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add isl_stream_read_map
[isl.git] / isl_map_simplify.c
blobd7512404307949d5cf6950d16487baa7deedcc82
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_set *isl_set_drop(struct isl_set *set,
246 enum isl_dim_type type, unsigned first, unsigned n)
247 {
248 return (isl_set *)isl_map_drop((isl_map *)set, type, first, n);
249 }
250
251 struct isl_map *isl_map_drop_inputs(
252 struct isl_map *map, unsigned first, unsigned n)
253 {
254 return isl_map_drop(map, isl_dim_in, first, n);
255 }
256
257 /*
258 * We don't cow, as the div is assumed to be redundant.
259 */
260 static struct isl_basic_map *isl_basic_map_drop_div(
261 struct isl_basic_map *bmap, unsigned div)
262 {
263 int i;
264 unsigned pos;
265
266 if (!bmap)
267 goto error;
268
269 pos = 1 + isl_dim_total(bmap->dim) + div;
270
271 isl_assert(bmap->ctx, div < bmap->n_div, goto error);
272
273 for (i = 0; i < bmap->n_eq; ++i)
274 constraint_drop_vars(bmap->eq[i]+pos, 1, bmap->extra-div-1);
275
276 for (i = 0; i < bmap->n_ineq; ++i) {
277 if (!isl_int_is_zero(bmap->ineq[i][pos])) {
278 isl_basic_map_drop_inequality(bmap, i);
279 --i;
280 continue;
281 }
282 constraint_drop_vars(bmap->ineq[i]+pos, 1, bmap->extra-div-1);
283 }
284
285 for (i = 0; i < bmap->n_div; ++i)
286 constraint_drop_vars(bmap->div[i]+1+pos, 1, bmap->extra-div-1);
287
288 if (div != bmap->n_div - 1) {
289 int j;
290 isl_int *t = bmap->div[div];
291
292 for (j = div; j < bmap->n_div - 1; ++j)
293 bmap->div[j] = bmap->div[j+1];
294
295 bmap->div[bmap->n_div - 1] = t;
296 }
297 ISL_F_CLR(bmap, ISL_BASIC_MAP_NORMALIZED);
298 isl_basic_map_free_div(bmap, 1);
299
300 return bmap;
301 error:
302 isl_basic_map_free(bmap);
303 return NULL;
304 }
305
306 struct isl_basic_map *isl_basic_map_normalize_constraints(
307 struct isl_basic_map *bmap)
308 {
309 int i;
310 isl_int gcd;
311 unsigned total = isl_basic_map_total_dim(bmap);
312
313 isl_int_init(gcd);
314 for (i = bmap->n_eq - 1; i >= 0; --i) {
315 isl_seq_gcd(bmap->eq[i]+1, total, &gcd);
316 if (isl_int_is_zero(gcd)) {
317 if (!isl_int_is_zero(bmap->eq[i][0])) {
318 bmap = isl_basic_map_set_to_empty(bmap);
319 break;
320 }
321 isl_basic_map_drop_equality(bmap, i);
322 continue;
323 }
324 if (ISL_F_ISSET(bmap, ISL_BASIC_MAP_RATIONAL))
325 isl_int_gcd(gcd, gcd, bmap->eq[i][0]);
326 if (isl_int_is_one(gcd))
327 continue;
328 if (!isl_int_is_divisible_by(bmap->eq[i][0], gcd)) {
329 bmap = isl_basic_map_set_to_empty(bmap);
330 break;
331 }
332 isl_seq_scale_down(bmap->eq[i], bmap->eq[i], gcd, 1+total);
333 }
334
335 for (i = bmap->n_ineq - 1; i >= 0; --i) {
336 isl_seq_gcd(bmap->ineq[i]+1, total, &gcd);
337 if (isl_int_is_zero(gcd)) {
338 if (isl_int_is_neg(bmap->ineq[i][0])) {
339 bmap = isl_basic_map_set_to_empty(bmap);
340 break;
341 }
342 isl_basic_map_drop_inequality(bmap, i);
343 continue;
344 }
345 if (ISL_F_ISSET(bmap, ISL_BASIC_MAP_RATIONAL))
346 isl_int_gcd(gcd, gcd, bmap->ineq[i][0]);
347 if (isl_int_is_one(gcd))
348 continue;
349 isl_int_fdiv_q(bmap->ineq[i][0], bmap->ineq[i][0], gcd);
350 isl_seq_scale_down(bmap->ineq[i]+1, bmap->ineq[i]+1, gcd, total);
351 }
352 isl_int_clear(gcd);
353
354 return bmap;
355 }
356
357 struct isl_basic_set *isl_basic_set_normalize_constraints(
358 struct isl_basic_set *bset)
359 {
360 return (struct isl_basic_set *)isl_basic_map_normalize_constraints(
361 (struct isl_basic_map *)bset);
362 }
363
364 /* Assumes divs have been ordered if keep_divs is set.
365 */
366 static void eliminate_var_using_equality(struct isl_basic_map *bmap,
367 unsigned pos, isl_int *eq, int keep_divs, int *progress)
368 {
369 unsigned total;
370 int k;
371 int last_div;
372
373 total = isl_basic_map_total_dim(bmap);
374 last_div = isl_seq_last_non_zero(eq + 1 + isl_dim_total(bmap->dim),
375 bmap->n_div);
376 for (k = 0; k < bmap->n_eq; ++k) {
377 if (bmap->eq[k] == eq)
378 continue;
379 if (isl_int_is_zero(bmap->eq[k][1+pos]))
380 continue;
381 if (progress)
382 *progress = 1;
383 isl_seq_elim(bmap->eq[k], eq, 1+pos, 1+total, NULL);
384 }
385
386 for (k = 0; k < bmap->n_ineq; ++k) {
387 if (isl_int_is_zero(bmap->ineq[k][1+pos]))
388 continue;
389 if (progress)
390 *progress = 1;
391 isl_seq_elim(bmap->ineq[k], eq, 1+pos, 1+total, NULL);
392 ISL_F_CLR(bmap, ISL_BASIC_MAP_NORMALIZED);
393 }
394
395 for (k = 0; k < bmap->n_div; ++k) {
396 if (isl_int_is_zero(bmap->div[k][0]))
397 continue;
398 if (isl_int_is_zero(bmap->div[k][1+1+pos]))
399 continue;
400 if (progress)
401 *progress = 1;
402 /* We need to be careful about circular definitions,
403 * so for now we just remove the definition of div k
404 * if the equality contains any divs.
405 * If keep_divs is set, then the divs have been ordered
406 * and we can keep the definition as long as the result
407 * is still ordered.
408 */
409 if (last_div == -1 || (keep_divs && last_div < k))
410 isl_seq_elim(bmap->div[k]+1, eq,
411 1+pos, 1+total, &bmap->div[k][0]);
412 else
413 isl_seq_clr(bmap->div[k], 1 + total);
414 ISL_F_CLR(bmap, ISL_BASIC_MAP_NORMALIZED);
415 }
416 }
417
418 /* Assumes divs have been ordered if keep_divs is set.
419 */
420 static void eliminate_div(struct isl_basic_map *bmap, isl_int *eq,
421 unsigned div, int keep_divs)
422 {
423 unsigned pos = isl_dim_total(bmap->dim) + div;
424
425 eliminate_var_using_equality(bmap, pos, eq, keep_divs, NULL);
426
427 isl_basic_map_drop_div(bmap, div);
428 }
429
430 /* Check if elimination of div "div" using equality "eq" would not
431 * result in a div depending on a later div.
