isl_map_gist_basic_map: drop empty pieces in result
[platform/upstream/isl.git] / isl_map_simplify.c
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 #include <isl_dim_private.h>
16 #include <isl_mat_private.h>
17
18 static void swap_equality(struct isl_basic_map *bmap, int a, int b)
19 {
20         isl_int *t = bmap->eq[a];
21         bmap->eq[a] = bmap->eq[b];
22         bmap->eq[b] = t;
23 }
24
25 static void swap_inequality(struct isl_basic_map *bmap, int a, int b)
26 {
27         if (a != b) {
28                 isl_int *t = bmap->ineq[a];
29                 bmap->ineq[a] = bmap->ineq[b];
30                 bmap->ineq[b] = t;
31         }
32 }
33
34 static void set_swap_inequality(struct isl_basic_set *bset, int a, int b)
35 {
36         swap_inequality((struct isl_basic_map *)bset, a, b);
37 }
38
39 static void constraint_drop_vars(isl_int *c, unsigned n, unsigned rem)
40 {
41         isl_seq_cpy(c, c + n, rem);
42         isl_seq_clr(c + rem, n);
43 }
44
45 /* Drop n dimensions starting at first.
46  *
47  * In principle, this frees up some extra variables as the number
48  * of columns remains constant, but we would have to extend
49  * the div array too as the number of rows in this array is assumed
50  * to be equal to extra.
51  */
52 struct isl_basic_set *isl_basic_set_drop_dims(
53                 struct isl_basic_set *bset, unsigned first, unsigned n)
54 {
55         int i;
56
57         if (!bset)
58                 goto error;
59
60         isl_assert(bset->ctx, first + n <= bset->dim->n_out, goto error);
61
62         if (n == 0 && !isl_dim_get_tuple_name(bset->dim, isl_dim_set))
63                 return bset;
64
65         bset = isl_basic_set_cow(bset);
66         if (!bset)
67                 return NULL;
68
69         for (i = 0; i < bset->n_eq; ++i)
70                 constraint_drop_vars(bset->eq[i]+1+bset->dim->nparam+first, n,
71                                      (bset->dim->n_out-first-n)+bset->extra);
72
73         for (i = 0; i < bset->n_ineq; ++i)
74                 constraint_drop_vars(bset->ineq[i]+1+bset->dim->nparam+first, n,
75                                      (bset->dim->n_out-first-n)+bset->extra);
76
77         for (i = 0; i < bset->n_div; ++i)
78                 constraint_drop_vars(bset->div[i]+1+1+bset->dim->nparam+first, n,
79                                      (bset->dim->n_out-first-n)+bset->extra);
80
81         bset->dim = isl_dim_drop_outputs(bset->dim, first, n);
82         if (!bset->dim)
83                 goto error;
84
85         ISL_F_CLR(bset, ISL_BASIC_SET_NORMALIZED);
86         bset = isl_basic_set_simplify(bset);
87         return isl_basic_set_finalize(bset);
88 error:
89         isl_basic_set_free(bset);
90         return NULL;
91 }
92
93 struct isl_set *isl_set_drop_dims(
94                 struct isl_set *set, unsigned first, unsigned n)
95 {
96         int i;
97
98         if (!set)
99                 goto error;
100
101         isl_assert(set->ctx, first + n <= set->dim->n_out, goto error);
102
103         if (n == 0 && !isl_dim_get_tuple_name(set->dim, isl_dim_set))
104                 return set;
105         set = isl_set_cow(set);
106         if (!set)
107                 goto error;
108         set->dim = isl_dim_drop_outputs(set->dim, first, n);
109         if (!set->dim)
110                 goto error;
111
112         for (i = 0; i < set->n; ++i) {
113                 set->p[i] = isl_basic_set_drop_dims(set->p[i], first, n);
114                 if (!set->p[i])
115                         goto error;
116         }
117
118         ISL_F_CLR(set, ISL_SET_NORMALIZED);
119         return set;
120 error:
121         isl_set_free(set);
122         return NULL;
123 }
124
125 /* Move "n" divs starting at "first" to the end of the list of divs.
126  */
127 static struct isl_basic_map *move_divs_last(struct isl_basic_map *bmap,
128         unsigned first, unsigned n)
129 {
130         isl_int **div;
131         int i;
132
133         if (first + n == bmap->n_div)
134                 return bmap;
135
136         div = isl_alloc_array(bmap->ctx, isl_int *, n);
137         if (!div)
138                 goto error;
139         for (i = 0; i < n; ++i)
140                 div[i] = bmap->div[first + i];
141         for (i = 0; i < bmap->n_div - first - n; ++i)
142                 bmap->div[first + i] = bmap->div[first + n + i];
143         for (i = 0; i < n; ++i)
144                 bmap->div[bmap->n_div - n + i] = div[i];
145         free(div);
146         return bmap;
147 error:
148         isl_basic_map_free(bmap);
149         return NULL;
150 }
151
152 /* Drop "n" dimensions of type "type" starting at "first".
153  *
154  * In principle, this frees up some extra variables as the number
155  * of columns remains constant, but we would have to extend
156  * the div array too as the number of rows in this array is assumed
157  * to be equal to extra.
158  */
159 struct isl_basic_map *isl_basic_map_drop(struct isl_basic_map *bmap,
160         enum isl_dim_type type, unsigned first, unsigned n)
161 {
162         int i;
163         unsigned dim;
164         unsigned offset;
165         unsigned left;
166
167         if (!bmap)
168                 goto error;
169
170         dim = isl_basic_map_dim(bmap, type);
171         isl_assert(bmap->ctx, first + n <= dim, goto error);
172
173         if (n == 0 && !isl_dim_get_tuple_name(bmap->dim, type))
174                 return bmap;
175
176         bmap = isl_basic_map_cow(bmap);
177         if (!bmap)
178                 return NULL;
179
180         offset = isl_basic_map_offset(bmap, type) + first;
181         left = isl_basic_map_total_dim(bmap) - (offset - 1) - n;
182         for (i = 0; i < bmap->n_eq; ++i)
183                 constraint_drop_vars(bmap->eq[i]+offset, n, left);
184
185         for (i = 0; i < bmap->n_ineq; ++i)
186                 constraint_drop_vars(bmap->ineq[i]+offset, n, left);
187
188         for (i = 0; i < bmap->n_div; ++i)
189                 constraint_drop_vars(bmap->div[i]+1+offset, n, left);
190
191         if (type == isl_dim_div) {
192                 bmap = move_divs_last(bmap, first, n);
193                 if (!bmap)
194                         goto error;
195                 isl_basic_map_free_div(bmap, n);
196         } else
197                 bmap->dim = isl_dim_drop(bmap->dim, type, first, n);
198         if (!bmap->dim)
199                 goto error;
200
201         ISL_F_CLR(bmap, ISL_BASIC_MAP_NORMALIZED);
202         bmap = isl_basic_map_simplify(bmap);
203         return isl_basic_map_finalize(bmap);
204 error:
205         isl_basic_map_free(bmap);
206         return NULL;
207 }
208
209 __isl_give isl_basic_set *isl_basic_set_drop(__isl_take isl_basic_set *bset,
210         enum isl_dim_type type, unsigned first, unsigned n)
211 {
212         return (isl_basic_set *)isl_basic_map_drop((isl_basic_map *)bset,
213                                                         type, first, n);
214 }
215
216 struct isl_basic_map *isl_basic_map_drop_inputs(
217                 struct isl_basic_map *bmap, unsigned first, unsigned n)
218 {
219         return isl_basic_map_drop(bmap, isl_dim_in, first, n);
220 }
221
222 struct isl_map *isl_map_drop(struct isl_map *map,
223         enum isl_dim_type type, unsigned first, unsigned n)
224 {
225         int i;
226
227         if (!map)
228                 goto error;
229
230         isl_assert(map->ctx, first + n <= isl_map_dim(map, type), goto error);
231
232         if (n == 0 && !isl_dim_get_tuple_name(map->dim, type))
233                 return map;
234         map = isl_map_cow(map);
235         if (!map)
236                 goto error;
237         map->dim = isl_dim_drop(map->dim, type, first, n);
238         if (!map->dim)
239                 goto error;
240
241         for (i = 0; i < map->n; ++i) {
242                 map->p[i] = isl_basic_map_drop(map->p[i], type, first, n);
243                 if (!map->p[i])
244                         goto error;
245         }
246         ISL_F_CLR(map, ISL_MAP_NORMALIZED);
247
248         return map;
249 error:
250         isl_map_free(map);
251         return NULL;
252 }
253
254 struct isl_set *isl_set_drop(struct isl_set *set,
255         enum isl_dim_type type, unsigned first, unsigned n)
256 {
257         return (isl_set *)isl_map_drop((isl_map *)set, type, first, n);
258 }
259
260 struct isl_map *isl_map_drop_inputs(
261                 struct isl_map *map, unsigned first, unsigned n)
262 {
263         return isl_map_drop(map, isl_dim_in, first, n);
264 }
265
266 /*
267  * We don't cow, as the div is assumed to be redundant.
268  */
269 static struct isl_basic_map *isl_basic_map_drop_div(
270                 struct isl_basic_map *bmap, unsigned div)
271 {
272         int i;
273         unsigned pos;
274
275         if (!bmap)
276                 goto error;
277
278         pos = 1 + isl_dim_total(bmap->dim) + div;
279
280         isl_assert(bmap->ctx, div < bmap->n_div, goto error);
281
282         for (i = 0; i < bmap->n_eq; ++i)
283                 constraint_drop_vars(bmap->eq[i]+pos, 1, bmap->extra-div-1);
284
285         for (i = 0; i < bmap->n_ineq; ++i) {
286                 if (!isl_int_is_zero(bmap->ineq[i][pos])) {
287                         isl_basic_map_drop_inequality(bmap, i);
288                         --i;
289                         continue;
290                 }
291                 constraint_drop_vars(bmap->ineq[i]+pos, 1, bmap->extra-div-1);
292         }
293
294         for (i = 0; i < bmap->n_div; ++i)
295                 constraint_drop_vars(bmap->div[i]+1+pos, 1, bmap->extra-div-1);
296
297         if (div != bmap->n_div - 1) {
298                 int j;
299                 isl_int *t = bmap->div[div];
300
301                 for (j = div; j < bmap->n_div - 1; ++j)
302                         bmap->div[j] = bmap->div[j+1];
303
304                 bmap->div[bmap->n_div - 1] = t;
305         }
306         ISL_F_CLR(bmap, ISL_BASIC_MAP_NORMALIZED);
307         isl_basic_map_free_div(bmap, 1);
308
309         return bmap;
310 error:
311         isl_basic_map_free(bmap);
312         return NULL;
313 }
314
315 struct isl_basic_map *isl_basic_map_normalize_constraints(
316         struct isl_basic_map *bmap)
317 {
318         int i;
319         isl_int gcd;
320         unsigned total = isl_basic_map_total_dim(bmap);
321
322         if (!bmap)
323                 return NULL;
324
325         isl_int_init(gcd);
326         for (i = bmap->n_eq - 1; i >= 0; --i) {
327                 isl_seq_gcd(bmap->eq[i]+1, total, &gcd);
328                 if (isl_int_is_zero(gcd)) {
329                         if (!isl_int_is_zero(bmap->eq[i][0])) {
330                                 bmap = isl_basic_map_set_to_empty(bmap);
331                                 break;
332                         }
333                         isl_basic_map_drop_equality(bmap, i);
334                         continue;
335                 }
336                 if (ISL_F_ISSET(bmap, ISL_BASIC_MAP_RATIONAL))
337                         isl_int_gcd(gcd, gcd, bmap->eq[i][0]);
338                 if (isl_int_is_one(gcd))
339                         continue;
340                 if (!isl_int_is_divisible_by(bmap->eq[i][0], gcd)) {
341                         bmap = isl_basic_map_set_to_empty(bmap);
342                         break;
343                 }
344                 isl_seq_scale_down(bmap->eq[i], bmap->eq[i], gcd, 1+total);
345         }
346
347         for (i = bmap->n_ineq - 1; i >= 0; --i) {
348                 isl_seq_gcd(bmap->ineq[i]+1, total, &gcd);
349                 if (isl_int_is_zero(gcd)) {
350                         if (isl_int_is_neg(bmap->ineq[i][0])) {
351                                 bmap = isl_basic_map_set_to_empty(bmap);
352                                 break;
353                         }
354                         isl_basic_map_drop_inequality(bmap, i);
355                         continue;
356                 }
357                 if (ISL_F_ISSET(bmap, ISL_BASIC_MAP_RATIONAL))
358                         isl_int_gcd(gcd, gcd, bmap->ineq[i][0]);
359                 if (isl_int_is_one(gcd))
360                         continue;
361                 isl_int_fdiv_q(bmap->ineq[i][0], bmap->ineq[i][0], gcd);
362                 isl_seq_scale_down(bmap->ineq[i]+1, bmap->ineq[i]+1, gcd, total);
363         }
364         isl_int_clear(gcd);
365
366         return bmap;
367 }
368
369 struct isl_basic_set *isl_basic_set_normalize_constraints(
370         struct isl_basic_set *bset)
371 {
372         return (struct isl_basic_set *)isl_basic_map_normalize_constraints(
373                 (struct isl_basic_map *)bset);
374 }
375
376 /* Assumes divs have been ordered if keep_divs is set.
