2 * Copyright 2008-2009 Katholieke Universiteit Leuven
3 * Copyright 2010 INRIA Saclay
4 * Copyright 2012 Ecole Normale Superieure
6 * Use of this software is governed by the MIT license
8 * Written by Sven Verdoolaege, K.U.Leuven, Departement
9 * Computerwetenschappen, Celestijnenlaan 200A, B-3001 Leuven, Belgium
10 * and INRIA Saclay - Ile-de-France, Parc Club Orsay Universite,
11 * ZAC des vignes, 4 rue Jacques Monod, 91893 Orsay, France
12 * and Ecole Normale Superieure, 45 rue d’Ulm, 75230 Paris, France
16 #include <isl_ctx_private.h>
17 #include <isl_map_private.h>
19 #include "isl_space_private.h"
20 #include "isl_equalities.h"
21 #include <isl_list_private.h>
26 #include "isl_map_piplib.h"
27 #include <isl_reordering.h>
28 #include "isl_sample.h"
31 #include <isl_mat_private.h>
32 #include <isl_dim_map.h>
33 #include <isl_local_space_private.h>
34 #include <isl_aff_private.h>
35 #include <isl_options_private.h>
37 static unsigned n(__isl_keep isl_space *dim, enum isl_dim_type type)
40 case isl_dim_param: return dim->nparam;
41 case isl_dim_in: return dim->n_in;
42 case isl_dim_out: return dim->n_out;
43 case isl_dim_all: return dim->nparam + dim->n_in + dim->n_out;
48 static unsigned pos(__isl_keep isl_space *dim, enum isl_dim_type type)
51 case isl_dim_param: return 1;
52 case isl_dim_in: return 1 + dim->nparam;
53 case isl_dim_out: return 1 + dim->nparam + dim->n_in;
58 unsigned isl_basic_map_dim(__isl_keep isl_basic_map *bmap,
59 enum isl_dim_type type)
64 case isl_dim_cst: return 1;
67 case isl_dim_out: return isl_space_dim(bmap->dim, type);
68 case isl_dim_div: return bmap->n_div;
69 case isl_dim_all: return isl_basic_map_total_dim(bmap);
74 unsigned isl_map_dim(__isl_keep isl_map *map, enum isl_dim_type type)
76 return map ? n(map->dim, type) : 0;
79 unsigned isl_set_dim(__isl_keep isl_set *set, enum isl_dim_type type)
81 return set ? n(set->dim, type) : 0;
84 unsigned isl_basic_map_offset(struct isl_basic_map *bmap,
85 enum isl_dim_type type)
87 isl_space *dim = bmap->dim;
89 case isl_dim_cst: return 0;
90 case isl_dim_param: return 1;
91 case isl_dim_in: return 1 + dim->nparam;
92 case isl_dim_out: return 1 + dim->nparam + dim->n_in;
93 case isl_dim_div: return 1 + dim->nparam + dim->n_in + dim->n_out;
98 unsigned isl_basic_set_offset(struct isl_basic_set *bset,
99 enum isl_dim_type type)
101 return isl_basic_map_offset(bset, type);
104 static unsigned map_offset(struct isl_map *map, enum isl_dim_type type)
106 return pos(map->dim, type);
109 unsigned isl_basic_set_dim(__isl_keep isl_basic_set *bset,
110 enum isl_dim_type type)
112 return isl_basic_map_dim(bset, type);
115 unsigned isl_basic_set_n_dim(__isl_keep isl_basic_set *bset)
117 return isl_basic_set_dim(bset, isl_dim_set);
120 unsigned isl_basic_set_n_param(__isl_keep isl_basic_set *bset)
122 return isl_basic_set_dim(bset, isl_dim_param);
125 unsigned isl_basic_set_total_dim(const struct isl_basic_set *bset)
129 return isl_space_dim(bset->dim, isl_dim_all) + bset->n_div;
132 unsigned isl_set_n_dim(__isl_keep isl_set *set)
134 return isl_set_dim(set, isl_dim_set);
137 unsigned isl_set_n_param(__isl_keep isl_set *set)
139 return isl_set_dim(set, isl_dim_param);
142 unsigned isl_basic_map_n_in(const struct isl_basic_map *bmap)
144 return bmap ? bmap->dim->n_in : 0;
147 unsigned isl_basic_map_n_out(const struct isl_basic_map *bmap)
149 return bmap ? bmap->dim->n_out : 0;
152 unsigned isl_basic_map_n_param(const struct isl_basic_map *bmap)
154 return bmap ? bmap->dim->nparam : 0;
157 unsigned isl_basic_map_n_div(const struct isl_basic_map *bmap)
159 return bmap ? bmap->n_div : 0;
162 unsigned isl_basic_map_total_dim(const struct isl_basic_map *bmap)
164 return bmap ? isl_space_dim(bmap->dim, isl_dim_all) + bmap->n_div : 0;
167 unsigned isl_map_n_in(const struct isl_map *map)
169 return map ? map->dim->n_in : 0;
172 unsigned isl_map_n_out(const struct isl_map *map)
174 return map ? map->dim->n_out : 0;
177 unsigned isl_map_n_param(const struct isl_map *map)
179 return map ? map->dim->nparam : 0;
182 int isl_map_compatible_domain(struct isl_map *map, struct isl_set *set)
187 m = isl_space_match(map->dim, isl_dim_param, set->dim, isl_dim_param);
190 return isl_space_tuple_match(map->dim, isl_dim_in, set->dim, isl_dim_set);
193 int isl_basic_map_compatible_domain(struct isl_basic_map *bmap,
194 struct isl_basic_set *bset)
199 m = isl_space_match(bmap->dim, isl_dim_param, bset->dim, isl_dim_param);
202 return isl_space_tuple_match(bmap->dim, isl_dim_in, bset->dim, isl_dim_set);
205 int isl_map_compatible_range(__isl_keep isl_map *map, __isl_keep isl_set *set)
210 m = isl_space_match(map->dim, isl_dim_param, set->dim, isl_dim_param);
213 return isl_space_tuple_match(map->dim, isl_dim_out, set->dim, isl_dim_set);
216 int isl_basic_map_compatible_range(struct isl_basic_map *bmap,
217 struct isl_basic_set *bset)
222 m = isl_space_match(bmap->dim, isl_dim_param, bset->dim, isl_dim_param);
225 return isl_space_tuple_match(bmap->dim, isl_dim_out, bset->dim, isl_dim_set);
228 isl_ctx *isl_basic_map_get_ctx(__isl_keep isl_basic_map *bmap)
230 return bmap ? bmap->ctx : NULL;
233 isl_ctx *isl_basic_set_get_ctx(__isl_keep isl_basic_set *bset)
235 return bset ? bset->ctx : NULL;
238 isl_ctx *isl_map_get_ctx(__isl_keep isl_map *map)
240 return map ? map->ctx : NULL;
243 isl_ctx *isl_set_get_ctx(__isl_keep isl_set *set)
245 return set ? set->ctx : NULL;
248 __isl_give isl_space *isl_basic_map_get_space(__isl_keep isl_basic_map *bmap)
252 return isl_space_copy(bmap->dim);
255 __isl_give isl_space *isl_basic_set_get_space(__isl_keep isl_basic_set *bset)
259 return isl_space_copy(bset->dim);
262 /* Extract the divs in "bmap" as a matrix.
264 __isl_give isl_mat *isl_basic_map_get_divs(__isl_keep isl_basic_map *bmap)
275 ctx = isl_basic_map_get_ctx(bmap);
276 total = isl_space_dim(bmap->dim, isl_dim_all);
277 cols = 1 + 1 + total + bmap->n_div;
278 div = isl_mat_alloc(ctx, bmap->n_div, cols);
282 for (i = 0; i < bmap->n_div; ++i)
283 isl_seq_cpy(div->row[i], bmap->div[i], cols);
288 __isl_give isl_local_space *isl_basic_map_get_local_space(
289 __isl_keep isl_basic_map *bmap)
296 div = isl_basic_map_get_divs(bmap);
297 return isl_local_space_alloc_div(isl_space_copy(bmap->dim), div);
300 __isl_give isl_local_space *isl_basic_set_get_local_space(
301 __isl_keep isl_basic_set *bset)
303 return isl_basic_map_get_local_space(bset);
306 __isl_give isl_basic_map *isl_basic_map_from_local_space(
307 __isl_take isl_local_space *ls)
316 n_div = isl_local_space_dim(ls, isl_dim_div);
317 bmap = isl_basic_map_alloc_space(isl_local_space_get_space(ls),
318 n_div, 0, 2 * n_div);
320 for (i = 0; i < n_div; ++i)
321 if (isl_basic_map_alloc_div(bmap) < 0)
324 for (i = 0; i < n_div; ++i) {
325 isl_seq_cpy(bmap->div[i], ls->div->row[i], ls->div->n_col);
326 if (isl_basic_map_add_div_constraints(bmap, i) < 0)
330 isl_local_space_free(ls);
333 isl_local_space_free(ls);
334 isl_basic_map_free(bmap);
338 __isl_give isl_basic_set *isl_basic_set_from_local_space(
339 __isl_take isl_local_space *ls)
341 return isl_basic_map_from_local_space(ls);
344 __isl_give isl_space *isl_map_get_space(__isl_keep isl_map *map)
348 return isl_space_copy(map->dim);
351 __isl_give isl_space *isl_set_get_space(__isl_keep isl_set *set)
355 return isl_space_copy(set->dim);
358 __isl_give isl_basic_map *isl_basic_map_set_tuple_name(
359 __isl_take isl_basic_map *bmap, enum isl_dim_type type, const char *s)
361 bmap = isl_basic_map_cow(bmap);
364 bmap->dim = isl_space_set_tuple_name(bmap->dim, type, s);
367 bmap = isl_basic_map_finalize(bmap);
370 isl_basic_map_free(bmap);
374 __isl_give isl_basic_set *isl_basic_set_set_tuple_name(
375 __isl_take isl_basic_set *bset, const char *s)
377 return isl_basic_map_set_tuple_name(bset, isl_dim_set, s);
380 const char *isl_basic_map_get_tuple_name(__isl_keep isl_basic_map *bmap,
381 enum isl_dim_type type)
383 return bmap ? isl_space_get_tuple_name(bmap->dim, type) : NULL;
386 __isl_give isl_map *isl_map_set_tuple_name(__isl_take isl_map *map,
387 enum isl_dim_type type, const char *s)
391 map = isl_map_cow(map);
395 map->dim = isl_space_set_tuple_name(map->dim, type, s);
399 for (i = 0; i < map->n; ++i) {
400 map->p[i] = isl_basic_map_set_tuple_name(map->p[i], type, s);
411 /* Does the input or output tuple have a name?
413 int isl_map_has_tuple_name(__isl_keep isl_map *map, enum isl_dim_type type)
415 return map ? isl_space_has_tuple_name(map->dim, type) : -1;
418 const char *isl_map_get_tuple_name(__isl_keep isl_map *map,
419 enum isl_dim_type type)
421 return map ? isl_space_get_tuple_name(map->dim, type) : NULL;
424 __isl_give isl_set *isl_set_set_tuple_name(__isl_take isl_set *set,
427 return (isl_set *)isl_map_set_tuple_name((isl_map *)set, isl_dim_set, s);
430 __isl_give isl_map *isl_map_set_tuple_id(__isl_take isl_map *map,
431 enum isl_dim_type type, __isl_take isl_id *id)
433 map = isl_map_cow(map);
435 return isl_id_free(id);
437 map->dim = isl_space_set_tuple_id(map->dim, type, id);
439 return isl_map_reset_space(map, isl_space_copy(map->dim));
442 __isl_give isl_set *isl_set_set_tuple_id(__isl_take isl_set *set,
443 __isl_take isl_id *id)
445 return isl_map_set_tuple_id(set, isl_dim_set, id);
448 __isl_give isl_map *isl_map_reset_tuple_id(__isl_take isl_map *map,
449 enum isl_dim_type type)
451 map = isl_map_cow(map);
455 map->dim = isl_space_reset_tuple_id(map->dim, type);
457 return isl_map_reset_space(map, isl_space_copy(map->dim));
460 __isl_give isl_set *isl_set_reset_tuple_id(__isl_take isl_set *set)
462 return isl_map_reset_tuple_id(set, isl_dim_set);
465 int isl_map_has_tuple_id(__isl_keep isl_map *map, enum isl_dim_type type)
467 return map ? isl_space_has_tuple_id(map->dim, type) : -1;
470 __isl_give isl_id *isl_map_get_tuple_id(__isl_keep isl_map *map,
471 enum isl_dim_type type)
473 return map ? isl_space_get_tuple_id(map->dim, type) : NULL;
476 int isl_set_has_tuple_id(__isl_keep isl_set *set)
478 return isl_map_has_tuple_id(set, isl_dim_set);
481 __isl_give isl_id *isl_set_get_tuple_id(__isl_keep isl_set *set)
483 return isl_map_get_tuple_id(set, isl_dim_set);
486 /* Does the set tuple have a name?
488 int isl_set_has_tuple_name(__isl_keep isl_set *set)
490 return set ? isl_space_has_tuple_name(set->dim, isl_dim_set) : -1;
494 const char *isl_basic_set_get_tuple_name(__isl_keep isl_basic_set *bset)
496 return bset ? isl_space_get_tuple_name(bset->dim, isl_dim_set) : NULL;
499 const char *isl_set_get_tuple_name(__isl_keep isl_set *set)
501 return set ? isl_space_get_tuple_name(set->dim, isl_dim_set) : NULL;
504 const char *isl_basic_map_get_dim_name(__isl_keep isl_basic_map *bmap,
505 enum isl_dim_type type, unsigned pos)
507 return bmap ? isl_space_get_dim_name(bmap->dim, type, pos) : NULL;
510 const char *isl_basic_set_get_dim_name(__isl_keep isl_basic_set *bset,
511 enum isl_dim_type type, unsigned pos)
513 return bset ? isl_space_get_dim_name(bset->dim, type, pos) : NULL;
516 /* Does the given dimension have a name?
518 int isl_map_has_dim_name(__isl_keep isl_map *map,
519 enum isl_dim_type type, unsigned pos)
521 return map ? isl_space_has_dim_name(map->dim, type, pos) : -1;
524 const char *isl_map_get_dim_name(__isl_keep isl_map *map,
525 enum isl_dim_type type, unsigned pos)
527 return map ? isl_space_get_dim_name(map->dim, type, pos) : NULL;
530 const char *isl_set_get_dim_name(__isl_keep isl_set *set,
531 enum isl_dim_type type, unsigned pos)
533 return set ? isl_space_get_dim_name(set->dim, type, pos) : NULL;
536 /* Does the given dimension have a name?
538 int isl_set_has_dim_name(__isl_keep isl_set *set,
539 enum isl_dim_type type, unsigned pos)
541 return set ? isl_space_has_dim_name(set->dim, type, pos) : -1;
544 __isl_give isl_basic_map *isl_basic_map_set_dim_name(
545 __isl_take isl_basic_map *bmap,
546 enum isl_dim_type type, unsigned pos, const char *s)
548 bmap = isl_basic_map_cow(bmap);
551 bmap->dim = isl_space_set_dim_name(bmap->dim, type, pos, s);
554 return isl_basic_map_finalize(bmap);
556 isl_basic_map_free(bmap);
560 __isl_give isl_map *isl_map_set_dim_name(__isl_take isl_map *map,
561 enum isl_dim_type type, unsigned pos, const char *s)
565 map = isl_map_cow(map);
569 map->dim = isl_space_set_dim_name(map->dim, type, pos, s);
573 for (i = 0; i < map->n; ++i) {
574 map->p[i] = isl_basic_map_set_dim_name(map->p[i], type, pos, s);
585 __isl_give isl_basic_set *isl_basic_set_set_dim_name(
586 __isl_take isl_basic_set *bset,
587 enum isl_dim_type type, unsigned pos, const char *s)
589 return (isl_basic_set *)isl_basic_map_set_dim_name(
590 (isl_basic_map *)bset, type, pos, s);
593 __isl_give isl_set *isl_set_set_dim_name(__isl_take isl_set *set,
594 enum isl_dim_type type, unsigned pos, const char *s)
596 return (isl_set *)isl_map_set_dim_name((isl_map *)set, type, pos, s);
599 int isl_basic_map_has_dim_id(__isl_keep isl_basic_map *bmap,
600 enum isl_dim_type type, unsigned pos)
602 return bmap ? isl_space_has_dim_id(bmap->dim, type, pos) : -1;
605 __isl_give isl_id *isl_basic_set_get_dim_id(__isl_keep isl_basic_set *bset,
606 enum isl_dim_type type, unsigned pos)
608 return bset ? isl_space_get_dim_id(bset->dim, type, pos) : NULL;
611 int isl_map_has_dim_id(__isl_keep isl_map *map,
612 enum isl_dim_type type, unsigned pos)
614 return map ? isl_space_has_dim_id(map->dim, type, pos) : -1;
617 __isl_give isl_id *isl_map_get_dim_id(__isl_keep isl_map *map,
618 enum isl_dim_type type, unsigned pos)
620 return map ? isl_space_get_dim_id(map->dim, type, pos) : NULL;
623 int isl_set_has_dim_id(__isl_keep isl_set *set,
624 enum isl_dim_type type, unsigned pos)
626 return isl_map_has_dim_id(set, type, pos);
629 __isl_give isl_id *isl_set_get_dim_id(__isl_keep isl_set *set,
630 enum isl_dim_type type, unsigned pos)
632 return isl_map_get_dim_id(set, type, pos);
635 __isl_give isl_map *isl_map_set_dim_id(__isl_take isl_map *map,
636 enum isl_dim_type type, unsigned pos, __isl_take isl_id *id)
638 map = isl_map_cow(map);
640 return isl_id_free(id);
642 map->dim = isl_space_set_dim_id(map->dim, type, pos, id);
644 return isl_map_reset_space(map, isl_space_copy(map->dim));
647 __isl_give isl_set *isl_set_set_dim_id(__isl_take isl_set *set,
648 enum isl_dim_type type, unsigned pos, __isl_take isl_id *id)
650 return isl_map_set_dim_id(set, type, pos, id);
653 int isl_map_find_dim_by_id(__isl_keep isl_map *map, enum isl_dim_type type,
654 __isl_keep isl_id *id)
658 return isl_space_find_dim_by_id(map->dim, type, id);
661 int isl_set_find_dim_by_id(__isl_keep isl_set *set, enum isl_dim_type type,
662 __isl_keep isl_id *id)
664 return isl_map_find_dim_by_id(set, type, id);
667 int isl_map_find_dim_by_name(__isl_keep isl_map *map, enum isl_dim_type type,
672 return isl_space_find_dim_by_name(map->dim, type, name);
675 int isl_set_find_dim_by_name(__isl_keep isl_set *set, enum isl_dim_type type,
678 return isl_map_find_dim_by_name(set, type, name);
681 int isl_basic_map_is_rational(__isl_keep isl_basic_map *bmap)
685 return ISL_F_ISSET(bmap, ISL_BASIC_MAP_RATIONAL);
688 int isl_basic_set_is_rational(__isl_keep isl_basic_set *bset)
690 return isl_basic_map_is_rational(bset);
693 /* Does "bmap" contain any rational points?
695 * If "bmap" has an equality for each dimension, equating the dimension
696 * to an integer constant, then it has no rational points, even if it
697 * is marked as rational.
699 int isl_basic_map_has_rational(__isl_keep isl_basic_map *bmap)
701 int has_rational = 1;
706 if (isl_basic_map_plain_is_empty(bmap))
708 if (!isl_basic_map_is_rational(bmap))
710 bmap = isl_basic_map_copy(bmap);
711 bmap = isl_basic_map_implicit_equalities(bmap);
714 total = isl_basic_map_total_dim(bmap);
715 if (bmap->n_eq == total) {
717 for (i = 0; i < bmap->n_eq; ++i) {
718 j = isl_seq_first_non_zero(bmap->eq[i] + 1, total);
721 if (!isl_int_is_one(bmap->eq[i][1 + j]) &&
722 !isl_int_is_negone(bmap->eq[i][1 + j]))
724 j = isl_seq_first_non_zero(bmap->eq[i] + 1 + j + 1,
732 isl_basic_map_free(bmap);
737 /* Does "map" contain any rational points?
739 int isl_map_has_rational(__isl_keep isl_map *map)
746 for (i = 0; i < map->n; ++i) {
747 has_rational = isl_basic_map_has_rational(map->p[i]);
748 if (has_rational < 0)
756 /* Does "set" contain any rational points?
758 int isl_set_has_rational(__isl_keep isl_set *set)
760 return isl_map_has_rational(set);
763 /* Is this basic set a parameter domain?
765 int isl_basic_set_is_params(__isl_keep isl_basic_set *bset)
769 return isl_space_is_params(bset->dim);
772 /* Is this set a parameter domain?
774 int isl_set_is_params(__isl_keep isl_set *set)
778 return isl_space_is_params(set->dim);
781 /* Is this map actually a parameter domain?
782 * Users should never call this function. Outside of isl,
783 * a map can never be a parameter domain.
785 int isl_map_is_params(__isl_keep isl_map *map)
789 return isl_space_is_params(map->dim);
792 static struct isl_basic_map *basic_map_init(struct isl_ctx *ctx,
793 struct isl_basic_map *bmap, unsigned extra,
794 unsigned n_eq, unsigned n_ineq)
797 size_t row_size = 1 + isl_space_dim(bmap->dim, isl_dim_all) + extra;
802 bmap->block = isl_blk_alloc(ctx, (n_ineq + n_eq) * row_size);
803 if (isl_blk_is_error(bmap->block))
806 bmap->ineq = isl_alloc_array(ctx, isl_int *, n_ineq + n_eq);
811 bmap->block2 = isl_blk_empty();
814 bmap->block2 = isl_blk_alloc(ctx, extra * (1 + row_size));
815 if (isl_blk_is_error(bmap->block2))
818 bmap->div = isl_alloc_array(ctx, isl_int *, extra);
823 for (i = 0; i < n_ineq + n_eq; ++i)
824 bmap->ineq[i] = bmap->block.data + i * row_size;
826 for (i = 0; i < extra; ++i)
827 bmap->div[i] = bmap->block2.data + i * (1 + row_size);
831 bmap->c_size = n_eq + n_ineq;
832 bmap->eq = bmap->ineq + n_ineq;
841 isl_basic_map_free(bmap);
845 struct isl_basic_set *isl_basic_set_alloc(struct isl_ctx *ctx,
846 unsigned nparam, unsigned dim, unsigned extra,
847 unsigned n_eq, unsigned n_ineq)
849 struct isl_basic_map *bmap;
852 space = isl_space_set_alloc(ctx, nparam, dim);
856 bmap = isl_basic_map_alloc_space(space, extra, n_eq, n_ineq);
857 return (struct isl_basic_set *)bmap;
860 struct isl_basic_set *isl_basic_set_alloc_space(__isl_take isl_space *dim,
861 unsigned extra, unsigned n_eq, unsigned n_ineq)
863 struct isl_basic_map *bmap;
866 isl_assert(dim->ctx, dim->n_in == 0, goto error);
867 bmap = isl_basic_map_alloc_space(dim, extra, n_eq, n_ineq);
868 return (struct isl_basic_set *)bmap;
874 struct isl_basic_map *isl_basic_map_alloc_space(__isl_take isl_space *dim,
875 unsigned extra, unsigned n_eq, unsigned n_ineq)
877 struct isl_basic_map *bmap;
881 bmap = isl_calloc_type(dim->ctx, struct isl_basic_map);
886 return basic_map_init(dim->ctx, bmap, extra, n_eq, n_ineq);
892 struct isl_basic_map *isl_basic_map_alloc(struct isl_ctx *ctx,
893 unsigned nparam, unsigned in, unsigned out, unsigned extra,
894 unsigned n_eq, unsigned n_ineq)
896 struct isl_basic_map *bmap;
899 dim = isl_space_alloc(ctx, nparam, in, out);
903 bmap = isl_basic_map_alloc_space(dim, extra, n_eq, n_ineq);
907 static void dup_constraints(
908 struct isl_basic_map *dst, struct isl_basic_map *src)
911 unsigned total = isl_basic_map_total_dim(src);
913 for (i = 0; i < src->n_eq; ++i) {
914 int j = isl_basic_map_alloc_equality(dst);
915 isl_seq_cpy(dst->eq[j], src->eq[i], 1+total);
918 for (i = 0; i < src->n_ineq; ++i) {
919 int j = isl_basic_map_alloc_inequality(dst);
920 isl_seq_cpy(dst->ineq[j], src->ineq[i], 1+total);
923 for (i = 0; i < src->n_div; ++i) {
924 int j = isl_basic_map_alloc_div(dst);
925 isl_seq_cpy(dst->div[j], src->div[i], 1+1+total);
927 ISL_F_SET(dst, ISL_BASIC_SET_FINAL);
930 struct isl_basic_map *isl_basic_map_dup(struct isl_basic_map *bmap)
932 struct isl_basic_map *dup;
936 dup = isl_basic_map_alloc_space(isl_space_copy(bmap->dim),
937 bmap->n_div, bmap->n_eq, bmap->n_ineq);
940 dup_constraints(dup, bmap);
941 dup->flags = bmap->flags;
942 dup->sample = isl_vec_copy(bmap->sample);
946 struct isl_basic_set *isl_basic_set_dup(struct isl_basic_set *bset)
948 struct isl_basic_map *dup;
950 dup = isl_basic_map_dup((struct isl_basic_map *)bset);
951 return (struct isl_basic_set *)dup;
954 struct isl_basic_set *isl_basic_set_copy(struct isl_basic_set *bset)
959 if (ISL_F_ISSET(bset, ISL_BASIC_SET_FINAL)) {
963 return isl_basic_set_dup(bset);
966 struct isl_set *isl_set_copy(struct isl_set *set)
975 struct isl_basic_map *isl_basic_map_copy(struct isl_basic_map *bmap)
980 if (ISL_F_ISSET(bmap, ISL_BASIC_SET_FINAL)) {
984 bmap = isl_basic_map_dup(bmap);
986 ISL_F_SET(bmap, ISL_BASIC_SET_FINAL);
990 struct isl_map *isl_map_copy(struct isl_map *map)
999 void *isl_basic_map_free(__isl_take isl_basic_map *bmap)
1004 if (--bmap->ref > 0)
1007 isl_ctx_deref(bmap->ctx);
1009 isl_blk_free(bmap->ctx, bmap->block2);
1011 isl_blk_free(bmap->ctx, bmap->block);
1012 isl_vec_free(bmap->sample);
1013 isl_space_free(bmap->dim);
1019 void *isl_basic_set_free(struct isl_basic_set *bset)
1021 return isl_basic_map_free((struct isl_basic_map *)bset);
1024 static int room_for_con(struct isl_basic_map *bmap, unsigned n)
1026 return bmap->n_eq + bmap->n_ineq + n <= bmap->c_size;
1029 __isl_give isl_map *isl_map_align_params_map_map_and(
1030 __isl_take isl_map *map1, __isl_take isl_map *map2,
1031 __isl_give isl_map *(*fn)(__isl_take isl_map *map1,
1032 __isl_take isl_map *map2))
1036 if (isl_space_match(map1->dim, isl_dim_param, map2->dim, isl_dim_param))
1037 return fn(map1, map2);
1038 if (!isl_space_has_named_params(map1->dim) ||
1039 !isl_space_has_named_params(map2->dim))
1040 isl_die(map1->ctx, isl_error_invalid,
1041 "unaligned unnamed parameters", goto error);
1042 map1 = isl_map_align_params(map1, isl_map_get_space(map2));
1043 map2 = isl_map_align_params(map2, isl_map_get_space(map1));
1044 return fn(map1, map2);
1051 int isl_map_align_params_map_map_and_test(__isl_keep isl_map *map1,
1052 __isl_keep isl_map *map2,
1053 int (*fn)(__isl_keep isl_map *map1, __isl_keep isl_map *map2))
1059 if (isl_space_match(map1->dim, isl_dim_param, map2->dim, isl_dim_param))
1060 return fn(map1, map2);
1061 if (!isl_space_has_named_params(map1->dim) ||
1062 !isl_space_has_named_params(map2->dim))
1063 isl_die(map1->ctx, isl_error_invalid,
1064 "unaligned unnamed parameters", return -1);
1065 map1 = isl_map_copy(map1);
1066 map2 = isl_map_copy(map2);
1067 map1 = isl_map_align_params(map1, isl_map_get_space(map2));
1068 map2 = isl_map_align_params(map2, isl_map_get_space(map1));
1075 int isl_basic_map_alloc_equality(struct isl_basic_map *bmap)
1077 struct isl_ctx *ctx;
1081 isl_assert(ctx, room_for_con(bmap, 1), return -1);
1082 isl_assert(ctx, (bmap->eq - bmap->ineq) + bmap->n_eq <= bmap->c_size,
1084 ISL_F_CLR(bmap, ISL_BASIC_MAP_NORMALIZED);
1085 ISL_F_CLR(bmap, ISL_BASIC_MAP_NO_REDUNDANT);
1086 ISL_F_CLR(bmap, ISL_BASIC_MAP_NO_IMPLICIT);
1087 ISL_F_CLR(bmap, ISL_BASIC_MAP_ALL_EQUALITIES);
1088 ISL_F_CLR(bmap, ISL_BASIC_MAP_NORMALIZED_DIVS);
1089 if ((bmap->eq - bmap->ineq) + bmap->n_eq == bmap->c_size) {
1091 int j = isl_basic_map_alloc_inequality(bmap);
1095 bmap->ineq[j] = bmap->ineq[bmap->n_ineq - 1];
1096 bmap->ineq[bmap->n_ineq - 1] = bmap->eq[-1];
1103 isl_seq_clr(bmap->eq[bmap->n_eq] + 1 + isl_basic_map_total_dim(bmap),
1104 bmap->extra - bmap->n_div);
1105 return bmap->n_eq++;
1108 int isl_basic_set_alloc_equality(struct isl_basic_set *bset)
1110 return isl_basic_map_alloc_equality((struct isl_basic_map *)bset);
1113 int isl_basic_map_free_equality(struct isl_basic_map *bmap, unsigned n)
1117 isl_assert(bmap->ctx, n <= bmap->n_eq, return -1);
1122 int isl_basic_set_free_equality(struct isl_basic_set *bset, unsigned n)
1124 return isl_basic_map_free_equality((struct isl_basic_map *)bset, n);
1127 int isl_basic_map_drop_equality(struct isl_basic_map *bmap, unsigned pos)
1132 isl_assert(bmap->ctx, pos < bmap->n_eq, return -1);
1134 if (pos != bmap->n_eq - 1) {
1136 bmap->eq[pos] = bmap->eq[bmap->n_eq - 1];
1137 bmap->eq[bmap->n_eq - 1] = t;
1143 int isl_basic_set_drop_equality(struct isl_basic_set *bset, unsigned pos)
1145 return isl_basic_map_drop_equality((struct isl_basic_map *)bset, pos);
1148 void isl_basic_map_inequality_to_equality(
1149 struct isl_basic_map *bmap, unsigned pos)
1153 t = bmap->ineq[pos];
1154 bmap->ineq[pos] = bmap->ineq[bmap->n_ineq - 1];
1155 bmap->ineq[bmap->n_ineq - 1] = bmap->eq[-1];
1160 ISL_F_CLR(bmap, ISL_BASIC_MAP_NO_REDUNDANT);
1161 ISL_F_CLR(bmap, ISL_BASIC_MAP_NORMALIZED);
1162 ISL_F_CLR(bmap, ISL_BASIC_MAP_NORMALIZED_DIVS);
1163 ISL_F_CLR(bmap, ISL_BASIC_MAP_ALL_EQUALITIES);
1166 static int room_for_ineq(struct isl_basic_map *bmap, unsigned n)
1168 return bmap->n_ineq + n <= bmap->eq - bmap->ineq;
1171 int isl_basic_map_alloc_inequality(struct isl_basic_map *bmap)
1173 struct isl_ctx *ctx;
1177 isl_assert(ctx, room_for_ineq(bmap, 1), return -1);
1178 ISL_F_CLR(bmap, ISL_BASIC_MAP_NO_IMPLICIT);
1179 ISL_F_CLR(bmap, ISL_BASIC_MAP_NO_REDUNDANT);
1180 ISL_F_CLR(bmap, ISL_BASIC_MAP_NORMALIZED);
1181 ISL_F_CLR(bmap, ISL_BASIC_MAP_ALL_EQUALITIES);
1182 isl_seq_clr(bmap->ineq[bmap->n_ineq] +
1183 1 + isl_basic_map_total_dim(bmap),
1184 bmap->extra - bmap->n_div);
1185 return bmap->n_ineq++;
1188 int isl_basic_set_alloc_inequality(struct isl_basic_set *bset)
1190 return isl_basic_map_alloc_inequality((struct isl_basic_map *)bset);
1193 int isl_basic_map_free_inequality(struct isl_basic_map *bmap, unsigned n)
1197 isl_assert(bmap->ctx, n <= bmap->n_ineq, return -1);
1202 int isl_basic_set_free_inequality(struct isl_basic_set *bset, unsigned n)
1204 return isl_basic_map_free_inequality((struct isl_basic_map *)bset, n);
1207 int isl_basic_map_drop_inequality(struct isl_basic_map *bmap, unsigned pos)
1212 isl_assert(bmap->ctx, pos < bmap->n_ineq, return -1);
1214 if (pos != bmap->n_ineq - 1) {
1215 t = bmap->ineq[pos];
1216 bmap->ineq[pos] = bmap->ineq[bmap->n_ineq - 1];
1217 bmap->ineq[bmap->n_ineq - 1] = t;
1218 ISL_F_CLR(bmap, ISL_BASIC_MAP_NORMALIZED);
1224 int isl_basic_set_drop_inequality(struct isl_basic_set *bset, unsigned pos)
1226 return isl_basic_map_drop_inequality((struct isl_basic_map *)bset, pos);
1229 __isl_give isl_basic_map *isl_basic_map_add_eq(__isl_take isl_basic_map *bmap,
1234 bmap = isl_basic_map_extend_constraints(bmap, 1, 0);
1237 k = isl_basic_map_alloc_equality(bmap);
1240 isl_seq_cpy(bmap->eq[k], eq, 1 + isl_basic_map_total_dim(bmap));
1243 isl_basic_map_free(bmap);
1247 __isl_give isl_basic_set *isl_basic_set_add_eq(__isl_take isl_basic_set *bset,
1250 return (isl_basic_set *)
1251 isl_basic_map_add_eq((isl_basic_map *)bset, eq);
1254 __isl_give isl_basic_map *isl_basic_map_add_ineq(__isl_take isl_basic_map *bmap,
1259 bmap = isl_basic_map_extend_constraints(bmap, 0, 1);
1262 k = isl_basic_map_alloc_inequality(bmap);
1265 isl_seq_cpy(bmap->ineq[k], ineq, 1 + isl_basic_map_total_dim(bmap));
1268 isl_basic_map_free(bmap);
1272 __isl_give isl_basic_set *isl_basic_set_add_ineq(__isl_take isl_basic_set *bset,
1275 return (isl_basic_set *)
1276 isl_basic_map_add_ineq((isl_basic_map *)bset, ineq);
1279 int isl_basic_map_alloc_div(struct isl_basic_map *bmap)
1283 isl_assert(bmap->ctx, bmap->n_div < bmap->extra, return -1);
1284 isl_seq_clr(bmap->div[bmap->n_div] +
1285 1 + 1 + isl_basic_map_total_dim(bmap),
1286 bmap->extra - bmap->n_div);
1287 ISL_F_CLR(bmap, ISL_BASIC_MAP_NORMALIZED_DIVS);
1288 return bmap->n_div++;
1291 int isl_basic_set_alloc_div(struct isl_basic_set *bset)
1293 return isl_basic_map_alloc_div((struct isl_basic_map *)bset);
1296 int isl_basic_map_free_div(struct isl_basic_map *bmap, unsigned n)
1300 isl_assert(bmap->ctx, n <= bmap->n_div, return -1);
1305 int isl_basic_set_free_div(struct isl_basic_set *bset, unsigned n)
1307 return isl_basic_map_free_div((struct isl_basic_map *)bset, n);
1310 /* Copy constraint from src to dst, putting the vars of src at offset
1311 * dim_off in dst and the divs of src at offset div_off in dst.
