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 /* Turn inequality "pos" of "bmap" into an equality.
1150 * In particular, we move the inequality in front of the equalities
1151 * and move the last inequality in the position of the moved inequality.
1152 * Note that isl_tab_make_equalities_explicit depends on this particular
1153 * change in the ordering of the constraints.
1155 void isl_basic_map_inequality_to_equality(
1156 struct isl_basic_map *bmap, unsigned pos)
1160 t = bmap->ineq[pos];
1161 bmap->ineq[pos] = bmap->ineq[bmap->n_ineq - 1];
1162 bmap->ineq[bmap->n_ineq - 1] = bmap->eq[-1];
1167 ISL_F_CLR(bmap, ISL_BASIC_MAP_NO_REDUNDANT);
1168 ISL_F_CLR(bmap, ISL_BASIC_MAP_NORMALIZED);
1169 ISL_F_CLR(bmap, ISL_BASIC_MAP_NORMALIZED_DIVS);
1170 ISL_F_CLR(bmap, ISL_BASIC_MAP_ALL_EQUALITIES);
1173 static int room_for_ineq(struct isl_basic_map *bmap, unsigned n)
1175 return bmap->n_ineq + n <= bmap->eq - bmap->ineq;
1178 int isl_basic_map_alloc_inequality(struct isl_basic_map *bmap)
1180 struct isl_ctx *ctx;
1184 isl_assert(ctx, room_for_ineq(bmap, 1), return -1);
1185 ISL_F_CLR(bmap, ISL_BASIC_MAP_NO_IMPLICIT);
1186 ISL_F_CLR(bmap, ISL_BASIC_MAP_NO_REDUNDANT);
1187 ISL_F_CLR(bmap, ISL_BASIC_MAP_NORMALIZED);
1188 ISL_F_CLR(bmap, ISL_BASIC_MAP_ALL_EQUALITIES);
1189 isl_seq_clr(bmap->ineq[bmap->n_ineq] +
1190 1 + isl_basic_map_total_dim(bmap),
1191 bmap->extra - bmap->n_div);
1192 return bmap->n_ineq++;
1195 int isl_basic_set_alloc_inequality(struct isl_basic_set *bset)
1197 return isl_basic_map_alloc_inequality((struct isl_basic_map *)bset);
1200 int isl_basic_map_free_inequality(struct isl_basic_map *bmap, unsigned n)
1204 isl_assert(bmap->ctx, n <= bmap->n_ineq, return -1);
1209 int isl_basic_set_free_inequality(struct isl_basic_set *bset, unsigned n)
1211 return isl_basic_map_free_inequality((struct isl_basic_map *)bset, n);
1214 int isl_basic_map_drop_inequality(struct isl_basic_map *bmap, unsigned pos)
1219 isl_assert(bmap->ctx, pos < bmap->n_ineq, return -1);
1221 if (pos != bmap->n_ineq - 1) {
1222 t = bmap->ineq[pos];
1223 bmap->ineq[pos] = bmap->ineq[bmap->n_ineq - 1];
1224 bmap->ineq[bmap->n_ineq - 1] = t;
1225 ISL_F_CLR(bmap, ISL_BASIC_MAP_NORMALIZED);
1231 int isl_basic_set_drop_inequality(struct isl_basic_set *bset, unsigned pos)
1233 return isl_basic_map_drop_inequality((struct isl_basic_map *)bset, pos);
1236 __isl_give isl_basic_map *isl_basic_map_add_eq(__isl_take isl_basic_map *bmap,
1241 bmap = isl_basic_map_extend_constraints(bmap, 1, 0);
1244 k = isl_basic_map_alloc_equality(bmap);
1247 isl_seq_cpy(bmap->eq[k], eq, 1 + isl_basic_map_total_dim(bmap));
1250 isl_basic_map_free(bmap);
1254 __isl_give isl_basic_set *isl_basic_set_add_eq(__isl_take isl_basic_set *bset,
1257 return (isl_basic_set *)
1258 isl_basic_map_add_eq((isl_basic_map *)bset, eq);
1261 __isl_give isl_basic_map *isl_basic_map_add_ineq(__isl_take isl_basic_map *bmap,
1266 bmap = isl_basic_map_extend_constraints(bmap, 0, 1);
1269 k = isl_basic_map_alloc_inequality(bmap);
1272 isl_seq_cpy(bmap->ineq[k], ineq, 1 + isl_basic_map_total_dim(bmap));
1275 isl_basic_map_free(bmap);
1279 __isl_give isl_basic_set *isl_basic_set_add_ineq(__isl_take isl_basic_set *bset,
1282 return (isl_basic_set *)
1283 isl_basic_map_add_ineq((isl_basic_map *)bset, ineq);
1286 int isl_basic_map_alloc_div(struct isl_basic_map *bmap)
1290 isl_assert(bmap->ctx, bmap->n_div < bmap->extra, return -1);
1291 isl_seq_clr(bmap->div[bmap->n_div] +
1292 1 + 1 + isl_basic_map_total_dim(bmap),
1293 bmap->extra - bmap->n_div);
1294 ISL_F_CLR(bmap, ISL_BASIC_MAP_NORMALIZED_DIVS);
1295 return bmap->n_div++;
1298 int isl_basic_set_alloc_div(struct isl_basic_set *bset)
1300 return isl_basic_map_alloc_div((struct isl_basic_map *)bset);
1303 int isl_basic_map_free_div(struct isl_basic_map *bmap, unsigned n)
1307 isl_assert(bmap->ctx, n <= bmap->n_div, return -1);
1312 int isl_basic_set_free_div(struct isl_basic_set *bset, unsigned n)
1314 return isl_basic_map_free_div((struct isl_basic_map *)bset, n);
1317 /* Copy constraint from src to dst, putting the vars of src at offset
1318 * dim_off in dst and the divs of src at offset div_off in dst.
1319 * If both sets are actually map, then dim_off applies to the input
1322 static void copy_constraint(struct isl_basic_map *dst_map, isl_int *dst,
1323 struct isl_basic_map *src_map, isl_int *src,
1324 unsigned in_off, unsigned out_off, unsigned div_off)
1326 unsigned src_nparam = isl_basic_map_n_param(src_map);
1327 unsigned dst_nparam = isl_basic_map_n_param(dst_map);
1328 unsigned src_in = isl_basic_map_n_in(src_map);
1329 unsigned dst_in = isl_basic_map_n_in(dst_map);
1330 unsigned src_out = isl_basic_map_n_out(src_map);
1331 unsigned dst_out = isl_basic_map_n_out(dst_map);
1332 isl_int_set(dst[0], src[0]);
1333 isl_seq_cpy(dst+1, src+1, isl_min(dst_nparam, src_nparam));
1334 if (dst_nparam > src_nparam)
1335 isl_seq_clr(dst+1+src_nparam,
1336 dst_nparam - src_nparam);
1337 isl_seq_clr(dst+1+dst_nparam, in_off);
1338 isl_seq_cpy(dst+1+dst_nparam+in_off,
1340 isl_min(dst_in-in_off, src_in));
1341 if (dst_in-in_off > src_in)
1342 isl_seq_clr(dst+1+dst_nparam+in_off+src_in,
1343 dst_in - in_off - src_in);
1344 isl_seq_clr(dst+1+dst_nparam+dst_in, out_off);
1345 isl_seq_cpy(dst+1+dst_nparam+dst_in+out_off,
1346 src+1+src_nparam+src_in,
1347 isl_min(dst_out-out_off, src_out));
1348 if (dst_out-out_off > src_out)
1349 isl_seq_clr(dst+1+dst_nparam+dst_in+out_off+src_out,
1350 dst_out - out_off - src_out);
1351 isl_seq_clr(dst+1+dst_nparam+dst_in+dst_out, div_off);
1352 isl_seq_cpy(dst+1+dst_nparam+dst_in+dst_out+div_off,
1353 src+1+src_nparam+src_in+src_out,
1354 isl_min(dst_map->extra-div_off, src_map->n_div));
1355 if (dst_map->n_div-div_off > src_map->n_div)
1356 isl_seq_clr(dst+1+dst_nparam+dst_in+dst_out+
1357 div_off+src_map->n_div,
1358 dst_map->n_div - div_off - src_map->n_div);
1361 static void copy_div(struct isl_basic_map *dst_map, isl_int *dst,
1362 struct isl_basic_map *src_map, isl_int *src,
1363 unsigned in_off, unsigned out_off, unsigned div_off)
1365 isl_int_set(dst[0], src[0]);
1366 copy_constraint(dst_map, dst+1, src_map, src+1, in_off, out_off, div_off);
1369 static struct isl_basic_map *add_constraints(struct isl_basic_map *bmap1,
1370 struct isl_basic_map *bmap2, unsigned i_pos, unsigned o_pos)
1375 if (!bmap1 || !bmap2)
1378 div_off = bmap1->n_div;
1380 for (i = 0; i < bmap2->n_eq; ++i) {
1381 int i1 = isl_basic_map_alloc_equality(bmap1);
1384 copy_constraint(bmap1, bmap1->eq[i1], bmap2, bmap2->eq[i],
1385 i_pos, o_pos, div_off);
1388 for (i = 0; i < bmap2->n_ineq; ++i) {
1389 int i1 = isl_basic_map_alloc_inequality(bmap1);
1392 copy_constraint(bmap1, bmap1->ineq[i1], bmap2, bmap2->ineq[i],
1393 i_pos, o_pos, div_off);
1396 for (i = 0; i < bmap2->n_div; ++i) {
1397 int i1 = isl_basic_map_alloc_div(bmap1);
1400 copy_div(bmap1, bmap1->div[i1], bmap2, bmap2->div[i],
1401 i_pos, o_pos, div_off);
1404 isl_basic_map_free(bmap2);
1409 isl_basic_map_free(bmap1);
1410 isl_basic_map_free(bmap2);
1414 struct isl_basic_set *isl_basic_set_add_constraints(struct isl_basic_set *bset1,
1415 struct isl_basic_set *bset2, unsigned pos)
1417 return (struct isl_basic_set *)
1418 add_constraints((struct isl_basic_map *)bset1,
1419 (struct isl_basic_map *)bset2, 0, pos);
1422 struct isl_basic_map *isl_basic_map_extend_space(struct isl_basic_map *base,
1423 __isl_take isl_space *dim, unsigned extra,
1424 unsigned n_eq, unsigned n_ineq)
1426 struct isl_basic_map *ext;
1436 dims_ok = isl_space_is_equal(base->dim, dim) &&
1437 base->extra >= base->n_div + extra;
1439 if (dims_ok && room_for_con(base, n_eq + n_ineq) &&
1440 room_for_ineq(base, n_ineq)) {
1441 isl_space_free(dim);
1445 isl_assert(base->ctx, base->dim->nparam <= dim->nparam, goto error);
1446 isl_assert(base->ctx, base->dim->n_in <= dim->n_in, goto error);
1447 isl_assert(base->ctx, base->dim->n_out <= dim->n_out, goto error);
1448 extra += base->extra;
1450 n_ineq += base->n_ineq;
1452 ext = isl_basic_map_alloc_space(dim, extra, n_eq, n_ineq);
1458 ext->sample = isl_vec_copy(base->sample);
1459 flags = base->flags;
1460 ext = add_constraints(ext, base, 0, 0);
1463 ISL_F_CLR(ext, ISL_BASIC_SET_FINAL);
1469 isl_space_free(dim);
1470 isl_basic_map_free(base);
1474 struct isl_basic_set *isl_basic_set_extend_space(struct isl_basic_set *base,
1475 __isl_take isl_space *dim, unsigned extra,
1476 unsigned n_eq, unsigned n_ineq)
1478 return (struct isl_basic_set *)
1479 isl_basic_map_extend_space((struct isl_basic_map *)base, dim,
1480 extra, n_eq, n_ineq);
1483 struct isl_basic_map *isl_basic_map_extend_constraints(
1484 struct isl_basic_map *base, unsigned n_eq, unsigned n_ineq)
1488 return isl_basic_map_extend_space(base, isl_space_copy(base->dim),
1492 struct isl_basic_map *isl_basic_map_extend(struct isl_basic_map *base,
1493 unsigned nparam, unsigned n_in, unsigned n_out, unsigned extra,
1494 unsigned n_eq, unsigned n_ineq)
1496 struct isl_basic_map *bmap;
1501 dim = isl_space_alloc(base->ctx, nparam, n_in, n_out);
1505 bmap = isl_basic_map_extend_space(base, dim, extra, n_eq, n_ineq);
1508 isl_basic_map_free(base);
1512 struct isl_basic_set *isl_basic_set_extend(struct isl_basic_set *base,
1513 unsigned nparam, unsigned dim, unsigned extra,
1514 unsigned n_eq, unsigned n_ineq)
1516 return (struct isl_basic_set *)
1517 isl_basic_map_extend((struct isl_basic_map *)base,
1518 nparam, 0, dim, extra, n_eq, n_ineq);
1521 struct isl_basic_set *isl_basic_set_extend_constraints(
1522 struct isl_basic_set *base, unsigned n_eq, unsigned n_ineq)
1524 return (struct isl_basic_set *)
1525 isl_basic_map_extend_constraints((struct isl_basic_map *)base,
1529 struct isl_basic_set *isl_basic_set_cow(struct isl_basic_set *bset)
1531 return (struct isl_basic_set *)
1532 isl_basic_map_cow((struct isl_basic_map *)bset);
1535 struct isl_basic_map *isl_basic_map_cow(struct isl_basic_map *bmap)
1540 if (bmap->ref > 1) {
1542 bmap = isl_basic_map_dup(bmap);
1545 ISL_F_CLR(bmap, ISL_BASIC_SET_FINAL);
1549 struct isl_set *isl_set_cow(struct isl_set *set)
1557 return isl_set_dup(set);
1560 struct isl_map *isl_map_cow(struct isl_map *map)
1568 return isl_map_dup(map);
1571 static void swap_vars(struct isl_blk blk, isl_int *a,
1572 unsigned a_len, unsigned b_len)
1574 isl_seq_cpy(blk.data, a+a_len, b_len);
1575 isl_seq_cpy(blk.data+b_len, a, a_len);
1576 isl_seq_cpy(a, blk.data, b_len+a_len);
1579 static __isl_give isl_basic_map *isl_basic_map_swap_vars(
1580 __isl_take isl_basic_map *bmap, unsigned pos, unsigned n1, unsigned n2)
1588 isl_assert(bmap->ctx,
1589 pos + n1 + n2 <= 1 + isl_basic_map_total_dim(bmap), goto error);
1591 if (n1 == 0 || n2 == 0)
1594 bmap = isl_basic_map_cow(bmap);
1598 blk = isl_blk_alloc(bmap->ctx, n1 + n2);
1599 if (isl_blk_is_error(blk))
1602 for (i = 0; i < bmap->n_eq; ++i)
1604 bmap->eq[i] + pos, n1, n2);
1606 for (i = 0; i < bmap->n_ineq; ++i)
1608 bmap->ineq[i] + pos, n1, n2);
1610 for (i = 0; i < bmap->n_div; ++i)
1612 bmap->div[i]+1 + pos, n1, n2);
1614 isl_blk_free(bmap->ctx, blk);
1616 ISL_F_CLR(bmap, ISL_BASIC_SET_NORMALIZED);
1617 bmap = isl_basic_map_gauss(bmap, NULL);
1618 return isl_basic_map_finalize(bmap);
1620 isl_basic_map_free(bmap);
1624 static __isl_give isl_basic_set *isl_basic_set_swap_vars(
1625 __isl_take isl_basic_set *bset, unsigned n)
1633 nparam = isl_basic_set_n_param(bset);
1634 dim = isl_basic_set_n_dim(bset);
1635 isl_assert(bset->ctx, n <= dim, goto error);
1637 return isl_basic_map_swap_vars(bset, 1 + nparam, n, dim - n);
1639 isl_basic_set_free(bset);
1643 struct isl_basic_map *isl_basic_map_set_to_empty(struct isl_basic_map *bmap)
1649 total = isl_basic_map_total_dim(bmap);
1650 isl_basic_map_free_div(bmap, bmap->n_div);
1651 isl_basic_map_free_inequality(bmap, bmap->n_ineq);
1653 isl_basic_map_free_equality(bmap, bmap->n_eq-1);
1655 i = isl_basic_map_alloc_equality(bmap);
1659 isl_int_set_si(bmap->eq[i][0], 1);
1660 isl_seq_clr(bmap->eq[i]+1, total);
1661 ISL_F_SET(bmap, ISL_BASIC_MAP_EMPTY);
1662 isl_vec_free(bmap->sample);
1663 bmap->sample = NULL;
1664 return isl_basic_map_finalize(bmap);
1666 isl_basic_map_free(bmap);
1670 struct isl_basic_set *isl_basic_set_set_to_empty(struct isl_basic_set *bset)
1672 return (struct isl_basic_set *)
1673 isl_basic_map_set_to_empty((struct isl_basic_map *)bset);
1676 /* Swap divs "a" and "b" in "bmap" (without modifying any of the constraints
1679 static void swap_div(__isl_keep isl_basic_map *bmap, int a, int b)
1681 isl_int *t = bmap->div[a];
1682 bmap->div[a] = bmap->div[b];
1686 /* Swap divs "a" and "b" in "bmap" and adjust the constraints and
1687 * div definitions accordingly.
1689 void isl_basic_map_swap_div(struct isl_basic_map *bmap, int a, int b)
1692 unsigned off = isl_space_dim(bmap->dim, isl_dim_all);
1694 swap_div(bmap, a, b);
1696 for (i = 0; i < bmap->n_eq; ++i)
1697 isl_int_swap(bmap->eq[i][1+off+a], bmap->eq[i][1+off+b]);
1699 for (i = 0; i < bmap->n_ineq; ++i)
1700 isl_int_swap(bmap->ineq[i][1+off+a], bmap->ineq[i][1+off+b]);
1702 for (i = 0; i < bmap->n_div; ++i)
1703 isl_int_swap(bmap->div[i][1+1+off+a], bmap->div[i][1+1+off+b]);
1704 ISL_F_CLR(bmap, ISL_BASIC_MAP_NORMALIZED);
1707 /* Eliminate the specified n dimensions starting at first from the
1708 * constraints, without removing the dimensions from the space.
1709 * If the set is rational, the dimensions are eliminated using Fourier-Motzkin.
1711 __isl_give isl_map *isl_map_eliminate(__isl_take isl_map *map,
1712 enum isl_dim_type type, unsigned first, unsigned n)
1721 if (first + n > isl_map_dim(map, type) || first + n < first)
1722 isl_die(map->ctx, isl_error_invalid,
1723 "index out of bounds", goto error);
1725 map = isl_map_cow(map);
1729 for (i = 0; i < map->n; ++i) {
1730 map->p[i] = isl_basic_map_eliminate(map->p[i], type, first, n);
1740 /* Eliminate the specified n dimensions starting at first from the
1741 * constraints, without removing the dimensions from the space.
1742 * If the set is rational, the dimensions are eliminated using Fourier-Motzkin.
1744 __isl_give isl_set *isl_set_eliminate(__isl_take isl_set *set,
1745 enum isl_dim_type type, unsigned first, unsigned n)
1747 return (isl_set *)isl_map_eliminate((isl_map *)set, type, first, n);
1750 /* Eliminate the specified n dimensions starting at first from the
1751 * constraints, without removing the dimensions from the space.
1752 * If the set is rational, the dimensions are eliminated using Fourier-Motzkin.
1754 __isl_give isl_set *isl_set_eliminate_dims(__isl_take isl_set *set,
1755 unsigned first, unsigned n)
1757 return isl_set_eliminate(set, isl_dim_set, first, n);
1760 __isl_give isl_basic_map *isl_basic_map_remove_divs(
1761 __isl_take isl_basic_map *bmap)
1765 bmap = isl_basic_map_eliminate_vars(bmap,
1766 isl_space_dim(bmap->dim, isl_dim_all), bmap->n_div);
1770 return isl_basic_map_finalize(bmap);
1773 __isl_give isl_basic_set *isl_basic_set_remove_divs(
1774 __isl_take isl_basic_set *bset)
1776 return (struct isl_basic_set *)isl_basic_map_remove_divs(
1777 (struct isl_basic_map *)bset);
1780 __isl_give isl_map *isl_map_remove_divs(__isl_take isl_map *map)
1789 map = isl_map_cow(map);
1793 for (i = 0; i < map->n; ++i) {
1794 map->p[i] = isl_basic_map_remove_divs(map->p[i]);
1804 __isl_give isl_set *isl_set_remove_divs(__isl_take isl_set *set)
1806 return isl_map_remove_divs(set);
1809 struct isl_basic_map *isl_basic_map_remove_dims(struct isl_basic_map *bmap,
1810 enum isl_dim_type type, unsigned first, unsigned n)
1814 isl_assert(bmap->ctx, first + n <= isl_basic_map_dim(bmap, type),
1816 if (n == 0 && !isl_space_is_named_or_nested(bmap->dim, type))
1818 bmap = isl_basic_map_eliminate_vars(bmap,
1819 isl_basic_map_offset(bmap, type) - 1 + first, n);
1822 if (ISL_F_ISSET(bmap, ISL_BASIC_MAP_EMPTY) && type == isl_dim_div)
1824 bmap = isl_basic_map_drop(bmap, type, first, n);
1827 isl_basic_map_free(bmap);
1831 /* Return true if the definition of the given div (recursively) involves
1832 * any of the given variables.
1834 static int div_involves_vars(__isl_keep isl_basic_map *bmap, int div,
1835 unsigned first, unsigned n)
1838 unsigned div_offset = isl_basic_map_offset(bmap, isl_dim_div);
1840 if (isl_int_is_zero(bmap->div[div][0]))
1842 if (isl_seq_first_non_zero(bmap->div[div] + 1 + first, n) >= 0)
1845 for (i = bmap->n_div - 1; i >= 0; --i) {
1846 if (isl_int_is_zero(bmap->div[div][1 + div_offset + i]))
1848 if (div_involves_vars(bmap, i, first, n))
1855 /* Try and add a lower and/or upper bound on "div" to "bmap"
1856 * based on inequality "i".
1857 * "total" is the total number of variables (excluding the divs).
1858 * "v" is a temporary object that can be used during the calculations.
1859 * If "lb" is set, then a lower bound should be constructed.
1860 * If "ub" is set, then an upper bound should be constructed.
1862 * The calling function has already checked that the inequality does not
1863 * reference "div", but we still need to check that the inequality is
1864 * of the right form. We'll consider the case where we want to construct
1865 * a lower bound. The construction of upper bounds is similar.
1867 * Let "div" be of the form
1869 * q = floor((a + f(x))/d)
1871 * We essentially check if constraint "i" is of the form
1875 * so that we can use it to derive a lower bound on "div".
1876 * However, we allow a slightly more general form
1880 * with the condition that the coefficients of g(x) - f(x) are all
1882 * Rewriting this constraint as
1886 * adding a + f(x) to both sides and dividing by d, we obtain
1888 * (a + f(x))/d >= (a-b)/d + (f(x)-g(x))/d
1890 * Taking the floor on both sides, we obtain
1892 * q >= floor((a-b)/d) + (f(x)-g(x))/d
1896 * (g(x)-f(x))/d + ceil((b-a)/d) + q >= 0
1898 * In the case of an upper bound, we construct the constraint
1900 * (g(x)+f(x))/d + floor((b+a)/d) - q >= 0
1903 static __isl_give isl_basic_map *insert_bounds_on_div_from_ineq(
1904 __isl_take isl_basic_map *bmap, int div, int i,
1905 unsigned total, isl_int v, int lb, int ub)
1909 for (j = 0; (lb || ub) && j < total + bmap->n_div; ++j) {
1911 isl_int_sub(v, bmap->ineq[i][1 + j],
1912 bmap->div[div][1 + 1 + j]);
1913 lb = isl_int_is_divisible_by(v, bmap->div[div][0]);
1916 isl_int_add(v, bmap->ineq[i][1 + j],
1917 bmap->div[div][1 + 1 + j]);
1918 ub = isl_int_is_divisible_by(v, bmap->div[div][0]);
1924 bmap = isl_basic_map_extend_constraints(bmap, 0, lb + ub);
1926 int k = isl_basic_map_alloc_inequality(bmap);
1929 for (j = 0; j < 1 + total + bmap->n_div; ++j) {
1930 isl_int_sub(bmap->ineq[k][j], bmap->ineq[i][j],
1931 bmap->div[div][1 + j]);
1932 isl_int_cdiv_q(bmap->ineq[k][j],
1933 bmap->ineq[k][j], bmap->div[div][0]);
1935 isl_int_set_si(bmap->ineq[k][1 + total + div], 1);
1938 int k = isl_basic_map_alloc_inequality(bmap);
1941 for (j = 0; j < 1 + total + bmap->n_div; ++j) {
1942 isl_int_add(bmap->ineq[k][j], bmap->ineq[i][j],
1943 bmap->div[div][1 + j]);
1944 isl_int_fdiv_q(bmap->ineq[k][j],
1945 bmap->ineq[k][j], bmap->div[div][0]);
1947 isl_int_set_si(bmap->ineq[k][1 + total + div], -1);
1952 isl_basic_map_free(bmap);
1956 /* This function is called right before "div" is eliminated from "bmap"
1957 * using Fourier-Motzkin.
1958 * Look through the constraints of "bmap" for constraints on the argument
1959 * of the integer division and use them to construct constraints on the
1960 * integer division itself. These constraints can then be combined
1961 * during the Fourier-Motzkin elimination.
1962 * Note that it is only useful to introduce lower bounds on "div"
1963 * if "bmap" already contains upper bounds on "div" as the newly
1964 * introduce lower bounds can then be combined with the pre-existing
1965 * upper bounds. Similarly for upper bounds.
1966 * We therefore first check if "bmap" contains any lower and/or upper bounds
1969 * It is interesting to note that the introduction of these constraints
1970 * can indeed lead to more accurate results, even when compared to
1971 * deriving constraints on the argument of "div" from constraints on "div".
1972 * Consider, for example, the set
1974 * { [i,j,k] : 3 + i + 2j >= 0 and 2 * [(i+2j)/4] <= k }
1976 * The second constraint can be rewritten as
1978 * 2 * [(-i-2j+3)/4] + k >= 0
1980 * from which we can derive
1982 * -i - 2j + 3 >= -2k
1988 * Combined with the first constraint, we obtain
1990 * -3 <= 3 + 2k or k >= -3
1992 * If, on the other hand we derive a constraint on [(i+2j)/4] from
1993 * the first constraint, we obtain
1995 * [(i + 2j)/4] >= [-3/4] = -1
1997 * Combining this constraint with the second constraint, we obtain
2001 static __isl_give isl_basic_map *insert_bounds_on_div(
2002 __isl_take isl_basic_map *bmap, int div)
2005 int check_lb, check_ub;
2012 if (isl_int_is_zero(bmap->div[div][0]))
2015 total = isl_space_dim(bmap->dim, isl_dim_all);
2019 for (i = 0; (!check_lb || !check_ub) && i < bmap->n_ineq; ++i) {
2020 int s = isl_int_sgn(bmap->ineq[i][1 + total + div]);
2027 if (!check_lb && !check_ub)
2032 for (i = 0; bmap && i < bmap->n_ineq; ++i) {
2033 if (!isl_int_is_zero(bmap->ineq[i][1 + total + div]))
2036 bmap = insert_bounds_on_div_from_ineq(bmap, div, i, total, v,
2037 check_lb, check_ub);
2045 /* Remove all divs (recursively) involving any of the given dimensions
2046 * in their definitions.
2048 __isl_give isl_basic_map *isl_basic_map_remove_divs_involving_dims(
2049 __isl_take isl_basic_map *bmap,
2050 enum isl_dim_type type, unsigned first, unsigned n)
2056 isl_assert(bmap->ctx, first + n <= isl_basic_map_dim(bmap, type),
2058 first += isl_basic_map_offset(bmap, type);
2060 for (i = bmap->n_div - 1; i >= 0; --i) {
2061 if (!div_involves_vars(bmap, i, first, n))
2063 bmap = insert_bounds_on_div(bmap, i);
2064 bmap = isl_basic_map_remove_dims(bmap, isl_dim_div, i, 1);
2072 isl_basic_map_free(bmap);
2076 __isl_give isl_basic_set *isl_basic_set_remove_divs_involving_dims(
2077 __isl_take isl_basic_set *bset,
2078 enum isl_dim_type type, unsigned first, unsigned n)
2080 return isl_basic_map_remove_divs_involving_dims(bset, type, first, n);
2083 __isl_give isl_map *isl_map_remove_divs_involving_dims(__isl_take isl_map *map,
2084 enum isl_dim_type type, unsigned first, unsigned n)
2093 map = isl_map_cow(map);
2097 for (i = 0; i < map->n; ++i) {
2098 map->p[i] = isl_basic_map_remove_divs_involving_dims(map->p[i],
2109 __isl_give isl_set *isl_set_remove_divs_involving_dims(__isl_take isl_set *set,
2110 enum isl_dim_type type, unsigned first, unsigned n)
2112 return (isl_set *)isl_map_remove_divs_involving_dims((isl_map *)set,
2116 /* Does the desciption of "bmap" depend on the specified dimensions?
2117 * We also check whether the dimensions appear in any of the div definitions.
2118 * In principle there is no need for this check. If the dimensions appear
2119 * in a div definition, they also appear in the defining constraints of that
2122 int isl_basic_map_involves_dims(__isl_keep isl_basic_map *bmap,
2123 enum isl_dim_type type, unsigned first, unsigned n)
2130 if (first + n > isl_basic_map_dim(bmap, type))
2131 isl_die(bmap->ctx, isl_error_invalid,
2132 "index out of bounds", return -1);
2134 first += isl_basic_map_offset(bmap, type);
2135 for (i = 0; i < bmap->n_eq; ++i)
2136 if (isl_seq_first_non_zero(bmap->eq[i] + first, n) >= 0)
2138 for (i = 0; i < bmap->n_ineq; ++i)
2139 if (isl_seq_first_non_zero(bmap->ineq[i] + first, n) >= 0)
2141 for (i = 0; i < bmap->n_div; ++i) {
2142 if (isl_int_is_zero(bmap->div[i][0]))
2144 if (isl_seq_first_non_zero(bmap->div[i] + 1 + first, n) >= 0)
2151 int isl_map_involves_dims(__isl_keep isl_map *map,
2152 enum isl_dim_type type, unsigned first, unsigned n)
2159 if (first + n > isl_map_dim(map, type))
2160 isl_die(map->ctx, isl_error_invalid,
2161 "index out of bounds", return -1);
2163 for (i = 0; i < map->n; ++i) {
2164 int involves = isl_basic_map_involves_dims(map->p[i],
2166 if (involves < 0 || involves)
2173 int isl_basic_set_involves_dims(__isl_keep isl_basic_set *bset,
2174 enum isl_dim_type type, unsigned first, unsigned n)
2176 return isl_basic_map_involves_dims(bset, type, first, n);
2179 int isl_set_involves_dims(__isl_keep isl_set *set,
2180 enum isl_dim_type type, unsigned first, unsigned n)
2182 return isl_map_involves_dims(set, type, first, n);
2185 /* Return true if the definition of the given div is unknown or depends
2188 static int div_is_unknown(__isl_keep isl_basic_map *bmap, int div)
2191 unsigned div_offset = isl_basic_map_offset(bmap, isl_dim_div);
2193 if (isl_int_is_zero(bmap->div[div][0]))
2196 for (i = bmap->n_div - 1; i >= 0; --i) {
2197 if (isl_int_is_zero(bmap->div[div][1 + div_offset + i]))
2199 if (div_is_unknown(bmap, i))
2206 /* Remove all divs that are unknown or defined in terms of unknown divs.
2208 __isl_give isl_basic_map *isl_basic_map_remove_unknown_divs(
2209 __isl_take isl_basic_map *bmap)
2216 for (i = bmap->n_div - 1; i >= 0; --i) {
2217 if (!div_is_unknown(bmap, i))
2219 bmap = isl_basic_map_remove_dims(bmap, isl_dim_div, i, 1);
2228 /* Remove all divs that are unknown or defined in terms of unknown divs.
2230 __isl_give isl_basic_set *isl_basic_set_remove_unknown_divs(
2231 __isl_take isl_basic_set *bset)
2233 return isl_basic_map_remove_unknown_divs(bset);
2236 __isl_give isl_map *isl_map_remove_unknown_divs(__isl_take isl_map *map)
2245 map = isl_map_cow(map);
2249 for (i = 0; i < map->n; ++i) {
2250 map->p[i] = isl_basic_map_remove_unknown_divs(map->p[i]);
2260 __isl_give isl_set *isl_set_remove_unknown_divs(__isl_take isl_set *set)
2262 return (isl_set *)isl_map_remove_unknown_divs((isl_map *)set);
2265 __isl_give isl_basic_set *isl_basic_set_remove_dims(
2266 __isl_take isl_basic_set *bset,
2267 enum isl_dim_type type, unsigned first, unsigned n)
2269 return (isl_basic_set *)
2270 isl_basic_map_remove_dims((isl_basic_map *)bset, type, first, n);
2273 struct isl_map *isl_map_remove_dims(struct isl_map *map,
2274 enum isl_dim_type type, unsigned first, unsigned n)
2281 map = isl_map_cow(map);
2284 isl_assert(map->ctx, first + n <= isl_map_dim(map, type), goto error);
2286 for (i = 0; i < map->n; ++i) {
2287 map->p[i] = isl_basic_map_eliminate_vars(map->p[i],
2288 isl_basic_map_offset(map->p[i], type) - 1 + first, n);
2292 map = isl_map_drop(map, type, first, n);
2299 __isl_give isl_set *isl_set_remove_dims(__isl_take isl_set *bset,
2300 enum isl_dim_type type, unsigned first, unsigned n)
2302 return (isl_set *)isl_map_remove_dims((isl_map *)bset, type, first, n);
2305 /* Project out n inputs starting at first using Fourier-Motzkin */
2306 struct isl_map *isl_map_remove_inputs(struct isl_map *map,
2307 unsigned first, unsigned n)
2309 return isl_map_remove_dims(map, isl_dim_in, first, n);
2312 static void dump_term(struct isl_basic_map *bmap,
2313 isl_int c, int pos, FILE *out)
2316 unsigned in = isl_basic_map_n_in(bmap);
2317 unsigned dim = in + isl_basic_map_n_out(bmap);
2318 unsigned nparam = isl_basic_map_n_param(bmap);
2320 isl_int_print(out, c, 0);
2322 if (!isl_int_is_one(c))
2323 isl_int_print(out, c, 0);
2324 if (pos < 1 + nparam) {
2325 name = isl_space_get_dim_name(bmap->dim,
2326 isl_dim_param, pos - 1);
2328 fprintf(out, "%s", name);
2330 fprintf(out, "p%d", pos - 1);
2331 } else if (pos < 1 + nparam + in)
2332 fprintf(out, "i%d", pos - 1 - nparam);
2333 else if (pos < 1 + nparam + dim)
2334 fprintf(out, "o%d", pos - 1 - nparam - in);
2336 fprintf(out, "e%d", pos - 1 - nparam - dim);
2340 static void dump_constraint_sign(struct isl_basic_map *bmap, isl_int *c,
2341 int sign, FILE *out)
2345 unsigned len = 1 + isl_basic_map_total_dim(bmap);
2349 for (i = 0, first = 1; i < len; ++i) {
2350 if (isl_int_sgn(c[i]) * sign <= 0)
2353 fprintf(out, " + ");
2355 isl_int_abs(v, c[i]);
2356 dump_term(bmap, v, i, out);
2363 static void dump_constraint(struct isl_basic_map *bmap, isl_int *c,
2364 const char *op, FILE *out, int indent)
2368 fprintf(out, "%*s", indent, "");
2370 dump_constraint_sign(bmap, c, 1, out);
2371 fprintf(out, " %s ", op);
2372 dump_constraint_sign(bmap, c, -1, out);
2376 for (i = bmap->n_div; i < bmap->extra; ++i) {
2377 if (isl_int_is_zero(c[1+isl_space_dim(bmap->dim, isl_dim_all)+i]))
2379 fprintf(out, "%*s", indent, "");
2380 fprintf(out, "ERROR: unused div coefficient not zero\n");
2385 static void dump_constraints(struct isl_basic_map *bmap,
2386 isl_int **c, unsigned n,
2387 const char *op, FILE *out, int indent)
2391 for (i = 0; i < n; ++i)
2392 dump_constraint(bmap, c[i], op, out, indent);
2395 static void dump_affine(struct isl_basic_map *bmap, isl_int *exp, FILE *out)
2399 unsigned total = isl_basic_map_total_dim(bmap);
2401 for (j = 0; j < 1 + total; ++j) {
2402 if (isl_int_is_zero(exp[j]))
2404 if (!first && isl_int_is_pos(exp[j]))
2406 dump_term(bmap, exp[j], j, out);
2411 static void dump(struct isl_basic_map *bmap, FILE *out, int indent)
2415 dump_constraints(bmap, bmap->eq, bmap->n_eq, "=", out, indent);
2416 dump_constraints(bmap, bmap->ineq, bmap->n_ineq, ">=", out, indent);
2418 for (i = 0; i < bmap->n_div; ++i) {
2419 fprintf(out, "%*s", indent, "");
2420 fprintf(out, "e%d = [(", i);
2421 dump_affine(bmap, bmap->div[i]+1, out);
2423 isl_int_print(out, bmap->div[i][0], 0);
2424 fprintf(out, "]\n");
2428 void isl_basic_set_print_internal(struct isl_basic_set *bset,
2429 FILE *out, int indent)
2432 fprintf(out, "null basic set\n");
2436 fprintf(out, "%*s", indent, "");
2437 fprintf(out, "ref: %d, nparam: %d, dim: %d, extra: %d, flags: %x\n",
2438 bset->ref, bset->dim->nparam, bset->dim->n_out,
2439 bset->extra, bset->flags);
2440 dump((struct isl_basic_map *)bset, out, indent);
2443 void isl_basic_map_print_internal(struct isl_basic_map *bmap,
2444 FILE *out, int indent)
2447 fprintf(out, "null basic map\n");
2451 fprintf(out, "%*s", indent, "");
2452 fprintf(out, "ref: %d, nparam: %d, in: %d, out: %d, extra: %d, "
2453 "flags: %x, n_name: %d\n",
2455 bmap->dim->nparam, bmap->dim->n_in, bmap->dim->n_out,
2456 bmap->extra, bmap->flags, bmap->dim->n_id);
2457 dump(bmap, out, indent);
2460 int isl_inequality_negate(struct isl_basic_map *bmap, unsigned pos)
2465 total = isl_basic_map_total_dim(bmap);
2466 isl_assert(bmap->ctx, pos < bmap->n_ineq, return -1);
2467 isl_seq_neg(bmap->ineq[pos], bmap->ineq[pos], 1 + total);
2468 isl_int_sub_ui(bmap->ineq[pos][0], bmap->ineq[pos][0], 1);
2469 ISL_F_CLR(bmap, ISL_BASIC_MAP_NORMALIZED);
2473 __isl_give isl_set *isl_set_alloc_space(__isl_take isl_space *dim, int n,
2476 struct isl_set *set;
2480 isl_assert(dim->ctx, dim->n_in == 0, goto error);
2481 isl_assert(dim->ctx, n >= 0, goto error);
2482 set = isl_alloc(dim->ctx, struct isl_set,
2483 sizeof(struct isl_set) +
2484 (n - 1) * sizeof(struct isl_basic_set *));
2488 set->ctx = dim->ctx;
2489 isl_ctx_ref(set->ctx);
2497 isl_space_free(dim);
2501 struct isl_set *isl_set_alloc(struct isl_ctx *ctx,
2502 unsigned nparam, unsigned dim, int n, unsigned flags)
2504 struct isl_set *set;
2507 dims = isl_space_alloc(ctx, nparam, 0, dim);
2511 set = isl_set_alloc_space(dims, n, flags);
2515 /* Make sure "map" has room for at least "n" more basic maps.
