2 * Copyright 2008-2009 Katholieke Universiteit Leuven
3 * Copyright 2010 INRIA Saclay
4 * Copyright 2012-2013 Ecole Normale Superieure
6 * Use of this software is governed by the MIT license
8 * Written by Sven Verdoolaege, K.U.Leuven, Departement
9 * Computerwetenschappen, Celestijnenlaan 200A, B-3001 Leuven, Belgium
10 * and INRIA Saclay - Ile-de-France, Parc Club Orsay Universite,
11 * ZAC des vignes, 4 rue Jacques Monod, 91893 Orsay, France
12 * and Ecole Normale Superieure, 45 rue d’Ulm, 75230 Paris, France
16 #include <isl_ctx_private.h>
17 #include <isl_map_private.h>
19 #include "isl_space_private.h"
20 #include "isl_equalities.h"
25 #include "isl_map_piplib.h"
26 #include <isl_reordering.h>
27 #include "isl_sample.h"
30 #include <isl_mat_private.h>
31 #include <isl_dim_map.h>
32 #include <isl_local_space_private.h>
33 #include <isl_aff_private.h>
34 #include <isl_options_private.h>
35 #include <isl_morph.h>
36 #include <isl_val_private.h>
38 static unsigned n(__isl_keep isl_space *dim, enum isl_dim_type type)
41 case isl_dim_param: return dim->nparam;
42 case isl_dim_in: return dim->n_in;
43 case isl_dim_out: return dim->n_out;
44 case isl_dim_all: return dim->nparam + dim->n_in + dim->n_out;
49 static unsigned pos(__isl_keep isl_space *dim, enum isl_dim_type type)
52 case isl_dim_param: return 1;
53 case isl_dim_in: return 1 + dim->nparam;
54 case isl_dim_out: return 1 + dim->nparam + dim->n_in;
59 unsigned isl_basic_map_dim(__isl_keep isl_basic_map *bmap,
60 enum isl_dim_type type)
65 case isl_dim_cst: return 1;
68 case isl_dim_out: return isl_space_dim(bmap->dim, type);
69 case isl_dim_div: return bmap->n_div;
70 case isl_dim_all: return isl_basic_map_total_dim(bmap);
75 unsigned isl_map_dim(__isl_keep isl_map *map, enum isl_dim_type type)
77 return map ? n(map->dim, type) : 0;
80 unsigned isl_set_dim(__isl_keep isl_set *set, enum isl_dim_type type)
82 return set ? n(set->dim, type) : 0;
85 unsigned isl_basic_map_offset(struct isl_basic_map *bmap,
86 enum isl_dim_type type)
88 isl_space *dim = bmap->dim;
90 case isl_dim_cst: return 0;
91 case isl_dim_param: return 1;
92 case isl_dim_in: return 1 + dim->nparam;
93 case isl_dim_out: return 1 + dim->nparam + dim->n_in;
94 case isl_dim_div: return 1 + dim->nparam + dim->n_in + dim->n_out;
99 unsigned isl_basic_set_offset(struct isl_basic_set *bset,
100 enum isl_dim_type type)
102 return isl_basic_map_offset(bset, type);
105 static unsigned map_offset(struct isl_map *map, enum isl_dim_type type)
107 return pos(map->dim, type);
110 unsigned isl_basic_set_dim(__isl_keep isl_basic_set *bset,
111 enum isl_dim_type type)
113 return isl_basic_map_dim(bset, type);
116 unsigned isl_basic_set_n_dim(__isl_keep isl_basic_set *bset)
118 return isl_basic_set_dim(bset, isl_dim_set);
121 unsigned isl_basic_set_n_param(__isl_keep isl_basic_set *bset)
123 return isl_basic_set_dim(bset, isl_dim_param);
126 unsigned isl_basic_set_total_dim(const struct isl_basic_set *bset)
130 return isl_space_dim(bset->dim, isl_dim_all) + bset->n_div;
133 unsigned isl_set_n_dim(__isl_keep isl_set *set)
135 return isl_set_dim(set, isl_dim_set);
138 unsigned isl_set_n_param(__isl_keep isl_set *set)
140 return isl_set_dim(set, isl_dim_param);
143 unsigned isl_basic_map_n_in(const struct isl_basic_map *bmap)
145 return bmap ? bmap->dim->n_in : 0;
148 unsigned isl_basic_map_n_out(const struct isl_basic_map *bmap)
150 return bmap ? bmap->dim->n_out : 0;
153 unsigned isl_basic_map_n_param(const struct isl_basic_map *bmap)
155 return bmap ? bmap->dim->nparam : 0;
158 unsigned isl_basic_map_n_div(const struct isl_basic_map *bmap)
160 return bmap ? bmap->n_div : 0;
163 unsigned isl_basic_map_total_dim(const struct isl_basic_map *bmap)
165 return bmap ? isl_space_dim(bmap->dim, isl_dim_all) + bmap->n_div : 0;
168 unsigned isl_map_n_in(const struct isl_map *map)
170 return map ? map->dim->n_in : 0;
173 unsigned isl_map_n_out(const struct isl_map *map)
175 return map ? map->dim->n_out : 0;
178 unsigned isl_map_n_param(const struct isl_map *map)
180 return map ? map->dim->nparam : 0;
183 int isl_map_compatible_domain(struct isl_map *map, struct isl_set *set)
188 m = isl_space_match(map->dim, isl_dim_param, set->dim, isl_dim_param);
191 return isl_space_tuple_match(map->dim, isl_dim_in, set->dim, isl_dim_set);
194 int isl_basic_map_compatible_domain(struct isl_basic_map *bmap,
195 struct isl_basic_set *bset)
200 m = isl_space_match(bmap->dim, isl_dim_param, bset->dim, isl_dim_param);
203 return isl_space_tuple_match(bmap->dim, isl_dim_in, bset->dim, isl_dim_set);
206 int isl_map_compatible_range(__isl_keep isl_map *map, __isl_keep isl_set *set)
211 m = isl_space_match(map->dim, isl_dim_param, set->dim, isl_dim_param);
214 return isl_space_tuple_match(map->dim, isl_dim_out, set->dim, isl_dim_set);
217 int isl_basic_map_compatible_range(struct isl_basic_map *bmap,
218 struct isl_basic_set *bset)
223 m = isl_space_match(bmap->dim, isl_dim_param, bset->dim, isl_dim_param);
226 return isl_space_tuple_match(bmap->dim, isl_dim_out, bset->dim, isl_dim_set);
229 isl_ctx *isl_basic_map_get_ctx(__isl_keep isl_basic_map *bmap)
231 return bmap ? bmap->ctx : NULL;
234 isl_ctx *isl_basic_set_get_ctx(__isl_keep isl_basic_set *bset)
236 return bset ? bset->ctx : NULL;
239 isl_ctx *isl_map_get_ctx(__isl_keep isl_map *map)
241 return map ? map->ctx : NULL;
244 isl_ctx *isl_set_get_ctx(__isl_keep isl_set *set)
246 return set ? set->ctx : NULL;
249 __isl_give isl_space *isl_basic_map_get_space(__isl_keep isl_basic_map *bmap)
253 return isl_space_copy(bmap->dim);
256 __isl_give isl_space *isl_basic_set_get_space(__isl_keep isl_basic_set *bset)
260 return isl_space_copy(bset->dim);
263 /* Extract the divs in "bmap" as a matrix.
265 __isl_give isl_mat *isl_basic_map_get_divs(__isl_keep isl_basic_map *bmap)
276 ctx = isl_basic_map_get_ctx(bmap);
277 total = isl_space_dim(bmap->dim, isl_dim_all);
278 cols = 1 + 1 + total + bmap->n_div;
279 div = isl_mat_alloc(ctx, bmap->n_div, cols);
283 for (i = 0; i < bmap->n_div; ++i)
284 isl_seq_cpy(div->row[i], bmap->div[i], cols);
289 /* Extract the divs in "bset" as a matrix.
291 __isl_give isl_mat *isl_basic_set_get_divs(__isl_keep isl_basic_set *bset)
293 return isl_basic_map_get_divs(bset);
296 __isl_give isl_local_space *isl_basic_map_get_local_space(
297 __isl_keep isl_basic_map *bmap)
304 div = isl_basic_map_get_divs(bmap);
305 return isl_local_space_alloc_div(isl_space_copy(bmap->dim), div);
308 __isl_give isl_local_space *isl_basic_set_get_local_space(
309 __isl_keep isl_basic_set *bset)
311 return isl_basic_map_get_local_space(bset);
314 __isl_give isl_basic_map *isl_basic_map_from_local_space(
315 __isl_take isl_local_space *ls)
324 n_div = isl_local_space_dim(ls, isl_dim_div);
325 bmap = isl_basic_map_alloc_space(isl_local_space_get_space(ls),
326 n_div, 0, 2 * n_div);
328 for (i = 0; i < n_div; ++i)
329 if (isl_basic_map_alloc_div(bmap) < 0)
332 for (i = 0; i < n_div; ++i) {
333 isl_seq_cpy(bmap->div[i], ls->div->row[i], ls->div->n_col);
334 if (isl_basic_map_add_div_constraints(bmap, i) < 0)
338 isl_local_space_free(ls);
341 isl_local_space_free(ls);
342 isl_basic_map_free(bmap);
346 __isl_give isl_basic_set *isl_basic_set_from_local_space(
347 __isl_take isl_local_space *ls)
349 return isl_basic_map_from_local_space(ls);
352 __isl_give isl_space *isl_map_get_space(__isl_keep isl_map *map)
356 return isl_space_copy(map->dim);
359 __isl_give isl_space *isl_set_get_space(__isl_keep isl_set *set)
363 return isl_space_copy(set->dim);
366 __isl_give isl_basic_map *isl_basic_map_set_tuple_name(
367 __isl_take isl_basic_map *bmap, enum isl_dim_type type, const char *s)
369 bmap = isl_basic_map_cow(bmap);
372 bmap->dim = isl_space_set_tuple_name(bmap->dim, type, s);
375 bmap = isl_basic_map_finalize(bmap);
378 isl_basic_map_free(bmap);
382 __isl_give isl_basic_set *isl_basic_set_set_tuple_name(
383 __isl_take isl_basic_set *bset, const char *s)
385 return isl_basic_map_set_tuple_name(bset, isl_dim_set, s);
388 const char *isl_basic_map_get_tuple_name(__isl_keep isl_basic_map *bmap,
389 enum isl_dim_type type)
391 return bmap ? isl_space_get_tuple_name(bmap->dim, type) : NULL;
394 __isl_give isl_map *isl_map_set_tuple_name(__isl_take isl_map *map,
395 enum isl_dim_type type, const char *s)
399 map = isl_map_cow(map);
403 map->dim = isl_space_set_tuple_name(map->dim, type, s);
407 for (i = 0; i < map->n; ++i) {
408 map->p[i] = isl_basic_map_set_tuple_name(map->p[i], type, s);
419 /* Does the input or output tuple have a name?
421 int isl_map_has_tuple_name(__isl_keep isl_map *map, enum isl_dim_type type)
423 return map ? isl_space_has_tuple_name(map->dim, type) : -1;
426 const char *isl_map_get_tuple_name(__isl_keep isl_map *map,
427 enum isl_dim_type type)
429 return map ? isl_space_get_tuple_name(map->dim, type) : NULL;
432 __isl_give isl_set *isl_set_set_tuple_name(__isl_take isl_set *set,
435 return (isl_set *)isl_map_set_tuple_name((isl_map *)set, isl_dim_set, s);
438 __isl_give isl_map *isl_map_set_tuple_id(__isl_take isl_map *map,
439 enum isl_dim_type type, __isl_take isl_id *id)
441 map = isl_map_cow(map);
443 return isl_id_free(id);
445 map->dim = isl_space_set_tuple_id(map->dim, type, id);
447 return isl_map_reset_space(map, isl_space_copy(map->dim));
450 __isl_give isl_set *isl_set_set_tuple_id(__isl_take isl_set *set,
451 __isl_take isl_id *id)
453 return isl_map_set_tuple_id(set, isl_dim_set, id);
456 __isl_give isl_map *isl_map_reset_tuple_id(__isl_take isl_map *map,
457 enum isl_dim_type type)
459 map = isl_map_cow(map);
463 map->dim = isl_space_reset_tuple_id(map->dim, type);
465 return isl_map_reset_space(map, isl_space_copy(map->dim));
468 __isl_give isl_set *isl_set_reset_tuple_id(__isl_take isl_set *set)
470 return isl_map_reset_tuple_id(set, isl_dim_set);
473 int isl_map_has_tuple_id(__isl_keep isl_map *map, enum isl_dim_type type)
475 return map ? isl_space_has_tuple_id(map->dim, type) : -1;
478 __isl_give isl_id *isl_map_get_tuple_id(__isl_keep isl_map *map,
479 enum isl_dim_type type)
481 return map ? isl_space_get_tuple_id(map->dim, type) : NULL;
484 int isl_set_has_tuple_id(__isl_keep isl_set *set)
486 return isl_map_has_tuple_id(set, isl_dim_set);
489 __isl_give isl_id *isl_set_get_tuple_id(__isl_keep isl_set *set)
491 return isl_map_get_tuple_id(set, isl_dim_set);
494 /* Does the set tuple have a name?
496 int isl_set_has_tuple_name(__isl_keep isl_set *set)
498 return set ? isl_space_has_tuple_name(set->dim, isl_dim_set) : -1;
502 const char *isl_basic_set_get_tuple_name(__isl_keep isl_basic_set *bset)
504 return bset ? isl_space_get_tuple_name(bset->dim, isl_dim_set) : NULL;
507 const char *isl_set_get_tuple_name(__isl_keep isl_set *set)
509 return set ? isl_space_get_tuple_name(set->dim, isl_dim_set) : NULL;
512 const char *isl_basic_map_get_dim_name(__isl_keep isl_basic_map *bmap,
513 enum isl_dim_type type, unsigned pos)
515 return bmap ? isl_space_get_dim_name(bmap->dim, type, pos) : NULL;
518 const char *isl_basic_set_get_dim_name(__isl_keep isl_basic_set *bset,
519 enum isl_dim_type type, unsigned pos)
521 return bset ? isl_space_get_dim_name(bset->dim, type, pos) : NULL;
524 /* Does the given dimension have a name?
526 int isl_map_has_dim_name(__isl_keep isl_map *map,
527 enum isl_dim_type type, unsigned pos)
529 return map ? isl_space_has_dim_name(map->dim, type, pos) : -1;
532 const char *isl_map_get_dim_name(__isl_keep isl_map *map,
533 enum isl_dim_type type, unsigned pos)
535 return map ? isl_space_get_dim_name(map->dim, type, pos) : NULL;
538 const char *isl_set_get_dim_name(__isl_keep isl_set *set,
539 enum isl_dim_type type, unsigned pos)
541 return set ? isl_space_get_dim_name(set->dim, type, pos) : NULL;
544 /* Does the given dimension have a name?
546 int isl_set_has_dim_name(__isl_keep isl_set *set,
547 enum isl_dim_type type, unsigned pos)
549 return set ? isl_space_has_dim_name(set->dim, type, pos) : -1;
552 __isl_give isl_basic_map *isl_basic_map_set_dim_name(
553 __isl_take isl_basic_map *bmap,
554 enum isl_dim_type type, unsigned pos, const char *s)
556 bmap = isl_basic_map_cow(bmap);
559 bmap->dim = isl_space_set_dim_name(bmap->dim, type, pos, s);
562 return isl_basic_map_finalize(bmap);
564 isl_basic_map_free(bmap);
568 __isl_give isl_map *isl_map_set_dim_name(__isl_take isl_map *map,
569 enum isl_dim_type type, unsigned pos, const char *s)
573 map = isl_map_cow(map);
577 map->dim = isl_space_set_dim_name(map->dim, type, pos, s);
581 for (i = 0; i < map->n; ++i) {
582 map->p[i] = isl_basic_map_set_dim_name(map->p[i], type, pos, s);
593 __isl_give isl_basic_set *isl_basic_set_set_dim_name(
594 __isl_take isl_basic_set *bset,
595 enum isl_dim_type type, unsigned pos, const char *s)
597 return (isl_basic_set *)isl_basic_map_set_dim_name(
598 (isl_basic_map *)bset, type, pos, s);
601 __isl_give isl_set *isl_set_set_dim_name(__isl_take isl_set *set,
602 enum isl_dim_type type, unsigned pos, const char *s)
604 return (isl_set *)isl_map_set_dim_name((isl_map *)set, type, pos, s);
607 int isl_basic_map_has_dim_id(__isl_keep isl_basic_map *bmap,
608 enum isl_dim_type type, unsigned pos)
610 return bmap ? isl_space_has_dim_id(bmap->dim, type, pos) : -1;
613 __isl_give isl_id *isl_basic_set_get_dim_id(__isl_keep isl_basic_set *bset,
614 enum isl_dim_type type, unsigned pos)
616 return bset ? isl_space_get_dim_id(bset->dim, type, pos) : NULL;
619 int isl_map_has_dim_id(__isl_keep isl_map *map,
620 enum isl_dim_type type, unsigned pos)
622 return map ? isl_space_has_dim_id(map->dim, type, pos) : -1;
625 __isl_give isl_id *isl_map_get_dim_id(__isl_keep isl_map *map,
626 enum isl_dim_type type, unsigned pos)
628 return map ? isl_space_get_dim_id(map->dim, type, pos) : NULL;
631 int isl_set_has_dim_id(__isl_keep isl_set *set,
632 enum isl_dim_type type, unsigned pos)
634 return isl_map_has_dim_id(set, type, pos);
637 __isl_give isl_id *isl_set_get_dim_id(__isl_keep isl_set *set,
638 enum isl_dim_type type, unsigned pos)
640 return isl_map_get_dim_id(set, type, pos);
643 __isl_give isl_map *isl_map_set_dim_id(__isl_take isl_map *map,
644 enum isl_dim_type type, unsigned pos, __isl_take isl_id *id)
646 map = isl_map_cow(map);
648 return isl_id_free(id);
650 map->dim = isl_space_set_dim_id(map->dim, type, pos, id);
652 return isl_map_reset_space(map, isl_space_copy(map->dim));
655 __isl_give isl_set *isl_set_set_dim_id(__isl_take isl_set *set,
656 enum isl_dim_type type, unsigned pos, __isl_take isl_id *id)
658 return isl_map_set_dim_id(set, type, pos, id);
661 int isl_map_find_dim_by_id(__isl_keep isl_map *map, enum isl_dim_type type,
662 __isl_keep isl_id *id)
666 return isl_space_find_dim_by_id(map->dim, type, id);
669 int isl_set_find_dim_by_id(__isl_keep isl_set *set, enum isl_dim_type type,
670 __isl_keep isl_id *id)
672 return isl_map_find_dim_by_id(set, type, id);
675 int isl_map_find_dim_by_name(__isl_keep isl_map *map, enum isl_dim_type type,
680 return isl_space_find_dim_by_name(map->dim, type, name);
683 int isl_set_find_dim_by_name(__isl_keep isl_set *set, enum isl_dim_type type,
686 return isl_map_find_dim_by_name(set, type, name);
689 int isl_basic_map_is_rational(__isl_keep isl_basic_map *bmap)
693 return ISL_F_ISSET(bmap, ISL_BASIC_MAP_RATIONAL);
696 int isl_basic_set_is_rational(__isl_keep isl_basic_set *bset)
698 return isl_basic_map_is_rational(bset);
701 /* Does "bmap" contain any rational points?
703 * If "bmap" has an equality for each dimension, equating the dimension
704 * to an integer constant, then it has no rational points, even if it
705 * is marked as rational.
707 int isl_basic_map_has_rational(__isl_keep isl_basic_map *bmap)
709 int has_rational = 1;
714 if (isl_basic_map_plain_is_empty(bmap))
716 if (!isl_basic_map_is_rational(bmap))
718 bmap = isl_basic_map_copy(bmap);
719 bmap = isl_basic_map_implicit_equalities(bmap);
722 total = isl_basic_map_total_dim(bmap);
723 if (bmap->n_eq == total) {
725 for (i = 0; i < bmap->n_eq; ++i) {
726 j = isl_seq_first_non_zero(bmap->eq[i] + 1, total);
729 if (!isl_int_is_one(bmap->eq[i][1 + j]) &&
730 !isl_int_is_negone(bmap->eq[i][1 + j]))
732 j = isl_seq_first_non_zero(bmap->eq[i] + 1 + j + 1,
740 isl_basic_map_free(bmap);
745 /* Does "map" contain any rational points?
747 int isl_map_has_rational(__isl_keep isl_map *map)
754 for (i = 0; i < map->n; ++i) {
755 has_rational = isl_basic_map_has_rational(map->p[i]);
756 if (has_rational < 0)
764 /* Does "set" contain any rational points?
766 int isl_set_has_rational(__isl_keep isl_set *set)
768 return isl_map_has_rational(set);
771 /* Is this basic set a parameter domain?
773 int isl_basic_set_is_params(__isl_keep isl_basic_set *bset)
777 return isl_space_is_params(bset->dim);
780 /* Is this set a parameter domain?
782 int isl_set_is_params(__isl_keep isl_set *set)
786 return isl_space_is_params(set->dim);
789 /* Is this map actually a parameter domain?
790 * Users should never call this function. Outside of isl,
791 * a map can never be a parameter domain.
793 int isl_map_is_params(__isl_keep isl_map *map)
797 return isl_space_is_params(map->dim);
800 static struct isl_basic_map *basic_map_init(struct isl_ctx *ctx,
801 struct isl_basic_map *bmap, unsigned extra,
802 unsigned n_eq, unsigned n_ineq)
805 size_t row_size = 1 + isl_space_dim(bmap->dim, isl_dim_all) + extra;
810 bmap->block = isl_blk_alloc(ctx, (n_ineq + n_eq) * row_size);
811 if (isl_blk_is_error(bmap->block))
814 bmap->ineq = isl_alloc_array(ctx, isl_int *, n_ineq + n_eq);
819 bmap->block2 = isl_blk_empty();
822 bmap->block2 = isl_blk_alloc(ctx, extra * (1 + row_size));
823 if (isl_blk_is_error(bmap->block2))
826 bmap->div = isl_alloc_array(ctx, isl_int *, extra);
831 for (i = 0; i < n_ineq + n_eq; ++i)
832 bmap->ineq[i] = bmap->block.data + i * row_size;
834 for (i = 0; i < extra; ++i)
835 bmap->div[i] = bmap->block2.data + i * (1 + row_size);
839 bmap->c_size = n_eq + n_ineq;
840 bmap->eq = bmap->ineq + n_ineq;
849 isl_basic_map_free(bmap);
853 struct isl_basic_set *isl_basic_set_alloc(struct isl_ctx *ctx,
854 unsigned nparam, unsigned dim, unsigned extra,
855 unsigned n_eq, unsigned n_ineq)
857 struct isl_basic_map *bmap;
860 space = isl_space_set_alloc(ctx, nparam, dim);
864 bmap = isl_basic_map_alloc_space(space, extra, n_eq, n_ineq);
865 return (struct isl_basic_set *)bmap;
868 struct isl_basic_set *isl_basic_set_alloc_space(__isl_take isl_space *dim,
869 unsigned extra, unsigned n_eq, unsigned n_ineq)
871 struct isl_basic_map *bmap;
874 isl_assert(dim->ctx, dim->n_in == 0, goto error);
875 bmap = isl_basic_map_alloc_space(dim, extra, n_eq, n_ineq);
876 return (struct isl_basic_set *)bmap;
882 struct isl_basic_map *isl_basic_map_alloc_space(__isl_take isl_space *dim,
883 unsigned extra, unsigned n_eq, unsigned n_ineq)
885 struct isl_basic_map *bmap;
889 bmap = isl_calloc_type(dim->ctx, struct isl_basic_map);
894 return basic_map_init(dim->ctx, bmap, extra, n_eq, n_ineq);
900 struct isl_basic_map *isl_basic_map_alloc(struct isl_ctx *ctx,
901 unsigned nparam, unsigned in, unsigned out, unsigned extra,
902 unsigned n_eq, unsigned n_ineq)
904 struct isl_basic_map *bmap;
907 dim = isl_space_alloc(ctx, nparam, in, out);
911 bmap = isl_basic_map_alloc_space(dim, extra, n_eq, n_ineq);
915 static void dup_constraints(
916 struct isl_basic_map *dst, struct isl_basic_map *src)
919 unsigned total = isl_basic_map_total_dim(src);
921 for (i = 0; i < src->n_eq; ++i) {
922 int j = isl_basic_map_alloc_equality(dst);
923 isl_seq_cpy(dst->eq[j], src->eq[i], 1+total);
926 for (i = 0; i < src->n_ineq; ++i) {
927 int j = isl_basic_map_alloc_inequality(dst);
928 isl_seq_cpy(dst->ineq[j], src->ineq[i], 1+total);
931 for (i = 0; i < src->n_div; ++i) {
932 int j = isl_basic_map_alloc_div(dst);
933 isl_seq_cpy(dst->div[j], src->div[i], 1+1+total);
935 ISL_F_SET(dst, ISL_BASIC_SET_FINAL);
938 struct isl_basic_map *isl_basic_map_dup(struct isl_basic_map *bmap)
940 struct isl_basic_map *dup;
944 dup = isl_basic_map_alloc_space(isl_space_copy(bmap->dim),
945 bmap->n_div, bmap->n_eq, bmap->n_ineq);
948 dup_constraints(dup, bmap);
949 dup->flags = bmap->flags;
950 dup->sample = isl_vec_copy(bmap->sample);
954 struct isl_basic_set *isl_basic_set_dup(struct isl_basic_set *bset)
956 struct isl_basic_map *dup;
958 dup = isl_basic_map_dup((struct isl_basic_map *)bset);
959 return (struct isl_basic_set *)dup;
962 struct isl_basic_set *isl_basic_set_copy(struct isl_basic_set *bset)
967 if (ISL_F_ISSET(bset, ISL_BASIC_SET_FINAL)) {
971 return isl_basic_set_dup(bset);
974 struct isl_set *isl_set_copy(struct isl_set *set)
983 struct isl_basic_map *isl_basic_map_copy(struct isl_basic_map *bmap)
988 if (ISL_F_ISSET(bmap, ISL_BASIC_SET_FINAL)) {
992 bmap = isl_basic_map_dup(bmap);
994 ISL_F_SET(bmap, ISL_BASIC_SET_FINAL);
998 struct isl_map *isl_map_copy(struct isl_map *map)
1007 void *isl_basic_map_free(__isl_take isl_basic_map *bmap)
1012 if (--bmap->ref > 0)
1015 isl_ctx_deref(bmap->ctx);
1017 isl_blk_free(bmap->ctx, bmap->block2);
1019 isl_blk_free(bmap->ctx, bmap->block);
1020 isl_vec_free(bmap->sample);
1021 isl_space_free(bmap->dim);
1027 void *isl_basic_set_free(struct isl_basic_set *bset)
1029 return isl_basic_map_free((struct isl_basic_map *)bset);
1032 static int room_for_con(struct isl_basic_map *bmap, unsigned n)
1034 return bmap->n_eq + bmap->n_ineq + n <= bmap->c_size;
1037 __isl_give isl_map *isl_map_align_params_map_map_and(
1038 __isl_take isl_map *map1, __isl_take isl_map *map2,
1039 __isl_give isl_map *(*fn)(__isl_take isl_map *map1,
1040 __isl_take isl_map *map2))
1044 if (isl_space_match(map1->dim, isl_dim_param, map2->dim, isl_dim_param))
1045 return fn(map1, map2);
1046 if (!isl_space_has_named_params(map1->dim) ||
1047 !isl_space_has_named_params(map2->dim))
1048 isl_die(map1->ctx, isl_error_invalid,
1049 "unaligned unnamed parameters", goto error);
1050 map1 = isl_map_align_params(map1, isl_map_get_space(map2));
1051 map2 = isl_map_align_params(map2, isl_map_get_space(map1));
1052 return fn(map1, map2);
1059 int isl_map_align_params_map_map_and_test(__isl_keep isl_map *map1,
1060 __isl_keep isl_map *map2,
1061 int (*fn)(__isl_keep isl_map *map1, __isl_keep isl_map *map2))
1067 if (isl_space_match(map1->dim, isl_dim_param, map2->dim, isl_dim_param))
1068 return fn(map1, map2);
1069 if (!isl_space_has_named_params(map1->dim) ||
1070 !isl_space_has_named_params(map2->dim))
1071 isl_die(map1->ctx, isl_error_invalid,
1072 "unaligned unnamed parameters", return -1);
1073 map1 = isl_map_copy(map1);
1074 map2 = isl_map_copy(map2);
1075 map1 = isl_map_align_params(map1, isl_map_get_space(map2));
1076 map2 = isl_map_align_params(map2, isl_map_get_space(map1));
1083 int isl_basic_map_alloc_equality(struct isl_basic_map *bmap)
1085 struct isl_ctx *ctx;
1089 isl_assert(ctx, room_for_con(bmap, 1), return -1);
1090 isl_assert(ctx, (bmap->eq - bmap->ineq) + bmap->n_eq <= bmap->c_size,
1092 ISL_F_CLR(bmap, ISL_BASIC_MAP_NORMALIZED);
1093 ISL_F_CLR(bmap, ISL_BASIC_MAP_NO_REDUNDANT);
1094 ISL_F_CLR(bmap, ISL_BASIC_MAP_NO_IMPLICIT);
1095 ISL_F_CLR(bmap, ISL_BASIC_MAP_ALL_EQUALITIES);
1096 ISL_F_CLR(bmap, ISL_BASIC_MAP_NORMALIZED_DIVS);
1097 if ((bmap->eq - bmap->ineq) + bmap->n_eq == bmap->c_size) {
1099 int j = isl_basic_map_alloc_inequality(bmap);
1103 bmap->ineq[j] = bmap->ineq[bmap->n_ineq - 1];
1104 bmap->ineq[bmap->n_ineq - 1] = bmap->eq[-1];
1111 isl_seq_clr(bmap->eq[bmap->n_eq] + 1 + isl_basic_map_total_dim(bmap),
1112 bmap->extra - bmap->n_div);
1113 return bmap->n_eq++;
1116 int isl_basic_set_alloc_equality(struct isl_basic_set *bset)
1118 return isl_basic_map_alloc_equality((struct isl_basic_map *)bset);
1121 int isl_basic_map_free_equality(struct isl_basic_map *bmap, unsigned n)
1125 isl_assert(bmap->ctx, n <= bmap->n_eq, return -1);
1130 int isl_basic_set_free_equality(struct isl_basic_set *bset, unsigned n)
1132 return isl_basic_map_free_equality((struct isl_basic_map *)bset, n);
1135 int isl_basic_map_drop_equality(struct isl_basic_map *bmap, unsigned pos)
1140 isl_assert(bmap->ctx, pos < bmap->n_eq, return -1);
1142 if (pos != bmap->n_eq - 1) {
1144 bmap->eq[pos] = bmap->eq[bmap->n_eq - 1];
1145 bmap->eq[bmap->n_eq - 1] = t;
1151 int isl_basic_set_drop_equality(struct isl_basic_set *bset, unsigned pos)
1153 return isl_basic_map_drop_equality((struct isl_basic_map *)bset, pos);
1156 /* Turn inequality "pos" of "bmap" into an equality.
1158 * In particular, we move the inequality in front of the equalities
1159 * and move the last inequality in the position of the moved inequality.
1160 * Note that isl_tab_make_equalities_explicit depends on this particular
1161 * change in the ordering of the constraints.
1163 void isl_basic_map_inequality_to_equality(
1164 struct isl_basic_map *bmap, unsigned pos)
1168 t = bmap->ineq[pos];
1169 bmap->ineq[pos] = bmap->ineq[bmap->n_ineq - 1];
1170 bmap->ineq[bmap->n_ineq - 1] = bmap->eq[-1];
1175 ISL_F_CLR(bmap, ISL_BASIC_MAP_NO_REDUNDANT);
1176 ISL_F_CLR(bmap, ISL_BASIC_MAP_NORMALIZED);
1177 ISL_F_CLR(bmap, ISL_BASIC_MAP_NORMALIZED_DIVS);
1178 ISL_F_CLR(bmap, ISL_BASIC_MAP_ALL_EQUALITIES);
1181 static int room_for_ineq(struct isl_basic_map *bmap, unsigned n)
1183 return bmap->n_ineq + n <= bmap->eq - bmap->ineq;
1186 int isl_basic_map_alloc_inequality(struct isl_basic_map *bmap)
1188 struct isl_ctx *ctx;
1192 isl_assert(ctx, room_for_ineq(bmap, 1), return -1);
1193 ISL_F_CLR(bmap, ISL_BASIC_MAP_NO_IMPLICIT);
1194 ISL_F_CLR(bmap, ISL_BASIC_MAP_NO_REDUNDANT);
1195 ISL_F_CLR(bmap, ISL_BASIC_MAP_NORMALIZED);
1196 ISL_F_CLR(bmap, ISL_BASIC_MAP_ALL_EQUALITIES);
1197 isl_seq_clr(bmap->ineq[bmap->n_ineq] +
1198 1 + isl_basic_map_total_dim(bmap),
1199 bmap->extra - bmap->n_div);
1200 return bmap->n_ineq++;
1203 int isl_basic_set_alloc_inequality(struct isl_basic_set *bset)
1205 return isl_basic_map_alloc_inequality((struct isl_basic_map *)bset);
1208 int isl_basic_map_free_inequality(struct isl_basic_map *bmap, unsigned n)
1212 isl_assert(bmap->ctx, n <= bmap->n_ineq, return -1);
1217 int isl_basic_set_free_inequality(struct isl_basic_set *bset, unsigned n)
1219 return isl_basic_map_free_inequality((struct isl_basic_map *)bset, n);
1222 int isl_basic_map_drop_inequality(struct isl_basic_map *bmap, unsigned pos)
1227 isl_assert(bmap->ctx, pos < bmap->n_ineq, return -1);
1229 if (pos != bmap->n_ineq - 1) {
1230 t = bmap->ineq[pos];
1231 bmap->ineq[pos] = bmap->ineq[bmap->n_ineq - 1];
1232 bmap->ineq[bmap->n_ineq - 1] = t;
1233 ISL_F_CLR(bmap, ISL_BASIC_MAP_NORMALIZED);
1239 int isl_basic_set_drop_inequality(struct isl_basic_set *bset, unsigned pos)
1241 return isl_basic_map_drop_inequality((struct isl_basic_map *)bset, pos);
1244 __isl_give isl_basic_map *isl_basic_map_add_eq(__isl_take isl_basic_map *bmap,
1249 bmap = isl_basic_map_extend_constraints(bmap, 1, 0);
1252 k = isl_basic_map_alloc_equality(bmap);
1255 isl_seq_cpy(bmap->eq[k], eq, 1 + isl_basic_map_total_dim(bmap));
1258 isl_basic_map_free(bmap);
1262 __isl_give isl_basic_set *isl_basic_set_add_eq(__isl_take isl_basic_set *bset,
1265 return (isl_basic_set *)
1266 isl_basic_map_add_eq((isl_basic_map *)bset, eq);
1269 __isl_give isl_basic_map *isl_basic_map_add_ineq(__isl_take isl_basic_map *bmap,
1274 bmap = isl_basic_map_extend_constraints(bmap, 0, 1);
1277 k = isl_basic_map_alloc_inequality(bmap);
1280 isl_seq_cpy(bmap->ineq[k], ineq, 1 + isl_basic_map_total_dim(bmap));
1283 isl_basic_map_free(bmap);
1287 __isl_give isl_basic_set *isl_basic_set_add_ineq(__isl_take isl_basic_set *bset,
1290 return (isl_basic_set *)
1291 isl_basic_map_add_ineq((isl_basic_map *)bset, ineq);
1294 int isl_basic_map_alloc_div(struct isl_basic_map *bmap)
1298 isl_assert(bmap->ctx, bmap->n_div < bmap->extra, return -1);
1299 isl_seq_clr(bmap->div[bmap->n_div] +
1300 1 + 1 + isl_basic_map_total_dim(bmap),
1301 bmap->extra - bmap->n_div);
1302 ISL_F_CLR(bmap, ISL_BASIC_MAP_NORMALIZED_DIVS);
1303 return bmap->n_div++;
1306 int isl_basic_set_alloc_div(struct isl_basic_set *bset)
1308 return isl_basic_map_alloc_div((struct isl_basic_map *)bset);
1311 int isl_basic_map_free_div(struct isl_basic_map *bmap, unsigned n)
1315 isl_assert(bmap->ctx, n <= bmap->n_div, return -1);
1320 int isl_basic_set_free_div(struct isl_basic_set *bset, unsigned n)
1322 return isl_basic_map_free_div((struct isl_basic_map *)bset, n);
1325 /* Copy constraint from src to dst, putting the vars of src at offset
1326 * dim_off in dst and the divs of src at offset div_off in dst.
1327 * If both sets are actually map, then dim_off applies to the input
1330 static void copy_constraint(struct isl_basic_map *dst_map, isl_int *dst,
1331 struct isl_basic_map *src_map, isl_int *src,
1332 unsigned in_off, unsigned out_off, unsigned div_off)
1334 unsigned src_nparam = isl_basic_map_n_param(src_map);
1335 unsigned dst_nparam = isl_basic_map_n_param(dst_map);
1336 unsigned src_in = isl_basic_map_n_in(src_map);
1337 unsigned dst_in = isl_basic_map_n_in(dst_map);
1338 unsigned src_out = isl_basic_map_n_out(src_map);
1339 unsigned dst_out = isl_basic_map_n_out(dst_map);
1340 isl_int_set(dst[0], src[0]);
1341 isl_seq_cpy(dst+1, src+1, isl_min(dst_nparam, src_nparam));
1342 if (dst_nparam > src_nparam)
1343 isl_seq_clr(dst+1+src_nparam,
1344 dst_nparam - src_nparam);
1345 isl_seq_clr(dst+1+dst_nparam, in_off);
1346 isl_seq_cpy(dst+1+dst_nparam+in_off,
1348 isl_min(dst_in-in_off, src_in));
1349 if (dst_in-in_off > src_in)
1350 isl_seq_clr(dst+1+dst_nparam+in_off+src_in,
1351 dst_in - in_off - src_in);
1352 isl_seq_clr(dst+1+dst_nparam+dst_in, out_off);
1353 isl_seq_cpy(dst+1+dst_nparam+dst_in+out_off,
1354 src+1+src_nparam+src_in,
1355 isl_min(dst_out-out_off, src_out));
1356 if (dst_out-out_off > src_out)
1357 isl_seq_clr(dst+1+dst_nparam+dst_in+out_off+src_out,
1358 dst_out - out_off - src_out);
1359 isl_seq_clr(dst+1+dst_nparam+dst_in+dst_out, div_off);
1360 isl_seq_cpy(dst+1+dst_nparam+dst_in+dst_out+div_off,
1361 src+1+src_nparam+src_in+src_out,
1362 isl_min(dst_map->extra-div_off, src_map->n_div));
1363 if (dst_map->n_div-div_off > src_map->n_div)
1364 isl_seq_clr(dst+1+dst_nparam+dst_in+dst_out+
1365 div_off+src_map->n_div,
1366 dst_map->n_div - div_off - src_map->n_div);
1369 static void copy_div(struct isl_basic_map *dst_map, isl_int *dst,
1370 struct isl_basic_map *src_map, isl_int *src,
1371 unsigned in_off, unsigned out_off, unsigned div_off)
1373 isl_int_set(dst[0], src[0]);
1374 copy_constraint(dst_map, dst+1, src_map, src+1, in_off, out_off, div_off);
1377 static struct isl_basic_map *add_constraints(struct isl_basic_map *bmap1,
1378 struct isl_basic_map *bmap2, unsigned i_pos, unsigned o_pos)
1383 if (!bmap1 || !bmap2)
1386 div_off = bmap1->n_div;
1388 for (i = 0; i < bmap2->n_eq; ++i) {
1389 int i1 = isl_basic_map_alloc_equality(bmap1);
1392 copy_constraint(bmap1, bmap1->eq[i1], bmap2, bmap2->eq[i],
1393 i_pos, o_pos, div_off);
1396 for (i = 0; i < bmap2->n_ineq; ++i) {
1397 int i1 = isl_basic_map_alloc_inequality(bmap1);
1400 copy_constraint(bmap1, bmap1->ineq[i1], bmap2, bmap2->ineq[i],
1401 i_pos, o_pos, div_off);
1404 for (i = 0; i < bmap2->n_div; ++i) {
1405 int i1 = isl_basic_map_alloc_div(bmap1);
1408 copy_div(bmap1, bmap1->div[i1], bmap2, bmap2->div[i],
1409 i_pos, o_pos, div_off);
1412 isl_basic_map_free(bmap2);
1417 isl_basic_map_free(bmap1);
1418 isl_basic_map_free(bmap2);
1422 struct isl_basic_set *isl_basic_set_add_constraints(struct isl_basic_set *bset1,
1423 struct isl_basic_set *bset2, unsigned pos)
1425 return (struct isl_basic_set *)
1426 add_constraints((struct isl_basic_map *)bset1,
1427 (struct isl_basic_map *)bset2, 0, pos);
1430 struct isl_basic_map *isl_basic_map_extend_space(struct isl_basic_map *base,
1431 __isl_take isl_space *dim, unsigned extra,
1432 unsigned n_eq, unsigned n_ineq)
1434 struct isl_basic_map *ext;
1444 dims_ok = isl_space_is_equal(base->dim, dim) &&
1445 base->extra >= base->n_div + extra;
1447 if (dims_ok && room_for_con(base, n_eq + n_ineq) &&
1448 room_for_ineq(base, n_ineq)) {
1449 isl_space_free(dim);
1453 isl_assert(base->ctx, base->dim->nparam <= dim->nparam, goto error);
1454 isl_assert(base->ctx, base->dim->n_in <= dim->n_in, goto error);
1455 isl_assert(base->ctx, base->dim->n_out <= dim->n_out, goto error);
1456 extra += base->extra;
1458 n_ineq += base->n_ineq;
1460 ext = isl_basic_map_alloc_space(dim, extra, n_eq, n_ineq);
1466 ext->sample = isl_vec_copy(base->sample);
1467 flags = base->flags;
1468 ext = add_constraints(ext, base, 0, 0);
1471 ISL_F_CLR(ext, ISL_BASIC_SET_FINAL);
1477 isl_space_free(dim);
1478 isl_basic_map_free(base);
1482 struct isl_basic_set *isl_basic_set_extend_space(struct isl_basic_set *base,
1483 __isl_take isl_space *dim, unsigned extra,
1484 unsigned n_eq, unsigned n_ineq)
1486 return (struct isl_basic_set *)
1487 isl_basic_map_extend_space((struct isl_basic_map *)base, dim,
1488 extra, n_eq, n_ineq);
1491 struct isl_basic_map *isl_basic_map_extend_constraints(
1492 struct isl_basic_map *base, unsigned n_eq, unsigned n_ineq)
1496 return isl_basic_map_extend_space(base, isl_space_copy(base->dim),
1500 struct isl_basic_map *isl_basic_map_extend(struct isl_basic_map *base,
1501 unsigned nparam, unsigned n_in, unsigned n_out, unsigned extra,
1502 unsigned n_eq, unsigned n_ineq)
1504 struct isl_basic_map *bmap;
1509 dim = isl_space_alloc(base->ctx, nparam, n_in, n_out);
1513 bmap = isl_basic_map_extend_space(base, dim, extra, n_eq, n_ineq);
1516 isl_basic_map_free(base);
1520 struct isl_basic_set *isl_basic_set_extend(struct isl_basic_set *base,
1521 unsigned nparam, unsigned dim, unsigned extra,
1522 unsigned n_eq, unsigned n_ineq)
1524 return (struct isl_basic_set *)
1525 isl_basic_map_extend((struct isl_basic_map *)base,
1526 nparam, 0, dim, extra, n_eq, n_ineq);
1529 struct isl_basic_set *isl_basic_set_extend_constraints(
1530 struct isl_basic_set *base, unsigned n_eq, unsigned n_ineq)
1532 return (struct isl_basic_set *)
1533 isl_basic_map_extend_constraints((struct isl_basic_map *)base,
1537 struct isl_basic_set *isl_basic_set_cow(struct isl_basic_set *bset)
1539 return (struct isl_basic_set *)
1540 isl_basic_map_cow((struct isl_basic_map *)bset);
1543 struct isl_basic_map *isl_basic_map_cow(struct isl_basic_map *bmap)
1548 if (bmap->ref > 1) {
1550 bmap = isl_basic_map_dup(bmap);
1553 ISL_F_CLR(bmap, ISL_BASIC_SET_FINAL);
1557 struct isl_set *isl_set_cow(struct isl_set *set)
1565 return isl_set_dup(set);
1568 struct isl_map *isl_map_cow(struct isl_map *map)
1576 return isl_map_dup(map);
1579 static void swap_vars(struct isl_blk blk, isl_int *a,
1580 unsigned a_len, unsigned b_len)
1582 isl_seq_cpy(blk.data, a+a_len, b_len);
1583 isl_seq_cpy(blk.data+b_len, a, a_len);
1584 isl_seq_cpy(a, blk.data, b_len+a_len);
1587 static __isl_give isl_basic_map *isl_basic_map_swap_vars(
1588 __isl_take isl_basic_map *bmap, unsigned pos, unsigned n1, unsigned n2)
1596 isl_assert(bmap->ctx,
1597 pos + n1 + n2 <= 1 + isl_basic_map_total_dim(bmap), goto error);
1599 if (n1 == 0 || n2 == 0)
1602 bmap = isl_basic_map_cow(bmap);
1606 blk = isl_blk_alloc(bmap->ctx, n1 + n2);
1607 if (isl_blk_is_error(blk))
1610 for (i = 0; i < bmap->n_eq; ++i)
1612 bmap->eq[i] + pos, n1, n2);
1614 for (i = 0; i < bmap->n_ineq; ++i)
1616 bmap->ineq[i] + pos, n1, n2);
1618 for (i = 0; i < bmap->n_div; ++i)
1620 bmap->div[i]+1 + pos, n1, n2);
1622 isl_blk_free(bmap->ctx, blk);
1624 ISL_F_CLR(bmap, ISL_BASIC_SET_NORMALIZED);
1625 bmap = isl_basic_map_gauss(bmap, NULL);
1626 return isl_basic_map_finalize(bmap);
1628 isl_basic_map_free(bmap);
1632 static __isl_give isl_basic_set *isl_basic_set_swap_vars(
1633 __isl_take isl_basic_set *bset, unsigned n)
1641 nparam = isl_basic_set_n_param(bset);
1642 dim = isl_basic_set_n_dim(bset);
1643 isl_assert(bset->ctx, n <= dim, goto error);
1645 return isl_basic_map_swap_vars(bset, 1 + nparam, n, dim - n);
1647 isl_basic_set_free(bset);
1651 struct isl_basic_map *isl_basic_map_set_to_empty(struct isl_basic_map *bmap)
1657 total = isl_basic_map_total_dim(bmap);
1658 isl_basic_map_free_div(bmap, bmap->n_div);
1659 isl_basic_map_free_inequality(bmap, bmap->n_ineq);
1661 isl_basic_map_free_equality(bmap, bmap->n_eq-1);
1663 i = isl_basic_map_alloc_equality(bmap);
1667 isl_int_set_si(bmap->eq[i][0], 1);
1668 isl_seq_clr(bmap->eq[i]+1, total);
1669 ISL_F_SET(bmap, ISL_BASIC_MAP_EMPTY);
1670 isl_vec_free(bmap->sample);
1671 bmap->sample = NULL;
1672 return isl_basic_map_finalize(bmap);
1674 isl_basic_map_free(bmap);
1678 struct isl_basic_set *isl_basic_set_set_to_empty(struct isl_basic_set *bset)
1680 return (struct isl_basic_set *)
1681 isl_basic_map_set_to_empty((struct isl_basic_map *)bset);
1684 /* Swap divs "a" and "b" in "bmap" (without modifying any of the constraints
1687 static void swap_div(__isl_keep isl_basic_map *bmap, int a, int b)
1689 isl_int *t = bmap->div[a];
1690 bmap->div[a] = bmap->div[b];
1694 /* Swap divs "a" and "b" in "bmap" and adjust the constraints and
1695 * div definitions accordingly.