377  */
378 static void eliminate_var_using_equality(struct isl_basic_map *bmap,
379         unsigned pos, isl_int *eq, int keep_divs, int *progress)
380 {
381         unsigned total;
382         int k;
383         int last_div;
384
385         total = isl_basic_map_total_dim(bmap);
386         last_div = isl_seq_last_non_zero(eq + 1 + isl_dim_total(bmap->dim),
387                                                 bmap->n_div);
388         for (k = 0; k < bmap->n_eq; ++k) {
389                 if (bmap->eq[k] == eq)
390                         continue;
391                 if (isl_int_is_zero(bmap->eq[k][1+pos]))
392                         continue;
393                 if (progress)
394                         *progress = 1;
395                 isl_seq_elim(bmap->eq[k], eq, 1+pos, 1+total, NULL);
396                 isl_seq_normalize(bmap->ctx, bmap->eq[k], 1 + total);
397         }
398
399         for (k = 0; k < bmap->n_ineq; ++k) {
400                 if (isl_int_is_zero(bmap->ineq[k][1+pos]))
401                         continue;
402                 if (progress)
403                         *progress = 1;
404                 isl_seq_elim(bmap->ineq[k], eq, 1+pos, 1+total, NULL);
405                 isl_seq_normalize(bmap->ctx, bmap->ineq[k], 1 + total);
406                 ISL_F_CLR(bmap, ISL_BASIC_MAP_NORMALIZED);
407         }
408
409         for (k = 0; k < bmap->n_div; ++k) {
410                 if (isl_int_is_zero(bmap->div[k][0]))
411                         continue;
412                 if (isl_int_is_zero(bmap->div[k][1+1+pos]))
413                         continue;
414                 if (progress)
415                         *progress = 1;
416                 /* We need to be careful about circular definitions,
417                  * so for now we just remove the definition of div k
418                  * if the equality contains any divs.
419                  * If keep_divs is set, then the divs have been ordered
420                  * and we can keep the definition as long as the result
421                  * is still ordered.
422                  */
423                 if (last_div == -1 || (keep_divs && last_div < k))
424                         isl_seq_elim(bmap->div[k]+1, eq,
425                                         1+pos, 1+total, &bmap->div[k][0]);
426                 else
427                         isl_seq_clr(bmap->div[k], 1 + total);
428                 ISL_F_CLR(bmap, ISL_BASIC_MAP_NORMALIZED);
429         }
430 }
431
432 /* Assumes divs have been ordered if keep_divs is set.
433  */
434 static void eliminate_div(struct isl_basic_map *bmap, isl_int *eq,
435         unsigned div, int keep_divs)
436 {
437         unsigned pos = isl_dim_total(bmap->dim) + div;
438
439         eliminate_var_using_equality(bmap, pos, eq, keep_divs, NULL);
440
441         isl_basic_map_drop_div(bmap, div);
442 }
443
444 /* Check if elimination of div "div" using equality "eq" would not
445  * result in a div depending on a later div.
446  */
447 static int ok_to_eliminate_div(struct isl_basic_map *bmap, isl_int *eq,
448         unsigned div)
449 {
450         int k;
451         int last_div;
452         unsigned pos = isl_dim_total(bmap->dim) + div;
453
454         last_div = isl_seq_last_non_zero(eq + 1 + isl_dim_total(bmap->dim),
455                                                 bmap->n_div);
456         if (last_div < 0 || last_div <= div)
457                 return 1;
458
459         for (k = 0; k <= last_div; ++k) {
460                 if (isl_int_is_zero(bmap->div[k][0]))
461                         return 1;
462                 if (!isl_int_is_zero(bmap->div[k][1 + 1 + pos]))
463                         return 0;
464         }
465
466         return 1;
467 }
468
469 /* Elimininate divs based on equalities
470  */
471 static struct isl_basic_map *eliminate_divs_eq(
472                 struct isl_basic_map *bmap, int *progress)
473 {
474         int d;
475         int i;
476         int modified = 0;
477         unsigned off;
478
479         bmap = isl_basic_map_order_divs(bmap);
480
481         if (!bmap)
482                 return NULL;
483
484         off = 1 + isl_dim_total(bmap->dim);
485
486         for (d = bmap->n_div - 1; d >= 0 ; --d) {
487                 for (i = 0; i < bmap->n_eq; ++i) {
488                         if (!isl_int_is_one(bmap->eq[i][off + d]) &&
489                             !isl_int_is_negone(bmap->eq[i][off + d]))
490                                 continue;
491                         if (!ok_to_eliminate_div(bmap, bmap->eq[i], d))
492                                 continue;
493                         modified = 1;
494                         *progress = 1;
495                         eliminate_div(bmap, bmap->eq[i], d, 1);
496                         isl_basic_map_drop_equality(bmap, i);
497                         break;
498                 }
499         }
500         if (modified)
501                 return eliminate_divs_eq(bmap, progress);
502         return bmap;
503 }
504
505 /* Elimininate divs based on inequalities
506  */
507 static struct isl_basic_map *eliminate_divs_ineq(
508                 struct isl_basic_map *bmap, int *progress)
509 {
510         int d;
511         int i;
512         unsigned off;
513         struct isl_ctx *ctx;
514
515         if (!bmap)
516                 return NULL;
517
518         ctx = bmap->ctx;
519         off = 1 + isl_dim_total(bmap->dim);
520
521         for (d = bmap->n_div - 1; d >= 0 ; --d) {
522                 for (i = 0; i < bmap->n_eq; ++i)
523                         if (!isl_int_is_zero(bmap->eq[i][off + d]))
524                                 break;
525                 if (i < bmap->n_eq)
526                         continue;
527                 for (i = 0; i < bmap->n_ineq; ++i)
528                         if (isl_int_abs_gt(bmap->ineq[i][off + d], ctx->one))
529                                 break;
530                 if (i < bmap->n_ineq)
531                         continue;
532                 *progress = 1;
533                 bmap = isl_basic_map_eliminate_vars(bmap, (off-1)+d, 1);
534                 if (!bmap || ISL_F_ISSET(bmap, ISL_BASIC_MAP_EMPTY))
535                         break;
536                 bmap = isl_basic_map_drop_div(bmap, d);
537                 if (!bmap)
538                         break;
539         }
540         return bmap;
541 }
542
543 struct isl_basic_map *isl_basic_map_gauss(
544         struct isl_basic_map *bmap, int *progress)
545 {
546         int k;
547         int done;
548         int last_var;
549         unsigned total_var;
550         unsigned total;
551
552         bmap = isl_basic_map_order_divs(bmap);
553
554         if (!bmap)
555                 return NULL;
556
557         total = isl_basic_map_total_dim(bmap);
558         total_var = total - bmap->n_div;
559
560         last_var = total - 1;
561         for (done = 0; done < bmap->n_eq; ++done) {
562                 for (; last_var >= 0; --last_var) {
563                         for (k = done; k < bmap->n_eq; ++k)
564                                 if (!isl_int_is_zero(bmap->eq[k][1+last_var]))
565                                         break;
566                         if (k < bmap->n_eq)
567                                 break;
568                 }
569                 if (last_var < 0)
570                         break;
571                 if (k != done)
572                         swap_equality(bmap, k, done);
573                 if (isl_int_is_neg(bmap->eq[done][1+last_var]))
574                         isl_seq_neg(bmap->eq[done], bmap->eq[done], 1+total);
575
576                 eliminate_var_using_equality(bmap, last_var, bmap->eq[done], 1,
577                                                 progress);
578
579                 if (last_var >= total_var &&
580                     isl_int_is_zero(bmap->div[last_var - total_var][0])) {
581                         unsigned div = last_var - total_var;
582                         isl_seq_neg(bmap->div[div]+1, bmap->eq[done], 1+total);
583                         isl_int_set_si(bmap->div[div][1+1+last_var], 0);
584                         isl_int_set(bmap->div[div][0],
585                                     bmap->eq[done][1+last_var]);
586                         ISL_F_CLR(bmap, ISL_BASIC_MAP_NORMALIZED);
587                 }
588         }
589         if (done == bmap->n_eq)
590                 return bmap;
591         for (k = done; k < bmap->n_eq; ++k) {
592                 if (isl_int_is_zero(bmap->eq[k][0]))
593                         continue;
594                 return isl_basic_map_set_to_empty(bmap);
595         }
596         isl_basic_map_free_equality(bmap, bmap->n_eq-done);
597         return bmap;
598 }
599
600 struct isl_basic_set *isl_basic_set_gauss(
601         struct isl_basic_set *bset, int *progress)
602 {
603         return (struct isl_basic_set*)isl_basic_map_gauss(
604                         (struct isl_basic_map *)bset, progress);
605 }
606
607
608 static unsigned int round_up(unsigned int v)
609 {
610         int old_v = v;
611
612         while (v) {
613                 old_v = v;
614                 v ^= v & -v;
615         }
616         return old_v << 1;
617 }
618
619 static int hash_index(isl_int ***index, unsigned int size, int bits,
620                         struct isl_basic_map *bmap, int k)
621 {
622         int h;
623         unsigned total = isl_basic_map_total_dim(bmap);
624         uint32_t hash = isl_seq_get_hash_bits(bmap->ineq[k]+1, total, bits);
625         for (h = hash; index[h]; h = (h+1) % size)
626                 if (&bmap->ineq[k] != index[h] &&
627                     isl_seq_eq(bmap->ineq[k]+1, index[h][0]+1, total))
628                         break;
629         return h;
630 }
631
632 static int set_hash_index(isl_int ***index, unsigned int size, int bits,
633                           struct isl_basic_set *bset, int k)
634 {
635         return hash_index(index, size, bits, (struct isl_basic_map *)bset, k);
636 }
637
638 /* If we can eliminate more than one div, then we need to make
639  * sure we do it from last div to first div, in order not to
640  * change the position of the other divs that still need to
641  * be removed.