2517 struct isl_map *isl_map_grow(struct isl_map *map, int n)
2520 struct isl_map *grown = NULL;
2524 isl_assert(map->ctx, n >= 0, goto error);
2525 if (map->n + n <= map->size)
2527 grown = isl_map_alloc_space(isl_map_get_space(map), map->n + n, map->flags);
2530 for (i = 0; i < map->n; ++i) {
2531 grown->p[i] = isl_basic_map_copy(map->p[i]);
2539 isl_map_free(grown);
2544 /* Make sure "set" has room for at least "n" more basic sets.
2546 struct isl_set *isl_set_grow(struct isl_set *set, int n)
2548 return (struct isl_set *)isl_map_grow((struct isl_map *)set, n);
2551 struct isl_set *isl_set_dup(struct isl_set *set)
2554 struct isl_set *dup;
2559 dup = isl_set_alloc_space(isl_space_copy(set->dim), set->n, set->flags);
2562 for (i = 0; i < set->n; ++i)
2563 dup = isl_set_add_basic_set(dup, isl_basic_set_copy(set->p[i]));
2567 struct isl_set *isl_set_from_basic_set(struct isl_basic_set *bset)
2569 return isl_map_from_basic_map(bset);
2572 struct isl_map *isl_map_from_basic_map(struct isl_basic_map *bmap)
2574 struct isl_map *map;
2579 map = isl_map_alloc_space(isl_space_copy(bmap->dim), 1, ISL_MAP_DISJOINT);
2580 return isl_map_add_basic_map(map, bmap);
2583 __isl_give isl_set *isl_set_add_basic_set(__isl_take isl_set *set,
2584 __isl_take isl_basic_set *bset)
2586 return (struct isl_set *)isl_map_add_basic_map((struct isl_map *)set,
2587 (struct isl_basic_map *)bset);
2590 void *isl_set_free(__isl_take isl_set *set)
2600 isl_ctx_deref(set->ctx);
2601 for (i = 0; i < set->n; ++i)
2602 isl_basic_set_free(set->p[i]);
2603 isl_space_free(set->dim);
2609 void isl_set_print_internal(struct isl_set *set, FILE *out, int indent)
2614 fprintf(out, "null set\n");
2618 fprintf(out, "%*s", indent, "");
2619 fprintf(out, "ref: %d, n: %d, nparam: %d, dim: %d, flags: %x\n",
2620 set->ref, set->n, set->dim->nparam, set->dim->n_out,
2622 for (i = 0; i < set->n; ++i) {
2623 fprintf(out, "%*s", indent, "");
2624 fprintf(out, "basic set %d:\n", i);
2625 isl_basic_set_print_internal(set->p[i], out, indent+4);
2629 void isl_map_print_internal(struct isl_map *map, FILE *out, int indent)
2634 fprintf(out, "null map\n");
2638 fprintf(out, "%*s", indent, "");
2639 fprintf(out, "ref: %d, n: %d, nparam: %d, in: %d, out: %d, "
2640 "flags: %x, n_name: %d\n",
2641 map->ref, map->n, map->dim->nparam, map->dim->n_in,
2642 map->dim->n_out, map->flags, map->dim->n_id);
2643 for (i = 0; i < map->n; ++i) {
2644 fprintf(out, "%*s", indent, "");
2645 fprintf(out, "basic map %d:\n", i);
2646 isl_basic_map_print_internal(map->p[i], out, indent+4);
2650 struct isl_basic_map *isl_basic_map_intersect_domain(
2651 struct isl_basic_map *bmap, struct isl_basic_set *bset)
2653 struct isl_basic_map *bmap_domain;
2658 isl_assert(bset->ctx, isl_space_match(bmap->dim, isl_dim_param,
2659 bset->dim, isl_dim_param), goto error);
2661 if (isl_space_dim(bset->dim, isl_dim_set) != 0)
2662 isl_assert(bset->ctx,
2663 isl_basic_map_compatible_domain(bmap, bset), goto error);
2665 bmap = isl_basic_map_cow(bmap);
2668 bmap = isl_basic_map_extend_space(bmap, isl_space_copy(bmap->dim),
2669 bset->n_div, bset->n_eq, bset->n_ineq);
2670 bmap_domain = isl_basic_map_from_domain(bset);
2671 bmap = add_constraints(bmap, bmap_domain, 0, 0);
2673 bmap = isl_basic_map_simplify(bmap);
2674 return isl_basic_map_finalize(bmap);
2676 isl_basic_map_free(bmap);
2677 isl_basic_set_free(bset);
2681 struct isl_basic_map *isl_basic_map_intersect_range(
2682 struct isl_basic_map *bmap, struct isl_basic_set *bset)
2684 struct isl_basic_map *bmap_range;
2689 isl_assert(bset->ctx, isl_space_match(bmap->dim, isl_dim_param,
2690 bset->dim, isl_dim_param), goto error);
2692 if (isl_space_dim(bset->dim, isl_dim_set) != 0)
2693 isl_assert(bset->ctx,
2694 isl_basic_map_compatible_range(bmap, bset), goto error);
2696 if (isl_basic_set_is_universe(bset)) {
2697 isl_basic_set_free(bset);
2701 bmap = isl_basic_map_cow(bmap);
2704 bmap = isl_basic_map_extend_space(bmap, isl_space_copy(bmap->dim),
2705 bset->n_div, bset->n_eq, bset->n_ineq);
2706 bmap_range = isl_basic_map_from_basic_set(bset, isl_space_copy(bset->dim));
2707 bmap = add_constraints(bmap, bmap_range, 0, 0);
2709 bmap = isl_basic_map_simplify(bmap);
2710 return isl_basic_map_finalize(bmap);
2712 isl_basic_map_free(bmap);
2713 isl_basic_set_free(bset);
2717 int isl_basic_map_contains(struct isl_basic_map *bmap, struct isl_vec *vec)
2723 total = 1 + isl_basic_map_total_dim(bmap);
2724 if (total != vec->size)
2729 for (i = 0; i < bmap->n_eq; ++i) {
2730 isl_seq_inner_product(vec->el, bmap->eq[i], total, &s);
2731 if (!isl_int_is_zero(s)) {
2737 for (i = 0; i < bmap->n_ineq; ++i) {
2738 isl_seq_inner_product(vec->el, bmap->ineq[i], total, &s);
2739 if (isl_int_is_neg(s)) {
2750 int isl_basic_set_contains(struct isl_basic_set *bset, struct isl_vec *vec)
2752 return isl_basic_map_contains((struct isl_basic_map *)bset, vec);
2755 struct isl_basic_map *isl_basic_map_intersect(
2756 struct isl_basic_map *bmap1, struct isl_basic_map *bmap2)
2758 struct isl_vec *sample = NULL;
2760 if (!bmap1 || !bmap2)
2763 isl_assert(bmap1->ctx, isl_space_match(bmap1->dim, isl_dim_param,
2764 bmap2->dim, isl_dim_param), goto error);
2765 if (isl_space_dim(bmap1->dim, isl_dim_all) ==
2766 isl_space_dim(bmap1->dim, isl_dim_param) &&
2767 isl_space_dim(bmap2->dim, isl_dim_all) !=
2768 isl_space_dim(bmap2->dim, isl_dim_param))
2769 return isl_basic_map_intersect(bmap2, bmap1);
2771 if (isl_space_dim(bmap2->dim, isl_dim_all) !=
2772 isl_space_dim(bmap2->dim, isl_dim_param))
2773 isl_assert(bmap1->ctx,
2774 isl_space_is_equal(bmap1->dim, bmap2->dim), goto error);
2776 if (bmap1->sample &&
2777 isl_basic_map_contains(bmap1, bmap1->sample) > 0 &&
2778 isl_basic_map_contains(bmap2, bmap1->sample) > 0)
2779 sample = isl_vec_copy(bmap1->sample);
2780 else if (bmap2->sample &&
2781 isl_basic_map_contains(bmap1, bmap2->sample) > 0 &&
2782 isl_basic_map_contains(bmap2, bmap2->sample) > 0)
2783 sample = isl_vec_copy(bmap2->sample);
2785 bmap1 = isl_basic_map_cow(bmap1);
2788 bmap1 = isl_basic_map_extend_space(bmap1, isl_space_copy(bmap1->dim),
2789 bmap2->n_div, bmap2->n_eq, bmap2->n_ineq);
2790 bmap1 = add_constraints(bmap1, bmap2, 0, 0);
2793 isl_vec_free(sample);
2795 isl_vec_free(bmap1->sample);
2796 bmap1->sample = sample;
2799 bmap1 = isl_basic_map_simplify(bmap1);
2800 return isl_basic_map_finalize(bmap1);
2803 isl_vec_free(sample);
2804 isl_basic_map_free(bmap1);
2805 isl_basic_map_free(bmap2);
2809 struct isl_basic_set *isl_basic_set_intersect(
2810 struct isl_basic_set *bset1, struct isl_basic_set *bset2)
2812 return (struct isl_basic_set *)
2813 isl_basic_map_intersect(
2814 (struct isl_basic_map *)bset1,
2815 (struct isl_basic_map *)bset2);
2818 __isl_give isl_basic_set *isl_basic_set_intersect_params(
2819 __isl_take isl_basic_set *bset1, __isl_take isl_basic_set *bset2)
2821 return isl_basic_set_intersect(bset1, bset2);
2824 /* Special case of isl_map_intersect, where both map1 and map2
2825 * are convex, without any divs and such that either map1 or map2
2826 * contains a single constraint. This constraint is then simply
2827 * added to the other map.
2829 static __isl_give isl_map *map_intersect_add_constraint(
2830 __isl_take isl_map *map1, __isl_take isl_map *map2)
2832 isl_assert(map1->ctx, map1->n == 1, goto error);
2833 isl_assert(map2->ctx, map1->n == 1, goto error);
2834 isl_assert(map1->ctx, map1->p[0]->n_div == 0, goto error);
2835 isl_assert(map2->ctx, map1->p[0]->n_div == 0, goto error);
2837 if (map2->p[0]->n_eq + map2->p[0]->n_ineq != 1)
2838 return isl_map_intersect(map2, map1);
2840 isl_assert(map2->ctx,
2841 map2->p[0]->n_eq + map2->p[0]->n_ineq == 1, goto error);
2843 map1 = isl_map_cow(map1);
2846 if (isl_map_plain_is_empty(map1)) {
2850 map1->p[0] = isl_basic_map_cow(map1->p[0]);
2851 if (map2->p[0]->n_eq == 1)
2852 map1->p[0] = isl_basic_map_add_eq(map1->p[0], map2->p[0]->eq[0]);
2854 map1->p[0] = isl_basic_map_add_ineq(map1->p[0],
2855 map2->p[0]->ineq[0]);
2857 map1->p[0] = isl_basic_map_simplify(map1->p[0]);
2858 map1->p[0] = isl_basic_map_finalize(map1->p[0]);
2862 if (isl_basic_map_plain_is_empty(map1->p[0])) {
2863 isl_basic_map_free(map1->p[0]);
2876 /* map2 may be either a parameter domain or a map living in the same
2879 static __isl_give isl_map *map_intersect_internal(__isl_take isl_map *map1,
2880 __isl_take isl_map *map2)
2889 if ((isl_map_plain_is_empty(map1) ||
2890 isl_map_plain_is_universe(map2)) &&
2891 isl_space_is_equal(map1->dim, map2->dim)) {
2895 if ((isl_map_plain_is_empty(map2) ||
2896 isl_map_plain_is_universe(map1)) &&
2897 isl_space_is_equal(map1->dim, map2->dim)) {
2902 if (map1->n == 1 && map2->n == 1 &&
2903 map1->p[0]->n_div == 0 && map2->p[0]->n_div == 0 &&
2904 isl_space_is_equal(map1->dim, map2->dim) &&
2905 (map1->p[0]->n_eq + map1->p[0]->n_ineq == 1 ||
2906 map2->p[0]->n_eq + map2->p[0]->n_ineq == 1))
2907 return map_intersect_add_constraint(map1, map2);
2909 if (isl_space_dim(map2->dim, isl_dim_all) !=
2910 isl_space_dim(map2->dim, isl_dim_param))
2911 isl_assert(map1->ctx,
2912 isl_space_is_equal(map1->dim, map2->dim), goto error);
2914 if (ISL_F_ISSET(map1, ISL_MAP_DISJOINT) &&
2915 ISL_F_ISSET(map2, ISL_MAP_DISJOINT))
2916 ISL_FL_SET(flags, ISL_MAP_DISJOINT);
2918 result = isl_map_alloc_space(isl_space_copy(map1->dim),
2919 map1->n * map2->n, flags);
2922 for (i = 0; i < map1->n; ++i)
2923 for (j = 0; j < map2->n; ++j) {
2924 struct isl_basic_map *part;
2925 part = isl_basic_map_intersect(
2926 isl_basic_map_copy(map1->p[i]),
2927 isl_basic_map_copy(map2->p[j]));
2928 if (isl_basic_map_is_empty(part) < 0)
2929 part = isl_basic_map_free(part);
2930 result = isl_map_add_basic_map(result, part);
2943 static __isl_give isl_map *map_intersect(__isl_take isl_map *map1,
2944 __isl_take isl_map *map2)
2948 if (!isl_space_is_equal(map1->dim, map2->dim))
2949 isl_die(isl_map_get_ctx(map1), isl_error_invalid,
2950 "spaces don't match", goto error);
2951 return map_intersect_internal(map1, map2);
2958 __isl_give isl_map *isl_map_intersect(__isl_take isl_map *map1,
2959 __isl_take isl_map *map2)
2961 return isl_map_align_params_map_map_and(map1, map2, &map_intersect);
2964 struct isl_set *isl_set_intersect(struct isl_set *set1, struct isl_set *set2)
2966 return (struct isl_set *)
2967 isl_map_intersect((struct isl_map *)set1,
2968 (struct isl_map *)set2);
2971 /* map_intersect_internal accepts intersections
2972 * with parameter domains, so we can just call that function.
2974 static __isl_give isl_map *map_intersect_params(__isl_take isl_map *map,
2975 __isl_take isl_set *params)
2977 return map_intersect_internal(map, params);
2980 __isl_give isl_map *isl_map_intersect_params(__isl_take isl_map *map1,
2981 __isl_take isl_map *map2)
2983 return isl_map_align_params_map_map_and(map1, map2, &map_intersect_params);
2986 __isl_give isl_set *isl_set_intersect_params(__isl_take isl_set *set,
2987 __isl_take isl_set *params)
2989 return isl_map_intersect_params(set, params);
2992 struct isl_basic_map *isl_basic_map_reverse(struct isl_basic_map *bmap)
2995 struct isl_basic_set *bset;
3000 bmap = isl_basic_map_cow(bmap);
3003 dim = isl_space_reverse(isl_space_copy(bmap->dim));
3004 in = isl_basic_map_n_in(bmap);
3005 bset = isl_basic_set_from_basic_map(bmap);
3006 bset = isl_basic_set_swap_vars(bset, in);
3007 return isl_basic_map_from_basic_set(bset, dim);
3010 static __isl_give isl_basic_map *basic_map_space_reset(
3011 __isl_take isl_basic_map *bmap, enum isl_dim_type type)
3017 if (!isl_space_is_named_or_nested(bmap->dim, type))
3020 space = isl_basic_map_get_space(bmap);
3021 space = isl_space_reset(space, type);
3022 bmap = isl_basic_map_reset_space(bmap, space);
3026 __isl_give isl_basic_map *isl_basic_map_insert_dims(
3027 __isl_take isl_basic_map *bmap, enum isl_dim_type type,
3028 unsigned pos, unsigned n)
3031 struct isl_basic_map *res;
3032 struct isl_dim_map *dim_map;
3033 unsigned total, off;
3034 enum isl_dim_type t;
3037 return basic_map_space_reset(bmap, type);
3042 res_dim = isl_space_insert_dims(isl_basic_map_get_space(bmap), type, pos, n);
3044 total = isl_basic_map_total_dim(bmap) + n;
3045 dim_map = isl_dim_map_alloc(bmap->ctx, total);
3047 for (t = isl_dim_param; t <= isl_dim_out; ++t) {
3049 isl_dim_map_dim(dim_map, bmap->dim, t, off);
3051 unsigned size = isl_basic_map_dim(bmap, t);
3052 isl_dim_map_dim_range(dim_map, bmap->dim, t,
3054 isl_dim_map_dim_range(dim_map, bmap->dim, t,
3055 pos, size - pos, off + pos + n);
3057 off += isl_space_dim(res_dim, t);
3059 isl_dim_map_div(dim_map, bmap, off);
3061 res = isl_basic_map_alloc_space(res_dim,
3062 bmap->n_div, bmap->n_eq, bmap->n_ineq);
3063 if (isl_basic_map_is_rational(bmap))
3064 res = isl_basic_map_set_rational(res);
3065 if (isl_basic_map_plain_is_empty(bmap)) {
3066 isl_basic_map_free(bmap);
3067 return isl_basic_map_set_to_empty(res);
3069 res = isl_basic_map_add_constraints_dim_map(res, bmap, dim_map);
3070 return isl_basic_map_finalize(res);
3073 __isl_give isl_basic_set *isl_basic_set_insert_dims(
3074 __isl_take isl_basic_set *bset,
3075 enum isl_dim_type type, unsigned pos, unsigned n)
3077 return isl_basic_map_insert_dims(bset, type, pos, n);
3080 __isl_give isl_basic_map *isl_basic_map_add(__isl_take isl_basic_map *bmap,
3081 enum isl_dim_type type, unsigned n)
3085 return isl_basic_map_insert_dims(bmap, type,
3086 isl_basic_map_dim(bmap, type), n);
3089 __isl_give isl_basic_set *isl_basic_set_add_dims(__isl_take isl_basic_set *bset,
3090 enum isl_dim_type type, unsigned n)
3094 isl_assert(bset->ctx, type != isl_dim_in, goto error);
3095 return (isl_basic_set *)isl_basic_map_add((isl_basic_map *)bset, type, n);
3097 isl_basic_set_free(bset);
3101 static __isl_give isl_map *map_space_reset(__isl_take isl_map *map,
3102 enum isl_dim_type type)
3106 if (!map || !isl_space_is_named_or_nested(map->dim, type))
3109 space = isl_map_get_space(map);
3110 space = isl_space_reset(space, type);
3111 map = isl_map_reset_space(map, space);
3115 __isl_give isl_map *isl_map_insert_dims(__isl_take isl_map *map,
3116 enum isl_dim_type type, unsigned pos, unsigned n)
3121 return map_space_reset(map, type);
3123 map = isl_map_cow(map);
3127 map->dim = isl_space_insert_dims(map->dim, type, pos, n);
3131 for (i = 0; i < map->n; ++i) {
3132 map->p[i] = isl_basic_map_insert_dims(map->p[i], type, pos, n);
3143 __isl_give isl_set *isl_set_insert_dims(__isl_take isl_set *set,
3144 enum isl_dim_type type, unsigned pos, unsigned n)
3146 return isl_map_insert_dims(set, type, pos, n);
3149 __isl_give isl_map *isl_map_add_dims(__isl_take isl_map *map,
3150 enum isl_dim_type type, unsigned n)
3154 return isl_map_insert_dims(map, type, isl_map_dim(map, type), n);
3157 __isl_give isl_set *isl_set_add_dims(__isl_take isl_set *set,
3158 enum isl_dim_type type, unsigned n)
3162 isl_assert(set->ctx, type != isl_dim_in, goto error);
3163 return (isl_set *)isl_map_add_dims((isl_map *)set, type, n);
3169 __isl_give isl_basic_map *isl_basic_map_move_dims(
3170 __isl_take isl_basic_map *bmap,
3171 enum isl_dim_type dst_type, unsigned dst_pos,
3172 enum isl_dim_type src_type, unsigned src_pos, unsigned n)
3174 struct isl_dim_map *dim_map;
3175 struct isl_basic_map *res;
3176 enum isl_dim_type t;
3177 unsigned total, off;
3184 isl_assert(bmap->ctx, src_pos + n <= isl_basic_map_dim(bmap, src_type),
3187 if (dst_type == src_type && dst_pos == src_pos)
3190 isl_assert(bmap->ctx, dst_type != src_type, goto error);
3192 if (pos(bmap->dim, dst_type) + dst_pos ==
3193 pos(bmap->dim, src_type) + src_pos +
3194 ((src_type < dst_type) ? n : 0)) {
3195 bmap = isl_basic_map_cow(bmap);
3199 bmap->dim = isl_space_move_dims(bmap->dim, dst_type, dst_pos,
3200 src_type, src_pos, n);
3204 bmap = isl_basic_map_finalize(bmap);
3209 total = isl_basic_map_total_dim(bmap);
3210 dim_map = isl_dim_map_alloc(bmap->ctx, total);
3213 for (t = isl_dim_param; t <= isl_dim_out; ++t) {
3214 unsigned size = isl_space_dim(bmap->dim, t);
3215 if (t == dst_type) {
3216 isl_dim_map_dim_range(dim_map, bmap->dim, t,
3219 isl_dim_map_dim_range(dim_map, bmap->dim, src_type,
3222 isl_dim_map_dim_range(dim_map, bmap->dim, t,
3223 dst_pos, size - dst_pos, off);
3224 off += size - dst_pos;
3225 } else if (t == src_type) {
3226 isl_dim_map_dim_range(dim_map, bmap->dim, t,
3229 isl_dim_map_dim_range(dim_map, bmap->dim, t,
3230 src_pos + n, size - src_pos - n, off);
3231 off += size - src_pos - n;
3233 isl_dim_map_dim(dim_map, bmap->dim, t, off);
3237 isl_dim_map_div(dim_map, bmap, off);
3239 res = isl_basic_map_alloc_space(isl_basic_map_get_space(bmap),
3240 bmap->n_div, bmap->n_eq, bmap->n_ineq);
3241 bmap = isl_basic_map_add_constraints_dim_map(res, bmap, dim_map);
3245 bmap->dim = isl_space_move_dims(bmap->dim, dst_type, dst_pos,
3246 src_type, src_pos, n);
3250 ISL_F_CLR(bmap, ISL_BASIC_MAP_NORMALIZED);
3251 bmap = isl_basic_map_gauss(bmap, NULL);
3252 bmap = isl_basic_map_finalize(bmap);
3256 isl_basic_map_free(bmap);
3260 __isl_give isl_basic_set *isl_basic_set_move_dims(__isl_take isl_basic_set *bset,
3261 enum isl_dim_type dst_type, unsigned dst_pos,
3262 enum isl_dim_type src_type, unsigned src_pos, unsigned n)
3264 return (isl_basic_set *)isl_basic_map_move_dims(
3265 (isl_basic_map *)bset, dst_type, dst_pos, src_type, src_pos, n);
3268 __isl_give isl_set *isl_set_move_dims(__isl_take isl_set *set,
3269 enum isl_dim_type dst_type, unsigned dst_pos,
3270 enum isl_dim_type src_type, unsigned src_pos, unsigned n)
3274 isl_assert(set->ctx, dst_type != isl_dim_in, goto error);
3275 return (isl_set *)isl_map_move_dims((isl_map *)set, dst_type, dst_pos,
3276 src_type, src_pos, n);
3282 __isl_give isl_map *isl_map_move_dims(__isl_take isl_map *map,
3283 enum isl_dim_type dst_type, unsigned dst_pos,
3284 enum isl_dim_type src_type, unsigned src_pos, unsigned n)
3293 isl_assert(map->ctx, src_pos + n <= isl_map_dim(map, src_type),
3296 if (dst_type == src_type && dst_pos == src_pos)
3299 isl_assert(map->ctx, dst_type != src_type, goto error);
3301 map = isl_map_cow(map);
3305 map->dim = isl_space_move_dims(map->dim, dst_type, dst_pos, src_type, src_pos, n);
3309 for (i = 0; i < map->n; ++i) {
3310 map->p[i] = isl_basic_map_move_dims(map->p[i],
3312 src_type, src_pos, n);
3323 /* Move the specified dimensions to the last columns right before
3324 * the divs. Don't change the dimension specification of bmap.
3325 * That's the responsibility of the caller.
3327 static __isl_give isl_basic_map *move_last(__isl_take isl_basic_map *bmap,
3328 enum isl_dim_type type, unsigned first, unsigned n)
3330 struct isl_dim_map *dim_map;
3331 struct isl_basic_map *res;
3332 enum isl_dim_type t;
3333 unsigned total, off;
3337 if (pos(bmap->dim, type) + first + n ==
3338 1 + isl_space_dim(bmap->dim, isl_dim_all))
3341 total = isl_basic_map_total_dim(bmap);
3342 dim_map = isl_dim_map_alloc(bmap->ctx, total);
3345 for (t = isl_dim_param; t <= isl_dim_out; ++t) {
3346 unsigned size = isl_space_dim(bmap->dim, t);
3348 isl_dim_map_dim_range(dim_map, bmap->dim, t,
3351 isl_dim_map_dim_range(dim_map, bmap->dim, t,
3352 first, n, total - bmap->n_div - n);
3353 isl_dim_map_dim_range(dim_map, bmap->dim, t,
3354 first + n, size - (first + n), off);
3355 off += size - (first + n);
3357 isl_dim_map_dim(dim_map, bmap->dim, t, off);
3361 isl_dim_map_div(dim_map, bmap, off + n);
3363 res = isl_basic_map_alloc_space(isl_basic_map_get_space(bmap),
3364 bmap->n_div, bmap->n_eq, bmap->n_ineq);
3365 res = isl_basic_map_add_constraints_dim_map(res, bmap, dim_map);
3369 /* Turn the n dimensions of type type, starting at first
3370 * into existentially quantified variables.
3372 __isl_give isl_basic_map *isl_basic_map_project_out(
3373 __isl_take isl_basic_map *bmap,
3374 enum isl_dim_type type, unsigned first, unsigned n)
3382 return basic_map_space_reset(bmap, type);
3387 if (ISL_F_ISSET(bmap, ISL_BASIC_MAP_RATIONAL))
3388 return isl_basic_map_remove_dims(bmap, type, first, n);
3390 isl_assert(bmap->ctx, first + n <= isl_basic_map_dim(bmap, type),
3393 bmap = move_last(bmap, type, first, n);
3394 bmap = isl_basic_map_cow(bmap);
3398 row_size = 1 + isl_space_dim(bmap->dim, isl_dim_all) + bmap->extra;
3399 old = bmap->block2.data;
3400 bmap->block2 = isl_blk_extend(bmap->ctx, bmap->block2,
3401 (bmap->extra + n) * (1 + row_size));
3402 if (!bmap->block2.data)
3404 new_div = isl_alloc_array(bmap->ctx, isl_int *, bmap->extra + n);
3407 for (i = 0; i < n; ++i) {
3408 new_div[i] = bmap->block2.data +
3409 (bmap->extra + i) * (1 + row_size);
3410 isl_seq_clr(new_div[i], 1 + row_size);
3412 for (i = 0; i < bmap->extra; ++i)
3413 new_div[n + i] = bmap->block2.data + (bmap->div[i] - old);
3415 bmap->div = new_div;
3419 bmap->dim = isl_space_drop_dims(bmap->dim, type, first, n);
3422 bmap = isl_basic_map_simplify(bmap);
3423 bmap = isl_basic_map_drop_redundant_divs(bmap);
3424 return isl_basic_map_finalize(bmap);
3426 isl_basic_map_free(bmap);
3430 /* Turn the n dimensions of type type, starting at first
3431 * into existentially quantified variables.
3433 struct isl_basic_set *isl_basic_set_project_out(struct isl_basic_set *bset,
3434 enum isl_dim_type type, unsigned first, unsigned n)
3436 return (isl_basic_set *)isl_basic_map_project_out(
3437 (isl_basic_map *)bset, type, first, n);
3440 /* Turn the n dimensions of type type, starting at first
3441 * into existentially quantified variables.
3443 __isl_give isl_map *isl_map_project_out(__isl_take isl_map *map,
3444 enum isl_dim_type type, unsigned first, unsigned n)
3452 return map_space_reset(map, type);
3454 isl_assert(map->ctx, first + n <= isl_map_dim(map, type), goto error);
3456 map = isl_map_cow(map);
3460 map->dim = isl_space_drop_dims(map->dim, type, first, n);
3464 for (i = 0; i < map->n; ++i) {
3465 map->p[i] = isl_basic_map_project_out(map->p[i], type, first, n);
3476 /* Turn the n dimensions of type type, starting at first
3477 * into existentially quantified variables.
3479 __isl_give isl_set *isl_set_project_out(__isl_take isl_set *set,
3480 enum isl_dim_type type, unsigned first, unsigned n)
3482 return (isl_set *)isl_map_project_out((isl_map *)set, type, first, n);
3485 static struct isl_basic_map *add_divs(struct isl_basic_map *bmap, unsigned n)
3489 for (i = 0; i < n; ++i) {
3490 j = isl_basic_map_alloc_div(bmap);
3493 isl_seq_clr(bmap->div[j], 1+1+isl_basic_map_total_dim(bmap));
3497 isl_basic_map_free(bmap);
3501 struct isl_basic_map *isl_basic_map_apply_range(
3502 struct isl_basic_map *bmap1, struct isl_basic_map *bmap2)
3504 isl_space *dim_result = NULL;
3505 struct isl_basic_map *bmap;
3506 unsigned n_in, n_out, n, nparam, total, pos;
3507 struct isl_dim_map *dim_map1, *dim_map2;
3509 if (!bmap1 || !bmap2)
3512 dim_result = isl_space_join(isl_space_copy(bmap1->dim),
3513 isl_space_copy(bmap2->dim));
3515 n_in = isl_basic_map_n_in(bmap1);
3516 n_out = isl_basic_map_n_out(bmap2);
3517 n = isl_basic_map_n_out(bmap1);
3518 nparam = isl_basic_map_n_param(bmap1);
3520 total = nparam + n_in + n_out + bmap1->n_div + bmap2->n_div + n;
3521 dim_map1 = isl_dim_map_alloc(bmap1->ctx, total);
3522 dim_map2 = isl_dim_map_alloc(bmap1->ctx, total);
3523 isl_dim_map_dim(dim_map1, bmap1->dim, isl_dim_param, pos = 0);
3524 isl_dim_map_dim(dim_map2, bmap2->dim, isl_dim_param, pos = 0);
3525 isl_dim_map_dim(dim_map1, bmap1->dim, isl_dim_in, pos += nparam);
3526 isl_dim_map_dim(dim_map2, bmap2->dim, isl_dim_out, pos += n_in);
3527 isl_dim_map_div(dim_map1, bmap1, pos += n_out);
3528 isl_dim_map_div(dim_map2, bmap2, pos += bmap1->n_div);
3529 isl_dim_map_dim(dim_map1, bmap1->dim, isl_dim_out, pos += bmap2->n_div);
3530 isl_dim_map_dim(dim_map2, bmap2->dim, isl_dim_in, pos);
3532 bmap = isl_basic_map_alloc_space(dim_result,
3533 bmap1->n_div + bmap2->n_div + n,
3534 bmap1->n_eq + bmap2->n_eq,
3535 bmap1->n_ineq + bmap2->n_ineq);
3536 bmap = isl_basic_map_add_constraints_dim_map(bmap, bmap1, dim_map1);
3537 bmap = isl_basic_map_add_constraints_dim_map(bmap, bmap2, dim_map2);
3538 bmap = add_divs(bmap, n);
3539 bmap = isl_basic_map_simplify(bmap);
3540 bmap = isl_basic_map_drop_redundant_divs(bmap);
3541 return isl_basic_map_finalize(bmap);
3543 isl_basic_map_free(bmap1);
3544 isl_basic_map_free(bmap2);
3548 struct isl_basic_set *isl_basic_set_apply(
3549 struct isl_basic_set *bset, struct isl_basic_map *bmap)
3554 isl_assert(bset->ctx, isl_basic_map_compatible_domain(bmap, bset),
3557 return (struct isl_basic_set *)
3558 isl_basic_map_apply_range((struct isl_basic_map *)bset, bmap);
3560 isl_basic_set_free(bset);
3561 isl_basic_map_free(bmap);
3565 struct isl_basic_map *isl_basic_map_apply_domain(
3566 struct isl_basic_map *bmap1, struct isl_basic_map *bmap2)
3568 if (!bmap1 || !bmap2)
3571 isl_assert(bmap1->ctx,
3572 isl_basic_map_n_in(bmap1) == isl_basic_map_n_in(bmap2), goto error);
3573 isl_assert(bmap1->ctx,
3574 isl_basic_map_n_param(bmap1) == isl_basic_map_n_param(bmap2),
3577 bmap1 = isl_basic_map_reverse(bmap1);
3578 bmap1 = isl_basic_map_apply_range(bmap1, bmap2);
3579 return isl_basic_map_reverse(bmap1);
3581 isl_basic_map_free(bmap1);
3582 isl_basic_map_free(bmap2);
3586 /* Given two basic maps A -> f(A) and B -> g(B), construct a basic map
3587 * A \cap B -> f(A) + f(B)
3589 struct isl_basic_map *isl_basic_map_sum(
3590 struct isl_basic_map *bmap1, struct isl_basic_map *bmap2)
3592 unsigned n_in, n_out, nparam, total, pos;
3593 struct isl_basic_map *bmap = NULL;
3594 struct isl_dim_map *dim_map1, *dim_map2;
3597 if (!bmap1 || !bmap2)
3600 isl_assert(bmap1->ctx, isl_space_is_equal(bmap1->dim, bmap2->dim),
3603 nparam = isl_basic_map_n_param(bmap1);
3604 n_in = isl_basic_map_n_in(bmap1);
3605 n_out = isl_basic_map_n_out(bmap1);
3607 total = nparam + n_in + n_out + bmap1->n_div + bmap2->n_div + 2 * n_out;
3608 dim_map1 = isl_dim_map_alloc(bmap1->ctx, total);
3609 dim_map2 = isl_dim_map_alloc(bmap2->ctx, total);
3610 isl_dim_map_dim(dim_map1, bmap1->dim, isl_dim_param, pos = 0);
3611 isl_dim_map_dim(dim_map2, bmap2->dim, isl_dim_param, pos);
3612 isl_dim_map_dim(dim_map1, bmap1->dim, isl_dim_in, pos += nparam);
3613 isl_dim_map_dim(dim_map2, bmap2->dim, isl_dim_in, pos);
3614 isl_dim_map_div(dim_map1, bmap1, pos += n_in + n_out);
3615 isl_dim_map_div(dim_map2, bmap2, pos += bmap1->n_div);
3616 isl_dim_map_dim(dim_map1, bmap1->dim, isl_dim_out, pos += bmap2->n_div);
3617 isl_dim_map_dim(dim_map2, bmap2->dim, isl_dim_out, pos += n_out);
3619 bmap = isl_basic_map_alloc_space(isl_space_copy(bmap1->dim),
3620 bmap1->n_div + bmap2->n_div + 2 * n_out,
3621 bmap1->n_eq + bmap2->n_eq + n_out,
3622 bmap1->n_ineq + bmap2->n_ineq);
3623 for (i = 0; i < n_out; ++i) {
3624 int j = isl_basic_map_alloc_equality(bmap);
3627 isl_seq_clr(bmap->eq[j], 1+total);
3628 isl_int_set_si(bmap->eq[j][1+nparam+n_in+i], -1);
3629 isl_int_set_si(bmap->eq[j][1+pos+i], 1);
3630 isl_int_set_si(bmap->eq[j][1+pos-n_out+i], 1);
3632 bmap = isl_basic_map_add_constraints_dim_map(bmap, bmap1, dim_map1);
3633 bmap = isl_basic_map_add_constraints_dim_map(bmap, bmap2, dim_map2);
3634 bmap = add_divs(bmap, 2 * n_out);
3636 bmap = isl_basic_map_simplify(bmap);
3637 return isl_basic_map_finalize(bmap);
3639 isl_basic_map_free(bmap);
3640 isl_basic_map_free(bmap1);
3641 isl_basic_map_free(bmap2);
3645 /* Given two maps A -> f(A) and B -> g(B), construct a map
3646 * A \cap B -> f(A) + f(B)
3648 struct isl_map *isl_map_sum(struct isl_map *map1, struct isl_map *map2)
3650 struct isl_map *result;
3656 isl_assert(map1->ctx, isl_space_is_equal(map1->dim, map2->dim), goto error);
3658 result = isl_map_alloc_space(isl_space_copy(map1->dim),
3659 map1->n * map2->n, 0);
3662 for (i = 0; i < map1->n; ++i)
3663 for (j = 0; j < map2->n; ++j) {
3664 struct isl_basic_map *part;
3665 part = isl_basic_map_sum(
3666 isl_basic_map_copy(map1->p[i]),
3667 isl_basic_map_copy(map2->p[j]));
3668 if (isl_basic_map_is_empty(part))
3669 isl_basic_map_free(part);
3671 result = isl_map_add_basic_map(result, part);
3684 __isl_give isl_set *isl_set_sum(__isl_take isl_set *set1,
3685 __isl_take isl_set *set2)
3687 return (isl_set *)isl_map_sum((isl_map *)set1, (isl_map *)set2);
3690 /* Given a basic map A -> f(A), construct A -> -f(A).
