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"
21 #include <isl_list_private.h>
26 #include "isl_map_piplib.h"
27 #include <isl_reordering.h>
28 #include "isl_sample.h"
31 #include <isl_mat_private.h>
32 #include <isl_dim_map.h>
33 #include <isl_local_space_private.h>
34 #include <isl_aff_private.h>
35 #include <isl_options_private.h>
36 #include <isl_morph.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 __isl_give isl_local_space *isl_basic_map_get_local_space(
290 __isl_keep isl_basic_map *bmap)
297 div = isl_basic_map_get_divs(bmap);
298 return isl_local_space_alloc_div(isl_space_copy(bmap->dim), div);
301 __isl_give isl_local_space *isl_basic_set_get_local_space(
302 __isl_keep isl_basic_set *bset)
304 return isl_basic_map_get_local_space(bset);
307 __isl_give isl_basic_map *isl_basic_map_from_local_space(
308 __isl_take isl_local_space *ls)
317 n_div = isl_local_space_dim(ls, isl_dim_div);
318 bmap = isl_basic_map_alloc_space(isl_local_space_get_space(ls),
319 n_div, 0, 2 * n_div);
321 for (i = 0; i < n_div; ++i)
322 if (isl_basic_map_alloc_div(bmap) < 0)
325 for (i = 0; i < n_div; ++i) {
326 isl_seq_cpy(bmap->div[i], ls->div->row[i], ls->div->n_col);
327 if (isl_basic_map_add_div_constraints(bmap, i) < 0)
331 isl_local_space_free(ls);
334 isl_local_space_free(ls);
335 isl_basic_map_free(bmap);
339 __isl_give isl_basic_set *isl_basic_set_from_local_space(
340 __isl_take isl_local_space *ls)
342 return isl_basic_map_from_local_space(ls);
345 __isl_give isl_space *isl_map_get_space(__isl_keep isl_map *map)
349 return isl_space_copy(map->dim);
352 __isl_give isl_space *isl_set_get_space(__isl_keep isl_set *set)
356 return isl_space_copy(set->dim);
359 __isl_give isl_basic_map *isl_basic_map_set_tuple_name(
360 __isl_take isl_basic_map *bmap, enum isl_dim_type type, const char *s)
362 bmap = isl_basic_map_cow(bmap);
365 bmap->dim = isl_space_set_tuple_name(bmap->dim, type, s);
368 bmap = isl_basic_map_finalize(bmap);
371 isl_basic_map_free(bmap);
375 __isl_give isl_basic_set *isl_basic_set_set_tuple_name(
376 __isl_take isl_basic_set *bset, const char *s)
378 return isl_basic_map_set_tuple_name(bset, isl_dim_set, s);
381 const char *isl_basic_map_get_tuple_name(__isl_keep isl_basic_map *bmap,
382 enum isl_dim_type type)
384 return bmap ? isl_space_get_tuple_name(bmap->dim, type) : NULL;
387 __isl_give isl_map *isl_map_set_tuple_name(__isl_take isl_map *map,
388 enum isl_dim_type type, const char *s)
392 map = isl_map_cow(map);
396 map->dim = isl_space_set_tuple_name(map->dim, type, s);
400 for (i = 0; i < map->n; ++i) {
401 map->p[i] = isl_basic_map_set_tuple_name(map->p[i], type, s);
412 /* Does the input or output tuple have a name?
414 int isl_map_has_tuple_name(__isl_keep isl_map *map, enum isl_dim_type type)
416 return map ? isl_space_has_tuple_name(map->dim, type) : -1;
419 const char *isl_map_get_tuple_name(__isl_keep isl_map *map,
420 enum isl_dim_type type)
422 return map ? isl_space_get_tuple_name(map->dim, type) : NULL;
425 __isl_give isl_set *isl_set_set_tuple_name(__isl_take isl_set *set,
428 return (isl_set *)isl_map_set_tuple_name((isl_map *)set, isl_dim_set, s);
431 __isl_give isl_map *isl_map_set_tuple_id(__isl_take isl_map *map,
432 enum isl_dim_type type, __isl_take isl_id *id)
434 map = isl_map_cow(map);
436 return isl_id_free(id);
438 map->dim = isl_space_set_tuple_id(map->dim, type, id);
440 return isl_map_reset_space(map, isl_space_copy(map->dim));
443 __isl_give isl_set *isl_set_set_tuple_id(__isl_take isl_set *set,
444 __isl_take isl_id *id)
446 return isl_map_set_tuple_id(set, isl_dim_set, id);
449 __isl_give isl_map *isl_map_reset_tuple_id(__isl_take isl_map *map,
450 enum isl_dim_type type)
452 map = isl_map_cow(map);
456 map->dim = isl_space_reset_tuple_id(map->dim, type);
458 return isl_map_reset_space(map, isl_space_copy(map->dim));
461 __isl_give isl_set *isl_set_reset_tuple_id(__isl_take isl_set *set)
463 return isl_map_reset_tuple_id(set, isl_dim_set);
466 int isl_map_has_tuple_id(__isl_keep isl_map *map, enum isl_dim_type type)
468 return map ? isl_space_has_tuple_id(map->dim, type) : -1;
471 __isl_give isl_id *isl_map_get_tuple_id(__isl_keep isl_map *map,
472 enum isl_dim_type type)
474 return map ? isl_space_get_tuple_id(map->dim, type) : NULL;
477 int isl_set_has_tuple_id(__isl_keep isl_set *set)
479 return isl_map_has_tuple_id(set, isl_dim_set);
482 __isl_give isl_id *isl_set_get_tuple_id(__isl_keep isl_set *set)
484 return isl_map_get_tuple_id(set, isl_dim_set);
487 /* Does the set tuple have a name?
489 int isl_set_has_tuple_name(__isl_keep isl_set *set)
491 return set ? isl_space_has_tuple_name(set->dim, isl_dim_set) : -1;
495 const char *isl_basic_set_get_tuple_name(__isl_keep isl_basic_set *bset)
497 return bset ? isl_space_get_tuple_name(bset->dim, isl_dim_set) : NULL;
500 const char *isl_set_get_tuple_name(__isl_keep isl_set *set)
502 return set ? isl_space_get_tuple_name(set->dim, isl_dim_set) : NULL;
505 const char *isl_basic_map_get_dim_name(__isl_keep isl_basic_map *bmap,
506 enum isl_dim_type type, unsigned pos)
508 return bmap ? isl_space_get_dim_name(bmap->dim, type, pos) : NULL;
511 const char *isl_basic_set_get_dim_name(__isl_keep isl_basic_set *bset,
512 enum isl_dim_type type, unsigned pos)
514 return bset ? isl_space_get_dim_name(bset->dim, type, pos) : NULL;
517 /* Does the given dimension have a name?
519 int isl_map_has_dim_name(__isl_keep isl_map *map,
520 enum isl_dim_type type, unsigned pos)
522 return map ? isl_space_has_dim_name(map->dim, type, pos) : -1;
525 const char *isl_map_get_dim_name(__isl_keep isl_map *map,
526 enum isl_dim_type type, unsigned pos)
528 return map ? isl_space_get_dim_name(map->dim, type, pos) : NULL;
531 const char *isl_set_get_dim_name(__isl_keep isl_set *set,
532 enum isl_dim_type type, unsigned pos)
534 return set ? isl_space_get_dim_name(set->dim, type, pos) : NULL;
537 /* Does the given dimension have a name?
539 int isl_set_has_dim_name(__isl_keep isl_set *set,
540 enum isl_dim_type type, unsigned pos)
542 return set ? isl_space_has_dim_name(set->dim, type, pos) : -1;
545 __isl_give isl_basic_map *isl_basic_map_set_dim_name(
546 __isl_take isl_basic_map *bmap,
547 enum isl_dim_type type, unsigned pos, const char *s)
549 bmap = isl_basic_map_cow(bmap);
552 bmap->dim = isl_space_set_dim_name(bmap->dim, type, pos, s);
555 return isl_basic_map_finalize(bmap);
557 isl_basic_map_free(bmap);
561 __isl_give isl_map *isl_map_set_dim_name(__isl_take isl_map *map,
562 enum isl_dim_type type, unsigned pos, const char *s)
566 map = isl_map_cow(map);
570 map->dim = isl_space_set_dim_name(map->dim, type, pos, s);
574 for (i = 0; i < map->n; ++i) {
575 map->p[i] = isl_basic_map_set_dim_name(map->p[i], type, pos, s);
586 __isl_give isl_basic_set *isl_basic_set_set_dim_name(
587 __isl_take isl_basic_set *bset,
588 enum isl_dim_type type, unsigned pos, const char *s)
590 return (isl_basic_set *)isl_basic_map_set_dim_name(
591 (isl_basic_map *)bset, type, pos, s);
594 __isl_give isl_set *isl_set_set_dim_name(__isl_take isl_set *set,
595 enum isl_dim_type type, unsigned pos, const char *s)
597 return (isl_set *)isl_map_set_dim_name((isl_map *)set, type, pos, s);
600 int isl_basic_map_has_dim_id(__isl_keep isl_basic_map *bmap,
601 enum isl_dim_type type, unsigned pos)
603 return bmap ? isl_space_has_dim_id(bmap->dim, type, pos) : -1;
606 __isl_give isl_id *isl_basic_set_get_dim_id(__isl_keep isl_basic_set *bset,
607 enum isl_dim_type type, unsigned pos)
609 return bset ? isl_space_get_dim_id(bset->dim, type, pos) : NULL;
612 int isl_map_has_dim_id(__isl_keep isl_map *map,
613 enum isl_dim_type type, unsigned pos)
615 return map ? isl_space_has_dim_id(map->dim, type, pos) : -1;
618 __isl_give isl_id *isl_map_get_dim_id(__isl_keep isl_map *map,
619 enum isl_dim_type type, unsigned pos)
621 return map ? isl_space_get_dim_id(map->dim, type, pos) : NULL;
624 int isl_set_has_dim_id(__isl_keep isl_set *set,
625 enum isl_dim_type type, unsigned pos)
627 return isl_map_has_dim_id(set, type, pos);
630 __isl_give isl_id *isl_set_get_dim_id(__isl_keep isl_set *set,
631 enum isl_dim_type type, unsigned pos)
633 return isl_map_get_dim_id(set, type, pos);
636 __isl_give isl_map *isl_map_set_dim_id(__isl_take isl_map *map,
637 enum isl_dim_type type, unsigned pos, __isl_take isl_id *id)
639 map = isl_map_cow(map);
641 return isl_id_free(id);
643 map->dim = isl_space_set_dim_id(map->dim, type, pos, id);
645 return isl_map_reset_space(map, isl_space_copy(map->dim));
648 __isl_give isl_set *isl_set_set_dim_id(__isl_take isl_set *set,
649 enum isl_dim_type type, unsigned pos, __isl_take isl_id *id)
651 return isl_map_set_dim_id(set, type, pos, id);
654 int isl_map_find_dim_by_id(__isl_keep isl_map *map, enum isl_dim_type type,
655 __isl_keep isl_id *id)
659 return isl_space_find_dim_by_id(map->dim, type, id);
662 int isl_set_find_dim_by_id(__isl_keep isl_set *set, enum isl_dim_type type,
663 __isl_keep isl_id *id)
665 return isl_map_find_dim_by_id(set, type, id);
668 int isl_map_find_dim_by_name(__isl_keep isl_map *map, enum isl_dim_type type,
673 return isl_space_find_dim_by_name(map->dim, type, name);
676 int isl_set_find_dim_by_name(__isl_keep isl_set *set, enum isl_dim_type type,
679 return isl_map_find_dim_by_name(set, type, name);
682 int isl_basic_map_is_rational(__isl_keep isl_basic_map *bmap)
686 return ISL_F_ISSET(bmap, ISL_BASIC_MAP_RATIONAL);
689 int isl_basic_set_is_rational(__isl_keep isl_basic_set *bset)
691 return isl_basic_map_is_rational(bset);
694 /* Does "bmap" contain any rational points?
696 * If "bmap" has an equality for each dimension, equating the dimension
697 * to an integer constant, then it has no rational points, even if it
698 * is marked as rational.
700 int isl_basic_map_has_rational(__isl_keep isl_basic_map *bmap)
702 int has_rational = 1;
707 if (isl_basic_map_plain_is_empty(bmap))
709 if (!isl_basic_map_is_rational(bmap))
711 bmap = isl_basic_map_copy(bmap);
712 bmap = isl_basic_map_implicit_equalities(bmap);
715 total = isl_basic_map_total_dim(bmap);
716 if (bmap->n_eq == total) {
718 for (i = 0; i < bmap->n_eq; ++i) {
719 j = isl_seq_first_non_zero(bmap->eq[i] + 1, total);
722 if (!isl_int_is_one(bmap->eq[i][1 + j]) &&
723 !isl_int_is_negone(bmap->eq[i][1 + j]))
725 j = isl_seq_first_non_zero(bmap->eq[i] + 1 + j + 1,
733 isl_basic_map_free(bmap);
738 /* Does "map" contain any rational points?
740 int isl_map_has_rational(__isl_keep isl_map *map)
747 for (i = 0; i < map->n; ++i) {
748 has_rational = isl_basic_map_has_rational(map->p[i]);
749 if (has_rational < 0)
757 /* Does "set" contain any rational points?
759 int isl_set_has_rational(__isl_keep isl_set *set)
761 return isl_map_has_rational(set);
764 /* Is this basic set a parameter domain?
766 int isl_basic_set_is_params(__isl_keep isl_basic_set *bset)
770 return isl_space_is_params(bset->dim);
773 /* Is this set a parameter domain?
775 int isl_set_is_params(__isl_keep isl_set *set)
779 return isl_space_is_params(set->dim);
782 /* Is this map actually a parameter domain?
783 * Users should never call this function. Outside of isl,
784 * a map can never be a parameter domain.
786 int isl_map_is_params(__isl_keep isl_map *map)
790 return isl_space_is_params(map->dim);
793 static struct isl_basic_map *basic_map_init(struct isl_ctx *ctx,
794 struct isl_basic_map *bmap, unsigned extra,
795 unsigned n_eq, unsigned n_ineq)
798 size_t row_size = 1 + isl_space_dim(bmap->dim, isl_dim_all) + extra;
803 bmap->block = isl_blk_alloc(ctx, (n_ineq + n_eq) * row_size);
804 if (isl_blk_is_error(bmap->block))
807 bmap->ineq = isl_alloc_array(ctx, isl_int *, n_ineq + n_eq);
812 bmap->block2 = isl_blk_empty();
815 bmap->block2 = isl_blk_alloc(ctx, extra * (1 + row_size));
816 if (isl_blk_is_error(bmap->block2))
819 bmap->div = isl_alloc_array(ctx, isl_int *, extra);
824 for (i = 0; i < n_ineq + n_eq; ++i)
825 bmap->ineq[i] = bmap->block.data + i * row_size;
827 for (i = 0; i < extra; ++i)
828 bmap->div[i] = bmap->block2.data + i * (1 + row_size);
832 bmap->c_size = n_eq + n_ineq;
833 bmap->eq = bmap->ineq + n_ineq;
842 isl_basic_map_free(bmap);
846 struct isl_basic_set *isl_basic_set_alloc(struct isl_ctx *ctx,
847 unsigned nparam, unsigned dim, unsigned extra,
848 unsigned n_eq, unsigned n_ineq)
850 struct isl_basic_map *bmap;
853 space = isl_space_set_alloc(ctx, nparam, dim);
857 bmap = isl_basic_map_alloc_space(space, extra, n_eq, n_ineq);
858 return (struct isl_basic_set *)bmap;
861 struct isl_basic_set *isl_basic_set_alloc_space(__isl_take isl_space *dim,
862 unsigned extra, unsigned n_eq, unsigned n_ineq)
864 struct isl_basic_map *bmap;
867 isl_assert(dim->ctx, dim->n_in == 0, goto error);
868 bmap = isl_basic_map_alloc_space(dim, extra, n_eq, n_ineq);
869 return (struct isl_basic_set *)bmap;
875 struct isl_basic_map *isl_basic_map_alloc_space(__isl_take isl_space *dim,
876 unsigned extra, unsigned n_eq, unsigned n_ineq)
878 struct isl_basic_map *bmap;
882 bmap = isl_calloc_type(dim->ctx, struct isl_basic_map);
887 return basic_map_init(dim->ctx, bmap, extra, n_eq, n_ineq);
893 struct isl_basic_map *isl_basic_map_alloc(struct isl_ctx *ctx,
894 unsigned nparam, unsigned in, unsigned out, unsigned extra,
895 unsigned n_eq, unsigned n_ineq)
897 struct isl_basic_map *bmap;
900 dim = isl_space_alloc(ctx, nparam, in, out);
904 bmap = isl_basic_map_alloc_space(dim, extra, n_eq, n_ineq);
908 static void dup_constraints(
909 struct isl_basic_map *dst, struct isl_basic_map *src)
912 unsigned total = isl_basic_map_total_dim(src);
914 for (i = 0; i < src->n_eq; ++i) {
915 int j = isl_basic_map_alloc_equality(dst);
916 isl_seq_cpy(dst->eq[j], src->eq[i], 1+total);
919 for (i = 0; i < src->n_ineq; ++i) {
920 int j = isl_basic_map_alloc_inequality(dst);
921 isl_seq_cpy(dst->ineq[j], src->ineq[i], 1+total);
924 for (i = 0; i < src->n_div; ++i) {
925 int j = isl_basic_map_alloc_div(dst);
926 isl_seq_cpy(dst->div[j], src->div[i], 1+1+total);
928 ISL_F_SET(dst, ISL_BASIC_SET_FINAL);
931 struct isl_basic_map *isl_basic_map_dup(struct isl_basic_map *bmap)
933 struct isl_basic_map *dup;
937 dup = isl_basic_map_alloc_space(isl_space_copy(bmap->dim),
938 bmap->n_div, bmap->n_eq, bmap->n_ineq);
941 dup_constraints(dup, bmap);
942 dup->flags = bmap->flags;
943 dup->sample = isl_vec_copy(bmap->sample);
947 struct isl_basic_set *isl_basic_set_dup(struct isl_basic_set *bset)
949 struct isl_basic_map *dup;
951 dup = isl_basic_map_dup((struct isl_basic_map *)bset);
952 return (struct isl_basic_set *)dup;
955 struct isl_basic_set *isl_basic_set_copy(struct isl_basic_set *bset)
960 if (ISL_F_ISSET(bset, ISL_BASIC_SET_FINAL)) {
964 return isl_basic_set_dup(bset);
967 struct isl_set *isl_set_copy(struct isl_set *set)
976 struct isl_basic_map *isl_basic_map_copy(struct isl_basic_map *bmap)
981 if (ISL_F_ISSET(bmap, ISL_BASIC_SET_FINAL)) {
985 bmap = isl_basic_map_dup(bmap);
987 ISL_F_SET(bmap, ISL_BASIC_SET_FINAL);
991 struct isl_map *isl_map_copy(struct isl_map *map)
1000 void *isl_basic_map_free(__isl_take isl_basic_map *bmap)
1005 if (--bmap->ref > 0)
1008 isl_ctx_deref(bmap->ctx);
1010 isl_blk_free(bmap->ctx, bmap->block2);
1012 isl_blk_free(bmap->ctx, bmap->block);
1013 isl_vec_free(bmap->sample);
1014 isl_space_free(bmap->dim);
1020 void *isl_basic_set_free(struct isl_basic_set *bset)
1022 return isl_basic_map_free((struct isl_basic_map *)bset);
1025 static int room_for_con(struct isl_basic_map *bmap, unsigned n)
1027 return bmap->n_eq + bmap->n_ineq + n <= bmap->c_size;
1030 __isl_give isl_map *isl_map_align_params_map_map_and(
1031 __isl_take isl_map *map1, __isl_take isl_map *map2,
1032 __isl_give isl_map *(*fn)(__isl_take isl_map *map1,
1033 __isl_take isl_map *map2))
1037 if (isl_space_match(map1->dim, isl_dim_param, map2->dim, isl_dim_param))
1038 return fn(map1, map2);
1039 if (!isl_space_has_named_params(map1->dim) ||
1040 !isl_space_has_named_params(map2->dim))
1041 isl_die(map1->ctx, isl_error_invalid,
1042 "unaligned unnamed parameters", goto error);
1043 map1 = isl_map_align_params(map1, isl_map_get_space(map2));
1044 map2 = isl_map_align_params(map2, isl_map_get_space(map1));
1045 return fn(map1, map2);
1052 int isl_map_align_params_map_map_and_test(__isl_keep isl_map *map1,
1053 __isl_keep isl_map *map2,
1054 int (*fn)(__isl_keep isl_map *map1, __isl_keep isl_map *map2))
1060 if (isl_space_match(map1->dim, isl_dim_param, map2->dim, isl_dim_param))
1061 return fn(map1, map2);
1062 if (!isl_space_has_named_params(map1->dim) ||
1063 !isl_space_has_named_params(map2->dim))
1064 isl_die(map1->ctx, isl_error_invalid,
1065 "unaligned unnamed parameters", return -1);
1066 map1 = isl_map_copy(map1);
1067 map2 = isl_map_copy(map2);
1068 map1 = isl_map_align_params(map1, isl_map_get_space(map2));
1069 map2 = isl_map_align_params(map2, isl_map_get_space(map1));
1076 int isl_basic_map_alloc_equality(struct isl_basic_map *bmap)
1078 struct isl_ctx *ctx;
1082 isl_assert(ctx, room_for_con(bmap, 1), return -1);
1083 isl_assert(ctx, (bmap->eq - bmap->ineq) + bmap->n_eq <= bmap->c_size,
1085 ISL_F_CLR(bmap, ISL_BASIC_MAP_NORMALIZED);
1086 ISL_F_CLR(bmap, ISL_BASIC_MAP_NO_REDUNDANT);
1087 ISL_F_CLR(bmap, ISL_BASIC_MAP_NO_IMPLICIT);
1088 ISL_F_CLR(bmap, ISL_BASIC_MAP_ALL_EQUALITIES);
1089 ISL_F_CLR(bmap, ISL_BASIC_MAP_NORMALIZED_DIVS);
1090 if ((bmap->eq - bmap->ineq) + bmap->n_eq == bmap->c_size) {
1092 int j = isl_basic_map_alloc_inequality(bmap);
1096 bmap->ineq[j] = bmap->ineq[bmap->n_ineq - 1];
1097 bmap->ineq[bmap->n_ineq - 1] = bmap->eq[-1];
1104 isl_seq_clr(bmap->eq[bmap->n_eq] + 1 + isl_basic_map_total_dim(bmap),
1105 bmap->extra - bmap->n_div);
1106 return bmap->n_eq++;
1109 int isl_basic_set_alloc_equality(struct isl_basic_set *bset)
1111 return isl_basic_map_alloc_equality((struct isl_basic_map *)bset);
1114 int isl_basic_map_free_equality(struct isl_basic_map *bmap, unsigned n)
1118 isl_assert(bmap->ctx, n <= bmap->n_eq, return -1);
1123 int isl_basic_set_free_equality(struct isl_basic_set *bset, unsigned n)
1125 return isl_basic_map_free_equality((struct isl_basic_map *)bset, n);
1128 int isl_basic_map_drop_equality(struct isl_basic_map *bmap, unsigned pos)
1133 isl_assert(bmap->ctx, pos < bmap->n_eq, return -1);
1135 if (pos != bmap->n_eq - 1) {
1137 bmap->eq[pos] = bmap->eq[bmap->n_eq - 1];
1138 bmap->eq[bmap->n_eq - 1] = t;
1144 int isl_basic_set_drop_equality(struct isl_basic_set *bset, unsigned pos)
1146 return isl_basic_map_drop_equality((struct isl_basic_map *)bset, pos);
1149 /* Turn inequality "pos" of "bmap" into an equality.
1151 * In particular, we move the inequality in front of the equalities
1152 * and move the last inequality in the position of the moved inequality.
1153 * Note that isl_tab_make_equalities_explicit depends on this particular
1154 * change in the ordering of the constraints.
1156 void isl_basic_map_inequality_to_equality(
1157 struct isl_basic_map *bmap, unsigned pos)
1161 t = bmap->ineq[pos];
1162 bmap->ineq[pos] = bmap->ineq[bmap->n_ineq - 1];
1163 bmap->ineq[bmap->n_ineq - 1] = bmap->eq[-1];
1168 ISL_F_CLR(bmap, ISL_BASIC_MAP_NO_REDUNDANT);
1169 ISL_F_CLR(bmap, ISL_BASIC_MAP_NORMALIZED);
1170 ISL_F_CLR(bmap, ISL_BASIC_MAP_NORMALIZED_DIVS);
1171 ISL_F_CLR(bmap, ISL_BASIC_MAP_ALL_EQUALITIES);
1174 static int room_for_ineq(struct isl_basic_map *bmap, unsigned n)
1176 return bmap->n_ineq + n <= bmap->eq - bmap->ineq;
1179 int isl_basic_map_alloc_inequality(struct isl_basic_map *bmap)
1181 struct isl_ctx *ctx;
1185 isl_assert(ctx, room_for_ineq(bmap, 1), return -1);
1186 ISL_F_CLR(bmap, ISL_BASIC_MAP_NO_IMPLICIT);
1187 ISL_F_CLR(bmap, ISL_BASIC_MAP_NO_REDUNDANT);
1188 ISL_F_CLR(bmap, ISL_BASIC_MAP_NORMALIZED);
1189 ISL_F_CLR(bmap, ISL_BASIC_MAP_ALL_EQUALITIES);
1190 isl_seq_clr(bmap->ineq[bmap->n_ineq] +
1191 1 + isl_basic_map_total_dim(bmap),
1192 bmap->extra - bmap->n_div);
1193 return bmap->n_ineq++;
1196 int isl_basic_set_alloc_inequality(struct isl_basic_set *bset)
1198 return isl_basic_map_alloc_inequality((struct isl_basic_map *)bset);
1201 int isl_basic_map_free_inequality(struct isl_basic_map *bmap, unsigned n)
1205 isl_assert(bmap->ctx, n <= bmap->n_ineq, return -1);
1210 int isl_basic_set_free_inequality(struct isl_basic_set *bset, unsigned n)
1212 return isl_basic_map_free_inequality((struct isl_basic_map *)bset, n);
1215 int isl_basic_map_drop_inequality(struct isl_basic_map *bmap, unsigned pos)
1220 isl_assert(bmap->ctx, pos < bmap->n_ineq, return -1);
1222 if (pos != bmap->n_ineq - 1) {
1223 t = bmap->ineq[pos];
1224 bmap->ineq[pos] = bmap->ineq[bmap->n_ineq - 1];
1225 bmap->ineq[bmap->n_ineq - 1] = t;
1226 ISL_F_CLR(bmap, ISL_BASIC_MAP_NORMALIZED);
1232 int isl_basic_set_drop_inequality(struct isl_basic_set *bset, unsigned pos)
1234 return isl_basic_map_drop_inequality((struct isl_basic_map *)bset, pos);
1237 __isl_give isl_basic_map *isl_basic_map_add_eq(__isl_take isl_basic_map *bmap,
1242 bmap = isl_basic_map_extend_constraints(bmap, 1, 0);
1245 k = isl_basic_map_alloc_equality(bmap);
1248 isl_seq_cpy(bmap->eq[k], eq, 1 + isl_basic_map_total_dim(bmap));
1251 isl_basic_map_free(bmap);
1255 __isl_give isl_basic_set *isl_basic_set_add_eq(__isl_take isl_basic_set *bset,
1258 return (isl_basic_set *)
1259 isl_basic_map_add_eq((isl_basic_map *)bset, eq);
1262 __isl_give isl_basic_map *isl_basic_map_add_ineq(__isl_take isl_basic_map *bmap,
1267 bmap = isl_basic_map_extend_constraints(bmap, 0, 1);
1270 k = isl_basic_map_alloc_inequality(bmap);
1273 isl_seq_cpy(bmap->ineq[k], ineq, 1 + isl_basic_map_total_dim(bmap));
1276 isl_basic_map_free(bmap);
1280 __isl_give isl_basic_set *isl_basic_set_add_ineq(__isl_take isl_basic_set *bset,
1283 return (isl_basic_set *)
1284 isl_basic_map_add_ineq((isl_basic_map *)bset, ineq);
1287 int isl_basic_map_alloc_div(struct isl_basic_map *bmap)
1291 isl_assert(bmap->ctx, bmap->n_div < bmap->extra, return -1);
1292 isl_seq_clr(bmap->div[bmap->n_div] +
1293 1 + 1 + isl_basic_map_total_dim(bmap),
1294 bmap->extra - bmap->n_div);
1295 ISL_F_CLR(bmap, ISL_BASIC_MAP_NORMALIZED_DIVS);
1296 return bmap->n_div++;
1299 int isl_basic_set_alloc_div(struct isl_basic_set *bset)
1301 return isl_basic_map_alloc_div((struct isl_basic_map *)bset);
1304 int isl_basic_map_free_div(struct isl_basic_map *bmap, unsigned n)
1308 isl_assert(bmap->ctx, n <= bmap->n_div, return -1);
1313 int isl_basic_set_free_div(struct isl_basic_set *bset, unsigned n)
1315 return isl_basic_map_free_div((struct isl_basic_map *)bset, n);
1318 /* Copy constraint from src to dst, putting the vars of src at offset
1319 * dim_off in dst and the divs of src at offset div_off in dst.
1320 * If both sets are actually map, then dim_off applies to the input
1323 static void copy_constraint(struct isl_basic_map *dst_map, isl_int *dst,
1324 struct isl_basic_map *src_map, isl_int *src,
1325 unsigned in_off, unsigned out_off, unsigned div_off)
1327 unsigned src_nparam = isl_basic_map_n_param(src_map);
1328 unsigned dst_nparam = isl_basic_map_n_param(dst_map);
1329 unsigned src_in = isl_basic_map_n_in(src_map);
1330 unsigned dst_in = isl_basic_map_n_in(dst_map);
1331 unsigned src_out = isl_basic_map_n_out(src_map);
1332 unsigned dst_out = isl_basic_map_n_out(dst_map);
1333 isl_int_set(dst[0], src[0]);
1334 isl_seq_cpy(dst+1, src+1, isl_min(dst_nparam, src_nparam));
1335 if (dst_nparam > src_nparam)
1336 isl_seq_clr(dst+1+src_nparam,
1337 dst_nparam - src_nparam);
1338 isl_seq_clr(dst+1+dst_nparam, in_off);
1339 isl_seq_cpy(dst+1+dst_nparam+in_off,
1341 isl_min(dst_in-in_off, src_in));
1342 if (dst_in-in_off > src_in)
1343 isl_seq_clr(dst+1+dst_nparam+in_off+src_in,
1344 dst_in - in_off - src_in);
1345 isl_seq_clr(dst+1+dst_nparam+dst_in, out_off);
1346 isl_seq_cpy(dst+1+dst_nparam+dst_in+out_off,
1347 src+1+src_nparam+src_in,
1348 isl_min(dst_out-out_off, src_out));
1349 if (dst_out-out_off > src_out)
1350 isl_seq_clr(dst+1+dst_nparam+dst_in+out_off+src_out,
1351 dst_out - out_off - src_out);
1352 isl_seq_clr(dst+1+dst_nparam+dst_in+dst_out, div_off);
1353 isl_seq_cpy(dst+1+dst_nparam+dst_in+dst_out+div_off,
1354 src+1+src_nparam+src_in+src_out,
1355 isl_min(dst_map->extra-div_off, src_map->n_div));
1356 if (dst_map->n_div-div_off > src_map->n_div)
1357 isl_seq_clr(dst+1+dst_nparam+dst_in+dst_out+
1358 div_off+src_map->n_div,
1359 dst_map->n_div - div_off - src_map->n_div);
1362 static void copy_div(struct isl_basic_map *dst_map, isl_int *dst,
1363 struct isl_basic_map *src_map, isl_int *src,
1364 unsigned in_off, unsigned out_off, unsigned div_off)
1366 isl_int_set(dst[0], src[0]);
1367 copy_constraint(dst_map, dst+1, src_map, src+1, in_off, out_off, div_off);
1370 static struct isl_basic_map *add_constraints(struct isl_basic_map *bmap1,
1371 struct isl_basic_map *bmap2, unsigned i_pos, unsigned o_pos)
1376 if (!bmap1 || !bmap2)
1379 div_off = bmap1->n_div;
1381 for (i = 0; i < bmap2->n_eq; ++i) {
1382 int i1 = isl_basic_map_alloc_equality(bmap1);
1385 copy_constraint(bmap1, bmap1->eq[i1], bmap2, bmap2->eq[i],
1386 i_pos, o_pos, div_off);
1389 for (i = 0; i < bmap2->n_ineq; ++i) {
1390 int i1 = isl_basic_map_alloc_inequality(bmap1);
1393 copy_constraint(bmap1, bmap1->ineq[i1], bmap2, bmap2->ineq[i],
1394 i_pos, o_pos, div_off);
1397 for (i = 0; i < bmap2->n_div; ++i) {
1398 int i1 = isl_basic_map_alloc_div(bmap1);
1401 copy_div(bmap1, bmap1->div[i1], bmap2, bmap2->div[i],
1402 i_pos, o_pos, div_off);
1405 isl_basic_map_free(bmap2);
1410 isl_basic_map_free(bmap1);
1411 isl_basic_map_free(bmap2);
1415 struct isl_basic_set *isl_basic_set_add_constraints(struct isl_basic_set *bset1,
1416 struct isl_basic_set *bset2, unsigned pos)
1418 return (struct isl_basic_set *)
1419 add_constraints((struct isl_basic_map *)bset1,
1420 (struct isl_basic_map *)bset2, 0, pos);
1423 struct isl_basic_map *isl_basic_map_extend_space(struct isl_basic_map *base,
1424 __isl_take isl_space *dim, unsigned extra,
1425 unsigned n_eq, unsigned n_ineq)
1427 struct isl_basic_map *ext;
1437 dims_ok = isl_space_is_equal(base->dim, dim) &&
1438 base->extra >= base->n_div + extra;
1440 if (dims_ok && room_for_con(base, n_eq + n_ineq) &&
1441 room_for_ineq(base, n_ineq)) {
1442 isl_space_free(dim);
1446 isl_assert(base->ctx, base->dim->nparam <= dim->nparam, goto error);
1447 isl_assert(base->ctx, base->dim->n_in <= dim->n_in, goto error);
1448 isl_assert(base->ctx, base->dim->n_out <= dim->n_out, goto error);
1449 extra += base->extra;
1451 n_ineq += base->n_ineq;
1453 ext = isl_basic_map_alloc_space(dim, extra, n_eq, n_ineq);
1459 ext->sample = isl_vec_copy(base->sample);
1460 flags = base->flags;
1461 ext = add_constraints(ext, base, 0, 0);
1464 ISL_F_CLR(ext, ISL_BASIC_SET_FINAL);
1470 isl_space_free(dim);
1471 isl_basic_map_free(base);
1475 struct isl_basic_set *isl_basic_set_extend_space(struct isl_basic_set *base,
1476 __isl_take isl_space *dim, unsigned extra,
1477 unsigned n_eq, unsigned n_ineq)
1479 return (struct isl_basic_set *)
1480 isl_basic_map_extend_space((struct isl_basic_map *)base, dim,
1481 extra, n_eq, n_ineq);
1484 struct isl_basic_map *isl_basic_map_extend_constraints(
1485 struct isl_basic_map *base, unsigned n_eq, unsigned n_ineq)
1489 return isl_basic_map_extend_space(base, isl_space_copy(base->dim),
1493 struct isl_basic_map *isl_basic_map_extend(struct isl_basic_map *base,
1494 unsigned nparam, unsigned n_in, unsigned n_out, unsigned extra,
1495 unsigned n_eq, unsigned n_ineq)
1497 struct isl_basic_map *bmap;
1502 dim = isl_space_alloc(base->ctx, nparam, n_in, n_out);
1506 bmap = isl_basic_map_extend_space(base, dim, extra, n_eq, n_ineq);
1509 isl_basic_map_free(base);
1513 struct isl_basic_set *isl_basic_set_extend(struct isl_basic_set *base,
1514 unsigned nparam, unsigned dim, unsigned extra,
1515 unsigned n_eq, unsigned n_ineq)
1517 return (struct isl_basic_set *)
1518 isl_basic_map_extend((struct isl_basic_map *)base,
1519 nparam, 0, dim, extra, n_eq, n_ineq);
1522 struct isl_basic_set *isl_basic_set_extend_constraints(
1523 struct isl_basic_set *base, unsigned n_eq, unsigned n_ineq)
1525 return (struct isl_basic_set *)
1526 isl_basic_map_extend_constraints((struct isl_basic_map *)base,
1530 struct isl_basic_set *isl_basic_set_cow(struct isl_basic_set *bset)
1532 return (struct isl_basic_set *)
1533 isl_basic_map_cow((struct isl_basic_map *)bset);
1536 struct isl_basic_map *isl_basic_map_cow(struct isl_basic_map *bmap)
1541 if (bmap->ref > 1) {
1543 bmap = isl_basic_map_dup(bmap);
1546 ISL_F_CLR(bmap, ISL_BASIC_SET_FINAL);
1550 struct isl_set *isl_set_cow(struct isl_set *set)
1558 return isl_set_dup(set);
1561 struct isl_map *isl_map_cow(struct isl_map *map)
1569 return isl_map_dup(map);
1572 static void swap_vars(struct isl_blk blk, isl_int *a,
1573 unsigned a_len, unsigned b_len)
1575 isl_seq_cpy(blk.data, a+a_len, b_len);
1576 isl_seq_cpy(blk.data+b_len, a, a_len);
1577 isl_seq_cpy(a, blk.data, b_len+a_len);
1580 static __isl_give isl_basic_map *isl_basic_map_swap_vars(
1581 __isl_take isl_basic_map *bmap, unsigned pos, unsigned n1, unsigned n2)
1589 isl_assert(bmap->ctx,
1590 pos + n1 + n2 <= 1 + isl_basic_map_total_dim(bmap), goto error);
1592 if (n1 == 0 || n2 == 0)
1595 bmap = isl_basic_map_cow(bmap);
1599 blk = isl_blk_alloc(bmap->ctx, n1 + n2);
1600 if (isl_blk_is_error(blk))
1603 for (i = 0; i < bmap->n_eq; ++i)
1605 bmap->eq[i] + pos, n1, n2);
1607 for (i = 0; i < bmap->n_ineq; ++i)
1609 bmap->ineq[i] + pos, n1, n2);
1611 for (i = 0; i < bmap->n_div; ++i)
1613 bmap->div[i]+1 + pos, n1, n2);
1615 isl_blk_free(bmap->ctx, blk);
1617 ISL_F_CLR(bmap, ISL_BASIC_SET_NORMALIZED);
1618 bmap = isl_basic_map_gauss(bmap, NULL);
1619 return isl_basic_map_finalize(bmap);
1621 isl_basic_map_free(bmap);
1625 static __isl_give isl_basic_set *isl_basic_set_swap_vars(
1626 __isl_take isl_basic_set *bset, unsigned n)
1634 nparam = isl_basic_set_n_param(bset);
1635 dim = isl_basic_set_n_dim(bset);
1636 isl_assert(bset->ctx, n <= dim, goto error);
1638 return isl_basic_map_swap_vars(bset, 1 + nparam, n, dim - n);
1640 isl_basic_set_free(bset);
1644 struct isl_basic_map *isl_basic_map_set_to_empty(struct isl_basic_map *bmap)
1650 total = isl_basic_map_total_dim(bmap);
1651 isl_basic_map_free_div(bmap, bmap->n_div);
1652 isl_basic_map_free_inequality(bmap, bmap->n_ineq);
1654 isl_basic_map_free_equality(bmap, bmap->n_eq-1);
1656 i = isl_basic_map_alloc_equality(bmap);
1660 isl_int_set_si(bmap->eq[i][0], 1);
1661 isl_seq_clr(bmap->eq[i]+1, total);
1662 ISL_F_SET(bmap, ISL_BASIC_MAP_EMPTY);
1663 isl_vec_free(bmap->sample);
1664 bmap->sample = NULL;
1665 return isl_basic_map_finalize(bmap);
1667 isl_basic_map_free(bmap);
1671 struct isl_basic_set *isl_basic_set_set_to_empty(struct isl_basic_set *bset)
1673 return (struct isl_basic_set *)
1674 isl_basic_map_set_to_empty((struct isl_basic_map *)bset);
1677 /* Swap divs "a" and "b" in "bmap" (without modifying any of the constraints
1680 static void swap_div(__isl_keep isl_basic_map *bmap, int a, int b)
1682 isl_int *t = bmap->div[a];
1683 bmap->div[a] = bmap->div[b];
1687 /* Swap divs "a" and "b" in "bmap" and adjust the constraints and
1688 * div definitions accordingly.