432 */
433 static int ok_to_eliminate_div(struct isl_basic_map *bmap, isl_int *eq,
434 unsigned div)
435 {
436 int k;
437 int last_div;
438 unsigned pos = isl_dim_total(bmap->dim) + div;
439
440 last_div = isl_seq_last_non_zero(eq + 1 + isl_dim_total(bmap->dim),
441 bmap->n_div);
442 if (last_div < 0 || last_div <= div)
443 return 1;
444
445 for (k = 0; k <= last_div; ++k) {
446 if (isl_int_is_zero(bmap->div[k][0]))
447 return 1;
448 if (!isl_int_is_zero(bmap->div[k][1 + 1 + pos]))
449 return 0;
450 }
451
452 return 1;
453 }
454
455 /* Elimininate divs based on equalities
456 */
457 static struct isl_basic_map *eliminate_divs_eq(
458 struct isl_basic_map *bmap, int *progress)
459 {
460 int d;
461 int i;
462 int modified = 0;
463 unsigned off;
464
465 bmap = isl_basic_map_order_divs(bmap);
466
467 if (!bmap)
468 return NULL;
469
470 off = 1 + isl_dim_total(bmap->dim);
471
472 for (d = bmap->n_div - 1; d >= 0 ; --d) {
473 for (i = 0; i < bmap->n_eq; ++i) {
474 if (!isl_int_is_one(bmap->eq[i][off + d]) &&
475 !isl_int_is_negone(bmap->eq[i][off + d]))
476 continue;
477 if (!ok_to_eliminate_div(bmap, bmap->eq[i], d))
478 continue;
479 modified = 1;
480 *progress = 1;
481 eliminate_div(bmap, bmap->eq[i], d, 1);
482 isl_basic_map_drop_equality(bmap, i);
483 break;
484 }
485 }
486 if (modified)
487 return eliminate_divs_eq(bmap, progress);
488 return bmap;
489 }
490
491 /* Elimininate divs based on inequalities
492 */
493 static struct isl_basic_map *eliminate_divs_ineq(
494 struct isl_basic_map *bmap, int *progress)
495 {
496 int d;
497 int i;
498 unsigned off;
499 struct isl_ctx *ctx;
500
501 if (!bmap)
502 return NULL;
503
504 ctx = bmap->ctx;
505 off = 1 + isl_dim_total(bmap->dim);
506
507 for (d = bmap->n_div - 1; d >= 0 ; --d) {
508 for (i = 0; i < bmap->n_eq; ++i)
509 if (!isl_int_is_zero(bmap->eq[i][off + d]))
510 break;
511 if (i < bmap->n_eq)
512 continue;
513 for (i = 0; i < bmap->n_ineq; ++i)
514 if (isl_int_abs_gt(bmap->ineq[i][off + d], ctx->one))
515 break;
516 if (i < bmap->n_ineq)
517 continue;
518 *progress = 1;
519 bmap = isl_basic_map_eliminate_vars(bmap, (off-1)+d, 1);
520 if (ISL_F_ISSET(bmap, ISL_BASIC_MAP_EMPTY))
521 break;
522 bmap = isl_basic_map_drop_div(bmap, d);
523 if (!bmap)
524 break;
525 }
526 return bmap;
527 }
528
529 struct isl_basic_map *isl_basic_map_gauss(
530 struct isl_basic_map *bmap, int *progress)
531 {
532 int k;
533 int done;
534 int last_var;
535 unsigned total_var;
536 unsigned total;
537
538 bmap = isl_basic_map_order_divs(bmap);
539
540 if (!bmap)
541 return NULL;
542
543 total = isl_basic_map_total_dim(bmap);
544 total_var = total - bmap->n_div;
545
546 last_var = total - 1;
547 for (done = 0; done < bmap->n_eq; ++done) {
548 for (; last_var >= 0; --last_var) {
549 for (k = done; k < bmap->n_eq; ++k)
550 if (!isl_int_is_zero(bmap->eq[k][1+last_var]))
551 break;
552 if (k < bmap->n_eq)
553 break;
554 }
555 if (last_var < 0)
556 break;
557 if (k != done)
558 swap_equality(bmap, k, done);
559 if (isl_int_is_neg(bmap->eq[done][1+last_var]))
560 isl_seq_neg(bmap->eq[done], bmap->eq[done], 1+total);
561
562 eliminate_var_using_equality(bmap, last_var, bmap->eq[done], 1,
563 progress);
564
565 if (last_var >= total_var &&
566 isl_int_is_zero(bmap->div[last_var - total_var][0])) {
567 unsigned div = last_var - total_var;
568 isl_seq_neg(bmap->div[div]+1, bmap->eq[done], 1+total);
569 isl_int_set_si(bmap->div[div][1+1+last_var], 0);
570 isl_int_set(bmap->div[div][0],
571 bmap->eq[done][1+last_var]);
572 ISL_F_CLR(bmap, ISL_BASIC_MAP_NORMALIZED);
573 }
574 }
575 if (done == bmap->n_eq)
576 return bmap;
577 for (k = done; k < bmap->n_eq; ++k) {
578 if (isl_int_is_zero(bmap->eq[k][0]))
579 continue;
580 return isl_basic_map_set_to_empty(bmap);
581 }
582 isl_basic_map_free_equality(bmap, bmap->n_eq-done);
583 return bmap;
584 }
585
586 struct isl_basic_set *isl_basic_set_gauss(
587 struct isl_basic_set *bset, int *progress)
588 {
589 return (struct isl_basic_set*)isl_basic_map_gauss(
590 (struct isl_basic_map *)bset, progress);
591 }
592
593
594 static unsigned int round_up(unsigned int v)
595 {
596 int old_v = v;
597
598 while (v) {
599 old_v = v;
600 v ^= v & -v;
601 }
602 return old_v << 1;
603 }
604
605 static int hash_index(isl_int ***index, unsigned int size, int bits,
606 struct isl_basic_map *bmap, int k)
607 {
608 int h;
609 unsigned total = isl_basic_map_total_dim(bmap);
610 uint32_t hash = isl_seq_get_hash_bits(bmap->ineq[k]+1, total, bits);
611 for (h = hash; index[h]; h = (h+1) % size)
612 if (&bmap->ineq[k] != index[h] &&
613 isl_seq_eq(bmap->ineq[k]+1, index[h][0]+1, total))
614 break;
615 return h;
616 }
617
618 static int set_hash_index(isl_int ***index, unsigned int size, int bits,
619 struct isl_basic_set *bset, int k)
620 {
621 return hash_index(index, size, bits, (struct isl_basic_map *)bset, k);
622 }
623
624 /* If we can eliminate more than one div, then we need to make
625 * sure we do it from last div to first div, in order not to
626 * change the position of the other divs that still need to
627 * be removed.
628 */
629 static struct isl_basic_map *remove_duplicate_divs(
630 struct isl_basic_map *bmap, int *progress)
631 {
632 unsigned int size;
633 int *index;
634 int *elim_for;
635 int k, l, h;
636 int bits;
637 struct isl_blk eq;
638 unsigned total_var = isl_dim_total(bmap->dim);
639 unsigned total = total_var + bmap->n_div;
640 struct isl_ctx *ctx;
641
642 if (bmap->n_div <= 1)
643 return bmap;
644
645 ctx = bmap->ctx;
646 for (k = bmap->n_div - 1; k >= 0; --k)
647 if (!isl_int_is_zero(bmap->div[k][0]))
648 break;
649 if (k <= 0)
650 return bmap;
651
652 elim_for = isl_calloc_array(ctx, int, bmap->n_div);
653 size = round_up(4 * bmap->n_div / 3 - 1);
654 bits = ffs(size) - 1;
655 index = isl_calloc_array(ctx, int, size);
656 if (!index)
657 return bmap;
658 eq = isl_blk_alloc(ctx, 1+total);
659 if (isl_blk_is_error(eq))
660 goto out;
661
662 isl_seq_clr(eq.data, 1+total);
663 index[isl_seq_get_hash_bits(bmap->div[k], 2+total, bits)] = k + 1;
664 for (--k; k >= 0; --k) {
665 uint32_t hash;
666
667 if (isl_int_is_zero(bmap->div[k][0]))
668 continue;
669
670 hash = isl_seq_get_hash_bits(bmap->div[k], 2+total, bits);
671 for (h = hash; index[h]; h = (h+1) % size)
672 if (isl_seq_eq(bmap->div[k],
673 bmap->div[index[h]-1], 2+total))
674 break;
675 if (index[h]) {
676 *progress = 1;
677 l = index[h] - 1;
678 elim_for[l] = k + 1;
679 }
680 index[h] = k+1;
681 }
682 for (l = bmap->n_div - 1; l >= 0; --l) {
683 if (!elim_for[l])
684 continue;
685 k = elim_for[l] - 1;
686 isl_int_set_si(eq.data[1+total_var+k], -1);
687 isl_int_set_si(eq.data[1+total_var+l], 1);
688 eliminate_div(bmap, eq.data, l, 0);
689 isl_int_set_si(eq.data[1+total_var+k], 0);
690 isl_int_set_si(eq.data[1+total_var+l], 0);
691 }
692
693 isl_blk_free(ctx, eq);
694 out:
695 free(index);
696 free(elim_for);
697 return bmap;
698 }
699
700 static int n_pure_div_eq(struct isl_basic_map *bmap)
701 {
702 int i, j;
703 unsigned total;
704
705 total = isl_dim_total(bmap->dim);
706 for (i = 0, j = bmap->n_div-1; i < bmap->n_eq; ++i) {
707 while (j >= 0 && isl_int_is_zero(bmap->eq[i][1 + total + j]))
708 --j;
709 if (j < 0)
710 break;
711 if (isl_seq_first_non_zero(bmap->eq[i] + 1 + total, j) != -1)
712 return 0;
713 }
714 return i;
715 }
716
717 /* Normalize divs that appear in equalities.
718 *
719 * In particular, we assume that bmap contains some equalities
720 * of the form
721 *
722 * a x = m * e_i
723 *
724 * and we want to replace the set of e_i by a minimal set and
725 * such that the new e_i have a canonical representation in terms
726 * of the vector x.
727 * If any of the equalities involves more than one divs, then
728 * we currently simply bail out.
729 *
730 * Let us first additionally assume that all equalities involve
731 * a div. The equalities then express modulo constraints on the
732 * remaining variables and we can use "parameter compression"
733 * to find a minimal set of constraints. The result is a transformation
734 *
735 * x = T(x') = x_0 + G x'
736 *
737 * with G a lower-triangular matrix with all elements below the diagonal
738 * non-negative and smaller than the diagonal element on the same row.
739 * We first normalize x_0 by making the same property hold in the affine
740 * T matrix.
741 * The rows i of G with a 1 on the diagonal do not impose any modulo
742 * constraint and simply express x_i = x'_i.
743 * For each of the remaining rows i, we introduce a div and a corresponding
744 * equality. In particular
745 *
746 * g_ii e_j = x_i - g_i(x')
747 *
748 * where each x'_k is replaced either by x_k (if g_kk = 1) or the
749 * corresponding div (if g_kk != 1).
750 *
751 * If there are any equalities not involving any div, then we
752 * first apply a variable compression on the variables x:
753 *
754 * x = C x'' x'' = C_2 x
755 *
756 * and perform the above parameter compression on A C instead of on A.
757 * The resulting compression is then of the form
758 *
759 * x'' = T(x') = x_0 + G x'
760 *
761 * and in constructing the new divs and the corresponding equalities,
762 * we have to replace each x'', i.e., the x'_k with (g_kk = 1),
763 * by the corresponding row from C_2.