642  */
643 static struct isl_basic_map *remove_duplicate_divs(
644         struct isl_basic_map *bmap, int *progress)
645 {
646         unsigned int size;
647         int *index;
648         int *elim_for;
649         int k, l, h;
650         int bits;
651         struct isl_blk eq;
652         unsigned total_var;
653         unsigned total;
654         struct isl_ctx *ctx;
655
656         if (!bmap || bmap->n_div <= 1)
657                 return bmap;
658
659         total_var = isl_dim_total(bmap->dim);
660         total = total_var + bmap->n_div;
661
662         ctx = bmap->ctx;
663         for (k = bmap->n_div - 1; k >= 0; --k)
664                 if (!isl_int_is_zero(bmap->div[k][0]))
665                         break;
666         if (k <= 0)
667                 return bmap;
668
669         elim_for = isl_calloc_array(ctx, int, bmap->n_div);
670         size = round_up(4 * bmap->n_div / 3 - 1);
671         bits = ffs(size) - 1;
672         index = isl_calloc_array(ctx, int, size);
673         if (!index)
674                 return bmap;
675         eq = isl_blk_alloc(ctx, 1+total);
676         if (isl_blk_is_error(eq))
677                 goto out;
678
679         isl_seq_clr(eq.data, 1+total);
680         index[isl_seq_get_hash_bits(bmap->div[k], 2+total, bits)] = k + 1;
681         for (--k; k >= 0; --k) {
682                 uint32_t hash;
683
684                 if (isl_int_is_zero(bmap->div[k][0]))
685                         continue;
686
687                 hash = isl_seq_get_hash_bits(bmap->div[k], 2+total, bits);
688                 for (h = hash; index[h]; h = (h+1) % size)
689                         if (isl_seq_eq(bmap->div[k],
690                                        bmap->div[index[h]-1], 2+total))
691                                 break;
692                 if (index[h]) {
693                         *progress = 1;
694                         l = index[h] - 1;
695                         elim_for[l] = k + 1;
696                 }
697                 index[h] = k+1;
698         }
699         for (l = bmap->n_div - 1; l >= 0; --l) {
700                 if (!elim_for[l])
701                         continue;
702                 k = elim_for[l] - 1;
703                 isl_int_set_si(eq.data[1+total_var+k], -1);
704                 isl_int_set_si(eq.data[1+total_var+l], 1);
705                 eliminate_div(bmap, eq.data, l, 0);
706                 isl_int_set_si(eq.data[1+total_var+k], 0);
707                 isl_int_set_si(eq.data[1+total_var+l], 0);
708         }
709
710         isl_blk_free(ctx, eq);
711 out:
712         free(index);
713         free(elim_for);
714         return bmap;
715 }
716
717 static int n_pure_div_eq(struct isl_basic_map *bmap)
718 {
719         int i, j;
720         unsigned total;
721
722         total = isl_dim_total(bmap->dim);
723         for (i = 0, j = bmap->n_div-1; i < bmap->n_eq; ++i) {
724                 while (j >= 0 && isl_int_is_zero(bmap->eq[i][1 + total + j]))
725                         --j;
726                 if (j < 0)
727                         break;
728                 if (isl_seq_first_non_zero(bmap->eq[i] + 1 + total, j) != -1)
729                         return 0;
730         }
731         return i;
732 }
733
734 /* Normalize divs that appear in equalities.
735  *
736  * In particular, we assume that bmap contains some equalities
737  * of the form
738  *
739  *      a x = m * e_i
740  *
741  * and we want to replace the set of e_i by a minimal set and
742  * such that the new e_i have a canonical representation in terms
743  * of the vector x.
744  * If any of the equalities involves more than one divs, then
745  * we currently simply bail out.
746  *
747  * Let us first additionally assume that all equalities involve
748  * a div.  The equalities then express modulo constraints on the
749  * remaining variables and we can use "parameter compression"
750  * to find a minimal set of constraints.  The result is a transformation
751  *
752  *      x = T(x') = x_0 + G x'
753  *
754  * with G a lower-triangular matrix with all elements below the diagonal
755  * non-negative and smaller than the diagonal element on the same row.
756  * We first normalize x_0 by making the same property hold in the affine
757  * T matrix.
758  * The rows i of G with a 1 on the diagonal do not impose any modulo
759  * constraint and simply express x_i = x'_i.
760  * For each of the remaining rows i, we introduce a div and a corresponding
761  * equality.  In particular
762  *
763  *      g_ii e_j = x_i - g_i(x')
764  *
765  * where each x'_k is replaced either by x_k (if g_kk = 1) or the
766  * corresponding div (if g_kk != 1).
767  *
768  * If there are any equalities not involving any div, then we
769  * first apply a variable compression on the variables x:
770  *
771  *      x = C x''       x'' = C_2 x
772  *
773  * and perform the above parameter compression on A C instead of on A.
774  * The resulting compression is then of the form
775  *
776  *      x'' = T(x') = x_0 + G x'
777  *
778  * and in constructing the new divs and the corresponding equalities,
779  * we have to replace each x'', i.e., the x'_k with (g_kk = 1),
780  * by the corresponding row from C_2.
781  */
782 static struct isl_basic_map *normalize_divs(
783         struct isl_basic_map *bmap, int *progress)
784 {
785         int i, j, k;
786         int total;
787         int div_eq;
788         struct isl_mat *B;
789         struct isl_vec *d;
790         struct isl_mat *T = NULL;
791         struct isl_mat *C = NULL;
792         struct isl_mat *C2 = NULL;
793         isl_int v;
794         int *pos;
795         int dropped, needed;
796
797         if (!bmap)
798                 return NULL;
799
800         if (bmap->n_div == 0)
801                 return bmap;
802
803         if (bmap->n_eq == 0)
804                 return bmap;
805
806         if (ISL_F_ISSET(bmap, ISL_BASIC_MAP_NORMALIZED_DIVS))
807                 return bmap;
808
809         total = isl_dim_total(bmap->dim);
810         div_eq = n_pure_div_eq(bmap);
811         if (div_eq == 0)
812                 return bmap;
813
814         if (div_eq < bmap->n_eq) {
815                 B = isl_mat_sub_alloc(bmap->ctx, bmap->eq, div_eq,
816                                         bmap->n_eq - div_eq, 0, 1 + total);
817                 C = isl_mat_variable_compression(B, &C2);
818                 if (!C || !C2)
819                         goto error;
820                 if (C->n_col == 0) {
821                         bmap = isl_basic_map_set_to_empty(bmap);
822                         isl_mat_free(C);
823                         isl_mat_free(C2);
824                         goto done;
825                 }
826         }
827
828         d = isl_vec_alloc(bmap->ctx, div_eq);
829         if (!d)
830                 goto error;
831         for (i = 0, j = bmap->n_div-1; i < div_eq; ++i) {
832                 while (j >= 0 && isl_int_is_zero(bmap->eq[i][1 + total + j]))
833                         --j;
834                 isl_int_set(d->block.data[i], bmap->eq[i][1 + total + j]);
835         }
836         B = isl_mat_sub_alloc(bmap->ctx, bmap->eq, 0, div_eq, 0, 1 + total);
837
838         if (C) {
839                 B = isl_mat_product(B, C);
840                 C = NULL;
841         }
842
843         T = isl_mat_parameter_compression(B, d);
844         if (!T)
845                 goto error;
846         if (T->n_col == 0) {
847                 bmap = isl_basic_map_set_to_empty(bmap);
848                 isl_mat_free(C2);
849                 isl_mat_free(T);
850                 goto done;
851         }
852         isl_int_init(v);
853         for (i = 0; i < T->n_row - 1; ++i) {
854                 isl_int_fdiv_q(v, T->row[1 + i][0], T->row[1 + i][1 + i]);
855                 if (isl_int_is_zero(v))
856                         continue;
857                 isl_mat_col_submul(T, 0, v, 1 + i);
858         }
859         isl_int_clear(v);
860         pos = isl_alloc_array(bmap->ctx, int, T->n_row);
861         if (!pos)
862                 goto error;
863         /* We have to be careful because dropping equalities may reorder them */
864         dropped = 0;
865         for (j = bmap->n_div - 1; j >= 0; --j) {
866                 for (i = 0; i < bmap->n_eq; ++i)
867                         if (!isl_int_is_zero(bmap->eq[i][1 + total + j]))
868                                 break;
869                 if (i < bmap->n_eq) {
870                         bmap = isl_basic_map_drop_div(bmap, j);
871                         isl_basic_map_drop_equality(bmap, i);
872                         ++dropped;
873                 }
874         }
875         pos[0] = 0;
876         needed = 0;
877         for (i = 1; i < T->n_row; ++i) {
878                 if (isl_int_is_one(T->row[i][i]))
879                         pos[i] = i;
880                 else
881                         needed++;
882         }
883         if (needed > dropped) {
884                 bmap = isl_basic_map_extend_dim(bmap, isl_dim_copy(bmap->dim),
885                                 needed, needed, 0);
886                 if (!bmap)
887                         goto error;
888         }
889         for (i = 1; i < T->n_row; ++i) {
890                 if (isl_int_is_one(T->row[i][i]))
891                         continue;
892                 k = isl_basic_map_alloc_div(bmap);
893                 pos[i] = 1 + total + k;
894                 isl_seq_clr(bmap->div[k] + 1, 1 + total + bmap->n_div);
895                 isl_int_set(bmap->div[k][0], T->row[i][i]);
896                 if (C2)
897                         isl_seq_cpy(bmap->div[k] + 1, C2->row[i], 1 + total);
898                 else
899                         isl_int_set_si(bmap->div[k][1 + i], 1);
900                 for (j = 0; j < i; ++j) {
901                         if (isl_int_is_zero(T->row[i][j]))
902                                 continue;
903                         if (pos[j] < T->n_row && C2)
904                                 isl_seq_submul(bmap->div[k] + 1, T->row[i][j],
905                                                 C2->row[pos[j]], 1 + total);
906                         else
907                                 isl_int_neg(bmap->div[k][1 + pos[j]],
908                                                                 T->row[i][j]);
909                 }
910                 j = isl_basic_map_alloc_equality(bmap);
911                 isl_seq_neg(bmap->eq[j], bmap->div[k]+1, 1+total+bmap->n_div);
912                 isl_int_set(bmap->eq[j][pos[i]], bmap->div[k][0]);
913         }
914         free(pos);
915         isl_mat_free(C2);
916         isl_mat_free(T);
917
918         if (progress)
919                 *progress = 1;
920 done:
921         ISL_F_SET(bmap, ISL_BASIC_MAP_NORMALIZED_DIVS);
922
923         return bmap;
924 error:
925         isl_mat_free(C);
926         isl_mat_free(C2);
927         isl_mat_free(T);
928         return bmap;
929 }
930
931 static struct isl_basic_map *set_div_from_lower_bound(
932         struct isl_basic_map *bmap, int div, int ineq)
933 {
934         unsigned total = 1 + isl_dim_total(bmap->dim);
935
936         isl_seq_neg(bmap->div[div] + 1, bmap->ineq[ineq], total + bmap->n_div);
937         isl_int_set(bmap->div[div][0], bmap->ineq[ineq][total + div]);
938         isl_int_add(bmap->div[div][1], bmap->div[div][1], bmap->div[div][0]);
939         isl_int_sub_ui(bmap->div[div][1], bmap->div[div][1], 1);
940         isl_int_set_si(bmap->div[div][1 + total + div], 0);
941
942         return bmap;
943 }
944
945 /* Check whether it is ok to define a div based on an inequality.
946  * To avoid the introduction of circular definitions of divs, we
947  * do not allow such a definition if the resulting expression would refer to
948  * any other undefined divs or if any known div is defined in
949  * terms of the unknown div.
950  */
951 static int ok_to_set_div_from_bound(struct isl_basic_map *bmap,
952         int div, int ineq)
953 {
954         int j;
955         unsigned total = 1 + isl_dim_total(bmap->dim);
956
957         /* Not defined in terms of unknown divs */
958         for (j = 0; j < bmap->n_div; ++j) {
959                 if (div == j)
960                         continue;
961                 if (isl_int_is_zero(bmap->ineq[ineq][total + j]))
962                         continue;
963                 if (isl_int_is_zero(bmap->div[j][0]))
964                         return 0;
965         }
966
967         /* No other div defined in terms of this one => avoid loops */
968         for (j = 0; j < bmap->n_div; ++j) {
969                 if (div == j)
970                         continue;
971                 if (isl_int_is_zero(bmap->div[j][0]))
972                         continue;
973                 if (!isl_int_is_zero(bmap->div[j][1 + total + div]))
974                         return 0;
975         }
976
977         return 1;
978 }
979
980 /* Given two constraints "k" and "l" that are opposite to each other,
981  * except for the constant term, check if we can use them
982  * to obtain an expression for one of the hitherto unknown divs.
983  * "sum" is the sum of the constant terms of the constraints.
984  * If this sum is strictly smaller than the coefficient of one
985  * of the divs, then this pair can be used define the div.
986  * To avoid the introduction of circular definitions of divs, we
987  * do not use the pair if the resulting expression would refer to
988  * any other undefined divs or if any known div is defined in
989  * terms of the unknown div.