1690 void isl_basic_map_swap_div(struct isl_basic_map *bmap, int a, int b)
1693 unsigned off = isl_space_dim(bmap->dim, isl_dim_all);
1695 swap_div(bmap, a, b);
1697 for (i = 0; i < bmap->n_eq; ++i)
1698 isl_int_swap(bmap->eq[i][1+off+a], bmap->eq[i][1+off+b]);
1700 for (i = 0; i < bmap->n_ineq; ++i)
1701 isl_int_swap(bmap->ineq[i][1+off+a], bmap->ineq[i][1+off+b]);
1703 for (i = 0; i < bmap->n_div; ++i)
1704 isl_int_swap(bmap->div[i][1+1+off+a], bmap->div[i][1+1+off+b]);
1705 ISL_F_CLR(bmap, ISL_BASIC_MAP_NORMALIZED);
1708 /* Eliminate the specified n dimensions starting at first from the
1709 * constraints, without removing the dimensions from the space.
1710 * If the set is rational, the dimensions are eliminated using Fourier-Motzkin.
1712 __isl_give isl_map *isl_map_eliminate(__isl_take isl_map *map,
1713 enum isl_dim_type type, unsigned first, unsigned n)
1722 if (first + n > isl_map_dim(map, type) || first + n < first)
1723 isl_die(map->ctx, isl_error_invalid,
1724 "index out of bounds", goto error);
1726 map = isl_map_cow(map);
1730 for (i = 0; i < map->n; ++i) {
1731 map->p[i] = isl_basic_map_eliminate(map->p[i], type, first, n);
1741 /* Eliminate the specified n dimensions starting at first from the
1742 * constraints, without removing the dimensions from the space.
1743 * If the set is rational, the dimensions are eliminated using Fourier-Motzkin.
1745 __isl_give isl_set *isl_set_eliminate(__isl_take isl_set *set,
1746 enum isl_dim_type type, unsigned first, unsigned n)
1748 return (isl_set *)isl_map_eliminate((isl_map *)set, type, first, n);
1751 /* Eliminate the specified n dimensions starting at first from the
1752 * constraints, without removing the dimensions from the space.
1753 * If the set is rational, the dimensions are eliminated using Fourier-Motzkin.
1755 __isl_give isl_set *isl_set_eliminate_dims(__isl_take isl_set *set,
1756 unsigned first, unsigned n)
1758 return isl_set_eliminate(set, isl_dim_set, first, n);
1761 __isl_give isl_basic_map *isl_basic_map_remove_divs(
1762 __isl_take isl_basic_map *bmap)
1766 bmap = isl_basic_map_eliminate_vars(bmap,
1767 isl_space_dim(bmap->dim, isl_dim_all), bmap->n_div);
1771 return isl_basic_map_finalize(bmap);
1774 __isl_give isl_basic_set *isl_basic_set_remove_divs(
1775 __isl_take isl_basic_set *bset)
1777 return (struct isl_basic_set *)isl_basic_map_remove_divs(
1778 (struct isl_basic_map *)bset);
1781 __isl_give isl_map *isl_map_remove_divs(__isl_take isl_map *map)
1790 map = isl_map_cow(map);
1794 for (i = 0; i < map->n; ++i) {
1795 map->p[i] = isl_basic_map_remove_divs(map->p[i]);
1805 __isl_give isl_set *isl_set_remove_divs(__isl_take isl_set *set)
1807 return isl_map_remove_divs(set);
1810 struct isl_basic_map *isl_basic_map_remove_dims(struct isl_basic_map *bmap,
1811 enum isl_dim_type type, unsigned first, unsigned n)
1815 isl_assert(bmap->ctx, first + n <= isl_basic_map_dim(bmap, type),
1817 if (n == 0 && !isl_space_is_named_or_nested(bmap->dim, type))
1819 bmap = isl_basic_map_eliminate_vars(bmap,
1820 isl_basic_map_offset(bmap, type) - 1 + first, n);
1823 if (ISL_F_ISSET(bmap, ISL_BASIC_MAP_EMPTY) && type == isl_dim_div)
1825 bmap = isl_basic_map_drop(bmap, type, first, n);
1828 isl_basic_map_free(bmap);
1832 /* Return true if the definition of the given div (recursively) involves
1833 * any of the given variables.
1835 static int div_involves_vars(__isl_keep isl_basic_map *bmap, int div,
1836 unsigned first, unsigned n)
1839 unsigned div_offset = isl_basic_map_offset(bmap, isl_dim_div);
1841 if (isl_int_is_zero(bmap->div[div][0]))
1843 if (isl_seq_first_non_zero(bmap->div[div] + 1 + first, n) >= 0)
1846 for (i = bmap->n_div - 1; i >= 0; --i) {
1847 if (isl_int_is_zero(bmap->div[div][1 + div_offset + i]))
1849 if (div_involves_vars(bmap, i, first, n))
1856 /* Try and add a lower and/or upper bound on "div" to "bmap"
1857 * based on inequality "i".
1858 * "total" is the total number of variables (excluding the divs).
1859 * "v" is a temporary object that can be used during the calculations.
1860 * If "lb" is set, then a lower bound should be constructed.
1861 * If "ub" is set, then an upper bound should be constructed.
1863 * The calling function has already checked that the inequality does not
1864 * reference "div", but we still need to check that the inequality is
1865 * of the right form. We'll consider the case where we want to construct
1866 * a lower bound. The construction of upper bounds is similar.
1868 * Let "div" be of the form
1870 * q = floor((a + f(x))/d)
1872 * We essentially check if constraint "i" is of the form
1876 * so that we can use it to derive a lower bound on "div".
1877 * However, we allow a slightly more general form
1881 * with the condition that the coefficients of g(x) - f(x) are all
1883 * Rewriting this constraint as
1887 * adding a + f(x) to both sides and dividing by d, we obtain
1889 * (a + f(x))/d >= (a-b)/d + (f(x)-g(x))/d
1891 * Taking the floor on both sides, we obtain
1893 * q >= floor((a-b)/d) + (f(x)-g(x))/d
1897 * (g(x)-f(x))/d + ceil((b-a)/d) + q >= 0
1899 * In the case of an upper bound, we construct the constraint
1901 * (g(x)+f(x))/d + floor((b+a)/d) - q >= 0
1904 static __isl_give isl_basic_map *insert_bounds_on_div_from_ineq(
1905 __isl_take isl_basic_map *bmap, int div, int i,
1906 unsigned total, isl_int v, int lb, int ub)
1910 for (j = 0; (lb || ub) && j < total + bmap->n_div; ++j) {
1912 isl_int_sub(v, bmap->ineq[i][1 + j],
1913 bmap->div[div][1 + 1 + j]);
1914 lb = isl_int_is_divisible_by(v, bmap->div[div][0]);
1917 isl_int_add(v, bmap->ineq[i][1 + j],
1918 bmap->div[div][1 + 1 + j]);
1919 ub = isl_int_is_divisible_by(v, bmap->div[div][0]);
1925 bmap = isl_basic_map_extend_constraints(bmap, 0, lb + ub);
1927 int k = isl_basic_map_alloc_inequality(bmap);
1930 for (j = 0; j < 1 + total + bmap->n_div; ++j) {
1931 isl_int_sub(bmap->ineq[k][j], bmap->ineq[i][j],
1932 bmap->div[div][1 + j]);
1933 isl_int_cdiv_q(bmap->ineq[k][j],
1934 bmap->ineq[k][j], bmap->div[div][0]);
1936 isl_int_set_si(bmap->ineq[k][1 + total + div], 1);
1939 int k = isl_basic_map_alloc_inequality(bmap);
1942 for (j = 0; j < 1 + total + bmap->n_div; ++j) {
1943 isl_int_add(bmap->ineq[k][j], bmap->ineq[i][j],
1944 bmap->div[div][1 + j]);
1945 isl_int_fdiv_q(bmap->ineq[k][j],
1946 bmap->ineq[k][j], bmap->div[div][0]);
1948 isl_int_set_si(bmap->ineq[k][1 + total + div], -1);
1953 isl_basic_map_free(bmap);
1957 /* This function is called right before "div" is eliminated from "bmap"
1958 * using Fourier-Motzkin.
1959 * Look through the constraints of "bmap" for constraints on the argument
1960 * of the integer division and use them to construct constraints on the
1961 * integer division itself. These constraints can then be combined
1962 * during the Fourier-Motzkin elimination.
1963 * Note that it is only useful to introduce lower bounds on "div"
1964 * if "bmap" already contains upper bounds on "div" as the newly
1965 * introduce lower bounds can then be combined with the pre-existing
1966 * upper bounds. Similarly for upper bounds.
1967 * We therefore first check if "bmap" contains any lower and/or upper bounds
1970 * It is interesting to note that the introduction of these constraints
1971 * can indeed lead to more accurate results, even when compared to
1972 * deriving constraints on the argument of "div" from constraints on "div".
1973 * Consider, for example, the set
1975 * { [i,j,k] : 3 + i + 2j >= 0 and 2 * [(i+2j)/4] <= k }
1977 * The second constraint can be rewritten as
1979 * 2 * [(-i-2j+3)/4] + k >= 0
1981 * from which we can derive
1983 * -i - 2j + 3 >= -2k
1989 * Combined with the first constraint, we obtain
1991 * -3 <= 3 + 2k or k >= -3
1993 * If, on the other hand we derive a constraint on [(i+2j)/4] from
1994 * the first constraint, we obtain
1996 * [(i + 2j)/4] >= [-3/4] = -1
1998 * Combining this constraint with the second constraint, we obtain
2002 static __isl_give isl_basic_map *insert_bounds_on_div(
2003 __isl_take isl_basic_map *bmap, int div)
2006 int check_lb, check_ub;
2013 if (isl_int_is_zero(bmap->div[div][0]))
2016 total = isl_space_dim(bmap->dim, isl_dim_all);
2020 for (i = 0; (!check_lb || !check_ub) && i < bmap->n_ineq; ++i) {
2021 int s = isl_int_sgn(bmap->ineq[i][1 + total + div]);
2028 if (!check_lb && !check_ub)
2033 for (i = 0; bmap && i < bmap->n_ineq; ++i) {
2034 if (!isl_int_is_zero(bmap->ineq[i][1 + total + div]))
2037 bmap = insert_bounds_on_div_from_ineq(bmap, div, i, total, v,
2038 check_lb, check_ub);
2046 /* Remove all divs (recursively) involving any of the given dimensions
2047 * in their definitions.
2049 __isl_give isl_basic_map *isl_basic_map_remove_divs_involving_dims(
2050 __isl_take isl_basic_map *bmap,
2051 enum isl_dim_type type, unsigned first, unsigned n)
2057 isl_assert(bmap->ctx, first + n <= isl_basic_map_dim(bmap, type),
2059 first += isl_basic_map_offset(bmap, type);
2061 for (i = bmap->n_div - 1; i >= 0; --i) {
2062 if (!div_involves_vars(bmap, i, first, n))
2064 bmap = insert_bounds_on_div(bmap, i);
2065 bmap = isl_basic_map_remove_dims(bmap, isl_dim_div, i, 1);
2073 isl_basic_map_free(bmap);
2077 __isl_give isl_basic_set *isl_basic_set_remove_divs_involving_dims(
2078 __isl_take isl_basic_set *bset,
2079 enum isl_dim_type type, unsigned first, unsigned n)
2081 return isl_basic_map_remove_divs_involving_dims(bset, type, first, n);
2084 __isl_give isl_map *isl_map_remove_divs_involving_dims(__isl_take isl_map *map,
2085 enum isl_dim_type type, unsigned first, unsigned n)
2094 map = isl_map_cow(map);
2098 for (i = 0; i < map->n; ++i) {
2099 map->p[i] = isl_basic_map_remove_divs_involving_dims(map->p[i],
2110 __isl_give isl_set *isl_set_remove_divs_involving_dims(__isl_take isl_set *set,
2111 enum isl_dim_type type, unsigned first, unsigned n)
2113 return (isl_set *)isl_map_remove_divs_involving_dims((isl_map *)set,
2117 /* Does the desciption of "bmap" depend on the specified dimensions?
2118 * We also check whether the dimensions appear in any of the div definitions.
2119 * In principle there is no need for this check. If the dimensions appear
2120 * in a div definition, they also appear in the defining constraints of that
2123 int isl_basic_map_involves_dims(__isl_keep isl_basic_map *bmap,
2124 enum isl_dim_type type, unsigned first, unsigned n)
2131 if (first + n > isl_basic_map_dim(bmap, type))
2132 isl_die(bmap->ctx, isl_error_invalid,
2133 "index out of bounds", return -1);
2135 first += isl_basic_map_offset(bmap, type);
2136 for (i = 0; i < bmap->n_eq; ++i)
2137 if (isl_seq_first_non_zero(bmap->eq[i] + first, n) >= 0)
2139 for (i = 0; i < bmap->n_ineq; ++i)
2140 if (isl_seq_first_non_zero(bmap->ineq[i] + first, n) >= 0)
2142 for (i = 0; i < bmap->n_div; ++i) {
2143 if (isl_int_is_zero(bmap->div[i][0]))
2145 if (isl_seq_first_non_zero(bmap->div[i] + 1 + first, n) >= 0)
2152 int isl_map_involves_dims(__isl_keep isl_map *map,
2153 enum isl_dim_type type, unsigned first, unsigned n)
2160 if (first + n > isl_map_dim(map, type))
2161 isl_die(map->ctx, isl_error_invalid,
2162 "index out of bounds", return -1);
2164 for (i = 0; i < map->n; ++i) {
2165 int involves = isl_basic_map_involves_dims(map->p[i],
2167 if (involves < 0 || involves)
2174 int isl_basic_set_involves_dims(__isl_keep isl_basic_set *bset,
2175 enum isl_dim_type type, unsigned first, unsigned n)
2177 return isl_basic_map_involves_dims(bset, type, first, n);
2180 int isl_set_involves_dims(__isl_keep isl_set *set,
2181 enum isl_dim_type type, unsigned first, unsigned n)
2183 return isl_map_involves_dims(set, type, first, n);
2186 /* Return true if the definition of the given div is unknown or depends
2189 static int div_is_unknown(__isl_keep isl_basic_map *bmap, int div)
2192 unsigned div_offset = isl_basic_map_offset(bmap, isl_dim_div);
2194 if (isl_int_is_zero(bmap->div[div][0]))
2197 for (i = bmap->n_div - 1; i >= 0; --i) {
2198 if (isl_int_is_zero(bmap->div[div][1 + div_offset + i]))
2200 if (div_is_unknown(bmap, i))
2207 /* Remove all divs that are unknown or defined in terms of unknown divs.
2209 __isl_give isl_basic_map *isl_basic_map_remove_unknown_divs(
2210 __isl_take isl_basic_map *bmap)
2217 for (i = bmap->n_div - 1; i >= 0; --i) {
2218 if (!div_is_unknown(bmap, i))
2220 bmap = isl_basic_map_remove_dims(bmap, isl_dim_div, i, 1);
2229 /* Remove all divs that are unknown or defined in terms of unknown divs.
2231 __isl_give isl_basic_set *isl_basic_set_remove_unknown_divs(
2232 __isl_take isl_basic_set *bset)
2234 return isl_basic_map_remove_unknown_divs(bset);
2237 __isl_give isl_map *isl_map_remove_unknown_divs(__isl_take isl_map *map)
2246 map = isl_map_cow(map);
2250 for (i = 0; i < map->n; ++i) {
2251 map->p[i] = isl_basic_map_remove_unknown_divs(map->p[i]);
2261 __isl_give isl_set *isl_set_remove_unknown_divs(__isl_take isl_set *set)
2263 return (isl_set *)isl_map_remove_unknown_divs((isl_map *)set);
2266 __isl_give isl_basic_set *isl_basic_set_remove_dims(
2267 __isl_take isl_basic_set *bset,
2268 enum isl_dim_type type, unsigned first, unsigned n)
2270 return (isl_basic_set *)
2271 isl_basic_map_remove_dims((isl_basic_map *)bset, type, first, n);
2274 struct isl_map *isl_map_remove_dims(struct isl_map *map,
2275 enum isl_dim_type type, unsigned first, unsigned n)
2282 map = isl_map_cow(map);
2285 isl_assert(map->ctx, first + n <= isl_map_dim(map, type), goto error);
2287 for (i = 0; i < map->n; ++i) {
2288 map->p[i] = isl_basic_map_eliminate_vars(map->p[i],
2289 isl_basic_map_offset(map->p[i], type) - 1 + first, n);
2293 map = isl_map_drop(map, type, first, n);
2300 __isl_give isl_set *isl_set_remove_dims(__isl_take isl_set *bset,
2301 enum isl_dim_type type, unsigned first, unsigned n)
2303 return (isl_set *)isl_map_remove_dims((isl_map *)bset, type, first, n);
2306 /* Project out n inputs starting at first using Fourier-Motzkin */
2307 struct isl_map *isl_map_remove_inputs(struct isl_map *map,
2308 unsigned first, unsigned n)
2310 return isl_map_remove_dims(map, isl_dim_in, first, n);
2313 static void dump_term(struct isl_basic_map *bmap,
2314 isl_int c, int pos, FILE *out)
2317 unsigned in = isl_basic_map_n_in(bmap);
2318 unsigned dim = in + isl_basic_map_n_out(bmap);
2319 unsigned nparam = isl_basic_map_n_param(bmap);
2321 isl_int_print(out, c, 0);
2323 if (!isl_int_is_one(c))
2324 isl_int_print(out, c, 0);
2325 if (pos < 1 + nparam) {
2326 name = isl_space_get_dim_name(bmap->dim,
2327 isl_dim_param, pos - 1);
2329 fprintf(out, "%s", name);
2331 fprintf(out, "p%d", pos - 1);
2332 } else if (pos < 1 + nparam + in)
2333 fprintf(out, "i%d", pos - 1 - nparam);
2334 else if (pos < 1 + nparam + dim)
2335 fprintf(out, "o%d", pos - 1 - nparam - in);
2337 fprintf(out, "e%d", pos - 1 - nparam - dim);
2341 static void dump_constraint_sign(struct isl_basic_map *bmap, isl_int *c,
2342 int sign, FILE *out)
2346 unsigned len = 1 + isl_basic_map_total_dim(bmap);
2350 for (i = 0, first = 1; i < len; ++i) {
2351 if (isl_int_sgn(c[i]) * sign <= 0)
2354 fprintf(out, " + ");
2356 isl_int_abs(v, c[i]);
2357 dump_term(bmap, v, i, out);
2364 static void dump_constraint(struct isl_basic_map *bmap, isl_int *c,
2365 const char *op, FILE *out, int indent)
2369 fprintf(out, "%*s", indent, "");
2371 dump_constraint_sign(bmap, c, 1, out);
2372 fprintf(out, " %s ", op);
2373 dump_constraint_sign(bmap, c, -1, out);
2377 for (i = bmap->n_div; i < bmap->extra; ++i) {
2378 if (isl_int_is_zero(c[1+isl_space_dim(bmap->dim, isl_dim_all)+i]))
2380 fprintf(out, "%*s", indent, "");
2381 fprintf(out, "ERROR: unused div coefficient not zero\n");
2386 static void dump_constraints(struct isl_basic_map *bmap,
2387 isl_int **c, unsigned n,
2388 const char *op, FILE *out, int indent)
2392 for (i = 0; i < n; ++i)
2393 dump_constraint(bmap, c[i], op, out, indent);
2396 static void dump_affine(struct isl_basic_map *bmap, isl_int *exp, FILE *out)
2400 unsigned total = isl_basic_map_total_dim(bmap);
2402 for (j = 0; j < 1 + total; ++j) {
2403 if (isl_int_is_zero(exp[j]))
2405 if (!first && isl_int_is_pos(exp[j]))
2407 dump_term(bmap, exp[j], j, out);
2412 static void dump(struct isl_basic_map *bmap, FILE *out, int indent)
2416 dump_constraints(bmap, bmap->eq, bmap->n_eq, "=", out, indent);
2417 dump_constraints(bmap, bmap->ineq, bmap->n_ineq, ">=", out, indent);
2419 for (i = 0; i < bmap->n_div; ++i) {
2420 fprintf(out, "%*s", indent, "");
2421 fprintf(out, "e%d = [(", i);
2422 dump_affine(bmap, bmap->div[i]+1, out);
2424 isl_int_print(out, bmap->div[i][0], 0);
2425 fprintf(out, "]\n");
2429 void isl_basic_set_print_internal(struct isl_basic_set *bset,
2430 FILE *out, int indent)
2433 fprintf(out, "null basic set\n");
2437 fprintf(out, "%*s", indent, "");
2438 fprintf(out, "ref: %d, nparam: %d, dim: %d, extra: %d, flags: %x\n",
2439 bset->ref, bset->dim->nparam, bset->dim->n_out,
2440 bset->extra, bset->flags);
2441 dump((struct isl_basic_map *)bset, out, indent);
2444 void isl_basic_map_print_internal(struct isl_basic_map *bmap,
2445 FILE *out, int indent)
2448 fprintf(out, "null basic map\n");
2452 fprintf(out, "%*s", indent, "");
2453 fprintf(out, "ref: %d, nparam: %d, in: %d, out: %d, extra: %d, "
2454 "flags: %x, n_name: %d\n",
2456 bmap->dim->nparam, bmap->dim->n_in, bmap->dim->n_out,
2457 bmap->extra, bmap->flags, bmap->dim->n_id);
2458 dump(bmap, out, indent);
2461 int isl_inequality_negate(struct isl_basic_map *bmap, unsigned pos)
2466 total = isl_basic_map_total_dim(bmap);
2467 isl_assert(bmap->ctx, pos < bmap->n_ineq, return -1);
2468 isl_seq_neg(bmap->ineq[pos], bmap->ineq[pos], 1 + total);
2469 isl_int_sub_ui(bmap->ineq[pos][0], bmap->ineq[pos][0], 1);
2470 ISL_F_CLR(bmap, ISL_BASIC_MAP_NORMALIZED);
2474 __isl_give isl_set *isl_set_alloc_space(__isl_take isl_space *dim, int n,
2477 struct isl_set *set;
2481 isl_assert(dim->ctx, dim->n_in == 0, goto error);
2482 isl_assert(dim->ctx, n >= 0, goto error);
2483 set = isl_alloc(dim->ctx, struct isl_set,
2484 sizeof(struct isl_set) +
2485 (n - 1) * sizeof(struct isl_basic_set *));
2489 set->ctx = dim->ctx;
2490 isl_ctx_ref(set->ctx);
2498 isl_space_free(dim);
2502 struct isl_set *isl_set_alloc(struct isl_ctx *ctx,
2503 unsigned nparam, unsigned dim, int n, unsigned flags)
2505 struct isl_set *set;
2508 dims = isl_space_alloc(ctx, nparam, 0, dim);
2512 set = isl_set_alloc_space(dims, n, flags);
2516 /* Make sure "map" has room for at least "n" more basic maps.
2518 struct isl_map *isl_map_grow(struct isl_map *map, int n)
2521 struct isl_map *grown = NULL;
2525 isl_assert(map->ctx, n >= 0, goto error);
2526 if (map->n + n <= map->size)
2528 grown = isl_map_alloc_space(isl_map_get_space(map), map->n + n, map->flags);
2531 for (i = 0; i < map->n; ++i) {
2532 grown->p[i] = isl_basic_map_copy(map->p[i]);
2540 isl_map_free(grown);
2545 /* Make sure "set" has room for at least "n" more basic sets.
2547 struct isl_set *isl_set_grow(struct isl_set *set, int n)
2549 return (struct isl_set *)isl_map_grow((struct isl_map *)set, n);
2552 struct isl_set *isl_set_dup(struct isl_set *set)
2555 struct isl_set *dup;
2560 dup = isl_set_alloc_space(isl_space_copy(set->dim), set->n, set->flags);
2563 for (i = 0; i < set->n; ++i)
2564 dup = isl_set_add_basic_set(dup, isl_basic_set_copy(set->p[i]));
2568 struct isl_set *isl_set_from_basic_set(struct isl_basic_set *bset)
2570 return isl_map_from_basic_map(bset);
2573 struct isl_map *isl_map_from_basic_map(struct isl_basic_map *bmap)
2575 struct isl_map *map;
2580 map = isl_map_alloc_space(isl_space_copy(bmap->dim), 1, ISL_MAP_DISJOINT);
2581 return isl_map_add_basic_map(map, bmap);
2584 __isl_give isl_set *isl_set_add_basic_set(__isl_take isl_set *set,
2585 __isl_take isl_basic_set *bset)
2587 return (struct isl_set *)isl_map_add_basic_map((struct isl_map *)set,
2588 (struct isl_basic_map *)bset);
2591 void *isl_set_free(__isl_take isl_set *set)
2601 isl_ctx_deref(set->ctx);
2602 for (i = 0; i < set->n; ++i)
2603 isl_basic_set_free(set->p[i]);
2604 isl_space_free(set->dim);
2610 void isl_set_print_internal(struct isl_set *set, FILE *out, int indent)
2615 fprintf(out, "null set\n");
2619 fprintf(out, "%*s", indent, "");
2620 fprintf(out, "ref: %d, n: %d, nparam: %d, dim: %d, flags: %x\n",
2621 set->ref, set->n, set->dim->nparam, set->dim->n_out,
2623 for (i = 0; i < set->n; ++i) {
2624 fprintf(out, "%*s", indent, "");
2625 fprintf(out, "basic set %d:\n", i);
2626 isl_basic_set_print_internal(set->p[i], out, indent+4);
2630 void isl_map_print_internal(struct isl_map *map, FILE *out, int indent)
2635 fprintf(out, "null map\n");
2639 fprintf(out, "%*s", indent, "");
2640 fprintf(out, "ref: %d, n: %d, nparam: %d, in: %d, out: %d, "
2641 "flags: %x, n_name: %d\n",
2642 map->ref, map->n, map->dim->nparam, map->dim->n_in,
2643 map->dim->n_out, map->flags, map->dim->n_id);
2644 for (i = 0; i < map->n; ++i) {
2645 fprintf(out, "%*s", indent, "");
2646 fprintf(out, "basic map %d:\n", i);
2647 isl_basic_map_print_internal(map->p[i], out, indent+4);
2651 struct isl_basic_map *isl_basic_map_intersect_domain(
2652 struct isl_basic_map *bmap, struct isl_basic_set *bset)
2654 struct isl_basic_map *bmap_domain;
2659 isl_assert(bset->ctx, isl_space_match(bmap->dim, isl_dim_param,
2660 bset->dim, isl_dim_param), goto error);
2662 if (isl_space_dim(bset->dim, isl_dim_set) != 0)
2663 isl_assert(bset->ctx,
2664 isl_basic_map_compatible_domain(bmap, bset), goto error);
2666 bmap = isl_basic_map_cow(bmap);
2669 bmap = isl_basic_map_extend_space(bmap, isl_space_copy(bmap->dim),
2670 bset->n_div, bset->n_eq, bset->n_ineq);
2671 bmap_domain = isl_basic_map_from_domain(bset);
2672 bmap = add_constraints(bmap, bmap_domain, 0, 0);
2674 bmap = isl_basic_map_simplify(bmap);
2675 return isl_basic_map_finalize(bmap);
2677 isl_basic_map_free(bmap);
2678 isl_basic_set_free(bset);
2682 struct isl_basic_map *isl_basic_map_intersect_range(
2683 struct isl_basic_map *bmap, struct isl_basic_set *bset)
2685 struct isl_basic_map *bmap_range;
2690 isl_assert(bset->ctx, isl_space_match(bmap->dim, isl_dim_param,
2691 bset->dim, isl_dim_param), goto error);
2693 if (isl_space_dim(bset->dim, isl_dim_set) != 0)
2694 isl_assert(bset->ctx,
2695 isl_basic_map_compatible_range(bmap, bset), goto error);
2697 if (isl_basic_set_is_universe(bset)) {
2698 isl_basic_set_free(bset);
2702 bmap = isl_basic_map_cow(bmap);
2705 bmap = isl_basic_map_extend_space(bmap, isl_space_copy(bmap->dim),
2706 bset->n_div, bset->n_eq, bset->n_ineq);
2707 bmap_range = isl_basic_map_from_basic_set(bset, isl_space_copy(bset->dim));
2708 bmap = add_constraints(bmap, bmap_range, 0, 0);
2710 bmap = isl_basic_map_simplify(bmap);
2711 return isl_basic_map_finalize(bmap);
2713 isl_basic_map_free(bmap);
2714 isl_basic_set_free(bset);
2718 int isl_basic_map_contains(struct isl_basic_map *bmap, struct isl_vec *vec)
2724 total = 1 + isl_basic_map_total_dim(bmap);
2725 if (total != vec->size)
2730 for (i = 0; i < bmap->n_eq; ++i) {
2731 isl_seq_inner_product(vec->el, bmap->eq[i], total, &s);
2732 if (!isl_int_is_zero(s)) {
2738 for (i = 0; i < bmap->n_ineq; ++i) {
2739 isl_seq_inner_product(vec->el, bmap->ineq[i], total, &s);
2740 if (isl_int_is_neg(s)) {
2751 int isl_basic_set_contains(struct isl_basic_set *bset, struct isl_vec *vec)
2753 return isl_basic_map_contains((struct isl_basic_map *)bset, vec);
2756 struct isl_basic_map *isl_basic_map_intersect(
2757 struct isl_basic_map *bmap1, struct isl_basic_map *bmap2)
2759 struct isl_vec *sample = NULL;
2761 if (!bmap1 || !bmap2)
2764 isl_assert(bmap1->ctx, isl_space_match(bmap1->dim, isl_dim_param,
2765 bmap2->dim, isl_dim_param), goto error);
2766 if (isl_space_dim(bmap1->dim, isl_dim_all) ==
2767 isl_space_dim(bmap1->dim, isl_dim_param) &&
2768 isl_space_dim(bmap2->dim, isl_dim_all) !=
2769 isl_space_dim(bmap2->dim, isl_dim_param))
2770 return isl_basic_map_intersect(bmap2, bmap1);
2772 if (isl_space_dim(bmap2->dim, isl_dim_all) !=
2773 isl_space_dim(bmap2->dim, isl_dim_param))
2774 isl_assert(bmap1->ctx,
2775 isl_space_is_equal(bmap1->dim, bmap2->dim), goto error);
2777 if (bmap1->sample &&
2778 isl_basic_map_contains(bmap1, bmap1->sample) > 0 &&
2779 isl_basic_map_contains(bmap2, bmap1->sample) > 0)
2780 sample = isl_vec_copy(bmap1->sample);
2781 else if (bmap2->sample &&
2782 isl_basic_map_contains(bmap1, bmap2->sample) > 0 &&
2783 isl_basic_map_contains(bmap2, bmap2->sample) > 0)
2784 sample = isl_vec_copy(bmap2->sample);
2786 bmap1 = isl_basic_map_cow(bmap1);
2789 bmap1 = isl_basic_map_extend_space(bmap1, isl_space_copy(bmap1->dim),
2790 bmap2->n_div, bmap2->n_eq, bmap2->n_ineq);
2791 bmap1 = add_constraints(bmap1, bmap2, 0, 0);
2794 isl_vec_free(sample);
2796 isl_vec_free(bmap1->sample);
2797 bmap1->sample = sample;
2800 bmap1 = isl_basic_map_simplify(bmap1);
2801 return isl_basic_map_finalize(bmap1);
2804 isl_vec_free(sample);
2805 isl_basic_map_free(bmap1);
2806 isl_basic_map_free(bmap2);
2810 struct isl_basic_set *isl_basic_set_intersect(
2811 struct isl_basic_set *bset1, struct isl_basic_set *bset2)
2813 return (struct isl_basic_set *)
2814 isl_basic_map_intersect(
2815 (struct isl_basic_map *)bset1,
2816 (struct isl_basic_map *)bset2);
2819 __isl_give isl_basic_set *isl_basic_set_intersect_params(
2820 __isl_take isl_basic_set *bset1, __isl_take isl_basic_set *bset2)
2822 return isl_basic_set_intersect(bset1, bset2);
2825 /* Special case of isl_map_intersect, where both map1 and map2
2826 * are convex, without any divs and such that either map1 or map2
2827 * contains a single constraint. This constraint is then simply
2828 * added to the other map.
2830 static __isl_give isl_map *map_intersect_add_constraint(
2831 __isl_take isl_map *map1, __isl_take isl_map *map2)
2833 isl_assert(map1->ctx, map1->n == 1, goto error);
2834 isl_assert(map2->ctx, map1->n == 1, goto error);
2835 isl_assert(map1->ctx, map1->p[0]->n_div == 0, goto error);
2836 isl_assert(map2->ctx, map1->p[0]->n_div == 0, goto error);
2838 if (map2->p[0]->n_eq + map2->p[0]->n_ineq != 1)
2839 return isl_map_intersect(map2, map1);
2841 isl_assert(map2->ctx,
2842 map2->p[0]->n_eq + map2->p[0]->n_ineq == 1, goto error);
2844 map1 = isl_map_cow(map1);
2847 if (isl_map_plain_is_empty(map1)) {
2851 map1->p[0] = isl_basic_map_cow(map1->p[0]);
2852 if (map2->p[0]->n_eq == 1)
2853 map1->p[0] = isl_basic_map_add_eq(map1->p[0], map2->p[0]->eq[0]);
2855 map1->p[0] = isl_basic_map_add_ineq(map1->p[0],
2856 map2->p[0]->ineq[0]);
2858 map1->p[0] = isl_basic_map_simplify(map1->p[0]);
2859 map1->p[0] = isl_basic_map_finalize(map1->p[0]);
2863 if (isl_basic_map_plain_is_empty(map1->p[0])) {
2864 isl_basic_map_free(map1->p[0]);
2877 /* map2 may be either a parameter domain or a map living in the same
2880 static __isl_give isl_map *map_intersect_internal(__isl_take isl_map *map1,
2881 __isl_take isl_map *map2)
2890 if ((isl_map_plain_is_empty(map1) ||
2891 isl_map_plain_is_universe(map2)) &&
2892 isl_space_is_equal(map1->dim, map2->dim)) {
2896 if ((isl_map_plain_is_empty(map2) ||
2897 isl_map_plain_is_universe(map1)) &&
2898 isl_space_is_equal(map1->dim, map2->dim)) {
2903 if (map1->n == 1 && map2->n == 1 &&
2904 map1->p[0]->n_div == 0 && map2->p[0]->n_div == 0 &&
2905 isl_space_is_equal(map1->dim, map2->dim) &&
2906 (map1->p[0]->n_eq + map1->p[0]->n_ineq == 1 ||
2907 map2->p[0]->n_eq + map2->p[0]->n_ineq == 1))
2908 return map_intersect_add_constraint(map1, map2);
2910 if (isl_space_dim(map2->dim, isl_dim_all) !=
2911 isl_space_dim(map2->dim, isl_dim_param))
2912 isl_assert(map1->ctx,
2913 isl_space_is_equal(map1->dim, map2->dim), goto error);
2915 if (ISL_F_ISSET(map1, ISL_MAP_DISJOINT) &&
2916 ISL_F_ISSET(map2, ISL_MAP_DISJOINT))
2917 ISL_FL_SET(flags, ISL_MAP_DISJOINT);
2919 result = isl_map_alloc_space(isl_space_copy(map1->dim),
2920 map1->n * map2->n, flags);
2923 for (i = 0; i < map1->n; ++i)
2924 for (j = 0; j < map2->n; ++j) {
2925 struct isl_basic_map *part;
2926 part = isl_basic_map_intersect(
2927 isl_basic_map_copy(map1->p[i]),
2928 isl_basic_map_copy(map2->p[j]));
2929 if (isl_basic_map_is_empty(part) < 0)
2930 part = isl_basic_map_free(part);
2931 result = isl_map_add_basic_map(result, part);
2944 static __isl_give isl_map *map_intersect(__isl_take isl_map *map1,
2945 __isl_take isl_map *map2)
2949 if (!isl_space_is_equal(map1->dim, map2->dim))
2950 isl_die(isl_map_get_ctx(map1), isl_error_invalid,
2951 "spaces don't match", goto error);
2952 return map_intersect_internal(map1, map2);
2959 __isl_give isl_map *isl_map_intersect(__isl_take isl_map *map1,
2960 __isl_take isl_map *map2)
2962 return isl_map_align_params_map_map_and(map1, map2, &map_intersect);
2965 struct isl_set *isl_set_intersect(struct isl_set *set1, struct isl_set *set2)
2967 return (struct isl_set *)
2968 isl_map_intersect((struct isl_map *)set1,
2969 (struct isl_map *)set2);
2972 /* map_intersect_internal accepts intersections
2973 * with parameter domains, so we can just call that function.