1312 * If both sets are actually map, then dim_off applies to the input
1315 static void copy_constraint(struct isl_basic_map *dst_map, isl_int *dst,
1316 struct isl_basic_map *src_map, isl_int *src,
1317 unsigned in_off, unsigned out_off, unsigned div_off)
1319 unsigned src_nparam = isl_basic_map_n_param(src_map);
1320 unsigned dst_nparam = isl_basic_map_n_param(dst_map);
1321 unsigned src_in = isl_basic_map_n_in(src_map);
1322 unsigned dst_in = isl_basic_map_n_in(dst_map);
1323 unsigned src_out = isl_basic_map_n_out(src_map);
1324 unsigned dst_out = isl_basic_map_n_out(dst_map);
1325 isl_int_set(dst[0], src[0]);
1326 isl_seq_cpy(dst+1, src+1, isl_min(dst_nparam, src_nparam));
1327 if (dst_nparam > src_nparam)
1328 isl_seq_clr(dst+1+src_nparam,
1329 dst_nparam - src_nparam);
1330 isl_seq_clr(dst+1+dst_nparam, in_off);
1331 isl_seq_cpy(dst+1+dst_nparam+in_off,
1333 isl_min(dst_in-in_off, src_in));
1334 if (dst_in-in_off > src_in)
1335 isl_seq_clr(dst+1+dst_nparam+in_off+src_in,
1336 dst_in - in_off - src_in);
1337 isl_seq_clr(dst+1+dst_nparam+dst_in, out_off);
1338 isl_seq_cpy(dst+1+dst_nparam+dst_in+out_off,
1339 src+1+src_nparam+src_in,
1340 isl_min(dst_out-out_off, src_out));
1341 if (dst_out-out_off > src_out)
1342 isl_seq_clr(dst+1+dst_nparam+dst_in+out_off+src_out,
1343 dst_out - out_off - src_out);
1344 isl_seq_clr(dst+1+dst_nparam+dst_in+dst_out, div_off);
1345 isl_seq_cpy(dst+1+dst_nparam+dst_in+dst_out+div_off,
1346 src+1+src_nparam+src_in+src_out,
1347 isl_min(dst_map->extra-div_off, src_map->n_div));
1348 if (dst_map->n_div-div_off > src_map->n_div)
1349 isl_seq_clr(dst+1+dst_nparam+dst_in+dst_out+
1350 div_off+src_map->n_div,
1351 dst_map->n_div - div_off - src_map->n_div);
1354 static void copy_div(struct isl_basic_map *dst_map, isl_int *dst,
1355 struct isl_basic_map *src_map, isl_int *src,
1356 unsigned in_off, unsigned out_off, unsigned div_off)
1358 isl_int_set(dst[0], src[0]);
1359 copy_constraint(dst_map, dst+1, src_map, src+1, in_off, out_off, div_off);
1362 static struct isl_basic_map *add_constraints(struct isl_basic_map *bmap1,
1363 struct isl_basic_map *bmap2, unsigned i_pos, unsigned o_pos)
1368 if (!bmap1 || !bmap2)
1371 div_off = bmap1->n_div;
1373 for (i = 0; i < bmap2->n_eq; ++i) {
1374 int i1 = isl_basic_map_alloc_equality(bmap1);
1377 copy_constraint(bmap1, bmap1->eq[i1], bmap2, bmap2->eq[i],
1378 i_pos, o_pos, div_off);
1381 for (i = 0; i < bmap2->n_ineq; ++i) {
1382 int i1 = isl_basic_map_alloc_inequality(bmap1);
1385 copy_constraint(bmap1, bmap1->ineq[i1], bmap2, bmap2->ineq[i],
1386 i_pos, o_pos, div_off);
1389 for (i = 0; i < bmap2->n_div; ++i) {
1390 int i1 = isl_basic_map_alloc_div(bmap1);
1393 copy_div(bmap1, bmap1->div[i1], bmap2, bmap2->div[i],
1394 i_pos, o_pos, div_off);
1397 isl_basic_map_free(bmap2);
1402 isl_basic_map_free(bmap1);
1403 isl_basic_map_free(bmap2);
1407 struct isl_basic_set *isl_basic_set_add_constraints(struct isl_basic_set *bset1,
1408 struct isl_basic_set *bset2, unsigned pos)
1410 return (struct isl_basic_set *)
1411 add_constraints((struct isl_basic_map *)bset1,
1412 (struct isl_basic_map *)bset2, 0, pos);
1415 struct isl_basic_map *isl_basic_map_extend_space(struct isl_basic_map *base,
1416 __isl_take isl_space *dim, unsigned extra,
1417 unsigned n_eq, unsigned n_ineq)
1419 struct isl_basic_map *ext;
1429 dims_ok = isl_space_is_equal(base->dim, dim) &&
1430 base->extra >= base->n_div + extra;
1432 if (dims_ok && room_for_con(base, n_eq + n_ineq) &&
1433 room_for_ineq(base, n_ineq)) {
1434 isl_space_free(dim);
1438 isl_assert(base->ctx, base->dim->nparam <= dim->nparam, goto error);
1439 isl_assert(base->ctx, base->dim->n_in <= dim->n_in, goto error);
1440 isl_assert(base->ctx, base->dim->n_out <= dim->n_out, goto error);
1441 extra += base->extra;
1443 n_ineq += base->n_ineq;
1445 ext = isl_basic_map_alloc_space(dim, extra, n_eq, n_ineq);
1451 ext->sample = isl_vec_copy(base->sample);
1452 flags = base->flags;
1453 ext = add_constraints(ext, base, 0, 0);
1456 ISL_F_CLR(ext, ISL_BASIC_SET_FINAL);
1462 isl_space_free(dim);
1463 isl_basic_map_free(base);
1467 struct isl_basic_set *isl_basic_set_extend_space(struct isl_basic_set *base,
1468 __isl_take isl_space *dim, unsigned extra,
1469 unsigned n_eq, unsigned n_ineq)
1471 return (struct isl_basic_set *)
1472 isl_basic_map_extend_space((struct isl_basic_map *)base, dim,
1473 extra, n_eq, n_ineq);
1476 struct isl_basic_map *isl_basic_map_extend_constraints(
1477 struct isl_basic_map *base, unsigned n_eq, unsigned n_ineq)
1481 return isl_basic_map_extend_space(base, isl_space_copy(base->dim),
1485 struct isl_basic_map *isl_basic_map_extend(struct isl_basic_map *base,
1486 unsigned nparam, unsigned n_in, unsigned n_out, unsigned extra,
1487 unsigned n_eq, unsigned n_ineq)
1489 struct isl_basic_map *bmap;
1494 dim = isl_space_alloc(base->ctx, nparam, n_in, n_out);
1498 bmap = isl_basic_map_extend_space(base, dim, extra, n_eq, n_ineq);
1501 isl_basic_map_free(base);
1505 struct isl_basic_set *isl_basic_set_extend(struct isl_basic_set *base,
1506 unsigned nparam, unsigned dim, unsigned extra,
1507 unsigned n_eq, unsigned n_ineq)
1509 return (struct isl_basic_set *)
1510 isl_basic_map_extend((struct isl_basic_map *)base,
1511 nparam, 0, dim, extra, n_eq, n_ineq);
1514 struct isl_basic_set *isl_basic_set_extend_constraints(
1515 struct isl_basic_set *base, unsigned n_eq, unsigned n_ineq)
1517 return (struct isl_basic_set *)
1518 isl_basic_map_extend_constraints((struct isl_basic_map *)base,
1522 struct isl_basic_set *isl_basic_set_cow(struct isl_basic_set *bset)
1524 return (struct isl_basic_set *)
1525 isl_basic_map_cow((struct isl_basic_map *)bset);
1528 struct isl_basic_map *isl_basic_map_cow(struct isl_basic_map *bmap)
1533 if (bmap->ref > 1) {
1535 bmap = isl_basic_map_dup(bmap);
1538 ISL_F_CLR(bmap, ISL_BASIC_SET_FINAL);
1542 struct isl_set *isl_set_cow(struct isl_set *set)
1550 return isl_set_dup(set);
1553 struct isl_map *isl_map_cow(struct isl_map *map)
1561 return isl_map_dup(map);
1564 static void swap_vars(struct isl_blk blk, isl_int *a,
1565 unsigned a_len, unsigned b_len)
1567 isl_seq_cpy(blk.data, a+a_len, b_len);
1568 isl_seq_cpy(blk.data+b_len, a, a_len);
1569 isl_seq_cpy(a, blk.data, b_len+a_len);
1572 static __isl_give isl_basic_map *isl_basic_map_swap_vars(
1573 __isl_take isl_basic_map *bmap, unsigned pos, unsigned n1, unsigned n2)
1581 isl_assert(bmap->ctx,
1582 pos + n1 + n2 <= 1 + isl_basic_map_total_dim(bmap), goto error);
1584 if (n1 == 0 || n2 == 0)
1587 bmap = isl_basic_map_cow(bmap);
1591 blk = isl_blk_alloc(bmap->ctx, n1 + n2);
1592 if (isl_blk_is_error(blk))
1595 for (i = 0; i < bmap->n_eq; ++i)
1597 bmap->eq[i] + pos, n1, n2);
1599 for (i = 0; i < bmap->n_ineq; ++i)
1601 bmap->ineq[i] + pos, n1, n2);
1603 for (i = 0; i < bmap->n_div; ++i)
1605 bmap->div[i]+1 + pos, n1, n2);
1607 isl_blk_free(bmap->ctx, blk);
1609 ISL_F_CLR(bmap, ISL_BASIC_SET_NORMALIZED);
1610 bmap = isl_basic_map_gauss(bmap, NULL);
1611 return isl_basic_map_finalize(bmap);
1613 isl_basic_map_free(bmap);
1617 static __isl_give isl_basic_set *isl_basic_set_swap_vars(
1618 __isl_take isl_basic_set *bset, unsigned n)
1623 nparam = isl_basic_set_n_param(bset);
1624 dim = isl_basic_set_n_dim(bset);
1625 isl_assert(bset->ctx, n <= dim, goto error);
1627 return isl_basic_map_swap_vars(bset, 1 + nparam, n, dim - n);
1629 isl_basic_set_free(bset);
1633 struct isl_basic_map *isl_basic_map_set_to_empty(struct isl_basic_map *bmap)
1639 total = isl_basic_map_total_dim(bmap);
1640 isl_basic_map_free_div(bmap, bmap->n_div);
1641 isl_basic_map_free_inequality(bmap, bmap->n_ineq);
1643 isl_basic_map_free_equality(bmap, bmap->n_eq-1);
1645 i = isl_basic_map_alloc_equality(bmap);
1649 isl_int_set_si(bmap->eq[i][0], 1);
1650 isl_seq_clr(bmap->eq[i]+1, total);
1651 ISL_F_SET(bmap, ISL_BASIC_MAP_EMPTY);
1652 isl_vec_free(bmap->sample);
1653 bmap->sample = NULL;
1654 return isl_basic_map_finalize(bmap);
1656 isl_basic_map_free(bmap);
1660 struct isl_basic_set *isl_basic_set_set_to_empty(struct isl_basic_set *bset)
1662 return (struct isl_basic_set *)
1663 isl_basic_map_set_to_empty((struct isl_basic_map *)bset);
1666 void isl_basic_map_swap_div(struct isl_basic_map *bmap, int a, int b)
1669 unsigned off = isl_space_dim(bmap->dim, isl_dim_all);
1670 isl_int *t = bmap->div[a];
1671 bmap->div[a] = bmap->div[b];
1674 for (i = 0; i < bmap->n_eq; ++i)
1675 isl_int_swap(bmap->eq[i][1+off+a], bmap->eq[i][1+off+b]);
1677 for (i = 0; i < bmap->n_ineq; ++i)
1678 isl_int_swap(bmap->ineq[i][1+off+a], bmap->ineq[i][1+off+b]);
1680 for (i = 0; i < bmap->n_div; ++i)
1681 isl_int_swap(bmap->div[i][1+1+off+a], bmap->div[i][1+1+off+b]);
1682 ISL_F_CLR(bmap, ISL_BASIC_MAP_NORMALIZED);
1685 /* Eliminate the specified n dimensions starting at first from the
1686 * constraints, without removing the dimensions from the space.
1687 * If the set is rational, the dimensions are eliminated using Fourier-Motzkin.
1689 __isl_give isl_map *isl_map_eliminate(__isl_take isl_map *map,
1690 enum isl_dim_type type, unsigned first, unsigned n)
1699 if (first + n > isl_map_dim(map, type) || first + n < first)
1700 isl_die(map->ctx, isl_error_invalid,
1701 "index out of bounds", goto error);
1703 map = isl_map_cow(map);
1707 for (i = 0; i < map->n; ++i) {
1708 map->p[i] = isl_basic_map_eliminate(map->p[i], type, first, n);
1718 /* Eliminate the specified n dimensions starting at first from the
1719 * constraints, without removing the dimensions from the space.
1720 * If the set is rational, the dimensions are eliminated using Fourier-Motzkin.
1722 __isl_give isl_set *isl_set_eliminate(__isl_take isl_set *set,
1723 enum isl_dim_type type, unsigned first, unsigned n)
1725 return (isl_set *)isl_map_eliminate((isl_map *)set, type, first, n);
1728 /* Eliminate the specified n dimensions starting at first from the
1729 * constraints, without removing the dimensions from the space.
1730 * If the set is rational, the dimensions are eliminated using Fourier-Motzkin.
1732 __isl_give isl_set *isl_set_eliminate_dims(__isl_take isl_set *set,
1733 unsigned first, unsigned n)
1735 return isl_set_eliminate(set, isl_dim_set, first, n);
1738 __isl_give isl_basic_map *isl_basic_map_remove_divs(
1739 __isl_take isl_basic_map *bmap)
1743 bmap = isl_basic_map_eliminate_vars(bmap,
1744 isl_space_dim(bmap->dim, isl_dim_all), bmap->n_div);
1748 return isl_basic_map_finalize(bmap);
1751 __isl_give isl_basic_set *isl_basic_set_remove_divs(
1752 __isl_take isl_basic_set *bset)
1754 return (struct isl_basic_set *)isl_basic_map_remove_divs(
1755 (struct isl_basic_map *)bset);
1758 __isl_give isl_map *isl_map_remove_divs(__isl_take isl_map *map)
1767 map = isl_map_cow(map);
1771 for (i = 0; i < map->n; ++i) {
1772 map->p[i] = isl_basic_map_remove_divs(map->p[i]);
1782 __isl_give isl_set *isl_set_remove_divs(__isl_take isl_set *set)
1784 return isl_map_remove_divs(set);
1787 struct isl_basic_map *isl_basic_map_remove_dims(struct isl_basic_map *bmap,
1788 enum isl_dim_type type, unsigned first, unsigned n)
1792 isl_assert(bmap->ctx, first + n <= isl_basic_map_dim(bmap, type),
1794 if (n == 0 && !isl_space_is_named_or_nested(bmap->dim, type))
1796 bmap = isl_basic_map_eliminate_vars(bmap,
1797 isl_basic_map_offset(bmap, type) - 1 + first, n);
1800 if (ISL_F_ISSET(bmap, ISL_BASIC_MAP_EMPTY) && type == isl_dim_div)
1802 bmap = isl_basic_map_drop(bmap, type, first, n);
1805 isl_basic_map_free(bmap);
1809 /* Return true if the definition of the given div (recursively) involves
1810 * any of the given variables.
1812 static int div_involves_vars(__isl_keep isl_basic_map *bmap, int div,
1813 unsigned first, unsigned n)
1816 unsigned div_offset = isl_basic_map_offset(bmap, isl_dim_div);
1818 if (isl_int_is_zero(bmap->div[div][0]))
1820 if (isl_seq_first_non_zero(bmap->div[div] + 1 + first, n) >= 0)
1823 for (i = bmap->n_div - 1; i >= 0; --i) {
1824 if (isl_int_is_zero(bmap->div[div][1 + div_offset + i]))
1826 if (div_involves_vars(bmap, i, first, n))
1833 /* Try and add a lower and/or upper bound on "div" to "bmap"
1834 * based on inequality "i".
1835 * "total" is the total number of variables (excluding the divs).
1836 * "v" is a temporary object that can be used during the calculations.
1837 * If "lb" is set, then a lower bound should be constructed.
1838 * If "ub" is set, then an upper bound should be constructed.
1840 * The calling function has already checked that the inequality does not
1841 * reference "div", but we still need to check that the inequality is
1842 * of the right form. We'll consider the case where we want to construct
1843 * a lower bound. The construction of upper bounds is similar.
1845 * Let "div" be of the form
1847 * q = floor((a + f(x))/d)
1849 * We essentially check if constraint "i" is of the form
1853 * so that we can use it to derive a lower bound on "div".
1854 * However, we allow a slightly more general form
1858 * with the condition that the coefficients of g(x) - f(x) are all
1860 * Rewriting this constraint as
1864 * adding a + f(x) to both sides and dividing by d, we obtain
1866 * (a + f(x))/d >= (a-b)/d + (f(x)-g(x))/d
1868 * Taking the floor on both sides, we obtain
1870 * q >= floor((a-b)/d) + (f(x)-g(x))/d
1874 * (g(x)-f(x))/d + ceil((b-a)/d) + q >= 0
1876 * In the case of an upper bound, we construct the constraint
1878 * (g(x)+f(x))/d + floor((b+a)/d) - q >= 0
1881 static __isl_give isl_basic_map *insert_bounds_on_div_from_ineq(
1882 __isl_take isl_basic_map *bmap, int div, int i,
1883 unsigned total, isl_int v, int lb, int ub)
1887 for (j = 0; (lb || ub) && j < total + bmap->n_div; ++j) {
1889 isl_int_sub(v, bmap->ineq[i][1 + j],
1890 bmap->div[div][1 + 1 + j]);
1891 lb = isl_int_is_divisible_by(v, bmap->div[div][0]);
1894 isl_int_add(v, bmap->ineq[i][1 + j],
1895 bmap->div[div][1 + 1 + j]);
1896 ub = isl_int_is_divisible_by(v, bmap->div[div][0]);
1902 bmap = isl_basic_map_extend_constraints(bmap, 0, lb + ub);
1904 int k = isl_basic_map_alloc_inequality(bmap);
1907 for (j = 0; j < 1 + total + bmap->n_div; ++j) {
1908 isl_int_sub(bmap->ineq[k][j], bmap->ineq[i][j],
1909 bmap->div[div][1 + j]);
1910 isl_int_cdiv_q(bmap->ineq[k][j],
1911 bmap->ineq[k][j], bmap->div[div][0]);
1913 isl_int_set_si(bmap->ineq[k][1 + total + div], 1);
1916 int k = isl_basic_map_alloc_inequality(bmap);
1919 for (j = 0; j < 1 + total + bmap->n_div; ++j) {
1920 isl_int_add(bmap->ineq[k][j], bmap->ineq[i][j],
1921 bmap->div[div][1 + j]);
1922 isl_int_fdiv_q(bmap->ineq[k][j],
1923 bmap->ineq[k][j], bmap->div[div][0]);
1925 isl_int_set_si(bmap->ineq[k][1 + total + div], -1);
1930 isl_basic_map_free(bmap);
1934 /* This function is called right before "div" is eliminated from "bmap"
1935 * using Fourier-Motzkin.
1936 * Look through the constraints of "bmap" for constraints on the argument
1937 * of the integer division and use them to construct constraints on the
1938 * integer division itself. These constraints can then be combined
1939 * during the Fourier-Motzkin elimination.
1940 * Note that it is only useful to introduce lower bounds on "div"
1941 * if "bmap" already contains upper bounds on "div" as the newly
1942 * introduce lower bounds can then be combined with the pre-existing
1943 * upper bounds. Similarly for upper bounds.
1944 * We therefore first check if "bmap" contains any lower and/or upper bounds
1947 * It is interesting to note that the introduction of these constraints
1948 * can indeed lead to more accurate results, even when compared to
1949 * deriving constraints on the argument of "div" from constraints on "div".
1950 * Consider, for example, the set
1952 * { [i,j,k] : 3 + i + 2j >= 0 and 2 * [(i+2j)/4] <= k }
1954 * The second constraint can be rewritten as
1956 * 2 * [(-i-2j+3)/4] + k >= 0
1958 * from which we can derive
1960 * -i - 2j + 3 >= -2k
1966 * Combined with the first constraint, we obtain
1968 * -3 <= 3 + 2k or k >= -3
1970 * If, on the other hand we derive a constraint on [(i+2j)/4] from
1971 * the first constraint, we obtain
1973 * [(i + 2j)/4] >= [-3/4] = -1
1975 * Combining this constraint with the second constraint, we obtain
1979 static __isl_give isl_basic_map *insert_bounds_on_div(
1980 __isl_take isl_basic_map *bmap, int div)
1983 int check_lb, check_ub;
1990 if (isl_int_is_zero(bmap->div[div][0]))
1993 total = isl_space_dim(bmap->dim, isl_dim_all);
1997 for (i = 0; (!check_lb || !check_ub) && i < bmap->n_ineq; ++i) {
1998 int s = isl_int_sgn(bmap->ineq[i][1 + total + div]);
2005 if (!check_lb && !check_ub)
2010 for (i = 0; bmap && i < bmap->n_ineq; ++i) {
2011 if (!isl_int_is_zero(bmap->ineq[i][1 + total + div]))
2014 bmap = insert_bounds_on_div_from_ineq(bmap, div, i, total, v,
2015 check_lb, check_ub);
2023 /* Remove all divs (recursively) involving any of the given dimensions
2024 * in their definitions.
2026 __isl_give isl_basic_map *isl_basic_map_remove_divs_involving_dims(
2027 __isl_take isl_basic_map *bmap,
2028 enum isl_dim_type type, unsigned first, unsigned n)
2034 isl_assert(bmap->ctx, first + n <= isl_basic_map_dim(bmap, type),
2036 first += isl_basic_map_offset(bmap, type);
2038 for (i = bmap->n_div - 1; i >= 0; --i) {
2039 if (!div_involves_vars(bmap, i, first, n))
2041 bmap = insert_bounds_on_div(bmap, i);
2042 bmap = isl_basic_map_remove_dims(bmap, isl_dim_div, i, 1);
2050 isl_basic_map_free(bmap);
2054 __isl_give isl_basic_set *isl_basic_set_remove_divs_involving_dims(
2055 __isl_take isl_basic_set *bset,
2056 enum isl_dim_type type, unsigned first, unsigned n)
2058 return isl_basic_map_remove_divs_involving_dims(bset, type, first, n);
2061 __isl_give isl_map *isl_map_remove_divs_involving_dims(__isl_take isl_map *map,
2062 enum isl_dim_type type, unsigned first, unsigned n)
2071 map = isl_map_cow(map);
2075 for (i = 0; i < map->n; ++i) {
2076 map->p[i] = isl_basic_map_remove_divs_involving_dims(map->p[i],
2087 __isl_give isl_set *isl_set_remove_divs_involving_dims(__isl_take isl_set *set,
2088 enum isl_dim_type type, unsigned first, unsigned n)
2090 return (isl_set *)isl_map_remove_divs_involving_dims((isl_map *)set,
2094 /* Does the desciption of "bmap" depend on the specified dimensions?
2095 * We also check whether the dimensions appear in any of the div definitions.
2096 * In principle there is no need for this check. If the dimensions appear
2097 * in a div definition, they also appear in the defining constraints of that
2100 int isl_basic_map_involves_dims(__isl_keep isl_basic_map *bmap,
2101 enum isl_dim_type type, unsigned first, unsigned n)
2108 if (first + n > isl_basic_map_dim(bmap, type))
2109 isl_die(bmap->ctx, isl_error_invalid,
2110 "index out of bounds", return -1);
2112 first += isl_basic_map_offset(bmap, type);
2113 for (i = 0; i < bmap->n_eq; ++i)
2114 if (isl_seq_first_non_zero(bmap->eq[i] + first, n) >= 0)
2116 for (i = 0; i < bmap->n_ineq; ++i)
2117 if (isl_seq_first_non_zero(bmap->ineq[i] + first, n) >= 0)
2119 for (i = 0; i < bmap->n_div; ++i) {
2120 if (isl_int_is_zero(bmap->div[i][0]))
2122 if (isl_seq_first_non_zero(bmap->div[i] + 1 + first, n) >= 0)
2129 int isl_map_involves_dims(__isl_keep isl_map *map,
2130 enum isl_dim_type type, unsigned first, unsigned n)
2137 if (first + n > isl_map_dim(map, type))
2138 isl_die(map->ctx, isl_error_invalid,
2139 "index out of bounds", return -1);
2141 for (i = 0; i < map->n; ++i) {
2142 int involves = isl_basic_map_involves_dims(map->p[i],
2144 if (involves < 0 || involves)
2151 int isl_basic_set_involves_dims(__isl_keep isl_basic_set *bset,
2152 enum isl_dim_type type, unsigned first, unsigned n)
2154 return isl_basic_map_involves_dims(bset, type, first, n);
2157 int isl_set_involves_dims(__isl_keep isl_set *set,
2158 enum isl_dim_type type, unsigned first, unsigned n)
2160 return isl_map_involves_dims(set, type, first, n);
2163 /* Return true if the definition of the given div is unknown or depends
2166 static int div_is_unknown(__isl_keep isl_basic_map *bmap, int div)
2169 unsigned div_offset = isl_basic_map_offset(bmap, isl_dim_div);
2171 if (isl_int_is_zero(bmap->div[div][0]))
2174 for (i = bmap->n_div - 1; i >= 0; --i) {
2175 if (isl_int_is_zero(bmap->div[div][1 + div_offset + i]))
2177 if (div_is_unknown(bmap, i))
2184 /* Remove all divs that are unknown or defined in terms of unknown divs.
2186 __isl_give isl_basic_map *isl_basic_map_remove_unknown_divs(
2187 __isl_take isl_basic_map *bmap)
2194 for (i = bmap->n_div - 1; i >= 0; --i) {
2195 if (!div_is_unknown(bmap, i))
2197 bmap = isl_basic_map_remove_dims(bmap, isl_dim_div, i, 1);
2206 /* Remove all divs that are unknown or defined in terms of unknown divs.
2208 __isl_give isl_basic_set *isl_basic_set_remove_unknown_divs(
2209 __isl_take isl_basic_set *bset)
2211 return isl_basic_map_remove_unknown_divs(bset);
2214 __isl_give isl_map *isl_map_remove_unknown_divs(__isl_take isl_map *map)
2223 map = isl_map_cow(map);
2227 for (i = 0; i < map->n; ++i) {
2228 map->p[i] = isl_basic_map_remove_unknown_divs(map->p[i]);
2238 __isl_give isl_set *isl_set_remove_unknown_divs(__isl_take isl_set *set)
2240 return (isl_set *)isl_map_remove_unknown_divs((isl_map *)set);
2243 __isl_give isl_basic_set *isl_basic_set_remove_dims(
2244 __isl_take isl_basic_set *bset,
2245 enum isl_dim_type type, unsigned first, unsigned n)
2247 return (isl_basic_set *)
2248 isl_basic_map_remove_dims((isl_basic_map *)bset, type, first, n);
2251 struct isl_map *isl_map_remove_dims(struct isl_map *map,
2252 enum isl_dim_type type, unsigned first, unsigned n)
2259 map = isl_map_cow(map);
2262 isl_assert(map->ctx, first + n <= isl_map_dim(map, type), goto error);
2264 for (i = 0; i < map->n; ++i) {
2265 map->p[i] = isl_basic_map_eliminate_vars(map->p[i],
2266 isl_basic_map_offset(map->p[i], type) - 1 + first, n);
2270 map = isl_map_drop(map, type, first, n);
2277 __isl_give isl_set *isl_set_remove_dims(__isl_take isl_set *bset,
2278 enum isl_dim_type type, unsigned first, unsigned n)
2280 return (isl_set *)isl_map_remove_dims((isl_map *)bset, type, first, n);
2283 /* Project out n inputs starting at first using Fourier-Motzkin */
2284 struct isl_map *isl_map_remove_inputs(struct isl_map *map,
2285 unsigned first, unsigned n)
2287 return isl_map_remove_dims(map, isl_dim_in, first, n);
2290 static void dump_term(struct isl_basic_map *bmap,
2291 isl_int c, int pos, FILE *out)
2294 unsigned in = isl_basic_map_n_in(bmap);
2295 unsigned dim = in + isl_basic_map_n_out(bmap);
2296 unsigned nparam = isl_basic_map_n_param(bmap);
2298 isl_int_print(out, c, 0);
2300 if (!isl_int_is_one(c))
2301 isl_int_print(out, c, 0);
2302 if (pos < 1 + nparam) {
2303 name = isl_space_get_dim_name(bmap->dim,
2304 isl_dim_param, pos - 1);
2306 fprintf(out, "%s", name);
2308 fprintf(out, "p%d", pos - 1);
2309 } else if (pos < 1 + nparam + in)
2310 fprintf(out, "i%d", pos - 1 - nparam);
2311 else if (pos < 1 + nparam + dim)
2312 fprintf(out, "o%d", pos - 1 - nparam - in);
2314 fprintf(out, "e%d", pos - 1 - nparam - dim);
2318 static void dump_constraint_sign(struct isl_basic_map *bmap, isl_int *c,
2319 int sign, FILE *out)
2323 unsigned len = 1 + isl_basic_map_total_dim(bmap);
2327 for (i = 0, first = 1; i < len; ++i) {
2328 if (isl_int_sgn(c[i]) * sign <= 0)
2331 fprintf(out, " + ");
2333 isl_int_abs(v, c[i]);
2334 dump_term(bmap, v, i, out);
2341 static void dump_constraint(struct isl_basic_map *bmap, isl_int *c,
2342 const char *op, FILE *out, int indent)
2346 fprintf(out, "%*s", indent, "");
2348 dump_constraint_sign(bmap, c, 1, out);
2349 fprintf(out, " %s ", op);
2350 dump_constraint_sign(bmap, c, -1, out);
2354 for (i = bmap->n_div; i < bmap->extra; ++i) {
2355 if (isl_int_is_zero(c[1+isl_space_dim(bmap->dim, isl_dim_all)+i]))
2357 fprintf(out, "%*s", indent, "");
2358 fprintf(out, "ERROR: unused div coefficient not zero\n");
2363 static void dump_constraints(struct isl_basic_map *bmap,
2364 isl_int **c, unsigned n,
2365 const char *op, FILE *out, int indent)
2369 for (i = 0; i < n; ++i)
2370 dump_constraint(bmap, c[i], op, out, indent);
2373 static void dump_affine(struct isl_basic_map *bmap, isl_int *exp, FILE *out)
2377 unsigned total = isl_basic_map_total_dim(bmap);
2379 for (j = 0; j < 1 + total; ++j) {
2380 if (isl_int_is_zero(exp[j]))
2382 if (!first && isl_int_is_pos(exp[j]))
2384 dump_term(bmap, exp[j], j, out);
2389 static void dump(struct isl_basic_map *bmap, FILE *out, int indent)
2393 dump_constraints(bmap, bmap->eq, bmap->n_eq, "=", out, indent);
2394 dump_constraints(bmap, bmap->ineq, bmap->n_ineq, ">=", out, indent);
2396 for (i = 0; i < bmap->n_div; ++i) {
2397 fprintf(out, "%*s", indent, "");
2398 fprintf(out, "e%d = [(", i);
2399 dump_affine(bmap, bmap->div[i]+1, out);
2401 isl_int_print(out, bmap->div[i][0], 0);
2402 fprintf(out, "]\n");
2406 void isl_basic_set_print_internal(struct isl_basic_set *bset,
2407 FILE *out, int indent)
2410 fprintf(out, "null basic set\n");
2414 fprintf(out, "%*s", indent, "");
2415 fprintf(out, "ref: %d, nparam: %d, dim: %d, extra: %d, flags: %x\n",
2416 bset->ref, bset->dim->nparam, bset->dim->n_out,
2417 bset->extra, bset->flags);
2418 dump((struct isl_basic_map *)bset, out, indent);
2421 void isl_basic_map_print_internal(struct isl_basic_map *bmap,
2422 FILE *out, int indent)
2425 fprintf(out, "null basic map\n");
2429 fprintf(out, "%*s", indent, "");
2430 fprintf(out, "ref: %d, nparam: %d, in: %d, out: %d, extra: %d, "
2431 "flags: %x, n_name: %d\n",
2433 bmap->dim->nparam, bmap->dim->n_in, bmap->dim->n_out,
2434 bmap->extra, bmap->flags, bmap->dim->n_id);
2435 dump(bmap, out, indent);
2438 int isl_inequality_negate(struct isl_basic_map *bmap, unsigned pos)
2443 total = isl_basic_map_total_dim(bmap);
2444 isl_assert(bmap->ctx, pos < bmap->n_ineq, return -1);
2445 isl_seq_neg(bmap->ineq[pos], bmap->ineq[pos], 1 + total);
2446 isl_int_sub_ui(bmap->ineq[pos][0], bmap->ineq[pos][0], 1);
2447 ISL_F_CLR(bmap, ISL_BASIC_MAP_NORMALIZED);
2451 __isl_give isl_set *isl_set_alloc_space(__isl_take isl_space *dim, int n,
2454 struct isl_set *set;
2458 isl_assert(dim->ctx, dim->n_in == 0, goto error);
2459 isl_assert(dim->ctx, n >= 0, goto error);
2460 set = isl_alloc(dim->ctx, struct isl_set,
2461 sizeof(struct isl_set) +
2462 (n - 1) * sizeof(struct isl_basic_set *));
2466 set->ctx = dim->ctx;
2467 isl_ctx_ref(set->ctx);
2475 isl_space_free(dim);
2479 struct isl_set *isl_set_alloc(struct isl_ctx *ctx,
2480 unsigned nparam, unsigned dim, int n, unsigned flags)
2482 struct isl_set *set;
2485 dims = isl_space_alloc(ctx, nparam, 0, dim);
2489 set = isl_set_alloc_space(dims, n, flags);
2493 /* Make sure "map" has room for at least "n" more basic maps.
2495 struct isl_map *isl_map_grow(struct isl_map *map, int n)
2498 struct isl_map *grown = NULL;
2502 isl_assert(map->ctx, n >= 0, goto error);
2503 if (map->n + n <= map->size)
2505 grown = isl_map_alloc_space(isl_map_get_space(map), map->n + n, map->flags);
2508 for (i = 0; i < map->n; ++i) {
2509 grown->p[i] = isl_basic_map_copy(map->p[i]);
2517 isl_map_free(grown);
2522 /* Make sure "set" has room for at least "n" more basic sets.
2524 struct isl_set *isl_set_grow(struct isl_set *set, int n)
2526 return (struct isl_set *)isl_map_grow((struct isl_map *)set, n);
2529 struct isl_set *isl_set_dup(struct isl_set *set)
2532 struct isl_set *dup;
2537 dup = isl_set_alloc_space(isl_space_copy(set->dim), set->n, set->flags);
2540 for (i = 0; i < set->n; ++i)
2541 dup = isl_set_add_basic_set(dup, isl_basic_set_copy(set->p[i]));
2545 struct isl_set *isl_set_from_basic_set(struct isl_basic_set *bset)
2547 return isl_map_from_basic_map(bset);
2550 struct isl_map *isl_map_from_basic_map(struct isl_basic_map *bmap)
2552 struct isl_map *map;
2557 map = isl_map_alloc_space(isl_space_copy(bmap->dim), 1, ISL_MAP_DISJOINT);
2558 return isl_map_add_basic_map(map, bmap);
2561 __isl_give isl_set *isl_set_add_basic_set(__isl_take isl_set *set,
2562 __isl_take isl_basic_set *bset)
2564 return (struct isl_set *)isl_map_add_basic_map((struct isl_map *)set,
2565 (struct isl_basic_map *)bset);
2568 void *isl_set_free(__isl_take isl_set *set)
2578 isl_ctx_deref(set->ctx);
2579 for (i = 0; i < set->n; ++i)
2580 isl_basic_set_free(set->p[i]);
2581 isl_space_free(set->dim);
2587 void isl_set_print_internal(struct isl_set *set, FILE *out, int indent)
2592 fprintf(out, "null set\n");
2596 fprintf(out, "%*s", indent, "");
2597 fprintf(out, "ref: %d, n: %d, nparam: %d, dim: %d, flags: %x\n",
2598 set->ref, set->n, set->dim->nparam, set->dim->n_out,
2600 for (i = 0; i < set->n; ++i) {
2601 fprintf(out, "%*s", indent, "");
2602 fprintf(out, "basic set %d:\n", i);
2603 isl_basic_set_print_internal(set->p[i], out, indent+4);
2607 void isl_map_print_internal(struct isl_map *map, FILE *out, int indent)
2612 fprintf(out, "null map\n");
2616 fprintf(out, "%*s", indent, "");
2617 fprintf(out, "ref: %d, n: %d, nparam: %d, in: %d, out: %d, "
2618 "flags: %x, n_name: %d\n",
2619 map->ref, map->n, map->dim->nparam, map->dim->n_in,
2620 map->dim->n_out, map->flags, map->dim->n_id);
2621 for (i = 0; i < map->n; ++i) {
2622 fprintf(out, "%*s", indent, "");
2623 fprintf(out, "basic map %d:\n", i);
2624 isl_basic_map_print_internal(map->p[i], out, indent+4);
2628 struct isl_basic_map *isl_basic_map_intersect_domain(
2629 struct isl_basic_map *bmap, struct isl_basic_set *bset)
2631 struct isl_basic_map *bmap_domain;
2636 isl_assert(bset->ctx, isl_space_match(bmap->dim, isl_dim_param,
2637 bset->dim, isl_dim_param), goto error);
2639 if (isl_space_dim(bset->dim, isl_dim_set) != 0)
2640 isl_assert(bset->ctx,
2641 isl_basic_map_compatible_domain(bmap, bset), goto error);
2643 bmap = isl_basic_map_cow(bmap);
2646 bmap = isl_basic_map_extend_space(bmap, isl_space_copy(bmap->dim),
2647 bset->n_div, bset->n_eq, bset->n_ineq);
2648 bmap_domain = isl_basic_map_from_domain(bset);
2649 bmap = add_constraints(bmap, bmap_domain, 0, 0);
2651 bmap = isl_basic_map_simplify(bmap);
2652 return isl_basic_map_finalize(bmap);
2654 isl_basic_map_free(bmap);
2655 isl_basic_set_free(bset);
2659 struct isl_basic_map *isl_basic_map_intersect_range(
2660 struct isl_basic_map *bmap, struct isl_basic_set *bset)
2662 struct isl_basic_map *bmap_range;
2667 isl_assert(bset->ctx, isl_space_match(bmap->dim, isl_dim_param,
2668 bset->dim, isl_dim_param), goto error);
2670 if (isl_space_dim(bset->dim, isl_dim_set) != 0)
2671 isl_assert(bset->ctx,
2672 isl_basic_map_compatible_range(bmap, bset), goto error);
2674 if (isl_basic_set_is_universe(bset)) {
2675 isl_basic_set_free(bset);
2679 bmap = isl_basic_map_cow(bmap);
2682 bmap = isl_basic_map_extend_space(bmap, isl_space_copy(bmap->dim),
2683 bset->n_div, bset->n_eq, bset->n_ineq);
2684 bmap_range = isl_basic_map_from_basic_set(bset, isl_space_copy(bset->dim));
2685 bmap = add_constraints(bmap, bmap_range, 0, 0);
2687 bmap = isl_basic_map_simplify(bmap);
2688 return isl_basic_map_finalize(bmap);
2690 isl_basic_map_free(bmap);
2691 isl_basic_set_free(bset);
2695 int isl_basic_map_contains(struct isl_basic_map *bmap, struct isl_vec *vec)
2701 total = 1 + isl_basic_map_total_dim(bmap);
2702 if (total != vec->size)
2707 for (i = 0; i < bmap->n_eq; ++i) {
2708 isl_seq_inner_product(vec->el, bmap->eq[i], total, &s);
2709 if (!isl_int_is_zero(s)) {
2715 for (i = 0; i < bmap->n_ineq; ++i) {
2716 isl_seq_inner_product(vec->el, bmap->ineq[i], total, &s);
2717 if (isl_int_is_neg(s)) {
2728 int isl_basic_set_contains(struct isl_basic_set *bset, struct isl_vec *vec)
2730 return isl_basic_map_contains((struct isl_basic_map *)bset, vec);
2733 struct isl_basic_map *isl_basic_map_intersect(
2734 struct isl_basic_map *bmap1, struct isl_basic_map *bmap2)
2736 struct isl_vec *sample = NULL;
2738 if (!bmap1 || !bmap2)
2741 isl_assert(bmap1->ctx, isl_space_match(bmap1->dim, isl_dim_param,
2742 bmap2->dim, isl_dim_param), goto error);
2743 if (isl_space_dim(bmap1->dim, isl_dim_all) ==
2744 isl_space_dim(bmap1->dim, isl_dim_param) &&
2745 isl_space_dim(bmap2->dim, isl_dim_all) !=
2746 isl_space_dim(bmap2->dim, isl_dim_param))
2747 return isl_basic_map_intersect(bmap2, bmap1);
2749 if (isl_space_dim(bmap2->dim, isl_dim_all) !=
2750 isl_space_dim(bmap2->dim, isl_dim_param))
2751 isl_assert(bmap1->ctx,
2752 isl_space_is_equal(bmap1->dim, bmap2->dim), goto error);
2754 if (bmap1->sample &&
2755 isl_basic_map_contains(bmap1, bmap1->sample) > 0 &&
2756 isl_basic_map_contains(bmap2, bmap1->sample) > 0)
2757 sample = isl_vec_copy(bmap1->sample);
2758 else if (bmap2->sample &&
2759 isl_basic_map_contains(bmap1, bmap2->sample) > 0 &&
2760 isl_basic_map_contains(bmap2, bmap2->sample) > 0)
2761 sample = isl_vec_copy(bmap2->sample);
2763 bmap1 = isl_basic_map_cow(bmap1);
2766 bmap1 = isl_basic_map_extend_space(bmap1, isl_space_copy(bmap1->dim),
2767 bmap2->n_div, bmap2->n_eq, bmap2->n_ineq);
2768 bmap1 = add_constraints(bmap1, bmap2, 0, 0);
2771 isl_vec_free(sample);
2773 isl_vec_free(bmap1->sample);
2774 bmap1->sample = sample;
2777 bmap1 = isl_basic_map_simplify(bmap1);
2778 return isl_basic_map_finalize(bmap1);
2781 isl_vec_free(sample);
2782 isl_basic_map_free(bmap1);
2783 isl_basic_map_free(bmap2);
2787 struct isl_basic_set *isl_basic_set_intersect(
2788 struct isl_basic_set *bset1, struct isl_basic_set *bset2)
2790 return (struct isl_basic_set *)
2791 isl_basic_map_intersect(
2792 (struct isl_basic_map *)bset1,
2793 (struct isl_basic_map *)bset2);
2796 __isl_give isl_basic_set *isl_basic_set_intersect_params(
2797 __isl_take isl_basic_set *bset1, __isl_take isl_basic_set *bset2)
2799 return isl_basic_set_intersect(bset1, bset2);
2802 /* Special case of isl_map_intersect, where both map1 and map2
2803 * are convex, without any divs and such that either map1 or map2
2804 * contains a single constraint. This constraint is then simply
2805 * added to the other map.