1697 void isl_basic_map_swap_div(struct isl_basic_map *bmap, int a, int b)
1700 unsigned off = isl_space_dim(bmap->dim, isl_dim_all);
1702 swap_div(bmap, a, b);
1704 for (i = 0; i < bmap->n_eq; ++i)
1705 isl_int_swap(bmap->eq[i][1+off+a], bmap->eq[i][1+off+b]);
1707 for (i = 0; i < bmap->n_ineq; ++i)
1708 isl_int_swap(bmap->ineq[i][1+off+a], bmap->ineq[i][1+off+b]);
1710 for (i = 0; i < bmap->n_div; ++i)
1711 isl_int_swap(bmap->div[i][1+1+off+a], bmap->div[i][1+1+off+b]);
1712 ISL_F_CLR(bmap, ISL_BASIC_MAP_NORMALIZED);
1715 /* Eliminate the specified n dimensions starting at first from the
1716 * constraints, without removing the dimensions from the space.
1717 * If the set is rational, the dimensions are eliminated using Fourier-Motzkin.
1719 __isl_give isl_map *isl_map_eliminate(__isl_take isl_map *map,
1720 enum isl_dim_type type, unsigned first, unsigned n)
1729 if (first + n > isl_map_dim(map, type) || first + n < first)
1730 isl_die(map->ctx, isl_error_invalid,
1731 "index out of bounds", goto error);
1733 map = isl_map_cow(map);
1737 for (i = 0; i < map->n; ++i) {
1738 map->p[i] = isl_basic_map_eliminate(map->p[i], type, first, n);
1748 /* Eliminate the specified n dimensions starting at first from the
1749 * constraints, without removing the dimensions from the space.
1750 * If the set is rational, the dimensions are eliminated using Fourier-Motzkin.
1752 __isl_give isl_set *isl_set_eliminate(__isl_take isl_set *set,
1753 enum isl_dim_type type, unsigned first, unsigned n)
1755 return (isl_set *)isl_map_eliminate((isl_map *)set, type, first, n);
1758 /* Eliminate the specified n dimensions starting at first from the
1759 * constraints, without removing the dimensions from the space.
1760 * If the set is rational, the dimensions are eliminated using Fourier-Motzkin.
1762 __isl_give isl_set *isl_set_eliminate_dims(__isl_take isl_set *set,
1763 unsigned first, unsigned n)
1765 return isl_set_eliminate(set, isl_dim_set, first, n);
1768 __isl_give isl_basic_map *isl_basic_map_remove_divs(
1769 __isl_take isl_basic_map *bmap)
1773 bmap = isl_basic_map_eliminate_vars(bmap,
1774 isl_space_dim(bmap->dim, isl_dim_all), bmap->n_div);
1778 return isl_basic_map_finalize(bmap);
1781 __isl_give isl_basic_set *isl_basic_set_remove_divs(
1782 __isl_take isl_basic_set *bset)
1784 return (struct isl_basic_set *)isl_basic_map_remove_divs(
1785 (struct isl_basic_map *)bset);
1788 __isl_give isl_map *isl_map_remove_divs(__isl_take isl_map *map)
1797 map = isl_map_cow(map);
1801 for (i = 0; i < map->n; ++i) {
1802 map->p[i] = isl_basic_map_remove_divs(map->p[i]);
1812 __isl_give isl_set *isl_set_remove_divs(__isl_take isl_set *set)
1814 return isl_map_remove_divs(set);
1817 struct isl_basic_map *isl_basic_map_remove_dims(struct isl_basic_map *bmap,
1818 enum isl_dim_type type, unsigned first, unsigned n)
1822 isl_assert(bmap->ctx, first + n <= isl_basic_map_dim(bmap, type),
1824 if (n == 0 && !isl_space_is_named_or_nested(bmap->dim, type))
1826 bmap = isl_basic_map_eliminate_vars(bmap,
1827 isl_basic_map_offset(bmap, type) - 1 + first, n);
1830 if (ISL_F_ISSET(bmap, ISL_BASIC_MAP_EMPTY) && type == isl_dim_div)
1832 bmap = isl_basic_map_drop(bmap, type, first, n);
1835 isl_basic_map_free(bmap);
1839 /* Return true if the definition of the given div (recursively) involves
1840 * any of the given variables.
1842 static int div_involves_vars(__isl_keep isl_basic_map *bmap, int div,
1843 unsigned first, unsigned n)
1846 unsigned div_offset = isl_basic_map_offset(bmap, isl_dim_div);
1848 if (isl_int_is_zero(bmap->div[div][0]))
1850 if (isl_seq_first_non_zero(bmap->div[div] + 1 + first, n) >= 0)
1853 for (i = bmap->n_div - 1; i >= 0; --i) {
1854 if (isl_int_is_zero(bmap->div[div][1 + div_offset + i]))
1856 if (div_involves_vars(bmap, i, first, n))
1863 /* Try and add a lower and/or upper bound on "div" to "bmap"
1864 * based on inequality "i".
1865 * "total" is the total number of variables (excluding the divs).
1866 * "v" is a temporary object that can be used during the calculations.
1867 * If "lb" is set, then a lower bound should be constructed.
1868 * If "ub" is set, then an upper bound should be constructed.
1870 * The calling function has already checked that the inequality does not
1871 * reference "div", but we still need to check that the inequality is
1872 * of the right form. We'll consider the case where we want to construct
1873 * a lower bound. The construction of upper bounds is similar.
1875 * Let "div" be of the form
1877 * q = floor((a + f(x))/d)
1879 * We essentially check if constraint "i" is of the form
1883 * so that we can use it to derive a lower bound on "div".
1884 * However, we allow a slightly more general form
1888 * with the condition that the coefficients of g(x) - f(x) are all
1890 * Rewriting this constraint as
1894 * adding a + f(x) to both sides and dividing by d, we obtain
1896 * (a + f(x))/d >= (a-b)/d + (f(x)-g(x))/d
1898 * Taking the floor on both sides, we obtain
1900 * q >= floor((a-b)/d) + (f(x)-g(x))/d
1904 * (g(x)-f(x))/d + ceil((b-a)/d) + q >= 0
1906 * In the case of an upper bound, we construct the constraint
1908 * (g(x)+f(x))/d + floor((b+a)/d) - q >= 0
1911 static __isl_give isl_basic_map *insert_bounds_on_div_from_ineq(
1912 __isl_take isl_basic_map *bmap, int div, int i,
1913 unsigned total, isl_int v, int lb, int ub)
1917 for (j = 0; (lb || ub) && j < total + bmap->n_div; ++j) {
1919 isl_int_sub(v, bmap->ineq[i][1 + j],
1920 bmap->div[div][1 + 1 + j]);
1921 lb = isl_int_is_divisible_by(v, bmap->div[div][0]);
1924 isl_int_add(v, bmap->ineq[i][1 + j],
1925 bmap->div[div][1 + 1 + j]);
1926 ub = isl_int_is_divisible_by(v, bmap->div[div][0]);
1932 bmap = isl_basic_map_extend_constraints(bmap, 0, lb + ub);
1934 int k = isl_basic_map_alloc_inequality(bmap);
1937 for (j = 0; j < 1 + total + bmap->n_div; ++j) {
1938 isl_int_sub(bmap->ineq[k][j], bmap->ineq[i][j],
1939 bmap->div[div][1 + j]);
1940 isl_int_cdiv_q(bmap->ineq[k][j],
1941 bmap->ineq[k][j], bmap->div[div][0]);
1943 isl_int_set_si(bmap->ineq[k][1 + total + div], 1);
1946 int k = isl_basic_map_alloc_inequality(bmap);
1949 for (j = 0; j < 1 + total + bmap->n_div; ++j) {
1950 isl_int_add(bmap->ineq[k][j], bmap->ineq[i][j],
1951 bmap->div[div][1 + j]);
1952 isl_int_fdiv_q(bmap->ineq[k][j],
1953 bmap->ineq[k][j], bmap->div[div][0]);
1955 isl_int_set_si(bmap->ineq[k][1 + total + div], -1);
1960 isl_basic_map_free(bmap);
1964 /* This function is called right before "div" is eliminated from "bmap"
1965 * using Fourier-Motzkin.
1966 * Look through the constraints of "bmap" for constraints on the argument
1967 * of the integer division and use them to construct constraints on the
1968 * integer division itself. These constraints can then be combined
1969 * during the Fourier-Motzkin elimination.
1970 * Note that it is only useful to introduce lower bounds on "div"
1971 * if "bmap" already contains upper bounds on "div" as the newly
1972 * introduce lower bounds can then be combined with the pre-existing
1973 * upper bounds. Similarly for upper bounds.
1974 * We therefore first check if "bmap" contains any lower and/or upper bounds
1977 * It is interesting to note that the introduction of these constraints
1978 * can indeed lead to more accurate results, even when compared to
1979 * deriving constraints on the argument of "div" from constraints on "div".
1980 * Consider, for example, the set
1982 * { [i,j,k] : 3 + i + 2j >= 0 and 2 * [(i+2j)/4] <= k }
1984 * The second constraint can be rewritten as
1986 * 2 * [(-i-2j+3)/4] + k >= 0
1988 * from which we can derive
1990 * -i - 2j + 3 >= -2k
1996 * Combined with the first constraint, we obtain
1998 * -3 <= 3 + 2k or k >= -3
2000 * If, on the other hand we derive a constraint on [(i+2j)/4] from
2001 * the first constraint, we obtain
2003 * [(i + 2j)/4] >= [-3/4] = -1
2005 * Combining this constraint with the second constraint, we obtain
2009 static __isl_give isl_basic_map *insert_bounds_on_div(
2010 __isl_take isl_basic_map *bmap, int div)
2013 int check_lb, check_ub;
2020 if (isl_int_is_zero(bmap->div[div][0]))
2023 total = isl_space_dim(bmap->dim, isl_dim_all);
2027 for (i = 0; (!check_lb || !check_ub) && i < bmap->n_ineq; ++i) {
2028 int s = isl_int_sgn(bmap->ineq[i][1 + total + div]);
2035 if (!check_lb && !check_ub)
2040 for (i = 0; bmap && i < bmap->n_ineq; ++i) {
2041 if (!isl_int_is_zero(bmap->ineq[i][1 + total + div]))
2044 bmap = insert_bounds_on_div_from_ineq(bmap, div, i, total, v,
2045 check_lb, check_ub);
2053 /* Remove all divs (recursively) involving any of the given dimensions
2054 * in their definitions.
2056 __isl_give isl_basic_map *isl_basic_map_remove_divs_involving_dims(
2057 __isl_take isl_basic_map *bmap,
2058 enum isl_dim_type type, unsigned first, unsigned n)
2064 isl_assert(bmap->ctx, first + n <= isl_basic_map_dim(bmap, type),
2066 first += isl_basic_map_offset(bmap, type);
2068 for (i = bmap->n_div - 1; i >= 0; --i) {
2069 if (!div_involves_vars(bmap, i, first, n))
2071 bmap = insert_bounds_on_div(bmap, i);
2072 bmap = isl_basic_map_remove_dims(bmap, isl_dim_div, i, 1);
2080 isl_basic_map_free(bmap);
2084 __isl_give isl_basic_set *isl_basic_set_remove_divs_involving_dims(
2085 __isl_take isl_basic_set *bset,
2086 enum isl_dim_type type, unsigned first, unsigned n)
2088 return isl_basic_map_remove_divs_involving_dims(bset, type, first, n);
2091 __isl_give isl_map *isl_map_remove_divs_involving_dims(__isl_take isl_map *map,
2092 enum isl_dim_type type, unsigned first, unsigned n)
2101 map = isl_map_cow(map);
2105 for (i = 0; i < map->n; ++i) {
2106 map->p[i] = isl_basic_map_remove_divs_involving_dims(map->p[i],
2117 __isl_give isl_set *isl_set_remove_divs_involving_dims(__isl_take isl_set *set,
2118 enum isl_dim_type type, unsigned first, unsigned n)
2120 return (isl_set *)isl_map_remove_divs_involving_dims((isl_map *)set,
2124 /* Does the desciption of "bmap" depend on the specified dimensions?
2125 * We also check whether the dimensions appear in any of the div definitions.
2126 * In principle there is no need for this check. If the dimensions appear
2127 * in a div definition, they also appear in the defining constraints of that
2130 int isl_basic_map_involves_dims(__isl_keep isl_basic_map *bmap,
2131 enum isl_dim_type type, unsigned first, unsigned n)
2138 if (first + n > isl_basic_map_dim(bmap, type))
2139 isl_die(bmap->ctx, isl_error_invalid,
2140 "index out of bounds", return -1);
2142 first += isl_basic_map_offset(bmap, type);
2143 for (i = 0; i < bmap->n_eq; ++i)
2144 if (isl_seq_first_non_zero(bmap->eq[i] + first, n) >= 0)
2146 for (i = 0; i < bmap->n_ineq; ++i)
2147 if (isl_seq_first_non_zero(bmap->ineq[i] + first, n) >= 0)
2149 for (i = 0; i < bmap->n_div; ++i) {
2150 if (isl_int_is_zero(bmap->div[i][0]))
2152 if (isl_seq_first_non_zero(bmap->div[i] + 1 + first, n) >= 0)
2159 int isl_map_involves_dims(__isl_keep isl_map *map,
2160 enum isl_dim_type type, unsigned first, unsigned n)
2167 if (first + n > isl_map_dim(map, type))
2168 isl_die(map->ctx, isl_error_invalid,
2169 "index out of bounds", return -1);
2171 for (i = 0; i < map->n; ++i) {
2172 int involves = isl_basic_map_involves_dims(map->p[i],
2174 if (involves < 0 || involves)
2181 int isl_basic_set_involves_dims(__isl_keep isl_basic_set *bset,
2182 enum isl_dim_type type, unsigned first, unsigned n)
2184 return isl_basic_map_involves_dims(bset, type, first, n);
2187 int isl_set_involves_dims(__isl_keep isl_set *set,
2188 enum isl_dim_type type, unsigned first, unsigned n)
2190 return isl_map_involves_dims(set, type, first, n);
2193 /* Return true if the definition of the given div is unknown or depends
2196 static int div_is_unknown(__isl_keep isl_basic_map *bmap, int div)
2199 unsigned div_offset = isl_basic_map_offset(bmap, isl_dim_div);
2201 if (isl_int_is_zero(bmap->div[div][0]))
2204 for (i = bmap->n_div - 1; i >= 0; --i) {
2205 if (isl_int_is_zero(bmap->div[div][1 + div_offset + i]))
2207 if (div_is_unknown(bmap, i))
2214 /* Remove all divs that are unknown or defined in terms of unknown divs.
2216 __isl_give isl_basic_map *isl_basic_map_remove_unknown_divs(
2217 __isl_take isl_basic_map *bmap)
2224 for (i = bmap->n_div - 1; i >= 0; --i) {
2225 if (!div_is_unknown(bmap, i))
2227 bmap = isl_basic_map_remove_dims(bmap, isl_dim_div, i, 1);
2236 /* Remove all divs that are unknown or defined in terms of unknown divs.
2238 __isl_give isl_basic_set *isl_basic_set_remove_unknown_divs(
2239 __isl_take isl_basic_set *bset)
2241 return isl_basic_map_remove_unknown_divs(bset);
2244 __isl_give isl_map *isl_map_remove_unknown_divs(__isl_take isl_map *map)
2253 map = isl_map_cow(map);
2257 for (i = 0; i < map->n; ++i) {
2258 map->p[i] = isl_basic_map_remove_unknown_divs(map->p[i]);
2268 __isl_give isl_set *isl_set_remove_unknown_divs(__isl_take isl_set *set)
2270 return (isl_set *)isl_map_remove_unknown_divs((isl_map *)set);
2273 __isl_give isl_basic_set *isl_basic_set_remove_dims(
2274 __isl_take isl_basic_set *bset,
2275 enum isl_dim_type type, unsigned first, unsigned n)
2277 return (isl_basic_set *)
2278 isl_basic_map_remove_dims((isl_basic_map *)bset, type, first, n);
2281 struct isl_map *isl_map_remove_dims(struct isl_map *map,
2282 enum isl_dim_type type, unsigned first, unsigned n)
2289 map = isl_map_cow(map);
2292 isl_assert(map->ctx, first + n <= isl_map_dim(map, type), goto error);
2294 for (i = 0; i < map->n; ++i) {
2295 map->p[i] = isl_basic_map_eliminate_vars(map->p[i],
2296 isl_basic_map_offset(map->p[i], type) - 1 + first, n);
2300 map = isl_map_drop(map, type, first, n);
2307 __isl_give isl_set *isl_set_remove_dims(__isl_take isl_set *bset,
2308 enum isl_dim_type type, unsigned first, unsigned n)
2310 return (isl_set *)isl_map_remove_dims((isl_map *)bset, type, first, n);
2313 /* Project out n inputs starting at first using Fourier-Motzkin */
2314 struct isl_map *isl_map_remove_inputs(struct isl_map *map,
2315 unsigned first, unsigned n)
2317 return isl_map_remove_dims(map, isl_dim_in, first, n);
2320 static void dump_term(struct isl_basic_map *bmap,
2321 isl_int c, int pos, FILE *out)
2324 unsigned in = isl_basic_map_n_in(bmap);
2325 unsigned dim = in + isl_basic_map_n_out(bmap);
2326 unsigned nparam = isl_basic_map_n_param(bmap);
2328 isl_int_print(out, c, 0);
2330 if (!isl_int_is_one(c))
2331 isl_int_print(out, c, 0);
2332 if (pos < 1 + nparam) {
2333 name = isl_space_get_dim_name(bmap->dim,
2334 isl_dim_param, pos - 1);
2336 fprintf(out, "%s", name);
2338 fprintf(out, "p%d", pos - 1);
2339 } else if (pos < 1 + nparam + in)
2340 fprintf(out, "i%d", pos - 1 - nparam);
2341 else if (pos < 1 + nparam + dim)
2342 fprintf(out, "o%d", pos - 1 - nparam - in);
2344 fprintf(out, "e%d", pos - 1 - nparam - dim);
2348 static void dump_constraint_sign(struct isl_basic_map *bmap, isl_int *c,
2349 int sign, FILE *out)
2353 unsigned len = 1 + isl_basic_map_total_dim(bmap);
2357 for (i = 0, first = 1; i < len; ++i) {
2358 if (isl_int_sgn(c[i]) * sign <= 0)
2361 fprintf(out, " + ");
2363 isl_int_abs(v, c[i]);
2364 dump_term(bmap, v, i, out);
2371 static void dump_constraint(struct isl_basic_map *bmap, isl_int *c,
2372 const char *op, FILE *out, int indent)
2376 fprintf(out, "%*s", indent, "");
2378 dump_constraint_sign(bmap, c, 1, out);
2379 fprintf(out, " %s ", op);
2380 dump_constraint_sign(bmap, c, -1, out);
2384 for (i = bmap->n_div; i < bmap->extra; ++i) {
2385 if (isl_int_is_zero(c[1+isl_space_dim(bmap->dim, isl_dim_all)+i]))
2387 fprintf(out, "%*s", indent, "");
2388 fprintf(out, "ERROR: unused div coefficient not zero\n");
2393 static void dump_constraints(struct isl_basic_map *bmap,
2394 isl_int **c, unsigned n,
2395 const char *op, FILE *out, int indent)
2399 for (i = 0; i < n; ++i)
2400 dump_constraint(bmap, c[i], op, out, indent);
2403 static void dump_affine(struct isl_basic_map *bmap, isl_int *exp, FILE *out)
2407 unsigned total = isl_basic_map_total_dim(bmap);
2409 for (j = 0; j < 1 + total; ++j) {
2410 if (isl_int_is_zero(exp[j]))
2412 if (!first && isl_int_is_pos(exp[j]))
2414 dump_term(bmap, exp[j], j, out);
2419 static void dump(struct isl_basic_map *bmap, FILE *out, int indent)
2423 dump_constraints(bmap, bmap->eq, bmap->n_eq, "=", out, indent);
2424 dump_constraints(bmap, bmap->ineq, bmap->n_ineq, ">=", out, indent);
2426 for (i = 0; i < bmap->n_div; ++i) {
2427 fprintf(out, "%*s", indent, "");
2428 fprintf(out, "e%d = [(", i);
2429 dump_affine(bmap, bmap->div[i]+1, out);
2431 isl_int_print(out, bmap->div[i][0], 0);
2432 fprintf(out, "]\n");
2436 void isl_basic_set_print_internal(struct isl_basic_set *bset,
2437 FILE *out, int indent)
2440 fprintf(out, "null basic set\n");
2444 fprintf(out, "%*s", indent, "");
2445 fprintf(out, "ref: %d, nparam: %d, dim: %d, extra: %d, flags: %x\n",
2446 bset->ref, bset->dim->nparam, bset->dim->n_out,
2447 bset->extra, bset->flags);
2448 dump((struct isl_basic_map *)bset, out, indent);
2451 void isl_basic_map_print_internal(struct isl_basic_map *bmap,
2452 FILE *out, int indent)
2455 fprintf(out, "null basic map\n");
2459 fprintf(out, "%*s", indent, "");
2460 fprintf(out, "ref: %d, nparam: %d, in: %d, out: %d, extra: %d, "
2461 "flags: %x, n_name: %d\n",
2463 bmap->dim->nparam, bmap->dim->n_in, bmap->dim->n_out,
2464 bmap->extra, bmap->flags, bmap->dim->n_id);
2465 dump(bmap, out, indent);
2468 int isl_inequality_negate(struct isl_basic_map *bmap, unsigned pos)
2473 total = isl_basic_map_total_dim(bmap);
2474 isl_assert(bmap->ctx, pos < bmap->n_ineq, return -1);
2475 isl_seq_neg(bmap->ineq[pos], bmap->ineq[pos], 1 + total);
2476 isl_int_sub_ui(bmap->ineq[pos][0], bmap->ineq[pos][0], 1);
2477 ISL_F_CLR(bmap, ISL_BASIC_MAP_NORMALIZED);
2481 __isl_give isl_set *isl_set_alloc_space(__isl_take isl_space *dim, int n,
2484 struct isl_set *set;
2488 isl_assert(dim->ctx, dim->n_in == 0, goto error);
2489 isl_assert(dim->ctx, n >= 0, goto error);
2490 set = isl_alloc(dim->ctx, struct isl_set,
2491 sizeof(struct isl_set) +
2492 (n - 1) * sizeof(struct isl_basic_set *));
2496 set->ctx = dim->ctx;
2497 isl_ctx_ref(set->ctx);
2505 isl_space_free(dim);
2509 struct isl_set *isl_set_alloc(struct isl_ctx *ctx,
2510 unsigned nparam, unsigned dim, int n, unsigned flags)
2512 struct isl_set *set;
2515 dims = isl_space_alloc(ctx, nparam, 0, dim);
2519 set = isl_set_alloc_space(dims, n, flags);
2523 /* Make sure "map" has room for at least "n" more basic maps.
2525 struct isl_map *isl_map_grow(struct isl_map *map, int n)
2528 struct isl_map *grown = NULL;
2532 isl_assert(map->ctx, n >= 0, goto error);
2533 if (map->n + n <= map->size)
2535 grown = isl_map_alloc_space(isl_map_get_space(map), map->n + n, map->flags);
2538 for (i = 0; i < map->n; ++i) {
2539 grown->p[i] = isl_basic_map_copy(map->p[i]);
2547 isl_map_free(grown);
2552 /* Make sure "set" has room for at least "n" more basic sets.
2554 struct isl_set *isl_set_grow(struct isl_set *set, int n)
2556 return (struct isl_set *)isl_map_grow((struct isl_map *)set, n);
2559 struct isl_set *isl_set_dup(struct isl_set *set)
2562 struct isl_set *dup;
2567 dup = isl_set_alloc_space(isl_space_copy(set->dim), set->n, set->flags);
2570 for (i = 0; i < set->n; ++i)
2571 dup = isl_set_add_basic_set(dup, isl_basic_set_copy(set->p[i]));
2575 struct isl_set *isl_set_from_basic_set(struct isl_basic_set *bset)
2577 return isl_map_from_basic_map(bset);
2580 struct isl_map *isl_map_from_basic_map(struct isl_basic_map *bmap)
2582 struct isl_map *map;
2587 map = isl_map_alloc_space(isl_space_copy(bmap->dim), 1, ISL_MAP_DISJOINT);
2588 return isl_map_add_basic_map(map, bmap);
2591 __isl_give isl_set *isl_set_add_basic_set(__isl_take isl_set *set,
2592 __isl_take isl_basic_set *bset)
2594 return (struct isl_set *)isl_map_add_basic_map((struct isl_map *)set,
2595 (struct isl_basic_map *)bset);
2598 void *isl_set_free(__isl_take isl_set *set)
2608 isl_ctx_deref(set->ctx);
2609 for (i = 0; i < set->n; ++i)
2610 isl_basic_set_free(set->p[i]);
2611 isl_space_free(set->dim);
2617 void isl_set_print_internal(struct isl_set *set, FILE *out, int indent)
2622 fprintf(out, "null set\n");
2626 fprintf(out, "%*s", indent, "");
2627 fprintf(out, "ref: %d, n: %d, nparam: %d, dim: %d, flags: %x\n",
2628 set->ref, set->n, set->dim->nparam, set->dim->n_out,
2630 for (i = 0; i < set->n; ++i) {
2631 fprintf(out, "%*s", indent, "");
2632 fprintf(out, "basic set %d:\n", i);
2633 isl_basic_set_print_internal(set->p[i], out, indent+4);
2637 void isl_map_print_internal(struct isl_map *map, FILE *out, int indent)
2642 fprintf(out, "null map\n");
2646 fprintf(out, "%*s", indent, "");
2647 fprintf(out, "ref: %d, n: %d, nparam: %d, in: %d, out: %d, "
2648 "flags: %x, n_name: %d\n",
2649 map->ref, map->n, map->dim->nparam, map->dim->n_in,
2650 map->dim->n_out, map->flags, map->dim->n_id);
2651 for (i = 0; i < map->n; ++i) {
2652 fprintf(out, "%*s", indent, "");
2653 fprintf(out, "basic map %d:\n", i);
2654 isl_basic_map_print_internal(map->p[i], out, indent+4);
2658 struct isl_basic_map *isl_basic_map_intersect_domain(
2659 struct isl_basic_map *bmap, struct isl_basic_set *bset)
2661 struct isl_basic_map *bmap_domain;
2666 isl_assert(bset->ctx, isl_space_match(bmap->dim, isl_dim_param,
2667 bset->dim, isl_dim_param), goto error);
2669 if (isl_space_dim(bset->dim, isl_dim_set) != 0)
2670 isl_assert(bset->ctx,
2671 isl_basic_map_compatible_domain(bmap, bset), goto error);
2673 bmap = isl_basic_map_cow(bmap);
2676 bmap = isl_basic_map_extend_space(bmap, isl_space_copy(bmap->dim),
2677 bset->n_div, bset->n_eq, bset->n_ineq);
2678 bmap_domain = isl_basic_map_from_domain(bset);
2679 bmap = add_constraints(bmap, bmap_domain, 0, 0);
2681 bmap = isl_basic_map_simplify(bmap);
2682 return isl_basic_map_finalize(bmap);
2684 isl_basic_map_free(bmap);
2685 isl_basic_set_free(bset);
2689 struct isl_basic_map *isl_basic_map_intersect_range(
2690 struct isl_basic_map *bmap, struct isl_basic_set *bset)
2692 struct isl_basic_map *bmap_range;
2697 isl_assert(bset->ctx, isl_space_match(bmap->dim, isl_dim_param,
2698 bset->dim, isl_dim_param), goto error);
2700 if (isl_space_dim(bset->dim, isl_dim_set) != 0)
2701 isl_assert(bset->ctx,
2702 isl_basic_map_compatible_range(bmap, bset), goto error);
2704 if (isl_basic_set_is_universe(bset)) {
2705 isl_basic_set_free(bset);
2709 bmap = isl_basic_map_cow(bmap);
2712 bmap = isl_basic_map_extend_space(bmap, isl_space_copy(bmap->dim),
2713 bset->n_div, bset->n_eq, bset->n_ineq);
2714 bmap_range = isl_basic_map_from_basic_set(bset, isl_space_copy(bset->dim));
2715 bmap = add_constraints(bmap, bmap_range, 0, 0);
2717 bmap = isl_basic_map_simplify(bmap);
2718 return isl_basic_map_finalize(bmap);
2720 isl_basic_map_free(bmap);
2721 isl_basic_set_free(bset);
2725 int isl_basic_map_contains(struct isl_basic_map *bmap, struct isl_vec *vec)
2731 total = 1 + isl_basic_map_total_dim(bmap);
2732 if (total != vec->size)
2737 for (i = 0; i < bmap->n_eq; ++i) {
2738 isl_seq_inner_product(vec->el, bmap->eq[i], total, &s);
2739 if (!isl_int_is_zero(s)) {
2745 for (i = 0; i < bmap->n_ineq; ++i) {
2746 isl_seq_inner_product(vec->el, bmap->ineq[i], total, &s);
2747 if (isl_int_is_neg(s)) {
2758 int isl_basic_set_contains(struct isl_basic_set *bset, struct isl_vec *vec)
2760 return isl_basic_map_contains((struct isl_basic_map *)bset, vec);
2763 struct isl_basic_map *isl_basic_map_intersect(
2764 struct isl_basic_map *bmap1, struct isl_basic_map *bmap2)
2766 struct isl_vec *sample = NULL;
2768 if (!bmap1 || !bmap2)
2771 isl_assert(bmap1->ctx, isl_space_match(bmap1->dim, isl_dim_param,
2772 bmap2->dim, isl_dim_param), goto error);
2773 if (isl_space_dim(bmap1->dim, isl_dim_all) ==
2774 isl_space_dim(bmap1->dim, isl_dim_param) &&
2775 isl_space_dim(bmap2->dim, isl_dim_all) !=
2776 isl_space_dim(bmap2->dim, isl_dim_param))
2777 return isl_basic_map_intersect(bmap2, bmap1);
2779 if (isl_space_dim(bmap2->dim, isl_dim_all) !=
2780 isl_space_dim(bmap2->dim, isl_dim_param))
2781 isl_assert(bmap1->ctx,
2782 isl_space_is_equal(bmap1->dim, bmap2->dim), goto error);
2784 if (bmap1->sample &&
2785 isl_basic_map_contains(bmap1, bmap1->sample) > 0 &&
2786 isl_basic_map_contains(bmap2, bmap1->sample) > 0)
2787 sample = isl_vec_copy(bmap1->sample);
2788 else if (bmap2->sample &&
2789 isl_basic_map_contains(bmap1, bmap2->sample) > 0 &&
2790 isl_basic_map_contains(bmap2, bmap2->sample) > 0)
2791 sample = isl_vec_copy(bmap2->sample);
2793 bmap1 = isl_basic_map_cow(bmap1);
2796 bmap1 = isl_basic_map_extend_space(bmap1, isl_space_copy(bmap1->dim),
2797 bmap2->n_div, bmap2->n_eq, bmap2->n_ineq);
2798 bmap1 = add_constraints(bmap1, bmap2, 0, 0);
2801 isl_vec_free(sample);
2803 isl_vec_free(bmap1->sample);
2804 bmap1->sample = sample;
2807 bmap1 = isl_basic_map_simplify(bmap1);
2808 return isl_basic_map_finalize(bmap1);
2811 isl_vec_free(sample);
2812 isl_basic_map_free(bmap1);
2813 isl_basic_map_free(bmap2);
2817 struct isl_basic_set *isl_basic_set_intersect(
2818 struct isl_basic_set *bset1, struct isl_basic_set *bset2)
2820 return (struct isl_basic_set *)
2821 isl_basic_map_intersect(
2822 (struct isl_basic_map *)bset1,
2823 (struct isl_basic_map *)bset2);
2826 __isl_give isl_basic_set *isl_basic_set_intersect_params(
2827 __isl_take isl_basic_set *bset1, __isl_take isl_basic_set *bset2)
2829 return isl_basic_set_intersect(bset1, bset2);
2832 /* Special case of isl_map_intersect, where both map1 and map2
2833 * are convex, without any divs and such that either map1 or map2
2834 * contains a single constraint. This constraint is then simply
2835 * added to the other map.
2837 static __isl_give isl_map *map_intersect_add_constraint(
2838 __isl_take isl_map *map1, __isl_take isl_map *map2)
2840 isl_assert(map1->ctx, map1->n == 1, goto error);
2841 isl_assert(map2->ctx, map1->n == 1, goto error);
2842 isl_assert(map1->ctx, map1->p[0]->n_div == 0, goto error);
2843 isl_assert(map2->ctx, map1->p[0]->n_div == 0, goto error);
2845 if (map2->p[0]->n_eq + map2->p[0]->n_ineq != 1)
2846 return isl_map_intersect(map2, map1);
2848 isl_assert(map2->ctx,
2849 map2->p[0]->n_eq + map2->p[0]->n_ineq == 1, goto error);
2851 map1 = isl_map_cow(map1);
2854 if (isl_map_plain_is_empty(map1)) {
2858 map1->p[0] = isl_basic_map_cow(map1->p[0]);
2859 if (map2->p[0]->n_eq == 1)
2860 map1->p[0] = isl_basic_map_add_eq(map1->p[0], map2->p[0]->eq[0]);
2862 map1->p[0] = isl_basic_map_add_ineq(map1->p[0],
2863 map2->p[0]->ineq[0]);
2865 map1->p[0] = isl_basic_map_simplify(map1->p[0]);
2866 map1->p[0] = isl_basic_map_finalize(map1->p[0]);
2870 if (isl_basic_map_plain_is_empty(map1->p[0])) {
2871 isl_basic_map_free(map1->p[0]);
2884 /* map2 may be either a parameter domain or a map living in the same
2887 static __isl_give isl_map *map_intersect_internal(__isl_take isl_map *map1,
2888 __isl_take isl_map *map2)
2897 if ((isl_map_plain_is_empty(map1) ||
2898 isl_map_plain_is_universe(map2)) &&
2899 isl_space_is_equal(map1->dim, map2->dim)) {
2903 if ((isl_map_plain_is_empty(map2) ||
2904 isl_map_plain_is_universe(map1)) &&
2905 isl_space_is_equal(map1->dim, map2->dim)) {
2910 if (map1->n == 1 && map2->n == 1 &&
2911 map1->p[0]->n_div == 0 && map2->p[0]->n_div == 0 &&
2912 isl_space_is_equal(map1->dim, map2->dim) &&
2913 (map1->p[0]->n_eq + map1->p[0]->n_ineq == 1 ||
2914 map2->p[0]->n_eq + map2->p[0]->n_ineq == 1))
2915 return map_intersect_add_constraint(map1, map2);
2917 if (isl_space_dim(map2->dim, isl_dim_all) !=
2918 isl_space_dim(map2->dim, isl_dim_param))
2919 isl_assert(map1->ctx,
2920 isl_space_is_equal(map1->dim, map2->dim), goto error);
2922 if (ISL_F_ISSET(map1, ISL_MAP_DISJOINT) &&
2923 ISL_F_ISSET(map2, ISL_MAP_DISJOINT))
2924 ISL_FL_SET(flags, ISL_MAP_DISJOINT);
2926 result = isl_map_alloc_space(isl_space_copy(map1->dim),
2927 map1->n * map2->n, flags);
2930 for (i = 0; i < map1->n; ++i)
2931 for (j = 0; j < map2->n; ++j) {
2932 struct isl_basic_map *part;
2933 part = isl_basic_map_intersect(
2934 isl_basic_map_copy(map1->p[i]),
2935 isl_basic_map_copy(map2->p[j]));
2936 if (isl_basic_map_is_empty(part) < 0)
2937 part = isl_basic_map_free(part);
2938 result = isl_map_add_basic_map(result, part);
2951 static __isl_give isl_map *map_intersect(__isl_take isl_map *map1,
2952 __isl_take isl_map *map2)
2956 if (!isl_space_is_equal(map1->dim, map2->dim))
2957 isl_die(isl_map_get_ctx(map1), isl_error_invalid,
2958 "spaces don't match", goto error);
2959 return map_intersect_internal(map1, map2);
2966 __isl_give isl_map *isl_map_intersect(__isl_take isl_map *map1,
2967 __isl_take isl_map *map2)
2969 return isl_map_align_params_map_map_and(map1, map2, &map_intersect);
2972 struct isl_set *isl_set_intersect(struct isl_set *set1, struct isl_set *set2)
2974 return (struct isl_set *)
2975 isl_map_intersect((struct isl_map *)set1,
2976 (struct isl_map *)set2);
2979 /* map_intersect_internal accepts intersections
2980 * with parameter domains, so we can just call that function.