3692 struct isl_basic_map *isl_basic_map_neg(struct isl_basic_map *bmap)
3697 bmap = isl_basic_map_cow(bmap);
3701 n = isl_basic_map_dim(bmap, isl_dim_out);
3702 off = isl_basic_map_offset(bmap, isl_dim_out);
3703 for (i = 0; i < bmap->n_eq; ++i)
3704 for (j = 0; j < n; ++j)
3705 isl_int_neg(bmap->eq[i][off+j], bmap->eq[i][off+j]);
3706 for (i = 0; i < bmap->n_ineq; ++i)
3707 for (j = 0; j < n; ++j)
3708 isl_int_neg(bmap->ineq[i][off+j], bmap->ineq[i][off+j]);
3709 for (i = 0; i < bmap->n_div; ++i)
3710 for (j = 0; j < n; ++j)
3711 isl_int_neg(bmap->div[i][1+off+j], bmap->div[i][1+off+j]);
3712 bmap = isl_basic_map_gauss(bmap, NULL);
3713 return isl_basic_map_finalize(bmap);
3716 __isl_give isl_basic_set *isl_basic_set_neg(__isl_take isl_basic_set *bset)
3718 return isl_basic_map_neg(bset);
3721 /* Given a map A -> f(A), construct A -> -f(A).
3723 struct isl_map *isl_map_neg(struct isl_map *map)
3727 map = isl_map_cow(map);
3731 for (i = 0; i < map->n; ++i) {
3732 map->p[i] = isl_basic_map_neg(map->p[i]);
3743 __isl_give isl_set *isl_set_neg(__isl_take isl_set *set)
3745 return (isl_set *)isl_map_neg((isl_map *)set);
3748 /* Given a basic map A -> f(A) and an integer d, construct a basic map
3749 * A -> floor(f(A)/d).
3751 struct isl_basic_map *isl_basic_map_floordiv(struct isl_basic_map *bmap,
3754 unsigned n_in, n_out, nparam, total, pos;
3755 struct isl_basic_map *result = NULL;
3756 struct isl_dim_map *dim_map;
3762 nparam = isl_basic_map_n_param(bmap);
3763 n_in = isl_basic_map_n_in(bmap);
3764 n_out = isl_basic_map_n_out(bmap);
3766 total = nparam + n_in + n_out + bmap->n_div + n_out;
3767 dim_map = isl_dim_map_alloc(bmap->ctx, total);
3768 isl_dim_map_dim(dim_map, bmap->dim, isl_dim_param, pos = 0);
3769 isl_dim_map_dim(dim_map, bmap->dim, isl_dim_in, pos += nparam);
3770 isl_dim_map_div(dim_map, bmap, pos += n_in + n_out);
3771 isl_dim_map_dim(dim_map, bmap->dim, isl_dim_out, pos += bmap->n_div);
3773 result = isl_basic_map_alloc_space(isl_space_copy(bmap->dim),
3774 bmap->n_div + n_out,
3775 bmap->n_eq, bmap->n_ineq + 2 * n_out);
3776 result = isl_basic_map_add_constraints_dim_map(result, bmap, dim_map);
3777 result = add_divs(result, n_out);
3778 for (i = 0; i < n_out; ++i) {
3780 j = isl_basic_map_alloc_inequality(result);
3783 isl_seq_clr(result->ineq[j], 1+total);
3784 isl_int_neg(result->ineq[j][1+nparam+n_in+i], d);
3785 isl_int_set_si(result->ineq[j][1+pos+i], 1);
3786 j = isl_basic_map_alloc_inequality(result);
3789 isl_seq_clr(result->ineq[j], 1+total);
3790 isl_int_set(result->ineq[j][1+nparam+n_in+i], d);
3791 isl_int_set_si(result->ineq[j][1+pos+i], -1);
3792 isl_int_sub_ui(result->ineq[j][0], d, 1);
3795 result = isl_basic_map_simplify(result);
3796 return isl_basic_map_finalize(result);
3798 isl_basic_map_free(result);
3802 /* Given a map A -> f(A) and an integer d, construct a map
3803 * A -> floor(f(A)/d).
3805 struct isl_map *isl_map_floordiv(struct isl_map *map, isl_int d)
3809 map = isl_map_cow(map);
3813 ISL_F_CLR(map, ISL_MAP_DISJOINT);
3814 ISL_F_CLR(map, ISL_MAP_NORMALIZED);
3815 for (i = 0; i < map->n; ++i) {
3816 map->p[i] = isl_basic_map_floordiv(map->p[i], d);
3827 static struct isl_basic_map *var_equal(struct isl_basic_map *bmap, unsigned pos)
3833 i = isl_basic_map_alloc_equality(bmap);
3836 nparam = isl_basic_map_n_param(bmap);
3837 n_in = isl_basic_map_n_in(bmap);
3838 isl_seq_clr(bmap->eq[i], 1 + isl_basic_map_total_dim(bmap));
3839 isl_int_set_si(bmap->eq[i][1+nparam+pos], -1);
3840 isl_int_set_si(bmap->eq[i][1+nparam+n_in+pos], 1);
3841 return isl_basic_map_finalize(bmap);
3843 isl_basic_map_free(bmap);
3847 /* Add a constraints to "bmap" expressing i_pos < o_pos
3849 static struct isl_basic_map *var_less(struct isl_basic_map *bmap, unsigned pos)
3855 i = isl_basic_map_alloc_inequality(bmap);
3858 nparam = isl_basic_map_n_param(bmap);
3859 n_in = isl_basic_map_n_in(bmap);
3860 isl_seq_clr(bmap->ineq[i], 1 + isl_basic_map_total_dim(bmap));
3861 isl_int_set_si(bmap->ineq[i][0], -1);
3862 isl_int_set_si(bmap->ineq[i][1+nparam+pos], -1);
3863 isl_int_set_si(bmap->ineq[i][1+nparam+n_in+pos], 1);
3864 return isl_basic_map_finalize(bmap);
3866 isl_basic_map_free(bmap);
3870 /* Add a constraint to "bmap" expressing i_pos <= o_pos
3872 static __isl_give isl_basic_map *var_less_or_equal(
3873 __isl_take isl_basic_map *bmap, unsigned pos)
3879 i = isl_basic_map_alloc_inequality(bmap);
3882 nparam = isl_basic_map_n_param(bmap);
3883 n_in = isl_basic_map_n_in(bmap);
3884 isl_seq_clr(bmap->ineq[i], 1 + isl_basic_map_total_dim(bmap));
3885 isl_int_set_si(bmap->ineq[i][1+nparam+pos], -1);
3886 isl_int_set_si(bmap->ineq[i][1+nparam+n_in+pos], 1);
3887 return isl_basic_map_finalize(bmap);
3889 isl_basic_map_free(bmap);
3893 /* Add a constraints to "bmap" expressing i_pos > o_pos
3895 static struct isl_basic_map *var_more(struct isl_basic_map *bmap, unsigned pos)
3901 i = isl_basic_map_alloc_inequality(bmap);
3904 nparam = isl_basic_map_n_param(bmap);
3905 n_in = isl_basic_map_n_in(bmap);
3906 isl_seq_clr(bmap->ineq[i], 1 + isl_basic_map_total_dim(bmap));
3907 isl_int_set_si(bmap->ineq[i][0], -1);
3908 isl_int_set_si(bmap->ineq[i][1+nparam+pos], 1);
3909 isl_int_set_si(bmap->ineq[i][1+nparam+n_in+pos], -1);
3910 return isl_basic_map_finalize(bmap);
3912 isl_basic_map_free(bmap);
3916 /* Add a constraint to "bmap" expressing i_pos >= o_pos
3918 static __isl_give isl_basic_map *var_more_or_equal(
3919 __isl_take isl_basic_map *bmap, unsigned pos)
3925 i = isl_basic_map_alloc_inequality(bmap);
3928 nparam = isl_basic_map_n_param(bmap);
3929 n_in = isl_basic_map_n_in(bmap);
3930 isl_seq_clr(bmap->ineq[i], 1 + isl_basic_map_total_dim(bmap));
3931 isl_int_set_si(bmap->ineq[i][1+nparam+pos], 1);
3932 isl_int_set_si(bmap->ineq[i][1+nparam+n_in+pos], -1);
3933 return isl_basic_map_finalize(bmap);
3935 isl_basic_map_free(bmap);
3939 __isl_give isl_basic_map *isl_basic_map_equal(
3940 __isl_take isl_space *dim, unsigned n_equal)
3943 struct isl_basic_map *bmap;
3944 bmap = isl_basic_map_alloc_space(dim, 0, n_equal, 0);
3947 for (i = 0; i < n_equal && bmap; ++i)
3948 bmap = var_equal(bmap, i);
3949 return isl_basic_map_finalize(bmap);
3952 /* Return a relation on of dimension "dim" expressing i_[0..pos] << o_[0..pos]
3954 __isl_give isl_basic_map *isl_basic_map_less_at(__isl_take isl_space *dim,
3958 struct isl_basic_map *bmap;
3959 bmap = isl_basic_map_alloc_space(dim, 0, pos, 1);
3962 for (i = 0; i < pos && bmap; ++i)
3963 bmap = var_equal(bmap, i);
3965 bmap = var_less(bmap, pos);
3966 return isl_basic_map_finalize(bmap);
3969 /* Return a relation on of dimension "dim" expressing i_[0..pos] <<= o_[0..pos]
3971 __isl_give isl_basic_map *isl_basic_map_less_or_equal_at(
3972 __isl_take isl_space *dim, unsigned pos)
3975 isl_basic_map *bmap;
3977 bmap = isl_basic_map_alloc_space(dim, 0, pos, 1);
3978 for (i = 0; i < pos; ++i)
3979 bmap = var_equal(bmap, i);
3980 bmap = var_less_or_equal(bmap, pos);
3981 return isl_basic_map_finalize(bmap);
3984 /* Return a relation on pairs of sets of dimension "dim" expressing i_pos > o_pos
3986 __isl_give isl_basic_map *isl_basic_map_more_at(__isl_take isl_space *dim,
3990 struct isl_basic_map *bmap;
3991 bmap = isl_basic_map_alloc_space(dim, 0, pos, 1);
3994 for (i = 0; i < pos && bmap; ++i)
3995 bmap = var_equal(bmap, i);
3997 bmap = var_more(bmap, pos);
3998 return isl_basic_map_finalize(bmap);
4001 /* Return a relation on of dimension "dim" expressing i_[0..pos] >>= o_[0..pos]
4003 __isl_give isl_basic_map *isl_basic_map_more_or_equal_at(
4004 __isl_take isl_space *dim, unsigned pos)
4007 isl_basic_map *bmap;
4009 bmap = isl_basic_map_alloc_space(dim, 0, pos, 1);
4010 for (i = 0; i < pos; ++i)
4011 bmap = var_equal(bmap, i);
4012 bmap = var_more_or_equal(bmap, pos);
4013 return isl_basic_map_finalize(bmap);
4016 static __isl_give isl_map *map_lex_lte_first(__isl_take isl_space *dims,
4017 unsigned n, int equal)
4019 struct isl_map *map;
4022 if (n == 0 && equal)
4023 return isl_map_universe(dims);
4025 map = isl_map_alloc_space(isl_space_copy(dims), n, ISL_MAP_DISJOINT);
4027 for (i = 0; i + 1 < n; ++i)
4028 map = isl_map_add_basic_map(map,
4029 isl_basic_map_less_at(isl_space_copy(dims), i));
4032 map = isl_map_add_basic_map(map,
4033 isl_basic_map_less_or_equal_at(dims, n - 1));
4035 map = isl_map_add_basic_map(map,
4036 isl_basic_map_less_at(dims, n - 1));
4038 isl_space_free(dims);
4043 static __isl_give isl_map *map_lex_lte(__isl_take isl_space *dims, int equal)
4047 return map_lex_lte_first(dims, dims->n_out, equal);
4050 __isl_give isl_map *isl_map_lex_lt_first(__isl_take isl_space *dim, unsigned n)
4052 return map_lex_lte_first(dim, n, 0);
4055 __isl_give isl_map *isl_map_lex_le_first(__isl_take isl_space *dim, unsigned n)
4057 return map_lex_lte_first(dim, n, 1);
4060 __isl_give isl_map *isl_map_lex_lt(__isl_take isl_space *set_dim)
4062 return map_lex_lte(isl_space_map_from_set(set_dim), 0);
4065 __isl_give isl_map *isl_map_lex_le(__isl_take isl_space *set_dim)
4067 return map_lex_lte(isl_space_map_from_set(set_dim), 1);
4070 static __isl_give isl_map *map_lex_gte_first(__isl_take isl_space *dims,
4071 unsigned n, int equal)
4073 struct isl_map *map;
4076 if (n == 0 && equal)
4077 return isl_map_universe(dims);
4079 map = isl_map_alloc_space(isl_space_copy(dims), n, ISL_MAP_DISJOINT);
4081 for (i = 0; i + 1 < n; ++i)
4082 map = isl_map_add_basic_map(map,
4083 isl_basic_map_more_at(isl_space_copy(dims), i));
4086 map = isl_map_add_basic_map(map,
4087 isl_basic_map_more_or_equal_at(dims, n - 1));
4089 map = isl_map_add_basic_map(map,
4090 isl_basic_map_more_at(dims, n - 1));
4092 isl_space_free(dims);
4097 static __isl_give isl_map *map_lex_gte(__isl_take isl_space *dims, int equal)
4101 return map_lex_gte_first(dims, dims->n_out, equal);
4104 __isl_give isl_map *isl_map_lex_gt_first(__isl_take isl_space *dim, unsigned n)
4106 return map_lex_gte_first(dim, n, 0);
4109 __isl_give isl_map *isl_map_lex_ge_first(__isl_take isl_space *dim, unsigned n)
4111 return map_lex_gte_first(dim, n, 1);
4114 __isl_give isl_map *isl_map_lex_gt(__isl_take isl_space *set_dim)
4116 return map_lex_gte(isl_space_map_from_set(set_dim), 0);
4119 __isl_give isl_map *isl_map_lex_ge(__isl_take isl_space *set_dim)
4121 return map_lex_gte(isl_space_map_from_set(set_dim), 1);
4124 __isl_give isl_map *isl_set_lex_le_set(__isl_take isl_set *set1,
4125 __isl_take isl_set *set2)
4128 map = isl_map_lex_le(isl_set_get_space(set1));
4129 map = isl_map_intersect_domain(map, set1);
4130 map = isl_map_intersect_range(map, set2);
4134 __isl_give isl_map *isl_set_lex_lt_set(__isl_take isl_set *set1,
4135 __isl_take isl_set *set2)
4138 map = isl_map_lex_lt(isl_set_get_space(set1));
4139 map = isl_map_intersect_domain(map, set1);
4140 map = isl_map_intersect_range(map, set2);
4144 __isl_give isl_map *isl_set_lex_ge_set(__isl_take isl_set *set1,
4145 __isl_take isl_set *set2)
4148 map = isl_map_lex_ge(isl_set_get_space(set1));
4149 map = isl_map_intersect_domain(map, set1);
4150 map = isl_map_intersect_range(map, set2);
4154 __isl_give isl_map *isl_set_lex_gt_set(__isl_take isl_set *set1,
4155 __isl_take isl_set *set2)
4158 map = isl_map_lex_gt(isl_set_get_space(set1));
4159 map = isl_map_intersect_domain(map, set1);
4160 map = isl_map_intersect_range(map, set2);
4164 __isl_give isl_map *isl_map_lex_le_map(__isl_take isl_map *map1,
4165 __isl_take isl_map *map2)
4168 map = isl_map_lex_le(isl_space_range(isl_map_get_space(map1)));
4169 map = isl_map_apply_domain(map, isl_map_reverse(map1));
4170 map = isl_map_apply_range(map, isl_map_reverse(map2));
4174 __isl_give isl_map *isl_map_lex_lt_map(__isl_take isl_map *map1,
4175 __isl_take isl_map *map2)
4178 map = isl_map_lex_lt(isl_space_range(isl_map_get_space(map1)));
4179 map = isl_map_apply_domain(map, isl_map_reverse(map1));
4180 map = isl_map_apply_range(map, isl_map_reverse(map2));
4184 __isl_give isl_map *isl_map_lex_ge_map(__isl_take isl_map *map1,
4185 __isl_take isl_map *map2)
4188 map = isl_map_lex_ge(isl_space_range(isl_map_get_space(map1)));
4189 map = isl_map_apply_domain(map, isl_map_reverse(map1));
4190 map = isl_map_apply_range(map, isl_map_reverse(map2));
4194 __isl_give isl_map *isl_map_lex_gt_map(__isl_take isl_map *map1,
4195 __isl_take isl_map *map2)
4198 map = isl_map_lex_gt(isl_space_range(isl_map_get_space(map1)));
4199 map = isl_map_apply_domain(map, isl_map_reverse(map1));
4200 map = isl_map_apply_range(map, isl_map_reverse(map2));
4204 __isl_give isl_basic_map *isl_basic_map_from_basic_set(
4205 __isl_take isl_basic_set *bset, __isl_take isl_space *dim)
4207 struct isl_basic_map *bmap;
4209 bset = isl_basic_set_cow(bset);
4213 isl_assert(bset->ctx, isl_space_compatible(bset->dim, dim), goto error);
4214 isl_space_free(bset->dim);
4215 bmap = (struct isl_basic_map *) bset;
4217 return isl_basic_map_finalize(bmap);
4219 isl_basic_set_free(bset);
4220 isl_space_free(dim);
4224 struct isl_basic_set *isl_basic_set_from_basic_map(struct isl_basic_map *bmap)
4228 if (bmap->dim->n_in == 0)
4229 return (struct isl_basic_set *)bmap;
4230 bmap = isl_basic_map_cow(bmap);
4233 bmap->dim = isl_space_as_set_space(bmap->dim);
4236 bmap = isl_basic_map_finalize(bmap);
4237 return (struct isl_basic_set *)bmap;
4239 isl_basic_map_free(bmap);
4243 /* For a div d = floor(f/m), add the constraints
4246 * -(f-(n-1)) + m d >= 0
4248 * Note that the second constraint is the negation of
4252 int isl_basic_map_add_div_constraints_var(__isl_keep isl_basic_map *bmap,
4253 unsigned pos, isl_int *div)
4256 unsigned total = isl_basic_map_total_dim(bmap);
4258 i = isl_basic_map_alloc_inequality(bmap);
4261 isl_seq_cpy(bmap->ineq[i], div + 1, 1 + total);
4262 isl_int_neg(bmap->ineq[i][1 + pos], div[0]);
4264 j = isl_basic_map_alloc_inequality(bmap);
4267 isl_seq_neg(bmap->ineq[j], bmap->ineq[i], 1 + total);
4268 isl_int_add(bmap->ineq[j][0], bmap->ineq[j][0], bmap->ineq[j][1 + pos]);
4269 isl_int_sub_ui(bmap->ineq[j][0], bmap->ineq[j][0], 1);
4273 int isl_basic_set_add_div_constraints_var(__isl_keep isl_basic_set *bset,
4274 unsigned pos, isl_int *div)
4276 return isl_basic_map_add_div_constraints_var((isl_basic_map *)bset,
4280 int isl_basic_map_add_div_constraints(struct isl_basic_map *bmap, unsigned div)
4282 unsigned total = isl_basic_map_total_dim(bmap);
4283 unsigned div_pos = total - bmap->n_div + div;
4285 return isl_basic_map_add_div_constraints_var(bmap, div_pos,
4289 int isl_basic_set_add_div_constraints(struct isl_basic_set *bset, unsigned div)
4291 return isl_basic_map_add_div_constraints(bset, div);
4294 struct isl_basic_set *isl_basic_map_underlying_set(
4295 struct isl_basic_map *bmap)
4299 if (bmap->dim->nparam == 0 && bmap->dim->n_in == 0 &&
4301 !isl_space_is_named_or_nested(bmap->dim, isl_dim_in) &&
4302 !isl_space_is_named_or_nested(bmap->dim, isl_dim_out))
4303 return (struct isl_basic_set *)bmap;
4304 bmap = isl_basic_map_cow(bmap);
4307 bmap->dim = isl_space_underlying(bmap->dim, bmap->n_div);
4310 bmap->extra -= bmap->n_div;
4312 bmap = isl_basic_map_finalize(bmap);
4313 return (struct isl_basic_set *)bmap;
4315 isl_basic_map_free(bmap);
4319 __isl_give isl_basic_set *isl_basic_set_underlying_set(
4320 __isl_take isl_basic_set *bset)
4322 return isl_basic_map_underlying_set((isl_basic_map *)bset);
4325 struct isl_basic_map *isl_basic_map_overlying_set(
4326 struct isl_basic_set *bset, struct isl_basic_map *like)
4328 struct isl_basic_map *bmap;
4329 struct isl_ctx *ctx;
4336 isl_assert(ctx, bset->n_div == 0, goto error);
4337 isl_assert(ctx, isl_basic_set_n_param(bset) == 0, goto error);
4338 isl_assert(ctx, bset->dim->n_out == isl_basic_map_total_dim(like),
4340 if (isl_space_is_equal(bset->dim, like->dim) && like->n_div == 0) {
4341 isl_basic_map_free(like);
4342 return (struct isl_basic_map *)bset;
4344 bset = isl_basic_set_cow(bset);
4347 total = bset->dim->n_out + bset->extra;
4348 bmap = (struct isl_basic_map *)bset;
4349 isl_space_free(bmap->dim);
4350 bmap->dim = isl_space_copy(like->dim);
4353 bmap->n_div = like->n_div;
4354 bmap->extra += like->n_div;
4358 ltotal = total - bmap->extra + like->extra;
4361 bmap->block2 = isl_blk_extend(ctx, bmap->block2,
4362 bmap->extra * (1 + 1 + total));
4363 if (isl_blk_is_error(bmap->block2))
4365 div = isl_realloc_array(ctx, bmap->div, isl_int *, bmap->extra);
4369 for (i = 0; i < bmap->extra; ++i)
4370 bmap->div[i] = bmap->block2.data + i * (1 + 1 + total);
4371 for (i = 0; i < like->n_div; ++i) {
4372 isl_seq_cpy(bmap->div[i], like->div[i], 1 + 1 + ltotal);
4373 isl_seq_clr(bmap->div[i]+1+1+ltotal, total - ltotal);
4375 bmap = isl_basic_map_extend_constraints(bmap,
4376 0, 2 * like->n_div);
4377 for (i = 0; i < like->n_div; ++i) {
4380 if (isl_int_is_zero(bmap->div[i][0]))
4382 if (isl_basic_map_add_div_constraints(bmap, i) < 0)
4383 bmap = isl_basic_map_free(bmap);
4386 isl_basic_map_free(like);
4387 bmap = isl_basic_map_simplify(bmap);
4388 bmap = isl_basic_map_finalize(bmap);
4391 isl_basic_map_free(like);
4392 isl_basic_set_free(bset);
4396 struct isl_basic_set *isl_basic_set_from_underlying_set(
4397 struct isl_basic_set *bset, struct isl_basic_set *like)
4399 return (struct isl_basic_set *)
4400 isl_basic_map_overlying_set(bset, (struct isl_basic_map *)like);
4403 struct isl_set *isl_set_from_underlying_set(
4404 struct isl_set *set, struct isl_basic_set *like)
4410 isl_assert(set->ctx, set->dim->n_out == isl_basic_set_total_dim(like),
4412 if (isl_space_is_equal(set->dim, like->dim) && like->n_div == 0) {
4413 isl_basic_set_free(like);
4416 set = isl_set_cow(set);
4419 for (i = 0; i < set->n; ++i) {
4420 set->p[i] = isl_basic_set_from_underlying_set(set->p[i],
4421 isl_basic_set_copy(like));
4425 isl_space_free(set->dim);
4426 set->dim = isl_space_copy(like->dim);
4429 isl_basic_set_free(like);
4432 isl_basic_set_free(like);
4437 struct isl_set *isl_map_underlying_set(struct isl_map *map)
4441 map = isl_map_cow(map);
4444 map->dim = isl_space_cow(map->dim);
4448 for (i = 1; i < map->n; ++i)
4449 isl_assert(map->ctx, map->p[0]->n_div == map->p[i]->n_div,
4451 for (i = 0; i < map->n; ++i) {
4452 map->p[i] = (struct isl_basic_map *)
4453 isl_basic_map_underlying_set(map->p[i]);
4458 map->dim = isl_space_underlying(map->dim, 0);
4460 isl_space_free(map->dim);
4461 map->dim = isl_space_copy(map->p[0]->dim);
4465 return (struct isl_set *)map;
4471 struct isl_set *isl_set_to_underlying_set(struct isl_set *set)
4473 return (struct isl_set *)isl_map_underlying_set((struct isl_map *)set);
4476 __isl_give isl_basic_map *isl_basic_map_reset_space(
4477 __isl_take isl_basic_map *bmap, __isl_take isl_space *dim)
4479 bmap = isl_basic_map_cow(bmap);
4483 isl_space_free(bmap->dim);
4486 bmap = isl_basic_map_finalize(bmap);
4490 isl_basic_map_free(bmap);
4491 isl_space_free(dim);
4495 __isl_give isl_basic_set *isl_basic_set_reset_space(
4496 __isl_take isl_basic_set *bset, __isl_take isl_space *dim)
4498 return (isl_basic_set *)isl_basic_map_reset_space((isl_basic_map *)bset,
4502 __isl_give isl_map *isl_map_reset_space(__isl_take isl_map *map,
4503 __isl_take isl_space *dim)
4507 map = isl_map_cow(map);
4511 for (i = 0; i < map->n; ++i) {
4512 map->p[i] = isl_basic_map_reset_space(map->p[i],
4513 isl_space_copy(dim));
4517 isl_space_free(map->dim);
4523 isl_space_free(dim);
4527 __isl_give isl_set *isl_set_reset_space(__isl_take isl_set *set,
4528 __isl_take isl_space *dim)
4530 return (struct isl_set *) isl_map_reset_space((struct isl_map *)set, dim);
4533 /* Compute the parameter domain of the given basic set.
4535 __isl_give isl_basic_set *isl_basic_set_params(__isl_take isl_basic_set *bset)
4540 if (isl_basic_set_is_params(bset))
4543 n = isl_basic_set_dim(bset, isl_dim_set);
4544 bset = isl_basic_set_project_out(bset, isl_dim_set, 0, n);
4545 space = isl_basic_set_get_space(bset);
4546 space = isl_space_params(space);
4547 bset = isl_basic_set_reset_space(bset, space);
4551 /* Construct a zero-dimensional basic set with the given parameter domain.
4553 __isl_give isl_basic_set *isl_basic_set_from_params(
4554 __isl_take isl_basic_set *bset)
4557 space = isl_basic_set_get_space(bset);
4558 space = isl_space_set_from_params(space);
4559 bset = isl_basic_set_reset_space(bset, space);
4563 /* Compute the parameter domain of the given set.
4565 __isl_give isl_set *isl_set_params(__isl_take isl_set *set)
4570 if (isl_set_is_params(set))
4573 n = isl_set_dim(set, isl_dim_set);
4574 set = isl_set_project_out(set, isl_dim_set, 0, n);
4575 space = isl_set_get_space(set);
4576 space = isl_space_params(space);
4577 set = isl_set_reset_space(set, space);
4581 /* Construct a zero-dimensional set with the given parameter domain.
4583 __isl_give isl_set *isl_set_from_params(__isl_take isl_set *set)
4586 space = isl_set_get_space(set);
4587 space = isl_space_set_from_params(space);
4588 set = isl_set_reset_space(set, space);
4592 /* Compute the parameter domain of the given map.
4594 __isl_give isl_set *isl_map_params(__isl_take isl_map *map)
4599 n = isl_map_dim(map, isl_dim_in);
4600 map = isl_map_project_out(map, isl_dim_in, 0, n);
4601 n = isl_map_dim(map, isl_dim_out);
4602 map = isl_map_project_out(map, isl_dim_out, 0, n);
4603 space = isl_map_get_space(map);
4604 space = isl_space_params(space);
4605 map = isl_map_reset_space(map, space);
4609 struct isl_basic_set *isl_basic_map_domain(struct isl_basic_map *bmap)
4612 struct isl_basic_set *domain;
4618 dim = isl_space_domain(isl_basic_map_get_space(bmap));
4620 n_in = isl_basic_map_n_in(bmap);
4621 n_out = isl_basic_map_n_out(bmap);
4622 domain = isl_basic_set_from_basic_map(bmap);
4623 domain = isl_basic_set_project_out(domain, isl_dim_set, n_in, n_out);
4625 domain = isl_basic_set_reset_space(domain, dim);
4630 int isl_basic_map_may_be_set(__isl_keep isl_basic_map *bmap)
4634 return isl_space_may_be_set(bmap->dim);
4637 /* Is this basic map actually a set?
4638 * Users should never call this function. Outside of isl,
4639 * the type should indicate whether something is a set or a map.
4641 int isl_basic_map_is_set(__isl_keep isl_basic_map *bmap)
4645 return isl_space_is_set(bmap->dim);
4648 struct isl_basic_set *isl_basic_map_range(struct isl_basic_map *bmap)
4652 if (isl_basic_map_is_set(bmap))
4654 return isl_basic_map_domain(isl_basic_map_reverse(bmap));
4657 __isl_give isl_basic_map *isl_basic_map_domain_map(
4658 __isl_take isl_basic_map *bmap)
4662 isl_basic_map *domain;
4663 int nparam, n_in, n_out;
4666 nparam = isl_basic_map_dim(bmap, isl_dim_param);
4667 n_in = isl_basic_map_dim(bmap, isl_dim_in);
4668 n_out = isl_basic_map_dim(bmap, isl_dim_out);
4670 dim = isl_space_from_range(isl_space_domain(isl_basic_map_get_space(bmap)));
4671 domain = isl_basic_map_universe(dim);
4673 bmap = isl_basic_map_from_domain(isl_basic_map_wrap(bmap));
4674 bmap = isl_basic_map_apply_range(bmap, domain);
4675 bmap = isl_basic_map_extend_constraints(bmap, n_in, 0);
4677 total = isl_basic_map_total_dim(bmap);
4679 for (i = 0; i < n_in; ++i) {
4680 k = isl_basic_map_alloc_equality(bmap);
4683 isl_seq_clr(bmap->eq[k], 1 + total);
4684 isl_int_set_si(bmap->eq[k][1 + nparam + i], -1);
4685 isl_int_set_si(bmap->eq[k][1 + nparam + n_in + n_out + i], 1);
4688 bmap = isl_basic_map_gauss(bmap, NULL);
4689 return isl_basic_map_finalize(bmap);
4691 isl_basic_map_free(bmap);
4695 __isl_give isl_basic_map *isl_basic_map_range_map(
4696 __isl_take isl_basic_map *bmap)
4700 isl_basic_map *range;
4701 int nparam, n_in, n_out;
4704 nparam = isl_basic_map_dim(bmap, isl_dim_param);
4705 n_in = isl_basic_map_dim(bmap, isl_dim_in);
4706 n_out = isl_basic_map_dim(bmap, isl_dim_out);
4708 dim = isl_space_from_range(isl_space_range(isl_basic_map_get_space(bmap)));
4709 range = isl_basic_map_universe(dim);
4711 bmap = isl_basic_map_from_domain(isl_basic_map_wrap(bmap));
4712 bmap = isl_basic_map_apply_range(bmap, range);
4713 bmap = isl_basic_map_extend_constraints(bmap, n_out, 0);
4715 total = isl_basic_map_total_dim(bmap);
4717 for (i = 0; i < n_out; ++i) {
4718 k = isl_basic_map_alloc_equality(bmap);
4721 isl_seq_clr(bmap->eq[k], 1 + total);
4722 isl_int_set_si(bmap->eq[k][1 + nparam + n_in + i], -1);
4723 isl_int_set_si(bmap->eq[k][1 + nparam + n_in + n_out + i], 1);
4726 bmap = isl_basic_map_gauss(bmap, NULL);
4727 return isl_basic_map_finalize(bmap);
4729 isl_basic_map_free(bmap);
4733 int isl_map_may_be_set(__isl_keep isl_map *map)
4737 return isl_space_may_be_set(map->dim);
4740 /* Is this map actually a set?
4741 * Users should never call this function. Outside of isl,
4742 * the type should indicate whether something is a set or a map.