2975 static __isl_give isl_map *map_intersect_params(__isl_take isl_map *map,
2976 __isl_take isl_set *params)
2978 return map_intersect_internal(map, params);
2981 __isl_give isl_map *isl_map_intersect_params(__isl_take isl_map *map1,
2982 __isl_take isl_map *map2)
2984 return isl_map_align_params_map_map_and(map1, map2, &map_intersect_params);
2987 __isl_give isl_set *isl_set_intersect_params(__isl_take isl_set *set,
2988 __isl_take isl_set *params)
2990 return isl_map_intersect_params(set, params);
2993 struct isl_basic_map *isl_basic_map_reverse(struct isl_basic_map *bmap)
2996 struct isl_basic_set *bset;
3001 bmap = isl_basic_map_cow(bmap);
3004 dim = isl_space_reverse(isl_space_copy(bmap->dim));
3005 in = isl_basic_map_n_in(bmap);
3006 bset = isl_basic_set_from_basic_map(bmap);
3007 bset = isl_basic_set_swap_vars(bset, in);
3008 return isl_basic_map_from_basic_set(bset, dim);
3011 static __isl_give isl_basic_map *basic_map_space_reset(
3012 __isl_take isl_basic_map *bmap, enum isl_dim_type type)
3018 if (!isl_space_is_named_or_nested(bmap->dim, type))
3021 space = isl_basic_map_get_space(bmap);
3022 space = isl_space_reset(space, type);
3023 bmap = isl_basic_map_reset_space(bmap, space);
3027 __isl_give isl_basic_map *isl_basic_map_insert_dims(
3028 __isl_take isl_basic_map *bmap, enum isl_dim_type type,
3029 unsigned pos, unsigned n)
3032 struct isl_basic_map *res;
3033 struct isl_dim_map *dim_map;
3034 unsigned total, off;
3035 enum isl_dim_type t;
3038 return basic_map_space_reset(bmap, type);
3043 res_dim = isl_space_insert_dims(isl_basic_map_get_space(bmap), type, pos, n);
3045 total = isl_basic_map_total_dim(bmap) + n;
3046 dim_map = isl_dim_map_alloc(bmap->ctx, total);
3048 for (t = isl_dim_param; t <= isl_dim_out; ++t) {
3050 isl_dim_map_dim(dim_map, bmap->dim, t, off);
3052 unsigned size = isl_basic_map_dim(bmap, t);
3053 isl_dim_map_dim_range(dim_map, bmap->dim, t,
3055 isl_dim_map_dim_range(dim_map, bmap->dim, t,
3056 pos, size - pos, off + pos + n);
3058 off += isl_space_dim(res_dim, t);
3060 isl_dim_map_div(dim_map, bmap, off);
3062 res = isl_basic_map_alloc_space(res_dim,
3063 bmap->n_div, bmap->n_eq, bmap->n_ineq);
3064 if (isl_basic_map_is_rational(bmap))
3065 res = isl_basic_map_set_rational(res);
3066 if (isl_basic_map_plain_is_empty(bmap)) {
3067 isl_basic_map_free(bmap);
3068 return isl_basic_map_set_to_empty(res);
3070 res = isl_basic_map_add_constraints_dim_map(res, bmap, dim_map);
3071 return isl_basic_map_finalize(res);
3074 __isl_give isl_basic_set *isl_basic_set_insert_dims(
3075 __isl_take isl_basic_set *bset,
3076 enum isl_dim_type type, unsigned pos, unsigned n)
3078 return isl_basic_map_insert_dims(bset, type, pos, n);
3081 __isl_give isl_basic_map *isl_basic_map_add(__isl_take isl_basic_map *bmap,
3082 enum isl_dim_type type, unsigned n)
3086 return isl_basic_map_insert_dims(bmap, type,
3087 isl_basic_map_dim(bmap, type), n);
3090 __isl_give isl_basic_set *isl_basic_set_add_dims(__isl_take isl_basic_set *bset,
3091 enum isl_dim_type type, unsigned n)
3095 isl_assert(bset->ctx, type != isl_dim_in, goto error);
3096 return (isl_basic_set *)isl_basic_map_add((isl_basic_map *)bset, type, n);
3098 isl_basic_set_free(bset);
3102 static __isl_give isl_map *map_space_reset(__isl_take isl_map *map,
3103 enum isl_dim_type type)
3107 if (!map || !isl_space_is_named_or_nested(map->dim, type))
3110 space = isl_map_get_space(map);
3111 space = isl_space_reset(space, type);
3112 map = isl_map_reset_space(map, space);
3116 __isl_give isl_map *isl_map_insert_dims(__isl_take isl_map *map,
3117 enum isl_dim_type type, unsigned pos, unsigned n)
3122 return map_space_reset(map, type);
3124 map = isl_map_cow(map);
3128 map->dim = isl_space_insert_dims(map->dim, type, pos, n);
3132 for (i = 0; i < map->n; ++i) {
3133 map->p[i] = isl_basic_map_insert_dims(map->p[i], type, pos, n);
3144 __isl_give isl_set *isl_set_insert_dims(__isl_take isl_set *set,
3145 enum isl_dim_type type, unsigned pos, unsigned n)
3147 return isl_map_insert_dims(set, type, pos, n);
3150 __isl_give isl_map *isl_map_add_dims(__isl_take isl_map *map,
3151 enum isl_dim_type type, unsigned n)
3155 return isl_map_insert_dims(map, type, isl_map_dim(map, type), n);
3158 __isl_give isl_set *isl_set_add_dims(__isl_take isl_set *set,
3159 enum isl_dim_type type, unsigned n)
3163 isl_assert(set->ctx, type != isl_dim_in, goto error);
3164 return (isl_set *)isl_map_add_dims((isl_map *)set, type, n);
3170 __isl_give isl_basic_map *isl_basic_map_move_dims(
3171 __isl_take isl_basic_map *bmap,
3172 enum isl_dim_type dst_type, unsigned dst_pos,
3173 enum isl_dim_type src_type, unsigned src_pos, unsigned n)
3175 struct isl_dim_map *dim_map;
3176 struct isl_basic_map *res;
3177 enum isl_dim_type t;
3178 unsigned total, off;
3185 isl_assert(bmap->ctx, src_pos + n <= isl_basic_map_dim(bmap, src_type),
3188 if (dst_type == src_type && dst_pos == src_pos)
3191 isl_assert(bmap->ctx, dst_type != src_type, goto error);
3193 if (pos(bmap->dim, dst_type) + dst_pos ==
3194 pos(bmap->dim, src_type) + src_pos +
3195 ((src_type < dst_type) ? n : 0)) {
3196 bmap = isl_basic_map_cow(bmap);
3200 bmap->dim = isl_space_move_dims(bmap->dim, dst_type, dst_pos,
3201 src_type, src_pos, n);
3205 bmap = isl_basic_map_finalize(bmap);
3210 total = isl_basic_map_total_dim(bmap);
3211 dim_map = isl_dim_map_alloc(bmap->ctx, total);
3214 for (t = isl_dim_param; t <= isl_dim_out; ++t) {
3215 unsigned size = isl_space_dim(bmap->dim, t);
3216 if (t == dst_type) {
3217 isl_dim_map_dim_range(dim_map, bmap->dim, t,
3220 isl_dim_map_dim_range(dim_map, bmap->dim, src_type,
3223 isl_dim_map_dim_range(dim_map, bmap->dim, t,
3224 dst_pos, size - dst_pos, off);
3225 off += size - dst_pos;
3226 } else if (t == src_type) {
3227 isl_dim_map_dim_range(dim_map, bmap->dim, t,
3230 isl_dim_map_dim_range(dim_map, bmap->dim, t,
3231 src_pos + n, size - src_pos - n, off);
3232 off += size - src_pos - n;
3234 isl_dim_map_dim(dim_map, bmap->dim, t, off);
3238 isl_dim_map_div(dim_map, bmap, off);
3240 res = isl_basic_map_alloc_space(isl_basic_map_get_space(bmap),
3241 bmap->n_div, bmap->n_eq, bmap->n_ineq);
3242 bmap = isl_basic_map_add_constraints_dim_map(res, bmap, dim_map);
3246 bmap->dim = isl_space_move_dims(bmap->dim, dst_type, dst_pos,
3247 src_type, src_pos, n);
3251 ISL_F_CLR(bmap, ISL_BASIC_MAP_NORMALIZED);
3252 bmap = isl_basic_map_gauss(bmap, NULL);
3253 bmap = isl_basic_map_finalize(bmap);
3257 isl_basic_map_free(bmap);
3261 __isl_give isl_basic_set *isl_basic_set_move_dims(__isl_take isl_basic_set *bset,
3262 enum isl_dim_type dst_type, unsigned dst_pos,
3263 enum isl_dim_type src_type, unsigned src_pos, unsigned n)
3265 return (isl_basic_set *)isl_basic_map_move_dims(
3266 (isl_basic_map *)bset, dst_type, dst_pos, src_type, src_pos, n);
3269 __isl_give isl_set *isl_set_move_dims(__isl_take isl_set *set,
3270 enum isl_dim_type dst_type, unsigned dst_pos,
3271 enum isl_dim_type src_type, unsigned src_pos, unsigned n)
3275 isl_assert(set->ctx, dst_type != isl_dim_in, goto error);
3276 return (isl_set *)isl_map_move_dims((isl_map *)set, dst_type, dst_pos,
3277 src_type, src_pos, n);
3283 __isl_give isl_map *isl_map_move_dims(__isl_take isl_map *map,
3284 enum isl_dim_type dst_type, unsigned dst_pos,
3285 enum isl_dim_type src_type, unsigned src_pos, unsigned n)
3294 isl_assert(map->ctx, src_pos + n <= isl_map_dim(map, src_type),
3297 if (dst_type == src_type && dst_pos == src_pos)
3300 isl_assert(map->ctx, dst_type != src_type, goto error);
3302 map = isl_map_cow(map);
3306 map->dim = isl_space_move_dims(map->dim, dst_type, dst_pos, src_type, src_pos, n);
3310 for (i = 0; i < map->n; ++i) {
3311 map->p[i] = isl_basic_map_move_dims(map->p[i],
3313 src_type, src_pos, n);
3324 /* Move the specified dimensions to the last columns right before
3325 * the divs. Don't change the dimension specification of bmap.
3326 * That's the responsibility of the caller.
3328 static __isl_give isl_basic_map *move_last(__isl_take isl_basic_map *bmap,
3329 enum isl_dim_type type, unsigned first, unsigned n)
3331 struct isl_dim_map *dim_map;
3332 struct isl_basic_map *res;
3333 enum isl_dim_type t;
3334 unsigned total, off;
3338 if (pos(bmap->dim, type) + first + n ==
3339 1 + isl_space_dim(bmap->dim, isl_dim_all))
3342 total = isl_basic_map_total_dim(bmap);
3343 dim_map = isl_dim_map_alloc(bmap->ctx, total);
3346 for (t = isl_dim_param; t <= isl_dim_out; ++t) {
3347 unsigned size = isl_space_dim(bmap->dim, t);
3349 isl_dim_map_dim_range(dim_map, bmap->dim, t,
3352 isl_dim_map_dim_range(dim_map, bmap->dim, t,
3353 first, n, total - bmap->n_div - n);
3354 isl_dim_map_dim_range(dim_map, bmap->dim, t,
3355 first + n, size - (first + n), off);
3356 off += size - (first + n);
3358 isl_dim_map_dim(dim_map, bmap->dim, t, off);
3362 isl_dim_map_div(dim_map, bmap, off + n);
3364 res = isl_basic_map_alloc_space(isl_basic_map_get_space(bmap),
3365 bmap->n_div, bmap->n_eq, bmap->n_ineq);
3366 res = isl_basic_map_add_constraints_dim_map(res, bmap, dim_map);
3370 /* Insert "n" rows in the divs of "bmap".
3372 * The number of columns is not changed, which means that the last
3373 * dimensions of "bmap" are being reintepreted as the new divs.
3374 * The space of "bmap" is not adjusted, however, which means
3375 * that "bmap" is left in an inconsistent state. Removing "n" dimensions
3376 * from the space of "bmap" is the responsibility of the caller.
3378 static __isl_give isl_basic_map *insert_div_rows(__isl_take isl_basic_map *bmap,
3386 bmap = isl_basic_map_cow(bmap);
3390 row_size = 1 + isl_space_dim(bmap->dim, isl_dim_all) + bmap->extra;
3391 old = bmap->block2.data;
3392 bmap->block2 = isl_blk_extend(bmap->ctx, bmap->block2,
3393 (bmap->extra + n) * (1 + row_size));
3394 if (!bmap->block2.data)
3395 return isl_basic_map_free(bmap);
3396 new_div = isl_alloc_array(bmap->ctx, isl_int *, bmap->extra + n);
3398 return isl_basic_map_free(bmap);
3399 for (i = 0; i < n; ++i) {
3400 new_div[i] = bmap->block2.data +
3401 (bmap->extra + i) * (1 + row_size);
3402 isl_seq_clr(new_div[i], 1 + row_size);
3404 for (i = 0; i < bmap->extra; ++i)
3405 new_div[n + i] = bmap->block2.data + (bmap->div[i] - old);
3407 bmap->div = new_div;
3414 /* Turn the n dimensions of type type, starting at first
3415 * into existentially quantified variables.
3417 __isl_give isl_basic_map *isl_basic_map_project_out(
3418 __isl_take isl_basic_map *bmap,
3419 enum isl_dim_type type, unsigned first, unsigned n)
3422 return basic_map_space_reset(bmap, type);
3427 if (ISL_F_ISSET(bmap, ISL_BASIC_MAP_RATIONAL))
3428 return isl_basic_map_remove_dims(bmap, type, first, n);
3430 isl_assert(bmap->ctx, first + n <= isl_basic_map_dim(bmap, type),
3433 bmap = move_last(bmap, type, first, n);
3434 bmap = isl_basic_map_cow(bmap);
3435 bmap = insert_div_rows(bmap, n);
3439 bmap->dim = isl_space_drop_dims(bmap->dim, type, first, n);
3442 bmap = isl_basic_map_simplify(bmap);
3443 bmap = isl_basic_map_drop_redundant_divs(bmap);
3444 return isl_basic_map_finalize(bmap);
3446 isl_basic_map_free(bmap);
3450 /* Turn the n dimensions of type type, starting at first
3451 * into existentially quantified variables.
3453 struct isl_basic_set *isl_basic_set_project_out(struct isl_basic_set *bset,
3454 enum isl_dim_type type, unsigned first, unsigned n)
3456 return (isl_basic_set *)isl_basic_map_project_out(
3457 (isl_basic_map *)bset, type, first, n);
3460 /* Turn the n dimensions of type type, starting at first
3461 * into existentially quantified variables.
3463 __isl_give isl_map *isl_map_project_out(__isl_take isl_map *map,
3464 enum isl_dim_type type, unsigned first, unsigned n)
3472 return map_space_reset(map, type);
3474 isl_assert(map->ctx, first + n <= isl_map_dim(map, type), goto error);
3476 map = isl_map_cow(map);
3480 map->dim = isl_space_drop_dims(map->dim, type, first, n);
3484 for (i = 0; i < map->n; ++i) {
3485 map->p[i] = isl_basic_map_project_out(map->p[i], type, first, n);
3496 /* Turn the n dimensions of type type, starting at first
3497 * into existentially quantified variables.
3499 __isl_give isl_set *isl_set_project_out(__isl_take isl_set *set,
3500 enum isl_dim_type type, unsigned first, unsigned n)
3502 return (isl_set *)isl_map_project_out((isl_map *)set, type, first, n);
3505 static struct isl_basic_map *add_divs(struct isl_basic_map *bmap, unsigned n)
3509 for (i = 0; i < n; ++i) {
3510 j = isl_basic_map_alloc_div(bmap);
3513 isl_seq_clr(bmap->div[j], 1+1+isl_basic_map_total_dim(bmap));
3517 isl_basic_map_free(bmap);
3521 struct isl_basic_map *isl_basic_map_apply_range(
3522 struct isl_basic_map *bmap1, struct isl_basic_map *bmap2)
3524 isl_space *dim_result = NULL;
3525 struct isl_basic_map *bmap;
3526 unsigned n_in, n_out, n, nparam, total, pos;
3527 struct isl_dim_map *dim_map1, *dim_map2;
3529 if (!bmap1 || !bmap2)
3532 dim_result = isl_space_join(isl_space_copy(bmap1->dim),
3533 isl_space_copy(bmap2->dim));
3535 n_in = isl_basic_map_n_in(bmap1);
3536 n_out = isl_basic_map_n_out(bmap2);
3537 n = isl_basic_map_n_out(bmap1);
3538 nparam = isl_basic_map_n_param(bmap1);
3540 total = nparam + n_in + n_out + bmap1->n_div + bmap2->n_div + n;
3541 dim_map1 = isl_dim_map_alloc(bmap1->ctx, total);
3542 dim_map2 = isl_dim_map_alloc(bmap1->ctx, total);
3543 isl_dim_map_dim(dim_map1, bmap1->dim, isl_dim_param, pos = 0);
3544 isl_dim_map_dim(dim_map2, bmap2->dim, isl_dim_param, pos = 0);
3545 isl_dim_map_dim(dim_map1, bmap1->dim, isl_dim_in, pos += nparam);
3546 isl_dim_map_dim(dim_map2, bmap2->dim, isl_dim_out, pos += n_in);
3547 isl_dim_map_div(dim_map1, bmap1, pos += n_out);
3548 isl_dim_map_div(dim_map2, bmap2, pos += bmap1->n_div);
3549 isl_dim_map_dim(dim_map1, bmap1->dim, isl_dim_out, pos += bmap2->n_div);
3550 isl_dim_map_dim(dim_map2, bmap2->dim, isl_dim_in, pos);
3552 bmap = isl_basic_map_alloc_space(dim_result,
3553 bmap1->n_div + bmap2->n_div + n,
3554 bmap1->n_eq + bmap2->n_eq,
3555 bmap1->n_ineq + bmap2->n_ineq);
3556 bmap = isl_basic_map_add_constraints_dim_map(bmap, bmap1, dim_map1);
3557 bmap = isl_basic_map_add_constraints_dim_map(bmap, bmap2, dim_map2);
3558 bmap = add_divs(bmap, n);
3559 bmap = isl_basic_map_simplify(bmap);
3560 bmap = isl_basic_map_drop_redundant_divs(bmap);
3561 return isl_basic_map_finalize(bmap);
3563 isl_basic_map_free(bmap1);
3564 isl_basic_map_free(bmap2);
3568 struct isl_basic_set *isl_basic_set_apply(
3569 struct isl_basic_set *bset, struct isl_basic_map *bmap)
3574 isl_assert(bset->ctx, isl_basic_map_compatible_domain(bmap, bset),
3577 return (struct isl_basic_set *)
3578 isl_basic_map_apply_range((struct isl_basic_map *)bset, bmap);
3580 isl_basic_set_free(bset);
3581 isl_basic_map_free(bmap);
3585 struct isl_basic_map *isl_basic_map_apply_domain(
3586 struct isl_basic_map *bmap1, struct isl_basic_map *bmap2)
3588 if (!bmap1 || !bmap2)
3591 isl_assert(bmap1->ctx,
3592 isl_basic_map_n_in(bmap1) == isl_basic_map_n_in(bmap2), goto error);
3593 isl_assert(bmap1->ctx,
3594 isl_basic_map_n_param(bmap1) == isl_basic_map_n_param(bmap2),
3597 bmap1 = isl_basic_map_reverse(bmap1);
3598 bmap1 = isl_basic_map_apply_range(bmap1, bmap2);
3599 return isl_basic_map_reverse(bmap1);
3601 isl_basic_map_free(bmap1);
3602 isl_basic_map_free(bmap2);
3606 /* Given two basic maps A -> f(A) and B -> g(B), construct a basic map
3607 * A \cap B -> f(A) + f(B)
3609 struct isl_basic_map *isl_basic_map_sum(
3610 struct isl_basic_map *bmap1, struct isl_basic_map *bmap2)
3612 unsigned n_in, n_out, nparam, total, pos;
3613 struct isl_basic_map *bmap = NULL;
3614 struct isl_dim_map *dim_map1, *dim_map2;
3617 if (!bmap1 || !bmap2)
3620 isl_assert(bmap1->ctx, isl_space_is_equal(bmap1->dim, bmap2->dim),
3623 nparam = isl_basic_map_n_param(bmap1);
3624 n_in = isl_basic_map_n_in(bmap1);
3625 n_out = isl_basic_map_n_out(bmap1);
3627 total = nparam + n_in + n_out + bmap1->n_div + bmap2->n_div + 2 * n_out;
3628 dim_map1 = isl_dim_map_alloc(bmap1->ctx, total);
3629 dim_map2 = isl_dim_map_alloc(bmap2->ctx, total);
3630 isl_dim_map_dim(dim_map1, bmap1->dim, isl_dim_param, pos = 0);
3631 isl_dim_map_dim(dim_map2, bmap2->dim, isl_dim_param, pos);
3632 isl_dim_map_dim(dim_map1, bmap1->dim, isl_dim_in, pos += nparam);
3633 isl_dim_map_dim(dim_map2, bmap2->dim, isl_dim_in, pos);
3634 isl_dim_map_div(dim_map1, bmap1, pos += n_in + n_out);
3635 isl_dim_map_div(dim_map2, bmap2, pos += bmap1->n_div);
3636 isl_dim_map_dim(dim_map1, bmap1->dim, isl_dim_out, pos += bmap2->n_div);
3637 isl_dim_map_dim(dim_map2, bmap2->dim, isl_dim_out, pos += n_out);
3639 bmap = isl_basic_map_alloc_space(isl_space_copy(bmap1->dim),
3640 bmap1->n_div + bmap2->n_div + 2 * n_out,
3641 bmap1->n_eq + bmap2->n_eq + n_out,
3642 bmap1->n_ineq + bmap2->n_ineq);
3643 for (i = 0; i < n_out; ++i) {
3644 int j = isl_basic_map_alloc_equality(bmap);
3647 isl_seq_clr(bmap->eq[j], 1+total);
3648 isl_int_set_si(bmap->eq[j][1+nparam+n_in+i], -1);
3649 isl_int_set_si(bmap->eq[j][1+pos+i], 1);
3650 isl_int_set_si(bmap->eq[j][1+pos-n_out+i], 1);
3652 bmap = isl_basic_map_add_constraints_dim_map(bmap, bmap1, dim_map1);
3653 bmap = isl_basic_map_add_constraints_dim_map(bmap, bmap2, dim_map2);
3654 bmap = add_divs(bmap, 2 * n_out);
3656 bmap = isl_basic_map_simplify(bmap);
3657 return isl_basic_map_finalize(bmap);
3659 isl_basic_map_free(bmap);
3660 isl_basic_map_free(bmap1);
3661 isl_basic_map_free(bmap2);
3665 /* Given two maps A -> f(A) and B -> g(B), construct a map
3666 * A \cap B -> f(A) + f(B)
3668 struct isl_map *isl_map_sum(struct isl_map *map1, struct isl_map *map2)
3670 struct isl_map *result;
3676 isl_assert(map1->ctx, isl_space_is_equal(map1->dim, map2->dim), goto error);
3678 result = isl_map_alloc_space(isl_space_copy(map1->dim),
3679 map1->n * map2->n, 0);
3682 for (i = 0; i < map1->n; ++i)
3683 for (j = 0; j < map2->n; ++j) {
3684 struct isl_basic_map *part;
3685 part = isl_basic_map_sum(
3686 isl_basic_map_copy(map1->p[i]),
3687 isl_basic_map_copy(map2->p[j]));
3688 if (isl_basic_map_is_empty(part))
3689 isl_basic_map_free(part);
3691 result = isl_map_add_basic_map(result, part);
3704 __isl_give isl_set *isl_set_sum(__isl_take isl_set *set1,
3705 __isl_take isl_set *set2)
3707 return (isl_set *)isl_map_sum((isl_map *)set1, (isl_map *)set2);
3710 /* Given a basic map A -> f(A), construct A -> -f(A).
3712 struct isl_basic_map *isl_basic_map_neg(struct isl_basic_map *bmap)
3717 bmap = isl_basic_map_cow(bmap);
3721 n = isl_basic_map_dim(bmap, isl_dim_out);
3722 off = isl_basic_map_offset(bmap, isl_dim_out);
3723 for (i = 0; i < bmap->n_eq; ++i)
3724 for (j = 0; j < n; ++j)
3725 isl_int_neg(bmap->eq[i][off+j], bmap->eq[i][off+j]);
3726 for (i = 0; i < bmap->n_ineq; ++i)
3727 for (j = 0; j < n; ++j)
3728 isl_int_neg(bmap->ineq[i][off+j], bmap->ineq[i][off+j]);
3729 for (i = 0; i < bmap->n_div; ++i)
3730 for (j = 0; j < n; ++j)
3731 isl_int_neg(bmap->div[i][1+off+j], bmap->div[i][1+off+j]);
3732 bmap = isl_basic_map_gauss(bmap, NULL);
3733 return isl_basic_map_finalize(bmap);
3736 __isl_give isl_basic_set *isl_basic_set_neg(__isl_take isl_basic_set *bset)
3738 return isl_basic_map_neg(bset);
3741 /* Given a map A -> f(A), construct A -> -f(A).
3743 struct isl_map *isl_map_neg(struct isl_map *map)
3747 map = isl_map_cow(map);
3751 for (i = 0; i < map->n; ++i) {
3752 map->p[i] = isl_basic_map_neg(map->p[i]);
3763 __isl_give isl_set *isl_set_neg(__isl_take isl_set *set)
3765 return (isl_set *)isl_map_neg((isl_map *)set);
3768 /* Given a basic map A -> f(A) and an integer d, construct a basic map
3769 * A -> floor(f(A)/d).
3771 struct isl_basic_map *isl_basic_map_floordiv(struct isl_basic_map *bmap,
3774 unsigned n_in, n_out, nparam, total, pos;
3775 struct isl_basic_map *result = NULL;
3776 struct isl_dim_map *dim_map;
3782 nparam = isl_basic_map_n_param(bmap);
3783 n_in = isl_basic_map_n_in(bmap);
3784 n_out = isl_basic_map_n_out(bmap);
3786 total = nparam + n_in + n_out + bmap->n_div + n_out;
3787 dim_map = isl_dim_map_alloc(bmap->ctx, total);
3788 isl_dim_map_dim(dim_map, bmap->dim, isl_dim_param, pos = 0);
3789 isl_dim_map_dim(dim_map, bmap->dim, isl_dim_in, pos += nparam);
3790 isl_dim_map_div(dim_map, bmap, pos += n_in + n_out);
3791 isl_dim_map_dim(dim_map, bmap->dim, isl_dim_out, pos += bmap->n_div);
3793 result = isl_basic_map_alloc_space(isl_space_copy(bmap->dim),
3794 bmap->n_div + n_out,
3795 bmap->n_eq, bmap->n_ineq + 2 * n_out);
3796 result = isl_basic_map_add_constraints_dim_map(result, bmap, dim_map);
3797 result = add_divs(result, n_out);
3798 for (i = 0; i < n_out; ++i) {
3800 j = isl_basic_map_alloc_inequality(result);
3803 isl_seq_clr(result->ineq[j], 1+total);
3804 isl_int_neg(result->ineq[j][1+nparam+n_in+i], d);
3805 isl_int_set_si(result->ineq[j][1+pos+i], 1);
3806 j = isl_basic_map_alloc_inequality(result);
3809 isl_seq_clr(result->ineq[j], 1+total);
3810 isl_int_set(result->ineq[j][1+nparam+n_in+i], d);
3811 isl_int_set_si(result->ineq[j][1+pos+i], -1);
3812 isl_int_sub_ui(result->ineq[j][0], d, 1);
3815 result = isl_basic_map_simplify(result);
3816 return isl_basic_map_finalize(result);
3818 isl_basic_map_free(result);
3822 /* Given a map A -> f(A) and an integer d, construct a map
3823 * A -> floor(f(A)/d).
3825 struct isl_map *isl_map_floordiv(struct isl_map *map, isl_int d)
3829 map = isl_map_cow(map);
3833 ISL_F_CLR(map, ISL_MAP_DISJOINT);
3834 ISL_F_CLR(map, ISL_MAP_NORMALIZED);
3835 for (i = 0; i < map->n; ++i) {
3836 map->p[i] = isl_basic_map_floordiv(map->p[i], d);
3847 static struct isl_basic_map *var_equal(struct isl_basic_map *bmap, unsigned pos)
3853 i = isl_basic_map_alloc_equality(bmap);
3856 nparam = isl_basic_map_n_param(bmap);
3857 n_in = isl_basic_map_n_in(bmap);
3858 isl_seq_clr(bmap->eq[i], 1 + isl_basic_map_total_dim(bmap));
3859 isl_int_set_si(bmap->eq[i][1+nparam+pos], -1);
3860 isl_int_set_si(bmap->eq[i][1+nparam+n_in+pos], 1);
3861 return isl_basic_map_finalize(bmap);
3863 isl_basic_map_free(bmap);
3867 /* Add a constraints to "bmap" expressing i_pos < o_pos
3869 static struct isl_basic_map *var_less(struct isl_basic_map *bmap, unsigned pos)
3875 i = isl_basic_map_alloc_inequality(bmap);
3878 nparam = isl_basic_map_n_param(bmap);
3879 n_in = isl_basic_map_n_in(bmap);
3880 isl_seq_clr(bmap->ineq[i], 1 + isl_basic_map_total_dim(bmap));
3881 isl_int_set_si(bmap->ineq[i][0], -1);
3882 isl_int_set_si(bmap->ineq[i][1+nparam+pos], -1);
3883 isl_int_set_si(bmap->ineq[i][1+nparam+n_in+pos], 1);
3884 return isl_basic_map_finalize(bmap);
3886 isl_basic_map_free(bmap);
3890 /* Add a constraint to "bmap" expressing i_pos <= o_pos
3892 static __isl_give isl_basic_map *var_less_or_equal(
3893 __isl_take isl_basic_map *bmap, unsigned pos)
3899 i = isl_basic_map_alloc_inequality(bmap);
3902 nparam = isl_basic_map_n_param(bmap);
3903 n_in = isl_basic_map_n_in(bmap);
3904 isl_seq_clr(bmap->ineq[i], 1 + isl_basic_map_total_dim(bmap));
3905 isl_int_set_si(bmap->ineq[i][1+nparam+pos], -1);
3906 isl_int_set_si(bmap->ineq[i][1+nparam+n_in+pos], 1);
3907 return isl_basic_map_finalize(bmap);
3909 isl_basic_map_free(bmap);
3913 /* Add a constraints to "bmap" expressing i_pos > o_pos
3915 static struct isl_basic_map *var_more(struct isl_basic_map *bmap, unsigned pos)
3921 i = isl_basic_map_alloc_inequality(bmap);
3924 nparam = isl_basic_map_n_param(bmap);
3925 n_in = isl_basic_map_n_in(bmap);
3926 isl_seq_clr(bmap->ineq[i], 1 + isl_basic_map_total_dim(bmap));
3927 isl_int_set_si(bmap->ineq[i][0], -1);
3928 isl_int_set_si(bmap->ineq[i][1+nparam+pos], 1);
3929 isl_int_set_si(bmap->ineq[i][1+nparam+n_in+pos], -1);
3930 return isl_basic_map_finalize(bmap);
3932 isl_basic_map_free(bmap);
3936 /* Add a constraint to "bmap" expressing i_pos >= o_pos
3938 static __isl_give isl_basic_map *var_more_or_equal(
3939 __isl_take isl_basic_map *bmap, unsigned pos)
3945 i = isl_basic_map_alloc_inequality(bmap);
3948 nparam = isl_basic_map_n_param(bmap);
3949 n_in = isl_basic_map_n_in(bmap);
3950 isl_seq_clr(bmap->ineq[i], 1 + isl_basic_map_total_dim(bmap));
3951 isl_int_set_si(bmap->ineq[i][1+nparam+pos], 1);
3952 isl_int_set_si(bmap->ineq[i][1+nparam+n_in+pos], -1);
3953 return isl_basic_map_finalize(bmap);
3955 isl_basic_map_free(bmap);
3959 __isl_give isl_basic_map *isl_basic_map_equal(
3960 __isl_take isl_space *dim, unsigned n_equal)
3963 struct isl_basic_map *bmap;
3964 bmap = isl_basic_map_alloc_space(dim, 0, n_equal, 0);
3967 for (i = 0; i < n_equal && bmap; ++i)
3968 bmap = var_equal(bmap, i);
3969 return isl_basic_map_finalize(bmap);
3972 /* Return a relation on of dimension "dim" expressing i_[0..pos] << o_[0..pos]
3974 __isl_give isl_basic_map *isl_basic_map_less_at(__isl_take isl_space *dim,
3978 struct isl_basic_map *bmap;
3979 bmap = isl_basic_map_alloc_space(dim, 0, pos, 1);
3982 for (i = 0; i < pos && bmap; ++i)
3983 bmap = var_equal(bmap, i);
3985 bmap = var_less(bmap, pos);
3986 return isl_basic_map_finalize(bmap);
3989 /* Return a relation on of dimension "dim" expressing i_[0..pos] <<= o_[0..pos]
3991 __isl_give isl_basic_map *isl_basic_map_less_or_equal_at(
3992 __isl_take isl_space *dim, unsigned pos)
3995 isl_basic_map *bmap;
3997 bmap = isl_basic_map_alloc_space(dim, 0, pos, 1);
3998 for (i = 0; i < pos; ++i)
3999 bmap = var_equal(bmap, i);
4000 bmap = var_less_or_equal(bmap, pos);
4001 return isl_basic_map_finalize(bmap);
4004 /* Return a relation on pairs of sets of dimension "dim" expressing i_pos > o_pos
4006 __isl_give isl_basic_map *isl_basic_map_more_at(__isl_take isl_space *dim,
4010 struct isl_basic_map *bmap;
4011 bmap = isl_basic_map_alloc_space(dim, 0, pos, 1);
4014 for (i = 0; i < pos && bmap; ++i)
4015 bmap = var_equal(bmap, i);
4017 bmap = var_more(bmap, pos);
4018 return isl_basic_map_finalize(bmap);
4021 /* Return a relation on of dimension "dim" expressing i_[0..pos] >>= o_[0..pos]
4023 __isl_give isl_basic_map *isl_basic_map_more_or_equal_at(
4024 __isl_take isl_space *dim, unsigned pos)
4027 isl_basic_map *bmap;
4029 bmap = isl_basic_map_alloc_space(dim, 0, pos, 1);
4030 for (i = 0; i < pos; ++i)
4031 bmap = var_equal(bmap, i);
4032 bmap = var_more_or_equal(bmap, pos);
4033 return isl_basic_map_finalize(bmap);
4036 static __isl_give isl_map *map_lex_lte_first(__isl_take isl_space *dims,
4037 unsigned n, int equal)
4039 struct isl_map *map;
4042 if (n == 0 && equal)
4043 return isl_map_universe(dims);
4045 map = isl_map_alloc_space(isl_space_copy(dims), n, ISL_MAP_DISJOINT);
4047 for (i = 0; i + 1 < n; ++i)
4048 map = isl_map_add_basic_map(map,
4049 isl_basic_map_less_at(isl_space_copy(dims), i));
4052 map = isl_map_add_basic_map(map,
4053 isl_basic_map_less_or_equal_at(dims, n - 1));
4055 map = isl_map_add_basic_map(map,
4056 isl_basic_map_less_at(dims, n - 1));
4058 isl_space_free(dims);
4063 static __isl_give isl_map *map_lex_lte(__isl_take isl_space *dims, int equal)
4067 return map_lex_lte_first(dims, dims->n_out, equal);
4070 __isl_give isl_map *isl_map_lex_lt_first(__isl_take isl_space *dim, unsigned n)
4072 return map_lex_lte_first(dim, n, 0);
4075 __isl_give isl_map *isl_map_lex_le_first(__isl_take isl_space *dim, unsigned n)
4077 return map_lex_lte_first(dim, n, 1);
4080 __isl_give isl_map *isl_map_lex_lt(__isl_take isl_space *set_dim)
4082 return map_lex_lte(isl_space_map_from_set(set_dim), 0);
4085 __isl_give isl_map *isl_map_lex_le(__isl_take isl_space *set_dim)
4087 return map_lex_lte(isl_space_map_from_set(set_dim), 1);
4090 static __isl_give isl_map *map_lex_gte_first(__isl_take isl_space *dims,
4091 unsigned n, int equal)
4093 struct isl_map *map;
4096 if (n == 0 && equal)
4097 return isl_map_universe(dims);
4099 map = isl_map_alloc_space(isl_space_copy(dims), n, ISL_MAP_DISJOINT);
4101 for (i = 0; i + 1 < n; ++i)
4102 map = isl_map_add_basic_map(map,
4103 isl_basic_map_more_at(isl_space_copy(dims), i));
4106 map = isl_map_add_basic_map(map,
4107 isl_basic_map_more_or_equal_at(dims, n - 1));
4109 map = isl_map_add_basic_map(map,
4110 isl_basic_map_more_at(dims, n - 1));
4112 isl_space_free(dims);
4117 static __isl_give isl_map *map_lex_gte(__isl_take isl_space *dims, int equal)
4121 return map_lex_gte_first(dims, dims->n_out, equal);
4124 __isl_give isl_map *isl_map_lex_gt_first(__isl_take isl_space *dim, unsigned n)
4126 return map_lex_gte_first(dim, n, 0);
4129 __isl_give isl_map *isl_map_lex_ge_first(__isl_take isl_space *dim, unsigned n)
4131 return map_lex_gte_first(dim, n, 1);
4134 __isl_give isl_map *isl_map_lex_gt(__isl_take isl_space *set_dim)
4136 return map_lex_gte(isl_space_map_from_set(set_dim), 0);
4139 __isl_give isl_map *isl_map_lex_ge(__isl_take isl_space *set_dim)
4141 return map_lex_gte(isl_space_map_from_set(set_dim), 1);
4144 __isl_give isl_map *isl_set_lex_le_set(__isl_take isl_set *set1,
4145 __isl_take isl_set *set2)
4148 map = isl_map_lex_le(isl_set_get_space(set1));
4149 map = isl_map_intersect_domain(map, set1);
4150 map = isl_map_intersect_range(map, set2);
4154 __isl_give isl_map *isl_set_lex_lt_set(__isl_take isl_set *set1,
4155 __isl_take isl_set *set2)
4158 map = isl_map_lex_lt(isl_set_get_space(set1));
4159 map = isl_map_intersect_domain(map, set1);
4160 map = isl_map_intersect_range(map, set2);
4164 __isl_give isl_map *isl_set_lex_ge_set(__isl_take isl_set *set1,
4165 __isl_take isl_set *set2)
4168 map = isl_map_lex_ge(isl_set_get_space(set1));
4169 map = isl_map_intersect_domain(map, set1);
4170 map = isl_map_intersect_range(map, set2);
4174 __isl_give isl_map *isl_set_lex_gt_set(__isl_take isl_set *set1,
4175 __isl_take isl_set *set2)
4178 map = isl_map_lex_gt(isl_set_get_space(set1));
4179 map = isl_map_intersect_domain(map, set1);
4180 map = isl_map_intersect_range(map, set2);
4184 __isl_give isl_map *isl_map_lex_le_map(__isl_take isl_map *map1,
4185 __isl_take isl_map *map2)
4188 map = isl_map_lex_le(isl_space_range(isl_map_get_space(map1)));
4189 map = isl_map_apply_domain(map, isl_map_reverse(map1));
4190 map = isl_map_apply_range(map, isl_map_reverse(map2));
4194 __isl_give isl_map *isl_map_lex_lt_map(__isl_take isl_map *map1,
4195 __isl_take isl_map *map2)
4198 map = isl_map_lex_lt(isl_space_range(isl_map_get_space(map1)));
4199 map = isl_map_apply_domain(map, isl_map_reverse(map1));
4200 map = isl_map_apply_range(map, isl_map_reverse(map2));
4204 __isl_give isl_map *isl_map_lex_ge_map(__isl_take isl_map *map1,
4205 __isl_take isl_map *map2)
4208 map = isl_map_lex_ge(isl_space_range(isl_map_get_space(map1)));
4209 map = isl_map_apply_domain(map, isl_map_reverse(map1));
4210 map = isl_map_apply_range(map, isl_map_reverse(map2));
4214 __isl_give isl_map *isl_map_lex_gt_map(__isl_take isl_map *map1,
4215 __isl_take isl_map *map2)
4218 map = isl_map_lex_gt(isl_space_range(isl_map_get_space(map1)));
4219 map = isl_map_apply_domain(map, isl_map_reverse(map1));
4220 map = isl_map_apply_range(map, isl_map_reverse(map2));
4224 __isl_give isl_basic_map *isl_basic_map_from_basic_set(
4225 __isl_take isl_basic_set *bset, __isl_take isl_space *dim)
4227 struct isl_basic_map *bmap;
4229 bset = isl_basic_set_cow(bset);
4233 isl_assert(bset->ctx, isl_space_compatible(bset->dim, dim), goto error);
4234 isl_space_free(bset->dim);
4235 bmap = (struct isl_basic_map *) bset;
4237 return isl_basic_map_finalize(bmap);
4239 isl_basic_set_free(bset);
4240 isl_space_free(dim);
4244 struct isl_basic_set *isl_basic_set_from_basic_map(struct isl_basic_map *bmap)
4248 if (bmap->dim->n_in == 0)
4249 return (struct isl_basic_set *)bmap;
4250 bmap = isl_basic_map_cow(bmap);
4253 bmap->dim = isl_space_as_set_space(bmap->dim);
4256 bmap = isl_basic_map_finalize(bmap);
4257 return (struct isl_basic_set *)bmap;
4259 isl_basic_map_free(bmap);
4263 /* For a div d = floor(f/m), add the constraints
4266 * -(f-(n-1)) + m d >= 0
4268 * Note that the second constraint is the negation of
4272 int isl_basic_map_add_div_constraints_var(__isl_keep isl_basic_map *bmap,
4273 unsigned pos, isl_int *div)
4276 unsigned total = isl_basic_map_total_dim(bmap);
4278 i = isl_basic_map_alloc_inequality(bmap);
4281 isl_seq_cpy(bmap->ineq[i], div + 1, 1 + total);
4282 isl_int_neg(bmap->ineq[i][1 + pos], div[0]);
4284 j = isl_basic_map_alloc_inequality(bmap);
4287 isl_seq_neg(bmap->ineq[j], bmap->ineq[i], 1 + total);
4288 isl_int_add(bmap->ineq[j][0], bmap->ineq[j][0], bmap->ineq[j][1 + pos]);
4289 isl_int_sub_ui(bmap->ineq[j][0], bmap->ineq[j][0], 1);
4293 int isl_basic_set_add_div_constraints_var(__isl_keep isl_basic_set *bset,
4294 unsigned pos, isl_int *div)
4296 return isl_basic_map_add_div_constraints_var((isl_basic_map *)bset,
4300 int isl_basic_map_add_div_constraints(struct isl_basic_map *bmap, unsigned div)
4302 unsigned total = isl_basic_map_total_dim(bmap);
4303 unsigned div_pos = total - bmap->n_div + div;
4305 return isl_basic_map_add_div_constraints_var(bmap, div_pos,
4309 int isl_basic_set_add_div_constraints(struct isl_basic_set *bset, unsigned div)
4311 return isl_basic_map_add_div_constraints(bset, div);
4314 struct isl_basic_set *isl_basic_map_underlying_set(
4315 struct isl_basic_map *bmap)
4319 if (bmap->dim->nparam == 0 && bmap->dim->n_in == 0 &&
4321 !isl_space_is_named_or_nested(bmap->dim, isl_dim_in) &&
4322 !isl_space_is_named_or_nested(bmap->dim, isl_dim_out))
4323 return (struct isl_basic_set *)bmap;
4324 bmap = isl_basic_map_cow(bmap);
4327 bmap->dim = isl_space_underlying(bmap->dim, bmap->n_div);
4330 bmap->extra -= bmap->n_div;
4332 bmap = isl_basic_map_finalize(bmap);
4333 return (struct isl_basic_set *)bmap;
4335 isl_basic_map_free(bmap);
4339 __isl_give isl_basic_set *isl_basic_set_underlying_set(
4340 __isl_take isl_basic_set *bset)
4342 return isl_basic_map_underlying_set((isl_basic_map *)bset);
4345 struct isl_basic_map *isl_basic_map_overlying_set(
4346 struct isl_basic_set *bset, struct isl_basic_map *like)
4348 struct isl_basic_map *bmap;
4349 struct isl_ctx *ctx;
4356 isl_assert(ctx, bset->n_div == 0, goto error);
4357 isl_assert(ctx, isl_basic_set_n_param(bset) == 0, goto error);
4358 isl_assert(ctx, bset->dim->n_out == isl_basic_map_total_dim(like),
4360 if (isl_space_is_equal(bset->dim, like->dim) && like->n_div == 0) {
4361 isl_basic_map_free(like);
4362 return (struct isl_basic_map *)bset;
4364 bset = isl_basic_set_cow(bset);
4367 total = bset->dim->n_out + bset->extra;
4368 bmap = (struct isl_basic_map *)bset;
4369 isl_space_free(bmap->dim);
4370 bmap->dim = isl_space_copy(like->dim);
4373 bmap->n_div = like->n_div;
4374 bmap->extra += like->n_div;
4378 ltotal = total - bmap->extra + like->extra;
4381 bmap->block2 = isl_blk_extend(ctx, bmap->block2,
4382 bmap->extra * (1 + 1 + total));
4383 if (isl_blk_is_error(bmap->block2))
4385 div = isl_realloc_array(ctx, bmap->div, isl_int *, bmap->extra);
4389 for (i = 0; i < bmap->extra; ++i)
4390 bmap->div[i] = bmap->block2.data + i * (1 + 1 + total);
4391 for (i = 0; i < like->n_div; ++i) {
4392 isl_seq_cpy(bmap->div[i], like->div[i], 1 + 1 + ltotal);
4393 isl_seq_clr(bmap->div[i]+1+1+ltotal, total - ltotal);
4395 bmap = isl_basic_map_extend_constraints(bmap,
4396 0, 2 * like->n_div);
4397 for (i = 0; i < like->n_div; ++i) {
4400 if (isl_int_is_zero(bmap->div[i][0]))
4402 if (isl_basic_map_add_div_constraints(bmap, i) < 0)
4403 bmap = isl_basic_map_free(bmap);
4406 isl_basic_map_free(like);
4407 bmap = isl_basic_map_simplify(bmap);
4408 bmap = isl_basic_map_finalize(bmap);
4411 isl_basic_map_free(like);
4412 isl_basic_set_free(bset);
4416 struct isl_basic_set *isl_basic_set_from_underlying_set(
4417 struct isl_basic_set *bset, struct isl_basic_set *like)
4419 return (struct isl_basic_set *)
4420 isl_basic_map_overlying_set(bset, (struct isl_basic_map *)like);
4423 struct isl_set *isl_set_from_underlying_set(
4424 struct isl_set *set, struct isl_basic_set *like)
4430 isl_assert(set->ctx, set->dim->n_out == isl_basic_set_total_dim(like),
4432 if (isl_space_is_equal(set->dim, like->dim) && like->n_div == 0) {
4433 isl_basic_set_free(like);
4436 set = isl_set_cow(set);
4439 for (i = 0; i < set->n; ++i) {
4440 set->p[i] = isl_basic_set_from_underlying_set(set->p[i],
4441 isl_basic_set_copy(like));
4445 isl_space_free(set->dim);
4446 set->dim = isl_space_copy(like->dim);
4449 isl_basic_set_free(like);
4452 isl_basic_set_free(like);
4457 struct isl_set *isl_map_underlying_set(struct isl_map *map)
4461 map = isl_map_cow(map);
4464 map->dim = isl_space_cow(map->dim);
4468 for (i = 1; i < map->n; ++i)
4469 isl_assert(map->ctx, map->p[0]->n_div == map->p[i]->n_div,
4471 for (i = 0; i < map->n; ++i) {
4472 map->p[i] = (struct isl_basic_map *)
4473 isl_basic_map_underlying_set(map->p[i]);
4478 map->dim = isl_space_underlying(map->dim, 0);
4480 isl_space_free(map->dim);
4481 map->dim = isl_space_copy(map->p[0]->dim);
4485 return (struct isl_set *)map;
4491 struct isl_set *isl_set_to_underlying_set(struct isl_set *set)
4493 return (struct isl_set *)isl_map_underlying_set((struct isl_map *)set);
4496 __isl_give isl_basic_map *isl_basic_map_reset_space(
4497 __isl_take isl_basic_map *bmap, __isl_take isl_space *dim)
4499 bmap = isl_basic_map_cow(bmap);
4503 isl_space_free(bmap->dim);
4506 bmap = isl_basic_map_finalize(bmap);
4510 isl_basic_map_free(bmap);
4511 isl_space_free(dim);
4515 __isl_give isl_basic_set *isl_basic_set_reset_space(
4516 __isl_take isl_basic_set *bset, __isl_take isl_space *dim)
4518 return (isl_basic_set *)isl_basic_map_reset_space((isl_basic_map *)bset,
4522 __isl_give isl_map *isl_map_reset_space(__isl_take isl_map *map,
4523 __isl_take isl_space *dim)
4527 map = isl_map_cow(map);
4531 for (i = 0; i < map->n; ++i) {
4532 map->p[i] = isl_basic_map_reset_space(map->p[i],
4533 isl_space_copy(dim));
4537 isl_space_free(map->dim);
4543 isl_space_free(dim);
4547 __isl_give isl_set *isl_set_reset_space(__isl_take isl_set *set,
4548 __isl_take isl_space *dim)
4550 return (struct isl_set *) isl_map_reset_space((struct isl_map *)set, dim);
4553 /* Compute the parameter domain of the given basic set.