2982 static __isl_give isl_map *map_intersect_params(__isl_take isl_map *map,
2983 __isl_take isl_set *params)
2985 return map_intersect_internal(map, params);
2988 __isl_give isl_map *isl_map_intersect_params(__isl_take isl_map *map1,
2989 __isl_take isl_map *map2)
2991 return isl_map_align_params_map_map_and(map1, map2, &map_intersect_params);
2994 __isl_give isl_set *isl_set_intersect_params(__isl_take isl_set *set,
2995 __isl_take isl_set *params)
2997 return isl_map_intersect_params(set, params);
3000 struct isl_basic_map *isl_basic_map_reverse(struct isl_basic_map *bmap)
3003 struct isl_basic_set *bset;
3008 bmap = isl_basic_map_cow(bmap);
3011 dim = isl_space_reverse(isl_space_copy(bmap->dim));
3012 in = isl_basic_map_n_in(bmap);
3013 bset = isl_basic_set_from_basic_map(bmap);
3014 bset = isl_basic_set_swap_vars(bset, in);
3015 return isl_basic_map_from_basic_set(bset, dim);
3018 static __isl_give isl_basic_map *basic_map_space_reset(
3019 __isl_take isl_basic_map *bmap, enum isl_dim_type type)
3025 if (!isl_space_is_named_or_nested(bmap->dim, type))
3028 space = isl_basic_map_get_space(bmap);
3029 space = isl_space_reset(space, type);
3030 bmap = isl_basic_map_reset_space(bmap, space);
3034 __isl_give isl_basic_map *isl_basic_map_insert_dims(
3035 __isl_take isl_basic_map *bmap, enum isl_dim_type type,
3036 unsigned pos, unsigned n)
3039 struct isl_basic_map *res;
3040 struct isl_dim_map *dim_map;
3041 unsigned total, off;
3042 enum isl_dim_type t;
3045 return basic_map_space_reset(bmap, type);
3050 res_dim = isl_space_insert_dims(isl_basic_map_get_space(bmap), type, pos, n);
3052 total = isl_basic_map_total_dim(bmap) + n;
3053 dim_map = isl_dim_map_alloc(bmap->ctx, total);
3055 for (t = isl_dim_param; t <= isl_dim_out; ++t) {
3057 isl_dim_map_dim(dim_map, bmap->dim, t, off);
3059 unsigned size = isl_basic_map_dim(bmap, t);
3060 isl_dim_map_dim_range(dim_map, bmap->dim, t,
3062 isl_dim_map_dim_range(dim_map, bmap->dim, t,
3063 pos, size - pos, off + pos + n);
3065 off += isl_space_dim(res_dim, t);
3067 isl_dim_map_div(dim_map, bmap, off);
3069 res = isl_basic_map_alloc_space(res_dim,
3070 bmap->n_div, bmap->n_eq, bmap->n_ineq);
3071 if (isl_basic_map_is_rational(bmap))
3072 res = isl_basic_map_set_rational(res);
3073 if (isl_basic_map_plain_is_empty(bmap)) {
3074 isl_basic_map_free(bmap);
3076 return isl_basic_map_set_to_empty(res);
3078 res = isl_basic_map_add_constraints_dim_map(res, bmap, dim_map);
3079 return isl_basic_map_finalize(res);
3082 __isl_give isl_basic_set *isl_basic_set_insert_dims(
3083 __isl_take isl_basic_set *bset,
3084 enum isl_dim_type type, unsigned pos, unsigned n)
3086 return isl_basic_map_insert_dims(bset, type, pos, n);
3089 __isl_give isl_basic_map *isl_basic_map_add(__isl_take isl_basic_map *bmap,
3090 enum isl_dim_type type, unsigned n)
3094 return isl_basic_map_insert_dims(bmap, type,
3095 isl_basic_map_dim(bmap, type), n);
3098 __isl_give isl_basic_set *isl_basic_set_add_dims(__isl_take isl_basic_set *bset,
3099 enum isl_dim_type type, unsigned n)
3103 isl_assert(bset->ctx, type != isl_dim_in, goto error);
3104 return (isl_basic_set *)isl_basic_map_add((isl_basic_map *)bset, type, n);
3106 isl_basic_set_free(bset);
3110 static __isl_give isl_map *map_space_reset(__isl_take isl_map *map,
3111 enum isl_dim_type type)
3115 if (!map || !isl_space_is_named_or_nested(map->dim, type))
3118 space = isl_map_get_space(map);
3119 space = isl_space_reset(space, type);
3120 map = isl_map_reset_space(map, space);
3124 __isl_give isl_map *isl_map_insert_dims(__isl_take isl_map *map,
3125 enum isl_dim_type type, unsigned pos, unsigned n)
3130 return map_space_reset(map, type);
3132 map = isl_map_cow(map);
3136 map->dim = isl_space_insert_dims(map->dim, type, pos, n);
3140 for (i = 0; i < map->n; ++i) {
3141 map->p[i] = isl_basic_map_insert_dims(map->p[i], type, pos, n);
3152 __isl_give isl_set *isl_set_insert_dims(__isl_take isl_set *set,
3153 enum isl_dim_type type, unsigned pos, unsigned n)
3155 return isl_map_insert_dims(set, type, pos, n);
3158 __isl_give isl_map *isl_map_add_dims(__isl_take isl_map *map,
3159 enum isl_dim_type type, unsigned n)
3163 return isl_map_insert_dims(map, type, isl_map_dim(map, type), n);
3166 __isl_give isl_set *isl_set_add_dims(__isl_take isl_set *set,
3167 enum isl_dim_type type, unsigned n)
3171 isl_assert(set->ctx, type != isl_dim_in, goto error);
3172 return (isl_set *)isl_map_add_dims((isl_map *)set, type, n);
3178 __isl_give isl_basic_map *isl_basic_map_move_dims(
3179 __isl_take isl_basic_map *bmap,
3180 enum isl_dim_type dst_type, unsigned dst_pos,
3181 enum isl_dim_type src_type, unsigned src_pos, unsigned n)
3183 struct isl_dim_map *dim_map;
3184 struct isl_basic_map *res;
3185 enum isl_dim_type t;
3186 unsigned total, off;
3193 isl_assert(bmap->ctx, src_pos + n <= isl_basic_map_dim(bmap, src_type),
3196 if (dst_type == src_type && dst_pos == src_pos)
3199 isl_assert(bmap->ctx, dst_type != src_type, goto error);
3201 if (pos(bmap->dim, dst_type) + dst_pos ==
3202 pos(bmap->dim, src_type) + src_pos +
3203 ((src_type < dst_type) ? n : 0)) {
3204 bmap = isl_basic_map_cow(bmap);
3208 bmap->dim = isl_space_move_dims(bmap->dim, dst_type, dst_pos,
3209 src_type, src_pos, n);
3213 bmap = isl_basic_map_finalize(bmap);
3218 total = isl_basic_map_total_dim(bmap);
3219 dim_map = isl_dim_map_alloc(bmap->ctx, total);
3222 for (t = isl_dim_param; t <= isl_dim_out; ++t) {
3223 unsigned size = isl_space_dim(bmap->dim, t);
3224 if (t == dst_type) {
3225 isl_dim_map_dim_range(dim_map, bmap->dim, t,
3228 isl_dim_map_dim_range(dim_map, bmap->dim, src_type,
3231 isl_dim_map_dim_range(dim_map, bmap->dim, t,
3232 dst_pos, size - dst_pos, off);
3233 off += size - dst_pos;
3234 } else if (t == src_type) {
3235 isl_dim_map_dim_range(dim_map, bmap->dim, t,
3238 isl_dim_map_dim_range(dim_map, bmap->dim, t,
3239 src_pos + n, size - src_pos - n, off);
3240 off += size - src_pos - n;
3242 isl_dim_map_dim(dim_map, bmap->dim, t, off);
3246 isl_dim_map_div(dim_map, bmap, off);
3248 res = isl_basic_map_alloc_space(isl_basic_map_get_space(bmap),
3249 bmap->n_div, bmap->n_eq, bmap->n_ineq);
3250 bmap = isl_basic_map_add_constraints_dim_map(res, bmap, dim_map);
3254 bmap->dim = isl_space_move_dims(bmap->dim, dst_type, dst_pos,
3255 src_type, src_pos, n);
3259 ISL_F_CLR(bmap, ISL_BASIC_MAP_NORMALIZED);
3260 bmap = isl_basic_map_gauss(bmap, NULL);
3261 bmap = isl_basic_map_finalize(bmap);
3265 isl_basic_map_free(bmap);
3269 __isl_give isl_basic_set *isl_basic_set_move_dims(__isl_take isl_basic_set *bset,
3270 enum isl_dim_type dst_type, unsigned dst_pos,
3271 enum isl_dim_type src_type, unsigned src_pos, unsigned n)
3273 return (isl_basic_set *)isl_basic_map_move_dims(
3274 (isl_basic_map *)bset, dst_type, dst_pos, src_type, src_pos, n);
3277 __isl_give isl_set *isl_set_move_dims(__isl_take isl_set *set,
3278 enum isl_dim_type dst_type, unsigned dst_pos,
3279 enum isl_dim_type src_type, unsigned src_pos, unsigned n)
3283 isl_assert(set->ctx, dst_type != isl_dim_in, goto error);
3284 return (isl_set *)isl_map_move_dims((isl_map *)set, dst_type, dst_pos,
3285 src_type, src_pos, n);
3291 __isl_give isl_map *isl_map_move_dims(__isl_take isl_map *map,
3292 enum isl_dim_type dst_type, unsigned dst_pos,
3293 enum isl_dim_type src_type, unsigned src_pos, unsigned n)
3302 isl_assert(map->ctx, src_pos + n <= isl_map_dim(map, src_type),
3305 if (dst_type == src_type && dst_pos == src_pos)
3308 isl_assert(map->ctx, dst_type != src_type, goto error);
3310 map = isl_map_cow(map);
3314 map->dim = isl_space_move_dims(map->dim, dst_type, dst_pos, src_type, src_pos, n);
3318 for (i = 0; i < map->n; ++i) {
3319 map->p[i] = isl_basic_map_move_dims(map->p[i],
3321 src_type, src_pos, n);
3332 /* Move the specified dimensions to the last columns right before
3333 * the divs. Don't change the dimension specification of bmap.
3334 * That's the responsibility of the caller.
3336 static __isl_give isl_basic_map *move_last(__isl_take isl_basic_map *bmap,
3337 enum isl_dim_type type, unsigned first, unsigned n)
3339 struct isl_dim_map *dim_map;
3340 struct isl_basic_map *res;
3341 enum isl_dim_type t;
3342 unsigned total, off;
3346 if (pos(bmap->dim, type) + first + n ==
3347 1 + isl_space_dim(bmap->dim, isl_dim_all))
3350 total = isl_basic_map_total_dim(bmap);
3351 dim_map = isl_dim_map_alloc(bmap->ctx, total);
3354 for (t = isl_dim_param; t <= isl_dim_out; ++t) {
3355 unsigned size = isl_space_dim(bmap->dim, t);
3357 isl_dim_map_dim_range(dim_map, bmap->dim, t,
3360 isl_dim_map_dim_range(dim_map, bmap->dim, t,
3361 first, n, total - bmap->n_div - n);
3362 isl_dim_map_dim_range(dim_map, bmap->dim, t,
3363 first + n, size - (first + n), off);
3364 off += size - (first + n);
3366 isl_dim_map_dim(dim_map, bmap->dim, t, off);
3370 isl_dim_map_div(dim_map, bmap, off + n);
3372 res = isl_basic_map_alloc_space(isl_basic_map_get_space(bmap),
3373 bmap->n_div, bmap->n_eq, bmap->n_ineq);
3374 res = isl_basic_map_add_constraints_dim_map(res, bmap, dim_map);
3378 /* Insert "n" rows in the divs of "bmap".
3380 * The number of columns is not changed, which means that the last
3381 * dimensions of "bmap" are being reintepreted as the new divs.
3382 * The space of "bmap" is not adjusted, however, which means
3383 * that "bmap" is left in an inconsistent state. Removing "n" dimensions
3384 * from the space of "bmap" is the responsibility of the caller.
3386 static __isl_give isl_basic_map *insert_div_rows(__isl_take isl_basic_map *bmap,
3394 bmap = isl_basic_map_cow(bmap);
3398 row_size = 1 + isl_space_dim(bmap->dim, isl_dim_all) + bmap->extra;
3399 old = bmap->block2.data;
3400 bmap->block2 = isl_blk_extend(bmap->ctx, bmap->block2,
3401 (bmap->extra + n) * (1 + row_size));
3402 if (!bmap->block2.data)
3403 return isl_basic_map_free(bmap);
3404 new_div = isl_alloc_array(bmap->ctx, isl_int *, bmap->extra + n);
3406 return isl_basic_map_free(bmap);
3407 for (i = 0; i < n; ++i) {
3408 new_div[i] = bmap->block2.data +
3409 (bmap->extra + i) * (1 + row_size);
3410 isl_seq_clr(new_div[i], 1 + row_size);
3412 for (i = 0; i < bmap->extra; ++i)
3413 new_div[n + i] = bmap->block2.data + (bmap->div[i] - old);
3415 bmap->div = new_div;
3422 /* Turn the n dimensions of type type, starting at first
3423 * into existentially quantified variables.
3425 __isl_give isl_basic_map *isl_basic_map_project_out(
3426 __isl_take isl_basic_map *bmap,
3427 enum isl_dim_type type, unsigned first, unsigned n)
3430 return basic_map_space_reset(bmap, type);
3435 if (ISL_F_ISSET(bmap, ISL_BASIC_MAP_RATIONAL))
3436 return isl_basic_map_remove_dims(bmap, type, first, n);
3438 isl_assert(bmap->ctx, first + n <= isl_basic_map_dim(bmap, type),
3441 bmap = move_last(bmap, type, first, n);
3442 bmap = isl_basic_map_cow(bmap);
3443 bmap = insert_div_rows(bmap, n);
3447 bmap->dim = isl_space_drop_dims(bmap->dim, type, first, n);
3450 bmap = isl_basic_map_simplify(bmap);
3451 bmap = isl_basic_map_drop_redundant_divs(bmap);
3452 return isl_basic_map_finalize(bmap);
3454 isl_basic_map_free(bmap);
3458 /* Turn the n dimensions of type type, starting at first
3459 * into existentially quantified variables.
3461 struct isl_basic_set *isl_basic_set_project_out(struct isl_basic_set *bset,
3462 enum isl_dim_type type, unsigned first, unsigned n)
3464 return (isl_basic_set *)isl_basic_map_project_out(
3465 (isl_basic_map *)bset, type, first, n);
3468 /* Turn the n dimensions of type type, starting at first
3469 * into existentially quantified variables.
3471 __isl_give isl_map *isl_map_project_out(__isl_take isl_map *map,
3472 enum isl_dim_type type, unsigned first, unsigned n)
3480 return map_space_reset(map, type);
3482 isl_assert(map->ctx, first + n <= isl_map_dim(map, type), goto error);
3484 map = isl_map_cow(map);
3488 map->dim = isl_space_drop_dims(map->dim, type, first, n);
3492 for (i = 0; i < map->n; ++i) {
3493 map->p[i] = isl_basic_map_project_out(map->p[i], type, first, n);
3504 /* Turn the n dimensions of type type, starting at first
3505 * into existentially quantified variables.
3507 __isl_give isl_set *isl_set_project_out(__isl_take isl_set *set,
3508 enum isl_dim_type type, unsigned first, unsigned n)
3510 return (isl_set *)isl_map_project_out((isl_map *)set, type, first, n);
3513 static struct isl_basic_map *add_divs(struct isl_basic_map *bmap, unsigned n)
3517 for (i = 0; i < n; ++i) {
3518 j = isl_basic_map_alloc_div(bmap);
3521 isl_seq_clr(bmap->div[j], 1+1+isl_basic_map_total_dim(bmap));
3525 isl_basic_map_free(bmap);
3529 struct isl_basic_map *isl_basic_map_apply_range(
3530 struct isl_basic_map *bmap1, struct isl_basic_map *bmap2)
3532 isl_space *dim_result = NULL;
3533 struct isl_basic_map *bmap;
3534 unsigned n_in, n_out, n, nparam, total, pos;
3535 struct isl_dim_map *dim_map1, *dim_map2;
3537 if (!bmap1 || !bmap2)
3540 dim_result = isl_space_join(isl_space_copy(bmap1->dim),
3541 isl_space_copy(bmap2->dim));
3543 n_in = isl_basic_map_n_in(bmap1);
3544 n_out = isl_basic_map_n_out(bmap2);
3545 n = isl_basic_map_n_out(bmap1);
3546 nparam = isl_basic_map_n_param(bmap1);
3548 total = nparam + n_in + n_out + bmap1->n_div + bmap2->n_div + n;
3549 dim_map1 = isl_dim_map_alloc(bmap1->ctx, total);
3550 dim_map2 = isl_dim_map_alloc(bmap1->ctx, total);
3551 isl_dim_map_dim(dim_map1, bmap1->dim, isl_dim_param, pos = 0);
3552 isl_dim_map_dim(dim_map2, bmap2->dim, isl_dim_param, pos = 0);
3553 isl_dim_map_dim(dim_map1, bmap1->dim, isl_dim_in, pos += nparam);
3554 isl_dim_map_dim(dim_map2, bmap2->dim, isl_dim_out, pos += n_in);
3555 isl_dim_map_div(dim_map1, bmap1, pos += n_out);
3556 isl_dim_map_div(dim_map2, bmap2, pos += bmap1->n_div);
3557 isl_dim_map_dim(dim_map1, bmap1->dim, isl_dim_out, pos += bmap2->n_div);
3558 isl_dim_map_dim(dim_map2, bmap2->dim, isl_dim_in, pos);
3560 bmap = isl_basic_map_alloc_space(dim_result,
3561 bmap1->n_div + bmap2->n_div + n,
3562 bmap1->n_eq + bmap2->n_eq,
3563 bmap1->n_ineq + bmap2->n_ineq);
3564 bmap = isl_basic_map_add_constraints_dim_map(bmap, bmap1, dim_map1);
3565 bmap = isl_basic_map_add_constraints_dim_map(bmap, bmap2, dim_map2);
3566 bmap = add_divs(bmap, n);
3567 bmap = isl_basic_map_simplify(bmap);
3568 bmap = isl_basic_map_drop_redundant_divs(bmap);
3569 return isl_basic_map_finalize(bmap);
3571 isl_basic_map_free(bmap1);
3572 isl_basic_map_free(bmap2);
3576 struct isl_basic_set *isl_basic_set_apply(
3577 struct isl_basic_set *bset, struct isl_basic_map *bmap)
3582 isl_assert(bset->ctx, isl_basic_map_compatible_domain(bmap, bset),
3585 return (struct isl_basic_set *)
3586 isl_basic_map_apply_range((struct isl_basic_map *)bset, bmap);
3588 isl_basic_set_free(bset);
3589 isl_basic_map_free(bmap);
3593 struct isl_basic_map *isl_basic_map_apply_domain(
3594 struct isl_basic_map *bmap1, struct isl_basic_map *bmap2)
3596 if (!bmap1 || !bmap2)
3599 isl_assert(bmap1->ctx,
3600 isl_basic_map_n_in(bmap1) == isl_basic_map_n_in(bmap2), goto error);
3601 isl_assert(bmap1->ctx,
3602 isl_basic_map_n_param(bmap1) == isl_basic_map_n_param(bmap2),
3605 bmap1 = isl_basic_map_reverse(bmap1);
3606 bmap1 = isl_basic_map_apply_range(bmap1, bmap2);
3607 return isl_basic_map_reverse(bmap1);
3609 isl_basic_map_free(bmap1);
3610 isl_basic_map_free(bmap2);
3614 /* Given two basic maps A -> f(A) and B -> g(B), construct a basic map
3615 * A \cap B -> f(A) + f(B)
3617 struct isl_basic_map *isl_basic_map_sum(
3618 struct isl_basic_map *bmap1, struct isl_basic_map *bmap2)
3620 unsigned n_in, n_out, nparam, total, pos;
3621 struct isl_basic_map *bmap = NULL;
3622 struct isl_dim_map *dim_map1, *dim_map2;
3625 if (!bmap1 || !bmap2)
3628 isl_assert(bmap1->ctx, isl_space_is_equal(bmap1->dim, bmap2->dim),
3631 nparam = isl_basic_map_n_param(bmap1);
3632 n_in = isl_basic_map_n_in(bmap1);
3633 n_out = isl_basic_map_n_out(bmap1);
3635 total = nparam + n_in + n_out + bmap1->n_div + bmap2->n_div + 2 * n_out;
3636 dim_map1 = isl_dim_map_alloc(bmap1->ctx, total);
3637 dim_map2 = isl_dim_map_alloc(bmap2->ctx, total);
3638 isl_dim_map_dim(dim_map1, bmap1->dim, isl_dim_param, pos = 0);
3639 isl_dim_map_dim(dim_map2, bmap2->dim, isl_dim_param, pos);
3640 isl_dim_map_dim(dim_map1, bmap1->dim, isl_dim_in, pos += nparam);
3641 isl_dim_map_dim(dim_map2, bmap2->dim, isl_dim_in, pos);
3642 isl_dim_map_div(dim_map1, bmap1, pos += n_in + n_out);
3643 isl_dim_map_div(dim_map2, bmap2, pos += bmap1->n_div);
3644 isl_dim_map_dim(dim_map1, bmap1->dim, isl_dim_out, pos += bmap2->n_div);
3645 isl_dim_map_dim(dim_map2, bmap2->dim, isl_dim_out, pos += n_out);
3647 bmap = isl_basic_map_alloc_space(isl_space_copy(bmap1->dim),
3648 bmap1->n_div + bmap2->n_div + 2 * n_out,
3649 bmap1->n_eq + bmap2->n_eq + n_out,
3650 bmap1->n_ineq + bmap2->n_ineq);
3651 for (i = 0; i < n_out; ++i) {
3652 int j = isl_basic_map_alloc_equality(bmap);
3655 isl_seq_clr(bmap->eq[j], 1+total);
3656 isl_int_set_si(bmap->eq[j][1+nparam+n_in+i], -1);
3657 isl_int_set_si(bmap->eq[j][1+pos+i], 1);
3658 isl_int_set_si(bmap->eq[j][1+pos-n_out+i], 1);
3660 bmap = isl_basic_map_add_constraints_dim_map(bmap, bmap1, dim_map1);
3661 bmap = isl_basic_map_add_constraints_dim_map(bmap, bmap2, dim_map2);
3662 bmap = add_divs(bmap, 2 * n_out);
3664 bmap = isl_basic_map_simplify(bmap);
3665 return isl_basic_map_finalize(bmap);
3667 isl_basic_map_free(bmap);
3668 isl_basic_map_free(bmap1);
3669 isl_basic_map_free(bmap2);
3673 /* Given two maps A -> f(A) and B -> g(B), construct a map
3674 * A \cap B -> f(A) + f(B)
3676 struct isl_map *isl_map_sum(struct isl_map *map1, struct isl_map *map2)
3678 struct isl_map *result;
3684 isl_assert(map1->ctx, isl_space_is_equal(map1->dim, map2->dim), goto error);
3686 result = isl_map_alloc_space(isl_space_copy(map1->dim),
3687 map1->n * map2->n, 0);
3690 for (i = 0; i < map1->n; ++i)
3691 for (j = 0; j < map2->n; ++j) {
3692 struct isl_basic_map *part;
3693 part = isl_basic_map_sum(
3694 isl_basic_map_copy(map1->p[i]),
3695 isl_basic_map_copy(map2->p[j]));
3696 if (isl_basic_map_is_empty(part))
3697 isl_basic_map_free(part);
3699 result = isl_map_add_basic_map(result, part);
3712 __isl_give isl_set *isl_set_sum(__isl_take isl_set *set1,
3713 __isl_take isl_set *set2)
3715 return (isl_set *)isl_map_sum((isl_map *)set1, (isl_map *)set2);
3718 /* Given a basic map A -> f(A), construct A -> -f(A).
3720 struct isl_basic_map *isl_basic_map_neg(struct isl_basic_map *bmap)
3725 bmap = isl_basic_map_cow(bmap);
3729 n = isl_basic_map_dim(bmap, isl_dim_out);
3730 off = isl_basic_map_offset(bmap, isl_dim_out);
3731 for (i = 0; i < bmap->n_eq; ++i)
3732 for (j = 0; j < n; ++j)
3733 isl_int_neg(bmap->eq[i][off+j], bmap->eq[i][off+j]);
3734 for (i = 0; i < bmap->n_ineq; ++i)
3735 for (j = 0; j < n; ++j)
3736 isl_int_neg(bmap->ineq[i][off+j], bmap->ineq[i][off+j]);
3737 for (i = 0; i < bmap->n_div; ++i)
3738 for (j = 0; j < n; ++j)
3739 isl_int_neg(bmap->div[i][1+off+j], bmap->div[i][1+off+j]);
3740 bmap = isl_basic_map_gauss(bmap, NULL);
3741 return isl_basic_map_finalize(bmap);
3744 __isl_give isl_basic_set *isl_basic_set_neg(__isl_take isl_basic_set *bset)
3746 return isl_basic_map_neg(bset);
3749 /* Given a map A -> f(A), construct A -> -f(A).
3751 struct isl_map *isl_map_neg(struct isl_map *map)
3755 map = isl_map_cow(map);
3759 for (i = 0; i < map->n; ++i) {
3760 map->p[i] = isl_basic_map_neg(map->p[i]);
3771 __isl_give isl_set *isl_set_neg(__isl_take isl_set *set)
3773 return (isl_set *)isl_map_neg((isl_map *)set);
3776 /* Given a basic map A -> f(A) and an integer d, construct a basic map
3777 * A -> floor(f(A)/d).
3779 struct isl_basic_map *isl_basic_map_floordiv(struct isl_basic_map *bmap,
3782 unsigned n_in, n_out, nparam, total, pos;
3783 struct isl_basic_map *result = NULL;
3784 struct isl_dim_map *dim_map;
3790 nparam = isl_basic_map_n_param(bmap);
3791 n_in = isl_basic_map_n_in(bmap);
3792 n_out = isl_basic_map_n_out(bmap);
3794 total = nparam + n_in + n_out + bmap->n_div + n_out;
3795 dim_map = isl_dim_map_alloc(bmap->ctx, total);
3796 isl_dim_map_dim(dim_map, bmap->dim, isl_dim_param, pos = 0);
3797 isl_dim_map_dim(dim_map, bmap->dim, isl_dim_in, pos += nparam);
3798 isl_dim_map_div(dim_map, bmap, pos += n_in + n_out);
3799 isl_dim_map_dim(dim_map, bmap->dim, isl_dim_out, pos += bmap->n_div);
3801 result = isl_basic_map_alloc_space(isl_space_copy(bmap->dim),
3802 bmap->n_div + n_out,
3803 bmap->n_eq, bmap->n_ineq + 2 * n_out);
3804 result = isl_basic_map_add_constraints_dim_map(result, bmap, dim_map);
3805 result = add_divs(result, n_out);
3806 for (i = 0; i < n_out; ++i) {
3808 j = isl_basic_map_alloc_inequality(result);
3811 isl_seq_clr(result->ineq[j], 1+total);
3812 isl_int_neg(result->ineq[j][1+nparam+n_in+i], d);
3813 isl_int_set_si(result->ineq[j][1+pos+i], 1);
3814 j = isl_basic_map_alloc_inequality(result);
3817 isl_seq_clr(result->ineq[j], 1+total);
3818 isl_int_set(result->ineq[j][1+nparam+n_in+i], d);
3819 isl_int_set_si(result->ineq[j][1+pos+i], -1);
3820 isl_int_sub_ui(result->ineq[j][0], d, 1);
3823 result = isl_basic_map_simplify(result);
3824 return isl_basic_map_finalize(result);
3826 isl_basic_map_free(result);
3830 /* Given a map A -> f(A) and an integer d, construct a map
3831 * A -> floor(f(A)/d).
3833 struct isl_map *isl_map_floordiv(struct isl_map *map, isl_int d)
3837 map = isl_map_cow(map);
3841 ISL_F_CLR(map, ISL_MAP_DISJOINT);
3842 ISL_F_CLR(map, ISL_MAP_NORMALIZED);
3843 for (i = 0; i < map->n; ++i) {
3844 map->p[i] = isl_basic_map_floordiv(map->p[i], d);
3855 static struct isl_basic_map *var_equal(struct isl_basic_map *bmap, unsigned pos)
3861 i = isl_basic_map_alloc_equality(bmap);
3864 nparam = isl_basic_map_n_param(bmap);
3865 n_in = isl_basic_map_n_in(bmap);
3866 isl_seq_clr(bmap->eq[i], 1 + isl_basic_map_total_dim(bmap));
3867 isl_int_set_si(bmap->eq[i][1+nparam+pos], -1);
3868 isl_int_set_si(bmap->eq[i][1+nparam+n_in+pos], 1);
3869 return isl_basic_map_finalize(bmap);
3871 isl_basic_map_free(bmap);
3875 /* Add a constraints to "bmap" expressing i_pos < o_pos
3877 static struct isl_basic_map *var_less(struct isl_basic_map *bmap, unsigned pos)
3883 i = isl_basic_map_alloc_inequality(bmap);
3886 nparam = isl_basic_map_n_param(bmap);
3887 n_in = isl_basic_map_n_in(bmap);
3888 isl_seq_clr(bmap->ineq[i], 1 + isl_basic_map_total_dim(bmap));
3889 isl_int_set_si(bmap->ineq[i][0], -1);
3890 isl_int_set_si(bmap->ineq[i][1+nparam+pos], -1);
3891 isl_int_set_si(bmap->ineq[i][1+nparam+n_in+pos], 1);
3892 return isl_basic_map_finalize(bmap);
3894 isl_basic_map_free(bmap);
3898 /* Add a constraint to "bmap" expressing i_pos <= o_pos
3900 static __isl_give isl_basic_map *var_less_or_equal(
3901 __isl_take isl_basic_map *bmap, unsigned pos)
3907 i = isl_basic_map_alloc_inequality(bmap);
3910 nparam = isl_basic_map_n_param(bmap);
3911 n_in = isl_basic_map_n_in(bmap);
3912 isl_seq_clr(bmap->ineq[i], 1 + isl_basic_map_total_dim(bmap));
3913 isl_int_set_si(bmap->ineq[i][1+nparam+pos], -1);
3914 isl_int_set_si(bmap->ineq[i][1+nparam+n_in+pos], 1);
3915 return isl_basic_map_finalize(bmap);
3917 isl_basic_map_free(bmap);
3921 /* Add a constraints to "bmap" expressing i_pos > o_pos
3923 static struct isl_basic_map *var_more(struct isl_basic_map *bmap, unsigned pos)
3929 i = isl_basic_map_alloc_inequality(bmap);
3932 nparam = isl_basic_map_n_param(bmap);
3933 n_in = isl_basic_map_n_in(bmap);
3934 isl_seq_clr(bmap->ineq[i], 1 + isl_basic_map_total_dim(bmap));
3935 isl_int_set_si(bmap->ineq[i][0], -1);
3936 isl_int_set_si(bmap->ineq[i][1+nparam+pos], 1);
3937 isl_int_set_si(bmap->ineq[i][1+nparam+n_in+pos], -1);
3938 return isl_basic_map_finalize(bmap);
3940 isl_basic_map_free(bmap);
3944 /* Add a constraint to "bmap" expressing i_pos >= o_pos
3946 static __isl_give isl_basic_map *var_more_or_equal(
3947 __isl_take isl_basic_map *bmap, unsigned pos)
3953 i = isl_basic_map_alloc_inequality(bmap);
3956 nparam = isl_basic_map_n_param(bmap);
3957 n_in = isl_basic_map_n_in(bmap);
3958 isl_seq_clr(bmap->ineq[i], 1 + isl_basic_map_total_dim(bmap));
3959 isl_int_set_si(bmap->ineq[i][1+nparam+pos], 1);
3960 isl_int_set_si(bmap->ineq[i][1+nparam+n_in+pos], -1);
3961 return isl_basic_map_finalize(bmap);
3963 isl_basic_map_free(bmap);
3967 __isl_give isl_basic_map *isl_basic_map_equal(
3968 __isl_take isl_space *dim, unsigned n_equal)
3971 struct isl_basic_map *bmap;
3972 bmap = isl_basic_map_alloc_space(dim, 0, n_equal, 0);
3975 for (i = 0; i < n_equal && bmap; ++i)
3976 bmap = var_equal(bmap, i);
3977 return isl_basic_map_finalize(bmap);
3980 /* Return a relation on of dimension "dim" expressing i_[0..pos] << o_[0..pos]
3982 __isl_give isl_basic_map *isl_basic_map_less_at(__isl_take isl_space *dim,
3986 struct isl_basic_map *bmap;
3987 bmap = isl_basic_map_alloc_space(dim, 0, pos, 1);
3990 for (i = 0; i < pos && bmap; ++i)
3991 bmap = var_equal(bmap, i);
3993 bmap = var_less(bmap, pos);
3994 return isl_basic_map_finalize(bmap);
3997 /* Return a relation on of dimension "dim" expressing i_[0..pos] <<= o_[0..pos]
3999 __isl_give isl_basic_map *isl_basic_map_less_or_equal_at(
4000 __isl_take isl_space *dim, unsigned pos)
4003 isl_basic_map *bmap;
4005 bmap = isl_basic_map_alloc_space(dim, 0, pos, 1);
4006 for (i = 0; i < pos; ++i)
4007 bmap = var_equal(bmap, i);
4008 bmap = var_less_or_equal(bmap, pos);
4009 return isl_basic_map_finalize(bmap);
4012 /* Return a relation on pairs of sets of dimension "dim" expressing i_pos > o_pos
4014 __isl_give isl_basic_map *isl_basic_map_more_at(__isl_take isl_space *dim,
4018 struct isl_basic_map *bmap;
4019 bmap = isl_basic_map_alloc_space(dim, 0, pos, 1);
4022 for (i = 0; i < pos && bmap; ++i)
4023 bmap = var_equal(bmap, i);
4025 bmap = var_more(bmap, pos);
4026 return isl_basic_map_finalize(bmap);
4029 /* Return a relation on of dimension "dim" expressing i_[0..pos] >>= o_[0..pos]
4031 __isl_give isl_basic_map *isl_basic_map_more_or_equal_at(
4032 __isl_take isl_space *dim, unsigned pos)
4035 isl_basic_map *bmap;
4037 bmap = isl_basic_map_alloc_space(dim, 0, pos, 1);
4038 for (i = 0; i < pos; ++i)
4039 bmap = var_equal(bmap, i);
4040 bmap = var_more_or_equal(bmap, pos);
4041 return isl_basic_map_finalize(bmap);
4044 static __isl_give isl_map *map_lex_lte_first(__isl_take isl_space *dims,
4045 unsigned n, int equal)
4047 struct isl_map *map;
4050 if (n == 0 && equal)
4051 return isl_map_universe(dims);
4053 map = isl_map_alloc_space(isl_space_copy(dims), n, ISL_MAP_DISJOINT);
4055 for (i = 0; i + 1 < n; ++i)
4056 map = isl_map_add_basic_map(map,
4057 isl_basic_map_less_at(isl_space_copy(dims), i));
4060 map = isl_map_add_basic_map(map,
4061 isl_basic_map_less_or_equal_at(dims, n - 1));
4063 map = isl_map_add_basic_map(map,
4064 isl_basic_map_less_at(dims, n - 1));
4066 isl_space_free(dims);
4071 static __isl_give isl_map *map_lex_lte(__isl_take isl_space *dims, int equal)
4075 return map_lex_lte_first(dims, dims->n_out, equal);
4078 __isl_give isl_map *isl_map_lex_lt_first(__isl_take isl_space *dim, unsigned n)
4080 return map_lex_lte_first(dim, n, 0);
4083 __isl_give isl_map *isl_map_lex_le_first(__isl_take isl_space *dim, unsigned n)
4085 return map_lex_lte_first(dim, n, 1);
4088 __isl_give isl_map *isl_map_lex_lt(__isl_take isl_space *set_dim)
4090 return map_lex_lte(isl_space_map_from_set(set_dim), 0);
4093 __isl_give isl_map *isl_map_lex_le(__isl_take isl_space *set_dim)
4095 return map_lex_lte(isl_space_map_from_set(set_dim), 1);
4098 static __isl_give isl_map *map_lex_gte_first(__isl_take isl_space *dims,
4099 unsigned n, int equal)
4101 struct isl_map *map;
4104 if (n == 0 && equal)
4105 return isl_map_universe(dims);
4107 map = isl_map_alloc_space(isl_space_copy(dims), n, ISL_MAP_DISJOINT);
4109 for (i = 0; i + 1 < n; ++i)
4110 map = isl_map_add_basic_map(map,
4111 isl_basic_map_more_at(isl_space_copy(dims), i));
4114 map = isl_map_add_basic_map(map,
4115 isl_basic_map_more_or_equal_at(dims, n - 1));
4117 map = isl_map_add_basic_map(map,
4118 isl_basic_map_more_at(dims, n - 1));
4120 isl_space_free(dims);
4125 static __isl_give isl_map *map_lex_gte(__isl_take isl_space *dims, int equal)
4129 return map_lex_gte_first(dims, dims->n_out, equal);
4132 __isl_give isl_map *isl_map_lex_gt_first(__isl_take isl_space *dim, unsigned n)
4134 return map_lex_gte_first(dim, n, 0);
4137 __isl_give isl_map *isl_map_lex_ge_first(__isl_take isl_space *dim, unsigned n)
4139 return map_lex_gte_first(dim, n, 1);
4142 __isl_give isl_map *isl_map_lex_gt(__isl_take isl_space *set_dim)
4144 return map_lex_gte(isl_space_map_from_set(set_dim), 0);
4147 __isl_give isl_map *isl_map_lex_ge(__isl_take isl_space *set_dim)
4149 return map_lex_gte(isl_space_map_from_set(set_dim), 1);
4152 __isl_give isl_map *isl_set_lex_le_set(__isl_take isl_set *set1,
4153 __isl_take isl_set *set2)
4156 map = isl_map_lex_le(isl_set_get_space(set1));
4157 map = isl_map_intersect_domain(map, set1);
4158 map = isl_map_intersect_range(map, set2);
4162 __isl_give isl_map *isl_set_lex_lt_set(__isl_take isl_set *set1,
4163 __isl_take isl_set *set2)
4166 map = isl_map_lex_lt(isl_set_get_space(set1));
4167 map = isl_map_intersect_domain(map, set1);
4168 map = isl_map_intersect_range(map, set2);
4172 __isl_give isl_map *isl_set_lex_ge_set(__isl_take isl_set *set1,
4173 __isl_take isl_set *set2)
4176 map = isl_map_lex_ge(isl_set_get_space(set1));
4177 map = isl_map_intersect_domain(map, set1);
4178 map = isl_map_intersect_range(map, set2);
4182 __isl_give isl_map *isl_set_lex_gt_set(__isl_take isl_set *set1,
4183 __isl_take isl_set *set2)
4186 map = isl_map_lex_gt(isl_set_get_space(set1));
4187 map = isl_map_intersect_domain(map, set1);
4188 map = isl_map_intersect_range(map, set2);
4192 __isl_give isl_map *isl_map_lex_le_map(__isl_take isl_map *map1,
4193 __isl_take isl_map *map2)
4196 map = isl_map_lex_le(isl_space_range(isl_map_get_space(map1)));
4197 map = isl_map_apply_domain(map, isl_map_reverse(map1));
4198 map = isl_map_apply_range(map, isl_map_reverse(map2));
4202 __isl_give isl_map *isl_map_lex_lt_map(__isl_take isl_map *map1,
4203 __isl_take isl_map *map2)
4206 map = isl_map_lex_lt(isl_space_range(isl_map_get_space(map1)));
4207 map = isl_map_apply_domain(map, isl_map_reverse(map1));
4208 map = isl_map_apply_range(map, isl_map_reverse(map2));
4212 __isl_give isl_map *isl_map_lex_ge_map(__isl_take isl_map *map1,
4213 __isl_take isl_map *map2)
4216 map = isl_map_lex_ge(isl_space_range(isl_map_get_space(map1)));
4217 map = isl_map_apply_domain(map, isl_map_reverse(map1));
4218 map = isl_map_apply_range(map, isl_map_reverse(map2));
4222 __isl_give isl_map *isl_map_lex_gt_map(__isl_take isl_map *map1,
4223 __isl_take isl_map *map2)
4226 map = isl_map_lex_gt(isl_space_range(isl_map_get_space(map1)));
4227 map = isl_map_apply_domain(map, isl_map_reverse(map1));
4228 map = isl_map_apply_range(map, isl_map_reverse(map2));
4232 __isl_give isl_basic_map *isl_basic_map_from_basic_set(
4233 __isl_take isl_basic_set *bset, __isl_take isl_space *dim)
4235 struct isl_basic_map *bmap;
4237 bset = isl_basic_set_cow(bset);
4241 isl_assert(bset->ctx, isl_space_compatible(bset->dim, dim), goto error);
4242 isl_space_free(bset->dim);
4243 bmap = (struct isl_basic_map *) bset;
4245 return isl_basic_map_finalize(bmap);
4247 isl_basic_set_free(bset);
4248 isl_space_free(dim);
4252 struct isl_basic_set *isl_basic_set_from_basic_map(struct isl_basic_map *bmap)
4256 if (bmap->dim->n_in == 0)
4257 return (struct isl_basic_set *)bmap;
4258 bmap = isl_basic_map_cow(bmap);
4261 bmap->dim = isl_space_as_set_space(bmap->dim);
4264 bmap = isl_basic_map_finalize(bmap);
4265 return (struct isl_basic_set *)bmap;
4267 isl_basic_map_free(bmap);
4271 /* For a div d = floor(f/m), add the constraints
4274 * -(f-(n-1)) + m d >= 0
4276 * Note that the second constraint is the negation of
4280 int isl_basic_map_add_div_constraints_var(__isl_keep isl_basic_map *bmap,
4281 unsigned pos, isl_int *div)
4284 unsigned total = isl_basic_map_total_dim(bmap);
4286 i = isl_basic_map_alloc_inequality(bmap);
4289 isl_seq_cpy(bmap->ineq[i], div + 1, 1 + total);
4290 isl_int_neg(bmap->ineq[i][1 + pos], div[0]);
4292 j = isl_basic_map_alloc_inequality(bmap);
4295 isl_seq_neg(bmap->ineq[j], bmap->ineq[i], 1 + total);
4296 isl_int_add(bmap->ineq[j][0], bmap->ineq[j][0], bmap->ineq[j][1 + pos]);
4297 isl_int_sub_ui(bmap->ineq[j][0], bmap->ineq[j][0], 1);
4301 int isl_basic_set_add_div_constraints_var(__isl_keep isl_basic_set *bset,
4302 unsigned pos, isl_int *div)
4304 return isl_basic_map_add_div_constraints_var((isl_basic_map *)bset,
4308 int isl_basic_map_add_div_constraints(struct isl_basic_map *bmap, unsigned div)
4310 unsigned total = isl_basic_map_total_dim(bmap);
4311 unsigned div_pos = total - bmap->n_div + div;
4313 return isl_basic_map_add_div_constraints_var(bmap, div_pos,
4317 int isl_basic_set_add_div_constraints(struct isl_basic_set *bset, unsigned div)
4319 return isl_basic_map_add_div_constraints(bset, div);
4322 struct isl_basic_set *isl_basic_map_underlying_set(
4323 struct isl_basic_map *bmap)
4327 if (bmap->dim->nparam == 0 && bmap->dim->n_in == 0 &&
4329 !isl_space_is_named_or_nested(bmap->dim, isl_dim_in) &&
4330 !isl_space_is_named_or_nested(bmap->dim, isl_dim_out))
4331 return (struct isl_basic_set *)bmap;
4332 bmap = isl_basic_map_cow(bmap);
4335 bmap->dim = isl_space_underlying(bmap->dim, bmap->n_div);
4338 bmap->extra -= bmap->n_div;
4340 bmap = isl_basic_map_finalize(bmap);
4341 return (struct isl_basic_set *)bmap;
4343 isl_basic_map_free(bmap);
4347 __isl_give isl_basic_set *isl_basic_set_underlying_set(
4348 __isl_take isl_basic_set *bset)
4350 return isl_basic_map_underlying_set((isl_basic_map *)bset);
4353 struct isl_basic_map *isl_basic_map_overlying_set(
4354 struct isl_basic_set *bset, struct isl_basic_map *like)
4356 struct isl_basic_map *bmap;
4357 struct isl_ctx *ctx;
4364 isl_assert(ctx, bset->n_div == 0, goto error);
4365 isl_assert(ctx, isl_basic_set_n_param(bset) == 0, goto error);
4366 isl_assert(ctx, bset->dim->n_out == isl_basic_map_total_dim(like),
4368 if (isl_space_is_equal(bset->dim, like->dim) && like->n_div == 0) {
4369 isl_basic_map_free(like);
4370 return (struct isl_basic_map *)bset;
4372 bset = isl_basic_set_cow(bset);
4375 total = bset->dim->n_out + bset->extra;
4376 bmap = (struct isl_basic_map *)bset;
4377 isl_space_free(bmap->dim);
4378 bmap->dim = isl_space_copy(like->dim);
4381 bmap->n_div = like->n_div;
4382 bmap->extra += like->n_div;
4386 ltotal = total - bmap->extra + like->extra;
4389 bmap->block2 = isl_blk_extend(ctx, bmap->block2,
4390 bmap->extra * (1 + 1 + total));
4391 if (isl_blk_is_error(bmap->block2))
4393 div = isl_realloc_array(ctx, bmap->div, isl_int *, bmap->extra);
4397 for (i = 0; i < bmap->extra; ++i)
4398 bmap->div[i] = bmap->block2.data + i * (1 + 1 + total);
4399 for (i = 0; i < like->n_div; ++i) {
4400 isl_seq_cpy(bmap->div[i], like->div[i], 1 + 1 + ltotal);
4401 isl_seq_clr(bmap->div[i]+1+1+ltotal, total - ltotal);
4403 bmap = isl_basic_map_extend_constraints(bmap,
4404 0, 2 * like->n_div);
4405 for (i = 0; i < like->n_div; ++i) {
4408 if (isl_int_is_zero(bmap->div[i][0]))
4410 if (isl_basic_map_add_div_constraints(bmap, i) < 0)
4411 bmap = isl_basic_map_free(bmap);
4414 isl_basic_map_free(like);
4415 bmap = isl_basic_map_simplify(bmap);
4416 bmap = isl_basic_map_finalize(bmap);
4419 isl_basic_map_free(like);
4420 isl_basic_set_free(bset);
4424 struct isl_basic_set *isl_basic_set_from_underlying_set(
4425 struct isl_basic_set *bset, struct isl_basic_set *like)
4427 return (struct isl_basic_set *)
4428 isl_basic_map_overlying_set(bset, (struct isl_basic_map *)like);
4431 struct isl_set *isl_set_from_underlying_set(
4432 struct isl_set *set, struct isl_basic_set *like)
4438 isl_assert(set->ctx, set->dim->n_out == isl_basic_set_total_dim(like),
4440 if (isl_space_is_equal(set->dim, like->dim) && like->n_div == 0) {
4441 isl_basic_set_free(like);
4444 set = isl_set_cow(set);
4447 for (i = 0; i < set->n; ++i) {
4448 set->p[i] = isl_basic_set_from_underlying_set(set->p[i],
4449 isl_basic_set_copy(like));
4453 isl_space_free(set->dim);
4454 set->dim = isl_space_copy(like->dim);
4457 isl_basic_set_free(like);
4460 isl_basic_set_free(like);
4465 struct isl_set *isl_map_underlying_set(struct isl_map *map)
4469 map = isl_map_cow(map);
4472 map->dim = isl_space_cow(map->dim);
4476 for (i = 1; i < map->n; ++i)
4477 isl_assert(map->ctx, map->p[0]->n_div == map->p[i]->n_div,
4479 for (i = 0; i < map->n; ++i) {
4480 map->p[i] = (struct isl_basic_map *)
4481 isl_basic_map_underlying_set(map->p[i]);
4486 map->dim = isl_space_underlying(map->dim, 0);
4488 isl_space_free(map->dim);
4489 map->dim = isl_space_copy(map->p[0]->dim);
4493 return (struct isl_set *)map;
4499 struct isl_set *isl_set_to_underlying_set(struct isl_set *set)
4501 return (struct isl_set *)isl_map_underlying_set((struct isl_map *)set);
4504 __isl_give isl_basic_map *isl_basic_map_reset_space(
4505 __isl_take isl_basic_map *bmap, __isl_take isl_space *dim)
4507 bmap = isl_basic_map_cow(bmap);
4511 isl_space_free(bmap->dim);
4514 bmap = isl_basic_map_finalize(bmap);
4518 isl_basic_map_free(bmap);
4519 isl_space_free(dim);
4523 __isl_give isl_basic_set *isl_basic_set_reset_space(
4524 __isl_take isl_basic_set *bset, __isl_take isl_space *dim)
4526 return (isl_basic_set *)isl_basic_map_reset_space((isl_basic_map *)bset,
4530 __isl_give isl_map *isl_map_reset_space(__isl_take isl_map *map,
4531 __isl_take isl_space *dim)
4535 map = isl_map_cow(map);
4539 for (i = 0; i < map->n; ++i) {
4540 map->p[i] = isl_basic_map_reset_space(map->p[i],
4541 isl_space_copy(dim));
4545 isl_space_free(map->dim);
4551 isl_space_free(dim);
4555 __isl_give isl_set *isl_set_reset_space(__isl_take isl_set *set,
4556 __isl_take isl_space *dim)
4558 return (struct isl_set *) isl_map_reset_space((struct isl_map *)set, dim);
4561 /* Compute the parameter domain of the given basic set.