764 */
765 static struct isl_basic_map *normalize_divs(
766 struct isl_basic_map *bmap, int *progress)
767 {
768 int i, j, k;
769 int total;
770 int div_eq;
771 struct isl_mat *B;
772 struct isl_vec *d;
773 struct isl_mat *T = NULL;
774 struct isl_mat *C = NULL;
775 struct isl_mat *C2 = NULL;
776 isl_int v;
777 int *pos;
778 int dropped, needed;
779
780 if (!bmap)
781 return NULL;
782
783 if (bmap->n_div == 0)
784 return bmap;
785
786 if (bmap->n_eq == 0)
787 return bmap;
788
789 if (ISL_F_ISSET(bmap, ISL_BASIC_MAP_NORMALIZED_DIVS))
790 return bmap;
791
792 total = isl_dim_total(bmap->dim);
793 div_eq = n_pure_div_eq(bmap);
794 if (div_eq == 0)
795 return bmap;
796
797 if (div_eq < bmap->n_eq) {
798 B = isl_mat_sub_alloc(bmap->ctx, bmap->eq, div_eq,
799 bmap->n_eq - div_eq, 0, 1 + total);
800 C = isl_mat_variable_compression(B, &C2);
801 if (!C || !C2)
802 goto error;
803 if (C->n_col == 0) {
804 bmap = isl_basic_map_set_to_empty(bmap);
805 isl_mat_free(C);
806 isl_mat_free(C2);
807 goto done;
808 }
809 }
810
811 d = isl_vec_alloc(bmap->ctx, div_eq);
812 if (!d)
813 goto error;
814 for (i = 0, j = bmap->n_div-1; i < div_eq; ++i) {
815 while (j >= 0 && isl_int_is_zero(bmap->eq[i][1 + total + j]))
816 --j;
817 isl_int_set(d->block.data[i], bmap->eq[i][1 + total + j]);
818 }
819 B = isl_mat_sub_alloc(bmap->ctx, bmap->eq, 0, div_eq, 0, 1 + total);
820
821 if (C) {
822 B = isl_mat_product(B, C);
823 C = NULL;
824 }
825
826 T = isl_mat_parameter_compression(B, d);
827 if (!T)
828 goto error;
829 if (T->n_col == 0) {
830 bmap = isl_basic_map_set_to_empty(bmap);
831 isl_mat_free(C2);
832 isl_mat_free(T);
833 goto done;
834 }
835 isl_int_init(v);
836 for (i = 0; i < T->n_row - 1; ++i) {
837 isl_int_fdiv_q(v, T->row[1 + i][0], T->row[1 + i][1 + i]);
838 if (isl_int_is_zero(v))
839 continue;
840 isl_mat_col_submul(T, 0, v, 1 + i);
841 }
842 isl_int_clear(v);
843 pos = isl_alloc_array(bmap->ctx, int, T->n_row);
844 /* We have to be careful because dropping equalities may reorder them */
845 dropped = 0;
846 for (j = bmap->n_div - 1; j >= 0; --j) {
847 for (i = 0; i < bmap->n_eq; ++i)
848 if (!isl_int_is_zero(bmap->eq[i][1 + total + j]))
849 break;
850 if (i < bmap->n_eq) {
851 bmap = isl_basic_map_drop_div(bmap, j);
852 isl_basic_map_drop_equality(bmap, i);
853 ++dropped;
854 }
855 }
856 pos[0] = 0;
857 needed = 0;
858 for (i = 1; i < T->n_row; ++i) {
859 if (isl_int_is_one(T->row[i][i]))
860 pos[i] = i;
861 else
862 needed++;
863 }
864 if (needed > dropped) {
865 bmap = isl_basic_map_extend_dim(bmap, isl_dim_copy(bmap->dim),
866 needed, needed, 0);
867 if (!bmap)
868 goto error;
869 }
870 for (i = 1; i < T->n_row; ++i) {
871 if (isl_int_is_one(T->row[i][i]))
872 continue;
873 k = isl_basic_map_alloc_div(bmap);
874 pos[i] = 1 + total + k;
875 isl_seq_clr(bmap->div[k] + 1, 1 + total + bmap->n_div);
876 isl_int_set(bmap->div[k][0], T->row[i][i]);
877 if (C2)
878 isl_seq_cpy(bmap->div[k] + 1, C2->row[i], 1 + total);
879 else
880 isl_int_set_si(bmap->div[k][1 + i], 1);
881 for (j = 0; j < i; ++j) {
882 if (isl_int_is_zero(T->row[i][j]))
883 continue;
884 if (pos[j] < T->n_row && C2)
885 isl_seq_submul(bmap->div[k] + 1, T->row[i][j],
886 C2->row[pos[j]], 1 + total);
887 else
888 isl_int_neg(bmap->div[k][1 + pos[j]],
889 T->row[i][j]);
890 }
891 j = isl_basic_map_alloc_equality(bmap);
892 isl_seq_neg(bmap->eq[j], bmap->div[k]+1, 1+total+bmap->n_div);
893 isl_int_set(bmap->eq[j][pos[i]], bmap->div[k][0]);
894 }
895 free(pos);
896 isl_mat_free(C2);
897 isl_mat_free(T);
898
899 if (progress)
900 *progress = 1;
901 done:
902 ISL_F_SET(bmap, ISL_BASIC_MAP_NORMALIZED_DIVS);
903
904 return bmap;
905 error:
906 isl_mat_free(C);
907 isl_mat_free(C2);
908 isl_mat_free(T);
909 return bmap;
910 }
911
912 static struct isl_basic_map *set_div_from_lower_bound(
913 struct isl_basic_map *bmap, int div, int ineq)
914 {
915 unsigned total = 1 + isl_dim_total(bmap->dim);
916
917 isl_seq_neg(bmap->div[div] + 1, bmap->ineq[ineq], total + bmap->n_div);
918 isl_int_set(bmap->div[div][0], bmap->ineq[ineq][total + div]);
919 isl_int_add(bmap->div[div][1], bmap->div[div][1], bmap->div[div][0]);
920 isl_int_sub_ui(bmap->div[div][1], bmap->div[div][1], 1);
921 isl_int_set_si(bmap->div[div][1 + total + div], 0);
922
923 return bmap;
924 }
925
926 /* Check whether it is ok to define a div based on an inequality.
927 * To avoid the introduction of circular definitions of divs, we
928 * do not allow such a definition if the resulting expression would refer to
929 * any other undefined divs or if any known div is defined in
930 * terms of the unknown div.
931 */
932 static int ok_to_set_div_from_bound(struct isl_basic_map *bmap,
933 int div, int ineq)
934 {
935 int j;
936 unsigned total = 1 + isl_dim_total(bmap->dim);
937
938 /* Not defined in terms of unknown divs */
939 for (j = 0; j < bmap->n_div; ++j) {
940 if (div == j)
941 continue;
942 if (isl_int_is_zero(bmap->ineq[ineq][total + j]))
943 continue;
944 if (isl_int_is_zero(bmap->div[j][0]))
945 return 0;
946 }
947
948 /* No other div defined in terms of this one => avoid loops */
949 for (j = 0; j < bmap->n_div; ++j) {
950 if (div == j)
951 continue;
952 if (isl_int_is_zero(bmap->div[j][0]))
953 continue;
954 if (!isl_int_is_zero(bmap->div[j][1 + total + div]))
955 return 0;
956 }
957
958 return 1;
959 }
960
961 /* Given two constraints "k" and "l" that are opposite to each other,
962 * except for the constant term, check if we can use them
963 * to obtain an expression for one of the hitherto unknown divs.
964 * "sum" is the sum of the constant terms of the constraints.
965 * If this sum is strictly smaller than the coefficient of one
966 * of the divs, then this pair can be used define the div.
967 * To avoid the introduction of circular definitions of divs, we
968 * do not use the pair if the resulting expression would refer to
969 * any other undefined divs or if any known div is defined in
970 * terms of the unknown div.
971 */
972 static struct isl_basic_map *check_for_div_constraints(
973 struct isl_basic_map *bmap, int k, int l, isl_int sum, int *progress)
974 {
975 int i;
976 unsigned total = 1 + isl_dim_total(bmap->dim);
977
978 for (i = 0; i < bmap->n_div; ++i) {
979 if (!isl_int_is_zero(bmap->div[i][0]))
980 continue;
981 if (isl_int_is_zero(bmap->ineq[k][total + i]))
982 continue;
983 if (isl_int_abs_ge(sum, bmap->ineq[k][total + i]))
984 continue;
985 if (!ok_to_set_div_from_bound(bmap, i, k))
986 break;
987 if (isl_int_is_pos(bmap->ineq[k][total + i]))
988 bmap = set_div_from_lower_bound(bmap, i, k);
989 else
990 bmap = set_div_from_lower_bound(bmap, i, l);
991 if (progress)
992 *progress = 1;
993 break;
994 }
995 return bmap;
996 }
997
998 static struct isl_basic_map *remove_duplicate_constraints(
999 struct isl_basic_map *bmap, int *progress)
1000 {
1001 unsigned int size;
1002 isl_int ***index;
1003 int k, l, h;
1004 int bits;
1005 unsigned total = isl_basic_map_total_dim(bmap);
1006 isl_int sum;
1007
1008 if (bmap->n_ineq <= 1)
1009 return bmap;
1010
1011 size = round_up(4 * (bmap->n_ineq+1) / 3 - 1);
1012 bits = ffs(size) - 1;
1013 index = isl_calloc_array(ctx, isl_int **, size);
1014 if (!index)
1015 return bmap;
1016
1017 index[isl_seq_get_hash_bits(bmap->ineq[0]+1, total, bits)] = &bmap->ineq[0];
1018 for (k = 1; k < bmap->n_ineq; ++k) {
1019 h = hash_index(index, size, bits, bmap, k);
1020 if (!index[h]) {
1021 index[h] = &bmap->ineq[k];
1022 continue;
1023 }
1024 if (progress)
1025 *progress = 1;
1026 l = index[h] - &bmap->ineq[0];
1027 if (isl_int_lt(bmap->ineq[k][0], bmap->ineq[l][0]))
1028 swap_inequality(bmap, k, l);
1029 isl_basic_map_drop_inequality(bmap, k);
1030 --k;
1031 }
1032 isl_int_init(sum);
1033 for (k = 0; k < bmap->n_ineq-1; ++k) {
1034 isl_seq_neg(bmap->ineq[k]+1, bmap->ineq[k]+1, total);
1035 h = hash_index(index, size, bits, bmap, k);
1036 isl_seq_neg(bmap->ineq[k]+1, bmap->ineq[k]+1, total);
1037 if (!index[h])
1038 continue;
1039 l = index[h] - &bmap->ineq[0];
1040 isl_int_add(sum, bmap->ineq[k][0], bmap->ineq[l][0]);
1041 if (isl_int_is_pos(sum)) {
1042 bmap = check_for_div_constraints(bmap, k, l, sum,
1043 progress);
1044 continue;
1045 }
1046 if (isl_int_is_zero(sum)) {
1047 /* We need to break out of the loop after these
1048 * changes since the contents of the hash
1049 * will no longer be valid.
1050 * Plus, we probably we want to regauss first.
1051 */
1052 if (progress)
1053 *progress = 1;
1054 isl_basic_map_drop_inequality(bmap, l);
1055 isl_basic_map_inequality_to_equality(bmap, k);
1056 } else
1057 bmap = isl_basic_map_set_to_empty(bmap);
1058 break;
1059 }
1060 isl_int_clear(sum);
1061
1062 free(index);
1063 return bmap;
1064 }
1065
1066
1067 struct isl_basic_map *isl_basic_map_simplify(struct isl_basic_map *bmap)
1068 {
1069 int progress = 1;
1070 if (!bmap)
1071 return NULL;
1072 while (progress) {
1073 progress = 0;
1074 bmap = isl_basic_map_normalize_constraints(bmap);
1075 bmap = remove_duplicate_divs(bmap, &progress);
1076 bmap = eliminate_divs_eq(bmap, &progress);
1077 bmap = eliminate_divs_ineq(bmap, &progress);
1078 bmap = isl_basic_map_gauss(bmap, &progress);
1079 /* requires equalities in normal form */
1080 bmap = normalize_divs(bmap, &progress);
1081 bmap = remove_duplicate_constraints(bmap, &progress);
1082 }
1083 return bmap;
1084 }
1085
1086 struct isl_basic_set *isl_basic_set_simplify(struct isl_basic_set *bset)
1087 {
1088 return (struct isl_basic_set *)
1089 isl_basic_map_simplify((struct isl_basic_map *)bset);
1090 }
1091
1092
1093 /* If the only constraints a div d=floor(f/m)
1094 * appears in are its two defining constraints
1095 *
1096 * f - m d >=0
1097 * -(f - (m - 1)) + m d >= 0
1098 *
1099 * then it can safely be removed.