990  */
991 static struct isl_basic_map *check_for_div_constraints(
992         struct isl_basic_map *bmap, int k, int l, isl_int sum, int *progress)
993 {
994         int i;
995         unsigned total = 1 + isl_dim_total(bmap->dim);
996
997         for (i = 0; i < bmap->n_div; ++i) {
998                 if (!isl_int_is_zero(bmap->div[i][0]))
999                         continue;
1000                 if (isl_int_is_zero(bmap->ineq[k][total + i]))
1001                         continue;
1002                 if (isl_int_abs_ge(sum, bmap->ineq[k][total + i]))
1003                         continue;
1004                 if (!ok_to_set_div_from_bound(bmap, i, k))
1005                         break;
1006                 if (isl_int_is_pos(bmap->ineq[k][total + i]))
1007                         bmap = set_div_from_lower_bound(bmap, i, k);
1008                 else
1009                         bmap = set_div_from_lower_bound(bmap, i, l);
1010                 if (progress)
1011                         *progress = 1;
1012                 break;
1013         }
1014         return bmap;
1015 }
1016
1017 static struct isl_basic_map *remove_duplicate_constraints(
1018         struct isl_basic_map *bmap, int *progress)
1019 {
1020         unsigned int size;
1021         isl_int ***index;
1022         int k, l, h;
1023         int bits;
1024         unsigned total = isl_basic_map_total_dim(bmap);
1025         isl_int sum;
1026
1027         if (!bmap || bmap->n_ineq <= 1)
1028                 return bmap;
1029
1030         size = round_up(4 * (bmap->n_ineq+1) / 3 - 1);
1031         bits = ffs(size) - 1;
1032         index = isl_calloc_array(ctx, isl_int **, size);
1033         if (!index)
1034                 return bmap;
1035
1036         index[isl_seq_get_hash_bits(bmap->ineq[0]+1, total, bits)] = &bmap->ineq[0];
1037         for (k = 1; k < bmap->n_ineq; ++k) {
1038                 h = hash_index(index, size, bits, bmap, k);
1039                 if (!index[h]) {
1040                         index[h] = &bmap->ineq[k];
1041                         continue;
1042                 }
1043                 if (progress)
1044                         *progress = 1;
1045                 l = index[h] - &bmap->ineq[0];
1046                 if (isl_int_lt(bmap->ineq[k][0], bmap->ineq[l][0]))
1047                         swap_inequality(bmap, k, l);
1048                 isl_basic_map_drop_inequality(bmap, k);
1049                 --k;
1050         }
1051         isl_int_init(sum);
1052         for (k = 0; k < bmap->n_ineq-1; ++k) {
1053                 isl_seq_neg(bmap->ineq[k]+1, bmap->ineq[k]+1, total);
1054                 h = hash_index(index, size, bits, bmap, k);
1055                 isl_seq_neg(bmap->ineq[k]+1, bmap->ineq[k]+1, total);
1056                 if (!index[h])
1057                         continue;
1058                 l = index[h] - &bmap->ineq[0];
1059                 isl_int_add(sum, bmap->ineq[k][0], bmap->ineq[l][0]);
1060                 if (isl_int_is_pos(sum)) {
1061                         bmap = check_for_div_constraints(bmap, k, l, sum,
1062                                                          progress);
1063                         continue;
1064                 }
1065                 if (isl_int_is_zero(sum)) {
1066                         /* We need to break out of the loop after these
1067                          * changes since the contents of the hash
1068                          * will no longer be valid.
1069                          * Plus, we probably we want to regauss first.
1070                          */
1071                         if (progress)
1072                                 *progress = 1;
1073                         isl_basic_map_drop_inequality(bmap, l);
1074                         isl_basic_map_inequality_to_equality(bmap, k);
1075                 } else
1076                         bmap = isl_basic_map_set_to_empty(bmap);
1077                 break;
1078         }
1079         isl_int_clear(sum);
1080
1081         free(index);
1082         return bmap;
1083 }
1084
1085
1086 struct isl_basic_map *isl_basic_map_simplify(struct isl_basic_map *bmap)
1087 {
1088         int progress = 1;
1089         if (!bmap)
1090                 return NULL;
1091         while (progress) {
1092                 progress = 0;
1093                 bmap = isl_basic_map_normalize_constraints(bmap);
1094                 bmap = remove_duplicate_divs(bmap, &progress);
1095                 bmap = eliminate_divs_eq(bmap, &progress);
1096                 bmap = eliminate_divs_ineq(bmap, &progress);
1097                 bmap = isl_basic_map_gauss(bmap, &progress);
1098                 /* requires equalities in normal form */
1099                 bmap = normalize_divs(bmap, &progress);
1100                 bmap = remove_duplicate_constraints(bmap, &progress);
1101         }
1102         return bmap;
1103 }
1104
1105 struct isl_basic_set *isl_basic_set_simplify(struct isl_basic_set *bset)
1106 {
1107         return (struct isl_basic_set *)
1108                 isl_basic_map_simplify((struct isl_basic_map *)bset);
1109 }
1110
1111
1112 int isl_basic_map_is_div_constraint(__isl_keep isl_basic_map *bmap,
1113         isl_int *constraint, unsigned div)
1114 {
1115         unsigned pos;
1116
1117         if (!bmap)
1118                 return -1;
1119
1120         pos = 1 + isl_dim_total(bmap->dim) + div;
1121
1122         if (isl_int_eq(constraint[pos], bmap->div[div][0])) {
1123                 int neg;
1124                 isl_int_sub(bmap->div[div][1],
1125                                 bmap->div[div][1], bmap->div[div][0]);
1126                 isl_int_add_ui(bmap->div[div][1], bmap->div[div][1], 1);
1127                 neg = isl_seq_is_neg(constraint, bmap->div[div]+1, pos);
1128                 isl_int_sub_ui(bmap->div[div][1], bmap->div[div][1], 1);
1129                 isl_int_add(bmap->div[div][1],
1130                                 bmap->div[div][1], bmap->div[div][0]);
1131                 if (!neg)
1132                         return 0;
1133                 if (isl_seq_first_non_zero(constraint+pos+1,
1134                                             bmap->n_div-div-1) != -1)
1135                         return 0;
1136         } else if (isl_int_abs_eq(constraint[pos], bmap->div[div][0])) {
1137                 if (!isl_seq_eq(constraint, bmap->div[div]+1, pos))
1138                         return 0;
1139                 if (isl_seq_first_non_zero(constraint+pos+1,
1140                                             bmap->n_div-div-1) != -1)
1141                         return 0;
1142         } else
1143                 return 0;
1144
1145         return 1;
1146 }
1147
1148
1149 /* If the only constraints a div d=floor(f/m)
1150  * appears in are its two defining constraints
1151  *
1152  *      f - m d >=0
1153  *      -(f - (m - 1)) + m d >= 0
1154  *
1155  * then it can safely be removed.
1156  */
1157 static int div_is_redundant(struct isl_basic_map *bmap, int div)
1158 {
1159         int i;
1160         unsigned pos = 1 + isl_dim_total(bmap->dim) + div;
1161
1162         for (i = 0; i < bmap->n_eq; ++i)
1163                 if (!isl_int_is_zero(bmap->eq[i][pos]))
1164                         return 0;
1165
1166         for (i = 0; i < bmap->n_ineq; ++i) {
1167                 if (isl_int_is_zero(bmap->ineq[i][pos]))
1168                         continue;
1169                 if (!isl_basic_map_is_div_constraint(bmap, bmap->ineq[i], div))
1170                         return 0;
1171         }
1172
1173         for (i = 0; i < bmap->n_div; ++i)
1174                 if (!isl_int_is_zero(bmap->div[i][1+pos]))
1175                         return 0;
1176
1177         return 1;
1178 }
1179
1180 /*
1181  * Remove divs that don't occur in any of the constraints or other divs.
1182  * These can arise when dropping some of the variables in a quast
1183  * returned by piplib.
1184  */
1185 static struct isl_basic_map *remove_redundant_divs(struct isl_basic_map *bmap)
1186 {
1187         int i;
1188
1189         if (!bmap)
1190                 return NULL;
1191
1192         for (i = bmap->n_div-1; i >= 0; --i) {
1193                 if (!div_is_redundant(bmap, i))
1194                         continue;
1195                 bmap = isl_basic_map_drop_div(bmap, i);
1196         }
1197         return bmap;
1198 }
1199
1200 struct isl_basic_map *isl_basic_map_finalize(struct isl_basic_map *bmap)
1201 {
1202         bmap = remove_redundant_divs(bmap);
1203         if (!bmap)
1204                 return NULL;
1205         ISL_F_SET(bmap, ISL_BASIC_SET_FINAL);
1206         return bmap;
1207 }
1208
1209 struct isl_basic_set *isl_basic_set_finalize(struct isl_basic_set *bset)
1210 {
1211         return (struct isl_basic_set *)
1212                 isl_basic_map_finalize((struct isl_basic_map *)bset);
1213 }
1214
1215 struct isl_set *isl_set_finalize(struct isl_set *set)
1216 {
1217         int i;
1218
1219         if (!set)
1220                 return NULL;
1221         for (i = 0; i < set->n; ++i) {
1222                 set->p[i] = isl_basic_set_finalize(set->p[i]);
1223                 if (!set->p[i])
1224                         goto error;
1225         }
1226         return set;
1227 error:
1228         isl_set_free(set);
1229         return NULL;
1230 }
1231
1232 struct isl_map *isl_map_finalize(struct isl_map *map)
1233 {
1234         int i;
1235
1236         if (!map)
1237                 return NULL;
1238         for (i = 0; i < map->n; ++i) {
1239                 map->p[i] = isl_basic_map_finalize(map->p[i]);
1240                 if (!map->p[i])
1241                         goto error;
1242         }
1243         ISL_F_CLR(map, ISL_MAP_NORMALIZED);
1244         return map;
1245 error:
1246         isl_map_free(map);
1247         return NULL;
1248 }
1249
1250
1251 /* Remove definition of any div that is defined in terms of the given variable.
1252  * The div itself is not removed.  Functions such as
1253  * eliminate_divs_ineq depend on the other divs remaining in place.
1254  */
1255 static struct isl_basic_map *remove_dependent_vars(struct isl_basic_map *bmap,
1256                                                                         int pos)
1257 {
1258         int i;
1259
1260         for (i = 0; i < bmap->n_div; ++i) {
1261                 if (isl_int_is_zero(bmap->div[i][0]))
1262                         continue;
1263                 if (isl_int_is_zero(bmap->div[i][1+1+pos]))
1264                         continue;
1265                 isl_int_set_si(bmap->div[i][0], 0);
1266         }
1267         return bmap;
1268 }
1269
1270 /* Eliminate the specified variables from the constraints using
1271  * Fourier-Motzkin.  The variables themselves are not removed.
1272  */
1273 struct isl_basic_map *isl_basic_map_eliminate_vars(
1274         struct isl_basic_map *bmap, unsigned pos, unsigned n)
1275 {
1276         int d;
1277         int i, j, k;
1278         unsigned total;
1279
1280         if (n == 0)
1281                 return bmap;
1282         if (!bmap)
1283                 return NULL;
1284         total = isl_basic_map_total_dim(bmap);
1285
1286         bmap = isl_basic_map_cow(bmap);
1287         for (d = pos + n - 1; d >= 0 && d >= pos; --d)
1288                 bmap = remove_dependent_vars(bmap, d);
1289
1290         for (d = pos + n - 1;
1291              d >= 0 && d >= total - bmap->n_div && d >= pos; --d)
1292                 isl_seq_clr(bmap->div[d-(total-bmap->n_div)], 2+total);
1293         for (d = pos + n - 1; d >= 0 && d >= pos; --d) {
1294                 int n_lower, n_upper;
1295                 if (!bmap)
1296                         return NULL;
1297                 for (i = 0; i < bmap->n_eq; ++i) {
1298                         if (isl_int_is_zero(bmap->eq[i][1+d]))
1299                                 continue;
1300                         eliminate_var_using_equality(bmap, d, bmap->eq[i], 0, NULL);
1301                         isl_basic_map_drop_equality(bmap, i);
1302                         break;
1303                 }
1304                 if (i < bmap->n_eq)
1305                         continue;
1306                 n_lower = 0;
1307                 n_upper = 0;
1308                 for (i = 0; i < bmap->n_ineq; ++i) {
1309                         if (isl_int_is_pos(bmap->ineq[i][1+d]))
1310                                 n_lower++;
1311                         else if (isl_int_is_neg(bmap->ineq[i][1+d]))
1312                                 n_upper++;
1313                 }
1314                 bmap = isl_basic_map_extend_constraints(bmap,
1315                                 0, n_lower * n_upper);
1316                 if (!bmap)
1317                         goto error;
1318                 for (i = bmap->n_ineq - 1; i >= 0; --i) {
1319                         int last;
1320                         if (isl_int_is_zero(bmap->ineq[i][1+d]))
1321                                 continue;
1322                         last = -1;
1323                         for (j = 0; j < i; ++j) {
1324                                 if (isl_int_is_zero(bmap->ineq[j][1+d]))
1325                                         continue;
1326                                 last = j;
1327                                 if (isl_int_sgn(bmap->ineq[i][1+d]) ==
1328                                     isl_int_sgn(bmap->ineq[j][1+d]))
1329                                         continue;
1330                                 k = isl_basic_map_alloc_inequality(bmap);
1331                                 if (k < 0)
1332                                         goto error;
1333                                 isl_seq_cpy(bmap->ineq[k], bmap->ineq[i],
1334                                                 1+total);
1335                                 isl_seq_elim(bmap->ineq[k], bmap->ineq[j],
1336                                                 1+d, 1+total, NULL);
1337                         }
1338                         isl_basic_map_drop_inequality(bmap, i);
1339                         i = last + 1;
1340                 }
1341                 if (n_lower > 0 && n_upper > 0) {
1342                         bmap = isl_basic_map_normalize_constraints(bmap);
1343                         bmap = remove_duplicate_constraints(bmap, NULL);
1344                         bmap = isl_basic_map_gauss(bmap, NULL);
1345                         bmap = isl_basic_map_remove_redundancies(bmap);
1346                         if (!bmap)
1347                                 goto error;
1348                         if (ISL_F_ISSET(bmap, ISL_BASIC_MAP_EMPTY))
1349                                 break;
1350                 }
1351         }
1352         ISL_F_CLR(bmap, ISL_BASIC_MAP_NORMALIZED);
1353         return bmap;
1354 error:
1355         isl_basic_map_free(bmap);
1356         return NULL;
1357 }
1358
1359 struct isl_basic_set *isl_basic_set_eliminate_vars(
1360         struct isl_basic_set *bset, unsigned pos, unsigned n)
1361 {
1362         return (struct isl_basic_set *)isl_basic_map_eliminate_vars(
1363                         (struct isl_basic_map *)bset, pos, n);
1364 }
1365
1366 /* Don't assume equalities are in order, because align_divs
1367  * may have changed the order of the divs.