4563 __isl_give isl_basic_set *isl_basic_set_params(__isl_take isl_basic_set *bset)
4568 if (isl_basic_set_is_params(bset))
4571 n = isl_basic_set_dim(bset, isl_dim_set);
4572 bset = isl_basic_set_project_out(bset, isl_dim_set, 0, n);
4573 space = isl_basic_set_get_space(bset);
4574 space = isl_space_params(space);
4575 bset = isl_basic_set_reset_space(bset, space);
4579 /* Construct a zero-dimensional basic set with the given parameter domain.
4581 __isl_give isl_basic_set *isl_basic_set_from_params(
4582 __isl_take isl_basic_set *bset)
4585 space = isl_basic_set_get_space(bset);
4586 space = isl_space_set_from_params(space);
4587 bset = isl_basic_set_reset_space(bset, space);
4591 /* Compute the parameter domain of the given set.
4593 __isl_give isl_set *isl_set_params(__isl_take isl_set *set)
4598 if (isl_set_is_params(set))
4601 n = isl_set_dim(set, isl_dim_set);
4602 set = isl_set_project_out(set, isl_dim_set, 0, n);
4603 space = isl_set_get_space(set);
4604 space = isl_space_params(space);
4605 set = isl_set_reset_space(set, space);
4609 /* Construct a zero-dimensional set with the given parameter domain.
4611 __isl_give isl_set *isl_set_from_params(__isl_take isl_set *set)
4614 space = isl_set_get_space(set);
4615 space = isl_space_set_from_params(space);
4616 set = isl_set_reset_space(set, space);
4620 /* Compute the parameter domain of the given map.
4622 __isl_give isl_set *isl_map_params(__isl_take isl_map *map)
4627 n = isl_map_dim(map, isl_dim_in);
4628 map = isl_map_project_out(map, isl_dim_in, 0, n);
4629 n = isl_map_dim(map, isl_dim_out);
4630 map = isl_map_project_out(map, isl_dim_out, 0, n);
4631 space = isl_map_get_space(map);
4632 space = isl_space_params(space);
4633 map = isl_map_reset_space(map, space);
4637 struct isl_basic_set *isl_basic_map_domain(struct isl_basic_map *bmap)
4640 struct isl_basic_set *domain;
4646 dim = isl_space_domain(isl_basic_map_get_space(bmap));
4648 n_in = isl_basic_map_n_in(bmap);
4649 n_out = isl_basic_map_n_out(bmap);
4650 domain = isl_basic_set_from_basic_map(bmap);
4651 domain = isl_basic_set_project_out(domain, isl_dim_set, n_in, n_out);
4653 domain = isl_basic_set_reset_space(domain, dim);
4658 int isl_basic_map_may_be_set(__isl_keep isl_basic_map *bmap)
4662 return isl_space_may_be_set(bmap->dim);
4665 /* Is this basic map actually a set?
4666 * Users should never call this function. Outside of isl,
4667 * the type should indicate whether something is a set or a map.
4669 int isl_basic_map_is_set(__isl_keep isl_basic_map *bmap)
4673 return isl_space_is_set(bmap->dim);
4676 struct isl_basic_set *isl_basic_map_range(struct isl_basic_map *bmap)
4680 if (isl_basic_map_is_set(bmap))
4682 return isl_basic_map_domain(isl_basic_map_reverse(bmap));
4685 __isl_give isl_basic_map *isl_basic_map_domain_map(
4686 __isl_take isl_basic_map *bmap)
4690 isl_basic_map *domain;
4691 int nparam, n_in, n_out;
4694 nparam = isl_basic_map_dim(bmap, isl_dim_param);
4695 n_in = isl_basic_map_dim(bmap, isl_dim_in);
4696 n_out = isl_basic_map_dim(bmap, isl_dim_out);
4698 dim = isl_space_from_range(isl_space_domain(isl_basic_map_get_space(bmap)));
4699 domain = isl_basic_map_universe(dim);
4701 bmap = isl_basic_map_from_domain(isl_basic_map_wrap(bmap));
4702 bmap = isl_basic_map_apply_range(bmap, domain);
4703 bmap = isl_basic_map_extend_constraints(bmap, n_in, 0);
4705 total = isl_basic_map_total_dim(bmap);
4707 for (i = 0; i < n_in; ++i) {
4708 k = isl_basic_map_alloc_equality(bmap);
4711 isl_seq_clr(bmap->eq[k], 1 + total);
4712 isl_int_set_si(bmap->eq[k][1 + nparam + i], -1);
4713 isl_int_set_si(bmap->eq[k][1 + nparam + n_in + n_out + i], 1);
4716 bmap = isl_basic_map_gauss(bmap, NULL);
4717 return isl_basic_map_finalize(bmap);
4719 isl_basic_map_free(bmap);
4723 __isl_give isl_basic_map *isl_basic_map_range_map(
4724 __isl_take isl_basic_map *bmap)
4728 isl_basic_map *range;
4729 int nparam, n_in, n_out;
4732 nparam = isl_basic_map_dim(bmap, isl_dim_param);
4733 n_in = isl_basic_map_dim(bmap, isl_dim_in);
4734 n_out = isl_basic_map_dim(bmap, isl_dim_out);
4736 dim = isl_space_from_range(isl_space_range(isl_basic_map_get_space(bmap)));
4737 range = isl_basic_map_universe(dim);
4739 bmap = isl_basic_map_from_domain(isl_basic_map_wrap(bmap));
4740 bmap = isl_basic_map_apply_range(bmap, range);
4741 bmap = isl_basic_map_extend_constraints(bmap, n_out, 0);
4743 total = isl_basic_map_total_dim(bmap);
4745 for (i = 0; i < n_out; ++i) {
4746 k = isl_basic_map_alloc_equality(bmap);
4749 isl_seq_clr(bmap->eq[k], 1 + total);
4750 isl_int_set_si(bmap->eq[k][1 + nparam + n_in + i], -1);
4751 isl_int_set_si(bmap->eq[k][1 + nparam + n_in + n_out + i], 1);
4754 bmap = isl_basic_map_gauss(bmap, NULL);
4755 return isl_basic_map_finalize(bmap);
4757 isl_basic_map_free(bmap);
4761 int isl_map_may_be_set(__isl_keep isl_map *map)
4765 return isl_space_may_be_set(map->dim);
4768 /* Is this map actually a set?
4769 * Users should never call this function. Outside of isl,
4770 * the type should indicate whether something is a set or a map.
4772 int isl_map_is_set(__isl_keep isl_map *map)
4776 return isl_space_is_set(map->dim);
4779 struct isl_set *isl_map_range(struct isl_map *map)
4782 struct isl_set *set;
4786 if (isl_map_is_set(map))
4787 return (isl_set *)map;
4789 map = isl_map_cow(map);
4793 set = (struct isl_set *) map;
4794 set->dim = isl_space_range(set->dim);
4797 for (i = 0; i < map->n; ++i) {
4798 set->p[i] = isl_basic_map_range(map->p[i]);
4802 ISL_F_CLR(set, ISL_MAP_DISJOINT);
4803 ISL_F_CLR(set, ISL_SET_NORMALIZED);
4810 __isl_give isl_map *isl_map_domain_map(__isl_take isl_map *map)
4813 isl_space *domain_dim;
4815 map = isl_map_cow(map);
4819 domain_dim = isl_space_from_range(isl_space_domain(isl_map_get_space(map)));
4820 map->dim = isl_space_from_domain(isl_space_wrap(map->dim));
4821 map->dim = isl_space_join(map->dim, domain_dim);
4824 for (i = 0; i < map->n; ++i) {
4825 map->p[i] = isl_basic_map_domain_map(map->p[i]);
4829 ISL_F_CLR(map, ISL_MAP_DISJOINT);
4830 ISL_F_CLR(map, ISL_MAP_NORMALIZED);
4837 __isl_give isl_map *isl_map_range_map(__isl_take isl_map *map)
4840 isl_space *range_dim;
4842 map = isl_map_cow(map);
4846 range_dim = isl_space_range(isl_map_get_space(map));
4847 range_dim = isl_space_from_range(range_dim);
4848 map->dim = isl_space_from_domain(isl_space_wrap(map->dim));
4849 map->dim = isl_space_join(map->dim, range_dim);
4852 for (i = 0; i < map->n; ++i) {
4853 map->p[i] = isl_basic_map_range_map(map->p[i]);
4857 ISL_F_CLR(map, ISL_MAP_DISJOINT);
4858 ISL_F_CLR(map, ISL_MAP_NORMALIZED);
4865 __isl_give isl_map *isl_map_from_set(__isl_take isl_set *set,
4866 __isl_take isl_space *dim)
4869 struct isl_map *map = NULL;
4871 set = isl_set_cow(set);
4874 isl_assert(set->ctx, isl_space_compatible(set->dim, dim), goto error);
4875 map = (struct isl_map *)set;
4876 for (i = 0; i < set->n; ++i) {
4877 map->p[i] = isl_basic_map_from_basic_set(
4878 set->p[i], isl_space_copy(dim));
4882 isl_space_free(map->dim);
4886 isl_space_free(dim);
4891 __isl_give isl_basic_map *isl_basic_map_from_domain(
4892 __isl_take isl_basic_set *bset)
4894 return isl_basic_map_reverse(isl_basic_map_from_range(bset));
4897 __isl_give isl_basic_map *isl_basic_map_from_range(
4898 __isl_take isl_basic_set *bset)
4901 space = isl_basic_set_get_space(bset);
4902 space = isl_space_from_range(space);
4903 bset = isl_basic_set_reset_space(bset, space);
4904 return (isl_basic_map *)bset;
4907 struct isl_map *isl_map_from_range(struct isl_set *set)
4910 space = isl_set_get_space(set);
4911 space = isl_space_from_range(space);
4912 set = isl_set_reset_space(set, space);
4913 return (struct isl_map *)set;
4916 __isl_give isl_map *isl_map_from_domain(__isl_take isl_set *set)
4918 return isl_map_reverse(isl_map_from_range(set));
4921 __isl_give isl_basic_map *isl_basic_map_from_domain_and_range(
4922 __isl_take isl_basic_set *domain, __isl_take isl_basic_set *range)
4924 return isl_basic_map_apply_range(isl_basic_map_reverse(domain), range);
4927 __isl_give isl_map *isl_map_from_domain_and_range(__isl_take isl_set *domain,
4928 __isl_take isl_set *range)
4930 return isl_map_apply_range(isl_map_reverse(domain), range);
4933 struct isl_set *isl_set_from_map(struct isl_map *map)
4936 struct isl_set *set = NULL;
4940 map = isl_map_cow(map);
4943 map->dim = isl_space_as_set_space(map->dim);
4946 set = (struct isl_set *)map;
4947 for (i = 0; i < map->n; ++i) {
4948 set->p[i] = isl_basic_set_from_basic_map(map->p[i]);
4958 __isl_give isl_map *isl_map_alloc_space(__isl_take isl_space *dim, int n,
4961 struct isl_map *map;
4966 isl_die(dim->ctx, isl_error_internal,
4967 "negative number of basic maps", goto error);
4968 map = isl_alloc(dim->ctx, struct isl_map,
4969 sizeof(struct isl_map) +
4970 (n - 1) * sizeof(struct isl_basic_map *));
4974 map->ctx = dim->ctx;
4975 isl_ctx_ref(map->ctx);
4983 isl_space_free(dim);
4987 struct isl_map *isl_map_alloc(struct isl_ctx *ctx,
4988 unsigned nparam, unsigned in, unsigned out, int n,
4991 struct isl_map *map;
4994 dims = isl_space_alloc(ctx, nparam, in, out);
4998 map = isl_map_alloc_space(dims, n, flags);
5002 __isl_give isl_basic_map *isl_basic_map_empty(__isl_take isl_space *dim)
5004 struct isl_basic_map *bmap;
5005 bmap = isl_basic_map_alloc_space(dim, 0, 1, 0);
5006 bmap = isl_basic_map_set_to_empty(bmap);
5010 __isl_give isl_basic_set *isl_basic_set_empty(__isl_take isl_space *dim)
5012 struct isl_basic_set *bset;
5013 bset = isl_basic_set_alloc_space(dim, 0, 1, 0);
5014 bset = isl_basic_set_set_to_empty(bset);
5018 struct isl_basic_map *isl_basic_map_empty_like(struct isl_basic_map *model)
5020 struct isl_basic_map *bmap;
5023 bmap = isl_basic_map_alloc_space(isl_space_copy(model->dim), 0, 1, 0);
5024 bmap = isl_basic_map_set_to_empty(bmap);
5028 struct isl_basic_map *isl_basic_map_empty_like_map(struct isl_map *model)
5030 struct isl_basic_map *bmap;
5033 bmap = isl_basic_map_alloc_space(isl_space_copy(model->dim), 0, 1, 0);
5034 bmap = isl_basic_map_set_to_empty(bmap);
5038 struct isl_basic_set *isl_basic_set_empty_like(struct isl_basic_set *model)
5040 struct isl_basic_set *bset;
5043 bset = isl_basic_set_alloc_space(isl_space_copy(model->dim), 0, 1, 0);
5044 bset = isl_basic_set_set_to_empty(bset);
5048 __isl_give isl_basic_map *isl_basic_map_universe(__isl_take isl_space *dim)
5050 struct isl_basic_map *bmap;
5051 bmap = isl_basic_map_alloc_space(dim, 0, 0, 0);
5052 bmap = isl_basic_map_finalize(bmap);
5056 __isl_give isl_basic_set *isl_basic_set_universe(__isl_take isl_space *dim)
5058 struct isl_basic_set *bset;
5059 bset = isl_basic_set_alloc_space(dim, 0, 0, 0);
5060 bset = isl_basic_set_finalize(bset);
5064 __isl_give isl_basic_map *isl_basic_map_nat_universe(__isl_take isl_space *dim)
5067 unsigned total = isl_space_dim(dim, isl_dim_all);
5068 isl_basic_map *bmap;
5070 bmap= isl_basic_map_alloc_space(dim, 0, 0, total);
5071 for (i = 0; i < total; ++i) {
5072 int k = isl_basic_map_alloc_inequality(bmap);
5075 isl_seq_clr(bmap->ineq[k], 1 + total);
5076 isl_int_set_si(bmap->ineq[k][1 + i], 1);
5080 isl_basic_map_free(bmap);
5084 __isl_give isl_basic_set *isl_basic_set_nat_universe(__isl_take isl_space *dim)
5086 return isl_basic_map_nat_universe(dim);
5089 __isl_give isl_map *isl_map_nat_universe(__isl_take isl_space *dim)
5091 return isl_map_from_basic_map(isl_basic_map_nat_universe(dim));
5094 __isl_give isl_set *isl_set_nat_universe(__isl_take isl_space *dim)
5096 return isl_map_nat_universe(dim);
5099 __isl_give isl_basic_map *isl_basic_map_universe_like(
5100 __isl_keep isl_basic_map *model)
5104 return isl_basic_map_alloc_space(isl_space_copy(model->dim), 0, 0, 0);
5107 struct isl_basic_set *isl_basic_set_universe_like(struct isl_basic_set *model)
5111 return isl_basic_set_alloc_space(isl_space_copy(model->dim), 0, 0, 0);
5114 __isl_give isl_basic_set *isl_basic_set_universe_like_set(
5115 __isl_keep isl_set *model)
5119 return isl_basic_set_alloc_space(isl_space_copy(model->dim), 0, 0, 0);
5122 __isl_give isl_map *isl_map_empty(__isl_take isl_space *dim)
5124 return isl_map_alloc_space(dim, 0, ISL_MAP_DISJOINT);
5127 struct isl_map *isl_map_empty_like(struct isl_map *model)
5131 return isl_map_alloc_space(isl_space_copy(model->dim), 0, ISL_MAP_DISJOINT);
5134 struct isl_map *isl_map_empty_like_basic_map(struct isl_basic_map *model)
5138 return isl_map_alloc_space(isl_space_copy(model->dim), 0, ISL_MAP_DISJOINT);
5141 __isl_give isl_set *isl_set_empty(__isl_take isl_space *dim)
5143 return isl_set_alloc_space(dim, 0, ISL_MAP_DISJOINT);
5146 struct isl_set *isl_set_empty_like(struct isl_set *model)
5150 return isl_set_empty(isl_space_copy(model->dim));
5153 __isl_give isl_map *isl_map_universe(__isl_take isl_space *dim)
5155 struct isl_map *map;
5158 map = isl_map_alloc_space(isl_space_copy(dim), 1, ISL_MAP_DISJOINT);
5159 map = isl_map_add_basic_map(map, isl_basic_map_universe(dim));
5163 __isl_give isl_set *isl_set_universe(__isl_take isl_space *dim)
5165 struct isl_set *set;
5168 set = isl_set_alloc_space(isl_space_copy(dim), 1, ISL_MAP_DISJOINT);
5169 set = isl_set_add_basic_set(set, isl_basic_set_universe(dim));
5173 __isl_give isl_set *isl_set_universe_like(__isl_keep isl_set *model)
5177 return isl_set_universe(isl_space_copy(model->dim));
5180 struct isl_map *isl_map_dup(struct isl_map *map)
5183 struct isl_map *dup;
5187 dup = isl_map_alloc_space(isl_space_copy(map->dim), map->n, map->flags);
5188 for (i = 0; i < map->n; ++i)
5189 dup = isl_map_add_basic_map(dup, isl_basic_map_copy(map->p[i]));
5193 __isl_give isl_map *isl_map_add_basic_map(__isl_take isl_map *map,
5194 __isl_take isl_basic_map *bmap)
5198 if (isl_basic_map_plain_is_empty(bmap)) {
5199 isl_basic_map_free(bmap);
5202 isl_assert(map->ctx, isl_space_is_equal(map->dim, bmap->dim), goto error);
5203 isl_assert(map->ctx, map->n < map->size, goto error);
5204 map->p[map->n] = bmap;
5206 ISL_F_CLR(map, ISL_MAP_NORMALIZED);
5212 isl_basic_map_free(bmap);
5216 void *isl_map_free(struct isl_map *map)
5226 isl_ctx_deref(map->ctx);
5227 for (i = 0; i < map->n; ++i)
5228 isl_basic_map_free(map->p[i]);
5229 isl_space_free(map->dim);
5235 struct isl_map *isl_map_extend(struct isl_map *base,
5236 unsigned nparam, unsigned n_in, unsigned n_out)
5240 base = isl_map_cow(base);
5244 base->dim = isl_space_extend(base->dim, nparam, n_in, n_out);
5247 for (i = 0; i < base->n; ++i) {
5248 base->p[i] = isl_basic_map_extend_space(base->p[i],
5249 isl_space_copy(base->dim), 0, 0, 0);
5259 struct isl_set *isl_set_extend(struct isl_set *base,
5260 unsigned nparam, unsigned dim)
5262 return (struct isl_set *)isl_map_extend((struct isl_map *)base,
5266 static struct isl_basic_map *isl_basic_map_fix_pos_si(
5267 struct isl_basic_map *bmap, unsigned pos, int value)
5271 bmap = isl_basic_map_cow(bmap);
5272 bmap = isl_basic_map_extend_constraints(bmap, 1, 0);
5273 j = isl_basic_map_alloc_equality(bmap);
5276 isl_seq_clr(bmap->eq[j] + 1, isl_basic_map_total_dim(bmap));
5277 isl_int_set_si(bmap->eq[j][pos], -1);
5278 isl_int_set_si(bmap->eq[j][0], value);
5279 bmap = isl_basic_map_simplify(bmap);
5280 return isl_basic_map_finalize(bmap);
5282 isl_basic_map_free(bmap);
5286 static __isl_give isl_basic_map *isl_basic_map_fix_pos(
5287 __isl_take isl_basic_map *bmap, unsigned pos, isl_int value)
5291 bmap = isl_basic_map_cow(bmap);
5292 bmap = isl_basic_map_extend_constraints(bmap, 1, 0);
5293 j = isl_basic_map_alloc_equality(bmap);
5296 isl_seq_clr(bmap->eq[j] + 1, isl_basic_map_total_dim(bmap));
5297 isl_int_set_si(bmap->eq[j][pos], -1);
5298 isl_int_set(bmap->eq[j][0], value);
5299 bmap = isl_basic_map_simplify(bmap);
5300 return isl_basic_map_finalize(bmap);
5302 isl_basic_map_free(bmap);
5306 struct isl_basic_map *isl_basic_map_fix_si(struct isl_basic_map *bmap,
5307 enum isl_dim_type type, unsigned pos, int value)
5311 isl_assert(bmap->ctx, pos < isl_basic_map_dim(bmap, type), goto error);
5312 return isl_basic_map_fix_pos_si(bmap,
5313 isl_basic_map_offset(bmap, type) + pos, value);
5315 isl_basic_map_free(bmap);
5319 __isl_give isl_basic_map *isl_basic_map_fix(__isl_take isl_basic_map *bmap,
5320 enum isl_dim_type type, unsigned pos, isl_int value)
5324 isl_assert(bmap->ctx, pos < isl_basic_map_dim(bmap, type), goto error);
5325 return isl_basic_map_fix_pos(bmap,
5326 isl_basic_map_offset(bmap, type) + pos, value);
5328 isl_basic_map_free(bmap);
5332 /* Fix the value of the variable at position "pos" of type "type" of "bmap"
5333 * to be equal to "v".
5335 __isl_give isl_basic_map *isl_basic_map_fix_val(__isl_take isl_basic_map *bmap,
5336 enum isl_dim_type type, unsigned pos, __isl_take isl_val *v)
5340 if (!isl_val_is_int(v))
5341 isl_die(isl_basic_map_get_ctx(bmap), isl_error_invalid,
5342 "expecting integer value", goto error);
5343 if (pos >= isl_basic_map_dim(bmap, type))
5344 isl_die(isl_basic_map_get_ctx(bmap), isl_error_invalid,
5345 "index out of bounds", goto error);
5346 pos += isl_basic_map_offset(bmap, type);
5347 bmap = isl_basic_map_fix_pos(bmap, pos, v->n);
5351 isl_basic_map_free(bmap);
5356 /* Fix the value of the variable at position "pos" of type "type" of "bset"
5357 * to be equal to "v".
5359 __isl_give isl_basic_set *isl_basic_set_fix_val(__isl_take isl_basic_set *bset,
5360 enum isl_dim_type type, unsigned pos, __isl_take isl_val *v)
5362 return isl_basic_map_fix_val(bset, type, pos, v);
5365 struct isl_basic_set *isl_basic_set_fix_si(struct isl_basic_set *bset,
5366 enum isl_dim_type type, unsigned pos, int value)
5368 return (struct isl_basic_set *)
5369 isl_basic_map_fix_si((struct isl_basic_map *)bset,
5373 __isl_give isl_basic_set *isl_basic_set_fix(__isl_take isl_basic_set *bset,
5374 enum isl_dim_type type, unsigned pos, isl_int value)
5376 return (struct isl_basic_set *)
5377 isl_basic_map_fix((struct isl_basic_map *)bset,
5381 struct isl_basic_map *isl_basic_map_fix_input_si(struct isl_basic_map *bmap,
5382 unsigned input, int value)
5384 return isl_basic_map_fix_si(bmap, isl_dim_in, input, value);
5387 struct isl_basic_set *isl_basic_set_fix_dim_si(struct isl_basic_set *bset,
5388 unsigned dim, int value)
5390 return (struct isl_basic_set *)
5391 isl_basic_map_fix_si((struct isl_basic_map *)bset,
5392 isl_dim_set, dim, value);
5395 static int remove_if_empty(__isl_keep isl_map *map, int i)
5397 int empty = isl_basic_map_plain_is_empty(map->p[i]);
5404 isl_basic_map_free(map->p[i]);
5405 if (i != map->n - 1) {
5406 ISL_F_CLR(map, ISL_MAP_NORMALIZED);
5407 map->p[i] = map->p[map->n - 1];
5414 /* Perform "fn" on each basic map of "map", where we may not be holding
5415 * the only reference to "map".
5416 * In particular, "fn" should be a semantics preserving operation
5417 * that we want to apply to all copies of "map". We therefore need
5418 * to be careful not to modify "map" in a way that breaks "map"
5419 * in case anything goes wrong.
5421 __isl_give isl_map *isl_map_inline_foreach_basic_map(__isl_take isl_map *map,
5422 __isl_give isl_basic_map *(*fn)(__isl_take isl_basic_map *bmap))
5424 struct isl_basic_map *bmap;
5430 for (i = map->n - 1; i >= 0; --i) {
5431 bmap = isl_basic_map_copy(map->p[i]);
5435 isl_basic_map_free(map->p[i]);
5437 if (remove_if_empty(map, i) < 0)
5447 struct isl_map *isl_map_fix_si(struct isl_map *map,
5448 enum isl_dim_type type, unsigned pos, int value)
5452 map = isl_map_cow(map);
5456 isl_assert(map->ctx, pos < isl_map_dim(map, type), goto error);
5457 for (i = map->n - 1; i >= 0; --i) {
5458 map->p[i] = isl_basic_map_fix_si(map->p[i], type, pos, value);
5459 if (remove_if_empty(map, i) < 0)
5462 ISL_F_CLR(map, ISL_MAP_NORMALIZED);
5469 __isl_give isl_set *isl_set_fix_si(__isl_take isl_set *set,
5470 enum isl_dim_type type, unsigned pos, int value)
5472 return (struct isl_set *)
5473 isl_map_fix_si((struct isl_map *)set, type, pos, value);
5476 __isl_give isl_map *isl_map_fix(__isl_take isl_map *map,
5477 enum isl_dim_type type, unsigned pos, isl_int value)
5481 map = isl_map_cow(map);
5485 isl_assert(map->ctx, pos < isl_map_dim(map, type), goto error);
5486 for (i = 0; i < map->n; ++i) {
5487 map->p[i] = isl_basic_map_fix(map->p[i], type, pos, value);
5491 ISL_F_CLR(map, ISL_MAP_NORMALIZED);
5498 __isl_give isl_set *isl_set_fix(__isl_take isl_set *set,
5499 enum isl_dim_type type, unsigned pos, isl_int value)
5501 return (struct isl_set *)isl_map_fix((isl_map *)set, type, pos, value);
5504 /* Fix the value of the variable at position "pos" of type "type" of "map"
5505 * to be equal to "v".
5507 __isl_give isl_map *isl_map_fix_val(__isl_take isl_map *map,
5508 enum isl_dim_type type, unsigned pos, __isl_take isl_val *v)
5512 map = isl_map_cow(map);
5516 if (!isl_val_is_int(v))
5517 isl_die(isl_map_get_ctx(map), isl_error_invalid,
5518 "expecting integer value", goto error);
5519 if (pos >= isl_map_dim(map, type))
5520 isl_die(isl_map_get_ctx(map), isl_error_invalid,
5521 "index out of bounds", goto error);
5522 for (i = map->n - 1; i >= 0; --i) {
5523 map->p[i] = isl_basic_map_fix_val(map->p[i], type, pos,
5525 if (remove_if_empty(map, i) < 0)
5528 ISL_F_CLR(map, ISL_MAP_NORMALIZED);
5537 /* Fix the value of the variable at position "pos" of type "type" of "set"
5538 * to be equal to "v".
5540 __isl_give isl_set *isl_set_fix_val(__isl_take isl_set *set,
5541 enum isl_dim_type type, unsigned pos, __isl_take isl_val *v)
5543 return isl_map_fix_val(set, type, pos, v);
5546 struct isl_map *isl_map_fix_input_si(struct isl_map *map,
5547 unsigned input, int value)
5549 return isl_map_fix_si(map, isl_dim_in, input, value);
5552 struct isl_set *isl_set_fix_dim_si(struct isl_set *set, unsigned dim, int value)
5554 return (struct isl_set *)
5555 isl_map_fix_si((struct isl_map *)set, isl_dim_set, dim, value);
5558 static __isl_give isl_basic_map *basic_map_bound_si(
5559 __isl_take isl_basic_map *bmap,
5560 enum isl_dim_type type, unsigned pos, int value, int upper)
5566 isl_assert(bmap->ctx, pos < isl_basic_map_dim(bmap, type), goto error);
5567 pos += isl_basic_map_offset(bmap, type);
5568 bmap = isl_basic_map_cow(bmap);
5569 bmap = isl_basic_map_extend_constraints(bmap, 0, 1);
5570 j = isl_basic_map_alloc_inequality(bmap);
5573 isl_seq_clr(bmap->ineq[j], 1 + isl_basic_map_total_dim(bmap));
5575 isl_int_set_si(bmap->ineq[j][pos], -1);
5576 isl_int_set_si(bmap->ineq[j][0], value);
5578 isl_int_set_si(bmap->ineq[j][pos], 1);
5579 isl_int_set_si(bmap->ineq[j][0], -value);
5581 bmap = isl_basic_map_simplify(bmap);
5582 return isl_basic_map_finalize(bmap);
5584 isl_basic_map_free(bmap);
5588 __isl_give isl_basic_map *isl_basic_map_lower_bound_si(
5589 __isl_take isl_basic_map *bmap,
5590 enum isl_dim_type type, unsigned pos, int value)
5592 return basic_map_bound_si(bmap, type, pos, value, 0);
5595 /* Constrain the values of the given dimension to be no greater than "value".
5597 __isl_give isl_basic_map *isl_basic_map_upper_bound_si(
5598 __isl_take isl_basic_map *bmap,
5599 enum isl_dim_type type, unsigned pos, int value)
5601 return basic_map_bound_si(bmap, type, pos, value, 1);
5604 struct isl_basic_set *isl_basic_set_lower_bound_dim(struct isl_basic_set *bset,
5605 unsigned dim, isl_int value)
5609 bset = isl_basic_set_cow(bset);
5610 bset = isl_basic_set_extend_constraints(bset, 0, 1);
5611 j = isl_basic_set_alloc_inequality(bset);
5614 isl_seq_clr(bset->ineq[j], 1 + isl_basic_set_total_dim(bset));
5615 isl_int_set_si(bset->ineq[j][1 + isl_basic_set_n_param(bset) + dim], 1);
5616 isl_int_neg(bset->ineq[j][0], value);
5617 bset = isl_basic_set_simplify(bset);
5618 return isl_basic_set_finalize(bset);
5620 isl_basic_set_free(bset);
5624 static __isl_give isl_map *map_bound_si(__isl_take isl_map *map,
5625 enum isl_dim_type type, unsigned pos, int value, int upper)
5629 map = isl_map_cow(map);
5633 isl_assert(map->ctx, pos < isl_map_dim(map, type), goto error);
5634 for (i = 0; i < map->n; ++i) {
5635 map->p[i] = basic_map_bound_si(map->p[i],
5636 type, pos, value, upper);
5640 ISL_F_CLR(map, ISL_MAP_NORMALIZED);
5647 __isl_give isl_map *isl_map_lower_bound_si(__isl_take isl_map *map,
5648 enum isl_dim_type type, unsigned pos, int value)
5650 return map_bound_si(map, type, pos, value, 0);
5653 __isl_give isl_map *isl_map_upper_bound_si(__isl_take isl_map *map,
5654 enum isl_dim_type type, unsigned pos, int value)
5656 return map_bound_si(map, type, pos, value, 1);
5659 __isl_give isl_set *isl_set_lower_bound_si(__isl_take isl_set *set,
5660 enum isl_dim_type type, unsigned pos, int value)
5662 return (struct isl_set *)
5663 isl_map_lower_bound_si((struct isl_map *)set, type, pos, value);
5666 __isl_give isl_set *isl_set_upper_bound_si(__isl_take isl_set *set,
5667 enum isl_dim_type type, unsigned pos, int value)
5669 return isl_map_upper_bound_si(set, type, pos, value);
5672 /* Bound the given variable of "bmap" from below (or above is "upper"
5673 * is set) to "value".
5675 static __isl_give isl_basic_map *basic_map_bound(
5676 __isl_take isl_basic_map *bmap,
5677 enum isl_dim_type type, unsigned pos, isl_int value, int upper)
5683 if (pos >= isl_basic_map_dim(bmap, type))
5684 isl_die(bmap->ctx, isl_error_invalid,
5685 "index out of bounds", goto error);
5686 pos += isl_basic_map_offset(bmap, type);
5687 bmap = isl_basic_map_cow(bmap);
5688 bmap = isl_basic_map_extend_constraints(bmap, 0, 1);
5689 j = isl_basic_map_alloc_inequality(bmap);
5692 isl_seq_clr(bmap->ineq[j], 1 + isl_basic_map_total_dim(bmap));
5694 isl_int_set_si(bmap->ineq[j][pos], -1);
5695 isl_int_set(bmap->ineq[j][0], value);
5697 isl_int_set_si(bmap->ineq[j][pos], 1);
5698 isl_int_neg(bmap->ineq[j][0], value);
5700 bmap = isl_basic_map_simplify(bmap);
5701 return isl_basic_map_finalize(bmap);
5703 isl_basic_map_free(bmap);
5707 /* Bound the given variable of "map" from below (or above is "upper"
5708 * is set) to "value".
5710 static __isl_give isl_map *map_bound(__isl_take isl_map *map,
5711 enum isl_dim_type type, unsigned pos, isl_int value, int upper)
5715 map = isl_map_cow(map);
5719 if (pos >= isl_map_dim(map, type))
5720 isl_die(map->ctx, isl_error_invalid,
5721 "index out of bounds", goto error);
5722 for (i = map->n - 1; i >= 0; --i) {
5723 map->p[i] = basic_map_bound(map->p[i], type, pos, value, upper);
5724 if (remove_if_empty(map, i) < 0)
5727 ISL_F_CLR(map, ISL_MAP_NORMALIZED);
5734 __isl_give isl_map *isl_map_lower_bound(__isl_take isl_map *map,
5735 enum isl_dim_type type, unsigned pos, isl_int value)
5737 return map_bound(map, type, pos, value, 0);
5740 __isl_give isl_map *isl_map_upper_bound(__isl_take isl_map *map,
5741 enum isl_dim_type type, unsigned pos, isl_int value)
5743 return map_bound(map, type, pos, value, 1);
5746 __isl_give isl_set *isl_set_lower_bound(__isl_take isl_set *set,
5747 enum isl_dim_type type, unsigned pos, isl_int value)
5749 return isl_map_lower_bound(set, type, pos, value);
5752 __isl_give isl_set *isl_set_upper_bound(__isl_take isl_set *set,
5753 enum isl_dim_type type, unsigned pos, isl_int value)
5755 return isl_map_upper_bound(set, type, pos, value);
5758 /* Force the values of the variable at position "pos" of type "type" of "set"
5759 * to be no smaller than "value".
5761 __isl_give isl_set *isl_set_lower_bound_val(__isl_take isl_set *set,
5762 enum isl_dim_type type, unsigned pos, __isl_take isl_val *value)
5766 if (!isl_val_is_int(value))
5767 isl_die(isl_set_get_ctx(set), isl_error_invalid,
5768 "expecting integer value", goto error);
5769 set = isl_set_lower_bound(set, type, pos, value->n);
5770 isl_val_free(value);
5773 isl_val_free(value);
5778 /* Force the values of the variable at position "pos" of type "type" of "set"
5779 * to be no greater than "value".