4555 __isl_give isl_basic_set *isl_basic_set_params(__isl_take isl_basic_set *bset)
4560 if (isl_basic_set_is_params(bset))
4563 n = isl_basic_set_dim(bset, isl_dim_set);
4564 bset = isl_basic_set_project_out(bset, isl_dim_set, 0, n);
4565 space = isl_basic_set_get_space(bset);
4566 space = isl_space_params(space);
4567 bset = isl_basic_set_reset_space(bset, space);
4571 /* Construct a zero-dimensional basic set with the given parameter domain.
4573 __isl_give isl_basic_set *isl_basic_set_from_params(
4574 __isl_take isl_basic_set *bset)
4577 space = isl_basic_set_get_space(bset);
4578 space = isl_space_set_from_params(space);
4579 bset = isl_basic_set_reset_space(bset, space);
4583 /* Compute the parameter domain of the given set.
4585 __isl_give isl_set *isl_set_params(__isl_take isl_set *set)
4590 if (isl_set_is_params(set))
4593 n = isl_set_dim(set, isl_dim_set);
4594 set = isl_set_project_out(set, isl_dim_set, 0, n);
4595 space = isl_set_get_space(set);
4596 space = isl_space_params(space);
4597 set = isl_set_reset_space(set, space);
4601 /* Construct a zero-dimensional set with the given parameter domain.
4603 __isl_give isl_set *isl_set_from_params(__isl_take isl_set *set)
4606 space = isl_set_get_space(set);
4607 space = isl_space_set_from_params(space);
4608 set = isl_set_reset_space(set, space);
4612 /* Compute the parameter domain of the given map.
4614 __isl_give isl_set *isl_map_params(__isl_take isl_map *map)
4619 n = isl_map_dim(map, isl_dim_in);
4620 map = isl_map_project_out(map, isl_dim_in, 0, n);
4621 n = isl_map_dim(map, isl_dim_out);
4622 map = isl_map_project_out(map, isl_dim_out, 0, n);
4623 space = isl_map_get_space(map);
4624 space = isl_space_params(space);
4625 map = isl_map_reset_space(map, space);
4629 struct isl_basic_set *isl_basic_map_domain(struct isl_basic_map *bmap)
4632 struct isl_basic_set *domain;
4638 dim = isl_space_domain(isl_basic_map_get_space(bmap));
4640 n_in = isl_basic_map_n_in(bmap);
4641 n_out = isl_basic_map_n_out(bmap);
4642 domain = isl_basic_set_from_basic_map(bmap);
4643 domain = isl_basic_set_project_out(domain, isl_dim_set, n_in, n_out);
4645 domain = isl_basic_set_reset_space(domain, dim);
4650 int isl_basic_map_may_be_set(__isl_keep isl_basic_map *bmap)
4654 return isl_space_may_be_set(bmap->dim);
4657 /* Is this basic map actually a set?
4658 * Users should never call this function. Outside of isl,
4659 * the type should indicate whether something is a set or a map.
4661 int isl_basic_map_is_set(__isl_keep isl_basic_map *bmap)
4665 return isl_space_is_set(bmap->dim);
4668 struct isl_basic_set *isl_basic_map_range(struct isl_basic_map *bmap)
4672 if (isl_basic_map_is_set(bmap))
4674 return isl_basic_map_domain(isl_basic_map_reverse(bmap));
4677 __isl_give isl_basic_map *isl_basic_map_domain_map(
4678 __isl_take isl_basic_map *bmap)
4682 isl_basic_map *domain;
4683 int nparam, n_in, n_out;
4686 nparam = isl_basic_map_dim(bmap, isl_dim_param);
4687 n_in = isl_basic_map_dim(bmap, isl_dim_in);
4688 n_out = isl_basic_map_dim(bmap, isl_dim_out);
4690 dim = isl_space_from_range(isl_space_domain(isl_basic_map_get_space(bmap)));
4691 domain = isl_basic_map_universe(dim);
4693 bmap = isl_basic_map_from_domain(isl_basic_map_wrap(bmap));
4694 bmap = isl_basic_map_apply_range(bmap, domain);
4695 bmap = isl_basic_map_extend_constraints(bmap, n_in, 0);
4697 total = isl_basic_map_total_dim(bmap);
4699 for (i = 0; i < n_in; ++i) {
4700 k = isl_basic_map_alloc_equality(bmap);
4703 isl_seq_clr(bmap->eq[k], 1 + total);
4704 isl_int_set_si(bmap->eq[k][1 + nparam + i], -1);
4705 isl_int_set_si(bmap->eq[k][1 + nparam + n_in + n_out + i], 1);
4708 bmap = isl_basic_map_gauss(bmap, NULL);
4709 return isl_basic_map_finalize(bmap);
4711 isl_basic_map_free(bmap);
4715 __isl_give isl_basic_map *isl_basic_map_range_map(
4716 __isl_take isl_basic_map *bmap)
4720 isl_basic_map *range;
4721 int nparam, n_in, n_out;
4724 nparam = isl_basic_map_dim(bmap, isl_dim_param);
4725 n_in = isl_basic_map_dim(bmap, isl_dim_in);
4726 n_out = isl_basic_map_dim(bmap, isl_dim_out);
4728 dim = isl_space_from_range(isl_space_range(isl_basic_map_get_space(bmap)));
4729 range = isl_basic_map_universe(dim);
4731 bmap = isl_basic_map_from_domain(isl_basic_map_wrap(bmap));
4732 bmap = isl_basic_map_apply_range(bmap, range);
4733 bmap = isl_basic_map_extend_constraints(bmap, n_out, 0);
4735 total = isl_basic_map_total_dim(bmap);
4737 for (i = 0; i < n_out; ++i) {
4738 k = isl_basic_map_alloc_equality(bmap);
4741 isl_seq_clr(bmap->eq[k], 1 + total);
4742 isl_int_set_si(bmap->eq[k][1 + nparam + n_in + i], -1);
4743 isl_int_set_si(bmap->eq[k][1 + nparam + n_in + n_out + i], 1);
4746 bmap = isl_basic_map_gauss(bmap, NULL);
4747 return isl_basic_map_finalize(bmap);
4749 isl_basic_map_free(bmap);
4753 int isl_map_may_be_set(__isl_keep isl_map *map)
4757 return isl_space_may_be_set(map->dim);
4760 /* Is this map actually a set?
4761 * Users should never call this function. Outside of isl,
4762 * the type should indicate whether something is a set or a map.
4764 int isl_map_is_set(__isl_keep isl_map *map)
4768 return isl_space_is_set(map->dim);
4771 struct isl_set *isl_map_range(struct isl_map *map)
4774 struct isl_set *set;
4778 if (isl_map_is_set(map))
4779 return (isl_set *)map;
4781 map = isl_map_cow(map);
4785 set = (struct isl_set *) map;
4786 set->dim = isl_space_range(set->dim);
4789 for (i = 0; i < map->n; ++i) {
4790 set->p[i] = isl_basic_map_range(map->p[i]);
4794 ISL_F_CLR(set, ISL_MAP_DISJOINT);
4795 ISL_F_CLR(set, ISL_SET_NORMALIZED);
4802 __isl_give isl_map *isl_map_domain_map(__isl_take isl_map *map)
4805 isl_space *domain_dim;
4807 map = isl_map_cow(map);
4811 domain_dim = isl_space_from_range(isl_space_domain(isl_map_get_space(map)));
4812 map->dim = isl_space_from_domain(isl_space_wrap(map->dim));
4813 map->dim = isl_space_join(map->dim, domain_dim);
4816 for (i = 0; i < map->n; ++i) {
4817 map->p[i] = isl_basic_map_domain_map(map->p[i]);
4821 ISL_F_CLR(map, ISL_MAP_DISJOINT);
4822 ISL_F_CLR(map, ISL_MAP_NORMALIZED);
4829 __isl_give isl_map *isl_map_range_map(__isl_take isl_map *map)
4832 isl_space *range_dim;
4834 map = isl_map_cow(map);
4838 range_dim = isl_space_range(isl_map_get_space(map));
4839 range_dim = isl_space_from_range(range_dim);
4840 map->dim = isl_space_from_domain(isl_space_wrap(map->dim));
4841 map->dim = isl_space_join(map->dim, range_dim);
4844 for (i = 0; i < map->n; ++i) {
4845 map->p[i] = isl_basic_map_range_map(map->p[i]);
4849 ISL_F_CLR(map, ISL_MAP_DISJOINT);
4850 ISL_F_CLR(map, ISL_MAP_NORMALIZED);
4857 __isl_give isl_map *isl_map_from_set(__isl_take isl_set *set,
4858 __isl_take isl_space *dim)
4861 struct isl_map *map = NULL;
4863 set = isl_set_cow(set);
4866 isl_assert(set->ctx, isl_space_compatible(set->dim, dim), goto error);
4867 map = (struct isl_map *)set;
4868 for (i = 0; i < set->n; ++i) {
4869 map->p[i] = isl_basic_map_from_basic_set(
4870 set->p[i], isl_space_copy(dim));
4874 isl_space_free(map->dim);
4878 isl_space_free(dim);
4883 __isl_give isl_basic_map *isl_basic_map_from_domain(
4884 __isl_take isl_basic_set *bset)
4886 return isl_basic_map_reverse(isl_basic_map_from_range(bset));
4889 __isl_give isl_basic_map *isl_basic_map_from_range(
4890 __isl_take isl_basic_set *bset)
4893 space = isl_basic_set_get_space(bset);
4894 space = isl_space_from_range(space);
4895 bset = isl_basic_set_reset_space(bset, space);
4896 return (isl_basic_map *)bset;
4899 struct isl_map *isl_map_from_range(struct isl_set *set)
4902 space = isl_set_get_space(set);
4903 space = isl_space_from_range(space);
4904 set = isl_set_reset_space(set, space);
4905 return (struct isl_map *)set;
4908 __isl_give isl_map *isl_map_from_domain(__isl_take isl_set *set)
4910 return isl_map_reverse(isl_map_from_range(set));
4913 __isl_give isl_basic_map *isl_basic_map_from_domain_and_range(
4914 __isl_take isl_basic_set *domain, __isl_take isl_basic_set *range)
4916 return isl_basic_map_apply_range(isl_basic_map_reverse(domain), range);
4919 __isl_give isl_map *isl_map_from_domain_and_range(__isl_take isl_set *domain,
4920 __isl_take isl_set *range)
4922 return isl_map_apply_range(isl_map_reverse(domain), range);
4925 struct isl_set *isl_set_from_map(struct isl_map *map)
4928 struct isl_set *set = NULL;
4932 map = isl_map_cow(map);
4935 map->dim = isl_space_as_set_space(map->dim);
4938 set = (struct isl_set *)map;
4939 for (i = 0; i < map->n; ++i) {
4940 set->p[i] = isl_basic_set_from_basic_map(map->p[i]);
4950 __isl_give isl_map *isl_map_alloc_space(__isl_take isl_space *dim, int n,
4953 struct isl_map *map;
4958 isl_die(dim->ctx, isl_error_internal,
4959 "negative number of basic maps", goto error);
4960 map = isl_alloc(dim->ctx, struct isl_map,
4961 sizeof(struct isl_map) +
4962 (n - 1) * sizeof(struct isl_basic_map *));
4966 map->ctx = dim->ctx;
4967 isl_ctx_ref(map->ctx);
4975 isl_space_free(dim);
4979 struct isl_map *isl_map_alloc(struct isl_ctx *ctx,
4980 unsigned nparam, unsigned in, unsigned out, int n,
4983 struct isl_map *map;
4986 dims = isl_space_alloc(ctx, nparam, in, out);
4990 map = isl_map_alloc_space(dims, n, flags);
4994 __isl_give isl_basic_map *isl_basic_map_empty(__isl_take isl_space *dim)
4996 struct isl_basic_map *bmap;
4997 bmap = isl_basic_map_alloc_space(dim, 0, 1, 0);
4998 bmap = isl_basic_map_set_to_empty(bmap);
5002 __isl_give isl_basic_set *isl_basic_set_empty(__isl_take isl_space *dim)
5004 struct isl_basic_set *bset;
5005 bset = isl_basic_set_alloc_space(dim, 0, 1, 0);
5006 bset = isl_basic_set_set_to_empty(bset);
5010 struct isl_basic_map *isl_basic_map_empty_like(struct isl_basic_map *model)
5012 struct isl_basic_map *bmap;
5015 bmap = isl_basic_map_alloc_space(isl_space_copy(model->dim), 0, 1, 0);
5016 bmap = isl_basic_map_set_to_empty(bmap);
5020 struct isl_basic_map *isl_basic_map_empty_like_map(struct isl_map *model)
5022 struct isl_basic_map *bmap;
5025 bmap = isl_basic_map_alloc_space(isl_space_copy(model->dim), 0, 1, 0);
5026 bmap = isl_basic_map_set_to_empty(bmap);
5030 struct isl_basic_set *isl_basic_set_empty_like(struct isl_basic_set *model)
5032 struct isl_basic_set *bset;
5035 bset = isl_basic_set_alloc_space(isl_space_copy(model->dim), 0, 1, 0);
5036 bset = isl_basic_set_set_to_empty(bset);
5040 __isl_give isl_basic_map *isl_basic_map_universe(__isl_take isl_space *dim)
5042 struct isl_basic_map *bmap;
5043 bmap = isl_basic_map_alloc_space(dim, 0, 0, 0);
5044 bmap = isl_basic_map_finalize(bmap);
5048 __isl_give isl_basic_set *isl_basic_set_universe(__isl_take isl_space *dim)
5050 struct isl_basic_set *bset;
5051 bset = isl_basic_set_alloc_space(dim, 0, 0, 0);
5052 bset = isl_basic_set_finalize(bset);
5056 __isl_give isl_basic_map *isl_basic_map_nat_universe(__isl_take isl_space *dim)
5059 unsigned total = isl_space_dim(dim, isl_dim_all);
5060 isl_basic_map *bmap;
5062 bmap= isl_basic_map_alloc_space(dim, 0, 0, total);
5063 for (i = 0; i < total; ++i) {
5064 int k = isl_basic_map_alloc_inequality(bmap);
5067 isl_seq_clr(bmap->ineq[k], 1 + total);
5068 isl_int_set_si(bmap->ineq[k][1 + i], 1);
5072 isl_basic_map_free(bmap);
5076 __isl_give isl_basic_set *isl_basic_set_nat_universe(__isl_take isl_space *dim)
5078 return isl_basic_map_nat_universe(dim);
5081 __isl_give isl_map *isl_map_nat_universe(__isl_take isl_space *dim)
5083 return isl_map_from_basic_map(isl_basic_map_nat_universe(dim));
5086 __isl_give isl_set *isl_set_nat_universe(__isl_take isl_space *dim)
5088 return isl_map_nat_universe(dim);
5091 __isl_give isl_basic_map *isl_basic_map_universe_like(
5092 __isl_keep isl_basic_map *model)
5096 return isl_basic_map_alloc_space(isl_space_copy(model->dim), 0, 0, 0);
5099 struct isl_basic_set *isl_basic_set_universe_like(struct isl_basic_set *model)
5103 return isl_basic_set_alloc_space(isl_space_copy(model->dim), 0, 0, 0);
5106 __isl_give isl_basic_set *isl_basic_set_universe_like_set(
5107 __isl_keep isl_set *model)
5111 return isl_basic_set_alloc_space(isl_space_copy(model->dim), 0, 0, 0);
5114 __isl_give isl_map *isl_map_empty(__isl_take isl_space *dim)
5116 return isl_map_alloc_space(dim, 0, ISL_MAP_DISJOINT);
5119 struct isl_map *isl_map_empty_like(struct isl_map *model)
5123 return isl_map_alloc_space(isl_space_copy(model->dim), 0, ISL_MAP_DISJOINT);
5126 struct isl_map *isl_map_empty_like_basic_map(struct isl_basic_map *model)
5130 return isl_map_alloc_space(isl_space_copy(model->dim), 0, ISL_MAP_DISJOINT);
5133 __isl_give isl_set *isl_set_empty(__isl_take isl_space *dim)
5135 return isl_set_alloc_space(dim, 0, ISL_MAP_DISJOINT);
5138 struct isl_set *isl_set_empty_like(struct isl_set *model)
5142 return isl_set_empty(isl_space_copy(model->dim));
5145 __isl_give isl_map *isl_map_universe(__isl_take isl_space *dim)
5147 struct isl_map *map;
5150 map = isl_map_alloc_space(isl_space_copy(dim), 1, ISL_MAP_DISJOINT);
5151 map = isl_map_add_basic_map(map, isl_basic_map_universe(dim));
5155 __isl_give isl_set *isl_set_universe(__isl_take isl_space *dim)
5157 struct isl_set *set;
5160 set = isl_set_alloc_space(isl_space_copy(dim), 1, ISL_MAP_DISJOINT);
5161 set = isl_set_add_basic_set(set, isl_basic_set_universe(dim));
5165 __isl_give isl_set *isl_set_universe_like(__isl_keep isl_set *model)
5169 return isl_set_universe(isl_space_copy(model->dim));
5172 struct isl_map *isl_map_dup(struct isl_map *map)
5175 struct isl_map *dup;
5179 dup = isl_map_alloc_space(isl_space_copy(map->dim), map->n, map->flags);
5180 for (i = 0; i < map->n; ++i)
5181 dup = isl_map_add_basic_map(dup, isl_basic_map_copy(map->p[i]));
5185 __isl_give isl_map *isl_map_add_basic_map(__isl_take isl_map *map,
5186 __isl_take isl_basic_map *bmap)
5190 if (isl_basic_map_plain_is_empty(bmap)) {
5191 isl_basic_map_free(bmap);
5194 isl_assert(map->ctx, isl_space_is_equal(map->dim, bmap->dim), goto error);
5195 isl_assert(map->ctx, map->n < map->size, goto error);
5196 map->p[map->n] = bmap;
5198 ISL_F_CLR(map, ISL_MAP_NORMALIZED);
5204 isl_basic_map_free(bmap);
5208 void *isl_map_free(struct isl_map *map)
5218 isl_ctx_deref(map->ctx);
5219 for (i = 0; i < map->n; ++i)
5220 isl_basic_map_free(map->p[i]);
5221 isl_space_free(map->dim);
5227 struct isl_map *isl_map_extend(struct isl_map *base,
5228 unsigned nparam, unsigned n_in, unsigned n_out)
5232 base = isl_map_cow(base);
5236 base->dim = isl_space_extend(base->dim, nparam, n_in, n_out);
5239 for (i = 0; i < base->n; ++i) {
5240 base->p[i] = isl_basic_map_extend_space(base->p[i],
5241 isl_space_copy(base->dim), 0, 0, 0);
5251 struct isl_set *isl_set_extend(struct isl_set *base,
5252 unsigned nparam, unsigned dim)
5254 return (struct isl_set *)isl_map_extend((struct isl_map *)base,
5258 static struct isl_basic_map *isl_basic_map_fix_pos_si(
5259 struct isl_basic_map *bmap, unsigned pos, int value)
5263 bmap = isl_basic_map_cow(bmap);
5264 bmap = isl_basic_map_extend_constraints(bmap, 1, 0);
5265 j = isl_basic_map_alloc_equality(bmap);
5268 isl_seq_clr(bmap->eq[j] + 1, isl_basic_map_total_dim(bmap));
5269 isl_int_set_si(bmap->eq[j][pos], -1);
5270 isl_int_set_si(bmap->eq[j][0], value);
5271 bmap = isl_basic_map_simplify(bmap);
5272 return isl_basic_map_finalize(bmap);
5274 isl_basic_map_free(bmap);
5278 static __isl_give isl_basic_map *isl_basic_map_fix_pos(
5279 __isl_take isl_basic_map *bmap, unsigned pos, isl_int value)
5283 bmap = isl_basic_map_cow(bmap);
5284 bmap = isl_basic_map_extend_constraints(bmap, 1, 0);
5285 j = isl_basic_map_alloc_equality(bmap);
5288 isl_seq_clr(bmap->eq[j] + 1, isl_basic_map_total_dim(bmap));
5289 isl_int_set_si(bmap->eq[j][pos], -1);
5290 isl_int_set(bmap->eq[j][0], value);
5291 bmap = isl_basic_map_simplify(bmap);
5292 return isl_basic_map_finalize(bmap);
5294 isl_basic_map_free(bmap);
5298 struct isl_basic_map *isl_basic_map_fix_si(struct isl_basic_map *bmap,
5299 enum isl_dim_type type, unsigned pos, int value)
5303 isl_assert(bmap->ctx, pos < isl_basic_map_dim(bmap, type), goto error);
5304 return isl_basic_map_fix_pos_si(bmap,
5305 isl_basic_map_offset(bmap, type) + pos, value);
5307 isl_basic_map_free(bmap);
5311 __isl_give isl_basic_map *isl_basic_map_fix(__isl_take isl_basic_map *bmap,
5312 enum isl_dim_type type, unsigned pos, isl_int value)
5316 isl_assert(bmap->ctx, pos < isl_basic_map_dim(bmap, type), goto error);
5317 return isl_basic_map_fix_pos(bmap,
5318 isl_basic_map_offset(bmap, type) + pos, value);
5320 isl_basic_map_free(bmap);
5324 struct isl_basic_set *isl_basic_set_fix_si(struct isl_basic_set *bset,
5325 enum isl_dim_type type, unsigned pos, int value)
5327 return (struct isl_basic_set *)
5328 isl_basic_map_fix_si((struct isl_basic_map *)bset,
5332 __isl_give isl_basic_set *isl_basic_set_fix(__isl_take isl_basic_set *bset,
5333 enum isl_dim_type type, unsigned pos, isl_int value)
5335 return (struct isl_basic_set *)
5336 isl_basic_map_fix((struct isl_basic_map *)bset,
5340 struct isl_basic_map *isl_basic_map_fix_input_si(struct isl_basic_map *bmap,
5341 unsigned input, int value)
5343 return isl_basic_map_fix_si(bmap, isl_dim_in, input, value);
5346 struct isl_basic_set *isl_basic_set_fix_dim_si(struct isl_basic_set *bset,
5347 unsigned dim, int value)
5349 return (struct isl_basic_set *)
5350 isl_basic_map_fix_si((struct isl_basic_map *)bset,
5351 isl_dim_set, dim, value);
5354 static int remove_if_empty(__isl_keep isl_map *map, int i)
5356 int empty = isl_basic_map_plain_is_empty(map->p[i]);
5363 isl_basic_map_free(map->p[i]);
5364 if (i != map->n - 1) {
5365 ISL_F_CLR(map, ISL_MAP_NORMALIZED);
5366 map->p[i] = map->p[map->n - 1];
5373 /* Perform "fn" on each basic map of "map", where we may not be holding
5374 * the only reference to "map".
5375 * In particular, "fn" should be a semantics preserving operation
5376 * that we want to apply to all copies of "map". We therefore need
5377 * to be careful not to modify "map" in a way that breaks "map"
5378 * in case anything goes wrong.
5380 __isl_give isl_map *isl_map_inline_foreach_basic_map(__isl_take isl_map *map,
5381 __isl_give isl_basic_map *(*fn)(__isl_take isl_basic_map *bmap))
5383 struct isl_basic_map *bmap;
5389 for (i = map->n - 1; i >= 0; --i) {
5390 bmap = isl_basic_map_copy(map->p[i]);
5394 isl_basic_map_free(map->p[i]);
5396 if (remove_if_empty(map, i) < 0)
5406 struct isl_map *isl_map_fix_si(struct isl_map *map,
5407 enum isl_dim_type type, unsigned pos, int value)
5411 map = isl_map_cow(map);
5415 isl_assert(map->ctx, pos < isl_map_dim(map, type), goto error);
5416 for (i = map->n - 1; i >= 0; --i) {
5417 map->p[i] = isl_basic_map_fix_si(map->p[i], type, pos, value);
5418 if (remove_if_empty(map, i) < 0)
5421 ISL_F_CLR(map, ISL_MAP_NORMALIZED);
5428 __isl_give isl_set *isl_set_fix_si(__isl_take isl_set *set,
5429 enum isl_dim_type type, unsigned pos, int value)
5431 return (struct isl_set *)
5432 isl_map_fix_si((struct isl_map *)set, type, pos, value);
5435 __isl_give isl_map *isl_map_fix(__isl_take isl_map *map,
5436 enum isl_dim_type type, unsigned pos, isl_int value)
5440 map = isl_map_cow(map);
5444 isl_assert(map->ctx, pos < isl_map_dim(map, type), goto error);
5445 for (i = 0; i < map->n; ++i) {
5446 map->p[i] = isl_basic_map_fix(map->p[i], type, pos, value);
5450 ISL_F_CLR(map, ISL_MAP_NORMALIZED);
5457 __isl_give isl_set *isl_set_fix(__isl_take isl_set *set,
5458 enum isl_dim_type type, unsigned pos, isl_int value)
5460 return (struct isl_set *)isl_map_fix((isl_map *)set, type, pos, value);
5463 struct isl_map *isl_map_fix_input_si(struct isl_map *map,
5464 unsigned input, int value)
5466 return isl_map_fix_si(map, isl_dim_in, input, value);
5469 struct isl_set *isl_set_fix_dim_si(struct isl_set *set, unsigned dim, int value)
5471 return (struct isl_set *)
5472 isl_map_fix_si((struct isl_map *)set, isl_dim_set, dim, value);
5475 static __isl_give isl_basic_map *basic_map_bound_si(
5476 __isl_take isl_basic_map *bmap,
5477 enum isl_dim_type type, unsigned pos, int value, int upper)
5483 isl_assert(bmap->ctx, pos < isl_basic_map_dim(bmap, type), goto error);
5484 pos += isl_basic_map_offset(bmap, type);
5485 bmap = isl_basic_map_cow(bmap);
5486 bmap = isl_basic_map_extend_constraints(bmap, 0, 1);
5487 j = isl_basic_map_alloc_inequality(bmap);
5490 isl_seq_clr(bmap->ineq[j], 1 + isl_basic_map_total_dim(bmap));
5492 isl_int_set_si(bmap->ineq[j][pos], -1);
5493 isl_int_set_si(bmap->ineq[j][0], value);
5495 isl_int_set_si(bmap->ineq[j][pos], 1);
5496 isl_int_set_si(bmap->ineq[j][0], -value);
5498 bmap = isl_basic_map_simplify(bmap);
5499 return isl_basic_map_finalize(bmap);
5501 isl_basic_map_free(bmap);
5505 __isl_give isl_basic_map *isl_basic_map_lower_bound_si(
5506 __isl_take isl_basic_map *bmap,
5507 enum isl_dim_type type, unsigned pos, int value)
5509 return basic_map_bound_si(bmap, type, pos, value, 0);
5512 /* Constrain the values of the given dimension to be no greater than "value".
5514 __isl_give isl_basic_map *isl_basic_map_upper_bound_si(
5515 __isl_take isl_basic_map *bmap,
5516 enum isl_dim_type type, unsigned pos, int value)
5518 return basic_map_bound_si(bmap, type, pos, value, 1);
5521 struct isl_basic_set *isl_basic_set_lower_bound_dim(struct isl_basic_set *bset,
5522 unsigned dim, isl_int value)
5526 bset = isl_basic_set_cow(bset);
5527 bset = isl_basic_set_extend_constraints(bset, 0, 1);
5528 j = isl_basic_set_alloc_inequality(bset);
5531 isl_seq_clr(bset->ineq[j], 1 + isl_basic_set_total_dim(bset));
5532 isl_int_set_si(bset->ineq[j][1 + isl_basic_set_n_param(bset) + dim], 1);
5533 isl_int_neg(bset->ineq[j][0], value);
5534 bset = isl_basic_set_simplify(bset);
5535 return isl_basic_set_finalize(bset);
5537 isl_basic_set_free(bset);
5541 static __isl_give isl_map *map_bound_si(__isl_take isl_map *map,
5542 enum isl_dim_type type, unsigned pos, int value, int upper)
5546 map = isl_map_cow(map);
5550 isl_assert(map->ctx, pos < isl_map_dim(map, type), goto error);
5551 for (i = 0; i < map->n; ++i) {
5552 map->p[i] = basic_map_bound_si(map->p[i],
5553 type, pos, value, upper);
5557 ISL_F_CLR(map, ISL_MAP_NORMALIZED);
5564 __isl_give isl_map *isl_map_lower_bound_si(__isl_take isl_map *map,
5565 enum isl_dim_type type, unsigned pos, int value)
5567 return map_bound_si(map, type, pos, value, 0);
5570 __isl_give isl_map *isl_map_upper_bound_si(__isl_take isl_map *map,
5571 enum isl_dim_type type, unsigned pos, int value)
5573 return map_bound_si(map, type, pos, value, 1);
5576 __isl_give isl_set *isl_set_lower_bound_si(__isl_take isl_set *set,
5577 enum isl_dim_type type, unsigned pos, int value)
5579 return (struct isl_set *)
5580 isl_map_lower_bound_si((struct isl_map *)set, type, pos, value);
5583 __isl_give isl_set *isl_set_upper_bound_si(__isl_take isl_set *set,
5584 enum isl_dim_type type, unsigned pos, int value)
5586 return isl_map_upper_bound_si(set, type, pos, value);
5589 /* Bound the given variable of "bmap" from below (or above is "upper"
5590 * is set) to "value".
5592 static __isl_give isl_basic_map *basic_map_bound(
5593 __isl_take isl_basic_map *bmap,
5594 enum isl_dim_type type, unsigned pos, isl_int value, int upper)
5600 if (pos >= isl_basic_map_dim(bmap, type))
5601 isl_die(bmap->ctx, isl_error_invalid,
5602 "index out of bounds", goto error);
5603 pos += isl_basic_map_offset(bmap, type);
5604 bmap = isl_basic_map_cow(bmap);
5605 bmap = isl_basic_map_extend_constraints(bmap, 0, 1);
5606 j = isl_basic_map_alloc_inequality(bmap);
5609 isl_seq_clr(bmap->ineq[j], 1 + isl_basic_map_total_dim(bmap));
5611 isl_int_set_si(bmap->ineq[j][pos], -1);
5612 isl_int_set(bmap->ineq[j][0], value);
5614 isl_int_set_si(bmap->ineq[j][pos], 1);
5615 isl_int_neg(bmap->ineq[j][0], value);
5617 bmap = isl_basic_map_simplify(bmap);
5618 return isl_basic_map_finalize(bmap);
5620 isl_basic_map_free(bmap);
5624 /* Bound the given variable of "map" from below (or above is "upper"
5625 * is set) to "value".
5627 static __isl_give isl_map *map_bound(__isl_take isl_map *map,
5628 enum isl_dim_type type, unsigned pos, isl_int value, int upper)
5632 map = isl_map_cow(map);
5636 if (pos >= isl_map_dim(map, type))
5637 isl_die(map->ctx, isl_error_invalid,
5638 "index out of bounds", goto error);
5639 for (i = map->n - 1; i >= 0; --i) {
5640 map->p[i] = basic_map_bound(map->p[i], type, pos, value, upper);
5641 if (remove_if_empty(map, i) < 0)
5644 ISL_F_CLR(map, ISL_MAP_NORMALIZED);
5651 __isl_give isl_map *isl_map_lower_bound(__isl_take isl_map *map,
5652 enum isl_dim_type type, unsigned pos, isl_int value)
5654 return map_bound(map, type, pos, value, 0);
5657 __isl_give isl_map *isl_map_upper_bound(__isl_take isl_map *map,
5658 enum isl_dim_type type, unsigned pos, isl_int value)
5660 return map_bound(map, type, pos, value, 1);
5663 __isl_give isl_set *isl_set_lower_bound(__isl_take isl_set *set,
5664 enum isl_dim_type type, unsigned pos, isl_int value)
5666 return isl_map_lower_bound(set, type, pos, value);
5669 __isl_give isl_set *isl_set_upper_bound(__isl_take isl_set *set,
5670 enum isl_dim_type type, unsigned pos, isl_int value)
5672 return isl_map_upper_bound(set, type, pos, value);
5675 struct isl_set *isl_set_lower_bound_dim(struct isl_set *set, unsigned dim,
5680 set = isl_set_cow(set);
5684 isl_assert(set->ctx, dim < isl_set_n_dim(set), goto error);
5685 for (i = 0; i < set->n; ++i) {
5686 set->p[i] = isl_basic_set_lower_bound_dim(set->p[i], dim, value);
5696 struct isl_map *isl_map_reverse(struct isl_map *map)
5700 map = isl_map_cow(map);
5704 map->dim = isl_space_reverse(map->dim);
5707 for (i = 0; i < map->n; ++i) {
5708 map->p[i] = isl_basic_map_reverse(map->p[i]);
5712 ISL_F_CLR(map, ISL_MAP_NORMALIZED);
5719 static struct isl_map *isl_basic_map_partial_lexopt(
5720 struct isl_basic_map *bmap, struct isl_basic_set *dom,
5721 struct isl_set **empty, int max)
5725 if (bmap->ctx->opt->pip == ISL_PIP_PIP)
5726 return isl_pip_basic_map_lexopt(bmap, dom, empty, max);
5728 return isl_tab_basic_map_partial_lexopt(bmap, dom, empty, max);
5730 isl_basic_map_free(bmap);
5731 isl_basic_set_free(dom);
5737 struct isl_map *isl_basic_map_partial_lexmax(
5738 struct isl_basic_map *bmap, struct isl_basic_set *dom,
5739 struct isl_set **empty)
5741 return isl_basic_map_partial_lexopt(bmap, dom, empty, 1);
5744 struct isl_map *isl_basic_map_partial_lexmin(
5745 struct isl_basic_map *bmap, struct isl_basic_set *dom,
5746 struct isl_set **empty)
5748 return isl_basic_map_partial_lexopt(bmap, dom, empty, 0);
5751 struct isl_set *isl_basic_set_partial_lexmin(
5752 struct isl_basic_set *bset, struct isl_basic_set *dom,
5753 struct isl_set **empty)
5755 return (struct isl_set *)
5756 isl_basic_map_partial_lexmin((struct isl_basic_map *)bset,
5760 struct isl_set *isl_basic_set_partial_lexmax(
5761 struct isl_basic_set *bset, struct isl_basic_set *dom,
5762 struct isl_set **empty)
5764 return (struct isl_set *)
5765 isl_basic_map_partial_lexmax((struct isl_basic_map *)bset,
5769 __isl_give isl_pw_multi_aff *isl_basic_map_partial_lexmin_pw_multi_aff(
5770 __isl_take isl_basic_map *bmap, __isl_take isl_basic_set *dom,
5771 __isl_give isl_set **empty)
5773 return isl_basic_map_partial_lexopt_pw_multi_aff(bmap, dom, empty, 0);
5776 __isl_give isl_pw_multi_aff *isl_basic_map_partial_lexmax_pw_multi_aff(
5777 __isl_take isl_basic_map *bmap, __isl_take isl_basic_set *dom,
5778 __isl_give isl_set **empty)
5780 return isl_basic_map_partial_lexopt_pw_multi_aff(bmap, dom, empty, 1);
5783 __isl_give isl_pw_multi_aff *isl_basic_set_partial_lexmin_pw_multi_aff(
5784 __isl_take isl_basic_set *bset, __isl_take isl_basic_set *dom,
5785 __isl_give isl_set **empty)
5787 return isl_basic_map_partial_lexmin_pw_multi_aff(bset, dom, empty);
5790 __isl_give isl_pw_multi_aff *isl_basic_set_partial_lexmax_pw_multi_aff(
5791 __isl_take isl_basic_set *bset, __isl_take isl_basic_set *dom,
5792 __isl_give isl_set **empty)
5794 return isl_basic_map_partial_lexmax_pw_multi_aff(bset, dom, empty);
5797 __isl_give isl_pw_multi_aff *isl_basic_map_lexopt_pw_multi_aff(
5798 __isl_take isl_basic_map *bmap, int max)
5800 isl_basic_set *dom = NULL;
5801 isl_space *dom_space;
5805 dom_space = isl_space_domain(isl_space_copy(bmap->dim));
5806 dom = isl_basic_set_universe(dom_space);
5807 return isl_basic_map_partial_lexopt_pw_multi_aff(bmap, dom, NULL, max);
5809 isl_basic_map_free(bmap);
5813 __isl_give isl_pw_multi_aff *isl_basic_map_lexmin_pw_multi_aff(
5814 __isl_take isl_basic_map *bmap)
5816 return isl_basic_map_lexopt_pw_multi_aff(bmap, 0);
5820 #define TYPE isl_pw_multi_aff
5822 #define SUFFIX _pw_multi_aff
5824 #define EMPTY isl_pw_multi_aff_empty
5826 #define ADD isl_pw_multi_aff_union_add
5827 #include "isl_map_lexopt_templ.c"
5829 /* Given a map "map", compute the lexicographically minimal
5830 * (or maximal) image element for each domain element in dom,
5831 * in the form of an isl_pw_multi_aff.