1368  */
1369 static void compute_elimination_index(struct isl_basic_map *bmap, int *elim)
1370 {
1371         int d, i;
1372         unsigned total;
1373
1374         total = isl_dim_total(bmap->dim);
1375         for (d = 0; d < total; ++d)
1376                 elim[d] = -1;
1377         for (i = 0; i < bmap->n_eq; ++i) {
1378                 for (d = total - 1; d >= 0; --d) {
1379                         if (isl_int_is_zero(bmap->eq[i][1+d]))
1380                                 continue;
1381                         elim[d] = i;
1382                         break;
1383                 }
1384         }
1385 }
1386
1387 static void set_compute_elimination_index(struct isl_basic_set *bset, int *elim)
1388 {
1389         compute_elimination_index((struct isl_basic_map *)bset, elim);
1390 }
1391
1392 static int reduced_using_equalities(isl_int *dst, isl_int *src,
1393         struct isl_basic_map *bmap, int *elim)
1394 {
1395         int d;
1396         int copied = 0;
1397         unsigned total;
1398
1399         total = isl_dim_total(bmap->dim);
1400         for (d = total - 1; d >= 0; --d) {
1401                 if (isl_int_is_zero(src[1+d]))
1402                         continue;
1403                 if (elim[d] == -1)
1404                         continue;
1405                 if (!copied) {
1406                         isl_seq_cpy(dst, src, 1 + total);
1407                         copied = 1;
1408                 }
1409                 isl_seq_elim(dst, bmap->eq[elim[d]], 1 + d, 1 + total, NULL);
1410         }
1411         return copied;
1412 }
1413
1414 static int set_reduced_using_equalities(isl_int *dst, isl_int *src,
1415         struct isl_basic_set *bset, int *elim)
1416 {
1417         return reduced_using_equalities(dst, src,
1418                                         (struct isl_basic_map *)bset, elim);
1419 }
1420
1421 static struct isl_basic_set *isl_basic_set_reduce_using_equalities(
1422         struct isl_basic_set *bset, struct isl_basic_set *context)
1423 {
1424         int i;
1425         int *elim;
1426
1427         if (!bset || !context)
1428                 goto error;
1429
1430         if (context->n_eq == 0) {
1431                 isl_basic_set_free(context);
1432                 return bset;
1433         }
1434
1435         bset = isl_basic_set_cow(bset);
1436         if (!bset)
1437                 goto error;
1438
1439         elim = isl_alloc_array(bset->ctx, int, isl_basic_set_n_dim(bset));
1440         if (!elim)
1441                 goto error;
1442         set_compute_elimination_index(context, elim);
1443         for (i = 0; i < bset->n_eq; ++i)
1444                 set_reduced_using_equalities(bset->eq[i], bset->eq[i],
1445                                                         context, elim);
1446         for (i = 0; i < bset->n_ineq; ++i)
1447                 set_reduced_using_equalities(bset->ineq[i], bset->ineq[i],
1448                                                         context, elim);
1449         isl_basic_set_free(context);
1450         free(elim);
1451         bset = isl_basic_set_simplify(bset);
1452         bset = isl_basic_set_finalize(bset);
1453         return bset;
1454 error:
1455         isl_basic_set_free(bset);
1456         isl_basic_set_free(context);
1457         return NULL;
1458 }
1459
1460 static struct isl_basic_set *remove_shifted_constraints(
1461         struct isl_basic_set *bset, struct isl_basic_set *context)
1462 {
1463         unsigned int size;
1464         isl_int ***index;
1465         int bits;
1466         int k, h, l;
1467
1468         if (!bset)
1469                 return NULL;
1470
1471         size = round_up(4 * (context->n_ineq+1) / 3 - 1);
1472         bits = ffs(size) - 1;
1473         index = isl_calloc_array(ctx, isl_int **, size);
1474         if (!index)
1475                 return bset;
1476
1477         for (k = 0; k < context->n_ineq; ++k) {
1478                 h = set_hash_index(index, size, bits, context, k);
1479                 index[h] = &context->ineq[k];
1480         }
1481         for (k = 0; k < bset->n_ineq; ++k) {
1482                 h = set_hash_index(index, size, bits, bset, k);
1483                 if (!index[h])
1484                         continue;
1485                 l = index[h] - &context->ineq[0];
1486                 if (isl_int_lt(bset->ineq[k][0], context->ineq[l][0]))
1487                         continue;
1488                 bset = isl_basic_set_cow(bset);
1489                 if (!bset)
1490                         goto error;
1491                 isl_basic_set_drop_inequality(bset, k);
1492                 --k;
1493         }
1494         free(index);
1495         return bset;
1496 error:
1497         free(index);
1498         return bset;
1499 }
1500
1501 /* Tighten (decrease) the constant terms of the inequalities based
1502  * on the equalities, without removing any integer points.
1503  * For example, if there is an equality
1504  *
1505  *              i = 3 * j
1506  *
1507  * and an inequality
1508  *
1509  *              i >= 1
1510  *
1511  * then we want to replace the inequality by
1512  *
1513  *              i >= 3
1514  *
1515  * We do this by computing a variable compression and translating
1516  * the constraints to the compressed space.
1517  * If any constraint has coefficients (except the contant term)
1518  * with a common factor "f", then we can replace the constant term "c"
1519  * by
1520  *
1521  *              f * floor(c/f)
1522  *
1523  * That is, we add
1524  *
1525  *              f * floor(c/f) - c = -fract(c/f)
1526  *
1527  * and we can add the same value to the original constraint.
1528  *
1529  * In the example, the compressed space only contains "j",
1530  * and the inequality translates to
1531  *
1532  *              3 * j - 1 >= 0
1533  *
1534  * We add -fract(-1/3) = -2 to the original constraint to obtain
1535  *
1536  *              i - 3 >= 0
1537  */
1538 static struct isl_basic_set *normalize_constraints_in_compressed_space(
1539         struct isl_basic_set *bset)
1540 {
1541         int i;
1542         unsigned total;
1543         struct isl_mat *B, *C;
1544         isl_int gcd;
1545
1546         if (!bset)
1547                 return NULL;
1548
1549         if (ISL_F_ISSET(bset, ISL_BASIC_SET_RATIONAL))
1550                 return bset;
1551
1552         if (!bset->n_ineq)
1553                 return bset;
1554
1555         bset = isl_basic_set_cow(bset);
1556         if (!bset)
1557                 return NULL;
1558
1559         total = isl_basic_set_total_dim(bset);
1560         B = isl_mat_sub_alloc(bset->ctx, bset->eq, 0, bset->n_eq, 0, 1 + total);
1561         C = isl_mat_variable_compression(B, NULL);
1562         if (!C)
1563                 return bset;
1564         if (C->n_col == 0) {
1565                 isl_mat_free(C);
1566                 return isl_basic_set_set_to_empty(bset);
1567         }
1568         B = isl_mat_sub_alloc(bset->ctx, bset->ineq,
1569                                                 0, bset->n_ineq, 0, 1 + total);
1570         C = isl_mat_product(B, C);
1571         if (!C)
1572                 return bset;
1573
1574         isl_int_init(gcd);
1575         for (i = 0; i < bset->n_ineq; ++i) {
1576                 isl_seq_gcd(C->row[i] + 1, C->n_col - 1, &gcd);
1577                 if (isl_int_is_one(gcd))
1578                         continue;
1579                 isl_int_fdiv_r(C->row[i][0], C->row[i][0], gcd);
1580                 isl_int_sub(bset->ineq[i][0], bset->ineq[i][0], C->row[i][0]);
1581         }
1582         isl_int_clear(gcd);
1583
1584         isl_mat_free(C);
1585
1586         return bset;
1587 }
1588
1589 /* Remove all information from bset that is redundant in the context
1590  * of context.  Both bset and context are assumed to be full-dimensional.
1591  *
1592  * We first * remove the inequalities from "bset"
1593  * that are obviously redundant with respect to some inequality in "context".
1594  *
1595  * If there are any inequalities left, we construct a tableau for
1596  * the context and then add the inequalities of "bset".
1597  * Before adding these inequalities, we freeze all constraints such that
1598  * they won't be considered redundant in terms of the constraints of "bset".
1599  * Then we detect all redundant constraints (among the
1600  * constraints that weren't frozen), first by checking for redundancy in the
1601  * the tableau and then by checking if replacing a constraint by its negation
1602  * would lead to an empty set.  This last step is fairly expensive
1603  * and could be optimized by more reuse of the tableau.
1604  * Finally, we update bset according to the results.
1605  */
1606 static __isl_give isl_basic_set *uset_gist_full(__isl_take isl_basic_set *bset,
1607         __isl_take isl_basic_set *context)
1608 {
1609         int i, k;
1610         isl_basic_set *combined = NULL;
1611         struct isl_tab *tab = NULL;
1612         unsigned context_ineq;
1613         unsigned total;
1614
1615         if (!bset || !context)
1616                 goto error;
1617
1618         if (isl_basic_set_is_universe(bset)) {
1619                 isl_basic_set_free(context);
1620                 return bset;
1621         }
1622
1623         if (isl_basic_set_is_universe(context)) {
1624                 isl_basic_set_free(context);
1625                 return bset;
1626         }
1627
1628         bset = remove_shifted_constraints(bset, context);
1629         if (!bset)
1630                 goto error;
1631         if (bset->n_ineq == 0)
1632                 goto done;
1633
1634         context_ineq = context->n_ineq;
1635         combined = isl_basic_set_cow(isl_basic_set_copy(context));
1636         combined = isl_basic_set_extend_constraints(combined, 0, bset->n_ineq);
1637         tab = isl_tab_from_basic_set(combined);
1638         for (i = 0; i < context_ineq; ++i)
1639                 if (isl_tab_freeze_constraint(tab, i) < 0)
1640                         goto error;
1641         tab = isl_tab_extend(tab, bset->n_ineq);
1642         for (i = 0; i < bset->n_ineq; ++i)
1643                 if (isl_tab_add_ineq(tab, bset->ineq[i]) < 0)
1644                         goto error;
1645         bset = isl_basic_set_add_constraints(combined, bset, 0);
1646         combined = NULL;
1647         if (!bset)
1648                 goto error;
1649         if (isl_tab_detect_redundant(tab) < 0)
1650                 goto error;
1651         total = isl_basic_set_total_dim(bset);
1652         for (i = context_ineq; i < bset->n_ineq; ++i) {
1653                 int is_empty;
1654                 if (tab->con[i].is_redundant)
1655                         continue;
1656                 tab->con[i].is_redundant = 1;
1657                 combined = isl_basic_set_dup(bset);
1658                 combined = isl_basic_set_update_from_tab(combined, tab);
1659                 combined = isl_basic_set_extend_constraints(combined, 0, 1);
1660                 k = isl_basic_set_alloc_inequality(combined);
1661                 if (k < 0)
1662                         goto error;
1663                 isl_seq_neg(combined->ineq[k], bset->ineq[i], 1 + total);
1664                 isl_int_sub_ui(combined->ineq[k][0], combined->ineq[k][0], 1);
1665                 is_empty = isl_basic_set_is_empty(combined);
1666                 if (is_empty < 0)
1667                         goto error;
1668                 isl_basic_set_free(combined);
1669                 combined = NULL;
1670                 if (!is_empty)
1671                         tab->con[i].is_redundant = 0;
1672         }
1673         for (i = 0; i < context_ineq; ++i)
1674                 tab->con[i].is_redundant = 1;
1675         bset = isl_basic_set_update_from_tab(bset, tab);
1676         if (bset) {
1677                 ISL_F_SET(bset, ISL_BASIC_SET_NO_IMPLICIT);
1678                 ISL_F_SET(bset, ISL_BASIC_SET_NO_REDUNDANT);
1679         }
1680
1681         isl_tab_free(tab);
1682 done:
1683         bset = isl_basic_set_simplify(bset);
1684         bset = isl_basic_set_finalize(bset);
1685         isl_basic_set_free(context);
1686         return bset;
1687 error:
1688         isl_tab_free(tab);
1689         isl_basic_set_free(combined);
1690         isl_basic_set_free(context);
1691         isl_basic_set_free(bset);
1692         return NULL;
1693 }
1694
1695 /* Remove all information from bset that is redundant in the context
1696  * of context.  In particular, equalities that are linear combinations
1697  * of those in context are removed.  Then the inequalities that are
1698  * redundant in the context of the equalities and inequalities of
1699  * context are removed.