2807 static __isl_give isl_map *map_intersect_add_constraint(
2808 __isl_take isl_map *map1, __isl_take isl_map *map2)
2810 isl_assert(map1->ctx, map1->n == 1, goto error);
2811 isl_assert(map2->ctx, map1->n == 1, goto error);
2812 isl_assert(map1->ctx, map1->p[0]->n_div == 0, goto error);
2813 isl_assert(map2->ctx, map1->p[0]->n_div == 0, goto error);
2815 if (map2->p[0]->n_eq + map2->p[0]->n_ineq != 1)
2816 return isl_map_intersect(map2, map1);
2818 isl_assert(map2->ctx,
2819 map2->p[0]->n_eq + map2->p[0]->n_ineq == 1, goto error);
2821 map1 = isl_map_cow(map1);
2824 if (isl_map_plain_is_empty(map1)) {
2828 map1->p[0] = isl_basic_map_cow(map1->p[0]);
2829 if (map2->p[0]->n_eq == 1)
2830 map1->p[0] = isl_basic_map_add_eq(map1->p[0], map2->p[0]->eq[0]);
2832 map1->p[0] = isl_basic_map_add_ineq(map1->p[0],
2833 map2->p[0]->ineq[0]);
2835 map1->p[0] = isl_basic_map_simplify(map1->p[0]);
2836 map1->p[0] = isl_basic_map_finalize(map1->p[0]);
2840 if (isl_basic_map_plain_is_empty(map1->p[0])) {
2841 isl_basic_map_free(map1->p[0]);
2854 /* map2 may be either a parameter domain or a map living in the same
2857 static __isl_give isl_map *map_intersect_internal(__isl_take isl_map *map1,
2858 __isl_take isl_map *map2)
2861 struct isl_map *result;
2867 if ((isl_map_plain_is_empty(map1) ||
2868 isl_map_plain_is_universe(map2)) &&
2869 isl_space_is_equal(map1->dim, map2->dim)) {
2873 if ((isl_map_plain_is_empty(map2) ||
2874 isl_map_plain_is_universe(map1)) &&
2875 isl_space_is_equal(map1->dim, map2->dim)) {
2880 if (map1->n == 1 && map2->n == 1 &&
2881 map1->p[0]->n_div == 0 && map2->p[0]->n_div == 0 &&
2882 isl_space_is_equal(map1->dim, map2->dim) &&
2883 (map1->p[0]->n_eq + map1->p[0]->n_ineq == 1 ||
2884 map2->p[0]->n_eq + map2->p[0]->n_ineq == 1))
2885 return map_intersect_add_constraint(map1, map2);
2887 if (isl_space_dim(map2->dim, isl_dim_all) !=
2888 isl_space_dim(map2->dim, isl_dim_param))
2889 isl_assert(map1->ctx,
2890 isl_space_is_equal(map1->dim, map2->dim), goto error);
2892 if (ISL_F_ISSET(map1, ISL_MAP_DISJOINT) &&
2893 ISL_F_ISSET(map2, ISL_MAP_DISJOINT))
2894 ISL_FL_SET(flags, ISL_MAP_DISJOINT);
2896 result = isl_map_alloc_space(isl_space_copy(map1->dim),
2897 map1->n * map2->n, flags);
2900 for (i = 0; i < map1->n; ++i)
2901 for (j = 0; j < map2->n; ++j) {
2902 struct isl_basic_map *part;
2903 part = isl_basic_map_intersect(
2904 isl_basic_map_copy(map1->p[i]),
2905 isl_basic_map_copy(map2->p[j]));
2906 if (isl_basic_map_is_empty(part) < 0)
2908 result = isl_map_add_basic_map(result, part);
2921 static __isl_give isl_map *map_intersect(__isl_take isl_map *map1,
2922 __isl_take isl_map *map2)
2926 if (!isl_space_is_equal(map1->dim, map2->dim))
2927 isl_die(isl_map_get_ctx(map1), isl_error_invalid,
2928 "spaces don't match", goto error);
2929 return map_intersect_internal(map1, map2);
2936 __isl_give isl_map *isl_map_intersect(__isl_take isl_map *map1,
2937 __isl_take isl_map *map2)
2939 return isl_map_align_params_map_map_and(map1, map2, &map_intersect);
2942 struct isl_set *isl_set_intersect(struct isl_set *set1, struct isl_set *set2)
2944 return (struct isl_set *)
2945 isl_map_intersect((struct isl_map *)set1,
2946 (struct isl_map *)set2);
2949 /* map_intersect_internal accepts intersections
2950 * with parameter domains, so we can just call that function.
2952 static __isl_give isl_map *map_intersect_params(__isl_take isl_map *map,
2953 __isl_take isl_set *params)
2955 return map_intersect_internal(map, params);
2958 __isl_give isl_map *isl_map_intersect_params(__isl_take isl_map *map1,
2959 __isl_take isl_map *map2)
2961 return isl_map_align_params_map_map_and(map1, map2, &map_intersect_params);
2964 __isl_give isl_set *isl_set_intersect_params(__isl_take isl_set *set,
2965 __isl_take isl_set *params)
2967 return isl_map_intersect_params(set, params);
2970 struct isl_basic_map *isl_basic_map_reverse(struct isl_basic_map *bmap)
2973 struct isl_basic_set *bset;
2978 bmap = isl_basic_map_cow(bmap);
2981 dim = isl_space_reverse(isl_space_copy(bmap->dim));
2982 in = isl_basic_map_n_in(bmap);
2983 bset = isl_basic_set_from_basic_map(bmap);
2984 bset = isl_basic_set_swap_vars(bset, in);
2985 return isl_basic_map_from_basic_set(bset, dim);
2988 static __isl_give isl_basic_map *basic_map_space_reset(
2989 __isl_take isl_basic_map *bmap, enum isl_dim_type type)
2993 if (!isl_space_is_named_or_nested(bmap->dim, type))
2996 space = isl_basic_map_get_space(bmap);
2997 space = isl_space_reset(space, type);
2998 bmap = isl_basic_map_reset_space(bmap, space);
3002 __isl_give isl_basic_map *isl_basic_map_insert_dims(
3003 __isl_take isl_basic_map *bmap, enum isl_dim_type type,
3004 unsigned pos, unsigned n)
3007 struct isl_basic_map *res;
3008 struct isl_dim_map *dim_map;
3009 unsigned total, off;
3010 enum isl_dim_type t;
3013 return basic_map_space_reset(bmap, type);
3018 res_dim = isl_space_insert_dims(isl_basic_map_get_space(bmap), type, pos, n);
3020 total = isl_basic_map_total_dim(bmap) + n;
3021 dim_map = isl_dim_map_alloc(bmap->ctx, total);
3023 for (t = isl_dim_param; t <= isl_dim_out; ++t) {
3025 isl_dim_map_dim(dim_map, bmap->dim, t, off);
3027 unsigned size = isl_basic_map_dim(bmap, t);
3028 isl_dim_map_dim_range(dim_map, bmap->dim, t,
3030 isl_dim_map_dim_range(dim_map, bmap->dim, t,
3031 pos, size - pos, off + pos + n);
3033 off += isl_space_dim(res_dim, t);
3035 isl_dim_map_div(dim_map, bmap, off);
3037 res = isl_basic_map_alloc_space(res_dim,
3038 bmap->n_div, bmap->n_eq, bmap->n_ineq);
3039 if (isl_basic_map_is_rational(bmap))
3040 res = isl_basic_map_set_rational(res);
3041 if (isl_basic_map_plain_is_empty(bmap)) {
3042 isl_basic_map_free(bmap);
3043 return isl_basic_map_set_to_empty(res);
3045 res = isl_basic_map_add_constraints_dim_map(res, bmap, dim_map);
3046 return isl_basic_map_finalize(res);
3049 __isl_give isl_basic_set *isl_basic_set_insert_dims(
3050 __isl_take isl_basic_set *bset,
3051 enum isl_dim_type type, unsigned pos, unsigned n)
3053 return isl_basic_map_insert_dims(bset, type, pos, n);
3056 __isl_give isl_basic_map *isl_basic_map_add(__isl_take isl_basic_map *bmap,
3057 enum isl_dim_type type, unsigned n)
3061 return isl_basic_map_insert_dims(bmap, type,
3062 isl_basic_map_dim(bmap, type), n);
3065 __isl_give isl_basic_set *isl_basic_set_add(__isl_take isl_basic_set *bset,
3066 enum isl_dim_type type, unsigned n)
3070 isl_assert(bset->ctx, type != isl_dim_in, goto error);
3071 return (isl_basic_set *)isl_basic_map_add((isl_basic_map *)bset, type, n);
3073 isl_basic_set_free(bset);
3077 static __isl_give isl_map *map_space_reset(__isl_take isl_map *map,
3078 enum isl_dim_type type)
3082 if (!map || !isl_space_is_named_or_nested(map->dim, type))
3085 space = isl_map_get_space(map);
3086 space = isl_space_reset(space, type);
3087 map = isl_map_reset_space(map, space);
3091 __isl_give isl_map *isl_map_insert_dims(__isl_take isl_map *map,
3092 enum isl_dim_type type, unsigned pos, unsigned n)
3097 return map_space_reset(map, type);
3099 map = isl_map_cow(map);
3103 map->dim = isl_space_insert_dims(map->dim, type, pos, n);
3107 for (i = 0; i < map->n; ++i) {
3108 map->p[i] = isl_basic_map_insert_dims(map->p[i], type, pos, n);
3119 __isl_give isl_set *isl_set_insert_dims(__isl_take isl_set *set,
3120 enum isl_dim_type type, unsigned pos, unsigned n)
3122 return isl_map_insert_dims(set, type, pos, n);
3125 __isl_give isl_map *isl_map_add_dims(__isl_take isl_map *map,
3126 enum isl_dim_type type, unsigned n)
3130 return isl_map_insert_dims(map, type, isl_map_dim(map, type), n);
3133 __isl_give isl_set *isl_set_add_dims(__isl_take isl_set *set,
3134 enum isl_dim_type type, unsigned n)
3138 isl_assert(set->ctx, type != isl_dim_in, goto error);
3139 return (isl_set *)isl_map_add_dims((isl_map *)set, type, n);
3145 __isl_give isl_basic_map *isl_basic_map_move_dims(
3146 __isl_take isl_basic_map *bmap,
3147 enum isl_dim_type dst_type, unsigned dst_pos,
3148 enum isl_dim_type src_type, unsigned src_pos, unsigned n)
3150 struct isl_dim_map *dim_map;
3151 struct isl_basic_map *res;
3152 enum isl_dim_type t;
3153 unsigned total, off;
3160 isl_assert(bmap->ctx, src_pos + n <= isl_basic_map_dim(bmap, src_type),
3163 if (dst_type == src_type && dst_pos == src_pos)
3166 isl_assert(bmap->ctx, dst_type != src_type, goto error);
3168 if (pos(bmap->dim, dst_type) + dst_pos ==
3169 pos(bmap->dim, src_type) + src_pos +
3170 ((src_type < dst_type) ? n : 0)) {
3171 bmap = isl_basic_map_cow(bmap);
3175 bmap->dim = isl_space_move_dims(bmap->dim, dst_type, dst_pos,
3176 src_type, src_pos, n);
3180 bmap = isl_basic_map_finalize(bmap);
3185 total = isl_basic_map_total_dim(bmap);
3186 dim_map = isl_dim_map_alloc(bmap->ctx, total);
3189 for (t = isl_dim_param; t <= isl_dim_out; ++t) {
3190 unsigned size = isl_space_dim(bmap->dim, t);
3191 if (t == dst_type) {
3192 isl_dim_map_dim_range(dim_map, bmap->dim, t,
3195 isl_dim_map_dim_range(dim_map, bmap->dim, src_type,
3198 isl_dim_map_dim_range(dim_map, bmap->dim, t,
3199 dst_pos, size - dst_pos, off);
3200 off += size - dst_pos;
3201 } else if (t == src_type) {
3202 isl_dim_map_dim_range(dim_map, bmap->dim, t,
3205 isl_dim_map_dim_range(dim_map, bmap->dim, t,
3206 src_pos + n, size - src_pos - n, off);
3207 off += size - src_pos - n;
3209 isl_dim_map_dim(dim_map, bmap->dim, t, off);
3213 isl_dim_map_div(dim_map, bmap, off);
3215 res = isl_basic_map_alloc_space(isl_basic_map_get_space(bmap),
3216 bmap->n_div, bmap->n_eq, bmap->n_ineq);
3217 bmap = isl_basic_map_add_constraints_dim_map(res, bmap, dim_map);
3219 bmap->dim = isl_space_move_dims(bmap->dim, dst_type, dst_pos,
3220 src_type, src_pos, n);
3224 ISL_F_CLR(bmap, ISL_BASIC_MAP_NORMALIZED);
3225 bmap = isl_basic_map_gauss(bmap, NULL);
3226 bmap = isl_basic_map_finalize(bmap);
3230 isl_basic_map_free(bmap);
3234 __isl_give isl_basic_set *isl_basic_set_move_dims(__isl_take isl_basic_set *bset,
3235 enum isl_dim_type dst_type, unsigned dst_pos,
3236 enum isl_dim_type src_type, unsigned src_pos, unsigned n)
3238 return (isl_basic_set *)isl_basic_map_move_dims(
3239 (isl_basic_map *)bset, dst_type, dst_pos, src_type, src_pos, n);
3242 __isl_give isl_set *isl_set_move_dims(__isl_take isl_set *set,
3243 enum isl_dim_type dst_type, unsigned dst_pos,
3244 enum isl_dim_type src_type, unsigned src_pos, unsigned n)
3248 isl_assert(set->ctx, dst_type != isl_dim_in, goto error);
3249 return (isl_set *)isl_map_move_dims((isl_map *)set, dst_type, dst_pos,
3250 src_type, src_pos, n);
3256 __isl_give isl_map *isl_map_move_dims(__isl_take isl_map *map,
3257 enum isl_dim_type dst_type, unsigned dst_pos,
3258 enum isl_dim_type src_type, unsigned src_pos, unsigned n)
3267 isl_assert(map->ctx, src_pos + n <= isl_map_dim(map, src_type),
3270 if (dst_type == src_type && dst_pos == src_pos)
3273 isl_assert(map->ctx, dst_type != src_type, goto error);
3275 map = isl_map_cow(map);
3279 map->dim = isl_space_move_dims(map->dim, dst_type, dst_pos, src_type, src_pos, n);
3283 for (i = 0; i < map->n; ++i) {
3284 map->p[i] = isl_basic_map_move_dims(map->p[i],
3286 src_type, src_pos, n);
3297 /* Move the specified dimensions to the last columns right before
3298 * the divs. Don't change the dimension specification of bmap.
3299 * That's the responsibility of the caller.
3301 static __isl_give isl_basic_map *move_last(__isl_take isl_basic_map *bmap,
3302 enum isl_dim_type type, unsigned first, unsigned n)
3304 struct isl_dim_map *dim_map;
3305 struct isl_basic_map *res;
3306 enum isl_dim_type t;
3307 unsigned total, off;
3311 if (pos(bmap->dim, type) + first + n ==
3312 1 + isl_space_dim(bmap->dim, isl_dim_all))
3315 total = isl_basic_map_total_dim(bmap);
3316 dim_map = isl_dim_map_alloc(bmap->ctx, total);
3319 for (t = isl_dim_param; t <= isl_dim_out; ++t) {
3320 unsigned size = isl_space_dim(bmap->dim, t);
3322 isl_dim_map_dim_range(dim_map, bmap->dim, t,
3325 isl_dim_map_dim_range(dim_map, bmap->dim, t,
3326 first, n, total - bmap->n_div - n);
3327 isl_dim_map_dim_range(dim_map, bmap->dim, t,
3328 first + n, size - (first + n), off);
3329 off += size - (first + n);
3331 isl_dim_map_dim(dim_map, bmap->dim, t, off);
3335 isl_dim_map_div(dim_map, bmap, off + n);
3337 res = isl_basic_map_alloc_space(isl_basic_map_get_space(bmap),
3338 bmap->n_div, bmap->n_eq, bmap->n_ineq);
3339 res = isl_basic_map_add_constraints_dim_map(res, bmap, dim_map);
3343 /* Turn the n dimensions of type type, starting at first
3344 * into existentially quantified variables.
3346 __isl_give isl_basic_map *isl_basic_map_project_out(
3347 __isl_take isl_basic_map *bmap,
3348 enum isl_dim_type type, unsigned first, unsigned n)
3356 return basic_map_space_reset(bmap, type);
3361 if (ISL_F_ISSET(bmap, ISL_BASIC_MAP_RATIONAL))
3362 return isl_basic_map_remove_dims(bmap, type, first, n);
3364 isl_assert(bmap->ctx, first + n <= isl_basic_map_dim(bmap, type),
3367 bmap = move_last(bmap, type, first, n);
3368 bmap = isl_basic_map_cow(bmap);
3372 row_size = 1 + isl_space_dim(bmap->dim, isl_dim_all) + bmap->extra;
3373 old = bmap->block2.data;
3374 bmap->block2 = isl_blk_extend(bmap->ctx, bmap->block2,
3375 (bmap->extra + n) * (1 + row_size));
3376 if (!bmap->block2.data)
3378 new_div = isl_alloc_array(bmap->ctx, isl_int *, bmap->extra + n);
3381 for (i = 0; i < n; ++i) {
3382 new_div[i] = bmap->block2.data +
3383 (bmap->extra + i) * (1 + row_size);
3384 isl_seq_clr(new_div[i], 1 + row_size);
3386 for (i = 0; i < bmap->extra; ++i)
3387 new_div[n + i] = bmap->block2.data + (bmap->div[i] - old);
3389 bmap->div = new_div;
3393 bmap->dim = isl_space_drop_dims(bmap->dim, type, first, n);
3396 bmap = isl_basic_map_simplify(bmap);
3397 bmap = isl_basic_map_drop_redundant_divs(bmap);
3398 return isl_basic_map_finalize(bmap);
3400 isl_basic_map_free(bmap);
3404 /* Turn the n dimensions of type type, starting at first
3405 * into existentially quantified variables.
3407 struct isl_basic_set *isl_basic_set_project_out(struct isl_basic_set *bset,
3408 enum isl_dim_type type, unsigned first, unsigned n)
3410 return (isl_basic_set *)isl_basic_map_project_out(
3411 (isl_basic_map *)bset, type, first, n);
3414 /* Turn the n dimensions of type type, starting at first
3415 * into existentially quantified variables.
3417 __isl_give isl_map *isl_map_project_out(__isl_take isl_map *map,
3418 enum isl_dim_type type, unsigned first, unsigned n)
3426 return map_space_reset(map, type);
3428 isl_assert(map->ctx, first + n <= isl_map_dim(map, type), goto error);
3430 map = isl_map_cow(map);
3434 map->dim = isl_space_drop_dims(map->dim, type, first, n);
3438 for (i = 0; i < map->n; ++i) {
3439 map->p[i] = isl_basic_map_project_out(map->p[i], type, first, n);
3450 /* Turn the n dimensions of type type, starting at first
3451 * into existentially quantified variables.
3453 __isl_give isl_set *isl_set_project_out(__isl_take isl_set *set,
3454 enum isl_dim_type type, unsigned first, unsigned n)
3456 return (isl_set *)isl_map_project_out((isl_map *)set, type, first, n);
3459 static struct isl_basic_map *add_divs(struct isl_basic_map *bmap, unsigned n)
3463 for (i = 0; i < n; ++i) {
3464 j = isl_basic_map_alloc_div(bmap);
3467 isl_seq_clr(bmap->div[j], 1+1+isl_basic_map_total_dim(bmap));
3471 isl_basic_map_free(bmap);
3475 struct isl_basic_map *isl_basic_map_apply_range(
3476 struct isl_basic_map *bmap1, struct isl_basic_map *bmap2)
3478 isl_space *dim_result = NULL;
3479 struct isl_basic_map *bmap;
3480 unsigned n_in, n_out, n, nparam, total, pos;
3481 struct isl_dim_map *dim_map1, *dim_map2;
3483 if (!bmap1 || !bmap2)
3486 dim_result = isl_space_join(isl_space_copy(bmap1->dim),
3487 isl_space_copy(bmap2->dim));
3489 n_in = isl_basic_map_n_in(bmap1);
3490 n_out = isl_basic_map_n_out(bmap2);
3491 n = isl_basic_map_n_out(bmap1);
3492 nparam = isl_basic_map_n_param(bmap1);
3494 total = nparam + n_in + n_out + bmap1->n_div + bmap2->n_div + n;
3495 dim_map1 = isl_dim_map_alloc(bmap1->ctx, total);
3496 dim_map2 = isl_dim_map_alloc(bmap1->ctx, total);
3497 isl_dim_map_dim(dim_map1, bmap1->dim, isl_dim_param, pos = 0);
3498 isl_dim_map_dim(dim_map2, bmap2->dim, isl_dim_param, pos = 0);
3499 isl_dim_map_dim(dim_map1, bmap1->dim, isl_dim_in, pos += nparam);
3500 isl_dim_map_dim(dim_map2, bmap2->dim, isl_dim_out, pos += n_in);
3501 isl_dim_map_div(dim_map1, bmap1, pos += n_out);
3502 isl_dim_map_div(dim_map2, bmap2, pos += bmap1->n_div);
3503 isl_dim_map_dim(dim_map1, bmap1->dim, isl_dim_out, pos += bmap2->n_div);
3504 isl_dim_map_dim(dim_map2, bmap2->dim, isl_dim_in, pos);
3506 bmap = isl_basic_map_alloc_space(dim_result,
3507 bmap1->n_div + bmap2->n_div + n,
3508 bmap1->n_eq + bmap2->n_eq,
3509 bmap1->n_ineq + bmap2->n_ineq);
3510 bmap = isl_basic_map_add_constraints_dim_map(bmap, bmap1, dim_map1);
3511 bmap = isl_basic_map_add_constraints_dim_map(bmap, bmap2, dim_map2);
3512 bmap = add_divs(bmap, n);
3513 bmap = isl_basic_map_simplify(bmap);
3514 bmap = isl_basic_map_drop_redundant_divs(bmap);
3515 return isl_basic_map_finalize(bmap);
3517 isl_basic_map_free(bmap1);
3518 isl_basic_map_free(bmap2);
3522 struct isl_basic_set *isl_basic_set_apply(
3523 struct isl_basic_set *bset, struct isl_basic_map *bmap)
3528 isl_assert(bset->ctx, isl_basic_map_compatible_domain(bmap, bset),
3531 return (struct isl_basic_set *)
3532 isl_basic_map_apply_range((struct isl_basic_map *)bset, bmap);
3534 isl_basic_set_free(bset);
3535 isl_basic_map_free(bmap);
3539 struct isl_basic_map *isl_basic_map_apply_domain(
3540 struct isl_basic_map *bmap1, struct isl_basic_map *bmap2)
3542 if (!bmap1 || !bmap2)
3545 isl_assert(bmap1->ctx,
3546 isl_basic_map_n_in(bmap1) == isl_basic_map_n_in(bmap2), goto error);
3547 isl_assert(bmap1->ctx,
3548 isl_basic_map_n_param(bmap1) == isl_basic_map_n_param(bmap2),
3551 bmap1 = isl_basic_map_reverse(bmap1);
3552 bmap1 = isl_basic_map_apply_range(bmap1, bmap2);
3553 return isl_basic_map_reverse(bmap1);
3555 isl_basic_map_free(bmap1);
3556 isl_basic_map_free(bmap2);
3560 /* Given two basic maps A -> f(A) and B -> g(B), construct a basic map
3561 * A \cap B -> f(A) + f(B)
3563 struct isl_basic_map *isl_basic_map_sum(
3564 struct isl_basic_map *bmap1, struct isl_basic_map *bmap2)
3566 unsigned n_in, n_out, nparam, total, pos;
3567 struct isl_basic_map *bmap = NULL;
3568 struct isl_dim_map *dim_map1, *dim_map2;
3571 if (!bmap1 || !bmap2)
3574 isl_assert(bmap1->ctx, isl_space_is_equal(bmap1->dim, bmap2->dim),
3577 nparam = isl_basic_map_n_param(bmap1);
3578 n_in = isl_basic_map_n_in(bmap1);
3579 n_out = isl_basic_map_n_out(bmap1);
3581 total = nparam + n_in + n_out + bmap1->n_div + bmap2->n_div + 2 * n_out;
3582 dim_map1 = isl_dim_map_alloc(bmap1->ctx, total);
3583 dim_map2 = isl_dim_map_alloc(bmap2->ctx, total);
3584 isl_dim_map_dim(dim_map1, bmap1->dim, isl_dim_param, pos = 0);
3585 isl_dim_map_dim(dim_map2, bmap2->dim, isl_dim_param, pos);
3586 isl_dim_map_dim(dim_map1, bmap1->dim, isl_dim_in, pos += nparam);
3587 isl_dim_map_dim(dim_map2, bmap2->dim, isl_dim_in, pos);
3588 isl_dim_map_div(dim_map1, bmap1, pos += n_in + n_out);
3589 isl_dim_map_div(dim_map2, bmap2, pos += bmap1->n_div);
3590 isl_dim_map_dim(dim_map1, bmap1->dim, isl_dim_out, pos += bmap2->n_div);
3591 isl_dim_map_dim(dim_map2, bmap2->dim, isl_dim_out, pos += n_out);
3593 bmap = isl_basic_map_alloc_space(isl_space_copy(bmap1->dim),
3594 bmap1->n_div + bmap2->n_div + 2 * n_out,
3595 bmap1->n_eq + bmap2->n_eq + n_out,
3596 bmap1->n_ineq + bmap2->n_ineq);
3597 for (i = 0; i < n_out; ++i) {
3598 int j = isl_basic_map_alloc_equality(bmap);
3601 isl_seq_clr(bmap->eq[j], 1+total);
3602 isl_int_set_si(bmap->eq[j][1+nparam+n_in+i], -1);
3603 isl_int_set_si(bmap->eq[j][1+pos+i], 1);
3604 isl_int_set_si(bmap->eq[j][1+pos-n_out+i], 1);
3606 bmap = isl_basic_map_add_constraints_dim_map(bmap, bmap1, dim_map1);
3607 bmap = isl_basic_map_add_constraints_dim_map(bmap, bmap2, dim_map2);
3608 bmap = add_divs(bmap, 2 * n_out);
3610 bmap = isl_basic_map_simplify(bmap);
3611 return isl_basic_map_finalize(bmap);
3613 isl_basic_map_free(bmap);
3614 isl_basic_map_free(bmap1);
3615 isl_basic_map_free(bmap2);
3619 /* Given two maps A -> f(A) and B -> g(B), construct a map
3620 * A \cap B -> f(A) + f(B)
3622 struct isl_map *isl_map_sum(struct isl_map *map1, struct isl_map *map2)
3624 struct isl_map *result;
3630 isl_assert(map1->ctx, isl_space_is_equal(map1->dim, map2->dim), goto error);
3632 result = isl_map_alloc_space(isl_space_copy(map1->dim),
3633 map1->n * map2->n, 0);
3636 for (i = 0; i < map1->n; ++i)
3637 for (j = 0; j < map2->n; ++j) {
3638 struct isl_basic_map *part;
3639 part = isl_basic_map_sum(
3640 isl_basic_map_copy(map1->p[i]),
3641 isl_basic_map_copy(map2->p[j]));
3642 if (isl_basic_map_is_empty(part))
3643 isl_basic_map_free(part);
3645 result = isl_map_add_basic_map(result, part);
3658 __isl_give isl_set *isl_set_sum(__isl_take isl_set *set1,
3659 __isl_take isl_set *set2)
3661 return (isl_set *)isl_map_sum((isl_map *)set1, (isl_map *)set2);
3664 /* Given a basic map A -> f(A), construct A -> -f(A).
3666 struct isl_basic_map *isl_basic_map_neg(struct isl_basic_map *bmap)
3671 bmap = isl_basic_map_cow(bmap);
3675 n = isl_basic_map_dim(bmap, isl_dim_out);
3676 off = isl_basic_map_offset(bmap, isl_dim_out);
3677 for (i = 0; i < bmap->n_eq; ++i)
3678 for (j = 0; j < n; ++j)
3679 isl_int_neg(bmap->eq[i][off+j], bmap->eq[i][off+j]);
3680 for (i = 0; i < bmap->n_ineq; ++i)
3681 for (j = 0; j < n; ++j)
3682 isl_int_neg(bmap->ineq[i][off+j], bmap->ineq[i][off+j]);
3683 for (i = 0; i < bmap->n_div; ++i)
3684 for (j = 0; j < n; ++j)
3685 isl_int_neg(bmap->div[i][1+off+j], bmap->div[i][1+off+j]);
3686 bmap = isl_basic_map_gauss(bmap, NULL);
3687 return isl_basic_map_finalize(bmap);
3690 __isl_give isl_basic_set *isl_basic_set_neg(__isl_take isl_basic_set *bset)
3692 return isl_basic_map_neg(bset);
3695 /* Given a map A -> f(A), construct A -> -f(A).
3697 struct isl_map *isl_map_neg(struct isl_map *map)
3701 map = isl_map_cow(map);
3705 for (i = 0; i < map->n; ++i) {
3706 map->p[i] = isl_basic_map_neg(map->p[i]);
3717 __isl_give isl_set *isl_set_neg(__isl_take isl_set *set)
3719 return (isl_set *)isl_map_neg((isl_map *)set);
3722 /* Given a basic map A -> f(A) and an integer d, construct a basic map
3723 * A -> floor(f(A)/d).
3725 struct isl_basic_map *isl_basic_map_floordiv(struct isl_basic_map *bmap,
3728 unsigned n_in, n_out, nparam, total, pos;
3729 struct isl_basic_map *result = NULL;
3730 struct isl_dim_map *dim_map;
3736 nparam = isl_basic_map_n_param(bmap);
3737 n_in = isl_basic_map_n_in(bmap);
3738 n_out = isl_basic_map_n_out(bmap);
3740 total = nparam + n_in + n_out + bmap->n_div + n_out;
3741 dim_map = isl_dim_map_alloc(bmap->ctx, total);
3742 isl_dim_map_dim(dim_map, bmap->dim, isl_dim_param, pos = 0);
3743 isl_dim_map_dim(dim_map, bmap->dim, isl_dim_in, pos += nparam);
3744 isl_dim_map_div(dim_map, bmap, pos += n_in + n_out);
3745 isl_dim_map_dim(dim_map, bmap->dim, isl_dim_out, pos += bmap->n_div);
3747 result = isl_basic_map_alloc_space(isl_space_copy(bmap->dim),
3748 bmap->n_div + n_out,
3749 bmap->n_eq, bmap->n_ineq + 2 * n_out);
3750 result = isl_basic_map_add_constraints_dim_map(result, bmap, dim_map);
3751 result = add_divs(result, n_out);
3752 for (i = 0; i < n_out; ++i) {
3754 j = isl_basic_map_alloc_inequality(result);
3757 isl_seq_clr(result->ineq[j], 1+total);
3758 isl_int_neg(result->ineq[j][1+nparam+n_in+i], d);
3759 isl_int_set_si(result->ineq[j][1+pos+i], 1);
3760 j = isl_basic_map_alloc_inequality(result);
3763 isl_seq_clr(result->ineq[j], 1+total);
3764 isl_int_set(result->ineq[j][1+nparam+n_in+i], d);
3765 isl_int_set_si(result->ineq[j][1+pos+i], -1);
3766 isl_int_sub_ui(result->ineq[j][0], d, 1);
3769 result = isl_basic_map_simplify(result);
3770 return isl_basic_map_finalize(result);
3772 isl_basic_map_free(result);
3776 /* Given a map A -> f(A) and an integer d, construct a map
3777 * A -> floor(f(A)/d).