5832 * Set *empty to those elements in dom that do not have an image element.
5834 * We first compute the lexicographically minimal or maximal element
5835 * in the first basic map. This results in a partial solution "res"
5836 * and a subset "todo" of dom that still need to be handled.
5837 * We then consider each of the remaining maps in "map" and successively
5838 * update both "res" and "todo".
5840 static __isl_give isl_pw_multi_aff *isl_map_partial_lexopt_aligned_pw_multi_aff(
5841 __isl_take isl_map *map, __isl_take isl_set *dom,
5842 __isl_give isl_set **empty, int max)
5845 isl_pw_multi_aff *res;
5851 if (isl_map_plain_is_empty(map)) {
5856 return isl_pw_multi_aff_from_map(map);
5859 res = basic_map_partial_lexopt_pw_multi_aff(
5860 isl_basic_map_copy(map->p[0]),
5861 isl_set_copy(dom), &todo, max);
5863 for (i = 1; i < map->n; ++i) {
5864 isl_pw_multi_aff *res_i;
5867 res_i = basic_map_partial_lexopt_pw_multi_aff(
5868 isl_basic_map_copy(map->p[i]),
5869 isl_set_copy(dom), &todo_i, max);
5872 res = isl_pw_multi_aff_union_lexmax(res, res_i);
5874 res = isl_pw_multi_aff_union_lexmin(res, res_i);
5876 todo = isl_set_intersect(todo, todo_i);
5897 #define TYPE isl_map
5901 #define EMPTY isl_map_empty
5903 #define ADD isl_map_union_disjoint
5904 #include "isl_map_lexopt_templ.c"
5906 /* Given a map "map", compute the lexicographically minimal
5907 * (or maximal) image element for each domain element in dom.
5908 * Set *empty to those elements in dom that do not have an image element.
5910 * We first compute the lexicographically minimal or maximal element
5911 * in the first basic map. This results in a partial solution "res"
5912 * and a subset "todo" of dom that still need to be handled.
5913 * We then consider each of the remaining maps in "map" and successively
5914 * update both "res" and "todo".
5916 * Let res^k and todo^k be the results after k steps and let i = k + 1.
5917 * Assume we are computing the lexicographical maximum.
5918 * We first compute the lexicographically maximal element in basic map i.
5919 * This results in a partial solution res_i and a subset todo_i.
5920 * Then we combine these results with those obtain for the first k basic maps
5921 * to obtain a result that is valid for the first k+1 basic maps.
5922 * In particular, the set where there is no solution is the set where
5923 * there is no solution for the first k basic maps and also no solution
5924 * for the ith basic map, i.e.,
5926 * todo^i = todo^k * todo_i
5928 * On dom(res^k) * dom(res_i), we need to pick the larger of the two
5929 * solutions, arbitrarily breaking ties in favor of res^k.
5930 * That is, when res^k(a) >= res_i(a), we pick res^k and
5931 * when res^k(a) < res_i(a), we pick res_i. (Here, ">=" and "<" denote
5932 * the lexicographic order.)
5933 * In practice, we compute
5935 * res^k * (res_i . "<=")
5939 * res_i * (res^k . "<")
5941 * Finally, we consider the symmetric difference of dom(res^k) and dom(res_i),
5942 * where only one of res^k and res_i provides a solution and we simply pick
5949 * Note that we only compute these intersections when dom(res^k) intersects
5950 * dom(res_i). Otherwise, the only effect of these intersections is to
5951 * potentially break up res^k and res_i into smaller pieces.
5952 * We want to avoid such splintering as much as possible.
5953 * In fact, an earlier implementation of this function would look for
5954 * better results in the domain of res^k and for extra results in todo^k,
5955 * but this would always result in a splintering according to todo^k,
5956 * even when the domain of basic map i is disjoint from the domains of
5957 * the previous basic maps.
5959 static __isl_give isl_map *isl_map_partial_lexopt_aligned(
5960 __isl_take isl_map *map, __isl_take isl_set *dom,
5961 __isl_give isl_set **empty, int max)
5964 struct isl_map *res;
5965 struct isl_set *todo;
5970 if (isl_map_plain_is_empty(map)) {
5978 res = basic_map_partial_lexopt(isl_basic_map_copy(map->p[0]),
5979 isl_set_copy(dom), &todo, max);
5981 for (i = 1; i < map->n; ++i) {
5985 isl_space *dim = isl_space_range(isl_map_get_space(res));
5987 res_i = basic_map_partial_lexopt(isl_basic_map_copy(map->p[i]),
5988 isl_set_copy(dom), &todo_i, max);
5991 lt = isl_map_lex_lt(isl_space_copy(dim));
5992 le = isl_map_lex_le(dim);
5994 lt = isl_map_lex_gt(isl_space_copy(dim));
5995 le = isl_map_lex_ge(dim);
5997 lt = isl_map_apply_range(isl_map_copy(res), lt);
5998 lt = isl_map_intersect(lt, isl_map_copy(res_i));
5999 le = isl_map_apply_range(isl_map_copy(res_i), le);
6000 le = isl_map_intersect(le, isl_map_copy(res));
6002 if (!isl_map_is_empty(lt) || !isl_map_is_empty(le)) {
6003 res = isl_map_intersect_domain(res,
6004 isl_set_copy(todo_i));
6005 res_i = isl_map_intersect_domain(res_i,
6006 isl_set_copy(todo));
6009 res = isl_map_union_disjoint(res, res_i);
6010 res = isl_map_union_disjoint(res, lt);
6011 res = isl_map_union_disjoint(res, le);
6013 todo = isl_set_intersect(todo, todo_i);
6033 __isl_give isl_map *isl_map_partial_lexmax(
6034 __isl_take isl_map *map, __isl_take isl_set *dom,
6035 __isl_give isl_set **empty)
6037 return isl_map_partial_lexopt(map, dom, empty, 1);
6040 __isl_give isl_map *isl_map_partial_lexmin(
6041 __isl_take isl_map *map, __isl_take isl_set *dom,
6042 __isl_give isl_set **empty)
6044 return isl_map_partial_lexopt(map, dom, empty, 0);
6047 __isl_give isl_set *isl_set_partial_lexmin(
6048 __isl_take isl_set *set, __isl_take isl_set *dom,
6049 __isl_give isl_set **empty)
6051 return (struct isl_set *)
6052 isl_map_partial_lexmin((struct isl_map *)set,
6056 __isl_give isl_set *isl_set_partial_lexmax(
6057 __isl_take isl_set *set, __isl_take isl_set *dom,
6058 __isl_give isl_set **empty)
6060 return (struct isl_set *)
6061 isl_map_partial_lexmax((struct isl_map *)set,
6065 /* Compute the lexicographic minimum (or maximum if "max" is set)
6066 * of "bmap" over its domain.
6068 * Since we are not interested in the part of the domain space where
6069 * there is no solution, we initialize the domain to those constraints
6070 * of "bmap" that only involve the parameters and the input dimensions.
6071 * This relieves the parametric programming engine from detecting those
6072 * inequalities and transferring them to the context. More importantly,
6073 * it ensures that those inequalities are transferred first and not
6074 * intermixed with inequalities that actually split the domain.
6076 __isl_give isl_map *isl_basic_map_lexopt(__isl_take isl_basic_map *bmap, int max)
6080 isl_basic_map *copy;
6083 n_div = isl_basic_map_dim(bmap, isl_dim_div);
6084 n_out = isl_basic_map_dim(bmap, isl_dim_out);
6085 copy = isl_basic_map_copy(bmap);
6086 copy = isl_basic_map_drop_constraints_involving_dims(copy,
6087 isl_dim_div, 0, n_div);
6088 copy = isl_basic_map_drop_constraints_involving_dims(copy,
6089 isl_dim_out, 0, n_out);
6090 dom = isl_basic_map_domain(copy);
6091 return isl_basic_map_partial_lexopt(bmap, dom, NULL, max);
6094 __isl_give isl_map *isl_basic_map_lexmin(__isl_take isl_basic_map *bmap)
6096 return isl_basic_map_lexopt(bmap, 0);
6099 __isl_give isl_map *isl_basic_map_lexmax(__isl_take isl_basic_map *bmap)
6101 return isl_basic_map_lexopt(bmap, 1);
6104 __isl_give isl_set *isl_basic_set_lexmin(__isl_take isl_basic_set *bset)
6106 return (isl_set *)isl_basic_map_lexmin((isl_basic_map *)bset);
6109 __isl_give isl_set *isl_basic_set_lexmax(__isl_take isl_basic_set *bset)
6111 return (isl_set *)isl_basic_map_lexmax((isl_basic_map *)bset);
6114 /* Extract the first and only affine expression from list
6115 * and then add it to *pwaff with the given dom.
6116 * This domain is known to be disjoint from other domains
6117 * because of the way isl_basic_map_foreach_lexmax works.
6119 static int update_dim_opt(__isl_take isl_basic_set *dom,
6120 __isl_take isl_aff_list *list, void *user)
6122 isl_ctx *ctx = isl_basic_set_get_ctx(dom);
6124 isl_pw_aff **pwaff = user;
6125 isl_pw_aff *pwaff_i;
6129 if (isl_aff_list_n_aff(list) != 1)
6130 isl_die(ctx, isl_error_internal,
6131 "expecting single element list", goto error);
6133 aff = isl_aff_list_get_aff(list, 0);
6134 pwaff_i = isl_pw_aff_alloc(isl_set_from_basic_set(dom), aff);
6136 *pwaff = isl_pw_aff_add_disjoint(*pwaff, pwaff_i);
6138 isl_aff_list_free(list);
6142 isl_basic_set_free(dom);
6143 isl_aff_list_free(list);
6147 /* Given a basic map with one output dimension, compute the minimum or
6148 * maximum of that dimension as an isl_pw_aff.
6150 * The isl_pw_aff is constructed by having isl_basic_map_foreach_lexopt
6151 * call update_dim_opt on each leaf of the result.
6153 static __isl_give isl_pw_aff *basic_map_dim_opt(__isl_keep isl_basic_map *bmap,
6156 isl_space *dim = isl_basic_map_get_space(bmap);
6160 dim = isl_space_from_domain(isl_space_domain(dim));
6161 dim = isl_space_add_dims(dim, isl_dim_out, 1);
6162 pwaff = isl_pw_aff_empty(dim);
6164 r = isl_basic_map_foreach_lexopt(bmap, max, &update_dim_opt, &pwaff);
6166 return isl_pw_aff_free(pwaff);
6171 /* Compute the minimum or maximum of the given output dimension
6172 * as a function of the parameters and the input dimensions,
6173 * but independently of the other output dimensions.
6175 * We first project out the other output dimension and then compute
6176 * the "lexicographic" maximum in each basic map, combining the results
6177 * using isl_pw_aff_union_max.
6179 static __isl_give isl_pw_aff *map_dim_opt(__isl_take isl_map *map, int pos,
6186 n_out = isl_map_dim(map, isl_dim_out);
6187 map = isl_map_project_out(map, isl_dim_out, pos + 1, n_out - (pos + 1));
6188 map = isl_map_project_out(map, isl_dim_out, 0, pos);
6193 isl_space *dim = isl_map_get_space(map);
6194 dim = isl_space_domain(isl_space_from_range(dim));
6196 return isl_pw_aff_empty(dim);
6199 pwaff = basic_map_dim_opt(map->p[0], max);
6200 for (i = 1; i < map->n; ++i) {
6201 isl_pw_aff *pwaff_i;
6203 pwaff_i = basic_map_dim_opt(map->p[i], max);
6204 pwaff = isl_pw_aff_union_opt(pwaff, pwaff_i, max);
6212 /* Compute the maximum of the given output dimension as a function of the
6213 * parameters and input dimensions, but independently of
6214 * the other output dimensions.
6216 __isl_give isl_pw_aff *isl_map_dim_max(__isl_take isl_map *map, int pos)
6218 return map_dim_opt(map, pos, 1);
6221 /* Compute the minimum or maximum of the given set dimension
6222 * as a function of the parameters,
6223 * but independently of the other set dimensions.
6225 static __isl_give isl_pw_aff *set_dim_opt(__isl_take isl_set *set, int pos,
6228 return map_dim_opt(set, pos, max);
6231 /* Compute the maximum of the given set dimension as a function of the
6232 * parameters, but independently of the other set dimensions.
6234 __isl_give isl_pw_aff *isl_set_dim_max(__isl_take isl_set *set, int pos)
6236 return set_dim_opt(set, pos, 1);
6239 /* Compute the minimum of the given set dimension as a function of the
6240 * parameters, but independently of the other set dimensions.
6242 __isl_give isl_pw_aff *isl_set_dim_min(__isl_take isl_set *set, int pos)
6244 return set_dim_opt(set, pos, 0);
6247 /* Apply a preimage specified by "mat" on the parameters of "bset".
6248 * bset is assumed to have only parameters and divs.
6250 static struct isl_basic_set *basic_set_parameter_preimage(
6251 struct isl_basic_set *bset, struct isl_mat *mat)
6258 bset->dim = isl_space_cow(bset->dim);
6262 nparam = isl_basic_set_dim(bset, isl_dim_param);
6264 isl_assert(bset->ctx, mat->n_row == 1 + nparam, goto error);
6266 bset->dim->nparam = 0;
6267 bset->dim->n_out = nparam;
6268 bset = isl_basic_set_preimage(bset, mat);
6270 bset->dim->nparam = bset->dim->n_out;
6271 bset->dim->n_out = 0;
6276 isl_basic_set_free(bset);
6280 /* Apply a preimage specified by "mat" on the parameters of "set".
6281 * set is assumed to have only parameters and divs.
6283 static struct isl_set *set_parameter_preimage(
6284 struct isl_set *set, struct isl_mat *mat)
6286 isl_space *dim = NULL;
6292 dim = isl_space_copy(set->dim);
6293 dim = isl_space_cow(dim);
6297 nparam = isl_set_dim(set, isl_dim_param);
6299 isl_assert(set->ctx, mat->n_row == 1 + nparam, goto error);
6302 dim->n_out = nparam;
6303 isl_set_reset_space(set, dim);
6304 set = isl_set_preimage(set, mat);
6307 dim = isl_space_copy(set->dim);
6308 dim = isl_space_cow(dim);
6311 dim->nparam = dim->n_out;
6313 isl_set_reset_space(set, dim);
6316 isl_space_free(dim);
6323 /* Intersect the basic set "bset" with the affine space specified by the
6324 * equalities in "eq".
6326 static struct isl_basic_set *basic_set_append_equalities(
6327 struct isl_basic_set *bset, struct isl_mat *eq)
6335 bset = isl_basic_set_extend_space(bset, isl_space_copy(bset->dim), 0,
6340 len = 1 + isl_space_dim(bset->dim, isl_dim_all) + bset->extra;
6341 for (i = 0; i < eq->n_row; ++i) {
6342 k = isl_basic_set_alloc_equality(bset);
6345 isl_seq_cpy(bset->eq[k], eq->row[i], eq->n_col);
6346 isl_seq_clr(bset->eq[k] + eq->n_col, len - eq->n_col);
6350 bset = isl_basic_set_gauss(bset, NULL);
6351 bset = isl_basic_set_finalize(bset);
6356 isl_basic_set_free(bset);
6360 /* Intersect the set "set" with the affine space specified by the
6361 * equalities in "eq".
6363 static struct isl_set *set_append_equalities(struct isl_set *set,
6371 for (i = 0; i < set->n; ++i) {
6372 set->p[i] = basic_set_append_equalities(set->p[i],
6385 /* Given a basic set "bset" that only involves parameters and existentially
6386 * quantified variables, return the index of the first equality
6387 * that only involves parameters. If there is no such equality then
6388 * return bset->n_eq.
6390 * This function assumes that isl_basic_set_gauss has been called on "bset".
6392 static int first_parameter_equality(__isl_keep isl_basic_set *bset)
6395 unsigned nparam, n_div;
6400 nparam = isl_basic_set_dim(bset, isl_dim_param);
6401 n_div = isl_basic_set_dim(bset, isl_dim_div);
6403 for (i = 0, j = n_div - 1; i < bset->n_eq && j >= 0; --j) {
6404 if (!isl_int_is_zero(bset->eq[i][1 + nparam + j]))
6411 /* Compute an explicit representation for the existentially quantified
6412 * variables in "bset" by computing the "minimal value" of the set
6413 * variables. Since there are no set variables, the computation of
6414 * the minimal value essentially computes an explicit representation
6415 * of the non-empty part(s) of "bset".
6417 * The input only involves parameters and existentially quantified variables.
6418 * All equalities among parameters have been removed.
6420 * Since the existentially quantified variables in the result are in general
6421 * going to be different from those in the input, we first replace
6422 * them by the minimal number of variables based on their equalities.
6423 * This should simplify the parametric integer programming.
6425 static __isl_give isl_set *base_compute_divs(__isl_take isl_basic_set *bset)
6427 isl_morph *morph1, *morph2;
6433 if (bset->n_eq == 0)
6434 return isl_basic_set_lexmin(bset);
6436 morph1 = isl_basic_set_parameter_compression(bset);
6437 bset = isl_morph_basic_set(isl_morph_copy(morph1), bset);
6438 bset = isl_basic_set_lift(bset);
6439 morph2 = isl_basic_set_variable_compression(bset, isl_dim_set);
6440 bset = isl_morph_basic_set(morph2, bset);
6441 n = isl_basic_set_dim(bset, isl_dim_set);
6442 bset = isl_basic_set_project_out(bset, isl_dim_set, 0, n);
6444 set = isl_basic_set_lexmin(bset);
6446 set = isl_morph_set(isl_morph_inverse(morph1), set);
6451 /* Project the given basic set onto its parameter domain, possibly introducing
6452 * new, explicit, existential variables in the constraints.
6453 * The input has parameters and (possibly implicit) existential variables.
6454 * The output has the same parameters, but only
6455 * explicit existentially quantified variables.
6457 * The actual projection is performed by pip, but pip doesn't seem
6458 * to like equalities very much, so we first remove the equalities
6459 * among the parameters by performing a variable compression on
6460 * the parameters. Afterward, an inverse transformation is performed
6461 * and the equalities among the parameters are inserted back in.
6463 * The variable compression on the parameters may uncover additional
6464 * equalities that were only implicit before. We therefore check
6465 * if there are any new parameter equalities in the result and
6466 * if so recurse. The removal of parameter equalities is required
6467 * for the parameter compression performed by base_compute_divs.
6469 static struct isl_set *parameter_compute_divs(struct isl_basic_set *bset)
6473 struct isl_mat *T, *T2;
6474 struct isl_set *set;
6477 bset = isl_basic_set_cow(bset);
6481 if (bset->n_eq == 0)
6482 return base_compute_divs(bset);
6484 bset = isl_basic_set_gauss(bset, NULL);
6487 if (isl_basic_set_plain_is_empty(bset))
6488 return isl_set_from_basic_set(bset);
6490 i = first_parameter_equality(bset);
6491 if (i == bset->n_eq)
6492 return base_compute_divs(bset);
6494 nparam = isl_basic_set_dim(bset, isl_dim_param);
6495 eq = isl_mat_sub_alloc6(bset->ctx, bset->eq, i, bset->n_eq - i,
6497 eq = isl_mat_cow(eq);
6498 T = isl_mat_variable_compression(isl_mat_copy(eq), &T2);
6499 if (T && T->n_col == 0) {
6503 bset = isl_basic_set_set_to_empty(bset);
6504 return isl_set_from_basic_set(bset);
6506 bset = basic_set_parameter_preimage(bset, T);
6508 i = first_parameter_equality(bset);
6511 else if (i == bset->n_eq)
6512 set = base_compute_divs(bset);
6514 set = parameter_compute_divs(bset);
6515 set = set_parameter_preimage(set, T2);
6516 set = set_append_equalities(set, eq);
6520 /* Insert the divs from "ls" before those of "bmap".
6522 * The number of columns is not changed, which means that the last
6523 * dimensions of "bmap" are being reintepreted as the divs from "ls".
6524 * The caller is responsible for removing the same number of dimensions
6525 * from the space of "bmap".
6527 static __isl_give isl_basic_map *insert_divs_from_local_space(
6528 __isl_take isl_basic_map *bmap, __isl_keep isl_local_space *ls)
6534 n_div = isl_local_space_dim(ls, isl_dim_div);
6538 old_n_div = bmap->n_div;
6539 bmap = insert_div_rows(bmap, n_div);
6543 for (i = 0; i < n_div; ++i) {
6544 isl_seq_cpy(bmap->div[i], ls->div->row[i], ls->div->n_col);
6545 isl_seq_clr(bmap->div[i] + ls->div->n_col, old_n_div);
6551 /* Replace the space of "bmap" by the space and divs of "ls".
6553 * If "ls" has any divs, then we simplify the result since we may
6554 * have discovered some additional equalities that could simplify
6555 * the div expressions.
6557 static __isl_give isl_basic_map *basic_replace_space_by_local_space(
6558 __isl_take isl_basic_map *bmap, __isl_take isl_local_space *ls)
6562 bmap = isl_basic_map_cow(bmap);
6566 n_div = isl_local_space_dim(ls, isl_dim_div);
6567 bmap = insert_divs_from_local_space(bmap, ls);
6571 isl_space_free(bmap->dim);
6572 bmap->dim = isl_local_space_get_space(ls);
6576 isl_local_space_free(ls);
6578 bmap = isl_basic_map_simplify(bmap);
6579 bmap = isl_basic_map_finalize(bmap);
6582 isl_basic_map_free(bmap);
6583 isl_local_space_free(ls);
6587 /* Replace the space of "map" by the space and divs of "ls".
6589 static __isl_give isl_map *replace_space_by_local_space(__isl_take isl_map *map,
6590 __isl_take isl_local_space *ls)
6594 map = isl_map_cow(map);
6598 for (i = 0; i < map->n; ++i) {
6599 map->p[i] = basic_replace_space_by_local_space(map->p[i],
6600 isl_local_space_copy(ls));
6604 isl_space_free(map->dim);
6605 map->dim = isl_local_space_get_space(ls);
6609 isl_local_space_free(ls);
6612 isl_local_space_free(ls);
6617 /* Compute an explicit representation for the existentially
6618 * quantified variables for which do not know any explicit representation yet.
6620 * We first sort the existentially quantified variables so that the
6621 * existentially quantified variables for which we already have an explicit
6622 * representation are placed before those for which we do not.
6623 * The input dimensions, the output dimensions and the existentially
6624 * quantified variables for which we already have an explicit
6625 * representation are then turned into parameters.
6626 * compute_divs returns a map with the same parameters and
6627 * no input or output dimensions and the dimension specification
6628 * is reset to that of the input, including the existentially quantified
6629 * variables for which we already had an explicit representation.
6631 static struct isl_map *compute_divs(struct isl_basic_map *bmap)
6633 struct isl_basic_set *bset;
6634 struct isl_set *set;
6635 struct isl_map *map;
6637 isl_local_space *ls;
6644 bmap = isl_basic_map_sort_divs(bmap);
6645 bmap = isl_basic_map_cow(bmap);
6649 for (n_known = 0; n_known < bmap->n_div; ++n_known)
6650 if (isl_int_is_zero(bmap->div[n_known][0]))
6653 nparam = isl_basic_map_dim(bmap, isl_dim_param);
6654 n_in = isl_basic_map_dim(bmap, isl_dim_in);
6655 n_out = isl_basic_map_dim(bmap, isl_dim_out);
6656 dim = isl_space_set_alloc(bmap->ctx,
6657 nparam + n_in + n_out + n_known, 0);
6661 ls = isl_basic_map_get_local_space(bmap);
6662 ls = isl_local_space_drop_dims(ls, isl_dim_div,
6663 n_known, bmap->n_div - n_known);
6665 for (i = n_known; i < bmap->n_div; ++i)
6666 swap_div(bmap, i - n_known, i);
6667 bmap->n_div -= n_known;
6668 bmap->extra -= n_known;
6670 bmap = isl_basic_map_reset_space(bmap, dim);
6671 bset = (struct isl_basic_set *)bmap;
6673 set = parameter_compute_divs(bset);
6674 map = (struct isl_map *)set;
6675 map = replace_space_by_local_space(map, ls);
6679 isl_basic_map_free(bmap);
6683 int isl_basic_map_divs_known(__isl_keep isl_basic_map *bmap)
6691 off = isl_space_dim(bmap->dim, isl_dim_all);
6692 for (i = 0; i < bmap->n_div; ++i) {
6693 if (isl_int_is_zero(bmap->div[i][0]))
6695 isl_assert(bmap->ctx, isl_int_is_zero(bmap->div[i][1+1+off+i]),
6701 static int map_divs_known(__isl_keep isl_map *map)
6708 for (i = 0; i < map->n; ++i) {
6709 int known = isl_basic_map_divs_known(map->p[i]);
6717 /* If bmap contains any unknown divs, then compute explicit
6718 * expressions for them. However, this computation may be
6719 * quite expensive, so first try to remove divs that aren't
6722 struct isl_map *isl_basic_map_compute_divs(struct isl_basic_map *bmap)
6725 struct isl_map *map;
6727 known = isl_basic_map_divs_known(bmap);
6731 return isl_map_from_basic_map(bmap);
6733 bmap = isl_basic_map_drop_redundant_divs(bmap);
6735 known = isl_basic_map_divs_known(bmap);
6739 return isl_map_from_basic_map(bmap);
6741 map = compute_divs(bmap);
6744 isl_basic_map_free(bmap);
6748 struct isl_map *isl_map_compute_divs(struct isl_map *map)
6752 struct isl_map *res;
6759 known = map_divs_known(map);
6767 res = isl_basic_map_compute_divs(isl_basic_map_copy(map->p[0]));
6768 for (i = 1 ; i < map->n; ++i) {
6770 r2 = isl_basic_map_compute_divs(isl_basic_map_copy(map->p[i]));
6771 if (ISL_F_ISSET(map, ISL_MAP_DISJOINT))
6772 res = isl_map_union_disjoint(res, r2);
6774 res = isl_map_union(res, r2);
6781 struct isl_set *isl_basic_set_compute_divs(struct isl_basic_set *bset)
6783 return (struct isl_set *)
6784 isl_basic_map_compute_divs((struct isl_basic_map *)bset);
6787 struct isl_set *isl_set_compute_divs(struct isl_set *set)
6789 return (struct isl_set *)
6790 isl_map_compute_divs((struct isl_map *)set);
6793 struct isl_set *isl_map_domain(struct isl_map *map)
6796 struct isl_set *set;
6801 map = isl_map_cow(map);
6805 set = (struct isl_set *)map;
6806 set->dim = isl_space_domain(set->dim);
6809 for (i = 0; i < map->n; ++i) {
6810 set->p[i] = isl_basic_map_domain(map->p[i]);
6814 ISL_F_CLR(set, ISL_MAP_DISJOINT);
6815 ISL_F_CLR(set, ISL_SET_NORMALIZED);
6822 /* Return the union of "map1" and "map2", where we assume for now that
6823 * "map1" and "map2" are disjoint. Note that the basic maps inside
6824 * "map1" or "map2" may not be disjoint from each other.
6825 * Also note that this function is also called from isl_map_union,
6826 * which takes care of handling the situation where "map1" and "map2"
6827 * may not be disjoint.
6829 * If one of the inputs is empty, we can simply return the other input.
6830 * Similarly, if one of the inputs is universal, then it is equal to the union.
6832 static __isl_give isl_map *map_union_disjoint(__isl_take isl_map *map1,
6833 __isl_take isl_map *map2)
6837 struct isl_map *map = NULL;
6852 is_universe = isl_map_plain_is_universe(map1);
6853 if (is_universe < 0)
6860 is_universe = isl_map_plain_is_universe(map2);
6861 if (is_universe < 0)
6868 isl_assert(map1->ctx, isl_space_is_equal(map1->dim, map2->dim), goto error);
6870 if (ISL_F_ISSET(map1, ISL_MAP_DISJOINT) &&
6871 ISL_F_ISSET(map2, ISL_MAP_DISJOINT))
6872 ISL_FL_SET(flags, ISL_MAP_DISJOINT);
6874 map = isl_map_alloc_space(isl_space_copy(map1->dim),
6875 map1->n + map2->n, flags);
6878 for (i = 0; i < map1->n; ++i) {
6879 map = isl_map_add_basic_map(map,
6880 isl_basic_map_copy(map1->p[i]));
6884 for (i = 0; i < map2->n; ++i) {
6885 map = isl_map_add_basic_map(map,
6886 isl_basic_map_copy(map2->p[i]));
6900 __isl_give isl_map *isl_map_union_disjoint(__isl_take isl_map *map1,
6901 __isl_take isl_map *map2)
6903 return isl_map_align_params_map_map_and(map1, map2, &map_union_disjoint);
6906 struct isl_map *isl_map_union(struct isl_map *map1, struct isl_map *map2)
6908 map1 = isl_map_union_disjoint(map1, map2);
6912 ISL_F_CLR(map1, ISL_MAP_DISJOINT);
6916 struct isl_set *isl_set_union_disjoint(
6917 struct isl_set *set1, struct isl_set *set2)
6919 return (struct isl_set *)
6920 isl_map_union_disjoint(
6921 (struct isl_map *)set1, (struct isl_map *)set2);
6924 struct isl_set *isl_set_union(struct isl_set *set1, struct isl_set *set2)
6926 return (struct isl_set *)
6927 isl_map_union((struct isl_map *)set1, (struct isl_map *)set2);
6930 /* Apply "fn" to pairs of elements from "map" and "set" and collect
6933 * "map" and "set" are assumed to be compatible and non-NULL.
6935 static __isl_give isl_map *map_intersect_set(__isl_take isl_map *map,
6936 __isl_take isl_set *set,
6937 __isl_give isl_basic_map *fn(__isl_take isl_basic_map *bmap,
6938 __isl_take isl_basic_set *bset))
6941 struct isl_map *result;
6944 if (isl_set_plain_is_universe(set)) {
6949 if (ISL_F_ISSET(map, ISL_MAP_DISJOINT) &&
6950 ISL_F_ISSET(set, ISL_MAP_DISJOINT))
6951 ISL_FL_SET(flags, ISL_MAP_DISJOINT);
6953 result = isl_map_alloc_space(isl_space_copy(map->dim),
6954 map->n * set->n, flags);
6955 for (i = 0; result && i < map->n; ++i)
6956 for (j = 0; j < set->n; ++j) {
6957 result = isl_map_add_basic_map(result,
6958 fn(isl_basic_map_copy(map->p[i]),
6959 isl_basic_set_copy(set->p[j])));
6969 static __isl_give isl_map *map_intersect_range(__isl_take isl_map *map,
6970 __isl_take isl_set *set)
6975 if (!isl_map_compatible_range(map, set))
6976 isl_die(set->ctx, isl_error_invalid,
6977 "incompatible spaces", goto error);
6979 return map_intersect_set(map, set, &isl_basic_map_intersect_range);
6986 __isl_give isl_map *isl_map_intersect_range(__isl_take isl_map *map,
6987 __isl_take isl_set *set)
6989 return isl_map_align_params_map_map_and(map, set, &map_intersect_range);
6992 static __isl_give isl_map *map_intersect_domain(__isl_take isl_map *map,
6993 __isl_take isl_set *set)
6998 if (!isl_map_compatible_domain(map, set))
6999 isl_die(set->ctx, isl_error_invalid,
7000 "incompatible spaces", goto error);
7002 return map_intersect_set(map, set, &isl_basic_map_intersect_domain);
7009 __isl_give isl_map *isl_map_intersect_domain(__isl_take isl_map *map,
7010 __isl_take isl_set *set)
7012 return isl_map_align_params_map_map_and(map, set,
7013 &map_intersect_domain);
7016 static __isl_give isl_map *map_apply_domain(__isl_take isl_map *map1,
7017 __isl_take isl_map *map2)
7021 map1 = isl_map_reverse(map1);
7022 map1 = isl_map_apply_range(map1, map2);
7023 return isl_map_reverse(map1);
7030 __isl_give isl_map *isl_map_apply_domain(__isl_take isl_map *map1,
7031 __isl_take isl_map *map2)
7033 return isl_map_align_params_map_map_and(map1, map2, &map_apply_domain);
7036 static __isl_give isl_map *map_apply_range(__isl_take isl_map *map1,
7037 __isl_take isl_map *map2)
7039 isl_space *dim_result;
7040 struct isl_map *result;
7046 dim_result = isl_space_join(isl_space_copy(map1->dim),
7047 isl_space_copy(map2->dim));
7049 result = isl_map_alloc_space(dim_result, map1->n * map2->n, 0);
7052 for (i = 0; i < map1->n; ++i)
7053 for (j = 0; j < map2->n; ++j) {
7054 result = isl_map_add_basic_map(result,
7055 isl_basic_map_apply_range(
7056 isl_basic_map_copy(map1->p[i]),
7057 isl_basic_map_copy(map2->p[j])));
7063 if (result && result->n <= 1)
7064 ISL_F_SET(result, ISL_MAP_DISJOINT);
7072 __isl_give isl_map *isl_map_apply_range(__isl_take isl_map *map1,
7073 __isl_take isl_map *map2)
7075 return isl_map_align_params_map_map_and(map1, map2, &map_apply_range);
7079 * returns range - domain
7081 struct isl_basic_set *isl_basic_map_deltas(struct isl_basic_map *bmap)
7083 isl_space *dims, *target_dim;
7084 struct isl_basic_set *bset;
7091 isl_assert(bmap->ctx, isl_space_tuple_match(bmap->dim, isl_dim_in,
7092 bmap->dim, isl_dim_out),
7094 target_dim = isl_space_domain(isl_basic_map_get_space(bmap));
7095 dim = isl_basic_map_n_in(bmap);
7096 nparam = isl_basic_map_n_param(bmap);
7097 bset = isl_basic_set_from_basic_map(bmap);
7098 bset = isl_basic_set_cow(bset);
7099 dims = isl_basic_set_get_space(bset);
7100 dims = isl_space_add_dims(dims, isl_dim_set, dim);
7101 bset = isl_basic_set_extend_space(bset, dims, 0, dim, 0);
7102 bset = isl_basic_set_swap_vars(bset, 2*dim);
7103 for (i = 0; i < dim; ++i) {
7104 int j = isl_basic_map_alloc_equality(
7105 (struct isl_basic_map *)bset);
7107 bset = isl_basic_set_free(bset);
7110 isl_seq_clr(bset->eq[j], 1 + isl_basic_set_total_dim(bset));
7111 isl_int_set_si(bset->eq[j][1+nparam+i], 1);
7112 isl_int_set_si(bset->eq[j][1+nparam+dim+i], 1);
7113 isl_int_set_si(bset->eq[j][1+nparam+2*dim+i], -1);
7115 bset = isl_basic_set_project_out(bset, isl_dim_set, dim, 2*dim);
7116 bset = isl_basic_set_reset_space(bset, target_dim);
7119 isl_basic_map_free(bmap);
7124 * returns range - domain
7126 __isl_give isl_set *isl_map_deltas(__isl_take isl_map *map)
7130 struct isl_set *result;
7135 isl_assert(map->ctx, isl_space_tuple_match(map->dim, isl_dim_in,
7136 map->dim, isl_dim_out),
7138 dim = isl_map_get_space(map);
7139 dim = isl_space_domain(dim);
7140 result = isl_set_alloc_space(dim, map->n, 0);
7143 for (i = 0; i < map->n; ++i)
7144 result = isl_set_add_basic_set(result,
7145 isl_basic_map_deltas(isl_basic_map_copy(map->p[i])));
7154 * returns [domain -> range] -> range - domain
7156 __isl_give isl_basic_map *isl_basic_map_deltas_map(
7157 __isl_take isl_basic_map *bmap)
7161 isl_basic_map *domain;
7165 if (!isl_space_tuple_match(bmap->dim, isl_dim_in, bmap->dim, isl_dim_out))
7166 isl_die(bmap->ctx, isl_error_invalid,
7167 "domain and range don't match", goto error);
7169 nparam = isl_basic_map_dim(bmap, isl_dim_param);
7170 n = isl_basic_map_dim(bmap, isl_dim_in);
7172 dim = isl_space_from_range(isl_space_domain(isl_basic_map_get_space(bmap)));
7173 domain = isl_basic_map_universe(dim);
7175 bmap = isl_basic_map_from_domain(isl_basic_map_wrap(bmap));
7176 bmap = isl_basic_map_apply_range(bmap, domain);
7177 bmap = isl_basic_map_extend_constraints(bmap, n, 0);
7179 total = isl_basic_map_total_dim(bmap);
7181 for (i = 0; i < n; ++i) {
7182 k = isl_basic_map_alloc_equality(bmap);
7185 isl_seq_clr(bmap->eq[k], 1 + total);
7186 isl_int_set_si(bmap->eq[k][1 + nparam + i], 1);
7187 isl_int_set_si(bmap->eq[k][1 + nparam + n + i], -1);
7188 isl_int_set_si(bmap->eq[k][1 + nparam + n + n + i], 1);
7191 bmap = isl_basic_map_gauss(bmap, NULL);
7192 return isl_basic_map_finalize(bmap);
7194 isl_basic_map_free(bmap);
7199 * returns [domain -> range] -> range - domain
7201 __isl_give isl_map *isl_map_deltas_map(__isl_take isl_map *map)
7204 isl_space *domain_dim;
7209 if (!isl_space_tuple_match(map->dim, isl_dim_in, map->dim, isl_dim_out))
7210 isl_die(map->ctx, isl_error_invalid,
7211 "domain and range don't match", goto error);
7213 map = isl_map_cow(map);
7217 domain_dim = isl_space_from_range(isl_space_domain(isl_map_get_space(map)));
7218 map->dim = isl_space_from_domain(isl_space_wrap(map->dim));
7219 map->dim = isl_space_join(map->dim, domain_dim);
7222 for (i = 0; i < map->n; ++i) {
7223 map->p[i] = isl_basic_map_deltas_map(map->p[i]);
7227 ISL_F_CLR(map, ISL_MAP_NORMALIZED);
7234 static __isl_give isl_basic_map *basic_map_identity(__isl_take isl_space *dims)
7236 struct isl_basic_map *bmap;
7244 nparam = dims->nparam;
7246 bmap = isl_basic_map_alloc_space(dims, 0, dim, 0);
7250 for (i = 0; i < dim; ++i) {
7251 int j = isl_basic_map_alloc_equality(bmap);
7254 isl_seq_clr(bmap->eq[j], 1 + isl_basic_map_total_dim(bmap));
7255 isl_int_set_si(bmap->eq[j][1+nparam+i], 1);
7256 isl_int_set_si(bmap->eq[j][1+nparam+dim+i], -1);
7258 return isl_basic_map_finalize(bmap);
7260 isl_basic_map_free(bmap);
7264 __isl_give isl_basic_map *isl_basic_map_identity(__isl_take isl_space *dim)
7268 if (dim->n_in != dim->n_out)
7269 isl_die(dim->ctx, isl_error_invalid,
7270 "number of input and output dimensions needs to be "
7271 "the same", goto error);
7272 return basic_map_identity(dim);
7274 isl_space_free(dim);
7278 struct isl_basic_map *isl_basic_map_identity_like(struct isl_basic_map *model)
7280 if (!model || !model->dim)
7282 return isl_basic_map_identity(isl_space_copy(model->dim));
7285 __isl_give isl_map *isl_map_identity(__isl_take isl_space *dim)
7287 return isl_map_from_basic_map(isl_basic_map_identity(dim));
7290 struct isl_map *isl_map_identity_like(struct isl_map *model)
7292 if (!model || !model->dim)
7294 return isl_map_identity(isl_space_copy(model->dim));
7297 struct isl_map *isl_map_identity_like_basic_map(struct isl_basic_map *model)
7299 if (!model || !model->dim)
7301 return isl_map_identity(isl_space_copy(model->dim));
7304 __isl_give isl_map *isl_set_identity(__isl_take isl_set *set)
7306 isl_space *dim = isl_set_get_space(set);
7308 id = isl_map_identity(isl_space_map_from_set(dim));
7309 return isl_map_intersect_range(id, set);
7312 /* Construct a basic set with all set dimensions having only non-negative
7315 __isl_give isl_basic_set *isl_basic_set_positive_orthant(
7316 __isl_take isl_space *space)
7321 struct isl_basic_set *bset;
7325 nparam = space->nparam;
7327 bset = isl_basic_set_alloc_space(space, 0, 0, dim);
7330 for (i = 0; i < dim; ++i) {
7331 int k = isl_basic_set_alloc_inequality(bset);
7334 isl_seq_clr(bset->ineq[k], 1 + isl_basic_set_total_dim(bset));
7335 isl_int_set_si(bset->ineq[k][1 + nparam + i], 1);
7339 isl_basic_set_free(bset);
7343 /* Construct the half-space x_pos >= 0.