1700  *
1701  * We first compute the integer affine hull of the intersection,
1702  * compute the gist inside this affine hull and then add back
1703  * those equalities that are not implied by the context.
1704  */
1705 static __isl_give isl_basic_set *uset_gist(__isl_take isl_basic_set *bset,
1706         __isl_take isl_basic_set *context)
1707 {
1708         isl_mat *eq;
1709         isl_mat *T, *T2;
1710         isl_basic_set *aff;
1711         isl_basic_set *aff_context;
1712         unsigned total;
1713
1714         if (!bset || !context)
1715                 goto error;
1716
1717         bset = isl_basic_set_intersect(bset, isl_basic_set_copy(context));
1718         if (isl_basic_set_fast_is_empty(bset)) {
1719                 isl_basic_set_free(context);
1720                 return bset;
1721         }
1722         aff = isl_basic_set_affine_hull(isl_basic_set_copy(bset));
1723         if (!aff)
1724                 goto error;
1725         if (isl_basic_set_fast_is_empty(aff)) {
1726                 isl_basic_set_free(aff);
1727                 isl_basic_set_free(context);
1728                 return bset;
1729         }
1730         if (aff->n_eq == 0) {
1731                 isl_basic_set_free(aff);
1732                 return uset_gist_full(bset, context);
1733         }
1734         total = isl_basic_set_total_dim(bset);
1735         eq = isl_mat_sub_alloc(bset->ctx, aff->eq, 0, aff->n_eq, 0, 1 + total);
1736         eq = isl_mat_cow(eq);
1737         T = isl_mat_variable_compression(eq, &T2);
1738         if (T && T->n_col == 0) {
1739                 isl_mat_free(T);
1740                 isl_mat_free(T2);
1741                 isl_basic_set_free(context);
1742                 isl_basic_set_free(aff);
1743                 return isl_basic_set_set_to_empty(bset);
1744         }
1745
1746         aff_context = isl_basic_set_affine_hull(isl_basic_set_copy(context));
1747
1748         bset = isl_basic_set_preimage(bset, isl_mat_copy(T));
1749         context = isl_basic_set_preimage(context, T);
1750
1751         bset = uset_gist_full(bset, context);
1752         bset = isl_basic_set_preimage(bset, T2);
1753         bset = isl_basic_set_intersect(bset, aff);
1754         bset = isl_basic_set_reduce_using_equalities(bset, aff_context);
1755
1756         if (bset) {
1757                 ISL_F_SET(bset, ISL_BASIC_SET_NO_IMPLICIT);
1758                 ISL_F_SET(bset, ISL_BASIC_SET_NO_REDUNDANT);
1759         }
1760
1761         return bset;
1762 error:
1763         isl_basic_set_free(bset);
1764         isl_basic_set_free(context);
1765         return NULL;
1766 }
1767
1768 /* Normalize the divs in "bmap" in the context of the equalities in "context".
1769  * We simply add the equalities in context to bmap and then do a regular
1770  * div normalizations.  Better results can be obtained by normalizing
1771  * only the divs in bmap than do not also appear in context.
1772  * We need to be careful to reduce the divs using the equalities
1773  * so that later calls to isl_basic_map_overlying_set wouldn't introduce
1774  * spurious constraints.
1775  */
1776 static struct isl_basic_map *normalize_divs_in_context(
1777         struct isl_basic_map *bmap, struct isl_basic_map *context)
1778 {
1779         int i;
1780         unsigned total_context;
1781         int div_eq;
1782
1783         div_eq = n_pure_div_eq(bmap);
1784         if (div_eq == 0)
1785                 return bmap;
1786
1787         if (context->n_div > 0)
1788                 bmap = isl_basic_map_align_divs(bmap, context);
1789
1790         total_context = isl_basic_map_total_dim(context);
1791         bmap = isl_basic_map_extend_constraints(bmap, context->n_eq, 0);
1792         for (i = 0; i < context->n_eq; ++i) {
1793                 int k;
1794                 k = isl_basic_map_alloc_equality(bmap);
1795                 isl_seq_cpy(bmap->eq[k], context->eq[i], 1 + total_context);
1796                 isl_seq_clr(bmap->eq[k] + 1 + total_context,
1797                                 isl_basic_map_total_dim(bmap) - total_context);
1798         }
1799         bmap = isl_basic_map_gauss(bmap, NULL);
1800         bmap = normalize_divs(bmap, NULL);
1801         bmap = isl_basic_map_gauss(bmap, NULL);
1802         return bmap;
1803 }
1804
1805 struct isl_basic_map *isl_basic_map_gist(struct isl_basic_map *bmap,
1806         struct isl_basic_map *context)
1807 {
1808         struct isl_basic_set *bset;
1809
1810         if (!bmap || !context)
1811                 goto error;
1812
1813         if (isl_basic_map_is_universe(bmap)) {
1814                 isl_basic_map_free(context);
1815                 return bmap;
1816         }
1817         if (isl_basic_map_fast_is_empty(context)) {
1818                 struct isl_dim *dim = isl_dim_copy(bmap->dim);
1819                 isl_basic_map_free(context);
1820                 isl_basic_map_free(bmap);
1821                 return isl_basic_map_universe(dim);
1822         }
1823         if (isl_basic_map_fast_is_empty(bmap)) {
1824                 isl_basic_map_free(context);
1825                 return bmap;
1826         }
1827
1828         bmap = isl_basic_map_remove_redundancies(bmap);
1829         context = isl_basic_map_remove_redundancies(context);
1830
1831         if (context->n_eq)
1832                 bmap = normalize_divs_in_context(bmap, context);
1833
1834         context = isl_basic_map_align_divs(context, bmap);
1835         bmap = isl_basic_map_align_divs(bmap, context);
1836
1837         bset = uset_gist(isl_basic_map_underlying_set(isl_basic_map_copy(bmap)),
1838                          isl_basic_map_underlying_set(context));
1839
1840         return isl_basic_map_overlying_set(bset, bmap);
1841 error:
1842         isl_basic_map_free(bmap);
1843         isl_basic_map_free(context);
1844         return NULL;
1845 }
1846
1847 /*
1848  * Assumes context has no implicit divs.
1849  */
1850 __isl_give isl_map *isl_map_gist_basic_map(__isl_take isl_map *map,
1851         __isl_take isl_basic_map *context)
1852 {
1853         int i;
1854
1855         if (!map || !context)
1856                 goto error;;
1857
1858         if (isl_basic_map_fast_is_empty(context)) {
1859                 struct isl_dim *dim = isl_dim_copy(map->dim);
1860                 isl_basic_map_free(context);
1861                 isl_map_free(map);
1862                 return isl_map_universe(dim);
1863         }
1864
1865         context = isl_basic_map_remove_redundancies(context);
1866         map = isl_map_cow(map);
1867         if (!map || !context)
1868                 goto error;;
1869         isl_assert(map->ctx, isl_dim_equal(map->dim, context->dim), goto error);
1870         map = isl_map_compute_divs(map);
1871         for (i = 0; i < map->n; ++i)
1872                 context = isl_basic_map_align_divs(context, map->p[i]);
1873         for (i = map->n - 1; i >= 0; --i) {
1874                 map->p[i] = isl_basic_map_gist(map->p[i],
1875                                                 isl_basic_map_copy(context));
1876                 if (!map->p[i])
1877                         goto error;
1878                 if (isl_basic_map_fast_is_empty(map->p[i])) {
1879                         isl_basic_map_free(map->p[i]);
1880                         if (i != map->n - 1)
1881                                 map->p[i] = map->p[map->n - 1];
1882                         map->n--;
1883                 }
1884         }
1885         isl_basic_map_free(context);
1886         ISL_F_CLR(map, ISL_MAP_NORMALIZED);
1887         return map;
1888 error:
1889         isl_map_free(map);
1890         isl_basic_map_free(context);
1891         return NULL;
1892 }
1893
1894 __isl_give isl_map *isl_map_gist(__isl_take isl_map *map,
1895         __isl_take isl_map *context)
1896 {
1897         context = isl_map_compute_divs(context);
1898         return isl_map_gist_basic_map(map, isl_map_simple_hull(context));
1899 }
1900
1901 struct isl_basic_set *isl_basic_set_gist(struct isl_basic_set *bset,
1902                                                 struct isl_basic_set *context)
1903 {
1904         return (struct isl_basic_set *)isl_basic_map_gist(
1905                 (struct isl_basic_map *)bset, (struct isl_basic_map *)context);
1906 }
1907
1908 __isl_give isl_set *isl_set_gist_basic_set(__isl_take isl_set *set,
1909         __isl_take isl_basic_set *context)
1910 {
1911         return (struct isl_set *)isl_map_gist_basic_map((struct isl_map *)set,
1912                                         (struct isl_basic_map *)context);
1913 }
1914
1915 __isl_give isl_set *isl_set_gist(__isl_take isl_set *set,
1916         __isl_take isl_set *context)
1917 {
1918         return (struct isl_set *)isl_map_gist((struct isl_map *)set,
1919                                         (struct isl_map *)context);
1920 }
1921
1922 /* Quick check to see if two basic maps are disjoint.
1923  * In particular, we reduce the equalities and inequalities of
1924  * one basic map in the context of the equalities of the other
1925  * basic map and check if we get a contradiction.