3779 struct isl_map *isl_map_floordiv(struct isl_map *map, isl_int d)
3783 map = isl_map_cow(map);
3787 ISL_F_CLR(map, ISL_MAP_DISJOINT);
3788 ISL_F_CLR(map, ISL_MAP_NORMALIZED);
3789 for (i = 0; i < map->n; ++i) {
3790 map->p[i] = isl_basic_map_floordiv(map->p[i], d);
3801 static struct isl_basic_map *var_equal(struct isl_basic_map *bmap, unsigned pos)
3807 i = isl_basic_map_alloc_equality(bmap);
3810 nparam = isl_basic_map_n_param(bmap);
3811 n_in = isl_basic_map_n_in(bmap);
3812 isl_seq_clr(bmap->eq[i], 1 + isl_basic_map_total_dim(bmap));
3813 isl_int_set_si(bmap->eq[i][1+nparam+pos], -1);
3814 isl_int_set_si(bmap->eq[i][1+nparam+n_in+pos], 1);
3815 return isl_basic_map_finalize(bmap);
3817 isl_basic_map_free(bmap);
3821 /* Add a constraints to "bmap" expressing i_pos < o_pos
3823 static struct isl_basic_map *var_less(struct isl_basic_map *bmap, unsigned pos)
3829 i = isl_basic_map_alloc_inequality(bmap);
3832 nparam = isl_basic_map_n_param(bmap);
3833 n_in = isl_basic_map_n_in(bmap);
3834 isl_seq_clr(bmap->ineq[i], 1 + isl_basic_map_total_dim(bmap));
3835 isl_int_set_si(bmap->ineq[i][0], -1);
3836 isl_int_set_si(bmap->ineq[i][1+nparam+pos], -1);
3837 isl_int_set_si(bmap->ineq[i][1+nparam+n_in+pos], 1);
3838 return isl_basic_map_finalize(bmap);
3840 isl_basic_map_free(bmap);
3844 /* Add a constraint to "bmap" expressing i_pos <= o_pos
3846 static __isl_give isl_basic_map *var_less_or_equal(
3847 __isl_take isl_basic_map *bmap, unsigned pos)
3853 i = isl_basic_map_alloc_inequality(bmap);
3856 nparam = isl_basic_map_n_param(bmap);
3857 n_in = isl_basic_map_n_in(bmap);
3858 isl_seq_clr(bmap->ineq[i], 1 + isl_basic_map_total_dim(bmap));
3859 isl_int_set_si(bmap->ineq[i][1+nparam+pos], -1);
3860 isl_int_set_si(bmap->ineq[i][1+nparam+n_in+pos], 1);
3861 return isl_basic_map_finalize(bmap);
3863 isl_basic_map_free(bmap);
3867 /* Add a constraints to "bmap" expressing i_pos > o_pos
3869 static struct isl_basic_map *var_more(struct isl_basic_map *bmap, unsigned pos)
3875 i = isl_basic_map_alloc_inequality(bmap);
3878 nparam = isl_basic_map_n_param(bmap);
3879 n_in = isl_basic_map_n_in(bmap);
3880 isl_seq_clr(bmap->ineq[i], 1 + isl_basic_map_total_dim(bmap));
3881 isl_int_set_si(bmap->ineq[i][0], -1);
3882 isl_int_set_si(bmap->ineq[i][1+nparam+pos], 1);
3883 isl_int_set_si(bmap->ineq[i][1+nparam+n_in+pos], -1);
3884 return isl_basic_map_finalize(bmap);
3886 isl_basic_map_free(bmap);
3890 /* Add a constraint to "bmap" expressing i_pos >= o_pos
3892 static __isl_give isl_basic_map *var_more_or_equal(
3893 __isl_take isl_basic_map *bmap, unsigned pos)
3899 i = isl_basic_map_alloc_inequality(bmap);
3902 nparam = isl_basic_map_n_param(bmap);
3903 n_in = isl_basic_map_n_in(bmap);
3904 isl_seq_clr(bmap->ineq[i], 1 + isl_basic_map_total_dim(bmap));
3905 isl_int_set_si(bmap->ineq[i][1+nparam+pos], 1);
3906 isl_int_set_si(bmap->ineq[i][1+nparam+n_in+pos], -1);
3907 return isl_basic_map_finalize(bmap);
3909 isl_basic_map_free(bmap);
3913 __isl_give isl_basic_map *isl_basic_map_equal(
3914 __isl_take isl_space *dim, unsigned n_equal)
3917 struct isl_basic_map *bmap;
3918 bmap = isl_basic_map_alloc_space(dim, 0, n_equal, 0);
3921 for (i = 0; i < n_equal && bmap; ++i)
3922 bmap = var_equal(bmap, i);
3923 return isl_basic_map_finalize(bmap);
3926 /* Return a relation on of dimension "dim" expressing i_[0..pos] << o_[0..pos]
3928 __isl_give isl_basic_map *isl_basic_map_less_at(__isl_take isl_space *dim,
3932 struct isl_basic_map *bmap;
3933 bmap = isl_basic_map_alloc_space(dim, 0, pos, 1);
3936 for (i = 0; i < pos && bmap; ++i)
3937 bmap = var_equal(bmap, i);
3939 bmap = var_less(bmap, pos);
3940 return isl_basic_map_finalize(bmap);
3943 /* Return a relation on of dimension "dim" expressing i_[0..pos] <<= o_[0..pos]
3945 __isl_give isl_basic_map *isl_basic_map_less_or_equal_at(
3946 __isl_take isl_space *dim, unsigned pos)
3949 isl_basic_map *bmap;
3951 bmap = isl_basic_map_alloc_space(dim, 0, pos, 1);
3952 for (i = 0; i < pos; ++i)
3953 bmap = var_equal(bmap, i);
3954 bmap = var_less_or_equal(bmap, pos);
3955 return isl_basic_map_finalize(bmap);
3958 /* Return a relation on pairs of sets of dimension "dim" expressing i_pos > o_pos
3960 __isl_give isl_basic_map *isl_basic_map_more_at(__isl_take isl_space *dim,
3964 struct isl_basic_map *bmap;
3965 bmap = isl_basic_map_alloc_space(dim, 0, pos, 1);
3968 for (i = 0; i < pos && bmap; ++i)
3969 bmap = var_equal(bmap, i);
3971 bmap = var_more(bmap, pos);
3972 return isl_basic_map_finalize(bmap);
3975 /* Return a relation on of dimension "dim" expressing i_[0..pos] >>= o_[0..pos]
3977 __isl_give isl_basic_map *isl_basic_map_more_or_equal_at(
3978 __isl_take isl_space *dim, unsigned pos)
3981 isl_basic_map *bmap;
3983 bmap = isl_basic_map_alloc_space(dim, 0, pos, 1);
3984 for (i = 0; i < pos; ++i)
3985 bmap = var_equal(bmap, i);
3986 bmap = var_more_or_equal(bmap, pos);
3987 return isl_basic_map_finalize(bmap);
3990 static __isl_give isl_map *map_lex_lte_first(__isl_take isl_space *dims,
3991 unsigned n, int equal)
3993 struct isl_map *map;
3996 if (n == 0 && equal)
3997 return isl_map_universe(dims);
3999 map = isl_map_alloc_space(isl_space_copy(dims), n, ISL_MAP_DISJOINT);
4001 for (i = 0; i + 1 < n; ++i)
4002 map = isl_map_add_basic_map(map,
4003 isl_basic_map_less_at(isl_space_copy(dims), i));
4006 map = isl_map_add_basic_map(map,
4007 isl_basic_map_less_or_equal_at(dims, n - 1));
4009 map = isl_map_add_basic_map(map,
4010 isl_basic_map_less_at(dims, n - 1));
4012 isl_space_free(dims);
4017 static __isl_give isl_map *map_lex_lte(__isl_take isl_space *dims, int equal)
4021 return map_lex_lte_first(dims, dims->n_out, equal);
4024 __isl_give isl_map *isl_map_lex_lt_first(__isl_take isl_space *dim, unsigned n)
4026 return map_lex_lte_first(dim, n, 0);
4029 __isl_give isl_map *isl_map_lex_le_first(__isl_take isl_space *dim, unsigned n)
4031 return map_lex_lte_first(dim, n, 1);
4034 __isl_give isl_map *isl_map_lex_lt(__isl_take isl_space *set_dim)
4036 return map_lex_lte(isl_space_map_from_set(set_dim), 0);
4039 __isl_give isl_map *isl_map_lex_le(__isl_take isl_space *set_dim)
4041 return map_lex_lte(isl_space_map_from_set(set_dim), 1);
4044 static __isl_give isl_map *map_lex_gte_first(__isl_take isl_space *dims,
4045 unsigned n, int equal)
4047 struct isl_map *map;
4050 if (n == 0 && equal)
4051 return isl_map_universe(dims);
4053 map = isl_map_alloc_space(isl_space_copy(dims), n, ISL_MAP_DISJOINT);
4055 for (i = 0; i + 1 < n; ++i)
4056 map = isl_map_add_basic_map(map,
4057 isl_basic_map_more_at(isl_space_copy(dims), i));
4060 map = isl_map_add_basic_map(map,
4061 isl_basic_map_more_or_equal_at(dims, n - 1));
4063 map = isl_map_add_basic_map(map,
4064 isl_basic_map_more_at(dims, n - 1));
4066 isl_space_free(dims);
4071 static __isl_give isl_map *map_lex_gte(__isl_take isl_space *dims, int equal)
4075 return map_lex_gte_first(dims, dims->n_out, equal);
4078 __isl_give isl_map *isl_map_lex_gt_first(__isl_take isl_space *dim, unsigned n)
4080 return map_lex_gte_first(dim, n, 0);
4083 __isl_give isl_map *isl_map_lex_ge_first(__isl_take isl_space *dim, unsigned n)
4085 return map_lex_gte_first(dim, n, 1);
4088 __isl_give isl_map *isl_map_lex_gt(__isl_take isl_space *set_dim)
4090 return map_lex_gte(isl_space_map_from_set(set_dim), 0);
4093 __isl_give isl_map *isl_map_lex_ge(__isl_take isl_space *set_dim)
4095 return map_lex_gte(isl_space_map_from_set(set_dim), 1);
4098 __isl_give isl_map *isl_set_lex_le_set(__isl_take isl_set *set1,
4099 __isl_take isl_set *set2)
4102 map = isl_map_lex_le(isl_set_get_space(set1));
4103 map = isl_map_intersect_domain(map, set1);
4104 map = isl_map_intersect_range(map, set2);
4108 __isl_give isl_map *isl_set_lex_lt_set(__isl_take isl_set *set1,
4109 __isl_take isl_set *set2)
4112 map = isl_map_lex_lt(isl_set_get_space(set1));
4113 map = isl_map_intersect_domain(map, set1);
4114 map = isl_map_intersect_range(map, set2);
4118 __isl_give isl_map *isl_set_lex_ge_set(__isl_take isl_set *set1,
4119 __isl_take isl_set *set2)
4122 map = isl_map_lex_ge(isl_set_get_space(set1));
4123 map = isl_map_intersect_domain(map, set1);
4124 map = isl_map_intersect_range(map, set2);
4128 __isl_give isl_map *isl_set_lex_gt_set(__isl_take isl_set *set1,
4129 __isl_take isl_set *set2)
4132 map = isl_map_lex_gt(isl_set_get_space(set1));
4133 map = isl_map_intersect_domain(map, set1);
4134 map = isl_map_intersect_range(map, set2);
4138 __isl_give isl_map *isl_map_lex_le_map(__isl_take isl_map *map1,
4139 __isl_take isl_map *map2)
4142 map = isl_map_lex_le(isl_space_range(isl_map_get_space(map1)));
4143 map = isl_map_apply_domain(map, isl_map_reverse(map1));
4144 map = isl_map_apply_range(map, isl_map_reverse(map2));
4148 __isl_give isl_map *isl_map_lex_lt_map(__isl_take isl_map *map1,
4149 __isl_take isl_map *map2)
4152 map = isl_map_lex_lt(isl_space_range(isl_map_get_space(map1)));
4153 map = isl_map_apply_domain(map, isl_map_reverse(map1));
4154 map = isl_map_apply_range(map, isl_map_reverse(map2));
4158 __isl_give isl_map *isl_map_lex_ge_map(__isl_take isl_map *map1,
4159 __isl_take isl_map *map2)
4162 map = isl_map_lex_ge(isl_space_range(isl_map_get_space(map1)));
4163 map = isl_map_apply_domain(map, isl_map_reverse(map1));
4164 map = isl_map_apply_range(map, isl_map_reverse(map2));
4168 __isl_give isl_map *isl_map_lex_gt_map(__isl_take isl_map *map1,
4169 __isl_take isl_map *map2)
4172 map = isl_map_lex_gt(isl_space_range(isl_map_get_space(map1)));
4173 map = isl_map_apply_domain(map, isl_map_reverse(map1));
4174 map = isl_map_apply_range(map, isl_map_reverse(map2));
4178 __isl_give isl_basic_map *isl_basic_map_from_basic_set(
4179 __isl_take isl_basic_set *bset, __isl_take isl_space *dim)
4181 struct isl_basic_map *bmap;
4183 bset = isl_basic_set_cow(bset);
4187 isl_assert(bset->ctx, isl_space_compatible(bset->dim, dim), goto error);
4188 isl_space_free(bset->dim);
4189 bmap = (struct isl_basic_map *) bset;
4191 return isl_basic_map_finalize(bmap);
4193 isl_basic_set_free(bset);
4194 isl_space_free(dim);
4198 struct isl_basic_set *isl_basic_set_from_basic_map(struct isl_basic_map *bmap)
4202 if (bmap->dim->n_in == 0)
4203 return (struct isl_basic_set *)bmap;
4204 bmap = isl_basic_map_cow(bmap);
4207 bmap->dim = isl_space_as_set_space(bmap->dim);
4210 bmap = isl_basic_map_finalize(bmap);
4211 return (struct isl_basic_set *)bmap;
4213 isl_basic_map_free(bmap);
4217 /* For a div d = floor(f/m), add the constraints
4220 * -(f-(n-1)) + m d >= 0
4222 * Note that the second constraint is the negation of
4226 int isl_basic_map_add_div_constraints_var(__isl_keep isl_basic_map *bmap,
4227 unsigned pos, isl_int *div)
4230 unsigned total = isl_basic_map_total_dim(bmap);
4232 i = isl_basic_map_alloc_inequality(bmap);
4235 isl_seq_cpy(bmap->ineq[i], div + 1, 1 + total);
4236 isl_int_neg(bmap->ineq[i][1 + pos], div[0]);
4238 j = isl_basic_map_alloc_inequality(bmap);
4241 isl_seq_neg(bmap->ineq[j], bmap->ineq[i], 1 + total);
4242 isl_int_add(bmap->ineq[j][0], bmap->ineq[j][0], bmap->ineq[j][1 + pos]);
4243 isl_int_sub_ui(bmap->ineq[j][0], bmap->ineq[j][0], 1);
4247 int isl_basic_set_add_div_constraints_var(__isl_keep isl_basic_set *bset,
4248 unsigned pos, isl_int *div)
4250 return isl_basic_map_add_div_constraints_var((isl_basic_map *)bset,
4254 int isl_basic_map_add_div_constraints(struct isl_basic_map *bmap, unsigned div)
4256 unsigned total = isl_basic_map_total_dim(bmap);
4257 unsigned div_pos = total - bmap->n_div + div;
4259 return isl_basic_map_add_div_constraints_var(bmap, div_pos,
4263 int isl_basic_set_add_div_constraints(struct isl_basic_set *bset, unsigned div)
4265 return isl_basic_map_add_div_constraints(bset, div);
4268 struct isl_basic_set *isl_basic_map_underlying_set(
4269 struct isl_basic_map *bmap)
4273 if (bmap->dim->nparam == 0 && bmap->dim->n_in == 0 &&
4275 !isl_space_is_named_or_nested(bmap->dim, isl_dim_in) &&
4276 !isl_space_is_named_or_nested(bmap->dim, isl_dim_out))
4277 return (struct isl_basic_set *)bmap;
4278 bmap = isl_basic_map_cow(bmap);
4281 bmap->dim = isl_space_underlying(bmap->dim, bmap->n_div);
4284 bmap->extra -= bmap->n_div;
4286 bmap = isl_basic_map_finalize(bmap);
4287 return (struct isl_basic_set *)bmap;
4292 __isl_give isl_basic_set *isl_basic_set_underlying_set(
4293 __isl_take isl_basic_set *bset)
4295 return isl_basic_map_underlying_set((isl_basic_map *)bset);
4298 struct isl_basic_map *isl_basic_map_overlying_set(
4299 struct isl_basic_set *bset, struct isl_basic_map *like)
4301 struct isl_basic_map *bmap;
4302 struct isl_ctx *ctx;
4309 isl_assert(ctx, bset->n_div == 0, goto error);
4310 isl_assert(ctx, isl_basic_set_n_param(bset) == 0, goto error);
4311 isl_assert(ctx, bset->dim->n_out == isl_basic_map_total_dim(like),
4313 if (isl_space_is_equal(bset->dim, like->dim) && like->n_div == 0) {
4314 isl_basic_map_free(like);
4315 return (struct isl_basic_map *)bset;
4317 bset = isl_basic_set_cow(bset);
4320 total = bset->dim->n_out + bset->extra;
4321 bmap = (struct isl_basic_map *)bset;
4322 isl_space_free(bmap->dim);
4323 bmap->dim = isl_space_copy(like->dim);
4326 bmap->n_div = like->n_div;
4327 bmap->extra += like->n_div;
4331 ltotal = total - bmap->extra + like->extra;
4334 bmap->block2 = isl_blk_extend(ctx, bmap->block2,
4335 bmap->extra * (1 + 1 + total));
4336 if (isl_blk_is_error(bmap->block2))
4338 div = isl_realloc_array(ctx, bmap->div, isl_int *, bmap->extra);
4342 for (i = 0; i < bmap->extra; ++i)
4343 bmap->div[i] = bmap->block2.data + i * (1 + 1 + total);
4344 for (i = 0; i < like->n_div; ++i) {
4345 isl_seq_cpy(bmap->div[i], like->div[i], 1 + 1 + ltotal);
4346 isl_seq_clr(bmap->div[i]+1+1+ltotal, total - ltotal);
4348 bmap = isl_basic_map_extend_constraints(bmap,
4349 0, 2 * like->n_div);
4350 for (i = 0; i < like->n_div; ++i) {
4351 if (isl_int_is_zero(bmap->div[i][0]))
4353 if (isl_basic_map_add_div_constraints(bmap, i) < 0)
4357 isl_basic_map_free(like);
4358 bmap = isl_basic_map_simplify(bmap);
4359 bmap = isl_basic_map_finalize(bmap);
4362 isl_basic_map_free(like);
4363 isl_basic_set_free(bset);
4367 struct isl_basic_set *isl_basic_set_from_underlying_set(
4368 struct isl_basic_set *bset, struct isl_basic_set *like)
4370 return (struct isl_basic_set *)
4371 isl_basic_map_overlying_set(bset, (struct isl_basic_map *)like);
4374 struct isl_set *isl_set_from_underlying_set(
4375 struct isl_set *set, struct isl_basic_set *like)
4381 isl_assert(set->ctx, set->dim->n_out == isl_basic_set_total_dim(like),
4383 if (isl_space_is_equal(set->dim, like->dim) && like->n_div == 0) {
4384 isl_basic_set_free(like);
4387 set = isl_set_cow(set);
4390 for (i = 0; i < set->n; ++i) {
4391 set->p[i] = isl_basic_set_from_underlying_set(set->p[i],
4392 isl_basic_set_copy(like));
4396 isl_space_free(set->dim);
4397 set->dim = isl_space_copy(like->dim);
4400 isl_basic_set_free(like);
4403 isl_basic_set_free(like);
4408 struct isl_set *isl_map_underlying_set(struct isl_map *map)
4412 map = isl_map_cow(map);
4415 map->dim = isl_space_cow(map->dim);
4419 for (i = 1; i < map->n; ++i)
4420 isl_assert(map->ctx, map->p[0]->n_div == map->p[i]->n_div,
4422 for (i = 0; i < map->n; ++i) {
4423 map->p[i] = (struct isl_basic_map *)
4424 isl_basic_map_underlying_set(map->p[i]);
4429 map->dim = isl_space_underlying(map->dim, 0);
4431 isl_space_free(map->dim);
4432 map->dim = isl_space_copy(map->p[0]->dim);
4436 return (struct isl_set *)map;
4442 struct isl_set *isl_set_to_underlying_set(struct isl_set *set)
4444 return (struct isl_set *)isl_map_underlying_set((struct isl_map *)set);
4447 __isl_give isl_basic_map *isl_basic_map_reset_space(
4448 __isl_take isl_basic_map *bmap, __isl_take isl_space *dim)
4450 bmap = isl_basic_map_cow(bmap);
4454 isl_space_free(bmap->dim);
4457 bmap = isl_basic_map_finalize(bmap);
4461 isl_basic_map_free(bmap);
4462 isl_space_free(dim);
4466 __isl_give isl_basic_set *isl_basic_set_reset_space(
4467 __isl_take isl_basic_set *bset, __isl_take isl_space *dim)
4469 return (isl_basic_set *)isl_basic_map_reset_space((isl_basic_map *)bset,
4473 __isl_give isl_map *isl_map_reset_space(__isl_take isl_map *map,
4474 __isl_take isl_space *dim)
4478 map = isl_map_cow(map);
4482 for (i = 0; i < map->n; ++i) {
4483 map->p[i] = isl_basic_map_reset_space(map->p[i],
4484 isl_space_copy(dim));
4488 isl_space_free(map->dim);
4494 isl_space_free(dim);
4498 __isl_give isl_set *isl_set_reset_space(__isl_take isl_set *set,
4499 __isl_take isl_space *dim)
4501 return (struct isl_set *) isl_map_reset_space((struct isl_map *)set, dim);
4504 /* Compute the parameter domain of the given basic set.
4506 __isl_give isl_basic_set *isl_basic_set_params(__isl_take isl_basic_set *bset)
4511 if (isl_basic_set_is_params(bset))
4514 n = isl_basic_set_dim(bset, isl_dim_set);
4515 bset = isl_basic_set_project_out(bset, isl_dim_set, 0, n);
4516 space = isl_basic_set_get_space(bset);
4517 space = isl_space_params(space);
4518 bset = isl_basic_set_reset_space(bset, space);
4522 /* Construct a zero-dimensional basic set with the given parameter domain.
4524 __isl_give isl_basic_set *isl_basic_set_from_params(
4525 __isl_take isl_basic_set *bset)
4528 space = isl_basic_set_get_space(bset);
4529 space = isl_space_set_from_params(space);
4530 bset = isl_basic_set_reset_space(bset, space);
4534 /* Compute the parameter domain of the given set.
4536 __isl_give isl_set *isl_set_params(__isl_take isl_set *set)
4541 if (isl_set_is_params(set))
4544 n = isl_set_dim(set, isl_dim_set);
4545 set = isl_set_project_out(set, isl_dim_set, 0, n);
4546 space = isl_set_get_space(set);
4547 space = isl_space_params(space);
4548 set = isl_set_reset_space(set, space);
4552 /* Construct a zero-dimensional set with the given parameter domain.
4554 __isl_give isl_set *isl_set_from_params(__isl_take isl_set *set)
4557 space = isl_set_get_space(set);
4558 space = isl_space_set_from_params(space);
4559 set = isl_set_reset_space(set, space);
4563 /* Compute the parameter domain of the given map.
4565 __isl_give isl_set *isl_map_params(__isl_take isl_map *map)
4570 n = isl_map_dim(map, isl_dim_in);
4571 map = isl_map_project_out(map, isl_dim_in, 0, n);
4572 n = isl_map_dim(map, isl_dim_out);
4573 map = isl_map_project_out(map, isl_dim_out, 0, n);
4574 space = isl_map_get_space(map);
4575 space = isl_space_params(space);
4576 map = isl_map_reset_space(map, space);
4580 struct isl_basic_set *isl_basic_map_domain(struct isl_basic_map *bmap)
4583 struct isl_basic_set *domain;
4589 dim = isl_space_domain(isl_basic_map_get_space(bmap));
4591 n_in = isl_basic_map_n_in(bmap);
4592 n_out = isl_basic_map_n_out(bmap);
4593 domain = isl_basic_set_from_basic_map(bmap);
4594 domain = isl_basic_set_project_out(domain, isl_dim_set, n_in, n_out);
4596 domain = isl_basic_set_reset_space(domain, dim);
4601 int isl_basic_map_may_be_set(__isl_keep isl_basic_map *bmap)
4605 return isl_space_may_be_set(bmap->dim);
4608 /* Is this basic map actually a set?
4609 * Users should never call this function. Outside of isl,
4610 * the type should indicate whether something is a set or a map.
4612 int isl_basic_map_is_set(__isl_keep isl_basic_map *bmap)
4616 return isl_space_is_set(bmap->dim);
4619 struct isl_basic_set *isl_basic_map_range(struct isl_basic_map *bmap)
4623 if (isl_basic_map_is_set(bmap))
4625 return isl_basic_map_domain(isl_basic_map_reverse(bmap));
4628 __isl_give isl_basic_map *isl_basic_map_domain_map(
4629 __isl_take isl_basic_map *bmap)
4633 isl_basic_map *domain;
4634 int nparam, n_in, n_out;
4637 nparam = isl_basic_map_dim(bmap, isl_dim_param);
4638 n_in = isl_basic_map_dim(bmap, isl_dim_in);
4639 n_out = isl_basic_map_dim(bmap, isl_dim_out);
4641 dim = isl_space_from_range(isl_space_domain(isl_basic_map_get_space(bmap)));
4642 domain = isl_basic_map_universe(dim);
4644 bmap = isl_basic_map_from_domain(isl_basic_map_wrap(bmap));
4645 bmap = isl_basic_map_apply_range(bmap, domain);
4646 bmap = isl_basic_map_extend_constraints(bmap, n_in, 0);
4648 total = isl_basic_map_total_dim(bmap);
4650 for (i = 0; i < n_in; ++i) {
4651 k = isl_basic_map_alloc_equality(bmap);
4654 isl_seq_clr(bmap->eq[k], 1 + total);
4655 isl_int_set_si(bmap->eq[k][1 + nparam + i], -1);
4656 isl_int_set_si(bmap->eq[k][1 + nparam + n_in + n_out + i], 1);
4659 bmap = isl_basic_map_gauss(bmap, NULL);
4660 return isl_basic_map_finalize(bmap);
4662 isl_basic_map_free(bmap);
4666 __isl_give isl_basic_map *isl_basic_map_range_map(
4667 __isl_take isl_basic_map *bmap)
4671 isl_basic_map *range;
4672 int nparam, n_in, n_out;
4675 nparam = isl_basic_map_dim(bmap, isl_dim_param);
4676 n_in = isl_basic_map_dim(bmap, isl_dim_in);
4677 n_out = isl_basic_map_dim(bmap, isl_dim_out);
4679 dim = isl_space_from_range(isl_space_range(isl_basic_map_get_space(bmap)));
4680 range = isl_basic_map_universe(dim);
4682 bmap = isl_basic_map_from_domain(isl_basic_map_wrap(bmap));
4683 bmap = isl_basic_map_apply_range(bmap, range);
4684 bmap = isl_basic_map_extend_constraints(bmap, n_out, 0);
4686 total = isl_basic_map_total_dim(bmap);
4688 for (i = 0; i < n_out; ++i) {
4689 k = isl_basic_map_alloc_equality(bmap);
4692 isl_seq_clr(bmap->eq[k], 1 + total);
4693 isl_int_set_si(bmap->eq[k][1 + nparam + n_in + i], -1);
4694 isl_int_set_si(bmap->eq[k][1 + nparam + n_in + n_out + i], 1);
4697 bmap = isl_basic_map_gauss(bmap, NULL);
4698 return isl_basic_map_finalize(bmap);
4700 isl_basic_map_free(bmap);
4704 int isl_map_may_be_set(__isl_keep isl_map *map)
4708 return isl_space_may_be_set(map->dim);
4711 /* Is this map actually a set?
4712 * Users should never call this function. Outside of isl,
4713 * the type should indicate whether something is a set or a map.
4715 int isl_map_is_set(__isl_keep isl_map *map)
4719 return isl_space_is_set(map->dim);
4722 struct isl_set *isl_map_range(struct isl_map *map)
4725 struct isl_set *set;
4729 if (isl_map_is_set(map))
4730 return (isl_set *)map;
4732 map = isl_map_cow(map);
4736 set = (struct isl_set *) map;
4737 set->dim = isl_space_range(set->dim);
4740 for (i = 0; i < map->n; ++i) {
4741 set->p[i] = isl_basic_map_range(map->p[i]);
4745 ISL_F_CLR(set, ISL_MAP_DISJOINT);
4746 ISL_F_CLR(set, ISL_SET_NORMALIZED);
4753 __isl_give isl_map *isl_map_domain_map(__isl_take isl_map *map)
4756 isl_space *domain_dim;
4758 map = isl_map_cow(map);
4762 domain_dim = isl_space_from_range(isl_space_domain(isl_map_get_space(map)));
4763 map->dim = isl_space_from_domain(isl_space_wrap(map->dim));
4764 map->dim = isl_space_join(map->dim, domain_dim);
4767 for (i = 0; i < map->n; ++i) {
4768 map->p[i] = isl_basic_map_domain_map(map->p[i]);
4772 ISL_F_CLR(map, ISL_MAP_DISJOINT);
4773 ISL_F_CLR(map, ISL_MAP_NORMALIZED);
4780 __isl_give isl_map *isl_map_range_map(__isl_take isl_map *map)
4783 isl_space *range_dim;
4785 map = isl_map_cow(map);
4789 range_dim = isl_space_range(isl_map_get_space(map));
4790 range_dim = isl_space_from_range(range_dim);
4791 map->dim = isl_space_from_domain(isl_space_wrap(map->dim));
4792 map->dim = isl_space_join(map->dim, range_dim);
4795 for (i = 0; i < map->n; ++i) {
4796 map->p[i] = isl_basic_map_range_map(map->p[i]);
4800 ISL_F_CLR(map, ISL_MAP_DISJOINT);
4801 ISL_F_CLR(map, ISL_MAP_NORMALIZED);
4808 __isl_give isl_map *isl_map_from_set(__isl_take isl_set *set,
4809 __isl_take isl_space *dim)
4812 struct isl_map *map = NULL;
4814 set = isl_set_cow(set);
4817 isl_assert(set->ctx, isl_space_compatible(set->dim, dim), goto error);
4818 map = (struct isl_map *)set;
4819 for (i = 0; i < set->n; ++i) {
4820 map->p[i] = isl_basic_map_from_basic_set(
4821 set->p[i], isl_space_copy(dim));
4825 isl_space_free(map->dim);
4829 isl_space_free(dim);
4834 __isl_give isl_basic_map *isl_basic_map_from_domain(
4835 __isl_take isl_basic_set *bset)
4837 return isl_basic_map_reverse(isl_basic_map_from_range(bset));
4840 __isl_give isl_basic_map *isl_basic_map_from_range(
4841 __isl_take isl_basic_set *bset)
4844 space = isl_basic_set_get_space(bset);
4845 space = isl_space_from_range(space);
4846 bset = isl_basic_set_reset_space(bset, space);
4847 return (isl_basic_map *)bset;
4850 struct isl_map *isl_map_from_range(struct isl_set *set)
4853 space = isl_set_get_space(set);
4854 space = isl_space_from_range(space);
4855 set = isl_set_reset_space(set, space);
4856 return (struct isl_map *)set;
4859 __isl_give isl_map *isl_map_from_domain(__isl_take isl_set *set)
4861 return isl_map_reverse(isl_map_from_range(set));
4864 __isl_give isl_basic_map *isl_basic_map_from_domain_and_range(
4865 __isl_take isl_basic_set *domain, __isl_take isl_basic_set *range)
4867 return isl_basic_map_apply_range(isl_basic_map_reverse(domain), range);
4870 __isl_give isl_map *isl_map_from_domain_and_range(__isl_take isl_set *domain,
4871 __isl_take isl_set *range)
4873 return isl_map_apply_range(isl_map_reverse(domain), range);
4876 struct isl_set *isl_set_from_map(struct isl_map *map)
4879 struct isl_set *set = NULL;
4883 map = isl_map_cow(map);
4886 map->dim = isl_space_as_set_space(map->dim);
4889 set = (struct isl_set *)map;
4890 for (i = 0; i < map->n; ++i) {
4891 set->p[i] = isl_basic_set_from_basic_map(map->p[i]);
4901 __isl_give isl_map *isl_map_alloc_space(__isl_take isl_space *dim, int n,
4904 struct isl_map *map;
4909 isl_die(dim->ctx, isl_error_internal,
4910 "negative number of basic maps", goto error);
4911 map = isl_alloc(dim->ctx, struct isl_map,
4912 sizeof(struct isl_map) +
4913 (n - 1) * sizeof(struct isl_basic_map *));
4917 map->ctx = dim->ctx;
4918 isl_ctx_ref(map->ctx);
4926 isl_space_free(dim);
4930 struct isl_map *isl_map_alloc(struct isl_ctx *ctx,
4931 unsigned nparam, unsigned in, unsigned out, int n,
4934 struct isl_map *map;
4937 dims = isl_space_alloc(ctx, nparam, in, out);
4941 map = isl_map_alloc_space(dims, n, flags);
4945 __isl_give isl_basic_map *isl_basic_map_empty(__isl_take isl_space *dim)
4947 struct isl_basic_map *bmap;
4948 bmap = isl_basic_map_alloc_space(dim, 0, 1, 0);
4949 bmap = isl_basic_map_set_to_empty(bmap);
4953 __isl_give isl_basic_set *isl_basic_set_empty(__isl_take isl_space *dim)
4955 struct isl_basic_set *bset;
4956 bset = isl_basic_set_alloc_space(dim, 0, 1, 0);
4957 bset = isl_basic_set_set_to_empty(bset);
4961 struct isl_basic_map *isl_basic_map_empty_like(struct isl_basic_map *model)
4963 struct isl_basic_map *bmap;
4966 bmap = isl_basic_map_alloc_space(isl_space_copy(model->dim), 0, 1, 0);
4967 bmap = isl_basic_map_set_to_empty(bmap);
4971 struct isl_basic_map *isl_basic_map_empty_like_map(struct isl_map *model)
4973 struct isl_basic_map *bmap;
4976 bmap = isl_basic_map_alloc_space(isl_space_copy(model->dim), 0, 1, 0);
4977 bmap = isl_basic_map_set_to_empty(bmap);
4981 struct isl_basic_set *isl_basic_set_empty_like(struct isl_basic_set *model)
4983 struct isl_basic_set *bset;
4986 bset = isl_basic_set_alloc_space(isl_space_copy(model->dim), 0, 1, 0);
4987 bset = isl_basic_set_set_to_empty(bset);
4991 __isl_give isl_basic_map *isl_basic_map_universe(__isl_take isl_space *dim)
4993 struct isl_basic_map *bmap;
4994 bmap = isl_basic_map_alloc_space(dim, 0, 0, 0);
4995 bmap = isl_basic_map_finalize(bmap);
4999 __isl_give isl_basic_set *isl_basic_set_universe(__isl_take isl_space *dim)
5001 struct isl_basic_set *bset;
5002 bset = isl_basic_set_alloc_space(dim, 0, 0, 0);
5003 bset = isl_basic_set_finalize(bset);
5007 __isl_give isl_basic_map *isl_basic_map_nat_universe(__isl_take isl_space *dim)
5010 unsigned total = isl_space_dim(dim, isl_dim_all);
5011 isl_basic_map *bmap;
5013 bmap= isl_basic_map_alloc_space(dim, 0, 0, total);
5014 for (i = 0; i < total; ++i) {
5015 int k = isl_basic_map_alloc_inequality(bmap);
5018 isl_seq_clr(bmap->ineq[k], 1 + total);
5019 isl_int_set_si(bmap->ineq[k][1 + i], 1);
5023 isl_basic_map_free(bmap);
5027 __isl_give isl_basic_set *isl_basic_set_nat_universe(__isl_take isl_space *dim)
5029 return isl_basic_map_nat_universe(dim);
5032 __isl_give isl_map *isl_map_nat_universe(__isl_take isl_space *dim)
5034 return isl_map_from_basic_map(isl_basic_map_nat_universe(dim));
5037 __isl_give isl_set *isl_set_nat_universe(__isl_take isl_space *dim)
5039 return isl_map_nat_universe(dim);
5042 __isl_give isl_basic_map *isl_basic_map_universe_like(
5043 __isl_keep isl_basic_map *model)
5047 return isl_basic_map_alloc_space(isl_space_copy(model->dim), 0, 0, 0);
5050 struct isl_basic_set *isl_basic_set_universe_like(struct isl_basic_set *model)
5054 return isl_basic_set_alloc_space(isl_space_copy(model->dim), 0, 0, 0);
5057 __isl_give isl_basic_set *isl_basic_set_universe_like_set(
5058 __isl_keep isl_set *model)
5062 return isl_basic_set_alloc_space(isl_space_copy(model->dim), 0, 0, 0);
5065 __isl_give isl_map *isl_map_empty(__isl_take isl_space *dim)
5067 return isl_map_alloc_space(dim, 0, ISL_MAP_DISJOINT);
5070 struct isl_map *isl_map_empty_like(struct isl_map *model)
5074 return isl_map_alloc_space(isl_space_copy(model->dim), 0, ISL_MAP_DISJOINT);
5077 struct isl_map *isl_map_empty_like_basic_map(struct isl_basic_map *model)
5081 return isl_map_alloc_space(isl_space_copy(model->dim), 0, ISL_MAP_DISJOINT);
5084 __isl_give isl_set *isl_set_empty(__isl_take isl_space *dim)
5086 return isl_set_alloc_space(dim, 0, ISL_MAP_DISJOINT);
5089 struct isl_set *isl_set_empty_like(struct isl_set *model)
5093 return isl_set_empty(isl_space_copy(model->dim));
5096 __isl_give isl_map *isl_map_universe(__isl_take isl_space *dim)
5098 struct isl_map *map;
5101 map = isl_map_alloc_space(isl_space_copy(dim), 1, ISL_MAP_DISJOINT);
5102 map = isl_map_add_basic_map(map, isl_basic_map_universe(dim));
5106 __isl_give isl_set *isl_set_universe(__isl_take isl_space *dim)
5108 struct isl_set *set;
5111 set = isl_set_alloc_space(isl_space_copy(dim), 1, ISL_MAP_DISJOINT);
5112 set = isl_set_add_basic_set(set, isl_basic_set_universe(dim));
5116 __isl_give isl_set *isl_set_universe_like(__isl_keep isl_set *model)
5120 return isl_set_universe(isl_space_copy(model->dim));
5123 struct isl_map *isl_map_dup(struct isl_map *map)
5126 struct isl_map *dup;
5130 dup = isl_map_alloc_space(isl_space_copy(map->dim), map->n, map->flags);
5131 for (i = 0; i < map->n; ++i)
5132 dup = isl_map_add_basic_map(dup, isl_basic_map_copy(map->p[i]));
5136 __isl_give isl_map *isl_map_add_basic_map(__isl_take isl_map *map,
5137 __isl_take isl_basic_map *bmap)
5141 if (isl_basic_map_plain_is_empty(bmap)) {
5142 isl_basic_map_free(bmap);
5145 isl_assert(map->ctx, isl_space_is_equal(map->dim, bmap->dim), goto error);
5146 isl_assert(map->ctx, map->n < map->size, goto error);
5147 map->p[map->n] = bmap;
5149 ISL_F_CLR(map, ISL_MAP_NORMALIZED);
5155 isl_basic_map_free(bmap);
5159 void *isl_map_free(struct isl_map *map)
5169 isl_ctx_deref(map->ctx);
5170 for (i = 0; i < map->n; ++i)
5171 isl_basic_map_free(map->p[i]);
5172 isl_space_free(map->dim);
5178 struct isl_map *isl_map_extend(struct isl_map *base,
5179 unsigned nparam, unsigned n_in, unsigned n_out)
5183 base = isl_map_cow(base);
5187 base->dim = isl_space_extend(base->dim, nparam, n_in, n_out);
5190 for (i = 0; i < base->n; ++i) {
5191 base->p[i] = isl_basic_map_extend_space(base->p[i],
5192 isl_space_copy(base->dim), 0, 0, 0);
5202 struct isl_set *isl_set_extend(struct isl_set *base,
5203 unsigned nparam, unsigned dim)
5205 return (struct isl_set *)isl_map_extend((struct isl_map *)base,
5209 static struct isl_basic_map *isl_basic_map_fix_pos_si(
5210 struct isl_basic_map *bmap, unsigned pos, int value)
5214 bmap = isl_basic_map_cow(bmap);
5215 bmap = isl_basic_map_extend_constraints(bmap, 1, 0);
5216 j = isl_basic_map_alloc_equality(bmap);
5219 isl_seq_clr(bmap->eq[j] + 1, isl_basic_map_total_dim(bmap));
5220 isl_int_set_si(bmap->eq[j][pos], -1);
5221 isl_int_set_si(bmap->eq[j][0], value);
5222 bmap = isl_basic_map_simplify(bmap);
5223 return isl_basic_map_finalize(bmap);
5225 isl_basic_map_free(bmap);
5229 static __isl_give isl_basic_map *isl_basic_map_fix_pos(
5230 __isl_take isl_basic_map *bmap, unsigned pos, isl_int value)
5234 bmap = isl_basic_map_cow(bmap);
5235 bmap = isl_basic_map_extend_constraints(bmap, 1, 0);
5236 j = isl_basic_map_alloc_equality(bmap);
5239 isl_seq_clr(bmap->eq[j] + 1, isl_basic_map_total_dim(bmap));
5240 isl_int_set_si(bmap->eq[j][pos], -1);
5241 isl_int_set(bmap->eq[j][0], value);
5242 bmap = isl_basic_map_simplify(bmap);
5243 return isl_basic_map_finalize(bmap);
5245 isl_basic_map_free(bmap);
5249 struct isl_basic_map *isl_basic_map_fix_si(struct isl_basic_map *bmap,
5250 enum isl_dim_type type, unsigned pos, int value)
5254 isl_assert(bmap->ctx, pos < isl_basic_map_dim(bmap, type), goto error);
5255 return isl_basic_map_fix_pos_si(bmap,
5256 isl_basic_map_offset(bmap, type) + pos, value);
5258 isl_basic_map_free(bmap);
5262 __isl_give isl_basic_map *isl_basic_map_fix(__isl_take isl_basic_map *bmap,
5263 enum isl_dim_type type, unsigned pos, isl_int value)
5267 isl_assert(bmap->ctx, pos < isl_basic_map_dim(bmap, type), goto error);
5268 return isl_basic_map_fix_pos(bmap,
5269 isl_basic_map_offset(bmap, type) + pos, value);
5271 isl_basic_map_free(bmap);
5275 struct isl_basic_set *isl_basic_set_fix_si(struct isl_basic_set *bset,
5276 enum isl_dim_type type, unsigned pos, int value)
5278 return (struct isl_basic_set *)
5279 isl_basic_map_fix_si((struct isl_basic_map *)bset,
5283 __isl_give isl_basic_set *isl_basic_set_fix(__isl_take isl_basic_set *bset,
5284 enum isl_dim_type type, unsigned pos, isl_int value)
5286 return (struct isl_basic_set *)
5287 isl_basic_map_fix((struct isl_basic_map *)bset,
5291 struct isl_basic_map *isl_basic_map_fix_input_si(struct isl_basic_map *bmap,
5292 unsigned input, int value)
5294 return isl_basic_map_fix_si(bmap, isl_dim_in, input, value);
5297 struct isl_basic_set *isl_basic_set_fix_dim_si(struct isl_basic_set *bset,
5298 unsigned dim, int value)
5300 return (struct isl_basic_set *)
5301 isl_basic_map_fix_si((struct isl_basic_map *)bset,
5302 isl_dim_set, dim, value);
5305 static int remove_if_empty(__isl_keep isl_map *map, int i)
5307 int empty = isl_basic_map_plain_is_empty(map->p[i]);
5314 isl_basic_map_free(map->p[i]);
5315 if (i != map->n - 1) {
5316 ISL_F_CLR(map, ISL_MAP_NORMALIZED);
5317 map->p[i] = map->p[map->n - 1];
5324 struct isl_map *isl_map_fix_si(struct isl_map *map,
5325 enum isl_dim_type type, unsigned pos, int value)
5329 map = isl_map_cow(map);
5333 isl_assert(map->ctx, pos < isl_map_dim(map, type), goto error);
5334 for (i = map->n - 1; i >= 0; --i) {
5335 map->p[i] = isl_basic_map_fix_si(map->p[i], type, pos, value);
5336 if (remove_if_empty(map, i) < 0)
5339 ISL_F_CLR(map, ISL_MAP_NORMALIZED);
5346 __isl_give isl_set *isl_set_fix_si(__isl_take isl_set *set,
5347 enum isl_dim_type type, unsigned pos, int value)
5349 return (struct isl_set *)
5350 isl_map_fix_si((struct isl_map *)set, type, pos, value);
5353 __isl_give isl_map *isl_map_fix(__isl_take isl_map *map,
5354 enum isl_dim_type type, unsigned pos, isl_int value)
5358 map = isl_map_cow(map);
5362 isl_assert(map->ctx, pos < isl_map_dim(map, type), goto error);
5363 for (i = 0; i < map->n; ++i) {
5364 map->p[i] = isl_basic_map_fix(map->p[i], type, pos, value);
5368 ISL_F_CLR(map, ISL_MAP_NORMALIZED);
5375 __isl_give isl_set *isl_set_fix(__isl_take isl_set *set,
5376 enum isl_dim_type type, unsigned pos, isl_int value)
5378 return (struct isl_set *)isl_map_fix((isl_map *)set, type, pos, value);
5381 struct isl_map *isl_map_fix_input_si(struct isl_map *map,
5382 unsigned input, int value)
5384 return isl_map_fix_si(map, isl_dim_in, input, value);
5387 struct isl_set *isl_set_fix_dim_si(struct isl_set *set, unsigned dim, int value)
5389 return (struct isl_set *)
5390 isl_map_fix_si((struct isl_map *)set, isl_dim_set, dim, value);
5393 static __isl_give isl_basic_map *basic_map_bound_si(
5394 __isl_take isl_basic_map *bmap,
5395 enum isl_dim_type type, unsigned pos, int value, int upper)
5401 isl_assert(bmap->ctx, pos < isl_basic_map_dim(bmap, type), goto error);
5402 pos += isl_basic_map_offset(bmap, type);
5403 bmap = isl_basic_map_cow(bmap);
5404 bmap = isl_basic_map_extend_constraints(bmap, 0, 1);
5405 j = isl_basic_map_alloc_inequality(bmap);
5408 isl_seq_clr(bmap->ineq[j], 1 + isl_basic_map_total_dim(bmap));
5410 isl_int_set_si(bmap->ineq[j][pos], -1);
5411 isl_int_set_si(bmap->ineq[j][0], value);
5413 isl_int_set_si(bmap->ineq[j][pos], 1);
5414 isl_int_set_si(bmap->ineq[j][0], -value);
5416 bmap = isl_basic_map_simplify(bmap);
5417 return isl_basic_map_finalize(bmap);
5419 isl_basic_map_free(bmap);
5423 __isl_give isl_basic_map *isl_basic_map_lower_bound_si(
5424 __isl_take isl_basic_map *bmap,
5425 enum isl_dim_type type, unsigned pos, int value)
5427 return basic_map_bound_si(bmap, type, pos, value, 0);
5430 /* Constrain the values of the given dimension to be no greater than "value".