7345 static __isl_give isl_basic_set *nonneg_halfspace(__isl_take isl_space *dim,
7349 isl_basic_set *nonneg;
7351 nonneg = isl_basic_set_alloc_space(dim, 0, 0, 1);
7352 k = isl_basic_set_alloc_inequality(nonneg);
7355 isl_seq_clr(nonneg->ineq[k], 1 + isl_basic_set_total_dim(nonneg));
7356 isl_int_set_si(nonneg->ineq[k][pos], 1);
7358 return isl_basic_set_finalize(nonneg);
7360 isl_basic_set_free(nonneg);
7364 /* Construct the half-space x_pos <= -1.
7366 static __isl_give isl_basic_set *neg_halfspace(__isl_take isl_space *dim, int pos)
7371 neg = isl_basic_set_alloc_space(dim, 0, 0, 1);
7372 k = isl_basic_set_alloc_inequality(neg);
7375 isl_seq_clr(neg->ineq[k], 1 + isl_basic_set_total_dim(neg));
7376 isl_int_set_si(neg->ineq[k][0], -1);
7377 isl_int_set_si(neg->ineq[k][pos], -1);
7379 return isl_basic_set_finalize(neg);
7381 isl_basic_set_free(neg);
7385 __isl_give isl_set *isl_set_split_dims(__isl_take isl_set *set,
7386 enum isl_dim_type type, unsigned first, unsigned n)
7389 isl_basic_set *nonneg;
7397 isl_assert(set->ctx, first + n <= isl_set_dim(set, type), goto error);
7399 for (i = 0; i < n; ++i) {
7400 nonneg = nonneg_halfspace(isl_set_get_space(set),
7401 pos(set->dim, type) + first + i);
7402 neg = neg_halfspace(isl_set_get_space(set),
7403 pos(set->dim, type) + first + i);
7405 set = isl_set_intersect(set, isl_basic_set_union(nonneg, neg));
7414 static int foreach_orthant(__isl_take isl_set *set, int *signs, int first,
7415 int len, int (*fn)(__isl_take isl_set *orthant, int *signs, void *user),
7422 if (isl_set_plain_is_empty(set)) {
7427 return fn(set, signs, user);
7430 half = isl_set_from_basic_set(nonneg_halfspace(isl_set_get_space(set),
7432 half = isl_set_intersect(half, isl_set_copy(set));
7433 if (foreach_orthant(half, signs, first + 1, len, fn, user) < 0)
7437 half = isl_set_from_basic_set(neg_halfspace(isl_set_get_space(set),
7439 half = isl_set_intersect(half, set);
7440 return foreach_orthant(half, signs, first + 1, len, fn, user);
7446 /* Call "fn" on the intersections of "set" with each of the orthants
7447 * (except for obviously empty intersections). The orthant is identified
7448 * by the signs array, with each entry having value 1 or -1 according
7449 * to the sign of the corresponding variable.
7451 int isl_set_foreach_orthant(__isl_keep isl_set *set,
7452 int (*fn)(__isl_take isl_set *orthant, int *signs, void *user),
7462 if (isl_set_plain_is_empty(set))
7465 nparam = isl_set_dim(set, isl_dim_param);
7466 nvar = isl_set_dim(set, isl_dim_set);
7468 signs = isl_alloc_array(set->ctx, int, nparam + nvar);
7470 r = foreach_orthant(isl_set_copy(set), signs, 0, nparam + nvar,
7478 int isl_set_is_equal(struct isl_set *set1, struct isl_set *set2)
7480 return isl_map_is_equal((struct isl_map *)set1, (struct isl_map *)set2);
7483 int isl_basic_map_is_subset(
7484 struct isl_basic_map *bmap1, struct isl_basic_map *bmap2)
7487 struct isl_map *map1;
7488 struct isl_map *map2;
7490 if (!bmap1 || !bmap2)
7493 map1 = isl_map_from_basic_map(isl_basic_map_copy(bmap1));
7494 map2 = isl_map_from_basic_map(isl_basic_map_copy(bmap2));
7496 is_subset = isl_map_is_subset(map1, map2);
7504 int isl_basic_set_is_subset(__isl_keep isl_basic_set *bset1,
7505 __isl_keep isl_basic_set *bset2)
7507 return isl_basic_map_is_subset(bset1, bset2);
7510 int isl_basic_map_is_equal(
7511 struct isl_basic_map *bmap1, struct isl_basic_map *bmap2)
7515 if (!bmap1 || !bmap2)
7517 is_subset = isl_basic_map_is_subset(bmap1, bmap2);
7520 is_subset = isl_basic_map_is_subset(bmap2, bmap1);
7524 int isl_basic_set_is_equal(
7525 struct isl_basic_set *bset1, struct isl_basic_set *bset2)
7527 return isl_basic_map_is_equal(
7528 (struct isl_basic_map *)bset1, (struct isl_basic_map *)bset2);
7531 int isl_map_is_empty(struct isl_map *map)
7538 for (i = 0; i < map->n; ++i) {
7539 is_empty = isl_basic_map_is_empty(map->p[i]);
7548 int isl_map_plain_is_empty(__isl_keep isl_map *map)
7550 return map ? map->n == 0 : -1;
7553 int isl_map_fast_is_empty(__isl_keep isl_map *map)
7555 return isl_map_plain_is_empty(map);
7558 int isl_set_plain_is_empty(struct isl_set *set)
7560 return set ? set->n == 0 : -1;
7563 int isl_set_fast_is_empty(__isl_keep isl_set *set)
7565 return isl_set_plain_is_empty(set);
7568 int isl_set_is_empty(struct isl_set *set)
7570 return isl_map_is_empty((struct isl_map *)set);
7573 int isl_map_has_equal_space(__isl_keep isl_map *map1, __isl_keep isl_map *map2)
7578 return isl_space_is_equal(map1->dim, map2->dim);
7581 int isl_set_has_equal_space(__isl_keep isl_set *set1, __isl_keep isl_set *set2)
7586 return isl_space_is_equal(set1->dim, set2->dim);
7589 static int map_is_equal(__isl_keep isl_map *map1, __isl_keep isl_map *map2)
7595 is_subset = isl_map_is_subset(map1, map2);
7598 is_subset = isl_map_is_subset(map2, map1);
7602 int isl_map_is_equal(__isl_keep isl_map *map1, __isl_keep isl_map *map2)
7604 return isl_map_align_params_map_map_and_test(map1, map2, &map_is_equal);
7607 int isl_basic_map_is_strict_subset(
7608 struct isl_basic_map *bmap1, struct isl_basic_map *bmap2)
7612 if (!bmap1 || !bmap2)
7614 is_subset = isl_basic_map_is_subset(bmap1, bmap2);
7617 is_subset = isl_basic_map_is_subset(bmap2, bmap1);
7618 if (is_subset == -1)
7623 int isl_map_is_strict_subset(struct isl_map *map1, struct isl_map *map2)
7629 is_subset = isl_map_is_subset(map1, map2);
7632 is_subset = isl_map_is_subset(map2, map1);
7633 if (is_subset == -1)
7638 int isl_set_is_strict_subset(__isl_keep isl_set *set1, __isl_keep isl_set *set2)
7640 return isl_map_is_strict_subset((isl_map *)set1, (isl_map *)set2);
7643 int isl_basic_map_is_universe(struct isl_basic_map *bmap)
7647 return bmap->n_eq == 0 && bmap->n_ineq == 0;
7650 int isl_basic_set_is_universe(struct isl_basic_set *bset)
7654 return bset->n_eq == 0 && bset->n_ineq == 0;
7657 int isl_map_plain_is_universe(__isl_keep isl_map *map)
7664 for (i = 0; i < map->n; ++i) {
7665 int r = isl_basic_map_is_universe(map->p[i]);
7673 int isl_set_plain_is_universe(__isl_keep isl_set *set)
7675 return isl_map_plain_is_universe((isl_map *) set);
7678 int isl_set_fast_is_universe(__isl_keep isl_set *set)
7680 return isl_set_plain_is_universe(set);
7683 int isl_basic_map_is_empty(struct isl_basic_map *bmap)
7685 struct isl_basic_set *bset = NULL;
7686 struct isl_vec *sample = NULL;
7693 if (ISL_F_ISSET(bmap, ISL_BASIC_MAP_EMPTY))
7696 if (isl_basic_map_is_universe(bmap))
7699 if (ISL_F_ISSET(bmap, ISL_BASIC_MAP_RATIONAL)) {
7700 struct isl_basic_map *copy = isl_basic_map_copy(bmap);
7701 copy = isl_basic_map_remove_redundancies(copy);
7702 empty = isl_basic_map_plain_is_empty(copy);
7703 isl_basic_map_free(copy);
7707 total = 1 + isl_basic_map_total_dim(bmap);
7708 if (bmap->sample && bmap->sample->size == total) {
7709 int contains = isl_basic_map_contains(bmap, bmap->sample);
7715 isl_vec_free(bmap->sample);
7716 bmap->sample = NULL;
7717 bset = isl_basic_map_underlying_set(isl_basic_map_copy(bmap));
7720 sample = isl_basic_set_sample_vec(bset);
7723 empty = sample->size == 0;
7724 isl_vec_free(bmap->sample);
7725 bmap->sample = sample;
7727 ISL_F_SET(bmap, ISL_BASIC_MAP_EMPTY);
7732 int isl_basic_map_plain_is_empty(__isl_keep isl_basic_map *bmap)
7736 return ISL_F_ISSET(bmap, ISL_BASIC_MAP_EMPTY);
7739 int isl_basic_map_fast_is_empty(__isl_keep isl_basic_map *bmap)
7741 return isl_basic_map_plain_is_empty(bmap);
7744 int isl_basic_set_plain_is_empty(__isl_keep isl_basic_set *bset)
7748 return ISL_F_ISSET(bset, ISL_BASIC_SET_EMPTY);
7751 int isl_basic_set_fast_is_empty(__isl_keep isl_basic_set *bset)
7753 return isl_basic_set_plain_is_empty(bset);
7756 int isl_basic_set_is_empty(struct isl_basic_set *bset)
7758 return isl_basic_map_is_empty((struct isl_basic_map *)bset);
7761 struct isl_map *isl_basic_map_union(
7762 struct isl_basic_map *bmap1, struct isl_basic_map *bmap2)
7764 struct isl_map *map;
7765 if (!bmap1 || !bmap2)
7768 isl_assert(bmap1->ctx, isl_space_is_equal(bmap1->dim, bmap2->dim), goto error);
7770 map = isl_map_alloc_space(isl_space_copy(bmap1->dim), 2, 0);
7773 map = isl_map_add_basic_map(map, bmap1);
7774 map = isl_map_add_basic_map(map, bmap2);
7777 isl_basic_map_free(bmap1);
7778 isl_basic_map_free(bmap2);
7782 struct isl_set *isl_basic_set_union(
7783 struct isl_basic_set *bset1, struct isl_basic_set *bset2)
7785 return (struct isl_set *)isl_basic_map_union(
7786 (struct isl_basic_map *)bset1,
7787 (struct isl_basic_map *)bset2);
7790 /* Order divs such that any div only depends on previous divs */
7791 struct isl_basic_map *isl_basic_map_order_divs(struct isl_basic_map *bmap)
7799 off = isl_space_dim(bmap->dim, isl_dim_all);
7801 for (i = 0; i < bmap->n_div; ++i) {
7803 if (isl_int_is_zero(bmap->div[i][0]))
7805 pos = isl_seq_first_non_zero(bmap->div[i]+1+1+off+i,
7809 isl_basic_map_swap_div(bmap, i, i + pos);
7815 struct isl_basic_set *isl_basic_set_order_divs(struct isl_basic_set *bset)
7817 return (struct isl_basic_set *)
7818 isl_basic_map_order_divs((struct isl_basic_map *)bset);
7821 __isl_give isl_map *isl_map_order_divs(__isl_take isl_map *map)
7828 for (i = 0; i < map->n; ++i) {
7829 map->p[i] = isl_basic_map_order_divs(map->p[i]);
7840 /* Apply the expansion computed by isl_merge_divs.
7841 * The expansion itself is given by "exp" while the resulting
7842 * list of divs is given by "div".
7844 __isl_give isl_basic_set *isl_basic_set_expand_divs(
7845 __isl_take isl_basic_set *bset, __isl_take isl_mat *div, int *exp)
7850 bset = isl_basic_set_cow(bset);
7854 if (div->n_row < bset->n_div)
7855 isl_die(isl_mat_get_ctx(div), isl_error_invalid,
7856 "not an expansion", goto error);
7858 n_div = bset->n_div;
7859 bset = isl_basic_map_extend_space(bset, isl_space_copy(bset->dim),
7860 div->n_row - n_div, 0,
7861 2 * (div->n_row - n_div));
7863 for (i = n_div; i < div->n_row; ++i)
7864 if (isl_basic_set_alloc_div(bset) < 0)
7868 for (i = div->n_row - 1; i >= 0; --i) {
7869 if (j >= 0 && exp[j] == i) {
7871 isl_basic_map_swap_div(bset, i, j);
7874 isl_seq_cpy(bset->div[i], div->row[i], div->n_col);
7875 if (isl_basic_map_add_div_constraints(bset, i) < 0)
7883 isl_basic_set_free(bset);
7888 /* Look for a div in dst that corresponds to the div "div" in src.
7889 * The divs before "div" in src and dst are assumed to be the same.
7891 * Returns -1 if no corresponding div was found and the position
7892 * of the corresponding div in dst otherwise.
7894 static int find_div(struct isl_basic_map *dst,
7895 struct isl_basic_map *src, unsigned div)
7899 unsigned total = isl_space_dim(src->dim, isl_dim_all);
7901 isl_assert(dst->ctx, div <= dst->n_div, return -1);
7902 for (i = div; i < dst->n_div; ++i)
7903 if (isl_seq_eq(dst->div[i], src->div[div], 1+1+total+div) &&
7904 isl_seq_first_non_zero(dst->div[i]+1+1+total+div,
7905 dst->n_div - div) == -1)
7910 struct isl_basic_map *isl_basic_map_align_divs(
7911 struct isl_basic_map *dst, struct isl_basic_map *src)
7919 if (src->n_div == 0)
7922 for (i = 0; i < src->n_div; ++i)
7923 isl_assert(src->ctx, !isl_int_is_zero(src->div[i][0]), goto error);
7925 src = isl_basic_map_order_divs(src);
7926 dst = isl_basic_map_cow(dst);
7927 dst = isl_basic_map_extend_space(dst, isl_space_copy(dst->dim),
7928 src->n_div, 0, 2 * src->n_div);
7931 total = isl_space_dim(src->dim, isl_dim_all);
7932 for (i = 0; i < src->n_div; ++i) {
7933 int j = find_div(dst, src, i);
7935 j = isl_basic_map_alloc_div(dst);
7938 isl_seq_cpy(dst->div[j], src->div[i], 1+1+total+i);
7939 isl_seq_clr(dst->div[j]+1+1+total+i, dst->n_div - i);
7940 if (isl_basic_map_add_div_constraints(dst, j) < 0)
7944 isl_basic_map_swap_div(dst, i, j);
7948 isl_basic_map_free(dst);
7952 struct isl_basic_set *isl_basic_set_align_divs(
7953 struct isl_basic_set *dst, struct isl_basic_set *src)
7955 return (struct isl_basic_set *)isl_basic_map_align_divs(
7956 (struct isl_basic_map *)dst, (struct isl_basic_map *)src);
7959 struct isl_map *isl_map_align_divs(struct isl_map *map)
7967 map = isl_map_compute_divs(map);
7968 map = isl_map_cow(map);
7972 for (i = 1; i < map->n; ++i)
7973 map->p[0] = isl_basic_map_align_divs(map->p[0], map->p[i]);
7974 for (i = 1; i < map->n; ++i)
7975 map->p[i] = isl_basic_map_align_divs(map->p[i], map->p[0]);
7977 ISL_F_CLR(map, ISL_MAP_NORMALIZED);
7981 struct isl_set *isl_set_align_divs(struct isl_set *set)
7983 return (struct isl_set *)isl_map_align_divs((struct isl_map *)set);
7986 static __isl_give isl_set *set_apply( __isl_take isl_set *set,
7987 __isl_take isl_map *map)
7991 isl_assert(set->ctx, isl_map_compatible_domain(map, set), goto error);
7992 map = isl_map_intersect_domain(map, set);
7993 set = isl_map_range(map);
8001 __isl_give isl_set *isl_set_apply( __isl_take isl_set *set,
8002 __isl_take isl_map *map)
8004 return isl_map_align_params_map_map_and(set, map, &set_apply);
8007 /* There is no need to cow as removing empty parts doesn't change
8008 * the meaning of the set.
8010 struct isl_map *isl_map_remove_empty_parts(struct isl_map *map)
8017 for (i = map->n - 1; i >= 0; --i)
8018 remove_if_empty(map, i);
8023 struct isl_set *isl_set_remove_empty_parts(struct isl_set *set)
8025 return (struct isl_set *)
8026 isl_map_remove_empty_parts((struct isl_map *)set);
8029 struct isl_basic_map *isl_map_copy_basic_map(struct isl_map *map)
8031 struct isl_basic_map *bmap;
8032 if (!map || map->n == 0)
8034 bmap = map->p[map->n-1];
8035 isl_assert(map->ctx, ISL_F_ISSET(bmap, ISL_BASIC_SET_FINAL), return NULL);
8036 return isl_basic_map_copy(bmap);
8039 struct isl_basic_set *isl_set_copy_basic_set(struct isl_set *set)
8041 return (struct isl_basic_set *)
8042 isl_map_copy_basic_map((struct isl_map *)set);
8045 __isl_give isl_map *isl_map_drop_basic_map(__isl_take isl_map *map,
8046 __isl_keep isl_basic_map *bmap)
8052 for (i = map->n-1; i >= 0; --i) {
8053 if (map->p[i] != bmap)
8055 map = isl_map_cow(map);
8058 isl_basic_map_free(map->p[i]);
8059 if (i != map->n-1) {
8060 ISL_F_CLR(map, ISL_SET_NORMALIZED);
8061 map->p[i] = map->p[map->n-1];
8072 struct isl_set *isl_set_drop_basic_set(struct isl_set *set,
8073 struct isl_basic_set *bset)
8075 return (struct isl_set *)isl_map_drop_basic_map((struct isl_map *)set,
8076 (struct isl_basic_map *)bset);
8079 /* Given two basic sets bset1 and bset2, compute the maximal difference
8080 * between the values of dimension pos in bset1 and those in bset2
8081 * for any common value of the parameters and dimensions preceding pos.
8083 static enum isl_lp_result basic_set_maximal_difference_at(
8084 __isl_keep isl_basic_set *bset1, __isl_keep isl_basic_set *bset2,
8085 int pos, isl_int *opt)
8088 struct isl_basic_map *bmap1 = NULL;
8089 struct isl_basic_map *bmap2 = NULL;
8090 struct isl_ctx *ctx;
8091 struct isl_vec *obj;
8094 unsigned dim1, dim2;
8095 enum isl_lp_result res;
8097 if (!bset1 || !bset2)
8098 return isl_lp_error;
8100 nparam = isl_basic_set_n_param(bset1);
8101 dim1 = isl_basic_set_n_dim(bset1);
8102 dim2 = isl_basic_set_n_dim(bset2);
8103 dims = isl_space_alloc(bset1->ctx, nparam, pos, dim1 - pos);
8104 bmap1 = isl_basic_map_from_basic_set(isl_basic_set_copy(bset1), dims);
8105 dims = isl_space_alloc(bset2->ctx, nparam, pos, dim2 - pos);
8106 bmap2 = isl_basic_map_from_basic_set(isl_basic_set_copy(bset2), dims);
8107 if (!bmap1 || !bmap2)
8109 bmap1 = isl_basic_map_cow(bmap1);
8110 bmap1 = isl_basic_map_extend(bmap1, nparam,
8111 pos, (dim1 - pos) + (dim2 - pos),
8112 bmap2->n_div, bmap2->n_eq, bmap2->n_ineq);
8113 bmap1 = add_constraints(bmap1, bmap2, 0, dim1 - pos);
8116 total = isl_basic_map_total_dim(bmap1);
8118 obj = isl_vec_alloc(ctx, 1 + total);
8121 isl_seq_clr(obj->block.data, 1 + total);
8122 isl_int_set_si(obj->block.data[1+nparam+pos], 1);
8123 isl_int_set_si(obj->block.data[1+nparam+pos+(dim1-pos)], -1);
8124 res = isl_basic_map_solve_lp(bmap1, 1, obj->block.data, ctx->one,
8126 isl_basic_map_free(bmap1);
8130 isl_basic_map_free(bmap2);
8132 isl_basic_map_free(bmap1);
8133 return isl_lp_error;
8136 /* Given two _disjoint_ basic sets bset1 and bset2, check whether
8137 * for any common value of the parameters and dimensions preceding pos
8138 * in both basic sets, the values of dimension pos in bset1 are
8139 * smaller or larger than those in bset2.
8142 * 1 if bset1 follows bset2
8143 * -1 if bset1 precedes bset2
8144 * 0 if bset1 and bset2 are incomparable
8145 * -2 if some error occurred.
8147 int isl_basic_set_compare_at(struct isl_basic_set *bset1,
8148 struct isl_basic_set *bset2, int pos)
8151 enum isl_lp_result res;
8156 res = basic_set_maximal_difference_at(bset1, bset2, pos, &opt);
8158 if (res == isl_lp_empty)
8160 else if ((res == isl_lp_ok && isl_int_is_pos(opt)) ||
8161 res == isl_lp_unbounded)
8163 else if (res == isl_lp_ok && isl_int_is_neg(opt))
8172 /* Given two basic sets bset1 and bset2, check whether
8173 * for any common value of the parameters and dimensions preceding pos
8174 * there is a value of dimension pos in bset1 that is larger
8175 * than a value of the same dimension in bset2.
8178 * 1 if there exists such a pair
8179 * 0 if there is no such pair, but there is a pair of equal values
8181 * -2 if some error occurred.
8183 int isl_basic_set_follows_at(__isl_keep isl_basic_set *bset1,
8184 __isl_keep isl_basic_set *bset2, int pos)
8187 enum isl_lp_result res;
8192 res = basic_set_maximal_difference_at(bset1, bset2, pos, &opt);
8194 if (res == isl_lp_empty)
8196 else if ((res == isl_lp_ok && isl_int_is_pos(opt)) ||
8197 res == isl_lp_unbounded)
8199 else if (res == isl_lp_ok && isl_int_is_neg(opt))
8201 else if (res == isl_lp_ok)
8210 /* Given two sets set1 and set2, check whether
8211 * for any common value of the parameters and dimensions preceding pos
8212 * there is a value of dimension pos in set1 that is larger
8213 * than a value of the same dimension in set2.
8216 * 1 if there exists such a pair
8217 * 0 if there is no such pair, but there is a pair of equal values
8219 * -2 if some error occurred.
8221 int isl_set_follows_at(__isl_keep isl_set *set1,
8222 __isl_keep isl_set *set2, int pos)
8230 for (i = 0; i < set1->n; ++i)
8231 for (j = 0; j < set2->n; ++j) {
8233 f = isl_basic_set_follows_at(set1->p[i], set2->p[j], pos);
8234 if (f == 1 || f == -2)
8243 static int isl_basic_map_plain_has_fixed_var(__isl_keep isl_basic_map *bmap,
8244 unsigned pos, isl_int *val)
8252 total = isl_basic_map_total_dim(bmap);
8253 for (i = 0, d = total-1; i < bmap->n_eq && d+1 > pos; ++i) {
8254 for (; d+1 > pos; --d)
8255 if (!isl_int_is_zero(bmap->eq[i][1+d]))
8259 if (isl_seq_first_non_zero(bmap->eq[i]+1, d) != -1)
8261 if (isl_seq_first_non_zero(bmap->eq[i]+1+d+1, total-d-1) != -1)
8263 if (!isl_int_is_one(bmap->eq[i][1+d]))
8266 isl_int_neg(*val, bmap->eq[i][0]);
8272 static int isl_map_plain_has_fixed_var(__isl_keep isl_map *map,
8273 unsigned pos, isl_int *val)
8285 return isl_basic_map_plain_has_fixed_var(map->p[0], pos, val);
8288 fixed = isl_basic_map_plain_has_fixed_var(map->p[0], pos, &v);
8289 for (i = 1; fixed == 1 && i < map->n; ++i) {
8290 fixed = isl_basic_map_plain_has_fixed_var(map->p[i], pos, &tmp);
8291 if (fixed == 1 && isl_int_ne(tmp, v))
8295 isl_int_set(*val, v);
8301 static int isl_basic_set_plain_has_fixed_var(__isl_keep isl_basic_set *bset,
8302 unsigned pos, isl_int *val)
8304 return isl_basic_map_plain_has_fixed_var((struct isl_basic_map *)bset,
8308 static int isl_set_plain_has_fixed_var(__isl_keep isl_set *set, unsigned pos,
8311 return isl_map_plain_has_fixed_var((struct isl_map *)set, pos, val);
8314 int isl_basic_map_plain_is_fixed(__isl_keep isl_basic_map *bmap,
8315 enum isl_dim_type type, unsigned pos, isl_int *val)
8317 if (pos >= isl_basic_map_dim(bmap, type))
8319 return isl_basic_map_plain_has_fixed_var(bmap,
8320 isl_basic_map_offset(bmap, type) - 1 + pos, val);
8323 int isl_map_plain_is_fixed(__isl_keep isl_map *map,
8324 enum isl_dim_type type, unsigned pos, isl_int *val)
8326 if (pos >= isl_map_dim(map, type))
8328 return isl_map_plain_has_fixed_var(map,
8329 map_offset(map, type) - 1 + pos, val);
8332 int isl_set_plain_is_fixed(__isl_keep isl_set *set,
8333 enum isl_dim_type type, unsigned pos, isl_int *val)
8335 return isl_map_plain_is_fixed(set, type, pos, val);
8338 int isl_map_fast_is_fixed(__isl_keep isl_map *map,
8339 enum isl_dim_type type, unsigned pos, isl_int *val)
8341 return isl_map_plain_is_fixed(map, type, pos, val);
8344 /* Check if dimension dim has fixed value and if so and if val is not NULL,
8345 * then return this fixed value in *val.
8347 int isl_basic_set_plain_dim_is_fixed(__isl_keep isl_basic_set *bset,
8348 unsigned dim, isl_int *val)
8350 return isl_basic_set_plain_has_fixed_var(bset,
8351 isl_basic_set_n_param(bset) + dim, val);
8354 /* Check if dimension dim has fixed value and if so and if val is not NULL,
8355 * then return this fixed value in *val.
8357 int isl_set_plain_dim_is_fixed(__isl_keep isl_set *set,
8358 unsigned dim, isl_int *val)
8360 return isl_set_plain_has_fixed_var(set, isl_set_n_param(set) + dim, val);
8363 int isl_set_fast_dim_is_fixed(__isl_keep isl_set *set,
8364 unsigned dim, isl_int *val)
8366 return isl_set_plain_dim_is_fixed(set, dim, val);
8369 /* Check if input variable in has fixed value and if so and if val is not NULL,
8370 * then return this fixed value in *val.
8372 int isl_map_plain_input_is_fixed(__isl_keep isl_map *map,
8373 unsigned in, isl_int *val)
8375 return isl_map_plain_has_fixed_var(map, isl_map_n_param(map) + in, val);
8378 /* Check if dimension dim has an (obvious) fixed lower bound and if so
8379 * and if val is not NULL, then return this lower bound in *val.
8381 int isl_basic_set_plain_dim_has_fixed_lower_bound(
8382 __isl_keep isl_basic_set *bset, unsigned dim, isl_int *val)
8384 int i, i_eq = -1, i_ineq = -1;
8391 total = isl_basic_set_total_dim(bset);
8392 nparam = isl_basic_set_n_param(bset);
8393 for (i = 0; i < bset->n_eq; ++i) {
8394 if (isl_int_is_zero(bset->eq[i][1+nparam+dim]))
8400 for (i = 0; i < bset->n_ineq; ++i) {
8401 if (!isl_int_is_pos(bset->ineq[i][1+nparam+dim]))
8403 if (i_eq != -1 || i_ineq != -1)
8407 if (i_eq == -1 && i_ineq == -1)
8409 c = i_eq != -1 ? bset->eq[i_eq] : bset->ineq[i_ineq];
8410 /* The coefficient should always be one due to normalization. */
8411 if (!isl_int_is_one(c[1+nparam+dim]))
8413 if (isl_seq_first_non_zero(c+1, nparam+dim) != -1)
8415 if (isl_seq_first_non_zero(c+1+nparam+dim+1,
8416 total - nparam - dim - 1) != -1)
8419 isl_int_neg(*val, c[0]);
8423 int isl_set_plain_dim_has_fixed_lower_bound(__isl_keep isl_set *set,
8424 unsigned dim, isl_int *val)
8436 return isl_basic_set_plain_dim_has_fixed_lower_bound(set->p[0],
8440 fixed = isl_basic_set_plain_dim_has_fixed_lower_bound(set->p[0],
8442 for (i = 1; fixed == 1 && i < set->n; ++i) {
8443 fixed = isl_basic_set_plain_dim_has_fixed_lower_bound(set->p[i],
8445 if (fixed == 1 && isl_int_ne(tmp, v))
8449 isl_int_set(*val, v);
8460 /* uset_gist depends on constraints without existentially quantified
8461 * variables sorting first.
8463 static int qsort_constraint_cmp(const void *p1, const void *p2)
8465 const struct constraint *c1 = (const struct constraint *)p1;
8466 const struct constraint *c2 = (const struct constraint *)p2;
8468 unsigned size = isl_min(c1->size, c2->size);
8470 l1 = isl_seq_last_non_zero(c1->c + 1, size);
8471 l2 = isl_seq_last_non_zero(c2->c + 1, size);
8476 return isl_seq_cmp(c1->c + 1, c2->c + 1, size);
8479 static struct isl_basic_map *isl_basic_map_sort_constraints(
8480 struct isl_basic_map *bmap)
8483 struct constraint *c;
8488 total = isl_basic_map_total_dim(bmap);
8489 c = isl_alloc_array(bmap->ctx, struct constraint, bmap->n_ineq);
8492 for (i = 0; i < bmap->n_ineq; ++i) {
8494 c[i].c = bmap->ineq[i];
8496 qsort(c, bmap->n_ineq, sizeof(struct constraint), qsort_constraint_cmp);
8497 for (i = 0; i < bmap->n_ineq; ++i)
8498 bmap->ineq[i] = c[i].c;
8502 isl_basic_map_free(bmap);
8506 __isl_give isl_basic_set *isl_basic_set_sort_constraints(
8507 __isl_take isl_basic_set *bset)
8509 return (struct isl_basic_set *)isl_basic_map_sort_constraints(
8510 (struct isl_basic_map *)bset);
8513 struct isl_basic_map *isl_basic_map_normalize(struct isl_basic_map *bmap)
8517 if (ISL_F_ISSET(bmap, ISL_BASIC_MAP_NORMALIZED))
8519 bmap = isl_basic_map_remove_redundancies(bmap);
8520 bmap = isl_basic_map_sort_constraints(bmap);
8522 ISL_F_SET(bmap, ISL_BASIC_MAP_NORMALIZED);
8526 struct isl_basic_set *isl_basic_set_normalize(struct isl_basic_set *bset)
8528 return (struct isl_basic_set *)isl_basic_map_normalize(
8529 (struct isl_basic_map *)bset);
8532 int isl_basic_map_plain_cmp(const __isl_keep isl_basic_map *bmap1,
8533 const __isl_keep isl_basic_map *bmap2)
8540 if (ISL_F_ISSET(bmap1, ISL_BASIC_MAP_RATIONAL) !=
8541 ISL_F_ISSET(bmap2, ISL_BASIC_MAP_RATIONAL))
8542 return ISL_F_ISSET(bmap1, ISL_BASIC_MAP_RATIONAL) ? -1 : 1;
8543 if (isl_basic_map_n_param(bmap1) != isl_basic_map_n_param(bmap2))
8544 return isl_basic_map_n_param(bmap1) - isl_basic_map_n_param(bmap2);
8545 if (isl_basic_map_n_in(bmap1) != isl_basic_map_n_in(bmap2))
8546 return isl_basic_map_n_out(bmap1) - isl_basic_map_n_out(bmap2);
8547 if (isl_basic_map_n_out(bmap1) != isl_basic_map_n_out(bmap2))
8548 return isl_basic_map_n_out(bmap1) - isl_basic_map_n_out(bmap2);
8549 if (ISL_F_ISSET(bmap1, ISL_BASIC_MAP_EMPTY) &&
8550 ISL_F_ISSET(bmap2, ISL_BASIC_MAP_EMPTY))
8552 if (ISL_F_ISSET(bmap1, ISL_BASIC_MAP_EMPTY))
8554 if (ISL_F_ISSET(bmap2, ISL_BASIC_MAP_EMPTY))
8556 if (bmap1->n_eq != bmap2->n_eq)
8557 return bmap1->n_eq - bmap2->n_eq;
8558 if (bmap1->n_ineq != bmap2->n_ineq)
8559 return bmap1->n_ineq - bmap2->n_ineq;
8560 if (bmap1->n_div != bmap2->n_div)
8561 return bmap1->n_div - bmap2->n_div;
8562 total = isl_basic_map_total_dim(bmap1);
8563 for (i = 0; i < bmap1->n_eq; ++i) {
8564 cmp = isl_seq_cmp(bmap1->eq[i], bmap2->eq[i], 1+total);
8568 for (i = 0; i < bmap1->n_ineq; ++i) {
8569 cmp = isl_seq_cmp(bmap1->ineq[i], bmap2->ineq[i], 1+total);
8573 for (i = 0; i < bmap1->n_div; ++i) {
8574 cmp = isl_seq_cmp(bmap1->div[i], bmap2->div[i], 1+1+total);
8581 int isl_basic_set_plain_cmp(const __isl_keep isl_basic_set *bset1,
8582 const __isl_keep isl_basic_set *bset2)
8584 return isl_basic_map_plain_cmp(bset1, bset2);
8587 int isl_set_plain_cmp(__isl_keep isl_set *set1, __isl_keep isl_set *set2)
8593 if (set1->n != set2->n)
8594 return set1->n - set2->n;
8596 for (i = 0; i < set1->n; ++i) {
8597 cmp = isl_basic_set_plain_cmp(set1->p[i], set2->p[i]);
8605 int isl_basic_map_plain_is_equal(__isl_keep isl_basic_map *bmap1,
8606 __isl_keep isl_basic_map *bmap2)
8608 return isl_basic_map_plain_cmp(bmap1, bmap2) == 0;
8611 int isl_basic_set_plain_is_equal(__isl_keep isl_basic_set *bset1,
8612 __isl_keep isl_basic_set *bset2)
8614 return isl_basic_map_plain_is_equal((isl_basic_map *)bset1,
8615 (isl_basic_map *)bset2);
8618 static int qsort_bmap_cmp(const void *p1, const void *p2)
8620 const struct isl_basic_map *bmap1 = *(const struct isl_basic_map **)p1;
8621 const struct isl_basic_map *bmap2 = *(const struct isl_basic_map **)p2;
8623 return isl_basic_map_plain_cmp(bmap1, bmap2);
8626 /* We normalize in place, but if anything goes wrong we need
8627 * to return NULL, so we need to make sure we don't change the
8628 * meaning of any possible other copies of map.
8630 struct isl_map *isl_map_normalize(struct isl_map *map)
8633 struct isl_basic_map *bmap;
8637 if (ISL_F_ISSET(map, ISL_MAP_NORMALIZED))
8639 for (i = 0; i < map->n; ++i) {
8640 bmap = isl_basic_map_normalize(isl_basic_map_copy(map->p[i]));
8643 isl_basic_map_free(map->p[i]);
8646 qsort(map->p, map->n, sizeof(struct isl_basic_map *), qsort_bmap_cmp);
8647 ISL_F_SET(map, ISL_MAP_NORMALIZED);
8648 map = isl_map_remove_empty_parts(map);
8651 for (i = map->n - 1; i >= 1; --i) {
8652 if (!isl_basic_map_plain_is_equal(map->p[i-1], map->p[i]))
8654 isl_basic_map_free(map->p[i-1]);
8655 for (j = i; j < map->n; ++j)
8656 map->p[j-1] = map->p[j];
8666 struct isl_set *isl_set_normalize(struct isl_set *set)
8668 return (struct isl_set *)isl_map_normalize((struct isl_map *)set);
8671 int isl_map_plain_is_equal(__isl_keep isl_map *map1, __isl_keep isl_map *map2)
8681 if (!isl_space_is_equal(map1->dim, map2->dim))
8684 map1 = isl_map_copy(map1);
8685 map2 = isl_map_copy(map2);
8686 map1 = isl_map_normalize(map1);
8687 map2 = isl_map_normalize(map2);
8690 equal = map1->n == map2->n;
8691 for (i = 0; equal && i < map1->n; ++i) {
8692 equal = isl_basic_map_plain_is_equal(map1->p[i], map2->p[i]);
8705 int isl_map_fast_is_equal(__isl_keep isl_map *map1, __isl_keep isl_map *map2)
8707 return isl_map_plain_is_equal(map1, map2);
8710 int isl_set_plain_is_equal(__isl_keep isl_set *set1, __isl_keep isl_set *set2)
8712 return isl_map_plain_is_equal((struct isl_map *)set1,
8713 (struct isl_map *)set2);
8716 int isl_set_fast_is_equal(__isl_keep isl_set *set1, __isl_keep isl_set *set2)
8718 return isl_set_plain_is_equal(set1, set2);
8721 /* Return an interval that ranges from min to max (inclusive)
8723 struct isl_basic_set *isl_basic_set_interval(struct isl_ctx *ctx,
8724 isl_int min, isl_int max)
8727 struct isl_basic_set *bset = NULL;
8729 bset = isl_basic_set_alloc(ctx, 0, 1, 0, 0, 2);
8733 k = isl_basic_set_alloc_inequality(bset);
8736 isl_int_set_si(bset->ineq[k][1], 1);
8737 isl_int_neg(bset->ineq[k][0], min);
8739 k = isl_basic_set_alloc_inequality(bset);
8742 isl_int_set_si(bset->ineq[k][1], -1);
8743 isl_int_set(bset->ineq[k][0], max);
8747 isl_basic_set_free(bset);
8751 /* Return the Cartesian product of the basic sets in list (in the given order).