5781 __isl_give isl_set *isl_set_upper_bound_val(__isl_take isl_set *set,
5782 enum isl_dim_type type, unsigned pos, __isl_take isl_val *value)
5786 if (!isl_val_is_int(value))
5787 isl_die(isl_set_get_ctx(set), isl_error_invalid,
5788 "expecting integer value", goto error);
5789 set = isl_set_upper_bound(set, type, pos, value->n);
5790 isl_val_free(value);
5793 isl_val_free(value);
5798 struct isl_set *isl_set_lower_bound_dim(struct isl_set *set, unsigned dim,
5803 set = isl_set_cow(set);
5807 isl_assert(set->ctx, dim < isl_set_n_dim(set), goto error);
5808 for (i = 0; i < set->n; ++i) {
5809 set->p[i] = isl_basic_set_lower_bound_dim(set->p[i], dim, value);
5819 struct isl_map *isl_map_reverse(struct isl_map *map)
5823 map = isl_map_cow(map);
5827 map->dim = isl_space_reverse(map->dim);
5830 for (i = 0; i < map->n; ++i) {
5831 map->p[i] = isl_basic_map_reverse(map->p[i]);
5835 ISL_F_CLR(map, ISL_MAP_NORMALIZED);
5842 static struct isl_map *isl_basic_map_partial_lexopt(
5843 struct isl_basic_map *bmap, struct isl_basic_set *dom,
5844 struct isl_set **empty, int max)
5848 if (bmap->ctx->opt->pip == ISL_PIP_PIP)
5849 return isl_pip_basic_map_lexopt(bmap, dom, empty, max);
5851 return isl_tab_basic_map_partial_lexopt(bmap, dom, empty, max);
5853 isl_basic_map_free(bmap);
5854 isl_basic_set_free(dom);
5860 struct isl_map *isl_basic_map_partial_lexmax(
5861 struct isl_basic_map *bmap, struct isl_basic_set *dom,
5862 struct isl_set **empty)
5864 return isl_basic_map_partial_lexopt(bmap, dom, empty, 1);
5867 struct isl_map *isl_basic_map_partial_lexmin(
5868 struct isl_basic_map *bmap, struct isl_basic_set *dom,
5869 struct isl_set **empty)
5871 return isl_basic_map_partial_lexopt(bmap, dom, empty, 0);
5874 struct isl_set *isl_basic_set_partial_lexmin(
5875 struct isl_basic_set *bset, struct isl_basic_set *dom,
5876 struct isl_set **empty)
5878 return (struct isl_set *)
5879 isl_basic_map_partial_lexmin((struct isl_basic_map *)bset,
5883 struct isl_set *isl_basic_set_partial_lexmax(
5884 struct isl_basic_set *bset, struct isl_basic_set *dom,
5885 struct isl_set **empty)
5887 return (struct isl_set *)
5888 isl_basic_map_partial_lexmax((struct isl_basic_map *)bset,
5892 __isl_give isl_pw_multi_aff *isl_basic_map_partial_lexmin_pw_multi_aff(
5893 __isl_take isl_basic_map *bmap, __isl_take isl_basic_set *dom,
5894 __isl_give isl_set **empty)
5896 return isl_basic_map_partial_lexopt_pw_multi_aff(bmap, dom, empty, 0);
5899 __isl_give isl_pw_multi_aff *isl_basic_map_partial_lexmax_pw_multi_aff(
5900 __isl_take isl_basic_map *bmap, __isl_take isl_basic_set *dom,
5901 __isl_give isl_set **empty)
5903 return isl_basic_map_partial_lexopt_pw_multi_aff(bmap, dom, empty, 1);
5906 __isl_give isl_pw_multi_aff *isl_basic_set_partial_lexmin_pw_multi_aff(
5907 __isl_take isl_basic_set *bset, __isl_take isl_basic_set *dom,
5908 __isl_give isl_set **empty)
5910 return isl_basic_map_partial_lexmin_pw_multi_aff(bset, dom, empty);
5913 __isl_give isl_pw_multi_aff *isl_basic_set_partial_lexmax_pw_multi_aff(
5914 __isl_take isl_basic_set *bset, __isl_take isl_basic_set *dom,
5915 __isl_give isl_set **empty)
5917 return isl_basic_map_partial_lexmax_pw_multi_aff(bset, dom, empty);
5920 __isl_give isl_pw_multi_aff *isl_basic_map_lexopt_pw_multi_aff(
5921 __isl_take isl_basic_map *bmap, int max)
5923 isl_basic_set *dom = NULL;
5924 isl_space *dom_space;
5928 dom_space = isl_space_domain(isl_space_copy(bmap->dim));
5929 dom = isl_basic_set_universe(dom_space);
5930 return isl_basic_map_partial_lexopt_pw_multi_aff(bmap, dom, NULL, max);
5932 isl_basic_map_free(bmap);
5936 __isl_give isl_pw_multi_aff *isl_basic_map_lexmin_pw_multi_aff(
5937 __isl_take isl_basic_map *bmap)
5939 return isl_basic_map_lexopt_pw_multi_aff(bmap, 0);
5943 #define TYPE isl_pw_multi_aff
5945 #define SUFFIX _pw_multi_aff
5947 #define EMPTY isl_pw_multi_aff_empty
5949 #define ADD isl_pw_multi_aff_union_add
5950 #include "isl_map_lexopt_templ.c"
5952 /* Given a map "map", compute the lexicographically minimal
5953 * (or maximal) image element for each domain element in dom,
5954 * in the form of an isl_pw_multi_aff.
5955 * Set *empty to those elements in dom that do not have an image element.
5957 * We first compute the lexicographically minimal or maximal element
5958 * in the first basic map. This results in a partial solution "res"
5959 * and a subset "todo" of dom that still need to be handled.
5960 * We then consider each of the remaining maps in "map" and successively
5961 * update both "res" and "todo".
5963 static __isl_give isl_pw_multi_aff *isl_map_partial_lexopt_aligned_pw_multi_aff(
5964 __isl_take isl_map *map, __isl_take isl_set *dom,
5965 __isl_give isl_set **empty, int max)
5968 isl_pw_multi_aff *res;
5974 if (isl_map_plain_is_empty(map)) {
5979 return isl_pw_multi_aff_from_map(map);
5982 res = basic_map_partial_lexopt_pw_multi_aff(
5983 isl_basic_map_copy(map->p[0]),
5984 isl_set_copy(dom), &todo, max);
5986 for (i = 1; i < map->n; ++i) {
5987 isl_pw_multi_aff *res_i;
5990 res_i = basic_map_partial_lexopt_pw_multi_aff(
5991 isl_basic_map_copy(map->p[i]),
5992 isl_set_copy(dom), &todo_i, max);
5995 res = isl_pw_multi_aff_union_lexmax(res, res_i);
5997 res = isl_pw_multi_aff_union_lexmin(res, res_i);
5999 todo = isl_set_intersect(todo, todo_i);
6020 #define TYPE isl_map
6024 #define EMPTY isl_map_empty
6026 #define ADD isl_map_union_disjoint
6027 #include "isl_map_lexopt_templ.c"
6029 /* Given a map "map", compute the lexicographically minimal
6030 * (or maximal) image element for each domain element in dom.
6031 * Set *empty to those elements in dom that do not have an image element.
6033 * We first compute the lexicographically minimal or maximal element
6034 * in the first basic map. This results in a partial solution "res"
6035 * and a subset "todo" of dom that still need to be handled.
6036 * We then consider each of the remaining maps in "map" and successively
6037 * update both "res" and "todo".
6039 * Let res^k and todo^k be the results after k steps and let i = k + 1.
6040 * Assume we are computing the lexicographical maximum.
6041 * We first compute the lexicographically maximal element in basic map i.
6042 * This results in a partial solution res_i and a subset todo_i.
6043 * Then we combine these results with those obtain for the first k basic maps
6044 * to obtain a result that is valid for the first k+1 basic maps.
6045 * In particular, the set where there is no solution is the set where
6046 * there is no solution for the first k basic maps and also no solution
6047 * for the ith basic map, i.e.,
6049 * todo^i = todo^k * todo_i
6051 * On dom(res^k) * dom(res_i), we need to pick the larger of the two
6052 * solutions, arbitrarily breaking ties in favor of res^k.
6053 * That is, when res^k(a) >= res_i(a), we pick res^k and
6054 * when res^k(a) < res_i(a), we pick res_i. (Here, ">=" and "<" denote
6055 * the lexicographic order.)
6056 * In practice, we compute
6058 * res^k * (res_i . "<=")
6062 * res_i * (res^k . "<")
6064 * Finally, we consider the symmetric difference of dom(res^k) and dom(res_i),
6065 * where only one of res^k and res_i provides a solution and we simply pick
6072 * Note that we only compute these intersections when dom(res^k) intersects
6073 * dom(res_i). Otherwise, the only effect of these intersections is to
6074 * potentially break up res^k and res_i into smaller pieces.
6075 * We want to avoid such splintering as much as possible.
6076 * In fact, an earlier implementation of this function would look for
6077 * better results in the domain of res^k and for extra results in todo^k,
6078 * but this would always result in a splintering according to todo^k,
6079 * even when the domain of basic map i is disjoint from the domains of
6080 * the previous basic maps.
6082 static __isl_give isl_map *isl_map_partial_lexopt_aligned(
6083 __isl_take isl_map *map, __isl_take isl_set *dom,
6084 __isl_give isl_set **empty, int max)
6087 struct isl_map *res;
6088 struct isl_set *todo;
6093 if (isl_map_plain_is_empty(map)) {
6101 res = basic_map_partial_lexopt(isl_basic_map_copy(map->p[0]),
6102 isl_set_copy(dom), &todo, max);
6104 for (i = 1; i < map->n; ++i) {
6108 isl_space *dim = isl_space_range(isl_map_get_space(res));
6110 res_i = basic_map_partial_lexopt(isl_basic_map_copy(map->p[i]),
6111 isl_set_copy(dom), &todo_i, max);
6114 lt = isl_map_lex_lt(isl_space_copy(dim));
6115 le = isl_map_lex_le(dim);
6117 lt = isl_map_lex_gt(isl_space_copy(dim));
6118 le = isl_map_lex_ge(dim);
6120 lt = isl_map_apply_range(isl_map_copy(res), lt);
6121 lt = isl_map_intersect(lt, isl_map_copy(res_i));
6122 le = isl_map_apply_range(isl_map_copy(res_i), le);
6123 le = isl_map_intersect(le, isl_map_copy(res));
6125 if (!isl_map_is_empty(lt) || !isl_map_is_empty(le)) {
6126 res = isl_map_intersect_domain(res,
6127 isl_set_copy(todo_i));
6128 res_i = isl_map_intersect_domain(res_i,
6129 isl_set_copy(todo));
6132 res = isl_map_union_disjoint(res, res_i);
6133 res = isl_map_union_disjoint(res, lt);
6134 res = isl_map_union_disjoint(res, le);
6136 todo = isl_set_intersect(todo, todo_i);
6156 __isl_give isl_map *isl_map_partial_lexmax(
6157 __isl_take isl_map *map, __isl_take isl_set *dom,
6158 __isl_give isl_set **empty)
6160 return isl_map_partial_lexopt(map, dom, empty, 1);
6163 __isl_give isl_map *isl_map_partial_lexmin(
6164 __isl_take isl_map *map, __isl_take isl_set *dom,
6165 __isl_give isl_set **empty)
6167 return isl_map_partial_lexopt(map, dom, empty, 0);
6170 __isl_give isl_set *isl_set_partial_lexmin(
6171 __isl_take isl_set *set, __isl_take isl_set *dom,
6172 __isl_give isl_set **empty)
6174 return (struct isl_set *)
6175 isl_map_partial_lexmin((struct isl_map *)set,
6179 __isl_give isl_set *isl_set_partial_lexmax(
6180 __isl_take isl_set *set, __isl_take isl_set *dom,
6181 __isl_give isl_set **empty)
6183 return (struct isl_set *)
6184 isl_map_partial_lexmax((struct isl_map *)set,
6188 /* Compute the lexicographic minimum (or maximum if "max" is set)
6189 * of "bmap" over its domain.
6191 * Since we are not interested in the part of the domain space where
6192 * there is no solution, we initialize the domain to those constraints
6193 * of "bmap" that only involve the parameters and the input dimensions.
6194 * This relieves the parametric programming engine from detecting those
6195 * inequalities and transferring them to the context. More importantly,
6196 * it ensures that those inequalities are transferred first and not
6197 * intermixed with inequalities that actually split the domain.
6199 __isl_give isl_map *isl_basic_map_lexopt(__isl_take isl_basic_map *bmap, int max)
6203 isl_basic_map *copy;
6206 n_div = isl_basic_map_dim(bmap, isl_dim_div);
6207 n_out = isl_basic_map_dim(bmap, isl_dim_out);
6208 copy = isl_basic_map_copy(bmap);
6209 copy = isl_basic_map_drop_constraints_involving_dims(copy,
6210 isl_dim_div, 0, n_div);
6211 copy = isl_basic_map_drop_constraints_involving_dims(copy,
6212 isl_dim_out, 0, n_out);
6213 dom = isl_basic_map_domain(copy);
6214 return isl_basic_map_partial_lexopt(bmap, dom, NULL, max);
6217 __isl_give isl_map *isl_basic_map_lexmin(__isl_take isl_basic_map *bmap)
6219 return isl_basic_map_lexopt(bmap, 0);
6222 __isl_give isl_map *isl_basic_map_lexmax(__isl_take isl_basic_map *bmap)
6224 return isl_basic_map_lexopt(bmap, 1);
6227 __isl_give isl_set *isl_basic_set_lexmin(__isl_take isl_basic_set *bset)
6229 return (isl_set *)isl_basic_map_lexmin((isl_basic_map *)bset);
6232 __isl_give isl_set *isl_basic_set_lexmax(__isl_take isl_basic_set *bset)
6234 return (isl_set *)isl_basic_map_lexmax((isl_basic_map *)bset);
6237 /* Extract the first and only affine expression from list
6238 * and then add it to *pwaff with the given dom.
6239 * This domain is known to be disjoint from other domains
6240 * because of the way isl_basic_map_foreach_lexmax works.
6242 static int update_dim_opt(__isl_take isl_basic_set *dom,
6243 __isl_take isl_aff_list *list, void *user)
6245 isl_ctx *ctx = isl_basic_set_get_ctx(dom);
6247 isl_pw_aff **pwaff = user;
6248 isl_pw_aff *pwaff_i;
6252 if (isl_aff_list_n_aff(list) != 1)
6253 isl_die(ctx, isl_error_internal,
6254 "expecting single element list", goto error);
6256 aff = isl_aff_list_get_aff(list, 0);
6257 pwaff_i = isl_pw_aff_alloc(isl_set_from_basic_set(dom), aff);
6259 *pwaff = isl_pw_aff_add_disjoint(*pwaff, pwaff_i);
6261 isl_aff_list_free(list);
6265 isl_basic_set_free(dom);
6266 isl_aff_list_free(list);
6270 /* Given a basic map with one output dimension, compute the minimum or
6271 * maximum of that dimension as an isl_pw_aff.
6273 * The isl_pw_aff is constructed by having isl_basic_map_foreach_lexopt
6274 * call update_dim_opt on each leaf of the result.
6276 static __isl_give isl_pw_aff *basic_map_dim_opt(__isl_keep isl_basic_map *bmap,
6279 isl_space *dim = isl_basic_map_get_space(bmap);
6283 dim = isl_space_from_domain(isl_space_domain(dim));
6284 dim = isl_space_add_dims(dim, isl_dim_out, 1);
6285 pwaff = isl_pw_aff_empty(dim);
6287 r = isl_basic_map_foreach_lexopt(bmap, max, &update_dim_opt, &pwaff);
6289 return isl_pw_aff_free(pwaff);
6294 /* Compute the minimum or maximum of the given output dimension
6295 * as a function of the parameters and the input dimensions,
6296 * but independently of the other output dimensions.
6298 * We first project out the other output dimension and then compute
6299 * the "lexicographic" maximum in each basic map, combining the results
6300 * using isl_pw_aff_union_max.
6302 static __isl_give isl_pw_aff *map_dim_opt(__isl_take isl_map *map, int pos,
6309 n_out = isl_map_dim(map, isl_dim_out);
6310 map = isl_map_project_out(map, isl_dim_out, pos + 1, n_out - (pos + 1));
6311 map = isl_map_project_out(map, isl_dim_out, 0, pos);
6316 isl_space *dim = isl_map_get_space(map);
6317 dim = isl_space_domain(isl_space_from_range(dim));
6319 return isl_pw_aff_empty(dim);
6322 pwaff = basic_map_dim_opt(map->p[0], max);
6323 for (i = 1; i < map->n; ++i) {
6324 isl_pw_aff *pwaff_i;
6326 pwaff_i = basic_map_dim_opt(map->p[i], max);
6327 pwaff = isl_pw_aff_union_opt(pwaff, pwaff_i, max);
6335 /* Compute the maximum of the given output dimension as a function of the
6336 * parameters and input dimensions, but independently of
6337 * the other output dimensions.
6339 __isl_give isl_pw_aff *isl_map_dim_max(__isl_take isl_map *map, int pos)
6341 return map_dim_opt(map, pos, 1);
6344 /* Compute the minimum or maximum of the given set dimension
6345 * as a function of the parameters,
6346 * but independently of the other set dimensions.
6348 static __isl_give isl_pw_aff *set_dim_opt(__isl_take isl_set *set, int pos,
6351 return map_dim_opt(set, pos, max);
6354 /* Compute the maximum of the given set dimension as a function of the
6355 * parameters, but independently of the other set dimensions.
6357 __isl_give isl_pw_aff *isl_set_dim_max(__isl_take isl_set *set, int pos)
6359 return set_dim_opt(set, pos, 1);
6362 /* Compute the minimum of the given set dimension as a function of the
6363 * parameters, but independently of the other set dimensions.
6365 __isl_give isl_pw_aff *isl_set_dim_min(__isl_take isl_set *set, int pos)
6367 return set_dim_opt(set, pos, 0);
6370 /* Apply a preimage specified by "mat" on the parameters of "bset".
6371 * bset is assumed to have only parameters and divs.
6373 static struct isl_basic_set *basic_set_parameter_preimage(
6374 struct isl_basic_set *bset, struct isl_mat *mat)
6381 bset->dim = isl_space_cow(bset->dim);
6385 nparam = isl_basic_set_dim(bset, isl_dim_param);
6387 isl_assert(bset->ctx, mat->n_row == 1 + nparam, goto error);
6389 bset->dim->nparam = 0;
6390 bset->dim->n_out = nparam;
6391 bset = isl_basic_set_preimage(bset, mat);
6393 bset->dim->nparam = bset->dim->n_out;
6394 bset->dim->n_out = 0;
6399 isl_basic_set_free(bset);
6403 /* Apply a preimage specified by "mat" on the parameters of "set".
6404 * set is assumed to have only parameters and divs.
6406 static struct isl_set *set_parameter_preimage(
6407 struct isl_set *set, struct isl_mat *mat)
6409 isl_space *dim = NULL;
6415 dim = isl_space_copy(set->dim);
6416 dim = isl_space_cow(dim);
6420 nparam = isl_set_dim(set, isl_dim_param);
6422 isl_assert(set->ctx, mat->n_row == 1 + nparam, goto error);
6425 dim->n_out = nparam;
6426 isl_set_reset_space(set, dim);
6427 set = isl_set_preimage(set, mat);
6430 dim = isl_space_copy(set->dim);
6431 dim = isl_space_cow(dim);
6434 dim->nparam = dim->n_out;
6436 isl_set_reset_space(set, dim);
6439 isl_space_free(dim);
6446 /* Intersect the basic set "bset" with the affine space specified by the
6447 * equalities in "eq".
6449 static struct isl_basic_set *basic_set_append_equalities(
6450 struct isl_basic_set *bset, struct isl_mat *eq)
6458 bset = isl_basic_set_extend_space(bset, isl_space_copy(bset->dim), 0,
6463 len = 1 + isl_space_dim(bset->dim, isl_dim_all) + bset->extra;
6464 for (i = 0; i < eq->n_row; ++i) {
6465 k = isl_basic_set_alloc_equality(bset);
6468 isl_seq_cpy(bset->eq[k], eq->row[i], eq->n_col);
6469 isl_seq_clr(bset->eq[k] + eq->n_col, len - eq->n_col);
6473 bset = isl_basic_set_gauss(bset, NULL);
6474 bset = isl_basic_set_finalize(bset);
6479 isl_basic_set_free(bset);
6483 /* Intersect the set "set" with the affine space specified by the
6484 * equalities in "eq".
6486 static struct isl_set *set_append_equalities(struct isl_set *set,
6494 for (i = 0; i < set->n; ++i) {
6495 set->p[i] = basic_set_append_equalities(set->p[i],
6508 /* Given a basic set "bset" that only involves parameters and existentially
6509 * quantified variables, return the index of the first equality
6510 * that only involves parameters. If there is no such equality then
6511 * return bset->n_eq.
6513 * This function assumes that isl_basic_set_gauss has been called on "bset".
6515 static int first_parameter_equality(__isl_keep isl_basic_set *bset)
6518 unsigned nparam, n_div;
6523 nparam = isl_basic_set_dim(bset, isl_dim_param);
6524 n_div = isl_basic_set_dim(bset, isl_dim_div);
6526 for (i = 0, j = n_div - 1; i < bset->n_eq && j >= 0; --j) {
6527 if (!isl_int_is_zero(bset->eq[i][1 + nparam + j]))
6534 /* Compute an explicit representation for the existentially quantified
6535 * variables in "bset" by computing the "minimal value" of the set
6536 * variables. Since there are no set variables, the computation of
6537 * the minimal value essentially computes an explicit representation
6538 * of the non-empty part(s) of "bset".
6540 * The input only involves parameters and existentially quantified variables.
6541 * All equalities among parameters have been removed.
6543 * Since the existentially quantified variables in the result are in general
6544 * going to be different from those in the input, we first replace
6545 * them by the minimal number of variables based on their equalities.
6546 * This should simplify the parametric integer programming.
6548 static __isl_give isl_set *base_compute_divs(__isl_take isl_basic_set *bset)
6550 isl_morph *morph1, *morph2;
6556 if (bset->n_eq == 0)
6557 return isl_basic_set_lexmin(bset);
6559 morph1 = isl_basic_set_parameter_compression(bset);
6560 bset = isl_morph_basic_set(isl_morph_copy(morph1), bset);
6561 bset = isl_basic_set_lift(bset);
6562 morph2 = isl_basic_set_variable_compression(bset, isl_dim_set);
6563 bset = isl_morph_basic_set(morph2, bset);
6564 n = isl_basic_set_dim(bset, isl_dim_set);
6565 bset = isl_basic_set_project_out(bset, isl_dim_set, 0, n);
6567 set = isl_basic_set_lexmin(bset);
6569 set = isl_morph_set(isl_morph_inverse(morph1), set);
6574 /* Project the given basic set onto its parameter domain, possibly introducing
6575 * new, explicit, existential variables in the constraints.
6576 * The input has parameters and (possibly implicit) existential variables.
6577 * The output has the same parameters, but only
6578 * explicit existentially quantified variables.
6580 * The actual projection is performed by pip, but pip doesn't seem
6581 * to like equalities very much, so we first remove the equalities
6582 * among the parameters by performing a variable compression on
6583 * the parameters. Afterward, an inverse transformation is performed
6584 * and the equalities among the parameters are inserted back in.
6586 * The variable compression on the parameters may uncover additional
6587 * equalities that were only implicit before. We therefore check
6588 * if there are any new parameter equalities in the result and
6589 * if so recurse. The removal of parameter equalities is required
6590 * for the parameter compression performed by base_compute_divs.
6592 static struct isl_set *parameter_compute_divs(struct isl_basic_set *bset)
6596 struct isl_mat *T, *T2;
6597 struct isl_set *set;
6600 bset = isl_basic_set_cow(bset);
6604 if (bset->n_eq == 0)
6605 return base_compute_divs(bset);
6607 bset = isl_basic_set_gauss(bset, NULL);
6610 if (isl_basic_set_plain_is_empty(bset))
6611 return isl_set_from_basic_set(bset);
6613 i = first_parameter_equality(bset);
6614 if (i == bset->n_eq)
6615 return base_compute_divs(bset);
6617 nparam = isl_basic_set_dim(bset, isl_dim_param);
6618 eq = isl_mat_sub_alloc6(bset->ctx, bset->eq, i, bset->n_eq - i,
6620 eq = isl_mat_cow(eq);
6621 T = isl_mat_variable_compression(isl_mat_copy(eq), &T2);
6622 if (T && T->n_col == 0) {
6626 bset = isl_basic_set_set_to_empty(bset);
6627 return isl_set_from_basic_set(bset);
6629 bset = basic_set_parameter_preimage(bset, T);
6631 i = first_parameter_equality(bset);
6634 else if (i == bset->n_eq)
6635 set = base_compute_divs(bset);
6637 set = parameter_compute_divs(bset);
6638 set = set_parameter_preimage(set, T2);
6639 set = set_append_equalities(set, eq);
6643 /* Insert the divs from "ls" before those of "bmap".
6645 * The number of columns is not changed, which means that the last
6646 * dimensions of "bmap" are being reintepreted as the divs from "ls".
6647 * The caller is responsible for removing the same number of dimensions
6648 * from the space of "bmap".
6650 static __isl_give isl_basic_map *insert_divs_from_local_space(
6651 __isl_take isl_basic_map *bmap, __isl_keep isl_local_space *ls)
6657 n_div = isl_local_space_dim(ls, isl_dim_div);
6661 old_n_div = bmap->n_div;
6662 bmap = insert_div_rows(bmap, n_div);
6666 for (i = 0; i < n_div; ++i) {
6667 isl_seq_cpy(bmap->div[i], ls->div->row[i], ls->div->n_col);
6668 isl_seq_clr(bmap->div[i] + ls->div->n_col, old_n_div);
6674 /* Replace the space of "bmap" by the space and divs of "ls".
6676 * If "ls" has any divs, then we simplify the result since we may
6677 * have discovered some additional equalities that could simplify
6678 * the div expressions.
6680 static __isl_give isl_basic_map *basic_replace_space_by_local_space(
6681 __isl_take isl_basic_map *bmap, __isl_take isl_local_space *ls)
6685 bmap = isl_basic_map_cow(bmap);
6689 n_div = isl_local_space_dim(ls, isl_dim_div);
6690 bmap = insert_divs_from_local_space(bmap, ls);
6694 isl_space_free(bmap->dim);
6695 bmap->dim = isl_local_space_get_space(ls);
6699 isl_local_space_free(ls);
6701 bmap = isl_basic_map_simplify(bmap);
6702 bmap = isl_basic_map_finalize(bmap);
6705 isl_basic_map_free(bmap);
6706 isl_local_space_free(ls);
6710 /* Replace the space of "map" by the space and divs of "ls".
6712 static __isl_give isl_map *replace_space_by_local_space(__isl_take isl_map *map,
6713 __isl_take isl_local_space *ls)
6717 map = isl_map_cow(map);
6721 for (i = 0; i < map->n; ++i) {
6722 map->p[i] = basic_replace_space_by_local_space(map->p[i],
6723 isl_local_space_copy(ls));
6727 isl_space_free(map->dim);
6728 map->dim = isl_local_space_get_space(ls);
6732 isl_local_space_free(ls);
6735 isl_local_space_free(ls);
6740 /* Compute an explicit representation for the existentially
6741 * quantified variables for which do not know any explicit representation yet.
6743 * We first sort the existentially quantified variables so that the
6744 * existentially quantified variables for which we already have an explicit
6745 * representation are placed before those for which we do not.
6746 * The input dimensions, the output dimensions and the existentially
6747 * quantified variables for which we already have an explicit
6748 * representation are then turned into parameters.
6749 * compute_divs returns a map with the same parameters and
6750 * no input or output dimensions and the dimension specification
6751 * is reset to that of the input, including the existentially quantified
6752 * variables for which we already had an explicit representation.
6754 static struct isl_map *compute_divs(struct isl_basic_map *bmap)
6756 struct isl_basic_set *bset;
6757 struct isl_set *set;
6758 struct isl_map *map;
6760 isl_local_space *ls;
6767 bmap = isl_basic_map_sort_divs(bmap);
6768 bmap = isl_basic_map_cow(bmap);
6772 for (n_known = 0; n_known < bmap->n_div; ++n_known)
6773 if (isl_int_is_zero(bmap->div[n_known][0]))
6776 nparam = isl_basic_map_dim(bmap, isl_dim_param);
6777 n_in = isl_basic_map_dim(bmap, isl_dim_in);
6778 n_out = isl_basic_map_dim(bmap, isl_dim_out);
6779 dim = isl_space_set_alloc(bmap->ctx,
6780 nparam + n_in + n_out + n_known, 0);
6784 ls = isl_basic_map_get_local_space(bmap);
6785 ls = isl_local_space_drop_dims(ls, isl_dim_div,
6786 n_known, bmap->n_div - n_known);
6788 for (i = n_known; i < bmap->n_div; ++i)
6789 swap_div(bmap, i - n_known, i);
6790 bmap->n_div -= n_known;
6791 bmap->extra -= n_known;
6793 bmap = isl_basic_map_reset_space(bmap, dim);
6794 bset = (struct isl_basic_set *)bmap;
6796 set = parameter_compute_divs(bset);
6797 map = (struct isl_map *)set;
6798 map = replace_space_by_local_space(map, ls);
6802 isl_basic_map_free(bmap);
6806 int isl_basic_map_divs_known(__isl_keep isl_basic_map *bmap)
6814 off = isl_space_dim(bmap->dim, isl_dim_all);
6815 for (i = 0; i < bmap->n_div; ++i) {
6816 if (isl_int_is_zero(bmap->div[i][0]))
6818 isl_assert(bmap->ctx, isl_int_is_zero(bmap->div[i][1+1+off+i]),
6824 static int map_divs_known(__isl_keep isl_map *map)
6831 for (i = 0; i < map->n; ++i) {
6832 int known = isl_basic_map_divs_known(map->p[i]);
6840 /* If bmap contains any unknown divs, then compute explicit
6841 * expressions for them. However, this computation may be
6842 * quite expensive, so first try to remove divs that aren't
6845 struct isl_map *isl_basic_map_compute_divs(struct isl_basic_map *bmap)
6848 struct isl_map *map;
6850 known = isl_basic_map_divs_known(bmap);
6854 return isl_map_from_basic_map(bmap);
6856 bmap = isl_basic_map_drop_redundant_divs(bmap);
6858 known = isl_basic_map_divs_known(bmap);
6862 return isl_map_from_basic_map(bmap);
6864 map = compute_divs(bmap);
6867 isl_basic_map_free(bmap);
6871 struct isl_map *isl_map_compute_divs(struct isl_map *map)
6875 struct isl_map *res;
6882 known = map_divs_known(map);
6890 res = isl_basic_map_compute_divs(isl_basic_map_copy(map->p[0]));
6891 for (i = 1 ; i < map->n; ++i) {
6893 r2 = isl_basic_map_compute_divs(isl_basic_map_copy(map->p[i]));
6894 if (ISL_F_ISSET(map, ISL_MAP_DISJOINT))
6895 res = isl_map_union_disjoint(res, r2);
6897 res = isl_map_union(res, r2);
6904 struct isl_set *isl_basic_set_compute_divs(struct isl_basic_set *bset)
6906 return (struct isl_set *)
6907 isl_basic_map_compute_divs((struct isl_basic_map *)bset);
6910 struct isl_set *isl_set_compute_divs(struct isl_set *set)
6912 return (struct isl_set *)
6913 isl_map_compute_divs((struct isl_map *)set);
6916 struct isl_set *isl_map_domain(struct isl_map *map)
6919 struct isl_set *set;
6924 map = isl_map_cow(map);
6928 set = (struct isl_set *)map;
6929 set->dim = isl_space_domain(set->dim);
6932 for (i = 0; i < map->n; ++i) {
6933 set->p[i] = isl_basic_map_domain(map->p[i]);
6937 ISL_F_CLR(set, ISL_MAP_DISJOINT);
6938 ISL_F_CLR(set, ISL_SET_NORMALIZED);
6945 /* Return the union of "map1" and "map2", where we assume for now that
6946 * "map1" and "map2" are disjoint. Note that the basic maps inside
6947 * "map1" or "map2" may not be disjoint from each other.
6948 * Also note that this function is also called from isl_map_union,
6949 * which takes care of handling the situation where "map1" and "map2"
6950 * may not be disjoint.
6952 * If one of the inputs is empty, we can simply return the other input.
6953 * Similarly, if one of the inputs is universal, then it is equal to the union.
6955 static __isl_give isl_map *map_union_disjoint(__isl_take isl_map *map1,
6956 __isl_take isl_map *map2)
6960 struct isl_map *map = NULL;
6975 is_universe = isl_map_plain_is_universe(map1);
6976 if (is_universe < 0)
6983 is_universe = isl_map_plain_is_universe(map2);
6984 if (is_universe < 0)
6991 isl_assert(map1->ctx, isl_space_is_equal(map1->dim, map2->dim), goto error);
6993 if (ISL_F_ISSET(map1, ISL_MAP_DISJOINT) &&
6994 ISL_F_ISSET(map2, ISL_MAP_DISJOINT))
6995 ISL_FL_SET(flags, ISL_MAP_DISJOINT);
6997 map = isl_map_alloc_space(isl_space_copy(map1->dim),
6998 map1->n + map2->n, flags);
7001 for (i = 0; i < map1->n; ++i) {
7002 map = isl_map_add_basic_map(map,
7003 isl_basic_map_copy(map1->p[i]));
7007 for (i = 0; i < map2->n; ++i) {
7008 map = isl_map_add_basic_map(map,
7009 isl_basic_map_copy(map2->p[i]));
7023 __isl_give isl_map *isl_map_union_disjoint(__isl_take isl_map *map1,
7024 __isl_take isl_map *map2)
7026 return isl_map_align_params_map_map_and(map1, map2, &map_union_disjoint);
7029 struct isl_map *isl_map_union(struct isl_map *map1, struct isl_map *map2)
7031 map1 = isl_map_union_disjoint(map1, map2);
7035 ISL_F_CLR(map1, ISL_MAP_DISJOINT);
7039 struct isl_set *isl_set_union_disjoint(
7040 struct isl_set *set1, struct isl_set *set2)
7042 return (struct isl_set *)
7043 isl_map_union_disjoint(
7044 (struct isl_map *)set1, (struct isl_map *)set2);
7047 struct isl_set *isl_set_union(struct isl_set *set1, struct isl_set *set2)
7049 return (struct isl_set *)
7050 isl_map_union((struct isl_map *)set1, (struct isl_map *)set2);
7053 /* Apply "fn" to pairs of elements from "map" and "set" and collect
7056 * "map" and "set" are assumed to be compatible and non-NULL.
7058 static __isl_give isl_map *map_intersect_set(__isl_take isl_map *map,
7059 __isl_take isl_set *set,
7060 __isl_give isl_basic_map *fn(__isl_take isl_basic_map *bmap,
7061 __isl_take isl_basic_set *bset))
7064 struct isl_map *result;
7067 if (isl_set_plain_is_universe(set)) {
7072 if (ISL_F_ISSET(map, ISL_MAP_DISJOINT) &&
7073 ISL_F_ISSET(set, ISL_MAP_DISJOINT))
7074 ISL_FL_SET(flags, ISL_MAP_DISJOINT);
7076 result = isl_map_alloc_space(isl_space_copy(map->dim),
7077 map->n * set->n, flags);
7078 for (i = 0; result && i < map->n; ++i)
7079 for (j = 0; j < set->n; ++j) {
7080 result = isl_map_add_basic_map(result,
7081 fn(isl_basic_map_copy(map->p[i]),
7082 isl_basic_set_copy(set->p[j])));
7092 static __isl_give isl_map *map_intersect_range(__isl_take isl_map *map,
7093 __isl_take isl_set *set)
7098 if (!isl_map_compatible_range(map, set))
7099 isl_die(set->ctx, isl_error_invalid,
7100 "incompatible spaces", goto error);
7102 return map_intersect_set(map, set, &isl_basic_map_intersect_range);
7109 __isl_give isl_map *isl_map_intersect_range(__isl_take isl_map *map,
7110 __isl_take isl_set *set)
7112 return isl_map_align_params_map_map_and(map, set, &map_intersect_range);
7115 static __isl_give isl_map *map_intersect_domain(__isl_take isl_map *map,
7116 __isl_take isl_set *set)
7121 if (!isl_map_compatible_domain(map, set))
7122 isl_die(set->ctx, isl_error_invalid,
7123 "incompatible spaces", goto error);
7125 return map_intersect_set(map, set, &isl_basic_map_intersect_domain);
7132 __isl_give isl_map *isl_map_intersect_domain(__isl_take isl_map *map,
7133 __isl_take isl_set *set)
7135 return isl_map_align_params_map_map_and(map, set,
7136 &map_intersect_domain);
7139 static __isl_give isl_map *map_apply_domain(__isl_take isl_map *map1,
7140 __isl_take isl_map *map2)
7144 map1 = isl_map_reverse(map1);
7145 map1 = isl_map_apply_range(map1, map2);
7146 return isl_map_reverse(map1);
7153 __isl_give isl_map *isl_map_apply_domain(__isl_take isl_map *map1,
7154 __isl_take isl_map *map2)
7156 return isl_map_align_params_map_map_and(map1, map2, &map_apply_domain);
7159 static __isl_give isl_map *map_apply_range(__isl_take isl_map *map1,
7160 __isl_take isl_map *map2)
7162 isl_space *dim_result;
7163 struct isl_map *result;
7169 dim_result = isl_space_join(isl_space_copy(map1->dim),
7170 isl_space_copy(map2->dim));
7172 result = isl_map_alloc_space(dim_result, map1->n * map2->n, 0);
7175 for (i = 0; i < map1->n; ++i)
7176 for (j = 0; j < map2->n; ++j) {
7177 result = isl_map_add_basic_map(result,
7178 isl_basic_map_apply_range(
7179 isl_basic_map_copy(map1->p[i]),
7180 isl_basic_map_copy(map2->p[j])));
7186 if (result && result->n <= 1)
7187 ISL_F_SET(result, ISL_MAP_DISJOINT);
7195 __isl_give isl_map *isl_map_apply_range(__isl_take isl_map *map1,
7196 __isl_take isl_map *map2)
7198 return isl_map_align_params_map_map_and(map1, map2, &map_apply_range);
7202 * returns range - domain
7204 struct isl_basic_set *isl_basic_map_deltas(struct isl_basic_map *bmap)
7206 isl_space *dims, *target_dim;
7207 struct isl_basic_set *bset;
7214 isl_assert(bmap->ctx, isl_space_tuple_match(bmap->dim, isl_dim_in,
7215 bmap->dim, isl_dim_out),
7217 target_dim = isl_space_domain(isl_basic_map_get_space(bmap));
7218 dim = isl_basic_map_n_in(bmap);
7219 nparam = isl_basic_map_n_param(bmap);
7220 bset = isl_basic_set_from_basic_map(bmap);
7221 bset = isl_basic_set_cow(bset);
7222 dims = isl_basic_set_get_space(bset);
7223 dims = isl_space_add_dims(dims, isl_dim_set, dim);
7224 bset = isl_basic_set_extend_space(bset, dims, 0, dim, 0);
7225 bset = isl_basic_set_swap_vars(bset, 2*dim);
7226 for (i = 0; i < dim; ++i) {
7227 int j = isl_basic_map_alloc_equality(
7228 (struct isl_basic_map *)bset);
7230 bset = isl_basic_set_free(bset);
7233 isl_seq_clr(bset->eq[j], 1 + isl_basic_set_total_dim(bset));
7234 isl_int_set_si(bset->eq[j][1+nparam+i], 1);
7235 isl_int_set_si(bset->eq[j][1+nparam+dim+i], 1);
7236 isl_int_set_si(bset->eq[j][1+nparam+2*dim+i], -1);
7238 bset = isl_basic_set_project_out(bset, isl_dim_set, dim, 2*dim);
7239 bset = isl_basic_set_reset_space(bset, target_dim);
7242 isl_basic_map_free(bmap);
7247 * returns range - domain
7249 __isl_give isl_set *isl_map_deltas(__isl_take isl_map *map)
7253 struct isl_set *result;
7258 isl_assert(map->ctx, isl_space_tuple_match(map->dim, isl_dim_in,
7259 map->dim, isl_dim_out),
7261 dim = isl_map_get_space(map);
7262 dim = isl_space_domain(dim);
7263 result = isl_set_alloc_space(dim, map->n, 0);
7266 for (i = 0; i < map->n; ++i)
7267 result = isl_set_add_basic_set(result,
7268 isl_basic_map_deltas(isl_basic_map_copy(map->p[i])));
7277 * returns [domain -> range] -> range - domain
7279 __isl_give isl_basic_map *isl_basic_map_deltas_map(
7280 __isl_take isl_basic_map *bmap)
7284 isl_basic_map *domain;
7288 if (!isl_space_tuple_match(bmap->dim, isl_dim_in, bmap->dim, isl_dim_out))
7289 isl_die(bmap->ctx, isl_error_invalid,
7290 "domain and range don't match", goto error);
7292 nparam = isl_basic_map_dim(bmap, isl_dim_param);
7293 n = isl_basic_map_dim(bmap, isl_dim_in);
7295 dim = isl_space_from_range(isl_space_domain(isl_basic_map_get_space(bmap)));
7296 domain = isl_basic_map_universe(dim);
7298 bmap = isl_basic_map_from_domain(isl_basic_map_wrap(bmap));
7299 bmap = isl_basic_map_apply_range(bmap, domain);
7300 bmap = isl_basic_map_extend_constraints(bmap, n, 0);
7302 total = isl_basic_map_total_dim(bmap);
7304 for (i = 0; i < n; ++i) {
7305 k = isl_basic_map_alloc_equality(bmap);
7308 isl_seq_clr(bmap->eq[k], 1 + total);
7309 isl_int_set_si(bmap->eq[k][1 + nparam + i], 1);
7310 isl_int_set_si(bmap->eq[k][1 + nparam + n + i], -1);
7311 isl_int_set_si(bmap->eq[k][1 + nparam + n + n + i], 1);
7314 bmap = isl_basic_map_gauss(bmap, NULL);
7315 return isl_basic_map_finalize(bmap);
7317 isl_basic_map_free(bmap);
7322 * returns [domain -> range] -> range - domain
7324 __isl_give isl_map *isl_map_deltas_map(__isl_take isl_map *map)
7327 isl_space *domain_dim;
7332 if (!isl_space_tuple_match(map->dim, isl_dim_in, map->dim, isl_dim_out))
7333 isl_die(map->ctx, isl_error_invalid,
7334 "domain and range don't match", goto error);
7336 map = isl_map_cow(map);
7340 domain_dim = isl_space_from_range(isl_space_domain(isl_map_get_space(map)));
7341 map->dim = isl_space_from_domain(isl_space_wrap(map->dim));
7342 map->dim = isl_space_join(map->dim, domain_dim);
7345 for (i = 0; i < map->n; ++i) {
7346 map->p[i] = isl_basic_map_deltas_map(map->p[i]);
7350 ISL_F_CLR(map, ISL_MAP_NORMALIZED);
7357 static __isl_give isl_basic_map *basic_map_identity(__isl_take isl_space *dims)
7359 struct isl_basic_map *bmap;
7367 nparam = dims->nparam;
7369 bmap = isl_basic_map_alloc_space(dims, 0, dim, 0);
7373 for (i = 0; i < dim; ++i) {
7374 int j = isl_basic_map_alloc_equality(bmap);
7377 isl_seq_clr(bmap->eq[j], 1 + isl_basic_map_total_dim(bmap));
7378 isl_int_set_si(bmap->eq[j][1+nparam+i], 1);
7379 isl_int_set_si(bmap->eq[j][1+nparam+dim+i], -1);
7381 return isl_basic_map_finalize(bmap);
7383 isl_basic_map_free(bmap);
7387 __isl_give isl_basic_map *isl_basic_map_identity(__isl_take isl_space *dim)
7391 if (dim->n_in != dim->n_out)
7392 isl_die(dim->ctx, isl_error_invalid,
7393 "number of input and output dimensions needs to be "
7394 "the same", goto error);
7395 return basic_map_identity(dim);
7397 isl_space_free(dim);
7401 struct isl_basic_map *isl_basic_map_identity_like(struct isl_basic_map *model)
7403 if (!model || !model->dim)
7405 return isl_basic_map_identity(isl_space_copy(model->dim));
7408 __isl_give isl_map *isl_map_identity(__isl_take isl_space *dim)
7410 return isl_map_from_basic_map(isl_basic_map_identity(dim));
7413 struct isl_map *isl_map_identity_like(struct isl_map *model)
7415 if (!model || !model->dim)
7417 return isl_map_identity(isl_space_copy(model->dim));
7420 struct isl_map *isl_map_identity_like_basic_map(struct isl_basic_map *model)
7422 if (!model || !model->dim)
7424 return isl_map_identity(isl_space_copy(model->dim));
7427 __isl_give isl_map *isl_set_identity(__isl_take isl_set *set)
7429 isl_space *dim = isl_set_get_space(set);
7431 id = isl_map_identity(isl_space_map_from_set(dim));
7432 return isl_map_intersect_range(id, set);
7435 /* Construct a basic set with all set dimensions having only non-negative
7438 __isl_give isl_basic_set *isl_basic_set_positive_orthant(
7439 __isl_take isl_space *space)
7444 struct isl_basic_set *bset;
7448 nparam = space->nparam;
7450 bset = isl_basic_set_alloc_space(space, 0, 0, dim);
7453 for (i = 0; i < dim; ++i) {
7454 int k = isl_basic_set_alloc_inequality(bset);
7457 isl_seq_clr(bset->ineq[k], 1 + isl_basic_set_total_dim(bset));
7458 isl_int_set_si(bset->ineq[k][1 + nparam + i], 1);
7462 isl_basic_set_free(bset);
7466 /* Construct the half-space x_pos >= 0.