1100 */
1101 static int div_is_redundant(struct isl_basic_map *bmap, int div)
1102 {
1103 int i;
1104 unsigned pos = 1 + isl_dim_total(bmap->dim) + div;
1105
1106 for (i = 0; i < bmap->n_eq; ++i)
1107 if (!isl_int_is_zero(bmap->eq[i][pos]))
1108 return 0;
1109
1110 for (i = 0; i < bmap->n_ineq; ++i) {
1111 if (isl_int_is_zero(bmap->ineq[i][pos]))
1112 continue;
1113 if (isl_int_eq(bmap->ineq[i][pos], bmap->div[div][0])) {
1114 int neg;
1115 isl_int_sub(bmap->div[div][1],
1116 bmap->div[div][1], bmap->div[div][0]);
1117 isl_int_add_ui(bmap->div[div][1], bmap->div[div][1], 1);
1118 neg = isl_seq_is_neg(bmap->ineq[i], bmap->div[div]+1, pos);
1119 isl_int_sub_ui(bmap->div[div][1], bmap->div[div][1], 1);
1120 isl_int_add(bmap->div[div][1],
1121 bmap->div[div][1], bmap->div[div][0]);
1122 if (!neg)
1123 return 0;
1124 if (isl_seq_first_non_zero(bmap->ineq[i]+pos+1,
1125 bmap->n_div-div-1) != -1)
1126 return 0;
1127 } else if (isl_int_abs_eq(bmap->ineq[i][pos], bmap->div[div][0])) {
1128 if (!isl_seq_eq(bmap->ineq[i], bmap->div[div]+1, pos))
1129 return 0;
1130 if (isl_seq_first_non_zero(bmap->ineq[i]+pos+1,
1131 bmap->n_div-div-1) != -1)
1132 return 0;
1133 } else
1134 return 0;
1135 }
1136
1137 for (i = 0; i < bmap->n_div; ++i)
1138 if (!isl_int_is_zero(bmap->div[i][1+pos]))
1139 return 0;
1140
1141 return 1;
1142 }
1143
1144 /*
1145 * Remove divs that don't occur in any of the constraints or other divs.
1146 * These can arise when dropping some of the variables in a quast
1147 * returned by piplib.
1148 */
1149 static struct isl_basic_map *remove_redundant_divs(struct isl_basic_map *bmap)
1150 {
1151 int i;
1152
1153 if (!bmap)
1154 return NULL;
1155
1156 for (i = bmap->n_div-1; i >= 0; --i) {
1157 if (!div_is_redundant(bmap, i))
1158 continue;
1159 bmap = isl_basic_map_drop_div(bmap, i);
1160 }
1161 return bmap;
1162 }
1163
1164 struct isl_basic_map *isl_basic_map_finalize(struct isl_basic_map *bmap)
1165 {
1166 bmap = remove_redundant_divs(bmap);
1167 if (!bmap)
1168 return NULL;
1169 ISL_F_SET(bmap, ISL_BASIC_SET_FINAL);
1170 return bmap;
1171 }
1172
1173 struct isl_basic_set *isl_basic_set_finalize(struct isl_basic_set *bset)
1174 {
1175 return (struct isl_basic_set *)
1176 isl_basic_map_finalize((struct isl_basic_map *)bset);
1177 }
1178
1179 struct isl_set *isl_set_finalize(struct isl_set *set)
1180 {
1181 int i;
1182
1183 if (!set)
1184 return NULL;
1185 for (i = 0; i < set->n; ++i) {
1186 set->p[i] = isl_basic_set_finalize(set->p[i]);
1187 if (!set->p[i])
1188 goto error;
1189 }
1190 return set;
1191 error:
1192 isl_set_free(set);
1193 return NULL;
1194 }
1195
1196 struct isl_map *isl_map_finalize(struct isl_map *map)
1197 {
1198 int i;
1199
1200 if (!map)
1201 return NULL;
1202 for (i = 0; i < map->n; ++i) {
1203 map->p[i] = isl_basic_map_finalize(map->p[i]);
1204 if (!map->p[i])
1205 goto error;
1206 }
1207 ISL_F_CLR(map, ISL_MAP_NORMALIZED);
1208 return map;
1209 error:
1210 isl_map_free(map);
1211 return NULL;
1212 }
1213
1214
1215 /* Remove definition of any div that is defined in terms of the given variable.
1216 * The div itself is not removed. Functions such as
1217 * eliminate_divs_ineq depend on the other divs remaining in place.
1218 */
1219 static struct isl_basic_map *remove_dependent_vars(struct isl_basic_map *bmap,
1220 int pos)
1221 {
1222 int i;
1223
1224 for (i = 0; i < bmap->n_div; ++i) {
1225 if (isl_int_is_zero(bmap->div[i][0]))
1226 continue;
1227 if (isl_int_is_zero(bmap->div[i][1+1+pos]))
1228 continue;
1229 isl_int_set_si(bmap->div[i][0], 0);
1230 }
1231 return bmap;
1232 }
1233
1234 /* Eliminate the specified variables from the constraints using
1235 * Fourier-Motzkin. The variables themselves are not removed.
1236 */
1237 struct isl_basic_map *isl_basic_map_eliminate_vars(
1238 struct isl_basic_map *bmap, unsigned pos, unsigned n)
1239 {
1240 int d;
1241 int i, j, k;
1242 unsigned total;
1243
1244 if (n == 0)
1245 return bmap;
1246 if (!bmap)
1247 return NULL;
1248 total = isl_basic_map_total_dim(bmap);
1249
1250 bmap = isl_basic_map_cow(bmap);
1251 for (d = pos + n - 1; d >= 0 && d >= pos; --d)
1252 bmap = remove_dependent_vars(bmap, d);
1253
1254 for (d = pos + n - 1;
1255 d >= 0 && d >= total - bmap->n_div && d >= pos; --d)
1256 isl_seq_clr(bmap->div[d-(total-bmap->n_div)], 2+total);
1257 for (d = pos + n - 1; d >= 0 && d >= pos; --d) {
1258 int n_lower, n_upper;
1259 if (!bmap)
1260 return NULL;
1261 for (i = 0; i < bmap->n_eq; ++i) {
1262 if (isl_int_is_zero(bmap->eq[i][1+d]))
1263 continue;
1264 eliminate_var_using_equality(bmap, d, bmap->eq[i], 0, NULL);
1265 isl_basic_map_drop_equality(bmap, i);
1266 break;
1267 }
1268 if (i < bmap->n_eq)
1269 continue;
1270 n_lower = 0;
1271 n_upper = 0;
1272 for (i = 0; i < bmap->n_ineq; ++i) {
1273 if (isl_int_is_pos(bmap->ineq[i][1+d]))
1274 n_lower++;
1275 else if (isl_int_is_neg(bmap->ineq[i][1+d]))
1276 n_upper++;
1277 }
1278 bmap = isl_basic_map_extend_constraints(bmap,
1279 0, n_lower * n_upper);
1280 for (i = bmap->n_ineq - 1; i >= 0; --i) {
1281 int last;
1282 if (isl_int_is_zero(bmap->ineq[i][1+d]))
1283 continue;
1284 last = -1;
1285 for (j = 0; j < i; ++j) {
1286 if (isl_int_is_zero(bmap->ineq[j][1+d]))
1287 continue;
1288 last = j;
1289 if (isl_int_sgn(bmap->ineq[i][1+d]) ==
1290 isl_int_sgn(bmap->ineq[j][1+d]))
1291 continue;
1292 k = isl_basic_map_alloc_inequality(bmap);
1293 if (k < 0)
1294 goto error;
1295 isl_seq_cpy(bmap->ineq[k], bmap->ineq[i],
1296 1+total);
1297 isl_seq_elim(bmap->ineq[k], bmap->ineq[j],
1298 1+d, 1+total, NULL);
1299 }
1300 isl_basic_map_drop_inequality(bmap, i);
1301 i = last + 1;
1302 }
1303 if (n_lower > 0 && n_upper > 0) {
1304 bmap = isl_basic_map_normalize_constraints(bmap);
1305 bmap = remove_duplicate_constraints(bmap, NULL);
1306 bmap = isl_basic_map_gauss(bmap, NULL);
1307 bmap = isl_basic_map_convex_hull(bmap);
1308 if (!bmap)
1309 goto error;
1310 if (ISL_F_ISSET(bmap, ISL_BASIC_MAP_EMPTY))
1311 break;
1312 }
1313 }
1314 ISL_F_CLR(bmap, ISL_BASIC_MAP_NORMALIZED);
1315 return bmap;
1316 error:
1317 isl_basic_map_free(bmap);
1318 return NULL;
1319 }
1320
1321 struct isl_basic_set *isl_basic_set_eliminate_vars(
1322 struct isl_basic_set *bset, unsigned pos, unsigned n)
1323 {
1324 return (struct isl_basic_set *)isl_basic_map_eliminate_vars(
1325 (struct isl_basic_map *)bset, pos, n);
1326 }
1327
1328 /* Don't assume equalities are in order, because align_divs
1329 * may have changed the order of the divs.