4744 int isl_map_is_set(__isl_keep isl_map *map)
4748 return isl_space_is_set(map->dim);
4751 struct isl_set *isl_map_range(struct isl_map *map)
4754 struct isl_set *set;
4758 if (isl_map_is_set(map))
4759 return (isl_set *)map;
4761 map = isl_map_cow(map);
4765 set = (struct isl_set *) map;
4766 set->dim = isl_space_range(set->dim);
4769 for (i = 0; i < map->n; ++i) {
4770 set->p[i] = isl_basic_map_range(map->p[i]);
4774 ISL_F_CLR(set, ISL_MAP_DISJOINT);
4775 ISL_F_CLR(set, ISL_SET_NORMALIZED);
4782 __isl_give isl_map *isl_map_domain_map(__isl_take isl_map *map)
4785 isl_space *domain_dim;
4787 map = isl_map_cow(map);
4791 domain_dim = isl_space_from_range(isl_space_domain(isl_map_get_space(map)));
4792 map->dim = isl_space_from_domain(isl_space_wrap(map->dim));
4793 map->dim = isl_space_join(map->dim, domain_dim);
4796 for (i = 0; i < map->n; ++i) {
4797 map->p[i] = isl_basic_map_domain_map(map->p[i]);
4801 ISL_F_CLR(map, ISL_MAP_DISJOINT);
4802 ISL_F_CLR(map, ISL_MAP_NORMALIZED);
4809 __isl_give isl_map *isl_map_range_map(__isl_take isl_map *map)
4812 isl_space *range_dim;
4814 map = isl_map_cow(map);
4818 range_dim = isl_space_range(isl_map_get_space(map));
4819 range_dim = isl_space_from_range(range_dim);
4820 map->dim = isl_space_from_domain(isl_space_wrap(map->dim));
4821 map->dim = isl_space_join(map->dim, range_dim);
4824 for (i = 0; i < map->n; ++i) {
4825 map->p[i] = isl_basic_map_range_map(map->p[i]);
4829 ISL_F_CLR(map, ISL_MAP_DISJOINT);
4830 ISL_F_CLR(map, ISL_MAP_NORMALIZED);
4837 __isl_give isl_map *isl_map_from_set(__isl_take isl_set *set,
4838 __isl_take isl_space *dim)
4841 struct isl_map *map = NULL;
4843 set = isl_set_cow(set);
4846 isl_assert(set->ctx, isl_space_compatible(set->dim, dim), goto error);
4847 map = (struct isl_map *)set;
4848 for (i = 0; i < set->n; ++i) {
4849 map->p[i] = isl_basic_map_from_basic_set(
4850 set->p[i], isl_space_copy(dim));
4854 isl_space_free(map->dim);
4858 isl_space_free(dim);
4863 __isl_give isl_basic_map *isl_basic_map_from_domain(
4864 __isl_take isl_basic_set *bset)
4866 return isl_basic_map_reverse(isl_basic_map_from_range(bset));
4869 __isl_give isl_basic_map *isl_basic_map_from_range(
4870 __isl_take isl_basic_set *bset)
4873 space = isl_basic_set_get_space(bset);
4874 space = isl_space_from_range(space);
4875 bset = isl_basic_set_reset_space(bset, space);
4876 return (isl_basic_map *)bset;
4879 struct isl_map *isl_map_from_range(struct isl_set *set)
4882 space = isl_set_get_space(set);
4883 space = isl_space_from_range(space);
4884 set = isl_set_reset_space(set, space);
4885 return (struct isl_map *)set;
4888 __isl_give isl_map *isl_map_from_domain(__isl_take isl_set *set)
4890 return isl_map_reverse(isl_map_from_range(set));
4893 __isl_give isl_basic_map *isl_basic_map_from_domain_and_range(
4894 __isl_take isl_basic_set *domain, __isl_take isl_basic_set *range)
4896 return isl_basic_map_apply_range(isl_basic_map_reverse(domain), range);
4899 __isl_give isl_map *isl_map_from_domain_and_range(__isl_take isl_set *domain,
4900 __isl_take isl_set *range)
4902 return isl_map_apply_range(isl_map_reverse(domain), range);
4905 struct isl_set *isl_set_from_map(struct isl_map *map)
4908 struct isl_set *set = NULL;
4912 map = isl_map_cow(map);
4915 map->dim = isl_space_as_set_space(map->dim);
4918 set = (struct isl_set *)map;
4919 for (i = 0; i < map->n; ++i) {
4920 set->p[i] = isl_basic_set_from_basic_map(map->p[i]);
4930 __isl_give isl_map *isl_map_alloc_space(__isl_take isl_space *dim, int n,
4933 struct isl_map *map;
4938 isl_die(dim->ctx, isl_error_internal,
4939 "negative number of basic maps", goto error);
4940 map = isl_alloc(dim->ctx, struct isl_map,
4941 sizeof(struct isl_map) +
4942 (n - 1) * sizeof(struct isl_basic_map *));
4946 map->ctx = dim->ctx;
4947 isl_ctx_ref(map->ctx);
4955 isl_space_free(dim);
4959 struct isl_map *isl_map_alloc(struct isl_ctx *ctx,
4960 unsigned nparam, unsigned in, unsigned out, int n,
4963 struct isl_map *map;
4966 dims = isl_space_alloc(ctx, nparam, in, out);
4970 map = isl_map_alloc_space(dims, n, flags);
4974 __isl_give isl_basic_map *isl_basic_map_empty(__isl_take isl_space *dim)
4976 struct isl_basic_map *bmap;
4977 bmap = isl_basic_map_alloc_space(dim, 0, 1, 0);
4978 bmap = isl_basic_map_set_to_empty(bmap);
4982 __isl_give isl_basic_set *isl_basic_set_empty(__isl_take isl_space *dim)
4984 struct isl_basic_set *bset;
4985 bset = isl_basic_set_alloc_space(dim, 0, 1, 0);
4986 bset = isl_basic_set_set_to_empty(bset);
4990 struct isl_basic_map *isl_basic_map_empty_like(struct isl_basic_map *model)
4992 struct isl_basic_map *bmap;
4995 bmap = isl_basic_map_alloc_space(isl_space_copy(model->dim), 0, 1, 0);
4996 bmap = isl_basic_map_set_to_empty(bmap);
5000 struct isl_basic_map *isl_basic_map_empty_like_map(struct isl_map *model)
5002 struct isl_basic_map *bmap;
5005 bmap = isl_basic_map_alloc_space(isl_space_copy(model->dim), 0, 1, 0);
5006 bmap = isl_basic_map_set_to_empty(bmap);
5010 struct isl_basic_set *isl_basic_set_empty_like(struct isl_basic_set *model)
5012 struct isl_basic_set *bset;
5015 bset = isl_basic_set_alloc_space(isl_space_copy(model->dim), 0, 1, 0);
5016 bset = isl_basic_set_set_to_empty(bset);
5020 __isl_give isl_basic_map *isl_basic_map_universe(__isl_take isl_space *dim)
5022 struct isl_basic_map *bmap;
5023 bmap = isl_basic_map_alloc_space(dim, 0, 0, 0);
5024 bmap = isl_basic_map_finalize(bmap);
5028 __isl_give isl_basic_set *isl_basic_set_universe(__isl_take isl_space *dim)
5030 struct isl_basic_set *bset;
5031 bset = isl_basic_set_alloc_space(dim, 0, 0, 0);
5032 bset = isl_basic_set_finalize(bset);
5036 __isl_give isl_basic_map *isl_basic_map_nat_universe(__isl_take isl_space *dim)
5039 unsigned total = isl_space_dim(dim, isl_dim_all);
5040 isl_basic_map *bmap;
5042 bmap= isl_basic_map_alloc_space(dim, 0, 0, total);
5043 for (i = 0; i < total; ++i) {
5044 int k = isl_basic_map_alloc_inequality(bmap);
5047 isl_seq_clr(bmap->ineq[k], 1 + total);
5048 isl_int_set_si(bmap->ineq[k][1 + i], 1);
5052 isl_basic_map_free(bmap);
5056 __isl_give isl_basic_set *isl_basic_set_nat_universe(__isl_take isl_space *dim)
5058 return isl_basic_map_nat_universe(dim);
5061 __isl_give isl_map *isl_map_nat_universe(__isl_take isl_space *dim)
5063 return isl_map_from_basic_map(isl_basic_map_nat_universe(dim));
5066 __isl_give isl_set *isl_set_nat_universe(__isl_take isl_space *dim)
5068 return isl_map_nat_universe(dim);
5071 __isl_give isl_basic_map *isl_basic_map_universe_like(
5072 __isl_keep isl_basic_map *model)
5076 return isl_basic_map_alloc_space(isl_space_copy(model->dim), 0, 0, 0);
5079 struct isl_basic_set *isl_basic_set_universe_like(struct isl_basic_set *model)
5083 return isl_basic_set_alloc_space(isl_space_copy(model->dim), 0, 0, 0);
5086 __isl_give isl_basic_set *isl_basic_set_universe_like_set(
5087 __isl_keep isl_set *model)
5091 return isl_basic_set_alloc_space(isl_space_copy(model->dim), 0, 0, 0);
5094 __isl_give isl_map *isl_map_empty(__isl_take isl_space *dim)
5096 return isl_map_alloc_space(dim, 0, ISL_MAP_DISJOINT);
5099 struct isl_map *isl_map_empty_like(struct isl_map *model)
5103 return isl_map_alloc_space(isl_space_copy(model->dim), 0, ISL_MAP_DISJOINT);
5106 struct isl_map *isl_map_empty_like_basic_map(struct isl_basic_map *model)
5110 return isl_map_alloc_space(isl_space_copy(model->dim), 0, ISL_MAP_DISJOINT);
5113 __isl_give isl_set *isl_set_empty(__isl_take isl_space *dim)
5115 return isl_set_alloc_space(dim, 0, ISL_MAP_DISJOINT);
5118 struct isl_set *isl_set_empty_like(struct isl_set *model)
5122 return isl_set_empty(isl_space_copy(model->dim));
5125 __isl_give isl_map *isl_map_universe(__isl_take isl_space *dim)
5127 struct isl_map *map;
5130 map = isl_map_alloc_space(isl_space_copy(dim), 1, ISL_MAP_DISJOINT);
5131 map = isl_map_add_basic_map(map, isl_basic_map_universe(dim));
5135 __isl_give isl_set *isl_set_universe(__isl_take isl_space *dim)
5137 struct isl_set *set;
5140 set = isl_set_alloc_space(isl_space_copy(dim), 1, ISL_MAP_DISJOINT);
5141 set = isl_set_add_basic_set(set, isl_basic_set_universe(dim));
5145 __isl_give isl_set *isl_set_universe_like(__isl_keep isl_set *model)
5149 return isl_set_universe(isl_space_copy(model->dim));
5152 struct isl_map *isl_map_dup(struct isl_map *map)
5155 struct isl_map *dup;
5159 dup = isl_map_alloc_space(isl_space_copy(map->dim), map->n, map->flags);
5160 for (i = 0; i < map->n; ++i)
5161 dup = isl_map_add_basic_map(dup, isl_basic_map_copy(map->p[i]));
5165 __isl_give isl_map *isl_map_add_basic_map(__isl_take isl_map *map,
5166 __isl_take isl_basic_map *bmap)
5170 if (isl_basic_map_plain_is_empty(bmap)) {
5171 isl_basic_map_free(bmap);
5174 isl_assert(map->ctx, isl_space_is_equal(map->dim, bmap->dim), goto error);
5175 isl_assert(map->ctx, map->n < map->size, goto error);
5176 map->p[map->n] = bmap;
5178 ISL_F_CLR(map, ISL_MAP_NORMALIZED);
5184 isl_basic_map_free(bmap);
5188 void *isl_map_free(struct isl_map *map)
5198 isl_ctx_deref(map->ctx);
5199 for (i = 0; i < map->n; ++i)
5200 isl_basic_map_free(map->p[i]);
5201 isl_space_free(map->dim);
5207 struct isl_map *isl_map_extend(struct isl_map *base,
5208 unsigned nparam, unsigned n_in, unsigned n_out)
5212 base = isl_map_cow(base);
5216 base->dim = isl_space_extend(base->dim, nparam, n_in, n_out);
5219 for (i = 0; i < base->n; ++i) {
5220 base->p[i] = isl_basic_map_extend_space(base->p[i],
5221 isl_space_copy(base->dim), 0, 0, 0);
5231 struct isl_set *isl_set_extend(struct isl_set *base,
5232 unsigned nparam, unsigned dim)
5234 return (struct isl_set *)isl_map_extend((struct isl_map *)base,
5238 static struct isl_basic_map *isl_basic_map_fix_pos_si(
5239 struct isl_basic_map *bmap, unsigned pos, int value)
5243 bmap = isl_basic_map_cow(bmap);
5244 bmap = isl_basic_map_extend_constraints(bmap, 1, 0);
5245 j = isl_basic_map_alloc_equality(bmap);
5248 isl_seq_clr(bmap->eq[j] + 1, isl_basic_map_total_dim(bmap));
5249 isl_int_set_si(bmap->eq[j][pos], -1);
5250 isl_int_set_si(bmap->eq[j][0], value);
5251 bmap = isl_basic_map_simplify(bmap);
5252 return isl_basic_map_finalize(bmap);
5254 isl_basic_map_free(bmap);
5258 static __isl_give isl_basic_map *isl_basic_map_fix_pos(
5259 __isl_take isl_basic_map *bmap, unsigned pos, isl_int value)
5263 bmap = isl_basic_map_cow(bmap);
5264 bmap = isl_basic_map_extend_constraints(bmap, 1, 0);
5265 j = isl_basic_map_alloc_equality(bmap);
5268 isl_seq_clr(bmap->eq[j] + 1, isl_basic_map_total_dim(bmap));
5269 isl_int_set_si(bmap->eq[j][pos], -1);
5270 isl_int_set(bmap->eq[j][0], value);
5271 bmap = isl_basic_map_simplify(bmap);
5272 return isl_basic_map_finalize(bmap);
5274 isl_basic_map_free(bmap);
5278 struct isl_basic_map *isl_basic_map_fix_si(struct isl_basic_map *bmap,
5279 enum isl_dim_type type, unsigned pos, int value)
5283 isl_assert(bmap->ctx, pos < isl_basic_map_dim(bmap, type), goto error);
5284 return isl_basic_map_fix_pos_si(bmap,
5285 isl_basic_map_offset(bmap, type) + pos, value);
5287 isl_basic_map_free(bmap);
5291 __isl_give isl_basic_map *isl_basic_map_fix(__isl_take isl_basic_map *bmap,
5292 enum isl_dim_type type, unsigned pos, isl_int value)
5296 isl_assert(bmap->ctx, pos < isl_basic_map_dim(bmap, type), goto error);
5297 return isl_basic_map_fix_pos(bmap,
5298 isl_basic_map_offset(bmap, type) + pos, value);
5300 isl_basic_map_free(bmap);
5304 struct isl_basic_set *isl_basic_set_fix_si(struct isl_basic_set *bset,
5305 enum isl_dim_type type, unsigned pos, int value)
5307 return (struct isl_basic_set *)
5308 isl_basic_map_fix_si((struct isl_basic_map *)bset,
5312 __isl_give isl_basic_set *isl_basic_set_fix(__isl_take isl_basic_set *bset,
5313 enum isl_dim_type type, unsigned pos, isl_int value)
5315 return (struct isl_basic_set *)
5316 isl_basic_map_fix((struct isl_basic_map *)bset,
5320 struct isl_basic_map *isl_basic_map_fix_input_si(struct isl_basic_map *bmap,
5321 unsigned input, int value)
5323 return isl_basic_map_fix_si(bmap, isl_dim_in, input, value);
5326 struct isl_basic_set *isl_basic_set_fix_dim_si(struct isl_basic_set *bset,
5327 unsigned dim, int value)
5329 return (struct isl_basic_set *)
5330 isl_basic_map_fix_si((struct isl_basic_map *)bset,
5331 isl_dim_set, dim, value);
5334 static int remove_if_empty(__isl_keep isl_map *map, int i)
5336 int empty = isl_basic_map_plain_is_empty(map->p[i]);
5343 isl_basic_map_free(map->p[i]);
5344 if (i != map->n - 1) {
5345 ISL_F_CLR(map, ISL_MAP_NORMALIZED);
5346 map->p[i] = map->p[map->n - 1];
5353 /* Perform "fn" on each basic map of "map", where we may not be holding
5354 * the only reference to "map".
5355 * In particular, "fn" should be a semantics preserving operation
5356 * that we want to apply to all copies of "map". We therefore need
5357 * to be careful not to modify "map" in a way that breaks "map"
5358 * in case anything goes wrong.
5360 __isl_give isl_map *isl_map_inline_foreach_basic_map(__isl_take isl_map *map,
5361 __isl_give isl_basic_map *(*fn)(__isl_take isl_basic_map *bmap))
5363 struct isl_basic_map *bmap;
5369 for (i = map->n - 1; i >= 0; --i) {
5370 bmap = isl_basic_map_copy(map->p[i]);
5374 isl_basic_map_free(map->p[i]);
5376 if (remove_if_empty(map, i) < 0)
5386 struct isl_map *isl_map_fix_si(struct isl_map *map,
5387 enum isl_dim_type type, unsigned pos, int value)
5391 map = isl_map_cow(map);
5395 isl_assert(map->ctx, pos < isl_map_dim(map, type), goto error);
5396 for (i = map->n - 1; i >= 0; --i) {
5397 map->p[i] = isl_basic_map_fix_si(map->p[i], type, pos, value);
5398 if (remove_if_empty(map, i) < 0)
5401 ISL_F_CLR(map, ISL_MAP_NORMALIZED);
5408 __isl_give isl_set *isl_set_fix_si(__isl_take isl_set *set,
5409 enum isl_dim_type type, unsigned pos, int value)
5411 return (struct isl_set *)
5412 isl_map_fix_si((struct isl_map *)set, type, pos, value);
5415 __isl_give isl_map *isl_map_fix(__isl_take isl_map *map,
5416 enum isl_dim_type type, unsigned pos, isl_int value)
5420 map = isl_map_cow(map);
5424 isl_assert(map->ctx, pos < isl_map_dim(map, type), goto error);
5425 for (i = 0; i < map->n; ++i) {
5426 map->p[i] = isl_basic_map_fix(map->p[i], type, pos, value);
5430 ISL_F_CLR(map, ISL_MAP_NORMALIZED);
5437 __isl_give isl_set *isl_set_fix(__isl_take isl_set *set,
5438 enum isl_dim_type type, unsigned pos, isl_int value)
5440 return (struct isl_set *)isl_map_fix((isl_map *)set, type, pos, value);
5443 struct isl_map *isl_map_fix_input_si(struct isl_map *map,
5444 unsigned input, int value)
5446 return isl_map_fix_si(map, isl_dim_in, input, value);
5449 struct isl_set *isl_set_fix_dim_si(struct isl_set *set, unsigned dim, int value)
5451 return (struct isl_set *)
5452 isl_map_fix_si((struct isl_map *)set, isl_dim_set, dim, value);
5455 static __isl_give isl_basic_map *basic_map_bound_si(
5456 __isl_take isl_basic_map *bmap,
5457 enum isl_dim_type type, unsigned pos, int value, int upper)
5463 isl_assert(bmap->ctx, pos < isl_basic_map_dim(bmap, type), goto error);
5464 pos += isl_basic_map_offset(bmap, type);
5465 bmap = isl_basic_map_cow(bmap);
5466 bmap = isl_basic_map_extend_constraints(bmap, 0, 1);
5467 j = isl_basic_map_alloc_inequality(bmap);
5470 isl_seq_clr(bmap->ineq[j], 1 + isl_basic_map_total_dim(bmap));
5472 isl_int_set_si(bmap->ineq[j][pos], -1);
5473 isl_int_set_si(bmap->ineq[j][0], value);
5475 isl_int_set_si(bmap->ineq[j][pos], 1);
5476 isl_int_set_si(bmap->ineq[j][0], -value);
5478 bmap = isl_basic_map_simplify(bmap);
5479 return isl_basic_map_finalize(bmap);
5481 isl_basic_map_free(bmap);
5485 __isl_give isl_basic_map *isl_basic_map_lower_bound_si(
5486 __isl_take isl_basic_map *bmap,
5487 enum isl_dim_type type, unsigned pos, int value)
5489 return basic_map_bound_si(bmap, type, pos, value, 0);
5492 /* Constrain the values of the given dimension to be no greater than "value".
5494 __isl_give isl_basic_map *isl_basic_map_upper_bound_si(
5495 __isl_take isl_basic_map *bmap,
5496 enum isl_dim_type type, unsigned pos, int value)
5498 return basic_map_bound_si(bmap, type, pos, value, 1);
5501 struct isl_basic_set *isl_basic_set_lower_bound_dim(struct isl_basic_set *bset,
5502 unsigned dim, isl_int value)
5506 bset = isl_basic_set_cow(bset);
5507 bset = isl_basic_set_extend_constraints(bset, 0, 1);
5508 j = isl_basic_set_alloc_inequality(bset);
5511 isl_seq_clr(bset->ineq[j], 1 + isl_basic_set_total_dim(bset));
5512 isl_int_set_si(bset->ineq[j][1 + isl_basic_set_n_param(bset) + dim], 1);
5513 isl_int_neg(bset->ineq[j][0], value);
5514 bset = isl_basic_set_simplify(bset);
5515 return isl_basic_set_finalize(bset);
5517 isl_basic_set_free(bset);
5521 static __isl_give isl_map *map_bound_si(__isl_take isl_map *map,
5522 enum isl_dim_type type, unsigned pos, int value, int upper)
5526 map = isl_map_cow(map);
5530 isl_assert(map->ctx, pos < isl_map_dim(map, type), goto error);
5531 for (i = 0; i < map->n; ++i) {
5532 map->p[i] = basic_map_bound_si(map->p[i],
5533 type, pos, value, upper);
5537 ISL_F_CLR(map, ISL_MAP_NORMALIZED);
5544 __isl_give isl_map *isl_map_lower_bound_si(__isl_take isl_map *map,
5545 enum isl_dim_type type, unsigned pos, int value)
5547 return map_bound_si(map, type, pos, value, 0);
5550 __isl_give isl_map *isl_map_upper_bound_si(__isl_take isl_map *map,
5551 enum isl_dim_type type, unsigned pos, int value)
5553 return map_bound_si(map, type, pos, value, 1);
5556 __isl_give isl_set *isl_set_lower_bound_si(__isl_take isl_set *set,
5557 enum isl_dim_type type, unsigned pos, int value)
5559 return (struct isl_set *)
5560 isl_map_lower_bound_si((struct isl_map *)set, type, pos, value);
5563 __isl_give isl_set *isl_set_upper_bound_si(__isl_take isl_set *set,
5564 enum isl_dim_type type, unsigned pos, int value)
5566 return isl_map_upper_bound_si(set, type, pos, value);
5569 /* Bound the given variable of "bmap" from below (or above is "upper"
5570 * is set) to "value".
5572 static __isl_give isl_basic_map *basic_map_bound(
5573 __isl_take isl_basic_map *bmap,
5574 enum isl_dim_type type, unsigned pos, isl_int value, int upper)
5580 if (pos >= isl_basic_map_dim(bmap, type))
5581 isl_die(bmap->ctx, isl_error_invalid,
5582 "index out of bounds", goto error);
5583 pos += isl_basic_map_offset(bmap, type);
5584 bmap = isl_basic_map_cow(bmap);
5585 bmap = isl_basic_map_extend_constraints(bmap, 0, 1);
5586 j = isl_basic_map_alloc_inequality(bmap);
5589 isl_seq_clr(bmap->ineq[j], 1 + isl_basic_map_total_dim(bmap));
5591 isl_int_set_si(bmap->ineq[j][pos], -1);
5592 isl_int_set(bmap->ineq[j][0], value);
5594 isl_int_set_si(bmap->ineq[j][pos], 1);
5595 isl_int_neg(bmap->ineq[j][0], value);
5597 bmap = isl_basic_map_simplify(bmap);
5598 return isl_basic_map_finalize(bmap);
5600 isl_basic_map_free(bmap);
5604 /* Bound the given variable of "map" from below (or above is "upper"
5605 * is set) to "value".
5607 static __isl_give isl_map *map_bound(__isl_take isl_map *map,
5608 enum isl_dim_type type, unsigned pos, isl_int value, int upper)
5612 map = isl_map_cow(map);
5616 if (pos >= isl_map_dim(map, type))
5617 isl_die(map->ctx, isl_error_invalid,
5618 "index out of bounds", goto error);
5619 for (i = map->n - 1; i >= 0; --i) {
5620 map->p[i] = basic_map_bound(map->p[i], type, pos, value, upper);
5621 if (remove_if_empty(map, i) < 0)
5624 ISL_F_CLR(map, ISL_MAP_NORMALIZED);
5631 __isl_give isl_map *isl_map_lower_bound(__isl_take isl_map *map,
5632 enum isl_dim_type type, unsigned pos, isl_int value)
5634 return map_bound(map, type, pos, value, 0);
5637 __isl_give isl_map *isl_map_upper_bound(__isl_take isl_map *map,
5638 enum isl_dim_type type, unsigned pos, isl_int value)
5640 return map_bound(map, type, pos, value, 1);
5643 __isl_give isl_set *isl_set_lower_bound(__isl_take isl_set *set,
5644 enum isl_dim_type type, unsigned pos, isl_int value)
5646 return isl_map_lower_bound(set, type, pos, value);
5649 __isl_give isl_set *isl_set_upper_bound(__isl_take isl_set *set,
5650 enum isl_dim_type type, unsigned pos, isl_int value)
5652 return isl_map_upper_bound(set, type, pos, value);
5655 struct isl_set *isl_set_lower_bound_dim(struct isl_set *set, unsigned dim,
5660 set = isl_set_cow(set);
5664 isl_assert(set->ctx, dim < isl_set_n_dim(set), goto error);
5665 for (i = 0; i < set->n; ++i) {
5666 set->p[i] = isl_basic_set_lower_bound_dim(set->p[i], dim, value);
5676 struct isl_map *isl_map_reverse(struct isl_map *map)
5680 map = isl_map_cow(map);
5684 map->dim = isl_space_reverse(map->dim);
5687 for (i = 0; i < map->n; ++i) {
5688 map->p[i] = isl_basic_map_reverse(map->p[i]);
5692 ISL_F_CLR(map, ISL_MAP_NORMALIZED);
5699 static struct isl_map *isl_basic_map_partial_lexopt(
5700 struct isl_basic_map *bmap, struct isl_basic_set *dom,
5701 struct isl_set **empty, int max)
5705 if (bmap->ctx->opt->pip == ISL_PIP_PIP)
5706 return isl_pip_basic_map_lexopt(bmap, dom, empty, max);
5708 return isl_tab_basic_map_partial_lexopt(bmap, dom, empty, max);
5710 isl_basic_map_free(bmap);
5711 isl_basic_set_free(dom);
5717 struct isl_map *isl_basic_map_partial_lexmax(
5718 struct isl_basic_map *bmap, struct isl_basic_set *dom,
5719 struct isl_set **empty)
5721 return isl_basic_map_partial_lexopt(bmap, dom, empty, 1);
5724 struct isl_map *isl_basic_map_partial_lexmin(
5725 struct isl_basic_map *bmap, struct isl_basic_set *dom,
5726 struct isl_set **empty)
5728 return isl_basic_map_partial_lexopt(bmap, dom, empty, 0);
5731 struct isl_set *isl_basic_set_partial_lexmin(
5732 struct isl_basic_set *bset, struct isl_basic_set *dom,
5733 struct isl_set **empty)
5735 return (struct isl_set *)
5736 isl_basic_map_partial_lexmin((struct isl_basic_map *)bset,
5740 struct isl_set *isl_basic_set_partial_lexmax(
5741 struct isl_basic_set *bset, struct isl_basic_set *dom,
5742 struct isl_set **empty)
5744 return (struct isl_set *)
5745 isl_basic_map_partial_lexmax((struct isl_basic_map *)bset,
5749 __isl_give isl_pw_multi_aff *isl_basic_map_partial_lexmin_pw_multi_aff(
5750 __isl_take isl_basic_map *bmap, __isl_take isl_basic_set *dom,
5751 __isl_give isl_set **empty)
5753 return isl_basic_map_partial_lexopt_pw_multi_aff(bmap, dom, empty, 0);
5756 __isl_give isl_pw_multi_aff *isl_basic_map_partial_lexmax_pw_multi_aff(
5757 __isl_take isl_basic_map *bmap, __isl_take isl_basic_set *dom,
5758 __isl_give isl_set **empty)
5760 return isl_basic_map_partial_lexopt_pw_multi_aff(bmap, dom, empty, 1);
5763 __isl_give isl_pw_multi_aff *isl_basic_set_partial_lexmin_pw_multi_aff(
5764 __isl_take isl_basic_set *bset, __isl_take isl_basic_set *dom,
5765 __isl_give isl_set **empty)
5767 return isl_basic_map_partial_lexmin_pw_multi_aff(bset, dom, empty);
5770 __isl_give isl_pw_multi_aff *isl_basic_set_partial_lexmax_pw_multi_aff(
5771 __isl_take isl_basic_set *bset, __isl_take isl_basic_set *dom,
5772 __isl_give isl_set **empty)
5774 return isl_basic_map_partial_lexmax_pw_multi_aff(bset, dom, empty);
5777 __isl_give isl_pw_multi_aff *isl_basic_map_lexopt_pw_multi_aff(
5778 __isl_take isl_basic_map *bmap, int max)
5780 isl_basic_set *dom = NULL;
5781 isl_space *dom_space;
5785 dom_space = isl_space_domain(isl_space_copy(bmap->dim));
5786 dom = isl_basic_set_universe(dom_space);
5787 return isl_basic_map_partial_lexopt_pw_multi_aff(bmap, dom, NULL, max);
5789 isl_basic_map_free(bmap);
5793 __isl_give isl_pw_multi_aff *isl_basic_map_lexmin_pw_multi_aff(
5794 __isl_take isl_basic_map *bmap)
5796 return isl_basic_map_lexopt_pw_multi_aff(bmap, 0);
5800 #define TYPE isl_pw_multi_aff
5802 #define SUFFIX _pw_multi_aff
5804 #define EMPTY isl_pw_multi_aff_empty
5806 #define ADD isl_pw_multi_aff_union_add
5807 #include "isl_map_lexopt_templ.c"
5809 /* Given a map "map", compute the lexicographically minimal
5810 * (or maximal) image element for each domain element in dom,
5811 * in the form of an isl_pw_multi_aff.
5812 * Set *empty to those elements in dom that do not have an image element.
5814 * We first compute the lexicographically minimal or maximal element
5815 * in the first basic map. This results in a partial solution "res"
5816 * and a subset "todo" of dom that still need to be handled.
5817 * We then consider each of the remaining maps in "map" and successively
5818 * update both "res" and "todo".
5820 static __isl_give isl_pw_multi_aff *isl_map_partial_lexopt_aligned_pw_multi_aff(
5821 __isl_take isl_map *map, __isl_take isl_set *dom,
5822 __isl_give isl_set **empty, int max)
5825 isl_pw_multi_aff *res;
5831 if (isl_map_plain_is_empty(map)) {
5836 return isl_pw_multi_aff_from_map(map);
5839 res = basic_map_partial_lexopt_pw_multi_aff(
5840 isl_basic_map_copy(map->p[0]),
5841 isl_set_copy(dom), &todo, max);
5843 for (i = 1; i < map->n; ++i) {
5844 isl_pw_multi_aff *res_i;
5847 res_i = basic_map_partial_lexopt_pw_multi_aff(
5848 isl_basic_map_copy(map->p[i]),
5849 isl_set_copy(dom), &todo_i, max);
5852 res = isl_pw_multi_aff_union_lexmax(res, res_i);
5854 res = isl_pw_multi_aff_union_lexmin(res, res_i);
5856 todo = isl_set_intersect(todo, todo_i);
5877 #define TYPE isl_map
5881 #define EMPTY isl_map_empty
5883 #define ADD isl_map_union_disjoint
5884 #include "isl_map_lexopt_templ.c"
5886 /* Given a map "map", compute the lexicographically minimal
5887 * (or maximal) image element for each domain element in dom.
5888 * Set *empty to those elements in dom that do not have an image element.
5890 * We first compute the lexicographically minimal or maximal element
5891 * in the first basic map. This results in a partial solution "res"
5892 * and a subset "todo" of dom that still need to be handled.
5893 * We then consider each of the remaining maps in "map" and successively
5894 * update both "res" and "todo".
5896 * Let res^k and todo^k be the results after k steps and let i = k + 1.
5897 * Assume we are computing the lexicographical maximum.
5898 * We first compute the lexicographically maximal element in basic map i.
5899 * This results in a partial solution res_i and a subset todo_i.
5900 * Then we combine these results with those obtain for the first k basic maps
5901 * to obtain a result that is valid for the first k+1 basic maps.
5902 * In particular, the set where there is no solution is the set where
5903 * there is no solution for the first k basic maps and also no solution
5904 * for the ith basic map, i.e.,
5906 * todo^i = todo^k * todo_i
5908 * On dom(res^k) * dom(res_i), we need to pick the larger of the two
5909 * solutions, arbitrarily breaking ties in favor of res^k.
5910 * That is, when res^k(a) >= res_i(a), we pick res^k and
5911 * when res^k(a) < res_i(a), we pick res_i. (Here, ">=" and "<" denote
5912 * the lexicographic order.)
5913 * In practice, we compute
5915 * res^k * (res_i . "<=")
5919 * res_i * (res^k . "<")
5921 * Finally, we consider the symmetric difference of dom(res^k) and dom(res_i),
5922 * where only one of res^k and res_i provides a solution and we simply pick
5929 * Note that we only compute these intersections when dom(res^k) intersects
5930 * dom(res_i). Otherwise, the only effect of these intersections is to
5931 * potentially break up res^k and res_i into smaller pieces.
5932 * We want to avoid such splintering as much as possible.
5933 * In fact, an earlier implementation of this function would look for
5934 * better results in the domain of res^k and for extra results in todo^k,
5935 * but this would always result in a splintering according to todo^k,
5936 * even when the domain of basic map i is disjoint from the domains of
5937 * the previous basic maps.
5939 static __isl_give isl_map *isl_map_partial_lexopt_aligned(
5940 __isl_take isl_map *map, __isl_take isl_set *dom,
5941 __isl_give isl_set **empty, int max)
5944 struct isl_map *res;
5945 struct isl_set *todo;
5950 if (isl_map_plain_is_empty(map)) {
5958 res = basic_map_partial_lexopt(isl_basic_map_copy(map->p[0]),
5959 isl_set_copy(dom), &todo, max);
5961 for (i = 1; i < map->n; ++i) {
5965 isl_space *dim = isl_space_range(isl_map_get_space(res));
5967 res_i = basic_map_partial_lexopt(isl_basic_map_copy(map->p[i]),
5968 isl_set_copy(dom), &todo_i, max);
5971 lt = isl_map_lex_lt(isl_space_copy(dim));
5972 le = isl_map_lex_le(dim);
5974 lt = isl_map_lex_gt(isl_space_copy(dim));
5975 le = isl_map_lex_ge(dim);
5977 lt = isl_map_apply_range(isl_map_copy(res), lt);
5978 lt = isl_map_intersect(lt, isl_map_copy(res_i));
5979 le = isl_map_apply_range(isl_map_copy(res_i), le);
5980 le = isl_map_intersect(le, isl_map_copy(res));
5982 if (!isl_map_is_empty(lt) || !isl_map_is_empty(le)) {
5983 res = isl_map_intersect_domain(res,
5984 isl_set_copy(todo_i));
5985 res_i = isl_map_intersect_domain(res_i,
5986 isl_set_copy(todo));
5989 res = isl_map_union_disjoint(res, res_i);
5990 res = isl_map_union_disjoint(res, lt);
5991 res = isl_map_union_disjoint(res, le);
5993 todo = isl_set_intersect(todo, todo_i);
6013 __isl_give isl_map *isl_map_partial_lexmax(
6014 __isl_take isl_map *map, __isl_take isl_set *dom,
6015 __isl_give isl_set **empty)
6017 return isl_map_partial_lexopt(map, dom, empty, 1);
6020 __isl_give isl_map *isl_map_partial_lexmin(
6021 __isl_take isl_map *map, __isl_take isl_set *dom,
6022 __isl_give isl_set **empty)
6024 return isl_map_partial_lexopt(map, dom, empty, 0);
6027 __isl_give isl_set *isl_set_partial_lexmin(
6028 __isl_take isl_set *set, __isl_take isl_set *dom,
6029 __isl_give isl_set **empty)
6031 return (struct isl_set *)
6032 isl_map_partial_lexmin((struct isl_map *)set,
6036 __isl_give isl_set *isl_set_partial_lexmax(
6037 __isl_take isl_set *set, __isl_take isl_set *dom,
6038 __isl_give isl_set **empty)
6040 return (struct isl_set *)
6041 isl_map_partial_lexmax((struct isl_map *)set,
6045 __isl_give isl_map *isl_basic_map_lexopt(__isl_take isl_basic_map *bmap, int max)
6047 struct isl_basic_set *dom = NULL;
6052 dom_dim = isl_space_domain(isl_space_copy(bmap->dim));
6053 dom = isl_basic_set_universe(dom_dim);
6054 return isl_basic_map_partial_lexopt(bmap, dom, NULL, max);
6056 isl_basic_map_free(bmap);
6060 __isl_give isl_map *isl_basic_map_lexmin(__isl_take isl_basic_map *bmap)
6062 return isl_basic_map_lexopt(bmap, 0);
6065 __isl_give isl_map *isl_basic_map_lexmax(__isl_take isl_basic_map *bmap)
6067 return isl_basic_map_lexopt(bmap, 1);
6070 __isl_give isl_set *isl_basic_set_lexmin(__isl_take isl_basic_set *bset)
6072 return (isl_set *)isl_basic_map_lexmin((isl_basic_map *)bset);
6075 __isl_give isl_set *isl_basic_set_lexmax(__isl_take isl_basic_set *bset)
6077 return (isl_set *)isl_basic_map_lexmax((isl_basic_map *)bset);
6080 __isl_give isl_set *isl_set_lexmin(__isl_take isl_set *set)
6082 return (isl_set *)isl_map_lexmin((isl_map *)set);
6085 __isl_give isl_set *isl_set_lexmax(__isl_take isl_set *set)
6087 return (isl_set *)isl_map_lexmax((isl_map *)set);
6090 /* Extract the first and only affine expression from list
6091 * and then add it to *pwaff with the given dom.