7468 static __isl_give isl_basic_set *nonneg_halfspace(__isl_take isl_space *dim,
7472 isl_basic_set *nonneg;
7474 nonneg = isl_basic_set_alloc_space(dim, 0, 0, 1);
7475 k = isl_basic_set_alloc_inequality(nonneg);
7478 isl_seq_clr(nonneg->ineq[k], 1 + isl_basic_set_total_dim(nonneg));
7479 isl_int_set_si(nonneg->ineq[k][pos], 1);
7481 return isl_basic_set_finalize(nonneg);
7483 isl_basic_set_free(nonneg);
7487 /* Construct the half-space x_pos <= -1.
7489 static __isl_give isl_basic_set *neg_halfspace(__isl_take isl_space *dim, int pos)
7494 neg = isl_basic_set_alloc_space(dim, 0, 0, 1);
7495 k = isl_basic_set_alloc_inequality(neg);
7498 isl_seq_clr(neg->ineq[k], 1 + isl_basic_set_total_dim(neg));
7499 isl_int_set_si(neg->ineq[k][0], -1);
7500 isl_int_set_si(neg->ineq[k][pos], -1);
7502 return isl_basic_set_finalize(neg);
7504 isl_basic_set_free(neg);
7508 __isl_give isl_set *isl_set_split_dims(__isl_take isl_set *set,
7509 enum isl_dim_type type, unsigned first, unsigned n)
7512 isl_basic_set *nonneg;
7520 isl_assert(set->ctx, first + n <= isl_set_dim(set, type), goto error);
7522 for (i = 0; i < n; ++i) {
7523 nonneg = nonneg_halfspace(isl_set_get_space(set),
7524 pos(set->dim, type) + first + i);
7525 neg = neg_halfspace(isl_set_get_space(set),
7526 pos(set->dim, type) + first + i);
7528 set = isl_set_intersect(set, isl_basic_set_union(nonneg, neg));
7537 static int foreach_orthant(__isl_take isl_set *set, int *signs, int first,
7538 int len, int (*fn)(__isl_take isl_set *orthant, int *signs, void *user),
7545 if (isl_set_plain_is_empty(set)) {
7550 return fn(set, signs, user);
7553 half = isl_set_from_basic_set(nonneg_halfspace(isl_set_get_space(set),
7555 half = isl_set_intersect(half, isl_set_copy(set));
7556 if (foreach_orthant(half, signs, first + 1, len, fn, user) < 0)
7560 half = isl_set_from_basic_set(neg_halfspace(isl_set_get_space(set),
7562 half = isl_set_intersect(half, set);
7563 return foreach_orthant(half, signs, first + 1, len, fn, user);
7569 /* Call "fn" on the intersections of "set" with each of the orthants
7570 * (except for obviously empty intersections). The orthant is identified
7571 * by the signs array, with each entry having value 1 or -1 according
7572 * to the sign of the corresponding variable.
7574 int isl_set_foreach_orthant(__isl_keep isl_set *set,
7575 int (*fn)(__isl_take isl_set *orthant, int *signs, void *user),
7585 if (isl_set_plain_is_empty(set))
7588 nparam = isl_set_dim(set, isl_dim_param);
7589 nvar = isl_set_dim(set, isl_dim_set);
7591 signs = isl_alloc_array(set->ctx, int, nparam + nvar);
7593 r = foreach_orthant(isl_set_copy(set), signs, 0, nparam + nvar,
7601 int isl_set_is_equal(struct isl_set *set1, struct isl_set *set2)
7603 return isl_map_is_equal((struct isl_map *)set1, (struct isl_map *)set2);
7606 int isl_basic_map_is_subset(
7607 struct isl_basic_map *bmap1, struct isl_basic_map *bmap2)
7610 struct isl_map *map1;
7611 struct isl_map *map2;
7613 if (!bmap1 || !bmap2)
7616 map1 = isl_map_from_basic_map(isl_basic_map_copy(bmap1));
7617 map2 = isl_map_from_basic_map(isl_basic_map_copy(bmap2));
7619 is_subset = isl_map_is_subset(map1, map2);
7627 int isl_basic_set_is_subset(__isl_keep isl_basic_set *bset1,
7628 __isl_keep isl_basic_set *bset2)
7630 return isl_basic_map_is_subset(bset1, bset2);
7633 int isl_basic_map_is_equal(
7634 struct isl_basic_map *bmap1, struct isl_basic_map *bmap2)
7638 if (!bmap1 || !bmap2)
7640 is_subset = isl_basic_map_is_subset(bmap1, bmap2);
7643 is_subset = isl_basic_map_is_subset(bmap2, bmap1);
7647 int isl_basic_set_is_equal(
7648 struct isl_basic_set *bset1, struct isl_basic_set *bset2)
7650 return isl_basic_map_is_equal(
7651 (struct isl_basic_map *)bset1, (struct isl_basic_map *)bset2);
7654 int isl_map_is_empty(struct isl_map *map)
7661 for (i = 0; i < map->n; ++i) {
7662 is_empty = isl_basic_map_is_empty(map->p[i]);
7671 int isl_map_plain_is_empty(__isl_keep isl_map *map)
7673 return map ? map->n == 0 : -1;
7676 int isl_map_fast_is_empty(__isl_keep isl_map *map)
7678 return isl_map_plain_is_empty(map);
7681 int isl_set_plain_is_empty(struct isl_set *set)
7683 return set ? set->n == 0 : -1;
7686 int isl_set_fast_is_empty(__isl_keep isl_set *set)
7688 return isl_set_plain_is_empty(set);
7691 int isl_set_is_empty(struct isl_set *set)
7693 return isl_map_is_empty((struct isl_map *)set);
7696 int isl_map_has_equal_space(__isl_keep isl_map *map1, __isl_keep isl_map *map2)
7701 return isl_space_is_equal(map1->dim, map2->dim);
7704 int isl_set_has_equal_space(__isl_keep isl_set *set1, __isl_keep isl_set *set2)
7709 return isl_space_is_equal(set1->dim, set2->dim);
7712 static int map_is_equal(__isl_keep isl_map *map1, __isl_keep isl_map *map2)
7718 is_subset = isl_map_is_subset(map1, map2);
7721 is_subset = isl_map_is_subset(map2, map1);
7725 int isl_map_is_equal(__isl_keep isl_map *map1, __isl_keep isl_map *map2)
7727 return isl_map_align_params_map_map_and_test(map1, map2, &map_is_equal);
7730 int isl_basic_map_is_strict_subset(
7731 struct isl_basic_map *bmap1, struct isl_basic_map *bmap2)
7735 if (!bmap1 || !bmap2)
7737 is_subset = isl_basic_map_is_subset(bmap1, bmap2);
7740 is_subset = isl_basic_map_is_subset(bmap2, bmap1);
7741 if (is_subset == -1)
7746 int isl_map_is_strict_subset(struct isl_map *map1, struct isl_map *map2)
7752 is_subset = isl_map_is_subset(map1, map2);
7755 is_subset = isl_map_is_subset(map2, map1);
7756 if (is_subset == -1)
7761 int isl_set_is_strict_subset(__isl_keep isl_set *set1, __isl_keep isl_set *set2)
7763 return isl_map_is_strict_subset((isl_map *)set1, (isl_map *)set2);
7766 int isl_basic_map_is_universe(struct isl_basic_map *bmap)
7770 return bmap->n_eq == 0 && bmap->n_ineq == 0;
7773 int isl_basic_set_is_universe(struct isl_basic_set *bset)
7777 return bset->n_eq == 0 && bset->n_ineq == 0;
7780 int isl_map_plain_is_universe(__isl_keep isl_map *map)
7787 for (i = 0; i < map->n; ++i) {
7788 int r = isl_basic_map_is_universe(map->p[i]);
7796 int isl_set_plain_is_universe(__isl_keep isl_set *set)
7798 return isl_map_plain_is_universe((isl_map *) set);
7801 int isl_set_fast_is_universe(__isl_keep isl_set *set)
7803 return isl_set_plain_is_universe(set);
7806 int isl_basic_map_is_empty(struct isl_basic_map *bmap)
7808 struct isl_basic_set *bset = NULL;
7809 struct isl_vec *sample = NULL;
7816 if (ISL_F_ISSET(bmap, ISL_BASIC_MAP_EMPTY))
7819 if (isl_basic_map_is_universe(bmap))
7822 if (ISL_F_ISSET(bmap, ISL_BASIC_MAP_RATIONAL)) {
7823 struct isl_basic_map *copy = isl_basic_map_copy(bmap);
7824 copy = isl_basic_map_remove_redundancies(copy);
7825 empty = isl_basic_map_plain_is_empty(copy);
7826 isl_basic_map_free(copy);
7830 total = 1 + isl_basic_map_total_dim(bmap);
7831 if (bmap->sample && bmap->sample->size == total) {
7832 int contains = isl_basic_map_contains(bmap, bmap->sample);
7838 isl_vec_free(bmap->sample);
7839 bmap->sample = NULL;
7840 bset = isl_basic_map_underlying_set(isl_basic_map_copy(bmap));
7843 sample = isl_basic_set_sample_vec(bset);
7846 empty = sample->size == 0;
7847 isl_vec_free(bmap->sample);
7848 bmap->sample = sample;
7850 ISL_F_SET(bmap, ISL_BASIC_MAP_EMPTY);
7855 int isl_basic_map_plain_is_empty(__isl_keep isl_basic_map *bmap)
7859 return ISL_F_ISSET(bmap, ISL_BASIC_MAP_EMPTY);
7862 int isl_basic_map_fast_is_empty(__isl_keep isl_basic_map *bmap)
7864 return isl_basic_map_plain_is_empty(bmap);
7867 int isl_basic_set_plain_is_empty(__isl_keep isl_basic_set *bset)
7871 return ISL_F_ISSET(bset, ISL_BASIC_SET_EMPTY);
7874 int isl_basic_set_fast_is_empty(__isl_keep isl_basic_set *bset)
7876 return isl_basic_set_plain_is_empty(bset);
7879 int isl_basic_set_is_empty(struct isl_basic_set *bset)
7881 return isl_basic_map_is_empty((struct isl_basic_map *)bset);
7884 struct isl_map *isl_basic_map_union(
7885 struct isl_basic_map *bmap1, struct isl_basic_map *bmap2)
7887 struct isl_map *map;
7888 if (!bmap1 || !bmap2)
7891 isl_assert(bmap1->ctx, isl_space_is_equal(bmap1->dim, bmap2->dim), goto error);
7893 map = isl_map_alloc_space(isl_space_copy(bmap1->dim), 2, 0);
7896 map = isl_map_add_basic_map(map, bmap1);
7897 map = isl_map_add_basic_map(map, bmap2);
7900 isl_basic_map_free(bmap1);
7901 isl_basic_map_free(bmap2);
7905 struct isl_set *isl_basic_set_union(
7906 struct isl_basic_set *bset1, struct isl_basic_set *bset2)
7908 return (struct isl_set *)isl_basic_map_union(
7909 (struct isl_basic_map *)bset1,
7910 (struct isl_basic_map *)bset2);
7913 /* Order divs such that any div only depends on previous divs */
7914 struct isl_basic_map *isl_basic_map_order_divs(struct isl_basic_map *bmap)
7922 off = isl_space_dim(bmap->dim, isl_dim_all);
7924 for (i = 0; i < bmap->n_div; ++i) {
7926 if (isl_int_is_zero(bmap->div[i][0]))
7928 pos = isl_seq_first_non_zero(bmap->div[i]+1+1+off+i,
7932 isl_basic_map_swap_div(bmap, i, i + pos);
7938 struct isl_basic_set *isl_basic_set_order_divs(struct isl_basic_set *bset)
7940 return (struct isl_basic_set *)
7941 isl_basic_map_order_divs((struct isl_basic_map *)bset);
7944 __isl_give isl_map *isl_map_order_divs(__isl_take isl_map *map)
7951 for (i = 0; i < map->n; ++i) {
7952 map->p[i] = isl_basic_map_order_divs(map->p[i]);
7963 /* Apply the expansion computed by isl_merge_divs.
7964 * The expansion itself is given by "exp" while the resulting
7965 * list of divs is given by "div".
7967 __isl_give isl_basic_set *isl_basic_set_expand_divs(
7968 __isl_take isl_basic_set *bset, __isl_take isl_mat *div, int *exp)
7973 bset = isl_basic_set_cow(bset);
7977 if (div->n_row < bset->n_div)
7978 isl_die(isl_mat_get_ctx(div), isl_error_invalid,
7979 "not an expansion", goto error);
7981 n_div = bset->n_div;
7982 bset = isl_basic_map_extend_space(bset, isl_space_copy(bset->dim),
7983 div->n_row - n_div, 0,
7984 2 * (div->n_row - n_div));
7986 for (i = n_div; i < div->n_row; ++i)
7987 if (isl_basic_set_alloc_div(bset) < 0)
7991 for (i = div->n_row - 1; i >= 0; --i) {
7992 if (j >= 0 && exp[j] == i) {
7994 isl_basic_map_swap_div(bset, i, j);
7997 isl_seq_cpy(bset->div[i], div->row[i], div->n_col);
7998 if (isl_basic_map_add_div_constraints(bset, i) < 0)
8006 isl_basic_set_free(bset);
8011 /* Look for a div in dst that corresponds to the div "div" in src.
8012 * The divs before "div" in src and dst are assumed to be the same.
8014 * Returns -1 if no corresponding div was found and the position
8015 * of the corresponding div in dst otherwise.
8017 static int find_div(struct isl_basic_map *dst,
8018 struct isl_basic_map *src, unsigned div)
8022 unsigned total = isl_space_dim(src->dim, isl_dim_all);
8024 isl_assert(dst->ctx, div <= dst->n_div, return -1);
8025 for (i = div; i < dst->n_div; ++i)
8026 if (isl_seq_eq(dst->div[i], src->div[div], 1+1+total+div) &&
8027 isl_seq_first_non_zero(dst->div[i]+1+1+total+div,
8028 dst->n_div - div) == -1)
8033 struct isl_basic_map *isl_basic_map_align_divs(
8034 struct isl_basic_map *dst, struct isl_basic_map *src)
8042 if (src->n_div == 0)
8045 for (i = 0; i < src->n_div; ++i)
8046 isl_assert(src->ctx, !isl_int_is_zero(src->div[i][0]), goto error);
8048 src = isl_basic_map_order_divs(src);
8049 dst = isl_basic_map_cow(dst);
8050 dst = isl_basic_map_extend_space(dst, isl_space_copy(dst->dim),
8051 src->n_div, 0, 2 * src->n_div);
8054 total = isl_space_dim(src->dim, isl_dim_all);
8055 for (i = 0; i < src->n_div; ++i) {
8056 int j = find_div(dst, src, i);
8058 j = isl_basic_map_alloc_div(dst);
8061 isl_seq_cpy(dst->div[j], src->div[i], 1+1+total+i);
8062 isl_seq_clr(dst->div[j]+1+1+total+i, dst->n_div - i);
8063 if (isl_basic_map_add_div_constraints(dst, j) < 0)
8067 isl_basic_map_swap_div(dst, i, j);
8071 isl_basic_map_free(dst);
8075 struct isl_basic_set *isl_basic_set_align_divs(
8076 struct isl_basic_set *dst, struct isl_basic_set *src)
8078 return (struct isl_basic_set *)isl_basic_map_align_divs(
8079 (struct isl_basic_map *)dst, (struct isl_basic_map *)src);
8082 struct isl_map *isl_map_align_divs(struct isl_map *map)
8090 map = isl_map_compute_divs(map);
8091 map = isl_map_cow(map);
8095 for (i = 1; i < map->n; ++i)
8096 map->p[0] = isl_basic_map_align_divs(map->p[0], map->p[i]);
8097 for (i = 1; i < map->n; ++i)
8098 map->p[i] = isl_basic_map_align_divs(map->p[i], map->p[0]);
8100 ISL_F_CLR(map, ISL_MAP_NORMALIZED);
8104 struct isl_set *isl_set_align_divs(struct isl_set *set)
8106 return (struct isl_set *)isl_map_align_divs((struct isl_map *)set);
8109 static __isl_give isl_set *set_apply( __isl_take isl_set *set,
8110 __isl_take isl_map *map)
8114 isl_assert(set->ctx, isl_map_compatible_domain(map, set), goto error);
8115 map = isl_map_intersect_domain(map, set);
8116 set = isl_map_range(map);
8124 __isl_give isl_set *isl_set_apply( __isl_take isl_set *set,
8125 __isl_take isl_map *map)
8127 return isl_map_align_params_map_map_and(set, map, &set_apply);
8130 /* There is no need to cow as removing empty parts doesn't change
8131 * the meaning of the set.
8133 struct isl_map *isl_map_remove_empty_parts(struct isl_map *map)
8140 for (i = map->n - 1; i >= 0; --i)
8141 remove_if_empty(map, i);
8146 struct isl_set *isl_set_remove_empty_parts(struct isl_set *set)
8148 return (struct isl_set *)
8149 isl_map_remove_empty_parts((struct isl_map *)set);
8152 struct isl_basic_map *isl_map_copy_basic_map(struct isl_map *map)
8154 struct isl_basic_map *bmap;
8155 if (!map || map->n == 0)
8157 bmap = map->p[map->n-1];
8158 isl_assert(map->ctx, ISL_F_ISSET(bmap, ISL_BASIC_SET_FINAL), return NULL);
8159 return isl_basic_map_copy(bmap);
8162 struct isl_basic_set *isl_set_copy_basic_set(struct isl_set *set)
8164 return (struct isl_basic_set *)
8165 isl_map_copy_basic_map((struct isl_map *)set);
8168 __isl_give isl_map *isl_map_drop_basic_map(__isl_take isl_map *map,
8169 __isl_keep isl_basic_map *bmap)
8175 for (i = map->n-1; i >= 0; --i) {
8176 if (map->p[i] != bmap)
8178 map = isl_map_cow(map);
8181 isl_basic_map_free(map->p[i]);
8182 if (i != map->n-1) {
8183 ISL_F_CLR(map, ISL_SET_NORMALIZED);
8184 map->p[i] = map->p[map->n-1];
8195 struct isl_set *isl_set_drop_basic_set(struct isl_set *set,
8196 struct isl_basic_set *bset)
8198 return (struct isl_set *)isl_map_drop_basic_map((struct isl_map *)set,
8199 (struct isl_basic_map *)bset);
8202 /* Given two basic sets bset1 and bset2, compute the maximal difference
8203 * between the values of dimension pos in bset1 and those in bset2
8204 * for any common value of the parameters and dimensions preceding pos.
8206 static enum isl_lp_result basic_set_maximal_difference_at(
8207 __isl_keep isl_basic_set *bset1, __isl_keep isl_basic_set *bset2,
8208 int pos, isl_int *opt)
8211 struct isl_basic_map *bmap1 = NULL;
8212 struct isl_basic_map *bmap2 = NULL;
8213 struct isl_ctx *ctx;
8214 struct isl_vec *obj;
8217 unsigned dim1, dim2;
8218 enum isl_lp_result res;
8220 if (!bset1 || !bset2)
8221 return isl_lp_error;
8223 nparam = isl_basic_set_n_param(bset1);
8224 dim1 = isl_basic_set_n_dim(bset1);
8225 dim2 = isl_basic_set_n_dim(bset2);
8226 dims = isl_space_alloc(bset1->ctx, nparam, pos, dim1 - pos);
8227 bmap1 = isl_basic_map_from_basic_set(isl_basic_set_copy(bset1), dims);
8228 dims = isl_space_alloc(bset2->ctx, nparam, pos, dim2 - pos);
8229 bmap2 = isl_basic_map_from_basic_set(isl_basic_set_copy(bset2), dims);
8230 if (!bmap1 || !bmap2)
8232 bmap1 = isl_basic_map_cow(bmap1);
8233 bmap1 = isl_basic_map_extend(bmap1, nparam,
8234 pos, (dim1 - pos) + (dim2 - pos),
8235 bmap2->n_div, bmap2->n_eq, bmap2->n_ineq);
8236 bmap1 = add_constraints(bmap1, bmap2, 0, dim1 - pos);
8239 total = isl_basic_map_total_dim(bmap1);
8241 obj = isl_vec_alloc(ctx, 1 + total);
8244 isl_seq_clr(obj->block.data, 1 + total);
8245 isl_int_set_si(obj->block.data[1+nparam+pos], 1);
8246 isl_int_set_si(obj->block.data[1+nparam+pos+(dim1-pos)], -1);
8247 res = isl_basic_map_solve_lp(bmap1, 1, obj->block.data, ctx->one,
8249 isl_basic_map_free(bmap1);
8253 isl_basic_map_free(bmap2);
8255 isl_basic_map_free(bmap1);
8256 return isl_lp_error;
8259 /* Given two _disjoint_ basic sets bset1 and bset2, check whether
8260 * for any common value of the parameters and dimensions preceding pos
8261 * in both basic sets, the values of dimension pos in bset1 are
8262 * smaller or larger than those in bset2.
8265 * 1 if bset1 follows bset2
8266 * -1 if bset1 precedes bset2
8267 * 0 if bset1 and bset2 are incomparable
8268 * -2 if some error occurred.
8270 int isl_basic_set_compare_at(struct isl_basic_set *bset1,
8271 struct isl_basic_set *bset2, int pos)
8274 enum isl_lp_result res;
8279 res = basic_set_maximal_difference_at(bset1, bset2, pos, &opt);
8281 if (res == isl_lp_empty)
8283 else if ((res == isl_lp_ok && isl_int_is_pos(opt)) ||
8284 res == isl_lp_unbounded)
8286 else if (res == isl_lp_ok && isl_int_is_neg(opt))
8295 /* Given two basic sets bset1 and bset2, check whether
8296 * for any common value of the parameters and dimensions preceding pos
8297 * there is a value of dimension pos in bset1 that is larger
8298 * than a value of the same dimension in bset2.
8301 * 1 if there exists such a pair
8302 * 0 if there is no such pair, but there is a pair of equal values
8304 * -2 if some error occurred.
8306 int isl_basic_set_follows_at(__isl_keep isl_basic_set *bset1,
8307 __isl_keep isl_basic_set *bset2, int pos)
8310 enum isl_lp_result res;
8315 res = basic_set_maximal_difference_at(bset1, bset2, pos, &opt);
8317 if (res == isl_lp_empty)
8319 else if ((res == isl_lp_ok && isl_int_is_pos(opt)) ||
8320 res == isl_lp_unbounded)
8322 else if (res == isl_lp_ok && isl_int_is_neg(opt))
8324 else if (res == isl_lp_ok)
8333 /* Given two sets set1 and set2, check whether
8334 * for any common value of the parameters and dimensions preceding pos
8335 * there is a value of dimension pos in set1 that is larger
8336 * than a value of the same dimension in set2.
8339 * 1 if there exists such a pair
8340 * 0 if there is no such pair, but there is a pair of equal values
8342 * -2 if some error occurred.
8344 int isl_set_follows_at(__isl_keep isl_set *set1,
8345 __isl_keep isl_set *set2, int pos)
8353 for (i = 0; i < set1->n; ++i)
8354 for (j = 0; j < set2->n; ++j) {
8356 f = isl_basic_set_follows_at(set1->p[i], set2->p[j], pos);
8357 if (f == 1 || f == -2)
8366 static int isl_basic_map_plain_has_fixed_var(__isl_keep isl_basic_map *bmap,
8367 unsigned pos, isl_int *val)
8375 total = isl_basic_map_total_dim(bmap);
8376 for (i = 0, d = total-1; i < bmap->n_eq && d+1 > pos; ++i) {
8377 for (; d+1 > pos; --d)
8378 if (!isl_int_is_zero(bmap->eq[i][1+d]))
8382 if (isl_seq_first_non_zero(bmap->eq[i]+1, d) != -1)
8384 if (isl_seq_first_non_zero(bmap->eq[i]+1+d+1, total-d-1) != -1)
8386 if (!isl_int_is_one(bmap->eq[i][1+d]))
8389 isl_int_neg(*val, bmap->eq[i][0]);
8395 static int isl_map_plain_has_fixed_var(__isl_keep isl_map *map,
8396 unsigned pos, isl_int *val)
8408 return isl_basic_map_plain_has_fixed_var(map->p[0], pos, val);
8411 fixed = isl_basic_map_plain_has_fixed_var(map->p[0], pos, &v);
8412 for (i = 1; fixed == 1 && i < map->n; ++i) {
8413 fixed = isl_basic_map_plain_has_fixed_var(map->p[i], pos, &tmp);
8414 if (fixed == 1 && isl_int_ne(tmp, v))
8418 isl_int_set(*val, v);
8424 static int isl_basic_set_plain_has_fixed_var(__isl_keep isl_basic_set *bset,
8425 unsigned pos, isl_int *val)
8427 return isl_basic_map_plain_has_fixed_var((struct isl_basic_map *)bset,
8431 static int isl_set_plain_has_fixed_var(__isl_keep isl_set *set, unsigned pos,
8434 return isl_map_plain_has_fixed_var((struct isl_map *)set, pos, val);
8437 int isl_basic_map_plain_is_fixed(__isl_keep isl_basic_map *bmap,
8438 enum isl_dim_type type, unsigned pos, isl_int *val)
8440 if (pos >= isl_basic_map_dim(bmap, type))
8442 return isl_basic_map_plain_has_fixed_var(bmap,
8443 isl_basic_map_offset(bmap, type) - 1 + pos, val);
8446 /* If "bmap" obviously lies on a hyperplane where the given dimension
8447 * has a fixed value, then return that value.
8448 * Otherwise return NaN.
8450 __isl_give isl_val *isl_basic_map_plain_get_val_if_fixed(
8451 __isl_keep isl_basic_map *bmap,
8452 enum isl_dim_type type, unsigned pos)
8460 ctx = isl_basic_map_get_ctx(bmap);
8461 v = isl_val_alloc(ctx);
8464 fixed = isl_basic_map_plain_is_fixed(bmap, type, pos, &v->n);
8466 return isl_val_free(v);
8468 isl_int_set_si(v->d, 1);
8472 return isl_val_nan(ctx);
8475 int isl_map_plain_is_fixed(__isl_keep isl_map *map,
8476 enum isl_dim_type type, unsigned pos, isl_int *val)
8478 if (pos >= isl_map_dim(map, type))
8480 return isl_map_plain_has_fixed_var(map,
8481 map_offset(map, type) - 1 + pos, val);
8484 /* If "map" obviously lies on a hyperplane where the given dimension
8485 * has a fixed value, then return that value.
8486 * Otherwise return NaN.
8488 __isl_give isl_val *isl_map_plain_get_val_if_fixed(__isl_keep isl_map *map,
8489 enum isl_dim_type type, unsigned pos)
8497 ctx = isl_map_get_ctx(map);
8498 v = isl_val_alloc(ctx);
8501 fixed = isl_map_plain_is_fixed(map, type, pos, &v->n);
8503 return isl_val_free(v);
8505 isl_int_set_si(v->d, 1);
8509 return isl_val_nan(ctx);
8512 /* If "set" obviously lies on a hyperplane where the given dimension
8513 * has a fixed value, then return that value.
8514 * Otherwise return NaN.
8516 __isl_give isl_val *isl_set_plain_get_val_if_fixed(__isl_keep isl_set *set,
8517 enum isl_dim_type type, unsigned pos)
8519 return isl_map_plain_get_val_if_fixed(set, type, pos);
8522 int isl_set_plain_is_fixed(__isl_keep isl_set *set,
8523 enum isl_dim_type type, unsigned pos, isl_int *val)
8525 return isl_map_plain_is_fixed(set, type, pos, val);
8528 int isl_map_fast_is_fixed(__isl_keep isl_map *map,
8529 enum isl_dim_type type, unsigned pos, isl_int *val)
8531 return isl_map_plain_is_fixed(map, type, pos, val);
8534 /* Check if dimension dim has fixed value and if so and if val is not NULL,
8535 * then return this fixed value in *val.
8537 int isl_basic_set_plain_dim_is_fixed(__isl_keep isl_basic_set *bset,
8538 unsigned dim, isl_int *val)
8540 return isl_basic_set_plain_has_fixed_var(bset,
8541 isl_basic_set_n_param(bset) + dim, val);
8544 /* Check if dimension dim has fixed value and if so and if val is not NULL,
8545 * then return this fixed value in *val.
8547 int isl_set_plain_dim_is_fixed(__isl_keep isl_set *set,
8548 unsigned dim, isl_int *val)
8550 return isl_set_plain_has_fixed_var(set, isl_set_n_param(set) + dim, val);
8553 int isl_set_fast_dim_is_fixed(__isl_keep isl_set *set,
8554 unsigned dim, isl_int *val)
8556 return isl_set_plain_dim_is_fixed(set, dim, val);
8559 /* Check if input variable in has fixed value and if so and if val is not NULL,
8560 * then return this fixed value in *val.
8562 int isl_map_plain_input_is_fixed(__isl_keep isl_map *map,
8563 unsigned in, isl_int *val)
8565 return isl_map_plain_has_fixed_var(map, isl_map_n_param(map) + in, val);
8568 /* Check if dimension dim has an (obvious) fixed lower bound and if so
8569 * and if val is not NULL, then return this lower bound in *val.
8571 int isl_basic_set_plain_dim_has_fixed_lower_bound(
8572 __isl_keep isl_basic_set *bset, unsigned dim, isl_int *val)
8574 int i, i_eq = -1, i_ineq = -1;
8581 total = isl_basic_set_total_dim(bset);
8582 nparam = isl_basic_set_n_param(bset);
8583 for (i = 0; i < bset->n_eq; ++i) {
8584 if (isl_int_is_zero(bset->eq[i][1+nparam+dim]))
8590 for (i = 0; i < bset->n_ineq; ++i) {
8591 if (!isl_int_is_pos(bset->ineq[i][1+nparam+dim]))
8593 if (i_eq != -1 || i_ineq != -1)
8597 if (i_eq == -1 && i_ineq == -1)
8599 c = i_eq != -1 ? bset->eq[i_eq] : bset->ineq[i_ineq];
8600 /* The coefficient should always be one due to normalization. */
8601 if (!isl_int_is_one(c[1+nparam+dim]))
8603 if (isl_seq_first_non_zero(c+1, nparam+dim) != -1)
8605 if (isl_seq_first_non_zero(c+1+nparam+dim+1,
8606 total - nparam - dim - 1) != -1)
8609 isl_int_neg(*val, c[0]);
8613 int isl_set_plain_dim_has_fixed_lower_bound(__isl_keep isl_set *set,
8614 unsigned dim, isl_int *val)
8626 return isl_basic_set_plain_dim_has_fixed_lower_bound(set->p[0],
8630 fixed = isl_basic_set_plain_dim_has_fixed_lower_bound(set->p[0],
8632 for (i = 1; fixed == 1 && i < set->n; ++i) {
8633 fixed = isl_basic_set_plain_dim_has_fixed_lower_bound(set->p[i],
8635 if (fixed == 1 && isl_int_ne(tmp, v))
8639 isl_int_set(*val, v);
8650 /* uset_gist depends on constraints without existentially quantified
8651 * variables sorting first.
8653 static int qsort_constraint_cmp(const void *p1, const void *p2)
8655 const struct constraint *c1 = (const struct constraint *)p1;
8656 const struct constraint *c2 = (const struct constraint *)p2;
8658 unsigned size = isl_min(c1->size, c2->size);
8660 l1 = isl_seq_last_non_zero(c1->c + 1, size);
8661 l2 = isl_seq_last_non_zero(c2->c + 1, size);
8666 return isl_seq_cmp(c1->c + 1, c2->c + 1, size);
8669 static struct isl_basic_map *isl_basic_map_sort_constraints(
8670 struct isl_basic_map *bmap)
8673 struct constraint *c;
8678 total = isl_basic_map_total_dim(bmap);
8679 c = isl_alloc_array(bmap->ctx, struct constraint, bmap->n_ineq);
8682 for (i = 0; i < bmap->n_ineq; ++i) {
8684 c[i].c = bmap->ineq[i];
8686 qsort(c, bmap->n_ineq, sizeof(struct constraint), qsort_constraint_cmp);
8687 for (i = 0; i < bmap->n_ineq; ++i)
8688 bmap->ineq[i] = c[i].c;
8692 isl_basic_map_free(bmap);
8696 __isl_give isl_basic_set *isl_basic_set_sort_constraints(
8697 __isl_take isl_basic_set *bset)
8699 return (struct isl_basic_set *)isl_basic_map_sort_constraints(
8700 (struct isl_basic_map *)bset);
8703 struct isl_basic_map *isl_basic_map_normalize(struct isl_basic_map *bmap)
8707 if (ISL_F_ISSET(bmap, ISL_BASIC_MAP_NORMALIZED))
8709 bmap = isl_basic_map_remove_redundancies(bmap);
8710 bmap = isl_basic_map_sort_constraints(bmap);
8712 ISL_F_SET(bmap, ISL_BASIC_MAP_NORMALIZED);
8716 struct isl_basic_set *isl_basic_set_normalize(struct isl_basic_set *bset)
8718 return (struct isl_basic_set *)isl_basic_map_normalize(
8719 (struct isl_basic_map *)bset);
8722 int isl_basic_map_plain_cmp(const __isl_keep isl_basic_map *bmap1,
8723 const __isl_keep isl_basic_map *bmap2)
8730 if (ISL_F_ISSET(bmap1, ISL_BASIC_MAP_RATIONAL) !=
8731 ISL_F_ISSET(bmap2, ISL_BASIC_MAP_RATIONAL))
8732 return ISL_F_ISSET(bmap1, ISL_BASIC_MAP_RATIONAL) ? -1 : 1;
8733 if (isl_basic_map_n_param(bmap1) != isl_basic_map_n_param(bmap2))
8734 return isl_basic_map_n_param(bmap1) - isl_basic_map_n_param(bmap2);
8735 if (isl_basic_map_n_in(bmap1) != isl_basic_map_n_in(bmap2))
8736 return isl_basic_map_n_out(bmap1) - isl_basic_map_n_out(bmap2);
8737 if (isl_basic_map_n_out(bmap1) != isl_basic_map_n_out(bmap2))
8738 return isl_basic_map_n_out(bmap1) - isl_basic_map_n_out(bmap2);
8739 if (ISL_F_ISSET(bmap1, ISL_BASIC_MAP_EMPTY) &&
8740 ISL_F_ISSET(bmap2, ISL_BASIC_MAP_EMPTY))
8742 if (ISL_F_ISSET(bmap1, ISL_BASIC_MAP_EMPTY))
8744 if (ISL_F_ISSET(bmap2, ISL_BASIC_MAP_EMPTY))
8746 if (bmap1->n_eq != bmap2->n_eq)
8747 return bmap1->n_eq - bmap2->n_eq;
8748 if (bmap1->n_ineq != bmap2->n_ineq)
8749 return bmap1->n_ineq - bmap2->n_ineq;
8750 if (bmap1->n_div != bmap2->n_div)
8751 return bmap1->n_div - bmap2->n_div;
8752 total = isl_basic_map_total_dim(bmap1);
8753 for (i = 0; i < bmap1->n_eq; ++i) {
8754 cmp = isl_seq_cmp(bmap1->eq[i], bmap2->eq[i], 1+total);
8758 for (i = 0; i < bmap1->n_ineq; ++i) {
8759 cmp = isl_seq_cmp(bmap1->ineq[i], bmap2->ineq[i], 1+total);
8763 for (i = 0; i < bmap1->n_div; ++i) {
8764 cmp = isl_seq_cmp(bmap1->div[i], bmap2->div[i], 1+1+total);
8771 int isl_basic_set_plain_cmp(const __isl_keep isl_basic_set *bset1,
8772 const __isl_keep isl_basic_set *bset2)
8774 return isl_basic_map_plain_cmp(bset1, bset2);
8777 int isl_set_plain_cmp(__isl_keep isl_set *set1, __isl_keep isl_set *set2)
8783 if (set1->n != set2->n)
8784 return set1->n - set2->n;
8786 for (i = 0; i < set1->n; ++i) {
8787 cmp = isl_basic_set_plain_cmp(set1->p[i], set2->p[i]);
8795 int isl_basic_map_plain_is_equal(__isl_keep isl_basic_map *bmap1,
8796 __isl_keep isl_basic_map *bmap2)
8798 return isl_basic_map_plain_cmp(bmap1, bmap2) == 0;
8801 int isl_basic_set_plain_is_equal(__isl_keep isl_basic_set *bset1,
8802 __isl_keep isl_basic_set *bset2)
8804 return isl_basic_map_plain_is_equal((isl_basic_map *)bset1,
8805 (isl_basic_map *)bset2);
8808 static int qsort_bmap_cmp(const void *p1, const void *p2)
8810 const struct isl_basic_map *bmap1 = *(const struct isl_basic_map **)p1;
8811 const struct isl_basic_map *bmap2 = *(const struct isl_basic_map **)p2;
8813 return isl_basic_map_plain_cmp(bmap1, bmap2);
8816 /* We normalize in place, but if anything goes wrong we need
8817 * to return NULL, so we need to make sure we don't change the
8818 * meaning of any possible other copies of map.
8820 struct isl_map *isl_map_normalize(struct isl_map *map)
8823 struct isl_basic_map *bmap;
8827 if (ISL_F_ISSET(map, ISL_MAP_NORMALIZED))
8829 for (i = 0; i < map->n; ++i) {
8830 bmap = isl_basic_map_normalize(isl_basic_map_copy(map->p[i]));
8833 isl_basic_map_free(map->p[i]);
8836 qsort(map->p, map->n, sizeof(struct isl_basic_map *), qsort_bmap_cmp);
8837 ISL_F_SET(map, ISL_MAP_NORMALIZED);
8838 map = isl_map_remove_empty_parts(map);
8841 for (i = map->n - 1; i >= 1; --i) {
8842 if (!isl_basic_map_plain_is_equal(map->p[i-1], map->p[i]))
8844 isl_basic_map_free(map->p[i-1]);
8845 for (j = i; j < map->n; ++j)
8846 map->p[j-1] = map->p[j];
8856 struct isl_set *isl_set_normalize(struct isl_set *set)
8858 return (struct isl_set *)isl_map_normalize((struct isl_map *)set);
8861 int isl_map_plain_is_equal(__isl_keep isl_map *map1, __isl_keep isl_map *map2)
8871 if (!isl_space_is_equal(map1->dim, map2->dim))
8874 map1 = isl_map_copy(map1);
8875 map2 = isl_map_copy(map2);
8876 map1 = isl_map_normalize(map1);
8877 map2 = isl_map_normalize(map2);
8880 equal = map1->n == map2->n;
8881 for (i = 0; equal && i < map1->n; ++i) {
8882 equal = isl_basic_map_plain_is_equal(map1->p[i], map2->p[i]);
8895 int isl_map_fast_is_equal(__isl_keep isl_map *map1, __isl_keep isl_map *map2)
8897 return isl_map_plain_is_equal(map1, map2);
8900 int isl_set_plain_is_equal(__isl_keep isl_set *set1, __isl_keep isl_set *set2)
8902 return isl_map_plain_is_equal((struct isl_map *)set1,
8903 (struct isl_map *)set2);
8906 int isl_set_fast_is_equal(__isl_keep isl_set *set1, __isl_keep isl_set *set2)
8908 return isl_set_plain_is_equal(set1, set2);
8911 /* Return an interval that ranges from min to max (inclusive)
8913 struct isl_basic_set *isl_basic_set_interval(struct isl_ctx *ctx,
8914 isl_int min, isl_int max)
8917 struct isl_basic_set *bset = NULL;
8919 bset = isl_basic_set_alloc(ctx, 0, 1, 0, 0, 2);
8923 k = isl_basic_set_alloc_inequality(bset);
8926 isl_int_set_si(bset->ineq[k][1], 1);
8927 isl_int_neg(bset->ineq[k][0], min);
8929 k = isl_basic_set_alloc_inequality(bset);
8932 isl_int_set_si(bset->ineq[k][1], -1);
8933 isl_int_set(bset->ineq[k][0], max);
8937 isl_basic_set_free(bset);
8941 /* Return the Cartesian product of the basic sets in list (in the given order).