8753 __isl_give isl_basic_set *isl_basic_set_list_product(
8754 __isl_take struct isl_basic_set_list *list)
8762 struct isl_basic_set *product = NULL;
8766 isl_assert(list->ctx, list->n > 0, goto error);
8767 isl_assert(list->ctx, list->p[0], goto error);
8768 nparam = isl_basic_set_n_param(list->p[0]);
8769 dim = isl_basic_set_n_dim(list->p[0]);
8770 extra = list->p[0]->n_div;
8771 n_eq = list->p[0]->n_eq;
8772 n_ineq = list->p[0]->n_ineq;
8773 for (i = 1; i < list->n; ++i) {
8774 isl_assert(list->ctx, list->p[i], goto error);
8775 isl_assert(list->ctx,
8776 nparam == isl_basic_set_n_param(list->p[i]), goto error);
8777 dim += isl_basic_set_n_dim(list->p[i]);
8778 extra += list->p[i]->n_div;
8779 n_eq += list->p[i]->n_eq;
8780 n_ineq += list->p[i]->n_ineq;
8782 product = isl_basic_set_alloc(list->ctx, nparam, dim, extra,
8787 for (i = 0; i < list->n; ++i) {
8788 isl_basic_set_add_constraints(product,
8789 isl_basic_set_copy(list->p[i]), dim);
8790 dim += isl_basic_set_n_dim(list->p[i]);
8792 isl_basic_set_list_free(list);
8795 isl_basic_set_free(product);
8796 isl_basic_set_list_free(list);
8800 struct isl_basic_map *isl_basic_map_product(
8801 struct isl_basic_map *bmap1, struct isl_basic_map *bmap2)
8803 isl_space *dim_result = NULL;
8804 struct isl_basic_map *bmap;
8805 unsigned in1, in2, out1, out2, nparam, total, pos;
8806 struct isl_dim_map *dim_map1, *dim_map2;
8808 if (!bmap1 || !bmap2)
8811 isl_assert(bmap1->ctx, isl_space_match(bmap1->dim, isl_dim_param,
8812 bmap2->dim, isl_dim_param), goto error);
8813 dim_result = isl_space_product(isl_space_copy(bmap1->dim),
8814 isl_space_copy(bmap2->dim));
8816 in1 = isl_basic_map_n_in(bmap1);
8817 in2 = isl_basic_map_n_in(bmap2);
8818 out1 = isl_basic_map_n_out(bmap1);
8819 out2 = isl_basic_map_n_out(bmap2);
8820 nparam = isl_basic_map_n_param(bmap1);
8822 total = nparam + in1 + in2 + out1 + out2 + bmap1->n_div + bmap2->n_div;
8823 dim_map1 = isl_dim_map_alloc(bmap1->ctx, total);
8824 dim_map2 = isl_dim_map_alloc(bmap1->ctx, total);
8825 isl_dim_map_dim(dim_map1, bmap1->dim, isl_dim_param, pos = 0);
8826 isl_dim_map_dim(dim_map2, bmap2->dim, isl_dim_param, pos = 0);
8827 isl_dim_map_dim(dim_map1, bmap1->dim, isl_dim_in, pos += nparam);
8828 isl_dim_map_dim(dim_map2, bmap2->dim, isl_dim_in, pos += in1);
8829 isl_dim_map_dim(dim_map1, bmap1->dim, isl_dim_out, pos += in2);
8830 isl_dim_map_dim(dim_map2, bmap2->dim, isl_dim_out, pos += out1);
8831 isl_dim_map_div(dim_map1, bmap1, pos += out2);
8832 isl_dim_map_div(dim_map2, bmap2, pos += bmap1->n_div);
8834 bmap = isl_basic_map_alloc_space(dim_result,
8835 bmap1->n_div + bmap2->n_div,
8836 bmap1->n_eq + bmap2->n_eq,
8837 bmap1->n_ineq + bmap2->n_ineq);
8838 bmap = isl_basic_map_add_constraints_dim_map(bmap, bmap1, dim_map1);
8839 bmap = isl_basic_map_add_constraints_dim_map(bmap, bmap2, dim_map2);
8840 bmap = isl_basic_map_simplify(bmap);
8841 return isl_basic_map_finalize(bmap);
8843 isl_basic_map_free(bmap1);
8844 isl_basic_map_free(bmap2);
8848 __isl_give isl_basic_map *isl_basic_map_flat_product(
8849 __isl_take isl_basic_map *bmap1, __isl_take isl_basic_map *bmap2)
8851 isl_basic_map *prod;
8853 prod = isl_basic_map_product(bmap1, bmap2);
8854 prod = isl_basic_map_flatten(prod);
8858 __isl_give isl_basic_set *isl_basic_set_flat_product(
8859 __isl_take isl_basic_set *bset1, __isl_take isl_basic_set *bset2)
8861 return isl_basic_map_flat_range_product(bset1, bset2);
8864 __isl_give isl_basic_map *isl_basic_map_domain_product(
8865 __isl_take isl_basic_map *bmap1, __isl_take isl_basic_map *bmap2)
8867 isl_space *space_result = NULL;
8868 isl_basic_map *bmap;
8869 unsigned in1, in2, out, nparam, total, pos;
8870 struct isl_dim_map *dim_map1, *dim_map2;
8872 if (!bmap1 || !bmap2)
8875 space_result = isl_space_domain_product(isl_space_copy(bmap1->dim),
8876 isl_space_copy(bmap2->dim));
8878 in1 = isl_basic_map_dim(bmap1, isl_dim_in);
8879 in2 = isl_basic_map_dim(bmap2, isl_dim_in);
8880 out = isl_basic_map_dim(bmap1, isl_dim_out);
8881 nparam = isl_basic_map_dim(bmap1, isl_dim_param);
8883 total = nparam + in1 + in2 + out + bmap1->n_div + bmap2->n_div;
8884 dim_map1 = isl_dim_map_alloc(bmap1->ctx, total);
8885 dim_map2 = isl_dim_map_alloc(bmap1->ctx, total);
8886 isl_dim_map_dim(dim_map1, bmap1->dim, isl_dim_param, pos = 0);
8887 isl_dim_map_dim(dim_map2, bmap2->dim, isl_dim_param, pos = 0);
8888 isl_dim_map_dim(dim_map1, bmap1->dim, isl_dim_in, pos += nparam);
8889 isl_dim_map_dim(dim_map2, bmap2->dim, isl_dim_in, pos += in1);
8890 isl_dim_map_dim(dim_map1, bmap1->dim, isl_dim_out, pos += in2);
8891 isl_dim_map_dim(dim_map2, bmap2->dim, isl_dim_out, pos);
8892 isl_dim_map_div(dim_map1, bmap1, pos += out);
8893 isl_dim_map_div(dim_map2, bmap2, pos += bmap1->n_div);
8895 bmap = isl_basic_map_alloc_space(space_result,
8896 bmap1->n_div + bmap2->n_div,
8897 bmap1->n_eq + bmap2->n_eq,
8898 bmap1->n_ineq + bmap2->n_ineq);
8899 bmap = isl_basic_map_add_constraints_dim_map(bmap, bmap1, dim_map1);
8900 bmap = isl_basic_map_add_constraints_dim_map(bmap, bmap2, dim_map2);
8901 bmap = isl_basic_map_simplify(bmap);
8902 return isl_basic_map_finalize(bmap);
8904 isl_basic_map_free(bmap1);
8905 isl_basic_map_free(bmap2);
8909 __isl_give isl_basic_map *isl_basic_map_range_product(
8910 __isl_take isl_basic_map *bmap1, __isl_take isl_basic_map *bmap2)
8912 isl_space *dim_result = NULL;
8913 isl_basic_map *bmap;
8914 unsigned in, out1, out2, nparam, total, pos;
8915 struct isl_dim_map *dim_map1, *dim_map2;
8917 if (!bmap1 || !bmap2)
8920 if (!isl_space_match(bmap1->dim, isl_dim_param,
8921 bmap2->dim, isl_dim_param))
8922 isl_die(isl_basic_map_get_ctx(bmap1), isl_error_invalid,
8923 "parameters don't match", goto error);
8925 dim_result = isl_space_range_product(isl_space_copy(bmap1->dim),
8926 isl_space_copy(bmap2->dim));
8928 in = isl_basic_map_dim(bmap1, isl_dim_in);
8929 out1 = isl_basic_map_n_out(bmap1);
8930 out2 = isl_basic_map_n_out(bmap2);
8931 nparam = isl_basic_map_n_param(bmap1);
8933 total = nparam + in + out1 + out2 + bmap1->n_div + bmap2->n_div;
8934 dim_map1 = isl_dim_map_alloc(bmap1->ctx, total);
8935 dim_map2 = isl_dim_map_alloc(bmap1->ctx, total);
8936 isl_dim_map_dim(dim_map1, bmap1->dim, isl_dim_param, pos = 0);
8937 isl_dim_map_dim(dim_map2, bmap2->dim, isl_dim_param, pos = 0);
8938 isl_dim_map_dim(dim_map1, bmap1->dim, isl_dim_in, pos += nparam);
8939 isl_dim_map_dim(dim_map2, bmap2->dim, isl_dim_in, pos);
8940 isl_dim_map_dim(dim_map1, bmap1->dim, isl_dim_out, pos += in);
8941 isl_dim_map_dim(dim_map2, bmap2->dim, isl_dim_out, pos += out1);
8942 isl_dim_map_div(dim_map1, bmap1, pos += out2);
8943 isl_dim_map_div(dim_map2, bmap2, pos += bmap1->n_div);
8945 bmap = isl_basic_map_alloc_space(dim_result,
8946 bmap1->n_div + bmap2->n_div,
8947 bmap1->n_eq + bmap2->n_eq,
8948 bmap1->n_ineq + bmap2->n_ineq);
8949 bmap = isl_basic_map_add_constraints_dim_map(bmap, bmap1, dim_map1);
8950 bmap = isl_basic_map_add_constraints_dim_map(bmap, bmap2, dim_map2);
8951 bmap = isl_basic_map_simplify(bmap);
8952 return isl_basic_map_finalize(bmap);
8954 isl_basic_map_free(bmap1);
8955 isl_basic_map_free(bmap2);
8959 __isl_give isl_basic_map *isl_basic_map_flat_range_product(
8960 __isl_take isl_basic_map *bmap1, __isl_take isl_basic_map *bmap2)
8962 isl_basic_map *prod;
8964 prod = isl_basic_map_range_product(bmap1, bmap2);
8965 prod = isl_basic_map_flatten_range(prod);
8969 static __isl_give isl_map *map_product(__isl_take isl_map *map1,
8970 __isl_take isl_map *map2,
8971 __isl_give isl_space *(*dim_product)(__isl_take isl_space *left,
8972 __isl_take isl_space *right),
8973 __isl_give isl_basic_map *(*basic_map_product)(
8974 __isl_take isl_basic_map *left, __isl_take isl_basic_map *right))
8977 struct isl_map *result;
8983 isl_assert(map1->ctx, isl_space_match(map1->dim, isl_dim_param,
8984 map2->dim, isl_dim_param), goto error);
8986 if (ISL_F_ISSET(map1, ISL_MAP_DISJOINT) &&
8987 ISL_F_ISSET(map2, ISL_MAP_DISJOINT))
8988 ISL_FL_SET(flags, ISL_MAP_DISJOINT);
8990 result = isl_map_alloc_space(dim_product(isl_space_copy(map1->dim),
8991 isl_space_copy(map2->dim)),
8992 map1->n * map2->n, flags);
8995 for (i = 0; i < map1->n; ++i)
8996 for (j = 0; j < map2->n; ++j) {
8997 struct isl_basic_map *part;
8998 part = basic_map_product(isl_basic_map_copy(map1->p[i]),
8999 isl_basic_map_copy(map2->p[j]));
9000 if (isl_basic_map_is_empty(part))
9001 isl_basic_map_free(part);
9003 result = isl_map_add_basic_map(result, part);
9016 /* Given two maps A -> B and C -> D, construct a map [A -> C] -> [B -> D]
9018 static __isl_give isl_map *map_product_aligned(__isl_take isl_map *map1,
9019 __isl_take isl_map *map2)
9021 return map_product(map1, map2, &isl_space_product, &isl_basic_map_product);
9024 __isl_give isl_map *isl_map_product(__isl_take isl_map *map1,
9025 __isl_take isl_map *map2)
9027 return isl_map_align_params_map_map_and(map1, map2, &map_product_aligned);
9030 /* Given two maps A -> B and C -> D, construct a map (A, C) -> (B, D)
9032 __isl_give isl_map *isl_map_flat_product(__isl_take isl_map *map1,
9033 __isl_take isl_map *map2)
9037 prod = isl_map_product(map1, map2);
9038 prod = isl_map_flatten(prod);
9042 /* Given two set A and B, construct its Cartesian product A x B.
9044 struct isl_set *isl_set_product(struct isl_set *set1, struct isl_set *set2)
9046 return isl_map_range_product(set1, set2);
9049 __isl_give isl_set *isl_set_flat_product(__isl_take isl_set *set1,
9050 __isl_take isl_set *set2)
9052 return isl_map_flat_range_product(set1, set2);
9055 /* Given two maps A -> B and C -> D, construct a map [A -> C] -> (B * D)
9057 static __isl_give isl_map *map_domain_product_aligned(__isl_take isl_map *map1,
9058 __isl_take isl_map *map2)
9060 return map_product(map1, map2, &isl_space_domain_product,
9061 &isl_basic_map_domain_product);
9064 /* Given two maps A -> B and C -> D, construct a map (A * C) -> [B -> D]
9066 static __isl_give isl_map *map_range_product_aligned(__isl_take isl_map *map1,
9067 __isl_take isl_map *map2)
9069 return map_product(map1, map2, &isl_space_range_product,
9070 &isl_basic_map_range_product);
9073 __isl_give isl_map *isl_map_domain_product(__isl_take isl_map *map1,
9074 __isl_take isl_map *map2)
9076 return isl_map_align_params_map_map_and(map1, map2,
9077 &map_domain_product_aligned);
9080 __isl_give isl_map *isl_map_range_product(__isl_take isl_map *map1,
9081 __isl_take isl_map *map2)
9083 return isl_map_align_params_map_map_and(map1, map2,
9084 &map_range_product_aligned);
9087 /* Given two maps A -> B and C -> D, construct a map (A, C) -> (B * D)
9089 __isl_give isl_map *isl_map_flat_domain_product(__isl_take isl_map *map1,
9090 __isl_take isl_map *map2)
9094 prod = isl_map_domain_product(map1, map2);
9095 prod = isl_map_flatten_domain(prod);
9099 /* Given two maps A -> B and C -> D, construct a map (A * C) -> (B, D)
9101 __isl_give isl_map *isl_map_flat_range_product(__isl_take isl_map *map1,
9102 __isl_take isl_map *map2)
9106 prod = isl_map_range_product(map1, map2);
9107 prod = isl_map_flatten_range(prod);
9111 uint32_t isl_basic_map_get_hash(__isl_keep isl_basic_map *bmap)
9114 uint32_t hash = isl_hash_init();
9119 bmap = isl_basic_map_copy(bmap);
9120 bmap = isl_basic_map_normalize(bmap);
9123 total = isl_basic_map_total_dim(bmap);
9124 isl_hash_byte(hash, bmap->n_eq & 0xFF);
9125 for (i = 0; i < bmap->n_eq; ++i) {
9127 c_hash = isl_seq_get_hash(bmap->eq[i], 1 + total);
9128 isl_hash_hash(hash, c_hash);
9130 isl_hash_byte(hash, bmap->n_ineq & 0xFF);
9131 for (i = 0; i < bmap->n_ineq; ++i) {
9133 c_hash = isl_seq_get_hash(bmap->ineq[i], 1 + total);
9134 isl_hash_hash(hash, c_hash);
9136 isl_hash_byte(hash, bmap->n_div & 0xFF);
9137 for (i = 0; i < bmap->n_div; ++i) {
9139 if (isl_int_is_zero(bmap->div[i][0]))
9141 isl_hash_byte(hash, i & 0xFF);
9142 c_hash = isl_seq_get_hash(bmap->div[i], 1 + 1 + total);
9143 isl_hash_hash(hash, c_hash);
9145 isl_basic_map_free(bmap);
9149 uint32_t isl_basic_set_get_hash(__isl_keep isl_basic_set *bset)
9151 return isl_basic_map_get_hash((isl_basic_map *)bset);
9154 uint32_t isl_map_get_hash(__isl_keep isl_map *map)
9161 map = isl_map_copy(map);
9162 map = isl_map_normalize(map);
9166 hash = isl_hash_init();
9167 for (i = 0; i < map->n; ++i) {
9169 bmap_hash = isl_basic_map_get_hash(map->p[i]);
9170 isl_hash_hash(hash, bmap_hash);
9178 uint32_t isl_set_get_hash(__isl_keep isl_set *set)
9180 return isl_map_get_hash((isl_map *)set);
9183 /* Check if the value for dimension dim is completely determined
9184 * by the values of the other parameters and variables.
9185 * That is, check if dimension dim is involved in an equality.
9187 int isl_basic_set_dim_is_unique(struct isl_basic_set *bset, unsigned dim)
9194 nparam = isl_basic_set_n_param(bset);
9195 for (i = 0; i < bset->n_eq; ++i)
9196 if (!isl_int_is_zero(bset->eq[i][1 + nparam + dim]))
9201 /* Check if the value for dimension dim is completely determined
9202 * by the values of the other parameters and variables.
9203 * That is, check if dimension dim is involved in an equality
9204 * for each of the subsets.
9206 int isl_set_dim_is_unique(struct isl_set *set, unsigned dim)
9212 for (i = 0; i < set->n; ++i) {
9214 unique = isl_basic_set_dim_is_unique(set->p[i], dim);
9221 int isl_set_n_basic_set(__isl_keep isl_set *set)
9223 return set ? set->n : 0;
9226 int isl_map_foreach_basic_map(__isl_keep isl_map *map,
9227 int (*fn)(__isl_take isl_basic_map *bmap, void *user), void *user)
9234 for (i = 0; i < map->n; ++i)
9235 if (fn(isl_basic_map_copy(map->p[i]), user) < 0)
9241 int isl_set_foreach_basic_set(__isl_keep isl_set *set,
9242 int (*fn)(__isl_take isl_basic_set *bset, void *user), void *user)
9249 for (i = 0; i < set->n; ++i)
9250 if (fn(isl_basic_set_copy(set->p[i]), user) < 0)
9256 __isl_give isl_basic_set *isl_basic_set_lift(__isl_take isl_basic_set *bset)
9263 bset = isl_basic_set_cow(bset);
9267 dim = isl_basic_set_get_space(bset);
9268 dim = isl_space_lift(dim, bset->n_div);
9271 isl_space_free(bset->dim);
9273 bset->extra -= bset->n_div;
9276 bset = isl_basic_set_finalize(bset);
9280 isl_basic_set_free(bset);
9284 __isl_give isl_set *isl_set_lift(__isl_take isl_set *set)
9290 set = isl_set_align_divs(set);
9295 set = isl_set_cow(set);
9299 n_div = set->p[0]->n_div;
9300 dim = isl_set_get_space(set);
9301 dim = isl_space_lift(dim, n_div);
9304 isl_space_free(set->dim);
9307 for (i = 0; i < set->n; ++i) {
9308 set->p[i] = isl_basic_set_lift(set->p[i]);
9319 __isl_give isl_map *isl_set_lifting(__isl_take isl_set *set)
9322 struct isl_basic_map *bmap;
9329 set = isl_set_align_divs(set);
9334 dim = isl_set_get_space(set);
9335 if (set->n == 0 || set->p[0]->n_div == 0) {
9337 return isl_map_identity(isl_space_map_from_set(dim));
9340 n_div = set->p[0]->n_div;
9341 dim = isl_space_map_from_set(dim);
9342 n_param = isl_space_dim(dim, isl_dim_param);
9343 n_set = isl_space_dim(dim, isl_dim_in);
9344 dim = isl_space_extend(dim, n_param, n_set, n_set + n_div);
9345 bmap = isl_basic_map_alloc_space(dim, 0, n_set, 2 * n_div);
9346 for (i = 0; i < n_set; ++i)
9347 bmap = var_equal(bmap, i);
9349 total = n_param + n_set + n_set + n_div;
9350 for (i = 0; i < n_div; ++i) {
9351 k = isl_basic_map_alloc_inequality(bmap);
9354 isl_seq_cpy(bmap->ineq[k], set->p[0]->div[i]+1, 1+n_param);
9355 isl_seq_clr(bmap->ineq[k]+1+n_param, n_set);
9356 isl_seq_cpy(bmap->ineq[k]+1+n_param+n_set,
9357 set->p[0]->div[i]+1+1+n_param, n_set + n_div);
9358 isl_int_neg(bmap->ineq[k][1+n_param+n_set+n_set+i],
9359 set->p[0]->div[i][0]);
9361 l = isl_basic_map_alloc_inequality(bmap);
9364 isl_seq_neg(bmap->ineq[l], bmap->ineq[k], 1 + total);
9365 isl_int_add(bmap->ineq[l][0], bmap->ineq[l][0],
9366 set->p[0]->div[i][0]);
9367 isl_int_sub_ui(bmap->ineq[l][0], bmap->ineq[l][0], 1);
9371 bmap = isl_basic_map_simplify(bmap);
9372 bmap = isl_basic_map_finalize(bmap);
9373 return isl_map_from_basic_map(bmap);
9376 isl_basic_map_free(bmap);
9380 int isl_basic_set_size(__isl_keep isl_basic_set *bset)
9388 dim = isl_basic_set_total_dim(bset);
9389 size += bset->n_eq * (1 + dim);
9390 size += bset->n_ineq * (1 + dim);
9391 size += bset->n_div * (2 + dim);
9396 int isl_set_size(__isl_keep isl_set *set)
9404 for (i = 0; i < set->n; ++i)
9405 size += isl_basic_set_size(set->p[i]);
9410 /* Check if there is any lower bound (if lower == 0) and/or upper
9411 * bound (if upper == 0) on the specified dim.
9413 static int basic_map_dim_is_bounded(__isl_keep isl_basic_map *bmap,
9414 enum isl_dim_type type, unsigned pos, int lower, int upper)
9421 isl_assert(bmap->ctx, pos < isl_basic_map_dim(bmap, type), return -1);
9423 pos += isl_basic_map_offset(bmap, type);
9425 for (i = 0; i < bmap->n_div; ++i) {
9426 if (isl_int_is_zero(bmap->div[i][0]))
9428 if (!isl_int_is_zero(bmap->div[i][1 + pos]))
9432 for (i = 0; i < bmap->n_eq; ++i)
9433 if (!isl_int_is_zero(bmap->eq[i][pos]))
9436 for (i = 0; i < bmap->n_ineq; ++i) {
9437 int sgn = isl_int_sgn(bmap->ineq[i][pos]);
9444 return lower && upper;
9447 int isl_basic_map_dim_is_bounded(__isl_keep isl_basic_map *bmap,
9448 enum isl_dim_type type, unsigned pos)
9450 return basic_map_dim_is_bounded(bmap, type, pos, 0, 0);
9453 int isl_basic_map_dim_has_lower_bound(__isl_keep isl_basic_map *bmap,
9454 enum isl_dim_type type, unsigned pos)
9456 return basic_map_dim_is_bounded(bmap, type, pos, 0, 1);
9459 int isl_basic_map_dim_has_upper_bound(__isl_keep isl_basic_map *bmap,
9460 enum isl_dim_type type, unsigned pos)
9462 return basic_map_dim_is_bounded(bmap, type, pos, 1, 0);
9465 int isl_map_dim_is_bounded(__isl_keep isl_map *map,
9466 enum isl_dim_type type, unsigned pos)
9473 for (i = 0; i < map->n; ++i) {
9475 bounded = isl_basic_map_dim_is_bounded(map->p[i], type, pos);
9476 if (bounded < 0 || !bounded)
9483 /* Return 1 if the specified dim is involved in both an upper bound
9484 * and a lower bound.
9486 int isl_set_dim_is_bounded(__isl_keep isl_set *set,
9487 enum isl_dim_type type, unsigned pos)
9489 return isl_map_dim_is_bounded((isl_map *)set, type, pos);
9492 /* Does "map" have a bound (according to "fn") for any of its basic maps?
9494 static int has_any_bound(__isl_keep isl_map *map,
9495 enum isl_dim_type type, unsigned pos,
9496 int (*fn)(__isl_keep isl_basic_map *bmap,
9497 enum isl_dim_type type, unsigned pos))
9504 for (i = 0; i < map->n; ++i) {
9506 bounded = fn(map->p[i], type, pos);
9507 if (bounded < 0 || bounded)
9514 /* Return 1 if the specified dim is involved in any lower bound.
9516 int isl_set_dim_has_any_lower_bound(__isl_keep isl_set *set,
9517 enum isl_dim_type type, unsigned pos)
9519 return has_any_bound(set, type, pos,
9520 &isl_basic_map_dim_has_lower_bound);
9523 /* Return 1 if the specified dim is involved in any upper bound.
9525 int isl_set_dim_has_any_upper_bound(__isl_keep isl_set *set,
9526 enum isl_dim_type type, unsigned pos)
9528 return has_any_bound(set, type, pos,
9529 &isl_basic_map_dim_has_upper_bound);
9532 /* Does "map" have a bound (according to "fn") for all of its basic maps?
9534 static int has_bound(__isl_keep isl_map *map,
9535 enum isl_dim_type type, unsigned pos,
9536 int (*fn)(__isl_keep isl_basic_map *bmap,
9537 enum isl_dim_type type, unsigned pos))
9544 for (i = 0; i < map->n; ++i) {
9546 bounded = fn(map->p[i], type, pos);
9547 if (bounded < 0 || !bounded)
9554 /* Return 1 if the specified dim has a lower bound (in each of its basic sets).
9556 int isl_set_dim_has_lower_bound(__isl_keep isl_set *set,
9557 enum isl_dim_type type, unsigned pos)
9559 return has_bound(set, type, pos, &isl_basic_map_dim_has_lower_bound);
9562 /* Return 1 if the specified dim has an upper bound (in each of its basic sets).
9564 int isl_set_dim_has_upper_bound(__isl_keep isl_set *set,
9565 enum isl_dim_type type, unsigned pos)
9567 return has_bound(set, type, pos, &isl_basic_map_dim_has_upper_bound);
9570 /* For each of the "n" variables starting at "first", determine
9571 * the sign of the variable and put the results in the first "n"
9572 * elements of the array "signs".
9574 * 1 means that the variable is non-negative
9575 * -1 means that the variable is non-positive
9576 * 0 means the variable attains both positive and negative values.
9578 int isl_basic_set_vars_get_sign(__isl_keep isl_basic_set *bset,
9579 unsigned first, unsigned n, int *signs)
9581 isl_vec *bound = NULL;
9582 struct isl_tab *tab = NULL;
9583 struct isl_tab_undo *snap;
9586 if (!bset || !signs)
9589 bound = isl_vec_alloc(bset->ctx, 1 + isl_basic_set_total_dim(bset));
9590 tab = isl_tab_from_basic_set(bset, 0);
9594 isl_seq_clr(bound->el, bound->size);
9595 isl_int_set_si(bound->el[0], -1);
9597 snap = isl_tab_snap(tab);
9598 for (i = 0; i < n; ++i) {
9601 isl_int_set_si(bound->el[1 + first + i], -1);
9602 if (isl_tab_add_ineq(tab, bound->el) < 0)
9605 isl_int_set_si(bound->el[1 + first + i], 0);
9606 if (isl_tab_rollback(tab, snap) < 0)
9614 isl_int_set_si(bound->el[1 + first + i], 1);
9615 if (isl_tab_add_ineq(tab, bound->el) < 0)
9618 isl_int_set_si(bound->el[1 + first + i], 0);
9619 if (isl_tab_rollback(tab, snap) < 0)
9622 signs[i] = empty ? -1 : 0;
9626 isl_vec_free(bound);
9630 isl_vec_free(bound);
9634 int isl_basic_set_dims_get_sign(__isl_keep isl_basic_set *bset,
9635 enum isl_dim_type type, unsigned first, unsigned n, int *signs)
9637 if (!bset || !signs)
9639 isl_assert(bset->ctx, first + n <= isl_basic_set_dim(bset, type),
9642 first += pos(bset->dim, type) - 1;
9643 return isl_basic_set_vars_get_sign(bset, first, n, signs);
9646 /* Check if the given basic map is obviously single-valued.
9647 * In particular, for each output dimension, check that there is
9648 * an equality that defines the output dimension in terms of
9649 * earlier dimensions.
9651 int isl_basic_map_plain_is_single_valued(__isl_keep isl_basic_map *bmap)
9661 total = 1 + isl_basic_map_total_dim(bmap);
9662 n_out = isl_basic_map_dim(bmap, isl_dim_out);
9663 o_out = isl_basic_map_offset(bmap, isl_dim_out);
9665 for (i = 0; i < n_out; ++i) {
9666 for (j = 0; j < bmap->n_eq; ++j) {
9667 if (isl_int_is_zero(bmap->eq[j][o_out + i]))
9669 if (isl_seq_first_non_zero(bmap->eq[j] + o_out + i + 1,
9670 total - (o_out + i + 1)) == -1)
9673 if (j >= bmap->n_eq)
9680 /* Check if the given basic map is single-valued.
9685 * and check if the result is a subset of the identity mapping.
9687 int isl_basic_map_is_single_valued(__isl_keep isl_basic_map *bmap)
9690 isl_basic_map *test;
9694 sv = isl_basic_map_plain_is_single_valued(bmap);
9698 test = isl_basic_map_reverse(isl_basic_map_copy(bmap));
9699 test = isl_basic_map_apply_range(test, isl_basic_map_copy(bmap));
9701 space = isl_basic_map_get_space(bmap);
9702 space = isl_space_map_from_set(isl_space_range(space));
9703 id = isl_basic_map_identity(space);
9705 sv = isl_basic_map_is_subset(test, id);
9707 isl_basic_map_free(test);
9708 isl_basic_map_free(id);
9713 /* Check if the given map is obviously single-valued.
9715 int isl_map_plain_is_single_valued(__isl_keep isl_map *map)
9724 return isl_basic_map_plain_is_single_valued(map->p[0]);
9727 /* Check if the given map is single-valued.
9732 * and check if the result is a subset of the identity mapping.
9734 int isl_map_is_single_valued(__isl_keep isl_map *map)
9741 sv = isl_map_plain_is_single_valued(map);
9745 test = isl_map_reverse(isl_map_copy(map));
9746 test = isl_map_apply_range(test, isl_map_copy(map));
9748 dim = isl_space_map_from_set(isl_space_range(isl_map_get_space(map)));
9749 id = isl_map_identity(dim);
9751 sv = isl_map_is_subset(test, id);
9759 int isl_map_is_injective(__isl_keep isl_map *map)
9763 map = isl_map_copy(map);
9764 map = isl_map_reverse(map);
9765 in = isl_map_is_single_valued(map);
9771 /* Check if the given map is obviously injective.
9773 int isl_map_plain_is_injective(__isl_keep isl_map *map)
9777 map = isl_map_copy(map);
9778 map = isl_map_reverse(map);
9779 in = isl_map_plain_is_single_valued(map);
9785 int isl_map_is_bijective(__isl_keep isl_map *map)
9789 sv = isl_map_is_single_valued(map);
9793 return isl_map_is_injective(map);
9796 int isl_set_is_singleton(__isl_keep isl_set *set)
9798 return isl_map_is_single_valued((isl_map *)set);
9801 int isl_map_is_translation(__isl_keep isl_map *map)
9806 delta = isl_map_deltas(isl_map_copy(map));
9807 ok = isl_set_is_singleton(delta);
9808 isl_set_free(delta);
9813 static int unique(isl_int *p, unsigned pos, unsigned len)
9815 if (isl_seq_first_non_zero(p, pos) != -1)
9817 if (isl_seq_first_non_zero(p + pos + 1, len - pos - 1) != -1)
9822 int isl_basic_set_is_box(__isl_keep isl_basic_set *bset)
9831 if (isl_basic_set_dim(bset, isl_dim_div) != 0)
9834 nvar = isl_basic_set_dim(bset, isl_dim_set);
9835 ovar = isl_space_offset(bset->dim, isl_dim_set);
9836 for (j = 0; j < nvar; ++j) {
9837 int lower = 0, upper = 0;
9838 for (i = 0; i < bset->n_eq; ++i) {
9839 if (isl_int_is_zero(bset->eq[i][1 + ovar + j]))
9841 if (!unique(bset->eq[i] + 1 + ovar, j, nvar))
9847 for (i = 0; i < bset->n_ineq; ++i) {
9848 if (isl_int_is_zero(bset->ineq[i][1 + ovar + j]))
9850 if (!unique(bset->ineq[i] + 1 + ovar, j, nvar))
9852 if (isl_int_is_pos(bset->ineq[i][1 + ovar + j]))
9857 if (!lower || !upper)
9864 int isl_set_is_box(__isl_keep isl_set *set)
9871 return isl_basic_set_is_box(set->p[0]);
9874 int isl_basic_set_is_wrapping(__isl_keep isl_basic_set *bset)
9879 return isl_space_is_wrapping(bset->dim);
9882 int isl_set_is_wrapping(__isl_keep isl_set *set)
9887 return isl_space_is_wrapping(set->dim);
9890 __isl_give isl_basic_set *isl_basic_map_wrap(__isl_take isl_basic_map *bmap)
9892 bmap = isl_basic_map_cow(bmap);
9896 bmap->dim = isl_space_wrap(bmap->dim);
9900 bmap = isl_basic_map_finalize(bmap);
9902 return (isl_basic_set *)bmap;
9904 isl_basic_map_free(bmap);
9908 __isl_give isl_set *isl_map_wrap(__isl_take isl_map *map)
9912 map = isl_map_cow(map);
9916 for (i = 0; i < map->n; ++i) {
9917 map->p[i] = (isl_basic_map *)isl_basic_map_wrap(map->p[i]);
9921 map->dim = isl_space_wrap(map->dim);
9925 return (isl_set *)map;
9931 __isl_give isl_basic_map *isl_basic_set_unwrap(__isl_take isl_basic_set *bset)
9933 bset = isl_basic_set_cow(bset);
9937 bset->dim = isl_space_unwrap(bset->dim);
9941 bset = isl_basic_set_finalize(bset);
9943 return (isl_basic_map *)bset;
9945 isl_basic_set_free(bset);
9949 __isl_give isl_map *isl_set_unwrap(__isl_take isl_set *set)
9956 if (!isl_set_is_wrapping(set))
9957 isl_die(set->ctx, isl_error_invalid, "not a wrapping set",
9960 set = isl_set_cow(set);
9964 for (i = 0; i < set->n; ++i) {
9965 set->p[i] = (isl_basic_set *)isl_basic_set_unwrap(set->p[i]);
9970 set->dim = isl_space_unwrap(set->dim);
9974 return (isl_map *)set;
9980 __isl_give isl_basic_map *isl_basic_map_reset(__isl_take isl_basic_map *bmap,
9981 enum isl_dim_type type)
9986 if (!isl_space_is_named_or_nested(bmap->dim, type))
9989 bmap = isl_basic_map_cow(bmap);
9993 bmap->dim = isl_space_reset(bmap->dim, type);
9997 bmap = isl_basic_map_finalize(bmap);
10001 isl_basic_map_free(bmap);
10005 __isl_give isl_map *isl_map_reset(__isl_take isl_map *map,
10006 enum isl_dim_type type)
10013 if (!isl_space_is_named_or_nested(map->dim, type))
10016 map = isl_map_cow(map);
10020 for (i = 0; i < map->n; ++i) {
10021 map->p[i] = isl_basic_map_reset(map->p[i], type);
10025 map->dim = isl_space_reset(map->dim, type);
10035 __isl_give isl_basic_map *isl_basic_map_flatten(__isl_take isl_basic_map *bmap)
10040 if (!bmap->dim->nested[0] && !bmap->dim->nested[1])
10043 bmap = isl_basic_map_cow(bmap);
10047 bmap->dim = isl_space_flatten(bmap->dim);
10051 bmap = isl_basic_map_finalize(bmap);
10055 isl_basic_map_free(bmap);
10059 __isl_give isl_basic_set *isl_basic_set_flatten(__isl_take isl_basic_set *bset)
10061 return (isl_basic_set *)isl_basic_map_flatten((isl_basic_map *)bset);
10064 __isl_give isl_basic_map *isl_basic_map_flatten_domain(
10065 __isl_take isl_basic_map *bmap)
10070 if (!bmap->dim->nested[0])
10073 bmap = isl_basic_map_cow(bmap);
10077 bmap->dim = isl_space_flatten_domain(bmap->dim);
10081 bmap = isl_basic_map_finalize(bmap);
10085 isl_basic_map_free(bmap);
10089 __isl_give isl_basic_map *isl_basic_map_flatten_range(
10090 __isl_take isl_basic_map *bmap)
10095 if (!bmap->dim->nested[1])
10098 bmap = isl_basic_map_cow(bmap);
10102 bmap->dim = isl_space_flatten_range(bmap->dim);
10106 bmap = isl_basic_map_finalize(bmap);
10110 isl_basic_map_free(bmap);
10114 __isl_give isl_map *isl_map_flatten(__isl_take isl_map *map)
10121 if (!map->dim->nested[0] && !map->dim->nested[1])
10124 map = isl_map_cow(map);
10128 for (i = 0; i < map->n; ++i) {
10129 map->p[i] = isl_basic_map_flatten(map->p[i]);
10133 map->dim = isl_space_flatten(map->dim);
10143 __isl_give isl_set *isl_set_flatten(__isl_take isl_set *set)
10145 return (isl_set *)isl_map_flatten((isl_map *)set);
10148 __isl_give isl_map *isl_set_flatten_map(__isl_take isl_set *set)
10150 isl_space *dim, *flat_dim;
10153 dim = isl_set_get_space(set);
10154 flat_dim = isl_space_flatten(isl_space_copy(dim));
10155 map = isl_map_identity(isl_space_join(isl_space_reverse(dim), flat_dim));
10156 map = isl_map_intersect_domain(map, set);
10161 __isl_give isl_map *isl_map_flatten_domain(__isl_take isl_map *map)
10168 if (!map->dim->nested[0])
10171 map = isl_map_cow(map);
10175 for (i = 0; i < map->n; ++i) {
10176 map->p[i] = isl_basic_map_flatten_domain(map->p[i]);
10180 map->dim = isl_space_flatten_domain(map->dim);
10190 __isl_give isl_map *isl_map_flatten_range(__isl_take isl_map *map)
10197 if (!map->dim->nested[1])
10200 map = isl_map_cow(map);
10204 for (i = 0; i < map->n; ++i) {
10205 map->p[i] = isl_basic_map_flatten_range(map->p[i]);
10209 map->dim = isl_space_flatten_range(map->dim);
10219 /* Reorder the dimensions of "bmap" according to the given dim_map
10220 * and set the dimension specification to "dim".
10222 __isl_give isl_basic_map *isl_basic_map_realign(__isl_take isl_basic_map *bmap,
10223 __isl_take isl_space *dim, __isl_take struct isl_dim_map *dim_map)
10225 isl_basic_map *res;
10228 bmap = isl_basic_map_cow(bmap);
10229 if (!bmap || !dim || !dim_map)
10232 flags = bmap->flags;
10233 ISL_FL_CLR(flags, ISL_BASIC_MAP_FINAL);
10234 ISL_FL_CLR(flags, ISL_BASIC_MAP_NORMALIZED);
10235 ISL_FL_CLR(flags, ISL_BASIC_MAP_NORMALIZED_DIVS);
10236 res = isl_basic_map_alloc_space(dim,
10237 bmap->n_div, bmap->n_eq, bmap->n_ineq);
10238 res = isl_basic_map_add_constraints_dim_map(res, bmap, dim_map);
10240 res->flags = flags;
10241 res = isl_basic_map_finalize(res);
10245 isl_basic_map_free(bmap);
10246 isl_space_free(dim);
10250 /* Reorder the dimensions of "map" according to given reordering.
