2 * Copyright 2008-2009 Katholieke Universiteit Leuven
3 * Copyright 2010 INRIA Saclay
4 * Copyright 2012 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>
37 static unsigned n(__isl_keep isl_space *dim, enum isl_dim_type type)
40 case isl_dim_param: return dim->nparam;
41 case isl_dim_in: return dim->n_in;
42 case isl_dim_out: return dim->n_out;
43 case isl_dim_all: return dim->nparam + dim->n_in + dim->n_out;
48 static unsigned pos(__isl_keep isl_space *dim, enum isl_dim_type type)
51 case isl_dim_param: return 1;
52 case isl_dim_in: return 1 + dim->nparam;
53 case isl_dim_out: return 1 + dim->nparam + dim->n_in;
58 unsigned isl_basic_map_dim(__isl_keep isl_basic_map *bmap,
59 enum isl_dim_type type)
64 case isl_dim_cst: return 1;
67 case isl_dim_out: return isl_space_dim(bmap->dim, type);
68 case isl_dim_div: return bmap->n_div;
69 case isl_dim_all: return isl_basic_map_total_dim(bmap);
74 unsigned isl_map_dim(__isl_keep isl_map *map, enum isl_dim_type type)
76 return map ? n(map->dim, type) : 0;
79 unsigned isl_set_dim(__isl_keep isl_set *set, enum isl_dim_type type)
81 return set ? n(set->dim, type) : 0;
84 unsigned isl_basic_map_offset(struct isl_basic_map *bmap,
85 enum isl_dim_type type)
87 isl_space *dim = bmap->dim;
89 case isl_dim_cst: return 0;
90 case isl_dim_param: return 1;
91 case isl_dim_in: return 1 + dim->nparam;
92 case isl_dim_out: return 1 + dim->nparam + dim->n_in;
93 case isl_dim_div: return 1 + dim->nparam + dim->n_in + dim->n_out;
98 unsigned isl_basic_set_offset(struct isl_basic_set *bset,
99 enum isl_dim_type type)
101 return isl_basic_map_offset(bset, type);
104 static unsigned map_offset(struct isl_map *map, enum isl_dim_type type)
106 return pos(map->dim, type);
109 unsigned isl_basic_set_dim(__isl_keep isl_basic_set *bset,
110 enum isl_dim_type type)
112 return isl_basic_map_dim(bset, type);
115 unsigned isl_basic_set_n_dim(__isl_keep isl_basic_set *bset)
117 return isl_basic_set_dim(bset, isl_dim_set);
120 unsigned isl_basic_set_n_param(__isl_keep isl_basic_set *bset)
122 return isl_basic_set_dim(bset, isl_dim_param);
125 unsigned isl_basic_set_total_dim(const struct isl_basic_set *bset)
129 return isl_space_dim(bset->dim, isl_dim_all) + bset->n_div;
132 unsigned isl_set_n_dim(__isl_keep isl_set *set)
134 return isl_set_dim(set, isl_dim_set);
137 unsigned isl_set_n_param(__isl_keep isl_set *set)
139 return isl_set_dim(set, isl_dim_param);
142 unsigned isl_basic_map_n_in(const struct isl_basic_map *bmap)
144 return bmap ? bmap->dim->n_in : 0;
147 unsigned isl_basic_map_n_out(const struct isl_basic_map *bmap)
149 return bmap ? bmap->dim->n_out : 0;
152 unsigned isl_basic_map_n_param(const struct isl_basic_map *bmap)
154 return bmap ? bmap->dim->nparam : 0;
157 unsigned isl_basic_map_n_div(const struct isl_basic_map *bmap)
159 return bmap ? bmap->n_div : 0;
162 unsigned isl_basic_map_total_dim(const struct isl_basic_map *bmap)
164 return bmap ? isl_space_dim(bmap->dim, isl_dim_all) + bmap->n_div : 0;
167 unsigned isl_map_n_in(const struct isl_map *map)
169 return map ? map->dim->n_in : 0;
172 unsigned isl_map_n_out(const struct isl_map *map)
174 return map ? map->dim->n_out : 0;
177 unsigned isl_map_n_param(const struct isl_map *map)
179 return map ? map->dim->nparam : 0;
182 int isl_map_compatible_domain(struct isl_map *map, struct isl_set *set)
187 m = isl_space_match(map->dim, isl_dim_param, set->dim, isl_dim_param);
190 return isl_space_tuple_match(map->dim, isl_dim_in, set->dim, isl_dim_set);
193 int isl_basic_map_compatible_domain(struct isl_basic_map *bmap,
194 struct isl_basic_set *bset)
199 m = isl_space_match(bmap->dim, isl_dim_param, bset->dim, isl_dim_param);
202 return isl_space_tuple_match(bmap->dim, isl_dim_in, bset->dim, isl_dim_set);
205 int isl_map_compatible_range(__isl_keep isl_map *map, __isl_keep isl_set *set)
210 m = isl_space_match(map->dim, isl_dim_param, set->dim, isl_dim_param);
213 return isl_space_tuple_match(map->dim, isl_dim_out, set->dim, isl_dim_set);
216 int isl_basic_map_compatible_range(struct isl_basic_map *bmap,
217 struct isl_basic_set *bset)
222 m = isl_space_match(bmap->dim, isl_dim_param, bset->dim, isl_dim_param);
225 return isl_space_tuple_match(bmap->dim, isl_dim_out, bset->dim, isl_dim_set);
228 isl_ctx *isl_basic_map_get_ctx(__isl_keep isl_basic_map *bmap)
230 return bmap ? bmap->ctx : NULL;
233 isl_ctx *isl_basic_set_get_ctx(__isl_keep isl_basic_set *bset)
235 return bset ? bset->ctx : NULL;
238 isl_ctx *isl_map_get_ctx(__isl_keep isl_map *map)
240 return map ? map->ctx : NULL;
243 isl_ctx *isl_set_get_ctx(__isl_keep isl_set *set)
245 return set ? set->ctx : NULL;
248 __isl_give isl_space *isl_basic_map_get_space(__isl_keep isl_basic_map *bmap)
252 return isl_space_copy(bmap->dim);
255 __isl_give isl_space *isl_basic_set_get_space(__isl_keep isl_basic_set *bset)
259 return isl_space_copy(bset->dim);
262 /* Extract the divs in "bmap" as a matrix.
264 __isl_give isl_mat *isl_basic_map_get_divs(__isl_keep isl_basic_map *bmap)
275 ctx = isl_basic_map_get_ctx(bmap);
276 total = isl_space_dim(bmap->dim, isl_dim_all);
277 cols = 1 + 1 + total + bmap->n_div;
278 div = isl_mat_alloc(ctx, bmap->n_div, cols);
282 for (i = 0; i < bmap->n_div; ++i)
283 isl_seq_cpy(div->row[i], bmap->div[i], cols);
288 __isl_give isl_local_space *isl_basic_map_get_local_space(
289 __isl_keep isl_basic_map *bmap)
296 div = isl_basic_map_get_divs(bmap);
297 return isl_local_space_alloc_div(isl_space_copy(bmap->dim), div);
300 __isl_give isl_local_space *isl_basic_set_get_local_space(
301 __isl_keep isl_basic_set *bset)
303 return isl_basic_map_get_local_space(bset);
306 __isl_give isl_basic_map *isl_basic_map_from_local_space(
307 __isl_take isl_local_space *ls)
316 n_div = isl_local_space_dim(ls, isl_dim_div);
317 bmap = isl_basic_map_alloc_space(isl_local_space_get_space(ls),
318 n_div, 0, 2 * n_div);
320 for (i = 0; i < n_div; ++i)
321 if (isl_basic_map_alloc_div(bmap) < 0)
324 for (i = 0; i < n_div; ++i) {
325 isl_seq_cpy(bmap->div[i], ls->div->row[i], ls->div->n_col);
326 if (isl_basic_map_add_div_constraints(bmap, i) < 0)
330 isl_local_space_free(ls);
333 isl_local_space_free(ls);
334 isl_basic_map_free(bmap);
338 __isl_give isl_basic_set *isl_basic_set_from_local_space(
339 __isl_take isl_local_space *ls)
341 return isl_basic_map_from_local_space(ls);
344 __isl_give isl_space *isl_map_get_space(__isl_keep isl_map *map)
348 return isl_space_copy(map->dim);
351 __isl_give isl_space *isl_set_get_space(__isl_keep isl_set *set)
355 return isl_space_copy(set->dim);
358 __isl_give isl_basic_map *isl_basic_map_set_tuple_name(
359 __isl_take isl_basic_map *bmap, enum isl_dim_type type, const char *s)
361 bmap = isl_basic_map_cow(bmap);
364 bmap->dim = isl_space_set_tuple_name(bmap->dim, type, s);
367 bmap = isl_basic_map_finalize(bmap);
370 isl_basic_map_free(bmap);
374 __isl_give isl_basic_set *isl_basic_set_set_tuple_name(
375 __isl_take isl_basic_set *bset, const char *s)
377 return isl_basic_map_set_tuple_name(bset, isl_dim_set, s);
380 const char *isl_basic_map_get_tuple_name(__isl_keep isl_basic_map *bmap,
381 enum isl_dim_type type)
383 return bmap ? isl_space_get_tuple_name(bmap->dim, type) : NULL;
386 __isl_give isl_map *isl_map_set_tuple_name(__isl_take isl_map *map,
387 enum isl_dim_type type, const char *s)
391 map = isl_map_cow(map);
395 map->dim = isl_space_set_tuple_name(map->dim, type, s);
399 for (i = 0; i < map->n; ++i) {
400 map->p[i] = isl_basic_map_set_tuple_name(map->p[i], type, s);
411 /* Does the input or output tuple have a name?
413 int isl_map_has_tuple_name(__isl_keep isl_map *map, enum isl_dim_type type)
415 return map ? isl_space_has_tuple_name(map->dim, type) : -1;
418 const char *isl_map_get_tuple_name(__isl_keep isl_map *map,
419 enum isl_dim_type type)
421 return map ? isl_space_get_tuple_name(map->dim, type) : NULL;
424 __isl_give isl_set *isl_set_set_tuple_name(__isl_take isl_set *set,
427 return (isl_set *)isl_map_set_tuple_name((isl_map *)set, isl_dim_set, s);
430 __isl_give isl_map *isl_map_set_tuple_id(__isl_take isl_map *map,
431 enum isl_dim_type type, __isl_take isl_id *id)
433 map = isl_map_cow(map);
435 return isl_id_free(id);
437 map->dim = isl_space_set_tuple_id(map->dim, type, id);
439 return isl_map_reset_space(map, isl_space_copy(map->dim));
442 __isl_give isl_set *isl_set_set_tuple_id(__isl_take isl_set *set,
443 __isl_take isl_id *id)
445 return isl_map_set_tuple_id(set, isl_dim_set, id);
448 __isl_give isl_map *isl_map_reset_tuple_id(__isl_take isl_map *map,
449 enum isl_dim_type type)
451 map = isl_map_cow(map);
455 map->dim = isl_space_reset_tuple_id(map->dim, type);
457 return isl_map_reset_space(map, isl_space_copy(map->dim));
460 __isl_give isl_set *isl_set_reset_tuple_id(__isl_take isl_set *set)
462 return isl_map_reset_tuple_id(set, isl_dim_set);
465 int isl_map_has_tuple_id(__isl_keep isl_map *map, enum isl_dim_type type)
467 return map ? isl_space_has_tuple_id(map->dim, type) : -1;
470 __isl_give isl_id *isl_map_get_tuple_id(__isl_keep isl_map *map,
471 enum isl_dim_type type)
473 return map ? isl_space_get_tuple_id(map->dim, type) : NULL;
476 int isl_set_has_tuple_id(__isl_keep isl_set *set)
478 return isl_map_has_tuple_id(set, isl_dim_set);
481 __isl_give isl_id *isl_set_get_tuple_id(__isl_keep isl_set *set)
483 return isl_map_get_tuple_id(set, isl_dim_set);
486 /* Does the set tuple have a name?
488 int isl_set_has_tuple_name(__isl_keep isl_set *set)
490 return set ? isl_space_has_tuple_name(set->dim, isl_dim_set) : -1;
494 const char *isl_basic_set_get_tuple_name(__isl_keep isl_basic_set *bset)
496 return bset ? isl_space_get_tuple_name(bset->dim, isl_dim_set) : NULL;
499 const char *isl_set_get_tuple_name(__isl_keep isl_set *set)
501 return set ? isl_space_get_tuple_name(set->dim, isl_dim_set) : NULL;
504 const char *isl_basic_map_get_dim_name(__isl_keep isl_basic_map *bmap,
505 enum isl_dim_type type, unsigned pos)
507 return bmap ? isl_space_get_dim_name(bmap->dim, type, pos) : NULL;
510 const char *isl_basic_set_get_dim_name(__isl_keep isl_basic_set *bset,
511 enum isl_dim_type type, unsigned pos)
513 return bset ? isl_space_get_dim_name(bset->dim, type, pos) : NULL;
516 /* Does the given dimension have a name?
518 int isl_map_has_dim_name(__isl_keep isl_map *map,
519 enum isl_dim_type type, unsigned pos)
521 return map ? isl_space_has_dim_name(map->dim, type, pos) : -1;
524 const char *isl_map_get_dim_name(__isl_keep isl_map *map,
525 enum isl_dim_type type, unsigned pos)
527 return map ? isl_space_get_dim_name(map->dim, type, pos) : NULL;
530 const char *isl_set_get_dim_name(__isl_keep isl_set *set,
531 enum isl_dim_type type, unsigned pos)
533 return set ? isl_space_get_dim_name(set->dim, type, pos) : NULL;
536 /* Does the given dimension have a name?
538 int isl_set_has_dim_name(__isl_keep isl_set *set,
539 enum isl_dim_type type, unsigned pos)
541 return set ? isl_space_has_dim_name(set->dim, type, pos) : -1;
544 __isl_give isl_basic_map *isl_basic_map_set_dim_name(
545 __isl_take isl_basic_map *bmap,
546 enum isl_dim_type type, unsigned pos, const char *s)
548 bmap = isl_basic_map_cow(bmap);
551 bmap->dim = isl_space_set_dim_name(bmap->dim, type, pos, s);
554 return isl_basic_map_finalize(bmap);
556 isl_basic_map_free(bmap);
560 __isl_give isl_map *isl_map_set_dim_name(__isl_take isl_map *map,
561 enum isl_dim_type type, unsigned pos, const char *s)
565 map = isl_map_cow(map);
569 map->dim = isl_space_set_dim_name(map->dim, type, pos, s);
573 for (i = 0; i < map->n; ++i) {
574 map->p[i] = isl_basic_map_set_dim_name(map->p[i], type, pos, s);
585 __isl_give isl_basic_set *isl_basic_set_set_dim_name(
586 __isl_take isl_basic_set *bset,
587 enum isl_dim_type type, unsigned pos, const char *s)
589 return (isl_basic_set *)isl_basic_map_set_dim_name(
590 (isl_basic_map *)bset, type, pos, s);
593 __isl_give isl_set *isl_set_set_dim_name(__isl_take isl_set *set,
594 enum isl_dim_type type, unsigned pos, const char *s)
596 return (isl_set *)isl_map_set_dim_name((isl_map *)set, type, pos, s);
599 int isl_basic_map_has_dim_id(__isl_keep isl_basic_map *bmap,
600 enum isl_dim_type type, unsigned pos)
602 return bmap ? isl_space_has_dim_id(bmap->dim, type, pos) : -1;
605 __isl_give isl_id *isl_basic_set_get_dim_id(__isl_keep isl_basic_set *bset,
606 enum isl_dim_type type, unsigned pos)
608 return bset ? isl_space_get_dim_id(bset->dim, type, pos) : NULL;
611 int isl_map_has_dim_id(__isl_keep isl_map *map,
612 enum isl_dim_type type, unsigned pos)
614 return map ? isl_space_has_dim_id(map->dim, type, pos) : -1;
617 __isl_give isl_id *isl_map_get_dim_id(__isl_keep isl_map *map,
618 enum isl_dim_type type, unsigned pos)
620 return map ? isl_space_get_dim_id(map->dim, type, pos) : NULL;
623 int isl_set_has_dim_id(__isl_keep isl_set *set,
624 enum isl_dim_type type, unsigned pos)
626 return isl_map_has_dim_id(set, type, pos);
629 __isl_give isl_id *isl_set_get_dim_id(__isl_keep isl_set *set,
630 enum isl_dim_type type, unsigned pos)
632 return isl_map_get_dim_id(set, type, pos);
635 __isl_give isl_map *isl_map_set_dim_id(__isl_take isl_map *map,
636 enum isl_dim_type type, unsigned pos, __isl_take isl_id *id)
638 map = isl_map_cow(map);
640 return isl_id_free(id);
642 map->dim = isl_space_set_dim_id(map->dim, type, pos, id);
644 return isl_map_reset_space(map, isl_space_copy(map->dim));
647 __isl_give isl_set *isl_set_set_dim_id(__isl_take isl_set *set,
648 enum isl_dim_type type, unsigned pos, __isl_take isl_id *id)
650 return isl_map_set_dim_id(set, type, pos, id);
653 int isl_map_find_dim_by_id(__isl_keep isl_map *map, enum isl_dim_type type,
654 __isl_keep isl_id *id)
658 return isl_space_find_dim_by_id(map->dim, type, id);
661 int isl_set_find_dim_by_id(__isl_keep isl_set *set, enum isl_dim_type type,
662 __isl_keep isl_id *id)
664 return isl_map_find_dim_by_id(set, type, id);
667 int isl_map_find_dim_by_name(__isl_keep isl_map *map, enum isl_dim_type type,
672 return isl_space_find_dim_by_name(map->dim, type, name);
675 int isl_set_find_dim_by_name(__isl_keep isl_set *set, enum isl_dim_type type,
678 return isl_map_find_dim_by_name(set, type, name);
681 int isl_basic_map_is_rational(__isl_keep isl_basic_map *bmap)
685 return ISL_F_ISSET(bmap, ISL_BASIC_MAP_RATIONAL);
688 int isl_basic_set_is_rational(__isl_keep isl_basic_set *bset)
690 return isl_basic_map_is_rational(bset);
693 /* Does "bmap" contain any rational points?
695 * If "bmap" has an equality for each dimension, equating the dimension
696 * to an integer constant, then it has no rational points, even if it
697 * is marked as rational.
699 int isl_basic_map_has_rational(__isl_keep isl_basic_map *bmap)
701 int has_rational = 1;
706 if (isl_basic_map_plain_is_empty(bmap))
708 if (!isl_basic_map_is_rational(bmap))
710 bmap = isl_basic_map_copy(bmap);
711 bmap = isl_basic_map_implicit_equalities(bmap);
714 total = isl_basic_map_total_dim(bmap);
715 if (bmap->n_eq == total) {
717 for (i = 0; i < bmap->n_eq; ++i) {
718 j = isl_seq_first_non_zero(bmap->eq[i] + 1, total);
721 if (!isl_int_is_one(bmap->eq[i][1 + j]) &&
722 !isl_int_is_negone(bmap->eq[i][1 + j]))
724 j = isl_seq_first_non_zero(bmap->eq[i] + 1 + j + 1,
732 isl_basic_map_free(bmap);
737 /* Does "map" contain any rational points?
739 int isl_map_has_rational(__isl_keep isl_map *map)
746 for (i = 0; i < map->n; ++i) {
747 has_rational = isl_basic_map_has_rational(map->p[i]);
748 if (has_rational < 0)
756 /* Does "set" contain any rational points?
758 int isl_set_has_rational(__isl_keep isl_set *set)
760 return isl_map_has_rational(set);
763 /* Is this basic set a parameter domain?
765 int isl_basic_set_is_params(__isl_keep isl_basic_set *bset)
769 return isl_space_is_params(bset->dim);
772 /* Is this set a parameter domain?
774 int isl_set_is_params(__isl_keep isl_set *set)
778 return isl_space_is_params(set->dim);
781 /* Is this map actually a parameter domain?
782 * Users should never call this function. Outside of isl,
783 * a map can never be a parameter domain.
785 int isl_map_is_params(__isl_keep isl_map *map)
789 return isl_space_is_params(map->dim);
792 static struct isl_basic_map *basic_map_init(struct isl_ctx *ctx,
793 struct isl_basic_map *bmap, unsigned extra,
794 unsigned n_eq, unsigned n_ineq)
797 size_t row_size = 1 + isl_space_dim(bmap->dim, isl_dim_all) + extra;
802 bmap->block = isl_blk_alloc(ctx, (n_ineq + n_eq) * row_size);
803 if (isl_blk_is_error(bmap->block))
806 bmap->ineq = isl_alloc_array(ctx, isl_int *, n_ineq + n_eq);
811 bmap->block2 = isl_blk_empty();
814 bmap->block2 = isl_blk_alloc(ctx, extra * (1 + row_size));
815 if (isl_blk_is_error(bmap->block2))
818 bmap->div = isl_alloc_array(ctx, isl_int *, extra);
823 for (i = 0; i < n_ineq + n_eq; ++i)
824 bmap->ineq[i] = bmap->block.data + i * row_size;
826 for (i = 0; i < extra; ++i)
827 bmap->div[i] = bmap->block2.data + i * (1 + row_size);
831 bmap->c_size = n_eq + n_ineq;
832 bmap->eq = bmap->ineq + n_ineq;
841 isl_basic_map_free(bmap);
845 struct isl_basic_set *isl_basic_set_alloc(struct isl_ctx *ctx,
846 unsigned nparam, unsigned dim, unsigned extra,
847 unsigned n_eq, unsigned n_ineq)
849 struct isl_basic_map *bmap;
852 space = isl_space_set_alloc(ctx, nparam, dim);
856 bmap = isl_basic_map_alloc_space(space, extra, n_eq, n_ineq);
857 return (struct isl_basic_set *)bmap;
860 struct isl_basic_set *isl_basic_set_alloc_space(__isl_take isl_space *dim,
861 unsigned extra, unsigned n_eq, unsigned n_ineq)
863 struct isl_basic_map *bmap;
866 isl_assert(dim->ctx, dim->n_in == 0, goto error);
867 bmap = isl_basic_map_alloc_space(dim, extra, n_eq, n_ineq);
868 return (struct isl_basic_set *)bmap;
874 struct isl_basic_map *isl_basic_map_alloc_space(__isl_take isl_space *dim,
875 unsigned extra, unsigned n_eq, unsigned n_ineq)
877 struct isl_basic_map *bmap;
881 bmap = isl_calloc_type(dim->ctx, struct isl_basic_map);
886 return basic_map_init(dim->ctx, bmap, extra, n_eq, n_ineq);
892 struct isl_basic_map *isl_basic_map_alloc(struct isl_ctx *ctx,
893 unsigned nparam, unsigned in, unsigned out, unsigned extra,
894 unsigned n_eq, unsigned n_ineq)
896 struct isl_basic_map *bmap;
899 dim = isl_space_alloc(ctx, nparam, in, out);
903 bmap = isl_basic_map_alloc_space(dim, extra, n_eq, n_ineq);
907 static void dup_constraints(
908 struct isl_basic_map *dst, struct isl_basic_map *src)
911 unsigned total = isl_basic_map_total_dim(src);
913 for (i = 0; i < src->n_eq; ++i) {
914 int j = isl_basic_map_alloc_equality(dst);
915 isl_seq_cpy(dst->eq[j], src->eq[i], 1+total);
918 for (i = 0; i < src->n_ineq; ++i) {
919 int j = isl_basic_map_alloc_inequality(dst);
920 isl_seq_cpy(dst->ineq[j], src->ineq[i], 1+total);
923 for (i = 0; i < src->n_div; ++i) {
924 int j = isl_basic_map_alloc_div(dst);
925 isl_seq_cpy(dst->div[j], src->div[i], 1+1+total);
927 ISL_F_SET(dst, ISL_BASIC_SET_FINAL);
930 struct isl_basic_map *isl_basic_map_dup(struct isl_basic_map *bmap)
932 struct isl_basic_map *dup;
936 dup = isl_basic_map_alloc_space(isl_space_copy(bmap->dim),
937 bmap->n_div, bmap->n_eq, bmap->n_ineq);
940 dup_constraints(dup, bmap);
941 dup->flags = bmap->flags;
942 dup->sample = isl_vec_copy(bmap->sample);
946 struct isl_basic_set *isl_basic_set_dup(struct isl_basic_set *bset)
948 struct isl_basic_map *dup;
950 dup = isl_basic_map_dup((struct isl_basic_map *)bset);
951 return (struct isl_basic_set *)dup;
954 struct isl_basic_set *isl_basic_set_copy(struct isl_basic_set *bset)
959 if (ISL_F_ISSET(bset, ISL_BASIC_SET_FINAL)) {
963 return isl_basic_set_dup(bset);
966 struct isl_set *isl_set_copy(struct isl_set *set)
975 struct isl_basic_map *isl_basic_map_copy(struct isl_basic_map *bmap)
980 if (ISL_F_ISSET(bmap, ISL_BASIC_SET_FINAL)) {
984 bmap = isl_basic_map_dup(bmap);
986 ISL_F_SET(bmap, ISL_BASIC_SET_FINAL);
990 struct isl_map *isl_map_copy(struct isl_map *map)
999 void *isl_basic_map_free(__isl_take isl_basic_map *bmap)
1004 if (--bmap->ref > 0)
1007 isl_ctx_deref(bmap->ctx);
1009 isl_blk_free(bmap->ctx, bmap->block2);
1011 isl_blk_free(bmap->ctx, bmap->block);
1012 isl_vec_free(bmap->sample);
1013 isl_space_free(bmap->dim);
1019 void *isl_basic_set_free(struct isl_basic_set *bset)
1021 return isl_basic_map_free((struct isl_basic_map *)bset);
1024 static int room_for_con(struct isl_basic_map *bmap, unsigned n)
1026 return bmap->n_eq + bmap->n_ineq + n <= bmap->c_size;
1029 __isl_give isl_map *isl_map_align_params_map_map_and(
1030 __isl_take isl_map *map1, __isl_take isl_map *map2,
1031 __isl_give isl_map *(*fn)(__isl_take isl_map *map1,
1032 __isl_take isl_map *map2))
1036 if (isl_space_match(map1->dim, isl_dim_param, map2->dim, isl_dim_param))
1037 return fn(map1, map2);
1038 if (!isl_space_has_named_params(map1->dim) ||
1039 !isl_space_has_named_params(map2->dim))
1040 isl_die(map1->ctx, isl_error_invalid,
1041 "unaligned unnamed parameters", goto error);
1042 map1 = isl_map_align_params(map1, isl_map_get_space(map2));
1043 map2 = isl_map_align_params(map2, isl_map_get_space(map1));
1044 return fn(map1, map2);
1051 int isl_map_align_params_map_map_and_test(__isl_keep isl_map *map1,
1052 __isl_keep isl_map *map2,
1053 int (*fn)(__isl_keep isl_map *map1, __isl_keep isl_map *map2))
1059 if (isl_space_match(map1->dim, isl_dim_param, map2->dim, isl_dim_param))
1060 return fn(map1, map2);
1061 if (!isl_space_has_named_params(map1->dim) ||
1062 !isl_space_has_named_params(map2->dim))
1063 isl_die(map1->ctx, isl_error_invalid,
1064 "unaligned unnamed parameters", return -1);
1065 map1 = isl_map_copy(map1);
1066 map2 = isl_map_copy(map2);
1067 map1 = isl_map_align_params(map1, isl_map_get_space(map2));
1068 map2 = isl_map_align_params(map2, isl_map_get_space(map1));
1075 int isl_basic_map_alloc_equality(struct isl_basic_map *bmap)
1077 struct isl_ctx *ctx;
1081 isl_assert(ctx, room_for_con(bmap, 1), return -1);
1082 isl_assert(ctx, (bmap->eq - bmap->ineq) + bmap->n_eq <= bmap->c_size,
1084 ISL_F_CLR(bmap, ISL_BASIC_MAP_NORMALIZED);
1085 ISL_F_CLR(bmap, ISL_BASIC_MAP_NO_REDUNDANT);
1086 ISL_F_CLR(bmap, ISL_BASIC_MAP_NO_IMPLICIT);
1087 ISL_F_CLR(bmap, ISL_BASIC_MAP_ALL_EQUALITIES);
1088 ISL_F_CLR(bmap, ISL_BASIC_MAP_NORMALIZED_DIVS);
1089 if ((bmap->eq - bmap->ineq) + bmap->n_eq == bmap->c_size) {
1091 int j = isl_basic_map_alloc_inequality(bmap);
1095 bmap->ineq[j] = bmap->ineq[bmap->n_ineq - 1];
1096 bmap->ineq[bmap->n_ineq - 1] = bmap->eq[-1];
1103 isl_seq_clr(bmap->eq[bmap->n_eq] + 1 + isl_basic_map_total_dim(bmap),
1104 bmap->extra - bmap->n_div);
1105 return bmap->n_eq++;
1108 int isl_basic_set_alloc_equality(struct isl_basic_set *bset)
1110 return isl_basic_map_alloc_equality((struct isl_basic_map *)bset);
1113 int isl_basic_map_free_equality(struct isl_basic_map *bmap, unsigned n)
1117 isl_assert(bmap->ctx, n <= bmap->n_eq, return -1);
1122 int isl_basic_set_free_equality(struct isl_basic_set *bset, unsigned n)
1124 return isl_basic_map_free_equality((struct isl_basic_map *)bset, n);
1127 int isl_basic_map_drop_equality(struct isl_basic_map *bmap, unsigned pos)
1132 isl_assert(bmap->ctx, pos < bmap->n_eq, return -1);
1134 if (pos != bmap->n_eq - 1) {
1136 bmap->eq[pos] = bmap->eq[bmap->n_eq - 1];
1137 bmap->eq[bmap->n_eq - 1] = t;
1143 int isl_basic_set_drop_equality(struct isl_basic_set *bset, unsigned pos)
1145 return isl_basic_map_drop_equality((struct isl_basic_map *)bset, pos);
1148 void isl_basic_map_inequality_to_equality(
1149 struct isl_basic_map *bmap, unsigned pos)
1153 t = bmap->ineq[pos];
1154 bmap->ineq[pos] = bmap->ineq[bmap->n_ineq - 1];
1155 bmap->ineq[bmap->n_ineq - 1] = bmap->eq[-1];
1160 ISL_F_CLR(bmap, ISL_BASIC_MAP_NO_REDUNDANT);
1161 ISL_F_CLR(bmap, ISL_BASIC_MAP_NORMALIZED);
1162 ISL_F_CLR(bmap, ISL_BASIC_MAP_NORMALIZED_DIVS);
1163 ISL_F_CLR(bmap, ISL_BASIC_MAP_ALL_EQUALITIES);
1166 static int room_for_ineq(struct isl_basic_map *bmap, unsigned n)
1168 return bmap->n_ineq + n <= bmap->eq - bmap->ineq;
1171 int isl_basic_map_alloc_inequality(struct isl_basic_map *bmap)
1173 struct isl_ctx *ctx;
1177 isl_assert(ctx, room_for_ineq(bmap, 1), return -1);
1178 ISL_F_CLR(bmap, ISL_BASIC_MAP_NO_IMPLICIT);
1179 ISL_F_CLR(bmap, ISL_BASIC_MAP_NO_REDUNDANT);
1180 ISL_F_CLR(bmap, ISL_BASIC_MAP_NORMALIZED);
1181 ISL_F_CLR(bmap, ISL_BASIC_MAP_ALL_EQUALITIES);
1182 isl_seq_clr(bmap->ineq[bmap->n_ineq] +
1183 1 + isl_basic_map_total_dim(bmap),
1184 bmap->extra - bmap->n_div);
1185 return bmap->n_ineq++;
1188 int isl_basic_set_alloc_inequality(struct isl_basic_set *bset)
1190 return isl_basic_map_alloc_inequality((struct isl_basic_map *)bset);
1193 int isl_basic_map_free_inequality(struct isl_basic_map *bmap, unsigned n)
1197 isl_assert(bmap->ctx, n <= bmap->n_ineq, return -1);
1202 int isl_basic_set_free_inequality(struct isl_basic_set *bset, unsigned n)
1204 return isl_basic_map_free_inequality((struct isl_basic_map *)bset, n);
1207 int isl_basic_map_drop_inequality(struct isl_basic_map *bmap, unsigned pos)
1212 isl_assert(bmap->ctx, pos < bmap->n_ineq, return -1);
1214 if (pos != bmap->n_ineq - 1) {
1215 t = bmap->ineq[pos];
1216 bmap->ineq[pos] = bmap->ineq[bmap->n_ineq - 1];
1217 bmap->ineq[bmap->n_ineq - 1] = t;
1218 ISL_F_CLR(bmap, ISL_BASIC_MAP_NORMALIZED);
1224 int isl_basic_set_drop_inequality(struct isl_basic_set *bset, unsigned pos)
1226 return isl_basic_map_drop_inequality((struct isl_basic_map *)bset, pos);
1229 __isl_give isl_basic_map *isl_basic_map_add_eq(__isl_take isl_basic_map *bmap,
1234 bmap = isl_basic_map_extend_constraints(bmap, 1, 0);
1237 k = isl_basic_map_alloc_equality(bmap);
1240 isl_seq_cpy(bmap->eq[k], eq, 1 + isl_basic_map_total_dim(bmap));
1243 isl_basic_map_free(bmap);
1247 __isl_give isl_basic_set *isl_basic_set_add_eq(__isl_take isl_basic_set *bset,
1250 return (isl_basic_set *)
1251 isl_basic_map_add_eq((isl_basic_map *)bset, eq);
1254 __isl_give isl_basic_map *isl_basic_map_add_ineq(__isl_take isl_basic_map *bmap,
1259 bmap = isl_basic_map_extend_constraints(bmap, 0, 1);
1262 k = isl_basic_map_alloc_inequality(bmap);
1265 isl_seq_cpy(bmap->ineq[k], ineq, 1 + isl_basic_map_total_dim(bmap));
1268 isl_basic_map_free(bmap);
1272 __isl_give isl_basic_set *isl_basic_set_add_ineq(__isl_take isl_basic_set *bset,
1275 return (isl_basic_set *)
1276 isl_basic_map_add_ineq((isl_basic_map *)bset, ineq);
1279 int isl_basic_map_alloc_div(struct isl_basic_map *bmap)
1283 isl_assert(bmap->ctx, bmap->n_div < bmap->extra, return -1);
1284 isl_seq_clr(bmap->div[bmap->n_div] +
1285 1 + 1 + isl_basic_map_total_dim(bmap),
1286 bmap->extra - bmap->n_div);
1287 ISL_F_CLR(bmap, ISL_BASIC_MAP_NORMALIZED_DIVS);
1288 return bmap->n_div++;
1291 int isl_basic_set_alloc_div(struct isl_basic_set *bset)
1293 return isl_basic_map_alloc_div((struct isl_basic_map *)bset);
1296 int isl_basic_map_free_div(struct isl_basic_map *bmap, unsigned n)
1300 isl_assert(bmap->ctx, n <= bmap->n_div, return -1);
1305 int isl_basic_set_free_div(struct isl_basic_set *bset, unsigned n)
1307 return isl_basic_map_free_div((struct isl_basic_map *)bset, n);
1310 /* Copy constraint from src to dst, putting the vars of src at offset
1311 * dim_off in dst and the divs of src at offset div_off in dst.