8943 __isl_give isl_basic_set *isl_basic_set_list_product(
8944 __isl_take struct isl_basic_set_list *list)
8952 struct isl_basic_set *product = NULL;
8956 isl_assert(list->ctx, list->n > 0, goto error);
8957 isl_assert(list->ctx, list->p[0], goto error);
8958 nparam = isl_basic_set_n_param(list->p[0]);
8959 dim = isl_basic_set_n_dim(list->p[0]);
8960 extra = list->p[0]->n_div;
8961 n_eq = list->p[0]->n_eq;
8962 n_ineq = list->p[0]->n_ineq;
8963 for (i = 1; i < list->n; ++i) {
8964 isl_assert(list->ctx, list->p[i], goto error);
8965 isl_assert(list->ctx,
8966 nparam == isl_basic_set_n_param(list->p[i]), goto error);
8967 dim += isl_basic_set_n_dim(list->p[i]);
8968 extra += list->p[i]->n_div;
8969 n_eq += list->p[i]->n_eq;
8970 n_ineq += list->p[i]->n_ineq;
8972 product = isl_basic_set_alloc(list->ctx, nparam, dim, extra,
8977 for (i = 0; i < list->n; ++i) {
8978 isl_basic_set_add_constraints(product,
8979 isl_basic_set_copy(list->p[i]), dim);
8980 dim += isl_basic_set_n_dim(list->p[i]);
8982 isl_basic_set_list_free(list);
8985 isl_basic_set_free(product);
8986 isl_basic_set_list_free(list);
8990 struct isl_basic_map *isl_basic_map_product(
8991 struct isl_basic_map *bmap1, struct isl_basic_map *bmap2)
8993 isl_space *dim_result = NULL;
8994 struct isl_basic_map *bmap;
8995 unsigned in1, in2, out1, out2, nparam, total, pos;
8996 struct isl_dim_map *dim_map1, *dim_map2;
8998 if (!bmap1 || !bmap2)
9001 isl_assert(bmap1->ctx, isl_space_match(bmap1->dim, isl_dim_param,
9002 bmap2->dim, isl_dim_param), goto error);
9003 dim_result = isl_space_product(isl_space_copy(bmap1->dim),
9004 isl_space_copy(bmap2->dim));
9006 in1 = isl_basic_map_n_in(bmap1);
9007 in2 = isl_basic_map_n_in(bmap2);
9008 out1 = isl_basic_map_n_out(bmap1);
9009 out2 = isl_basic_map_n_out(bmap2);
9010 nparam = isl_basic_map_n_param(bmap1);
9012 total = nparam + in1 + in2 + out1 + out2 + bmap1->n_div + bmap2->n_div;
9013 dim_map1 = isl_dim_map_alloc(bmap1->ctx, total);
9014 dim_map2 = isl_dim_map_alloc(bmap1->ctx, total);
9015 isl_dim_map_dim(dim_map1, bmap1->dim, isl_dim_param, pos = 0);
9016 isl_dim_map_dim(dim_map2, bmap2->dim, isl_dim_param, pos = 0);
9017 isl_dim_map_dim(dim_map1, bmap1->dim, isl_dim_in, pos += nparam);
9018 isl_dim_map_dim(dim_map2, bmap2->dim, isl_dim_in, pos += in1);
9019 isl_dim_map_dim(dim_map1, bmap1->dim, isl_dim_out, pos += in2);
9020 isl_dim_map_dim(dim_map2, bmap2->dim, isl_dim_out, pos += out1);
9021 isl_dim_map_div(dim_map1, bmap1, pos += out2);
9022 isl_dim_map_div(dim_map2, bmap2, pos += bmap1->n_div);
9024 bmap = isl_basic_map_alloc_space(dim_result,
9025 bmap1->n_div + bmap2->n_div,
9026 bmap1->n_eq + bmap2->n_eq,
9027 bmap1->n_ineq + bmap2->n_ineq);
9028 bmap = isl_basic_map_add_constraints_dim_map(bmap, bmap1, dim_map1);
9029 bmap = isl_basic_map_add_constraints_dim_map(bmap, bmap2, dim_map2);
9030 bmap = isl_basic_map_simplify(bmap);
9031 return isl_basic_map_finalize(bmap);
9033 isl_basic_map_free(bmap1);
9034 isl_basic_map_free(bmap2);
9038 __isl_give isl_basic_map *isl_basic_map_flat_product(
9039 __isl_take isl_basic_map *bmap1, __isl_take isl_basic_map *bmap2)
9041 isl_basic_map *prod;
9043 prod = isl_basic_map_product(bmap1, bmap2);
9044 prod = isl_basic_map_flatten(prod);
9048 __isl_give isl_basic_set *isl_basic_set_flat_product(
9049 __isl_take isl_basic_set *bset1, __isl_take isl_basic_set *bset2)
9051 return isl_basic_map_flat_range_product(bset1, bset2);
9054 __isl_give isl_basic_map *isl_basic_map_domain_product(
9055 __isl_take isl_basic_map *bmap1, __isl_take isl_basic_map *bmap2)
9057 isl_space *space_result = NULL;
9058 isl_basic_map *bmap;
9059 unsigned in1, in2, out, nparam, total, pos;
9060 struct isl_dim_map *dim_map1, *dim_map2;
9062 if (!bmap1 || !bmap2)
9065 space_result = isl_space_domain_product(isl_space_copy(bmap1->dim),
9066 isl_space_copy(bmap2->dim));
9068 in1 = isl_basic_map_dim(bmap1, isl_dim_in);
9069 in2 = isl_basic_map_dim(bmap2, isl_dim_in);
9070 out = isl_basic_map_dim(bmap1, isl_dim_out);
9071 nparam = isl_basic_map_dim(bmap1, isl_dim_param);
9073 total = nparam + in1 + in2 + out + bmap1->n_div + bmap2->n_div;
9074 dim_map1 = isl_dim_map_alloc(bmap1->ctx, total);
9075 dim_map2 = isl_dim_map_alloc(bmap1->ctx, total);
9076 isl_dim_map_dim(dim_map1, bmap1->dim, isl_dim_param, pos = 0);
9077 isl_dim_map_dim(dim_map2, bmap2->dim, isl_dim_param, pos = 0);
9078 isl_dim_map_dim(dim_map1, bmap1->dim, isl_dim_in, pos += nparam);
9079 isl_dim_map_dim(dim_map2, bmap2->dim, isl_dim_in, pos += in1);
9080 isl_dim_map_dim(dim_map1, bmap1->dim, isl_dim_out, pos += in2);
9081 isl_dim_map_dim(dim_map2, bmap2->dim, isl_dim_out, pos);
9082 isl_dim_map_div(dim_map1, bmap1, pos += out);
9083 isl_dim_map_div(dim_map2, bmap2, pos += bmap1->n_div);
9085 bmap = isl_basic_map_alloc_space(space_result,
9086 bmap1->n_div + bmap2->n_div,
9087 bmap1->n_eq + bmap2->n_eq,
9088 bmap1->n_ineq + bmap2->n_ineq);
9089 bmap = isl_basic_map_add_constraints_dim_map(bmap, bmap1, dim_map1);
9090 bmap = isl_basic_map_add_constraints_dim_map(bmap, bmap2, dim_map2);
9091 bmap = isl_basic_map_simplify(bmap);
9092 return isl_basic_map_finalize(bmap);
9094 isl_basic_map_free(bmap1);
9095 isl_basic_map_free(bmap2);
9099 __isl_give isl_basic_map *isl_basic_map_range_product(
9100 __isl_take isl_basic_map *bmap1, __isl_take isl_basic_map *bmap2)
9102 isl_space *dim_result = NULL;
9103 isl_basic_map *bmap;
9104 unsigned in, out1, out2, nparam, total, pos;
9105 struct isl_dim_map *dim_map1, *dim_map2;
9107 if (!bmap1 || !bmap2)
9110 if (!isl_space_match(bmap1->dim, isl_dim_param,
9111 bmap2->dim, isl_dim_param))
9112 isl_die(isl_basic_map_get_ctx(bmap1), isl_error_invalid,
9113 "parameters don't match", goto error);
9115 dim_result = isl_space_range_product(isl_space_copy(bmap1->dim),
9116 isl_space_copy(bmap2->dim));
9118 in = isl_basic_map_dim(bmap1, isl_dim_in);
9119 out1 = isl_basic_map_n_out(bmap1);
9120 out2 = isl_basic_map_n_out(bmap2);
9121 nparam = isl_basic_map_n_param(bmap1);
9123 total = nparam + in + out1 + out2 + bmap1->n_div + bmap2->n_div;
9124 dim_map1 = isl_dim_map_alloc(bmap1->ctx, total);
9125 dim_map2 = isl_dim_map_alloc(bmap1->ctx, total);
9126 isl_dim_map_dim(dim_map1, bmap1->dim, isl_dim_param, pos = 0);
9127 isl_dim_map_dim(dim_map2, bmap2->dim, isl_dim_param, pos = 0);
9128 isl_dim_map_dim(dim_map1, bmap1->dim, isl_dim_in, pos += nparam);
9129 isl_dim_map_dim(dim_map2, bmap2->dim, isl_dim_in, pos);
9130 isl_dim_map_dim(dim_map1, bmap1->dim, isl_dim_out, pos += in);
9131 isl_dim_map_dim(dim_map2, bmap2->dim, isl_dim_out, pos += out1);
9132 isl_dim_map_div(dim_map1, bmap1, pos += out2);
9133 isl_dim_map_div(dim_map2, bmap2, pos += bmap1->n_div);
9135 bmap = isl_basic_map_alloc_space(dim_result,
9136 bmap1->n_div + bmap2->n_div,
9137 bmap1->n_eq + bmap2->n_eq,
9138 bmap1->n_ineq + bmap2->n_ineq);
9139 bmap = isl_basic_map_add_constraints_dim_map(bmap, bmap1, dim_map1);
9140 bmap = isl_basic_map_add_constraints_dim_map(bmap, bmap2, dim_map2);
9141 bmap = isl_basic_map_simplify(bmap);
9142 return isl_basic_map_finalize(bmap);
9144 isl_basic_map_free(bmap1);
9145 isl_basic_map_free(bmap2);
9149 __isl_give isl_basic_map *isl_basic_map_flat_range_product(
9150 __isl_take isl_basic_map *bmap1, __isl_take isl_basic_map *bmap2)
9152 isl_basic_map *prod;
9154 prod = isl_basic_map_range_product(bmap1, bmap2);
9155 prod = isl_basic_map_flatten_range(prod);
9159 static __isl_give isl_map *map_product(__isl_take isl_map *map1,
9160 __isl_take isl_map *map2,
9161 __isl_give isl_space *(*dim_product)(__isl_take isl_space *left,
9162 __isl_take isl_space *right),
9163 __isl_give isl_basic_map *(*basic_map_product)(
9164 __isl_take isl_basic_map *left, __isl_take isl_basic_map *right))
9167 struct isl_map *result;
9173 isl_assert(map1->ctx, isl_space_match(map1->dim, isl_dim_param,
9174 map2->dim, isl_dim_param), goto error);
9176 if (ISL_F_ISSET(map1, ISL_MAP_DISJOINT) &&
9177 ISL_F_ISSET(map2, ISL_MAP_DISJOINT))
9178 ISL_FL_SET(flags, ISL_MAP_DISJOINT);
9180 result = isl_map_alloc_space(dim_product(isl_space_copy(map1->dim),
9181 isl_space_copy(map2->dim)),
9182 map1->n * map2->n, flags);
9185 for (i = 0; i < map1->n; ++i)
9186 for (j = 0; j < map2->n; ++j) {
9187 struct isl_basic_map *part;
9188 part = basic_map_product(isl_basic_map_copy(map1->p[i]),
9189 isl_basic_map_copy(map2->p[j]));
9190 if (isl_basic_map_is_empty(part))
9191 isl_basic_map_free(part);
9193 result = isl_map_add_basic_map(result, part);
9206 /* Given two maps A -> B and C -> D, construct a map [A -> C] -> [B -> D]
9208 static __isl_give isl_map *map_product_aligned(__isl_take isl_map *map1,
9209 __isl_take isl_map *map2)
9211 return map_product(map1, map2, &isl_space_product, &isl_basic_map_product);
9214 __isl_give isl_map *isl_map_product(__isl_take isl_map *map1,
9215 __isl_take isl_map *map2)
9217 return isl_map_align_params_map_map_and(map1, map2, &map_product_aligned);
9220 /* Given two maps A -> B and C -> D, construct a map (A, C) -> (B, D)
9222 __isl_give isl_map *isl_map_flat_product(__isl_take isl_map *map1,
9223 __isl_take isl_map *map2)
9227 prod = isl_map_product(map1, map2);
9228 prod = isl_map_flatten(prod);
9232 /* Given two set A and B, construct its Cartesian product A x B.
9234 struct isl_set *isl_set_product(struct isl_set *set1, struct isl_set *set2)
9236 return isl_map_range_product(set1, set2);
9239 __isl_give isl_set *isl_set_flat_product(__isl_take isl_set *set1,
9240 __isl_take isl_set *set2)
9242 return isl_map_flat_range_product(set1, set2);
9245 /* Given two maps A -> B and C -> D, construct a map [A -> C] -> (B * D)
9247 static __isl_give isl_map *map_domain_product_aligned(__isl_take isl_map *map1,
9248 __isl_take isl_map *map2)
9250 return map_product(map1, map2, &isl_space_domain_product,
9251 &isl_basic_map_domain_product);
9254 /* Given two maps A -> B and C -> D, construct a map (A * C) -> [B -> D]
9256 static __isl_give isl_map *map_range_product_aligned(__isl_take isl_map *map1,
9257 __isl_take isl_map *map2)
9259 return map_product(map1, map2, &isl_space_range_product,
9260 &isl_basic_map_range_product);
9263 __isl_give isl_map *isl_map_domain_product(__isl_take isl_map *map1,
9264 __isl_take isl_map *map2)
9266 return isl_map_align_params_map_map_and(map1, map2,
9267 &map_domain_product_aligned);
9270 __isl_give isl_map *isl_map_range_product(__isl_take isl_map *map1,
9271 __isl_take isl_map *map2)
9273 return isl_map_align_params_map_map_and(map1, map2,
9274 &map_range_product_aligned);
9277 /* Given two maps A -> B and C -> D, construct a map (A, C) -> (B * D)
9279 __isl_give isl_map *isl_map_flat_domain_product(__isl_take isl_map *map1,
9280 __isl_take isl_map *map2)
9284 prod = isl_map_domain_product(map1, map2);
9285 prod = isl_map_flatten_domain(prod);
9289 /* Given two maps A -> B and C -> D, construct a map (A * C) -> (B, D)
9291 __isl_give isl_map *isl_map_flat_range_product(__isl_take isl_map *map1,
9292 __isl_take isl_map *map2)
9296 prod = isl_map_range_product(map1, map2);
9297 prod = isl_map_flatten_range(prod);
9301 uint32_t isl_basic_map_get_hash(__isl_keep isl_basic_map *bmap)
9304 uint32_t hash = isl_hash_init();
9309 bmap = isl_basic_map_copy(bmap);
9310 bmap = isl_basic_map_normalize(bmap);
9313 total = isl_basic_map_total_dim(bmap);
9314 isl_hash_byte(hash, bmap->n_eq & 0xFF);
9315 for (i = 0; i < bmap->n_eq; ++i) {
9317 c_hash = isl_seq_get_hash(bmap->eq[i], 1 + total);
9318 isl_hash_hash(hash, c_hash);
9320 isl_hash_byte(hash, bmap->n_ineq & 0xFF);
9321 for (i = 0; i < bmap->n_ineq; ++i) {
9323 c_hash = isl_seq_get_hash(bmap->ineq[i], 1 + total);
9324 isl_hash_hash(hash, c_hash);
9326 isl_hash_byte(hash, bmap->n_div & 0xFF);
9327 for (i = 0; i < bmap->n_div; ++i) {
9329 if (isl_int_is_zero(bmap->div[i][0]))
9331 isl_hash_byte(hash, i & 0xFF);
9332 c_hash = isl_seq_get_hash(bmap->div[i], 1 + 1 + total);
9333 isl_hash_hash(hash, c_hash);
9335 isl_basic_map_free(bmap);
9339 uint32_t isl_basic_set_get_hash(__isl_keep isl_basic_set *bset)
9341 return isl_basic_map_get_hash((isl_basic_map *)bset);
9344 uint32_t isl_map_get_hash(__isl_keep isl_map *map)
9351 map = isl_map_copy(map);
9352 map = isl_map_normalize(map);
9356 hash = isl_hash_init();
9357 for (i = 0; i < map->n; ++i) {
9359 bmap_hash = isl_basic_map_get_hash(map->p[i]);
9360 isl_hash_hash(hash, bmap_hash);
9368 uint32_t isl_set_get_hash(__isl_keep isl_set *set)
9370 return isl_map_get_hash((isl_map *)set);
9373 /* Check if the value for dimension dim is completely determined
9374 * by the values of the other parameters and variables.
9375 * That is, check if dimension dim is involved in an equality.
9377 int isl_basic_set_dim_is_unique(struct isl_basic_set *bset, unsigned dim)
9384 nparam = isl_basic_set_n_param(bset);
9385 for (i = 0; i < bset->n_eq; ++i)
9386 if (!isl_int_is_zero(bset->eq[i][1 + nparam + dim]))
9391 /* Check if the value for dimension dim is completely determined
9392 * by the values of the other parameters and variables.
9393 * That is, check if dimension dim is involved in an equality
9394 * for each of the subsets.
9396 int isl_set_dim_is_unique(struct isl_set *set, unsigned dim)
9402 for (i = 0; i < set->n; ++i) {
9404 unique = isl_basic_set_dim_is_unique(set->p[i], dim);
9411 int isl_set_n_basic_set(__isl_keep isl_set *set)
9413 return set ? set->n : 0;
9416 int isl_map_foreach_basic_map(__isl_keep isl_map *map,
9417 int (*fn)(__isl_take isl_basic_map *bmap, void *user), void *user)
9424 for (i = 0; i < map->n; ++i)
9425 if (fn(isl_basic_map_copy(map->p[i]), user) < 0)
9431 int isl_set_foreach_basic_set(__isl_keep isl_set *set,
9432 int (*fn)(__isl_take isl_basic_set *bset, void *user), void *user)
9439 for (i = 0; i < set->n; ++i)
9440 if (fn(isl_basic_set_copy(set->p[i]), user) < 0)
9446 __isl_give isl_basic_set *isl_basic_set_lift(__isl_take isl_basic_set *bset)
9453 bset = isl_basic_set_cow(bset);
9457 dim = isl_basic_set_get_space(bset);
9458 dim = isl_space_lift(dim, bset->n_div);
9461 isl_space_free(bset->dim);
9463 bset->extra -= bset->n_div;
9466 bset = isl_basic_set_finalize(bset);
9470 isl_basic_set_free(bset);
9474 __isl_give isl_set *isl_set_lift(__isl_take isl_set *set)
9480 set = isl_set_align_divs(set);
9485 set = isl_set_cow(set);
9489 n_div = set->p[0]->n_div;
9490 dim = isl_set_get_space(set);
9491 dim = isl_space_lift(dim, n_div);
9494 isl_space_free(set->dim);
9497 for (i = 0; i < set->n; ++i) {
9498 set->p[i] = isl_basic_set_lift(set->p[i]);
9509 __isl_give isl_map *isl_set_lifting(__isl_take isl_set *set)
9512 struct isl_basic_map *bmap;
9519 set = isl_set_align_divs(set);
9524 dim = isl_set_get_space(set);
9525 if (set->n == 0 || set->p[0]->n_div == 0) {
9527 return isl_map_identity(isl_space_map_from_set(dim));
9530 n_div = set->p[0]->n_div;
9531 dim = isl_space_map_from_set(dim);
9532 n_param = isl_space_dim(dim, isl_dim_param);
9533 n_set = isl_space_dim(dim, isl_dim_in);
9534 dim = isl_space_extend(dim, n_param, n_set, n_set + n_div);
9535 bmap = isl_basic_map_alloc_space(dim, 0, n_set, 2 * n_div);
9536 for (i = 0; i < n_set; ++i)
9537 bmap = var_equal(bmap, i);
9539 total = n_param + n_set + n_set + n_div;
9540 for (i = 0; i < n_div; ++i) {
9541 k = isl_basic_map_alloc_inequality(bmap);
9544 isl_seq_cpy(bmap->ineq[k], set->p[0]->div[i]+1, 1+n_param);
9545 isl_seq_clr(bmap->ineq[k]+1+n_param, n_set);
9546 isl_seq_cpy(bmap->ineq[k]+1+n_param+n_set,
9547 set->p[0]->div[i]+1+1+n_param, n_set + n_div);
9548 isl_int_neg(bmap->ineq[k][1+n_param+n_set+n_set+i],
9549 set->p[0]->div[i][0]);
9551 l = isl_basic_map_alloc_inequality(bmap);
9554 isl_seq_neg(bmap->ineq[l], bmap->ineq[k], 1 + total);
9555 isl_int_add(bmap->ineq[l][0], bmap->ineq[l][0],
9556 set->p[0]->div[i][0]);
9557 isl_int_sub_ui(bmap->ineq[l][0], bmap->ineq[l][0], 1);
9561 bmap = isl_basic_map_simplify(bmap);
9562 bmap = isl_basic_map_finalize(bmap);
9563 return isl_map_from_basic_map(bmap);
9566 isl_basic_map_free(bmap);
9570 int isl_basic_set_size(__isl_keep isl_basic_set *bset)
9578 dim = isl_basic_set_total_dim(bset);
9579 size += bset->n_eq * (1 + dim);
9580 size += bset->n_ineq * (1 + dim);
9581 size += bset->n_div * (2 + dim);
9586 int isl_set_size(__isl_keep isl_set *set)
9594 for (i = 0; i < set->n; ++i)
9595 size += isl_basic_set_size(set->p[i]);
9600 /* Check if there is any lower bound (if lower == 0) and/or upper
9601 * bound (if upper == 0) on the specified dim.
9603 static int basic_map_dim_is_bounded(__isl_keep isl_basic_map *bmap,
9604 enum isl_dim_type type, unsigned pos, int lower, int upper)
9611 isl_assert(bmap->ctx, pos < isl_basic_map_dim(bmap, type), return -1);
9613 pos += isl_basic_map_offset(bmap, type);
9615 for (i = 0; i < bmap->n_div; ++i) {
9616 if (isl_int_is_zero(bmap->div[i][0]))
9618 if (!isl_int_is_zero(bmap->div[i][1 + pos]))
9622 for (i = 0; i < bmap->n_eq; ++i)
9623 if (!isl_int_is_zero(bmap->eq[i][pos]))
9626 for (i = 0; i < bmap->n_ineq; ++i) {
9627 int sgn = isl_int_sgn(bmap->ineq[i][pos]);
9634 return lower && upper;
9637 int isl_basic_map_dim_is_bounded(__isl_keep isl_basic_map *bmap,
9638 enum isl_dim_type type, unsigned pos)
9640 return basic_map_dim_is_bounded(bmap, type, pos, 0, 0);
9643 int isl_basic_map_dim_has_lower_bound(__isl_keep isl_basic_map *bmap,
9644 enum isl_dim_type type, unsigned pos)
9646 return basic_map_dim_is_bounded(bmap, type, pos, 0, 1);
9649 int isl_basic_map_dim_has_upper_bound(__isl_keep isl_basic_map *bmap,
9650 enum isl_dim_type type, unsigned pos)
9652 return basic_map_dim_is_bounded(bmap, type, pos, 1, 0);
9655 int isl_map_dim_is_bounded(__isl_keep isl_map *map,
9656 enum isl_dim_type type, unsigned pos)
9663 for (i = 0; i < map->n; ++i) {
9665 bounded = isl_basic_map_dim_is_bounded(map->p[i], type, pos);
9666 if (bounded < 0 || !bounded)
9673 /* Return 1 if the specified dim is involved in both an upper bound
9674 * and a lower bound.
9676 int isl_set_dim_is_bounded(__isl_keep isl_set *set,
9677 enum isl_dim_type type, unsigned pos)
9679 return isl_map_dim_is_bounded((isl_map *)set, type, pos);
9682 /* Does "map" have a bound (according to "fn") for any of its basic maps?
9684 static int has_any_bound(__isl_keep isl_map *map,
9685 enum isl_dim_type type, unsigned pos,
9686 int (*fn)(__isl_keep isl_basic_map *bmap,
9687 enum isl_dim_type type, unsigned pos))
9694 for (i = 0; i < map->n; ++i) {
9696 bounded = fn(map->p[i], type, pos);
9697 if (bounded < 0 || bounded)
9704 /* Return 1 if the specified dim is involved in any lower bound.
9706 int isl_set_dim_has_any_lower_bound(__isl_keep isl_set *set,
9707 enum isl_dim_type type, unsigned pos)
9709 return has_any_bound(set, type, pos,
9710 &isl_basic_map_dim_has_lower_bound);
9713 /* Return 1 if the specified dim is involved in any upper bound.
9715 int isl_set_dim_has_any_upper_bound(__isl_keep isl_set *set,
9716 enum isl_dim_type type, unsigned pos)
9718 return has_any_bound(set, type, pos,
9719 &isl_basic_map_dim_has_upper_bound);
9722 /* Does "map" have a bound (according to "fn") for all of its basic maps?
9724 static int has_bound(__isl_keep isl_map *map,
9725 enum isl_dim_type type, unsigned pos,
9726 int (*fn)(__isl_keep isl_basic_map *bmap,
9727 enum isl_dim_type type, unsigned pos))
9734 for (i = 0; i < map->n; ++i) {
9736 bounded = fn(map->p[i], type, pos);
9737 if (bounded < 0 || !bounded)
9744 /* Return 1 if the specified dim has a lower bound (in each of its basic sets).
9746 int isl_set_dim_has_lower_bound(__isl_keep isl_set *set,
9747 enum isl_dim_type type, unsigned pos)
9749 return has_bound(set, type, pos, &isl_basic_map_dim_has_lower_bound);
9752 /* Return 1 if the specified dim has an upper bound (in each of its basic sets).
9754 int isl_set_dim_has_upper_bound(__isl_keep isl_set *set,
9755 enum isl_dim_type type, unsigned pos)
9757 return has_bound(set, type, pos, &isl_basic_map_dim_has_upper_bound);
9760 /* For each of the "n" variables starting at "first", determine
9761 * the sign of the variable and put the results in the first "n"
9762 * elements of the array "signs".
9764 * 1 means that the variable is non-negative
9765 * -1 means that the variable is non-positive
9766 * 0 means the variable attains both positive and negative values.
9768 int isl_basic_set_vars_get_sign(__isl_keep isl_basic_set *bset,
9769 unsigned first, unsigned n, int *signs)
9771 isl_vec *bound = NULL;
9772 struct isl_tab *tab = NULL;
9773 struct isl_tab_undo *snap;
9776 if (!bset || !signs)
9779 bound = isl_vec_alloc(bset->ctx, 1 + isl_basic_set_total_dim(bset));
9780 tab = isl_tab_from_basic_set(bset, 0);
9784 isl_seq_clr(bound->el, bound->size);
9785 isl_int_set_si(bound->el[0], -1);
9787 snap = isl_tab_snap(tab);
9788 for (i = 0; i < n; ++i) {
9791 isl_int_set_si(bound->el[1 + first + i], -1);
9792 if (isl_tab_add_ineq(tab, bound->el) < 0)
9795 isl_int_set_si(bound->el[1 + first + i], 0);
9796 if (isl_tab_rollback(tab, snap) < 0)
9804 isl_int_set_si(bound->el[1 + first + i], 1);
9805 if (isl_tab_add_ineq(tab, bound->el) < 0)
9808 isl_int_set_si(bound->el[1 + first + i], 0);
9809 if (isl_tab_rollback(tab, snap) < 0)
9812 signs[i] = empty ? -1 : 0;
9816 isl_vec_free(bound);
9820 isl_vec_free(bound);
9824 int isl_basic_set_dims_get_sign(__isl_keep isl_basic_set *bset,
9825 enum isl_dim_type type, unsigned first, unsigned n, int *signs)
9827 if (!bset || !signs)
9829 isl_assert(bset->ctx, first + n <= isl_basic_set_dim(bset, type),
9832 first += pos(bset->dim, type) - 1;
9833 return isl_basic_set_vars_get_sign(bset, first, n, signs);
9836 /* Check if the given basic map is obviously single-valued.
9837 * In particular, for each output dimension, check that there is
9838 * an equality that defines the output dimension in terms of
9839 * earlier dimensions.
9841 int isl_basic_map_plain_is_single_valued(__isl_keep isl_basic_map *bmap)
9851 total = 1 + isl_basic_map_total_dim(bmap);
9852 n_out = isl_basic_map_dim(bmap, isl_dim_out);
9853 o_out = isl_basic_map_offset(bmap, isl_dim_out);
9855 for (i = 0; i < n_out; ++i) {
9856 for (j = 0; j < bmap->n_eq; ++j) {
9857 if (isl_int_is_zero(bmap->eq[j][o_out + i]))
9859 if (isl_seq_first_non_zero(bmap->eq[j] + o_out + i + 1,
9860 total - (o_out + i + 1)) == -1)
9863 if (j >= bmap->n_eq)
9870 /* Check if the given basic map is single-valued.
9875 * and check if the result is a subset of the identity mapping.
9877 int isl_basic_map_is_single_valued(__isl_keep isl_basic_map *bmap)
9880 isl_basic_map *test;
9884 sv = isl_basic_map_plain_is_single_valued(bmap);
9888 test = isl_basic_map_reverse(isl_basic_map_copy(bmap));
9889 test = isl_basic_map_apply_range(test, isl_basic_map_copy(bmap));
9891 space = isl_basic_map_get_space(bmap);
9892 space = isl_space_map_from_set(isl_space_range(space));
9893 id = isl_basic_map_identity(space);
9895 sv = isl_basic_map_is_subset(test, id);
9897 isl_basic_map_free(test);
9898 isl_basic_map_free(id);
9903 /* Check if the given map is obviously single-valued.
9905 int isl_map_plain_is_single_valued(__isl_keep isl_map *map)
9914 return isl_basic_map_plain_is_single_valued(map->p[0]);
9917 /* Check if the given map is single-valued.
9922 * and check if the result is a subset of the identity mapping.
9924 int isl_map_is_single_valued(__isl_keep isl_map *map)
9931 sv = isl_map_plain_is_single_valued(map);
9935 test = isl_map_reverse(isl_map_copy(map));
9936 test = isl_map_apply_range(test, isl_map_copy(map));
9938 dim = isl_space_map_from_set(isl_space_range(isl_map_get_space(map)));
9939 id = isl_map_identity(dim);
9941 sv = isl_map_is_subset(test, id);
9949 int isl_map_is_injective(__isl_keep isl_map *map)
9953 map = isl_map_copy(map);
9954 map = isl_map_reverse(map);
9955 in = isl_map_is_single_valued(map);
9961 /* Check if the given map is obviously injective.
9963 int isl_map_plain_is_injective(__isl_keep isl_map *map)
9967 map = isl_map_copy(map);
9968 map = isl_map_reverse(map);
9969 in = isl_map_plain_is_single_valued(map);
9975 int isl_map_is_bijective(__isl_keep isl_map *map)
9979 sv = isl_map_is_single_valued(map);
9983 return isl_map_is_injective(map);
9986 int isl_set_is_singleton(__isl_keep isl_set *set)
9988 return isl_map_is_single_valued((isl_map *)set);
9991 int isl_map_is_translation(__isl_keep isl_map *map)
9996 delta = isl_map_deltas(isl_map_copy(map));
9997 ok = isl_set_is_singleton(delta);
9998 isl_set_free(delta);
10003 static int unique(isl_int *p, unsigned pos, unsigned len)
10005 if (isl_seq_first_non_zero(p, pos) != -1)
10007 if (isl_seq_first_non_zero(p + pos + 1, len - pos - 1) != -1)
10012 int isl_basic_set_is_box(__isl_keep isl_basic_set *bset)
10021 if (isl_basic_set_dim(bset, isl_dim_div) != 0)
10024 nvar = isl_basic_set_dim(bset, isl_dim_set);
10025 ovar = isl_space_offset(bset->dim, isl_dim_set);
10026 for (j = 0; j < nvar; ++j) {
10027 int lower = 0, upper = 0;
10028 for (i = 0; i < bset->n_eq; ++i) {
10029 if (isl_int_is_zero(bset->eq[i][1 + ovar + j]))
10031 if (!unique(bset->eq[i] + 1 + ovar, j, nvar))
10035 if (i < bset->n_eq)
10037 for (i = 0; i < bset->n_ineq; ++i) {
10038 if (isl_int_is_zero(bset->ineq[i][1 + ovar + j]))
10040 if (!unique(bset->ineq[i] + 1 + ovar, j, nvar))
10042 if (isl_int_is_pos(bset->ineq[i][1 + ovar + j]))
10047 if (!lower || !upper)
10054 int isl_set_is_box(__isl_keep isl_set *set)
10061 return isl_basic_set_is_box(set->p[0]);
10064 int isl_basic_set_is_wrapping(__isl_keep isl_basic_set *bset)
10069 return isl_space_is_wrapping(bset->dim);
10072 int isl_set_is_wrapping(__isl_keep isl_set *set)
10077 return isl_space_is_wrapping(set->dim);
10080 __isl_give isl_basic_set *isl_basic_map_wrap(__isl_take isl_basic_map *bmap)
10082 bmap = isl_basic_map_cow(bmap);
10086 bmap->dim = isl_space_wrap(bmap->dim);
10090 bmap = isl_basic_map_finalize(bmap);
10092 return (isl_basic_set *)bmap;
10094 isl_basic_map_free(bmap);
10098 __isl_give isl_set *isl_map_wrap(__isl_take isl_map *map)
10102 map = isl_map_cow(map);
10106 for (i = 0; i < map->n; ++i) {
10107 map->p[i] = (isl_basic_map *)isl_basic_map_wrap(map->p[i]);
10111 map->dim = isl_space_wrap(map->dim);
10115 return (isl_set *)map;
10121 __isl_give isl_basic_map *isl_basic_set_unwrap(__isl_take isl_basic_set *bset)
10123 bset = isl_basic_set_cow(bset);
10127 bset->dim = isl_space_unwrap(bset->dim);
10131 bset = isl_basic_set_finalize(bset);
10133 return (isl_basic_map *)bset;
10135 isl_basic_set_free(bset);
10139 __isl_give isl_map *isl_set_unwrap(__isl_take isl_set *set)
10146 if (!isl_set_is_wrapping(set))
10147 isl_die(set->ctx, isl_error_invalid, "not a wrapping set",
10150 set = isl_set_cow(set);
10154 for (i = 0; i < set->n; ++i) {
10155 set->p[i] = (isl_basic_set *)isl_basic_set_unwrap(set->p[i]);
10160 set->dim = isl_space_unwrap(set->dim);
10164 return (isl_map *)set;
10170 __isl_give isl_basic_map *isl_basic_map_reset(__isl_take isl_basic_map *bmap,
10171 enum isl_dim_type type)
10176 if (!isl_space_is_named_or_nested(bmap->dim, type))
10179 bmap = isl_basic_map_cow(bmap);
10183 bmap->dim = isl_space_reset(bmap->dim, type);
10187 bmap = isl_basic_map_finalize(bmap);
10191 isl_basic_map_free(bmap);
10195 __isl_give isl_map *isl_map_reset(__isl_take isl_map *map,
10196 enum isl_dim_type type)
10203 if (!isl_space_is_named_or_nested(map->dim, type))
10206 map = isl_map_cow(map);
10210 for (i = 0; i < map->n; ++i) {
10211 map->p[i] = isl_basic_map_reset(map->p[i], type);
10215 map->dim = isl_space_reset(map->dim, type);
10225 __isl_give isl_basic_map *isl_basic_map_flatten(__isl_take isl_basic_map *bmap)
10230 if (!bmap->dim->nested[0] && !bmap->dim->nested[1])
10233 bmap = isl_basic_map_cow(bmap);
10237 bmap->dim = isl_space_flatten(bmap->dim);
10241 bmap = isl_basic_map_finalize(bmap);
10245 isl_basic_map_free(bmap);
10249 __isl_give isl_basic_set *isl_basic_set_flatten(__isl_take isl_basic_set *bset)
10251 return (isl_basic_set *)isl_basic_map_flatten((isl_basic_map *)bset);
10254 __isl_give isl_basic_map *isl_basic_map_flatten_domain(
10255 __isl_take isl_basic_map *bmap)
10260 if (!bmap->dim->nested[0])
10263 bmap = isl_basic_map_cow(bmap);
10267 bmap->dim = isl_space_flatten_domain(bmap->dim);
10271 bmap = isl_basic_map_finalize(bmap);
10275 isl_basic_map_free(bmap);
10279 __isl_give isl_basic_map *isl_basic_map_flatten_range(
10280 __isl_take isl_basic_map *bmap)
10285 if (!bmap->dim->nested[1])
10288 bmap = isl_basic_map_cow(bmap);
10292 bmap->dim = isl_space_flatten_range(bmap->dim);
10296 bmap = isl_basic_map_finalize(bmap);
10300 isl_basic_map_free(bmap);
10304 __isl_give isl_map *isl_map_flatten(__isl_take isl_map *map)
10311 if (!map->dim->nested[0] && !map->dim->nested[1])
10314 map = isl_map_cow(map);
10318 for (i = 0; i < map->n; ++i) {
10319 map->p[i] = isl_basic_map_flatten(map->p[i]);
10323 map->dim = isl_space_flatten(map->dim);
10333 __isl_give isl_set *isl_set_flatten(__isl_take isl_set *set)
10335 return (isl_set *)isl_map_flatten((isl_map *)set);
10338 __isl_give isl_map *isl_set_flatten_map(__isl_take isl_set *set)
10340 isl_space *dim, *flat_dim;
10343 dim = isl_set_get_space(set);
10344 flat_dim = isl_space_flatten(isl_space_copy(dim));
10345 map = isl_map_identity(isl_space_join(isl_space_reverse(dim), flat_dim));
10346 map = isl_map_intersect_domain(map, set);
10351 __isl_give isl_map *isl_map_flatten_domain(__isl_take isl_map *map)
10358 if (!map->dim->nested[0])
10361 map = isl_map_cow(map);
10365 for (i = 0; i < map->n; ++i) {
10366 map->p[i] = isl_basic_map_flatten_domain(map->p[i]);
10370 map->dim = isl_space_flatten_domain(map->dim);
10380 __isl_give isl_map *isl_map_flatten_range(__isl_take isl_map *map)
10387 if (!map->dim->nested[1])
10390 map = isl_map_cow(map);
10394 for (i = 0; i < map->n; ++i) {
10395 map->p[i] = isl_basic_map_flatten_range(map->p[i]);
10399 map->dim = isl_space_flatten_range(map->dim);
10409 /* Reorder the dimensions of "bmap" according to the given dim_map
10410 * and set the dimension specification to "dim".
10412 __isl_give isl_basic_map *isl_basic_map_realign(__isl_take isl_basic_map *bmap,
10413 __isl_take isl_space *dim, __isl_take struct isl_dim_map *dim_map)
10415 isl_basic_map *res;
10418 bmap = isl_basic_map_cow(bmap);
10419 if (!bmap || !dim || !dim_map)
10422 flags = bmap->flags;
10423 ISL_FL_CLR(flags, ISL_BASIC_MAP_FINAL);
10424 ISL_FL_CLR(flags, ISL_BASIC_MAP_NORMALIZED);
10425 ISL_FL_CLR(flags, ISL_BASIC_MAP_NORMALIZED_DIVS);
10426 res = isl_basic_map_alloc_space(dim,
10427 bmap->n_div, bmap->n_eq, bmap->n_ineq);
10428 res = isl_basic_map_add_constraints_dim_map(res, bmap, dim_map);
10430 res->flags = flags;
10431 res = isl_basic_map_finalize(res);
10435 isl_basic_map_free(bmap);
10436 isl_space_free(dim);
10440 /* Reorder the dimensions of "map" according to given reordering.
10442 __isl_give isl_map *isl_map_realign(__isl_take isl_map *map,
10443 __isl_take isl_reordering *r)
10446 struct isl_dim_map *dim_map;
10448 map = isl_map_cow(map);
10449 dim_map = isl_dim_map_from_reordering(r);
10450 if (!map || !r || !dim_map)
10453 for (i = 0; i < map->n; ++i) {
10454 struct isl_dim_map *dim_map_i;
10456 dim_map_i = isl_dim_map_extend(dim_map, map->p[i]);
10458 map->p[i] = isl_basic_map_realign(map->p[i],
10459 isl_space_copy(r->dim), dim_map_i);
10465 map = isl_map_reset_space(map, isl_space_copy(r->dim));
10467 isl_reordering_free(r);
10473 isl_reordering_free(r);
10477 __isl_give isl_set *isl_set_realign(__isl_take isl_set *set,
10478 __isl_take isl_reordering *r)
10480 return (isl_set *)isl_map_realign((isl_map *)set, r);
10483 __isl_give isl_map *isl_map_align_params(__isl_take isl_map *map,
10484 __isl_take isl_space *model)
10488 if (!map || !model)
10491 ctx = isl_space_get_ctx(model);
10492 if (!isl_space_has_named_params(model))
10493 isl_die(ctx, isl_error_invalid,
10494 "model has unnamed parameters", goto error);
10495 if (!isl_space_has_named_params(map->dim))
10496 isl_die(ctx, isl_error_invalid,
10497 "relation has unnamed parameters", goto error);
10498 if (!isl_space_match(map->dim, isl_dim_param, model, isl_dim_param)) {
10499 isl_reordering *exp;
10501 model = isl_space_drop_dims(model, isl_dim_in,
10502 0, isl_space_dim(model, isl_dim_in));
10503 model = isl_space_drop_dims(model, isl_dim_out,
10504 0, isl_space_dim(model, isl_dim_out));
10505 exp = isl_parameter_alignment_reordering(map->dim, model);
10506 exp = isl_reordering_extend_space(exp, isl_map_get_space(map));
10507 map = isl_map_realign(map, exp);
10510 isl_space_free(model);
10513 isl_space_free(model);
10518 __isl_give isl_set *isl_set_align_params(__isl_take isl_set *set,
10519 __isl_take isl_space *model)
10521 return isl_map_align_params(set, model);
10524 /* Align the parameters of "bmap" to those of "model", introducing
10525 * additional parameters if needed.
10527 __isl_give isl_basic_map *isl_basic_map_align_params(
10528 __isl_take isl_basic_map *bmap, __isl_take isl_space *model)
10532 if (!bmap || !model)
10535 ctx = isl_space_get_ctx(model);
10536 if (!isl_space_has_named_params(model))
10537 isl_die(ctx, isl_error_invalid,
10538 "model has unnamed parameters", goto error);
10539 if (!isl_space_has_named_params(bmap->dim))
10540 isl_die(ctx, isl_error_invalid,
10541 "relation has unnamed parameters", goto error);
10542 if (!isl_space_match(bmap->dim, isl_dim_param, model, isl_dim_param)) {
10543 isl_reordering *exp;
10544 struct isl_dim_map *dim_map;
10546 model = isl_space_drop_dims(model, isl_dim_in,
10547 0, isl_space_dim(model, isl_dim_in));
10548 model = isl_space_drop_dims(model, isl_dim_out,
10549 0, isl_space_dim(model, isl_dim_out));
10550 exp = isl_parameter_alignment_reordering(bmap->dim, model);
10551 exp = isl_reordering_extend_space(exp,
10552 isl_basic_map_get_space(bmap));
10553 dim_map = isl_dim_map_from_reordering(exp);
10554 bmap = isl_basic_map_realign(bmap,
10555 exp ? isl_space_copy(exp->dim) : NULL,
10556 isl_dim_map_extend(dim_map, bmap));
10557 isl_reordering_free(exp);
10561 isl_space_free(model);
10564 isl_space_free(model);
10565 isl_basic_map_free(bmap);
10569 /* Align the parameters of "bset" to those of "model", introducing
10570 * additional parameters if needed.