1330 */
1331 static void compute_elimination_index(struct isl_basic_map *bmap, int *elim)
1332 {
1333 int d, i;
1334 unsigned total;
1335
1336 total = isl_dim_total(bmap->dim);
1337 for (d = 0; d < total; ++d)
1338 elim[d] = -1;
1339 for (i = 0; i < bmap->n_eq; ++i) {
1340 for (d = total - 1; d >= 0; --d) {
1341 if (isl_int_is_zero(bmap->eq[i][1+d]))
1342 continue;
1343 elim[d] = i;
1344 break;
1345 }
1346 }
1347 }
1348
1349 static void set_compute_elimination_index(struct isl_basic_set *bset, int *elim)
1350 {
1351 compute_elimination_index((struct isl_basic_map *)bset, elim);
1352 }
1353
1354 static int reduced_using_equalities(isl_int *dst, isl_int *src,
1355 struct isl_basic_map *bmap, int *elim)
1356 {
1357 int d;
1358 int copied = 0;
1359 unsigned total;
1360
1361 total = isl_dim_total(bmap->dim);
1362 for (d = total - 1; d >= 0; --d) {
1363 if (isl_int_is_zero(src[1+d]))
1364 continue;
1365 if (elim[d] == -1)
1366 continue;
1367 if (!copied) {
1368 isl_seq_cpy(dst, src, 1 + total);
1369 copied = 1;
1370 }
1371 isl_seq_elim(dst, bmap->eq[elim[d]], 1 + d, 1 + total, NULL);
1372 }
1373 return copied;
1374 }
1375
1376 static int set_reduced_using_equalities(isl_int *dst, isl_int *src,
1377 struct isl_basic_set *bset, int *elim)
1378 {
1379 return reduced_using_equalities(dst, src,
1380 (struct isl_basic_map *)bset, elim);
1381 }
1382
1383 static struct isl_basic_set *isl_basic_set_reduce_using_equalities(
1384 struct isl_basic_set *bset, struct isl_basic_set *context)
1385 {
1386 int i;
1387 int *elim;
1388
1389 if (!bset || !context)
1390 goto error;
1391
1392 bset = isl_basic_set_cow(bset);
1393 if (!bset)
1394 goto error;
1395
1396 elim = isl_alloc_array(ctx, int, isl_basic_set_n_dim(bset));
1397 if (!elim)
1398 goto error;
1399 set_compute_elimination_index(context, elim);
1400 for (i = 0; i < bset->n_eq; ++i)
1401 set_reduced_using_equalities(bset->eq[i], bset->eq[i],
1402 context, elim);
1403 for (i = 0; i < bset->n_ineq; ++i)
1404 set_reduced_using_equalities(bset->ineq[i], bset->ineq[i],
1405 context, elim);
1406 isl_basic_set_free(context);
1407 free(elim);
1408 bset = isl_basic_set_simplify(bset);
1409 bset = isl_basic_set_finalize(bset);
1410 return bset;
1411 error:
1412 isl_basic_set_free(bset);
1413 isl_basic_set_free(context);
1414 return NULL;
1415 }
1416
1417 static struct isl_basic_set *remove_shifted_constraints(
1418 struct isl_basic_set *bset, struct isl_basic_set *context)
1419 {
1420 unsigned int size;
1421 isl_int ***index;
1422 int bits;
1423 int k, h, l;
1424
1425 if (!bset)
1426 return NULL;
1427
1428 size = round_up(4 * (context->n_ineq+1) / 3 - 1);
1429 bits = ffs(size) - 1;
1430 index = isl_calloc_array(ctx, isl_int **, size);
1431 if (!index)
1432 return bset;
1433
1434 for (k = 0; k < context->n_ineq; ++k) {
1435 h = set_hash_index(index, size, bits, context, k);
1436 index[h] = &context->ineq[k];
1437 }
1438 for (k = 0; k < bset->n_ineq; ++k) {
1439 h = set_hash_index(index, size, bits, bset, k);
1440 if (!index[h])
1441 continue;
1442 l = index[h] - &context->ineq[0];
1443 if (isl_int_lt(bset->ineq[k][0], context->ineq[l][0]))
1444 continue;
1445 bset = isl_basic_set_cow(bset);
1446 if (!bset)
1447 goto error;
1448 isl_basic_set_drop_inequality(bset, k);
1449 --k;
1450 }
1451 free(index);
1452 return bset;
1453 error:
1454 free(index);
1455 return bset;
1456 }
1457
1458 /* Tighten (decrease) the constant terms of the inequalities based
1459 * on the equalities, without removing any integer points.
1460 * For example, if there is an equality
1461 *
1462 * i = 3 * j
1463 *
1464 * and an inequality
1465 *
1466 * i >= 1
1467 *
1468 * then we want to replace the inequality by
1469 *
1470 * i >= 3
1471 *
1472 * We do this by computing a variable compression and translating
1473 * the constraints to the compressed space.
1474 * If any constraint has coefficients (except the contant term)
1475 * with a common factor "f", then we can replace the constant term "c"
1476 * by
1477 *
1478 * f * floor(c/f)
1479 *
1480 * That is, we add
1481 *
1482 * f * floor(c/f) - c = -fract(c/f)
1483 *
1484 * and we can add the same value to the original constraint.
1485 *
1486 * In the example, the compressed space only contains "j",
1487 * and the inequality translates to
1488 *
1489 * 3 * j - 1 >= 0
1490 *
1491 * We add -fract(-1/3) = -2 to the original constraint to obtain
1492 *
1493 * i - 3 >= 0
1494 */
1495 static struct isl_basic_set *normalize_constraints_in_compressed_space(
1496 struct isl_basic_set *bset)
1497 {
1498 int i;
1499 unsigned total;
1500 struct isl_mat *B, *C;
1501 isl_int gcd;
1502
1503 if (!bset)
1504 return NULL;
1505
1506 if (ISL_F_ISSET(bset, ISL_BASIC_SET_RATIONAL))
1507 return bset;
1508
1509 if (!bset->n_ineq)
1510 return bset;
1511
1512 bset = isl_basic_set_cow(bset);
1513 if (!bset)
1514 return NULL;
1515
1516 total = isl_basic_set_total_dim(bset);
1517 B = isl_mat_sub_alloc(bset->ctx, bset->eq, 0, bset->n_eq, 0, 1 + total);
1518 C = isl_mat_variable_compression(B, NULL);
1519 if (!C)
1520 return bset;
1521 if (C->n_col == 0) {
1522 isl_mat_free(C);
1523 return isl_basic_set_set_to_empty(bset);
1524 }
1525 B = isl_mat_sub_alloc(bset->ctx, bset->ineq,
1526 0, bset->n_ineq, 0, 1 + total);
1527 C = isl_mat_product(B, C);
1528 if (!C)
1529 return bset;
1530
1531 isl_int_init(gcd);
1532 for (i = 0; i < bset->n_ineq; ++i) {
1533 isl_seq_gcd(C->row[i] + 1, C->n_col - 1, &gcd);
1534 if (isl_int_is_one(gcd))
1535 continue;
1536 isl_int_fdiv_r(C->row[i][0], C->row[i][0], gcd);
1537 isl_int_sub(bset->ineq[i][0], bset->ineq[i][0], C->row[i][0]);
1538 }
1539 isl_int_clear(gcd);
1540
1541 isl_mat_free(C);
1542
1543 return bset;
1544 }
1545
1546 /* Remove all information from bset that is redundant in the context
1547 * of context. In particular, equalities that are linear combinations
1548 * of those in context are removed. Then the inequalities that are
1549 * redundant in the context of the equalities and inequalities of
1550 * context are removed.
1551 *
1552 * We first simplify the constraints of "bset" in the context of the
1553 * equalities of "context".
1554 * Then we simplify the inequalities of the context in the context
1555 * of the equalities of bset and remove the inequalities from "bset"
1556 * that are obviously redundant with respect to some inequality in "context".
1557 *
1558 * If there are any inequalities left, we construct a tableau for
1559 * the context and then add the inequalities of "bset".
1560 * Before adding these equalities, we freeze all constraints such that
1561 * they won't be considered redundant in terms of the constraints of "bset".
1562 * Then we detect all equalities and redundant constraints (among the
1563 * constraints that weren't frozen) and update bset according to the results.
1564 * We have to be careful here because we don't want any of the context
1565 * constraints to remain and because we haven't added the equalities of "bset"
1566 * to the tableau so we temporarily have to pretend that there were no
1567 * equalities.
1568 */
1569 static struct isl_basic_set *uset_gist(struct isl_basic_set *bset,
1570 struct isl_basic_set *context)
1571 {
1572 int i;
1573 struct isl_tab *tab;
1574 unsigned context_ineq;
1575 struct isl_basic_set *combined = NULL;
1576
1577 if (!context || !bset)
1578 goto error;
1579
1580 if (context->n_eq > 0)
1581 bset = isl_basic_set_reduce_using_equalities(bset,
1582 isl_basic_set_copy(context));
1583 if (!bset)
1584 goto error;
1585 if (isl_basic_set_fast_is_empty(bset))
1586 goto done;
1587 if (!bset->n_ineq)
1588 goto done;
1589
1590 if (bset->n_eq > 0) {
1591 struct isl_basic_set *affine_hull;
1592 affine_hull = isl_basic_set_copy(bset);
1593 affine_hull = isl_basic_set_cow(affine_hull);
1594 if (!affine_hull)
1595 goto error;
1596 isl_basic_set_free_inequality(affine_hull, affine_hull->n_ineq);
1597 context = isl_basic_set_intersect(context, affine_hull);
1598 context = isl_basic_set_gauss(context, NULL);
1599 context = normalize_constraints_in_compressed_space(context);
1600 }
1601 if (!context)
1602 goto error;
1603 if (ISL_F_ISSET(context, ISL_BASIC_SET_EMPTY)) {
1604 isl_basic_set_free(bset);
1605 return context;
1606 }
1607 if (!context->n_ineq)
1608 goto done;
1609 bset = remove_shifted_constraints(bset, context);
1610 if (!bset->n_ineq)
1611 goto done;
1612 context_ineq = context->n_ineq;
1613 combined = isl_basic_set_cow(isl_basic_set_copy(context));
1614 if (isl_basic_set_free_equality(combined, context->n_eq) < 0)
1615 goto error;
1616 combined = isl_basic_set_extend_constraints(combined,
1617 bset->n_eq, bset->n_ineq);
1618 tab = isl_tab_from_basic_set(combined);
1619 if (!tab)
1620 goto error;
1621 for (i = 0; i < context_ineq; ++i)
1622 if (isl_tab_freeze_constraint(tab, i) < 0)
1623 goto error;
1624 tab = isl_tab_extend(tab, bset->n_ineq);
1625 if (!tab)
1626 goto error;
1627 for (i = 0; i < bset->n_ineq; ++i)
1628 if (isl_tab_add_ineq(tab, bset->ineq[i]) < 0)
1629 goto error;
1630 bset = isl_basic_set_add_constraints(combined, bset, 0);
1631 tab = isl_tab_detect_implicit_equalities(tab);
1632 if (isl_tab_detect_redundant(tab) < 0) {
1633 isl_tab_free(tab);
1634 goto error2;
1635 }
1636 for (i = 0; i < context_ineq; ++i) {
1637 tab->con[i].is_zero = 0;
1638 tab->con[i].is_redundant = 1;
1639 }
1640 bset = isl_basic_set_update_from_tab(bset, tab);
1641 isl_tab_free(tab);
1642 ISL_F_SET(bset, ISL_BASIC_SET_NO_IMPLICIT);
1643 ISL_F_SET(bset, ISL_BASIC_SET_NO_REDUNDANT);
1644 done:
1645 bset = isl_basic_set_simplify(bset);
1646 bset = isl_basic_set_finalize(bset);
1647 isl_basic_set_free(context);
1648 return bset;
1649 error:
1650 isl_basic_set_free(combined);
1651 error2:
1652 isl_basic_set_free(bset);
1653 isl_basic_set_free(context);
1654 return NULL;
1655 }
1656
1657 /* Normalize the divs in "bmap" in the context of the equalities in "context".