1312 * If both sets are actually map, then dim_off applies to the input
1315 static void copy_constraint(struct isl_basic_map *dst_map, isl_int *dst,
1316 struct isl_basic_map *src_map, isl_int *src,
1317 unsigned in_off, unsigned out_off, unsigned div_off)
1319 unsigned src_nparam = isl_basic_map_n_param(src_map);
1320 unsigned dst_nparam = isl_basic_map_n_param(dst_map);
1321 unsigned src_in = isl_basic_map_n_in(src_map);
1322 unsigned dst_in = isl_basic_map_n_in(dst_map);
1323 unsigned src_out = isl_basic_map_n_out(src_map);
1324 unsigned dst_out = isl_basic_map_n_out(dst_map);
1325 isl_int_set(dst[0], src[0]);
1326 isl_seq_cpy(dst+1, src+1, isl_min(dst_nparam, src_nparam));
1327 if (dst_nparam > src_nparam)
1328 isl_seq_clr(dst+1+src_nparam,
1329 dst_nparam - src_nparam);
1330 isl_seq_clr(dst+1+dst_nparam, in_off);
1331 isl_seq_cpy(dst+1+dst_nparam+in_off,
1333 isl_min(dst_in-in_off, src_in));
1334 if (dst_in-in_off > src_in)
1335 isl_seq_clr(dst+1+dst_nparam+in_off+src_in,
1336 dst_in - in_off - src_in);
1337 isl_seq_clr(dst+1+dst_nparam+dst_in, out_off);
1338 isl_seq_cpy(dst+1+dst_nparam+dst_in+out_off,
1339 src+1+src_nparam+src_in,
1340 isl_min(dst_out-out_off, src_out));
1341 if (dst_out-out_off > src_out)
1342 isl_seq_clr(dst+1+dst_nparam+dst_in+out_off+src_out,
1343 dst_out - out_off - src_out);
1344 isl_seq_clr(dst+1+dst_nparam+dst_in+dst_out, div_off);
1345 isl_seq_cpy(dst+1+dst_nparam+dst_in+dst_out+div_off,
1346 src+1+src_nparam+src_in+src_out,
1347 isl_min(dst_map->extra-div_off, src_map->n_div));
1348 if (dst_map->n_div-div_off > src_map->n_div)
1349 isl_seq_clr(dst+1+dst_nparam+dst_in+dst_out+
1350 div_off+src_map->n_div,
1351 dst_map->n_div - div_off - src_map->n_div);
1354 static void copy_div(struct isl_basic_map *dst_map, isl_int *dst,
1355 struct isl_basic_map *src_map, isl_int *src,
1356 unsigned in_off, unsigned out_off, unsigned div_off)
1358 isl_int_set(dst[0], src[0]);
1359 copy_constraint(dst_map, dst+1, src_map, src+1, in_off, out_off, div_off);
1362 static struct isl_basic_map *add_constraints(struct isl_basic_map *bmap1,
1363 struct isl_basic_map *bmap2, unsigned i_pos, unsigned o_pos)
1368 if (!bmap1 || !bmap2)
1371 div_off = bmap1->n_div;
1373 for (i = 0; i < bmap2->n_eq; ++i) {
1374 int i1 = isl_basic_map_alloc_equality(bmap1);
1377 copy_constraint(bmap1, bmap1->eq[i1], bmap2, bmap2->eq[i],
1378 i_pos, o_pos, div_off);
1381 for (i = 0; i < bmap2->n_ineq; ++i) {
1382 int i1 = isl_basic_map_alloc_inequality(bmap1);
1385 copy_constraint(bmap1, bmap1->ineq[i1], bmap2, bmap2->ineq[i],
1386 i_pos, o_pos, div_off);
1389 for (i = 0; i < bmap2->n_div; ++i) {
1390 int i1 = isl_basic_map_alloc_div(bmap1);
1393 copy_div(bmap1, bmap1->div[i1], bmap2, bmap2->div[i],
1394 i_pos, o_pos, div_off);
1397 isl_basic_map_free(bmap2);
1402 isl_basic_map_free(bmap1);
1403 isl_basic_map_free(bmap2);
1407 struct isl_basic_set *isl_basic_set_add_constraints(struct isl_basic_set *bset1,
1408 struct isl_basic_set *bset2, unsigned pos)
1410 return (struct isl_basic_set *)
1411 add_constraints((struct isl_basic_map *)bset1,
1412 (struct isl_basic_map *)bset2, 0, pos);
1415 struct isl_basic_map *isl_basic_map_extend_space(struct isl_basic_map *base,
1416 __isl_take isl_space *dim, unsigned extra,
1417 unsigned n_eq, unsigned n_ineq)
1419 struct isl_basic_map *ext;
1429 dims_ok = isl_space_is_equal(base->dim, dim) &&
1430 base->extra >= base->n_div + extra;
1432 if (dims_ok && room_for_con(base, n_eq + n_ineq) &&
1433 room_for_ineq(base, n_ineq)) {
1434 isl_space_free(dim);
1438 isl_assert(base->ctx, base->dim->nparam <= dim->nparam, goto error);
1439 isl_assert(base->ctx, base->dim->n_in <= dim->n_in, goto error);
1440 isl_assert(base->ctx, base->dim->n_out <= dim->n_out, goto error);
1441 extra += base->extra;
1443 n_ineq += base->n_ineq;
1445 ext = isl_basic_map_alloc_space(dim, extra, n_eq, n_ineq);
1451 ext->sample = isl_vec_copy(base->sample);
1452 flags = base->flags;
1453 ext = add_constraints(ext, base, 0, 0);
1456 ISL_F_CLR(ext, ISL_BASIC_SET_FINAL);
1462 isl_space_free(dim);
1463 isl_basic_map_free(base);
1467 struct isl_basic_set *isl_basic_set_extend_space(struct isl_basic_set *base,
1468 __isl_take isl_space *dim, unsigned extra,
1469 unsigned n_eq, unsigned n_ineq)
1471 return (struct isl_basic_set *)
1472 isl_basic_map_extend_space((struct isl_basic_map *)base, dim,
1473 extra, n_eq, n_ineq);
1476 struct isl_basic_map *isl_basic_map_extend_constraints(
1477 struct isl_basic_map *base, unsigned n_eq, unsigned n_ineq)
1481 return isl_basic_map_extend_space(base, isl_space_copy(base->dim),
1485 struct isl_basic_map *isl_basic_map_extend(struct isl_basic_map *base,
1486 unsigned nparam, unsigned n_in, unsigned n_out, unsigned extra,
1487 unsigned n_eq, unsigned n_ineq)
1489 struct isl_basic_map *bmap;
1494 dim = isl_space_alloc(base->ctx, nparam, n_in, n_out);
1498 bmap = isl_basic_map_extend_space(base, dim, extra, n_eq, n_ineq);
1501 isl_basic_map_free(base);
1505 struct isl_basic_set *isl_basic_set_extend(struct isl_basic_set *base,
1506 unsigned nparam, unsigned dim, unsigned extra,
1507 unsigned n_eq, unsigned n_ineq)
1509 return (struct isl_basic_set *)
1510 isl_basic_map_extend((struct isl_basic_map *)base,
1511 nparam, 0, dim, extra, n_eq, n_ineq);
1514 struct isl_basic_set *isl_basic_set_extend_constraints(
1515 struct isl_basic_set *base, unsigned n_eq, unsigned n_ineq)
1517 return (struct isl_basic_set *)
1518 isl_basic_map_extend_constraints((struct isl_basic_map *)base,
1522 struct isl_basic_set *isl_basic_set_cow(struct isl_basic_set *bset)
1524 return (struct isl_basic_set *)
1525 isl_basic_map_cow((struct isl_basic_map *)bset);
1528 struct isl_basic_map *isl_basic_map_cow(struct isl_basic_map *bmap)
1533 if (bmap->ref > 1) {
1535 bmap = isl_basic_map_dup(bmap);
1538 ISL_F_CLR(bmap, ISL_BASIC_SET_FINAL);
1542 struct isl_set *isl_set_cow(struct isl_set *set)
1550 return isl_set_dup(set);
1553 struct isl_map *isl_map_cow(struct isl_map *map)
1561 return isl_map_dup(map);
1564 static void swap_vars(struct isl_blk blk, isl_int *a,
1565 unsigned a_len, unsigned b_len)
1567 isl_seq_cpy(blk.data, a+a_len, b_len);
1568 isl_seq_cpy(blk.data+b_len, a, a_len);
1569 isl_seq_cpy(a, blk.data, b_len+a_len);
1572 static __isl_give isl_basic_map *isl_basic_map_swap_vars(
1573 __isl_take isl_basic_map *bmap, unsigned pos, unsigned n1, unsigned n2)
1581 isl_assert(bmap->ctx,
1582 pos + n1 + n2 <= 1 + isl_basic_map_total_dim(bmap), goto error);
1584 if (n1 == 0 || n2 == 0)
1587 bmap = isl_basic_map_cow(bmap);
1591 blk = isl_blk_alloc(bmap->ctx, n1 + n2);
1592 if (isl_blk_is_error(blk))
1595 for (i = 0; i < bmap->n_eq; ++i)
1597 bmap->eq[i] + pos, n1, n2);
1599 for (i = 0; i < bmap->n_ineq; ++i)
1601 bmap->ineq[i] + pos, n1, n2);
1603 for (i = 0; i < bmap->n_div; ++i)
1605 bmap->div[i]+1 + pos, n1, n2);
1607 isl_blk_free(bmap->ctx, blk);
1609 ISL_F_CLR(bmap, ISL_BASIC_SET_NORMALIZED);
1610 bmap = isl_basic_map_gauss(bmap, NULL);
1611 return isl_basic_map_finalize(bmap);
1613 isl_basic_map_free(bmap);
1617 static __isl_give isl_basic_set *isl_basic_set_swap_vars(
1618 __isl_take isl_basic_set *bset, unsigned n)
1626 nparam = isl_basic_set_n_param(bset);
1627 dim = isl_basic_set_n_dim(bset);
1628 isl_assert(bset->ctx, n <= dim, goto error);
1630 return isl_basic_map_swap_vars(bset, 1 + nparam, n, dim - n);
1632 isl_basic_set_free(bset);
1636 struct isl_basic_map *isl_basic_map_set_to_empty(struct isl_basic_map *bmap)
1642 total = isl_basic_map_total_dim(bmap);
1643 isl_basic_map_free_div(bmap, bmap->n_div);
1644 isl_basic_map_free_inequality(bmap, bmap->n_ineq);
1646 isl_basic_map_free_equality(bmap, bmap->n_eq-1);
1648 i = isl_basic_map_alloc_equality(bmap);
1652 isl_int_set_si(bmap->eq[i][0], 1);
1653 isl_seq_clr(bmap->eq[i]+1, total);
1654 ISL_F_SET(bmap, ISL_BASIC_MAP_EMPTY);
1655 isl_vec_free(bmap->sample);
1656 bmap->sample = NULL;
1657 return isl_basic_map_finalize(bmap);
1659 isl_basic_map_free(bmap);
1663 struct isl_basic_set *isl_basic_set_set_to_empty(struct isl_basic_set *bset)
1665 return (struct isl_basic_set *)
1666 isl_basic_map_set_to_empty((struct isl_basic_map *)bset);
1669 void isl_basic_map_swap_div(struct isl_basic_map *bmap, int a, int b)
1672 unsigned off = isl_space_dim(bmap->dim, isl_dim_all);
1673 isl_int *t = bmap->div[a];
1674 bmap->div[a] = bmap->div[b];
1677 for (i = 0; i < bmap->n_eq; ++i)
1678 isl_int_swap(bmap->eq[i][1+off+a], bmap->eq[i][1+off+b]);
1680 for (i = 0; i < bmap->n_ineq; ++i)
1681 isl_int_swap(bmap->ineq[i][1+off+a], bmap->ineq[i][1+off+b]);
1683 for (i = 0; i < bmap->n_div; ++i)
1684 isl_int_swap(bmap->div[i][1+1+off+a], bmap->div[i][1+1+off+b]);
1685 ISL_F_CLR(bmap, ISL_BASIC_MAP_NORMALIZED);
1688 /* Eliminate the specified n dimensions starting at first from the
1689 * constraints, without removing the dimensions from the space.
1690 * If the set is rational, the dimensions are eliminated using Fourier-Motzkin.
1692 __isl_give isl_map *isl_map_eliminate(__isl_take isl_map *map,
1693 enum isl_dim_type type, unsigned first, unsigned n)
1702 if (first + n > isl_map_dim(map, type) || first + n < first)
1703 isl_die(map->ctx, isl_error_invalid,
1704 "index out of bounds", goto error);
1706 map = isl_map_cow(map);
1710 for (i = 0; i < map->n; ++i) {
1711 map->p[i] = isl_basic_map_eliminate(map->p[i], type, first, n);
1721 /* Eliminate the specified n dimensions starting at first from the
1722 * constraints, without removing the dimensions from the space.
1723 * If the set is rational, the dimensions are eliminated using Fourier-Motzkin.
1725 __isl_give isl_set *isl_set_eliminate(__isl_take isl_set *set,
1726 enum isl_dim_type type, unsigned first, unsigned n)
1728 return (isl_set *)isl_map_eliminate((isl_map *)set, type, first, n);
1731 /* Eliminate the specified n dimensions starting at first from the
1732 * constraints, without removing the dimensions from the space.
1733 * If the set is rational, the dimensions are eliminated using Fourier-Motzkin.
1735 __isl_give isl_set *isl_set_eliminate_dims(__isl_take isl_set *set,
1736 unsigned first, unsigned n)
1738 return isl_set_eliminate(set, isl_dim_set, first, n);
1741 __isl_give isl_basic_map *isl_basic_map_remove_divs(
1742 __isl_take isl_basic_map *bmap)
1746 bmap = isl_basic_map_eliminate_vars(bmap,
1747 isl_space_dim(bmap->dim, isl_dim_all), bmap->n_div);
1751 return isl_basic_map_finalize(bmap);
1754 __isl_give isl_basic_set *isl_basic_set_remove_divs(
1755 __isl_take isl_basic_set *bset)
1757 return (struct isl_basic_set *)isl_basic_map_remove_divs(
1758 (struct isl_basic_map *)bset);
1761 __isl_give isl_map *isl_map_remove_divs(__isl_take isl_map *map)
1770 map = isl_map_cow(map);
1774 for (i = 0; i < map->n; ++i) {
1775 map->p[i] = isl_basic_map_remove_divs(map->p[i]);
1785 __isl_give isl_set *isl_set_remove_divs(__isl_take isl_set *set)
1787 return isl_map_remove_divs(set);
1790 struct isl_basic_map *isl_basic_map_remove_dims(struct isl_basic_map *bmap,
1791 enum isl_dim_type type, unsigned first, unsigned n)
1795 isl_assert(bmap->ctx, first + n <= isl_basic_map_dim(bmap, type),
1797 if (n == 0 && !isl_space_is_named_or_nested(bmap->dim, type))
1799 bmap = isl_basic_map_eliminate_vars(bmap,
1800 isl_basic_map_offset(bmap, type) - 1 + first, n);
1803 if (ISL_F_ISSET(bmap, ISL_BASIC_MAP_EMPTY) && type == isl_dim_div)
1805 bmap = isl_basic_map_drop(bmap, type, first, n);
1808 isl_basic_map_free(bmap);
1812 /* Return true if the definition of the given div (recursively) involves
1813 * any of the given variables.
1815 static int div_involves_vars(__isl_keep isl_basic_map *bmap, int div,
1816 unsigned first, unsigned n)
1819 unsigned div_offset = isl_basic_map_offset(bmap, isl_dim_div);
1821 if (isl_int_is_zero(bmap->div[div][0]))
1823 if (isl_seq_first_non_zero(bmap->div[div] + 1 + first, n) >= 0)
1826 for (i = bmap->n_div - 1; i >= 0; --i) {
1827 if (isl_int_is_zero(bmap->div[div][1 + div_offset + i]))
1829 if (div_involves_vars(bmap, i, first, n))
1836 /* Try and add a lower and/or upper bound on "div" to "bmap"
1837 * based on inequality "i".
1838 * "total" is the total number of variables (excluding the divs).
1839 * "v" is a temporary object that can be used during the calculations.
1840 * If "lb" is set, then a lower bound should be constructed.
1841 * If "ub" is set, then an upper bound should be constructed.
1843 * The calling function has already checked that the inequality does not
1844 * reference "div", but we still need to check that the inequality is
1845 * of the right form. We'll consider the case where we want to construct
1846 * a lower bound. The construction of upper bounds is similar.
1848 * Let "div" be of the form
1850 * q = floor((a + f(x))/d)
1852 * We essentially check if constraint "i" is of the form
1856 * so that we can use it to derive a lower bound on "div".
1857 * However, we allow a slightly more general form
1861 * with the condition that the coefficients of g(x) - f(x) are all
1863 * Rewriting this constraint as
1867 * adding a + f(x) to both sides and dividing by d, we obtain
1869 * (a + f(x))/d >= (a-b)/d + (f(x)-g(x))/d
1871 * Taking the floor on both sides, we obtain
1873 * q >= floor((a-b)/d) + (f(x)-g(x))/d
1877 * (g(x)-f(x))/d + ceil((b-a)/d) + q >= 0
1879 * In the case of an upper bound, we construct the constraint
1881 * (g(x)+f(x))/d + floor((b+a)/d) - q >= 0
1884 static __isl_give isl_basic_map *insert_bounds_on_div_from_ineq(
1885 __isl_take isl_basic_map *bmap, int div, int i,
1886 unsigned total, isl_int v, int lb, int ub)
1890 for (j = 0; (lb || ub) && j < total + bmap->n_div; ++j) {
1892 isl_int_sub(v, bmap->ineq[i][1 + j],
1893 bmap->div[div][1 + 1 + j]);
1894 lb = isl_int_is_divisible_by(v, bmap->div[div][0]);
1897 isl_int_add(v, bmap->ineq[i][1 + j],
1898 bmap->div[div][1 + 1 + j]);
1899 ub = isl_int_is_divisible_by(v, bmap->div[div][0]);
1905 bmap = isl_basic_map_extend_constraints(bmap, 0, lb + ub);
1907 int k = isl_basic_map_alloc_inequality(bmap);
1910 for (j = 0; j < 1 + total + bmap->n_div; ++j) {
1911 isl_int_sub(bmap->ineq[k][j], bmap->ineq[i][j],
1912 bmap->div[div][1 + j]);
1913 isl_int_cdiv_q(bmap->ineq[k][j],
1914 bmap->ineq[k][j], bmap->div[div][0]);
1916 isl_int_set_si(bmap->ineq[k][1 + total + div], 1);
1919 int k = isl_basic_map_alloc_inequality(bmap);
1922 for (j = 0; j < 1 + total + bmap->n_div; ++j) {
1923 isl_int_add(bmap->ineq[k][j], bmap->ineq[i][j],
1924 bmap->div[div][1 + j]);
1925 isl_int_fdiv_q(bmap->ineq[k][j],
1926 bmap->ineq[k][j], bmap->div[div][0]);
1928 isl_int_set_si(bmap->ineq[k][1 + total + div], -1);
1933 isl_basic_map_free(bmap);
1937 /* This function is called right before "div" is eliminated from "bmap"
1938 * using Fourier-Motzkin.
1939 * Look through the constraints of "bmap" for constraints on the argument
1940 * of the integer division and use them to construct constraints on the
1941 * integer division itself. These constraints can then be combined
1942 * during the Fourier-Motzkin elimination.
1943 * Note that it is only useful to introduce lower bounds on "div"
1944 * if "bmap" already contains upper bounds on "div" as the newly
1945 * introduce lower bounds can then be combined with the pre-existing
1946 * upper bounds. Similarly for upper bounds.
1947 * We therefore first check if "bmap" contains any lower and/or upper bounds
1950 * It is interesting to note that the introduction of these constraints
1951 * can indeed lead to more accurate results, even when compared to
1952 * deriving constraints on the argument of "div" from constraints on "div".
1953 * Consider, for example, the set
1955 * { [i,j,k] : 3 + i + 2j >= 0 and 2 * [(i+2j)/4] <= k }
1957 * The second constraint can be rewritten as
1959 * 2 * [(-i-2j+3)/4] + k >= 0
1961 * from which we can derive
1963 * -i - 2j + 3 >= -2k
1969 * Combined with the first constraint, we obtain
1971 * -3 <= 3 + 2k or k >= -3
1973 * If, on the other hand we derive a constraint on [(i+2j)/4] from
1974 * the first constraint, we obtain
1976 * [(i + 2j)/4] >= [-3/4] = -1
1978 * Combining this constraint with the second constraint, we obtain
1982 static __isl_give isl_basic_map *insert_bounds_on_div(
1983 __isl_take isl_basic_map *bmap, int div)
1986 int check_lb, check_ub;
1993 if (isl_int_is_zero(bmap->div[div][0]))
1996 total = isl_space_dim(bmap->dim, isl_dim_all);
2000 for (i = 0; (!check_lb || !check_ub) && i < bmap->n_ineq; ++i) {
2001 int s = isl_int_sgn(bmap->ineq[i][1 + total + div]);
2008 if (!check_lb && !check_ub)
2013 for (i = 0; bmap && i < bmap->n_ineq; ++i) {
2014 if (!isl_int_is_zero(bmap->ineq[i][1 + total + div]))
2017 bmap = insert_bounds_on_div_from_ineq(bmap, div, i, total, v,
2018 check_lb, check_ub);
2026 /* Remove all divs (recursively) involving any of the given dimensions
2027 * in their definitions.
2029 __isl_give isl_basic_map *isl_basic_map_remove_divs_involving_dims(
2030 __isl_take isl_basic_map *bmap,
2031 enum isl_dim_type type, unsigned first, unsigned n)
2037 isl_assert(bmap->ctx, first + n <= isl_basic_map_dim(bmap, type),
2039 first += isl_basic_map_offset(bmap, type);
2041 for (i = bmap->n_div - 1; i >= 0; --i) {
2042 if (!div_involves_vars(bmap, i, first, n))
2044 bmap = insert_bounds_on_div(bmap, i);
2045 bmap = isl_basic_map_remove_dims(bmap, isl_dim_div, i, 1);
2053 isl_basic_map_free(bmap);
2057 __isl_give isl_basic_set *isl_basic_set_remove_divs_involving_dims(
2058 __isl_take isl_basic_set *bset,
2059 enum isl_dim_type type, unsigned first, unsigned n)
2061 return isl_basic_map_remove_divs_involving_dims(bset, type, first, n);
2064 __isl_give isl_map *isl_map_remove_divs_involving_dims(__isl_take isl_map *map,
2065 enum isl_dim_type type, unsigned first, unsigned n)
2074 map = isl_map_cow(map);
2078 for (i = 0; i < map->n; ++i) {
2079 map->p[i] = isl_basic_map_remove_divs_involving_dims(map->p[i],
2090 __isl_give isl_set *isl_set_remove_divs_involving_dims(__isl_take isl_set *set,
2091 enum isl_dim_type type, unsigned first, unsigned n)
2093 return (isl_set *)isl_map_remove_divs_involving_dims((isl_map *)set,
2097 /* Does the desciption of "bmap" depend on the specified dimensions?
2098 * We also check whether the dimensions appear in any of the div definitions.
2099 * In principle there is no need for this check. If the dimensions appear
2100 * in a div definition, they also appear in the defining constraints of that
2103 int isl_basic_map_involves_dims(__isl_keep isl_basic_map *bmap,
2104 enum isl_dim_type type, unsigned first, unsigned n)
2111 if (first + n > isl_basic_map_dim(bmap, type))
2112 isl_die(bmap->ctx, isl_error_invalid,
2113 "index out of bounds", return -1);
2115 first += isl_basic_map_offset(bmap, type);
2116 for (i = 0; i < bmap->n_eq; ++i)
2117 if (isl_seq_first_non_zero(bmap->eq[i] + first, n) >= 0)
2119 for (i = 0; i < bmap->n_ineq; ++i)
2120 if (isl_seq_first_non_zero(bmap->ineq[i] + first, n) >= 0)
2122 for (i = 0; i < bmap->n_div; ++i) {
2123 if (isl_int_is_zero(bmap->div[i][0]))
2125 if (isl_seq_first_non_zero(bmap->div[i] + 1 + first, n) >= 0)
2132 int isl_map_involves_dims(__isl_keep isl_map *map,
2133 enum isl_dim_type type, unsigned first, unsigned n)
2140 if (first + n > isl_map_dim(map, type))
2141 isl_die(map->ctx, isl_error_invalid,
2142 "index out of bounds", return -1);
2144 for (i = 0; i < map->n; ++i) {
2145 int involves = isl_basic_map_involves_dims(map->p[i],
2147 if (involves < 0 || involves)
2154 int isl_basic_set_involves_dims(__isl_keep isl_basic_set *bset,
2155 enum isl_dim_type type, unsigned first, unsigned n)
2157 return isl_basic_map_involves_dims(bset, type, first, n);
2160 int isl_set_involves_dims(__isl_keep isl_set *set,
2161 enum isl_dim_type type, unsigned first, unsigned n)
2163 return isl_map_involves_dims(set, type, first, n);
2166 /* Return true if the definition of the given div is unknown or depends
2169 static int div_is_unknown(__isl_keep isl_basic_map *bmap, int div)
2172 unsigned div_offset = isl_basic_map_offset(bmap, isl_dim_div);
2174 if (isl_int_is_zero(bmap->div[div][0]))
2177 for (i = bmap->n_div - 1; i >= 0; --i) {
2178 if (isl_int_is_zero(bmap->div[div][1 + div_offset + i]))
2180 if (div_is_unknown(bmap, i))
2187 /* Remove all divs that are unknown or defined in terms of unknown divs.
2189 __isl_give isl_basic_map *isl_basic_map_remove_unknown_divs(
2190 __isl_take isl_basic_map *bmap)
2197 for (i = bmap->n_div - 1; i >= 0; --i) {
2198 if (!div_is_unknown(bmap, i))
2200 bmap = isl_basic_map_remove_dims(bmap, isl_dim_div, i, 1);
2209 /* Remove all divs that are unknown or defined in terms of unknown divs.
2211 __isl_give isl_basic_set *isl_basic_set_remove_unknown_divs(
2212 __isl_take isl_basic_set *bset)
2214 return isl_basic_map_remove_unknown_divs(bset);
2217 __isl_give isl_map *isl_map_remove_unknown_divs(__isl_take isl_map *map)
2226 map = isl_map_cow(map);
2230 for (i = 0; i < map->n; ++i) {
2231 map->p[i] = isl_basic_map_remove_unknown_divs(map->p[i]);
2241 __isl_give isl_set *isl_set_remove_unknown_divs(__isl_take isl_set *set)
2243 return (isl_set *)isl_map_remove_unknown_divs((isl_map *)set);
2246 __isl_give isl_basic_set *isl_basic_set_remove_dims(
2247 __isl_take isl_basic_set *bset,
2248 enum isl_dim_type type, unsigned first, unsigned n)
2250 return (isl_basic_set *)
2251 isl_basic_map_remove_dims((isl_basic_map *)bset, type, first, n);
2254 struct isl_map *isl_map_remove_dims(struct isl_map *map,
2255 enum isl_dim_type type, unsigned first, unsigned n)
2262 map = isl_map_cow(map);
2265 isl_assert(map->ctx, first + n <= isl_map_dim(map, type), goto error);
2267 for (i = 0; i < map->n; ++i) {
2268 map->p[i] = isl_basic_map_eliminate_vars(map->p[i],
2269 isl_basic_map_offset(map->p[i], type) - 1 + first, n);
2273 map = isl_map_drop(map, type, first, n);
2280 __isl_give isl_set *isl_set_remove_dims(__isl_take isl_set *bset,
2281 enum isl_dim_type type, unsigned first, unsigned n)
2283 return (isl_set *)isl_map_remove_dims((isl_map *)bset, type, first, n);
2286 /* Project out n inputs starting at first using Fourier-Motzkin */
2287 struct isl_map *isl_map_remove_inputs(struct isl_map *map,
2288 unsigned first, unsigned n)
2290 return isl_map_remove_dims(map, isl_dim_in, first, n);
2293 static void dump_term(struct isl_basic_map *bmap,
2294 isl_int c, int pos, FILE *out)
2297 unsigned in = isl_basic_map_n_in(bmap);
2298 unsigned dim = in + isl_basic_map_n_out(bmap);
2299 unsigned nparam = isl_basic_map_n_param(bmap);
2301 isl_int_print(out, c, 0);
2303 if (!isl_int_is_one(c))
2304 isl_int_print(out, c, 0);
2305 if (pos < 1 + nparam) {
2306 name = isl_space_get_dim_name(bmap->dim,
2307 isl_dim_param, pos - 1);
2309 fprintf(out, "%s", name);
2311 fprintf(out, "p%d", pos - 1);
2312 } else if (pos < 1 + nparam + in)
2313 fprintf(out, "i%d", pos - 1 - nparam);
2314 else if (pos < 1 + nparam + dim)
2315 fprintf(out, "o%d", pos - 1 - nparam - in);
2317 fprintf(out, "e%d", pos - 1 - nparam - dim);
2321 static void dump_constraint_sign(struct isl_basic_map *bmap, isl_int *c,
2322 int sign, FILE *out)
2326 unsigned len = 1 + isl_basic_map_total_dim(bmap);
2330 for (i = 0, first = 1; i < len; ++i) {
2331 if (isl_int_sgn(c[i]) * sign <= 0)
2334 fprintf(out, " + ");
2336 isl_int_abs(v, c[i]);
2337 dump_term(bmap, v, i, out);
2344 static void dump_constraint(struct isl_basic_map *bmap, isl_int *c,
2345 const char *op, FILE *out, int indent)
2349 fprintf(out, "%*s", indent, "");
2351 dump_constraint_sign(bmap, c, 1, out);
2352 fprintf(out, " %s ", op);
2353 dump_constraint_sign(bmap, c, -1, out);
2357 for (i = bmap->n_div; i < bmap->extra; ++i) {
2358 if (isl_int_is_zero(c[1+isl_space_dim(bmap->dim, isl_dim_all)+i]))
2360 fprintf(out, "%*s", indent, "");
2361 fprintf(out, "ERROR: unused div coefficient not zero\n");
2366 static void dump_constraints(struct isl_basic_map *bmap,
2367 isl_int **c, unsigned n,
2368 const char *op, FILE *out, int indent)
2372 for (i = 0; i < n; ++i)
2373 dump_constraint(bmap, c[i], op, out, indent);
2376 static void dump_affine(struct isl_basic_map *bmap, isl_int *exp, FILE *out)
2380 unsigned total = isl_basic_map_total_dim(bmap);
2382 for (j = 0; j < 1 + total; ++j) {
2383 if (isl_int_is_zero(exp[j]))
2385 if (!first && isl_int_is_pos(exp[j]))
2387 dump_term(bmap, exp[j], j, out);
2392 static void dump(struct isl_basic_map *bmap, FILE *out, int indent)
2396 dump_constraints(bmap, bmap->eq, bmap->n_eq, "=", out, indent);
2397 dump_constraints(bmap, bmap->ineq, bmap->n_ineq, ">=", out, indent);
2399 for (i = 0; i < bmap->n_div; ++i) {
2400 fprintf(out, "%*s", indent, "");
2401 fprintf(out, "e%d = [(", i);
2402 dump_affine(bmap, bmap->div[i]+1, out);
2404 isl_int_print(out, bmap->div[i][0], 0);
2405 fprintf(out, "]\n");
2409 void isl_basic_set_print_internal(struct isl_basic_set *bset,
2410 FILE *out, int indent)
2413 fprintf(out, "null basic set\n");
2417 fprintf(out, "%*s", indent, "");
2418 fprintf(out, "ref: %d, nparam: %d, dim: %d, extra: %d, flags: %x\n",
2419 bset->ref, bset->dim->nparam, bset->dim->n_out,
2420 bset->extra, bset->flags);
2421 dump((struct isl_basic_map *)bset, out, indent);
2424 void isl_basic_map_print_internal(struct isl_basic_map *bmap,
2425 FILE *out, int indent)
2428 fprintf(out, "null basic map\n");
2432 fprintf(out, "%*s", indent, "");
2433 fprintf(out, "ref: %d, nparam: %d, in: %d, out: %d, extra: %d, "
2434 "flags: %x, n_name: %d\n",
2436 bmap->dim->nparam, bmap->dim->n_in, bmap->dim->n_out,
2437 bmap->extra, bmap->flags, bmap->dim->n_id);
2438 dump(bmap, out, indent);
2441 int isl_inequality_negate(struct isl_basic_map *bmap, unsigned pos)
2446 total = isl_basic_map_total_dim(bmap);
2447 isl_assert(bmap->ctx, pos < bmap->n_ineq, return -1);
2448 isl_seq_neg(bmap->ineq[pos], bmap->ineq[pos], 1 + total);
2449 isl_int_sub_ui(bmap->ineq[pos][0], bmap->ineq[pos][0], 1);
2450 ISL_F_CLR(bmap, ISL_BASIC_MAP_NORMALIZED);
2454 __isl_give isl_set *isl_set_alloc_space(__isl_take isl_space *dim, int n,
2457 struct isl_set *set;
2461 isl_assert(dim->ctx, dim->n_in == 0, goto error);
2462 isl_assert(dim->ctx, n >= 0, goto error);
2463 set = isl_alloc(dim->ctx, struct isl_set,
2464 sizeof(struct isl_set) +
2465 (n - 1) * sizeof(struct isl_basic_set *));
2469 set->ctx = dim->ctx;
2470 isl_ctx_ref(set->ctx);
2478 isl_space_free(dim);
2482 struct isl_set *isl_set_alloc(struct isl_ctx *ctx,
2483 unsigned nparam, unsigned dim, int n, unsigned flags)
2485 struct isl_set *set;
2488 dims = isl_space_alloc(ctx, nparam, 0, dim);
2492 set = isl_set_alloc_space(dims, n, flags);
2496 /* Make sure "map" has room for at least "n" more basic maps.
2498 struct isl_map *isl_map_grow(struct isl_map *map, int n)
2501 struct isl_map *grown = NULL;
2505 isl_assert(map->ctx, n >= 0, goto error);
2506 if (map->n + n <= map->size)
2508 grown = isl_map_alloc_space(isl_map_get_space(map), map->n + n, map->flags);
2511 for (i = 0; i < map->n; ++i) {
2512 grown->p[i] = isl_basic_map_copy(map->p[i]);
2520 isl_map_free(grown);
2525 /* Make sure "set" has room for at least "n" more basic sets.
2527 struct isl_set *isl_set_grow(struct isl_set *set, int n)
2529 return (struct isl_set *)isl_map_grow((struct isl_map *)set, n);
2532 struct isl_set *isl_set_dup(struct isl_set *set)
2535 struct isl_set *dup;
2540 dup = isl_set_alloc_space(isl_space_copy(set->dim), set->n, set->flags);
2543 for (i = 0; i < set->n; ++i)
2544 dup = isl_set_add_basic_set(dup, isl_basic_set_copy(set->p[i]));
2548 struct isl_set *isl_set_from_basic_set(struct isl_basic_set *bset)
2550 return isl_map_from_basic_map(bset);
2553 struct isl_map *isl_map_from_basic_map(struct isl_basic_map *bmap)
2555 struct isl_map *map;
2560 map = isl_map_alloc_space(isl_space_copy(bmap->dim), 1, ISL_MAP_DISJOINT);
2561 return isl_map_add_basic_map(map, bmap);
2564 __isl_give isl_set *isl_set_add_basic_set(__isl_take isl_set *set,
2565 __isl_take isl_basic_set *bset)
2567 return (struct isl_set *)isl_map_add_basic_map((struct isl_map *)set,
2568 (struct isl_basic_map *)bset);
2571 void *isl_set_free(__isl_take isl_set *set)
2581 isl_ctx_deref(set->ctx);
2582 for (i = 0; i < set->n; ++i)
2583 isl_basic_set_free(set->p[i]);
2584 isl_space_free(set->dim);
2590 void isl_set_print_internal(struct isl_set *set, FILE *out, int indent)
2595 fprintf(out, "null set\n");
2599 fprintf(out, "%*s", indent, "");
2600 fprintf(out, "ref: %d, n: %d, nparam: %d, dim: %d, flags: %x\n",
2601 set->ref, set->n, set->dim->nparam, set->dim->n_out,
2603 for (i = 0; i < set->n; ++i) {
2604 fprintf(out, "%*s", indent, "");
2605 fprintf(out, "basic set %d:\n", i);
2606 isl_basic_set_print_internal(set->p[i], out, indent+4);
2610 void isl_map_print_internal(struct isl_map *map, FILE *out, int indent)
2615 fprintf(out, "null map\n");
2619 fprintf(out, "%*s", indent, "");
2620 fprintf(out, "ref: %d, n: %d, nparam: %d, in: %d, out: %d, "
2621 "flags: %x, n_name: %d\n",
2622 map->ref, map->n, map->dim->nparam, map->dim->n_in,
2623 map->dim->n_out, map->flags, map->dim->n_id);
2624 for (i = 0; i < map->n; ++i) {
2625 fprintf(out, "%*s", indent, "");
2626 fprintf(out, "basic map %d:\n", i);
2627 isl_basic_map_print_internal(map->p[i], out, indent+4);
2631 struct isl_basic_map *isl_basic_map_intersect_domain(
2632 struct isl_basic_map *bmap, struct isl_basic_set *bset)
2634 struct isl_basic_map *bmap_domain;
2639 isl_assert(bset->ctx, isl_space_match(bmap->dim, isl_dim_param,
2640 bset->dim, isl_dim_param), goto error);
2642 if (isl_space_dim(bset->dim, isl_dim_set) != 0)
2643 isl_assert(bset->ctx,
2644 isl_basic_map_compatible_domain(bmap, bset), goto error);
2646 bmap = isl_basic_map_cow(bmap);
2649 bmap = isl_basic_map_extend_space(bmap, isl_space_copy(bmap->dim),
2650 bset->n_div, bset->n_eq, bset->n_ineq);
2651 bmap_domain = isl_basic_map_from_domain(bset);
2652 bmap = add_constraints(bmap, bmap_domain, 0, 0);
2654 bmap = isl_basic_map_simplify(bmap);
2655 return isl_basic_map_finalize(bmap);
2657 isl_basic_map_free(bmap);
2658 isl_basic_set_free(bset);
2662 struct isl_basic_map *isl_basic_map_intersect_range(
2663 struct isl_basic_map *bmap, struct isl_basic_set *bset)
2665 struct isl_basic_map *bmap_range;
2670 isl_assert(bset->ctx, isl_space_match(bmap->dim, isl_dim_param,
2671 bset->dim, isl_dim_param), goto error);
2673 if (isl_space_dim(bset->dim, isl_dim_set) != 0)
2674 isl_assert(bset->ctx,
2675 isl_basic_map_compatible_range(bmap, bset), goto error);
2677 if (isl_basic_set_is_universe(bset)) {
2678 isl_basic_set_free(bset);
2682 bmap = isl_basic_map_cow(bmap);
2685 bmap = isl_basic_map_extend_space(bmap, isl_space_copy(bmap->dim),
2686 bset->n_div, bset->n_eq, bset->n_ineq);
2687 bmap_range = isl_basic_map_from_basic_set(bset, isl_space_copy(bset->dim));
2688 bmap = add_constraints(bmap, bmap_range, 0, 0);
2690 bmap = isl_basic_map_simplify(bmap);
2691 return isl_basic_map_finalize(bmap);
2693 isl_basic_map_free(bmap);
2694 isl_basic_set_free(bset);
2698 int isl_basic_map_contains(struct isl_basic_map *bmap, struct isl_vec *vec)
2704 total = 1 + isl_basic_map_total_dim(bmap);
2705 if (total != vec->size)
2710 for (i = 0; i < bmap->n_eq; ++i) {
2711 isl_seq_inner_product(vec->el, bmap->eq[i], total, &s);
2712 if (!isl_int_is_zero(s)) {
2718 for (i = 0; i < bmap->n_ineq; ++i) {
2719 isl_seq_inner_product(vec->el, bmap->ineq[i], total, &s);
2720 if (isl_int_is_neg(s)) {
2731 int isl_basic_set_contains(struct isl_basic_set *bset, struct isl_vec *vec)
2733 return isl_basic_map_contains((struct isl_basic_map *)bset, vec);
2736 struct isl_basic_map *isl_basic_map_intersect(
2737 struct isl_basic_map *bmap1, struct isl_basic_map *bmap2)
2739 struct isl_vec *sample = NULL;
2741 if (!bmap1 || !bmap2)
2744 isl_assert(bmap1->ctx, isl_space_match(bmap1->dim, isl_dim_param,
2745 bmap2->dim, isl_dim_param), goto error);
2746 if (isl_space_dim(bmap1->dim, isl_dim_all) ==
2747 isl_space_dim(bmap1->dim, isl_dim_param) &&
2748 isl_space_dim(bmap2->dim, isl_dim_all) !=
2749 isl_space_dim(bmap2->dim, isl_dim_param))
2750 return isl_basic_map_intersect(bmap2, bmap1);
2752 if (isl_space_dim(bmap2->dim, isl_dim_all) !=
2753 isl_space_dim(bmap2->dim, isl_dim_param))
2754 isl_assert(bmap1->ctx,
2755 isl_space_is_equal(bmap1->dim, bmap2->dim), goto error);
2757 if (bmap1->sample &&
2758 isl_basic_map_contains(bmap1, bmap1->sample) > 0 &&
2759 isl_basic_map_contains(bmap2, bmap1->sample) > 0)
2760 sample = isl_vec_copy(bmap1->sample);
2761 else if (bmap2->sample &&
2762 isl_basic_map_contains(bmap1, bmap2->sample) > 0 &&
2763 isl_basic_map_contains(bmap2, bmap2->sample) > 0)
2764 sample = isl_vec_copy(bmap2->sample);
2766 bmap1 = isl_basic_map_cow(bmap1);
2769 bmap1 = isl_basic_map_extend_space(bmap1, isl_space_copy(bmap1->dim),
2770 bmap2->n_div, bmap2->n_eq, bmap2->n_ineq);
2771 bmap1 = add_constraints(bmap1, bmap2, 0, 0);
2774 isl_vec_free(sample);
2776 isl_vec_free(bmap1->sample);
2777 bmap1->sample = sample;
2780 bmap1 = isl_basic_map_simplify(bmap1);
2781 return isl_basic_map_finalize(bmap1);
2784 isl_vec_free(sample);
2785 isl_basic_map_free(bmap1);
2786 isl_basic_map_free(bmap2);
2790 struct isl_basic_set *isl_basic_set_intersect(
2791 struct isl_basic_set *bset1, struct isl_basic_set *bset2)
2793 return (struct isl_basic_set *)
2794 isl_basic_map_intersect(
2795 (struct isl_basic_map *)bset1,
2796 (struct isl_basic_map *)bset2);
2799 __isl_give isl_basic_set *isl_basic_set_intersect_params(
2800 __isl_take isl_basic_set *bset1, __isl_take isl_basic_set *bset2)
2802 return isl_basic_set_intersect(bset1, bset2);
2805 /* Special case of isl_map_intersect, where both map1 and map2
2806 * are convex, without any divs and such that either map1 or map2
2807 * contains a single constraint. This constraint is then simply
2808 * added to the other map.