1926  */
1927 int isl_basic_map_fast_is_disjoint(struct isl_basic_map *bmap1,
1928         struct isl_basic_map *bmap2)
1929 {
1930         struct isl_vec *v = NULL;
1931         int *elim = NULL;
1932         unsigned total;
1933         int i;
1934
1935         if (!bmap1 || !bmap2)
1936                 return -1;
1937         isl_assert(bmap1->ctx, isl_dim_equal(bmap1->dim, bmap2->dim),
1938                         return -1);
1939         if (bmap1->n_div || bmap2->n_div)
1940                 return 0;
1941         if (!bmap1->n_eq && !bmap2->n_eq)
1942                 return 0;
1943
1944         total = isl_dim_total(bmap1->dim);
1945         if (total == 0)
1946                 return 0;
1947         v = isl_vec_alloc(bmap1->ctx, 1 + total);
1948         if (!v)
1949                 goto error;
1950         elim = isl_alloc_array(bmap1->ctx, int, total);
1951         if (!elim)
1952                 goto error;
1953         compute_elimination_index(bmap1, elim);
1954         for (i = 0; i < bmap2->n_eq; ++i) {
1955                 int reduced;
1956                 reduced = reduced_using_equalities(v->block.data, bmap2->eq[i],
1957                                                         bmap1, elim);
1958                 if (reduced && !isl_int_is_zero(v->block.data[0]) &&
1959                     isl_seq_first_non_zero(v->block.data + 1, total) == -1)
1960                         goto disjoint;
1961         }
1962         for (i = 0; i < bmap2->n_ineq; ++i) {
1963                 int reduced;
1964                 reduced = reduced_using_equalities(v->block.data,
1965                                                 bmap2->ineq[i], bmap1, elim);
1966                 if (reduced && isl_int_is_neg(v->block.data[0]) &&
1967                     isl_seq_first_non_zero(v->block.data + 1, total) == -1)
1968                         goto disjoint;
1969         }
1970         compute_elimination_index(bmap2, elim);
1971         for (i = 0; i < bmap1->n_ineq; ++i) {
1972                 int reduced;
1973                 reduced = reduced_using_equalities(v->block.data,
1974                                                 bmap1->ineq[i], bmap2, elim);
1975                 if (reduced && isl_int_is_neg(v->block.data[0]) &&
1976                     isl_seq_first_non_zero(v->block.data + 1, total) == -1)
1977                         goto disjoint;
1978         }
1979         isl_vec_free(v);
1980         free(elim);
1981         return 0;
1982 disjoint:
1983         isl_vec_free(v);
1984         free(elim);
1985         return 1;
1986 error:
1987         isl_vec_free(v);
1988         free(elim);
1989         return -1;
1990 }
1991
1992 int isl_basic_set_fast_is_disjoint(struct isl_basic_set *bset1,
1993         struct isl_basic_set *bset2)
1994 {
1995         return isl_basic_map_fast_is_disjoint((struct isl_basic_map *)bset1,
1996                                               (struct isl_basic_map *)bset2);
1997 }
1998
1999 int isl_map_fast_is_disjoint(struct isl_map *map1, struct isl_map *map2)
2000 {
2001         int i, j;
2002
2003         if (!map1 || !map2)
2004                 return -1;
2005
2006         if (isl_map_fast_is_equal(map1, map2))
2007                 return 0;
2008
2009         for (i = 0; i < map1->n; ++i) {
2010                 for (j = 0; j < map2->n; ++j) {
2011                         int d = isl_basic_map_fast_is_disjoint(map1->p[i],
2012                                                                map2->p[j]);
2013                         if (d != 1)
2014                                 return d;
2015                 }
2016         }
2017         return 1;
2018 }
2019
2020 int isl_set_fast_is_disjoint(struct isl_set *set1, struct isl_set *set2)
2021 {
2022         return isl_map_fast_is_disjoint((struct isl_map *)set1,
2023                                         (struct isl_map *)set2);
2024 }
2025
2026 /* Check if we can combine a given div with lower bound l and upper
2027  * bound u with some other div and if so return that other div.
2028  * Otherwise return -1.
2029  *
2030  * We first check that
2031  *      - the bounds are opposites of each other (except for the constant
2032  *        term)
2033  *      - the bounds do not reference any other div
2034  *      - no div is defined in terms of this div
2035  *
2036  * Let m be the size of the range allowed on the div by the bounds.
2037  * That is, the bounds are of the form
2038  *
2039  *      e <= a <= e + m - 1
2040  *
2041  * with e some expression in the other variables.
2042  * We look for another div b such that no third div is defined in terms
2043  * of this second div b and such that in any constraint that contains
2044  * a (except for the given lower and upper bound), also contains b
2045  * with a coefficient that is m times that of b.
2046  * That is, all constraints (execpt for the lower and upper bound)
2047  * are of the form
2048  *
2049  *      e + f (a + m b) >= 0
2050  *
2051  * If so, we return b so that "a + m b" can be replaced by
2052  * a single div "c = a + m b".
2053  */
2054 static int div_find_coalesce(struct isl_basic_map *bmap, int *pairs,
2055         unsigned div, unsigned l, unsigned u)
2056 {
2057         int i, j;
2058         unsigned dim;
2059         int coalesce = -1;
2060
2061         if (bmap->n_div <= 1)
2062                 return -1;
2063         dim = isl_dim_total(bmap->dim);
2064         if (isl_seq_first_non_zero(bmap->ineq[l] + 1 + dim, div) != -1)
2065                 return -1;
2066         if (isl_seq_first_non_zero(bmap->ineq[l] + 1 + dim + div + 1,
2067                                    bmap->n_div - div - 1) != -1)
2068                 return -1;
2069         if (!isl_seq_is_neg(bmap->ineq[l] + 1, bmap->ineq[u] + 1,
2070                             dim + bmap->n_div))
2071                 return -1;
2072
2073         for (i = 0; i < bmap->n_div; ++i) {
2074                 if (isl_int_is_zero(bmap->div[i][0]))
2075                         continue;
2076                 if (!isl_int_is_zero(bmap->div[i][1 + 1 + dim + div]))
2077                         return -1;
2078         }
2079
2080         isl_int_add(bmap->ineq[l][0], bmap->ineq[l][0], bmap->ineq[u][0]);
2081         if (isl_int_is_neg(bmap->ineq[l][0])) {
2082                 isl_int_sub(bmap->ineq[l][0],
2083                             bmap->ineq[l][0], bmap->ineq[u][0]);
2084                 bmap = isl_basic_map_copy(bmap);
2085                 bmap = isl_basic_map_set_to_empty(bmap);
2086                 isl_basic_map_free(bmap);
2087                 return -1;
2088         }
2089         isl_int_add_ui(bmap->ineq[l][0], bmap->ineq[l][0], 1);
2090         for (i = 0; i < bmap->n_div; ++i) {
2091                 if (i == div)
2092                         continue;
2093                 if (!pairs[i])
2094                         continue;
2095                 for (j = 0; j < bmap->n_div; ++j) {
2096                         if (isl_int_is_zero(bmap->div[j][0]))
2097                                 continue;
2098                         if (!isl_int_is_zero(bmap->div[j][1 + 1 + dim + i]))
2099                                 break;
2100                 }
2101                 if (j < bmap->n_div)
2102                         continue;
2103                 for (j = 0; j < bmap->n_ineq; ++j) {
2104                         int valid;
2105                         if (j == l || j == u)
2106                                 continue;
2107                         if (isl_int_is_zero(bmap->ineq[j][1 + dim + div]))
2108                                 continue;
2109                         if (isl_int_is_zero(bmap->ineq[j][1 + dim + i]))
2110                                 break;
2111                         isl_int_mul(bmap->ineq[j][1 + dim + div],
2112                                     bmap->ineq[j][1 + dim + div],
2113                                     bmap->ineq[l][0]);
2114                         valid = isl_int_eq(bmap->ineq[j][1 + dim + div],
2115                                            bmap->ineq[j][1 + dim + i]);
2116                         isl_int_divexact(bmap->ineq[j][1 + dim + div],
2117                                          bmap->ineq[j][1 + dim + div],
2118                                          bmap->ineq[l][0]);
2119                         if (!valid)
2120                                 break;
2121                 }
2122                 if (j < bmap->n_ineq)
2123                         continue;
2124                 coalesce = i;
2125                 break;
2126         }
2127         isl_int_sub_ui(bmap->ineq[l][0], bmap->ineq[l][0], 1);
2128         isl_int_sub(bmap->ineq[l][0], bmap->ineq[l][0], bmap->ineq[u][0]);
2129         return coalesce;
2130 }
2131
2132 /* Given a lower and an upper bound on div i, construct an inequality
2133  * that when nonnegative ensures that this pair of bounds always allows
2134  * for an integer value of the given div.
2135  * The lower bound is inequality l, while the upper bound is inequality u.
2136  * The constructed inequality is stored in ineq.
2137  * g, fl, fu are temporary scalars.
2138  *
2139  * Let the upper bound be
2140  *
2141  *      -n_u a + e_u >= 0
2142  *
2143  * and the lower bound
2144  *
2145  *      n_l a + e_l >= 0
2146  *
2147  * Let n_u = f_u g and n_l = f_l g, with g = gcd(n_u, n_l).
2148  * We have
2149  *
2150  *      - f_u e_l <= f_u f_l g a <= f_l e_u
2151  *
2152  * Since all variables are integer valued, this is equivalent to
2153  *
2154  *      - f_u e_l - (f_u - 1) <= f_u f_l g a <= f_l e_u + (f_l - 1)
2155  *
2156  * If this interval is at least f_u f_l g, then it contains at least
2157  * one integer value for a.
2158  * That is, the test constraint is
2159  *
2160  *      f_l e_u + f_u e_l + f_l - 1 + f_u - 1 + 1 >= f_u f_l g
2161  */
2162 static void construct_test_ineq(struct isl_basic_map *bmap, int i,
2163         int l, int u, isl_int *ineq, isl_int g, isl_int fl, isl_int fu)
2164 {
2165         unsigned dim;
2166         dim = isl_dim_total(bmap->dim);
2167
2168         isl_int_gcd(g, bmap->ineq[l][1 + dim + i], bmap->ineq[u][1 + dim + i]);
2169         isl_int_divexact(fl, bmap->ineq[l][1 + dim + i], g);
2170         isl_int_divexact(fu, bmap->ineq[u][1 + dim + i], g);
2171         isl_int_neg(fu, fu);
2172         isl_seq_combine(ineq, fl, bmap->ineq[u], fu, bmap->ineq[l],
2173                         1 + dim + bmap->n_div);
2174         isl_int_add(ineq[0], ineq[0], fl);
2175         isl_int_add(ineq[0], ineq[0], fu);
2176         isl_int_sub_ui(ineq[0], ineq[0], 1);
2177         isl_int_mul(g, g, fl);
2178         isl_int_mul(g, g, fu);
2179         isl_int_sub(ineq[0], ineq[0], g);
2180 }
2181
2182 /* Remove more kinds of divs that are not strictly needed.
2183  * In particular, if all pairs of lower and upper bounds on a div
2184  * are such that they allow at least one integer value of the div,
2185  * the we can eliminate the div using Fourier-Motzkin without
2186  * introducing any spurious solutions.
2187  */
2188 static struct isl_basic_map *drop_more_redundant_divs(
2189         struct isl_basic_map *bmap, int *pairs, int n)
2190 {
2191         struct isl_tab *tab = NULL;
2192         struct isl_vec *vec = NULL;
2193         unsigned dim;
2194         int remove = -1;
2195         isl_int g, fl, fu;
2196
2197         isl_int_init(g);
2198         isl_int_init(fl);
2199         isl_int_init(fu);
2200
2201         if (!bmap)
2202                 goto error;
2203
2204         dim = isl_dim_total(bmap->dim);
2205         vec = isl_vec_alloc(bmap->ctx, 1 + dim + bmap->n_div);
2206         if (!vec)
2207                 goto error;
2208
2209         tab = isl_tab_from_basic_map(bmap);
2210
2211         while (n > 0) {
2212                 int i, l, u;
2213                 int best = -1;
2214                 enum isl_lp_result res;
2215
2216                 for (i = 0; i < bmap->n_div; ++i) {
2217                         if (!pairs[i])
2218                                 continue;
2219                         if (best >= 0 && pairs[best] <= pairs[i])
2220                                 continue;
2221                         best = i;
2222                 }
2223
2224                 i = best;
2225                 for (l = 0; l < bmap->n_ineq; ++l) {
2226                         if (!isl_int_is_pos(bmap->ineq[l][1 + dim + i]))
2227                                 continue;
2228                         for (u = 0; u < bmap->n_ineq; ++u) {
2229                                 if (!isl_int_is_neg(bmap->ineq[u][1 + dim + i]))
2230                                         continue;
2231                                 construct_test_ineq(bmap, i, l, u,
2232                                                     vec->el, g, fl, fu);
2233                                 res = isl_tab_min(tab, vec->el,
2234                                                   bmap->ctx->one, &g, NULL, 0);
2235                                 if (res == isl_lp_error)
2236                                         goto error;
2237                                 if (res == isl_lp_empty) {
2238                                         bmap = isl_basic_map_set_to_empty(bmap);
2239                                         break;
2240                                 }
2241                                 if (res != isl_lp_ok || isl_int_is_neg(g))
2242                                         break;
2243                         }
2244                         if (u < bmap->n_ineq)
2245                                 break;
2246                 }
2247                 if (l == bmap->n_ineq) {
2248                         remove = i;
2249                         break;
2250                 }
2251                 pairs[i] = 0;
2252                 --n;
2253         }
2254
2255         isl_tab_free(tab);
2256         isl_vec_free(vec);
2257
2258         isl_int_clear(g);
2259         isl_int_clear(fl);
2260         isl_int_clear(fu);
2261
2262         free(pairs);
2263
2264         if (remove < 0)
2265                 return bmap;
2266
2267         bmap = isl_basic_map_remove_dims(bmap, isl_dim_div, remove, 1);
2268         return isl_basic_map_drop_redundant_divs(bmap);
2269 error:
2270         free(pairs);
2271         isl_basic_map_free(bmap);
2272         isl_tab_free(tab);
2273         isl_vec_free(vec);
2274         isl_int_clear(g);
2275         isl_int_clear(fl);
2276         isl_int_clear(fu);
2277         return NULL;
2278 }
2279
2280 /* Given a pair of divs div1 and div2 such that, expect for the lower bound l
2281  * and the upper bound u, div1 always occurs together with div2 in the form 
2282  * (div1 + m div2), where m is the constant range on the variable div1
2283  * allowed by l and u, replace the pair div1 and div2 by a single
2284  * div that is equal to div1 + m div2.