10572 __isl_give isl_basic_set *isl_basic_set_align_params(
10573 __isl_take isl_basic_set *bset, __isl_take isl_space *model)
10575 return isl_basic_map_align_params(bset, model);
10578 __isl_give isl_mat *isl_basic_map_equalities_matrix(
10579 __isl_keep isl_basic_map *bmap, enum isl_dim_type c1,
10580 enum isl_dim_type c2, enum isl_dim_type c3,
10581 enum isl_dim_type c4, enum isl_dim_type c5)
10583 enum isl_dim_type c[5] = { c1, c2, c3, c4, c5 };
10584 struct isl_mat *mat;
10590 mat = isl_mat_alloc(bmap->ctx, bmap->n_eq,
10591 isl_basic_map_total_dim(bmap) + 1);
10594 for (i = 0; i < bmap->n_eq; ++i)
10595 for (j = 0, pos = 0; j < 5; ++j) {
10596 int off = isl_basic_map_offset(bmap, c[j]);
10597 for (k = 0; k < isl_basic_map_dim(bmap, c[j]); ++k) {
10598 isl_int_set(mat->row[i][pos],
10599 bmap->eq[i][off + k]);
10607 __isl_give isl_mat *isl_basic_map_inequalities_matrix(
10608 __isl_keep isl_basic_map *bmap, enum isl_dim_type c1,
10609 enum isl_dim_type c2, enum isl_dim_type c3,
10610 enum isl_dim_type c4, enum isl_dim_type c5)
10612 enum isl_dim_type c[5] = { c1, c2, c3, c4, c5 };
10613 struct isl_mat *mat;
10619 mat = isl_mat_alloc(bmap->ctx, bmap->n_ineq,
10620 isl_basic_map_total_dim(bmap) + 1);
10623 for (i = 0; i < bmap->n_ineq; ++i)
10624 for (j = 0, pos = 0; j < 5; ++j) {
10625 int off = isl_basic_map_offset(bmap, c[j]);
10626 for (k = 0; k < isl_basic_map_dim(bmap, c[j]); ++k) {
10627 isl_int_set(mat->row[i][pos],
10628 bmap->ineq[i][off + k]);
10636 __isl_give isl_basic_map *isl_basic_map_from_constraint_matrices(
10637 __isl_take isl_space *dim,
10638 __isl_take isl_mat *eq, __isl_take isl_mat *ineq, enum isl_dim_type c1,
10639 enum isl_dim_type c2, enum isl_dim_type c3,
10640 enum isl_dim_type c4, enum isl_dim_type c5)
10642 enum isl_dim_type c[5] = { c1, c2, c3, c4, c5 };
10643 isl_basic_map *bmap;
10649 if (!dim || !eq || !ineq)
10652 if (eq->n_col != ineq->n_col)
10653 isl_die(dim->ctx, isl_error_invalid,
10654 "equalities and inequalities matrices should have "
10655 "same number of columns", goto error);
10657 total = 1 + isl_space_dim(dim, isl_dim_all);
10659 if (eq->n_col < total)
10660 isl_die(dim->ctx, isl_error_invalid,
10661 "number of columns too small", goto error);
10663 extra = eq->n_col - total;
10665 bmap = isl_basic_map_alloc_space(isl_space_copy(dim), extra,
10666 eq->n_row, ineq->n_row);
10669 for (i = 0; i < extra; ++i) {
10670 k = isl_basic_map_alloc_div(bmap);
10673 isl_int_set_si(bmap->div[k][0], 0);
10675 for (i = 0; i < eq->n_row; ++i) {
10676 l = isl_basic_map_alloc_equality(bmap);
10679 for (j = 0, pos = 0; j < 5; ++j) {
10680 int off = isl_basic_map_offset(bmap, c[j]);
10681 for (k = 0; k < isl_basic_map_dim(bmap, c[j]); ++k) {
10682 isl_int_set(bmap->eq[l][off + k],
10688 for (i = 0; i < ineq->n_row; ++i) {
10689 l = isl_basic_map_alloc_inequality(bmap);
10692 for (j = 0, pos = 0; j < 5; ++j) {
10693 int off = isl_basic_map_offset(bmap, c[j]);
10694 for (k = 0; k < isl_basic_map_dim(bmap, c[j]); ++k) {
10695 isl_int_set(bmap->ineq[l][off + k],
10696 ineq->row[i][pos]);
10702 isl_space_free(dim);
10704 isl_mat_free(ineq);
10706 bmap = isl_basic_map_simplify(bmap);
10707 return isl_basic_map_finalize(bmap);
10709 isl_space_free(dim);
10711 isl_mat_free(ineq);
10715 __isl_give isl_mat *isl_basic_set_equalities_matrix(
10716 __isl_keep isl_basic_set *bset, enum isl_dim_type c1,
10717 enum isl_dim_type c2, enum isl_dim_type c3, enum isl_dim_type c4)
10719 return isl_basic_map_equalities_matrix((isl_basic_map *)bset,
10720 c1, c2, c3, c4, isl_dim_in);
10723 __isl_give isl_mat *isl_basic_set_inequalities_matrix(
10724 __isl_keep isl_basic_set *bset, enum isl_dim_type c1,
10725 enum isl_dim_type c2, enum isl_dim_type c3, enum isl_dim_type c4)
10727 return isl_basic_map_inequalities_matrix((isl_basic_map *)bset,
10728 c1, c2, c3, c4, isl_dim_in);
10731 __isl_give isl_basic_set *isl_basic_set_from_constraint_matrices(
10732 __isl_take isl_space *dim,
10733 __isl_take isl_mat *eq, __isl_take isl_mat *ineq, enum isl_dim_type c1,
10734 enum isl_dim_type c2, enum isl_dim_type c3, enum isl_dim_type c4)
10736 return (isl_basic_set*)
10737 isl_basic_map_from_constraint_matrices(dim, eq, ineq,
10738 c1, c2, c3, c4, isl_dim_in);
10741 int isl_basic_map_can_zip(__isl_keep isl_basic_map *bmap)
10746 return isl_space_can_zip(bmap->dim);
10749 int isl_map_can_zip(__isl_keep isl_map *map)
10754 return isl_space_can_zip(map->dim);
10757 /* Given a basic map (A -> B) -> (C -> D), return the corresponding basic map
10758 * (A -> C) -> (B -> D).
10760 __isl_give isl_basic_map *isl_basic_map_zip(__isl_take isl_basic_map *bmap)
10769 if (!isl_basic_map_can_zip(bmap))
10770 isl_die(bmap->ctx, isl_error_invalid,
10771 "basic map cannot be zipped", goto error);
10772 pos = isl_basic_map_offset(bmap, isl_dim_in) +
10773 isl_space_dim(bmap->dim->nested[0], isl_dim_in);
10774 n1 = isl_space_dim(bmap->dim->nested[0], isl_dim_out);
10775 n2 = isl_space_dim(bmap->dim->nested[1], isl_dim_in);
10776 bmap = isl_basic_map_cow(bmap);
10777 bmap = isl_basic_map_swap_vars(bmap, pos, n1, n2);
10780 bmap->dim = isl_space_zip(bmap->dim);
10785 isl_basic_map_free(bmap);
10789 /* Given a map (A -> B) -> (C -> D), return the corresponding map
10790 * (A -> C) -> (B -> D).
10792 __isl_give isl_map *isl_map_zip(__isl_take isl_map *map)
10799 if (!isl_map_can_zip(map))
10800 isl_die(map->ctx, isl_error_invalid, "map cannot be zipped",
10803 map = isl_map_cow(map);
10807 for (i = 0; i < map->n; ++i) {
10808 map->p[i] = isl_basic_map_zip(map->p[i]);
10813 map->dim = isl_space_zip(map->dim);
10823 /* Can we apply isl_basic_map_curry to "bmap"?
10824 * That is, does it have a nested relation in its domain?
10826 int isl_basic_map_can_curry(__isl_keep isl_basic_map *bmap)
10831 return isl_space_can_curry(bmap->dim);
10834 /* Can we apply isl_map_curry to "map"?
10835 * That is, does it have a nested relation in its domain?
10837 int isl_map_can_curry(__isl_keep isl_map *map)
10842 return isl_space_can_curry(map->dim);
10845 /* Given a basic map (A -> B) -> C, return the corresponding basic map
10848 __isl_give isl_basic_map *isl_basic_map_curry(__isl_take isl_basic_map *bmap)
10854 if (!isl_basic_map_can_curry(bmap))
10855 isl_die(bmap->ctx, isl_error_invalid,
10856 "basic map cannot be curried", goto error);
10857 bmap = isl_basic_map_cow(bmap);
10860 bmap->dim = isl_space_curry(bmap->dim);
10865 isl_basic_map_free(bmap);
10869 /* Given a map (A -> B) -> C, return the corresponding map
10872 __isl_give isl_map *isl_map_curry(__isl_take isl_map *map)
10879 if (!isl_map_can_curry(map))
10880 isl_die(map->ctx, isl_error_invalid, "map cannot be curried",
10883 map = isl_map_cow(map);
10887 for (i = 0; i < map->n; ++i) {
10888 map->p[i] = isl_basic_map_curry(map->p[i]);
10893 map->dim = isl_space_curry(map->dim);
10903 /* Can we apply isl_basic_map_uncurry to "bmap"?
10904 * That is, does it have a nested relation in its domain?
10906 int isl_basic_map_can_uncurry(__isl_keep isl_basic_map *bmap)
10911 return isl_space_can_uncurry(bmap->dim);
10914 /* Can we apply isl_map_uncurry to "map"?
10915 * That is, does it have a nested relation in its domain?
10917 int isl_map_can_uncurry(__isl_keep isl_map *map)
10922 return isl_space_can_uncurry(map->dim);
10925 /* Given a basic map A -> (B -> C), return the corresponding basic map
10928 __isl_give isl_basic_map *isl_basic_map_uncurry(__isl_take isl_basic_map *bmap)
10934 if (!isl_basic_map_can_uncurry(bmap))
10935 isl_die(bmap->ctx, isl_error_invalid,
10936 "basic map cannot be uncurried",
10937 return isl_basic_map_free(bmap));
10938 bmap = isl_basic_map_cow(bmap);
10941 bmap->dim = isl_space_uncurry(bmap->dim);
10943 return isl_basic_map_free(bmap);
10947 /* Given a map A -> (B -> C), return the corresponding map
10950 __isl_give isl_map *isl_map_uncurry(__isl_take isl_map *map)
10957 if (!isl_map_can_uncurry(map))
10958 isl_die(map->ctx, isl_error_invalid, "map cannot be uncurried",
10959 return isl_map_free(map));
10961 map = isl_map_cow(map);
10965 for (i = 0; i < map->n; ++i) {
10966 map->p[i] = isl_basic_map_uncurry(map->p[i]);
10968 return isl_map_free(map);
10971 map->dim = isl_space_uncurry(map->dim);
10973 return isl_map_free(map);
10978 /* Construct a basic map mapping the domain of the affine expression
10979 * to a one-dimensional range prescribed by the affine expression.
10981 __isl_give isl_basic_map *isl_basic_map_from_aff(__isl_take isl_aff *aff)
10985 isl_local_space *ls;
10986 isl_basic_map *bmap;
10991 ls = isl_aff_get_local_space(aff);
10992 bmap = isl_basic_map_from_local_space(ls);
10993 bmap = isl_basic_map_extend_constraints(bmap, 1, 0);
10994 k = isl_basic_map_alloc_equality(bmap);
10998 pos = isl_basic_map_offset(bmap, isl_dim_out);
10999 isl_seq_cpy(bmap->eq[k], aff->v->el + 1, pos);
11000 isl_int_neg(bmap->eq[k][pos], aff->v->el[0]);
11001 isl_seq_cpy(bmap->eq[k] + pos + 1, aff->v->el + 1 + pos,
11002 aff->v->size - (pos + 1));
11005 bmap = isl_basic_map_finalize(bmap);
11009 isl_basic_map_free(bmap);
11013 /* Construct a map mapping the domain of the affine expression
11014 * to a one-dimensional range prescribed by the affine expression.
11016 __isl_give isl_map *isl_map_from_aff(__isl_take isl_aff *aff)
11018 isl_basic_map *bmap;
11020 bmap = isl_basic_map_from_aff(aff);
11021 return isl_map_from_basic_map(bmap);
11024 /* Construct a basic map mapping the domain the multi-affine expression
11025 * to its range, with each dimension in the range equated to the
11026 * corresponding affine expression.
11028 __isl_give isl_basic_map *isl_basic_map_from_multi_aff(
11029 __isl_take isl_multi_aff *maff)
11033 isl_basic_map *bmap;
11038 if (isl_space_dim(maff->space, isl_dim_out) != maff->n)
11039 isl_die(isl_multi_aff_get_ctx(maff), isl_error_internal,
11040 "invalid space", return isl_multi_aff_free(maff));
11042 space = isl_space_domain(isl_multi_aff_get_space(maff));
11043 bmap = isl_basic_map_universe(isl_space_from_domain(space));
11045 for (i = 0; i < maff->n; ++i) {
11047 isl_basic_map *bmap_i;
11049 aff = isl_aff_copy(maff->p[i]);
11050 bmap_i = isl_basic_map_from_aff(aff);
11052 bmap = isl_basic_map_flat_range_product(bmap, bmap_i);
11055 bmap = isl_basic_map_reset_space(bmap, isl_multi_aff_get_space(maff));
11057 isl_multi_aff_free(maff);
11061 /* Construct a map mapping the domain the multi-affine expression
11062 * to its range, with each dimension in the range equated to the
11063 * corresponding affine expression.
11065 __isl_give isl_map *isl_map_from_multi_aff(__isl_take isl_multi_aff *maff)
11067 isl_basic_map *bmap;
11069 bmap = isl_basic_map_from_multi_aff(maff);
11070 return isl_map_from_basic_map(bmap);
11073 /* Construct a basic map mapping a domain in the given space to
11074 * to an n-dimensional range, with n the number of elements in the list,
11075 * where each coordinate in the range is prescribed by the
11076 * corresponding affine expression.
11077 * The domains of all affine expressions in the list are assumed to match
11080 __isl_give isl_basic_map *isl_basic_map_from_aff_list(
11081 __isl_take isl_space *domain_dim, __isl_take isl_aff_list *list)
11085 isl_basic_map *bmap;
11090 dim = isl_space_from_domain(domain_dim);
11091 bmap = isl_basic_map_universe(dim);
11093 for (i = 0; i < list->n; ++i) {
11095 isl_basic_map *bmap_i;
11097 aff = isl_aff_copy(list->p[i]);
11098 bmap_i = isl_basic_map_from_aff(aff);
11100 bmap = isl_basic_map_flat_range_product(bmap, bmap_i);
11103 isl_aff_list_free(list);
11107 __isl_give isl_set *isl_set_equate(__isl_take isl_set *set,
11108 enum isl_dim_type type1, int pos1, enum isl_dim_type type2, int pos2)
11110 return isl_map_equate(set, type1, pos1, type2, pos2);
11113 /* Construct a basic map where the given dimensions are equal to each other.
11115 static __isl_give isl_basic_map *equator(__isl_take isl_space *space,
11116 enum isl_dim_type type1, int pos1, enum isl_dim_type type2, int pos2)
11118 isl_basic_map *bmap = NULL;
11124 if (pos1 >= isl_space_dim(space, type1))
11125 isl_die(isl_space_get_ctx(space), isl_error_invalid,
11126 "index out of bounds", goto error);
11127 if (pos2 >= isl_space_dim(space, type2))
11128 isl_die(isl_space_get_ctx(space), isl_error_invalid,
11129 "index out of bounds", goto error);
11131 if (type1 == type2 && pos1 == pos2)
11132 return isl_basic_map_universe(space);
11134 bmap = isl_basic_map_alloc_space(isl_space_copy(space), 0, 1, 0);
11135 i = isl_basic_map_alloc_equality(bmap);
11138 isl_seq_clr(bmap->eq[i], 1 + isl_basic_map_total_dim(bmap));
11139 pos1 += isl_basic_map_offset(bmap, type1);
11140 pos2 += isl_basic_map_offset(bmap, type2);
11141 isl_int_set_si(bmap->eq[i][pos1], -1);
11142 isl_int_set_si(bmap->eq[i][pos2], 1);
11143 bmap = isl_basic_map_finalize(bmap);
11144 isl_space_free(space);
11147 isl_space_free(space);
11148 isl_basic_map_free(bmap);
11152 /* Add a constraint imposing that the given two dimensions are equal.
11154 __isl_give isl_basic_map *isl_basic_map_equate(__isl_take isl_basic_map *bmap,
11155 enum isl_dim_type type1, int pos1, enum isl_dim_type type2, int pos2)
11159 eq = equator(isl_basic_map_get_space(bmap), type1, pos1, type2, pos2);
11161 bmap = isl_basic_map_intersect(bmap, eq);
11166 /* Add a constraint imposing that the given two dimensions are equal.
11168 __isl_give isl_map *isl_map_equate(__isl_take isl_map *map,
11169 enum isl_dim_type type1, int pos1, enum isl_dim_type type2, int pos2)
11171 isl_basic_map *bmap;
11173 bmap = equator(isl_map_get_space(map), type1, pos1, type2, pos2);
11175 map = isl_map_intersect(map, isl_map_from_basic_map(bmap));
11180 /* Add a constraint imposing that the given two dimensions have opposite values.
11182 __isl_give isl_map *isl_map_oppose(__isl_take isl_map *map,
11183 enum isl_dim_type type1, int pos1, enum isl_dim_type type2, int pos2)
11185 isl_basic_map *bmap = NULL;
11191 if (pos1 >= isl_map_dim(map, type1))
11192 isl_die(map->ctx, isl_error_invalid,
11193 "index out of bounds", goto error);
11194 if (pos2 >= isl_map_dim(map, type2))
11195 isl_die(map->ctx, isl_error_invalid,
11196 "index out of bounds", goto error);
11198 bmap = isl_basic_map_alloc_space(isl_map_get_space(map), 0, 1, 0);
11199 i = isl_basic_map_alloc_equality(bmap);
11202 isl_seq_clr(bmap->eq[i], 1 + isl_basic_map_total_dim(bmap));
11203 pos1 += isl_basic_map_offset(bmap, type1);
11204 pos2 += isl_basic_map_offset(bmap, type2);
11205 isl_int_set_si(bmap->eq[i][pos1], 1);
11206 isl_int_set_si(bmap->eq[i][pos2], 1);
11207 bmap = isl_basic_map_finalize(bmap);
11209 map = isl_map_intersect(map, isl_map_from_basic_map(bmap));
11213 isl_basic_map_free(bmap);
11218 /* Add a constraint imposing that the value of the first dimension is
11219 * greater than or equal to that of the second.
11221 __isl_give isl_basic_map *isl_basic_map_order_ge(__isl_take isl_basic_map *bmap,
11222 enum isl_dim_type type1, int pos1, enum isl_dim_type type2, int pos2)
11225 isl_local_space *ls;
11230 if (pos1 >= isl_basic_map_dim(bmap, type1))
11231 isl_die(bmap->ctx, isl_error_invalid,
11232 "index out of bounds", return isl_basic_map_free(bmap));
11233 if (pos2 >= isl_basic_map_dim(bmap, type2))
11234 isl_die(bmap->ctx, isl_error_invalid,
11235 "index out of bounds", return isl_basic_map_free(bmap));
11237 if (type1 == type2 && pos1 == pos2)
11240 ls = isl_local_space_from_space(isl_basic_map_get_space(bmap));
11241 c = isl_inequality_alloc(ls);
11242 c = isl_constraint_set_coefficient_si(c, type1, pos1, 1);
11243 c = isl_constraint_set_coefficient_si(c, type2, pos2, -1);
11244 bmap = isl_basic_map_add_constraint(bmap, c);
11249 /* Construct a basic map where the value of the first dimension is
11250 * greater than that of the second.
11252 static __isl_give isl_basic_map *greator(__isl_take isl_space *space,
11253 enum isl_dim_type type1, int pos1, enum isl_dim_type type2, int pos2)
11255 isl_basic_map *bmap = NULL;
11261 if (pos1 >= isl_space_dim(space, type1))
11262 isl_die(isl_space_get_ctx(space), isl_error_invalid,
11263 "index out of bounds", goto error);
11264 if (pos2 >= isl_space_dim(space, type2))
11265 isl_die(isl_space_get_ctx(space), isl_error_invalid,
11266 "index out of bounds", goto error);
11268 if (type1 == type2 && pos1 == pos2)
11269 return isl_basic_map_empty(space);
11271 bmap = isl_basic_map_alloc_space(space, 0, 0, 1);
11272 i = isl_basic_map_alloc_inequality(bmap);
11275 isl_seq_clr(bmap->ineq[i], 1 + isl_basic_map_total_dim(bmap));
11276 pos1 += isl_basic_map_offset(bmap, type1);
11277 pos2 += isl_basic_map_offset(bmap, type2);
11278 isl_int_set_si(bmap->ineq[i][pos1], 1);
11279 isl_int_set_si(bmap->ineq[i][pos2], -1);
11280 isl_int_set_si(bmap->ineq[i][0], -1);
11281 bmap = isl_basic_map_finalize(bmap);
11285 isl_space_free(space);
11286 isl_basic_map_free(bmap);
11290 /* Add a constraint imposing that the value of the first dimension is
11291 * greater than that of the second.
11293 __isl_give isl_basic_map *isl_basic_map_order_gt(__isl_take isl_basic_map *bmap,
11294 enum isl_dim_type type1, int pos1, enum isl_dim_type type2, int pos2)
11298 gt = greator(isl_basic_map_get_space(bmap), type1, pos1, type2, pos2);
11300 bmap = isl_basic_map_intersect(bmap, gt);
11305 /* Add a constraint imposing that the value of the first dimension is
11306 * greater than that of the second.
11308 __isl_give isl_map *isl_map_order_gt(__isl_take isl_map *map,
11309 enum isl_dim_type type1, int pos1, enum isl_dim_type type2, int pos2)
11311 isl_basic_map *bmap;
11313 bmap = greator(isl_map_get_space(map), type1, pos1, type2, pos2);
11315 map = isl_map_intersect(map, isl_map_from_basic_map(bmap));
11320 /* Add a constraint imposing that the value of the first dimension is
11321 * smaller than that of the second.
11323 __isl_give isl_map *isl_map_order_lt(__isl_take isl_map *map,
11324 enum isl_dim_type type1, int pos1, enum isl_dim_type type2, int pos2)
11326 return isl_map_order_gt(map, type2, pos2, type1, pos1);
11329 __isl_give isl_aff *isl_basic_map_get_div(__isl_keep isl_basic_map *bmap,
11333 isl_local_space *ls;
11338 if (!isl_basic_map_divs_known(bmap))
11339 isl_die(isl_basic_map_get_ctx(bmap), isl_error_invalid,
11340 "some divs are unknown", return NULL);
11342 ls = isl_basic_map_get_local_space(bmap);
11343 div = isl_local_space_get_div(ls, pos);
11344 isl_local_space_free(ls);
11349 __isl_give isl_aff *isl_basic_set_get_div(__isl_keep isl_basic_set *bset,
11352 return isl_basic_map_get_div(bset, pos);
11355 /* Plug in "subs" for dimension "type", "pos" of "bset".
11357 * Let i be the dimension to replace and let "subs" be of the form
11361 * Any integer division with a non-zero coefficient for i,
11363 * floor((a i + g)/m)
11367 * floor((a f + d g)/(m d))
11369 * Constraints of the form
11377 * We currently require that "subs" is an integral expression.
11378 * Handling rational expressions may require us to add stride constraints
11379 * as we do in isl_basic_set_preimage_multi_aff.
11381 __isl_give isl_basic_set *isl_basic_set_substitute(
11382 __isl_take isl_basic_set *bset,
11383 enum isl_dim_type type, unsigned pos, __isl_keep isl_aff *subs)
11389 if (bset && isl_basic_set_plain_is_empty(bset))
11392 bset = isl_basic_set_cow(bset);
11393 if (!bset || !subs)
11396 ctx = isl_basic_set_get_ctx(bset);
11397 if (!isl_space_is_equal(bset->dim, subs->ls->dim))
11398 isl_die(ctx, isl_error_invalid,
11399 "spaces don't match", goto error);
11400 if (isl_local_space_dim(subs->ls, isl_dim_div) != 0)
11401 isl_die(ctx, isl_error_unsupported,
11402 "cannot handle divs yet", goto error);
11403 if (!isl_int_is_one(subs->v->el[0]))
11404 isl_die(ctx, isl_error_invalid,
11405 "can only substitute integer expressions", goto error);
11407 pos += isl_basic_set_offset(bset, type);
11411 for (i = 0; i < bset->n_eq; ++i) {
11412 if (isl_int_is_zero(bset->eq[i][pos]))
11414 isl_int_set(v, bset->eq[i][pos]);
11415 isl_int_set_si(bset->eq[i][pos], 0);
11416 isl_seq_combine(bset->eq[i], subs->v->el[0], bset->eq[i],
11417 v, subs->v->el + 1, subs->v->size - 1);
11420 for (i = 0; i < bset->n_ineq; ++i) {
11421 if (isl_int_is_zero(bset->ineq[i][pos]))
11423 isl_int_set(v, bset->ineq[i][pos]);
11424 isl_int_set_si(bset->ineq[i][pos], 0);
11425 isl_seq_combine(bset->ineq[i], subs->v->el[0], bset->ineq[i],
11426 v, subs->v->el + 1, subs->v->size - 1);
11429 for (i = 0; i < bset->n_div; ++i) {
11430 if (isl_int_is_zero(bset->div[i][1 + pos]))
11432 isl_int_set(v, bset->div[i][1 + pos]);
11433 isl_int_set_si(bset->div[i][1 + pos], 0);
11434 isl_seq_combine(bset->div[i] + 1,
11435 subs->v->el[0], bset->div[i] + 1,
11436 v, subs->v->el + 1, subs->v->size - 1);
11437 isl_int_mul(bset->div[i][0], bset->div[i][0], subs->v->el[0]);
11442 bset = isl_basic_set_simplify(bset);
11443 return isl_basic_set_finalize(bset);
11445 isl_basic_set_free(bset);
11449 /* Plug in "subs" for dimension "type", "pos" of "set".
11451 __isl_give isl_set *isl_set_substitute(__isl_take isl_set *set,
11452 enum isl_dim_type type, unsigned pos, __isl_keep isl_aff *subs)
11456 if (set && isl_set_plain_is_empty(set))
11459 set = isl_set_cow(set);
11463 for (i = set->n - 1; i >= 0; --i) {
11464 set->p[i] = isl_basic_set_substitute(set->p[i], type, pos, subs);
11465 if (remove_if_empty(set, i) < 0)
11475 /* Check if the range of "ma" is compatible with the domain or range
11476 * (depending on "type") of "bmap".
11477 * Return -1 if anything is wrong.
11479 static int check_basic_map_compatible_range_multi_aff(
11480 __isl_keep isl_basic_map *bmap, enum isl_dim_type type,
11481 __isl_keep isl_multi_aff *ma)
11484 isl_space *ma_space;
11486 ma_space = isl_multi_aff_get_space(ma);
11487 m = isl_space_tuple_match(bmap->dim, type, ma_space, isl_dim_out);
11488 isl_space_free(ma_space);
11490 isl_die(isl_basic_map_get_ctx(bmap), isl_error_invalid,
11491 "spaces don't match", return -1);
11495 /* Copy the divs from "ma" to "bmap", adding zeros for the "n_before"
11496 * coefficients before the transformed range of dimensions,
11497 * the "n_after" coefficients after the transformed range of dimensions
11498 * and the coefficients of the other divs in "bmap".
11500 static int set_ma_divs(__isl_keep isl_basic_map *bmap,
11501 __isl_keep isl_multi_aff *ma, int n_before, int n_after, int n_div)
11506 isl_local_space *ls;
11511 ls = isl_aff_get_domain_local_space(ma->p[0]);
11515 n_param = isl_local_space_dim(ls, isl_dim_param);
11516 n_set = isl_local_space_dim(ls, isl_dim_set);
11517 for (i = 0; i < n_div; ++i) {
11518 int o_bmap = 0, o_ls = 0;
11520 isl_seq_cpy(bmap->div[i], ls->div->row[i], 1 + 1 + n_param);
11521 o_bmap += 1 + 1 + n_param;
11522 o_ls += 1 + 1 + n_param;
11523 isl_seq_clr(bmap->div[i] + o_bmap, n_before);
11524 o_bmap += n_before;
11525 isl_seq_cpy(bmap->div[i] + o_bmap,
11526 ls->div->row[i] + o_ls, n_set);
11529 isl_seq_clr(bmap->div[i] + o_bmap, n_after);
11531 isl_seq_cpy(bmap->div[i] + o_bmap,
11532 ls->div->row[i] + o_ls, n_div);
11535 isl_seq_clr(bmap->div[i] + o_bmap, bmap->n_div - n_div);
11536 if (isl_basic_set_add_div_constraints(bmap, i) < 0)
11540 isl_local_space_free(ls);
11543 isl_local_space_free(ls);
11547 /* How many stride constraints does "ma" enforce?
11548 * That is, how many of the affine expressions have a denominator
11549 * different from one?
11551 static int multi_aff_strides(__isl_keep isl_multi_aff *ma)
11556 for (i = 0; i < ma->n; ++i)
11557 if (!isl_int_is_one(ma->p[i]->v->el[0]))
11563 /* For each affine expression in ma of the form
11565 * x_i = (f_i y + h_i)/m_i
11567 * with m_i different from one, add a constraint to "bmap"
11570 * f_i y + h_i = m_i alpha_i
11572 * with alpha_i an additional existentially quantified variable.
11574 static __isl_give isl_basic_map *add_ma_strides(
11575 __isl_take isl_basic_map *bmap, __isl_keep isl_multi_aff *ma,
11576 int n_before, int n_after)
11585 total = isl_basic_map_total_dim(bmap);
11586 n_param = isl_multi_aff_dim(ma, isl_dim_param);
11587 n_in = isl_multi_aff_dim(ma, isl_dim_in);
11588 n_div = isl_multi_aff_dim(ma, isl_dim_div);
11589 for (i = 0; i < ma->n; ++i) {
11590 int o_bmap = 0, o_ma = 1;
11592 if (isl_int_is_one(ma->p[i]->v->el[0]))
11594 div = isl_basic_map_alloc_div(bmap);
11595 k = isl_basic_map_alloc_equality(bmap);
11596 if (div < 0 || k < 0)
11598 isl_int_set_si(bmap->div[div][0], 0);
11599 isl_seq_cpy(bmap->eq[k] + o_bmap,
11600 ma->p[i]->v->el + o_ma, 1 + n_param);
11601 o_bmap += 1 + n_param;
11602 o_ma += 1 + n_param;
11603 isl_seq_clr(bmap->eq[k] + o_bmap, n_before);
11604 o_bmap += n_before;
11605 isl_seq_cpy(bmap->eq[k] + o_bmap,
11606 ma->p[i]->v->el + o_ma, n_in);
11609 isl_seq_clr(bmap->eq[k] + o_bmap, n_after);
11611 isl_seq_cpy(bmap->eq[k] + o_bmap,
11612 ma->p[i]->v->el + o_ma, n_div);
11615 isl_seq_clr(bmap->eq[k] + o_bmap, 1 + total - o_bmap);
11616 isl_int_neg(bmap->eq[k][1 + total], ma->p[i]->v->el[0]);
11622 isl_basic_map_free(bmap);
11626 /* Replace the domain or range space (depending on "type) of "space" by "set".
11628 static __isl_give isl_space *isl_space_set(__isl_take isl_space *space,
11629 enum isl_dim_type type, __isl_take isl_space *set)
11631 if (type == isl_dim_in) {
11632 space = isl_space_range(space);
11633 space = isl_space_map_from_domain_and_range(set, space);
11635 space = isl_space_domain(space);
11636 space = isl_space_map_from_domain_and_range(space, set);
11642 /* Compute the preimage of the domain or range (depending on "type")
11643 * of "bmap" under the function represented by "ma".
11644 * In other words, plug in "ma" in the domain or range of "bmap".
11645 * The result is a basic map that lives in the same space as "bmap"
11646 * except that the domain or range has been replaced by
11647 * the domain space of "ma".
11649 * If bmap is represented by
11651 * A(p) + S u + B x + T v + C(divs) >= 0,
11653 * where u and x are input and output dimensions if type == isl_dim_out
11654 * while x and v are input and output dimensions if type == isl_dim_in,
11655 * and ma is represented by
11657 * x = D(p) + F(y) + G(divs')
11659 * then the result is
11661 * A(p) + B D(p) + S u + B F(y) + T v + B G(divs') + C(divs) >= 0
11663 * The divs in the input set are similarly adjusted.
11666 * floor((a_i(p) + s u + b_i x + t v + c_i(divs))/n_i)
11670 * floor((a_i(p) + b_i D(p) + s u + b_i F(y) + t v +
11671 * B_i G(divs') + c_i(divs))/n_i)
11673 * If bmap is not a rational map and if F(y) involves any denominators
11675 * x_i = (f_i y + h_i)/m_i
11677 * then additional constraints are added to ensure that we only
11678 * map back integer points. That is we enforce
11680 * f_i y + h_i = m_i alpha_i
11682 * with alpha_i an additional existentially quantified variable.
11684 * We first copy over the divs from "ma".
11685 * Then we add the modified constraints and divs from "bmap".
11686 * Finally, we add the stride constraints, if needed.
11688 __isl_give isl_basic_map *isl_basic_map_preimage_multi_aff(
11689 __isl_take isl_basic_map *bmap, enum isl_dim_type type,
11690 __isl_take isl_multi_aff *ma)
11694 isl_basic_map *res = NULL;
11695 int n_before, n_after, n_div_bmap, n_div_ma;
11696 isl_int f, c1, c2, g;
11697 int rational, strides;
11704 ma = isl_multi_aff_align_divs(ma);
11707 if (check_basic_map_compatible_range_multi_aff(bmap, type, ma) < 0)
11710 if (type == isl_dim_in) {
11712 n_after = isl_basic_map_dim(bmap, isl_dim_out);
11714 n_before = isl_basic_map_dim(bmap, isl_dim_in);
11717 n_div_bmap = isl_basic_map_dim(bmap, isl_dim_div);
11718 n_div_ma = ma->n ? isl_aff_dim(ma->p[0], isl_dim_div) : 0;
11720 space = isl_multi_aff_get_domain_space(ma);
11721 space = isl_space_set(isl_basic_map_get_space(bmap), type, space);
11722 rational = isl_basic_map_is_rational(bmap);
11723 strides = rational ? 0 : multi_aff_strides(ma);
11724 res = isl_basic_map_alloc_space(space, n_div_ma + n_div_bmap + strides,
11725 bmap->n_eq + strides, bmap->n_ineq + 2 * n_div_ma);
11727 res = isl_basic_map_set_rational(res);
11729 for (i = 0; i < n_div_ma + n_div_bmap; ++i)
11730 if (isl_basic_map_alloc_div(res) < 0)
11733 if (set_ma_divs(res, ma, n_before, n_after, n_div_ma) < 0)
11736 for (i = 0; i < bmap->n_eq; ++i) {
11737 k = isl_basic_map_alloc_equality(res);
11740 isl_seq_preimage(res->eq[k], bmap->eq[i], ma, n_before,
11741 n_after, n_div_ma, n_div_bmap, f, c1, c2, g, 0);
11744 for (i = 0; i < bmap->n_ineq; ++i) {
11745 k = isl_basic_map_alloc_inequality(res);
11748 isl_seq_preimage(res->ineq[k], bmap->ineq[i], ma, n_before,
11749 n_after, n_div_ma, n_div_bmap, f, c1, c2, g, 0);
11752 for (i = 0; i < bmap->n_div; ++i) {
11753 if (isl_int_is_zero(bmap->div[i][0])) {
11754 isl_int_set_si(res->div[n_div_ma + i][0], 0);
11757 isl_seq_preimage(res->div[n_div_ma + i], bmap->div[i], ma,
11758 n_before, n_after, n_div_ma, n_div_bmap,
11763 res = add_ma_strides(res, ma, n_before, n_after);
11769 isl_basic_map_free(bmap);
11770 isl_multi_aff_free(ma);
11771 res = isl_basic_set_simplify(res);
11772 return isl_basic_map_finalize(res);
11778 isl_basic_map_free(bmap);
11779 isl_multi_aff_free(ma);
11780 isl_basic_map_free(res);
11784 /* Compute the preimage of "bset" under the function represented by "ma".
11785 * In other words, plug in "ma" in "bset". The result is a basic set
11786 * that lives in the domain space of "ma".
11788 __isl_give isl_basic_set *isl_basic_set_preimage_multi_aff(
11789 __isl_take isl_basic_set *bset, __isl_take isl_multi_aff *ma)
11791 return isl_basic_map_preimage_multi_aff(bset, isl_dim_set, ma);
11794 /* Check if the range of "ma" is compatible with the domain or range
11795 * (depending on "type") of "map".
11796 * Return -1 if anything is wrong.
11798 static int check_map_compatible_range_multi_aff(
11799 __isl_keep isl_map *map, enum isl_dim_type type,
11800 __isl_keep isl_multi_aff *ma)
11803 isl_space *ma_space;
11805 ma_space = isl_multi_aff_get_space(ma);
11806 m = isl_space_tuple_match(map->dim, type, ma_space, isl_dim_out);
11807 isl_space_free(ma_space);
11809 isl_die(isl_map_get_ctx(map), isl_error_invalid,
11810 "spaces don't match", return -1);
11814 /* Compute the preimage of the domain or range (depending on "type")
11815 * of "map" under the function represented by "ma".
11816 * In other words, plug in "ma" in the domain or range of "map".
11817 * The result is a map that lives in the same space as "map"
11818 * except that the domain or range has been replaced by
11819 * the domain space of "ma".
11821 * The parameters are assumed to have been aligned.
11823 static __isl_give isl_map *map_preimage_multi_aff(__isl_take isl_map *map,
11824 enum isl_dim_type type, __isl_take isl_multi_aff *ma)
11829 map = isl_map_cow(map);
11830 ma = isl_multi_aff_align_divs(ma);
11833 if (check_map_compatible_range_multi_aff(map, type, ma) < 0)
11836 for (i = 0; i < map->n; ++i) {
11837 map->p[i] = isl_basic_map_preimage_multi_aff(map->p[i], type,
11838 isl_multi_aff_copy(ma));
11843 space = isl_multi_aff_get_domain_space(ma);
11844 space = isl_space_set(isl_map_get_space(map), type, space);
11846 isl_space_free(map->dim);
11851 isl_multi_aff_free(ma);
11853 ISL_F_CLR(map, ISL_MAP_DISJOINT);
11854 ISL_F_CLR(map, ISL_SET_NORMALIZED);
11857 isl_multi_aff_free(ma);
11862 /* Compute the preimage of the domain or range (depending on "type")
11863 * of "map" under the function represented by "ma".
11864 * In other words, plug in "ma" in the domain or range of "map".
11865 * The result is a map that lives in the same space as "map"
11866 * except that the domain or range has been replaced by
11867 * the domain space of "ma".
11869 __isl_give isl_map *isl_map_preimage_multi_aff(__isl_take isl_map *map,
11870 enum isl_dim_type type, __isl_take isl_multi_aff *ma)
11875 if (isl_space_match(map->dim, isl_dim_param, ma->space, isl_dim_param))
11876 return map_preimage_multi_aff(map, type, ma);
11878 if (!isl_space_has_named_params(map->dim) ||
11879 !isl_space_has_named_params(ma->space))
11880 isl_die(map->ctx, isl_error_invalid,
11881 "unaligned unnamed parameters", goto error);
11882 map = isl_map_align_params(map, isl_multi_aff_get_space(ma));
11883 ma = isl_multi_aff_align_params(ma, isl_map_get_space(map));
11885 return map_preimage_multi_aff(map, type, ma);
11887 isl_multi_aff_free(ma);
11888 return isl_map_free(map);
11891 /* Compute the preimage of "set" under the function represented by "ma".
11892 * In other words, plug in "ma" "set". The result is a set
11893 * that lives in the domain space of "ma".
11895 __isl_give isl_set *isl_set_preimage_multi_aff(__isl_take isl_set *set,
11896 __isl_take isl_multi_aff *ma)
11898 return isl_map_preimage_multi_aff(set, isl_dim_set, ma);
11901 /* Compute the preimage of the domain of "map" under the function
11902 * represented by "ma".
11903 * In other words, plug in "ma" in the domain of "map".
11904 * The result is a map that lives in the same space as "map"
11905 * except that the domain has been replaced by the domain space of "ma".
11907 __isl_give isl_map *isl_map_preimage_domain_multi_aff(__isl_take isl_map *map,
11908 __isl_take isl_multi_aff *ma)
11910 return isl_map_preimage_multi_aff(map, isl_dim_in, ma);
11913 /* Compute the preimage of "set" under the function represented by "pma".
11914 * In other words, plug in "pma" in "set. The result is a set
11915 * that lives in the domain space of "pma".
11917 static __isl_give isl_set *set_preimage_pw_multi_aff(__isl_take isl_set *set,
11918 __isl_take isl_pw_multi_aff *pma)
11927 isl_pw_multi_aff_free(pma);
11928 res = isl_set_empty(isl_set_get_space(set));
11933 res = isl_set_preimage_multi_aff(isl_set_copy(set),
11934 isl_multi_aff_copy(pma->p[0].maff));
11935 res = isl_set_intersect(res, isl_set_copy(pma->p[0].set));
11937 for (i = 1; i < pma->n; ++i) {
11940 res_i = isl_set_preimage_multi_aff(isl_set_copy(set),
11941 isl_multi_aff_copy(pma->p[i].maff));
11942 res_i = isl_set_intersect(res_i, isl_set_copy(pma->p[i].set));
11943 res = isl_set_union(res, res_i);
11946 isl_pw_multi_aff_free(pma);
11950 isl_pw_multi_aff_free(pma);
11955 __isl_give isl_set *isl_set_preimage_pw_multi_aff(__isl_take isl_set *set,
11956 __isl_take isl_pw_multi_aff *pma)
11961 if (isl_space_match(set->dim, isl_dim_param, pma->dim, isl_dim_param))
11962 return set_preimage_pw_multi_aff(set, pma);
11964 if (!isl_space_has_named_params(set->dim) ||
11965 !isl_space_has_named_params(pma->dim))
11966 isl_die(set->ctx, isl_error_invalid,
11967 "unaligned unnamed parameters", goto error);
11968 set = isl_set_align_params(set, isl_pw_multi_aff_get_space(pma));
11969 pma = isl_pw_multi_aff_align_params(pma, isl_set_get_space(set));
11971 return set_preimage_pw_multi_aff(set, pma);
11973 isl_pw_multi_aff_free(pma);
11974 return isl_set_free(set);