2810 static __isl_give isl_map *map_intersect_add_constraint(
2811 __isl_take isl_map *map1, __isl_take isl_map *map2)
2813 isl_assert(map1->ctx, map1->n == 1, goto error);
2814 isl_assert(map2->ctx, map1->n == 1, goto error);
2815 isl_assert(map1->ctx, map1->p[0]->n_div == 0, goto error);
2816 isl_assert(map2->ctx, map1->p[0]->n_div == 0, goto error);
2818 if (map2->p[0]->n_eq + map2->p[0]->n_ineq != 1)
2819 return isl_map_intersect(map2, map1);
2821 isl_assert(map2->ctx,
2822 map2->p[0]->n_eq + map2->p[0]->n_ineq == 1, goto error);
2824 map1 = isl_map_cow(map1);
2827 if (isl_map_plain_is_empty(map1)) {
2831 map1->p[0] = isl_basic_map_cow(map1->p[0]);
2832 if (map2->p[0]->n_eq == 1)
2833 map1->p[0] = isl_basic_map_add_eq(map1->p[0], map2->p[0]->eq[0]);
2835 map1->p[0] = isl_basic_map_add_ineq(map1->p[0],
2836 map2->p[0]->ineq[0]);
2838 map1->p[0] = isl_basic_map_simplify(map1->p[0]);
2839 map1->p[0] = isl_basic_map_finalize(map1->p[0]);
2843 if (isl_basic_map_plain_is_empty(map1->p[0])) {
2844 isl_basic_map_free(map1->p[0]);
2857 /* map2 may be either a parameter domain or a map living in the same
2860 static __isl_give isl_map *map_intersect_internal(__isl_take isl_map *map1,
2861 __isl_take isl_map *map2)
2870 if ((isl_map_plain_is_empty(map1) ||
2871 isl_map_plain_is_universe(map2)) &&
2872 isl_space_is_equal(map1->dim, map2->dim)) {
2876 if ((isl_map_plain_is_empty(map2) ||
2877 isl_map_plain_is_universe(map1)) &&
2878 isl_space_is_equal(map1->dim, map2->dim)) {
2883 if (map1->n == 1 && map2->n == 1 &&
2884 map1->p[0]->n_div == 0 && map2->p[0]->n_div == 0 &&
2885 isl_space_is_equal(map1->dim, map2->dim) &&
2886 (map1->p[0]->n_eq + map1->p[0]->n_ineq == 1 ||
2887 map2->p[0]->n_eq + map2->p[0]->n_ineq == 1))
2888 return map_intersect_add_constraint(map1, map2);
2890 if (isl_space_dim(map2->dim, isl_dim_all) !=
2891 isl_space_dim(map2->dim, isl_dim_param))
2892 isl_assert(map1->ctx,
2893 isl_space_is_equal(map1->dim, map2->dim), goto error);
2895 if (ISL_F_ISSET(map1, ISL_MAP_DISJOINT) &&
2896 ISL_F_ISSET(map2, ISL_MAP_DISJOINT))
2897 ISL_FL_SET(flags, ISL_MAP_DISJOINT);
2899 result = isl_map_alloc_space(isl_space_copy(map1->dim),
2900 map1->n * map2->n, flags);
2903 for (i = 0; i < map1->n; ++i)
2904 for (j = 0; j < map2->n; ++j) {
2905 struct isl_basic_map *part;
2906 part = isl_basic_map_intersect(
2907 isl_basic_map_copy(map1->p[i]),
2908 isl_basic_map_copy(map2->p[j]));
2909 if (isl_basic_map_is_empty(part) < 0)
2910 part = isl_basic_map_free(part);
2911 result = isl_map_add_basic_map(result, part);
2924 static __isl_give isl_map *map_intersect(__isl_take isl_map *map1,
2925 __isl_take isl_map *map2)
2929 if (!isl_space_is_equal(map1->dim, map2->dim))
2930 isl_die(isl_map_get_ctx(map1), isl_error_invalid,
2931 "spaces don't match", goto error);
2932 return map_intersect_internal(map1, map2);
2939 __isl_give isl_map *isl_map_intersect(__isl_take isl_map *map1,
2940 __isl_take isl_map *map2)
2942 return isl_map_align_params_map_map_and(map1, map2, &map_intersect);
2945 struct isl_set *isl_set_intersect(struct isl_set *set1, struct isl_set *set2)
2947 return (struct isl_set *)
2948 isl_map_intersect((struct isl_map *)set1,
2949 (struct isl_map *)set2);
2952 /* map_intersect_internal accepts intersections
2953 * with parameter domains, so we can just call that function.
2955 static __isl_give isl_map *map_intersect_params(__isl_take isl_map *map,
2956 __isl_take isl_set *params)
2958 return map_intersect_internal(map, params);
2961 __isl_give isl_map *isl_map_intersect_params(__isl_take isl_map *map1,
2962 __isl_take isl_map *map2)
2964 return isl_map_align_params_map_map_and(map1, map2, &map_intersect_params);
2967 __isl_give isl_set *isl_set_intersect_params(__isl_take isl_set *set,
2968 __isl_take isl_set *params)
2970 return isl_map_intersect_params(set, params);
2973 struct isl_basic_map *isl_basic_map_reverse(struct isl_basic_map *bmap)
2976 struct isl_basic_set *bset;
2981 bmap = isl_basic_map_cow(bmap);
2984 dim = isl_space_reverse(isl_space_copy(bmap->dim));
2985 in = isl_basic_map_n_in(bmap);
2986 bset = isl_basic_set_from_basic_map(bmap);
2987 bset = isl_basic_set_swap_vars(bset, in);
2988 return isl_basic_map_from_basic_set(bset, dim);
2991 static __isl_give isl_basic_map *basic_map_space_reset(
2992 __isl_take isl_basic_map *bmap, enum isl_dim_type type)
2998 if (!isl_space_is_named_or_nested(bmap->dim, type))
3001 space = isl_basic_map_get_space(bmap);
3002 space = isl_space_reset(space, type);
3003 bmap = isl_basic_map_reset_space(bmap, space);
3007 __isl_give isl_basic_map *isl_basic_map_insert_dims(
3008 __isl_take isl_basic_map *bmap, enum isl_dim_type type,
3009 unsigned pos, unsigned n)
3012 struct isl_basic_map *res;
3013 struct isl_dim_map *dim_map;
3014 unsigned total, off;
3015 enum isl_dim_type t;
3018 return basic_map_space_reset(bmap, type);
3023 res_dim = isl_space_insert_dims(isl_basic_map_get_space(bmap), type, pos, n);
3025 total = isl_basic_map_total_dim(bmap) + n;
3026 dim_map = isl_dim_map_alloc(bmap->ctx, total);
3028 for (t = isl_dim_param; t <= isl_dim_out; ++t) {
3030 isl_dim_map_dim(dim_map, bmap->dim, t, off);
3032 unsigned size = isl_basic_map_dim(bmap, t);
3033 isl_dim_map_dim_range(dim_map, bmap->dim, t,
3035 isl_dim_map_dim_range(dim_map, bmap->dim, t,
3036 pos, size - pos, off + pos + n);
3038 off += isl_space_dim(res_dim, t);
3040 isl_dim_map_div(dim_map, bmap, off);
3042 res = isl_basic_map_alloc_space(res_dim,
3043 bmap->n_div, bmap->n_eq, bmap->n_ineq);
3044 if (isl_basic_map_is_rational(bmap))
3045 res = isl_basic_map_set_rational(res);
3046 if (isl_basic_map_plain_is_empty(bmap)) {
3047 isl_basic_map_free(bmap);
3048 return isl_basic_map_set_to_empty(res);
3050 res = isl_basic_map_add_constraints_dim_map(res, bmap, dim_map);
3051 return isl_basic_map_finalize(res);
3054 __isl_give isl_basic_set *isl_basic_set_insert_dims(
3055 __isl_take isl_basic_set *bset,
3056 enum isl_dim_type type, unsigned pos, unsigned n)
3058 return isl_basic_map_insert_dims(bset, type, pos, n);
3061 __isl_give isl_basic_map *isl_basic_map_add(__isl_take isl_basic_map *bmap,
3062 enum isl_dim_type type, unsigned n)
3066 return isl_basic_map_insert_dims(bmap, type,
3067 isl_basic_map_dim(bmap, type), n);
3070 __isl_give isl_basic_set *isl_basic_set_add_dims(__isl_take isl_basic_set *bset,
3071 enum isl_dim_type type, unsigned n)
3075 isl_assert(bset->ctx, type != isl_dim_in, goto error);
3076 return (isl_basic_set *)isl_basic_map_add((isl_basic_map *)bset, type, n);
3078 isl_basic_set_free(bset);
3082 static __isl_give isl_map *map_space_reset(__isl_take isl_map *map,
3083 enum isl_dim_type type)
3087 if (!map || !isl_space_is_named_or_nested(map->dim, type))
3090 space = isl_map_get_space(map);
3091 space = isl_space_reset(space, type);
3092 map = isl_map_reset_space(map, space);
3096 __isl_give isl_map *isl_map_insert_dims(__isl_take isl_map *map,
3097 enum isl_dim_type type, unsigned pos, unsigned n)
3102 return map_space_reset(map, type);
3104 map = isl_map_cow(map);
3108 map->dim = isl_space_insert_dims(map->dim, type, pos, n);
3112 for (i = 0; i < map->n; ++i) {
3113 map->p[i] = isl_basic_map_insert_dims(map->p[i], type, pos, n);
3124 __isl_give isl_set *isl_set_insert_dims(__isl_take isl_set *set,
3125 enum isl_dim_type type, unsigned pos, unsigned n)
3127 return isl_map_insert_dims(set, type, pos, n);
3130 __isl_give isl_map *isl_map_add_dims(__isl_take isl_map *map,
3131 enum isl_dim_type type, unsigned n)
3135 return isl_map_insert_dims(map, type, isl_map_dim(map, type), n);
3138 __isl_give isl_set *isl_set_add_dims(__isl_take isl_set *set,
3139 enum isl_dim_type type, unsigned n)
3143 isl_assert(set->ctx, type != isl_dim_in, goto error);
3144 return (isl_set *)isl_map_add_dims((isl_map *)set, type, n);
3150 __isl_give isl_basic_map *isl_basic_map_move_dims(
3151 __isl_take isl_basic_map *bmap,
3152 enum isl_dim_type dst_type, unsigned dst_pos,
3153 enum isl_dim_type src_type, unsigned src_pos, unsigned n)
3155 struct isl_dim_map *dim_map;
3156 struct isl_basic_map *res;
3157 enum isl_dim_type t;
3158 unsigned total, off;
3165 isl_assert(bmap->ctx, src_pos + n <= isl_basic_map_dim(bmap, src_type),
3168 if (dst_type == src_type && dst_pos == src_pos)
3171 isl_assert(bmap->ctx, dst_type != src_type, goto error);
3173 if (pos(bmap->dim, dst_type) + dst_pos ==
3174 pos(bmap->dim, src_type) + src_pos +
3175 ((src_type < dst_type) ? n : 0)) {
3176 bmap = isl_basic_map_cow(bmap);
3180 bmap->dim = isl_space_move_dims(bmap->dim, dst_type, dst_pos,
3181 src_type, src_pos, n);
3185 bmap = isl_basic_map_finalize(bmap);
3190 total = isl_basic_map_total_dim(bmap);
3191 dim_map = isl_dim_map_alloc(bmap->ctx, total);
3194 for (t = isl_dim_param; t <= isl_dim_out; ++t) {
3195 unsigned size = isl_space_dim(bmap->dim, t);
3196 if (t == dst_type) {
3197 isl_dim_map_dim_range(dim_map, bmap->dim, t,
3200 isl_dim_map_dim_range(dim_map, bmap->dim, src_type,
3203 isl_dim_map_dim_range(dim_map, bmap->dim, t,
3204 dst_pos, size - dst_pos, off);
3205 off += size - dst_pos;
3206 } else if (t == src_type) {
3207 isl_dim_map_dim_range(dim_map, bmap->dim, t,
3210 isl_dim_map_dim_range(dim_map, bmap->dim, t,
3211 src_pos + n, size - src_pos - n, off);
3212 off += size - src_pos - n;
3214 isl_dim_map_dim(dim_map, bmap->dim, t, off);
3218 isl_dim_map_div(dim_map, bmap, off);
3220 res = isl_basic_map_alloc_space(isl_basic_map_get_space(bmap),
3221 bmap->n_div, bmap->n_eq, bmap->n_ineq);
3222 bmap = isl_basic_map_add_constraints_dim_map(res, bmap, dim_map);
3224 bmap->dim = isl_space_move_dims(bmap->dim, dst_type, dst_pos,
3225 src_type, src_pos, n);
3229 ISL_F_CLR(bmap, ISL_BASIC_MAP_NORMALIZED);
3230 bmap = isl_basic_map_gauss(bmap, NULL);
3231 bmap = isl_basic_map_finalize(bmap);
3235 isl_basic_map_free(bmap);
3239 __isl_give isl_basic_set *isl_basic_set_move_dims(__isl_take isl_basic_set *bset,
3240 enum isl_dim_type dst_type, unsigned dst_pos,
3241 enum isl_dim_type src_type, unsigned src_pos, unsigned n)
3243 return (isl_basic_set *)isl_basic_map_move_dims(
3244 (isl_basic_map *)bset, dst_type, dst_pos, src_type, src_pos, n);
3247 __isl_give isl_set *isl_set_move_dims(__isl_take isl_set *set,
3248 enum isl_dim_type dst_type, unsigned dst_pos,
3249 enum isl_dim_type src_type, unsigned src_pos, unsigned n)
3253 isl_assert(set->ctx, dst_type != isl_dim_in, goto error);
3254 return (isl_set *)isl_map_move_dims((isl_map *)set, dst_type, dst_pos,
3255 src_type, src_pos, n);
3261 __isl_give isl_map *isl_map_move_dims(__isl_take isl_map *map,
3262 enum isl_dim_type dst_type, unsigned dst_pos,
3263 enum isl_dim_type src_type, unsigned src_pos, unsigned n)
3272 isl_assert(map->ctx, src_pos + n <= isl_map_dim(map, src_type),
3275 if (dst_type == src_type && dst_pos == src_pos)
3278 isl_assert(map->ctx, dst_type != src_type, goto error);
3280 map = isl_map_cow(map);
3284 map->dim = isl_space_move_dims(map->dim, dst_type, dst_pos, src_type, src_pos, n);
3288 for (i = 0; i < map->n; ++i) {
3289 map->p[i] = isl_basic_map_move_dims(map->p[i],
3291 src_type, src_pos, n);
3302 /* Move the specified dimensions to the last columns right before
3303 * the divs. Don't change the dimension specification of bmap.
3304 * That's the responsibility of the caller.
3306 static __isl_give isl_basic_map *move_last(__isl_take isl_basic_map *bmap,
3307 enum isl_dim_type type, unsigned first, unsigned n)
3309 struct isl_dim_map *dim_map;
3310 struct isl_basic_map *res;
3311 enum isl_dim_type t;
3312 unsigned total, off;
3316 if (pos(bmap->dim, type) + first + n ==
3317 1 + isl_space_dim(bmap->dim, isl_dim_all))
3320 total = isl_basic_map_total_dim(bmap);
3321 dim_map = isl_dim_map_alloc(bmap->ctx, total);
3324 for (t = isl_dim_param; t <= isl_dim_out; ++t) {
3325 unsigned size = isl_space_dim(bmap->dim, t);
3327 isl_dim_map_dim_range(dim_map, bmap->dim, t,
3330 isl_dim_map_dim_range(dim_map, bmap->dim, t,
3331 first, n, total - bmap->n_div - n);
3332 isl_dim_map_dim_range(dim_map, bmap->dim, t,
3333 first + n, size - (first + n), off);
3334 off += size - (first + n);
3336 isl_dim_map_dim(dim_map, bmap->dim, t, off);
3340 isl_dim_map_div(dim_map, bmap, off + n);
3342 res = isl_basic_map_alloc_space(isl_basic_map_get_space(bmap),
3343 bmap->n_div, bmap->n_eq, bmap->n_ineq);
3344 res = isl_basic_map_add_constraints_dim_map(res, bmap, dim_map);
3348 /* Turn the n dimensions of type type, starting at first
3349 * into existentially quantified variables.
3351 __isl_give isl_basic_map *isl_basic_map_project_out(
3352 __isl_take isl_basic_map *bmap,
3353 enum isl_dim_type type, unsigned first, unsigned n)
3361 return basic_map_space_reset(bmap, type);
3366 if (ISL_F_ISSET(bmap, ISL_BASIC_MAP_RATIONAL))
3367 return isl_basic_map_remove_dims(bmap, type, first, n);
3369 isl_assert(bmap->ctx, first + n <= isl_basic_map_dim(bmap, type),
3372 bmap = move_last(bmap, type, first, n);
3373 bmap = isl_basic_map_cow(bmap);
3377 row_size = 1 + isl_space_dim(bmap->dim, isl_dim_all) + bmap->extra;
3378 old = bmap->block2.data;
3379 bmap->block2 = isl_blk_extend(bmap->ctx, bmap->block2,
3380 (bmap->extra + n) * (1 + row_size));
3381 if (!bmap->block2.data)
3383 new_div = isl_alloc_array(bmap->ctx, isl_int *, bmap->extra + n);
3386 for (i = 0; i < n; ++i) {
3387 new_div[i] = bmap->block2.data +
3388 (bmap->extra + i) * (1 + row_size);
3389 isl_seq_clr(new_div[i], 1 + row_size);
3391 for (i = 0; i < bmap->extra; ++i)
3392 new_div[n + i] = bmap->block2.data + (bmap->div[i] - old);
3394 bmap->div = new_div;
3398 bmap->dim = isl_space_drop_dims(bmap->dim, type, first, n);
3401 bmap = isl_basic_map_simplify(bmap);
3402 bmap = isl_basic_map_drop_redundant_divs(bmap);
3403 return isl_basic_map_finalize(bmap);
3405 isl_basic_map_free(bmap);
3409 /* Turn the n dimensions of type type, starting at first
3410 * into existentially quantified variables.
3412 struct isl_basic_set *isl_basic_set_project_out(struct isl_basic_set *bset,
3413 enum isl_dim_type type, unsigned first, unsigned n)
3415 return (isl_basic_set *)isl_basic_map_project_out(
3416 (isl_basic_map *)bset, type, first, n);
3419 /* Turn the n dimensions of type type, starting at first
3420 * into existentially quantified variables.
3422 __isl_give isl_map *isl_map_project_out(__isl_take isl_map *map,
3423 enum isl_dim_type type, unsigned first, unsigned n)
3431 return map_space_reset(map, type);
3433 isl_assert(map->ctx, first + n <= isl_map_dim(map, type), goto error);
3435 map = isl_map_cow(map);
3439 map->dim = isl_space_drop_dims(map->dim, type, first, n);
3443 for (i = 0; i < map->n; ++i) {
3444 map->p[i] = isl_basic_map_project_out(map->p[i], type, first, n);
3455 /* Turn the n dimensions of type type, starting at first
3456 * into existentially quantified variables.
3458 __isl_give isl_set *isl_set_project_out(__isl_take isl_set *set,
3459 enum isl_dim_type type, unsigned first, unsigned n)
3461 return (isl_set *)isl_map_project_out((isl_map *)set, type, first, n);
3464 static struct isl_basic_map *add_divs(struct isl_basic_map *bmap, unsigned n)
3468 for (i = 0; i < n; ++i) {
3469 j = isl_basic_map_alloc_div(bmap);
3472 isl_seq_clr(bmap->div[j], 1+1+isl_basic_map_total_dim(bmap));
3476 isl_basic_map_free(bmap);
3480 struct isl_basic_map *isl_basic_map_apply_range(
3481 struct isl_basic_map *bmap1, struct isl_basic_map *bmap2)
3483 isl_space *dim_result = NULL;
3484 struct isl_basic_map *bmap;
3485 unsigned n_in, n_out, n, nparam, total, pos;
3486 struct isl_dim_map *dim_map1, *dim_map2;
3488 if (!bmap1 || !bmap2)
3491 dim_result = isl_space_join(isl_space_copy(bmap1->dim),
3492 isl_space_copy(bmap2->dim));
3494 n_in = isl_basic_map_n_in(bmap1);
3495 n_out = isl_basic_map_n_out(bmap2);
3496 n = isl_basic_map_n_out(bmap1);
3497 nparam = isl_basic_map_n_param(bmap1);
3499 total = nparam + n_in + n_out + bmap1->n_div + bmap2->n_div + n;
3500 dim_map1 = isl_dim_map_alloc(bmap1->ctx, total);
3501 dim_map2 = isl_dim_map_alloc(bmap1->ctx, total);
3502 isl_dim_map_dim(dim_map1, bmap1->dim, isl_dim_param, pos = 0);
3503 isl_dim_map_dim(dim_map2, bmap2->dim, isl_dim_param, pos = 0);
3504 isl_dim_map_dim(dim_map1, bmap1->dim, isl_dim_in, pos += nparam);
3505 isl_dim_map_dim(dim_map2, bmap2->dim, isl_dim_out, pos += n_in);
3506 isl_dim_map_div(dim_map1, bmap1, pos += n_out);
3507 isl_dim_map_div(dim_map2, bmap2, pos += bmap1->n_div);
3508 isl_dim_map_dim(dim_map1, bmap1->dim, isl_dim_out, pos += bmap2->n_div);
3509 isl_dim_map_dim(dim_map2, bmap2->dim, isl_dim_in, pos);
3511 bmap = isl_basic_map_alloc_space(dim_result,
3512 bmap1->n_div + bmap2->n_div + n,
3513 bmap1->n_eq + bmap2->n_eq,
3514 bmap1->n_ineq + bmap2->n_ineq);
3515 bmap = isl_basic_map_add_constraints_dim_map(bmap, bmap1, dim_map1);
3516 bmap = isl_basic_map_add_constraints_dim_map(bmap, bmap2, dim_map2);
3517 bmap = add_divs(bmap, n);
3518 bmap = isl_basic_map_simplify(bmap);
3519 bmap = isl_basic_map_drop_redundant_divs(bmap);
3520 return isl_basic_map_finalize(bmap);
3522 isl_basic_map_free(bmap1);
3523 isl_basic_map_free(bmap2);
3527 struct isl_basic_set *isl_basic_set_apply(
3528 struct isl_basic_set *bset, struct isl_basic_map *bmap)
3533 isl_assert(bset->ctx, isl_basic_map_compatible_domain(bmap, bset),
3536 return (struct isl_basic_set *)
3537 isl_basic_map_apply_range((struct isl_basic_map *)bset, bmap);
3539 isl_basic_set_free(bset);
3540 isl_basic_map_free(bmap);
3544 struct isl_basic_map *isl_basic_map_apply_domain(
3545 struct isl_basic_map *bmap1, struct isl_basic_map *bmap2)
3547 if (!bmap1 || !bmap2)
3550 isl_assert(bmap1->ctx,
3551 isl_basic_map_n_in(bmap1) == isl_basic_map_n_in(bmap2), goto error);
3552 isl_assert(bmap1->ctx,
3553 isl_basic_map_n_param(bmap1) == isl_basic_map_n_param(bmap2),
3556 bmap1 = isl_basic_map_reverse(bmap1);
3557 bmap1 = isl_basic_map_apply_range(bmap1, bmap2);
3558 return isl_basic_map_reverse(bmap1);
3560 isl_basic_map_free(bmap1);
3561 isl_basic_map_free(bmap2);
3565 /* Given two basic maps A -> f(A) and B -> g(B), construct a basic map
3566 * A \cap B -> f(A) + f(B)
3568 struct isl_basic_map *isl_basic_map_sum(
3569 struct isl_basic_map *bmap1, struct isl_basic_map *bmap2)
3571 unsigned n_in, n_out, nparam, total, pos;
3572 struct isl_basic_map *bmap = NULL;
3573 struct isl_dim_map *dim_map1, *dim_map2;
3576 if (!bmap1 || !bmap2)
3579 isl_assert(bmap1->ctx, isl_space_is_equal(bmap1->dim, bmap2->dim),
3582 nparam = isl_basic_map_n_param(bmap1);
3583 n_in = isl_basic_map_n_in(bmap1);
3584 n_out = isl_basic_map_n_out(bmap1);
3586 total = nparam + n_in + n_out + bmap1->n_div + bmap2->n_div + 2 * n_out;
3587 dim_map1 = isl_dim_map_alloc(bmap1->ctx, total);
3588 dim_map2 = isl_dim_map_alloc(bmap2->ctx, total);
3589 isl_dim_map_dim(dim_map1, bmap1->dim, isl_dim_param, pos = 0);
3590 isl_dim_map_dim(dim_map2, bmap2->dim, isl_dim_param, pos);
3591 isl_dim_map_dim(dim_map1, bmap1->dim, isl_dim_in, pos += nparam);
3592 isl_dim_map_dim(dim_map2, bmap2->dim, isl_dim_in, pos);
3593 isl_dim_map_div(dim_map1, bmap1, pos += n_in + n_out);
3594 isl_dim_map_div(dim_map2, bmap2, pos += bmap1->n_div);
3595 isl_dim_map_dim(dim_map1, bmap1->dim, isl_dim_out, pos += bmap2->n_div);
3596 isl_dim_map_dim(dim_map2, bmap2->dim, isl_dim_out, pos += n_out);
3598 bmap = isl_basic_map_alloc_space(isl_space_copy(bmap1->dim),
3599 bmap1->n_div + bmap2->n_div + 2 * n_out,
3600 bmap1->n_eq + bmap2->n_eq + n_out,
3601 bmap1->n_ineq + bmap2->n_ineq);
3602 for (i = 0; i < n_out; ++i) {
3603 int j = isl_basic_map_alloc_equality(bmap);
3606 isl_seq_clr(bmap->eq[j], 1+total);
3607 isl_int_set_si(bmap->eq[j][1+nparam+n_in+i], -1);
3608 isl_int_set_si(bmap->eq[j][1+pos+i], 1);
3609 isl_int_set_si(bmap->eq[j][1+pos-n_out+i], 1);
3611 bmap = isl_basic_map_add_constraints_dim_map(bmap, bmap1, dim_map1);
3612 bmap = isl_basic_map_add_constraints_dim_map(bmap, bmap2, dim_map2);
3613 bmap = add_divs(bmap, 2 * n_out);
3615 bmap = isl_basic_map_simplify(bmap);
3616 return isl_basic_map_finalize(bmap);
3618 isl_basic_map_free(bmap);
3619 isl_basic_map_free(bmap1);
3620 isl_basic_map_free(bmap2);
3624 /* Given two maps A -> f(A) and B -> g(B), construct a map
3625 * A \cap B -> f(A) + f(B)
3627 struct isl_map *isl_map_sum(struct isl_map *map1, struct isl_map *map2)
3629 struct isl_map *result;
3635 isl_assert(map1->ctx, isl_space_is_equal(map1->dim, map2->dim), goto error);
3637 result = isl_map_alloc_space(isl_space_copy(map1->dim),
3638 map1->n * map2->n, 0);
3641 for (i = 0; i < map1->n; ++i)
3642 for (j = 0; j < map2->n; ++j) {
3643 struct isl_basic_map *part;
3644 part = isl_basic_map_sum(
3645 isl_basic_map_copy(map1->p[i]),
3646 isl_basic_map_copy(map2->p[j]));
3647 if (isl_basic_map_is_empty(part))
3648 isl_basic_map_free(part);
3650 result = isl_map_add_basic_map(result, part);
3663 __isl_give isl_set *isl_set_sum(__isl_take isl_set *set1,
3664 __isl_take isl_set *set2)
3666 return (isl_set *)isl_map_sum((isl_map *)set1, (isl_map *)set2);
3669 /* Given a basic map A -> f(A), construct A -> -f(A).
3671 struct isl_basic_map *isl_basic_map_neg(struct isl_basic_map *bmap)
3676 bmap = isl_basic_map_cow(bmap);
3680 n = isl_basic_map_dim(bmap, isl_dim_out);
3681 off = isl_basic_map_offset(bmap, isl_dim_out);
3682 for (i = 0; i < bmap->n_eq; ++i)
3683 for (j = 0; j < n; ++j)
3684 isl_int_neg(bmap->eq[i][off+j], bmap->eq[i][off+j]);
3685 for (i = 0; i < bmap->n_ineq; ++i)
3686 for (j = 0; j < n; ++j)
3687 isl_int_neg(bmap->ineq[i][off+j], bmap->ineq[i][off+j]);
3688 for (i = 0; i < bmap->n_div; ++i)
3689 for (j = 0; j < n; ++j)
3690 isl_int_neg(bmap->div[i][1+off+j], bmap->div[i][1+off+j]);
3691 bmap = isl_basic_map_gauss(bmap, NULL);
3692 return isl_basic_map_finalize(bmap);
3695 __isl_give isl_basic_set *isl_basic_set_neg(__isl_take isl_basic_set *bset)
3697 return isl_basic_map_neg(bset);
3700 /* Given a map A -> f(A), construct A -> -f(A).
3702 struct isl_map *isl_map_neg(struct isl_map *map)
3706 map = isl_map_cow(map);
3710 for (i = 0; i < map->n; ++i) {
3711 map->p[i] = isl_basic_map_neg(map->p[i]);
3722 __isl_give isl_set *isl_set_neg(__isl_take isl_set *set)
3724 return (isl_set *)isl_map_neg((isl_map *)set);
3727 /* Given a basic map A -> f(A) and an integer d, construct a basic map
3728 * A -> floor(f(A)/d).
3730 struct isl_basic_map *isl_basic_map_floordiv(struct isl_basic_map *bmap,
3733 unsigned n_in, n_out, nparam, total, pos;
3734 struct isl_basic_map *result = NULL;
3735 struct isl_dim_map *dim_map;
3741 nparam = isl_basic_map_n_param(bmap);
3742 n_in = isl_basic_map_n_in(bmap);
3743 n_out = isl_basic_map_n_out(bmap);
3745 total = nparam + n_in + n_out + bmap->n_div + n_out;
3746 dim_map = isl_dim_map_alloc(bmap->ctx, total);
3747 isl_dim_map_dim(dim_map, bmap->dim, isl_dim_param, pos = 0);
3748 isl_dim_map_dim(dim_map, bmap->dim, isl_dim_in, pos += nparam);
3749 isl_dim_map_div(dim_map, bmap, pos += n_in + n_out);
3750 isl_dim_map_dim(dim_map, bmap->dim, isl_dim_out, pos += bmap->n_div);
3752 result = isl_basic_map_alloc_space(isl_space_copy(bmap->dim),
3753 bmap->n_div + n_out,
3754 bmap->n_eq, bmap->n_ineq + 2 * n_out);
3755 result = isl_basic_map_add_constraints_dim_map(result, bmap, dim_map);
3756 result = add_divs(result, n_out);
3757 for (i = 0; i < n_out; ++i) {
3759 j = isl_basic_map_alloc_inequality(result);
3762 isl_seq_clr(result->ineq[j], 1+total);
3763 isl_int_neg(result->ineq[j][1+nparam+n_in+i], d);
3764 isl_int_set_si(result->ineq[j][1+pos+i], 1);
3765 j = isl_basic_map_alloc_inequality(result);
3768 isl_seq_clr(result->ineq[j], 1+total);
3769 isl_int_set(result->ineq[j][1+nparam+n_in+i], d);
3770 isl_int_set_si(result->ineq[j][1+pos+i], -1);
3771 isl_int_sub_ui(result->ineq[j][0], d, 1);
3774 result = isl_basic_map_simplify(result);
3775 return isl_basic_map_finalize(result);
3777 isl_basic_map_free(result);
3781 /* Given a map A -> f(A) and an integer d, construct a map
3782 * A -> floor(f(A)/d).