5432 __isl_give isl_basic_map *isl_basic_map_upper_bound_si(
5433 __isl_take isl_basic_map *bmap,
5434 enum isl_dim_type type, unsigned pos, int value)
5436 return basic_map_bound_si(bmap, type, pos, value, 1);
5439 struct isl_basic_set *isl_basic_set_lower_bound_dim(struct isl_basic_set *bset,
5440 unsigned dim, isl_int value)
5444 bset = isl_basic_set_cow(bset);
5445 bset = isl_basic_set_extend_constraints(bset, 0, 1);
5446 j = isl_basic_set_alloc_inequality(bset);
5449 isl_seq_clr(bset->ineq[j], 1 + isl_basic_set_total_dim(bset));
5450 isl_int_set_si(bset->ineq[j][1 + isl_basic_set_n_param(bset) + dim], 1);
5451 isl_int_neg(bset->ineq[j][0], value);
5452 bset = isl_basic_set_simplify(bset);
5453 return isl_basic_set_finalize(bset);
5455 isl_basic_set_free(bset);
5459 static __isl_give isl_map *map_bound_si(__isl_take isl_map *map,
5460 enum isl_dim_type type, unsigned pos, int value, int upper)
5464 map = isl_map_cow(map);
5468 isl_assert(map->ctx, pos < isl_map_dim(map, type), goto error);
5469 for (i = 0; i < map->n; ++i) {
5470 map->p[i] = basic_map_bound_si(map->p[i],
5471 type, pos, value, upper);
5475 ISL_F_CLR(map, ISL_MAP_NORMALIZED);
5482 __isl_give isl_map *isl_map_lower_bound_si(__isl_take isl_map *map,
5483 enum isl_dim_type type, unsigned pos, int value)
5485 return map_bound_si(map, type, pos, value, 0);
5488 __isl_give isl_map *isl_map_upper_bound_si(__isl_take isl_map *map,
5489 enum isl_dim_type type, unsigned pos, int value)
5491 return map_bound_si(map, type, pos, value, 1);
5494 __isl_give isl_set *isl_set_lower_bound_si(__isl_take isl_set *set,
5495 enum isl_dim_type type, unsigned pos, int value)
5497 return (struct isl_set *)
5498 isl_map_lower_bound_si((struct isl_map *)set, type, pos, value);
5501 __isl_give isl_set *isl_set_upper_bound_si(__isl_take isl_set *set,
5502 enum isl_dim_type type, unsigned pos, int value)
5504 return isl_map_upper_bound_si(set, type, pos, value);
5507 /* Bound the given variable of "bmap" from below (or above is "upper"
5508 * is set) to "value".
5510 static __isl_give isl_basic_map *basic_map_bound(
5511 __isl_take isl_basic_map *bmap,
5512 enum isl_dim_type type, unsigned pos, isl_int value, int upper)
5518 if (pos >= isl_basic_map_dim(bmap, type))
5519 isl_die(bmap->ctx, isl_error_invalid,
5520 "index out of bounds", goto error);
5521 pos += isl_basic_map_offset(bmap, type);
5522 bmap = isl_basic_map_cow(bmap);
5523 bmap = isl_basic_map_extend_constraints(bmap, 0, 1);
5524 j = isl_basic_map_alloc_inequality(bmap);
5527 isl_seq_clr(bmap->ineq[j], 1 + isl_basic_map_total_dim(bmap));
5529 isl_int_set_si(bmap->ineq[j][pos], -1);
5530 isl_int_set(bmap->ineq[j][0], value);
5532 isl_int_set_si(bmap->ineq[j][pos], 1);
5533 isl_int_neg(bmap->ineq[j][0], value);
5535 bmap = isl_basic_map_simplify(bmap);
5536 return isl_basic_map_finalize(bmap);
5538 isl_basic_map_free(bmap);
5542 /* Bound the given variable of "map" from below (or above is "upper"
5543 * is set) to "value".
5545 static __isl_give isl_map *map_bound(__isl_take isl_map *map,
5546 enum isl_dim_type type, unsigned pos, isl_int value, int upper)
5550 map = isl_map_cow(map);
5554 if (pos >= isl_map_dim(map, type))
5555 isl_die(map->ctx, isl_error_invalid,
5556 "index out of bounds", goto error);
5557 for (i = map->n - 1; i >= 0; --i) {
5558 map->p[i] = basic_map_bound(map->p[i], type, pos, value, upper);
5559 if (remove_if_empty(map, i) < 0)
5562 ISL_F_CLR(map, ISL_MAP_NORMALIZED);
5569 __isl_give isl_map *isl_map_lower_bound(__isl_take isl_map *map,
5570 enum isl_dim_type type, unsigned pos, isl_int value)
5572 return map_bound(map, type, pos, value, 0);
5575 __isl_give isl_map *isl_map_upper_bound(__isl_take isl_map *map,
5576 enum isl_dim_type type, unsigned pos, isl_int value)
5578 return map_bound(map, type, pos, value, 1);
5581 __isl_give isl_set *isl_set_lower_bound(__isl_take isl_set *set,
5582 enum isl_dim_type type, unsigned pos, isl_int value)
5584 return isl_map_lower_bound(set, type, pos, value);
5587 __isl_give isl_set *isl_set_upper_bound(__isl_take isl_set *set,
5588 enum isl_dim_type type, unsigned pos, isl_int value)
5590 return isl_map_upper_bound(set, type, pos, value);
5593 struct isl_set *isl_set_lower_bound_dim(struct isl_set *set, unsigned dim,
5598 set = isl_set_cow(set);
5602 isl_assert(set->ctx, dim < isl_set_n_dim(set), goto error);
5603 for (i = 0; i < set->n; ++i) {
5604 set->p[i] = isl_basic_set_lower_bound_dim(set->p[i], dim, value);
5614 struct isl_map *isl_map_reverse(struct isl_map *map)
5618 map = isl_map_cow(map);
5622 map->dim = isl_space_reverse(map->dim);
5625 for (i = 0; i < map->n; ++i) {
5626 map->p[i] = isl_basic_map_reverse(map->p[i]);
5630 ISL_F_CLR(map, ISL_MAP_NORMALIZED);
5637 static struct isl_map *isl_basic_map_partial_lexopt(
5638 struct isl_basic_map *bmap, struct isl_basic_set *dom,
5639 struct isl_set **empty, int max)
5643 if (bmap->ctx->opt->pip == ISL_PIP_PIP)
5644 return isl_pip_basic_map_lexopt(bmap, dom, empty, max);
5646 return isl_tab_basic_map_partial_lexopt(bmap, dom, empty, max);
5648 isl_basic_map_free(bmap);
5649 isl_basic_set_free(dom);
5655 struct isl_map *isl_basic_map_partial_lexmax(
5656 struct isl_basic_map *bmap, struct isl_basic_set *dom,
5657 struct isl_set **empty)
5659 return isl_basic_map_partial_lexopt(bmap, dom, empty, 1);
5662 struct isl_map *isl_basic_map_partial_lexmin(
5663 struct isl_basic_map *bmap, struct isl_basic_set *dom,
5664 struct isl_set **empty)
5666 return isl_basic_map_partial_lexopt(bmap, dom, empty, 0);
5669 struct isl_set *isl_basic_set_partial_lexmin(
5670 struct isl_basic_set *bset, struct isl_basic_set *dom,
5671 struct isl_set **empty)
5673 return (struct isl_set *)
5674 isl_basic_map_partial_lexmin((struct isl_basic_map *)bset,
5678 struct isl_set *isl_basic_set_partial_lexmax(
5679 struct isl_basic_set *bset, struct isl_basic_set *dom,
5680 struct isl_set **empty)
5682 return (struct isl_set *)
5683 isl_basic_map_partial_lexmax((struct isl_basic_map *)bset,
5687 __isl_give isl_pw_multi_aff *isl_basic_map_partial_lexmin_pw_multi_aff(
5688 __isl_take isl_basic_map *bmap, __isl_take isl_basic_set *dom,
5689 __isl_give isl_set **empty)
5691 return isl_basic_map_partial_lexopt_pw_multi_aff(bmap, dom, empty, 0);
5694 __isl_give isl_pw_multi_aff *isl_basic_map_partial_lexmax_pw_multi_aff(
5695 __isl_take isl_basic_map *bmap, __isl_take isl_basic_set *dom,
5696 __isl_give isl_set **empty)
5698 return isl_basic_map_partial_lexopt_pw_multi_aff(bmap, dom, empty, 1);
5701 __isl_give isl_pw_multi_aff *isl_basic_set_partial_lexmin_pw_multi_aff(
5702 __isl_take isl_basic_set *bset, __isl_take isl_basic_set *dom,
5703 __isl_give isl_set **empty)
5705 return isl_basic_map_partial_lexmin_pw_multi_aff(bset, dom, empty);
5708 __isl_give isl_pw_multi_aff *isl_basic_set_partial_lexmax_pw_multi_aff(
5709 __isl_take isl_basic_set *bset, __isl_take isl_basic_set *dom,
5710 __isl_give isl_set **empty)
5712 return isl_basic_map_partial_lexmax_pw_multi_aff(bset, dom, empty);
5715 __isl_give isl_pw_multi_aff *isl_basic_map_lexopt_pw_multi_aff(
5716 __isl_take isl_basic_map *bmap, int max)
5718 isl_basic_set *dom = NULL;
5719 isl_space *dom_space;
5723 dom_space = isl_space_domain(isl_space_copy(bmap->dim));
5724 dom = isl_basic_set_universe(dom_space);
5725 return isl_basic_map_partial_lexopt_pw_multi_aff(bmap, dom, NULL, max);
5727 isl_basic_map_free(bmap);
5731 __isl_give isl_pw_multi_aff *isl_basic_map_lexmin_pw_multi_aff(
5732 __isl_take isl_basic_map *bmap)
5734 return isl_basic_map_lexopt_pw_multi_aff(bmap, 0);
5738 #define TYPE isl_pw_multi_aff
5740 #define SUFFIX _pw_multi_aff
5742 #define EMPTY isl_pw_multi_aff_empty
5744 #define ADD isl_pw_multi_aff_union_add
5745 #include "isl_map_lexopt_templ.c"
5747 /* Given a map "map", compute the lexicographically minimal
5748 * (or maximal) image element for each domain element in dom,
5749 * in the form of an isl_pw_multi_aff.
5750 * Set *empty to those elements in dom that do not have an image element.
5752 * We first compute the lexicographically minimal or maximal element
5753 * in the first basic map. This results in a partial solution "res"
5754 * and a subset "todo" of dom that still need to be handled.
5755 * We then consider each of the remaining maps in "map" and successively
5756 * update both "res" and "todo".
5758 static __isl_give isl_pw_multi_aff *isl_map_partial_lexopt_aligned_pw_multi_aff(
5759 __isl_take isl_map *map, __isl_take isl_set *dom,
5760 __isl_give isl_set **empty, int max)
5763 isl_pw_multi_aff *res;
5769 if (isl_map_plain_is_empty(map)) {
5774 return isl_pw_multi_aff_from_map(map);
5777 res = basic_map_partial_lexopt_pw_multi_aff(
5778 isl_basic_map_copy(map->p[0]),
5779 isl_set_copy(dom), &todo, max);
5781 for (i = 1; i < map->n; ++i) {
5782 isl_pw_multi_aff *res_i;
5785 res_i = basic_map_partial_lexopt_pw_multi_aff(
5786 isl_basic_map_copy(map->p[i]),
5787 isl_set_copy(dom), &todo_i, max);
5790 res = isl_pw_multi_aff_union_lexmax(res, res_i);
5792 res = isl_pw_multi_aff_union_lexmin(res, res_i);
5794 todo = isl_set_intersect(todo, todo_i);
5815 #define TYPE isl_map
5819 #define EMPTY isl_map_empty
5821 #define ADD isl_map_union_disjoint
5822 #include "isl_map_lexopt_templ.c"
5824 /* Given a map "map", compute the lexicographically minimal
5825 * (or maximal) image element for each domain element in dom.
5826 * Set *empty to those elements in dom that do not have an image element.
5828 * We first compute the lexicographically minimal or maximal element
5829 * in the first basic map. This results in a partial solution "res"
5830 * and a subset "todo" of dom that still need to be handled.
5831 * We then consider each of the remaining maps in "map" and successively
5832 * update both "res" and "todo".
5834 * Let res^k and todo^k be the results after k steps and let i = k + 1.
5835 * Assume we are computing the lexicographical maximum.
5836 * We first compute the lexicographically maximal element in basic map i.
5837 * This results in a partial solution res_i and a subset todo_i.
5838 * Then we combine these results with those obtain for the first k basic maps
5839 * to obtain a result that is valid for the first k+1 basic maps.
5840 * In particular, the set where there is no solution is the set where
5841 * there is no solution for the first k basic maps and also no solution
5842 * for the ith basic map, i.e.,
5844 * todo^i = todo^k * todo_i
5846 * On dom(res^k) * dom(res_i), we need to pick the larger of the two
5847 * solutions, arbitrarily breaking ties in favor of res^k.
5848 * That is, when res^k(a) >= res_i(a), we pick res^k and
5849 * when res^k(a) < res_i(a), we pick res_i. (Here, ">=" and "<" denote
5850 * the lexicographic order.)
5851 * In practice, we compute
5853 * res^k * (res_i . "<=")
5857 * res_i * (res^k . "<")
5859 * Finally, we consider the symmetric difference of dom(res^k) and dom(res_i),
5860 * where only one of res^k and res_i provides a solution and we simply pick
5867 * Note that we only compute these intersections when dom(res^k) intersects
5868 * dom(res_i). Otherwise, the only effect of these intersections is to
5869 * potentially break up res^k and res_i into smaller pieces.
5870 * We want to avoid such splintering as much as possible.
5871 * In fact, an earlier implementation of this function would look for
5872 * better results in the domain of res^k and for extra results in todo^k,
5873 * but this would always result in a splintering according to todo^k,
5874 * even when the domain of basic map i is disjoint from the domains of
5875 * the previous basic maps.
5877 static __isl_give isl_map *isl_map_partial_lexopt_aligned(
5878 __isl_take isl_map *map, __isl_take isl_set *dom,
5879 __isl_give isl_set **empty, int max)
5882 struct isl_map *res;
5883 struct isl_set *todo;
5888 if (isl_map_plain_is_empty(map)) {
5896 res = basic_map_partial_lexopt(isl_basic_map_copy(map->p[0]),
5897 isl_set_copy(dom), &todo, max);
5899 for (i = 1; i < map->n; ++i) {
5903 isl_space *dim = isl_space_range(isl_map_get_space(res));
5905 res_i = basic_map_partial_lexopt(isl_basic_map_copy(map->p[i]),
5906 isl_set_copy(dom), &todo_i, max);
5909 lt = isl_map_lex_lt(isl_space_copy(dim));
5910 le = isl_map_lex_le(dim);
5912 lt = isl_map_lex_gt(isl_space_copy(dim));
5913 le = isl_map_lex_ge(dim);
5915 lt = isl_map_apply_range(isl_map_copy(res), lt);
5916 lt = isl_map_intersect(lt, isl_map_copy(res_i));
5917 le = isl_map_apply_range(isl_map_copy(res_i), le);
5918 le = isl_map_intersect(le, isl_map_copy(res));
5920 if (!isl_map_is_empty(lt) || !isl_map_is_empty(le)) {
5921 res = isl_map_intersect_domain(res,
5922 isl_set_copy(todo_i));
5923 res_i = isl_map_intersect_domain(res_i,
5924 isl_set_copy(todo));
5927 res = isl_map_union_disjoint(res, res_i);
5928 res = isl_map_union_disjoint(res, lt);
5929 res = isl_map_union_disjoint(res, le);
5931 todo = isl_set_intersect(todo, todo_i);
5951 __isl_give isl_map *isl_map_partial_lexmax(
5952 __isl_take isl_map *map, __isl_take isl_set *dom,
5953 __isl_give isl_set **empty)
5955 return isl_map_partial_lexopt(map, dom, empty, 1);
5958 __isl_give isl_map *isl_map_partial_lexmin(
5959 __isl_take isl_map *map, __isl_take isl_set *dom,
5960 __isl_give isl_set **empty)
5962 return isl_map_partial_lexopt(map, dom, empty, 0);
5965 __isl_give isl_set *isl_set_partial_lexmin(
5966 __isl_take isl_set *set, __isl_take isl_set *dom,
5967 __isl_give isl_set **empty)
5969 return (struct isl_set *)
5970 isl_map_partial_lexmin((struct isl_map *)set,
5974 __isl_give isl_set *isl_set_partial_lexmax(
5975 __isl_take isl_set *set, __isl_take isl_set *dom,
5976 __isl_give isl_set **empty)
5978 return (struct isl_set *)
5979 isl_map_partial_lexmax((struct isl_map *)set,
5983 __isl_give isl_map *isl_basic_map_lexopt(__isl_take isl_basic_map *bmap, int max)
5985 struct isl_basic_set *dom = NULL;
5990 dom_dim = isl_space_domain(isl_space_copy(bmap->dim));
5991 dom = isl_basic_set_universe(dom_dim);
5992 return isl_basic_map_partial_lexopt(bmap, dom, NULL, max);
5994 isl_basic_map_free(bmap);
5998 __isl_give isl_map *isl_basic_map_lexmin(__isl_take isl_basic_map *bmap)
6000 return isl_basic_map_lexopt(bmap, 0);
6003 __isl_give isl_map *isl_basic_map_lexmax(__isl_take isl_basic_map *bmap)
6005 return isl_basic_map_lexopt(bmap, 1);
6008 __isl_give isl_set *isl_basic_set_lexmin(__isl_take isl_basic_set *bset)
6010 return (isl_set *)isl_basic_map_lexmin((isl_basic_map *)bset);
6013 __isl_give isl_set *isl_basic_set_lexmax(__isl_take isl_basic_set *bset)
6015 return (isl_set *)isl_basic_map_lexmax((isl_basic_map *)bset);
6018 __isl_give isl_set *isl_set_lexmin(__isl_take isl_set *set)
6020 return (isl_set *)isl_map_lexmin((isl_map *)set);
6023 __isl_give isl_set *isl_set_lexmax(__isl_take isl_set *set)
6025 return (isl_set *)isl_map_lexmax((isl_map *)set);
6028 /* Extract the first and only affine expression from list
6029 * and then add it to *pwaff with the given dom.
6030 * This domain is known to be disjoint from other domains
6031 * because of the way isl_basic_map_foreach_lexmax works.
6033 static int update_dim_opt(__isl_take isl_basic_set *dom,
6034 __isl_take isl_aff_list *list, void *user)
6036 isl_ctx *ctx = isl_basic_set_get_ctx(dom);
6038 isl_pw_aff **pwaff = user;
6039 isl_pw_aff *pwaff_i;
6041 if (isl_aff_list_n_aff(list) != 1)
6042 isl_die(ctx, isl_error_internal,
6043 "expecting single element list", goto error);
6045 aff = isl_aff_list_get_aff(list, 0);
6046 pwaff_i = isl_pw_aff_alloc(isl_set_from_basic_set(dom), aff);
6048 *pwaff = isl_pw_aff_add_disjoint(*pwaff, pwaff_i);
6050 isl_aff_list_free(list);
6054 isl_basic_set_free(dom);
6055 isl_aff_list_free(list);
6059 /* Given a basic map with one output dimension, compute the minimum or
6060 * maximum of that dimension as an isl_pw_aff.
6062 * The isl_pw_aff is constructed by having isl_basic_map_foreach_lexopt
6063 * call update_dim_opt on each leaf of the result.
6065 static __isl_give isl_pw_aff *basic_map_dim_opt(__isl_keep isl_basic_map *bmap,
6068 isl_space *dim = isl_basic_map_get_space(bmap);
6072 dim = isl_space_from_domain(isl_space_domain(dim));
6073 dim = isl_space_add_dims(dim, isl_dim_out, 1);
6074 pwaff = isl_pw_aff_empty(dim);
6076 r = isl_basic_map_foreach_lexopt(bmap, max, &update_dim_opt, &pwaff);
6078 return isl_pw_aff_free(pwaff);
6083 /* Compute the minimum or maximum of the given output dimension
6084 * as a function of the parameters and the input dimensions,
6085 * but independently of the other output dimensions.
6087 * We first project out the other output dimension and then compute
6088 * the "lexicographic" maximum in each basic map, combining the results
6089 * using isl_pw_aff_union_max.
6091 static __isl_give isl_pw_aff *map_dim_opt(__isl_take isl_map *map, int pos,
6098 n_out = isl_map_dim(map, isl_dim_out);
6099 map = isl_map_project_out(map, isl_dim_out, pos + 1, n_out - (pos + 1));
6100 map = isl_map_project_out(map, isl_dim_out, 0, pos);
6105 isl_space *dim = isl_map_get_space(map);
6106 dim = isl_space_domain(isl_space_from_range(dim));
6108 return isl_pw_aff_empty(dim);
6111 pwaff = basic_map_dim_opt(map->p[0], max);
6112 for (i = 1; i < map->n; ++i) {
6113 isl_pw_aff *pwaff_i;
6115 pwaff_i = basic_map_dim_opt(map->p[i], max);
6116 pwaff = isl_pw_aff_union_opt(pwaff, pwaff_i, max);
6124 /* Compute the maximum of the given output dimension as a function of the
6125 * parameters and input dimensions, but independently of
6126 * the other output dimensions.
6128 __isl_give isl_pw_aff *isl_map_dim_max(__isl_take isl_map *map, int pos)
6130 return map_dim_opt(map, pos, 1);
6133 /* Compute the minimum or maximum of the given set dimension
6134 * as a function of the parameters,
6135 * but independently of the other set dimensions.
6137 static __isl_give isl_pw_aff *set_dim_opt(__isl_take isl_set *set, int pos,
6140 return map_dim_opt(set, pos, max);
6143 /* Compute the maximum of the given set dimension as a function of the
6144 * parameters, but independently of the other set dimensions.
6146 __isl_give isl_pw_aff *isl_set_dim_max(__isl_take isl_set *set, int pos)
6148 return set_dim_opt(set, pos, 1);
6151 /* Compute the minimum of the given set dimension as a function of the
6152 * parameters, but independently of the other set dimensions.
6154 __isl_give isl_pw_aff *isl_set_dim_min(__isl_take isl_set *set, int pos)
6156 return set_dim_opt(set, pos, 0);
6159 /* Apply a preimage specified by "mat" on the parameters of "bset".
6160 * bset is assumed to have only parameters and divs.
6162 static struct isl_basic_set *basic_set_parameter_preimage(
6163 struct isl_basic_set *bset, struct isl_mat *mat)
6170 bset->dim = isl_space_cow(bset->dim);
6174 nparam = isl_basic_set_dim(bset, isl_dim_param);
6176 isl_assert(bset->ctx, mat->n_row == 1 + nparam, goto error);
6178 bset->dim->nparam = 0;
6179 bset->dim->n_out = nparam;
6180 bset = isl_basic_set_preimage(bset, mat);
6182 bset->dim->nparam = bset->dim->n_out;
6183 bset->dim->n_out = 0;
6188 isl_basic_set_free(bset);
6192 /* Apply a preimage specified by "mat" on the parameters of "set".
6193 * set is assumed to have only parameters and divs.
6195 static struct isl_set *set_parameter_preimage(
6196 struct isl_set *set, struct isl_mat *mat)
6198 isl_space *dim = NULL;
6204 dim = isl_space_copy(set->dim);
6205 dim = isl_space_cow(dim);
6209 nparam = isl_set_dim(set, isl_dim_param);
6211 isl_assert(set->ctx, mat->n_row == 1 + nparam, goto error);
6214 dim->n_out = nparam;
6215 isl_set_reset_space(set, dim);
6216 set = isl_set_preimage(set, mat);
6219 dim = isl_space_copy(set->dim);
6220 dim = isl_space_cow(dim);
6223 dim->nparam = dim->n_out;
6225 isl_set_reset_space(set, dim);
6228 isl_space_free(dim);
6235 /* Intersect the basic set "bset" with the affine space specified by the
6236 * equalities in "eq".
6238 static struct isl_basic_set *basic_set_append_equalities(
6239 struct isl_basic_set *bset, struct isl_mat *eq)
6247 bset = isl_basic_set_extend_space(bset, isl_space_copy(bset->dim), 0,
6252 len = 1 + isl_space_dim(bset->dim, isl_dim_all) + bset->extra;
6253 for (i = 0; i < eq->n_row; ++i) {
6254 k = isl_basic_set_alloc_equality(bset);
6257 isl_seq_cpy(bset->eq[k], eq->row[i], eq->n_col);
6258 isl_seq_clr(bset->eq[k] + eq->n_col, len - eq->n_col);
6262 bset = isl_basic_set_gauss(bset, NULL);
6263 bset = isl_basic_set_finalize(bset);
6268 isl_basic_set_free(bset);
6272 /* Intersect the set "set" with the affine space specified by the
6273 * equalities in "eq".
6275 static struct isl_set *set_append_equalities(struct isl_set *set,
6283 for (i = 0; i < set->n; ++i) {
6284 set->p[i] = basic_set_append_equalities(set->p[i],
6297 /* Project the given basic set onto its parameter domain, possibly introducing
6298 * new, explicit, existential variables in the constraints.
6299 * The input has parameters and (possibly implicit) existential variables.
6300 * The output has the same parameters, but only
6301 * explicit existentially quantified variables.
6303 * The actual projection is performed by pip, but pip doesn't seem
6304 * to like equalities very much, so we first remove the equalities
6305 * among the parameters by performing a variable compression on
6306 * the parameters. Afterward, an inverse transformation is performed
6307 * and the equalities among the parameters are inserted back in.
6309 static struct isl_set *parameter_compute_divs(struct isl_basic_set *bset)
6313 struct isl_mat *T, *T2;
6314 struct isl_set *set;
6315 unsigned nparam, n_div;
6317 bset = isl_basic_set_cow(bset);
6321 if (bset->n_eq == 0)
6322 return isl_basic_set_lexmin(bset);
6324 isl_basic_set_gauss(bset, NULL);
6326 nparam = isl_basic_set_dim(bset, isl_dim_param);
6327 n_div = isl_basic_set_dim(bset, isl_dim_div);
6329 for (i = 0, j = n_div - 1; i < bset->n_eq && j >= 0; --j) {
6330 if (!isl_int_is_zero(bset->eq[i][1 + nparam + j]))
6333 if (i == bset->n_eq)
6334 return isl_basic_set_lexmin(bset);
6336 eq = isl_mat_sub_alloc6(bset->ctx, bset->eq, i, bset->n_eq - i,
6338 eq = isl_mat_cow(eq);
6339 T = isl_mat_variable_compression(isl_mat_copy(eq), &T2);
6340 if (T && T->n_col == 0) {
6344 bset = isl_basic_set_set_to_empty(bset);
6345 return isl_set_from_basic_set(bset);
6347 bset = basic_set_parameter_preimage(bset, T);
6349 set = isl_basic_set_lexmin(bset);
6350 set = set_parameter_preimage(set, T2);
6351 set = set_append_equalities(set, eq);
6355 /* Compute an explicit representation for all the existentially
6356 * quantified variables.
6357 * The input and output dimensions are first turned into parameters.
6358 * compute_divs then returns a map with the same parameters and
6359 * no input or output dimensions and the dimension specification
6360 * is reset to that of the input.
6362 static struct isl_map *compute_divs(struct isl_basic_map *bmap)
6364 struct isl_basic_set *bset;
6365 struct isl_set *set;
6366 struct isl_map *map;
6367 isl_space *dim, *orig_dim = NULL;
6372 bmap = isl_basic_map_cow(bmap);
6376 nparam = isl_basic_map_dim(bmap, isl_dim_param);
6377 n_in = isl_basic_map_dim(bmap, isl_dim_in);
6378 n_out = isl_basic_map_dim(bmap, isl_dim_out);
6379 dim = isl_space_set_alloc(bmap->ctx, nparam + n_in + n_out, 0);
6383 orig_dim = bmap->dim;
6385 bset = (struct isl_basic_set *)bmap;
6387 set = parameter_compute_divs(bset);
6388 map = (struct isl_map *)set;
6389 map = isl_map_reset_space(map, orig_dim);
6393 isl_basic_map_free(bmap);
6397 int isl_basic_map_divs_known(__isl_keep isl_basic_map *bmap)
6405 off = isl_space_dim(bmap->dim, isl_dim_all);
6406 for (i = 0; i < bmap->n_div; ++i) {
6407 if (isl_int_is_zero(bmap->div[i][0]))
6409 isl_assert(bmap->ctx, isl_int_is_zero(bmap->div[i][1+1+off+i]),
6415 static int map_divs_known(__isl_keep isl_map *map)
6422 for (i = 0; i < map->n; ++i) {
6423 int known = isl_basic_map_divs_known(map->p[i]);
6431 /* If bmap contains any unknown divs, then compute explicit
6432 * expressions for them. However, this computation may be
6433 * quite expensive, so first try to remove divs that aren't
6436 struct isl_map *isl_basic_map_compute_divs(struct isl_basic_map *bmap)
6439 struct isl_map *map;
6441 known = isl_basic_map_divs_known(bmap);
6445 return isl_map_from_basic_map(bmap);
6447 bmap = isl_basic_map_drop_redundant_divs(bmap);
6449 known = isl_basic_map_divs_known(bmap);
6453 return isl_map_from_basic_map(bmap);
6455 map = compute_divs(bmap);
6458 isl_basic_map_free(bmap);
6462 struct isl_map *isl_map_compute_divs(struct isl_map *map)
6466 struct isl_map *res;
6473 known = map_divs_known(map);
6481 res = isl_basic_map_compute_divs(isl_basic_map_copy(map->p[0]));
6482 for (i = 1 ; i < map->n; ++i) {
6484 r2 = isl_basic_map_compute_divs(isl_basic_map_copy(map->p[i]));
6485 if (ISL_F_ISSET(map, ISL_MAP_DISJOINT))
6486 res = isl_map_union_disjoint(res, r2);
6488 res = isl_map_union(res, r2);
6495 struct isl_set *isl_basic_set_compute_divs(struct isl_basic_set *bset)
6497 return (struct isl_set *)
6498 isl_basic_map_compute_divs((struct isl_basic_map *)bset);
6501 struct isl_set *isl_set_compute_divs(struct isl_set *set)
6503 return (struct isl_set *)
6504 isl_map_compute_divs((struct isl_map *)set);
6507 struct isl_set *isl_map_domain(struct isl_map *map)
6510 struct isl_set *set;
6515 map = isl_map_cow(map);
6519 set = (struct isl_set *)map;
6520 set->dim = isl_space_domain(set->dim);
6523 for (i = 0; i < map->n; ++i) {
6524 set->p[i] = isl_basic_map_domain(map->p[i]);
6528 ISL_F_CLR(set, ISL_MAP_DISJOINT);
6529 ISL_F_CLR(set, ISL_SET_NORMALIZED);
6536 /* Return the union of "map1" and "map2", where we assume for now that
6537 * "map1" and "map2" are disjoint. Note that the basic maps inside
6538 * "map1" or "map2" may not be disjoint from each other.
6539 * Also note that this function is also called from isl_map_union,
6540 * which takes care of handling the situation where "map1" and "map2"
6541 * may not be disjoint.
6543 * If one of the inputs is empty, we can simply return the other input.
6544 * Similarly, if one of the inputs is universal, then it is equal to the union.