1658 * We simply add the equalities in context to bmap and then do a regular
1659 * div normalizations. Better results can be obtained by normalizing
1660 * only the divs in bmap than do not also appear in context.
1661 * We need to be careful to reduce the divs using the equalities
1662 * so that later calls to isl_basic_map_overlying_set wouldn't introduce
1663 * spurious constraints.
1664 */
1665 static struct isl_basic_map *normalize_divs_in_context(
1666 struct isl_basic_map *bmap, struct isl_basic_map *context)
1667 {
1668 int i;
1669 unsigned total_context;
1670 int div_eq;
1671
1672 div_eq = n_pure_div_eq(bmap);
1673 if (div_eq == 0)
1674 return bmap;
1675
1676 if (context->n_div > 0)
1677 bmap = isl_basic_map_align_divs(bmap, context);
1678
1679 total_context = isl_basic_map_total_dim(context);
1680 bmap = isl_basic_map_extend_constraints(bmap, context->n_eq, 0);
1681 for (i = 0; i < context->n_eq; ++i) {
1682 int k;
1683 k = isl_basic_map_alloc_equality(bmap);
1684 isl_seq_cpy(bmap->eq[k], context->eq[i], 1 + total_context);
1685 isl_seq_clr(bmap->eq[k] + 1 + total_context,
1686 isl_basic_map_total_dim(bmap) - total_context);
1687 }
1688 bmap = isl_basic_map_gauss(bmap, NULL);
1689 bmap = normalize_divs(bmap, NULL);
1690 bmap = isl_basic_map_gauss(bmap, NULL);
1691 return bmap;
1692 }
1693
1694 struct isl_basic_map *isl_basic_map_gist(struct isl_basic_map *bmap,
1695 struct isl_basic_map *context)
1696 {
1697 struct isl_basic_set *bset;
1698
1699 if (!bmap || !context)
1700 goto error;
1701
1702 if (isl_basic_map_is_universe(context)) {
1703 isl_basic_map_free(context);
1704 return bmap;
1705 }
1706 if (isl_basic_map_is_universe(bmap)) {
1707 isl_basic_map_free(context);
1708 return bmap;
1709 }
1710 if (isl_basic_map_fast_is_empty(context)) {
1711 struct isl_dim *dim = isl_dim_copy(bmap->dim);
1712 isl_basic_map_free(context);
1713 isl_basic_map_free(bmap);
1714 return isl_basic_map_universe(dim);
1715 }
1716 if (isl_basic_map_fast_is_empty(bmap)) {
1717 isl_basic_map_free(context);
1718 return bmap;
1719 }
1720
1721 bmap = isl_basic_map_convex_hull(bmap);
1722 context = isl_basic_map_convex_hull(context);
1723
1724 if (context->n_eq)
1725 bmap = normalize_divs_in_context(bmap, context);
1726
1727 context = isl_basic_map_align_divs(context, bmap);
1728 bmap = isl_basic_map_align_divs(bmap, context);
1729
1730 bset = uset_gist(isl_basic_map_underlying_set(isl_basic_map_copy(bmap)),
1731 isl_basic_map_underlying_set(context));
1732
1733 return isl_basic_map_overlying_set(bset, bmap);
1734 error:
1735 isl_basic_map_free(bmap);
1736 isl_basic_map_free(context);
1737 return NULL;
1738 }
1739
1740 /*
1741 * Assumes context has no implicit divs.
1742 */
1743 struct isl_map *isl_map_gist(struct isl_map *map, struct isl_basic_map *context)
1744 {
1745 int i;
1746
1747 if (!map || !context)
1748 goto error;;
1749
1750 if (isl_basic_map_is_universe(context)) {
1751 isl_basic_map_free(context);
1752 return map;
1753 }
1754 if (isl_basic_map_fast_is_empty(context)) {
1755 struct isl_dim *dim = isl_dim_copy(map->dim);
1756 isl_basic_map_free(context);
1757 isl_map_free(map);
1758 return isl_map_universe(dim);
1759 }
1760
1761 context = isl_basic_map_convex_hull(context);
1762 map = isl_map_cow(map);
1763 if (!map || !context)
1764 goto error;;
1765 isl_assert(map->ctx, isl_dim_equal(map->dim, context->dim), goto error);
1766 map = isl_map_compute_divs(map);
1767 for (i = 0; i < map->n; ++i)
1768 context = isl_basic_map_align_divs(context, map->p[i]);
1769 for (i = 0; i < map->n; ++i) {
1770 map->p[i] = isl_basic_map_gist(map->p[i],
1771 isl_basic_map_copy(context));
1772 if (!map->p[i])
1773 goto error;
1774 }
1775 isl_basic_map_free(context);
1776 ISL_F_CLR(map, ISL_MAP_NORMALIZED);
1777 return map;
1778 error:
1779 isl_map_free(map);
1780 isl_basic_map_free(context);
1781 return NULL;
1782 }
1783
1784 struct isl_basic_set *isl_basic_set_gist(struct isl_basic_set *bset,
1785 struct isl_basic_set *context)
1786 {
1787 return (struct isl_basic_set *)isl_basic_map_gist(
1788 (struct isl_basic_map *)bset, (struct isl_basic_map *)context);
1789 }
1790
1791 struct isl_set *isl_set_gist(struct isl_set *set, struct isl_basic_set *context)
1792 {
1793 return (struct isl_set *)isl_map_gist((struct isl_map *)set,
1794 (struct isl_basic_map *)context);
1795 }
1796
1797 /* Quick check to see if two basic maps are disjoint.
1798 * In particular, we reduce the equalities and inequalities of
1799 * one basic map in the context of the equalities of the other
1800 * basic map and check if we get a contradiction.
1801 */
1802 int isl_basic_map_fast_is_disjoint(struct isl_basic_map *bmap1,
1803 struct isl_basic_map *bmap2)
1804 {
1805 struct isl_vec *v = NULL;
1806 int *elim = NULL;
1807 unsigned total;
1808 int i;
1809
1810 if (!bmap1 || !bmap2)
1811 return -1;
1812 isl_assert(bmap1->ctx, isl_dim_equal(bmap1->dim, bmap2->dim),
1813 return -1);
1814 if (bmap1->n_div || bmap2->n_div)
1815 return 0;
1816 if (!bmap1->n_eq && !bmap2->n_eq)
1817 return 0;
1818
1819 total = isl_dim_total(bmap1->dim);
1820 if (total == 0)
1821 return 0;
1822 v = isl_vec_alloc(bmap1->ctx, 1 + total);
1823 if (!v)
1824 goto error;
1825 elim = isl_alloc_array(bmap1->ctx, int, total);
1826 if (!elim)
1827 goto error;
1828 compute_elimination_index(bmap1, elim);
1829 for (i = 0; i < bmap2->n_eq; ++i) {
1830 int reduced;
1831 reduced = reduced_using_equalities(v->block.data, bmap2->eq[i],
1832 bmap1, elim);
1833 if (reduced && !isl_int_is_zero(v->block.data[0]) &&
1834 isl_seq_first_non_zero(v->block.data + 1, total) == -1)
1835 goto disjoint;
1836 }
1837 for (i = 0; i < bmap2->n_ineq; ++i) {
1838 int reduced;
1839 reduced = reduced_using_equalities(v->block.data,
1840 bmap2->ineq[i], bmap1, elim);
1841 if (reduced && isl_int_is_neg(v->block.data[0]) &&
1842 isl_seq_first_non_zero(v->block.data + 1, total) == -1)
1843 goto disjoint;
1844 }
1845 compute_elimination_index(bmap2, elim);
1846 for (i = 0; i < bmap1->n_ineq; ++i) {
1847 int reduced;
1848 reduced = reduced_using_equalities(v->block.data,
1849 bmap1->ineq[i], bmap2, elim);
1850 if (reduced && isl_int_is_neg(v->block.data[0]) &&
1851 isl_seq_first_non_zero(v->block.data + 1, total) == -1)
1852 goto disjoint;
1853 }
1854 isl_vec_free(v);
1855 free(elim);
1856 return 0;
1857 disjoint:
1858 isl_vec_free(v);
1859 free(elim);
1860 return 1;
1861 error:
1862 isl_vec_free(v);
1863 free(elim);
1864 return -1;
1865 }
1866
1867 int isl_basic_set_fast_is_disjoint(struct isl_basic_set *bset1,
1868 struct isl_basic_set *bset2)
1869 {
1870 return isl_basic_map_fast_is_disjoint((struct isl_basic_map *)bset1,
1871 (struct isl_basic_map *)bset2);
1872 }
1873
1874 int isl_map_fast_is_disjoint(struct isl_map *map1, struct isl_map *map2)
1875 {
1876 int i, j;
1877
1878 if (!map1 || !map2)
1879 return -1;
1880
1881 if (isl_map_fast_is_equal(map1, map2))
1882 return 0;
1883
1884 for (i = 0; i < map1->n; ++i) {
1885 for (j = 0; j < map2->n; ++j) {
1886 int d = isl_basic_map_fast_is_disjoint(map1->p[i],
1887 map2->p[j]);
1888 if (d != 1)
1889 return d;
1890 }
1891 }
1892 return 1;
1893 }
1894
1895 int isl_set_fast_is_disjoint(struct isl_set *set1, struct isl_set *set2)
1896 {
1897 return isl_map_fast_is_disjoint((struct isl_map *)set1,
1898 (struct isl_map *)set2);
1899 }
1900
1901 /* Check if we can combine a given div with lower bound l and upper
1902 * bound u with some other div and if so return that other div.
1903 * Otherwise return -1.
1904 *
1905 * We first check that
1906 * - the bounds are opposites of each other (except for the constant
1907 * term)
1908 * - the bounds do not reference any other div
1909 * - no div is defined in terms of this div
1910 *
1911 * Let m be the size of the range allowed on the div by the bounds.
1912 * That is, the bounds are of the form
1913 *
1914 * e <= a <= e + m - 1
1915 *
1916 * with e some expression in the other variables.
1917 * We look for another div b such that no third div is defined in terms
1918 * of this second div b and such that in any constraint that contains
1919 * a (except for the given lower and upper bound), also contains b
1920 * with a coefficient that is m times that of b.