3784 struct isl_map *isl_map_floordiv(struct isl_map *map, isl_int d)
3788 map = isl_map_cow(map);
3792 ISL_F_CLR(map, ISL_MAP_DISJOINT);
3793 ISL_F_CLR(map, ISL_MAP_NORMALIZED);
3794 for (i = 0; i < map->n; ++i) {
3795 map->p[i] = isl_basic_map_floordiv(map->p[i], d);
3806 static struct isl_basic_map *var_equal(struct isl_basic_map *bmap, unsigned pos)
3812 i = isl_basic_map_alloc_equality(bmap);
3815 nparam = isl_basic_map_n_param(bmap);
3816 n_in = isl_basic_map_n_in(bmap);
3817 isl_seq_clr(bmap->eq[i], 1 + isl_basic_map_total_dim(bmap));
3818 isl_int_set_si(bmap->eq[i][1+nparam+pos], -1);
3819 isl_int_set_si(bmap->eq[i][1+nparam+n_in+pos], 1);
3820 return isl_basic_map_finalize(bmap);
3822 isl_basic_map_free(bmap);
3826 /* Add a constraints to "bmap" expressing i_pos < o_pos
3828 static struct isl_basic_map *var_less(struct isl_basic_map *bmap, unsigned pos)
3834 i = isl_basic_map_alloc_inequality(bmap);
3837 nparam = isl_basic_map_n_param(bmap);
3838 n_in = isl_basic_map_n_in(bmap);
3839 isl_seq_clr(bmap->ineq[i], 1 + isl_basic_map_total_dim(bmap));
3840 isl_int_set_si(bmap->ineq[i][0], -1);
3841 isl_int_set_si(bmap->ineq[i][1+nparam+pos], -1);
3842 isl_int_set_si(bmap->ineq[i][1+nparam+n_in+pos], 1);
3843 return isl_basic_map_finalize(bmap);
3845 isl_basic_map_free(bmap);
3849 /* Add a constraint to "bmap" expressing i_pos <= o_pos
3851 static __isl_give isl_basic_map *var_less_or_equal(
3852 __isl_take isl_basic_map *bmap, unsigned pos)
3858 i = isl_basic_map_alloc_inequality(bmap);
3861 nparam = isl_basic_map_n_param(bmap);
3862 n_in = isl_basic_map_n_in(bmap);
3863 isl_seq_clr(bmap->ineq[i], 1 + isl_basic_map_total_dim(bmap));
3864 isl_int_set_si(bmap->ineq[i][1+nparam+pos], -1);
3865 isl_int_set_si(bmap->ineq[i][1+nparam+n_in+pos], 1);
3866 return isl_basic_map_finalize(bmap);
3868 isl_basic_map_free(bmap);
3872 /* Add a constraints to "bmap" expressing i_pos > o_pos
3874 static struct isl_basic_map *var_more(struct isl_basic_map *bmap, unsigned pos)
3880 i = isl_basic_map_alloc_inequality(bmap);
3883 nparam = isl_basic_map_n_param(bmap);
3884 n_in = isl_basic_map_n_in(bmap);
3885 isl_seq_clr(bmap->ineq[i], 1 + isl_basic_map_total_dim(bmap));
3886 isl_int_set_si(bmap->ineq[i][0], -1);
3887 isl_int_set_si(bmap->ineq[i][1+nparam+pos], 1);
3888 isl_int_set_si(bmap->ineq[i][1+nparam+n_in+pos], -1);
3889 return isl_basic_map_finalize(bmap);
3891 isl_basic_map_free(bmap);
3895 /* Add a constraint to "bmap" expressing i_pos >= o_pos
3897 static __isl_give isl_basic_map *var_more_or_equal(
3898 __isl_take isl_basic_map *bmap, unsigned pos)
3904 i = isl_basic_map_alloc_inequality(bmap);
3907 nparam = isl_basic_map_n_param(bmap);
3908 n_in = isl_basic_map_n_in(bmap);
3909 isl_seq_clr(bmap->ineq[i], 1 + isl_basic_map_total_dim(bmap));
3910 isl_int_set_si(bmap->ineq[i][1+nparam+pos], 1);
3911 isl_int_set_si(bmap->ineq[i][1+nparam+n_in+pos], -1);
3912 return isl_basic_map_finalize(bmap);
3914 isl_basic_map_free(bmap);
3918 __isl_give isl_basic_map *isl_basic_map_equal(
3919 __isl_take isl_space *dim, unsigned n_equal)
3922 struct isl_basic_map *bmap;
3923 bmap = isl_basic_map_alloc_space(dim, 0, n_equal, 0);
3926 for (i = 0; i < n_equal && bmap; ++i)
3927 bmap = var_equal(bmap, i);
3928 return isl_basic_map_finalize(bmap);
3931 /* Return a relation on of dimension "dim" expressing i_[0..pos] << o_[0..pos]
3933 __isl_give isl_basic_map *isl_basic_map_less_at(__isl_take isl_space *dim,
3937 struct isl_basic_map *bmap;
3938 bmap = isl_basic_map_alloc_space(dim, 0, pos, 1);
3941 for (i = 0; i < pos && bmap; ++i)
3942 bmap = var_equal(bmap, i);
3944 bmap = var_less(bmap, pos);
3945 return isl_basic_map_finalize(bmap);
3948 /* Return a relation on of dimension "dim" expressing i_[0..pos] <<= o_[0..pos]
3950 __isl_give isl_basic_map *isl_basic_map_less_or_equal_at(
3951 __isl_take isl_space *dim, unsigned pos)
3954 isl_basic_map *bmap;
3956 bmap = isl_basic_map_alloc_space(dim, 0, pos, 1);
3957 for (i = 0; i < pos; ++i)
3958 bmap = var_equal(bmap, i);
3959 bmap = var_less_or_equal(bmap, pos);
3960 return isl_basic_map_finalize(bmap);
3963 /* Return a relation on pairs of sets of dimension "dim" expressing i_pos > o_pos
3965 __isl_give isl_basic_map *isl_basic_map_more_at(__isl_take isl_space *dim,
3969 struct isl_basic_map *bmap;
3970 bmap = isl_basic_map_alloc_space(dim, 0, pos, 1);
3973 for (i = 0; i < pos && bmap; ++i)
3974 bmap = var_equal(bmap, i);
3976 bmap = var_more(bmap, pos);
3977 return isl_basic_map_finalize(bmap);
3980 /* Return a relation on of dimension "dim" expressing i_[0..pos] >>= o_[0..pos]
3982 __isl_give isl_basic_map *isl_basic_map_more_or_equal_at(
3983 __isl_take isl_space *dim, unsigned pos)
3986 isl_basic_map *bmap;
3988 bmap = isl_basic_map_alloc_space(dim, 0, pos, 1);
3989 for (i = 0; i < pos; ++i)
3990 bmap = var_equal(bmap, i);
3991 bmap = var_more_or_equal(bmap, pos);
3992 return isl_basic_map_finalize(bmap);
3995 static __isl_give isl_map *map_lex_lte_first(__isl_take isl_space *dims,
3996 unsigned n, int equal)
3998 struct isl_map *map;
4001 if (n == 0 && equal)
4002 return isl_map_universe(dims);
4004 map = isl_map_alloc_space(isl_space_copy(dims), n, ISL_MAP_DISJOINT);
4006 for (i = 0; i + 1 < n; ++i)
4007 map = isl_map_add_basic_map(map,
4008 isl_basic_map_less_at(isl_space_copy(dims), i));
4011 map = isl_map_add_basic_map(map,
4012 isl_basic_map_less_or_equal_at(dims, n - 1));
4014 map = isl_map_add_basic_map(map,
4015 isl_basic_map_less_at(dims, n - 1));
4017 isl_space_free(dims);
4022 static __isl_give isl_map *map_lex_lte(__isl_take isl_space *dims, int equal)
4026 return map_lex_lte_first(dims, dims->n_out, equal);
4029 __isl_give isl_map *isl_map_lex_lt_first(__isl_take isl_space *dim, unsigned n)
4031 return map_lex_lte_first(dim, n, 0);
4034 __isl_give isl_map *isl_map_lex_le_first(__isl_take isl_space *dim, unsigned n)
4036 return map_lex_lte_first(dim, n, 1);
4039 __isl_give isl_map *isl_map_lex_lt(__isl_take isl_space *set_dim)
4041 return map_lex_lte(isl_space_map_from_set(set_dim), 0);
4044 __isl_give isl_map *isl_map_lex_le(__isl_take isl_space *set_dim)
4046 return map_lex_lte(isl_space_map_from_set(set_dim), 1);
4049 static __isl_give isl_map *map_lex_gte_first(__isl_take isl_space *dims,
4050 unsigned n, int equal)
4052 struct isl_map *map;
4055 if (n == 0 && equal)
4056 return isl_map_universe(dims);
4058 map = isl_map_alloc_space(isl_space_copy(dims), n, ISL_MAP_DISJOINT);
4060 for (i = 0; i + 1 < n; ++i)
4061 map = isl_map_add_basic_map(map,
4062 isl_basic_map_more_at(isl_space_copy(dims), i));
4065 map = isl_map_add_basic_map(map,
4066 isl_basic_map_more_or_equal_at(dims, n - 1));
4068 map = isl_map_add_basic_map(map,
4069 isl_basic_map_more_at(dims, n - 1));
4071 isl_space_free(dims);
4076 static __isl_give isl_map *map_lex_gte(__isl_take isl_space *dims, int equal)
4080 return map_lex_gte_first(dims, dims->n_out, equal);
4083 __isl_give isl_map *isl_map_lex_gt_first(__isl_take isl_space *dim, unsigned n)
4085 return map_lex_gte_first(dim, n, 0);
4088 __isl_give isl_map *isl_map_lex_ge_first(__isl_take isl_space *dim, unsigned n)
4090 return map_lex_gte_first(dim, n, 1);
4093 __isl_give isl_map *isl_map_lex_gt(__isl_take isl_space *set_dim)
4095 return map_lex_gte(isl_space_map_from_set(set_dim), 0);
4098 __isl_give isl_map *isl_map_lex_ge(__isl_take isl_space *set_dim)
4100 return map_lex_gte(isl_space_map_from_set(set_dim), 1);
4103 __isl_give isl_map *isl_set_lex_le_set(__isl_take isl_set *set1,
4104 __isl_take isl_set *set2)
4107 map = isl_map_lex_le(isl_set_get_space(set1));
4108 map = isl_map_intersect_domain(map, set1);
4109 map = isl_map_intersect_range(map, set2);
4113 __isl_give isl_map *isl_set_lex_lt_set(__isl_take isl_set *set1,
4114 __isl_take isl_set *set2)
4117 map = isl_map_lex_lt(isl_set_get_space(set1));
4118 map = isl_map_intersect_domain(map, set1);
4119 map = isl_map_intersect_range(map, set2);
4123 __isl_give isl_map *isl_set_lex_ge_set(__isl_take isl_set *set1,
4124 __isl_take isl_set *set2)
4127 map = isl_map_lex_ge(isl_set_get_space(set1));
4128 map = isl_map_intersect_domain(map, set1);
4129 map = isl_map_intersect_range(map, set2);
4133 __isl_give isl_map *isl_set_lex_gt_set(__isl_take isl_set *set1,
4134 __isl_take isl_set *set2)
4137 map = isl_map_lex_gt(isl_set_get_space(set1));
4138 map = isl_map_intersect_domain(map, set1);
4139 map = isl_map_intersect_range(map, set2);
4143 __isl_give isl_map *isl_map_lex_le_map(__isl_take isl_map *map1,
4144 __isl_take isl_map *map2)
4147 map = isl_map_lex_le(isl_space_range(isl_map_get_space(map1)));
4148 map = isl_map_apply_domain(map, isl_map_reverse(map1));
4149 map = isl_map_apply_range(map, isl_map_reverse(map2));
4153 __isl_give isl_map *isl_map_lex_lt_map(__isl_take isl_map *map1,
4154 __isl_take isl_map *map2)
4157 map = isl_map_lex_lt(isl_space_range(isl_map_get_space(map1)));
4158 map = isl_map_apply_domain(map, isl_map_reverse(map1));
4159 map = isl_map_apply_range(map, isl_map_reverse(map2));
4163 __isl_give isl_map *isl_map_lex_ge_map(__isl_take isl_map *map1,
4164 __isl_take isl_map *map2)
4167 map = isl_map_lex_ge(isl_space_range(isl_map_get_space(map1)));
4168 map = isl_map_apply_domain(map, isl_map_reverse(map1));
4169 map = isl_map_apply_range(map, isl_map_reverse(map2));
4173 __isl_give isl_map *isl_map_lex_gt_map(__isl_take isl_map *map1,
4174 __isl_take isl_map *map2)
4177 map = isl_map_lex_gt(isl_space_range(isl_map_get_space(map1)));
4178 map = isl_map_apply_domain(map, isl_map_reverse(map1));
4179 map = isl_map_apply_range(map, isl_map_reverse(map2));
4183 __isl_give isl_basic_map *isl_basic_map_from_basic_set(
4184 __isl_take isl_basic_set *bset, __isl_take isl_space *dim)
4186 struct isl_basic_map *bmap;
4188 bset = isl_basic_set_cow(bset);
4192 isl_assert(bset->ctx, isl_space_compatible(bset->dim, dim), goto error);
4193 isl_space_free(bset->dim);
4194 bmap = (struct isl_basic_map *) bset;
4196 return isl_basic_map_finalize(bmap);
4198 isl_basic_set_free(bset);
4199 isl_space_free(dim);
4203 struct isl_basic_set *isl_basic_set_from_basic_map(struct isl_basic_map *bmap)
4207 if (bmap->dim->n_in == 0)
4208 return (struct isl_basic_set *)bmap;
4209 bmap = isl_basic_map_cow(bmap);
4212 bmap->dim = isl_space_as_set_space(bmap->dim);
4215 bmap = isl_basic_map_finalize(bmap);
4216 return (struct isl_basic_set *)bmap;
4218 isl_basic_map_free(bmap);
4222 /* For a div d = floor(f/m), add the constraints
4225 * -(f-(n-1)) + m d >= 0
4227 * Note that the second constraint is the negation of
4231 int isl_basic_map_add_div_constraints_var(__isl_keep isl_basic_map *bmap,
4232 unsigned pos, isl_int *div)
4235 unsigned total = isl_basic_map_total_dim(bmap);
4237 i = isl_basic_map_alloc_inequality(bmap);
4240 isl_seq_cpy(bmap->ineq[i], div + 1, 1 + total);
4241 isl_int_neg(bmap->ineq[i][1 + pos], div[0]);
4243 j = isl_basic_map_alloc_inequality(bmap);
4246 isl_seq_neg(bmap->ineq[j], bmap->ineq[i], 1 + total);
4247 isl_int_add(bmap->ineq[j][0], bmap->ineq[j][0], bmap->ineq[j][1 + pos]);
4248 isl_int_sub_ui(bmap->ineq[j][0], bmap->ineq[j][0], 1);
4252 int isl_basic_set_add_div_constraints_var(__isl_keep isl_basic_set *bset,
4253 unsigned pos, isl_int *div)
4255 return isl_basic_map_add_div_constraints_var((isl_basic_map *)bset,
4259 int isl_basic_map_add_div_constraints(struct isl_basic_map *bmap, unsigned div)
4261 unsigned total = isl_basic_map_total_dim(bmap);
4262 unsigned div_pos = total - bmap->n_div + div;
4264 return isl_basic_map_add_div_constraints_var(bmap, div_pos,
4268 int isl_basic_set_add_div_constraints(struct isl_basic_set *bset, unsigned div)
4270 return isl_basic_map_add_div_constraints(bset, div);
4273 struct isl_basic_set *isl_basic_map_underlying_set(
4274 struct isl_basic_map *bmap)
4278 if (bmap->dim->nparam == 0 && bmap->dim->n_in == 0 &&
4280 !isl_space_is_named_or_nested(bmap->dim, isl_dim_in) &&
4281 !isl_space_is_named_or_nested(bmap->dim, isl_dim_out))
4282 return (struct isl_basic_set *)bmap;
4283 bmap = isl_basic_map_cow(bmap);
4286 bmap->dim = isl_space_underlying(bmap->dim, bmap->n_div);
4289 bmap->extra -= bmap->n_div;
4291 bmap = isl_basic_map_finalize(bmap);
4292 return (struct isl_basic_set *)bmap;
4294 isl_basic_map_free(bmap);
4298 __isl_give isl_basic_set *isl_basic_set_underlying_set(
4299 __isl_take isl_basic_set *bset)
4301 return isl_basic_map_underlying_set((isl_basic_map *)bset);
4304 struct isl_basic_map *isl_basic_map_overlying_set(
4305 struct isl_basic_set *bset, struct isl_basic_map *like)
4307 struct isl_basic_map *bmap;
4308 struct isl_ctx *ctx;
4315 isl_assert(ctx, bset->n_div == 0, goto error);
4316 isl_assert(ctx, isl_basic_set_n_param(bset) == 0, goto error);
4317 isl_assert(ctx, bset->dim->n_out == isl_basic_map_total_dim(like),
4319 if (isl_space_is_equal(bset->dim, like->dim) && like->n_div == 0) {
4320 isl_basic_map_free(like);
4321 return (struct isl_basic_map *)bset;
4323 bset = isl_basic_set_cow(bset);
4326 total = bset->dim->n_out + bset->extra;
4327 bmap = (struct isl_basic_map *)bset;
4328 isl_space_free(bmap->dim);
4329 bmap->dim = isl_space_copy(like->dim);
4332 bmap->n_div = like->n_div;
4333 bmap->extra += like->n_div;
4337 ltotal = total - bmap->extra + like->extra;
4340 bmap->block2 = isl_blk_extend(ctx, bmap->block2,
4341 bmap->extra * (1 + 1 + total));
4342 if (isl_blk_is_error(bmap->block2))
4344 div = isl_realloc_array(ctx, bmap->div, isl_int *, bmap->extra);
4348 for (i = 0; i < bmap->extra; ++i)
4349 bmap->div[i] = bmap->block2.data + i * (1 + 1 + total);
4350 for (i = 0; i < like->n_div; ++i) {
4351 isl_seq_cpy(bmap->div[i], like->div[i], 1 + 1 + ltotal);
4352 isl_seq_clr(bmap->div[i]+1+1+ltotal, total - ltotal);
4354 bmap = isl_basic_map_extend_constraints(bmap,
4355 0, 2 * like->n_div);
4356 for (i = 0; i < like->n_div; ++i) {
4359 if (isl_int_is_zero(bmap->div[i][0]))
4361 if (isl_basic_map_add_div_constraints(bmap, i) < 0)
4362 bmap = isl_basic_map_free(bmap);
4365 isl_basic_map_free(like);
4366 bmap = isl_basic_map_simplify(bmap);
4367 bmap = isl_basic_map_finalize(bmap);
4370 isl_basic_map_free(like);
4371 isl_basic_set_free(bset);
4375 struct isl_basic_set *isl_basic_set_from_underlying_set(
4376 struct isl_basic_set *bset, struct isl_basic_set *like)
4378 return (struct isl_basic_set *)
4379 isl_basic_map_overlying_set(bset, (struct isl_basic_map *)like);
4382 struct isl_set *isl_set_from_underlying_set(
4383 struct isl_set *set, struct isl_basic_set *like)
4389 isl_assert(set->ctx, set->dim->n_out == isl_basic_set_total_dim(like),
4391 if (isl_space_is_equal(set->dim, like->dim) && like->n_div == 0) {
4392 isl_basic_set_free(like);
4395 set = isl_set_cow(set);
4398 for (i = 0; i < set->n; ++i) {
4399 set->p[i] = isl_basic_set_from_underlying_set(set->p[i],
4400 isl_basic_set_copy(like));
4404 isl_space_free(set->dim);
4405 set->dim = isl_space_copy(like->dim);
4408 isl_basic_set_free(like);
4411 isl_basic_set_free(like);
4416 struct isl_set *isl_map_underlying_set(struct isl_map *map)
4420 map = isl_map_cow(map);
4423 map->dim = isl_space_cow(map->dim);
4427 for (i = 1; i < map->n; ++i)
4428 isl_assert(map->ctx, map->p[0]->n_div == map->p[i]->n_div,
4430 for (i = 0; i < map->n; ++i) {
4431 map->p[i] = (struct isl_basic_map *)
4432 isl_basic_map_underlying_set(map->p[i]);
4437 map->dim = isl_space_underlying(map->dim, 0);
4439 isl_space_free(map->dim);
4440 map->dim = isl_space_copy(map->p[0]->dim);
4444 return (struct isl_set *)map;
4450 struct isl_set *isl_set_to_underlying_set(struct isl_set *set)
4452 return (struct isl_set *)isl_map_underlying_set((struct isl_map *)set);
4455 __isl_give isl_basic_map *isl_basic_map_reset_space(
4456 __isl_take isl_basic_map *bmap, __isl_take isl_space *dim)
4458 bmap = isl_basic_map_cow(bmap);
4462 isl_space_free(bmap->dim);
4465 bmap = isl_basic_map_finalize(bmap);
4469 isl_basic_map_free(bmap);
4470 isl_space_free(dim);
4474 __isl_give isl_basic_set *isl_basic_set_reset_space(
4475 __isl_take isl_basic_set *bset, __isl_take isl_space *dim)
4477 return (isl_basic_set *)isl_basic_map_reset_space((isl_basic_map *)bset,
4481 __isl_give isl_map *isl_map_reset_space(__isl_take isl_map *map,
4482 __isl_take isl_space *dim)
4486 map = isl_map_cow(map);
4490 for (i = 0; i < map->n; ++i) {
4491 map->p[i] = isl_basic_map_reset_space(map->p[i],
4492 isl_space_copy(dim));
4496 isl_space_free(map->dim);
4502 isl_space_free(dim);
4506 __isl_give isl_set *isl_set_reset_space(__isl_take isl_set *set,
4507 __isl_take isl_space *dim)
4509 return (struct isl_set *) isl_map_reset_space((struct isl_map *)set, dim);
4512 /* Compute the parameter domain of the given basic set.
4514 __isl_give isl_basic_set *isl_basic_set_params(__isl_take isl_basic_set *bset)
4519 if (isl_basic_set_is_params(bset))
4522 n = isl_basic_set_dim(bset, isl_dim_set);
4523 bset = isl_basic_set_project_out(bset, isl_dim_set, 0, n);
4524 space = isl_basic_set_get_space(bset);
4525 space = isl_space_params(space);
4526 bset = isl_basic_set_reset_space(bset, space);
4530 /* Construct a zero-dimensional basic set with the given parameter domain.
4532 __isl_give isl_basic_set *isl_basic_set_from_params(
4533 __isl_take isl_basic_set *bset)
4536 space = isl_basic_set_get_space(bset);
4537 space = isl_space_set_from_params(space);
4538 bset = isl_basic_set_reset_space(bset, space);
4542 /* Compute the parameter domain of the given set.
4544 __isl_give isl_set *isl_set_params(__isl_take isl_set *set)
4549 if (isl_set_is_params(set))
4552 n = isl_set_dim(set, isl_dim_set);
4553 set = isl_set_project_out(set, isl_dim_set, 0, n);
4554 space = isl_set_get_space(set);
4555 space = isl_space_params(space);
4556 set = isl_set_reset_space(set, space);
4560 /* Construct a zero-dimensional set with the given parameter domain.
4562 __isl_give isl_set *isl_set_from_params(__isl_take isl_set *set)
4565 space = isl_set_get_space(set);
4566 space = isl_space_set_from_params(space);
4567 set = isl_set_reset_space(set, space);
4571 /* Compute the parameter domain of the given map.
4573 __isl_give isl_set *isl_map_params(__isl_take isl_map *map)
4578 n = isl_map_dim(map, isl_dim_in);
4579 map = isl_map_project_out(map, isl_dim_in, 0, n);
4580 n = isl_map_dim(map, isl_dim_out);
4581 map = isl_map_project_out(map, isl_dim_out, 0, n);
4582 space = isl_map_get_space(map);
4583 space = isl_space_params(space);
4584 map = isl_map_reset_space(map, space);
4588 struct isl_basic_set *isl_basic_map_domain(struct isl_basic_map *bmap)
4591 struct isl_basic_set *domain;
4597 dim = isl_space_domain(isl_basic_map_get_space(bmap));
4599 n_in = isl_basic_map_n_in(bmap);
4600 n_out = isl_basic_map_n_out(bmap);
4601 domain = isl_basic_set_from_basic_map(bmap);
4602 domain = isl_basic_set_project_out(domain, isl_dim_set, n_in, n_out);
4604 domain = isl_basic_set_reset_space(domain, dim);
4609 int isl_basic_map_may_be_set(__isl_keep isl_basic_map *bmap)
4613 return isl_space_may_be_set(bmap->dim);
4616 /* Is this basic map actually a set?
4617 * Users should never call this function. Outside of isl,
4618 * the type should indicate whether something is a set or a map.
4620 int isl_basic_map_is_set(__isl_keep isl_basic_map *bmap)
4624 return isl_space_is_set(bmap->dim);
4627 struct isl_basic_set *isl_basic_map_range(struct isl_basic_map *bmap)
4631 if (isl_basic_map_is_set(bmap))
4633 return isl_basic_map_domain(isl_basic_map_reverse(bmap));
4636 __isl_give isl_basic_map *isl_basic_map_domain_map(
4637 __isl_take isl_basic_map *bmap)
4641 isl_basic_map *domain;
4642 int nparam, n_in, n_out;
4645 nparam = isl_basic_map_dim(bmap, isl_dim_param);
4646 n_in = isl_basic_map_dim(bmap, isl_dim_in);
4647 n_out = isl_basic_map_dim(bmap, isl_dim_out);
4649 dim = isl_space_from_range(isl_space_domain(isl_basic_map_get_space(bmap)));
4650 domain = isl_basic_map_universe(dim);
4652 bmap = isl_basic_map_from_domain(isl_basic_map_wrap(bmap));
4653 bmap = isl_basic_map_apply_range(bmap, domain);
4654 bmap = isl_basic_map_extend_constraints(bmap, n_in, 0);
4656 total = isl_basic_map_total_dim(bmap);
4658 for (i = 0; i < n_in; ++i) {
4659 k = isl_basic_map_alloc_equality(bmap);
4662 isl_seq_clr(bmap->eq[k], 1 + total);
4663 isl_int_set_si(bmap->eq[k][1 + nparam + i], -1);
4664 isl_int_set_si(bmap->eq[k][1 + nparam + n_in + n_out + i], 1);
4667 bmap = isl_basic_map_gauss(bmap, NULL);
4668 return isl_basic_map_finalize(bmap);
4670 isl_basic_map_free(bmap);
4674 __isl_give isl_basic_map *isl_basic_map_range_map(
4675 __isl_take isl_basic_map *bmap)
4679 isl_basic_map *range;
4680 int nparam, n_in, n_out;
4683 nparam = isl_basic_map_dim(bmap, isl_dim_param);
4684 n_in = isl_basic_map_dim(bmap, isl_dim_in);
4685 n_out = isl_basic_map_dim(bmap, isl_dim_out);
4687 dim = isl_space_from_range(isl_space_range(isl_basic_map_get_space(bmap)));
4688 range = isl_basic_map_universe(dim);
4690 bmap = isl_basic_map_from_domain(isl_basic_map_wrap(bmap));
4691 bmap = isl_basic_map_apply_range(bmap, range);
4692 bmap = isl_basic_map_extend_constraints(bmap, n_out, 0);
4694 total = isl_basic_map_total_dim(bmap);
4696 for (i = 0; i < n_out; ++i) {
4697 k = isl_basic_map_alloc_equality(bmap);
4700 isl_seq_clr(bmap->eq[k], 1 + total);
4701 isl_int_set_si(bmap->eq[k][1 + nparam + n_in + i], -1);
4702 isl_int_set_si(bmap->eq[k][1 + nparam + n_in + n_out + i], 1);
4705 bmap = isl_basic_map_gauss(bmap, NULL);
4706 return isl_basic_map_finalize(bmap);
4708 isl_basic_map_free(bmap);
4712 int isl_map_may_be_set(__isl_keep isl_map *map)
4716 return isl_space_may_be_set(map->dim);
4719 /* Is this map actually a set?
4720 * Users should never call this function. Outside of isl,
4721 * the type should indicate whether something is a set or a map.
4723 int isl_map_is_set(__isl_keep isl_map *map)
4727 return isl_space_is_set(map->dim);
4730 struct isl_set *isl_map_range(struct isl_map *map)
4733 struct isl_set *set;
4737 if (isl_map_is_set(map))
4738 return (isl_set *)map;
4740 map = isl_map_cow(map);
4744 set = (struct isl_set *) map;
4745 set->dim = isl_space_range(set->dim);
4748 for (i = 0; i < map->n; ++i) {
4749 set->p[i] = isl_basic_map_range(map->p[i]);
4753 ISL_F_CLR(set, ISL_MAP_DISJOINT);
4754 ISL_F_CLR(set, ISL_SET_NORMALIZED);
4761 __isl_give isl_map *isl_map_domain_map(__isl_take isl_map *map)
4764 isl_space *domain_dim;
4766 map = isl_map_cow(map);
4770 domain_dim = isl_space_from_range(isl_space_domain(isl_map_get_space(map)));
4771 map->dim = isl_space_from_domain(isl_space_wrap(map->dim));
4772 map->dim = isl_space_join(map->dim, domain_dim);
4775 for (i = 0; i < map->n; ++i) {
4776 map->p[i] = isl_basic_map_domain_map(map->p[i]);
4780 ISL_F_CLR(map, ISL_MAP_DISJOINT);
4781 ISL_F_CLR(map, ISL_MAP_NORMALIZED);
4788 __isl_give isl_map *isl_map_range_map(__isl_take isl_map *map)
4791 isl_space *range_dim;
4793 map = isl_map_cow(map);
4797 range_dim = isl_space_range(isl_map_get_space(map));
4798 range_dim = isl_space_from_range(range_dim);
4799 map->dim = isl_space_from_domain(isl_space_wrap(map->dim));
4800 map->dim = isl_space_join(map->dim, range_dim);
4803 for (i = 0; i < map->n; ++i) {
4804 map->p[i] = isl_basic_map_range_map(map->p[i]);
4808 ISL_F_CLR(map, ISL_MAP_DISJOINT);
4809 ISL_F_CLR(map, ISL_MAP_NORMALIZED);
4816 __isl_give isl_map *isl_map_from_set(__isl_take isl_set *set,
4817 __isl_take isl_space *dim)
4820 struct isl_map *map = NULL;
4822 set = isl_set_cow(set);
4825 isl_assert(set->ctx, isl_space_compatible(set->dim, dim), goto error);
4826 map = (struct isl_map *)set;
4827 for (i = 0; i < set->n; ++i) {
4828 map->p[i] = isl_basic_map_from_basic_set(
4829 set->p[i], isl_space_copy(dim));
4833 isl_space_free(map->dim);
4837 isl_space_free(dim);
4842 __isl_give isl_basic_map *isl_basic_map_from_domain(
4843 __isl_take isl_basic_set *bset)
4845 return isl_basic_map_reverse(isl_basic_map_from_range(bset));
4848 __isl_give isl_basic_map *isl_basic_map_from_range(
4849 __isl_take isl_basic_set *bset)
4852 space = isl_basic_set_get_space(bset);
4853 space = isl_space_from_range(space);
4854 bset = isl_basic_set_reset_space(bset, space);
4855 return (isl_basic_map *)bset;
4858 struct isl_map *isl_map_from_range(struct isl_set *set)
4861 space = isl_set_get_space(set);
4862 space = isl_space_from_range(space);
4863 set = isl_set_reset_space(set, space);
4864 return (struct isl_map *)set;
4867 __isl_give isl_map *isl_map_from_domain(__isl_take isl_set *set)
4869 return isl_map_reverse(isl_map_from_range(set));
4872 __isl_give isl_basic_map *isl_basic_map_from_domain_and_range(
4873 __isl_take isl_basic_set *domain, __isl_take isl_basic_set *range)
4875 return isl_basic_map_apply_range(isl_basic_map_reverse(domain), range);
4878 __isl_give isl_map *isl_map_from_domain_and_range(__isl_take isl_set *domain,
4879 __isl_take isl_set *range)
4881 return isl_map_apply_range(isl_map_reverse(domain), range);
4884 struct isl_set *isl_set_from_map(struct isl_map *map)
4887 struct isl_set *set = NULL;
4891 map = isl_map_cow(map);
4894 map->dim = isl_space_as_set_space(map->dim);
4897 set = (struct isl_set *)map;
4898 for (i = 0; i < map->n; ++i) {
4899 set->p[i] = isl_basic_set_from_basic_map(map->p[i]);
4909 __isl_give isl_map *isl_map_alloc_space(__isl_take isl_space *dim, int n,
4912 struct isl_map *map;
4917 isl_die(dim->ctx, isl_error_internal,
4918 "negative number of basic maps", goto error);
4919 map = isl_alloc(dim->ctx, struct isl_map,
4920 sizeof(struct isl_map) +
4921 (n - 1) * sizeof(struct isl_basic_map *));
4925 map->ctx = dim->ctx;
4926 isl_ctx_ref(map->ctx);
4934 isl_space_free(dim);
4938 struct isl_map *isl_map_alloc(struct isl_ctx *ctx,
4939 unsigned nparam, unsigned in, unsigned out, int n,
4942 struct isl_map *map;
4945 dims = isl_space_alloc(ctx, nparam, in, out);
4949 map = isl_map_alloc_space(dims, n, flags);
4953 __isl_give isl_basic_map *isl_basic_map_empty(__isl_take isl_space *dim)
4955 struct isl_basic_map *bmap;
4956 bmap = isl_basic_map_alloc_space(dim, 0, 1, 0);
4957 bmap = isl_basic_map_set_to_empty(bmap);
4961 __isl_give isl_basic_set *isl_basic_set_empty(__isl_take isl_space *dim)
4963 struct isl_basic_set *bset;
4964 bset = isl_basic_set_alloc_space(dim, 0, 1, 0);
4965 bset = isl_basic_set_set_to_empty(bset);
4969 struct isl_basic_map *isl_basic_map_empty_like(struct isl_basic_map *model)
4971 struct isl_basic_map *bmap;
4974 bmap = isl_basic_map_alloc_space(isl_space_copy(model->dim), 0, 1, 0);
4975 bmap = isl_basic_map_set_to_empty(bmap);
4979 struct isl_basic_map *isl_basic_map_empty_like_map(struct isl_map *model)
4981 struct isl_basic_map *bmap;
4984 bmap = isl_basic_map_alloc_space(isl_space_copy(model->dim), 0, 1, 0);
4985 bmap = isl_basic_map_set_to_empty(bmap);
4989 struct isl_basic_set *isl_basic_set_empty_like(struct isl_basic_set *model)
4991 struct isl_basic_set *bset;
4994 bset = isl_basic_set_alloc_space(isl_space_copy(model->dim), 0, 1, 0);
4995 bset = isl_basic_set_set_to_empty(bset);
4999 __isl_give isl_basic_map *isl_basic_map_universe(__isl_take isl_space *dim)
5001 struct isl_basic_map *bmap;
5002 bmap = isl_basic_map_alloc_space(dim, 0, 0, 0);
5003 bmap = isl_basic_map_finalize(bmap);
5007 __isl_give isl_basic_set *isl_basic_set_universe(__isl_take isl_space *dim)
5009 struct isl_basic_set *bset;
5010 bset = isl_basic_set_alloc_space(dim, 0, 0, 0);
5011 bset = isl_basic_set_finalize(bset);
5015 __isl_give isl_basic_map *isl_basic_map_nat_universe(__isl_take isl_space *dim)
5018 unsigned total = isl_space_dim(dim, isl_dim_all);
5019 isl_basic_map *bmap;
5021 bmap= isl_basic_map_alloc_space(dim, 0, 0, total);
5022 for (i = 0; i < total; ++i) {
5023 int k = isl_basic_map_alloc_inequality(bmap);
5026 isl_seq_clr(bmap->ineq[k], 1 + total);
5027 isl_int_set_si(bmap->ineq[k][1 + i], 1);
5031 isl_basic_map_free(bmap);
5035 __isl_give isl_basic_set *isl_basic_set_nat_universe(__isl_take isl_space *dim)
5037 return isl_basic_map_nat_universe(dim);
5040 __isl_give isl_map *isl_map_nat_universe(__isl_take isl_space *dim)
5042 return isl_map_from_basic_map(isl_basic_map_nat_universe(dim));
5045 __isl_give isl_set *isl_set_nat_universe(__isl_take isl_space *dim)
5047 return isl_map_nat_universe(dim);
5050 __isl_give isl_basic_map *isl_basic_map_universe_like(
5051 __isl_keep isl_basic_map *model)
5055 return isl_basic_map_alloc_space(isl_space_copy(model->dim), 0, 0, 0);
5058 struct isl_basic_set *isl_basic_set_universe_like(struct isl_basic_set *model)
5062 return isl_basic_set_alloc_space(isl_space_copy(model->dim), 0, 0, 0);
5065 __isl_give isl_basic_set *isl_basic_set_universe_like_set(
5066 __isl_keep isl_set *model)
5070 return isl_basic_set_alloc_space(isl_space_copy(model->dim), 0, 0, 0);
5073 __isl_give isl_map *isl_map_empty(__isl_take isl_space *dim)
5075 return isl_map_alloc_space(dim, 0, ISL_MAP_DISJOINT);
5078 struct isl_map *isl_map_empty_like(struct isl_map *model)
5082 return isl_map_alloc_space(isl_space_copy(model->dim), 0, ISL_MAP_DISJOINT);
5085 struct isl_map *isl_map_empty_like_basic_map(struct isl_basic_map *model)
5089 return isl_map_alloc_space(isl_space_copy(model->dim), 0, ISL_MAP_DISJOINT);
5092 __isl_give isl_set *isl_set_empty(__isl_take isl_space *dim)
5094 return isl_set_alloc_space(dim, 0, ISL_MAP_DISJOINT);
5097 struct isl_set *isl_set_empty_like(struct isl_set *model)
5101 return isl_set_empty(isl_space_copy(model->dim));
5104 __isl_give isl_map *isl_map_universe(__isl_take isl_space *dim)
5106 struct isl_map *map;
5109 map = isl_map_alloc_space(isl_space_copy(dim), 1, ISL_MAP_DISJOINT);
5110 map = isl_map_add_basic_map(map, isl_basic_map_universe(dim));
5114 __isl_give isl_set *isl_set_universe(__isl_take isl_space *dim)
5116 struct isl_set *set;
5119 set = isl_set_alloc_space(isl_space_copy(dim), 1, ISL_MAP_DISJOINT);
5120 set = isl_set_add_basic_set(set, isl_basic_set_universe(dim));
5124 __isl_give isl_set *isl_set_universe_like(__isl_keep isl_set *model)
5128 return isl_set_universe(isl_space_copy(model->dim));
5131 struct isl_map *isl_map_dup(struct isl_map *map)
5134 struct isl_map *dup;
5138 dup = isl_map_alloc_space(isl_space_copy(map->dim), map->n, map->flags);
5139 for (i = 0; i < map->n; ++i)
5140 dup = isl_map_add_basic_map(dup, isl_basic_map_copy(map->p[i]));
5144 __isl_give isl_map *isl_map_add_basic_map(__isl_take isl_map *map,
5145 __isl_take isl_basic_map *bmap)
5149 if (isl_basic_map_plain_is_empty(bmap)) {
5150 isl_basic_map_free(bmap);
5153 isl_assert(map->ctx, isl_space_is_equal(map->dim, bmap->dim), goto error);
5154 isl_assert(map->ctx, map->n < map->size, goto error);
5155 map->p[map->n] = bmap;
5157 ISL_F_CLR(map, ISL_MAP_NORMALIZED);
5163 isl_basic_map_free(bmap);
5167 void *isl_map_free(struct isl_map *map)
5177 isl_ctx_deref(map->ctx);
5178 for (i = 0; i < map->n; ++i)
5179 isl_basic_map_free(map->p[i]);
5180 isl_space_free(map->dim);
5186 struct isl_map *isl_map_extend(struct isl_map *base,
5187 unsigned nparam, unsigned n_in, unsigned n_out)
5191 base = isl_map_cow(base);
5195 base->dim = isl_space_extend(base->dim, nparam, n_in, n_out);
5198 for (i = 0; i < base->n; ++i) {
5199 base->p[i] = isl_basic_map_extend_space(base->p[i],
5200 isl_space_copy(base->dim), 0, 0, 0);
5210 struct isl_set *isl_set_extend(struct isl_set *base,
5211 unsigned nparam, unsigned dim)
5213 return (struct isl_set *)isl_map_extend((struct isl_map *)base,
5217 static struct isl_basic_map *isl_basic_map_fix_pos_si(
5218 struct isl_basic_map *bmap, unsigned pos, int value)
5222 bmap = isl_basic_map_cow(bmap);
5223 bmap = isl_basic_map_extend_constraints(bmap, 1, 0);
5224 j = isl_basic_map_alloc_equality(bmap);
5227 isl_seq_clr(bmap->eq[j] + 1, isl_basic_map_total_dim(bmap));
5228 isl_int_set_si(bmap->eq[j][pos], -1);
5229 isl_int_set_si(bmap->eq[j][0], value);
5230 bmap = isl_basic_map_simplify(bmap);
5231 return isl_basic_map_finalize(bmap);
5233 isl_basic_map_free(bmap);
5237 static __isl_give isl_basic_map *isl_basic_map_fix_pos(
5238 __isl_take isl_basic_map *bmap, unsigned pos, isl_int value)
5242 bmap = isl_basic_map_cow(bmap);
5243 bmap = isl_basic_map_extend_constraints(bmap, 1, 0);
5244 j = isl_basic_map_alloc_equality(bmap);
5247 isl_seq_clr(bmap->eq[j] + 1, isl_basic_map_total_dim(bmap));
5248 isl_int_set_si(bmap->eq[j][pos], -1);
5249 isl_int_set(bmap->eq[j][0], value);
5250 bmap = isl_basic_map_simplify(bmap);
5251 return isl_basic_map_finalize(bmap);
5253 isl_basic_map_free(bmap);
5257 struct isl_basic_map *isl_basic_map_fix_si(struct isl_basic_map *bmap,
5258 enum isl_dim_type type, unsigned pos, int value)
5262 isl_assert(bmap->ctx, pos < isl_basic_map_dim(bmap, type), goto error);
5263 return isl_basic_map_fix_pos_si(bmap,
5264 isl_basic_map_offset(bmap, type) + pos, value);
5266 isl_basic_map_free(bmap);
5270 __isl_give isl_basic_map *isl_basic_map_fix(__isl_take isl_basic_map *bmap,
5271 enum isl_dim_type type, unsigned pos, isl_int value)
5275 isl_assert(bmap->ctx, pos < isl_basic_map_dim(bmap, type), goto error);
5276 return isl_basic_map_fix_pos(bmap,
5277 isl_basic_map_offset(bmap, type) + pos, value);
5279 isl_basic_map_free(bmap);
5283 struct isl_basic_set *isl_basic_set_fix_si(struct isl_basic_set *bset,
5284 enum isl_dim_type type, unsigned pos, int value)
5286 return (struct isl_basic_set *)
5287 isl_basic_map_fix_si((struct isl_basic_map *)bset,
5291 __isl_give isl_basic_set *isl_basic_set_fix(__isl_take isl_basic_set *bset,
5292 enum isl_dim_type type, unsigned pos, isl_int value)
5294 return (struct isl_basic_set *)
5295 isl_basic_map_fix((struct isl_basic_map *)bset,
5299 struct isl_basic_map *isl_basic_map_fix_input_si(struct isl_basic_map *bmap,
5300 unsigned input, int value)
5302 return isl_basic_map_fix_si(bmap, isl_dim_in, input, value);
5305 struct isl_basic_set *isl_basic_set_fix_dim_si(struct isl_basic_set *bset,
5306 unsigned dim, int value)
5308 return (struct isl_basic_set *)
5309 isl_basic_map_fix_si((struct isl_basic_map *)bset,
5310 isl_dim_set, dim, value);
5313 static int remove_if_empty(__isl_keep isl_map *map, int i)
5315 int empty = isl_basic_map_plain_is_empty(map->p[i]);
5322 isl_basic_map_free(map->p[i]);
5323 if (i != map->n - 1) {
5324 ISL_F_CLR(map, ISL_MAP_NORMALIZED);
5325 map->p[i] = map->p[map->n - 1];
5332 struct isl_map *isl_map_fix_si(struct isl_map *map,
5333 enum isl_dim_type type, unsigned pos, int value)
5337 map = isl_map_cow(map);
5341 isl_assert(map->ctx, pos < isl_map_dim(map, type), goto error);
5342 for (i = map->n - 1; i >= 0; --i) {
5343 map->p[i] = isl_basic_map_fix_si(map->p[i], type, pos, value);
5344 if (remove_if_empty(map, i) < 0)
5347 ISL_F_CLR(map, ISL_MAP_NORMALIZED);
5354 __isl_give isl_set *isl_set_fix_si(__isl_take isl_set *set,
5355 enum isl_dim_type type, unsigned pos, int value)
5357 return (struct isl_set *)
5358 isl_map_fix_si((struct isl_map *)set, type, pos, value);
5361 __isl_give isl_map *isl_map_fix(__isl_take isl_map *map,
5362 enum isl_dim_type type, unsigned pos, isl_int value)
5366 map = isl_map_cow(map);
5370 isl_assert(map->ctx, pos < isl_map_dim(map, type), goto error);
5371 for (i = 0; i < map->n; ++i) {
5372 map->p[i] = isl_basic_map_fix(map->p[i], type, pos, value);
5376 ISL_F_CLR(map, ISL_MAP_NORMALIZED);
5383 __isl_give isl_set *isl_set_fix(__isl_take isl_set *set,
5384 enum isl_dim_type type, unsigned pos, isl_int value)
5386 return (struct isl_set *)isl_map_fix((isl_map *)set, type, pos, value);
5389 struct isl_map *isl_map_fix_input_si(struct isl_map *map,
5390 unsigned input, int value)
5392 return isl_map_fix_si(map, isl_dim_in, input, value);
5395 struct isl_set *isl_set_fix_dim_si(struct isl_set *set, unsigned dim, int value)
5397 return (struct isl_set *)
5398 isl_map_fix_si((struct isl_map *)set, isl_dim_set, dim, value);
5401 static __isl_give isl_basic_map *basic_map_bound_si(
5402 __isl_take isl_basic_map *bmap,
5403 enum isl_dim_type type, unsigned pos, int value, int upper)
5409 isl_assert(bmap->ctx, pos < isl_basic_map_dim(bmap, type), goto error);
5410 pos += isl_basic_map_offset(bmap, type);
5411 bmap = isl_basic_map_cow(bmap);
5412 bmap = isl_basic_map_extend_constraints(bmap, 0, 1);
5413 j = isl_basic_map_alloc_inequality(bmap);
5416 isl_seq_clr(bmap->ineq[j], 1 + isl_basic_map_total_dim(bmap));
5418 isl_int_set_si(bmap->ineq[j][pos], -1);
5419 isl_int_set_si(bmap->ineq[j][0], value);
5421 isl_int_set_si(bmap->ineq[j][pos], 1);
5422 isl_int_set_si(bmap->ineq[j][0], -value);
5424 bmap = isl_basic_map_simplify(bmap);
5425 return isl_basic_map_finalize(bmap);
5427 isl_basic_map_free(bmap);
5431 __isl_give isl_basic_map *isl_basic_map_lower_bound_si(
5432 __isl_take isl_basic_map *bmap,
5433 enum isl_dim_type type, unsigned pos, int value)
5435 return basic_map_bound_si(bmap, type, pos, value, 0);
5438 /* Constrain the values of the given dimension to be no greater than "value".
5440 __isl_give isl_basic_map *isl_basic_map_upper_bound_si(
5441 __isl_take isl_basic_map *bmap,
5442 enum isl_dim_type type, unsigned pos, int value)
5444 return basic_map_bound_si(bmap, type, pos, value, 1);
5447 struct isl_basic_set *isl_basic_set_lower_bound_dim(struct isl_basic_set *bset,
5448 unsigned dim, isl_int value)
5452 bset = isl_basic_set_cow(bset);
5453 bset = isl_basic_set_extend_constraints(bset, 0, 1);
5454 j = isl_basic_set_alloc_inequality(bset);
5457 isl_seq_clr(bset->ineq[j], 1 + isl_basic_set_total_dim(bset));
5458 isl_int_set_si(bset->ineq[j][1 + isl_basic_set_n_param(bset) + dim], 1);
5459 isl_int_neg(bset->ineq[j][0], value);
5460 bset = isl_basic_set_simplify(bset);
5461 return isl_basic_set_finalize(bset);
5463 isl_basic_set_free(bset);
5467 static __isl_give isl_map *map_bound_si(__isl_take isl_map *map,
5468 enum isl_dim_type type, unsigned pos, int value, int upper)
5472 map = isl_map_cow(map);
5476 isl_assert(map->ctx, pos < isl_map_dim(map, type), goto error);
5477 for (i = 0; i < map->n; ++i) {
5478 map->p[i] = basic_map_bound_si(map->p[i],
5479 type, pos, value, upper);
5483 ISL_F_CLR(map, ISL_MAP_NORMALIZED);
5490 __isl_give isl_map *isl_map_lower_bound_si(__isl_take isl_map *map,
5491 enum isl_dim_type type, unsigned pos, int value)
5493 return map_bound_si(map, type, pos, value, 0);
5496 __isl_give isl_map *isl_map_upper_bound_si(__isl_take isl_map *map,
5497 enum isl_dim_type type, unsigned pos, int value)
5499 return map_bound_si(map, type, pos, value, 1);
5502 __isl_give isl_set *isl_set_lower_bound_si(__isl_take isl_set *set,
5503 enum isl_dim_type type, unsigned pos, int value)
5505 return (struct isl_set *)
5506 isl_map_lower_bound_si((struct isl_map *)set, type, pos, value);
5509 __isl_give isl_set *isl_set_upper_bound_si(__isl_take isl_set *set,
5510 enum isl_dim_type type, unsigned pos, int value)
5512 return isl_map_upper_bound_si(set, type, pos, value);
5515 /* Bound the given variable of "bmap" from below (or above is "upper"
5516 * is set) to "value".