6546 static __isl_give isl_map *map_union_disjoint(__isl_take isl_map *map1,
6547 __isl_take isl_map *map2)
6551 struct isl_map *map = NULL;
6566 is_universe = isl_map_plain_is_universe(map1);
6567 if (is_universe < 0)
6574 is_universe = isl_map_plain_is_universe(map2);
6575 if (is_universe < 0)
6582 isl_assert(map1->ctx, isl_space_is_equal(map1->dim, map2->dim), goto error);
6584 if (ISL_F_ISSET(map1, ISL_MAP_DISJOINT) &&
6585 ISL_F_ISSET(map2, ISL_MAP_DISJOINT))
6586 ISL_FL_SET(flags, ISL_MAP_DISJOINT);
6588 map = isl_map_alloc_space(isl_space_copy(map1->dim),
6589 map1->n + map2->n, flags);
6592 for (i = 0; i < map1->n; ++i) {
6593 map = isl_map_add_basic_map(map,
6594 isl_basic_map_copy(map1->p[i]));
6598 for (i = 0; i < map2->n; ++i) {
6599 map = isl_map_add_basic_map(map,
6600 isl_basic_map_copy(map2->p[i]));
6614 __isl_give isl_map *isl_map_union_disjoint(__isl_take isl_map *map1,
6615 __isl_take isl_map *map2)
6617 return isl_map_align_params_map_map_and(map1, map2, &map_union_disjoint);
6620 struct isl_map *isl_map_union(struct isl_map *map1, struct isl_map *map2)
6622 map1 = isl_map_union_disjoint(map1, map2);
6626 ISL_F_CLR(map1, ISL_MAP_DISJOINT);
6630 struct isl_set *isl_set_union_disjoint(
6631 struct isl_set *set1, struct isl_set *set2)
6633 return (struct isl_set *)
6634 isl_map_union_disjoint(
6635 (struct isl_map *)set1, (struct isl_map *)set2);
6638 struct isl_set *isl_set_union(struct isl_set *set1, struct isl_set *set2)
6640 return (struct isl_set *)
6641 isl_map_union((struct isl_map *)set1, (struct isl_map *)set2);
6644 /* Apply "fn" to pairs of elements from "map" and "set" and collect
6647 * "map" and "set" are assumed to be compatible and non-NULL.
6649 static __isl_give isl_map *map_intersect_set(__isl_take isl_map *map,
6650 __isl_take isl_set *set,
6651 __isl_give isl_basic_map *fn(__isl_take isl_basic_map *bmap,
6652 __isl_take isl_basic_set *bset))
6655 struct isl_map *result;
6658 if (isl_set_plain_is_universe(set)) {
6663 if (ISL_F_ISSET(map, ISL_MAP_DISJOINT) &&
6664 ISL_F_ISSET(set, ISL_MAP_DISJOINT))
6665 ISL_FL_SET(flags, ISL_MAP_DISJOINT);
6667 result = isl_map_alloc_space(isl_space_copy(map->dim),
6668 map->n * set->n, flags);
6669 for (i = 0; result && i < map->n; ++i)
6670 for (j = 0; j < set->n; ++j) {
6671 result = isl_map_add_basic_map(result,
6672 fn(isl_basic_map_copy(map->p[i]),
6673 isl_basic_set_copy(set->p[j])));
6683 static __isl_give isl_map *map_intersect_range(__isl_take isl_map *map,
6684 __isl_take isl_set *set)
6689 if (!isl_map_compatible_range(map, set))
6690 isl_die(set->ctx, isl_error_invalid,
6691 "incompatible spaces", goto error);
6693 return map_intersect_set(map, set, &isl_basic_map_intersect_range);
6700 __isl_give isl_map *isl_map_intersect_range(__isl_take isl_map *map,
6701 __isl_take isl_set *set)
6703 return isl_map_align_params_map_map_and(map, set, &map_intersect_range);
6706 static __isl_give isl_map *map_intersect_domain(__isl_take isl_map *map,
6707 __isl_take isl_set *set)
6712 if (!isl_map_compatible_domain(map, set))
6713 isl_die(set->ctx, isl_error_invalid,
6714 "incompatible spaces", goto error);
6716 return map_intersect_set(map, set, &isl_basic_map_intersect_domain);
6723 __isl_give isl_map *isl_map_intersect_domain(__isl_take isl_map *map,
6724 __isl_take isl_set *set)
6726 return isl_map_align_params_map_map_and(map, set,
6727 &map_intersect_domain);
6730 static __isl_give isl_map *map_apply_domain(__isl_take isl_map *map1,
6731 __isl_take isl_map *map2)
6735 map1 = isl_map_reverse(map1);
6736 map1 = isl_map_apply_range(map1, map2);
6737 return isl_map_reverse(map1);
6744 __isl_give isl_map *isl_map_apply_domain(__isl_take isl_map *map1,
6745 __isl_take isl_map *map2)
6747 return isl_map_align_params_map_map_and(map1, map2, &map_apply_domain);
6750 static __isl_give isl_map *map_apply_range(__isl_take isl_map *map1,
6751 __isl_take isl_map *map2)
6753 isl_space *dim_result;
6754 struct isl_map *result;
6760 dim_result = isl_space_join(isl_space_copy(map1->dim),
6761 isl_space_copy(map2->dim));
6763 result = isl_map_alloc_space(dim_result, map1->n * map2->n, 0);
6766 for (i = 0; i < map1->n; ++i)
6767 for (j = 0; j < map2->n; ++j) {
6768 result = isl_map_add_basic_map(result,
6769 isl_basic_map_apply_range(
6770 isl_basic_map_copy(map1->p[i]),
6771 isl_basic_map_copy(map2->p[j])));
6777 if (result && result->n <= 1)
6778 ISL_F_SET(result, ISL_MAP_DISJOINT);
6786 __isl_give isl_map *isl_map_apply_range(__isl_take isl_map *map1,
6787 __isl_take isl_map *map2)
6789 return isl_map_align_params_map_map_and(map1, map2, &map_apply_range);
6793 * returns range - domain
6795 struct isl_basic_set *isl_basic_map_deltas(struct isl_basic_map *bmap)
6797 isl_space *dims, *target_dim;
6798 struct isl_basic_set *bset;
6805 isl_assert(bmap->ctx, isl_space_tuple_match(bmap->dim, isl_dim_in,
6806 bmap->dim, isl_dim_out),
6808 target_dim = isl_space_domain(isl_basic_map_get_space(bmap));
6809 dim = isl_basic_map_n_in(bmap);
6810 nparam = isl_basic_map_n_param(bmap);
6811 bset = isl_basic_set_from_basic_map(bmap);
6812 bset = isl_basic_set_cow(bset);
6813 dims = isl_basic_set_get_space(bset);
6814 dims = isl_space_add_dims(dims, isl_dim_set, dim);
6815 bset = isl_basic_set_extend_space(bset, dims, 0, dim, 0);
6816 bset = isl_basic_set_swap_vars(bset, 2*dim);
6817 for (i = 0; i < dim; ++i) {
6818 int j = isl_basic_map_alloc_equality(
6819 (struct isl_basic_map *)bset);
6822 isl_seq_clr(bset->eq[j], 1 + isl_basic_set_total_dim(bset));
6823 isl_int_set_si(bset->eq[j][1+nparam+i], 1);
6824 isl_int_set_si(bset->eq[j][1+nparam+dim+i], 1);
6825 isl_int_set_si(bset->eq[j][1+nparam+2*dim+i], -1);
6827 bset = isl_basic_set_project_out(bset, isl_dim_set, dim, 2*dim);
6828 bset = isl_basic_set_reset_space(bset, target_dim);
6831 isl_basic_map_free(bmap);
6836 * returns range - domain
6838 __isl_give isl_set *isl_map_deltas(__isl_take isl_map *map)
6842 struct isl_set *result;
6847 isl_assert(map->ctx, isl_space_tuple_match(map->dim, isl_dim_in,
6848 map->dim, isl_dim_out),
6850 dim = isl_map_get_space(map);
6851 dim = isl_space_domain(dim);
6852 result = isl_set_alloc_space(dim, map->n, 0);
6855 for (i = 0; i < map->n; ++i)
6856 result = isl_set_add_basic_set(result,
6857 isl_basic_map_deltas(isl_basic_map_copy(map->p[i])));
6866 * returns [domain -> range] -> range - domain
6868 __isl_give isl_basic_map *isl_basic_map_deltas_map(
6869 __isl_take isl_basic_map *bmap)
6873 isl_basic_map *domain;
6877 if (!isl_space_tuple_match(bmap->dim, isl_dim_in, bmap->dim, isl_dim_out))
6878 isl_die(bmap->ctx, isl_error_invalid,
6879 "domain and range don't match", goto error);
6881 nparam = isl_basic_map_dim(bmap, isl_dim_param);
6882 n = isl_basic_map_dim(bmap, isl_dim_in);
6884 dim = isl_space_from_range(isl_space_domain(isl_basic_map_get_space(bmap)));
6885 domain = isl_basic_map_universe(dim);
6887 bmap = isl_basic_map_from_domain(isl_basic_map_wrap(bmap));
6888 bmap = isl_basic_map_apply_range(bmap, domain);
6889 bmap = isl_basic_map_extend_constraints(bmap, n, 0);
6891 total = isl_basic_map_total_dim(bmap);
6893 for (i = 0; i < n; ++i) {
6894 k = isl_basic_map_alloc_equality(bmap);
6897 isl_seq_clr(bmap->eq[k], 1 + total);
6898 isl_int_set_si(bmap->eq[k][1 + nparam + i], 1);
6899 isl_int_set_si(bmap->eq[k][1 + nparam + n + i], -1);
6900 isl_int_set_si(bmap->eq[k][1 + nparam + n + n + i], 1);
6903 bmap = isl_basic_map_gauss(bmap, NULL);
6904 return isl_basic_map_finalize(bmap);
6906 isl_basic_map_free(bmap);
6911 * returns [domain -> range] -> range - domain
6913 __isl_give isl_map *isl_map_deltas_map(__isl_take isl_map *map)
6916 isl_space *domain_dim;
6921 if (!isl_space_tuple_match(map->dim, isl_dim_in, map->dim, isl_dim_out))
6922 isl_die(map->ctx, isl_error_invalid,
6923 "domain and range don't match", goto error);
6925 map = isl_map_cow(map);
6929 domain_dim = isl_space_from_range(isl_space_domain(isl_map_get_space(map)));
6930 map->dim = isl_space_from_domain(isl_space_wrap(map->dim));
6931 map->dim = isl_space_join(map->dim, domain_dim);
6934 for (i = 0; i < map->n; ++i) {
6935 map->p[i] = isl_basic_map_deltas_map(map->p[i]);
6939 ISL_F_CLR(map, ISL_MAP_NORMALIZED);
6946 static __isl_give isl_basic_map *basic_map_identity(__isl_take isl_space *dims)
6948 struct isl_basic_map *bmap;
6956 nparam = dims->nparam;
6958 bmap = isl_basic_map_alloc_space(dims, 0, dim, 0);
6962 for (i = 0; i < dim; ++i) {
6963 int j = isl_basic_map_alloc_equality(bmap);
6966 isl_seq_clr(bmap->eq[j], 1 + isl_basic_map_total_dim(bmap));
6967 isl_int_set_si(bmap->eq[j][1+nparam+i], 1);
6968 isl_int_set_si(bmap->eq[j][1+nparam+dim+i], -1);
6970 return isl_basic_map_finalize(bmap);
6972 isl_basic_map_free(bmap);
6976 __isl_give isl_basic_map *isl_basic_map_identity(__isl_take isl_space *dim)
6980 if (dim->n_in != dim->n_out)
6981 isl_die(dim->ctx, isl_error_invalid,
6982 "number of input and output dimensions needs to be "
6983 "the same", goto error);
6984 return basic_map_identity(dim);
6986 isl_space_free(dim);
6990 struct isl_basic_map *isl_basic_map_identity_like(struct isl_basic_map *model)
6992 if (!model || !model->dim)
6994 return isl_basic_map_identity(isl_space_copy(model->dim));
6997 __isl_give isl_map *isl_map_identity(__isl_take isl_space *dim)
6999 return isl_map_from_basic_map(isl_basic_map_identity(dim));
7002 struct isl_map *isl_map_identity_like(struct isl_map *model)
7004 if (!model || !model->dim)
7006 return isl_map_identity(isl_space_copy(model->dim));
7009 struct isl_map *isl_map_identity_like_basic_map(struct isl_basic_map *model)
7011 if (!model || !model->dim)
7013 return isl_map_identity(isl_space_copy(model->dim));
7016 __isl_give isl_map *isl_set_identity(__isl_take isl_set *set)
7018 isl_space *dim = isl_set_get_space(set);
7020 id = isl_map_identity(isl_space_map_from_set(dim));
7021 return isl_map_intersect_range(id, set);
7024 /* Construct a basic set with all set dimensions having only non-negative
7027 __isl_give isl_basic_set *isl_basic_set_positive_orthant(
7028 __isl_take isl_space *space)
7033 struct isl_basic_set *bset;
7037 nparam = space->nparam;
7039 bset = isl_basic_set_alloc_space(space, 0, 0, dim);
7042 for (i = 0; i < dim; ++i) {
7043 int k = isl_basic_set_alloc_inequality(bset);
7046 isl_seq_clr(bset->ineq[k], 1 + isl_basic_set_total_dim(bset));
7047 isl_int_set_si(bset->ineq[k][1 + nparam + i], 1);
7051 isl_basic_set_free(bset);
7055 /* Construct the half-space x_pos >= 0.
7057 static __isl_give isl_basic_set *nonneg_halfspace(__isl_take isl_space *dim,
7061 isl_basic_set *nonneg;
7063 nonneg = isl_basic_set_alloc_space(dim, 0, 0, 1);
7064 k = isl_basic_set_alloc_inequality(nonneg);
7067 isl_seq_clr(nonneg->ineq[k], 1 + isl_basic_set_total_dim(nonneg));
7068 isl_int_set_si(nonneg->ineq[k][pos], 1);
7070 return isl_basic_set_finalize(nonneg);
7072 isl_basic_set_free(nonneg);
7076 /* Construct the half-space x_pos <= -1.
7078 static __isl_give isl_basic_set *neg_halfspace(__isl_take isl_space *dim, int pos)
7083 neg = isl_basic_set_alloc_space(dim, 0, 0, 1);
7084 k = isl_basic_set_alloc_inequality(neg);
7087 isl_seq_clr(neg->ineq[k], 1 + isl_basic_set_total_dim(neg));
7088 isl_int_set_si(neg->ineq[k][0], -1);
7089 isl_int_set_si(neg->ineq[k][pos], -1);
7091 return isl_basic_set_finalize(neg);
7093 isl_basic_set_free(neg);
7097 __isl_give isl_set *isl_set_split_dims(__isl_take isl_set *set,
7098 enum isl_dim_type type, unsigned first, unsigned n)
7101 isl_basic_set *nonneg;
7109 isl_assert(set->ctx, first + n <= isl_set_dim(set, type), goto error);
7111 for (i = 0; i < n; ++i) {
7112 nonneg = nonneg_halfspace(isl_set_get_space(set),
7113 pos(set->dim, type) + first + i);
7114 neg = neg_halfspace(isl_set_get_space(set),
7115 pos(set->dim, type) + first + i);
7117 set = isl_set_intersect(set, isl_basic_set_union(nonneg, neg));
7126 static int foreach_orthant(__isl_take isl_set *set, int *signs, int first,
7127 int len, int (*fn)(__isl_take isl_set *orthant, int *signs, void *user),
7134 if (isl_set_plain_is_empty(set)) {
7139 return fn(set, signs, user);
7142 half = isl_set_from_basic_set(nonneg_halfspace(isl_set_get_space(set),
7144 half = isl_set_intersect(half, isl_set_copy(set));
7145 if (foreach_orthant(half, signs, first + 1, len, fn, user) < 0)
7149 half = isl_set_from_basic_set(neg_halfspace(isl_set_get_space(set),
7151 half = isl_set_intersect(half, set);
7152 return foreach_orthant(half, signs, first + 1, len, fn, user);
7158 /* Call "fn" on the intersections of "set" with each of the orthants
7159 * (except for obviously empty intersections). The orthant is identified
7160 * by the signs array, with each entry having value 1 or -1 according
7161 * to the sign of the corresponding variable.
7163 int isl_set_foreach_orthant(__isl_keep isl_set *set,
7164 int (*fn)(__isl_take isl_set *orthant, int *signs, void *user),
7174 if (isl_set_plain_is_empty(set))
7177 nparam = isl_set_dim(set, isl_dim_param);
7178 nvar = isl_set_dim(set, isl_dim_set);
7180 signs = isl_alloc_array(set->ctx, int, nparam + nvar);
7182 r = foreach_orthant(isl_set_copy(set), signs, 0, nparam + nvar,
7190 int isl_set_is_equal(struct isl_set *set1, struct isl_set *set2)
7192 return isl_map_is_equal((struct isl_map *)set1, (struct isl_map *)set2);
7195 int isl_basic_map_is_subset(
7196 struct isl_basic_map *bmap1, struct isl_basic_map *bmap2)
7199 struct isl_map *map1;
7200 struct isl_map *map2;
7202 if (!bmap1 || !bmap2)
7205 map1 = isl_map_from_basic_map(isl_basic_map_copy(bmap1));
7206 map2 = isl_map_from_basic_map(isl_basic_map_copy(bmap2));
7208 is_subset = isl_map_is_subset(map1, map2);
7216 int isl_basic_set_is_subset(__isl_keep isl_basic_set *bset1,
7217 __isl_keep isl_basic_set *bset2)
7219 return isl_basic_map_is_subset(bset1, bset2);
7222 int isl_basic_map_is_equal(
7223 struct isl_basic_map *bmap1, struct isl_basic_map *bmap2)
7227 if (!bmap1 || !bmap2)
7229 is_subset = isl_basic_map_is_subset(bmap1, bmap2);
7232 is_subset = isl_basic_map_is_subset(bmap2, bmap1);
7236 int isl_basic_set_is_equal(
7237 struct isl_basic_set *bset1, struct isl_basic_set *bset2)
7239 return isl_basic_map_is_equal(
7240 (struct isl_basic_map *)bset1, (struct isl_basic_map *)bset2);
7243 int isl_map_is_empty(struct isl_map *map)
7250 for (i = 0; i < map->n; ++i) {
7251 is_empty = isl_basic_map_is_empty(map->p[i]);
7260 int isl_map_plain_is_empty(__isl_keep isl_map *map)
7262 return map ? map->n == 0 : -1;
7265 int isl_map_fast_is_empty(__isl_keep isl_map *map)
7267 return isl_map_plain_is_empty(map);
7270 int isl_set_plain_is_empty(struct isl_set *set)
7272 return set ? set->n == 0 : -1;
7275 int isl_set_fast_is_empty(__isl_keep isl_set *set)
7277 return isl_set_plain_is_empty(set);
7280 int isl_set_is_empty(struct isl_set *set)
7282 return isl_map_is_empty((struct isl_map *)set);
7285 int isl_map_has_equal_space(__isl_keep isl_map *map1, __isl_keep isl_map *map2)
7290 return isl_space_is_equal(map1->dim, map2->dim);
7293 int isl_set_has_equal_space(__isl_keep isl_set *set1, __isl_keep isl_set *set2)
7298 return isl_space_is_equal(set1->dim, set2->dim);
7301 static int map_is_equal(__isl_keep isl_map *map1, __isl_keep isl_map *map2)
7307 is_subset = isl_map_is_subset(map1, map2);
7310 is_subset = isl_map_is_subset(map2, map1);
7314 int isl_map_is_equal(__isl_keep isl_map *map1, __isl_keep isl_map *map2)
7316 return isl_map_align_params_map_map_and_test(map1, map2, &map_is_equal);
7319 int isl_basic_map_is_strict_subset(
7320 struct isl_basic_map *bmap1, struct isl_basic_map *bmap2)
7324 if (!bmap1 || !bmap2)
7326 is_subset = isl_basic_map_is_subset(bmap1, bmap2);
7329 is_subset = isl_basic_map_is_subset(bmap2, bmap1);
7330 if (is_subset == -1)
7335 int isl_map_is_strict_subset(struct isl_map *map1, struct isl_map *map2)
7341 is_subset = isl_map_is_subset(map1, map2);
7344 is_subset = isl_map_is_subset(map2, map1);
7345 if (is_subset == -1)
7350 int isl_set_is_strict_subset(__isl_keep isl_set *set1, __isl_keep isl_set *set2)
7352 return isl_map_is_strict_subset((isl_map *)set1, (isl_map *)set2);
7355 int isl_basic_map_is_universe(struct isl_basic_map *bmap)
7359 return bmap->n_eq == 0 && bmap->n_ineq == 0;
7362 int isl_basic_set_is_universe(struct isl_basic_set *bset)
7366 return bset->n_eq == 0 && bset->n_ineq == 0;
7369 int isl_map_plain_is_universe(__isl_keep isl_map *map)
7376 for (i = 0; i < map->n; ++i) {
7377 int r = isl_basic_map_is_universe(map->p[i]);
7385 int isl_set_plain_is_universe(__isl_keep isl_set *set)
7387 return isl_map_plain_is_universe((isl_map *) set);
7390 int isl_set_fast_is_universe(__isl_keep isl_set *set)
7392 return isl_set_plain_is_universe(set);
7395 int isl_basic_map_is_empty(struct isl_basic_map *bmap)
7397 struct isl_basic_set *bset = NULL;
7398 struct isl_vec *sample = NULL;
7405 if (ISL_F_ISSET(bmap, ISL_BASIC_MAP_EMPTY))
7408 if (isl_basic_map_is_universe(bmap))
7411 if (ISL_F_ISSET(bmap, ISL_BASIC_MAP_RATIONAL)) {
7412 struct isl_basic_map *copy = isl_basic_map_copy(bmap);
7413 copy = isl_basic_map_remove_redundancies(copy);
7414 empty = ISL_F_ISSET(copy, ISL_BASIC_MAP_EMPTY);
7415 isl_basic_map_free(copy);
7419 total = 1 + isl_basic_map_total_dim(bmap);
7420 if (bmap->sample && bmap->sample->size == total) {
7421 int contains = isl_basic_map_contains(bmap, bmap->sample);
7427 isl_vec_free(bmap->sample);
7428 bmap->sample = NULL;
7429 bset = isl_basic_map_underlying_set(isl_basic_map_copy(bmap));
7432 sample = isl_basic_set_sample_vec(bset);
7435 empty = sample->size == 0;
7436 isl_vec_free(bmap->sample);
7437 bmap->sample = sample;
7439 ISL_F_SET(bmap, ISL_BASIC_MAP_EMPTY);
7444 int isl_basic_map_plain_is_empty(__isl_keep isl_basic_map *bmap)
7448 return ISL_F_ISSET(bmap, ISL_BASIC_MAP_EMPTY);
7451 int isl_basic_map_fast_is_empty(__isl_keep isl_basic_map *bmap)
7453 return isl_basic_map_plain_is_empty(bmap);
7456 int isl_basic_set_plain_is_empty(__isl_keep isl_basic_set *bset)
7460 return ISL_F_ISSET(bset, ISL_BASIC_SET_EMPTY);
7463 int isl_basic_set_fast_is_empty(__isl_keep isl_basic_set *bset)
7465 return isl_basic_set_plain_is_empty(bset);
7468 int isl_basic_set_is_empty(struct isl_basic_set *bset)
7470 return isl_basic_map_is_empty((struct isl_basic_map *)bset);
7473 struct isl_map *isl_basic_map_union(
7474 struct isl_basic_map *bmap1, struct isl_basic_map *bmap2)
7476 struct isl_map *map;
7477 if (!bmap1 || !bmap2)
7480 isl_assert(bmap1->ctx, isl_space_is_equal(bmap1->dim, bmap2->dim), goto error);
7482 map = isl_map_alloc_space(isl_space_copy(bmap1->dim), 2, 0);
7485 map = isl_map_add_basic_map(map, bmap1);
7486 map = isl_map_add_basic_map(map, bmap2);
7489 isl_basic_map_free(bmap1);
7490 isl_basic_map_free(bmap2);
7494 struct isl_set *isl_basic_set_union(
7495 struct isl_basic_set *bset1, struct isl_basic_set *bset2)
7497 return (struct isl_set *)isl_basic_map_union(
7498 (struct isl_basic_map *)bset1,
7499 (struct isl_basic_map *)bset2);
7502 /* Order divs such that any div only depends on previous divs */
7503 struct isl_basic_map *isl_basic_map_order_divs(struct isl_basic_map *bmap)
7511 off = isl_space_dim(bmap->dim, isl_dim_all);
7513 for (i = 0; i < bmap->n_div; ++i) {
7515 if (isl_int_is_zero(bmap->div[i][0]))
7517 pos = isl_seq_first_non_zero(bmap->div[i]+1+1+off+i,
7521 isl_basic_map_swap_div(bmap, i, i + pos);
7527 struct isl_basic_set *isl_basic_set_order_divs(struct isl_basic_set *bset)
7529 return (struct isl_basic_set *)
7530 isl_basic_map_order_divs((struct isl_basic_map *)bset);
7533 __isl_give isl_map *isl_map_order_divs(__isl_take isl_map *map)
7540 for (i = 0; i < map->n; ++i) {
7541 map->p[i] = isl_basic_map_order_divs(map->p[i]);
7552 /* Apply the expansion computed by isl_merge_divs.
7553 * The expansion itself is given by "exp" while the resulting
7554 * list of divs is given by "div".
7556 __isl_give isl_basic_set *isl_basic_set_expand_divs(
7557 __isl_take isl_basic_set *bset, __isl_take isl_mat *div, int *exp)
7562 bset = isl_basic_set_cow(bset);
7566 if (div->n_row < bset->n_div)
7567 isl_die(isl_mat_get_ctx(div), isl_error_invalid,
7568 "not an expansion", goto error);
7570 bset = isl_basic_map_extend_space(bset, isl_space_copy(bset->dim),
7571 div->n_row - bset->n_div, 0,
7572 2 * (div->n_row - bset->n_div));
7574 n_div = bset->n_div;
7575 for (i = n_div; i < div->n_row; ++i)
7576 if (isl_basic_set_alloc_div(bset) < 0)
7580 for (i = div->n_row - 1; i >= 0; --i) {
7581 if (j >= 0 && exp[j] == i) {
7583 isl_basic_map_swap_div(bset, i, j);
7586 isl_seq_cpy(bset->div[i], div->row[i], div->n_col);
7587 if (isl_basic_map_add_div_constraints(bset, i) < 0)
7595 isl_basic_set_free(bset);
7600 /* Look for a div in dst that corresponds to the div "div" in src.
7601 * The divs before "div" in src and dst are assumed to be the same.
7603 * Returns -1 if no corresponding div was found and the position
7604 * of the corresponding div in dst otherwise.
7606 static int find_div(struct isl_basic_map *dst,
7607 struct isl_basic_map *src, unsigned div)
7611 unsigned total = isl_space_dim(src->dim, isl_dim_all);
7613 isl_assert(dst->ctx, div <= dst->n_div, return -1);
7614 for (i = div; i < dst->n_div; ++i)
7615 if (isl_seq_eq(dst->div[i], src->div[div], 1+1+total+div) &&
7616 isl_seq_first_non_zero(dst->div[i]+1+1+total+div,
7617 dst->n_div - div) == -1)
7622 struct isl_basic_map *isl_basic_map_align_divs(
7623 struct isl_basic_map *dst, struct isl_basic_map *src)
7631 if (src->n_div == 0)
7634 for (i = 0; i < src->n_div; ++i)
7635 isl_assert(src->ctx, !isl_int_is_zero(src->div[i][0]), goto error);
7637 src = isl_basic_map_order_divs(src);
7638 dst = isl_basic_map_cow(dst);
7639 dst = isl_basic_map_extend_space(dst, isl_space_copy(dst->dim),
7640 src->n_div, 0, 2 * src->n_div);
7643 total = isl_space_dim(src->dim, isl_dim_all);
7644 for (i = 0; i < src->n_div; ++i) {
7645 int j = find_div(dst, src, i);
7647 j = isl_basic_map_alloc_div(dst);
7650 isl_seq_cpy(dst->div[j], src->div[i], 1+1+total+i);
7651 isl_seq_clr(dst->div[j]+1+1+total+i, dst->n_div - i);
7652 if (isl_basic_map_add_div_constraints(dst, j) < 0)
7656 isl_basic_map_swap_div(dst, i, j);
7660 isl_basic_map_free(dst);
7664 struct isl_basic_set *isl_basic_set_align_divs(
7665 struct isl_basic_set *dst, struct isl_basic_set *src)
7667 return (struct isl_basic_set *)isl_basic_map_align_divs(
7668 (struct isl_basic_map *)dst, (struct isl_basic_map *)src);
7671 struct isl_map *isl_map_align_divs(struct isl_map *map)
7679 map = isl_map_compute_divs(map);
7680 map = isl_map_cow(map);
7684 for (i = 1; i < map->n; ++i)
7685 map->p[0] = isl_basic_map_align_divs(map->p[0], map->p[i]);
7686 for (i = 1; i < map->n; ++i)
7687 map->p[i] = isl_basic_map_align_divs(map->p[i], map->p[0]);
7689 ISL_F_CLR(map, ISL_MAP_NORMALIZED);
7693 struct isl_set *isl_set_align_divs(struct isl_set *set)
7695 return (struct isl_set *)isl_map_align_divs((struct isl_map *)set);
7698 static __isl_give isl_set *set_apply( __isl_take isl_set *set,
7699 __isl_take isl_map *map)
7703 isl_assert(set->ctx, isl_map_compatible_domain(map, set), goto error);
7704 map = isl_map_intersect_domain(map, set);
7705 set = isl_map_range(map);
7713 __isl_give isl_set *isl_set_apply( __isl_take isl_set *set,
7714 __isl_take isl_map *map)
7716 return isl_map_align_params_map_map_and(set, map, &set_apply);
7719 /* There is no need to cow as removing empty parts doesn't change
7720 * the meaning of the set.
7722 struct isl_map *isl_map_remove_empty_parts(struct isl_map *map)
7729 for (i = map->n - 1; i >= 0; --i)
7730 remove_if_empty(map, i);
7735 struct isl_set *isl_set_remove_empty_parts(struct isl_set *set)
7737 return (struct isl_set *)
7738 isl_map_remove_empty_parts((struct isl_map *)set);
7741 struct isl_basic_map *isl_map_copy_basic_map(struct isl_map *map)
7743 struct isl_basic_map *bmap;
7744 if (!map || map->n == 0)
7746 bmap = map->p[map->n-1];
7747 isl_assert(map->ctx, ISL_F_ISSET(bmap, ISL_BASIC_SET_FINAL), return NULL);
7748 return isl_basic_map_copy(bmap);
7751 struct isl_basic_set *isl_set_copy_basic_set(struct isl_set *set)
7753 return (struct isl_basic_set *)
7754 isl_map_copy_basic_map((struct isl_map *)set);
7757 __isl_give isl_map *isl_map_drop_basic_map(__isl_take isl_map *map,
7758 __isl_keep isl_basic_map *bmap)
7764 for (i = map->n-1; i >= 0; --i) {
7765 if (map->p[i] != bmap)
7767 map = isl_map_cow(map);
7770 isl_basic_map_free(map->p[i]);
7771 if (i != map->n-1) {
7772 ISL_F_CLR(map, ISL_SET_NORMALIZED);
7773 map->p[i] = map->p[map->n-1];
7784 struct isl_set *isl_set_drop_basic_set(struct isl_set *set,
7785 struct isl_basic_set *bset)
7787 return (struct isl_set *)isl_map_drop_basic_map((struct isl_map *)set,
7788 (struct isl_basic_map *)bset);
7791 /* Given two basic sets bset1 and bset2, compute the maximal difference
7792 * between the values of dimension pos in bset1 and those in bset2
7793 * for any common value of the parameters and dimensions preceding pos.
7795 static enum isl_lp_result basic_set_maximal_difference_at(
7796 __isl_keep isl_basic_set *bset1, __isl_keep isl_basic_set *bset2,
7797 int pos, isl_int *opt)
7800 struct isl_basic_map *bmap1 = NULL;
7801 struct isl_basic_map *bmap2 = NULL;
7802 struct isl_ctx *ctx;
7803 struct isl_vec *obj;
7806 unsigned dim1, dim2;
7807 enum isl_lp_result res;
7809 if (!bset1 || !bset2)
7810 return isl_lp_error;
7812 nparam = isl_basic_set_n_param(bset1);
7813 dim1 = isl_basic_set_n_dim(bset1);
7814 dim2 = isl_basic_set_n_dim(bset2);
7815 dims = isl_space_alloc(bset1->ctx, nparam, pos, dim1 - pos);
7816 bmap1 = isl_basic_map_from_basic_set(isl_basic_set_copy(bset1), dims);
7817 dims = isl_space_alloc(bset2->ctx, nparam, pos, dim2 - pos);
7818 bmap2 = isl_basic_map_from_basic_set(isl_basic_set_copy(bset2), dims);
7819 if (!bmap1 || !bmap2)
7821 bmap1 = isl_basic_map_cow(bmap1);
7822 bmap1 = isl_basic_map_extend(bmap1, nparam,
7823 pos, (dim1 - pos) + (dim2 - pos),
7824 bmap2->n_div, bmap2->n_eq, bmap2->n_ineq);
7825 bmap1 = add_constraints(bmap1, bmap2, 0, dim1 - pos);
7828 total = isl_basic_map_total_dim(bmap1);
7830 obj = isl_vec_alloc(ctx, 1 + total);
7831 isl_seq_clr(obj->block.data, 1 + total);
7832 isl_int_set_si(obj->block.data[1+nparam+pos], 1);
7833 isl_int_set_si(obj->block.data[1+nparam+pos+(dim1-pos)], -1);
7836 res = isl_basic_map_solve_lp(bmap1, 1, obj->block.data, ctx->one,
7838 isl_basic_map_free(bmap1);
7842 isl_basic_map_free(bmap1);
7843 isl_basic_map_free(bmap2);
7844 return isl_lp_error;
7847 /* Given two _disjoint_ basic sets bset1 and bset2, check whether
7848 * for any common value of the parameters and dimensions preceding pos
7849 * in both basic sets, the values of dimension pos in bset1 are
7850 * smaller or larger than those in bset2.
7853 * 1 if bset1 follows bset2
7854 * -1 if bset1 precedes bset2
7855 * 0 if bset1 and bset2 are incomparable
7856 * -2 if some error occurred.
7858 int isl_basic_set_compare_at(struct isl_basic_set *bset1,
7859 struct isl_basic_set *bset2, int pos)
7862 enum isl_lp_result res;
7867 res = basic_set_maximal_difference_at(bset1, bset2, pos, &opt);
7869 if (res == isl_lp_empty)
7871 else if ((res == isl_lp_ok && isl_int_is_pos(opt)) ||
7872 res == isl_lp_unbounded)
7874 else if (res == isl_lp_ok && isl_int_is_neg(opt))
7883 /* Given two basic sets bset1 and bset2, check whether
7884 * for any common value of the parameters and dimensions preceding pos
7885 * there is a value of dimension pos in bset1 that is larger
7886 * than a value of the same dimension in bset2.
7889 * 1 if there exists such a pair
7890 * 0 if there is no such pair, but there is a pair of equal values
7892 * -2 if some error occurred.
7894 int isl_basic_set_follows_at(__isl_keep isl_basic_set *bset1,
7895 __isl_keep isl_basic_set *bset2, int pos)
7898 enum isl_lp_result res;
7903 res = basic_set_maximal_difference_at(bset1, bset2, pos, &opt);
7905 if (res == isl_lp_empty)
7907 else if ((res == isl_lp_ok && isl_int_is_pos(opt)) ||
7908 res == isl_lp_unbounded)
7910 else if (res == isl_lp_ok && isl_int_is_neg(opt))
7912 else if (res == isl_lp_ok)
7921 /* Given two sets set1 and set2, check whether
7922 * for any common value of the parameters and dimensions preceding pos
7923 * there is a value of dimension pos in set1 that is larger
7924 * than a value of the same dimension in set2.
7927 * 1 if there exists such a pair
7928 * 0 if there is no such pair, but there is a pair of equal values
7930 * -2 if some error occurred.
7932 int isl_set_follows_at(__isl_keep isl_set *set1,
7933 __isl_keep isl_set *set2, int pos)
7941 for (i = 0; i < set1->n; ++i)
7942 for (j = 0; j < set2->n; ++j) {
7944 f = isl_basic_set_follows_at(set1->p[i], set2->p[j], pos);
7945 if (f == 1 || f == -2)
7954 static int isl_basic_map_plain_has_fixed_var(__isl_keep isl_basic_map *bmap,
7955 unsigned pos, isl_int *val)
7963 total = isl_basic_map_total_dim(bmap);
7964 for (i = 0, d = total-1; i < bmap->n_eq && d+1 > pos; ++i) {
7965 for (; d+1 > pos; --d)
7966 if (!isl_int_is_zero(bmap->eq[i][1+d]))
7970 if (isl_seq_first_non_zero(bmap->eq[i]+1, d) != -1)
7972 if (isl_seq_first_non_zero(bmap->eq[i]+1+d+1, total-d-1) != -1)
7974 if (!isl_int_is_one(bmap->eq[i][1+d]))
7977 isl_int_neg(*val, bmap->eq[i][0]);
7983 static int isl_map_plain_has_fixed_var(__isl_keep isl_map *map,
7984 unsigned pos, isl_int *val)
7996 return isl_basic_map_plain_has_fixed_var(map->p[0], pos, val);
7999 fixed = isl_basic_map_plain_has_fixed_var(map->p[0], pos, &v);
8000 for (i = 1; fixed == 1 && i < map->n; ++i) {
8001 fixed = isl_basic_map_plain_has_fixed_var(map->p[i], pos, &tmp);
8002 if (fixed == 1 && isl_int_ne(tmp, v))
8006 isl_int_set(*val, v);
8012 static int isl_basic_set_plain_has_fixed_var(__isl_keep isl_basic_set *bset,
8013 unsigned pos, isl_int *val)
8015 return isl_basic_map_plain_has_fixed_var((struct isl_basic_map *)bset,
8019 static int isl_set_plain_has_fixed_var(__isl_keep isl_set *set, unsigned pos,
8022 return isl_map_plain_has_fixed_var((struct isl_map *)set, pos, val);
8025 int isl_basic_map_plain_is_fixed(__isl_keep isl_basic_map *bmap,
8026 enum isl_dim_type type, unsigned pos, isl_int *val)
8028 if (pos >= isl_basic_map_dim(bmap, type))
8030 return isl_basic_map_plain_has_fixed_var(bmap,
8031 isl_basic_map_offset(bmap, type) - 1 + pos, val);
8034 int isl_map_plain_is_fixed(__isl_keep isl_map *map,
8035 enum isl_dim_type type, unsigned pos, isl_int *val)
8037 if (pos >= isl_map_dim(map, type))
8039 return isl_map_plain_has_fixed_var(map,
8040 map_offset(map, type) - 1 + pos, val);
8043 int isl_set_plain_is_fixed(__isl_keep isl_set *set,
8044 enum isl_dim_type type, unsigned pos, isl_int *val)
8046 return isl_map_plain_is_fixed(set, type, pos, val);
8049 int isl_map_fast_is_fixed(__isl_keep isl_map *map,
8050 enum isl_dim_type type, unsigned pos, isl_int *val)
8052 return isl_map_plain_is_fixed(map, type, pos, val);
8055 /* Check if dimension dim has fixed value and if so and if val is not NULL,
8056 * then return this fixed value in *val.