6092 * This domain is known to be disjoint from other domains
6093 * because of the way isl_basic_map_foreach_lexmax works.
6095 static int update_dim_opt(__isl_take isl_basic_set *dom,
6096 __isl_take isl_aff_list *list, void *user)
6098 isl_ctx *ctx = isl_basic_set_get_ctx(dom);
6100 isl_pw_aff **pwaff = user;
6101 isl_pw_aff *pwaff_i;
6105 if (isl_aff_list_n_aff(list) != 1)
6106 isl_die(ctx, isl_error_internal,
6107 "expecting single element list", goto error);
6109 aff = isl_aff_list_get_aff(list, 0);
6110 pwaff_i = isl_pw_aff_alloc(isl_set_from_basic_set(dom), aff);
6112 *pwaff = isl_pw_aff_add_disjoint(*pwaff, pwaff_i);
6114 isl_aff_list_free(list);
6118 isl_basic_set_free(dom);
6119 isl_aff_list_free(list);
6123 /* Given a basic map with one output dimension, compute the minimum or
6124 * maximum of that dimension as an isl_pw_aff.
6126 * The isl_pw_aff is constructed by having isl_basic_map_foreach_lexopt
6127 * call update_dim_opt on each leaf of the result.
6129 static __isl_give isl_pw_aff *basic_map_dim_opt(__isl_keep isl_basic_map *bmap,
6132 isl_space *dim = isl_basic_map_get_space(bmap);
6136 dim = isl_space_from_domain(isl_space_domain(dim));
6137 dim = isl_space_add_dims(dim, isl_dim_out, 1);
6138 pwaff = isl_pw_aff_empty(dim);
6140 r = isl_basic_map_foreach_lexopt(bmap, max, &update_dim_opt, &pwaff);
6142 return isl_pw_aff_free(pwaff);
6147 /* Compute the minimum or maximum of the given output dimension
6148 * as a function of the parameters and the input dimensions,
6149 * but independently of the other output dimensions.
6151 * We first project out the other output dimension and then compute
6152 * the "lexicographic" maximum in each basic map, combining the results
6153 * using isl_pw_aff_union_max.
6155 static __isl_give isl_pw_aff *map_dim_opt(__isl_take isl_map *map, int pos,
6162 n_out = isl_map_dim(map, isl_dim_out);
6163 map = isl_map_project_out(map, isl_dim_out, pos + 1, n_out - (pos + 1));
6164 map = isl_map_project_out(map, isl_dim_out, 0, pos);
6169 isl_space *dim = isl_map_get_space(map);
6170 dim = isl_space_domain(isl_space_from_range(dim));
6172 return isl_pw_aff_empty(dim);
6175 pwaff = basic_map_dim_opt(map->p[0], max);
6176 for (i = 1; i < map->n; ++i) {
6177 isl_pw_aff *pwaff_i;
6179 pwaff_i = basic_map_dim_opt(map->p[i], max);
6180 pwaff = isl_pw_aff_union_opt(pwaff, pwaff_i, max);
6188 /* Compute the maximum of the given output dimension as a function of the
6189 * parameters and input dimensions, but independently of
6190 * the other output dimensions.
6192 __isl_give isl_pw_aff *isl_map_dim_max(__isl_take isl_map *map, int pos)
6194 return map_dim_opt(map, pos, 1);
6197 /* Compute the minimum or maximum of the given set dimension
6198 * as a function of the parameters,
6199 * but independently of the other set dimensions.
6201 static __isl_give isl_pw_aff *set_dim_opt(__isl_take isl_set *set, int pos,
6204 return map_dim_opt(set, pos, max);
6207 /* Compute the maximum of the given set dimension as a function of the
6208 * parameters, but independently of the other set dimensions.
6210 __isl_give isl_pw_aff *isl_set_dim_max(__isl_take isl_set *set, int pos)
6212 return set_dim_opt(set, pos, 1);
6215 /* Compute the minimum of the given set dimension as a function of the
6216 * parameters, but independently of the other set dimensions.
6218 __isl_give isl_pw_aff *isl_set_dim_min(__isl_take isl_set *set, int pos)
6220 return set_dim_opt(set, pos, 0);
6223 /* Apply a preimage specified by "mat" on the parameters of "bset".
6224 * bset is assumed to have only parameters and divs.
6226 static struct isl_basic_set *basic_set_parameter_preimage(
6227 struct isl_basic_set *bset, struct isl_mat *mat)
6234 bset->dim = isl_space_cow(bset->dim);
6238 nparam = isl_basic_set_dim(bset, isl_dim_param);
6240 isl_assert(bset->ctx, mat->n_row == 1 + nparam, goto error);
6242 bset->dim->nparam = 0;
6243 bset->dim->n_out = nparam;
6244 bset = isl_basic_set_preimage(bset, mat);
6246 bset->dim->nparam = bset->dim->n_out;
6247 bset->dim->n_out = 0;
6252 isl_basic_set_free(bset);
6256 /* Apply a preimage specified by "mat" on the parameters of "set".
6257 * set is assumed to have only parameters and divs.
6259 static struct isl_set *set_parameter_preimage(
6260 struct isl_set *set, struct isl_mat *mat)
6262 isl_space *dim = NULL;
6268 dim = isl_space_copy(set->dim);
6269 dim = isl_space_cow(dim);
6273 nparam = isl_set_dim(set, isl_dim_param);
6275 isl_assert(set->ctx, mat->n_row == 1 + nparam, goto error);
6278 dim->n_out = nparam;
6279 isl_set_reset_space(set, dim);
6280 set = isl_set_preimage(set, mat);
6283 dim = isl_space_copy(set->dim);
6284 dim = isl_space_cow(dim);
6287 dim->nparam = dim->n_out;
6289 isl_set_reset_space(set, dim);
6292 isl_space_free(dim);
6299 /* Intersect the basic set "bset" with the affine space specified by the
6300 * equalities in "eq".
6302 static struct isl_basic_set *basic_set_append_equalities(
6303 struct isl_basic_set *bset, struct isl_mat *eq)
6311 bset = isl_basic_set_extend_space(bset, isl_space_copy(bset->dim), 0,
6316 len = 1 + isl_space_dim(bset->dim, isl_dim_all) + bset->extra;
6317 for (i = 0; i < eq->n_row; ++i) {
6318 k = isl_basic_set_alloc_equality(bset);
6321 isl_seq_cpy(bset->eq[k], eq->row[i], eq->n_col);
6322 isl_seq_clr(bset->eq[k] + eq->n_col, len - eq->n_col);
6326 bset = isl_basic_set_gauss(bset, NULL);
6327 bset = isl_basic_set_finalize(bset);
6332 isl_basic_set_free(bset);
6336 /* Intersect the set "set" with the affine space specified by the
6337 * equalities in "eq".
6339 static struct isl_set *set_append_equalities(struct isl_set *set,
6347 for (i = 0; i < set->n; ++i) {
6348 set->p[i] = basic_set_append_equalities(set->p[i],
6361 /* Project the given basic set onto its parameter domain, possibly introducing
6362 * new, explicit, existential variables in the constraints.
6363 * The input has parameters and (possibly implicit) existential variables.
6364 * The output has the same parameters, but only
6365 * explicit existentially quantified variables.
6367 * The actual projection is performed by pip, but pip doesn't seem
6368 * to like equalities very much, so we first remove the equalities
6369 * among the parameters by performing a variable compression on
6370 * the parameters. Afterward, an inverse transformation is performed
6371 * and the equalities among the parameters are inserted back in.
6373 static struct isl_set *parameter_compute_divs(struct isl_basic_set *bset)
6377 struct isl_mat *T, *T2;
6378 struct isl_set *set;
6379 unsigned nparam, n_div;
6381 bset = isl_basic_set_cow(bset);
6385 if (bset->n_eq == 0)
6386 return isl_basic_set_lexmin(bset);
6388 bset = isl_basic_set_gauss(bset, NULL);
6391 if (isl_basic_set_plain_is_empty(bset))
6392 return isl_set_from_basic_set(bset);
6394 nparam = isl_basic_set_dim(bset, isl_dim_param);
6395 n_div = isl_basic_set_dim(bset, isl_dim_div);
6397 for (i = 0, j = n_div - 1; i < bset->n_eq && j >= 0; --j) {
6398 if (!isl_int_is_zero(bset->eq[i][1 + nparam + j]))
6401 if (i == bset->n_eq)
6402 return isl_basic_set_lexmin(bset);
6404 eq = isl_mat_sub_alloc6(bset->ctx, bset->eq, i, bset->n_eq - i,
6406 eq = isl_mat_cow(eq);
6407 T = isl_mat_variable_compression(isl_mat_copy(eq), &T2);
6408 if (T && T->n_col == 0) {
6412 bset = isl_basic_set_set_to_empty(bset);
6413 return isl_set_from_basic_set(bset);
6415 bset = basic_set_parameter_preimage(bset, T);
6417 set = isl_basic_set_lexmin(bset);
6418 set = set_parameter_preimage(set, T2);
6419 set = set_append_equalities(set, eq);
6423 /* Compute an explicit representation for all the existentially
6424 * quantified variables.
6425 * The input and output dimensions are first turned into parameters.
6426 * compute_divs then returns a map with the same parameters and
6427 * no input or output dimensions and the dimension specification
6428 * is reset to that of the input.
6430 static struct isl_map *compute_divs(struct isl_basic_map *bmap)
6432 struct isl_basic_set *bset;
6433 struct isl_set *set;
6434 struct isl_map *map;
6435 isl_space *dim, *orig_dim = NULL;
6440 bmap = isl_basic_map_cow(bmap);
6444 nparam = isl_basic_map_dim(bmap, isl_dim_param);
6445 n_in = isl_basic_map_dim(bmap, isl_dim_in);
6446 n_out = isl_basic_map_dim(bmap, isl_dim_out);
6447 dim = isl_space_set_alloc(bmap->ctx, nparam + n_in + n_out, 0);
6451 orig_dim = bmap->dim;
6453 bset = (struct isl_basic_set *)bmap;
6455 set = parameter_compute_divs(bset);
6456 map = (struct isl_map *)set;
6457 map = isl_map_reset_space(map, orig_dim);
6461 isl_basic_map_free(bmap);
6465 int isl_basic_map_divs_known(__isl_keep isl_basic_map *bmap)
6473 off = isl_space_dim(bmap->dim, isl_dim_all);
6474 for (i = 0; i < bmap->n_div; ++i) {
6475 if (isl_int_is_zero(bmap->div[i][0]))
6477 isl_assert(bmap->ctx, isl_int_is_zero(bmap->div[i][1+1+off+i]),
6483 static int map_divs_known(__isl_keep isl_map *map)
6490 for (i = 0; i < map->n; ++i) {
6491 int known = isl_basic_map_divs_known(map->p[i]);
6499 /* If bmap contains any unknown divs, then compute explicit
6500 * expressions for them. However, this computation may be
6501 * quite expensive, so first try to remove divs that aren't
6504 struct isl_map *isl_basic_map_compute_divs(struct isl_basic_map *bmap)
6507 struct isl_map *map;
6509 known = isl_basic_map_divs_known(bmap);
6513 return isl_map_from_basic_map(bmap);
6515 bmap = isl_basic_map_drop_redundant_divs(bmap);
6517 known = isl_basic_map_divs_known(bmap);
6521 return isl_map_from_basic_map(bmap);
6523 map = compute_divs(bmap);
6526 isl_basic_map_free(bmap);
6530 struct isl_map *isl_map_compute_divs(struct isl_map *map)
6534 struct isl_map *res;
6541 known = map_divs_known(map);
6549 res = isl_basic_map_compute_divs(isl_basic_map_copy(map->p[0]));
6550 for (i = 1 ; i < map->n; ++i) {
6552 r2 = isl_basic_map_compute_divs(isl_basic_map_copy(map->p[i]));
6553 if (ISL_F_ISSET(map, ISL_MAP_DISJOINT))
6554 res = isl_map_union_disjoint(res, r2);
6556 res = isl_map_union(res, r2);
6563 struct isl_set *isl_basic_set_compute_divs(struct isl_basic_set *bset)
6565 return (struct isl_set *)
6566 isl_basic_map_compute_divs((struct isl_basic_map *)bset);
6569 struct isl_set *isl_set_compute_divs(struct isl_set *set)
6571 return (struct isl_set *)
6572 isl_map_compute_divs((struct isl_map *)set);
6575 struct isl_set *isl_map_domain(struct isl_map *map)
6578 struct isl_set *set;
6583 map = isl_map_cow(map);
6587 set = (struct isl_set *)map;
6588 set->dim = isl_space_domain(set->dim);
6591 for (i = 0; i < map->n; ++i) {
6592 set->p[i] = isl_basic_map_domain(map->p[i]);
6596 ISL_F_CLR(set, ISL_MAP_DISJOINT);
6597 ISL_F_CLR(set, ISL_SET_NORMALIZED);
6604 /* Return the union of "map1" and "map2", where we assume for now that
6605 * "map1" and "map2" are disjoint. Note that the basic maps inside
6606 * "map1" or "map2" may not be disjoint from each other.
6607 * Also note that this function is also called from isl_map_union,
6608 * which takes care of handling the situation where "map1" and "map2"
6609 * may not be disjoint.
6611 * If one of the inputs is empty, we can simply return the other input.
6612 * Similarly, if one of the inputs is universal, then it is equal to the union.
6614 static __isl_give isl_map *map_union_disjoint(__isl_take isl_map *map1,
6615 __isl_take isl_map *map2)
6619 struct isl_map *map = NULL;
6634 is_universe = isl_map_plain_is_universe(map1);
6635 if (is_universe < 0)
6642 is_universe = isl_map_plain_is_universe(map2);
6643 if (is_universe < 0)
6650 isl_assert(map1->ctx, isl_space_is_equal(map1->dim, map2->dim), goto error);
6652 if (ISL_F_ISSET(map1, ISL_MAP_DISJOINT) &&
6653 ISL_F_ISSET(map2, ISL_MAP_DISJOINT))
6654 ISL_FL_SET(flags, ISL_MAP_DISJOINT);
6656 map = isl_map_alloc_space(isl_space_copy(map1->dim),
6657 map1->n + map2->n, flags);
6660 for (i = 0; i < map1->n; ++i) {
6661 map = isl_map_add_basic_map(map,
6662 isl_basic_map_copy(map1->p[i]));
6666 for (i = 0; i < map2->n; ++i) {
6667 map = isl_map_add_basic_map(map,
6668 isl_basic_map_copy(map2->p[i]));
6682 __isl_give isl_map *isl_map_union_disjoint(__isl_take isl_map *map1,
6683 __isl_take isl_map *map2)
6685 return isl_map_align_params_map_map_and(map1, map2, &map_union_disjoint);
6688 struct isl_map *isl_map_union(struct isl_map *map1, struct isl_map *map2)
6690 map1 = isl_map_union_disjoint(map1, map2);
6694 ISL_F_CLR(map1, ISL_MAP_DISJOINT);
6698 struct isl_set *isl_set_union_disjoint(
6699 struct isl_set *set1, struct isl_set *set2)
6701 return (struct isl_set *)
6702 isl_map_union_disjoint(
6703 (struct isl_map *)set1, (struct isl_map *)set2);
6706 struct isl_set *isl_set_union(struct isl_set *set1, struct isl_set *set2)
6708 return (struct isl_set *)
6709 isl_map_union((struct isl_map *)set1, (struct isl_map *)set2);
6712 /* Apply "fn" to pairs of elements from "map" and "set" and collect
6715 * "map" and "set" are assumed to be compatible and non-NULL.
6717 static __isl_give isl_map *map_intersect_set(__isl_take isl_map *map,
6718 __isl_take isl_set *set,
6719 __isl_give isl_basic_map *fn(__isl_take isl_basic_map *bmap,
6720 __isl_take isl_basic_set *bset))
6723 struct isl_map *result;
6726 if (isl_set_plain_is_universe(set)) {
6731 if (ISL_F_ISSET(map, ISL_MAP_DISJOINT) &&
6732 ISL_F_ISSET(set, ISL_MAP_DISJOINT))
6733 ISL_FL_SET(flags, ISL_MAP_DISJOINT);
6735 result = isl_map_alloc_space(isl_space_copy(map->dim),
6736 map->n * set->n, flags);
6737 for (i = 0; result && i < map->n; ++i)
6738 for (j = 0; j < set->n; ++j) {
6739 result = isl_map_add_basic_map(result,
6740 fn(isl_basic_map_copy(map->p[i]),
6741 isl_basic_set_copy(set->p[j])));
6751 static __isl_give isl_map *map_intersect_range(__isl_take isl_map *map,
6752 __isl_take isl_set *set)
6757 if (!isl_map_compatible_range(map, set))
6758 isl_die(set->ctx, isl_error_invalid,
6759 "incompatible spaces", goto error);
6761 return map_intersect_set(map, set, &isl_basic_map_intersect_range);
6768 __isl_give isl_map *isl_map_intersect_range(__isl_take isl_map *map,
6769 __isl_take isl_set *set)
6771 return isl_map_align_params_map_map_and(map, set, &map_intersect_range);
6774 static __isl_give isl_map *map_intersect_domain(__isl_take isl_map *map,
6775 __isl_take isl_set *set)
6780 if (!isl_map_compatible_domain(map, set))
6781 isl_die(set->ctx, isl_error_invalid,
6782 "incompatible spaces", goto error);
6784 return map_intersect_set(map, set, &isl_basic_map_intersect_domain);
6791 __isl_give isl_map *isl_map_intersect_domain(__isl_take isl_map *map,
6792 __isl_take isl_set *set)
6794 return isl_map_align_params_map_map_and(map, set,
6795 &map_intersect_domain);
6798 static __isl_give isl_map *map_apply_domain(__isl_take isl_map *map1,
6799 __isl_take isl_map *map2)
6803 map1 = isl_map_reverse(map1);
6804 map1 = isl_map_apply_range(map1, map2);
6805 return isl_map_reverse(map1);
6812 __isl_give isl_map *isl_map_apply_domain(__isl_take isl_map *map1,
6813 __isl_take isl_map *map2)
6815 return isl_map_align_params_map_map_and(map1, map2, &map_apply_domain);
6818 static __isl_give isl_map *map_apply_range(__isl_take isl_map *map1,
6819 __isl_take isl_map *map2)
6821 isl_space *dim_result;
6822 struct isl_map *result;
6828 dim_result = isl_space_join(isl_space_copy(map1->dim),
6829 isl_space_copy(map2->dim));
6831 result = isl_map_alloc_space(dim_result, map1->n * map2->n, 0);
6834 for (i = 0; i < map1->n; ++i)
6835 for (j = 0; j < map2->n; ++j) {
6836 result = isl_map_add_basic_map(result,
6837 isl_basic_map_apply_range(
6838 isl_basic_map_copy(map1->p[i]),
6839 isl_basic_map_copy(map2->p[j])));
6845 if (result && result->n <= 1)
6846 ISL_F_SET(result, ISL_MAP_DISJOINT);
6854 __isl_give isl_map *isl_map_apply_range(__isl_take isl_map *map1,
6855 __isl_take isl_map *map2)
6857 return isl_map_align_params_map_map_and(map1, map2, &map_apply_range);
6861 * returns range - domain
6863 struct isl_basic_set *isl_basic_map_deltas(struct isl_basic_map *bmap)
6865 isl_space *dims, *target_dim;
6866 struct isl_basic_set *bset;
6873 isl_assert(bmap->ctx, isl_space_tuple_match(bmap->dim, isl_dim_in,
6874 bmap->dim, isl_dim_out),
6876 target_dim = isl_space_domain(isl_basic_map_get_space(bmap));
6877 dim = isl_basic_map_n_in(bmap);
6878 nparam = isl_basic_map_n_param(bmap);
6879 bset = isl_basic_set_from_basic_map(bmap);
6880 bset = isl_basic_set_cow(bset);
6881 dims = isl_basic_set_get_space(bset);
6882 dims = isl_space_add_dims(dims, isl_dim_set, dim);
6883 bset = isl_basic_set_extend_space(bset, dims, 0, dim, 0);
6884 bset = isl_basic_set_swap_vars(bset, 2*dim);
6885 for (i = 0; i < dim; ++i) {
6886 int j = isl_basic_map_alloc_equality(
6887 (struct isl_basic_map *)bset);
6889 bset = isl_basic_set_free(bset);
6892 isl_seq_clr(bset->eq[j], 1 + isl_basic_set_total_dim(bset));
6893 isl_int_set_si(bset->eq[j][1+nparam+i], 1);
6894 isl_int_set_si(bset->eq[j][1+nparam+dim+i], 1);
6895 isl_int_set_si(bset->eq[j][1+nparam+2*dim+i], -1);
6897 bset = isl_basic_set_project_out(bset, isl_dim_set, dim, 2*dim);
6898 bset = isl_basic_set_reset_space(bset, target_dim);
6901 isl_basic_map_free(bmap);
6906 * returns range - domain
6908 __isl_give isl_set *isl_map_deltas(__isl_take isl_map *map)
6912 struct isl_set *result;
6917 isl_assert(map->ctx, isl_space_tuple_match(map->dim, isl_dim_in,
6918 map->dim, isl_dim_out),
6920 dim = isl_map_get_space(map);
6921 dim = isl_space_domain(dim);
6922 result = isl_set_alloc_space(dim, map->n, 0);
6925 for (i = 0; i < map->n; ++i)
6926 result = isl_set_add_basic_set(result,
6927 isl_basic_map_deltas(isl_basic_map_copy(map->p[i])));
6936 * returns [domain -> range] -> range - domain
6938 __isl_give isl_basic_map *isl_basic_map_deltas_map(
6939 __isl_take isl_basic_map *bmap)
6943 isl_basic_map *domain;
6947 if (!isl_space_tuple_match(bmap->dim, isl_dim_in, bmap->dim, isl_dim_out))
6948 isl_die(bmap->ctx, isl_error_invalid,
6949 "domain and range don't match", goto error);
6951 nparam = isl_basic_map_dim(bmap, isl_dim_param);
6952 n = isl_basic_map_dim(bmap, isl_dim_in);
6954 dim = isl_space_from_range(isl_space_domain(isl_basic_map_get_space(bmap)));
6955 domain = isl_basic_map_universe(dim);
6957 bmap = isl_basic_map_from_domain(isl_basic_map_wrap(bmap));
6958 bmap = isl_basic_map_apply_range(bmap, domain);
6959 bmap = isl_basic_map_extend_constraints(bmap, n, 0);
6961 total = isl_basic_map_total_dim(bmap);
6963 for (i = 0; i < n; ++i) {
6964 k = isl_basic_map_alloc_equality(bmap);
6967 isl_seq_clr(bmap->eq[k], 1 + total);
6968 isl_int_set_si(bmap->eq[k][1 + nparam + i], 1);
6969 isl_int_set_si(bmap->eq[k][1 + nparam + n + i], -1);
6970 isl_int_set_si(bmap->eq[k][1 + nparam + n + n + i], 1);
6973 bmap = isl_basic_map_gauss(bmap, NULL);
6974 return isl_basic_map_finalize(bmap);
6976 isl_basic_map_free(bmap);
6981 * returns [domain -> range] -> range - domain
6983 __isl_give isl_map *isl_map_deltas_map(__isl_take isl_map *map)
6986 isl_space *domain_dim;
6991 if (!isl_space_tuple_match(map->dim, isl_dim_in, map->dim, isl_dim_out))
6992 isl_die(map->ctx, isl_error_invalid,
6993 "domain and range don't match", goto error);
6995 map = isl_map_cow(map);
6999 domain_dim = isl_space_from_range(isl_space_domain(isl_map_get_space(map)));
7000 map->dim = isl_space_from_domain(isl_space_wrap(map->dim));
7001 map->dim = isl_space_join(map->dim, domain_dim);
7004 for (i = 0; i < map->n; ++i) {
7005 map->p[i] = isl_basic_map_deltas_map(map->p[i]);
7009 ISL_F_CLR(map, ISL_MAP_NORMALIZED);
7016 static __isl_give isl_basic_map *basic_map_identity(__isl_take isl_space *dims)
7018 struct isl_basic_map *bmap;
7026 nparam = dims->nparam;
7028 bmap = isl_basic_map_alloc_space(dims, 0, dim, 0);
7032 for (i = 0; i < dim; ++i) {
7033 int j = isl_basic_map_alloc_equality(bmap);
7036 isl_seq_clr(bmap->eq[j], 1 + isl_basic_map_total_dim(bmap));
7037 isl_int_set_si(bmap->eq[j][1+nparam+i], 1);
7038 isl_int_set_si(bmap->eq[j][1+nparam+dim+i], -1);
7040 return isl_basic_map_finalize(bmap);
7042 isl_basic_map_free(bmap);
7046 __isl_give isl_basic_map *isl_basic_map_identity(__isl_take isl_space *dim)
7050 if (dim->n_in != dim->n_out)
7051 isl_die(dim->ctx, isl_error_invalid,
7052 "number of input and output dimensions needs to be "
7053 "the same", goto error);
7054 return basic_map_identity(dim);
7056 isl_space_free(dim);
7060 struct isl_basic_map *isl_basic_map_identity_like(struct isl_basic_map *model)
7062 if (!model || !model->dim)
7064 return isl_basic_map_identity(isl_space_copy(model->dim));
7067 __isl_give isl_map *isl_map_identity(__isl_take isl_space *dim)
7069 return isl_map_from_basic_map(isl_basic_map_identity(dim));
7072 struct isl_map *isl_map_identity_like(struct isl_map *model)
7074 if (!model || !model->dim)
7076 return isl_map_identity(isl_space_copy(model->dim));
7079 struct isl_map *isl_map_identity_like_basic_map(struct isl_basic_map *model)
7081 if (!model || !model->dim)
7083 return isl_map_identity(isl_space_copy(model->dim));
7086 __isl_give isl_map *isl_set_identity(__isl_take isl_set *set)
7088 isl_space *dim = isl_set_get_space(set);
7090 id = isl_map_identity(isl_space_map_from_set(dim));
7091 return isl_map_intersect_range(id, set);
7094 /* Construct a basic set with all set dimensions having only non-negative
7097 __isl_give isl_basic_set *isl_basic_set_positive_orthant(
7098 __isl_take isl_space *space)
7103 struct isl_basic_set *bset;
7107 nparam = space->nparam;
7109 bset = isl_basic_set_alloc_space(space, 0, 0, dim);
7112 for (i = 0; i < dim; ++i) {
7113 int k = isl_basic_set_alloc_inequality(bset);
7116 isl_seq_clr(bset->ineq[k], 1 + isl_basic_set_total_dim(bset));
7117 isl_int_set_si(bset->ineq[k][1 + nparam + i], 1);
7121 isl_basic_set_free(bset);
7125 /* Construct the half-space x_pos >= 0.
7127 static __isl_give isl_basic_set *nonneg_halfspace(__isl_take isl_space *dim,
7131 isl_basic_set *nonneg;
7133 nonneg = isl_basic_set_alloc_space(dim, 0, 0, 1);
7134 k = isl_basic_set_alloc_inequality(nonneg);
7137 isl_seq_clr(nonneg->ineq[k], 1 + isl_basic_set_total_dim(nonneg));
7138 isl_int_set_si(nonneg->ineq[k][pos], 1);
7140 return isl_basic_set_finalize(nonneg);
7142 isl_basic_set_free(nonneg);
7146 /* Construct the half-space x_pos <= -1.
7148 static __isl_give isl_basic_set *neg_halfspace(__isl_take isl_space *dim, int pos)
7153 neg = isl_basic_set_alloc_space(dim, 0, 0, 1);
7154 k = isl_basic_set_alloc_inequality(neg);
7157 isl_seq_clr(neg->ineq[k], 1 + isl_basic_set_total_dim(neg));
7158 isl_int_set_si(neg->ineq[k][0], -1);
7159 isl_int_set_si(neg->ineq[k][pos], -1);
7161 return isl_basic_set_finalize(neg);
7163 isl_basic_set_free(neg);
7167 __isl_give isl_set *isl_set_split_dims(__isl_take isl_set *set,
7168 enum isl_dim_type type, unsigned first, unsigned n)
7171 isl_basic_set *nonneg;
7179 isl_assert(set->ctx, first + n <= isl_set_dim(set, type), goto error);
7181 for (i = 0; i < n; ++i) {
7182 nonneg = nonneg_halfspace(isl_set_get_space(set),
7183 pos(set->dim, type) + first + i);
7184 neg = neg_halfspace(isl_set_get_space(set),
7185 pos(set->dim, type) + first + i);
7187 set = isl_set_intersect(set, isl_basic_set_union(nonneg, neg));
7196 static int foreach_orthant(__isl_take isl_set *set, int *signs, int first,
7197 int len, int (*fn)(__isl_take isl_set *orthant, int *signs, void *user),
7204 if (isl_set_plain_is_empty(set)) {
7209 return fn(set, signs, user);
7212 half = isl_set_from_basic_set(nonneg_halfspace(isl_set_get_space(set),
7214 half = isl_set_intersect(half, isl_set_copy(set));
7215 if (foreach_orthant(half, signs, first + 1, len, fn, user) < 0)
7219 half = isl_set_from_basic_set(neg_halfspace(isl_set_get_space(set),
7221 half = isl_set_intersect(half, set);
7222 return foreach_orthant(half, signs, first + 1, len, fn, user);
7228 /* Call "fn" on the intersections of "set" with each of the orthants
7229 * (except for obviously empty intersections). The orthant is identified
7230 * by the signs array, with each entry having value 1 or -1 according
7231 * to the sign of the corresponding variable.
7233 int isl_set_foreach_orthant(__isl_keep isl_set *set,
7234 int (*fn)(__isl_take isl_set *orthant, int *signs, void *user),
7244 if (isl_set_plain_is_empty(set))
7247 nparam = isl_set_dim(set, isl_dim_param);
7248 nvar = isl_set_dim(set, isl_dim_set);
7250 signs = isl_alloc_array(set->ctx, int, nparam + nvar);
7252 r = foreach_orthant(isl_set_copy(set), signs, 0, nparam + nvar,
7260 int isl_set_is_equal(struct isl_set *set1, struct isl_set *set2)
7262 return isl_map_is_equal((struct isl_map *)set1, (struct isl_map *)set2);
7265 int isl_basic_map_is_subset(
7266 struct isl_basic_map *bmap1, struct isl_basic_map *bmap2)
7269 struct isl_map *map1;
7270 struct isl_map *map2;
7272 if (!bmap1 || !bmap2)
7275 map1 = isl_map_from_basic_map(isl_basic_map_copy(bmap1));
7276 map2 = isl_map_from_basic_map(isl_basic_map_copy(bmap2));
7278 is_subset = isl_map_is_subset(map1, map2);
7286 int isl_basic_set_is_subset(__isl_keep isl_basic_set *bset1,
7287 __isl_keep isl_basic_set *bset2)
7289 return isl_basic_map_is_subset(bset1, bset2);
7292 int isl_basic_map_is_equal(
7293 struct isl_basic_map *bmap1, struct isl_basic_map *bmap2)
7297 if (!bmap1 || !bmap2)
7299 is_subset = isl_basic_map_is_subset(bmap1, bmap2);
7302 is_subset = isl_basic_map_is_subset(bmap2, bmap1);
7306 int isl_basic_set_is_equal(
7307 struct isl_basic_set *bset1, struct isl_basic_set *bset2)
7309 return isl_basic_map_is_equal(
7310 (struct isl_basic_map *)bset1, (struct isl_basic_map *)bset2);
7313 int isl_map_is_empty(struct isl_map *map)
7320 for (i = 0; i < map->n; ++i) {
7321 is_empty = isl_basic_map_is_empty(map->p[i]);
7330 int isl_map_plain_is_empty(__isl_keep isl_map *map)
7332 return map ? map->n == 0 : -1;
7335 int isl_map_fast_is_empty(__isl_keep isl_map *map)
7337 return isl_map_plain_is_empty(map);
7340 int isl_set_plain_is_empty(struct isl_set *set)
7342 return set ? set->n == 0 : -1;
7345 int isl_set_fast_is_empty(__isl_keep isl_set *set)
7347 return isl_set_plain_is_empty(set);
7350 int isl_set_is_empty(struct isl_set *set)
7352 return isl_map_is_empty((struct isl_map *)set);
7355 int isl_map_has_equal_space(__isl_keep isl_map *map1, __isl_keep isl_map *map2)
7360 return isl_space_is_equal(map1->dim, map2->dim);
7363 int isl_set_has_equal_space(__isl_keep isl_set *set1, __isl_keep isl_set *set2)
7368 return isl_space_is_equal(set1->dim, set2->dim);
7371 static int map_is_equal(__isl_keep isl_map *map1, __isl_keep isl_map *map2)
7377 is_subset = isl_map_is_subset(map1, map2);
7380 is_subset = isl_map_is_subset(map2, map1);
7384 int isl_map_is_equal(__isl_keep isl_map *map1, __isl_keep isl_map *map2)
7386 return isl_map_align_params_map_map_and_test(map1, map2, &map_is_equal);
7389 int isl_basic_map_is_strict_subset(
7390 struct isl_basic_map *bmap1, struct isl_basic_map *bmap2)
7394 if (!bmap1 || !bmap2)
7396 is_subset = isl_basic_map_is_subset(bmap1, bmap2);
7399 is_subset = isl_basic_map_is_subset(bmap2, bmap1);
7400 if (is_subset == -1)
7405 int isl_map_is_strict_subset(struct isl_map *map1, struct isl_map *map2)
7411 is_subset = isl_map_is_subset(map1, map2);
7414 is_subset = isl_map_is_subset(map2, map1);
7415 if (is_subset == -1)
7420 int isl_set_is_strict_subset(__isl_keep isl_set *set1, __isl_keep isl_set *set2)
7422 return isl_map_is_strict_subset((isl_map *)set1, (isl_map *)set2);
7425 int isl_basic_map_is_universe(struct isl_basic_map *bmap)
7429 return bmap->n_eq == 0 && bmap->n_ineq == 0;
7432 int isl_basic_set_is_universe(struct isl_basic_set *bset)
7436 return bset->n_eq == 0 && bset->n_ineq == 0;
7439 int isl_map_plain_is_universe(__isl_keep isl_map *map)
7446 for (i = 0; i < map->n; ++i) {
7447 int r = isl_basic_map_is_universe(map->p[i]);
7455 int isl_set_plain_is_universe(__isl_keep isl_set *set)
7457 return isl_map_plain_is_universe((isl_map *) set);
7460 int isl_set_fast_is_universe(__isl_keep isl_set *set)
7462 return isl_set_plain_is_universe(set);
7465 int isl_basic_map_is_empty(struct isl_basic_map *bmap)
7467 struct isl_basic_set *bset = NULL;
7468 struct isl_vec *sample = NULL;
7475 if (ISL_F_ISSET(bmap, ISL_BASIC_MAP_EMPTY))
7478 if (isl_basic_map_is_universe(bmap))
7481 if (ISL_F_ISSET(bmap, ISL_BASIC_MAP_RATIONAL)) {
7482 struct isl_basic_map *copy = isl_basic_map_copy(bmap);
7483 copy = isl_basic_map_remove_redundancies(copy);
7484 empty = isl_basic_map_plain_is_empty(copy);
7485 isl_basic_map_free(copy);
7489 total = 1 + isl_basic_map_total_dim(bmap);
7490 if (bmap->sample && bmap->sample->size == total) {
7491 int contains = isl_basic_map_contains(bmap, bmap->sample);
7497 isl_vec_free(bmap->sample);
7498 bmap->sample = NULL;
7499 bset = isl_basic_map_underlying_set(isl_basic_map_copy(bmap));
7502 sample = isl_basic_set_sample_vec(bset);
7505 empty = sample->size == 0;
7506 isl_vec_free(bmap->sample);
7507 bmap->sample = sample;
7509 ISL_F_SET(bmap, ISL_BASIC_MAP_EMPTY);
7514 int isl_basic_map_plain_is_empty(__isl_keep isl_basic_map *bmap)
7518 return ISL_F_ISSET(bmap, ISL_BASIC_MAP_EMPTY);
7521 int isl_basic_map_fast_is_empty(__isl_keep isl_basic_map *bmap)
7523 return isl_basic_map_plain_is_empty(bmap);
7526 int isl_basic_set_plain_is_empty(__isl_keep isl_basic_set *bset)
7530 return ISL_F_ISSET(bset, ISL_BASIC_SET_EMPTY);
7533 int isl_basic_set_fast_is_empty(__isl_keep isl_basic_set *bset)
7535 return isl_basic_set_plain_is_empty(bset);
7538 int isl_basic_set_is_empty(struct isl_basic_set *bset)
7540 return isl_basic_map_is_empty((struct isl_basic_map *)bset);
7543 struct isl_map *isl_basic_map_union(
7544 struct isl_basic_map *bmap1, struct isl_basic_map *bmap2)
7546 struct isl_map *map;
7547 if (!bmap1 || !bmap2)
7550 isl_assert(bmap1->ctx, isl_space_is_equal(bmap1->dim, bmap2->dim), goto error);
7552 map = isl_map_alloc_space(isl_space_copy(bmap1->dim), 2, 0);
7555 map = isl_map_add_basic_map(map, bmap1);
7556 map = isl_map_add_basic_map(map, bmap2);
7559 isl_basic_map_free(bmap1);
7560 isl_basic_map_free(bmap2);
7564 struct isl_set *isl_basic_set_union(
7565 struct isl_basic_set *bset1, struct isl_basic_set *bset2)
7567 return (struct isl_set *)isl_basic_map_union(
7568 (struct isl_basic_map *)bset1,
7569 (struct isl_basic_map *)bset2);
7572 /* Order divs such that any div only depends on previous divs */
7573 struct isl_basic_map *isl_basic_map_order_divs(struct isl_basic_map *bmap)
7581 off = isl_space_dim(bmap->dim, isl_dim_all);
7583 for (i = 0; i < bmap->n_div; ++i) {
7585 if (isl_int_is_zero(bmap->div[i][0]))
7587 pos = isl_seq_first_non_zero(bmap->div[i]+1+1+off+i,
7591 isl_basic_map_swap_div(bmap, i, i + pos);
7597 struct isl_basic_set *isl_basic_set_order_divs(struct isl_basic_set *bset)
7599 return (struct isl_basic_set *)
7600 isl_basic_map_order_divs((struct isl_basic_map *)bset);
7603 __isl_give isl_map *isl_map_order_divs(__isl_take isl_map *map)
7610 for (i = 0; i < map->n; ++i) {
7611 map->p[i] = isl_basic_map_order_divs(map->p[i]);
7622 /* Apply the expansion computed by isl_merge_divs.