5518 static __isl_give isl_basic_map *basic_map_bound(
5519 __isl_take isl_basic_map *bmap,
5520 enum isl_dim_type type, unsigned pos, isl_int value, int upper)
5526 if (pos >= isl_basic_map_dim(bmap, type))
5527 isl_die(bmap->ctx, isl_error_invalid,
5528 "index out of bounds", goto error);
5529 pos += isl_basic_map_offset(bmap, type);
5530 bmap = isl_basic_map_cow(bmap);
5531 bmap = isl_basic_map_extend_constraints(bmap, 0, 1);
5532 j = isl_basic_map_alloc_inequality(bmap);
5535 isl_seq_clr(bmap->ineq[j], 1 + isl_basic_map_total_dim(bmap));
5537 isl_int_set_si(bmap->ineq[j][pos], -1);
5538 isl_int_set(bmap->ineq[j][0], value);
5540 isl_int_set_si(bmap->ineq[j][pos], 1);
5541 isl_int_neg(bmap->ineq[j][0], value);
5543 bmap = isl_basic_map_simplify(bmap);
5544 return isl_basic_map_finalize(bmap);
5546 isl_basic_map_free(bmap);
5550 /* Bound the given variable of "map" from below (or above is "upper"
5551 * is set) to "value".
5553 static __isl_give isl_map *map_bound(__isl_take isl_map *map,
5554 enum isl_dim_type type, unsigned pos, isl_int value, int upper)
5558 map = isl_map_cow(map);
5562 if (pos >= isl_map_dim(map, type))
5563 isl_die(map->ctx, isl_error_invalid,
5564 "index out of bounds", goto error);
5565 for (i = map->n - 1; i >= 0; --i) {
5566 map->p[i] = basic_map_bound(map->p[i], type, pos, value, upper);
5567 if (remove_if_empty(map, i) < 0)
5570 ISL_F_CLR(map, ISL_MAP_NORMALIZED);
5577 __isl_give isl_map *isl_map_lower_bound(__isl_take isl_map *map,
5578 enum isl_dim_type type, unsigned pos, isl_int value)
5580 return map_bound(map, type, pos, value, 0);
5583 __isl_give isl_map *isl_map_upper_bound(__isl_take isl_map *map,
5584 enum isl_dim_type type, unsigned pos, isl_int value)
5586 return map_bound(map, type, pos, value, 1);
5589 __isl_give isl_set *isl_set_lower_bound(__isl_take isl_set *set,
5590 enum isl_dim_type type, unsigned pos, isl_int value)
5592 return isl_map_lower_bound(set, type, pos, value);
5595 __isl_give isl_set *isl_set_upper_bound(__isl_take isl_set *set,
5596 enum isl_dim_type type, unsigned pos, isl_int value)
5598 return isl_map_upper_bound(set, type, pos, value);
5601 struct isl_set *isl_set_lower_bound_dim(struct isl_set *set, unsigned dim,
5606 set = isl_set_cow(set);
5610 isl_assert(set->ctx, dim < isl_set_n_dim(set), goto error);
5611 for (i = 0; i < set->n; ++i) {
5612 set->p[i] = isl_basic_set_lower_bound_dim(set->p[i], dim, value);
5622 struct isl_map *isl_map_reverse(struct isl_map *map)
5626 map = isl_map_cow(map);
5630 map->dim = isl_space_reverse(map->dim);
5633 for (i = 0; i < map->n; ++i) {
5634 map->p[i] = isl_basic_map_reverse(map->p[i]);
5638 ISL_F_CLR(map, ISL_MAP_NORMALIZED);
5645 static struct isl_map *isl_basic_map_partial_lexopt(
5646 struct isl_basic_map *bmap, struct isl_basic_set *dom,
5647 struct isl_set **empty, int max)
5651 if (bmap->ctx->opt->pip == ISL_PIP_PIP)
5652 return isl_pip_basic_map_lexopt(bmap, dom, empty, max);
5654 return isl_tab_basic_map_partial_lexopt(bmap, dom, empty, max);
5656 isl_basic_map_free(bmap);
5657 isl_basic_set_free(dom);
5663 struct isl_map *isl_basic_map_partial_lexmax(
5664 struct isl_basic_map *bmap, struct isl_basic_set *dom,
5665 struct isl_set **empty)
5667 return isl_basic_map_partial_lexopt(bmap, dom, empty, 1);
5670 struct isl_map *isl_basic_map_partial_lexmin(
5671 struct isl_basic_map *bmap, struct isl_basic_set *dom,
5672 struct isl_set **empty)
5674 return isl_basic_map_partial_lexopt(bmap, dom, empty, 0);
5677 struct isl_set *isl_basic_set_partial_lexmin(
5678 struct isl_basic_set *bset, struct isl_basic_set *dom,
5679 struct isl_set **empty)
5681 return (struct isl_set *)
5682 isl_basic_map_partial_lexmin((struct isl_basic_map *)bset,
5686 struct isl_set *isl_basic_set_partial_lexmax(
5687 struct isl_basic_set *bset, struct isl_basic_set *dom,
5688 struct isl_set **empty)
5690 return (struct isl_set *)
5691 isl_basic_map_partial_lexmax((struct isl_basic_map *)bset,
5695 __isl_give isl_pw_multi_aff *isl_basic_map_partial_lexmin_pw_multi_aff(
5696 __isl_take isl_basic_map *bmap, __isl_take isl_basic_set *dom,
5697 __isl_give isl_set **empty)
5699 return isl_basic_map_partial_lexopt_pw_multi_aff(bmap, dom, empty, 0);
5702 __isl_give isl_pw_multi_aff *isl_basic_map_partial_lexmax_pw_multi_aff(
5703 __isl_take isl_basic_map *bmap, __isl_take isl_basic_set *dom,
5704 __isl_give isl_set **empty)
5706 return isl_basic_map_partial_lexopt_pw_multi_aff(bmap, dom, empty, 1);
5709 __isl_give isl_pw_multi_aff *isl_basic_set_partial_lexmin_pw_multi_aff(
5710 __isl_take isl_basic_set *bset, __isl_take isl_basic_set *dom,
5711 __isl_give isl_set **empty)
5713 return isl_basic_map_partial_lexmin_pw_multi_aff(bset, dom, empty);
5716 __isl_give isl_pw_multi_aff *isl_basic_set_partial_lexmax_pw_multi_aff(
5717 __isl_take isl_basic_set *bset, __isl_take isl_basic_set *dom,
5718 __isl_give isl_set **empty)
5720 return isl_basic_map_partial_lexmax_pw_multi_aff(bset, dom, empty);
5723 __isl_give isl_pw_multi_aff *isl_basic_map_lexopt_pw_multi_aff(
5724 __isl_take isl_basic_map *bmap, int max)
5726 isl_basic_set *dom = NULL;
5727 isl_space *dom_space;
5731 dom_space = isl_space_domain(isl_space_copy(bmap->dim));
5732 dom = isl_basic_set_universe(dom_space);
5733 return isl_basic_map_partial_lexopt_pw_multi_aff(bmap, dom, NULL, max);
5735 isl_basic_map_free(bmap);
5739 __isl_give isl_pw_multi_aff *isl_basic_map_lexmin_pw_multi_aff(
5740 __isl_take isl_basic_map *bmap)
5742 return isl_basic_map_lexopt_pw_multi_aff(bmap, 0);
5746 #define TYPE isl_pw_multi_aff
5748 #define SUFFIX _pw_multi_aff
5750 #define EMPTY isl_pw_multi_aff_empty
5752 #define ADD isl_pw_multi_aff_union_add
5753 #include "isl_map_lexopt_templ.c"
5755 /* Given a map "map", compute the lexicographically minimal
5756 * (or maximal) image element for each domain element in dom,
5757 * in the form of an isl_pw_multi_aff.
5758 * Set *empty to those elements in dom that do not have an image element.
5760 * We first compute the lexicographically minimal or maximal element
5761 * in the first basic map. This results in a partial solution "res"
5762 * and a subset "todo" of dom that still need to be handled.
5763 * We then consider each of the remaining maps in "map" and successively
5764 * update both "res" and "todo".
5766 static __isl_give isl_pw_multi_aff *isl_map_partial_lexopt_aligned_pw_multi_aff(
5767 __isl_take isl_map *map, __isl_take isl_set *dom,
5768 __isl_give isl_set **empty, int max)
5771 isl_pw_multi_aff *res;
5777 if (isl_map_plain_is_empty(map)) {
5782 return isl_pw_multi_aff_from_map(map);
5785 res = basic_map_partial_lexopt_pw_multi_aff(
5786 isl_basic_map_copy(map->p[0]),
5787 isl_set_copy(dom), &todo, max);
5789 for (i = 1; i < map->n; ++i) {
5790 isl_pw_multi_aff *res_i;
5793 res_i = basic_map_partial_lexopt_pw_multi_aff(
5794 isl_basic_map_copy(map->p[i]),
5795 isl_set_copy(dom), &todo_i, max);
5798 res = isl_pw_multi_aff_union_lexmax(res, res_i);
5800 res = isl_pw_multi_aff_union_lexmin(res, res_i);
5802 todo = isl_set_intersect(todo, todo_i);
5823 #define TYPE isl_map
5827 #define EMPTY isl_map_empty
5829 #define ADD isl_map_union_disjoint
5830 #include "isl_map_lexopt_templ.c"
5832 /* Given a map "map", compute the lexicographically minimal
5833 * (or maximal) image element for each domain element in dom.
5834 * Set *empty to those elements in dom that do not have an image element.
5836 * We first compute the lexicographically minimal or maximal element
5837 * in the first basic map. This results in a partial solution "res"
5838 * and a subset "todo" of dom that still need to be handled.
5839 * We then consider each of the remaining maps in "map" and successively
5840 * update both "res" and "todo".
5842 * Let res^k and todo^k be the results after k steps and let i = k + 1.
5843 * Assume we are computing the lexicographical maximum.
5844 * We first compute the lexicographically maximal element in basic map i.
5845 * This results in a partial solution res_i and a subset todo_i.
5846 * Then we combine these results with those obtain for the first k basic maps
5847 * to obtain a result that is valid for the first k+1 basic maps.
5848 * In particular, the set where there is no solution is the set where
5849 * there is no solution for the first k basic maps and also no solution
5850 * for the ith basic map, i.e.,
5852 * todo^i = todo^k * todo_i
5854 * On dom(res^k) * dom(res_i), we need to pick the larger of the two
5855 * solutions, arbitrarily breaking ties in favor of res^k.
5856 * That is, when res^k(a) >= res_i(a), we pick res^k and
5857 * when res^k(a) < res_i(a), we pick res_i. (Here, ">=" and "<" denote
5858 * the lexicographic order.)
5859 * In practice, we compute
5861 * res^k * (res_i . "<=")
5865 * res_i * (res^k . "<")
5867 * Finally, we consider the symmetric difference of dom(res^k) and dom(res_i),
5868 * where only one of res^k and res_i provides a solution and we simply pick
5875 * Note that we only compute these intersections when dom(res^k) intersects
5876 * dom(res_i). Otherwise, the only effect of these intersections is to
5877 * potentially break up res^k and res_i into smaller pieces.
5878 * We want to avoid such splintering as much as possible.
5879 * In fact, an earlier implementation of this function would look for
5880 * better results in the domain of res^k and for extra results in todo^k,
5881 * but this would always result in a splintering according to todo^k,
5882 * even when the domain of basic map i is disjoint from the domains of
5883 * the previous basic maps.
5885 static __isl_give isl_map *isl_map_partial_lexopt_aligned(
5886 __isl_take isl_map *map, __isl_take isl_set *dom,
5887 __isl_give isl_set **empty, int max)
5890 struct isl_map *res;
5891 struct isl_set *todo;
5896 if (isl_map_plain_is_empty(map)) {
5904 res = basic_map_partial_lexopt(isl_basic_map_copy(map->p[0]),
5905 isl_set_copy(dom), &todo, max);
5907 for (i = 1; i < map->n; ++i) {
5911 isl_space *dim = isl_space_range(isl_map_get_space(res));
5913 res_i = basic_map_partial_lexopt(isl_basic_map_copy(map->p[i]),
5914 isl_set_copy(dom), &todo_i, max);
5917 lt = isl_map_lex_lt(isl_space_copy(dim));
5918 le = isl_map_lex_le(dim);
5920 lt = isl_map_lex_gt(isl_space_copy(dim));
5921 le = isl_map_lex_ge(dim);
5923 lt = isl_map_apply_range(isl_map_copy(res), lt);
5924 lt = isl_map_intersect(lt, isl_map_copy(res_i));
5925 le = isl_map_apply_range(isl_map_copy(res_i), le);
5926 le = isl_map_intersect(le, isl_map_copy(res));
5928 if (!isl_map_is_empty(lt) || !isl_map_is_empty(le)) {
5929 res = isl_map_intersect_domain(res,
5930 isl_set_copy(todo_i));
5931 res_i = isl_map_intersect_domain(res_i,
5932 isl_set_copy(todo));
5935 res = isl_map_union_disjoint(res, res_i);
5936 res = isl_map_union_disjoint(res, lt);
5937 res = isl_map_union_disjoint(res, le);
5939 todo = isl_set_intersect(todo, todo_i);
5959 __isl_give isl_map *isl_map_partial_lexmax(
5960 __isl_take isl_map *map, __isl_take isl_set *dom,
5961 __isl_give isl_set **empty)
5963 return isl_map_partial_lexopt(map, dom, empty, 1);
5966 __isl_give isl_map *isl_map_partial_lexmin(
5967 __isl_take isl_map *map, __isl_take isl_set *dom,
5968 __isl_give isl_set **empty)
5970 return isl_map_partial_lexopt(map, dom, empty, 0);
5973 __isl_give isl_set *isl_set_partial_lexmin(
5974 __isl_take isl_set *set, __isl_take isl_set *dom,
5975 __isl_give isl_set **empty)
5977 return (struct isl_set *)
5978 isl_map_partial_lexmin((struct isl_map *)set,
5982 __isl_give isl_set *isl_set_partial_lexmax(
5983 __isl_take isl_set *set, __isl_take isl_set *dom,
5984 __isl_give isl_set **empty)
5986 return (struct isl_set *)
5987 isl_map_partial_lexmax((struct isl_map *)set,
5991 __isl_give isl_map *isl_basic_map_lexopt(__isl_take isl_basic_map *bmap, int max)
5993 struct isl_basic_set *dom = NULL;
5998 dom_dim = isl_space_domain(isl_space_copy(bmap->dim));
5999 dom = isl_basic_set_universe(dom_dim);
6000 return isl_basic_map_partial_lexopt(bmap, dom, NULL, max);
6002 isl_basic_map_free(bmap);
6006 __isl_give isl_map *isl_basic_map_lexmin(__isl_take isl_basic_map *bmap)
6008 return isl_basic_map_lexopt(bmap, 0);
6011 __isl_give isl_map *isl_basic_map_lexmax(__isl_take isl_basic_map *bmap)
6013 return isl_basic_map_lexopt(bmap, 1);
6016 __isl_give isl_set *isl_basic_set_lexmin(__isl_take isl_basic_set *bset)
6018 return (isl_set *)isl_basic_map_lexmin((isl_basic_map *)bset);
6021 __isl_give isl_set *isl_basic_set_lexmax(__isl_take isl_basic_set *bset)
6023 return (isl_set *)isl_basic_map_lexmax((isl_basic_map *)bset);
6026 __isl_give isl_set *isl_set_lexmin(__isl_take isl_set *set)
6028 return (isl_set *)isl_map_lexmin((isl_map *)set);
6031 __isl_give isl_set *isl_set_lexmax(__isl_take isl_set *set)
6033 return (isl_set *)isl_map_lexmax((isl_map *)set);
6036 /* Extract the first and only affine expression from list
6037 * and then add it to *pwaff with the given dom.
6038 * This domain is known to be disjoint from other domains
6039 * because of the way isl_basic_map_foreach_lexmax works.
6041 static int update_dim_opt(__isl_take isl_basic_set *dom,
6042 __isl_take isl_aff_list *list, void *user)
6044 isl_ctx *ctx = isl_basic_set_get_ctx(dom);
6046 isl_pw_aff **pwaff = user;
6047 isl_pw_aff *pwaff_i;
6051 if (isl_aff_list_n_aff(list) != 1)
6052 isl_die(ctx, isl_error_internal,
6053 "expecting single element list", goto error);
6055 aff = isl_aff_list_get_aff(list, 0);
6056 pwaff_i = isl_pw_aff_alloc(isl_set_from_basic_set(dom), aff);
6058 *pwaff = isl_pw_aff_add_disjoint(*pwaff, pwaff_i);
6060 isl_aff_list_free(list);
6064 isl_basic_set_free(dom);
6065 isl_aff_list_free(list);
6069 /* Given a basic map with one output dimension, compute the minimum or
6070 * maximum of that dimension as an isl_pw_aff.
6072 * The isl_pw_aff is constructed by having isl_basic_map_foreach_lexopt
6073 * call update_dim_opt on each leaf of the result.
6075 static __isl_give isl_pw_aff *basic_map_dim_opt(__isl_keep isl_basic_map *bmap,
6078 isl_space *dim = isl_basic_map_get_space(bmap);
6082 dim = isl_space_from_domain(isl_space_domain(dim));
6083 dim = isl_space_add_dims(dim, isl_dim_out, 1);
6084 pwaff = isl_pw_aff_empty(dim);
6086 r = isl_basic_map_foreach_lexopt(bmap, max, &update_dim_opt, &pwaff);
6088 return isl_pw_aff_free(pwaff);
6093 /* Compute the minimum or maximum of the given output dimension
6094 * as a function of the parameters and the input dimensions,
6095 * but independently of the other output dimensions.
6097 * We first project out the other output dimension and then compute
6098 * the "lexicographic" maximum in each basic map, combining the results
6099 * using isl_pw_aff_union_max.
6101 static __isl_give isl_pw_aff *map_dim_opt(__isl_take isl_map *map, int pos,
6108 n_out = isl_map_dim(map, isl_dim_out);
6109 map = isl_map_project_out(map, isl_dim_out, pos + 1, n_out - (pos + 1));
6110 map = isl_map_project_out(map, isl_dim_out, 0, pos);
6115 isl_space *dim = isl_map_get_space(map);
6116 dim = isl_space_domain(isl_space_from_range(dim));
6118 return isl_pw_aff_empty(dim);
6121 pwaff = basic_map_dim_opt(map->p[0], max);
6122 for (i = 1; i < map->n; ++i) {
6123 isl_pw_aff *pwaff_i;
6125 pwaff_i = basic_map_dim_opt(map->p[i], max);
6126 pwaff = isl_pw_aff_union_opt(pwaff, pwaff_i, max);
6134 /* Compute the maximum of the given output dimension as a function of the
6135 * parameters and input dimensions, but independently of
6136 * the other output dimensions.
6138 __isl_give isl_pw_aff *isl_map_dim_max(__isl_take isl_map *map, int pos)
6140 return map_dim_opt(map, pos, 1);
6143 /* Compute the minimum or maximum of the given set dimension
6144 * as a function of the parameters,
6145 * but independently of the other set dimensions.
6147 static __isl_give isl_pw_aff *set_dim_opt(__isl_take isl_set *set, int pos,
6150 return map_dim_opt(set, pos, max);
6153 /* Compute the maximum of the given set dimension as a function of the
6154 * parameters, but independently of the other set dimensions.
6156 __isl_give isl_pw_aff *isl_set_dim_max(__isl_take isl_set *set, int pos)
6158 return set_dim_opt(set, pos, 1);
6161 /* Compute the minimum of the given set dimension as a function of the
6162 * parameters, but independently of the other set dimensions.
6164 __isl_give isl_pw_aff *isl_set_dim_min(__isl_take isl_set *set, int pos)
6166 return set_dim_opt(set, pos, 0);
6169 /* Apply a preimage specified by "mat" on the parameters of "bset".
6170 * bset is assumed to have only parameters and divs.
6172 static struct isl_basic_set *basic_set_parameter_preimage(
6173 struct isl_basic_set *bset, struct isl_mat *mat)
6180 bset->dim = isl_space_cow(bset->dim);
6184 nparam = isl_basic_set_dim(bset, isl_dim_param);
6186 isl_assert(bset->ctx, mat->n_row == 1 + nparam, goto error);
6188 bset->dim->nparam = 0;
6189 bset->dim->n_out = nparam;
6190 bset = isl_basic_set_preimage(bset, mat);
6192 bset->dim->nparam = bset->dim->n_out;
6193 bset->dim->n_out = 0;
6198 isl_basic_set_free(bset);
6202 /* Apply a preimage specified by "mat" on the parameters of "set".
6203 * set is assumed to have only parameters and divs.
6205 static struct isl_set *set_parameter_preimage(
6206 struct isl_set *set, struct isl_mat *mat)
6208 isl_space *dim = NULL;
6214 dim = isl_space_copy(set->dim);
6215 dim = isl_space_cow(dim);
6219 nparam = isl_set_dim(set, isl_dim_param);
6221 isl_assert(set->ctx, mat->n_row == 1 + nparam, goto error);
6224 dim->n_out = nparam;
6225 isl_set_reset_space(set, dim);
6226 set = isl_set_preimage(set, mat);
6229 dim = isl_space_copy(set->dim);
6230 dim = isl_space_cow(dim);
6233 dim->nparam = dim->n_out;
6235 isl_set_reset_space(set, dim);
6238 isl_space_free(dim);
6245 /* Intersect the basic set "bset" with the affine space specified by the
6246 * equalities in "eq".
6248 static struct isl_basic_set *basic_set_append_equalities(
6249 struct isl_basic_set *bset, struct isl_mat *eq)
6257 bset = isl_basic_set_extend_space(bset, isl_space_copy(bset->dim), 0,
6262 len = 1 + isl_space_dim(bset->dim, isl_dim_all) + bset->extra;
6263 for (i = 0; i < eq->n_row; ++i) {
6264 k = isl_basic_set_alloc_equality(bset);
6267 isl_seq_cpy(bset->eq[k], eq->row[i], eq->n_col);
6268 isl_seq_clr(bset->eq[k] + eq->n_col, len - eq->n_col);
6272 bset = isl_basic_set_gauss(bset, NULL);
6273 bset = isl_basic_set_finalize(bset);
6278 isl_basic_set_free(bset);
6282 /* Intersect the set "set" with the affine space specified by the
6283 * equalities in "eq".
6285 static struct isl_set *set_append_equalities(struct isl_set *set,
6293 for (i = 0; i < set->n; ++i) {
6294 set->p[i] = basic_set_append_equalities(set->p[i],
6307 /* Project the given basic set onto its parameter domain, possibly introducing
6308 * new, explicit, existential variables in the constraints.
6309 * The input has parameters and (possibly implicit) existential variables.
6310 * The output has the same parameters, but only
6311 * explicit existentially quantified variables.
6313 * The actual projection is performed by pip, but pip doesn't seem
6314 * to like equalities very much, so we first remove the equalities
6315 * among the parameters by performing a variable compression on
6316 * the parameters. Afterward, an inverse transformation is performed
6317 * and the equalities among the parameters are inserted back in.
6319 static struct isl_set *parameter_compute_divs(struct isl_basic_set *bset)
6323 struct isl_mat *T, *T2;
6324 struct isl_set *set;
6325 unsigned nparam, n_div;
6327 bset = isl_basic_set_cow(bset);
6331 if (bset->n_eq == 0)
6332 return isl_basic_set_lexmin(bset);
6334 isl_basic_set_gauss(bset, NULL);
6336 nparam = isl_basic_set_dim(bset, isl_dim_param);
6337 n_div = isl_basic_set_dim(bset, isl_dim_div);
6339 for (i = 0, j = n_div - 1; i < bset->n_eq && j >= 0; --j) {
6340 if (!isl_int_is_zero(bset->eq[i][1 + nparam + j]))
6343 if (i == bset->n_eq)
6344 return isl_basic_set_lexmin(bset);
6346 eq = isl_mat_sub_alloc6(bset->ctx, bset->eq, i, bset->n_eq - i,
6348 eq = isl_mat_cow(eq);
6349 T = isl_mat_variable_compression(isl_mat_copy(eq), &T2);
6350 if (T && T->n_col == 0) {
6354 bset = isl_basic_set_set_to_empty(bset);
6355 return isl_set_from_basic_set(bset);
6357 bset = basic_set_parameter_preimage(bset, T);
6359 set = isl_basic_set_lexmin(bset);
6360 set = set_parameter_preimage(set, T2);
6361 set = set_append_equalities(set, eq);
6365 /* Compute an explicit representation for all the existentially
6366 * quantified variables.
6367 * The input and output dimensions are first turned into parameters.
6368 * compute_divs then returns a map with the same parameters and
6369 * no input or output dimensions and the dimension specification
6370 * is reset to that of the input.
6372 static struct isl_map *compute_divs(struct isl_basic_map *bmap)
6374 struct isl_basic_set *bset;
6375 struct isl_set *set;
6376 struct isl_map *map;
6377 isl_space *dim, *orig_dim = NULL;
6382 bmap = isl_basic_map_cow(bmap);
6386 nparam = isl_basic_map_dim(bmap, isl_dim_param);
6387 n_in = isl_basic_map_dim(bmap, isl_dim_in);
6388 n_out = isl_basic_map_dim(bmap, isl_dim_out);
6389 dim = isl_space_set_alloc(bmap->ctx, nparam + n_in + n_out, 0);
6393 orig_dim = bmap->dim;
6395 bset = (struct isl_basic_set *)bmap;
6397 set = parameter_compute_divs(bset);
6398 map = (struct isl_map *)set;
6399 map = isl_map_reset_space(map, orig_dim);
6403 isl_basic_map_free(bmap);
6407 int isl_basic_map_divs_known(__isl_keep isl_basic_map *bmap)
6415 off = isl_space_dim(bmap->dim, isl_dim_all);
6416 for (i = 0; i < bmap->n_div; ++i) {
6417 if (isl_int_is_zero(bmap->div[i][0]))
6419 isl_assert(bmap->ctx, isl_int_is_zero(bmap->div[i][1+1+off+i]),
6425 static int map_divs_known(__isl_keep isl_map *map)
6432 for (i = 0; i < map->n; ++i) {
6433 int known = isl_basic_map_divs_known(map->p[i]);
6441 /* If bmap contains any unknown divs, then compute explicit
6442 * expressions for them. However, this computation may be
6443 * quite expensive, so first try to remove divs that aren't
6446 struct isl_map *isl_basic_map_compute_divs(struct isl_basic_map *bmap)
6449 struct isl_map *map;
6451 known = isl_basic_map_divs_known(bmap);
6455 return isl_map_from_basic_map(bmap);
6457 bmap = isl_basic_map_drop_redundant_divs(bmap);
6459 known = isl_basic_map_divs_known(bmap);
6463 return isl_map_from_basic_map(bmap);
6465 map = compute_divs(bmap);
6468 isl_basic_map_free(bmap);
6472 struct isl_map *isl_map_compute_divs(struct isl_map *map)
6476 struct isl_map *res;
6483 known = map_divs_known(map);
6491 res = isl_basic_map_compute_divs(isl_basic_map_copy(map->p[0]));
6492 for (i = 1 ; i < map->n; ++i) {
6494 r2 = isl_basic_map_compute_divs(isl_basic_map_copy(map->p[i]));
6495 if (ISL_F_ISSET(map, ISL_MAP_DISJOINT))
6496 res = isl_map_union_disjoint(res, r2);
6498 res = isl_map_union(res, r2);
6505 struct isl_set *isl_basic_set_compute_divs(struct isl_basic_set *bset)
6507 return (struct isl_set *)
6508 isl_basic_map_compute_divs((struct isl_basic_map *)bset);
6511 struct isl_set *isl_set_compute_divs(struct isl_set *set)
6513 return (struct isl_set *)
6514 isl_map_compute_divs((struct isl_map *)set);
6517 struct isl_set *isl_map_domain(struct isl_map *map)
6520 struct isl_set *set;
6525 map = isl_map_cow(map);
6529 set = (struct isl_set *)map;
6530 set->dim = isl_space_domain(set->dim);
6533 for (i = 0; i < map->n; ++i) {
6534 set->p[i] = isl_basic_map_domain(map->p[i]);
6538 ISL_F_CLR(set, ISL_MAP_DISJOINT);
6539 ISL_F_CLR(set, ISL_SET_NORMALIZED);
6546 /* Return the union of "map1" and "map2", where we assume for now that
6547 * "map1" and "map2" are disjoint. Note that the basic maps inside
6548 * "map1" or "map2" may not be disjoint from each other.
6549 * Also note that this function is also called from isl_map_union,
6550 * which takes care of handling the situation where "map1" and "map2"
6551 * may not be disjoint.
6553 * If one of the inputs is empty, we can simply return the other input.
6554 * Similarly, if one of the inputs is universal, then it is equal to the union.
6556 static __isl_give isl_map *map_union_disjoint(__isl_take isl_map *map1,
6557 __isl_take isl_map *map2)
6561 struct isl_map *map = NULL;
6576 is_universe = isl_map_plain_is_universe(map1);
6577 if (is_universe < 0)
6584 is_universe = isl_map_plain_is_universe(map2);
6585 if (is_universe < 0)
6592 isl_assert(map1->ctx, isl_space_is_equal(map1->dim, map2->dim), goto error);
6594 if (ISL_F_ISSET(map1, ISL_MAP_DISJOINT) &&
6595 ISL_F_ISSET(map2, ISL_MAP_DISJOINT))
6596 ISL_FL_SET(flags, ISL_MAP_DISJOINT);
6598 map = isl_map_alloc_space(isl_space_copy(map1->dim),
6599 map1->n + map2->n, flags);
6602 for (i = 0; i < map1->n; ++i) {
6603 map = isl_map_add_basic_map(map,
6604 isl_basic_map_copy(map1->p[i]));
6608 for (i = 0; i < map2->n; ++i) {
6609 map = isl_map_add_basic_map(map,
6610 isl_basic_map_copy(map2->p[i]));
6624 __isl_give isl_map *isl_map_union_disjoint(__isl_take isl_map *map1,
6625 __isl_take isl_map *map2)
6627 return isl_map_align_params_map_map_and(map1, map2, &map_union_disjoint);
6630 struct isl_map *isl_map_union(struct isl_map *map1, struct isl_map *map2)
6632 map1 = isl_map_union_disjoint(map1, map2);
6636 ISL_F_CLR(map1, ISL_MAP_DISJOINT);
6640 struct isl_set *isl_set_union_disjoint(
6641 struct isl_set *set1, struct isl_set *set2)
6643 return (struct isl_set *)
6644 isl_map_union_disjoint(
6645 (struct isl_map *)set1, (struct isl_map *)set2);
6648 struct isl_set *isl_set_union(struct isl_set *set1, struct isl_set *set2)
6650 return (struct isl_set *)
6651 isl_map_union((struct isl_map *)set1, (struct isl_map *)set2);
6654 /* Apply "fn" to pairs of elements from "map" and "set" and collect
6657 * "map" and "set" are assumed to be compatible and non-NULL.
6659 static __isl_give isl_map *map_intersect_set(__isl_take isl_map *map,
6660 __isl_take isl_set *set,
6661 __isl_give isl_basic_map *fn(__isl_take isl_basic_map *bmap,
6662 __isl_take isl_basic_set *bset))
6665 struct isl_map *result;
6668 if (isl_set_plain_is_universe(set)) {
6673 if (ISL_F_ISSET(map, ISL_MAP_DISJOINT) &&
6674 ISL_F_ISSET(set, ISL_MAP_DISJOINT))
6675 ISL_FL_SET(flags, ISL_MAP_DISJOINT);
6677 result = isl_map_alloc_space(isl_space_copy(map->dim),
6678 map->n * set->n, flags);
6679 for (i = 0; result && i < map->n; ++i)
6680 for (j = 0; j < set->n; ++j) {
6681 result = isl_map_add_basic_map(result,
6682 fn(isl_basic_map_copy(map->p[i]),
6683 isl_basic_set_copy(set->p[j])));
6693 static __isl_give isl_map *map_intersect_range(__isl_take isl_map *map,
6694 __isl_take isl_set *set)
6699 if (!isl_map_compatible_range(map, set))
6700 isl_die(set->ctx, isl_error_invalid,
6701 "incompatible spaces", goto error);
6703 return map_intersect_set(map, set, &isl_basic_map_intersect_range);
6710 __isl_give isl_map *isl_map_intersect_range(__isl_take isl_map *map,
6711 __isl_take isl_set *set)
6713 return isl_map_align_params_map_map_and(map, set, &map_intersect_range);
6716 static __isl_give isl_map *map_intersect_domain(__isl_take isl_map *map,
6717 __isl_take isl_set *set)
6722 if (!isl_map_compatible_domain(map, set))
6723 isl_die(set->ctx, isl_error_invalid,
6724 "incompatible spaces", goto error);
6726 return map_intersect_set(map, set, &isl_basic_map_intersect_domain);
6733 __isl_give isl_map *isl_map_intersect_domain(__isl_take isl_map *map,
6734 __isl_take isl_set *set)
6736 return isl_map_align_params_map_map_and(map, set,
6737 &map_intersect_domain);
6740 static __isl_give isl_map *map_apply_domain(__isl_take isl_map *map1,
6741 __isl_take isl_map *map2)
6745 map1 = isl_map_reverse(map1);
6746 map1 = isl_map_apply_range(map1, map2);
6747 return isl_map_reverse(map1);
6754 __isl_give isl_map *isl_map_apply_domain(__isl_take isl_map *map1,
6755 __isl_take isl_map *map2)
6757 return isl_map_align_params_map_map_and(map1, map2, &map_apply_domain);
6760 static __isl_give isl_map *map_apply_range(__isl_take isl_map *map1,
6761 __isl_take isl_map *map2)
6763 isl_space *dim_result;
6764 struct isl_map *result;
6770 dim_result = isl_space_join(isl_space_copy(map1->dim),
6771 isl_space_copy(map2->dim));
6773 result = isl_map_alloc_space(dim_result, map1->n * map2->n, 0);
6776 for (i = 0; i < map1->n; ++i)
6777 for (j = 0; j < map2->n; ++j) {
6778 result = isl_map_add_basic_map(result,
6779 isl_basic_map_apply_range(
6780 isl_basic_map_copy(map1->p[i]),
6781 isl_basic_map_copy(map2->p[j])));
6787 if (result && result->n <= 1)
6788 ISL_F_SET(result, ISL_MAP_DISJOINT);
6796 __isl_give isl_map *isl_map_apply_range(__isl_take isl_map *map1,
6797 __isl_take isl_map *map2)
6799 return isl_map_align_params_map_map_and(map1, map2, &map_apply_range);
6803 * returns range - domain
6805 struct isl_basic_set *isl_basic_map_deltas(struct isl_basic_map *bmap)
6807 isl_space *dims, *target_dim;
6808 struct isl_basic_set *bset;
6815 isl_assert(bmap->ctx, isl_space_tuple_match(bmap->dim, isl_dim_in,
6816 bmap->dim, isl_dim_out),
6818 target_dim = isl_space_domain(isl_basic_map_get_space(bmap));
6819 dim = isl_basic_map_n_in(bmap);
6820 nparam = isl_basic_map_n_param(bmap);
6821 bset = isl_basic_set_from_basic_map(bmap);
6822 bset = isl_basic_set_cow(bset);
6823 dims = isl_basic_set_get_space(bset);
6824 dims = isl_space_add_dims(dims, isl_dim_set, dim);
6825 bset = isl_basic_set_extend_space(bset, dims, 0, dim, 0);
6826 bset = isl_basic_set_swap_vars(bset, 2*dim);
6827 for (i = 0; i < dim; ++i) {
6828 int j = isl_basic_map_alloc_equality(
6829 (struct isl_basic_map *)bset);
6832 isl_seq_clr(bset->eq[j], 1 + isl_basic_set_total_dim(bset));
6833 isl_int_set_si(bset->eq[j][1+nparam+i], 1);
6834 isl_int_set_si(bset->eq[j][1+nparam+dim+i], 1);
6835 isl_int_set_si(bset->eq[j][1+nparam+2*dim+i], -1);
6837 bset = isl_basic_set_project_out(bset, isl_dim_set, dim, 2*dim);
6838 bset = isl_basic_set_reset_space(bset, target_dim);
6841 isl_basic_map_free(bmap);
6846 * returns range - domain
6848 __isl_give isl_set *isl_map_deltas(__isl_take isl_map *map)
6852 struct isl_set *result;
6857 isl_assert(map->ctx, isl_space_tuple_match(map->dim, isl_dim_in,
6858 map->dim, isl_dim_out),
6860 dim = isl_map_get_space(map);
6861 dim = isl_space_domain(dim);
6862 result = isl_set_alloc_space(dim, map->n, 0);
6865 for (i = 0; i < map->n; ++i)
6866 result = isl_set_add_basic_set(result,
6867 isl_basic_map_deltas(isl_basic_map_copy(map->p[i])));
6876 * returns [domain -> range] -> range - domain
6878 __isl_give isl_basic_map *isl_basic_map_deltas_map(
6879 __isl_take isl_basic_map *bmap)
6883 isl_basic_map *domain;
6887 if (!isl_space_tuple_match(bmap->dim, isl_dim_in, bmap->dim, isl_dim_out))
6888 isl_die(bmap->ctx, isl_error_invalid,
6889 "domain and range don't match", goto error);
6891 nparam = isl_basic_map_dim(bmap, isl_dim_param);
6892 n = isl_basic_map_dim(bmap, isl_dim_in);
6894 dim = isl_space_from_range(isl_space_domain(isl_basic_map_get_space(bmap)));
6895 domain = isl_basic_map_universe(dim);
6897 bmap = isl_basic_map_from_domain(isl_basic_map_wrap(bmap));
6898 bmap = isl_basic_map_apply_range(bmap, domain);
6899 bmap = isl_basic_map_extend_constraints(bmap, n, 0);
6901 total = isl_basic_map_total_dim(bmap);
6903 for (i = 0; i < n; ++i) {
6904 k = isl_basic_map_alloc_equality(bmap);
6907 isl_seq_clr(bmap->eq[k], 1 + total);
6908 isl_int_set_si(bmap->eq[k][1 + nparam + i], 1);
6909 isl_int_set_si(bmap->eq[k][1 + nparam + n + i], -1);
6910 isl_int_set_si(bmap->eq[k][1 + nparam + n + n + i], 1);
6913 bmap = isl_basic_map_gauss(bmap, NULL);
6914 return isl_basic_map_finalize(bmap);
6916 isl_basic_map_free(bmap);
6921 * returns [domain -> range] -> range - domain
6923 __isl_give isl_map *isl_map_deltas_map(__isl_take isl_map *map)
6926 isl_space *domain_dim;
6931 if (!isl_space_tuple_match(map->dim, isl_dim_in, map->dim, isl_dim_out))
6932 isl_die(map->ctx, isl_error_invalid,
6933 "domain and range don't match", goto error);
6935 map = isl_map_cow(map);
6939 domain_dim = isl_space_from_range(isl_space_domain(isl_map_get_space(map)));
6940 map->dim = isl_space_from_domain(isl_space_wrap(map->dim));
6941 map->dim = isl_space_join(map->dim, domain_dim);
6944 for (i = 0; i < map->n; ++i) {
6945 map->p[i] = isl_basic_map_deltas_map(map->p[i]);
6949 ISL_F_CLR(map, ISL_MAP_NORMALIZED);
6956 static __isl_give isl_basic_map *basic_map_identity(__isl_take isl_space *dims)
6958 struct isl_basic_map *bmap;
6966 nparam = dims->nparam;
6968 bmap = isl_basic_map_alloc_space(dims, 0, dim, 0);
6972 for (i = 0; i < dim; ++i) {
6973 int j = isl_basic_map_alloc_equality(bmap);
6976 isl_seq_clr(bmap->eq[j], 1 + isl_basic_map_total_dim(bmap));
6977 isl_int_set_si(bmap->eq[j][1+nparam+i], 1);
6978 isl_int_set_si(bmap->eq[j][1+nparam+dim+i], -1);
6980 return isl_basic_map_finalize(bmap);
6982 isl_basic_map_free(bmap);
6986 __isl_give isl_basic_map *isl_basic_map_identity(__isl_take isl_space *dim)
6990 if (dim->n_in != dim->n_out)
6991 isl_die(dim->ctx, isl_error_invalid,
6992 "number of input and output dimensions needs to be "
6993 "the same", goto error);
6994 return basic_map_identity(dim);
6996 isl_space_free(dim);
7000 struct isl_basic_map *isl_basic_map_identity_like(struct isl_basic_map *model)
7002 if (!model || !model->dim)
7004 return isl_basic_map_identity(isl_space_copy(model->dim));
7007 __isl_give isl_map *isl_map_identity(__isl_take isl_space *dim)
7009 return isl_map_from_basic_map(isl_basic_map_identity(dim));
7012 struct isl_map *isl_map_identity_like(struct isl_map *model)
7014 if (!model || !model->dim)
7016 return isl_map_identity(isl_space_copy(model->dim));
7019 struct isl_map *isl_map_identity_like_basic_map(struct isl_basic_map *model)
7021 if (!model || !model->dim)
7023 return isl_map_identity(isl_space_copy(model->dim));
7026 __isl_give isl_map *isl_set_identity(__isl_take isl_set *set)
7028 isl_space *dim = isl_set_get_space(set);
7030 id = isl_map_identity(isl_space_map_from_set(dim));
7031 return isl_map_intersect_range(id, set);
7034 /* Construct a basic set with all set dimensions having only non-negative
7037 __isl_give isl_basic_set *isl_basic_set_positive_orthant(
7038 __isl_take isl_space *space)
7043 struct isl_basic_set *bset;
7047 nparam = space->nparam;
7049 bset = isl_basic_set_alloc_space(space, 0, 0, dim);
7052 for (i = 0; i < dim; ++i) {
7053 int k = isl_basic_set_alloc_inequality(bset);
7056 isl_seq_clr(bset->ineq[k], 1 + isl_basic_set_total_dim(bset));
7057 isl_int_set_si(bset->ineq[k][1 + nparam + i], 1);
7061 isl_basic_set_free(bset);
7065 /* Construct the half-space x_pos >= 0.