8058 int isl_basic_set_plain_dim_is_fixed(__isl_keep isl_basic_set *bset,
8059 unsigned dim, isl_int *val)
8061 return isl_basic_set_plain_has_fixed_var(bset,
8062 isl_basic_set_n_param(bset) + dim, val);
8065 /* Check if dimension dim has fixed value and if so and if val is not NULL,
8066 * then return this fixed value in *val.
8068 int isl_set_plain_dim_is_fixed(__isl_keep isl_set *set,
8069 unsigned dim, isl_int *val)
8071 return isl_set_plain_has_fixed_var(set, isl_set_n_param(set) + dim, val);
8074 int isl_set_fast_dim_is_fixed(__isl_keep isl_set *set,
8075 unsigned dim, isl_int *val)
8077 return isl_set_plain_dim_is_fixed(set, dim, val);
8080 /* Check if input variable in has fixed value and if so and if val is not NULL,
8081 * then return this fixed value in *val.
8083 int isl_map_plain_input_is_fixed(__isl_keep isl_map *map,
8084 unsigned in, isl_int *val)
8086 return isl_map_plain_has_fixed_var(map, isl_map_n_param(map) + in, val);
8089 /* Check if dimension dim has an (obvious) fixed lower bound and if so
8090 * and if val is not NULL, then return this lower bound in *val.
8092 int isl_basic_set_plain_dim_has_fixed_lower_bound(
8093 __isl_keep isl_basic_set *bset, unsigned dim, isl_int *val)
8095 int i, i_eq = -1, i_ineq = -1;
8102 total = isl_basic_set_total_dim(bset);
8103 nparam = isl_basic_set_n_param(bset);
8104 for (i = 0; i < bset->n_eq; ++i) {
8105 if (isl_int_is_zero(bset->eq[i][1+nparam+dim]))
8111 for (i = 0; i < bset->n_ineq; ++i) {
8112 if (!isl_int_is_pos(bset->ineq[i][1+nparam+dim]))
8114 if (i_eq != -1 || i_ineq != -1)
8118 if (i_eq == -1 && i_ineq == -1)
8120 c = i_eq != -1 ? bset->eq[i_eq] : bset->ineq[i_ineq];
8121 /* The coefficient should always be one due to normalization. */
8122 if (!isl_int_is_one(c[1+nparam+dim]))
8124 if (isl_seq_first_non_zero(c+1, nparam+dim) != -1)
8126 if (isl_seq_first_non_zero(c+1+nparam+dim+1,
8127 total - nparam - dim - 1) != -1)
8130 isl_int_neg(*val, c[0]);
8134 int isl_set_plain_dim_has_fixed_lower_bound(__isl_keep isl_set *set,
8135 unsigned dim, isl_int *val)
8147 return isl_basic_set_plain_dim_has_fixed_lower_bound(set->p[0],
8151 fixed = isl_basic_set_plain_dim_has_fixed_lower_bound(set->p[0],
8153 for (i = 1; fixed == 1 && i < set->n; ++i) {
8154 fixed = isl_basic_set_plain_dim_has_fixed_lower_bound(set->p[i],
8156 if (fixed == 1 && isl_int_ne(tmp, v))
8160 isl_int_set(*val, v);
8171 /* uset_gist depends on constraints without existentially quantified
8172 * variables sorting first.
8174 static int qsort_constraint_cmp(const void *p1, const void *p2)
8176 const struct constraint *c1 = (const struct constraint *)p1;
8177 const struct constraint *c2 = (const struct constraint *)p2;
8179 unsigned size = isl_min(c1->size, c2->size);
8181 l1 = isl_seq_last_non_zero(c1->c, size);
8182 l2 = isl_seq_last_non_zero(c2->c, size);
8187 return isl_seq_cmp(c1->c, c2->c, size);
8190 static struct isl_basic_map *isl_basic_map_sort_constraints(
8191 struct isl_basic_map *bmap)
8194 struct constraint *c;
8199 total = isl_basic_map_total_dim(bmap);
8200 c = isl_alloc_array(bmap->ctx, struct constraint, bmap->n_ineq);
8203 for (i = 0; i < bmap->n_ineq; ++i) {
8205 c[i].c = bmap->ineq[i];
8207 qsort(c, bmap->n_ineq, sizeof(struct constraint), qsort_constraint_cmp);
8208 for (i = 0; i < bmap->n_ineq; ++i)
8209 bmap->ineq[i] = c[i].c;
8213 isl_basic_map_free(bmap);
8217 __isl_give isl_basic_set *isl_basic_set_sort_constraints(
8218 __isl_take isl_basic_set *bset)
8220 return (struct isl_basic_set *)isl_basic_map_sort_constraints(
8221 (struct isl_basic_map *)bset);
8224 struct isl_basic_map *isl_basic_map_normalize(struct isl_basic_map *bmap)
8228 if (ISL_F_ISSET(bmap, ISL_BASIC_MAP_NORMALIZED))
8230 bmap = isl_basic_map_remove_redundancies(bmap);
8231 bmap = isl_basic_map_sort_constraints(bmap);
8232 ISL_F_SET(bmap, ISL_BASIC_MAP_NORMALIZED);
8236 struct isl_basic_set *isl_basic_set_normalize(struct isl_basic_set *bset)
8238 return (struct isl_basic_set *)isl_basic_map_normalize(
8239 (struct isl_basic_map *)bset);
8242 int isl_basic_map_plain_cmp(const __isl_keep isl_basic_map *bmap1,
8243 const __isl_keep isl_basic_map *bmap2)
8250 if (ISL_F_ISSET(bmap1, ISL_BASIC_MAP_RATIONAL) !=
8251 ISL_F_ISSET(bmap2, ISL_BASIC_MAP_RATIONAL))
8252 return ISL_F_ISSET(bmap1, ISL_BASIC_MAP_RATIONAL) ? -1 : 1;
8253 if (isl_basic_map_n_param(bmap1) != isl_basic_map_n_param(bmap2))
8254 return isl_basic_map_n_param(bmap1) - isl_basic_map_n_param(bmap2);
8255 if (isl_basic_map_n_in(bmap1) != isl_basic_map_n_in(bmap2))
8256 return isl_basic_map_n_out(bmap1) - isl_basic_map_n_out(bmap2);
8257 if (isl_basic_map_n_out(bmap1) != isl_basic_map_n_out(bmap2))
8258 return isl_basic_map_n_out(bmap1) - isl_basic_map_n_out(bmap2);
8259 if (ISL_F_ISSET(bmap1, ISL_BASIC_MAP_EMPTY) &&
8260 ISL_F_ISSET(bmap2, ISL_BASIC_MAP_EMPTY))
8262 if (ISL_F_ISSET(bmap1, ISL_BASIC_MAP_EMPTY))
8264 if (ISL_F_ISSET(bmap2, ISL_BASIC_MAP_EMPTY))
8266 if (bmap1->n_eq != bmap2->n_eq)
8267 return bmap1->n_eq - bmap2->n_eq;
8268 if (bmap1->n_ineq != bmap2->n_ineq)
8269 return bmap1->n_ineq - bmap2->n_ineq;
8270 if (bmap1->n_div != bmap2->n_div)
8271 return bmap1->n_div - bmap2->n_div;
8272 total = isl_basic_map_total_dim(bmap1);
8273 for (i = 0; i < bmap1->n_eq; ++i) {
8274 cmp = isl_seq_cmp(bmap1->eq[i], bmap2->eq[i], 1+total);
8278 for (i = 0; i < bmap1->n_ineq; ++i) {
8279 cmp = isl_seq_cmp(bmap1->ineq[i], bmap2->ineq[i], 1+total);
8283 for (i = 0; i < bmap1->n_div; ++i) {
8284 cmp = isl_seq_cmp(bmap1->div[i], bmap2->div[i], 1+1+total);
8291 int isl_basic_set_plain_cmp(const __isl_keep isl_basic_set *bset1,
8292 const __isl_keep isl_basic_set *bset2)
8294 return isl_basic_map_plain_cmp(bset1, bset2);
8297 int isl_set_plain_cmp(__isl_keep isl_set *set1, __isl_keep isl_set *set2)
8303 if (set1->n != set2->n)
8304 return set1->n - set2->n;
8306 for (i = 0; i < set1->n; ++i) {
8307 cmp = isl_basic_set_plain_cmp(set1->p[i], set2->p[i]);
8315 int isl_basic_map_plain_is_equal(__isl_keep isl_basic_map *bmap1,
8316 __isl_keep isl_basic_map *bmap2)
8318 return isl_basic_map_plain_cmp(bmap1, bmap2) == 0;
8321 int isl_basic_set_plain_is_equal(__isl_keep isl_basic_set *bset1,
8322 __isl_keep isl_basic_set *bset2)
8324 return isl_basic_map_plain_is_equal((isl_basic_map *)bset1,
8325 (isl_basic_map *)bset2);
8328 static int qsort_bmap_cmp(const void *p1, const void *p2)
8330 const struct isl_basic_map *bmap1 = *(const struct isl_basic_map **)p1;
8331 const struct isl_basic_map *bmap2 = *(const struct isl_basic_map **)p2;
8333 return isl_basic_map_plain_cmp(bmap1, bmap2);
8336 /* We normalize in place, but if anything goes wrong we need
8337 * to return NULL, so we need to make sure we don't change the
8338 * meaning of any possible other copies of map.
8340 struct isl_map *isl_map_normalize(struct isl_map *map)
8343 struct isl_basic_map *bmap;
8347 if (ISL_F_ISSET(map, ISL_MAP_NORMALIZED))
8349 for (i = 0; i < map->n; ++i) {
8350 bmap = isl_basic_map_normalize(isl_basic_map_copy(map->p[i]));
8353 isl_basic_map_free(map->p[i]);
8356 qsort(map->p, map->n, sizeof(struct isl_basic_map *), qsort_bmap_cmp);
8357 ISL_F_SET(map, ISL_MAP_NORMALIZED);
8358 map = isl_map_remove_empty_parts(map);
8361 for (i = map->n - 1; i >= 1; --i) {
8362 if (!isl_basic_map_plain_is_equal(map->p[i-1], map->p[i]))
8364 isl_basic_map_free(map->p[i-1]);
8365 for (j = i; j < map->n; ++j)
8366 map->p[j-1] = map->p[j];
8376 struct isl_set *isl_set_normalize(struct isl_set *set)
8378 return (struct isl_set *)isl_map_normalize((struct isl_map *)set);
8381 int isl_map_plain_is_equal(__isl_keep isl_map *map1, __isl_keep isl_map *map2)
8391 if (!isl_space_is_equal(map1->dim, map2->dim))
8394 map1 = isl_map_copy(map1);
8395 map2 = isl_map_copy(map2);
8396 map1 = isl_map_normalize(map1);
8397 map2 = isl_map_normalize(map2);
8400 equal = map1->n == map2->n;
8401 for (i = 0; equal && i < map1->n; ++i) {
8402 equal = isl_basic_map_plain_is_equal(map1->p[i], map2->p[i]);
8415 int isl_map_fast_is_equal(__isl_keep isl_map *map1, __isl_keep isl_map *map2)
8417 return isl_map_plain_is_equal(map1, map2);
8420 int isl_set_plain_is_equal(__isl_keep isl_set *set1, __isl_keep isl_set *set2)
8422 return isl_map_plain_is_equal((struct isl_map *)set1,
8423 (struct isl_map *)set2);
8426 int isl_set_fast_is_equal(__isl_keep isl_set *set1, __isl_keep isl_set *set2)
8428 return isl_set_plain_is_equal(set1, set2);
8431 /* Return an interval that ranges from min to max (inclusive)
8433 struct isl_basic_set *isl_basic_set_interval(struct isl_ctx *ctx,
8434 isl_int min, isl_int max)
8437 struct isl_basic_set *bset = NULL;
8439 bset = isl_basic_set_alloc(ctx, 0, 1, 0, 0, 2);
8443 k = isl_basic_set_alloc_inequality(bset);
8446 isl_int_set_si(bset->ineq[k][1], 1);
8447 isl_int_neg(bset->ineq[k][0], min);
8449 k = isl_basic_set_alloc_inequality(bset);
8452 isl_int_set_si(bset->ineq[k][1], -1);
8453 isl_int_set(bset->ineq[k][0], max);
8457 isl_basic_set_free(bset);
8461 /* Return the Cartesian product of the basic sets in list (in the given order).
8463 __isl_give isl_basic_set *isl_basic_set_list_product(
8464 __isl_take struct isl_basic_set_list *list)
8472 struct isl_basic_set *product = NULL;
8476 isl_assert(list->ctx, list->n > 0, goto error);
8477 isl_assert(list->ctx, list->p[0], goto error);
8478 nparam = isl_basic_set_n_param(list->p[0]);
8479 dim = isl_basic_set_n_dim(list->p[0]);
8480 extra = list->p[0]->n_div;
8481 n_eq = list->p[0]->n_eq;
8482 n_ineq = list->p[0]->n_ineq;
8483 for (i = 1; i < list->n; ++i) {
8484 isl_assert(list->ctx, list->p[i], goto error);
8485 isl_assert(list->ctx,
8486 nparam == isl_basic_set_n_param(list->p[i]), goto error);
8487 dim += isl_basic_set_n_dim(list->p[i]);
8488 extra += list->p[i]->n_div;
8489 n_eq += list->p[i]->n_eq;
8490 n_ineq += list->p[i]->n_ineq;
8492 product = isl_basic_set_alloc(list->ctx, nparam, dim, extra,
8497 for (i = 0; i < list->n; ++i) {
8498 isl_basic_set_add_constraints(product,
8499 isl_basic_set_copy(list->p[i]), dim);
8500 dim += isl_basic_set_n_dim(list->p[i]);
8502 isl_basic_set_list_free(list);
8505 isl_basic_set_free(product);
8506 isl_basic_set_list_free(list);
8510 struct isl_basic_map *isl_basic_map_product(
8511 struct isl_basic_map *bmap1, struct isl_basic_map *bmap2)
8513 isl_space *dim_result = NULL;
8514 struct isl_basic_map *bmap;
8515 unsigned in1, in2, out1, out2, nparam, total, pos;
8516 struct isl_dim_map *dim_map1, *dim_map2;
8518 if (!bmap1 || !bmap2)
8521 isl_assert(bmap1->ctx, isl_space_match(bmap1->dim, isl_dim_param,
8522 bmap2->dim, isl_dim_param), goto error);
8523 dim_result = isl_space_product(isl_space_copy(bmap1->dim),
8524 isl_space_copy(bmap2->dim));
8526 in1 = isl_basic_map_n_in(bmap1);
8527 in2 = isl_basic_map_n_in(bmap2);
8528 out1 = isl_basic_map_n_out(bmap1);
8529 out2 = isl_basic_map_n_out(bmap2);
8530 nparam = isl_basic_map_n_param(bmap1);
8532 total = nparam + in1 + in2 + out1 + out2 + bmap1->n_div + bmap2->n_div;
8533 dim_map1 = isl_dim_map_alloc(bmap1->ctx, total);
8534 dim_map2 = isl_dim_map_alloc(bmap1->ctx, total);
8535 isl_dim_map_dim(dim_map1, bmap1->dim, isl_dim_param, pos = 0);
8536 isl_dim_map_dim(dim_map2, bmap2->dim, isl_dim_param, pos = 0);
8537 isl_dim_map_dim(dim_map1, bmap1->dim, isl_dim_in, pos += nparam);
8538 isl_dim_map_dim(dim_map2, bmap2->dim, isl_dim_in, pos += in1);
8539 isl_dim_map_dim(dim_map1, bmap1->dim, isl_dim_out, pos += in2);
8540 isl_dim_map_dim(dim_map2, bmap2->dim, isl_dim_out, pos += out1);
8541 isl_dim_map_div(dim_map1, bmap1, pos += out2);
8542 isl_dim_map_div(dim_map2, bmap2, pos += bmap1->n_div);
8544 bmap = isl_basic_map_alloc_space(dim_result,
8545 bmap1->n_div + bmap2->n_div,
8546 bmap1->n_eq + bmap2->n_eq,
8547 bmap1->n_ineq + bmap2->n_ineq);
8548 bmap = isl_basic_map_add_constraints_dim_map(bmap, bmap1, dim_map1);
8549 bmap = isl_basic_map_add_constraints_dim_map(bmap, bmap2, dim_map2);
8550 bmap = isl_basic_map_simplify(bmap);
8551 return isl_basic_map_finalize(bmap);
8553 isl_basic_map_free(bmap1);
8554 isl_basic_map_free(bmap2);
8558 __isl_give isl_basic_map *isl_basic_map_flat_product(
8559 __isl_take isl_basic_map *bmap1, __isl_take isl_basic_map *bmap2)
8561 isl_basic_map *prod;
8563 prod = isl_basic_map_product(bmap1, bmap2);
8564 prod = isl_basic_map_flatten(prod);
8568 __isl_give isl_basic_set *isl_basic_set_flat_product(
8569 __isl_take isl_basic_set *bset1, __isl_take isl_basic_set *bset2)
8571 return isl_basic_map_flat_range_product(bset1, bset2);
8574 __isl_give isl_basic_map *isl_basic_map_domain_product(
8575 __isl_take isl_basic_map *bmap1, __isl_take isl_basic_map *bmap2)
8577 isl_space *space_result = NULL;
8578 isl_basic_map *bmap;
8579 unsigned in1, in2, out, nparam, total, pos;
8580 struct isl_dim_map *dim_map1, *dim_map2;
8582 if (!bmap1 || !bmap2)
8585 space_result = isl_space_domain_product(isl_space_copy(bmap1->dim),
8586 isl_space_copy(bmap2->dim));
8588 in1 = isl_basic_map_dim(bmap1, isl_dim_in);
8589 in2 = isl_basic_map_dim(bmap2, isl_dim_in);
8590 out = isl_basic_map_dim(bmap1, isl_dim_out);
8591 nparam = isl_basic_map_dim(bmap1, isl_dim_param);
8593 total = nparam + in1 + in2 + out + bmap1->n_div + bmap2->n_div;
8594 dim_map1 = isl_dim_map_alloc(bmap1->ctx, total);
8595 dim_map2 = isl_dim_map_alloc(bmap1->ctx, total);
8596 isl_dim_map_dim(dim_map1, bmap1->dim, isl_dim_param, pos = 0);
8597 isl_dim_map_dim(dim_map2, bmap2->dim, isl_dim_param, pos = 0);
8598 isl_dim_map_dim(dim_map1, bmap1->dim, isl_dim_in, pos += nparam);
8599 isl_dim_map_dim(dim_map2, bmap2->dim, isl_dim_in, pos += in1);
8600 isl_dim_map_dim(dim_map1, bmap1->dim, isl_dim_out, pos += in2);
8601 isl_dim_map_dim(dim_map2, bmap2->dim, isl_dim_out, pos);
8602 isl_dim_map_div(dim_map1, bmap1, pos += out);
8603 isl_dim_map_div(dim_map2, bmap2, pos += bmap1->n_div);
8605 bmap = isl_basic_map_alloc_space(space_result,
8606 bmap1->n_div + bmap2->n_div,
8607 bmap1->n_eq + bmap2->n_eq,
8608 bmap1->n_ineq + bmap2->n_ineq);
8609 bmap = isl_basic_map_add_constraints_dim_map(bmap, bmap1, dim_map1);
8610 bmap = isl_basic_map_add_constraints_dim_map(bmap, bmap2, dim_map2);
8611 bmap = isl_basic_map_simplify(bmap);
8612 return isl_basic_map_finalize(bmap);
8614 isl_basic_map_free(bmap1);
8615 isl_basic_map_free(bmap2);
8619 __isl_give isl_basic_map *isl_basic_map_range_product(
8620 __isl_take isl_basic_map *bmap1, __isl_take isl_basic_map *bmap2)
8622 isl_space *dim_result = NULL;
8623 isl_basic_map *bmap;
8624 unsigned in, out1, out2, nparam, total, pos;
8625 struct isl_dim_map *dim_map1, *dim_map2;
8627 if (!bmap1 || !bmap2)
8630 if (!isl_space_match(bmap1->dim, isl_dim_param,
8631 bmap2->dim, isl_dim_param))
8632 isl_die(isl_basic_map_get_ctx(bmap1), isl_error_invalid,
8633 "parameters don't match", goto error);
8635 dim_result = isl_space_range_product(isl_space_copy(bmap1->dim),
8636 isl_space_copy(bmap2->dim));
8638 in = isl_basic_map_dim(bmap1, isl_dim_in);
8639 out1 = isl_basic_map_n_out(bmap1);
8640 out2 = isl_basic_map_n_out(bmap2);
8641 nparam = isl_basic_map_n_param(bmap1);
8643 total = nparam + in + out1 + out2 + bmap1->n_div + bmap2->n_div;
8644 dim_map1 = isl_dim_map_alloc(bmap1->ctx, total);
8645 dim_map2 = isl_dim_map_alloc(bmap1->ctx, total);
8646 isl_dim_map_dim(dim_map1, bmap1->dim, isl_dim_param, pos = 0);
8647 isl_dim_map_dim(dim_map2, bmap2->dim, isl_dim_param, pos = 0);
8648 isl_dim_map_dim(dim_map1, bmap1->dim, isl_dim_in, pos += nparam);
8649 isl_dim_map_dim(dim_map2, bmap2->dim, isl_dim_in, pos);
8650 isl_dim_map_dim(dim_map1, bmap1->dim, isl_dim_out, pos += in);
8651 isl_dim_map_dim(dim_map2, bmap2->dim, isl_dim_out, pos += out1);
8652 isl_dim_map_div(dim_map1, bmap1, pos += out2);
8653 isl_dim_map_div(dim_map2, bmap2, pos += bmap1->n_div);
8655 bmap = isl_basic_map_alloc_space(dim_result,
8656 bmap1->n_div + bmap2->n_div,
8657 bmap1->n_eq + bmap2->n_eq,
8658 bmap1->n_ineq + bmap2->n_ineq);
8659 bmap = isl_basic_map_add_constraints_dim_map(bmap, bmap1, dim_map1);
8660 bmap = isl_basic_map_add_constraints_dim_map(bmap, bmap2, dim_map2);
8661 bmap = isl_basic_map_simplify(bmap);
8662 return isl_basic_map_finalize(bmap);
8664 isl_basic_map_free(bmap1);
8665 isl_basic_map_free(bmap2);
8669 __isl_give isl_basic_map *isl_basic_map_flat_range_product(
8670 __isl_take isl_basic_map *bmap1, __isl_take isl_basic_map *bmap2)
8672 isl_basic_map *prod;
8674 prod = isl_basic_map_range_product(bmap1, bmap2);
8675 prod = isl_basic_map_flatten_range(prod);
8679 static __isl_give isl_map *map_product(__isl_take isl_map *map1,
8680 __isl_take isl_map *map2,
8681 __isl_give isl_space *(*dim_product)(__isl_take isl_space *left,
8682 __isl_take isl_space *right),
8683 __isl_give isl_basic_map *(*basic_map_product)(
8684 __isl_take isl_basic_map *left, __isl_take isl_basic_map *right))
8687 struct isl_map *result;
8693 isl_assert(map1->ctx, isl_space_match(map1->dim, isl_dim_param,
8694 map2->dim, isl_dim_param), goto error);
8696 if (ISL_F_ISSET(map1, ISL_MAP_DISJOINT) &&
8697 ISL_F_ISSET(map2, ISL_MAP_DISJOINT))
8698 ISL_FL_SET(flags, ISL_MAP_DISJOINT);
8700 result = isl_map_alloc_space(dim_product(isl_space_copy(map1->dim),
8701 isl_space_copy(map2->dim)),
8702 map1->n * map2->n, flags);
8705 for (i = 0; i < map1->n; ++i)
8706 for (j = 0; j < map2->n; ++j) {
8707 struct isl_basic_map *part;
8708 part = basic_map_product(isl_basic_map_copy(map1->p[i]),
8709 isl_basic_map_copy(map2->p[j]));
8710 if (isl_basic_map_is_empty(part))
8711 isl_basic_map_free(part);
8713 result = isl_map_add_basic_map(result, part);
8726 /* Given two maps A -> B and C -> D, construct a map [A -> C] -> [B -> D]
8728 static __isl_give isl_map *map_product_aligned(__isl_take isl_map *map1,
8729 __isl_take isl_map *map2)
8731 return map_product(map1, map2, &isl_space_product, &isl_basic_map_product);
8734 __isl_give isl_map *isl_map_product(__isl_take isl_map *map1,
8735 __isl_take isl_map *map2)
8737 return isl_map_align_params_map_map_and(map1, map2, &map_product_aligned);
8740 /* Given two maps A -> B and C -> D, construct a map (A, C) -> (B, D)
8742 __isl_give isl_map *isl_map_flat_product(__isl_take isl_map *map1,
8743 __isl_take isl_map *map2)
8747 prod = isl_map_product(map1, map2);
8748 prod = isl_map_flatten(prod);
8752 /* Given two set A and B, construct its Cartesian product A x B.
8754 struct isl_set *isl_set_product(struct isl_set *set1, struct isl_set *set2)
8756 return isl_map_range_product(set1, set2);
8759 __isl_give isl_set *isl_set_flat_product(__isl_take isl_set *set1,
8760 __isl_take isl_set *set2)
8762 return isl_map_flat_range_product(set1, set2);
8765 /* Given two maps A -> B and C -> D, construct a map [A -> C] -> (B * D)
8767 static __isl_give isl_map *map_domain_product_aligned(__isl_take isl_map *map1,
8768 __isl_take isl_map *map2)
8770 return map_product(map1, map2, &isl_space_domain_product,
8771 &isl_basic_map_domain_product);
8774 /* Given two maps A -> B and C -> D, construct a map (A * C) -> [B -> D]
8776 static __isl_give isl_map *map_range_product_aligned(__isl_take isl_map *map1,
8777 __isl_take isl_map *map2)
8779 return map_product(map1, map2, &isl_space_range_product,
8780 &isl_basic_map_range_product);
8783 __isl_give isl_map *isl_map_domain_product(__isl_take isl_map *map1,
8784 __isl_take isl_map *map2)
8786 return isl_map_align_params_map_map_and(map1, map2,
8787 &map_domain_product_aligned);
8790 __isl_give isl_map *isl_map_range_product(__isl_take isl_map *map1,
8791 __isl_take isl_map *map2)
8793 return isl_map_align_params_map_map_and(map1, map2,
8794 &map_range_product_aligned);
8797 /* Given two maps A -> B and C -> D, construct a map (A, C) -> (B * D)
8799 __isl_give isl_map *isl_map_flat_domain_product(__isl_take isl_map *map1,
8800 __isl_take isl_map *map2)
8804 prod = isl_map_domain_product(map1, map2);
8805 prod = isl_map_flatten_domain(prod);
8809 /* Given two maps A -> B and C -> D, construct a map (A * C) -> (B, D)
8811 __isl_give isl_map *isl_map_flat_range_product(__isl_take isl_map *map1,
8812 __isl_take isl_map *map2)
8816 prod = isl_map_range_product(map1, map2);
8817 prod = isl_map_flatten_range(prod);
8821 uint32_t isl_basic_map_get_hash(__isl_keep isl_basic_map *bmap)
8824 uint32_t hash = isl_hash_init();
8829 bmap = isl_basic_map_copy(bmap);
8830 bmap = isl_basic_map_normalize(bmap);
8833 total = isl_basic_map_total_dim(bmap);
8834 isl_hash_byte(hash, bmap->n_eq & 0xFF);
8835 for (i = 0; i < bmap->n_eq; ++i) {
8837 c_hash = isl_seq_get_hash(bmap->eq[i], 1 + total);
8838 isl_hash_hash(hash, c_hash);
8840 isl_hash_byte(hash, bmap->n_ineq & 0xFF);
8841 for (i = 0; i < bmap->n_ineq; ++i) {
8843 c_hash = isl_seq_get_hash(bmap->ineq[i], 1 + total);
8844 isl_hash_hash(hash, c_hash);
8846 isl_hash_byte(hash, bmap->n_div & 0xFF);
8847 for (i = 0; i < bmap->n_div; ++i) {
8849 if (isl_int_is_zero(bmap->div[i][0]))
8851 isl_hash_byte(hash, i & 0xFF);
8852 c_hash = isl_seq_get_hash(bmap->div[i], 1 + 1 + total);
8853 isl_hash_hash(hash, c_hash);
8855 isl_basic_map_free(bmap);
8859 uint32_t isl_basic_set_get_hash(__isl_keep isl_basic_set *bset)
8861 return isl_basic_map_get_hash((isl_basic_map *)bset);
8864 uint32_t isl_map_get_hash(__isl_keep isl_map *map)
8871 map = isl_map_copy(map);
8872 map = isl_map_normalize(map);
8876 hash = isl_hash_init();
8877 for (i = 0; i < map->n; ++i) {
8879 bmap_hash = isl_basic_map_get_hash(map->p[i]);
8880 isl_hash_hash(hash, bmap_hash);
8888 uint32_t isl_set_get_hash(__isl_keep isl_set *set)
8890 return isl_map_get_hash((isl_map *)set);
8893 /* Check if the value for dimension dim is completely determined
8894 * by the values of the other parameters and variables.
8895 * That is, check if dimension dim is involved in an equality.
8897 int isl_basic_set_dim_is_unique(struct isl_basic_set *bset, unsigned dim)
8904 nparam = isl_basic_set_n_param(bset);
8905 for (i = 0; i < bset->n_eq; ++i)
8906 if (!isl_int_is_zero(bset->eq[i][1 + nparam + dim]))
8911 /* Check if the value for dimension dim is completely determined
8912 * by the values of the other parameters and variables.
8913 * That is, check if dimension dim is involved in an equality
8914 * for each of the subsets.
8916 int isl_set_dim_is_unique(struct isl_set *set, unsigned dim)
8922 for (i = 0; i < set->n; ++i) {
8924 unique = isl_basic_set_dim_is_unique(set->p[i], dim);
8931 int isl_set_n_basic_set(__isl_keep isl_set *set)
8933 return set ? set->n : 0;
8936 int isl_map_foreach_basic_map(__isl_keep isl_map *map,
8937 int (*fn)(__isl_take isl_basic_map *bmap, void *user), void *user)
8944 for (i = 0; i < map->n; ++i)
8945 if (fn(isl_basic_map_copy(map->p[i]), user) < 0)
8951 int isl_set_foreach_basic_set(__isl_keep isl_set *set,
8952 int (*fn)(__isl_take isl_basic_set *bset, void *user), void *user)
8959 for (i = 0; i < set->n; ++i)
8960 if (fn(isl_basic_set_copy(set->p[i]), user) < 0)
8966 __isl_give isl_basic_set *isl_basic_set_lift(__isl_take isl_basic_set *bset)
8973 bset = isl_basic_set_cow(bset);
8977 dim = isl_basic_set_get_space(bset);
8978 dim = isl_space_lift(dim, bset->n_div);
8981 isl_space_free(bset->dim);
8983 bset->extra -= bset->n_div;
8986 bset = isl_basic_set_finalize(bset);
8990 isl_basic_set_free(bset);
8994 __isl_give isl_set *isl_set_lift(__isl_take isl_set *set)
9000 set = isl_set_align_divs(set);
9005 set = isl_set_cow(set);
9009 n_div = set->p[0]->n_div;
9010 dim = isl_set_get_space(set);
9011 dim = isl_space_lift(dim, n_div);
9014 isl_space_free(set->dim);
9017 for (i = 0; i < set->n; ++i) {
9018 set->p[i] = isl_basic_set_lift(set->p[i]);
9029 __isl_give isl_map *isl_set_lifting(__isl_take isl_set *set)
9032 struct isl_basic_map *bmap;
9039 set = isl_set_align_divs(set);
9044 dim = isl_set_get_space(set);
9045 if (set->n == 0 || set->p[0]->n_div == 0) {
9047 return isl_map_identity(isl_space_map_from_set(dim));
9050 n_div = set->p[0]->n_div;
9051 dim = isl_space_map_from_set(dim);
9052 n_param = isl_space_dim(dim, isl_dim_param);
9053 n_set = isl_space_dim(dim, isl_dim_in);
9054 dim = isl_space_extend(dim, n_param, n_set, n_set + n_div);
9055 bmap = isl_basic_map_alloc_space(dim, 0, n_set, 2 * n_div);
9056 for (i = 0; i < n_set; ++i)
9057 bmap = var_equal(bmap, i);
9059 total = n_param + n_set + n_set + n_div;
9060 for (i = 0; i < n_div; ++i) {
9061 k = isl_basic_map_alloc_inequality(bmap);
9064 isl_seq_cpy(bmap->ineq[k], set->p[0]->div[i]+1, 1+n_param);
9065 isl_seq_clr(bmap->ineq[k]+1+n_param, n_set);
9066 isl_seq_cpy(bmap->ineq[k]+1+n_param+n_set,
9067 set->p[0]->div[i]+1+1+n_param, n_set + n_div);
9068 isl_int_neg(bmap->ineq[k][1+n_param+n_set+n_set+i],
9069 set->p[0]->div[i][0]);
9071 l = isl_basic_map_alloc_inequality(bmap);
9074 isl_seq_neg(bmap->ineq[l], bmap->ineq[k], 1 + total);
9075 isl_int_add(bmap->ineq[l][0], bmap->ineq[l][0],
9076 set->p[0]->div[i][0]);
9077 isl_int_sub_ui(bmap->ineq[l][0], bmap->ineq[l][0], 1);
9081 bmap = isl_basic_map_simplify(bmap);
9082 bmap = isl_basic_map_finalize(bmap);
9083 return isl_map_from_basic_map(bmap);
9086 isl_basic_map_free(bmap);
9090 int isl_basic_set_size(__isl_keep isl_basic_set *bset)
9098 dim = isl_basic_set_total_dim(bset);
9099 size += bset->n_eq * (1 + dim);
9100 size += bset->n_ineq * (1 + dim);
9101 size += bset->n_div * (2 + dim);
9106 int isl_set_size(__isl_keep isl_set *set)
9114 for (i = 0; i < set->n; ++i)
9115 size += isl_basic_set_size(set->p[i]);
9120 /* Check if there is any lower bound (if lower == 0) and/or upper
9121 * bound (if upper == 0) on the specified dim.
9123 static int basic_map_dim_is_bounded(__isl_keep isl_basic_map *bmap,
9124 enum isl_dim_type type, unsigned pos, int lower, int upper)
9131 isl_assert(bmap->ctx, pos < isl_basic_map_dim(bmap, type), return -1);
9133 pos += isl_basic_map_offset(bmap, type);
9135 for (i = 0; i < bmap->n_div; ++i) {
9136 if (isl_int_is_zero(bmap->div[i][0]))
9138 if (!isl_int_is_zero(bmap->div[i][1 + pos]))
9142 for (i = 0; i < bmap->n_eq; ++i)
9143 if (!isl_int_is_zero(bmap->eq[i][pos]))
9146 for (i = 0; i < bmap->n_ineq; ++i) {
9147 int sgn = isl_int_sgn(bmap->ineq[i][pos]);
9154 return lower && upper;
9157 int isl_basic_map_dim_is_bounded(__isl_keep isl_basic_map *bmap,
9158 enum isl_dim_type type, unsigned pos)
9160 return basic_map_dim_is_bounded(bmap, type, pos, 0, 0);
9163 int isl_basic_map_dim_has_lower_bound(__isl_keep isl_basic_map *bmap,
9164 enum isl_dim_type type, unsigned pos)
9166 return basic_map_dim_is_bounded(bmap, type, pos, 0, 1);
9169 int isl_basic_map_dim_has_upper_bound(__isl_keep isl_basic_map *bmap,
9170 enum isl_dim_type type, unsigned pos)
9172 return basic_map_dim_is_bounded(bmap, type, pos, 1, 0);
9175 int isl_map_dim_is_bounded(__isl_keep isl_map *map,
9176 enum isl_dim_type type, unsigned pos)
9183 for (i = 0; i < map->n; ++i) {
9185 bounded = isl_basic_map_dim_is_bounded(map->p[i], type, pos);
9186 if (bounded < 0 || !bounded)
9193 /* Return 1 if the specified dim is involved in both an upper bound
9194 * and a lower bound.
9196 int isl_set_dim_is_bounded(__isl_keep isl_set *set,
9197 enum isl_dim_type type, unsigned pos)
9199 return isl_map_dim_is_bounded((isl_map *)set, type, pos);
9202 /* Does "map" have a bound (according to "fn") for any of its basic maps?
9204 static int has_any_bound(__isl_keep isl_map *map,
9205 enum isl_dim_type type, unsigned pos,
9206 int (*fn)(__isl_keep isl_basic_map *bmap,
9207 enum isl_dim_type type, unsigned pos))
9214 for (i = 0; i < map->n; ++i) {
9216 bounded = fn(map->p[i], type, pos);
9217 if (bounded < 0 || bounded)
9224 /* Return 1 if the specified dim is involved in any lower bound.
9226 int isl_set_dim_has_any_lower_bound(__isl_keep isl_set *set,
9227 enum isl_dim_type type, unsigned pos)
9229 return has_any_bound(set, type, pos,
9230 &isl_basic_map_dim_has_lower_bound);
9233 /* Return 1 if the specified dim is involved in any upper bound.
9235 int isl_set_dim_has_any_upper_bound(__isl_keep isl_set *set,
9236 enum isl_dim_type type, unsigned pos)
9238 return has_any_bound(set, type, pos,
9239 &isl_basic_map_dim_has_upper_bound);
9242 /* Does "map" have a bound (according to "fn") for all of its basic maps?
9244 static int has_bound(__isl_keep isl_map *map,
9245 enum isl_dim_type type, unsigned pos,
9246 int (*fn)(__isl_keep isl_basic_map *bmap,
9247 enum isl_dim_type type, unsigned pos))
9254 for (i = 0; i < map->n; ++i) {
9256 bounded = fn(map->p[i], type, pos);
9257 if (bounded < 0 || !bounded)
9264 /* Return 1 if the specified dim has a lower bound (in each of its basic sets).