7623 * The expansion itself is given by "exp" while the resulting
7624 * list of divs is given by "div".
7626 __isl_give isl_basic_set *isl_basic_set_expand_divs(
7627 __isl_take isl_basic_set *bset, __isl_take isl_mat *div, int *exp)
7632 bset = isl_basic_set_cow(bset);
7636 if (div->n_row < bset->n_div)
7637 isl_die(isl_mat_get_ctx(div), isl_error_invalid,
7638 "not an expansion", goto error);
7640 n_div = bset->n_div;
7641 bset = isl_basic_map_extend_space(bset, isl_space_copy(bset->dim),
7642 div->n_row - n_div, 0,
7643 2 * (div->n_row - n_div));
7645 for (i = n_div; i < div->n_row; ++i)
7646 if (isl_basic_set_alloc_div(bset) < 0)
7650 for (i = div->n_row - 1; i >= 0; --i) {
7651 if (j >= 0 && exp[j] == i) {
7653 isl_basic_map_swap_div(bset, i, j);
7656 isl_seq_cpy(bset->div[i], div->row[i], div->n_col);
7657 if (isl_basic_map_add_div_constraints(bset, i) < 0)
7665 isl_basic_set_free(bset);
7670 /* Look for a div in dst that corresponds to the div "div" in src.
7671 * The divs before "div" in src and dst are assumed to be the same.
7673 * Returns -1 if no corresponding div was found and the position
7674 * of the corresponding div in dst otherwise.
7676 static int find_div(struct isl_basic_map *dst,
7677 struct isl_basic_map *src, unsigned div)
7681 unsigned total = isl_space_dim(src->dim, isl_dim_all);
7683 isl_assert(dst->ctx, div <= dst->n_div, return -1);
7684 for (i = div; i < dst->n_div; ++i)
7685 if (isl_seq_eq(dst->div[i], src->div[div], 1+1+total+div) &&
7686 isl_seq_first_non_zero(dst->div[i]+1+1+total+div,
7687 dst->n_div - div) == -1)
7692 struct isl_basic_map *isl_basic_map_align_divs(
7693 struct isl_basic_map *dst, struct isl_basic_map *src)
7701 if (src->n_div == 0)
7704 for (i = 0; i < src->n_div; ++i)
7705 isl_assert(src->ctx, !isl_int_is_zero(src->div[i][0]), goto error);
7707 src = isl_basic_map_order_divs(src);
7708 dst = isl_basic_map_cow(dst);
7709 dst = isl_basic_map_extend_space(dst, isl_space_copy(dst->dim),
7710 src->n_div, 0, 2 * src->n_div);
7713 total = isl_space_dim(src->dim, isl_dim_all);
7714 for (i = 0; i < src->n_div; ++i) {
7715 int j = find_div(dst, src, i);
7717 j = isl_basic_map_alloc_div(dst);
7720 isl_seq_cpy(dst->div[j], src->div[i], 1+1+total+i);
7721 isl_seq_clr(dst->div[j]+1+1+total+i, dst->n_div - i);
7722 if (isl_basic_map_add_div_constraints(dst, j) < 0)
7726 isl_basic_map_swap_div(dst, i, j);
7730 isl_basic_map_free(dst);
7734 struct isl_basic_set *isl_basic_set_align_divs(
7735 struct isl_basic_set *dst, struct isl_basic_set *src)
7737 return (struct isl_basic_set *)isl_basic_map_align_divs(
7738 (struct isl_basic_map *)dst, (struct isl_basic_map *)src);
7741 struct isl_map *isl_map_align_divs(struct isl_map *map)
7749 map = isl_map_compute_divs(map);
7750 map = isl_map_cow(map);
7754 for (i = 1; i < map->n; ++i)
7755 map->p[0] = isl_basic_map_align_divs(map->p[0], map->p[i]);
7756 for (i = 1; i < map->n; ++i)
7757 map->p[i] = isl_basic_map_align_divs(map->p[i], map->p[0]);
7759 ISL_F_CLR(map, ISL_MAP_NORMALIZED);
7763 struct isl_set *isl_set_align_divs(struct isl_set *set)
7765 return (struct isl_set *)isl_map_align_divs((struct isl_map *)set);
7768 static __isl_give isl_set *set_apply( __isl_take isl_set *set,
7769 __isl_take isl_map *map)
7773 isl_assert(set->ctx, isl_map_compatible_domain(map, set), goto error);
7774 map = isl_map_intersect_domain(map, set);
7775 set = isl_map_range(map);
7783 __isl_give isl_set *isl_set_apply( __isl_take isl_set *set,
7784 __isl_take isl_map *map)
7786 return isl_map_align_params_map_map_and(set, map, &set_apply);
7789 /* There is no need to cow as removing empty parts doesn't change
7790 * the meaning of the set.
7792 struct isl_map *isl_map_remove_empty_parts(struct isl_map *map)
7799 for (i = map->n - 1; i >= 0; --i)
7800 remove_if_empty(map, i);
7805 struct isl_set *isl_set_remove_empty_parts(struct isl_set *set)
7807 return (struct isl_set *)
7808 isl_map_remove_empty_parts((struct isl_map *)set);
7811 struct isl_basic_map *isl_map_copy_basic_map(struct isl_map *map)
7813 struct isl_basic_map *bmap;
7814 if (!map || map->n == 0)
7816 bmap = map->p[map->n-1];
7817 isl_assert(map->ctx, ISL_F_ISSET(bmap, ISL_BASIC_SET_FINAL), return NULL);
7818 return isl_basic_map_copy(bmap);
7821 struct isl_basic_set *isl_set_copy_basic_set(struct isl_set *set)
7823 return (struct isl_basic_set *)
7824 isl_map_copy_basic_map((struct isl_map *)set);
7827 __isl_give isl_map *isl_map_drop_basic_map(__isl_take isl_map *map,
7828 __isl_keep isl_basic_map *bmap)
7834 for (i = map->n-1; i >= 0; --i) {
7835 if (map->p[i] != bmap)
7837 map = isl_map_cow(map);
7840 isl_basic_map_free(map->p[i]);
7841 if (i != map->n-1) {
7842 ISL_F_CLR(map, ISL_SET_NORMALIZED);
7843 map->p[i] = map->p[map->n-1];
7854 struct isl_set *isl_set_drop_basic_set(struct isl_set *set,
7855 struct isl_basic_set *bset)
7857 return (struct isl_set *)isl_map_drop_basic_map((struct isl_map *)set,
7858 (struct isl_basic_map *)bset);
7861 /* Given two basic sets bset1 and bset2, compute the maximal difference
7862 * between the values of dimension pos in bset1 and those in bset2
7863 * for any common value of the parameters and dimensions preceding pos.
7865 static enum isl_lp_result basic_set_maximal_difference_at(
7866 __isl_keep isl_basic_set *bset1, __isl_keep isl_basic_set *bset2,
7867 int pos, isl_int *opt)
7870 struct isl_basic_map *bmap1 = NULL;
7871 struct isl_basic_map *bmap2 = NULL;
7872 struct isl_ctx *ctx;
7873 struct isl_vec *obj;
7876 unsigned dim1, dim2;
7877 enum isl_lp_result res;
7879 if (!bset1 || !bset2)
7880 return isl_lp_error;
7882 nparam = isl_basic_set_n_param(bset1);
7883 dim1 = isl_basic_set_n_dim(bset1);
7884 dim2 = isl_basic_set_n_dim(bset2);
7885 dims = isl_space_alloc(bset1->ctx, nparam, pos, dim1 - pos);
7886 bmap1 = isl_basic_map_from_basic_set(isl_basic_set_copy(bset1), dims);
7887 dims = isl_space_alloc(bset2->ctx, nparam, pos, dim2 - pos);
7888 bmap2 = isl_basic_map_from_basic_set(isl_basic_set_copy(bset2), dims);
7889 if (!bmap1 || !bmap2)
7891 bmap1 = isl_basic_map_cow(bmap1);
7892 bmap1 = isl_basic_map_extend(bmap1, nparam,
7893 pos, (dim1 - pos) + (dim2 - pos),
7894 bmap2->n_div, bmap2->n_eq, bmap2->n_ineq);
7895 bmap1 = add_constraints(bmap1, bmap2, 0, dim1 - pos);
7898 total = isl_basic_map_total_dim(bmap1);
7900 obj = isl_vec_alloc(ctx, 1 + total);
7903 isl_seq_clr(obj->block.data, 1 + total);
7904 isl_int_set_si(obj->block.data[1+nparam+pos], 1);
7905 isl_int_set_si(obj->block.data[1+nparam+pos+(dim1-pos)], -1);
7906 res = isl_basic_map_solve_lp(bmap1, 1, obj->block.data, ctx->one,
7908 isl_basic_map_free(bmap1);
7912 isl_basic_map_free(bmap2);
7914 isl_basic_map_free(bmap1);
7915 return isl_lp_error;
7918 /* Given two _disjoint_ basic sets bset1 and bset2, check whether
7919 * for any common value of the parameters and dimensions preceding pos
7920 * in both basic sets, the values of dimension pos in bset1 are
7921 * smaller or larger than those in bset2.
7924 * 1 if bset1 follows bset2
7925 * -1 if bset1 precedes bset2
7926 * 0 if bset1 and bset2 are incomparable
7927 * -2 if some error occurred.
7929 int isl_basic_set_compare_at(struct isl_basic_set *bset1,
7930 struct isl_basic_set *bset2, int pos)
7933 enum isl_lp_result res;
7938 res = basic_set_maximal_difference_at(bset1, bset2, pos, &opt);
7940 if (res == isl_lp_empty)
7942 else if ((res == isl_lp_ok && isl_int_is_pos(opt)) ||
7943 res == isl_lp_unbounded)
7945 else if (res == isl_lp_ok && isl_int_is_neg(opt))
7954 /* Given two basic sets bset1 and bset2, check whether
7955 * for any common value of the parameters and dimensions preceding pos
7956 * there is a value of dimension pos in bset1 that is larger
7957 * than a value of the same dimension in bset2.
7960 * 1 if there exists such a pair
7961 * 0 if there is no such pair, but there is a pair of equal values
7963 * -2 if some error occurred.
7965 int isl_basic_set_follows_at(__isl_keep isl_basic_set *bset1,
7966 __isl_keep isl_basic_set *bset2, int pos)
7969 enum isl_lp_result res;
7974 res = basic_set_maximal_difference_at(bset1, bset2, pos, &opt);
7976 if (res == isl_lp_empty)
7978 else if ((res == isl_lp_ok && isl_int_is_pos(opt)) ||
7979 res == isl_lp_unbounded)
7981 else if (res == isl_lp_ok && isl_int_is_neg(opt))
7983 else if (res == isl_lp_ok)
7992 /* Given two sets set1 and set2, check whether
7993 * for any common value of the parameters and dimensions preceding pos
7994 * there is a value of dimension pos in set1 that is larger
7995 * than a value of the same dimension in set2.
7998 * 1 if there exists such a pair
7999 * 0 if there is no such pair, but there is a pair of equal values
8001 * -2 if some error occurred.
8003 int isl_set_follows_at(__isl_keep isl_set *set1,
8004 __isl_keep isl_set *set2, int pos)
8012 for (i = 0; i < set1->n; ++i)
8013 for (j = 0; j < set2->n; ++j) {
8015 f = isl_basic_set_follows_at(set1->p[i], set2->p[j], pos);
8016 if (f == 1 || f == -2)
8025 static int isl_basic_map_plain_has_fixed_var(__isl_keep isl_basic_map *bmap,
8026 unsigned pos, isl_int *val)
8034 total = isl_basic_map_total_dim(bmap);
8035 for (i = 0, d = total-1; i < bmap->n_eq && d+1 > pos; ++i) {
8036 for (; d+1 > pos; --d)
8037 if (!isl_int_is_zero(bmap->eq[i][1+d]))
8041 if (isl_seq_first_non_zero(bmap->eq[i]+1, d) != -1)
8043 if (isl_seq_first_non_zero(bmap->eq[i]+1+d+1, total-d-1) != -1)
8045 if (!isl_int_is_one(bmap->eq[i][1+d]))
8048 isl_int_neg(*val, bmap->eq[i][0]);
8054 static int isl_map_plain_has_fixed_var(__isl_keep isl_map *map,
8055 unsigned pos, isl_int *val)
8067 return isl_basic_map_plain_has_fixed_var(map->p[0], pos, val);
8070 fixed = isl_basic_map_plain_has_fixed_var(map->p[0], pos, &v);
8071 for (i = 1; fixed == 1 && i < map->n; ++i) {
8072 fixed = isl_basic_map_plain_has_fixed_var(map->p[i], pos, &tmp);
8073 if (fixed == 1 && isl_int_ne(tmp, v))
8077 isl_int_set(*val, v);
8083 static int isl_basic_set_plain_has_fixed_var(__isl_keep isl_basic_set *bset,
8084 unsigned pos, isl_int *val)
8086 return isl_basic_map_plain_has_fixed_var((struct isl_basic_map *)bset,
8090 static int isl_set_plain_has_fixed_var(__isl_keep isl_set *set, unsigned pos,
8093 return isl_map_plain_has_fixed_var((struct isl_map *)set, pos, val);
8096 int isl_basic_map_plain_is_fixed(__isl_keep isl_basic_map *bmap,
8097 enum isl_dim_type type, unsigned pos, isl_int *val)
8099 if (pos >= isl_basic_map_dim(bmap, type))
8101 return isl_basic_map_plain_has_fixed_var(bmap,
8102 isl_basic_map_offset(bmap, type) - 1 + pos, val);
8105 int isl_map_plain_is_fixed(__isl_keep isl_map *map,
8106 enum isl_dim_type type, unsigned pos, isl_int *val)
8108 if (pos >= isl_map_dim(map, type))
8110 return isl_map_plain_has_fixed_var(map,
8111 map_offset(map, type) - 1 + pos, val);
8114 int isl_set_plain_is_fixed(__isl_keep isl_set *set,
8115 enum isl_dim_type type, unsigned pos, isl_int *val)
8117 return isl_map_plain_is_fixed(set, type, pos, val);
8120 int isl_map_fast_is_fixed(__isl_keep isl_map *map,
8121 enum isl_dim_type type, unsigned pos, isl_int *val)
8123 return isl_map_plain_is_fixed(map, type, pos, val);
8126 /* Check if dimension dim has fixed value and if so and if val is not NULL,
8127 * then return this fixed value in *val.
8129 int isl_basic_set_plain_dim_is_fixed(__isl_keep isl_basic_set *bset,
8130 unsigned dim, isl_int *val)
8132 return isl_basic_set_plain_has_fixed_var(bset,
8133 isl_basic_set_n_param(bset) + dim, val);
8136 /* Check if dimension dim has fixed value and if so and if val is not NULL,
8137 * then return this fixed value in *val.
8139 int isl_set_plain_dim_is_fixed(__isl_keep isl_set *set,
8140 unsigned dim, isl_int *val)
8142 return isl_set_plain_has_fixed_var(set, isl_set_n_param(set) + dim, val);
8145 int isl_set_fast_dim_is_fixed(__isl_keep isl_set *set,
8146 unsigned dim, isl_int *val)
8148 return isl_set_plain_dim_is_fixed(set, dim, val);
8151 /* Check if input variable in has fixed value and if so and if val is not NULL,
8152 * then return this fixed value in *val.
8154 int isl_map_plain_input_is_fixed(__isl_keep isl_map *map,
8155 unsigned in, isl_int *val)
8157 return isl_map_plain_has_fixed_var(map, isl_map_n_param(map) + in, val);
8160 /* Check if dimension dim has an (obvious) fixed lower bound and if so
8161 * and if val is not NULL, then return this lower bound in *val.
8163 int isl_basic_set_plain_dim_has_fixed_lower_bound(
8164 __isl_keep isl_basic_set *bset, unsigned dim, isl_int *val)
8166 int i, i_eq = -1, i_ineq = -1;
8173 total = isl_basic_set_total_dim(bset);
8174 nparam = isl_basic_set_n_param(bset);
8175 for (i = 0; i < bset->n_eq; ++i) {
8176 if (isl_int_is_zero(bset->eq[i][1+nparam+dim]))
8182 for (i = 0; i < bset->n_ineq; ++i) {
8183 if (!isl_int_is_pos(bset->ineq[i][1+nparam+dim]))
8185 if (i_eq != -1 || i_ineq != -1)
8189 if (i_eq == -1 && i_ineq == -1)
8191 c = i_eq != -1 ? bset->eq[i_eq] : bset->ineq[i_ineq];
8192 /* The coefficient should always be one due to normalization. */
8193 if (!isl_int_is_one(c[1+nparam+dim]))
8195 if (isl_seq_first_non_zero(c+1, nparam+dim) != -1)
8197 if (isl_seq_first_non_zero(c+1+nparam+dim+1,
8198 total - nparam - dim - 1) != -1)
8201 isl_int_neg(*val, c[0]);
8205 int isl_set_plain_dim_has_fixed_lower_bound(__isl_keep isl_set *set,
8206 unsigned dim, isl_int *val)
8218 return isl_basic_set_plain_dim_has_fixed_lower_bound(set->p[0],
8222 fixed = isl_basic_set_plain_dim_has_fixed_lower_bound(set->p[0],
8224 for (i = 1; fixed == 1 && i < set->n; ++i) {
8225 fixed = isl_basic_set_plain_dim_has_fixed_lower_bound(set->p[i],
8227 if (fixed == 1 && isl_int_ne(tmp, v))
8231 isl_int_set(*val, v);
8242 /* uset_gist depends on constraints without existentially quantified
8243 * variables sorting first.
8245 static int qsort_constraint_cmp(const void *p1, const void *p2)
8247 const struct constraint *c1 = (const struct constraint *)p1;
8248 const struct constraint *c2 = (const struct constraint *)p2;
8250 unsigned size = isl_min(c1->size, c2->size);
8252 l1 = isl_seq_last_non_zero(c1->c + 1, size);
8253 l2 = isl_seq_last_non_zero(c2->c + 1, size);
8258 return isl_seq_cmp(c1->c + 1, c2->c + 1, size);
8261 static struct isl_basic_map *isl_basic_map_sort_constraints(
8262 struct isl_basic_map *bmap)
8265 struct constraint *c;
8270 total = isl_basic_map_total_dim(bmap);
8271 c = isl_alloc_array(bmap->ctx, struct constraint, bmap->n_ineq);
8274 for (i = 0; i < bmap->n_ineq; ++i) {
8276 c[i].c = bmap->ineq[i];
8278 qsort(c, bmap->n_ineq, sizeof(struct constraint), qsort_constraint_cmp);
8279 for (i = 0; i < bmap->n_ineq; ++i)
8280 bmap->ineq[i] = c[i].c;
8284 isl_basic_map_free(bmap);
8288 __isl_give isl_basic_set *isl_basic_set_sort_constraints(
8289 __isl_take isl_basic_set *bset)
8291 return (struct isl_basic_set *)isl_basic_map_sort_constraints(
8292 (struct isl_basic_map *)bset);
8295 struct isl_basic_map *isl_basic_map_normalize(struct isl_basic_map *bmap)
8299 if (ISL_F_ISSET(bmap, ISL_BASIC_MAP_NORMALIZED))
8301 bmap = isl_basic_map_remove_redundancies(bmap);
8302 bmap = isl_basic_map_sort_constraints(bmap);
8304 ISL_F_SET(bmap, ISL_BASIC_MAP_NORMALIZED);
8308 struct isl_basic_set *isl_basic_set_normalize(struct isl_basic_set *bset)
8310 return (struct isl_basic_set *)isl_basic_map_normalize(
8311 (struct isl_basic_map *)bset);
8314 int isl_basic_map_plain_cmp(const __isl_keep isl_basic_map *bmap1,
8315 const __isl_keep isl_basic_map *bmap2)
8322 if (ISL_F_ISSET(bmap1, ISL_BASIC_MAP_RATIONAL) !=
8323 ISL_F_ISSET(bmap2, ISL_BASIC_MAP_RATIONAL))
8324 return ISL_F_ISSET(bmap1, ISL_BASIC_MAP_RATIONAL) ? -1 : 1;
8325 if (isl_basic_map_n_param(bmap1) != isl_basic_map_n_param(bmap2))
8326 return isl_basic_map_n_param(bmap1) - isl_basic_map_n_param(bmap2);
8327 if (isl_basic_map_n_in(bmap1) != isl_basic_map_n_in(bmap2))
8328 return isl_basic_map_n_out(bmap1) - isl_basic_map_n_out(bmap2);
8329 if (isl_basic_map_n_out(bmap1) != isl_basic_map_n_out(bmap2))
8330 return isl_basic_map_n_out(bmap1) - isl_basic_map_n_out(bmap2);
8331 if (ISL_F_ISSET(bmap1, ISL_BASIC_MAP_EMPTY) &&
8332 ISL_F_ISSET(bmap2, ISL_BASIC_MAP_EMPTY))
8334 if (ISL_F_ISSET(bmap1, ISL_BASIC_MAP_EMPTY))
8336 if (ISL_F_ISSET(bmap2, ISL_BASIC_MAP_EMPTY))
8338 if (bmap1->n_eq != bmap2->n_eq)
8339 return bmap1->n_eq - bmap2->n_eq;
8340 if (bmap1->n_ineq != bmap2->n_ineq)
8341 return bmap1->n_ineq - bmap2->n_ineq;
8342 if (bmap1->n_div != bmap2->n_div)
8343 return bmap1->n_div - bmap2->n_div;
8344 total = isl_basic_map_total_dim(bmap1);
8345 for (i = 0; i < bmap1->n_eq; ++i) {
8346 cmp = isl_seq_cmp(bmap1->eq[i], bmap2->eq[i], 1+total);
8350 for (i = 0; i < bmap1->n_ineq; ++i) {
8351 cmp = isl_seq_cmp(bmap1->ineq[i], bmap2->ineq[i], 1+total);
8355 for (i = 0; i < bmap1->n_div; ++i) {
8356 cmp = isl_seq_cmp(bmap1->div[i], bmap2->div[i], 1+1+total);
8363 int isl_basic_set_plain_cmp(const __isl_keep isl_basic_set *bset1,
8364 const __isl_keep isl_basic_set *bset2)
8366 return isl_basic_map_plain_cmp(bset1, bset2);
8369 int isl_set_plain_cmp(__isl_keep isl_set *set1, __isl_keep isl_set *set2)
8375 if (set1->n != set2->n)
8376 return set1->n - set2->n;
8378 for (i = 0; i < set1->n; ++i) {
8379 cmp = isl_basic_set_plain_cmp(set1->p[i], set2->p[i]);
8387 int isl_basic_map_plain_is_equal(__isl_keep isl_basic_map *bmap1,
8388 __isl_keep isl_basic_map *bmap2)
8390 return isl_basic_map_plain_cmp(bmap1, bmap2) == 0;
8393 int isl_basic_set_plain_is_equal(__isl_keep isl_basic_set *bset1,
8394 __isl_keep isl_basic_set *bset2)
8396 return isl_basic_map_plain_is_equal((isl_basic_map *)bset1,
8397 (isl_basic_map *)bset2);
8400 static int qsort_bmap_cmp(const void *p1, const void *p2)
8402 const struct isl_basic_map *bmap1 = *(const struct isl_basic_map **)p1;
8403 const struct isl_basic_map *bmap2 = *(const struct isl_basic_map **)p2;
8405 return isl_basic_map_plain_cmp(bmap1, bmap2);
8408 /* We normalize in place, but if anything goes wrong we need
8409 * to return NULL, so we need to make sure we don't change the
8410 * meaning of any possible other copies of map.
8412 struct isl_map *isl_map_normalize(struct isl_map *map)
8415 struct isl_basic_map *bmap;
8419 if (ISL_F_ISSET(map, ISL_MAP_NORMALIZED))
8421 for (i = 0; i < map->n; ++i) {
8422 bmap = isl_basic_map_normalize(isl_basic_map_copy(map->p[i]));
8425 isl_basic_map_free(map->p[i]);
8428 qsort(map->p, map->n, sizeof(struct isl_basic_map *), qsort_bmap_cmp);
8429 ISL_F_SET(map, ISL_MAP_NORMALIZED);
8430 map = isl_map_remove_empty_parts(map);
8433 for (i = map->n - 1; i >= 1; --i) {
8434 if (!isl_basic_map_plain_is_equal(map->p[i-1], map->p[i]))
8436 isl_basic_map_free(map->p[i-1]);
8437 for (j = i; j < map->n; ++j)
8438 map->p[j-1] = map->p[j];
8448 struct isl_set *isl_set_normalize(struct isl_set *set)
8450 return (struct isl_set *)isl_map_normalize((struct isl_map *)set);
8453 int isl_map_plain_is_equal(__isl_keep isl_map *map1, __isl_keep isl_map *map2)
8463 if (!isl_space_is_equal(map1->dim, map2->dim))
8466 map1 = isl_map_copy(map1);
8467 map2 = isl_map_copy(map2);
8468 map1 = isl_map_normalize(map1);
8469 map2 = isl_map_normalize(map2);
8472 equal = map1->n == map2->n;
8473 for (i = 0; equal && i < map1->n; ++i) {
8474 equal = isl_basic_map_plain_is_equal(map1->p[i], map2->p[i]);
8487 int isl_map_fast_is_equal(__isl_keep isl_map *map1, __isl_keep isl_map *map2)
8489 return isl_map_plain_is_equal(map1, map2);
8492 int isl_set_plain_is_equal(__isl_keep isl_set *set1, __isl_keep isl_set *set2)
8494 return isl_map_plain_is_equal((struct isl_map *)set1,
8495 (struct isl_map *)set2);
8498 int isl_set_fast_is_equal(__isl_keep isl_set *set1, __isl_keep isl_set *set2)
8500 return isl_set_plain_is_equal(set1, set2);
8503 /* Return an interval that ranges from min to max (inclusive)
8505 struct isl_basic_set *isl_basic_set_interval(struct isl_ctx *ctx,
8506 isl_int min, isl_int max)
8509 struct isl_basic_set *bset = NULL;
8511 bset = isl_basic_set_alloc(ctx, 0, 1, 0, 0, 2);
8515 k = isl_basic_set_alloc_inequality(bset);
8518 isl_int_set_si(bset->ineq[k][1], 1);
8519 isl_int_neg(bset->ineq[k][0], min);
8521 k = isl_basic_set_alloc_inequality(bset);
8524 isl_int_set_si(bset->ineq[k][1], -1);
8525 isl_int_set(bset->ineq[k][0], max);
8529 isl_basic_set_free(bset);
8533 /* Return the Cartesian product of the basic sets in list (in the given order).
8535 __isl_give isl_basic_set *isl_basic_set_list_product(
8536 __isl_take struct isl_basic_set_list *list)
8544 struct isl_basic_set *product = NULL;
8548 isl_assert(list->ctx, list->n > 0, goto error);
8549 isl_assert(list->ctx, list->p[0], goto error);
8550 nparam = isl_basic_set_n_param(list->p[0]);
8551 dim = isl_basic_set_n_dim(list->p[0]);
8552 extra = list->p[0]->n_div;
8553 n_eq = list->p[0]->n_eq;
8554 n_ineq = list->p[0]->n_ineq;
8555 for (i = 1; i < list->n; ++i) {
8556 isl_assert(list->ctx, list->p[i], goto error);
8557 isl_assert(list->ctx,
8558 nparam == isl_basic_set_n_param(list->p[i]), goto error);
8559 dim += isl_basic_set_n_dim(list->p[i]);
8560 extra += list->p[i]->n_div;
8561 n_eq += list->p[i]->n_eq;
8562 n_ineq += list->p[i]->n_ineq;
8564 product = isl_basic_set_alloc(list->ctx, nparam, dim, extra,
8569 for (i = 0; i < list->n; ++i) {
8570 isl_basic_set_add_constraints(product,
8571 isl_basic_set_copy(list->p[i]), dim);
8572 dim += isl_basic_set_n_dim(list->p[i]);
8574 isl_basic_set_list_free(list);
8577 isl_basic_set_free(product);
8578 isl_basic_set_list_free(list);
8582 struct isl_basic_map *isl_basic_map_product(
8583 struct isl_basic_map *bmap1, struct isl_basic_map *bmap2)
8585 isl_space *dim_result = NULL;
8586 struct isl_basic_map *bmap;
8587 unsigned in1, in2, out1, out2, nparam, total, pos;
8588 struct isl_dim_map *dim_map1, *dim_map2;
8590 if (!bmap1 || !bmap2)
8593 isl_assert(bmap1->ctx, isl_space_match(bmap1->dim, isl_dim_param,
8594 bmap2->dim, isl_dim_param), goto error);
8595 dim_result = isl_space_product(isl_space_copy(bmap1->dim),
8596 isl_space_copy(bmap2->dim));
8598 in1 = isl_basic_map_n_in(bmap1);
8599 in2 = isl_basic_map_n_in(bmap2);
8600 out1 = isl_basic_map_n_out(bmap1);
8601 out2 = isl_basic_map_n_out(bmap2);
8602 nparam = isl_basic_map_n_param(bmap1);
8604 total = nparam + in1 + in2 + out1 + out2 + bmap1->n_div + bmap2->n_div;
8605 dim_map1 = isl_dim_map_alloc(bmap1->ctx, total);
8606 dim_map2 = isl_dim_map_alloc(bmap1->ctx, total);
8607 isl_dim_map_dim(dim_map1, bmap1->dim, isl_dim_param, pos = 0);
8608 isl_dim_map_dim(dim_map2, bmap2->dim, isl_dim_param, pos = 0);
8609 isl_dim_map_dim(dim_map1, bmap1->dim, isl_dim_in, pos += nparam);
8610 isl_dim_map_dim(dim_map2, bmap2->dim, isl_dim_in, pos += in1);
8611 isl_dim_map_dim(dim_map1, bmap1->dim, isl_dim_out, pos += in2);
8612 isl_dim_map_dim(dim_map2, bmap2->dim, isl_dim_out, pos += out1);
8613 isl_dim_map_div(dim_map1, bmap1, pos += out2);
8614 isl_dim_map_div(dim_map2, bmap2, pos += bmap1->n_div);
8616 bmap = isl_basic_map_alloc_space(dim_result,
8617 bmap1->n_div + bmap2->n_div,
8618 bmap1->n_eq + bmap2->n_eq,
8619 bmap1->n_ineq + bmap2->n_ineq);
8620 bmap = isl_basic_map_add_constraints_dim_map(bmap, bmap1, dim_map1);
8621 bmap = isl_basic_map_add_constraints_dim_map(bmap, bmap2, dim_map2);
8622 bmap = isl_basic_map_simplify(bmap);
8623 return isl_basic_map_finalize(bmap);
8625 isl_basic_map_free(bmap1);
8626 isl_basic_map_free(bmap2);
8630 __isl_give isl_basic_map *isl_basic_map_flat_product(
8631 __isl_take isl_basic_map *bmap1, __isl_take isl_basic_map *bmap2)
8633 isl_basic_map *prod;
8635 prod = isl_basic_map_product(bmap1, bmap2);
8636 prod = isl_basic_map_flatten(prod);
8640 __isl_give isl_basic_set *isl_basic_set_flat_product(
8641 __isl_take isl_basic_set *bset1, __isl_take isl_basic_set *bset2)
8643 return isl_basic_map_flat_range_product(bset1, bset2);
8646 __isl_give isl_basic_map *isl_basic_map_domain_product(
8647 __isl_take isl_basic_map *bmap1, __isl_take isl_basic_map *bmap2)
8649 isl_space *space_result = NULL;
8650 isl_basic_map *bmap;
8651 unsigned in1, in2, out, nparam, total, pos;
8652 struct isl_dim_map *dim_map1, *dim_map2;
8654 if (!bmap1 || !bmap2)
8657 space_result = isl_space_domain_product(isl_space_copy(bmap1->dim),
8658 isl_space_copy(bmap2->dim));
8660 in1 = isl_basic_map_dim(bmap1, isl_dim_in);
8661 in2 = isl_basic_map_dim(bmap2, isl_dim_in);
8662 out = isl_basic_map_dim(bmap1, isl_dim_out);
8663 nparam = isl_basic_map_dim(bmap1, isl_dim_param);
8665 total = nparam + in1 + in2 + out + bmap1->n_div + bmap2->n_div;
8666 dim_map1 = isl_dim_map_alloc(bmap1->ctx, total);
8667 dim_map2 = isl_dim_map_alloc(bmap1->ctx, total);
8668 isl_dim_map_dim(dim_map1, bmap1->dim, isl_dim_param, pos = 0);
8669 isl_dim_map_dim(dim_map2, bmap2->dim, isl_dim_param, pos = 0);
8670 isl_dim_map_dim(dim_map1, bmap1->dim, isl_dim_in, pos += nparam);
8671 isl_dim_map_dim(dim_map2, bmap2->dim, isl_dim_in, pos += in1);
8672 isl_dim_map_dim(dim_map1, bmap1->dim, isl_dim_out, pos += in2);
8673 isl_dim_map_dim(dim_map2, bmap2->dim, isl_dim_out, pos);
8674 isl_dim_map_div(dim_map1, bmap1, pos += out);
8675 isl_dim_map_div(dim_map2, bmap2, pos += bmap1->n_div);
8677 bmap = isl_basic_map_alloc_space(space_result,
8678 bmap1->n_div + bmap2->n_div,
8679 bmap1->n_eq + bmap2->n_eq,
8680 bmap1->n_ineq + bmap2->n_ineq);
8681 bmap = isl_basic_map_add_constraints_dim_map(bmap, bmap1, dim_map1);
8682 bmap = isl_basic_map_add_constraints_dim_map(bmap, bmap2, dim_map2);
8683 bmap = isl_basic_map_simplify(bmap);
8684 return isl_basic_map_finalize(bmap);
8686 isl_basic_map_free(bmap1);
8687 isl_basic_map_free(bmap2);
8691 __isl_give isl_basic_map *isl_basic_map_range_product(
8692 __isl_take isl_basic_map *bmap1, __isl_take isl_basic_map *bmap2)
8694 isl_space *dim_result = NULL;
8695 isl_basic_map *bmap;
8696 unsigned in, out1, out2, nparam, total, pos;
8697 struct isl_dim_map *dim_map1, *dim_map2;
8699 if (!bmap1 || !bmap2)
8702 if (!isl_space_match(bmap1->dim, isl_dim_param,
8703 bmap2->dim, isl_dim_param))
8704 isl_die(isl_basic_map_get_ctx(bmap1), isl_error_invalid,
8705 "parameters don't match", goto error);
8707 dim_result = isl_space_range_product(isl_space_copy(bmap1->dim),
8708 isl_space_copy(bmap2->dim));
8710 in = isl_basic_map_dim(bmap1, isl_dim_in);
8711 out1 = isl_basic_map_n_out(bmap1);
8712 out2 = isl_basic_map_n_out(bmap2);
8713 nparam = isl_basic_map_n_param(bmap1);
8715 total = nparam + in + out1 + out2 + bmap1->n_div + bmap2->n_div;
8716 dim_map1 = isl_dim_map_alloc(bmap1->ctx, total);
8717 dim_map2 = isl_dim_map_alloc(bmap1->ctx, total);
8718 isl_dim_map_dim(dim_map1, bmap1->dim, isl_dim_param, pos = 0);
8719 isl_dim_map_dim(dim_map2, bmap2->dim, isl_dim_param, pos = 0);
8720 isl_dim_map_dim(dim_map1, bmap1->dim, isl_dim_in, pos += nparam);
8721 isl_dim_map_dim(dim_map2, bmap2->dim, isl_dim_in, pos);
8722 isl_dim_map_dim(dim_map1, bmap1->dim, isl_dim_out, pos += in);
8723 isl_dim_map_dim(dim_map2, bmap2->dim, isl_dim_out, pos += out1);
8724 isl_dim_map_div(dim_map1, bmap1, pos += out2);
8725 isl_dim_map_div(dim_map2, bmap2, pos += bmap1->n_div);
8727 bmap = isl_basic_map_alloc_space(dim_result,
8728 bmap1->n_div + bmap2->n_div,
8729 bmap1->n_eq + bmap2->n_eq,
8730 bmap1->n_ineq + bmap2->n_ineq);
8731 bmap = isl_basic_map_add_constraints_dim_map(bmap, bmap1, dim_map1);
8732 bmap = isl_basic_map_add_constraints_dim_map(bmap, bmap2, dim_map2);
8733 bmap = isl_basic_map_simplify(bmap);
8734 return isl_basic_map_finalize(bmap);
8736 isl_basic_map_free(bmap1);
8737 isl_basic_map_free(bmap2);
8741 __isl_give isl_basic_map *isl_basic_map_flat_range_product(
8742 __isl_take isl_basic_map *bmap1, __isl_take isl_basic_map *bmap2)
8744 isl_basic_map *prod;
8746 prod = isl_basic_map_range_product(bmap1, bmap2);
8747 prod = isl_basic_map_flatten_range(prod);
8751 static __isl_give isl_map *map_product(__isl_take isl_map *map1,
8752 __isl_take isl_map *map2,
8753 __isl_give isl_space *(*dim_product)(__isl_take isl_space *left,
8754 __isl_take isl_space *right),
8755 __isl_give isl_basic_map *(*basic_map_product)(
8756 __isl_take isl_basic_map *left, __isl_take isl_basic_map *right))
8759 struct isl_map *result;
8765 isl_assert(map1->ctx, isl_space_match(map1->dim, isl_dim_param,
8766 map2->dim, isl_dim_param), goto error);
8768 if (ISL_F_ISSET(map1, ISL_MAP_DISJOINT) &&
8769 ISL_F_ISSET(map2, ISL_MAP_DISJOINT))
8770 ISL_FL_SET(flags, ISL_MAP_DISJOINT);
8772 result = isl_map_alloc_space(dim_product(isl_space_copy(map1->dim),
8773 isl_space_copy(map2->dim)),
8774 map1->n * map2->n, flags);
8777 for (i = 0; i < map1->n; ++i)
8778 for (j = 0; j < map2->n; ++j) {
8779 struct isl_basic_map *part;
8780 part = basic_map_product(isl_basic_map_copy(map1->p[i]),
8781 isl_basic_map_copy(map2->p[j]));
8782 if (isl_basic_map_is_empty(part))
8783 isl_basic_map_free(part);
8785 result = isl_map_add_basic_map(result, part);
8798 /* Given two maps A -> B and C -> D, construct a map [A -> C] -> [B -> D]
8800 static __isl_give isl_map *map_product_aligned(__isl_take isl_map *map1,
8801 __isl_take isl_map *map2)
8803 return map_product(map1, map2, &isl_space_product, &isl_basic_map_product);
8806 __isl_give isl_map *isl_map_product(__isl_take isl_map *map1,
8807 __isl_take isl_map *map2)
8809 return isl_map_align_params_map_map_and(map1, map2, &map_product_aligned);
8812 /* Given two maps A -> B and C -> D, construct a map (A, C) -> (B, D)
8814 __isl_give isl_map *isl_map_flat_product(__isl_take isl_map *map1,
8815 __isl_take isl_map *map2)
8819 prod = isl_map_product(map1, map2);
8820 prod = isl_map_flatten(prod);
8824 /* Given two set A and B, construct its Cartesian product A x B.