7067 static __isl_give isl_basic_set *nonneg_halfspace(__isl_take isl_space *dim,
7071 isl_basic_set *nonneg;
7073 nonneg = isl_basic_set_alloc_space(dim, 0, 0, 1);
7074 k = isl_basic_set_alloc_inequality(nonneg);
7077 isl_seq_clr(nonneg->ineq[k], 1 + isl_basic_set_total_dim(nonneg));
7078 isl_int_set_si(nonneg->ineq[k][pos], 1);
7080 return isl_basic_set_finalize(nonneg);
7082 isl_basic_set_free(nonneg);
7086 /* Construct the half-space x_pos <= -1.
7088 static __isl_give isl_basic_set *neg_halfspace(__isl_take isl_space *dim, int pos)
7093 neg = isl_basic_set_alloc_space(dim, 0, 0, 1);
7094 k = isl_basic_set_alloc_inequality(neg);
7097 isl_seq_clr(neg->ineq[k], 1 + isl_basic_set_total_dim(neg));
7098 isl_int_set_si(neg->ineq[k][0], -1);
7099 isl_int_set_si(neg->ineq[k][pos], -1);
7101 return isl_basic_set_finalize(neg);
7103 isl_basic_set_free(neg);
7107 __isl_give isl_set *isl_set_split_dims(__isl_take isl_set *set,
7108 enum isl_dim_type type, unsigned first, unsigned n)
7111 isl_basic_set *nonneg;
7119 isl_assert(set->ctx, first + n <= isl_set_dim(set, type), goto error);
7121 for (i = 0; i < n; ++i) {
7122 nonneg = nonneg_halfspace(isl_set_get_space(set),
7123 pos(set->dim, type) + first + i);
7124 neg = neg_halfspace(isl_set_get_space(set),
7125 pos(set->dim, type) + first + i);
7127 set = isl_set_intersect(set, isl_basic_set_union(nonneg, neg));
7136 static int foreach_orthant(__isl_take isl_set *set, int *signs, int first,
7137 int len, int (*fn)(__isl_take isl_set *orthant, int *signs, void *user),
7144 if (isl_set_plain_is_empty(set)) {
7149 return fn(set, signs, user);
7152 half = isl_set_from_basic_set(nonneg_halfspace(isl_set_get_space(set),
7154 half = isl_set_intersect(half, isl_set_copy(set));
7155 if (foreach_orthant(half, signs, first + 1, len, fn, user) < 0)
7159 half = isl_set_from_basic_set(neg_halfspace(isl_set_get_space(set),
7161 half = isl_set_intersect(half, set);
7162 return foreach_orthant(half, signs, first + 1, len, fn, user);
7168 /* Call "fn" on the intersections of "set" with each of the orthants
7169 * (except for obviously empty intersections). The orthant is identified
7170 * by the signs array, with each entry having value 1 or -1 according
7171 * to the sign of the corresponding variable.
7173 int isl_set_foreach_orthant(__isl_keep isl_set *set,
7174 int (*fn)(__isl_take isl_set *orthant, int *signs, void *user),
7184 if (isl_set_plain_is_empty(set))
7187 nparam = isl_set_dim(set, isl_dim_param);
7188 nvar = isl_set_dim(set, isl_dim_set);
7190 signs = isl_alloc_array(set->ctx, int, nparam + nvar);
7192 r = foreach_orthant(isl_set_copy(set), signs, 0, nparam + nvar,
7200 int isl_set_is_equal(struct isl_set *set1, struct isl_set *set2)
7202 return isl_map_is_equal((struct isl_map *)set1, (struct isl_map *)set2);
7205 int isl_basic_map_is_subset(
7206 struct isl_basic_map *bmap1, struct isl_basic_map *bmap2)
7209 struct isl_map *map1;
7210 struct isl_map *map2;
7212 if (!bmap1 || !bmap2)
7215 map1 = isl_map_from_basic_map(isl_basic_map_copy(bmap1));
7216 map2 = isl_map_from_basic_map(isl_basic_map_copy(bmap2));
7218 is_subset = isl_map_is_subset(map1, map2);
7226 int isl_basic_set_is_subset(__isl_keep isl_basic_set *bset1,
7227 __isl_keep isl_basic_set *bset2)
7229 return isl_basic_map_is_subset(bset1, bset2);
7232 int isl_basic_map_is_equal(
7233 struct isl_basic_map *bmap1, struct isl_basic_map *bmap2)
7237 if (!bmap1 || !bmap2)
7239 is_subset = isl_basic_map_is_subset(bmap1, bmap2);
7242 is_subset = isl_basic_map_is_subset(bmap2, bmap1);
7246 int isl_basic_set_is_equal(
7247 struct isl_basic_set *bset1, struct isl_basic_set *bset2)
7249 return isl_basic_map_is_equal(
7250 (struct isl_basic_map *)bset1, (struct isl_basic_map *)bset2);
7253 int isl_map_is_empty(struct isl_map *map)
7260 for (i = 0; i < map->n; ++i) {
7261 is_empty = isl_basic_map_is_empty(map->p[i]);
7270 int isl_map_plain_is_empty(__isl_keep isl_map *map)
7272 return map ? map->n == 0 : -1;
7275 int isl_map_fast_is_empty(__isl_keep isl_map *map)
7277 return isl_map_plain_is_empty(map);
7280 int isl_set_plain_is_empty(struct isl_set *set)
7282 return set ? set->n == 0 : -1;
7285 int isl_set_fast_is_empty(__isl_keep isl_set *set)
7287 return isl_set_plain_is_empty(set);
7290 int isl_set_is_empty(struct isl_set *set)
7292 return isl_map_is_empty((struct isl_map *)set);
7295 int isl_map_has_equal_space(__isl_keep isl_map *map1, __isl_keep isl_map *map2)
7300 return isl_space_is_equal(map1->dim, map2->dim);
7303 int isl_set_has_equal_space(__isl_keep isl_set *set1, __isl_keep isl_set *set2)
7308 return isl_space_is_equal(set1->dim, set2->dim);
7311 static int map_is_equal(__isl_keep isl_map *map1, __isl_keep isl_map *map2)
7317 is_subset = isl_map_is_subset(map1, map2);
7320 is_subset = isl_map_is_subset(map2, map1);
7324 int isl_map_is_equal(__isl_keep isl_map *map1, __isl_keep isl_map *map2)
7326 return isl_map_align_params_map_map_and_test(map1, map2, &map_is_equal);
7329 int isl_basic_map_is_strict_subset(
7330 struct isl_basic_map *bmap1, struct isl_basic_map *bmap2)
7334 if (!bmap1 || !bmap2)
7336 is_subset = isl_basic_map_is_subset(bmap1, bmap2);
7339 is_subset = isl_basic_map_is_subset(bmap2, bmap1);
7340 if (is_subset == -1)
7345 int isl_map_is_strict_subset(struct isl_map *map1, struct isl_map *map2)
7351 is_subset = isl_map_is_subset(map1, map2);
7354 is_subset = isl_map_is_subset(map2, map1);
7355 if (is_subset == -1)
7360 int isl_set_is_strict_subset(__isl_keep isl_set *set1, __isl_keep isl_set *set2)
7362 return isl_map_is_strict_subset((isl_map *)set1, (isl_map *)set2);
7365 int isl_basic_map_is_universe(struct isl_basic_map *bmap)
7369 return bmap->n_eq == 0 && bmap->n_ineq == 0;
7372 int isl_basic_set_is_universe(struct isl_basic_set *bset)
7376 return bset->n_eq == 0 && bset->n_ineq == 0;
7379 int isl_map_plain_is_universe(__isl_keep isl_map *map)
7386 for (i = 0; i < map->n; ++i) {
7387 int r = isl_basic_map_is_universe(map->p[i]);
7395 int isl_set_plain_is_universe(__isl_keep isl_set *set)
7397 return isl_map_plain_is_universe((isl_map *) set);
7400 int isl_set_fast_is_universe(__isl_keep isl_set *set)
7402 return isl_set_plain_is_universe(set);
7405 int isl_basic_map_is_empty(struct isl_basic_map *bmap)
7407 struct isl_basic_set *bset = NULL;
7408 struct isl_vec *sample = NULL;
7415 if (ISL_F_ISSET(bmap, ISL_BASIC_MAP_EMPTY))
7418 if (isl_basic_map_is_universe(bmap))
7421 if (ISL_F_ISSET(bmap, ISL_BASIC_MAP_RATIONAL)) {
7422 struct isl_basic_map *copy = isl_basic_map_copy(bmap);
7423 copy = isl_basic_map_remove_redundancies(copy);
7424 empty = isl_basic_map_plain_is_empty(copy);
7425 isl_basic_map_free(copy);
7429 total = 1 + isl_basic_map_total_dim(bmap);
7430 if (bmap->sample && bmap->sample->size == total) {
7431 int contains = isl_basic_map_contains(bmap, bmap->sample);
7437 isl_vec_free(bmap->sample);
7438 bmap->sample = NULL;
7439 bset = isl_basic_map_underlying_set(isl_basic_map_copy(bmap));
7442 sample = isl_basic_set_sample_vec(bset);
7445 empty = sample->size == 0;
7446 isl_vec_free(bmap->sample);
7447 bmap->sample = sample;
7449 ISL_F_SET(bmap, ISL_BASIC_MAP_EMPTY);
7454 int isl_basic_map_plain_is_empty(__isl_keep isl_basic_map *bmap)
7458 return ISL_F_ISSET(bmap, ISL_BASIC_MAP_EMPTY);
7461 int isl_basic_map_fast_is_empty(__isl_keep isl_basic_map *bmap)
7463 return isl_basic_map_plain_is_empty(bmap);
7466 int isl_basic_set_plain_is_empty(__isl_keep isl_basic_set *bset)
7470 return ISL_F_ISSET(bset, ISL_BASIC_SET_EMPTY);
7473 int isl_basic_set_fast_is_empty(__isl_keep isl_basic_set *bset)
7475 return isl_basic_set_plain_is_empty(bset);
7478 int isl_basic_set_is_empty(struct isl_basic_set *bset)
7480 return isl_basic_map_is_empty((struct isl_basic_map *)bset);
7483 struct isl_map *isl_basic_map_union(
7484 struct isl_basic_map *bmap1, struct isl_basic_map *bmap2)
7486 struct isl_map *map;
7487 if (!bmap1 || !bmap2)
7490 isl_assert(bmap1->ctx, isl_space_is_equal(bmap1->dim, bmap2->dim), goto error);
7492 map = isl_map_alloc_space(isl_space_copy(bmap1->dim), 2, 0);
7495 map = isl_map_add_basic_map(map, bmap1);
7496 map = isl_map_add_basic_map(map, bmap2);
7499 isl_basic_map_free(bmap1);
7500 isl_basic_map_free(bmap2);
7504 struct isl_set *isl_basic_set_union(
7505 struct isl_basic_set *bset1, struct isl_basic_set *bset2)
7507 return (struct isl_set *)isl_basic_map_union(
7508 (struct isl_basic_map *)bset1,
7509 (struct isl_basic_map *)bset2);
7512 /* Order divs such that any div only depends on previous divs */
7513 struct isl_basic_map *isl_basic_map_order_divs(struct isl_basic_map *bmap)
7521 off = isl_space_dim(bmap->dim, isl_dim_all);
7523 for (i = 0; i < bmap->n_div; ++i) {
7525 if (isl_int_is_zero(bmap->div[i][0]))
7527 pos = isl_seq_first_non_zero(bmap->div[i]+1+1+off+i,
7531 isl_basic_map_swap_div(bmap, i, i + pos);
7537 struct isl_basic_set *isl_basic_set_order_divs(struct isl_basic_set *bset)
7539 return (struct isl_basic_set *)
7540 isl_basic_map_order_divs((struct isl_basic_map *)bset);
7543 __isl_give isl_map *isl_map_order_divs(__isl_take isl_map *map)
7550 for (i = 0; i < map->n; ++i) {
7551 map->p[i] = isl_basic_map_order_divs(map->p[i]);
7562 /* Apply the expansion computed by isl_merge_divs.
7563 * The expansion itself is given by "exp" while the resulting
7564 * list of divs is given by "div".
7566 __isl_give isl_basic_set *isl_basic_set_expand_divs(
7567 __isl_take isl_basic_set *bset, __isl_take isl_mat *div, int *exp)
7572 bset = isl_basic_set_cow(bset);
7576 if (div->n_row < bset->n_div)
7577 isl_die(isl_mat_get_ctx(div), isl_error_invalid,
7578 "not an expansion", goto error);
7580 bset = isl_basic_map_extend_space(bset, isl_space_copy(bset->dim),
7581 div->n_row - bset->n_div, 0,
7582 2 * (div->n_row - bset->n_div));
7584 n_div = bset->n_div;
7585 for (i = n_div; i < div->n_row; ++i)
7586 if (isl_basic_set_alloc_div(bset) < 0)
7590 for (i = div->n_row - 1; i >= 0; --i) {
7591 if (j >= 0 && exp[j] == i) {
7593 isl_basic_map_swap_div(bset, i, j);
7596 isl_seq_cpy(bset->div[i], div->row[i], div->n_col);
7597 if (isl_basic_map_add_div_constraints(bset, i) < 0)
7605 isl_basic_set_free(bset);
7610 /* Look for a div in dst that corresponds to the div "div" in src.
7611 * The divs before "div" in src and dst are assumed to be the same.
7613 * Returns -1 if no corresponding div was found and the position
7614 * of the corresponding div in dst otherwise.
7616 static int find_div(struct isl_basic_map *dst,
7617 struct isl_basic_map *src, unsigned div)
7621 unsigned total = isl_space_dim(src->dim, isl_dim_all);
7623 isl_assert(dst->ctx, div <= dst->n_div, return -1);
7624 for (i = div; i < dst->n_div; ++i)
7625 if (isl_seq_eq(dst->div[i], src->div[div], 1+1+total+div) &&
7626 isl_seq_first_non_zero(dst->div[i]+1+1+total+div,
7627 dst->n_div - div) == -1)
7632 struct isl_basic_map *isl_basic_map_align_divs(
7633 struct isl_basic_map *dst, struct isl_basic_map *src)
7641 if (src->n_div == 0)
7644 for (i = 0; i < src->n_div; ++i)
7645 isl_assert(src->ctx, !isl_int_is_zero(src->div[i][0]), goto error);
7647 src = isl_basic_map_order_divs(src);
7648 dst = isl_basic_map_cow(dst);
7649 dst = isl_basic_map_extend_space(dst, isl_space_copy(dst->dim),
7650 src->n_div, 0, 2 * src->n_div);
7653 total = isl_space_dim(src->dim, isl_dim_all);
7654 for (i = 0; i < src->n_div; ++i) {
7655 int j = find_div(dst, src, i);
7657 j = isl_basic_map_alloc_div(dst);
7660 isl_seq_cpy(dst->div[j], src->div[i], 1+1+total+i);
7661 isl_seq_clr(dst->div[j]+1+1+total+i, dst->n_div - i);
7662 if (isl_basic_map_add_div_constraints(dst, j) < 0)
7666 isl_basic_map_swap_div(dst, i, j);
7670 isl_basic_map_free(dst);
7674 struct isl_basic_set *isl_basic_set_align_divs(
7675 struct isl_basic_set *dst, struct isl_basic_set *src)
7677 return (struct isl_basic_set *)isl_basic_map_align_divs(
7678 (struct isl_basic_map *)dst, (struct isl_basic_map *)src);
7681 struct isl_map *isl_map_align_divs(struct isl_map *map)
7689 map = isl_map_compute_divs(map);
7690 map = isl_map_cow(map);
7694 for (i = 1; i < map->n; ++i)
7695 map->p[0] = isl_basic_map_align_divs(map->p[0], map->p[i]);
7696 for (i = 1; i < map->n; ++i)
7697 map->p[i] = isl_basic_map_align_divs(map->p[i], map->p[0]);
7699 ISL_F_CLR(map, ISL_MAP_NORMALIZED);
7703 struct isl_set *isl_set_align_divs(struct isl_set *set)
7705 return (struct isl_set *)isl_map_align_divs((struct isl_map *)set);
7708 static __isl_give isl_set *set_apply( __isl_take isl_set *set,
7709 __isl_take isl_map *map)
7713 isl_assert(set->ctx, isl_map_compatible_domain(map, set), goto error);
7714 map = isl_map_intersect_domain(map, set);
7715 set = isl_map_range(map);
7723 __isl_give isl_set *isl_set_apply( __isl_take isl_set *set,
7724 __isl_take isl_map *map)
7726 return isl_map_align_params_map_map_and(set, map, &set_apply);
7729 /* There is no need to cow as removing empty parts doesn't change
7730 * the meaning of the set.
7732 struct isl_map *isl_map_remove_empty_parts(struct isl_map *map)
7739 for (i = map->n - 1; i >= 0; --i)
7740 remove_if_empty(map, i);
7745 struct isl_set *isl_set_remove_empty_parts(struct isl_set *set)
7747 return (struct isl_set *)
7748 isl_map_remove_empty_parts((struct isl_map *)set);
7751 struct isl_basic_map *isl_map_copy_basic_map(struct isl_map *map)
7753 struct isl_basic_map *bmap;
7754 if (!map || map->n == 0)
7756 bmap = map->p[map->n-1];
7757 isl_assert(map->ctx, ISL_F_ISSET(bmap, ISL_BASIC_SET_FINAL), return NULL);
7758 return isl_basic_map_copy(bmap);
7761 struct isl_basic_set *isl_set_copy_basic_set(struct isl_set *set)
7763 return (struct isl_basic_set *)
7764 isl_map_copy_basic_map((struct isl_map *)set);
7767 __isl_give isl_map *isl_map_drop_basic_map(__isl_take isl_map *map,
7768 __isl_keep isl_basic_map *bmap)
7774 for (i = map->n-1; i >= 0; --i) {
7775 if (map->p[i] != bmap)
7777 map = isl_map_cow(map);
7780 isl_basic_map_free(map->p[i]);
7781 if (i != map->n-1) {
7782 ISL_F_CLR(map, ISL_SET_NORMALIZED);
7783 map->p[i] = map->p[map->n-1];
7794 struct isl_set *isl_set_drop_basic_set(struct isl_set *set,
7795 struct isl_basic_set *bset)
7797 return (struct isl_set *)isl_map_drop_basic_map((struct isl_map *)set,
7798 (struct isl_basic_map *)bset);
7801 /* Given two basic sets bset1 and bset2, compute the maximal difference
7802 * between the values of dimension pos in bset1 and those in bset2
7803 * for any common value of the parameters and dimensions preceding pos.
7805 static enum isl_lp_result basic_set_maximal_difference_at(
7806 __isl_keep isl_basic_set *bset1, __isl_keep isl_basic_set *bset2,
7807 int pos, isl_int *opt)
7810 struct isl_basic_map *bmap1 = NULL;
7811 struct isl_basic_map *bmap2 = NULL;
7812 struct isl_ctx *ctx;
7813 struct isl_vec *obj;
7816 unsigned dim1, dim2;
7817 enum isl_lp_result res;
7819 if (!bset1 || !bset2)
7820 return isl_lp_error;
7822 nparam = isl_basic_set_n_param(bset1);
7823 dim1 = isl_basic_set_n_dim(bset1);
7824 dim2 = isl_basic_set_n_dim(bset2);
7825 dims = isl_space_alloc(bset1->ctx, nparam, pos, dim1 - pos);
7826 bmap1 = isl_basic_map_from_basic_set(isl_basic_set_copy(bset1), dims);
7827 dims = isl_space_alloc(bset2->ctx, nparam, pos, dim2 - pos);
7828 bmap2 = isl_basic_map_from_basic_set(isl_basic_set_copy(bset2), dims);
7829 if (!bmap1 || !bmap2)
7831 bmap1 = isl_basic_map_cow(bmap1);
7832 bmap1 = isl_basic_map_extend(bmap1, nparam,
7833 pos, (dim1 - pos) + (dim2 - pos),
7834 bmap2->n_div, bmap2->n_eq, bmap2->n_ineq);
7835 bmap1 = add_constraints(bmap1, bmap2, 0, dim1 - pos);
7838 total = isl_basic_map_total_dim(bmap1);
7840 obj = isl_vec_alloc(ctx, 1 + total);
7843 isl_seq_clr(obj->block.data, 1 + total);
7844 isl_int_set_si(obj->block.data[1+nparam+pos], 1);
7845 isl_int_set_si(obj->block.data[1+nparam+pos+(dim1-pos)], -1);
7846 res = isl_basic_map_solve_lp(bmap1, 1, obj->block.data, ctx->one,
7848 isl_basic_map_free(bmap1);
7852 isl_basic_map_free(bmap2);
7854 isl_basic_map_free(bmap1);
7855 return isl_lp_error;
7858 /* Given two _disjoint_ basic sets bset1 and bset2, check whether
7859 * for any common value of the parameters and dimensions preceding pos
7860 * in both basic sets, the values of dimension pos in bset1 are
7861 * smaller or larger than those in bset2.
7864 * 1 if bset1 follows bset2
7865 * -1 if bset1 precedes bset2
7866 * 0 if bset1 and bset2 are incomparable
7867 * -2 if some error occurred.
7869 int isl_basic_set_compare_at(struct isl_basic_set *bset1,
7870 struct isl_basic_set *bset2, int pos)
7873 enum isl_lp_result res;
7878 res = basic_set_maximal_difference_at(bset1, bset2, pos, &opt);
7880 if (res == isl_lp_empty)
7882 else if ((res == isl_lp_ok && isl_int_is_pos(opt)) ||
7883 res == isl_lp_unbounded)
7885 else if (res == isl_lp_ok && isl_int_is_neg(opt))
7894 /* Given two basic sets bset1 and bset2, check whether
7895 * for any common value of the parameters and dimensions preceding pos
7896 * there is a value of dimension pos in bset1 that is larger
7897 * than a value of the same dimension in bset2.
7900 * 1 if there exists such a pair
7901 * 0 if there is no such pair, but there is a pair of equal values
7903 * -2 if some error occurred.
7905 int isl_basic_set_follows_at(__isl_keep isl_basic_set *bset1,
7906 __isl_keep isl_basic_set *bset2, int pos)
7909 enum isl_lp_result res;
7914 res = basic_set_maximal_difference_at(bset1, bset2, pos, &opt);
7916 if (res == isl_lp_empty)
7918 else if ((res == isl_lp_ok && isl_int_is_pos(opt)) ||
7919 res == isl_lp_unbounded)
7921 else if (res == isl_lp_ok && isl_int_is_neg(opt))
7923 else if (res == isl_lp_ok)
7932 /* Given two sets set1 and set2, check whether
7933 * for any common value of the parameters and dimensions preceding pos
7934 * there is a value of dimension pos in set1 that is larger
7935 * than a value of the same dimension in set2.
7938 * 1 if there exists such a pair
7939 * 0 if there is no such pair, but there is a pair of equal values
7941 * -2 if some error occurred.
7943 int isl_set_follows_at(__isl_keep isl_set *set1,
7944 __isl_keep isl_set *set2, int pos)
7952 for (i = 0; i < set1->n; ++i)
7953 for (j = 0; j < set2->n; ++j) {
7955 f = isl_basic_set_follows_at(set1->p[i], set2->p[j], pos);
7956 if (f == 1 || f == -2)
7965 static int isl_basic_map_plain_has_fixed_var(__isl_keep isl_basic_map *bmap,
7966 unsigned pos, isl_int *val)
7974 total = isl_basic_map_total_dim(bmap);
7975 for (i = 0, d = total-1; i < bmap->n_eq && d+1 > pos; ++i) {
7976 for (; d+1 > pos; --d)
7977 if (!isl_int_is_zero(bmap->eq[i][1+d]))
7981 if (isl_seq_first_non_zero(bmap->eq[i]+1, d) != -1)
7983 if (isl_seq_first_non_zero(bmap->eq[i]+1+d+1, total-d-1) != -1)
7985 if (!isl_int_is_one(bmap->eq[i][1+d]))
7988 isl_int_neg(*val, bmap->eq[i][0]);
7994 static int isl_map_plain_has_fixed_var(__isl_keep isl_map *map,
7995 unsigned pos, isl_int *val)
8007 return isl_basic_map_plain_has_fixed_var(map->p[0], pos, val);
8010 fixed = isl_basic_map_plain_has_fixed_var(map->p[0], pos, &v);
8011 for (i = 1; fixed == 1 && i < map->n; ++i) {
8012 fixed = isl_basic_map_plain_has_fixed_var(map->p[i], pos, &tmp);
8013 if (fixed == 1 && isl_int_ne(tmp, v))
8017 isl_int_set(*val, v);
8023 static int isl_basic_set_plain_has_fixed_var(__isl_keep isl_basic_set *bset,
8024 unsigned pos, isl_int *val)
8026 return isl_basic_map_plain_has_fixed_var((struct isl_basic_map *)bset,
8030 static int isl_set_plain_has_fixed_var(__isl_keep isl_set *set, unsigned pos,
8033 return isl_map_plain_has_fixed_var((struct isl_map *)set, pos, val);
8036 int isl_basic_map_plain_is_fixed(__isl_keep isl_basic_map *bmap,
8037 enum isl_dim_type type, unsigned pos, isl_int *val)
8039 if (pos >= isl_basic_map_dim(bmap, type))
8041 return isl_basic_map_plain_has_fixed_var(bmap,
8042 isl_basic_map_offset(bmap, type) - 1 + pos, val);
8045 int isl_map_plain_is_fixed(__isl_keep isl_map *map,
8046 enum isl_dim_type type, unsigned pos, isl_int *val)
8048 if (pos >= isl_map_dim(map, type))
8050 return isl_map_plain_has_fixed_var(map,
8051 map_offset(map, type) - 1 + pos, val);
8054 int isl_set_plain_is_fixed(__isl_keep isl_set *set,
8055 enum isl_dim_type type, unsigned pos, isl_int *val)
8057 return isl_map_plain_is_fixed(set, type, pos, val);
8060 int isl_map_fast_is_fixed(__isl_keep isl_map *map,
8061 enum isl_dim_type type, unsigned pos, isl_int *val)
8063 return isl_map_plain_is_fixed(map, type, pos, val);
8066 /* Check if dimension dim has fixed value and if so and if val is not NULL,
8067 * then return this fixed value in *val.
8069 int isl_basic_set_plain_dim_is_fixed(__isl_keep isl_basic_set *bset,
8070 unsigned dim, isl_int *val)
8072 return isl_basic_set_plain_has_fixed_var(bset,
8073 isl_basic_set_n_param(bset) + dim, val);
8076 /* Check if dimension dim has fixed value and if so and if val is not NULL,
8077 * then return this fixed value in *val.
8079 int isl_set_plain_dim_is_fixed(__isl_keep isl_set *set,
8080 unsigned dim, isl_int *val)
8082 return isl_set_plain_has_fixed_var(set, isl_set_n_param(set) + dim, val);
8085 int isl_set_fast_dim_is_fixed(__isl_keep isl_set *set,
8086 unsigned dim, isl_int *val)
8088 return isl_set_plain_dim_is_fixed(set, dim, val);
8091 /* Check if input variable in has fixed value and if so and if val is not NULL,
8092 * then return this fixed value in *val.
8094 int isl_map_plain_input_is_fixed(__isl_keep isl_map *map,
8095 unsigned in, isl_int *val)
8097 return isl_map_plain_has_fixed_var(map, isl_map_n_param(map) + in, val);
8100 /* Check if dimension dim has an (obvious) fixed lower bound and if so
8101 * and if val is not NULL, then return this lower bound in *val.
8103 int isl_basic_set_plain_dim_has_fixed_lower_bound(
8104 __isl_keep isl_basic_set *bset, unsigned dim, isl_int *val)
8106 int i, i_eq = -1, i_ineq = -1;
8113 total = isl_basic_set_total_dim(bset);
8114 nparam = isl_basic_set_n_param(bset);
8115 for (i = 0; i < bset->n_eq; ++i) {
8116 if (isl_int_is_zero(bset->eq[i][1+nparam+dim]))
8122 for (i = 0; i < bset->n_ineq; ++i) {
8123 if (!isl_int_is_pos(bset->ineq[i][1+nparam+dim]))
8125 if (i_eq != -1 || i_ineq != -1)
8129 if (i_eq == -1 && i_ineq == -1)
8131 c = i_eq != -1 ? bset->eq[i_eq] : bset->ineq[i_ineq];
8132 /* The coefficient should always be one due to normalization. */
8133 if (!isl_int_is_one(c[1+nparam+dim]))
8135 if (isl_seq_first_non_zero(c+1, nparam+dim) != -1)
8137 if (isl_seq_first_non_zero(c+1+nparam+dim+1,
8138 total - nparam - dim - 1) != -1)
8141 isl_int_neg(*val, c[0]);
8145 int isl_set_plain_dim_has_fixed_lower_bound(__isl_keep isl_set *set,
8146 unsigned dim, isl_int *val)
8158 return isl_basic_set_plain_dim_has_fixed_lower_bound(set->p[0],
8162 fixed = isl_basic_set_plain_dim_has_fixed_lower_bound(set->p[0],
8164 for (i = 1; fixed == 1 && i < set->n; ++i) {
8165 fixed = isl_basic_set_plain_dim_has_fixed_lower_bound(set->p[i],
8167 if (fixed == 1 && isl_int_ne(tmp, v))
8171 isl_int_set(*val, v);
8182 /* uset_gist depends on constraints without existentially quantified
8183 * variables sorting first.
8185 static int qsort_constraint_cmp(const void *p1, const void *p2)
8187 const struct constraint *c1 = (const struct constraint *)p1;
8188 const struct constraint *c2 = (const struct constraint *)p2;
8190 unsigned size = isl_min(c1->size, c2->size);
8192 l1 = isl_seq_last_non_zero(c1->c, size);
8193 l2 = isl_seq_last_non_zero(c2->c, size);
8198 return isl_seq_cmp(c1->c, c2->c, size);
8201 static struct isl_basic_map *isl_basic_map_sort_constraints(
8202 struct isl_basic_map *bmap)
8205 struct constraint *c;
8210 total = isl_basic_map_total_dim(bmap);
8211 c = isl_alloc_array(bmap->ctx, struct constraint, bmap->n_ineq);
8214 for (i = 0; i < bmap->n_ineq; ++i) {
8216 c[i].c = bmap->ineq[i];
8218 qsort(c, bmap->n_ineq, sizeof(struct constraint), qsort_constraint_cmp);
8219 for (i = 0; i < bmap->n_ineq; ++i)
8220 bmap->ineq[i] = c[i].c;
8224 isl_basic_map_free(bmap);
8228 __isl_give isl_basic_set *isl_basic_set_sort_constraints(
8229 __isl_take isl_basic_set *bset)
8231 return (struct isl_basic_set *)isl_basic_map_sort_constraints(
8232 (struct isl_basic_map *)bset);
8235 struct isl_basic_map *isl_basic_map_normalize(struct isl_basic_map *bmap)
8239 if (ISL_F_ISSET(bmap, ISL_BASIC_MAP_NORMALIZED))
8241 bmap = isl_basic_map_remove_redundancies(bmap);
8242 bmap = isl_basic_map_sort_constraints(bmap);
8244 ISL_F_SET(bmap, ISL_BASIC_MAP_NORMALIZED);
8248 struct isl_basic_set *isl_basic_set_normalize(struct isl_basic_set *bset)
8250 return (struct isl_basic_set *)isl_basic_map_normalize(
8251 (struct isl_basic_map *)bset);
8254 int isl_basic_map_plain_cmp(const __isl_keep isl_basic_map *bmap1,
8255 const __isl_keep isl_basic_map *bmap2)
8262 if (ISL_F_ISSET(bmap1, ISL_BASIC_MAP_RATIONAL) !=
8263 ISL_F_ISSET(bmap2, ISL_BASIC_MAP_RATIONAL))
8264 return ISL_F_ISSET(bmap1, ISL_BASIC_MAP_RATIONAL) ? -1 : 1;
8265 if (isl_basic_map_n_param(bmap1) != isl_basic_map_n_param(bmap2))
8266 return isl_basic_map_n_param(bmap1) - isl_basic_map_n_param(bmap2);
8267 if (isl_basic_map_n_in(bmap1) != isl_basic_map_n_in(bmap2))
8268 return isl_basic_map_n_out(bmap1) - isl_basic_map_n_out(bmap2);
8269 if (isl_basic_map_n_out(bmap1) != isl_basic_map_n_out(bmap2))
8270 return isl_basic_map_n_out(bmap1) - isl_basic_map_n_out(bmap2);
8271 if (ISL_F_ISSET(bmap1, ISL_BASIC_MAP_EMPTY) &&
8272 ISL_F_ISSET(bmap2, ISL_BASIC_MAP_EMPTY))
8274 if (ISL_F_ISSET(bmap1, ISL_BASIC_MAP_EMPTY))
8276 if (ISL_F_ISSET(bmap2, ISL_BASIC_MAP_EMPTY))
8278 if (bmap1->n_eq != bmap2->n_eq)
8279 return bmap1->n_eq - bmap2->n_eq;
8280 if (bmap1->n_ineq != bmap2->n_ineq)
8281 return bmap1->n_ineq - bmap2->n_ineq;
8282 if (bmap1->n_div != bmap2->n_div)
8283 return bmap1->n_div - bmap2->n_div;
8284 total = isl_basic_map_total_dim(bmap1);
8285 for (i = 0; i < bmap1->n_eq; ++i) {
8286 cmp = isl_seq_cmp(bmap1->eq[i], bmap2->eq[i], 1+total);
8290 for (i = 0; i < bmap1->n_ineq; ++i) {
8291 cmp = isl_seq_cmp(bmap1->ineq[i], bmap2->ineq[i], 1+total);
8295 for (i = 0; i < bmap1->n_div; ++i) {
8296 cmp = isl_seq_cmp(bmap1->div[i], bmap2->div[i], 1+1+total);
8303 int isl_basic_set_plain_cmp(const __isl_keep isl_basic_set *bset1,
8304 const __isl_keep isl_basic_set *bset2)
8306 return isl_basic_map_plain_cmp(bset1, bset2);
8309 int isl_set_plain_cmp(__isl_keep isl_set *set1, __isl_keep isl_set *set2)
8315 if (set1->n != set2->n)
8316 return set1->n - set2->n;
8318 for (i = 0; i < set1->n; ++i) {
8319 cmp = isl_basic_set_plain_cmp(set1->p[i], set2->p[i]);
8327 int isl_basic_map_plain_is_equal(__isl_keep isl_basic_map *bmap1,
8328 __isl_keep isl_basic_map *bmap2)
8330 return isl_basic_map_plain_cmp(bmap1, bmap2) == 0;
8333 int isl_basic_set_plain_is_equal(__isl_keep isl_basic_set *bset1,
8334 __isl_keep isl_basic_set *bset2)
8336 return isl_basic_map_plain_is_equal((isl_basic_map *)bset1,
8337 (isl_basic_map *)bset2);
8340 static int qsort_bmap_cmp(const void *p1, const void *p2)
8342 const struct isl_basic_map *bmap1 = *(const struct isl_basic_map **)p1;
8343 const struct isl_basic_map *bmap2 = *(const struct isl_basic_map **)p2;
8345 return isl_basic_map_plain_cmp(bmap1, bmap2);
8348 /* We normalize in place, but if anything goes wrong we need
8349 * to return NULL, so we need to make sure we don't change the
8350 * meaning of any possible other copies of map.
8352 struct isl_map *isl_map_normalize(struct isl_map *map)
8355 struct isl_basic_map *bmap;
8359 if (ISL_F_ISSET(map, ISL_MAP_NORMALIZED))
8361 for (i = 0; i < map->n; ++i) {
8362 bmap = isl_basic_map_normalize(isl_basic_map_copy(map->p[i]));
8365 isl_basic_map_free(map->p[i]);
8368 qsort(map->p, map->n, sizeof(struct isl_basic_map *), qsort_bmap_cmp);
8369 ISL_F_SET(map, ISL_MAP_NORMALIZED);
8370 map = isl_map_remove_empty_parts(map);
8373 for (i = map->n - 1; i >= 1; --i) {
8374 if (!isl_basic_map_plain_is_equal(map->p[i-1], map->p[i]))
8376 isl_basic_map_free(map->p[i-1]);
8377 for (j = i; j < map->n; ++j)
8378 map->p[j-1] = map->p[j];
8388 struct isl_set *isl_set_normalize(struct isl_set *set)
8390 return (struct isl_set *)isl_map_normalize((struct isl_map *)set);
8393 int isl_map_plain_is_equal(__isl_keep isl_map *map1, __isl_keep isl_map *map2)
8403 if (!isl_space_is_equal(map1->dim, map2->dim))
8406 map1 = isl_map_copy(map1);
8407 map2 = isl_map_copy(map2);
8408 map1 = isl_map_normalize(map1);
8409 map2 = isl_map_normalize(map2);
8412 equal = map1->n == map2->n;
8413 for (i = 0; equal && i < map1->n; ++i) {
8414 equal = isl_basic_map_plain_is_equal(map1->p[i], map2->p[i]);
8427 int isl_map_fast_is_equal(__isl_keep isl_map *map1, __isl_keep isl_map *map2)
8429 return isl_map_plain_is_equal(map1, map2);
8432 int isl_set_plain_is_equal(__isl_keep isl_set *set1, __isl_keep isl_set *set2)
8434 return isl_map_plain_is_equal((struct isl_map *)set1,
8435 (struct isl_map *)set2);
8438 int isl_set_fast_is_equal(__isl_keep isl_set *set1, __isl_keep isl_set *set2)
8440 return isl_set_plain_is_equal(set1, set2);
8443 /* Return an interval that ranges from min to max (inclusive)
8445 struct isl_basic_set *isl_basic_set_interval(struct isl_ctx *ctx,
8446 isl_int min, isl_int max)
8449 struct isl_basic_set *bset = NULL;
8451 bset = isl_basic_set_alloc(ctx, 0, 1, 0, 0, 2);
8455 k = isl_basic_set_alloc_inequality(bset);
8458 isl_int_set_si(bset->ineq[k][1], 1);
8459 isl_int_neg(bset->ineq[k][0], min);
8461 k = isl_basic_set_alloc_inequality(bset);
8464 isl_int_set_si(bset->ineq[k][1], -1);
8465 isl_int_set(bset->ineq[k][0], max);
8469 isl_basic_set_free(bset);
8473 /* Return the Cartesian product of the basic sets in list (in the given order).