10252 __isl_give isl_map *isl_map_realign(__isl_take isl_map *map,
10253 __isl_take isl_reordering *r)
10256 struct isl_dim_map *dim_map;
10258 map = isl_map_cow(map);
10259 dim_map = isl_dim_map_from_reordering(r);
10260 if (!map || !r || !dim_map)
10263 for (i = 0; i < map->n; ++i) {
10264 struct isl_dim_map *dim_map_i;
10266 dim_map_i = isl_dim_map_extend(dim_map, map->p[i]);
10268 map->p[i] = isl_basic_map_realign(map->p[i],
10269 isl_space_copy(r->dim), dim_map_i);
10275 map = isl_map_reset_space(map, isl_space_copy(r->dim));
10277 isl_reordering_free(r);
10283 isl_reordering_free(r);
10287 __isl_give isl_set *isl_set_realign(__isl_take isl_set *set,
10288 __isl_take isl_reordering *r)
10290 return (isl_set *)isl_map_realign((isl_map *)set, r);
10293 __isl_give isl_map *isl_map_align_params(__isl_take isl_map *map,
10294 __isl_take isl_space *model)
10298 if (!map || !model)
10301 ctx = isl_space_get_ctx(model);
10302 if (!isl_space_has_named_params(model))
10303 isl_die(ctx, isl_error_invalid,
10304 "model has unnamed parameters", goto error);
10305 if (!isl_space_has_named_params(map->dim))
10306 isl_die(ctx, isl_error_invalid,
10307 "relation has unnamed parameters", goto error);
10308 if (!isl_space_match(map->dim, isl_dim_param, model, isl_dim_param)) {
10309 isl_reordering *exp;
10311 model = isl_space_drop_dims(model, isl_dim_in,
10312 0, isl_space_dim(model, isl_dim_in));
10313 model = isl_space_drop_dims(model, isl_dim_out,
10314 0, isl_space_dim(model, isl_dim_out));
10315 exp = isl_parameter_alignment_reordering(map->dim, model);
10316 exp = isl_reordering_extend_space(exp, isl_map_get_space(map));
10317 map = isl_map_realign(map, exp);
10320 isl_space_free(model);
10323 isl_space_free(model);
10328 __isl_give isl_set *isl_set_align_params(__isl_take isl_set *set,
10329 __isl_take isl_space *model)
10331 return isl_map_align_params(set, model);
10334 /* Align the parameters of "bmap" to those of "model", introducing
10335 * additional parameters if needed.
10337 __isl_give isl_basic_map *isl_basic_map_align_params(
10338 __isl_take isl_basic_map *bmap, __isl_take isl_space *model)
10342 if (!bmap || !model)
10345 ctx = isl_space_get_ctx(model);
10346 if (!isl_space_has_named_params(model))
10347 isl_die(ctx, isl_error_invalid,
10348 "model has unnamed parameters", goto error);
10349 if (!isl_space_has_named_params(bmap->dim))
10350 isl_die(ctx, isl_error_invalid,
10351 "relation has unnamed parameters", goto error);
10352 if (!isl_space_match(bmap->dim, isl_dim_param, model, isl_dim_param)) {
10353 isl_reordering *exp;
10354 struct isl_dim_map *dim_map;
10356 model = isl_space_drop_dims(model, isl_dim_in,
10357 0, isl_space_dim(model, isl_dim_in));
10358 model = isl_space_drop_dims(model, isl_dim_out,
10359 0, isl_space_dim(model, isl_dim_out));
10360 exp = isl_parameter_alignment_reordering(bmap->dim, model);
10361 exp = isl_reordering_extend_space(exp,
10362 isl_basic_map_get_space(bmap));
10363 dim_map = isl_dim_map_from_reordering(exp);
10364 bmap = isl_basic_map_realign(bmap,
10365 exp ? isl_space_copy(exp->dim) : NULL,
10366 isl_dim_map_extend(dim_map, bmap));
10367 isl_reordering_free(exp);
10371 isl_space_free(model);
10374 isl_space_free(model);
10375 isl_basic_map_free(bmap);
10379 /* Align the parameters of "bset" to those of "model", introducing
10380 * additional parameters if needed.
10382 __isl_give isl_basic_set *isl_basic_set_align_params(
10383 __isl_take isl_basic_set *bset, __isl_take isl_space *model)
10385 return isl_basic_map_align_params(bset, model);
10388 __isl_give isl_mat *isl_basic_map_equalities_matrix(
10389 __isl_keep isl_basic_map *bmap, enum isl_dim_type c1,
10390 enum isl_dim_type c2, enum isl_dim_type c3,
10391 enum isl_dim_type c4, enum isl_dim_type c5)
10393 enum isl_dim_type c[5] = { c1, c2, c3, c4, c5 };
10394 struct isl_mat *mat;
10400 mat = isl_mat_alloc(bmap->ctx, bmap->n_eq,
10401 isl_basic_map_total_dim(bmap) + 1);
10404 for (i = 0; i < bmap->n_eq; ++i)
10405 for (j = 0, pos = 0; j < 5; ++j) {
10406 int off = isl_basic_map_offset(bmap, c[j]);
10407 for (k = 0; k < isl_basic_map_dim(bmap, c[j]); ++k) {
10408 isl_int_set(mat->row[i][pos],
10409 bmap->eq[i][off + k]);
10417 __isl_give isl_mat *isl_basic_map_inequalities_matrix(
10418 __isl_keep isl_basic_map *bmap, enum isl_dim_type c1,
10419 enum isl_dim_type c2, enum isl_dim_type c3,
10420 enum isl_dim_type c4, enum isl_dim_type c5)
10422 enum isl_dim_type c[5] = { c1, c2, c3, c4, c5 };
10423 struct isl_mat *mat;
10429 mat = isl_mat_alloc(bmap->ctx, bmap->n_ineq,
10430 isl_basic_map_total_dim(bmap) + 1);
10433 for (i = 0; i < bmap->n_ineq; ++i)
10434 for (j = 0, pos = 0; j < 5; ++j) {
10435 int off = isl_basic_map_offset(bmap, c[j]);
10436 for (k = 0; k < isl_basic_map_dim(bmap, c[j]); ++k) {
10437 isl_int_set(mat->row[i][pos],
10438 bmap->ineq[i][off + k]);
10446 __isl_give isl_basic_map *isl_basic_map_from_constraint_matrices(
10447 __isl_take isl_space *dim,
10448 __isl_take isl_mat *eq, __isl_take isl_mat *ineq, enum isl_dim_type c1,
10449 enum isl_dim_type c2, enum isl_dim_type c3,
10450 enum isl_dim_type c4, enum isl_dim_type c5)
10452 enum isl_dim_type c[5] = { c1, c2, c3, c4, c5 };
10453 isl_basic_map *bmap;
10459 if (!dim || !eq || !ineq)
10462 if (eq->n_col != ineq->n_col)
10463 isl_die(dim->ctx, isl_error_invalid,
10464 "equalities and inequalities matrices should have "
10465 "same number of columns", goto error);
10467 total = 1 + isl_space_dim(dim, isl_dim_all);
10469 if (eq->n_col < total)
10470 isl_die(dim->ctx, isl_error_invalid,
10471 "number of columns too small", goto error);
10473 extra = eq->n_col - total;
10475 bmap = isl_basic_map_alloc_space(isl_space_copy(dim), extra,
10476 eq->n_row, ineq->n_row);
10479 for (i = 0; i < extra; ++i) {
10480 k = isl_basic_map_alloc_div(bmap);
10483 isl_int_set_si(bmap->div[k][0], 0);
10485 for (i = 0; i < eq->n_row; ++i) {
10486 l = isl_basic_map_alloc_equality(bmap);
10489 for (j = 0, pos = 0; j < 5; ++j) {
10490 int off = isl_basic_map_offset(bmap, c[j]);
10491 for (k = 0; k < isl_basic_map_dim(bmap, c[j]); ++k) {
10492 isl_int_set(bmap->eq[l][off + k],
10498 for (i = 0; i < ineq->n_row; ++i) {
10499 l = isl_basic_map_alloc_inequality(bmap);
10502 for (j = 0, pos = 0; j < 5; ++j) {
10503 int off = isl_basic_map_offset(bmap, c[j]);
10504 for (k = 0; k < isl_basic_map_dim(bmap, c[j]); ++k) {
10505 isl_int_set(bmap->ineq[l][off + k],
10506 ineq->row[i][pos]);
10512 isl_space_free(dim);
10514 isl_mat_free(ineq);
10516 bmap = isl_basic_map_simplify(bmap);
10517 return isl_basic_map_finalize(bmap);
10519 isl_space_free(dim);
10521 isl_mat_free(ineq);
10525 __isl_give isl_mat *isl_basic_set_equalities_matrix(
10526 __isl_keep isl_basic_set *bset, enum isl_dim_type c1,
10527 enum isl_dim_type c2, enum isl_dim_type c3, enum isl_dim_type c4)
10529 return isl_basic_map_equalities_matrix((isl_basic_map *)bset,
10530 c1, c2, c3, c4, isl_dim_in);
10533 __isl_give isl_mat *isl_basic_set_inequalities_matrix(
10534 __isl_keep isl_basic_set *bset, enum isl_dim_type c1,
10535 enum isl_dim_type c2, enum isl_dim_type c3, enum isl_dim_type c4)
10537 return isl_basic_map_inequalities_matrix((isl_basic_map *)bset,
10538 c1, c2, c3, c4, isl_dim_in);
10541 __isl_give isl_basic_set *isl_basic_set_from_constraint_matrices(
10542 __isl_take isl_space *dim,
10543 __isl_take isl_mat *eq, __isl_take isl_mat *ineq, enum isl_dim_type c1,
10544 enum isl_dim_type c2, enum isl_dim_type c3, enum isl_dim_type c4)
10546 return (isl_basic_set*)
10547 isl_basic_map_from_constraint_matrices(dim, eq, ineq,
10548 c1, c2, c3, c4, isl_dim_in);
10551 int isl_basic_map_can_zip(__isl_keep isl_basic_map *bmap)
10556 return isl_space_can_zip(bmap->dim);
10559 int isl_map_can_zip(__isl_keep isl_map *map)
10564 return isl_space_can_zip(map->dim);
10567 /* Given a basic map (A -> B) -> (C -> D), return the corresponding basic map
10568 * (A -> C) -> (B -> D).
10570 __isl_give isl_basic_map *isl_basic_map_zip(__isl_take isl_basic_map *bmap)
10579 if (!isl_basic_map_can_zip(bmap))
10580 isl_die(bmap->ctx, isl_error_invalid,
10581 "basic map cannot be zipped", goto error);
10582 pos = isl_basic_map_offset(bmap, isl_dim_in) +
10583 isl_space_dim(bmap->dim->nested[0], isl_dim_in);
10584 n1 = isl_space_dim(bmap->dim->nested[0], isl_dim_out);
10585 n2 = isl_space_dim(bmap->dim->nested[1], isl_dim_in);
10586 bmap = isl_basic_map_cow(bmap);
10587 bmap = isl_basic_map_swap_vars(bmap, pos, n1, n2);
10590 bmap->dim = isl_space_zip(bmap->dim);
10595 isl_basic_map_free(bmap);
10599 /* Given a map (A -> B) -> (C -> D), return the corresponding map
10600 * (A -> C) -> (B -> D).
10602 __isl_give isl_map *isl_map_zip(__isl_take isl_map *map)
10609 if (!isl_map_can_zip(map))
10610 isl_die(map->ctx, isl_error_invalid, "map cannot be zipped",
10613 map = isl_map_cow(map);
10617 for (i = 0; i < map->n; ++i) {
10618 map->p[i] = isl_basic_map_zip(map->p[i]);
10623 map->dim = isl_space_zip(map->dim);
10633 /* Can we apply isl_basic_map_curry to "bmap"?
10634 * That is, does it have a nested relation in its domain?
10636 int isl_basic_map_can_curry(__isl_keep isl_basic_map *bmap)
10641 return isl_space_can_curry(bmap->dim);
10644 /* Can we apply isl_map_curry to "map"?
10645 * That is, does it have a nested relation in its domain?
10647 int isl_map_can_curry(__isl_keep isl_map *map)
10652 return isl_space_can_curry(map->dim);
10655 /* Given a basic map (A -> B) -> C, return the corresponding basic map
10658 __isl_give isl_basic_map *isl_basic_map_curry(__isl_take isl_basic_map *bmap)
10664 if (!isl_basic_map_can_curry(bmap))
10665 isl_die(bmap->ctx, isl_error_invalid,
10666 "basic map cannot be curried", goto error);
10667 bmap = isl_basic_map_cow(bmap);
10670 bmap->dim = isl_space_curry(bmap->dim);
10675 isl_basic_map_free(bmap);
10679 /* Given a map (A -> B) -> C, return the corresponding map
10682 __isl_give isl_map *isl_map_curry(__isl_take isl_map *map)
10689 if (!isl_map_can_curry(map))
10690 isl_die(map->ctx, isl_error_invalid, "map cannot be curried",
10693 map = isl_map_cow(map);
10697 for (i = 0; i < map->n; ++i) {
10698 map->p[i] = isl_basic_map_curry(map->p[i]);
10703 map->dim = isl_space_curry(map->dim);
10713 /* Can we apply isl_basic_map_uncurry to "bmap"?
10714 * That is, does it have a nested relation in its domain?
10716 int isl_basic_map_can_uncurry(__isl_keep isl_basic_map *bmap)
10721 return isl_space_can_uncurry(bmap->dim);
10724 /* Can we apply isl_map_uncurry to "map"?
10725 * That is, does it have a nested relation in its domain?
10727 int isl_map_can_uncurry(__isl_keep isl_map *map)
10732 return isl_space_can_uncurry(map->dim);
10735 /* Given a basic map A -> (B -> C), return the corresponding basic map
10738 __isl_give isl_basic_map *isl_basic_map_uncurry(__isl_take isl_basic_map *bmap)
10744 if (!isl_basic_map_can_uncurry(bmap))
10745 isl_die(bmap->ctx, isl_error_invalid,
10746 "basic map cannot be uncurried",
10747 return isl_basic_map_free(bmap));
10748 bmap = isl_basic_map_cow(bmap);
10751 bmap->dim = isl_space_uncurry(bmap->dim);
10753 return isl_basic_map_free(bmap);
10757 /* Given a map A -> (B -> C), return the corresponding map
10760 __isl_give isl_map *isl_map_uncurry(__isl_take isl_map *map)
10767 if (!isl_map_can_uncurry(map))
10768 isl_die(map->ctx, isl_error_invalid, "map cannot be uncurried",
10769 return isl_map_free(map));
10771 map = isl_map_cow(map);
10775 for (i = 0; i < map->n; ++i) {
10776 map->p[i] = isl_basic_map_uncurry(map->p[i]);
10778 return isl_map_free(map);
10781 map->dim = isl_space_uncurry(map->dim);
10783 return isl_map_free(map);
10788 /* Construct a basic map mapping the domain of the affine expression
10789 * to a one-dimensional range prescribed by the affine expression.
10791 __isl_give isl_basic_map *isl_basic_map_from_aff(__isl_take isl_aff *aff)
10795 isl_local_space *ls;
10796 isl_basic_map *bmap;
10801 ls = isl_aff_get_local_space(aff);
10802 bmap = isl_basic_map_from_local_space(ls);
10803 bmap = isl_basic_map_extend_constraints(bmap, 1, 0);
10804 k = isl_basic_map_alloc_equality(bmap);
10808 pos = isl_basic_map_offset(bmap, isl_dim_out);
10809 isl_seq_cpy(bmap->eq[k], aff->v->el + 1, pos);
10810 isl_int_neg(bmap->eq[k][pos], aff->v->el[0]);
10811 isl_seq_cpy(bmap->eq[k] + pos + 1, aff->v->el + 1 + pos,
10812 aff->v->size - (pos + 1));
10815 bmap = isl_basic_map_finalize(bmap);
10819 isl_basic_map_free(bmap);
10823 /* Construct a map mapping the domain of the affine expression
10824 * to a one-dimensional range prescribed by the affine expression.
10826 __isl_give isl_map *isl_map_from_aff(__isl_take isl_aff *aff)
10828 isl_basic_map *bmap;
10830 bmap = isl_basic_map_from_aff(aff);
10831 return isl_map_from_basic_map(bmap);
10834 /* Construct a basic map mapping the domain the multi-affine expression
10835 * to its range, with each dimension in the range equated to the
10836 * corresponding affine expression.
10838 __isl_give isl_basic_map *isl_basic_map_from_multi_aff(
10839 __isl_take isl_multi_aff *maff)
10843 isl_basic_map *bmap;
10848 if (isl_space_dim(maff->space, isl_dim_out) != maff->n)
10849 isl_die(isl_multi_aff_get_ctx(maff), isl_error_internal,
10850 "invalid space", return isl_multi_aff_free(maff));
10852 space = isl_space_domain(isl_multi_aff_get_space(maff));
10853 bmap = isl_basic_map_universe(isl_space_from_domain(space));
10855 for (i = 0; i < maff->n; ++i) {
10857 isl_basic_map *bmap_i;
10859 aff = isl_aff_copy(maff->p[i]);
10860 bmap_i = isl_basic_map_from_aff(aff);
10862 bmap = isl_basic_map_flat_range_product(bmap, bmap_i);
10865 bmap = isl_basic_map_reset_space(bmap, isl_multi_aff_get_space(maff));
10867 isl_multi_aff_free(maff);
10871 /* Construct a map mapping the domain the multi-affine expression
10872 * to its range, with each dimension in the range equated to the
10873 * corresponding affine expression.
10875 __isl_give isl_map *isl_map_from_multi_aff(__isl_take isl_multi_aff *maff)
10877 isl_basic_map *bmap;
10879 bmap = isl_basic_map_from_multi_aff(maff);
10880 return isl_map_from_basic_map(bmap);
10883 /* Construct a basic map mapping a domain in the given space to
10884 * to an n-dimensional range, with n the number of elements in the list,
10885 * where each coordinate in the range is prescribed by the
10886 * corresponding affine expression.
10887 * The domains of all affine expressions in the list are assumed to match
10890 __isl_give isl_basic_map *isl_basic_map_from_aff_list(
10891 __isl_take isl_space *domain_dim, __isl_take isl_aff_list *list)
10895 isl_basic_map *bmap;
10900 dim = isl_space_from_domain(domain_dim);
10901 bmap = isl_basic_map_universe(dim);
10903 for (i = 0; i < list->n; ++i) {
10905 isl_basic_map *bmap_i;
10907 aff = isl_aff_copy(list->p[i]);
10908 bmap_i = isl_basic_map_from_aff(aff);
10910 bmap = isl_basic_map_flat_range_product(bmap, bmap_i);
10913 isl_aff_list_free(list);
10917 __isl_give isl_set *isl_set_equate(__isl_take isl_set *set,
10918 enum isl_dim_type type1, int pos1, enum isl_dim_type type2, int pos2)
10920 return isl_map_equate(set, type1, pos1, type2, pos2);
10923 /* Construct a basic map where the given dimensions are equal to each other.
10925 static __isl_give isl_basic_map *equator(__isl_take isl_space *space,
10926 enum isl_dim_type type1, int pos1, enum isl_dim_type type2, int pos2)
10928 isl_basic_map *bmap = NULL;
10934 if (pos1 >= isl_space_dim(space, type1))
10935 isl_die(isl_space_get_ctx(space), isl_error_invalid,
10936 "index out of bounds", goto error);
10937 if (pos2 >= isl_space_dim(space, type2))
10938 isl_die(isl_space_get_ctx(space), isl_error_invalid,
10939 "index out of bounds", goto error);
10941 if (type1 == type2 && pos1 == pos2)
10942 return isl_basic_map_universe(space);
10944 bmap = isl_basic_map_alloc_space(isl_space_copy(space), 0, 1, 0);
10945 i = isl_basic_map_alloc_equality(bmap);
10948 isl_seq_clr(bmap->eq[i], 1 + isl_basic_map_total_dim(bmap));
10949 pos1 += isl_basic_map_offset(bmap, type1);
10950 pos2 += isl_basic_map_offset(bmap, type2);
10951 isl_int_set_si(bmap->eq[i][pos1], -1);
10952 isl_int_set_si(bmap->eq[i][pos2], 1);
10953 bmap = isl_basic_map_finalize(bmap);
10954 isl_space_free(space);
10957 isl_space_free(space);
10958 isl_basic_map_free(bmap);
10962 /* Add a constraint imposing that the given two dimensions are equal.
10964 __isl_give isl_basic_map *isl_basic_map_equate(__isl_take isl_basic_map *bmap,
10965 enum isl_dim_type type1, int pos1, enum isl_dim_type type2, int pos2)
10969 eq = equator(isl_basic_map_get_space(bmap), type1, pos1, type2, pos2);
10971 bmap = isl_basic_map_intersect(bmap, eq);
10976 /* Add a constraint imposing that the given two dimensions are equal.
10978 __isl_give isl_map *isl_map_equate(__isl_take isl_map *map,
10979 enum isl_dim_type type1, int pos1, enum isl_dim_type type2, int pos2)
10981 isl_basic_map *bmap;
10983 bmap = equator(isl_map_get_space(map), type1, pos1, type2, pos2);
10985 map = isl_map_intersect(map, isl_map_from_basic_map(bmap));
10990 /* Add a constraint imposing that the given two dimensions have opposite values.
10992 __isl_give isl_map *isl_map_oppose(__isl_take isl_map *map,
10993 enum isl_dim_type type1, int pos1, enum isl_dim_type type2, int pos2)
10995 isl_basic_map *bmap = NULL;
11001 if (pos1 >= isl_map_dim(map, type1))
11002 isl_die(map->ctx, isl_error_invalid,
11003 "index out of bounds", goto error);
11004 if (pos2 >= isl_map_dim(map, type2))
11005 isl_die(map->ctx, isl_error_invalid,
11006 "index out of bounds", goto error);
11008 bmap = isl_basic_map_alloc_space(isl_map_get_space(map), 0, 1, 0);
11009 i = isl_basic_map_alloc_equality(bmap);
11012 isl_seq_clr(bmap->eq[i], 1 + isl_basic_map_total_dim(bmap));
11013 pos1 += isl_basic_map_offset(bmap, type1);
11014 pos2 += isl_basic_map_offset(bmap, type2);
11015 isl_int_set_si(bmap->eq[i][pos1], 1);
11016 isl_int_set_si(bmap->eq[i][pos2], 1);
11017 bmap = isl_basic_map_finalize(bmap);
11019 map = isl_map_intersect(map, isl_map_from_basic_map(bmap));
11023 isl_basic_map_free(bmap);
11028 /* Add a constraint imposing that the value of the first dimension is
11029 * greater than or equal to that of the second.
11031 __isl_give isl_basic_map *isl_basic_map_order_ge(__isl_take isl_basic_map *bmap,
11032 enum isl_dim_type type1, int pos1, enum isl_dim_type type2, int pos2)
11035 isl_local_space *ls;
11040 if (pos1 >= isl_basic_map_dim(bmap, type1))
11041 isl_die(bmap->ctx, isl_error_invalid,
11042 "index out of bounds", return isl_basic_map_free(bmap));
11043 if (pos2 >= isl_basic_map_dim(bmap, type2))
11044 isl_die(bmap->ctx, isl_error_invalid,
11045 "index out of bounds", return isl_basic_map_free(bmap));
11047 if (type1 == type2 && pos1 == pos2)
11050 ls = isl_local_space_from_space(isl_basic_map_get_space(bmap));
11051 c = isl_inequality_alloc(ls);
11052 c = isl_constraint_set_coefficient_si(c, type1, pos1, 1);
11053 c = isl_constraint_set_coefficient_si(c, type2, pos2, -1);
11054 bmap = isl_basic_map_add_constraint(bmap, c);
11059 /* Add a constraint imposing that the value of the first dimension is
11060 * greater than that of the second.
11062 __isl_give isl_map *isl_map_order_gt(__isl_take isl_map *map,
11063 enum isl_dim_type type1, int pos1, enum isl_dim_type type2, int pos2)
11065 isl_basic_map *bmap = NULL;
11071 if (pos1 >= isl_map_dim(map, type1))
11072 isl_die(map->ctx, isl_error_invalid,
11073 "index out of bounds", goto error);
11074 if (pos2 >= isl_map_dim(map, type2))
11075 isl_die(map->ctx, isl_error_invalid,
11076 "index out of bounds", goto error);
11078 if (type1 == type2 && pos1 == pos2) {
11079 isl_space *space = isl_map_get_space(map);
11081 return isl_map_empty(space);
11084 bmap = isl_basic_map_alloc_space(isl_map_get_space(map), 0, 0, 1);
11085 i = isl_basic_map_alloc_inequality(bmap);
11088 isl_seq_clr(bmap->ineq[i], 1 + isl_basic_map_total_dim(bmap));
11089 pos1 += isl_basic_map_offset(bmap, type1);
11090 pos2 += isl_basic_map_offset(bmap, type2);
11091 isl_int_set_si(bmap->ineq[i][pos1], 1);
11092 isl_int_set_si(bmap->ineq[i][pos2], -1);
11093 isl_int_set_si(bmap->ineq[i][0], -1);
11094 bmap = isl_basic_map_finalize(bmap);
11096 map = isl_map_intersect(map, isl_map_from_basic_map(bmap));
11100 isl_basic_map_free(bmap);
11105 /* Add a constraint imposing that the value of the first dimension is
11106 * smaller than that of the second.
11108 __isl_give isl_map *isl_map_order_lt(__isl_take isl_map *map,
11109 enum isl_dim_type type1, int pos1, enum isl_dim_type type2, int pos2)
11111 return isl_map_order_gt(map, type2, pos2, type1, pos1);
11114 __isl_give isl_aff *isl_basic_map_get_div(__isl_keep isl_basic_map *bmap,
11118 isl_local_space *ls;
11123 if (!isl_basic_map_divs_known(bmap))
11124 isl_die(isl_basic_map_get_ctx(bmap), isl_error_invalid,
11125 "some divs are unknown", return NULL);
11127 ls = isl_basic_map_get_local_space(bmap);
11128 div = isl_local_space_get_div(ls, pos);
11129 isl_local_space_free(ls);
11134 __isl_give isl_aff *isl_basic_set_get_div(__isl_keep isl_basic_set *bset,
11137 return isl_basic_map_get_div(bset, pos);
11140 /* Plug in "subs" for dimension "type", "pos" of "bset".
11142 * Let i be the dimension to replace and let "subs" be of the form
11146 * Any integer division with a non-zero coefficient for i,
11148 * floor((a i + g)/m)
11152 * floor((a f + d g)/(m d))
11154 * Constraints of the form
11162 * We currently require that "subs" is an integral expression.
11163 * Handling rational expressions may require us to add stride constraints
11164 * as we do in isl_basic_set_preimage_multi_aff.
11166 __isl_give isl_basic_set *isl_basic_set_substitute(
11167 __isl_take isl_basic_set *bset,
11168 enum isl_dim_type type, unsigned pos, __isl_keep isl_aff *subs)
11174 if (bset && isl_basic_set_plain_is_empty(bset))
11177 bset = isl_basic_set_cow(bset);
11178 if (!bset || !subs)
11181 ctx = isl_basic_set_get_ctx(bset);
11182 if (!isl_space_is_equal(bset->dim, subs->ls->dim))
11183 isl_die(ctx, isl_error_invalid,
11184 "spaces don't match", goto error);
11185 if (isl_local_space_dim(subs->ls, isl_dim_div) != 0)
11186 isl_die(ctx, isl_error_unsupported,
11187 "cannot handle divs yet", goto error);
11188 if (!isl_int_is_one(subs->v->el[0]))
11189 isl_die(ctx, isl_error_invalid,
11190 "can only substitute integer expressions", goto error);
11192 pos += isl_basic_set_offset(bset, type);
11196 for (i = 0; i < bset->n_eq; ++i) {
11197 if (isl_int_is_zero(bset->eq[i][pos]))
11199 isl_int_set(v, bset->eq[i][pos]);
11200 isl_int_set_si(bset->eq[i][pos], 0);
11201 isl_seq_combine(bset->eq[i], subs->v->el[0], bset->eq[i],
11202 v, subs->v->el + 1, subs->v->size - 1);
11205 for (i = 0; i < bset->n_ineq; ++i) {
11206 if (isl_int_is_zero(bset->ineq[i][pos]))
11208 isl_int_set(v, bset->ineq[i][pos]);
11209 isl_int_set_si(bset->ineq[i][pos], 0);
11210 isl_seq_combine(bset->ineq[i], subs->v->el[0], bset->ineq[i],
11211 v, subs->v->el + 1, subs->v->size - 1);
11214 for (i = 0; i < bset->n_div; ++i) {
11215 if (isl_int_is_zero(bset->div[i][1 + pos]))
11217 isl_int_set(v, bset->div[i][1 + pos]);
11218 isl_int_set_si(bset->div[i][1 + pos], 0);
11219 isl_seq_combine(bset->div[i] + 1,
11220 subs->v->el[0], bset->div[i] + 1,
11221 v, subs->v->el + 1, subs->v->size - 1);
11222 isl_int_mul(bset->div[i][0], bset->div[i][0], subs->v->el[0]);
11227 bset = isl_basic_set_simplify(bset);
11228 return isl_basic_set_finalize(bset);
11230 isl_basic_set_free(bset);
11234 /* Plug in "subs" for dimension "type", "pos" of "set".
11236 __isl_give isl_set *isl_set_substitute(__isl_take isl_set *set,
11237 enum isl_dim_type type, unsigned pos, __isl_keep isl_aff *subs)
11241 if (set && isl_set_plain_is_empty(set))
11244 set = isl_set_cow(set);
11248 for (i = set->n - 1; i >= 0; --i) {
11249 set->p[i] = isl_basic_set_substitute(set->p[i], type, pos, subs);
11250 if (remove_if_empty(set, i) < 0)
11260 /* Check if the range of "ma" is compatible with "space".
11261 * Return -1 if anything is wrong.
11263 static int check_space_compatible_range_multi_aff(
11264 __isl_keep isl_space *space, __isl_keep isl_multi_aff *ma)
11267 isl_space *ma_space;
11269 ma_space = isl_multi_aff_get_space(ma);
11270 m = isl_space_is_range_internal(space, ma_space);
11271 isl_space_free(ma_space);
11273 isl_die(isl_space_get_ctx(space), isl_error_invalid,
11274 "spaces don't match", return -1);
11278 /* Check if the range of "ma" is compatible with "bset".
11279 * Return -1 if anything is wrong.
11281 static int check_basic_set_compatible_range_multi_aff(
11282 __isl_keep isl_basic_set *bset, __isl_keep isl_multi_aff *ma)
11284 return check_space_compatible_range_multi_aff(bset->dim, ma);
11287 /* Copy the divs from "ma" to "bset", adding zeros for the coefficients
11288 * of the other divs in "bset".
11290 static int set_ma_divs(__isl_keep isl_basic_set *bset,
11291 __isl_keep isl_multi_aff *ma, int n_div)
11294 isl_local_space *ls;
11299 ls = isl_aff_get_domain_local_space(ma->p[0]);
11303 for (i = 0; i < n_div; ++i) {
11304 isl_seq_cpy(bset->div[i], ls->div->row[i], ls->div->n_col);
11305 isl_seq_clr(bset->div[i] + ls->div->n_col, bset->n_div - n_div);
11306 if (isl_basic_set_add_div_constraints(bset, i) < 0)
11310 isl_local_space_free(ls);
11313 isl_local_space_free(ls);
11317 /* How many stride constraints does "ma" enforce?
11318 * That is, how many of the affine expressions have a denominator
11319 * different from one?
11321 static int multi_aff_strides(__isl_keep isl_multi_aff *ma)
11326 for (i = 0; i < ma->n; ++i)
11327 if (!isl_int_is_one(ma->p[i]->v->el[0]))
11333 /* For each affine expression in ma of the form
11335 * x_i = (f_i y + h_i)/m_i
11337 * with m_i different from one, add a constraint to "bset"
11340 * f_i y + h_i = m_i alpha_i
11342 * with alpha_i an additional existentially quantified variable.
11344 static __isl_give isl_basic_set *add_ma_strides(
11345 __isl_take isl_basic_set *bset, __isl_keep isl_multi_aff *ma)
11351 total = isl_basic_set_total_dim(bset);
11352 for (i = 0; i < ma->n; ++i) {
11355 if (isl_int_is_one(ma->p[i]->v->el[0]))
11357 div = isl_basic_set_alloc_div(bset);
11358 k = isl_basic_set_alloc_equality(bset);
11359 if (div < 0 || k < 0)
11361 isl_int_set_si(bset->div[div][0], 0);
11362 len = ma->p[i]->v->size;
11363 isl_seq_cpy(bset->eq[k], ma->p[i]->v->el + 1, len - 1);
11364 isl_seq_clr(bset->eq[k] + len - 1, 1 + total - (len - 1));
11365 isl_int_neg(bset->eq[k][1 + total], ma->p[i]->v->el[0]);
11371 isl_basic_set_free(bset);
11375 /* Compute the preimage of "bset" under the function represented by "ma".
11376 * In other words, plug in "ma" in "bset". The result is a basic set
11377 * that lives in the domain space of "ma".
11379 * If bset is represented by
11381 * A(p) + B x + C(divs) >= 0
11383 * and ma is represented by
11385 * x = D(p) + F(y) + G(divs')
11387 * then the result is
11389 * A(p) + B D(p) + B F(y) + B G(divs') + C(divs) >= 0
11391 * The divs in the input set are similarly adjusted.
11394 * floor((a_i(p) + b_i x + c_i(divs))/n_i)
11398 * floor((a_i(p) + b_i D(p) + b_i F(y) + B_i G(divs') + c_i(divs))/n_i)
11400 * If bset is not a rational set and if F(y) involves any denominators
11402 * x_i = (f_i y + h_i)/m_i
11404 * the additional constraints are added to ensure that we only
11405 * map back integer points. That is we enforce
11407 * f_i y + h_i = m_i alpha_i
11409 * with alpha_i an additional existentially quantified variable.
11411 * We first copy over the divs from "ma".
11412 * Then we add the modified constraints and divs from "bset".
11413 * Finally, we add the stride constraints, if needed.
11415 __isl_give isl_basic_set *isl_basic_set_preimage_multi_aff(
11416 __isl_take isl_basic_set *bset, __isl_take isl_multi_aff *ma)
11420 isl_basic_set *res = NULL;
11421 int n_div_bset, n_div_ma;
11422 isl_int f, c1, c2, g;
11423 int rational, strides;
11430 ma = isl_multi_aff_align_divs(ma);
11433 if (check_basic_set_compatible_range_multi_aff(bset, ma) < 0)
11436 n_div_bset = isl_basic_set_dim(bset, isl_dim_div);
11437 n_div_ma = ma->n ? isl_aff_dim(ma->p[0], isl_dim_div) : 0;
11439 space = isl_space_domain(isl_multi_aff_get_space(ma));
11440 rational = isl_basic_set_is_rational(bset);
11441 strides = rational ? 0 : multi_aff_strides(ma);
11442 res = isl_basic_set_alloc_space(space, n_div_ma + n_div_bset + strides,
11443 bset->n_eq + strides, bset->n_ineq + 2 * n_div_ma);
11445 res = isl_basic_set_set_rational(res);
11447 for (i = 0; i < n_div_ma + n_div_bset; ++i)
11448 if (isl_basic_set_alloc_div(res) < 0)
11451 if (set_ma_divs(res, ma, n_div_ma) < 0)
11454 for (i = 0; i < bset->n_eq; ++i) {
11455 k = isl_basic_set_alloc_equality(res);
11458 isl_seq_preimage(res->eq[k], bset->eq[i], ma, n_div_ma,
11459 n_div_bset, f, c1, c2, g, 0);
11462 for (i = 0; i < bset->n_ineq; ++i) {
11463 k = isl_basic_set_alloc_inequality(res);
11466 isl_seq_preimage(res->ineq[k], bset->ineq[i], ma, n_div_ma,
11467 n_div_bset, f, c1, c2, g, 0);
11470 for (i = 0; i < bset->n_div; ++i) {
11471 if (isl_int_is_zero(bset->div[i][0])) {
11472 isl_int_set_si(res->div[n_div_ma + i][0], 0);
11475 isl_seq_preimage(res->div[n_div_ma + i], bset->div[i],
11476 ma, n_div_ma, n_div_bset, f, c1, c2, g, 1);
11480 res = add_ma_strides(res, ma);
11486 isl_basic_set_free(bset);
11487 isl_multi_aff_free(ma);
11488 res = isl_basic_set_simplify(res);
11489 return isl_basic_set_finalize(res);
11495 isl_basic_set_free(bset);
11496 isl_multi_aff_free(ma);
11497 isl_basic_set_free(res);
11501 /* Check if the range of "ma" is compatible with "set".
11502 * Return -1 if anything is wrong.
11504 static int check_set_compatible_range_multi_aff(
11505 __isl_keep isl_set *set, __isl_keep isl_multi_aff *ma)
11507 return check_space_compatible_range_multi_aff(set->dim, ma);
11510 /* Compute the preimage of "set" under the function represented by "ma".
11511 * In other words, plug in "ma" in "set. The result is a set
11512 * that lives in the domain space of "ma".
11514 static __isl_give isl_set *set_preimage_multi_aff(__isl_take isl_set *set,
11515 __isl_take isl_multi_aff *ma)
11519 set = isl_set_cow(set);
11520 ma = isl_multi_aff_align_divs(ma);
11523 if (check_set_compatible_range_multi_aff(set, ma) < 0)
11526 for (i = 0; i < set->n; ++i) {
11527 set->p[i] = isl_basic_set_preimage_multi_aff(set->p[i],
11528 isl_multi_aff_copy(ma));
11533 isl_space_free(set->dim);
11534 set->dim = isl_multi_aff_get_domain_space(ma);
11538 isl_multi_aff_free(ma);
11540 ISL_F_CLR(set, ISL_MAP_DISJOINT);
11541 ISL_F_CLR(set, ISL_SET_NORMALIZED);
11544 isl_multi_aff_free(ma);
11549 __isl_give isl_set *isl_set_preimage_multi_aff(__isl_take isl_set *set,
11550 __isl_take isl_multi_aff *ma)
11555 if (isl_space_match(set->dim, isl_dim_param, ma->space, isl_dim_param))
11556 return set_preimage_multi_aff(set, ma);
11558 if (!isl_space_has_named_params(set->dim) ||
11559 !isl_space_has_named_params(ma->space))
11560 isl_die(set->ctx, isl_error_invalid,
11561 "unaligned unnamed parameters", goto error);
11562 set = isl_set_align_params(set, isl_multi_aff_get_space(ma));
11563 ma = isl_multi_aff_align_params(ma, isl_set_get_space(set));
11565 return set_preimage_multi_aff(set, ma);
11567 isl_multi_aff_free(ma);
11568 return isl_set_free(set);
11571 /* Compute the preimage of "set" under the function represented by "pma".
11572 * In other words, plug in "pma" in "set. The result is a set
11573 * that lives in the domain space of "pma".
11575 static __isl_give isl_set *set_preimage_pw_multi_aff(__isl_take isl_set *set,
11576 __isl_take isl_pw_multi_aff *pma)
11585 isl_pw_multi_aff_free(pma);
11586 res = isl_set_empty(isl_set_get_space(set));
11591 res = isl_set_preimage_multi_aff(isl_set_copy(set),
11592 isl_multi_aff_copy(pma->p[0].maff));
11593 res = isl_set_intersect(res, isl_set_copy(pma->p[0].set));
11595 for (i = 1; i < pma->n; ++i) {
11598 res_i = isl_set_preimage_multi_aff(isl_set_copy(set),
11599 isl_multi_aff_copy(pma->p[i].maff));
11600 res_i = isl_set_intersect(res_i, isl_set_copy(pma->p[i].set));
11601 res = isl_set_union(res, res_i);
11604 isl_pw_multi_aff_free(pma);
11608 isl_pw_multi_aff_free(pma);
11613 __isl_give isl_set *isl_set_preimage_pw_multi_aff(__isl_take isl_set *set,
11614 __isl_take isl_pw_multi_aff *pma)
11619 if (isl_space_match(set->dim, isl_dim_param, pma->dim, isl_dim_param))
11620 return set_preimage_pw_multi_aff(set, pma);
11622 if (!isl_space_has_named_params(set->dim) ||
11623 !isl_space_has_named_params(pma->dim))
11624 isl_die(set->ctx, isl_error_invalid,
11625 "unaligned unnamed parameters", goto error);
11626 set = isl_set_align_params(set, isl_pw_multi_aff_get_space(pma));
11627 pma = isl_pw_multi_aff_align_params(pma, isl_set_get_space(set));
11629 return set_preimage_pw_multi_aff(set, pma);
11631 isl_pw_multi_aff_free(pma);
11632 return isl_set_free(set);