2285  *
2286  * The new div will appear in the location that contains div2.
2287  * We need to modify all constraints that contain
2288  * div2 = (div - div1) / m
2289  * (If a constraint does not contain div2, it will also not contain div1.)
2290  * If the constraint also contains div1, then we know they appear
2291  * as f (div1 + m div2) and we can simply replace (div1 + m div2) by div,
2292  * i.e., the coefficient of div is f.
2293  *
2294  * Otherwise, we first need to introduce div1 into the constraint.
2295  * Let the l be
2296  *
2297  *      div1 + f >=0
2298  *
2299  * and u
2300  *
2301  *      -div1 + f' >= 0
2302  *
2303  * A lower bound on div2
2304  *
2305  *      n div2 + t >= 0
2306  *
2307  * can be replaced by
2308  *
2309  *      (n * (m div 2 + div1) + m t + n f)/g >= 0
2310  *
2311  * with g = gcd(m,n).
2312  * An upper bound
2313  *
2314  *      -n div2 + t >= 0
2315  *
2316  * can be replaced by
2317  *
2318  *      (-n * (m div2 + div1) + m t + n f')/g >= 0
2319  *
2320  * These constraint are those that we would obtain from eliminating
2321  * div1 using Fourier-Motzkin.
2322  *
2323  * After all constraints have been modified, we drop the lower and upper
2324  * bound and then drop div1.
2325  */
2326 static struct isl_basic_map *coalesce_divs(struct isl_basic_map *bmap,
2327         unsigned div1, unsigned div2, unsigned l, unsigned u)
2328 {
2329         isl_int a;
2330         isl_int b;
2331         isl_int m;
2332         unsigned dim, total;
2333         int i;
2334
2335         dim = isl_dim_total(bmap->dim);
2336         total = 1 + dim + bmap->n_div;
2337
2338         isl_int_init(a);
2339         isl_int_init(b);
2340         isl_int_init(m);
2341         isl_int_add(m, bmap->ineq[l][0], bmap->ineq[u][0]);
2342         isl_int_add_ui(m, m, 1);
2343
2344         for (i = 0; i < bmap->n_ineq; ++i) {
2345                 if (i == l || i == u)
2346                         continue;
2347                 if (isl_int_is_zero(bmap->ineq[i][1 + dim + div2]))
2348                         continue;
2349                 if (isl_int_is_zero(bmap->ineq[i][1 + dim + div1])) {
2350                         isl_int_gcd(b, m, bmap->ineq[i][1 + dim + div2]);
2351                         isl_int_divexact(a, m, b);
2352                         isl_int_divexact(b, bmap->ineq[i][1 + dim + div2], b);
2353                         if (isl_int_is_pos(b)) {
2354                                 isl_seq_combine(bmap->ineq[i], a, bmap->ineq[i],
2355                                                 b, bmap->ineq[l], total);
2356                         } else {
2357                                 isl_int_neg(b, b);
2358                                 isl_seq_combine(bmap->ineq[i], a, bmap->ineq[i],
2359                                                 b, bmap->ineq[u], total);
2360                         }
2361                 }
2362                 isl_int_set(bmap->ineq[i][1 + dim + div2],
2363                             bmap->ineq[i][1 + dim + div1]);
2364                 isl_int_set_si(bmap->ineq[i][1 + dim + div1], 0);
2365         }
2366
2367         isl_int_clear(a);
2368         isl_int_clear(b);
2369         isl_int_clear(m);
2370         if (l > u) {
2371                 isl_basic_map_drop_inequality(bmap, l);
2372                 isl_basic_map_drop_inequality(bmap, u);
2373         } else {
2374                 isl_basic_map_drop_inequality(bmap, u);
2375                 isl_basic_map_drop_inequality(bmap, l);
2376         }
2377         bmap = isl_basic_map_drop_div(bmap, div1);
2378         return bmap;
2379 }
2380
2381 /* First check if we can coalesce any pair of divs and
2382  * then continue with dropping more redundant divs.
2383  *
2384  * We loop over all pairs of lower and upper bounds on a div
2385  * with coefficient 1 and -1, respectively, check if there
2386  * is any other div "c" with which we can coalesce the div
2387  * and if so, perform the coalescing.
2388  */
2389 static struct isl_basic_map *coalesce_or_drop_more_redundant_divs(
2390         struct isl_basic_map *bmap, int *pairs, int n)
2391 {
2392         int i, l, u;
2393         unsigned dim;
2394
2395         dim = isl_dim_total(bmap->dim);
2396
2397         for (i = 0; i < bmap->n_div; ++i) {
2398                 if (!pairs[i])
2399                         continue;
2400                 for (l = 0; l < bmap->n_ineq; ++l) {
2401                         if (!isl_int_is_one(bmap->ineq[l][1 + dim + i]))
2402                                 continue;
2403                         for (u = 0; u < bmap->n_ineq; ++u) {
2404                                 int c;
2405
2406                                 if (!isl_int_is_negone(bmap->ineq[u][1+dim+i]))
2407                                         continue;
2408                                 c = div_find_coalesce(bmap, pairs, i, l, u);
2409                                 if (c < 0)
2410                                         continue;
2411                                 free(pairs);
2412                                 bmap = coalesce_divs(bmap, i, c, l, u);
2413                                 return isl_basic_map_drop_redundant_divs(bmap);
2414                         }
2415                 }
2416         }
2417
2418         if (ISL_F_ISSET(bmap, ISL_BASIC_MAP_EMPTY))
2419                 return bmap;
2420
2421         return drop_more_redundant_divs(bmap, pairs, n);
2422 }
2423
2424 /* Remove divs that are not strictly needed.
2425  * In particular, if a div only occurs positively (or negatively)
2426  * in constraints, then it can simply be dropped.
2427  * Also, if a div occurs only occurs in two constraints and if moreover
2428  * those two constraints are opposite to each other, except for the constant
2429  * term and if the sum of the constant terms is such that for any value
2430  * of the other values, there is always at least one integer value of the
2431  * div, i.e., if one plus this sum is greater than or equal to
2432  * the (absolute value) of the coefficent of the div in the constraints,
2433  * then we can also simply drop the div.
2434  *
2435  * If any divs are left after these simple checks then we move on
2436  * to more complicated cases in drop_more_redundant_divs.
2437  */
2438 struct isl_basic_map *isl_basic_map_drop_redundant_divs(
2439         struct isl_basic_map *bmap)
2440 {
2441         int i, j;
2442         unsigned off;
2443         int *pairs = NULL;
2444         int n = 0;
2445
2446         if (!bmap)
2447                 goto error;
2448
2449         off = isl_dim_total(bmap->dim);
2450         pairs = isl_calloc_array(bmap->ctx, int, bmap->n_div);
2451         if (!pairs)
2452                 goto error;
2453
2454         for (i = 0; i < bmap->n_div; ++i) {
2455                 int pos, neg;
2456                 int last_pos, last_neg;
2457                 int redundant;
2458                 int defined;
2459
2460                 defined = !isl_int_is_zero(bmap->div[i][0]);
2461                 for (j = 0; j < bmap->n_eq; ++j)
2462                         if (!isl_int_is_zero(bmap->eq[j][1 + off + i]))
2463                                 break;
2464                 if (j < bmap->n_eq)
2465                         continue;
2466                 ++n;
2467                 pos = neg = 0;
2468                 for (j = 0; j < bmap->n_ineq; ++j) {
2469                         if (isl_int_is_pos(bmap->ineq[j][1 + off + i])) {
2470                                 last_pos = j;
2471                                 ++pos;
2472                         }
2473                         if (isl_int_is_neg(bmap->ineq[j][1 + off + i])) {
2474                                 last_neg = j;
2475                                 ++neg;
2476                         }
2477                 }
2478                 pairs[i] = pos * neg;
2479                 if (pairs[i] == 0) {
2480                         for (j = bmap->n_ineq - 1; j >= 0; --j)
2481                                 if (!isl_int_is_zero(bmap->ineq[j][1+off+i]))
2482                                         isl_basic_map_drop_inequality(bmap, j);
2483                         bmap = isl_basic_map_drop_div(bmap, i);
2484                         free(pairs);
2485                         return isl_basic_map_drop_redundant_divs(bmap);
2486                 }
2487                 if (pairs[i] != 1)
2488                         continue;
2489                 if (!isl_seq_is_neg(bmap->ineq[last_pos] + 1,
2490                                     bmap->ineq[last_neg] + 1,
2491                                     off + bmap->n_div))
2492                         continue;
2493
2494                 isl_int_add(bmap->ineq[last_pos][0],
2495                             bmap->ineq[last_pos][0], bmap->ineq[last_neg][0]);
2496                 isl_int_add_ui(bmap->ineq[last_pos][0],
2497                                bmap->ineq[last_pos][0], 1);
2498                 redundant = isl_int_ge(bmap->ineq[last_pos][0],
2499                                 bmap->ineq[last_pos][1+off+i]);
2500                 isl_int_sub_ui(bmap->ineq[last_pos][0],
2501                                bmap->ineq[last_pos][0], 1);
2502                 isl_int_sub(bmap->ineq[last_pos][0],
2503                             bmap->ineq[last_pos][0], bmap->ineq[last_neg][0]);
2504                 if (!redundant) {
2505                         if (defined ||
2506                             !ok_to_set_div_from_bound(bmap, i, last_pos)) {
2507                                 pairs[i] = 0;
2508                                 --n;
2509                                 continue;
2510                         }
2511                         bmap = set_div_from_lower_bound(bmap, i, last_pos);
2512                         bmap = isl_basic_map_simplify(bmap);
2513                         free(pairs);
2514                         return isl_basic_map_drop_redundant_divs(bmap);
2515                 }
2516                 if (last_pos > last_neg) {
2517                         isl_basic_map_drop_inequality(bmap, last_pos);
2518                         isl_basic_map_drop_inequality(bmap, last_neg);
2519                 } else {
2520                         isl_basic_map_drop_inequality(bmap, last_neg);
2521                         isl_basic_map_drop_inequality(bmap, last_pos);
2522                 }
2523                 bmap = isl_basic_map_drop_div(bmap, i);
2524                 free(pairs);
2525                 return isl_basic_map_drop_redundant_divs(bmap);
2526         }
2527
2528         if (n > 0)
2529                 return coalesce_or_drop_more_redundant_divs(bmap, pairs, n);
2530
2531         free(pairs);
2532         return bmap;
2533 error:
2534         free(pairs);
2535         isl_basic_map_free(bmap);
2536         return NULL;
2537 }
2538
2539 struct isl_basic_set *isl_basic_set_drop_redundant_divs(
2540         struct isl_basic_set *bset)
2541 {
2542         return (struct isl_basic_set *)
2543             isl_basic_map_drop_redundant_divs((struct isl_basic_map *)bset);
2544 }
2545
2546 struct isl_map *isl_map_drop_redundant_divs(struct isl_map *map)
2547 {
2548         int i;
2549
2550         if (!map)
2551                 return NULL;
2552         for (i = 0; i < map->n; ++i) {
2553                 map->p[i] = isl_basic_map_drop_redundant_divs(map->p[i]);
2554                 if (!map->p[i])
2555                         goto error;
2556         }
2557         ISL_F_CLR(map, ISL_MAP_NORMALIZED);
2558         return map;
2559 error:
2560         isl_map_free(map);
2561         return NULL;
2562 }
2563
2564 struct isl_set *isl_set_drop_redundant_divs(struct isl_set *set)
2565 {
2566         return (struct isl_set *)
2567             isl_map_drop_redundant_divs((struct isl_map *)set);
2568 }