8826 struct isl_set *isl_set_product(struct isl_set *set1, struct isl_set *set2)
8828 return isl_map_range_product(set1, set2);
8831 __isl_give isl_set *isl_set_flat_product(__isl_take isl_set *set1,
8832 __isl_take isl_set *set2)
8834 return isl_map_flat_range_product(set1, set2);
8837 /* Given two maps A -> B and C -> D, construct a map [A -> C] -> (B * D)
8839 static __isl_give isl_map *map_domain_product_aligned(__isl_take isl_map *map1,
8840 __isl_take isl_map *map2)
8842 return map_product(map1, map2, &isl_space_domain_product,
8843 &isl_basic_map_domain_product);
8846 /* Given two maps A -> B and C -> D, construct a map (A * C) -> [B -> D]
8848 static __isl_give isl_map *map_range_product_aligned(__isl_take isl_map *map1,
8849 __isl_take isl_map *map2)
8851 return map_product(map1, map2, &isl_space_range_product,
8852 &isl_basic_map_range_product);
8855 __isl_give isl_map *isl_map_domain_product(__isl_take isl_map *map1,
8856 __isl_take isl_map *map2)
8858 return isl_map_align_params_map_map_and(map1, map2,
8859 &map_domain_product_aligned);
8862 __isl_give isl_map *isl_map_range_product(__isl_take isl_map *map1,
8863 __isl_take isl_map *map2)
8865 return isl_map_align_params_map_map_and(map1, map2,
8866 &map_range_product_aligned);
8869 /* Given two maps A -> B and C -> D, construct a map (A, C) -> (B * D)
8871 __isl_give isl_map *isl_map_flat_domain_product(__isl_take isl_map *map1,
8872 __isl_take isl_map *map2)
8876 prod = isl_map_domain_product(map1, map2);
8877 prod = isl_map_flatten_domain(prod);
8881 /* Given two maps A -> B and C -> D, construct a map (A * C) -> (B, D)
8883 __isl_give isl_map *isl_map_flat_range_product(__isl_take isl_map *map1,
8884 __isl_take isl_map *map2)
8888 prod = isl_map_range_product(map1, map2);
8889 prod = isl_map_flatten_range(prod);
8893 uint32_t isl_basic_map_get_hash(__isl_keep isl_basic_map *bmap)
8896 uint32_t hash = isl_hash_init();
8901 bmap = isl_basic_map_copy(bmap);
8902 bmap = isl_basic_map_normalize(bmap);
8905 total = isl_basic_map_total_dim(bmap);
8906 isl_hash_byte(hash, bmap->n_eq & 0xFF);
8907 for (i = 0; i < bmap->n_eq; ++i) {
8909 c_hash = isl_seq_get_hash(bmap->eq[i], 1 + total);
8910 isl_hash_hash(hash, c_hash);
8912 isl_hash_byte(hash, bmap->n_ineq & 0xFF);
8913 for (i = 0; i < bmap->n_ineq; ++i) {
8915 c_hash = isl_seq_get_hash(bmap->ineq[i], 1 + total);
8916 isl_hash_hash(hash, c_hash);
8918 isl_hash_byte(hash, bmap->n_div & 0xFF);
8919 for (i = 0; i < bmap->n_div; ++i) {
8921 if (isl_int_is_zero(bmap->div[i][0]))
8923 isl_hash_byte(hash, i & 0xFF);
8924 c_hash = isl_seq_get_hash(bmap->div[i], 1 + 1 + total);
8925 isl_hash_hash(hash, c_hash);
8927 isl_basic_map_free(bmap);
8931 uint32_t isl_basic_set_get_hash(__isl_keep isl_basic_set *bset)
8933 return isl_basic_map_get_hash((isl_basic_map *)bset);
8936 uint32_t isl_map_get_hash(__isl_keep isl_map *map)
8943 map = isl_map_copy(map);
8944 map = isl_map_normalize(map);
8948 hash = isl_hash_init();
8949 for (i = 0; i < map->n; ++i) {
8951 bmap_hash = isl_basic_map_get_hash(map->p[i]);
8952 isl_hash_hash(hash, bmap_hash);
8960 uint32_t isl_set_get_hash(__isl_keep isl_set *set)
8962 return isl_map_get_hash((isl_map *)set);
8965 /* Check if the value for dimension dim is completely determined
8966 * by the values of the other parameters and variables.
8967 * That is, check if dimension dim is involved in an equality.
8969 int isl_basic_set_dim_is_unique(struct isl_basic_set *bset, unsigned dim)
8976 nparam = isl_basic_set_n_param(bset);
8977 for (i = 0; i < bset->n_eq; ++i)
8978 if (!isl_int_is_zero(bset->eq[i][1 + nparam + dim]))
8983 /* Check if the value for dimension dim is completely determined
8984 * by the values of the other parameters and variables.
8985 * That is, check if dimension dim is involved in an equality
8986 * for each of the subsets.
8988 int isl_set_dim_is_unique(struct isl_set *set, unsigned dim)
8994 for (i = 0; i < set->n; ++i) {
8996 unique = isl_basic_set_dim_is_unique(set->p[i], dim);
9003 int isl_set_n_basic_set(__isl_keep isl_set *set)
9005 return set ? set->n : 0;
9008 int isl_map_foreach_basic_map(__isl_keep isl_map *map,
9009 int (*fn)(__isl_take isl_basic_map *bmap, void *user), void *user)
9016 for (i = 0; i < map->n; ++i)
9017 if (fn(isl_basic_map_copy(map->p[i]), user) < 0)
9023 int isl_set_foreach_basic_set(__isl_keep isl_set *set,
9024 int (*fn)(__isl_take isl_basic_set *bset, void *user), void *user)
9031 for (i = 0; i < set->n; ++i)
9032 if (fn(isl_basic_set_copy(set->p[i]), user) < 0)
9038 __isl_give isl_basic_set *isl_basic_set_lift(__isl_take isl_basic_set *bset)
9045 bset = isl_basic_set_cow(bset);
9049 dim = isl_basic_set_get_space(bset);
9050 dim = isl_space_lift(dim, bset->n_div);
9053 isl_space_free(bset->dim);
9055 bset->extra -= bset->n_div;
9058 bset = isl_basic_set_finalize(bset);
9062 isl_basic_set_free(bset);
9066 __isl_give isl_set *isl_set_lift(__isl_take isl_set *set)
9072 set = isl_set_align_divs(set);
9077 set = isl_set_cow(set);
9081 n_div = set->p[0]->n_div;
9082 dim = isl_set_get_space(set);
9083 dim = isl_space_lift(dim, n_div);
9086 isl_space_free(set->dim);
9089 for (i = 0; i < set->n; ++i) {
9090 set->p[i] = isl_basic_set_lift(set->p[i]);
9101 __isl_give isl_map *isl_set_lifting(__isl_take isl_set *set)
9104 struct isl_basic_map *bmap;
9111 set = isl_set_align_divs(set);
9116 dim = isl_set_get_space(set);
9117 if (set->n == 0 || set->p[0]->n_div == 0) {
9119 return isl_map_identity(isl_space_map_from_set(dim));
9122 n_div = set->p[0]->n_div;
9123 dim = isl_space_map_from_set(dim);
9124 n_param = isl_space_dim(dim, isl_dim_param);
9125 n_set = isl_space_dim(dim, isl_dim_in);
9126 dim = isl_space_extend(dim, n_param, n_set, n_set + n_div);
9127 bmap = isl_basic_map_alloc_space(dim, 0, n_set, 2 * n_div);
9128 for (i = 0; i < n_set; ++i)
9129 bmap = var_equal(bmap, i);
9131 total = n_param + n_set + n_set + n_div;
9132 for (i = 0; i < n_div; ++i) {
9133 k = isl_basic_map_alloc_inequality(bmap);
9136 isl_seq_cpy(bmap->ineq[k], set->p[0]->div[i]+1, 1+n_param);
9137 isl_seq_clr(bmap->ineq[k]+1+n_param, n_set);
9138 isl_seq_cpy(bmap->ineq[k]+1+n_param+n_set,
9139 set->p[0]->div[i]+1+1+n_param, n_set + n_div);
9140 isl_int_neg(bmap->ineq[k][1+n_param+n_set+n_set+i],
9141 set->p[0]->div[i][0]);
9143 l = isl_basic_map_alloc_inequality(bmap);
9146 isl_seq_neg(bmap->ineq[l], bmap->ineq[k], 1 + total);
9147 isl_int_add(bmap->ineq[l][0], bmap->ineq[l][0],
9148 set->p[0]->div[i][0]);
9149 isl_int_sub_ui(bmap->ineq[l][0], bmap->ineq[l][0], 1);
9153 bmap = isl_basic_map_simplify(bmap);
9154 bmap = isl_basic_map_finalize(bmap);
9155 return isl_map_from_basic_map(bmap);
9158 isl_basic_map_free(bmap);
9162 int isl_basic_set_size(__isl_keep isl_basic_set *bset)
9170 dim = isl_basic_set_total_dim(bset);
9171 size += bset->n_eq * (1 + dim);
9172 size += bset->n_ineq * (1 + dim);
9173 size += bset->n_div * (2 + dim);
9178 int isl_set_size(__isl_keep isl_set *set)
9186 for (i = 0; i < set->n; ++i)
9187 size += isl_basic_set_size(set->p[i]);
9192 /* Check if there is any lower bound (if lower == 0) and/or upper
9193 * bound (if upper == 0) on the specified dim.
9195 static int basic_map_dim_is_bounded(__isl_keep isl_basic_map *bmap,
9196 enum isl_dim_type type, unsigned pos, int lower, int upper)
9203 isl_assert(bmap->ctx, pos < isl_basic_map_dim(bmap, type), return -1);
9205 pos += isl_basic_map_offset(bmap, type);
9207 for (i = 0; i < bmap->n_div; ++i) {
9208 if (isl_int_is_zero(bmap->div[i][0]))
9210 if (!isl_int_is_zero(bmap->div[i][1 + pos]))
9214 for (i = 0; i < bmap->n_eq; ++i)
9215 if (!isl_int_is_zero(bmap->eq[i][pos]))
9218 for (i = 0; i < bmap->n_ineq; ++i) {
9219 int sgn = isl_int_sgn(bmap->ineq[i][pos]);
9226 return lower && upper;
9229 int isl_basic_map_dim_is_bounded(__isl_keep isl_basic_map *bmap,
9230 enum isl_dim_type type, unsigned pos)
9232 return basic_map_dim_is_bounded(bmap, type, pos, 0, 0);
9235 int isl_basic_map_dim_has_lower_bound(__isl_keep isl_basic_map *bmap,
9236 enum isl_dim_type type, unsigned pos)
9238 return basic_map_dim_is_bounded(bmap, type, pos, 0, 1);
9241 int isl_basic_map_dim_has_upper_bound(__isl_keep isl_basic_map *bmap,
9242 enum isl_dim_type type, unsigned pos)
9244 return basic_map_dim_is_bounded(bmap, type, pos, 1, 0);
9247 int isl_map_dim_is_bounded(__isl_keep isl_map *map,
9248 enum isl_dim_type type, unsigned pos)
9255 for (i = 0; i < map->n; ++i) {
9257 bounded = isl_basic_map_dim_is_bounded(map->p[i], type, pos);
9258 if (bounded < 0 || !bounded)
9265 /* Return 1 if the specified dim is involved in both an upper bound
9266 * and a lower bound.
9268 int isl_set_dim_is_bounded(__isl_keep isl_set *set,
9269 enum isl_dim_type type, unsigned pos)
9271 return isl_map_dim_is_bounded((isl_map *)set, type, pos);
9274 /* Does "map" have a bound (according to "fn") for any of its basic maps?
9276 static int has_any_bound(__isl_keep isl_map *map,
9277 enum isl_dim_type type, unsigned pos,
9278 int (*fn)(__isl_keep isl_basic_map *bmap,
9279 enum isl_dim_type type, unsigned pos))
9286 for (i = 0; i < map->n; ++i) {
9288 bounded = fn(map->p[i], type, pos);
9289 if (bounded < 0 || bounded)
9296 /* Return 1 if the specified dim is involved in any lower bound.
9298 int isl_set_dim_has_any_lower_bound(__isl_keep isl_set *set,
9299 enum isl_dim_type type, unsigned pos)
9301 return has_any_bound(set, type, pos,
9302 &isl_basic_map_dim_has_lower_bound);
9305 /* Return 1 if the specified dim is involved in any upper bound.
9307 int isl_set_dim_has_any_upper_bound(__isl_keep isl_set *set,
9308 enum isl_dim_type type, unsigned pos)
9310 return has_any_bound(set, type, pos,
9311 &isl_basic_map_dim_has_upper_bound);
9314 /* Does "map" have a bound (according to "fn") for all of its basic maps?
9316 static int has_bound(__isl_keep isl_map *map,
9317 enum isl_dim_type type, unsigned pos,
9318 int (*fn)(__isl_keep isl_basic_map *bmap,
9319 enum isl_dim_type type, unsigned pos))
9326 for (i = 0; i < map->n; ++i) {
9328 bounded = fn(map->p[i], type, pos);
9329 if (bounded < 0 || !bounded)
9336 /* Return 1 if the specified dim has a lower bound (in each of its basic sets).
9338 int isl_set_dim_has_lower_bound(__isl_keep isl_set *set,
9339 enum isl_dim_type type, unsigned pos)
9341 return has_bound(set, type, pos, &isl_basic_map_dim_has_lower_bound);
9344 /* Return 1 if the specified dim has an upper bound (in each of its basic sets).
9346 int isl_set_dim_has_upper_bound(__isl_keep isl_set *set,
9347 enum isl_dim_type type, unsigned pos)
9349 return has_bound(set, type, pos, &isl_basic_map_dim_has_upper_bound);
9352 /* For each of the "n" variables starting at "first", determine
9353 * the sign of the variable and put the results in the first "n"
9354 * elements of the array "signs".
9356 * 1 means that the variable is non-negative
9357 * -1 means that the variable is non-positive
9358 * 0 means the variable attains both positive and negative values.
9360 int isl_basic_set_vars_get_sign(__isl_keep isl_basic_set *bset,
9361 unsigned first, unsigned n, int *signs)
9363 isl_vec *bound = NULL;
9364 struct isl_tab *tab = NULL;
9365 struct isl_tab_undo *snap;
9368 if (!bset || !signs)
9371 bound = isl_vec_alloc(bset->ctx, 1 + isl_basic_set_total_dim(bset));
9372 tab = isl_tab_from_basic_set(bset, 0);
9376 isl_seq_clr(bound->el, bound->size);
9377 isl_int_set_si(bound->el[0], -1);
9379 snap = isl_tab_snap(tab);
9380 for (i = 0; i < n; ++i) {
9383 isl_int_set_si(bound->el[1 + first + i], -1);
9384 if (isl_tab_add_ineq(tab, bound->el) < 0)
9387 isl_int_set_si(bound->el[1 + first + i], 0);
9388 if (isl_tab_rollback(tab, snap) < 0)
9396 isl_int_set_si(bound->el[1 + first + i], 1);
9397 if (isl_tab_add_ineq(tab, bound->el) < 0)
9400 isl_int_set_si(bound->el[1 + first + i], 0);
9401 if (isl_tab_rollback(tab, snap) < 0)
9404 signs[i] = empty ? -1 : 0;
9408 isl_vec_free(bound);
9412 isl_vec_free(bound);
9416 int isl_basic_set_dims_get_sign(__isl_keep isl_basic_set *bset,
9417 enum isl_dim_type type, unsigned first, unsigned n, int *signs)
9419 if (!bset || !signs)
9421 isl_assert(bset->ctx, first + n <= isl_basic_set_dim(bset, type),
9424 first += pos(bset->dim, type) - 1;
9425 return isl_basic_set_vars_get_sign(bset, first, n, signs);
9428 /* Check if the given basic map is obviously single-valued.
9429 * In particular, for each output dimension, check that there is
9430 * an equality that defines the output dimension in terms of
9431 * earlier dimensions.
9433 int isl_basic_map_plain_is_single_valued(__isl_keep isl_basic_map *bmap)
9443 total = 1 + isl_basic_map_total_dim(bmap);
9444 n_out = isl_basic_map_dim(bmap, isl_dim_out);
9445 o_out = isl_basic_map_offset(bmap, isl_dim_out);
9447 for (i = 0; i < n_out; ++i) {
9448 for (j = 0; j < bmap->n_eq; ++j) {
9449 if (isl_int_is_zero(bmap->eq[j][o_out + i]))
9451 if (isl_seq_first_non_zero(bmap->eq[j] + o_out + i + 1,
9452 total - (o_out + i + 1)) == -1)
9455 if (j >= bmap->n_eq)
9462 /* Check if the given basic map is single-valued.
9467 * and check if the result is a subset of the identity mapping.
9469 int isl_basic_map_is_single_valued(__isl_keep isl_basic_map *bmap)
9472 isl_basic_map *test;
9476 sv = isl_basic_map_plain_is_single_valued(bmap);
9480 test = isl_basic_map_reverse(isl_basic_map_copy(bmap));
9481 test = isl_basic_map_apply_range(test, isl_basic_map_copy(bmap));
9483 space = isl_basic_map_get_space(bmap);
9484 space = isl_space_map_from_set(isl_space_range(space));
9485 id = isl_basic_map_identity(space);
9487 sv = isl_basic_map_is_subset(test, id);
9489 isl_basic_map_free(test);
9490 isl_basic_map_free(id);
9495 /* Check if the given map is obviously single-valued.
9497 int isl_map_plain_is_single_valued(__isl_keep isl_map *map)
9506 return isl_basic_map_plain_is_single_valued(map->p[0]);
9509 /* Check if the given map is single-valued.
9514 * and check if the result is a subset of the identity mapping.
9516 int isl_map_is_single_valued(__isl_keep isl_map *map)
9523 sv = isl_map_plain_is_single_valued(map);
9527 test = isl_map_reverse(isl_map_copy(map));
9528 test = isl_map_apply_range(test, isl_map_copy(map));
9530 dim = isl_space_map_from_set(isl_space_range(isl_map_get_space(map)));
9531 id = isl_map_identity(dim);
9533 sv = isl_map_is_subset(test, id);
9541 int isl_map_is_injective(__isl_keep isl_map *map)
9545 map = isl_map_copy(map);
9546 map = isl_map_reverse(map);
9547 in = isl_map_is_single_valued(map);
9553 /* Check if the given map is obviously injective.
9555 int isl_map_plain_is_injective(__isl_keep isl_map *map)
9559 map = isl_map_copy(map);
9560 map = isl_map_reverse(map);
9561 in = isl_map_plain_is_single_valued(map);
9567 int isl_map_is_bijective(__isl_keep isl_map *map)
9571 sv = isl_map_is_single_valued(map);
9575 return isl_map_is_injective(map);
9578 int isl_set_is_singleton(__isl_keep isl_set *set)
9580 return isl_map_is_single_valued((isl_map *)set);
9583 int isl_map_is_translation(__isl_keep isl_map *map)
9588 delta = isl_map_deltas(isl_map_copy(map));
9589 ok = isl_set_is_singleton(delta);
9590 isl_set_free(delta);
9595 static int unique(isl_int *p, unsigned pos, unsigned len)
9597 if (isl_seq_first_non_zero(p, pos) != -1)
9599 if (isl_seq_first_non_zero(p + pos + 1, len - pos - 1) != -1)
9604 int isl_basic_set_is_box(__isl_keep isl_basic_set *bset)
9613 if (isl_basic_set_dim(bset, isl_dim_div) != 0)
9616 nvar = isl_basic_set_dim(bset, isl_dim_set);
9617 ovar = isl_space_offset(bset->dim, isl_dim_set);
9618 for (j = 0; j < nvar; ++j) {
9619 int lower = 0, upper = 0;
9620 for (i = 0; i < bset->n_eq; ++i) {
9621 if (isl_int_is_zero(bset->eq[i][1 + ovar + j]))
9623 if (!unique(bset->eq[i] + 1 + ovar, j, nvar))
9629 for (i = 0; i < bset->n_ineq; ++i) {
9630 if (isl_int_is_zero(bset->ineq[i][1 + ovar + j]))
9632 if (!unique(bset->ineq[i] + 1 + ovar, j, nvar))
9634 if (isl_int_is_pos(bset->ineq[i][1 + ovar + j]))
9639 if (!lower || !upper)
9646 int isl_set_is_box(__isl_keep isl_set *set)
9653 return isl_basic_set_is_box(set->p[0]);
9656 int isl_basic_set_is_wrapping(__isl_keep isl_basic_set *bset)
9661 return isl_space_is_wrapping(bset->dim);
9664 int isl_set_is_wrapping(__isl_keep isl_set *set)
9669 return isl_space_is_wrapping(set->dim);
9672 __isl_give isl_basic_set *isl_basic_map_wrap(__isl_take isl_basic_map *bmap)
9674 bmap = isl_basic_map_cow(bmap);
9678 bmap->dim = isl_space_wrap(bmap->dim);
9682 bmap = isl_basic_map_finalize(bmap);
9684 return (isl_basic_set *)bmap;
9686 isl_basic_map_free(bmap);
9690 __isl_give isl_set *isl_map_wrap(__isl_take isl_map *map)
9694 map = isl_map_cow(map);
9698 for (i = 0; i < map->n; ++i) {
9699 map->p[i] = (isl_basic_map *)isl_basic_map_wrap(map->p[i]);
9703 map->dim = isl_space_wrap(map->dim);
9707 return (isl_set *)map;
9713 __isl_give isl_basic_map *isl_basic_set_unwrap(__isl_take isl_basic_set *bset)
9715 bset = isl_basic_set_cow(bset);
9719 bset->dim = isl_space_unwrap(bset->dim);
9723 bset = isl_basic_set_finalize(bset);
9725 return (isl_basic_map *)bset;
9727 isl_basic_set_free(bset);
9731 __isl_give isl_map *isl_set_unwrap(__isl_take isl_set *set)
9738 if (!isl_set_is_wrapping(set))
9739 isl_die(set->ctx, isl_error_invalid, "not a wrapping set",
9742 set = isl_set_cow(set);
9746 for (i = 0; i < set->n; ++i) {
9747 set->p[i] = (isl_basic_set *)isl_basic_set_unwrap(set->p[i]);
9752 set->dim = isl_space_unwrap(set->dim);
9756 return (isl_map *)set;
9762 __isl_give isl_basic_map *isl_basic_map_reset(__isl_take isl_basic_map *bmap,
9763 enum isl_dim_type type)
9768 if (!isl_space_is_named_or_nested(bmap->dim, type))
9771 bmap = isl_basic_map_cow(bmap);
9775 bmap->dim = isl_space_reset(bmap->dim, type);
9779 bmap = isl_basic_map_finalize(bmap);
9783 isl_basic_map_free(bmap);
9787 __isl_give isl_map *isl_map_reset(__isl_take isl_map *map,
9788 enum isl_dim_type type)
9795 if (!isl_space_is_named_or_nested(map->dim, type))
9798 map = isl_map_cow(map);
9802 for (i = 0; i < map->n; ++i) {
9803 map->p[i] = isl_basic_map_reset(map->p[i], type);
9807 map->dim = isl_space_reset(map->dim, type);
9817 __isl_give isl_basic_map *isl_basic_map_flatten(__isl_take isl_basic_map *bmap)
9822 if (!bmap->dim->nested[0] && !bmap->dim->nested[1])
9825 bmap = isl_basic_map_cow(bmap);
9829 bmap->dim = isl_space_flatten(bmap->dim);
9833 bmap = isl_basic_map_finalize(bmap);
9837 isl_basic_map_free(bmap);
9841 __isl_give isl_basic_set *isl_basic_set_flatten(__isl_take isl_basic_set *bset)
9843 return (isl_basic_set *)isl_basic_map_flatten((isl_basic_map *)bset);
9846 __isl_give isl_basic_map *isl_basic_map_flatten_domain(
9847 __isl_take isl_basic_map *bmap)
9852 if (!bmap->dim->nested[0])
9855 bmap = isl_basic_map_cow(bmap);
9859 bmap->dim = isl_space_flatten_domain(bmap->dim);
9863 bmap = isl_basic_map_finalize(bmap);
9867 isl_basic_map_free(bmap);
9871 __isl_give isl_basic_map *isl_basic_map_flatten_range(
9872 __isl_take isl_basic_map *bmap)
9877 if (!bmap->dim->nested[1])
9880 bmap = isl_basic_map_cow(bmap);
9884 bmap->dim = isl_space_flatten_range(bmap->dim);
9888 bmap = isl_basic_map_finalize(bmap);
9892 isl_basic_map_free(bmap);
9896 __isl_give isl_map *isl_map_flatten(__isl_take isl_map *map)
9903 if (!map->dim->nested[0] && !map->dim->nested[1])
9906 map = isl_map_cow(map);
9910 for (i = 0; i < map->n; ++i) {
9911 map->p[i] = isl_basic_map_flatten(map->p[i]);
9915 map->dim = isl_space_flatten(map->dim);
9925 __isl_give isl_set *isl_set_flatten(__isl_take isl_set *set)
9927 return (isl_set *)isl_map_flatten((isl_map *)set);
9930 __isl_give isl_map *isl_set_flatten_map(__isl_take isl_set *set)
9932 isl_space *dim, *flat_dim;
9935 dim = isl_set_get_space(set);
9936 flat_dim = isl_space_flatten(isl_space_copy(dim));
9937 map = isl_map_identity(isl_space_join(isl_space_reverse(dim), flat_dim));
9938 map = isl_map_intersect_domain(map, set);
9943 __isl_give isl_map *isl_map_flatten_domain(__isl_take isl_map *map)
9950 if (!map->dim->nested[0])
9953 map = isl_map_cow(map);
9957 for (i = 0; i < map->n; ++i) {
9958 map->p[i] = isl_basic_map_flatten_domain(map->p[i]);
9962 map->dim = isl_space_flatten_domain(map->dim);
9972 __isl_give isl_map *isl_map_flatten_range(__isl_take isl_map *map)
9979 if (!map->dim->nested[1])
9982 map = isl_map_cow(map);
9986 for (i = 0; i < map->n; ++i) {
9987 map->p[i] = isl_basic_map_flatten_range(map->p[i]);
9991 map->dim = isl_space_flatten_range(map->dim);
10001 /* Reorder the dimensions of "bmap" according to the given dim_map
10002 * and set the dimension specification to "dim".
10004 __isl_give isl_basic_map *isl_basic_map_realign(__isl_take isl_basic_map *bmap,
10005 __isl_take isl_space *dim, __isl_take struct isl_dim_map *dim_map)
10007 isl_basic_map *res;
10010 bmap = isl_basic_map_cow(bmap);
10011 if (!bmap || !dim || !dim_map)
10014 flags = bmap->flags;
10015 ISL_FL_CLR(flags, ISL_BASIC_MAP_FINAL);
10016 ISL_FL_CLR(flags, ISL_BASIC_MAP_NORMALIZED);
10017 ISL_FL_CLR(flags, ISL_BASIC_MAP_NORMALIZED_DIVS);
10018 res = isl_basic_map_alloc_space(dim,
10019 bmap->n_div, bmap->n_eq, bmap->n_ineq);
10020 res = isl_basic_map_add_constraints_dim_map(res, bmap, dim_map);
10022 res->flags = flags;
10023 res = isl_basic_map_finalize(res);
10027 isl_basic_map_free(bmap);
10028 isl_space_free(dim);
10032 /* Reorder the dimensions of "map" according to given reordering.
10034 __isl_give isl_map *isl_map_realign(__isl_take isl_map *map,
10035 __isl_take isl_reordering *r)
10038 struct isl_dim_map *dim_map;
10040 map = isl_map_cow(map);
10041 dim_map = isl_dim_map_from_reordering(r);
10042 if (!map || !r || !dim_map)
10045 for (i = 0; i < map->n; ++i) {
10046 struct isl_dim_map *dim_map_i;
10048 dim_map_i = isl_dim_map_extend(dim_map, map->p[i]);
10050 map->p[i] = isl_basic_map_realign(map->p[i],
10051 isl_space_copy(r->dim), dim_map_i);
10057 map = isl_map_reset_space(map, isl_space_copy(r->dim));
10059 isl_reordering_free(r);
10065 isl_reordering_free(r);
10069 __isl_give isl_set *isl_set_realign(__isl_take isl_set *set,
10070 __isl_take isl_reordering *r)
10072 return (isl_set *)isl_map_realign((isl_map *)set, r);
10075 __isl_give isl_map *isl_map_align_params(__isl_take isl_map *map,
10076 __isl_take isl_space *model)
10080 if (!map || !model)
10083 ctx = isl_space_get_ctx(model);
10084 if (!isl_space_has_named_params(model))
10085 isl_die(ctx, isl_error_invalid,
10086 "model has unnamed parameters", goto error);
10087 if (!isl_space_has_named_params(map->dim))
10088 isl_die(ctx, isl_error_invalid,
10089 "relation has unnamed parameters", goto error);
10090 if (!isl_space_match(map->dim, isl_dim_param, model, isl_dim_param)) {
10091 isl_reordering *exp;
10093 model = isl_space_drop_dims(model, isl_dim_in,
10094 0, isl_space_dim(model, isl_dim_in));
10095 model = isl_space_drop_dims(model, isl_dim_out,
10096 0, isl_space_dim(model, isl_dim_out));
10097 exp = isl_parameter_alignment_reordering(map->dim, model);
10098 exp = isl_reordering_extend_space(exp, isl_map_get_space(map));
10099 map = isl_map_realign(map, exp);
10102 isl_space_free(model);
10105 isl_space_free(model);
10110 __isl_give isl_set *isl_set_align_params(__isl_take isl_set *set,
10111 __isl_take isl_space *model)
10113 return isl_map_align_params(set, model);
10116 /* Align the parameters of "bmap" to those of "model", introducing
10117 * additional parameters if needed.
10119 __isl_give isl_basic_map *isl_basic_map_align_params(
10120 __isl_take isl_basic_map *bmap, __isl_take isl_space *model)
10124 if (!bmap || !model)
10127 ctx = isl_space_get_ctx(model);
10128 if (!isl_space_has_named_params(model))
10129 isl_die(ctx, isl_error_invalid,
10130 "model has unnamed parameters", goto error);
10131 if (!isl_space_has_named_params(bmap->dim))
10132 isl_die(ctx, isl_error_invalid,
10133 "relation has unnamed parameters", goto error);
10134 if (!isl_space_match(bmap->dim, isl_dim_param, model, isl_dim_param)) {
10135 isl_reordering *exp;
10136 struct isl_dim_map *dim_map;
10138 model = isl_space_drop_dims(model, isl_dim_in,
10139 0, isl_space_dim(model, isl_dim_in));
10140 model = isl_space_drop_dims(model, isl_dim_out,
10141 0, isl_space_dim(model, isl_dim_out));
10142 exp = isl_parameter_alignment_reordering(bmap->dim, model);
10143 exp = isl_reordering_extend_space(exp,
10144 isl_basic_map_get_space(bmap));
10145 dim_map = isl_dim_map_from_reordering(exp);
10146 bmap = isl_basic_map_realign(bmap,
10147 exp ? isl_space_copy(exp->dim) : NULL,
10148 isl_dim_map_extend(dim_map, bmap));
10149 isl_reordering_free(exp);
10153 isl_space_free(model);
10156 isl_space_free(model);
10157 isl_basic_map_free(bmap);
10161 /* Align the parameters of "bset" to those of "model", introducing
10162 * additional parameters if needed.