8475 __isl_give isl_basic_set *isl_basic_set_list_product(
8476 __isl_take struct isl_basic_set_list *list)
8484 struct isl_basic_set *product = NULL;
8488 isl_assert(list->ctx, list->n > 0, goto error);
8489 isl_assert(list->ctx, list->p[0], goto error);
8490 nparam = isl_basic_set_n_param(list->p[0]);
8491 dim = isl_basic_set_n_dim(list->p[0]);
8492 extra = list->p[0]->n_div;
8493 n_eq = list->p[0]->n_eq;
8494 n_ineq = list->p[0]->n_ineq;
8495 for (i = 1; i < list->n; ++i) {
8496 isl_assert(list->ctx, list->p[i], goto error);
8497 isl_assert(list->ctx,
8498 nparam == isl_basic_set_n_param(list->p[i]), goto error);
8499 dim += isl_basic_set_n_dim(list->p[i]);
8500 extra += list->p[i]->n_div;
8501 n_eq += list->p[i]->n_eq;
8502 n_ineq += list->p[i]->n_ineq;
8504 product = isl_basic_set_alloc(list->ctx, nparam, dim, extra,
8509 for (i = 0; i < list->n; ++i) {
8510 isl_basic_set_add_constraints(product,
8511 isl_basic_set_copy(list->p[i]), dim);
8512 dim += isl_basic_set_n_dim(list->p[i]);
8514 isl_basic_set_list_free(list);
8517 isl_basic_set_free(product);
8518 isl_basic_set_list_free(list);
8522 struct isl_basic_map *isl_basic_map_product(
8523 struct isl_basic_map *bmap1, struct isl_basic_map *bmap2)
8525 isl_space *dim_result = NULL;
8526 struct isl_basic_map *bmap;
8527 unsigned in1, in2, out1, out2, nparam, total, pos;
8528 struct isl_dim_map *dim_map1, *dim_map2;
8530 if (!bmap1 || !bmap2)
8533 isl_assert(bmap1->ctx, isl_space_match(bmap1->dim, isl_dim_param,
8534 bmap2->dim, isl_dim_param), goto error);
8535 dim_result = isl_space_product(isl_space_copy(bmap1->dim),
8536 isl_space_copy(bmap2->dim));
8538 in1 = isl_basic_map_n_in(bmap1);
8539 in2 = isl_basic_map_n_in(bmap2);
8540 out1 = isl_basic_map_n_out(bmap1);
8541 out2 = isl_basic_map_n_out(bmap2);
8542 nparam = isl_basic_map_n_param(bmap1);
8544 total = nparam + in1 + in2 + out1 + out2 + bmap1->n_div + bmap2->n_div;
8545 dim_map1 = isl_dim_map_alloc(bmap1->ctx, total);
8546 dim_map2 = isl_dim_map_alloc(bmap1->ctx, total);
8547 isl_dim_map_dim(dim_map1, bmap1->dim, isl_dim_param, pos = 0);
8548 isl_dim_map_dim(dim_map2, bmap2->dim, isl_dim_param, pos = 0);
8549 isl_dim_map_dim(dim_map1, bmap1->dim, isl_dim_in, pos += nparam);
8550 isl_dim_map_dim(dim_map2, bmap2->dim, isl_dim_in, pos += in1);
8551 isl_dim_map_dim(dim_map1, bmap1->dim, isl_dim_out, pos += in2);
8552 isl_dim_map_dim(dim_map2, bmap2->dim, isl_dim_out, pos += out1);
8553 isl_dim_map_div(dim_map1, bmap1, pos += out2);
8554 isl_dim_map_div(dim_map2, bmap2, pos += bmap1->n_div);
8556 bmap = isl_basic_map_alloc_space(dim_result,
8557 bmap1->n_div + bmap2->n_div,
8558 bmap1->n_eq + bmap2->n_eq,
8559 bmap1->n_ineq + bmap2->n_ineq);
8560 bmap = isl_basic_map_add_constraints_dim_map(bmap, bmap1, dim_map1);
8561 bmap = isl_basic_map_add_constraints_dim_map(bmap, bmap2, dim_map2);
8562 bmap = isl_basic_map_simplify(bmap);
8563 return isl_basic_map_finalize(bmap);
8565 isl_basic_map_free(bmap1);
8566 isl_basic_map_free(bmap2);
8570 __isl_give isl_basic_map *isl_basic_map_flat_product(
8571 __isl_take isl_basic_map *bmap1, __isl_take isl_basic_map *bmap2)
8573 isl_basic_map *prod;
8575 prod = isl_basic_map_product(bmap1, bmap2);
8576 prod = isl_basic_map_flatten(prod);
8580 __isl_give isl_basic_set *isl_basic_set_flat_product(
8581 __isl_take isl_basic_set *bset1, __isl_take isl_basic_set *bset2)
8583 return isl_basic_map_flat_range_product(bset1, bset2);
8586 __isl_give isl_basic_map *isl_basic_map_domain_product(
8587 __isl_take isl_basic_map *bmap1, __isl_take isl_basic_map *bmap2)
8589 isl_space *space_result = NULL;
8590 isl_basic_map *bmap;
8591 unsigned in1, in2, out, nparam, total, pos;
8592 struct isl_dim_map *dim_map1, *dim_map2;
8594 if (!bmap1 || !bmap2)
8597 space_result = isl_space_domain_product(isl_space_copy(bmap1->dim),
8598 isl_space_copy(bmap2->dim));
8600 in1 = isl_basic_map_dim(bmap1, isl_dim_in);
8601 in2 = isl_basic_map_dim(bmap2, isl_dim_in);
8602 out = isl_basic_map_dim(bmap1, isl_dim_out);
8603 nparam = isl_basic_map_dim(bmap1, isl_dim_param);
8605 total = nparam + in1 + in2 + out + bmap1->n_div + bmap2->n_div;
8606 dim_map1 = isl_dim_map_alloc(bmap1->ctx, total);
8607 dim_map2 = isl_dim_map_alloc(bmap1->ctx, total);
8608 isl_dim_map_dim(dim_map1, bmap1->dim, isl_dim_param, pos = 0);
8609 isl_dim_map_dim(dim_map2, bmap2->dim, isl_dim_param, pos = 0);
8610 isl_dim_map_dim(dim_map1, bmap1->dim, isl_dim_in, pos += nparam);
8611 isl_dim_map_dim(dim_map2, bmap2->dim, isl_dim_in, pos += in1);
8612 isl_dim_map_dim(dim_map1, bmap1->dim, isl_dim_out, pos += in2);
8613 isl_dim_map_dim(dim_map2, bmap2->dim, isl_dim_out, pos);
8614 isl_dim_map_div(dim_map1, bmap1, pos += out);
8615 isl_dim_map_div(dim_map2, bmap2, pos += bmap1->n_div);
8617 bmap = isl_basic_map_alloc_space(space_result,
8618 bmap1->n_div + bmap2->n_div,
8619 bmap1->n_eq + bmap2->n_eq,
8620 bmap1->n_ineq + bmap2->n_ineq);
8621 bmap = isl_basic_map_add_constraints_dim_map(bmap, bmap1, dim_map1);
8622 bmap = isl_basic_map_add_constraints_dim_map(bmap, bmap2, dim_map2);
8623 bmap = isl_basic_map_simplify(bmap);
8624 return isl_basic_map_finalize(bmap);
8626 isl_basic_map_free(bmap1);
8627 isl_basic_map_free(bmap2);
8631 __isl_give isl_basic_map *isl_basic_map_range_product(
8632 __isl_take isl_basic_map *bmap1, __isl_take isl_basic_map *bmap2)
8634 isl_space *dim_result = NULL;
8635 isl_basic_map *bmap;
8636 unsigned in, out1, out2, nparam, total, pos;
8637 struct isl_dim_map *dim_map1, *dim_map2;
8639 if (!bmap1 || !bmap2)
8642 if (!isl_space_match(bmap1->dim, isl_dim_param,
8643 bmap2->dim, isl_dim_param))
8644 isl_die(isl_basic_map_get_ctx(bmap1), isl_error_invalid,
8645 "parameters don't match", goto error);
8647 dim_result = isl_space_range_product(isl_space_copy(bmap1->dim),
8648 isl_space_copy(bmap2->dim));
8650 in = isl_basic_map_dim(bmap1, isl_dim_in);
8651 out1 = isl_basic_map_n_out(bmap1);
8652 out2 = isl_basic_map_n_out(bmap2);
8653 nparam = isl_basic_map_n_param(bmap1);
8655 total = nparam + in + out1 + out2 + bmap1->n_div + bmap2->n_div;
8656 dim_map1 = isl_dim_map_alloc(bmap1->ctx, total);
8657 dim_map2 = isl_dim_map_alloc(bmap1->ctx, total);
8658 isl_dim_map_dim(dim_map1, bmap1->dim, isl_dim_param, pos = 0);
8659 isl_dim_map_dim(dim_map2, bmap2->dim, isl_dim_param, pos = 0);
8660 isl_dim_map_dim(dim_map1, bmap1->dim, isl_dim_in, pos += nparam);
8661 isl_dim_map_dim(dim_map2, bmap2->dim, isl_dim_in, pos);
8662 isl_dim_map_dim(dim_map1, bmap1->dim, isl_dim_out, pos += in);
8663 isl_dim_map_dim(dim_map2, bmap2->dim, isl_dim_out, pos += out1);
8664 isl_dim_map_div(dim_map1, bmap1, pos += out2);
8665 isl_dim_map_div(dim_map2, bmap2, pos += bmap1->n_div);
8667 bmap = isl_basic_map_alloc_space(dim_result,
8668 bmap1->n_div + bmap2->n_div,
8669 bmap1->n_eq + bmap2->n_eq,
8670 bmap1->n_ineq + bmap2->n_ineq);
8671 bmap = isl_basic_map_add_constraints_dim_map(bmap, bmap1, dim_map1);
8672 bmap = isl_basic_map_add_constraints_dim_map(bmap, bmap2, dim_map2);
8673 bmap = isl_basic_map_simplify(bmap);
8674 return isl_basic_map_finalize(bmap);
8676 isl_basic_map_free(bmap1);
8677 isl_basic_map_free(bmap2);
8681 __isl_give isl_basic_map *isl_basic_map_flat_range_product(
8682 __isl_take isl_basic_map *bmap1, __isl_take isl_basic_map *bmap2)
8684 isl_basic_map *prod;
8686 prod = isl_basic_map_range_product(bmap1, bmap2);
8687 prod = isl_basic_map_flatten_range(prod);
8691 static __isl_give isl_map *map_product(__isl_take isl_map *map1,
8692 __isl_take isl_map *map2,
8693 __isl_give isl_space *(*dim_product)(__isl_take isl_space *left,
8694 __isl_take isl_space *right),
8695 __isl_give isl_basic_map *(*basic_map_product)(
8696 __isl_take isl_basic_map *left, __isl_take isl_basic_map *right))
8699 struct isl_map *result;
8705 isl_assert(map1->ctx, isl_space_match(map1->dim, isl_dim_param,
8706 map2->dim, isl_dim_param), goto error);
8708 if (ISL_F_ISSET(map1, ISL_MAP_DISJOINT) &&
8709 ISL_F_ISSET(map2, ISL_MAP_DISJOINT))
8710 ISL_FL_SET(flags, ISL_MAP_DISJOINT);
8712 result = isl_map_alloc_space(dim_product(isl_space_copy(map1->dim),
8713 isl_space_copy(map2->dim)),
8714 map1->n * map2->n, flags);
8717 for (i = 0; i < map1->n; ++i)
8718 for (j = 0; j < map2->n; ++j) {
8719 struct isl_basic_map *part;
8720 part = basic_map_product(isl_basic_map_copy(map1->p[i]),
8721 isl_basic_map_copy(map2->p[j]));
8722 if (isl_basic_map_is_empty(part))
8723 isl_basic_map_free(part);
8725 result = isl_map_add_basic_map(result, part);
8738 /* Given two maps A -> B and C -> D, construct a map [A -> C] -> [B -> D]
8740 static __isl_give isl_map *map_product_aligned(__isl_take isl_map *map1,
8741 __isl_take isl_map *map2)
8743 return map_product(map1, map2, &isl_space_product, &isl_basic_map_product);
8746 __isl_give isl_map *isl_map_product(__isl_take isl_map *map1,
8747 __isl_take isl_map *map2)
8749 return isl_map_align_params_map_map_and(map1, map2, &map_product_aligned);
8752 /* Given two maps A -> B and C -> D, construct a map (A, C) -> (B, D)
8754 __isl_give isl_map *isl_map_flat_product(__isl_take isl_map *map1,
8755 __isl_take isl_map *map2)
8759 prod = isl_map_product(map1, map2);
8760 prod = isl_map_flatten(prod);
8764 /* Given two set A and B, construct its Cartesian product A x B.
8766 struct isl_set *isl_set_product(struct isl_set *set1, struct isl_set *set2)
8768 return isl_map_range_product(set1, set2);
8771 __isl_give isl_set *isl_set_flat_product(__isl_take isl_set *set1,
8772 __isl_take isl_set *set2)
8774 return isl_map_flat_range_product(set1, set2);
8777 /* Given two maps A -> B and C -> D, construct a map [A -> C] -> (B * D)
8779 static __isl_give isl_map *map_domain_product_aligned(__isl_take isl_map *map1,
8780 __isl_take isl_map *map2)
8782 return map_product(map1, map2, &isl_space_domain_product,
8783 &isl_basic_map_domain_product);
8786 /* Given two maps A -> B and C -> D, construct a map (A * C) -> [B -> D]
8788 static __isl_give isl_map *map_range_product_aligned(__isl_take isl_map *map1,
8789 __isl_take isl_map *map2)
8791 return map_product(map1, map2, &isl_space_range_product,
8792 &isl_basic_map_range_product);
8795 __isl_give isl_map *isl_map_domain_product(__isl_take isl_map *map1,
8796 __isl_take isl_map *map2)
8798 return isl_map_align_params_map_map_and(map1, map2,
8799 &map_domain_product_aligned);
8802 __isl_give isl_map *isl_map_range_product(__isl_take isl_map *map1,
8803 __isl_take isl_map *map2)
8805 return isl_map_align_params_map_map_and(map1, map2,
8806 &map_range_product_aligned);
8809 /* Given two maps A -> B and C -> D, construct a map (A, C) -> (B * D)
8811 __isl_give isl_map *isl_map_flat_domain_product(__isl_take isl_map *map1,
8812 __isl_take isl_map *map2)
8816 prod = isl_map_domain_product(map1, map2);
8817 prod = isl_map_flatten_domain(prod);
8821 /* Given two maps A -> B and C -> D, construct a map (A * C) -> (B, D)
8823 __isl_give isl_map *isl_map_flat_range_product(__isl_take isl_map *map1,
8824 __isl_take isl_map *map2)
8828 prod = isl_map_range_product(map1, map2);
8829 prod = isl_map_flatten_range(prod);
8833 uint32_t isl_basic_map_get_hash(__isl_keep isl_basic_map *bmap)
8836 uint32_t hash = isl_hash_init();
8841 bmap = isl_basic_map_copy(bmap);
8842 bmap = isl_basic_map_normalize(bmap);
8845 total = isl_basic_map_total_dim(bmap);
8846 isl_hash_byte(hash, bmap->n_eq & 0xFF);
8847 for (i = 0; i < bmap->n_eq; ++i) {
8849 c_hash = isl_seq_get_hash(bmap->eq[i], 1 + total);
8850 isl_hash_hash(hash, c_hash);
8852 isl_hash_byte(hash, bmap->n_ineq & 0xFF);
8853 for (i = 0; i < bmap->n_ineq; ++i) {
8855 c_hash = isl_seq_get_hash(bmap->ineq[i], 1 + total);
8856 isl_hash_hash(hash, c_hash);
8858 isl_hash_byte(hash, bmap->n_div & 0xFF);
8859 for (i = 0; i < bmap->n_div; ++i) {
8861 if (isl_int_is_zero(bmap->div[i][0]))
8863 isl_hash_byte(hash, i & 0xFF);
8864 c_hash = isl_seq_get_hash(bmap->div[i], 1 + 1 + total);
8865 isl_hash_hash(hash, c_hash);
8867 isl_basic_map_free(bmap);
8871 uint32_t isl_basic_set_get_hash(__isl_keep isl_basic_set *bset)
8873 return isl_basic_map_get_hash((isl_basic_map *)bset);
8876 uint32_t isl_map_get_hash(__isl_keep isl_map *map)
8883 map = isl_map_copy(map);
8884 map = isl_map_normalize(map);
8888 hash = isl_hash_init();
8889 for (i = 0; i < map->n; ++i) {
8891 bmap_hash = isl_basic_map_get_hash(map->p[i]);
8892 isl_hash_hash(hash, bmap_hash);
8900 uint32_t isl_set_get_hash(__isl_keep isl_set *set)
8902 return isl_map_get_hash((isl_map *)set);
8905 /* Check if the value for dimension dim is completely determined
8906 * by the values of the other parameters and variables.
8907 * That is, check if dimension dim is involved in an equality.
8909 int isl_basic_set_dim_is_unique(struct isl_basic_set *bset, unsigned dim)
8916 nparam = isl_basic_set_n_param(bset);
8917 for (i = 0; i < bset->n_eq; ++i)
8918 if (!isl_int_is_zero(bset->eq[i][1 + nparam + dim]))
8923 /* Check if the value for dimension dim is completely determined
8924 * by the values of the other parameters and variables.
8925 * That is, check if dimension dim is involved in an equality
8926 * for each of the subsets.
8928 int isl_set_dim_is_unique(struct isl_set *set, unsigned dim)
8934 for (i = 0; i < set->n; ++i) {
8936 unique = isl_basic_set_dim_is_unique(set->p[i], dim);
8943 int isl_set_n_basic_set(__isl_keep isl_set *set)
8945 return set ? set->n : 0;
8948 int isl_map_foreach_basic_map(__isl_keep isl_map *map,
8949 int (*fn)(__isl_take isl_basic_map *bmap, void *user), void *user)
8956 for (i = 0; i < map->n; ++i)
8957 if (fn(isl_basic_map_copy(map->p[i]), user) < 0)
8963 int isl_set_foreach_basic_set(__isl_keep isl_set *set,
8964 int (*fn)(__isl_take isl_basic_set *bset, void *user), void *user)
8971 for (i = 0; i < set->n; ++i)
8972 if (fn(isl_basic_set_copy(set->p[i]), user) < 0)
8978 __isl_give isl_basic_set *isl_basic_set_lift(__isl_take isl_basic_set *bset)
8985 bset = isl_basic_set_cow(bset);
8989 dim = isl_basic_set_get_space(bset);
8990 dim = isl_space_lift(dim, bset->n_div);
8993 isl_space_free(bset->dim);
8995 bset->extra -= bset->n_div;
8998 bset = isl_basic_set_finalize(bset);
9002 isl_basic_set_free(bset);
9006 __isl_give isl_set *isl_set_lift(__isl_take isl_set *set)
9012 set = isl_set_align_divs(set);
9017 set = isl_set_cow(set);
9021 n_div = set->p[0]->n_div;
9022 dim = isl_set_get_space(set);
9023 dim = isl_space_lift(dim, n_div);
9026 isl_space_free(set->dim);
9029 for (i = 0; i < set->n; ++i) {
9030 set->p[i] = isl_basic_set_lift(set->p[i]);
9041 __isl_give isl_map *isl_set_lifting(__isl_take isl_set *set)
9044 struct isl_basic_map *bmap;
9051 set = isl_set_align_divs(set);
9056 dim = isl_set_get_space(set);
9057 if (set->n == 0 || set->p[0]->n_div == 0) {
9059 return isl_map_identity(isl_space_map_from_set(dim));
9062 n_div = set->p[0]->n_div;
9063 dim = isl_space_map_from_set(dim);
9064 n_param = isl_space_dim(dim, isl_dim_param);
9065 n_set = isl_space_dim(dim, isl_dim_in);
9066 dim = isl_space_extend(dim, n_param, n_set, n_set + n_div);
9067 bmap = isl_basic_map_alloc_space(dim, 0, n_set, 2 * n_div);
9068 for (i = 0; i < n_set; ++i)
9069 bmap = var_equal(bmap, i);
9071 total = n_param + n_set + n_set + n_div;
9072 for (i = 0; i < n_div; ++i) {
9073 k = isl_basic_map_alloc_inequality(bmap);
9076 isl_seq_cpy(bmap->ineq[k], set->p[0]->div[i]+1, 1+n_param);
9077 isl_seq_clr(bmap->ineq[k]+1+n_param, n_set);
9078 isl_seq_cpy(bmap->ineq[k]+1+n_param+n_set,
9079 set->p[0]->div[i]+1+1+n_param, n_set + n_div);
9080 isl_int_neg(bmap->ineq[k][1+n_param+n_set+n_set+i],
9081 set->p[0]->div[i][0]);
9083 l = isl_basic_map_alloc_inequality(bmap);
9086 isl_seq_neg(bmap->ineq[l], bmap->ineq[k], 1 + total);
9087 isl_int_add(bmap->ineq[l][0], bmap->ineq[l][0],
9088 set->p[0]->div[i][0]);
9089 isl_int_sub_ui(bmap->ineq[l][0], bmap->ineq[l][0], 1);
9093 bmap = isl_basic_map_simplify(bmap);
9094 bmap = isl_basic_map_finalize(bmap);
9095 return isl_map_from_basic_map(bmap);
9098 isl_basic_map_free(bmap);
9102 int isl_basic_set_size(__isl_keep isl_basic_set *bset)
9110 dim = isl_basic_set_total_dim(bset);
9111 size += bset->n_eq * (1 + dim);
9112 size += bset->n_ineq * (1 + dim);
9113 size += bset->n_div * (2 + dim);
9118 int isl_set_size(__isl_keep isl_set *set)
9126 for (i = 0; i < set->n; ++i)
9127 size += isl_basic_set_size(set->p[i]);
9132 /* Check if there is any lower bound (if lower == 0) and/or upper
9133 * bound (if upper == 0) on the specified dim.
9135 static int basic_map_dim_is_bounded(__isl_keep isl_basic_map *bmap,
9136 enum isl_dim_type type, unsigned pos, int lower, int upper)
9143 isl_assert(bmap->ctx, pos < isl_basic_map_dim(bmap, type), return -1);
9145 pos += isl_basic_map_offset(bmap, type);
9147 for (i = 0; i < bmap->n_div; ++i) {
9148 if (isl_int_is_zero(bmap->div[i][0]))
9150 if (!isl_int_is_zero(bmap->div[i][1 + pos]))
9154 for (i = 0; i < bmap->n_eq; ++i)
9155 if (!isl_int_is_zero(bmap->eq[i][pos]))
9158 for (i = 0; i < bmap->n_ineq; ++i) {
9159 int sgn = isl_int_sgn(bmap->ineq[i][pos]);
9166 return lower && upper;
9169 int isl_basic_map_dim_is_bounded(__isl_keep isl_basic_map *bmap,
9170 enum isl_dim_type type, unsigned pos)
9172 return basic_map_dim_is_bounded(bmap, type, pos, 0, 0);
9175 int isl_basic_map_dim_has_lower_bound(__isl_keep isl_basic_map *bmap,
9176 enum isl_dim_type type, unsigned pos)
9178 return basic_map_dim_is_bounded(bmap, type, pos, 0, 1);
9181 int isl_basic_map_dim_has_upper_bound(__isl_keep isl_basic_map *bmap,
9182 enum isl_dim_type type, unsigned pos)
9184 return basic_map_dim_is_bounded(bmap, type, pos, 1, 0);
9187 int isl_map_dim_is_bounded(__isl_keep isl_map *map,
9188 enum isl_dim_type type, unsigned pos)
9195 for (i = 0; i < map->n; ++i) {
9197 bounded = isl_basic_map_dim_is_bounded(map->p[i], type, pos);
9198 if (bounded < 0 || !bounded)
9205 /* Return 1 if the specified dim is involved in both an upper bound
9206 * and a lower bound.
9208 int isl_set_dim_is_bounded(__isl_keep isl_set *set,
9209 enum isl_dim_type type, unsigned pos)
9211 return isl_map_dim_is_bounded((isl_map *)set, type, pos);
9214 /* Does "map" have a bound (according to "fn") for any of its basic maps?
9216 static int has_any_bound(__isl_keep isl_map *map,
9217 enum isl_dim_type type, unsigned pos,
9218 int (*fn)(__isl_keep isl_basic_map *bmap,
9219 enum isl_dim_type type, unsigned pos))
9226 for (i = 0; i < map->n; ++i) {
9228 bounded = fn(map->p[i], type, pos);
9229 if (bounded < 0 || bounded)
9236 /* Return 1 if the specified dim is involved in any lower bound.
9238 int isl_set_dim_has_any_lower_bound(__isl_keep isl_set *set,
9239 enum isl_dim_type type, unsigned pos)
9241 return has_any_bound(set, type, pos,
9242 &isl_basic_map_dim_has_lower_bound);
9245 /* Return 1 if the specified dim is involved in any upper bound.
9247 int isl_set_dim_has_any_upper_bound(__isl_keep isl_set *set,
9248 enum isl_dim_type type, unsigned pos)
9250 return has_any_bound(set, type, pos,
9251 &isl_basic_map_dim_has_upper_bound);
9254 /* Does "map" have a bound (according to "fn") for all of its basic maps?
9256 static int has_bound(__isl_keep isl_map *map,
9257 enum isl_dim_type type, unsigned pos,
9258 int (*fn)(__isl_keep isl_basic_map *bmap,
9259 enum isl_dim_type type, unsigned pos))
9266 for (i = 0; i < map->n; ++i) {
9268 bounded = fn(map->p[i], type, pos);
9269 if (bounded < 0 || !bounded)
9276 /* Return 1 if the specified dim has a lower bound (in each of its basic sets).
9278 int isl_set_dim_has_lower_bound(__isl_keep isl_set *set,
9279 enum isl_dim_type type, unsigned pos)
9281 return has_bound(set, type, pos, &isl_basic_map_dim_has_lower_bound);
9284 /* Return 1 if the specified dim has an upper bound (in each of its basic sets).
9286 int isl_set_dim_has_upper_bound(__isl_keep isl_set *set,
9287 enum isl_dim_type type, unsigned pos)
9289 return has_bound(set, type, pos, &isl_basic_map_dim_has_upper_bound);
9292 /* For each of the "n" variables starting at "first", determine
9293 * the sign of the variable and put the results in the first "n"
9294 * elements of the array "signs".
9296 * 1 means that the variable is non-negative
9297 * -1 means that the variable is non-positive
9298 * 0 means the variable attains both positive and negative values.
9300 int isl_basic_set_vars_get_sign(__isl_keep isl_basic_set *bset,
9301 unsigned first, unsigned n, int *signs)
9303 isl_vec *bound = NULL;
9304 struct isl_tab *tab = NULL;
9305 struct isl_tab_undo *snap;
9308 if (!bset || !signs)
9311 bound = isl_vec_alloc(bset->ctx, 1 + isl_basic_set_total_dim(bset));
9312 tab = isl_tab_from_basic_set(bset, 0);
9316 isl_seq_clr(bound->el, bound->size);
9317 isl_int_set_si(bound->el[0], -1);
9319 snap = isl_tab_snap(tab);
9320 for (i = 0; i < n; ++i) {
9323 isl_int_set_si(bound->el[1 + first + i], -1);
9324 if (isl_tab_add_ineq(tab, bound->el) < 0)
9327 isl_int_set_si(bound->el[1 + first + i], 0);
9328 if (isl_tab_rollback(tab, snap) < 0)
9336 isl_int_set_si(bound->el[1 + first + i], 1);
9337 if (isl_tab_add_ineq(tab, bound->el) < 0)
9340 isl_int_set_si(bound->el[1 + first + i], 0);
9341 if (isl_tab_rollback(tab, snap) < 0)
9344 signs[i] = empty ? -1 : 0;
9348 isl_vec_free(bound);
9352 isl_vec_free(bound);
9356 int isl_basic_set_dims_get_sign(__isl_keep isl_basic_set *bset,
9357 enum isl_dim_type type, unsigned first, unsigned n, int *signs)
9359 if (!bset || !signs)
9361 isl_assert(bset->ctx, first + n <= isl_basic_set_dim(bset, type),
9364 first += pos(bset->dim, type) - 1;
9365 return isl_basic_set_vars_get_sign(bset, first, n, signs);
9368 /* Check if the given basic map is obviously single-valued.
9369 * In particular, for each output dimension, check that there is
9370 * an equality that defines the output dimension in terms of
9371 * earlier dimensions.
9373 int isl_basic_map_plain_is_single_valued(__isl_keep isl_basic_map *bmap)
9383 total = 1 + isl_basic_map_total_dim(bmap);
9384 n_out = isl_basic_map_dim(bmap, isl_dim_out);
9385 o_out = isl_basic_map_offset(bmap, isl_dim_out);
9387 for (i = 0; i < n_out; ++i) {
9388 for (j = 0; j < bmap->n_eq; ++j) {
9389 if (isl_int_is_zero(bmap->eq[j][o_out + i]))
9391 if (isl_seq_first_non_zero(bmap->eq[j] + o_out + i + 1,
9392 total - (o_out + i + 1)) == -1)
9395 if (j >= bmap->n_eq)
9402 /* Check if the given basic map is single-valued.
9407 * and check if the result is a subset of the identity mapping.
9409 int isl_basic_map_is_single_valued(__isl_keep isl_basic_map *bmap)
9412 isl_basic_map *test;
9416 sv = isl_basic_map_plain_is_single_valued(bmap);
9420 test = isl_basic_map_reverse(isl_basic_map_copy(bmap));
9421 test = isl_basic_map_apply_range(test, isl_basic_map_copy(bmap));
9423 space = isl_basic_map_get_space(bmap);
9424 space = isl_space_map_from_set(isl_space_range(space));
9425 id = isl_basic_map_identity(space);
9427 sv = isl_basic_map_is_subset(test, id);
9429 isl_basic_map_free(test);
9430 isl_basic_map_free(id);
9435 /* Check if the given map is obviously single-valued.
9437 int isl_map_plain_is_single_valued(__isl_keep isl_map *map)
9446 return isl_basic_map_plain_is_single_valued(map->p[0]);
9449 /* Check if the given map is single-valued.
9454 * and check if the result is a subset of the identity mapping.
9456 int isl_map_is_single_valued(__isl_keep isl_map *map)
9463 sv = isl_map_plain_is_single_valued(map);
9467 test = isl_map_reverse(isl_map_copy(map));
9468 test = isl_map_apply_range(test, isl_map_copy(map));
9470 dim = isl_space_map_from_set(isl_space_range(isl_map_get_space(map)));
9471 id = isl_map_identity(dim);
9473 sv = isl_map_is_subset(test, id);
9481 int isl_map_is_injective(__isl_keep isl_map *map)
9485 map = isl_map_copy(map);
9486 map = isl_map_reverse(map);
9487 in = isl_map_is_single_valued(map);
9493 /* Check if the given map is obviously injective.
9495 int isl_map_plain_is_injective(__isl_keep isl_map *map)
9499 map = isl_map_copy(map);
9500 map = isl_map_reverse(map);
9501 in = isl_map_plain_is_single_valued(map);
9507 int isl_map_is_bijective(__isl_keep isl_map *map)
9511 sv = isl_map_is_single_valued(map);
9515 return isl_map_is_injective(map);
9518 int isl_set_is_singleton(__isl_keep isl_set *set)
9520 return isl_map_is_single_valued((isl_map *)set);
9523 int isl_map_is_translation(__isl_keep isl_map *map)
9528 delta = isl_map_deltas(isl_map_copy(map));
9529 ok = isl_set_is_singleton(delta);
9530 isl_set_free(delta);
9535 static int unique(isl_int *p, unsigned pos, unsigned len)
9537 if (isl_seq_first_non_zero(p, pos) != -1)
9539 if (isl_seq_first_non_zero(p + pos + 1, len - pos - 1) != -1)
9544 int isl_basic_set_is_box(__isl_keep isl_basic_set *bset)
9553 if (isl_basic_set_dim(bset, isl_dim_div) != 0)
9556 nvar = isl_basic_set_dim(bset, isl_dim_set);
9557 ovar = isl_space_offset(bset->dim, isl_dim_set);
9558 for (j = 0; j < nvar; ++j) {
9559 int lower = 0, upper = 0;
9560 for (i = 0; i < bset->n_eq; ++i) {
9561 if (isl_int_is_zero(bset->eq[i][1 + ovar + j]))
9563 if (!unique(bset->eq[i] + 1 + ovar, j, nvar))
9569 for (i = 0; i < bset->n_ineq; ++i) {
9570 if (isl_int_is_zero(bset->ineq[i][1 + ovar + j]))
9572 if (!unique(bset->ineq[i] + 1 + ovar, j, nvar))
9574 if (isl_int_is_pos(bset->ineq[i][1 + ovar + j]))
9579 if (!lower || !upper)
9586 int isl_set_is_box(__isl_keep isl_set *set)
9593 return isl_basic_set_is_box(set->p[0]);
9596 int isl_basic_set_is_wrapping(__isl_keep isl_basic_set *bset)
9601 return isl_space_is_wrapping(bset->dim);
9604 int isl_set_is_wrapping(__isl_keep isl_set *set)
9609 return isl_space_is_wrapping(set->dim);
9612 __isl_give isl_basic_set *isl_basic_map_wrap(__isl_take isl_basic_map *bmap)
9614 bmap = isl_basic_map_cow(bmap);
9618 bmap->dim = isl_space_wrap(bmap->dim);
9622 bmap = isl_basic_map_finalize(bmap);
9624 return (isl_basic_set *)bmap;
9626 isl_basic_map_free(bmap);
9630 __isl_give isl_set *isl_map_wrap(__isl_take isl_map *map)
9634 map = isl_map_cow(map);
9638 for (i = 0; i < map->n; ++i) {
9639 map->p[i] = (isl_basic_map *)isl_basic_map_wrap(map->p[i]);
9643 map->dim = isl_space_wrap(map->dim);
9647 return (isl_set *)map;
9653 __isl_give isl_basic_map *isl_basic_set_unwrap(__isl_take isl_basic_set *bset)
9655 bset = isl_basic_set_cow(bset);
9659 bset->dim = isl_space_unwrap(bset->dim);
9663 bset = isl_basic_set_finalize(bset);
9665 return (isl_basic_map *)bset;
9667 isl_basic_set_free(bset);
9671 __isl_give isl_map *isl_set_unwrap(__isl_take isl_set *set)
9678 if (!isl_set_is_wrapping(set))
9679 isl_die(set->ctx, isl_error_invalid, "not a wrapping set",
9682 set = isl_set_cow(set);
9686 for (i = 0; i < set->n; ++i) {
9687 set->p[i] = (isl_basic_set *)isl_basic_set_unwrap(set->p[i]);
9692 set->dim = isl_space_unwrap(set->dim);
9696 return (isl_map *)set;
9702 __isl_give isl_basic_map *isl_basic_map_reset(__isl_take isl_basic_map *bmap,
9703 enum isl_dim_type type)
9708 if (!isl_space_is_named_or_nested(bmap->dim, type))
9711 bmap = isl_basic_map_cow(bmap);
9715 bmap->dim = isl_space_reset(bmap->dim, type);
9719 bmap = isl_basic_map_finalize(bmap);
9723 isl_basic_map_free(bmap);
9727 __isl_give isl_map *isl_map_reset(__isl_take isl_map *map,
9728 enum isl_dim_type type)
9735 if (!isl_space_is_named_or_nested(map->dim, type))
9738 map = isl_map_cow(map);
9742 for (i = 0; i < map->n; ++i) {
9743 map->p[i] = isl_basic_map_reset(map->p[i], type);
9747 map->dim = isl_space_reset(map->dim, type);
9757 __isl_give isl_basic_map *isl_basic_map_flatten(__isl_take isl_basic_map *bmap)
9762 if (!bmap->dim->nested[0] && !bmap->dim->nested[1])
9765 bmap = isl_basic_map_cow(bmap);
9769 bmap->dim = isl_space_flatten(bmap->dim);
9773 bmap = isl_basic_map_finalize(bmap);
9777 isl_basic_map_free(bmap);
9781 __isl_give isl_basic_set *isl_basic_set_flatten(__isl_take isl_basic_set *bset)
9783 return (isl_basic_set *)isl_basic_map_flatten((isl_basic_map *)bset);
9786 __isl_give isl_basic_map *isl_basic_map_flatten_domain(
9787 __isl_take isl_basic_map *bmap)
9792 if (!bmap->dim->nested[0])
9795 bmap = isl_basic_map_cow(bmap);
9799 bmap->dim = isl_space_flatten_domain(bmap->dim);
9803 bmap = isl_basic_map_finalize(bmap);
9807 isl_basic_map_free(bmap);
9811 __isl_give isl_basic_map *isl_basic_map_flatten_range(
9812 __isl_take isl_basic_map *bmap)
9817 if (!bmap->dim->nested[1])
9820 bmap = isl_basic_map_cow(bmap);
9824 bmap->dim = isl_space_flatten_range(bmap->dim);
9828 bmap = isl_basic_map_finalize(bmap);
9832 isl_basic_map_free(bmap);
9836 __isl_give isl_map *isl_map_flatten(__isl_take isl_map *map)
9843 if (!map->dim->nested[0] && !map->dim->nested[1])
9846 map = isl_map_cow(map);
9850 for (i = 0; i < map->n; ++i) {
9851 map->p[i] = isl_basic_map_flatten(map->p[i]);
9855 map->dim = isl_space_flatten(map->dim);
9865 __isl_give isl_set *isl_set_flatten(__isl_take isl_set *set)
9867 return (isl_set *)isl_map_flatten((isl_map *)set);
9870 __isl_give isl_map *isl_set_flatten_map(__isl_take isl_set *set)
9872 isl_space *dim, *flat_dim;
9875 dim = isl_set_get_space(set);
9876 flat_dim = isl_space_flatten(isl_space_copy(dim));
9877 map = isl_map_identity(isl_space_join(isl_space_reverse(dim), flat_dim));
9878 map = isl_map_intersect_domain(map, set);
9883 __isl_give isl_map *isl_map_flatten_domain(__isl_take isl_map *map)
9890 if (!map->dim->nested[0])
9893 map = isl_map_cow(map);
9897 for (i = 0; i < map->n; ++i) {
9898 map->p[i] = isl_basic_map_flatten_domain(map->p[i]);
9902 map->dim = isl_space_flatten_domain(map->dim);
9912 __isl_give isl_map *isl_map_flatten_range(__isl_take isl_map *map)
9919 if (!map->dim->nested[1])
9922 map = isl_map_cow(map);
9926 for (i = 0; i < map->n; ++i) {
9927 map->p[i] = isl_basic_map_flatten_range(map->p[i]);
9931 map->dim = isl_space_flatten_range(map->dim);
9941 /* Reorder the dimensions of "bmap" according to the given dim_map
9942 * and set the dimension specification to "dim".
9944 __isl_give isl_basic_map *isl_basic_map_realign(__isl_take isl_basic_map *bmap,
9945 __isl_take isl_space *dim, __isl_take struct isl_dim_map *dim_map)
9950 bmap = isl_basic_map_cow(bmap);
9951 if (!bmap || !dim || !dim_map)
9954 flags = bmap->flags;
9955 ISL_FL_CLR(flags, ISL_BASIC_MAP_FINAL);
9956 ISL_FL_CLR(flags, ISL_BASIC_MAP_NORMALIZED);
9957 ISL_FL_CLR(flags, ISL_BASIC_MAP_NORMALIZED_DIVS);
9958 res = isl_basic_map_alloc_space(dim,
9959 bmap->n_div, bmap->n_eq, bmap->n_ineq);
9960 res = isl_basic_map_add_constraints_dim_map(res, bmap, dim_map);
9963 res = isl_basic_map_finalize(res);
9967 isl_basic_map_free(bmap);
9968 isl_space_free(dim);
9972 /* Reorder the dimensions of "map" according to given reordering.