1921 * That is, all constraints (execpt for the lower and upper bound)
1922 * are of the form
1923 *
1924 * e + f (a + m b) >= 0
1925 *
1926 * If so, we return b so that "a + m b" can be replaced by
1927 * a single div "c = a + m b".
1928 */
1929 static int div_find_coalesce(struct isl_basic_map *bmap, int *pairs,
1930 unsigned div, unsigned l, unsigned u)
1931 {
1932 int i, j;
1933 unsigned dim;
1934 int coalesce = -1;
1935
1936 if (bmap->n_div <= 1)
1937 return -1;
1938 dim = isl_dim_total(bmap->dim);
1939 if (isl_seq_first_non_zero(bmap->ineq[l] + 1 + dim, div) != -1)
1940 return -1;
1941 if (isl_seq_first_non_zero(bmap->ineq[l] + 1 + dim + div + 1,
1942 bmap->n_div - div - 1) != -1)
1943 return -1;
1944 if (!isl_seq_is_neg(bmap->ineq[l] + 1, bmap->ineq[u] + 1,
1945 dim + bmap->n_div))
1946 return -1;
1947
1948 for (i = 0; i < bmap->n_div; ++i) {
1949 if (isl_int_is_zero(bmap->div[i][0]))
1950 continue;
1951 if (!isl_int_is_zero(bmap->div[i][1 + 1 + dim + div]))
1952 return -1;
1953 }
1954
1955 isl_int_add(bmap->ineq[l][0], bmap->ineq[l][0], bmap->ineq[u][0]);
1956 if (isl_int_is_neg(bmap->ineq[l][0])) {
1957 isl_int_sub(bmap->ineq[l][0],
1958 bmap->ineq[l][0], bmap->ineq[u][0]);
1959 bmap = isl_basic_map_copy(bmap);
1960 bmap = isl_basic_map_set_to_empty(bmap);
1961 isl_basic_map_free(bmap);
1962 return -1;
1963 }
1964 isl_int_add_ui(bmap->ineq[l][0], bmap->ineq[l][0], 1);
1965 for (i = 0; i < bmap->n_div; ++i) {
1966 if (i == div)
1967 continue;
1968 if (!pairs[i])
1969 continue;
1970 for (j = 0; j < bmap->n_div; ++j) {
1971 if (isl_int_is_zero(bmap->div[j][0]))
1972 continue;
1973 if (!isl_int_is_zero(bmap->div[j][1 + 1 + dim + i]))
1974 break;
1975 }
1976 if (j < bmap->n_div)
1977 continue;
1978 for (j = 0; j < bmap->n_ineq; ++j) {
1979 int valid;
1980 if (j == l || j == u)
1981 continue;
1982 if (isl_int_is_zero(bmap->ineq[j][1 + dim + div]))
1983 continue;
1984 if (isl_int_is_zero(bmap->ineq[j][1 + dim + i]))
1985 break;
1986 isl_int_mul(bmap->ineq[j][1 + dim + div],
1987 bmap->ineq[j][1 + dim + div],
1988 bmap->ineq[l][0]);
1989 valid = isl_int_eq(bmap->ineq[j][1 + dim + div],
1990 bmap->ineq[j][1 + dim + i]);
1991 isl_int_divexact(bmap->ineq[j][1 + dim + div],
1992 bmap->ineq[j][1 + dim + div],
1993 bmap->ineq[l][0]);
1994 if (!valid)
1995 break;
1996 }
1997 if (j < bmap->n_ineq)
1998 continue;
1999 coalesce = i;
2000 break;
2001 }
2002 isl_int_sub_ui(bmap->ineq[l][0], bmap->ineq[l][0], 1);
2003 isl_int_sub(bmap->ineq[l][0], bmap->ineq[l][0], bmap->ineq[u][0]);
2004 return coalesce;
2005 }
2006
2007 /* Given a lower and an upper bound on div i, construct an inequality
2008 * that when nonnegative ensures that this pair of bounds always allows
2009 * for an integer value of the given div.
2010 * The lower bound is inequality l, while the upper bound is inequality u.
2011 * The constructed inequality is stored in ineq.
2012 * g, fl, fu are temporary scalars.
2013 *
2014 * Let the upper bound be
2015 *
2016 * -n_u a + e_u >= 0
2017 *
2018 * and the lower bound
2019 *
2020 * n_l a + e_l >= 0
2021 *
2022 * Let n_u = f_u g and n_l = f_l g, with g = gcd(n_u, n_l).
2023 * We have
2024 *
2025 * - f_u e_l <= f_u f_l g a <= f_l e_u
2026 *
2027 * Since all variables are integer valued, this is equivalent to
2028 *
2029 * - f_u e_l - (f_u - 1) <= f_u f_l g a <= f_l e_u + (f_l - 1)
2030 *
2031 * If this interval is at least f_u f_l g, then it contains at least
2032 * one integer value for a.
2033 * That is, the test constraint is
2034 *
2035 * f_l e_u + f_u e_l + f_l - 1 + f_u - 1 + 1 >= f_u f_l g
2036 */
2037 static void construct_test_ineq(struct isl_basic_map *bmap, int i,
2038 int l, int u, isl_int *ineq, isl_int g, isl_int fl, isl_int fu)
2039 {
2040 unsigned dim;
2041 dim = isl_dim_total(bmap->dim);
2042
2043 isl_int_gcd(g, bmap->ineq[l][1 + dim + i], bmap->ineq[u][1 + dim + i]);
2044 isl_int_divexact(fl, bmap->ineq[l][1 + dim + i], g);
2045 isl_int_divexact(fu, bmap->ineq[u][1 + dim + i], g);
2046 isl_int_neg(fu, fu);
2047 isl_seq_combine(ineq, fl, bmap->ineq[u], fu, bmap->ineq[l],
2048 1 + dim + bmap->n_div);
2049 isl_int_add(ineq[0], ineq[0], fl);
2050 isl_int_add(ineq[0], ineq[0], fu);
2051 isl_int_sub_ui(ineq[0], ineq[0], 1);
2052 isl_int_mul(g, g, fl);
2053 isl_int_mul(g, g, fu);
2054 isl_int_sub(ineq[0], ineq[0], g);
2055 }
2056
2057 /* Remove more kinds of divs that are not strictly needed.
2058 * In particular, if all pairs of lower and upper bounds on a div
2059 * are such that they allow at least one integer value of the div,
2060 * the we can eliminate the div using Fourier-Motzkin without
2061 * introducing any spurious solutions.
2062 */
2063 static struct isl_basic_map *drop_more_redundant_divs(
2064 struct isl_basic_map *bmap, int *pairs, int n)
2065 {
2066 struct isl_tab *tab = NULL;
2067 struct isl_vec *vec = NULL;
2068 unsigned dim;
2069 int remove = -1;
2070 isl_int g, fl, fu;
2071
2072 isl_int_init(g);
2073 isl_int_init(fl);
2074 isl_int_init(fu);
2075
2076 if (!bmap)
2077 goto error;
2078
2079 dim = isl_dim_total(bmap->dim);
2080 vec = isl_vec_alloc(bmap->ctx, 1 + dim + bmap->n_div);
2081 if (!vec)
2082 goto error;
2083
2084 tab = isl_tab_from_basic_map(bmap);
2085
2086 while (n > 0) {
2087 int i, l, u;
2088 int best = -1;
2089 enum isl_lp_result res;
2090
2091 for (i = 0; i < bmap->n_div; ++i) {
2092 if (!pairs[i])
2093 continue;
2094 if (best >= 0 && pairs[best] <= pairs[i])
2095 continue;
2096 best = i;
2097 }
2098
2099 i = best;
2100 for (l = 0; l < bmap->n_ineq; ++l) {
2101 if (!isl_int_is_pos(bmap->ineq[l][1 + dim + i]))
2102 continue;
2103 for (u = 0; u < bmap->n_ineq; ++u) {
2104 if (!isl_int_is_neg(bmap->ineq[u][1 + dim + i]))
2105 continue;
2106 construct_test_ineq(bmap, i, l, u,
2107 vec->el, g, fl, fu);
2108 res = isl_tab_min(tab, vec->el,
2109 bmap->ctx->one, &g, NULL, 0);
2110 if (res == isl_lp_error)
2111 goto error;
2112 if (res == isl_lp_empty) {
2113 bmap = isl_basic_map_set_to_empty(bmap);
2114 break;
2115 }
2116 if (res != isl_lp_ok || isl_int_is_neg(g))
2117 break;
2118 }
2119 if (u < bmap->n_ineq)
2120 break;
2121 }
2122 if (l == bmap->n_ineq) {
2123 remove = i;
2124 break;
2125 }
2126 pairs[i] = 0;
2127 --n;
2128 }
2129
2130 isl_tab_free(tab);
2131 isl_vec_free(vec);
2132
2133 isl_int_clear(g);
2134 isl_int_clear(fl);
2135 isl_int_clear(fu);
2136
2137 free(pairs);
2138
2139 if (remove < 0)
2140 return bmap;
2141
2142 bmap = isl_basic_map_remove(bmap, isl_dim_div, remove, 1);
2143 return isl_basic_map_drop_redundant_divs(bmap);
2144 error:
2145 free(pairs);
2146 isl_basic_map_free(bmap);
2147 isl_tab_free(tab);
2148 isl_vec_free(vec);
2149 isl_int_clear(g);
2150 isl_int_clear(fl);
2151 isl_int_clear(fu);
2152 return NULL;
2153 }
2154
2155 /* Given a pair of divs div1 and div2 such that, expect for the lower bound l
2156 * and the upper bound u, div1 always occurs together with div2 in the form
2157 * (div1 + m div2), where m is the constant range on the variable div1
2158 * allowed by l and u, replace the pair div1 and div2 by a single
2159 * div that is equal to div1 + m div2.
2160 *
2161 * The new div will appear in the location that contains div2.
2162 * We need to modify all constraints that contain
2163 * div2 = (div - div1) / m
2164 * (If a constraint does not contain div2, it will also not contain div1.)
2165 * If the constraint also contains div1, then we know they appear
2166 * as f (div1 + m div2) and we can simply replace (div1 + m div2) by div,
2167 * i.e., the coefficient of div is f.
2168 *
2169 * Otherwise, we first need to introduce div1 into the constraint.