10164 __isl_give isl_basic_set *isl_basic_set_align_params(
10165 __isl_take isl_basic_set *bset, __isl_take isl_space *model)
10167 return isl_basic_map_align_params(bset, model);
10170 __isl_give isl_mat *isl_basic_map_equalities_matrix(
10171 __isl_keep isl_basic_map *bmap, enum isl_dim_type c1,
10172 enum isl_dim_type c2, enum isl_dim_type c3,
10173 enum isl_dim_type c4, enum isl_dim_type c5)
10175 enum isl_dim_type c[5] = { c1, c2, c3, c4, c5 };
10176 struct isl_mat *mat;
10182 mat = isl_mat_alloc(bmap->ctx, bmap->n_eq,
10183 isl_basic_map_total_dim(bmap) + 1);
10186 for (i = 0; i < bmap->n_eq; ++i)
10187 for (j = 0, pos = 0; j < 5; ++j) {
10188 int off = isl_basic_map_offset(bmap, c[j]);
10189 for (k = 0; k < isl_basic_map_dim(bmap, c[j]); ++k) {
10190 isl_int_set(mat->row[i][pos],
10191 bmap->eq[i][off + k]);
10199 __isl_give isl_mat *isl_basic_map_inequalities_matrix(
10200 __isl_keep isl_basic_map *bmap, enum isl_dim_type c1,
10201 enum isl_dim_type c2, enum isl_dim_type c3,
10202 enum isl_dim_type c4, enum isl_dim_type c5)
10204 enum isl_dim_type c[5] = { c1, c2, c3, c4, c5 };
10205 struct isl_mat *mat;
10211 mat = isl_mat_alloc(bmap->ctx, bmap->n_ineq,
10212 isl_basic_map_total_dim(bmap) + 1);
10215 for (i = 0; i < bmap->n_ineq; ++i)
10216 for (j = 0, pos = 0; j < 5; ++j) {
10217 int off = isl_basic_map_offset(bmap, c[j]);
10218 for (k = 0; k < isl_basic_map_dim(bmap, c[j]); ++k) {
10219 isl_int_set(mat->row[i][pos],
10220 bmap->ineq[i][off + k]);
10228 __isl_give isl_basic_map *isl_basic_map_from_constraint_matrices(
10229 __isl_take isl_space *dim,
10230 __isl_take isl_mat *eq, __isl_take isl_mat *ineq, enum isl_dim_type c1,
10231 enum isl_dim_type c2, enum isl_dim_type c3,
10232 enum isl_dim_type c4, enum isl_dim_type c5)
10234 enum isl_dim_type c[5] = { c1, c2, c3, c4, c5 };
10235 isl_basic_map *bmap;
10241 if (!dim || !eq || !ineq)
10244 if (eq->n_col != ineq->n_col)
10245 isl_die(dim->ctx, isl_error_invalid,
10246 "equalities and inequalities matrices should have "
10247 "same number of columns", goto error);
10249 total = 1 + isl_space_dim(dim, isl_dim_all);
10251 if (eq->n_col < total)
10252 isl_die(dim->ctx, isl_error_invalid,
10253 "number of columns too small", goto error);
10255 extra = eq->n_col - total;
10257 bmap = isl_basic_map_alloc_space(isl_space_copy(dim), extra,
10258 eq->n_row, ineq->n_row);
10261 for (i = 0; i < extra; ++i) {
10262 k = isl_basic_map_alloc_div(bmap);
10265 isl_int_set_si(bmap->div[k][0], 0);
10267 for (i = 0; i < eq->n_row; ++i) {
10268 l = isl_basic_map_alloc_equality(bmap);
10271 for (j = 0, pos = 0; j < 5; ++j) {
10272 int off = isl_basic_map_offset(bmap, c[j]);
10273 for (k = 0; k < isl_basic_map_dim(bmap, c[j]); ++k) {
10274 isl_int_set(bmap->eq[l][off + k],
10280 for (i = 0; i < ineq->n_row; ++i) {
10281 l = isl_basic_map_alloc_inequality(bmap);
10284 for (j = 0, pos = 0; j < 5; ++j) {
10285 int off = isl_basic_map_offset(bmap, c[j]);
10286 for (k = 0; k < isl_basic_map_dim(bmap, c[j]); ++k) {
10287 isl_int_set(bmap->ineq[l][off + k],
10288 ineq->row[i][pos]);
10294 isl_space_free(dim);
10296 isl_mat_free(ineq);
10298 bmap = isl_basic_map_simplify(bmap);
10299 return isl_basic_map_finalize(bmap);
10301 isl_space_free(dim);
10303 isl_mat_free(ineq);
10307 __isl_give isl_mat *isl_basic_set_equalities_matrix(
10308 __isl_keep isl_basic_set *bset, enum isl_dim_type c1,
10309 enum isl_dim_type c2, enum isl_dim_type c3, enum isl_dim_type c4)
10311 return isl_basic_map_equalities_matrix((isl_basic_map *)bset,
10312 c1, c2, c3, c4, isl_dim_in);
10315 __isl_give isl_mat *isl_basic_set_inequalities_matrix(
10316 __isl_keep isl_basic_set *bset, enum isl_dim_type c1,
10317 enum isl_dim_type c2, enum isl_dim_type c3, enum isl_dim_type c4)
10319 return isl_basic_map_inequalities_matrix((isl_basic_map *)bset,
10320 c1, c2, c3, c4, isl_dim_in);
10323 __isl_give isl_basic_set *isl_basic_set_from_constraint_matrices(
10324 __isl_take isl_space *dim,
10325 __isl_take isl_mat *eq, __isl_take isl_mat *ineq, enum isl_dim_type c1,
10326 enum isl_dim_type c2, enum isl_dim_type c3, enum isl_dim_type c4)
10328 return (isl_basic_set*)
10329 isl_basic_map_from_constraint_matrices(dim, eq, ineq,
10330 c1, c2, c3, c4, isl_dim_in);
10333 int isl_basic_map_can_zip(__isl_keep isl_basic_map *bmap)
10338 return isl_space_can_zip(bmap->dim);
10341 int isl_map_can_zip(__isl_keep isl_map *map)
10346 return isl_space_can_zip(map->dim);
10349 /* Given a basic map (A -> B) -> (C -> D), return the corresponding basic map
10350 * (A -> C) -> (B -> D).
10352 __isl_give isl_basic_map *isl_basic_map_zip(__isl_take isl_basic_map *bmap)
10361 if (!isl_basic_map_can_zip(bmap))
10362 isl_die(bmap->ctx, isl_error_invalid,
10363 "basic map cannot be zipped", goto error);
10364 pos = isl_basic_map_offset(bmap, isl_dim_in) +
10365 isl_space_dim(bmap->dim->nested[0], isl_dim_in);
10366 n1 = isl_space_dim(bmap->dim->nested[0], isl_dim_out);
10367 n2 = isl_space_dim(bmap->dim->nested[1], isl_dim_in);
10368 bmap = isl_basic_map_cow(bmap);
10369 bmap = isl_basic_map_swap_vars(bmap, pos, n1, n2);
10372 bmap->dim = isl_space_zip(bmap->dim);
10377 isl_basic_map_free(bmap);
10381 /* Given a map (A -> B) -> (C -> D), return the corresponding map
10382 * (A -> C) -> (B -> D).
10384 __isl_give isl_map *isl_map_zip(__isl_take isl_map *map)
10391 if (!isl_map_can_zip(map))
10392 isl_die(map->ctx, isl_error_invalid, "map cannot be zipped",
10395 map = isl_map_cow(map);
10399 for (i = 0; i < map->n; ++i) {
10400 map->p[i] = isl_basic_map_zip(map->p[i]);
10405 map->dim = isl_space_zip(map->dim);
10415 /* Can we apply isl_basic_map_curry to "bmap"?
10416 * That is, does it have a nested relation in its domain?
10418 int isl_basic_map_can_curry(__isl_keep isl_basic_map *bmap)
10423 return isl_space_can_curry(bmap->dim);
10426 /* Can we apply isl_map_curry to "map"?
10427 * That is, does it have a nested relation in its domain?
10429 int isl_map_can_curry(__isl_keep isl_map *map)
10434 return isl_space_can_curry(map->dim);
10437 /* Given a basic map (A -> B) -> C, return the corresponding basic map
10440 __isl_give isl_basic_map *isl_basic_map_curry(__isl_take isl_basic_map *bmap)
10446 if (!isl_basic_map_can_curry(bmap))
10447 isl_die(bmap->ctx, isl_error_invalid,
10448 "basic map cannot be curried", goto error);
10449 bmap = isl_basic_map_cow(bmap);
10452 bmap->dim = isl_space_curry(bmap->dim);
10457 isl_basic_map_free(bmap);
10461 /* Given a map (A -> B) -> C, return the corresponding map
10464 __isl_give isl_map *isl_map_curry(__isl_take isl_map *map)
10471 if (!isl_map_can_curry(map))
10472 isl_die(map->ctx, isl_error_invalid, "map cannot be curried",
10475 map = isl_map_cow(map);
10479 for (i = 0; i < map->n; ++i) {
10480 map->p[i] = isl_basic_map_curry(map->p[i]);
10485 map->dim = isl_space_curry(map->dim);
10495 /* Can we apply isl_basic_map_uncurry to "bmap"?
10496 * That is, does it have a nested relation in its domain?
10498 int isl_basic_map_can_uncurry(__isl_keep isl_basic_map *bmap)
10503 return isl_space_can_uncurry(bmap->dim);
10506 /* Can we apply isl_map_uncurry to "map"?
10507 * That is, does it have a nested relation in its domain?
10509 int isl_map_can_uncurry(__isl_keep isl_map *map)
10514 return isl_space_can_uncurry(map->dim);
10517 /* Given a basic map A -> (B -> C), return the corresponding basic map
10520 __isl_give isl_basic_map *isl_basic_map_uncurry(__isl_take isl_basic_map *bmap)
10526 if (!isl_basic_map_can_uncurry(bmap))
10527 isl_die(bmap->ctx, isl_error_invalid,
10528 "basic map cannot be uncurried",
10529 return isl_basic_map_free(bmap));
10530 bmap = isl_basic_map_cow(bmap);
10533 bmap->dim = isl_space_uncurry(bmap->dim);
10535 return isl_basic_map_free(bmap);
10539 /* Given a map A -> (B -> C), return the corresponding map
10542 __isl_give isl_map *isl_map_uncurry(__isl_take isl_map *map)
10549 if (!isl_map_can_uncurry(map))
10550 isl_die(map->ctx, isl_error_invalid, "map cannot be uncurried",
10551 return isl_map_free(map));
10553 map = isl_map_cow(map);
10557 for (i = 0; i < map->n; ++i) {
10558 map->p[i] = isl_basic_map_uncurry(map->p[i]);
10560 return isl_map_free(map);
10563 map->dim = isl_space_uncurry(map->dim);
10565 return isl_map_free(map);
10570 /* Construct a basic map mapping the domain of the affine expression
10571 * to a one-dimensional range prescribed by the affine expression.
10573 __isl_give isl_basic_map *isl_basic_map_from_aff(__isl_take isl_aff *aff)
10577 isl_local_space *ls;
10578 isl_basic_map *bmap;
10583 ls = isl_aff_get_local_space(aff);
10584 bmap = isl_basic_map_from_local_space(ls);
10585 bmap = isl_basic_map_extend_constraints(bmap, 1, 0);
10586 k = isl_basic_map_alloc_equality(bmap);
10590 pos = isl_basic_map_offset(bmap, isl_dim_out);
10591 isl_seq_cpy(bmap->eq[k], aff->v->el + 1, pos);
10592 isl_int_neg(bmap->eq[k][pos], aff->v->el[0]);
10593 isl_seq_cpy(bmap->eq[k] + pos + 1, aff->v->el + 1 + pos,
10594 aff->v->size - (pos + 1));
10597 bmap = isl_basic_map_finalize(bmap);
10601 isl_basic_map_free(bmap);
10605 /* Construct a map mapping the domain of the affine expression
10606 * to a one-dimensional range prescribed by the affine expression.
10608 __isl_give isl_map *isl_map_from_aff(__isl_take isl_aff *aff)
10610 isl_basic_map *bmap;
10612 bmap = isl_basic_map_from_aff(aff);
10613 return isl_map_from_basic_map(bmap);
10616 /* Construct a basic map mapping the domain the multi-affine expression
10617 * to its range, with each dimension in the range equated to the
10618 * corresponding affine expression.
10620 __isl_give isl_basic_map *isl_basic_map_from_multi_aff(
10621 __isl_take isl_multi_aff *maff)
10625 isl_basic_map *bmap;
10630 if (isl_space_dim(maff->space, isl_dim_out) != maff->n)
10631 isl_die(isl_multi_aff_get_ctx(maff), isl_error_internal,
10632 "invalid space", return isl_multi_aff_free(maff));
10634 space = isl_space_domain(isl_multi_aff_get_space(maff));
10635 bmap = isl_basic_map_universe(isl_space_from_domain(space));
10637 for (i = 0; i < maff->n; ++i) {
10639 isl_basic_map *bmap_i;
10641 aff = isl_aff_copy(maff->p[i]);
10642 bmap_i = isl_basic_map_from_aff(aff);
10644 bmap = isl_basic_map_flat_range_product(bmap, bmap_i);
10647 bmap = isl_basic_map_reset_space(bmap, isl_multi_aff_get_space(maff));
10649 isl_multi_aff_free(maff);
10653 /* Construct a map mapping the domain the multi-affine expression
10654 * to its range, with each dimension in the range equated to the
10655 * corresponding affine expression.
10657 __isl_give isl_map *isl_map_from_multi_aff(__isl_take isl_multi_aff *maff)
10659 isl_basic_map *bmap;
10661 bmap = isl_basic_map_from_multi_aff(maff);
10662 return isl_map_from_basic_map(bmap);
10665 /* Construct a basic map mapping a domain in the given space to
10666 * to an n-dimensional range, with n the number of elements in the list,
10667 * where each coordinate in the range is prescribed by the
10668 * corresponding affine expression.
10669 * The domains of all affine expressions in the list are assumed to match
10672 __isl_give isl_basic_map *isl_basic_map_from_aff_list(
10673 __isl_take isl_space *domain_dim, __isl_take isl_aff_list *list)
10677 isl_basic_map *bmap;
10682 dim = isl_space_from_domain(domain_dim);
10683 bmap = isl_basic_map_universe(dim);
10685 for (i = 0; i < list->n; ++i) {
10687 isl_basic_map *bmap_i;
10689 aff = isl_aff_copy(list->p[i]);
10690 bmap_i = isl_basic_map_from_aff(aff);
10692 bmap = isl_basic_map_flat_range_product(bmap, bmap_i);
10695 isl_aff_list_free(list);
10699 __isl_give isl_set *isl_set_equate(__isl_take isl_set *set,
10700 enum isl_dim_type type1, int pos1, enum isl_dim_type type2, int pos2)
10702 return isl_map_equate(set, type1, pos1, type2, pos2);
10705 /* Construct a basic map where the given dimensions are equal to each other.
10707 static __isl_give isl_basic_map *equator(__isl_take isl_space *space,
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_space_dim(space, type1))
10717 isl_die(isl_space_get_ctx(space), isl_error_invalid,
10718 "index out of bounds", goto error);
10719 if (pos2 >= isl_space_dim(space, type2))
10720 isl_die(isl_space_get_ctx(space), isl_error_invalid,
10721 "index out of bounds", goto error);
10723 if (type1 == type2 && pos1 == pos2)
10724 return isl_basic_map_universe(space);
10726 bmap = isl_basic_map_alloc_space(isl_space_copy(space), 0, 1, 0);
10727 i = isl_basic_map_alloc_equality(bmap);
10730 isl_seq_clr(bmap->eq[i], 1 + isl_basic_map_total_dim(bmap));
10731 pos1 += isl_basic_map_offset(bmap, type1);
10732 pos2 += isl_basic_map_offset(bmap, type2);
10733 isl_int_set_si(bmap->eq[i][pos1], -1);
10734 isl_int_set_si(bmap->eq[i][pos2], 1);
10735 bmap = isl_basic_map_finalize(bmap);
10736 isl_space_free(space);
10739 isl_space_free(space);
10740 isl_basic_map_free(bmap);
10744 /* Add a constraint imposing that the given two dimensions are equal.
10746 __isl_give isl_basic_map *isl_basic_map_equate(__isl_take isl_basic_map *bmap,
10747 enum isl_dim_type type1, int pos1, enum isl_dim_type type2, int pos2)
10751 eq = equator(isl_basic_map_get_space(bmap), type1, pos1, type2, pos2);
10753 bmap = isl_basic_map_intersect(bmap, eq);
10758 /* Add a constraint imposing that the given two dimensions are equal.
10760 __isl_give isl_map *isl_map_equate(__isl_take isl_map *map,
10761 enum isl_dim_type type1, int pos1, enum isl_dim_type type2, int pos2)
10763 isl_basic_map *bmap;
10765 bmap = equator(isl_map_get_space(map), type1, pos1, type2, pos2);
10767 map = isl_map_intersect(map, isl_map_from_basic_map(bmap));
10772 /* Add a constraint imposing that the given two dimensions have opposite values.
10774 __isl_give isl_map *isl_map_oppose(__isl_take isl_map *map,
10775 enum isl_dim_type type1, int pos1, enum isl_dim_type type2, int pos2)
10777 isl_basic_map *bmap = NULL;
10783 if (pos1 >= isl_map_dim(map, type1))
10784 isl_die(map->ctx, isl_error_invalid,
10785 "index out of bounds", goto error);
10786 if (pos2 >= isl_map_dim(map, type2))
10787 isl_die(map->ctx, isl_error_invalid,
10788 "index out of bounds", goto error);
10790 bmap = isl_basic_map_alloc_space(isl_map_get_space(map), 0, 1, 0);
10791 i = isl_basic_map_alloc_equality(bmap);
10794 isl_seq_clr(bmap->eq[i], 1 + isl_basic_map_total_dim(bmap));
10795 pos1 += isl_basic_map_offset(bmap, type1);
10796 pos2 += isl_basic_map_offset(bmap, type2);
10797 isl_int_set_si(bmap->eq[i][pos1], 1);
10798 isl_int_set_si(bmap->eq[i][pos2], 1);
10799 bmap = isl_basic_map_finalize(bmap);
10801 map = isl_map_intersect(map, isl_map_from_basic_map(bmap));
10805 isl_basic_map_free(bmap);
10810 /* Add a constraint imposing that the value of the first dimension is
10811 * greater than or equal to that of the second.
10813 __isl_give isl_basic_map *isl_basic_map_order_ge(__isl_take isl_basic_map *bmap,
10814 enum isl_dim_type type1, int pos1, enum isl_dim_type type2, int pos2)
10817 isl_local_space *ls;
10822 if (pos1 >= isl_basic_map_dim(bmap, type1))
10823 isl_die(bmap->ctx, isl_error_invalid,
10824 "index out of bounds", return isl_basic_map_free(bmap));
10825 if (pos2 >= isl_basic_map_dim(bmap, type2))
10826 isl_die(bmap->ctx, isl_error_invalid,
10827 "index out of bounds", return isl_basic_map_free(bmap));
10829 if (type1 == type2 && pos1 == pos2)
10832 ls = isl_local_space_from_space(isl_basic_map_get_space(bmap));
10833 c = isl_inequality_alloc(ls);
10834 c = isl_constraint_set_coefficient_si(c, type1, pos1, 1);
10835 c = isl_constraint_set_coefficient_si(c, type2, pos2, -1);
10836 bmap = isl_basic_map_add_constraint(bmap, c);
10841 /* Add a constraint imposing that the value of the first dimension is
10842 * greater than that of the second.
10844 __isl_give isl_map *isl_map_order_gt(__isl_take isl_map *map,
10845 enum isl_dim_type type1, int pos1, enum isl_dim_type type2, int pos2)
10847 isl_basic_map *bmap = NULL;
10853 if (pos1 >= isl_map_dim(map, type1))
10854 isl_die(map->ctx, isl_error_invalid,
10855 "index out of bounds", goto error);
10856 if (pos2 >= isl_map_dim(map, type2))
10857 isl_die(map->ctx, isl_error_invalid,
10858 "index out of bounds", goto error);
10860 if (type1 == type2 && pos1 == pos2) {
10861 isl_space *space = isl_map_get_space(map);
10863 return isl_map_empty(space);
10866 bmap = isl_basic_map_alloc_space(isl_map_get_space(map), 0, 0, 1);
10867 i = isl_basic_map_alloc_inequality(bmap);
10870 isl_seq_clr(bmap->ineq[i], 1 + isl_basic_map_total_dim(bmap));
10871 pos1 += isl_basic_map_offset(bmap, type1);
10872 pos2 += isl_basic_map_offset(bmap, type2);
10873 isl_int_set_si(bmap->ineq[i][pos1], 1);
10874 isl_int_set_si(bmap->ineq[i][pos2], -1);
10875 isl_int_set_si(bmap->ineq[i][0], -1);
10876 bmap = isl_basic_map_finalize(bmap);
10878 map = isl_map_intersect(map, isl_map_from_basic_map(bmap));
10882 isl_basic_map_free(bmap);
10887 /* Add a constraint imposing that the value of the first dimension is
10888 * smaller than that of the second.
10890 __isl_give isl_map *isl_map_order_lt(__isl_take isl_map *map,
10891 enum isl_dim_type type1, int pos1, enum isl_dim_type type2, int pos2)
10893 return isl_map_order_gt(map, type2, pos2, type1, pos1);
10896 __isl_give isl_aff *isl_basic_map_get_div(__isl_keep isl_basic_map *bmap,
10900 isl_local_space *ls;
10905 if (!isl_basic_map_divs_known(bmap))
10906 isl_die(isl_basic_map_get_ctx(bmap), isl_error_invalid,
10907 "some divs are unknown", return NULL);
10909 ls = isl_basic_map_get_local_space(bmap);
10910 div = isl_local_space_get_div(ls, pos);
10911 isl_local_space_free(ls);
10916 __isl_give isl_aff *isl_basic_set_get_div(__isl_keep isl_basic_set *bset,
10919 return isl_basic_map_get_div(bset, pos);
10922 /* Plug in "subs" for dimension "type", "pos" of "bset".
10924 * Let i be the dimension to replace and let "subs" be of the form
10928 * Any integer division with a non-zero coefficient for i,
10930 * floor((a i + g)/m)
10934 * floor((a f + d g)/(m d))
10936 * Constraints of the form
10944 * We currently require that "subs" is an integral expression.
10945 * Handling rational expressions may require us to add stride constraints
10946 * as we do in isl_basic_set_preimage_multi_aff.
10948 __isl_give isl_basic_set *isl_basic_set_substitute(
10949 __isl_take isl_basic_set *bset,
10950 enum isl_dim_type type, unsigned pos, __isl_keep isl_aff *subs)
10956 if (bset && isl_basic_set_plain_is_empty(bset))
10959 bset = isl_basic_set_cow(bset);
10960 if (!bset || !subs)
10963 ctx = isl_basic_set_get_ctx(bset);
10964 if (!isl_space_is_equal(bset->dim, subs->ls->dim))
10965 isl_die(ctx, isl_error_invalid,
10966 "spaces don't match", goto error);
10967 if (isl_local_space_dim(subs->ls, isl_dim_div) != 0)
10968 isl_die(ctx, isl_error_unsupported,
10969 "cannot handle divs yet", goto error);
10970 if (!isl_int_is_one(subs->v->el[0]))
10971 isl_die(ctx, isl_error_invalid,
10972 "can only substitute integer expressions", goto error);
10974 pos += isl_basic_set_offset(bset, type);
10978 for (i = 0; i < bset->n_eq; ++i) {
10979 if (isl_int_is_zero(bset->eq[i][pos]))
10981 isl_int_set(v, bset->eq[i][pos]);
10982 isl_int_set_si(bset->eq[i][pos], 0);
10983 isl_seq_combine(bset->eq[i], subs->v->el[0], bset->eq[i],
10984 v, subs->v->el + 1, subs->v->size - 1);
10987 for (i = 0; i < bset->n_ineq; ++i) {
10988 if (isl_int_is_zero(bset->ineq[i][pos]))
10990 isl_int_set(v, bset->ineq[i][pos]);
10991 isl_int_set_si(bset->ineq[i][pos], 0);
10992 isl_seq_combine(bset->ineq[i], subs->v->el[0], bset->ineq[i],
10993 v, subs->v->el + 1, subs->v->size - 1);
10996 for (i = 0; i < bset->n_div; ++i) {
10997 if (isl_int_is_zero(bset->div[i][1 + pos]))
10999 isl_int_set(v, bset->div[i][1 + pos]);
11000 isl_int_set_si(bset->div[i][1 + pos], 0);
11001 isl_seq_combine(bset->div[i] + 1,
11002 subs->v->el[0], bset->div[i] + 1,
11003 v, subs->v->el + 1, subs->v->size - 1);
11004 isl_int_mul(bset->div[i][0], bset->div[i][0], subs->v->el[0]);
11009 bset = isl_basic_set_simplify(bset);
11010 return isl_basic_set_finalize(bset);
11012 isl_basic_set_free(bset);
11016 /* Plug in "subs" for dimension "type", "pos" of "set".
11018 __isl_give isl_set *isl_set_substitute(__isl_take isl_set *set,
11019 enum isl_dim_type type, unsigned pos, __isl_keep isl_aff *subs)
11023 if (set && isl_set_plain_is_empty(set))
11026 set = isl_set_cow(set);
11030 for (i = set->n - 1; i >= 0; --i) {
11031 set->p[i] = isl_basic_set_substitute(set->p[i], type, pos, subs);
11032 if (remove_if_empty(set, i) < 0)
11042 /* Check if the range of "ma" is compatible with "space".
11043 * Return -1 if anything is wrong.
11045 static int check_space_compatible_range_multi_aff(
11046 __isl_keep isl_space *space, __isl_keep isl_multi_aff *ma)
11049 isl_space *ma_space;
11051 ma_space = isl_multi_aff_get_space(ma);
11052 m = isl_space_is_range_internal(space, ma_space);
11053 isl_space_free(ma_space);
11055 isl_die(isl_space_get_ctx(space), isl_error_invalid,
11056 "spaces don't match", return -1);
11060 /* Check if the range of "ma" is compatible with "bset".
11061 * Return -1 if anything is wrong.
11063 static int check_basic_set_compatible_range_multi_aff(
11064 __isl_keep isl_basic_set *bset, __isl_keep isl_multi_aff *ma)
11066 return check_space_compatible_range_multi_aff(bset->dim, ma);
11069 /* Copy the divs from "ma" to "bset", adding zeros for the coefficients
11070 * of the other divs in "bset".
11072 static int set_ma_divs(__isl_keep isl_basic_set *bset,
11073 __isl_keep isl_multi_aff *ma, int n_div)
11076 isl_local_space *ls;
11081 ls = isl_aff_get_domain_local_space(ma->p[0]);
11085 for (i = 0; i < n_div; ++i) {
11086 isl_seq_cpy(bset->div[i], ls->div->row[i], ls->div->n_col);
11087 isl_seq_clr(bset->div[i] + ls->div->n_col, bset->n_div - n_div);
11088 if (isl_basic_set_add_div_constraints(bset, i) < 0)
11092 isl_local_space_free(ls);
11095 isl_local_space_free(ls);
11099 /* How many stride constraints does "ma" enforce?
11100 * That is, how many of the affine expressions have a denominator
11101 * different from one?
11103 static int multi_aff_strides(__isl_keep isl_multi_aff *ma)
11108 for (i = 0; i < ma->n; ++i)
11109 if (!isl_int_is_one(ma->p[i]->v->el[0]))
11115 /* For each affine expression in ma of the form
11117 * x_i = (f_i y + h_i)/m_i
11119 * with m_i different from one, add a constraint to "bset"
11122 * f_i y + h_i = m_i alpha_i
11124 * with alpha_i an additional existentially quantified variable.
11126 static __isl_give isl_basic_set *add_ma_strides(
11127 __isl_take isl_basic_set *bset, __isl_keep isl_multi_aff *ma)
11133 total = isl_basic_set_total_dim(bset);
11134 for (i = 0; i < ma->n; ++i) {
11137 if (isl_int_is_one(ma->p[i]->v->el[0]))
11139 div = isl_basic_set_alloc_div(bset);
11140 k = isl_basic_set_alloc_equality(bset);
11141 if (div < 0 || k < 0)
11143 isl_int_set_si(bset->div[div][0], 0);
11144 len = ma->p[i]->v->size;
11145 isl_seq_cpy(bset->eq[k], ma->p[i]->v->el + 1, len - 1);
11146 isl_seq_clr(bset->eq[k] + len - 1, 1 + total - (len - 1));
11147 isl_int_neg(bset->eq[k][1 + total], ma->p[i]->v->el[0]);
11153 isl_basic_set_free(bset);
11157 /* Compute the preimage of "bset" under the function represented by "ma".
11158 * In other words, plug in "ma" in "bset". The result is a basic set
11159 * that lives in the domain space of "ma".
11161 * If bset is represented by
11163 * A(p) + B x + C(divs) >= 0
11165 * and ma is represented by
11167 * x = D(p) + F(y) + G(divs')
11169 * then the result is
11171 * A(p) + B D(p) + B F(y) + B G(divs') + C(divs) >= 0
11173 * The divs in the input set are similarly adjusted.
11176 * floor((a_i(p) + b_i x + c_i(divs))/n_i)
11180 * floor((a_i(p) + b_i D(p) + b_i F(y) + B_i G(divs') + c_i(divs))/n_i)
11182 * If bset is not a rational set and if F(y) involves any denominators
11184 * x_i = (f_i y + h_i)/m_i
11186 * the additional constraints are added to ensure that we only
11187 * map back integer points. That is we enforce
11189 * f_i y + h_i = m_i alpha_i
11191 * with alpha_i an additional existentially quantified variable.
11193 * We first copy over the divs from "ma".
11194 * Then we add the modified constraints and divs from "bset".
11195 * Finally, we add the stride constraints, if needed.
11197 __isl_give isl_basic_set *isl_basic_set_preimage_multi_aff(
11198 __isl_take isl_basic_set *bset, __isl_take isl_multi_aff *ma)
11202 isl_basic_set *res = NULL;
11203 int n_div_bset, n_div_ma;
11204 isl_int f, c1, c2, g;
11205 int rational, strides;
11212 ma = isl_multi_aff_align_divs(ma);
11215 if (check_basic_set_compatible_range_multi_aff(bset, ma) < 0)
11218 n_div_bset = isl_basic_set_dim(bset, isl_dim_div);
11219 n_div_ma = ma->n ? isl_aff_dim(ma->p[0], isl_dim_div) : 0;
11221 space = isl_space_domain(isl_multi_aff_get_space(ma));
11222 rational = isl_basic_set_is_rational(bset);
11223 strides = rational ? 0 : multi_aff_strides(ma);
11224 res = isl_basic_set_alloc_space(space, n_div_ma + n_div_bset + strides,
11225 bset->n_eq + strides, bset->n_ineq + 2 * n_div_ma);
11227 res = isl_basic_set_set_rational(res);
11229 for (i = 0; i < n_div_ma + n_div_bset; ++i)
11230 if (isl_basic_set_alloc_div(res) < 0)
11233 if (set_ma_divs(res, ma, n_div_ma) < 0)
11236 for (i = 0; i < bset->n_eq; ++i) {
11237 k = isl_basic_set_alloc_equality(res);
11240 isl_seq_preimage(res->eq[k], bset->eq[i], ma, n_div_ma,
11241 n_div_bset, f, c1, c2, g, 0);
11244 for (i = 0; i < bset->n_ineq; ++i) {
11245 k = isl_basic_set_alloc_inequality(res);
11248 isl_seq_preimage(res->ineq[k], bset->ineq[i], ma, n_div_ma,
11249 n_div_bset, f, c1, c2, g, 0);
11252 for (i = 0; i < bset->n_div; ++i) {
11253 if (isl_int_is_zero(bset->div[i][0])) {
11254 isl_int_set_si(res->div[n_div_ma + i][0], 0);
11257 isl_seq_preimage(res->div[n_div_ma + i], bset->div[i],
11258 ma, n_div_ma, n_div_bset, f, c1, c2, g, 1);
11262 res = add_ma_strides(res, ma);
11268 isl_basic_set_free(bset);
11269 isl_multi_aff_free(ma);
11270 res = isl_basic_set_simplify(res);
11271 return isl_basic_set_finalize(res);
11277 isl_basic_set_free(bset);
11278 isl_multi_aff_free(ma);
11279 isl_basic_set_free(res);
11283 /* Check if the range of "ma" is compatible with "set".
11284 * Return -1 if anything is wrong.
11286 static int check_set_compatible_range_multi_aff(
11287 __isl_keep isl_set *set, __isl_keep isl_multi_aff *ma)
11289 return check_space_compatible_range_multi_aff(set->dim, ma);
11292 /* Compute the preimage of "set" under the function represented by "ma".
11293 * In other words, plug in "ma" in "set. The result is a set
11294 * that lives in the domain space of "ma".
11296 static __isl_give isl_set *set_preimage_multi_aff(__isl_take isl_set *set,
11297 __isl_take isl_multi_aff *ma)
11301 set = isl_set_cow(set);
11302 ma = isl_multi_aff_align_divs(ma);
11305 if (check_set_compatible_range_multi_aff(set, ma) < 0)
11308 for (i = 0; i < set->n; ++i) {
11309 set->p[i] = isl_basic_set_preimage_multi_aff(set->p[i],
11310 isl_multi_aff_copy(ma));
11315 isl_space_free(set->dim);
11316 set->dim = isl_multi_aff_get_domain_space(ma);
11320 isl_multi_aff_free(ma);
11322 ISL_F_CLR(set, ISL_MAP_DISJOINT);
11323 ISL_F_CLR(set, ISL_SET_NORMALIZED);
11326 isl_multi_aff_free(ma);
11331 __isl_give isl_set *isl_set_preimage_multi_aff(__isl_take isl_set *set,
11332 __isl_take isl_multi_aff *ma)
11337 if (isl_space_match(set->dim, isl_dim_param, ma->space, isl_dim_param))
11338 return set_preimage_multi_aff(set, ma);
11340 if (!isl_space_has_named_params(set->dim) ||
11341 !isl_space_has_named_params(ma->space))
11342 isl_die(set->ctx, isl_error_invalid,
11343 "unaligned unnamed parameters", goto error);
11344 set = isl_set_align_params(set, isl_multi_aff_get_space(ma));
11345 ma = isl_multi_aff_align_params(ma, isl_set_get_space(set));
11347 return set_preimage_multi_aff(set, ma);
11349 isl_multi_aff_free(ma);
11350 return isl_set_free(set);
11353 /* Compute the preimage of "set" under the function represented by "pma".
11354 * In other words, plug in "pma" in "set. The result is a set
11355 * that lives in the domain space of "pma".
11357 static __isl_give isl_set *set_preimage_pw_multi_aff(__isl_take isl_set *set,
11358 __isl_take isl_pw_multi_aff *pma)
11367 isl_pw_multi_aff_free(pma);
11368 res = isl_set_empty(isl_set_get_space(set));
11373 res = isl_set_preimage_multi_aff(isl_set_copy(set),
11374 isl_multi_aff_copy(pma->p[0].maff));
11375 res = isl_set_intersect(res, isl_set_copy(pma->p[0].set));
11377 for (i = 1; i < pma->n; ++i) {
11380 res_i = isl_set_preimage_multi_aff(isl_set_copy(set),
11381 isl_multi_aff_copy(pma->p[i].maff));
11382 res_i = isl_set_intersect(res_i, isl_set_copy(pma->p[i].set));
11383 res = isl_set_union(res, res_i);
11386 isl_pw_multi_aff_free(pma);
11390 isl_pw_multi_aff_free(pma);
11395 __isl_give isl_set *isl_set_preimage_pw_multi_aff(__isl_take isl_set *set,
11396 __isl_take isl_pw_multi_aff *pma)
11401 if (isl_space_match(set->dim, isl_dim_param, pma->dim, isl_dim_param))
11402 return set_preimage_pw_multi_aff(set, pma);
11404 if (!isl_space_has_named_params(set->dim) ||
11405 !isl_space_has_named_params(pma->dim))
11406 isl_die(set->ctx, isl_error_invalid,
11407 "unaligned unnamed parameters", goto error);
11408 set = isl_set_align_params(set, isl_pw_multi_aff_get_space(pma));
11409 pma = isl_pw_multi_aff_align_params(pma, isl_set_get_space(set));
11411 return set_preimage_pw_multi_aff(set, pma);
11413 isl_pw_multi_aff_free(pma);
11414 return isl_set_free(set);