9974 __isl_give isl_map *isl_map_realign(__isl_take isl_map *map,
9975 __isl_take isl_reordering *r)
9978 struct isl_dim_map *dim_map;
9980 map = isl_map_cow(map);
9981 dim_map = isl_dim_map_from_reordering(r);
9982 if (!map || !r || !dim_map)
9985 for (i = 0; i < map->n; ++i) {
9986 struct isl_dim_map *dim_map_i;
9988 dim_map_i = isl_dim_map_extend(dim_map, map->p[i]);
9990 map->p[i] = isl_basic_map_realign(map->p[i],
9991 isl_space_copy(r->dim), dim_map_i);
9997 map = isl_map_reset_space(map, isl_space_copy(r->dim));
9999 isl_reordering_free(r);
10005 isl_reordering_free(r);
10009 __isl_give isl_set *isl_set_realign(__isl_take isl_set *set,
10010 __isl_take isl_reordering *r)
10012 return (isl_set *)isl_map_realign((isl_map *)set, r);
10015 __isl_give isl_map *isl_map_align_params(__isl_take isl_map *map,
10016 __isl_take isl_space *model)
10020 if (!map || !model)
10023 ctx = isl_space_get_ctx(model);
10024 if (!isl_space_has_named_params(model))
10025 isl_die(ctx, isl_error_invalid,
10026 "model has unnamed parameters", goto error);
10027 if (!isl_space_has_named_params(map->dim))
10028 isl_die(ctx, isl_error_invalid,
10029 "relation has unnamed parameters", goto error);
10030 if (!isl_space_match(map->dim, isl_dim_param, model, isl_dim_param)) {
10031 isl_reordering *exp;
10033 model = isl_space_drop_dims(model, isl_dim_in,
10034 0, isl_space_dim(model, isl_dim_in));
10035 model = isl_space_drop_dims(model, isl_dim_out,
10036 0, isl_space_dim(model, isl_dim_out));
10037 exp = isl_parameter_alignment_reordering(map->dim, model);
10038 exp = isl_reordering_extend_space(exp, isl_map_get_space(map));
10039 map = isl_map_realign(map, exp);
10042 isl_space_free(model);
10045 isl_space_free(model);
10050 __isl_give isl_set *isl_set_align_params(__isl_take isl_set *set,
10051 __isl_take isl_space *model)
10053 return isl_map_align_params(set, model);
10056 /* Align the parameters of "bmap" to those of "model", introducing
10057 * additional parameters if needed.
10059 __isl_give isl_basic_map *isl_basic_map_align_params(
10060 __isl_take isl_basic_map *bmap, __isl_take isl_space *model)
10064 if (!bmap || !model)
10067 ctx = isl_space_get_ctx(model);
10068 if (!isl_space_has_named_params(model))
10069 isl_die(ctx, isl_error_invalid,
10070 "model has unnamed parameters", goto error);
10071 if (!isl_space_has_named_params(bmap->dim))
10072 isl_die(ctx, isl_error_invalid,
10073 "relation has unnamed parameters", goto error);
10074 if (!isl_space_match(bmap->dim, isl_dim_param, model, isl_dim_param)) {
10075 isl_reordering *exp;
10076 struct isl_dim_map *dim_map;
10078 model = isl_space_drop_dims(model, isl_dim_in,
10079 0, isl_space_dim(model, isl_dim_in));
10080 model = isl_space_drop_dims(model, isl_dim_out,
10081 0, isl_space_dim(model, isl_dim_out));
10082 exp = isl_parameter_alignment_reordering(bmap->dim, model);
10083 exp = isl_reordering_extend_space(exp,
10084 isl_basic_map_get_space(bmap));
10085 dim_map = isl_dim_map_from_reordering(exp);
10086 bmap = isl_basic_map_realign(bmap,
10087 exp ? isl_space_copy(exp->dim) : NULL,
10088 isl_dim_map_extend(dim_map, bmap));
10089 isl_reordering_free(exp);
10093 isl_space_free(model);
10096 isl_space_free(model);
10097 isl_basic_map_free(bmap);
10101 /* Align the parameters of "bset" to those of "model", introducing
10102 * additional parameters if needed.
10104 __isl_give isl_basic_set *isl_basic_set_align_params(
10105 __isl_take isl_basic_set *bset, __isl_take isl_space *model)
10107 return isl_basic_map_align_params(bset, model);
10110 __isl_give isl_mat *isl_basic_map_equalities_matrix(
10111 __isl_keep isl_basic_map *bmap, enum isl_dim_type c1,
10112 enum isl_dim_type c2, enum isl_dim_type c3,
10113 enum isl_dim_type c4, enum isl_dim_type c5)
10115 enum isl_dim_type c[5] = { c1, c2, c3, c4, c5 };
10116 struct isl_mat *mat;
10122 mat = isl_mat_alloc(bmap->ctx, bmap->n_eq,
10123 isl_basic_map_total_dim(bmap) + 1);
10126 for (i = 0; i < bmap->n_eq; ++i)
10127 for (j = 0, pos = 0; j < 5; ++j) {
10128 int off = isl_basic_map_offset(bmap, c[j]);
10129 for (k = 0; k < isl_basic_map_dim(bmap, c[j]); ++k) {
10130 isl_int_set(mat->row[i][pos],
10131 bmap->eq[i][off + k]);
10139 __isl_give isl_mat *isl_basic_map_inequalities_matrix(
10140 __isl_keep isl_basic_map *bmap, enum isl_dim_type c1,
10141 enum isl_dim_type c2, enum isl_dim_type c3,
10142 enum isl_dim_type c4, enum isl_dim_type c5)
10144 enum isl_dim_type c[5] = { c1, c2, c3, c4, c5 };
10145 struct isl_mat *mat;
10151 mat = isl_mat_alloc(bmap->ctx, bmap->n_ineq,
10152 isl_basic_map_total_dim(bmap) + 1);
10155 for (i = 0; i < bmap->n_ineq; ++i)
10156 for (j = 0, pos = 0; j < 5; ++j) {
10157 int off = isl_basic_map_offset(bmap, c[j]);
10158 for (k = 0; k < isl_basic_map_dim(bmap, c[j]); ++k) {
10159 isl_int_set(mat->row[i][pos],
10160 bmap->ineq[i][off + k]);
10168 __isl_give isl_basic_map *isl_basic_map_from_constraint_matrices(
10169 __isl_take isl_space *dim,
10170 __isl_take isl_mat *eq, __isl_take isl_mat *ineq, enum isl_dim_type c1,
10171 enum isl_dim_type c2, enum isl_dim_type c3,
10172 enum isl_dim_type c4, enum isl_dim_type c5)
10174 enum isl_dim_type c[5] = { c1, c2, c3, c4, c5 };
10175 isl_basic_map *bmap;
10181 if (!dim || !eq || !ineq)
10184 if (eq->n_col != ineq->n_col)
10185 isl_die(dim->ctx, isl_error_invalid,
10186 "equalities and inequalities matrices should have "
10187 "same number of columns", goto error);
10189 total = 1 + isl_space_dim(dim, isl_dim_all);
10191 if (eq->n_col < total)
10192 isl_die(dim->ctx, isl_error_invalid,
10193 "number of columns too small", goto error);
10195 extra = eq->n_col - total;
10197 bmap = isl_basic_map_alloc_space(isl_space_copy(dim), extra,
10198 eq->n_row, ineq->n_row);
10201 for (i = 0; i < extra; ++i) {
10202 k = isl_basic_map_alloc_div(bmap);
10205 isl_int_set_si(bmap->div[k][0], 0);
10207 for (i = 0; i < eq->n_row; ++i) {
10208 l = isl_basic_map_alloc_equality(bmap);
10211 for (j = 0, pos = 0; j < 5; ++j) {
10212 int off = isl_basic_map_offset(bmap, c[j]);
10213 for (k = 0; k < isl_basic_map_dim(bmap, c[j]); ++k) {
10214 isl_int_set(bmap->eq[l][off + k],
10220 for (i = 0; i < ineq->n_row; ++i) {
10221 l = isl_basic_map_alloc_inequality(bmap);
10224 for (j = 0, pos = 0; j < 5; ++j) {
10225 int off = isl_basic_map_offset(bmap, c[j]);
10226 for (k = 0; k < isl_basic_map_dim(bmap, c[j]); ++k) {
10227 isl_int_set(bmap->ineq[l][off + k],
10228 ineq->row[i][pos]);
10234 isl_space_free(dim);
10236 isl_mat_free(ineq);
10240 isl_space_free(dim);
10242 isl_mat_free(ineq);
10246 __isl_give isl_mat *isl_basic_set_equalities_matrix(
10247 __isl_keep isl_basic_set *bset, enum isl_dim_type c1,
10248 enum isl_dim_type c2, enum isl_dim_type c3, enum isl_dim_type c4)
10250 return isl_basic_map_equalities_matrix((isl_basic_map *)bset,
10251 c1, c2, c3, c4, isl_dim_in);
10254 __isl_give isl_mat *isl_basic_set_inequalities_matrix(
10255 __isl_keep isl_basic_set *bset, enum isl_dim_type c1,
10256 enum isl_dim_type c2, enum isl_dim_type c3, enum isl_dim_type c4)
10258 return isl_basic_map_inequalities_matrix((isl_basic_map *)bset,
10259 c1, c2, c3, c4, isl_dim_in);
10262 __isl_give isl_basic_set *isl_basic_set_from_constraint_matrices(
10263 __isl_take isl_space *dim,
10264 __isl_take isl_mat *eq, __isl_take isl_mat *ineq, enum isl_dim_type c1,
10265 enum isl_dim_type c2, enum isl_dim_type c3, enum isl_dim_type c4)
10267 return (isl_basic_set*)
10268 isl_basic_map_from_constraint_matrices(dim, eq, ineq,
10269 c1, c2, c3, c4, isl_dim_in);
10272 int isl_basic_map_can_zip(__isl_keep isl_basic_map *bmap)
10277 return isl_space_can_zip(bmap->dim);
10280 int isl_map_can_zip(__isl_keep isl_map *map)
10285 return isl_space_can_zip(map->dim);
10288 /* Given a basic map (A -> B) -> (C -> D), return the corresponding basic map
10289 * (A -> C) -> (B -> D).
10291 __isl_give isl_basic_map *isl_basic_map_zip(__isl_take isl_basic_map *bmap)
10300 if (!isl_basic_map_can_zip(bmap))
10301 isl_die(bmap->ctx, isl_error_invalid,
10302 "basic map cannot be zipped", goto error);
10303 pos = isl_basic_map_offset(bmap, isl_dim_in) +
10304 isl_space_dim(bmap->dim->nested[0], isl_dim_in);
10305 n1 = isl_space_dim(bmap->dim->nested[0], isl_dim_out);
10306 n2 = isl_space_dim(bmap->dim->nested[1], isl_dim_in);
10307 bmap = isl_basic_map_cow(bmap);
10308 bmap = isl_basic_map_swap_vars(bmap, pos, n1, n2);
10311 bmap->dim = isl_space_zip(bmap->dim);
10316 isl_basic_map_free(bmap);
10320 /* Given a map (A -> B) -> (C -> D), return the corresponding map
10321 * (A -> C) -> (B -> D).
10323 __isl_give isl_map *isl_map_zip(__isl_take isl_map *map)
10330 if (!isl_map_can_zip(map))
10331 isl_die(map->ctx, isl_error_invalid, "map cannot be zipped",
10334 map = isl_map_cow(map);
10338 for (i = 0; i < map->n; ++i) {
10339 map->p[i] = isl_basic_map_zip(map->p[i]);
10344 map->dim = isl_space_zip(map->dim);
10354 /* Can we apply isl_basic_map_curry to "bmap"?
10355 * That is, does it have a nested relation in its domain?
10357 int isl_basic_map_can_curry(__isl_keep isl_basic_map *bmap)
10362 return isl_space_can_curry(bmap->dim);
10365 /* Can we apply isl_map_curry to "map"?
10366 * That is, does it have a nested relation in its domain?
10368 int isl_map_can_curry(__isl_keep isl_map *map)
10373 return isl_space_can_curry(map->dim);
10376 /* Given a basic map (A -> B) -> C, return the corresponding basic map
10379 __isl_give isl_basic_map *isl_basic_map_curry(__isl_take isl_basic_map *bmap)
10385 if (!isl_basic_map_can_curry(bmap))
10386 isl_die(bmap->ctx, isl_error_invalid,
10387 "basic map cannot be curried", goto error);
10388 bmap->dim = isl_space_curry(bmap->dim);
10393 isl_basic_map_free(bmap);
10397 /* Given a map (A -> B) -> C, return the corresponding map
10400 __isl_give isl_map *isl_map_curry(__isl_take isl_map *map)
10407 if (!isl_map_can_curry(map))
10408 isl_die(map->ctx, isl_error_invalid, "map cannot be curried",
10411 map = isl_map_cow(map);
10415 for (i = 0; i < map->n; ++i) {
10416 map->p[i] = isl_basic_map_curry(map->p[i]);
10421 map->dim = isl_space_curry(map->dim);
10431 /* Can we apply isl_basic_map_uncurry to "bmap"?
10432 * That is, does it have a nested relation in its domain?
10434 int isl_basic_map_can_uncurry(__isl_keep isl_basic_map *bmap)
10439 return isl_space_can_uncurry(bmap->dim);
10442 /* Can we apply isl_map_uncurry to "map"?
10443 * That is, does it have a nested relation in its domain?
10445 int isl_map_can_uncurry(__isl_keep isl_map *map)
10450 return isl_space_can_uncurry(map->dim);
10453 /* Given a basic map A -> (B -> C), return the corresponding basic map
10456 __isl_give isl_basic_map *isl_basic_map_uncurry(__isl_take isl_basic_map *bmap)
10462 if (!isl_basic_map_can_uncurry(bmap))
10463 isl_die(bmap->ctx, isl_error_invalid,
10464 "basic map cannot be uncurried",
10465 return isl_basic_map_free(bmap));
10466 bmap->dim = isl_space_uncurry(bmap->dim);
10468 return isl_basic_map_free(bmap);
10472 /* Given a map A -> (B -> C), return the corresponding map
10475 __isl_give isl_map *isl_map_uncurry(__isl_take isl_map *map)
10482 if (!isl_map_can_uncurry(map))
10483 isl_die(map->ctx, isl_error_invalid, "map cannot be uncurried",
10484 return isl_map_free(map));
10486 map = isl_map_cow(map);
10490 for (i = 0; i < map->n; ++i) {
10491 map->p[i] = isl_basic_map_uncurry(map->p[i]);
10493 return isl_map_free(map);
10496 map->dim = isl_space_uncurry(map->dim);
10498 return isl_map_free(map);
10503 /* Construct a basic map mapping the domain of the affine expression
10504 * to a one-dimensional range prescribed by the affine expression.
10506 __isl_give isl_basic_map *isl_basic_map_from_aff(__isl_take isl_aff *aff)
10510 isl_local_space *ls;
10511 isl_basic_map *bmap;
10516 ls = isl_aff_get_local_space(aff);
10517 bmap = isl_basic_map_from_local_space(ls);
10518 bmap = isl_basic_map_extend_constraints(bmap, 1, 0);
10519 k = isl_basic_map_alloc_equality(bmap);
10523 pos = isl_basic_map_offset(bmap, isl_dim_out);
10524 isl_seq_cpy(bmap->eq[k], aff->v->el + 1, pos);
10525 isl_int_neg(bmap->eq[k][pos], aff->v->el[0]);
10526 isl_seq_cpy(bmap->eq[k] + pos + 1, aff->v->el + 1 + pos,
10527 aff->v->size - (pos + 1));
10530 bmap = isl_basic_map_finalize(bmap);
10534 isl_basic_map_free(bmap);
10538 /* Construct a map mapping the domain of the affine expression
10539 * to a one-dimensional range prescribed by the affine expression.
10541 __isl_give isl_map *isl_map_from_aff(__isl_take isl_aff *aff)
10543 isl_basic_map *bmap;
10545 bmap = isl_basic_map_from_aff(aff);
10546 return isl_map_from_basic_map(bmap);
10549 /* Construct a basic map mapping the domain the multi-affine expression
10550 * to its range, with each dimension in the range equated to the
10551 * corresponding affine expression.
10553 __isl_give isl_basic_map *isl_basic_map_from_multi_aff(
10554 __isl_take isl_multi_aff *maff)
10558 isl_basic_map *bmap;
10563 if (isl_space_dim(maff->space, isl_dim_out) != maff->n)
10564 isl_die(isl_multi_aff_get_ctx(maff), isl_error_internal,
10565 "invalid space", return isl_multi_aff_free(maff));
10567 space = isl_space_domain(isl_multi_aff_get_space(maff));
10568 bmap = isl_basic_map_universe(isl_space_from_domain(space));
10570 for (i = 0; i < maff->n; ++i) {
10572 isl_basic_map *bmap_i;
10574 aff = isl_aff_copy(maff->p[i]);
10575 bmap_i = isl_basic_map_from_aff(aff);
10577 bmap = isl_basic_map_flat_range_product(bmap, bmap_i);
10580 bmap = isl_basic_map_reset_space(bmap, isl_multi_aff_get_space(maff));
10582 isl_multi_aff_free(maff);
10586 /* Construct a map mapping the domain the multi-affine expression
10587 * to its range, with each dimension in the range equated to the
10588 * corresponding affine expression.
10590 __isl_give isl_map *isl_map_from_multi_aff(__isl_take isl_multi_aff *maff)
10592 isl_basic_map *bmap;
10594 bmap = isl_basic_map_from_multi_aff(maff);
10595 return isl_map_from_basic_map(bmap);
10598 /* Construct a basic map mapping a domain in the given space to
10599 * to an n-dimensional range, with n the number of elements in the list,
10600 * where each coordinate in the range is prescribed by the
10601 * corresponding affine expression.
10602 * The domains of all affine expressions in the list are assumed to match
10605 __isl_give isl_basic_map *isl_basic_map_from_aff_list(
10606 __isl_take isl_space *domain_dim, __isl_take isl_aff_list *list)
10610 isl_basic_map *bmap;
10615 dim = isl_space_from_domain(domain_dim);
10616 bmap = isl_basic_map_universe(dim);
10618 for (i = 0; i < list->n; ++i) {
10620 isl_basic_map *bmap_i;
10622 aff = isl_aff_copy(list->p[i]);
10623 bmap_i = isl_basic_map_from_aff(aff);
10625 bmap = isl_basic_map_flat_range_product(bmap, bmap_i);
10628 isl_aff_list_free(list);
10632 __isl_give isl_set *isl_set_equate(__isl_take isl_set *set,
10633 enum isl_dim_type type1, int pos1, enum isl_dim_type type2, int pos2)
10635 return isl_map_equate(set, type1, pos1, type2, pos2);
10638 /* Construct a basic map where the given dimensions are equal to each other.
10640 static __isl_give isl_basic_map *equator(__isl_take isl_space *space,
10641 enum isl_dim_type type1, int pos1, enum isl_dim_type type2, int pos2)
10643 isl_basic_map *bmap = NULL;
10649 if (pos1 >= isl_space_dim(space, type1))
10650 isl_die(isl_space_get_ctx(space), isl_error_invalid,
10651 "index out of bounds", goto error);
10652 if (pos2 >= isl_space_dim(space, type2))
10653 isl_die(isl_space_get_ctx(space), isl_error_invalid,
10654 "index out of bounds", goto error);
10656 if (type1 == type2 && pos1 == pos2)
10657 return isl_basic_map_universe(space);
10659 bmap = isl_basic_map_alloc_space(isl_space_copy(space), 0, 1, 0);
10660 i = isl_basic_map_alloc_equality(bmap);
10663 isl_seq_clr(bmap->eq[i], 1 + isl_basic_map_total_dim(bmap));
10664 pos1 += isl_basic_map_offset(bmap, type1);
10665 pos2 += isl_basic_map_offset(bmap, type2);
10666 isl_int_set_si(bmap->eq[i][pos1], -1);
10667 isl_int_set_si(bmap->eq[i][pos2], 1);
10668 bmap = isl_basic_map_finalize(bmap);
10669 isl_space_free(space);
10672 isl_space_free(space);
10673 isl_basic_map_free(bmap);
10677 /* Add a constraint imposing that the given two dimensions are equal.
10679 __isl_give isl_basic_map *isl_basic_map_equate(__isl_take isl_basic_map *bmap,
10680 enum isl_dim_type type1, int pos1, enum isl_dim_type type2, int pos2)
10684 eq = equator(isl_basic_map_get_space(bmap), type1, pos1, type2, pos2);
10686 bmap = isl_basic_map_intersect(bmap, eq);
10691 /* Add a constraint imposing that the given two dimensions are equal.
10693 __isl_give isl_map *isl_map_equate(__isl_take isl_map *map,
10694 enum isl_dim_type type1, int pos1, enum isl_dim_type type2, int pos2)
10696 isl_basic_map *bmap;
10698 bmap = equator(isl_map_get_space(map), type1, pos1, type2, pos2);
10700 map = isl_map_intersect(map, isl_map_from_basic_map(bmap));
10705 /* Add a constraint imposing that the given two dimensions have opposite values.
10707 __isl_give isl_map *isl_map_oppose(__isl_take isl_map *map,
10708 enum isl_dim_type type1, int pos1, enum isl_dim_type type2, int pos2)
10710 isl_basic_map *bmap = NULL;
10716 if (pos1 >= isl_map_dim(map, type1))
10717 isl_die(map->ctx, isl_error_invalid,
10718 "index out of bounds", goto error);
10719 if (pos2 >= isl_map_dim(map, type2))
10720 isl_die(map->ctx, isl_error_invalid,
10721 "index out of bounds", goto error);
10723 bmap = isl_basic_map_alloc_space(isl_map_get_space(map), 0, 1, 0);
10724 i = isl_basic_map_alloc_equality(bmap);
10727 isl_seq_clr(bmap->eq[i], 1 + isl_basic_map_total_dim(bmap));
10728 pos1 += isl_basic_map_offset(bmap, type1);
10729 pos2 += isl_basic_map_offset(bmap, type2);
10730 isl_int_set_si(bmap->eq[i][pos1], 1);
10731 isl_int_set_si(bmap->eq[i][pos2], 1);
10732 bmap = isl_basic_map_finalize(bmap);
10734 map = isl_map_intersect(map, isl_map_from_basic_map(bmap));
10738 isl_basic_map_free(bmap);
10743 /* Add a constraint imposing that the value of the first dimension is
10744 * greater than or equal to that of the second.
10746 __isl_give isl_basic_map *isl_basic_map_order_ge(__isl_take isl_basic_map *bmap,
10747 enum isl_dim_type type1, int pos1, enum isl_dim_type type2, int pos2)
10750 isl_local_space *ls;
10755 if (pos1 >= isl_basic_map_dim(bmap, type1))
10756 isl_die(bmap->ctx, isl_error_invalid,
10757 "index out of bounds", return isl_basic_map_free(bmap));
10758 if (pos2 >= isl_basic_map_dim(bmap, type2))
10759 isl_die(bmap->ctx, isl_error_invalid,
10760 "index out of bounds", return isl_basic_map_free(bmap));
10762 if (type1 == type2 && pos1 == pos2)
10765 ls = isl_local_space_from_space(isl_basic_map_get_space(bmap));
10766 c = isl_inequality_alloc(ls);
10767 c = isl_constraint_set_coefficient_si(c, type1, pos1, 1);
10768 c = isl_constraint_set_coefficient_si(c, type2, pos2, -1);
10769 bmap = isl_basic_map_add_constraint(bmap, c);
10774 /* Add a constraint imposing that the value of the first dimension is
10775 * greater than that of the second.
10777 __isl_give isl_map *isl_map_order_gt(__isl_take isl_map *map,
10778 enum isl_dim_type type1, int pos1, enum isl_dim_type type2, int pos2)
10780 isl_basic_map *bmap = NULL;
10786 if (pos1 >= isl_map_dim(map, type1))
10787 isl_die(map->ctx, isl_error_invalid,
10788 "index out of bounds", goto error);
10789 if (pos2 >= isl_map_dim(map, type2))
10790 isl_die(map->ctx, isl_error_invalid,
10791 "index out of bounds", goto error);
10793 if (type1 == type2 && pos1 == pos2) {
10794 isl_space *space = isl_map_get_space(map);
10796 return isl_map_empty(space);
10799 bmap = isl_basic_map_alloc_space(isl_map_get_space(map), 0, 0, 1);
10800 i = isl_basic_map_alloc_inequality(bmap);
10803 isl_seq_clr(bmap->ineq[i], 1 + isl_basic_map_total_dim(bmap));
10804 pos1 += isl_basic_map_offset(bmap, type1);
10805 pos2 += isl_basic_map_offset(bmap, type2);
10806 isl_int_set_si(bmap->ineq[i][pos1], 1);
10807 isl_int_set_si(bmap->ineq[i][pos2], -1);
10808 isl_int_set_si(bmap->ineq[i][0], -1);
10809 bmap = isl_basic_map_finalize(bmap);
10811 map = isl_map_intersect(map, isl_map_from_basic_map(bmap));
10815 isl_basic_map_free(bmap);
10820 /* Add a constraint imposing that the value of the first dimension is
10821 * smaller than that of the second.
10823 __isl_give isl_map *isl_map_order_lt(__isl_take isl_map *map,
10824 enum isl_dim_type type1, int pos1, enum isl_dim_type type2, int pos2)
10826 return isl_map_order_gt(map, type2, pos2, type1, pos1);
10829 __isl_give isl_aff *isl_basic_map_get_div(__isl_keep isl_basic_map *bmap,
10833 isl_local_space *ls;
10838 if (!isl_basic_map_divs_known(bmap))
10839 isl_die(isl_basic_map_get_ctx(bmap), isl_error_invalid,
10840 "some divs are unknown", return NULL);
10842 ls = isl_basic_map_get_local_space(bmap);
10843 div = isl_local_space_get_div(ls, pos);
10844 isl_local_space_free(ls);
10849 __isl_give isl_aff *isl_basic_set_get_div(__isl_keep isl_basic_set *bset,
10852 return isl_basic_map_get_div(bset, pos);
10855 /* Plug in "subs" for dimension "type", "pos" of "bset".
10857 * Let i be the dimension to replace and let "subs" be of the form
10861 * Any integer division with a non-zero coefficient for i,
10863 * floor((a i + g)/m)
10867 * floor((a f + d g)/(m d))
10869 * Constraints of the form
10877 * We currently require that "subs" is an integral expression.
10878 * Handling rational expressions may require us to add stride constraints
10879 * as we do in isl_basic_set_preimage_multi_aff.
10881 __isl_give isl_basic_set *isl_basic_set_substitute(
10882 __isl_take isl_basic_set *bset,
10883 enum isl_dim_type type, unsigned pos, __isl_keep isl_aff *subs)
10889 if (bset && isl_basic_set_plain_is_empty(bset))
10892 bset = isl_basic_set_cow(bset);
10893 if (!bset || !subs)
10896 ctx = isl_basic_set_get_ctx(bset);
10897 if (!isl_space_is_equal(bset->dim, subs->ls->dim))
10898 isl_die(ctx, isl_error_invalid,
10899 "spaces don't match", goto error);
10900 if (isl_local_space_dim(subs->ls, isl_dim_div) != 0)
10901 isl_die(ctx, isl_error_unsupported,
10902 "cannot handle divs yet", goto error);
10903 if (!isl_int_is_one(subs->v->el[0]))
10904 isl_die(ctx, isl_error_invalid,
10905 "can only substitute integer expressions", goto error);
10907 pos += isl_basic_set_offset(bset, type);
10911 for (i = 0; i < bset->n_eq; ++i) {
10912 if (isl_int_is_zero(bset->eq[i][pos]))
10914 isl_int_set(v, bset->eq[i][pos]);
10915 isl_int_set_si(bset->eq[i][pos], 0);
10916 isl_seq_combine(bset->eq[i], subs->v->el[0], bset->eq[i],
10917 v, subs->v->el + 1, subs->v->size - 1);
10920 for (i = 0; i < bset->n_ineq; ++i) {
10921 if (isl_int_is_zero(bset->ineq[i][pos]))
10923 isl_int_set(v, bset->ineq[i][pos]);
10924 isl_int_set_si(bset->ineq[i][pos], 0);
10925 isl_seq_combine(bset->ineq[i], subs->v->el[0], bset->ineq[i],
10926 v, subs->v->el + 1, subs->v->size - 1);
10929 for (i = 0; i < bset->n_div; ++i) {
10930 if (isl_int_is_zero(bset->div[i][1 + pos]))
10932 isl_int_set(v, bset->div[i][1 + pos]);
10933 isl_int_set_si(bset->div[i][1 + pos], 0);
10934 isl_seq_combine(bset->div[i] + 1,
10935 subs->v->el[0], bset->div[i] + 1,
10936 v, subs->v->el + 1, subs->v->size - 1);
10937 isl_int_mul(bset->div[i][0], bset->div[i][0], subs->v->el[0]);
10942 bset = isl_basic_set_simplify(bset);
10943 return isl_basic_set_finalize(bset);
10945 isl_basic_set_free(bset);
10949 /* Plug in "subs" for dimension "type", "pos" of "set".
10951 __isl_give isl_set *isl_set_substitute(__isl_take isl_set *set,
10952 enum isl_dim_type type, unsigned pos, __isl_keep isl_aff *subs)
10956 if (set && isl_set_plain_is_empty(set))
10959 set = isl_set_cow(set);
10963 for (i = set->n - 1; i >= 0; --i) {
10964 set->p[i] = isl_basic_set_substitute(set->p[i], type, pos, subs);
10965 if (remove_if_empty(set, i) < 0)
10975 /* Check if the range of "ma" is compatible with "space".
10976 * Return -1 if anything is wrong.
10978 static int check_space_compatible_range_multi_aff(
10979 __isl_keep isl_space *space, __isl_keep isl_multi_aff *ma)
10982 isl_space *ma_space;
10984 ma_space = isl_multi_aff_get_space(ma);
10985 m = isl_space_is_range_internal(space, ma_space);
10986 isl_space_free(ma_space);
10988 isl_die(isl_space_get_ctx(space), isl_error_invalid,
10989 "spaces don't match", return -1);
10993 /* Check if the range of "ma" is compatible with "bset".
10994 * Return -1 if anything is wrong.
10996 static int check_basic_set_compatible_range_multi_aff(
10997 __isl_keep isl_basic_set *bset, __isl_keep isl_multi_aff *ma)
10999 return check_space_compatible_range_multi_aff(bset->dim, ma);
11002 /* Copy the divs from "ma" to "bset", adding zeros for the coefficients
11003 * of the other divs in "bset".
11005 static int set_ma_divs(__isl_keep isl_basic_set *bset,
11006 __isl_keep isl_multi_aff *ma, int n_div)
11009 isl_local_space *ls;
11014 ls = isl_aff_get_domain_local_space(ma->p[0]);
11018 for (i = 0; i < n_div; ++i) {
11019 isl_seq_cpy(bset->div[i], ls->div->row[i], ls->div->n_col);
11020 isl_seq_clr(bset->div[i] + ls->div->n_col, bset->n_div - n_div);
11021 if (isl_basic_set_add_div_constraints(bset, i) < 0)
11025 isl_local_space_free(ls);
11028 isl_local_space_free(ls);
11032 /* How many stride constraints does "ma" enforce?
11033 * That is, how many of the affine expressions have a denominator
11034 * different from one?
11036 static int multi_aff_strides(__isl_keep isl_multi_aff *ma)
11041 for (i = 0; i < ma->n; ++i)
11042 if (!isl_int_is_one(ma->p[i]->v->el[0]))
11048 /* For each affine expression in ma of the form
11050 * x_i = (f_i y + h_i)/m_i
11052 * with m_i different from one, add a constraint to "bset"
11055 * f_i y + h_i = m_i alpha_i
11057 * with alpha_i an additional existentially quantified variable.
11059 static __isl_give isl_basic_set *add_ma_strides(
11060 __isl_take isl_basic_set *bset, __isl_keep isl_multi_aff *ma)
11066 total = isl_basic_set_total_dim(bset);
11067 for (i = 0; i < ma->n; ++i) {
11070 if (isl_int_is_one(ma->p[i]->v->el[0]))
11072 div = isl_basic_set_alloc_div(bset);
11073 k = isl_basic_set_alloc_equality(bset);
11074 if (div < 0 || k < 0)
11076 isl_int_set_si(bset->div[div][0], 0);
11077 len = ma->p[i]->v->size;
11078 isl_seq_cpy(bset->eq[k], ma->p[i]->v->el + 1, len - 1);
11079 isl_seq_clr(bset->eq[k] + len - 1, 1 + total - (len - 1));
11080 isl_int_neg(bset->eq[k][1 + total], ma->p[i]->v->el[0]);
11086 isl_basic_set_free(bset);
11090 /* Compute the preimage of "bset" under the function represented by "ma".
11091 * In other words, plug in "ma" in "bset". The result is a basic set
11092 * that lives in the domain space of "ma".
11094 * If bset is represented by
11096 * A(p) + B x + C(divs) >= 0
11098 * and ma is represented by
11100 * x = D(p) + F(y) + G(divs')
11102 * then the result is
11104 * A(p) + B D(p) + B F(y) + B G(divs') + C(divs) >= 0
11106 * The divs in the input set are similarly adjusted.
11109 * floor((a_i(p) + b_i x + c_i(divs))/n_i)
11113 * floor((a_i(p) + b_i D(p) + b_i F(y) + B_i G(divs') + c_i(divs))/n_i)
11115 * If bset is not a rational set and if F(y) involves any denominators
11117 * x_i = (f_i y + h_i)/m_i
11119 * the additional constraints are added to ensure that we only
11120 * map back integer points. That is we enforce
11122 * f_i y + h_i = m_i alpha_i
11124 * with alpha_i an additional existentially quantified variable.
11126 * We first copy over the divs from "ma".
11127 * Then we add the modified constraints and divs from "bset".
11128 * Finally, we add the stride constraints, if needed.
11130 __isl_give isl_basic_set *isl_basic_set_preimage_multi_aff(
11131 __isl_take isl_basic_set *bset, __isl_take isl_multi_aff *ma)
11135 isl_basic_set *res = NULL;
11136 int n_div_bset, n_div_ma;
11137 isl_int f, c1, c2, g;
11138 int rational, strides;
11145 ma = isl_multi_aff_align_divs(ma);
11148 if (check_basic_set_compatible_range_multi_aff(bset, ma) < 0)
11151 n_div_bset = isl_basic_set_dim(bset, isl_dim_div);
11152 n_div_ma = ma->n ? isl_aff_dim(ma->p[0], isl_dim_div) : 0;
11154 space = isl_space_domain(isl_multi_aff_get_space(ma));
11155 rational = isl_basic_set_is_rational(bset);
11156 strides = rational ? 0 : multi_aff_strides(ma);
11157 res = isl_basic_set_alloc_space(space, n_div_ma + n_div_bset + strides,
11158 bset->n_eq + strides, bset->n_ineq + 2 * n_div_ma);
11160 res = isl_basic_set_set_rational(res);
11162 for (i = 0; i < n_div_ma + n_div_bset; ++i)
11163 if (isl_basic_set_alloc_div(res) < 0)
11166 if (set_ma_divs(res, ma, n_div_ma) < 0)
11169 for (i = 0; i < bset->n_eq; ++i) {
11170 k = isl_basic_set_alloc_equality(res);
11173 isl_seq_preimage(res->eq[k], bset->eq[i], ma, n_div_ma,
11174 n_div_bset, f, c1, c2, g, 0);
11177 for (i = 0; i < bset->n_ineq; ++i) {
11178 k = isl_basic_set_alloc_inequality(res);
11181 isl_seq_preimage(res->ineq[k], bset->ineq[i], ma, n_div_ma,
11182 n_div_bset, f, c1, c2, g, 0);
11185 for (i = 0; i < bset->n_div; ++i) {
11186 if (isl_int_is_zero(bset->div[i][0])) {
11187 isl_int_set_si(res->div[n_div_ma + i][0], 0);
11190 isl_seq_preimage(res->div[n_div_ma + i], bset->div[i],
11191 ma, n_div_ma, n_div_bset, f, c1, c2, g, 1);
11195 res = add_ma_strides(res, ma);
11201 isl_basic_set_free(bset);
11202 isl_multi_aff_free(ma);
11203 res = isl_basic_set_simplify(res);
11204 return isl_basic_set_finalize(res);
11210 isl_basic_set_free(bset);
11211 isl_multi_aff_free(ma);
11212 isl_basic_set_free(res);
11216 /* Check if the range of "ma" is compatible with "set".
11217 * Return -1 if anything is wrong.
11219 static int check_set_compatible_range_multi_aff(
11220 __isl_keep isl_set *set, __isl_keep isl_multi_aff *ma)
11222 return check_space_compatible_range_multi_aff(set->dim, ma);
11225 /* Compute the preimage of "set" under the function represented by "ma".
11226 * In other words, plug in "ma" in "set. The result is a set
11227 * that lives in the domain space of "ma".
11229 static __isl_give isl_set *set_preimage_multi_aff(__isl_take isl_set *set,
11230 __isl_take isl_multi_aff *ma)
11234 set = isl_set_cow(set);
11235 ma = isl_multi_aff_align_divs(ma);
11238 if (check_set_compatible_range_multi_aff(set, ma) < 0)
11241 for (i = 0; i < set->n; ++i) {
11242 set->p[i] = isl_basic_set_preimage_multi_aff(set->p[i],
11243 isl_multi_aff_copy(ma));
11248 isl_space_free(set->dim);
11249 set->dim = isl_multi_aff_get_domain_space(ma);
11253 isl_multi_aff_free(ma);
11255 ISL_F_CLR(set, ISL_MAP_DISJOINT);
11256 ISL_F_CLR(set, ISL_SET_NORMALIZED);
11259 isl_multi_aff_free(ma);
11264 __isl_give isl_set *isl_set_preimage_multi_aff(__isl_take isl_set *set,
11265 __isl_take isl_multi_aff *ma)
11270 if (isl_space_match(set->dim, isl_dim_param, ma->space, isl_dim_param))
11271 return set_preimage_multi_aff(set, ma);
11273 if (!isl_space_has_named_params(set->dim) ||
11274 !isl_space_has_named_params(ma->space))
11275 isl_die(set->ctx, isl_error_invalid,
11276 "unaligned unnamed parameters", goto error);
11277 set = isl_set_align_params(set, isl_multi_aff_get_space(ma));
11278 ma = isl_multi_aff_align_params(ma, isl_set_get_space(set));
11280 return set_preimage_multi_aff(set, ma);
11282 isl_multi_aff_free(ma);
11283 return isl_set_free(set);
11286 /* Compute the preimage of "set" under the function represented by "pma".
11287 * In other words, plug in "pma" in "set. The result is a set
11288 * that lives in the domain space of "pma".
11290 static __isl_give isl_set *set_preimage_pw_multi_aff(__isl_take isl_set *set,
11291 __isl_take isl_pw_multi_aff *pma)
11300 isl_pw_multi_aff_free(pma);
11301 res = isl_set_empty(isl_set_get_space(set));
11306 res = isl_set_preimage_multi_aff(isl_set_copy(set),
11307 isl_multi_aff_copy(pma->p[0].maff));
11308 res = isl_set_intersect(res, isl_set_copy(pma->p[0].set));
11310 for (i = 1; i < pma->n; ++i) {
11313 res_i = isl_set_preimage_multi_aff(isl_set_copy(set),
11314 isl_multi_aff_copy(pma->p[i].maff));
11315 res_i = isl_set_intersect(res_i, isl_set_copy(pma->p[i].set));
11316 res = isl_set_union(res, res_i);
11319 isl_pw_multi_aff_free(pma);
11323 isl_pw_multi_aff_free(pma);
11328 __isl_give isl_set *isl_set_preimage_pw_multi_aff(__isl_take isl_set *set,
11329 __isl_take isl_pw_multi_aff *pma)
11334 if (isl_space_match(set->dim, isl_dim_param, pma->dim, isl_dim_param))
11335 return set_preimage_pw_multi_aff(set, pma);
11337 if (!isl_space_has_named_params(set->dim) ||
11338 !isl_space_has_named_params(pma->dim))
11339 isl_die(set->ctx, isl_error_invalid,
11340 "unaligned unnamed parameters", goto error);
11341 set = isl_set_align_params(set, isl_pw_multi_aff_get_space(pma));
11342 pma = isl_pw_multi_aff_align_params(pma, isl_set_get_space(set));
11344 return set_preimage_pw_multi_aff(set, pma);
11346 isl_pw_multi_aff_free(pma);
11347 return isl_set_free(set);