2170 * Let the l be
2171 *
2172 * div1 + f >=0
2173 *
2174 * and u
2175 *
2176 * -div1 + f' >= 0
2177 *
2178 * A lower bound on div2
2179 *
2180 * n div2 + t >= 0
2181 *
2182 * can be replaced by
2183 *
2184 * (n * (m div 2 + div1) + m t + n f)/g >= 0
2185 *
2186 * with g = gcd(m,n).
2187 * An upper bound
2188 *
2189 * -n div2 + t >= 0
2190 *
2191 * can be replaced by
2192 *
2193 * (-n * (m div2 + div1) + m t + n f')/g >= 0
2194 *
2195 * These constraint are those that we would obtain from eliminating
2196 * div1 using Fourier-Motzkin.
2197 *
2198 * After all constraints have been modified, we drop the lower and upper
2199 * bound and then drop div1.
2200 */
2201 static struct isl_basic_map *coalesce_divs(struct isl_basic_map *bmap,
2202 unsigned div1, unsigned div2, unsigned l, unsigned u)
2203 {
2204 isl_int a;
2205 isl_int b;
2206 isl_int m;
2207 unsigned dim, total;
2208 int i;
2209
2210 dim = isl_dim_total(bmap->dim);
2211 total = 1 + dim + bmap->n_div;
2212
2213 isl_int_init(a);
2214 isl_int_init(b);
2215 isl_int_init(m);
2216 isl_int_add(m, bmap->ineq[l][0], bmap->ineq[u][0]);
2217 isl_int_add_ui(m, m, 1);
2218
2219 for (i = 0; i < bmap->n_ineq; ++i) {
2220 if (i == l || i == u)
2221 continue;
2222 if (isl_int_is_zero(bmap->ineq[i][1 + dim + div2]))
2223 continue;
2224 if (isl_int_is_zero(bmap->ineq[i][1 + dim + div1])) {
2225 isl_int_gcd(b, m, bmap->ineq[i][1 + dim + div2]);
2226 isl_int_divexact(a, m, b);
2227 isl_int_divexact(b, bmap->ineq[i][1 + dim + div2], b);
2228 if (isl_int_is_pos(b)) {
2229 isl_seq_combine(bmap->ineq[i], a, bmap->ineq[i],
2230 b, bmap->ineq[l], total);
2231 } else {
2232 isl_int_neg(b, b);
2233 isl_seq_combine(bmap->ineq[i], a, bmap->ineq[i],
2234 b, bmap->ineq[u], total);
2235 }
2236 }
2237 isl_int_set(bmap->ineq[i][1 + dim + div2],
2238 bmap->ineq[i][1 + dim + div1]);
2239 isl_int_set_si(bmap->ineq[i][1 + dim + div1], 0);
2240 }
2241
2242 isl_int_clear(a);
2243 isl_int_clear(b);
2244 isl_int_clear(m);
2245 if (l > u) {
2246 isl_basic_map_drop_inequality(bmap, l);
2247 isl_basic_map_drop_inequality(bmap, u);
2248 } else {
2249 isl_basic_map_drop_inequality(bmap, u);
2250 isl_basic_map_drop_inequality(bmap, l);
2251 }
2252 bmap = isl_basic_map_drop_div(bmap, div1);
2253 return bmap;
2254 }
2255
2256 /* First check if we can coalesce any pair of divs and
2257 * then continue with dropping more redundant divs.
2258 *
2259 * We loop over all pairs of lower and upper bounds on a div
2260 * with coefficient 1 and -1, respectively, check if there
2261 * is any other div "c" with which we can coalesce the div
2262 * and if so, perform the coalescing.
2263 */
2264 static struct isl_basic_map *coalesce_or_drop_more_redundant_divs(
2265 struct isl_basic_map *bmap, int *pairs, int n)
2266 {
2267 int i, l, u;
2268 unsigned dim;
2269
2270 dim = isl_dim_total(bmap->dim);
2271
2272 for (i = 0; i < bmap->n_div; ++i) {
2273 if (!pairs[i])
2274 continue;
2275 for (l = 0; l < bmap->n_ineq; ++l) {
2276 if (!isl_int_is_one(bmap->ineq[l][1 + dim + i]))
2277 continue;
2278 for (u = 0; u < bmap->n_ineq; ++u) {
2279 int c;
2280
2281 if (!isl_int_is_negone(bmap->ineq[u][1+dim+i]))
2282 continue;
2283 c = div_find_coalesce(bmap, pairs, i, l, u);
2284 if (c < 0)
2285 continue;
2286 free(pairs);
2287 bmap = coalesce_divs(bmap, i, c, l, u);
2288 return isl_basic_map_drop_redundant_divs(bmap);
2289 }
2290 }
2291 }
2292
2293 if (ISL_F_ISSET(bmap, ISL_BASIC_MAP_EMPTY))
2294 return bmap;
2295
2296 return drop_more_redundant_divs(bmap, pairs, n);
2297 }
2298
2299 /* Remove divs that are not strictly needed.
2300 * In particular, if a div only occurs positively (or negatively)
2301 * in constraints, then it can simply be dropped.
2302 * Also, if a div occurs only occurs in two constraints and if moreover
2303 * those two constraints are opposite to each other, except for the constant
2304 * term and if the sum of the constant terms is such that for any value
2305 * of the other values, there is always at least one integer value of the
2306 * div, i.e., if one plus this sum is greater than or equal to
2307 * the (absolute value) of the coefficent of the div in the constraints,
2308 * then we can also simply drop the div.
2309 *
2310 * If any divs are left after these simple checks then we move on
2311 * to more complicated cases in drop_more_redundant_divs.
2312 */
2313 struct isl_basic_map *isl_basic_map_drop_redundant_divs(
2314 struct isl_basic_map *bmap)
2315 {
2316 int i, j;
2317 unsigned off;
2318 int *pairs = NULL;
2319 int n = 0;
2320
2321 if (!bmap)
2322 goto error;
2323
2324 off = isl_dim_total(bmap->dim);
2325 pairs = isl_calloc_array(bmap->ctx, int, bmap->n_div);
2326 if (!pairs)
2327 goto error;
2328
2329 for (i = 0; i < bmap->n_div; ++i) {
2330 int pos, neg;
2331 int last_pos, last_neg;
2332 int redundant;
2333 int defined;
2334
2335 defined = !isl_int_is_zero(bmap->div[i][0]);
2336 for (j = 0; j < bmap->n_eq; ++j)
2337 if (!isl_int_is_zero(bmap->eq[j][1 + off + i]))
2338 break;
2339 if (j < bmap->n_eq)
2340 continue;
2341 ++n;
2342 pos = neg = 0;
2343 for (j = 0; j < bmap->n_ineq; ++j) {
2344 if (isl_int_is_pos(bmap->ineq[j][1 + off + i])) {
2345 last_pos = j;
2346 ++pos;
2347 }
2348 if (isl_int_is_neg(bmap->ineq[j][1 + off + i])) {
2349 last_neg = j;
2350 ++neg;
2351 }
2352 }
2353 pairs[i] = pos * neg;
2354 if (pairs[i] == 0) {
2355 for (j = bmap->n_ineq - 1; j >= 0; --j)
2356 if (!isl_int_is_zero(bmap->ineq[j][1+off+i]))
2357 isl_basic_map_drop_inequality(bmap, j);
2358 bmap = isl_basic_map_drop_div(bmap, i);
2359 free(pairs);
2360 return isl_basic_map_drop_redundant_divs(bmap);
2361 }
2362 if (pairs[i] != 1)
2363 continue;
2364 if (!isl_seq_is_neg(bmap->ineq[last_pos] + 1,
2365 bmap->ineq[last_neg] + 1,
2366 off + bmap->n_div))
2367 continue;
2368
2369 isl_int_add(bmap->ineq[last_pos][0],
2370 bmap->ineq[last_pos][0], bmap->ineq[last_neg][0]);
2371 isl_int_add_ui(bmap->ineq[last_pos][0],
2372 bmap->ineq[last_pos][0], 1);
2373 redundant = isl_int_ge(bmap->ineq[last_pos][0],
2374 bmap->ineq[last_pos][1+off+i]);
2375 isl_int_sub_ui(bmap->ineq[last_pos][0],
2376 bmap->ineq[last_pos][0], 1);
2377 isl_int_sub(bmap->ineq[last_pos][0],
2378 bmap->ineq[last_pos][0], bmap->ineq[last_neg][0]);
2379 if (!redundant) {
2380 if (defined ||
2381 !ok_to_set_div_from_bound(bmap, i, last_pos)) {
2382 pairs[i] = 0;
2383 --n;
2384 continue;
2385 }
2386 bmap = set_div_from_lower_bound(bmap, i, last_pos);
2387 bmap = isl_basic_map_simplify(bmap);
2388 free(pairs);
2389 return isl_basic_map_drop_redundant_divs(bmap);
2390 }
2391 if (last_pos > last_neg) {
2392 isl_basic_map_drop_inequality(bmap, last_pos);
2393 isl_basic_map_drop_inequality(bmap, last_neg);
2394 } else {
2395 isl_basic_map_drop_inequality(bmap, last_neg);
2396 isl_basic_map_drop_inequality(bmap, last_pos);
2397 }
2398 bmap = isl_basic_map_drop_div(bmap, i);
2399 free(pairs);
2400 return isl_basic_map_drop_redundant_divs(bmap);
2401 }
2402
2403 if (n > 0)
2404 return coalesce_or_drop_more_redundant_divs(bmap, pairs, n);
2405
2406 free(pairs);
2407 return bmap;
2408 error:
2409 free(pairs);
2410 isl_basic_map_free(bmap);
2411 return NULL;
2412 }
2413
2414 struct isl_basic_set *isl_basic_set_drop_redundant_divs(
2415 struct isl_basic_set *bset)
2416 {
2417 return (struct isl_basic_set *)
2418 isl_basic_map_drop_redundant_divs((struct isl_basic_map *)bset);
2419 }
2420
2421 struct isl_map *isl_map_drop_redundant_divs(struct isl_map *map)
2422 {
2423 int i;
2424
2425 if (!map)
2426 return NULL;
2427 for (i = 0; i < map->n; ++i) {
2428 map->p[i] = isl_basic_map_drop_redundant_divs(map->p[i]);
2429 if (!map->p[i])
2430 goto error;
2431 }
2432 ISL_F_CLR(map, ISL_MAP_NORMALIZED);
2433 return map;
2434 error:
2435 isl_map_free(map);
2436 return NULL;
2437 }
2438
2439 struct isl_set *isl_set_drop_redundant_divs(struct isl_set *set)
2440 {
2441 return (struct isl_set *)
2442 isl_map_drop_redundant_divs((struct isl_map *)set);
2443 }
Integer set library