9266 int isl_set_dim_has_lower_bound(__isl_keep isl_set *set,
9267 enum isl_dim_type type, unsigned pos)
9269 return has_bound(set, type, pos, &isl_basic_map_dim_has_lower_bound);
9272 /* Return 1 if the specified dim has an upper bound (in each of its basic sets).
9274 int isl_set_dim_has_upper_bound(__isl_keep isl_set *set,
9275 enum isl_dim_type type, unsigned pos)
9277 return has_bound(set, type, pos, &isl_basic_map_dim_has_upper_bound);
9280 /* For each of the "n" variables starting at "first", determine
9281 * the sign of the variable and put the results in the first "n"
9282 * elements of the array "signs".
9284 * 1 means that the variable is non-negative
9285 * -1 means that the variable is non-positive
9286 * 0 means the variable attains both positive and negative values.
9288 int isl_basic_set_vars_get_sign(__isl_keep isl_basic_set *bset,
9289 unsigned first, unsigned n, int *signs)
9291 isl_vec *bound = NULL;
9292 struct isl_tab *tab = NULL;
9293 struct isl_tab_undo *snap;
9296 if (!bset || !signs)
9299 bound = isl_vec_alloc(bset->ctx, 1 + isl_basic_set_total_dim(bset));
9300 tab = isl_tab_from_basic_set(bset, 0);
9304 isl_seq_clr(bound->el, bound->size);
9305 isl_int_set_si(bound->el[0], -1);
9307 snap = isl_tab_snap(tab);
9308 for (i = 0; i < n; ++i) {
9311 isl_int_set_si(bound->el[1 + first + i], -1);
9312 if (isl_tab_add_ineq(tab, bound->el) < 0)
9315 isl_int_set_si(bound->el[1 + first + i], 0);
9316 if (isl_tab_rollback(tab, snap) < 0)
9324 isl_int_set_si(bound->el[1 + first + i], 1);
9325 if (isl_tab_add_ineq(tab, bound->el) < 0)
9328 isl_int_set_si(bound->el[1 + first + i], 0);
9329 if (isl_tab_rollback(tab, snap) < 0)
9332 signs[i] = empty ? -1 : 0;
9336 isl_vec_free(bound);
9340 isl_vec_free(bound);
9344 int isl_basic_set_dims_get_sign(__isl_keep isl_basic_set *bset,
9345 enum isl_dim_type type, unsigned first, unsigned n, int *signs)
9347 if (!bset || !signs)
9349 isl_assert(bset->ctx, first + n <= isl_basic_set_dim(bset, type),
9352 first += pos(bset->dim, type) - 1;
9353 return isl_basic_set_vars_get_sign(bset, first, n, signs);
9356 /* Check if the given basic map is obviously single-valued.
9357 * In particular, for each output dimension, check that there is
9358 * an equality that defines the output dimension in terms of
9359 * earlier dimensions.
9361 int isl_basic_map_plain_is_single_valued(__isl_keep isl_basic_map *bmap)
9371 total = 1 + isl_basic_map_total_dim(bmap);
9372 n_out = isl_basic_map_dim(bmap, isl_dim_out);
9373 o_out = isl_basic_map_offset(bmap, isl_dim_out);
9375 for (i = 0; i < n_out; ++i) {
9376 for (j = 0; j < bmap->n_eq; ++j) {
9377 if (isl_int_is_zero(bmap->eq[j][o_out + i]))
9379 if (isl_seq_first_non_zero(bmap->eq[j] + o_out + i + 1,
9380 total - (o_out + i + 1)) == -1)
9383 if (j >= bmap->n_eq)
9390 /* Check if the given basic map is single-valued.
9395 * and check if the result is a subset of the identity mapping.
9397 int isl_basic_map_is_single_valued(__isl_keep isl_basic_map *bmap)
9400 isl_basic_map *test;
9404 sv = isl_basic_map_plain_is_single_valued(bmap);
9408 test = isl_basic_map_reverse(isl_basic_map_copy(bmap));
9409 test = isl_basic_map_apply_range(test, isl_basic_map_copy(bmap));
9411 space = isl_basic_map_get_space(bmap);
9412 space = isl_space_map_from_set(isl_space_range(space));
9413 id = isl_basic_map_identity(space);
9415 sv = isl_basic_map_is_subset(test, id);
9417 isl_basic_map_free(test);
9418 isl_basic_map_free(id);
9423 /* Check if the given map is obviously single-valued.
9425 int isl_map_plain_is_single_valued(__isl_keep isl_map *map)
9434 return isl_basic_map_plain_is_single_valued(map->p[0]);
9437 /* Check if the given map is single-valued.
9442 * and check if the result is a subset of the identity mapping.
9444 int isl_map_is_single_valued(__isl_keep isl_map *map)
9451 sv = isl_map_plain_is_single_valued(map);
9455 test = isl_map_reverse(isl_map_copy(map));
9456 test = isl_map_apply_range(test, isl_map_copy(map));
9458 dim = isl_space_map_from_set(isl_space_range(isl_map_get_space(map)));
9459 id = isl_map_identity(dim);
9461 sv = isl_map_is_subset(test, id);
9469 int isl_map_is_injective(__isl_keep isl_map *map)
9473 map = isl_map_copy(map);
9474 map = isl_map_reverse(map);
9475 in = isl_map_is_single_valued(map);
9481 /* Check if the given map is obviously injective.
9483 int isl_map_plain_is_injective(__isl_keep isl_map *map)
9487 map = isl_map_copy(map);
9488 map = isl_map_reverse(map);
9489 in = isl_map_plain_is_single_valued(map);
9495 int isl_map_is_bijective(__isl_keep isl_map *map)
9499 sv = isl_map_is_single_valued(map);
9503 return isl_map_is_injective(map);
9506 int isl_set_is_singleton(__isl_keep isl_set *set)
9508 return isl_map_is_single_valued((isl_map *)set);
9511 int isl_map_is_translation(__isl_keep isl_map *map)
9516 delta = isl_map_deltas(isl_map_copy(map));
9517 ok = isl_set_is_singleton(delta);
9518 isl_set_free(delta);
9523 static int unique(isl_int *p, unsigned pos, unsigned len)
9525 if (isl_seq_first_non_zero(p, pos) != -1)
9527 if (isl_seq_first_non_zero(p + pos + 1, len - pos - 1) != -1)
9532 int isl_basic_set_is_box(__isl_keep isl_basic_set *bset)
9541 if (isl_basic_set_dim(bset, isl_dim_div) != 0)
9544 nvar = isl_basic_set_dim(bset, isl_dim_set);
9545 ovar = isl_space_offset(bset->dim, isl_dim_set);
9546 for (j = 0; j < nvar; ++j) {
9547 int lower = 0, upper = 0;
9548 for (i = 0; i < bset->n_eq; ++i) {
9549 if (isl_int_is_zero(bset->eq[i][1 + ovar + j]))
9551 if (!unique(bset->eq[i] + 1 + ovar, j, nvar))
9557 for (i = 0; i < bset->n_ineq; ++i) {
9558 if (isl_int_is_zero(bset->ineq[i][1 + ovar + j]))
9560 if (!unique(bset->ineq[i] + 1 + ovar, j, nvar))
9562 if (isl_int_is_pos(bset->ineq[i][1 + ovar + j]))
9567 if (!lower || !upper)
9574 int isl_set_is_box(__isl_keep isl_set *set)
9581 return isl_basic_set_is_box(set->p[0]);
9584 int isl_basic_set_is_wrapping(__isl_keep isl_basic_set *bset)
9589 return isl_space_is_wrapping(bset->dim);
9592 int isl_set_is_wrapping(__isl_keep isl_set *set)
9597 return isl_space_is_wrapping(set->dim);
9600 __isl_give isl_basic_set *isl_basic_map_wrap(__isl_take isl_basic_map *bmap)
9602 bmap = isl_basic_map_cow(bmap);
9606 bmap->dim = isl_space_wrap(bmap->dim);
9610 bmap = isl_basic_map_finalize(bmap);
9612 return (isl_basic_set *)bmap;
9614 isl_basic_map_free(bmap);
9618 __isl_give isl_set *isl_map_wrap(__isl_take isl_map *map)
9622 map = isl_map_cow(map);
9626 for (i = 0; i < map->n; ++i) {
9627 map->p[i] = (isl_basic_map *)isl_basic_map_wrap(map->p[i]);
9631 map->dim = isl_space_wrap(map->dim);
9635 return (isl_set *)map;
9641 __isl_give isl_basic_map *isl_basic_set_unwrap(__isl_take isl_basic_set *bset)
9643 bset = isl_basic_set_cow(bset);
9647 bset->dim = isl_space_unwrap(bset->dim);
9651 bset = isl_basic_set_finalize(bset);
9653 return (isl_basic_map *)bset;
9655 isl_basic_set_free(bset);
9659 __isl_give isl_map *isl_set_unwrap(__isl_take isl_set *set)
9666 if (!isl_set_is_wrapping(set))
9667 isl_die(set->ctx, isl_error_invalid, "not a wrapping set",
9670 set = isl_set_cow(set);
9674 for (i = 0; i < set->n; ++i) {
9675 set->p[i] = (isl_basic_set *)isl_basic_set_unwrap(set->p[i]);
9680 set->dim = isl_space_unwrap(set->dim);
9684 return (isl_map *)set;
9690 __isl_give isl_basic_map *isl_basic_map_reset(__isl_take isl_basic_map *bmap,
9691 enum isl_dim_type type)
9696 if (!isl_space_is_named_or_nested(bmap->dim, type))
9699 bmap = isl_basic_map_cow(bmap);
9703 bmap->dim = isl_space_reset(bmap->dim, type);
9707 bmap = isl_basic_map_finalize(bmap);
9711 isl_basic_map_free(bmap);
9715 __isl_give isl_map *isl_map_reset(__isl_take isl_map *map,
9716 enum isl_dim_type type)
9723 if (!isl_space_is_named_or_nested(map->dim, type))
9726 map = isl_map_cow(map);
9730 for (i = 0; i < map->n; ++i) {
9731 map->p[i] = isl_basic_map_reset(map->p[i], type);
9735 map->dim = isl_space_reset(map->dim, type);
9745 __isl_give isl_basic_map *isl_basic_map_flatten(__isl_take isl_basic_map *bmap)
9750 if (!bmap->dim->nested[0] && !bmap->dim->nested[1])
9753 bmap = isl_basic_map_cow(bmap);
9757 bmap->dim = isl_space_flatten(bmap->dim);
9761 bmap = isl_basic_map_finalize(bmap);
9765 isl_basic_map_free(bmap);
9769 __isl_give isl_basic_set *isl_basic_set_flatten(__isl_take isl_basic_set *bset)
9771 return (isl_basic_set *)isl_basic_map_flatten((isl_basic_map *)bset);
9774 __isl_give isl_basic_map *isl_basic_map_flatten_domain(
9775 __isl_take isl_basic_map *bmap)
9780 if (!bmap->dim->nested[0])
9783 bmap = isl_basic_map_cow(bmap);
9787 bmap->dim = isl_space_flatten_domain(bmap->dim);
9791 bmap = isl_basic_map_finalize(bmap);
9795 isl_basic_map_free(bmap);
9799 __isl_give isl_basic_map *isl_basic_map_flatten_range(
9800 __isl_take isl_basic_map *bmap)
9805 if (!bmap->dim->nested[1])
9808 bmap = isl_basic_map_cow(bmap);
9812 bmap->dim = isl_space_flatten_range(bmap->dim);
9816 bmap = isl_basic_map_finalize(bmap);
9820 isl_basic_map_free(bmap);
9824 __isl_give isl_map *isl_map_flatten(__isl_take isl_map *map)
9831 if (!map->dim->nested[0] && !map->dim->nested[1])
9834 map = isl_map_cow(map);
9838 for (i = 0; i < map->n; ++i) {
9839 map->p[i] = isl_basic_map_flatten(map->p[i]);
9843 map->dim = isl_space_flatten(map->dim);
9853 __isl_give isl_set *isl_set_flatten(__isl_take isl_set *set)
9855 return (isl_set *)isl_map_flatten((isl_map *)set);
9858 __isl_give isl_map *isl_set_flatten_map(__isl_take isl_set *set)
9860 isl_space *dim, *flat_dim;
9863 dim = isl_set_get_space(set);
9864 flat_dim = isl_space_flatten(isl_space_copy(dim));
9865 map = isl_map_identity(isl_space_join(isl_space_reverse(dim), flat_dim));
9866 map = isl_map_intersect_domain(map, set);
9871 __isl_give isl_map *isl_map_flatten_domain(__isl_take isl_map *map)
9878 if (!map->dim->nested[0])
9881 map = isl_map_cow(map);
9885 for (i = 0; i < map->n; ++i) {
9886 map->p[i] = isl_basic_map_flatten_domain(map->p[i]);
9890 map->dim = isl_space_flatten_domain(map->dim);
9900 __isl_give isl_map *isl_map_flatten_range(__isl_take isl_map *map)
9907 if (!map->dim->nested[1])
9910 map = isl_map_cow(map);
9914 for (i = 0; i < map->n; ++i) {
9915 map->p[i] = isl_basic_map_flatten_range(map->p[i]);
9919 map->dim = isl_space_flatten_range(map->dim);
9929 /* Reorder the dimensions of "bmap" according to the given dim_map
9930 * and set the dimension specification to "dim".
9932 __isl_give isl_basic_map *isl_basic_map_realign(__isl_take isl_basic_map *bmap,
9933 __isl_take isl_space *dim, __isl_take struct isl_dim_map *dim_map)
9938 bmap = isl_basic_map_cow(bmap);
9939 if (!bmap || !dim || !dim_map)
9942 flags = bmap->flags;
9943 ISL_FL_CLR(flags, ISL_BASIC_MAP_FINAL);
9944 ISL_FL_CLR(flags, ISL_BASIC_MAP_NORMALIZED);
9945 ISL_FL_CLR(flags, ISL_BASIC_MAP_NORMALIZED_DIVS);
9946 res = isl_basic_map_alloc_space(dim,
9947 bmap->n_div, bmap->n_eq, bmap->n_ineq);
9948 res = isl_basic_map_add_constraints_dim_map(res, bmap, dim_map);
9951 res = isl_basic_map_finalize(res);
9955 isl_basic_map_free(bmap);
9956 isl_space_free(dim);
9960 /* Reorder the dimensions of "map" according to given reordering.
9962 __isl_give isl_map *isl_map_realign(__isl_take isl_map *map,
9963 __isl_take isl_reordering *r)
9966 struct isl_dim_map *dim_map;
9968 map = isl_map_cow(map);
9969 dim_map = isl_dim_map_from_reordering(r);
9970 if (!map || !r || !dim_map)
9973 for (i = 0; i < map->n; ++i) {
9974 struct isl_dim_map *dim_map_i;
9976 dim_map_i = isl_dim_map_extend(dim_map, map->p[i]);
9978 map->p[i] = isl_basic_map_realign(map->p[i],
9979 isl_space_copy(r->dim), dim_map_i);
9985 map = isl_map_reset_space(map, isl_space_copy(r->dim));
9987 isl_reordering_free(r);
9993 isl_reordering_free(r);
9997 __isl_give isl_set *isl_set_realign(__isl_take isl_set *set,
9998 __isl_take isl_reordering *r)
10000 return (isl_set *)isl_map_realign((isl_map *)set, r);
10003 __isl_give isl_map *isl_map_align_params(__isl_take isl_map *map,
10004 __isl_take isl_space *model)
10008 if (!map || !model)
10011 ctx = isl_space_get_ctx(model);
10012 if (!isl_space_has_named_params(model))
10013 isl_die(ctx, isl_error_invalid,
10014 "model has unnamed parameters", goto error);
10015 if (!isl_space_has_named_params(map->dim))
10016 isl_die(ctx, isl_error_invalid,
10017 "relation has unnamed parameters", goto error);
10018 if (!isl_space_match(map->dim, isl_dim_param, model, isl_dim_param)) {
10019 isl_reordering *exp;
10021 model = isl_space_drop_dims(model, isl_dim_in,
10022 0, isl_space_dim(model, isl_dim_in));
10023 model = isl_space_drop_dims(model, isl_dim_out,
10024 0, isl_space_dim(model, isl_dim_out));
10025 exp = isl_parameter_alignment_reordering(map->dim, model);
10026 exp = isl_reordering_extend_space(exp, isl_map_get_space(map));
10027 map = isl_map_realign(map, exp);
10030 isl_space_free(model);
10033 isl_space_free(model);
10038 __isl_give isl_set *isl_set_align_params(__isl_take isl_set *set,
10039 __isl_take isl_space *model)
10041 return isl_map_align_params(set, model);
10044 /* Align the parameters of "bmap" to those of "model", introducing
10045 * additional parameters if needed.
10047 __isl_give isl_basic_map *isl_basic_map_align_params(
10048 __isl_take isl_basic_map *bmap, __isl_take isl_space *model)
10052 if (!bmap || !model)
10055 ctx = isl_space_get_ctx(model);
10056 if (!isl_space_has_named_params(model))
10057 isl_die(ctx, isl_error_invalid,
10058 "model has unnamed parameters", goto error);
10059 if (!isl_space_has_named_params(bmap->dim))
10060 isl_die(ctx, isl_error_invalid,
10061 "relation has unnamed parameters", goto error);
10062 if (!isl_space_match(bmap->dim, isl_dim_param, model, isl_dim_param)) {
10063 isl_reordering *exp;
10064 struct isl_dim_map *dim_map;
10066 model = isl_space_drop_dims(model, isl_dim_in,
10067 0, isl_space_dim(model, isl_dim_in));
10068 model = isl_space_drop_dims(model, isl_dim_out,
10069 0, isl_space_dim(model, isl_dim_out));
10070 exp = isl_parameter_alignment_reordering(bmap->dim, model);
10071 exp = isl_reordering_extend_space(exp,
10072 isl_basic_map_get_space(bmap));
10073 dim_map = isl_dim_map_from_reordering(exp);
10074 bmap = isl_basic_map_realign(bmap,
10075 exp ? isl_space_copy(exp->dim) : NULL,
10076 isl_dim_map_extend(dim_map, bmap));
10077 isl_reordering_free(exp);
10081 isl_space_free(model);
10084 isl_space_free(model);
10085 isl_basic_map_free(bmap);
10089 /* Align the parameters of "bset" to those of "model", introducing
10090 * additional parameters if needed.
10092 __isl_give isl_basic_set *isl_basic_set_align_params(
10093 __isl_take isl_basic_set *bset, __isl_take isl_space *model)
10095 return isl_basic_map_align_params(bset, model);
10098 __isl_give isl_mat *isl_basic_map_equalities_matrix(
10099 __isl_keep isl_basic_map *bmap, enum isl_dim_type c1,
10100 enum isl_dim_type c2, enum isl_dim_type c3,
10101 enum isl_dim_type c4, enum isl_dim_type c5)
10103 enum isl_dim_type c[5] = { c1, c2, c3, c4, c5 };
10104 struct isl_mat *mat;
10110 mat = isl_mat_alloc(bmap->ctx, bmap->n_eq,
10111 isl_basic_map_total_dim(bmap) + 1);
10114 for (i = 0; i < bmap->n_eq; ++i)
10115 for (j = 0, pos = 0; j < 5; ++j) {
10116 int off = isl_basic_map_offset(bmap, c[j]);
10117 for (k = 0; k < isl_basic_map_dim(bmap, c[j]); ++k) {
10118 isl_int_set(mat->row[i][pos],
10119 bmap->eq[i][off + k]);
10127 __isl_give isl_mat *isl_basic_map_inequalities_matrix(
10128 __isl_keep isl_basic_map *bmap, enum isl_dim_type c1,
10129 enum isl_dim_type c2, enum isl_dim_type c3,
10130 enum isl_dim_type c4, enum isl_dim_type c5)
10132 enum isl_dim_type c[5] = { c1, c2, c3, c4, c5 };
10133 struct isl_mat *mat;
10139 mat = isl_mat_alloc(bmap->ctx, bmap->n_ineq,
10140 isl_basic_map_total_dim(bmap) + 1);
10143 for (i = 0; i < bmap->n_ineq; ++i)
10144 for (j = 0, pos = 0; j < 5; ++j) {
10145 int off = isl_basic_map_offset(bmap, c[j]);
10146 for (k = 0; k < isl_basic_map_dim(bmap, c[j]); ++k) {
10147 isl_int_set(mat->row[i][pos],
10148 bmap->ineq[i][off + k]);
10156 __isl_give isl_basic_map *isl_basic_map_from_constraint_matrices(
10157 __isl_take isl_space *dim,
10158 __isl_take isl_mat *eq, __isl_take isl_mat *ineq, enum isl_dim_type c1,
10159 enum isl_dim_type c2, enum isl_dim_type c3,
10160 enum isl_dim_type c4, enum isl_dim_type c5)
10162 enum isl_dim_type c[5] = { c1, c2, c3, c4, c5 };
10163 isl_basic_map *bmap;
10169 if (!dim || !eq || !ineq)
10172 if (eq->n_col != ineq->n_col)
10173 isl_die(dim->ctx, isl_error_invalid,
10174 "equalities and inequalities matrices should have "
10175 "same number of columns", goto error);
10177 total = 1 + isl_space_dim(dim, isl_dim_all);
10179 if (eq->n_col < total)
10180 isl_die(dim->ctx, isl_error_invalid,
10181 "number of columns too small", goto error);
10183 extra = eq->n_col - total;
10185 bmap = isl_basic_map_alloc_space(isl_space_copy(dim), extra,
10186 eq->n_row, ineq->n_row);
10189 for (i = 0; i < extra; ++i) {
10190 k = isl_basic_map_alloc_div(bmap);
10193 isl_int_set_si(bmap->div[k][0], 0);
10195 for (i = 0; i < eq->n_row; ++i) {
10196 l = isl_basic_map_alloc_equality(bmap);
10199 for (j = 0, pos = 0; j < 5; ++j) {
10200 int off = isl_basic_map_offset(bmap, c[j]);
10201 for (k = 0; k < isl_basic_map_dim(bmap, c[j]); ++k) {
10202 isl_int_set(bmap->eq[l][off + k],
10208 for (i = 0; i < ineq->n_row; ++i) {
10209 l = isl_basic_map_alloc_inequality(bmap);
10212 for (j = 0, pos = 0; j < 5; ++j) {
10213 int off = isl_basic_map_offset(bmap, c[j]);
10214 for (k = 0; k < isl_basic_map_dim(bmap, c[j]); ++k) {
10215 isl_int_set(bmap->ineq[l][off + k],
10216 ineq->row[i][pos]);
10222 isl_space_free(dim);
10224 isl_mat_free(ineq);
10228 isl_space_free(dim);
10230 isl_mat_free(ineq);
10234 __isl_give isl_mat *isl_basic_set_equalities_matrix(
10235 __isl_keep isl_basic_set *bset, enum isl_dim_type c1,
10236 enum isl_dim_type c2, enum isl_dim_type c3, enum isl_dim_type c4)
10238 return isl_basic_map_equalities_matrix((isl_basic_map *)bset,
10239 c1, c2, c3, c4, isl_dim_in);
10242 __isl_give isl_mat *isl_basic_set_inequalities_matrix(
10243 __isl_keep isl_basic_set *bset, enum isl_dim_type c1,
10244 enum isl_dim_type c2, enum isl_dim_type c3, enum isl_dim_type c4)
10246 return isl_basic_map_inequalities_matrix((isl_basic_map *)bset,
10247 c1, c2, c3, c4, isl_dim_in);
10250 __isl_give isl_basic_set *isl_basic_set_from_constraint_matrices(
10251 __isl_take isl_space *dim,
10252 __isl_take isl_mat *eq, __isl_take isl_mat *ineq, enum isl_dim_type c1,
10253 enum isl_dim_type c2, enum isl_dim_type c3, enum isl_dim_type c4)
10255 return (isl_basic_set*)
10256 isl_basic_map_from_constraint_matrices(dim, eq, ineq,
10257 c1, c2, c3, c4, isl_dim_in);
10260 int isl_basic_map_can_zip(__isl_keep isl_basic_map *bmap)
10265 return isl_space_can_zip(bmap->dim);
10268 int isl_map_can_zip(__isl_keep isl_map *map)
10273 return isl_space_can_zip(map->dim);
10276 /* Given a basic map (A -> B) -> (C -> D), return the corresponding basic map
10277 * (A -> C) -> (B -> D).
10279 __isl_give isl_basic_map *isl_basic_map_zip(__isl_take isl_basic_map *bmap)
10288 if (!isl_basic_map_can_zip(bmap))
10289 isl_die(bmap->ctx, isl_error_invalid,
10290 "basic map cannot be zipped", goto error);
10291 pos = isl_basic_map_offset(bmap, isl_dim_in) +
10292 isl_space_dim(bmap->dim->nested[0], isl_dim_in);
10293 n1 = isl_space_dim(bmap->dim->nested[0], isl_dim_out);
10294 n2 = isl_space_dim(bmap->dim->nested[1], isl_dim_in);
10295 bmap = isl_basic_map_cow(bmap);
10296 bmap = isl_basic_map_swap_vars(bmap, pos, n1, n2);
10299 bmap->dim = isl_space_zip(bmap->dim);
10304 isl_basic_map_free(bmap);
10308 /* Given a map (A -> B) -> (C -> D), return the corresponding map
10309 * (A -> C) -> (B -> D).
10311 __isl_give isl_map *isl_map_zip(__isl_take isl_map *map)
10318 if (!isl_map_can_zip(map))
10319 isl_die(map->ctx, isl_error_invalid, "map cannot be zipped",
10322 map = isl_map_cow(map);
10326 for (i = 0; i < map->n; ++i) {
10327 map->p[i] = isl_basic_map_zip(map->p[i]);
10332 map->dim = isl_space_zip(map->dim);
10342 /* Can we apply isl_basic_map_curry to "bmap"?
10343 * That is, does it have a nested relation in its domain?
10345 int isl_basic_map_can_curry(__isl_keep isl_basic_map *bmap)
10350 return isl_space_can_curry(bmap->dim);
10353 /* Can we apply isl_map_curry to "map"?
10354 * That is, does it have a nested relation in its domain?
10356 int isl_map_can_curry(__isl_keep isl_map *map)
10361 return isl_space_can_curry(map->dim);
10364 /* Given a basic map (A -> B) -> C, return the corresponding basic map
10367 __isl_give isl_basic_map *isl_basic_map_curry(__isl_take isl_basic_map *bmap)
10373 if (!isl_basic_map_can_curry(bmap))
10374 isl_die(bmap->ctx, isl_error_invalid,
10375 "basic map cannot be curried", goto error);
10376 bmap->dim = isl_space_curry(bmap->dim);
10381 isl_basic_map_free(bmap);
10385 /* Given a map (A -> B) -> C, return the corresponding map
10388 __isl_give isl_map *isl_map_curry(__isl_take isl_map *map)
10395 if (!isl_map_can_curry(map))
10396 isl_die(map->ctx, isl_error_invalid, "map cannot be curried",
10399 map = isl_map_cow(map);
10403 for (i = 0; i < map->n; ++i) {
10404 map->p[i] = isl_basic_map_curry(map->p[i]);
10409 map->dim = isl_space_curry(map->dim);
10419 /* Can we apply isl_basic_map_uncurry to "bmap"?
10420 * That is, does it have a nested relation in its domain?
10422 int isl_basic_map_can_uncurry(__isl_keep isl_basic_map *bmap)
10427 return isl_space_can_uncurry(bmap->dim);
10430 /* Can we apply isl_map_uncurry to "map"?
10431 * That is, does it have a nested relation in its domain?
10433 int isl_map_can_uncurry(__isl_keep isl_map *map)
10438 return isl_space_can_uncurry(map->dim);
10441 /* Given a basic map A -> (B -> C), return the corresponding basic map
10444 __isl_give isl_basic_map *isl_basic_map_uncurry(__isl_take isl_basic_map *bmap)
10450 if (!isl_basic_map_can_uncurry(bmap))
10451 isl_die(bmap->ctx, isl_error_invalid,
10452 "basic map cannot be uncurried",
10453 return isl_basic_map_free(bmap));
10454 bmap->dim = isl_space_uncurry(bmap->dim);
10456 return isl_basic_map_free(bmap);
10460 /* Given a map A -> (B -> C), return the corresponding map
10463 __isl_give isl_map *isl_map_uncurry(__isl_take isl_map *map)
10470 if (!isl_map_can_uncurry(map))
10471 isl_die(map->ctx, isl_error_invalid, "map cannot be uncurried",
10472 return isl_map_free(map));
10474 map = isl_map_cow(map);
10478 for (i = 0; i < map->n; ++i) {
10479 map->p[i] = isl_basic_map_uncurry(map->p[i]);
10481 return isl_map_free(map);
10484 map->dim = isl_space_uncurry(map->dim);
10486 return isl_map_free(map);
10491 /* Construct a basic map mapping the domain of the affine expression
10492 * to a one-dimensional range prescribed by the affine expression.
10494 __isl_give isl_basic_map *isl_basic_map_from_aff(__isl_take isl_aff *aff)
10498 isl_local_space *ls;
10499 isl_basic_map *bmap;
10504 ls = isl_aff_get_local_space(aff);
10505 bmap = isl_basic_map_from_local_space(ls);
10506 bmap = isl_basic_map_extend_constraints(bmap, 1, 0);
10507 k = isl_basic_map_alloc_equality(bmap);
10511 pos = isl_basic_map_offset(bmap, isl_dim_out);
10512 isl_seq_cpy(bmap->eq[k], aff->v->el + 1, pos);
10513 isl_int_neg(bmap->eq[k][pos], aff->v->el[0]);
10514 isl_seq_cpy(bmap->eq[k] + pos + 1, aff->v->el + 1 + pos,
10515 aff->v->size - (pos + 1));
10518 bmap = isl_basic_map_finalize(bmap);
10522 isl_basic_map_free(bmap);
10526 /* Construct a map mapping the domain of the affine expression
10527 * to a one-dimensional range prescribed by the affine expression.
10529 __isl_give isl_map *isl_map_from_aff(__isl_take isl_aff *aff)
10531 isl_basic_map *bmap;
10533 bmap = isl_basic_map_from_aff(aff);
10534 return isl_map_from_basic_map(bmap);
10537 /* Construct a basic map mapping the domain the multi-affine expression
10538 * to its range, with each dimension in the range equated to the
10539 * corresponding affine expression.
10541 __isl_give isl_basic_map *isl_basic_map_from_multi_aff(
10542 __isl_take isl_multi_aff *maff)
10546 isl_basic_map *bmap;
10551 if (isl_space_dim(maff->space, isl_dim_out) != maff->n)
10552 isl_die(isl_multi_aff_get_ctx(maff), isl_error_internal,
10553 "invalid space", return isl_multi_aff_free(maff));
10555 space = isl_space_domain(isl_multi_aff_get_space(maff));
10556 bmap = isl_basic_map_universe(isl_space_from_domain(space));
10558 for (i = 0; i < maff->n; ++i) {
10560 isl_basic_map *bmap_i;
10562 aff = isl_aff_copy(maff->p[i]);
10563 bmap_i = isl_basic_map_from_aff(aff);
10565 bmap = isl_basic_map_flat_range_product(bmap, bmap_i);
10568 bmap = isl_basic_map_reset_space(bmap, isl_multi_aff_get_space(maff));
10570 isl_multi_aff_free(maff);
10574 /* Construct a map mapping the domain the multi-affine expression
10575 * to its range, with each dimension in the range equated to the
10576 * corresponding affine expression.
10578 __isl_give isl_map *isl_map_from_multi_aff(__isl_take isl_multi_aff *maff)
10580 isl_basic_map *bmap;
10582 bmap = isl_basic_map_from_multi_aff(maff);
10583 return isl_map_from_basic_map(bmap);
10586 /* Construct a basic map mapping a domain in the given space to
10587 * to an n-dimensional range, with n the number of elements in the list,
10588 * where each coordinate in the range is prescribed by the
10589 * corresponding affine expression.
10590 * The domains of all affine expressions in the list are assumed to match
10593 __isl_give isl_basic_map *isl_basic_map_from_aff_list(
10594 __isl_take isl_space *domain_dim, __isl_take isl_aff_list *list)
10598 isl_basic_map *bmap;
10603 dim = isl_space_from_domain(domain_dim);
10604 bmap = isl_basic_map_universe(dim);
10606 for (i = 0; i < list->n; ++i) {
10608 isl_basic_map *bmap_i;
10610 aff = isl_aff_copy(list->p[i]);
10611 bmap_i = isl_basic_map_from_aff(aff);
10613 bmap = isl_basic_map_flat_range_product(bmap, bmap_i);
10616 isl_aff_list_free(list);
10620 __isl_give isl_set *isl_set_equate(__isl_take isl_set *set,
10621 enum isl_dim_type type1, int pos1, enum isl_dim_type type2, int pos2)
10623 return isl_map_equate(set, type1, pos1, type2, pos2);
10626 /* Construct a basic map where the given dimensions are equal to each other.
10628 static __isl_give isl_basic_map *equator(__isl_take isl_space *space,
10629 enum isl_dim_type type1, int pos1, enum isl_dim_type type2, int pos2)
10631 isl_basic_map *bmap = NULL;
10637 if (pos1 >= isl_space_dim(space, type1))
10638 isl_die(isl_space_get_ctx(space), isl_error_invalid,
10639 "index out of bounds", goto error);
10640 if (pos2 >= isl_space_dim(space, type2))
10641 isl_die(isl_space_get_ctx(space), isl_error_invalid,
10642 "index out of bounds", goto error);
10644 if (type1 == type2 && pos1 == pos2)
10645 return isl_basic_map_universe(space);
10647 bmap = isl_basic_map_alloc_space(isl_space_copy(space), 0, 1, 0);
10648 i = isl_basic_map_alloc_equality(bmap);
10651 isl_seq_clr(bmap->eq[i], 1 + isl_basic_map_total_dim(bmap));
10652 pos1 += isl_basic_map_offset(bmap, type1);
10653 pos2 += isl_basic_map_offset(bmap, type2);
10654 isl_int_set_si(bmap->eq[i][pos1], -1);
10655 isl_int_set_si(bmap->eq[i][pos2], 1);
10656 bmap = isl_basic_map_finalize(bmap);
10657 isl_space_free(space);
10660 isl_space_free(space);
10661 isl_basic_map_free(bmap);
10665 /* Add a constraint imposing that the given two dimensions are equal.
10667 __isl_give isl_basic_map *isl_basic_map_equate(__isl_take isl_basic_map *bmap,
10668 enum isl_dim_type type1, int pos1, enum isl_dim_type type2, int pos2)
10672 eq = equator(isl_basic_map_get_space(bmap), type1, pos1, type2, pos2);
10674 bmap = isl_basic_map_intersect(bmap, eq);
10679 /* Add a constraint imposing that the given two dimensions are equal.
10681 __isl_give isl_map *isl_map_equate(__isl_take isl_map *map,
10682 enum isl_dim_type type1, int pos1, enum isl_dim_type type2, int pos2)
10684 isl_basic_map *bmap;
10686 bmap = equator(isl_map_get_space(map), type1, pos1, type2, pos2);
10688 map = isl_map_intersect(map, isl_map_from_basic_map(bmap));
10693 /* Add a constraint imposing that the given two dimensions have opposite values.
10695 __isl_give isl_map *isl_map_oppose(__isl_take isl_map *map,
10696 enum isl_dim_type type1, int pos1, enum isl_dim_type type2, int pos2)
10698 isl_basic_map *bmap = NULL;
10704 if (pos1 >= isl_map_dim(map, type1))
10705 isl_die(map->ctx, isl_error_invalid,
10706 "index out of bounds", goto error);
10707 if (pos2 >= isl_map_dim(map, type2))
10708 isl_die(map->ctx, isl_error_invalid,
10709 "index out of bounds", goto error);
10711 bmap = isl_basic_map_alloc_space(isl_map_get_space(map), 0, 1, 0);
10712 i = isl_basic_map_alloc_equality(bmap);
10715 isl_seq_clr(bmap->eq[i], 1 + isl_basic_map_total_dim(bmap));
10716 pos1 += isl_basic_map_offset(bmap, type1);
10717 pos2 += isl_basic_map_offset(bmap, type2);
10718 isl_int_set_si(bmap->eq[i][pos1], 1);
10719 isl_int_set_si(bmap->eq[i][pos2], 1);
10720 bmap = isl_basic_map_finalize(bmap);
10722 map = isl_map_intersect(map, isl_map_from_basic_map(bmap));
10726 isl_basic_map_free(bmap);
10731 /* Add a constraint imposing that the value of the first dimension is
10732 * greater than or equal to that of the second.
10734 __isl_give isl_basic_map *isl_basic_map_order_ge(__isl_take isl_basic_map *bmap,
10735 enum isl_dim_type type1, int pos1, enum isl_dim_type type2, int pos2)
10738 isl_local_space *ls;
10743 if (pos1 >= isl_basic_map_dim(bmap, type1))
10744 isl_die(bmap->ctx, isl_error_invalid,
10745 "index out of bounds", return isl_basic_map_free(bmap));
10746 if (pos2 >= isl_basic_map_dim(bmap, type2))
10747 isl_die(bmap->ctx, isl_error_invalid,
10748 "index out of bounds", return isl_basic_map_free(bmap));
10750 if (type1 == type2 && pos1 == pos2)
10753 ls = isl_local_space_from_space(isl_basic_map_get_space(bmap));
10754 c = isl_inequality_alloc(ls);
10755 c = isl_constraint_set_coefficient_si(c, type1, pos1, 1);
10756 c = isl_constraint_set_coefficient_si(c, type2, pos2, -1);
10757 bmap = isl_basic_map_add_constraint(bmap, c);
10762 /* Add a constraint imposing that the value of the first dimension is
10763 * greater than that of the second.
10765 __isl_give isl_map *isl_map_order_gt(__isl_take isl_map *map,
10766 enum isl_dim_type type1, int pos1, enum isl_dim_type type2, int pos2)
10768 isl_basic_map *bmap = NULL;
10774 if (pos1 >= isl_map_dim(map, type1))
10775 isl_die(map->ctx, isl_error_invalid,
10776 "index out of bounds", goto error);
10777 if (pos2 >= isl_map_dim(map, type2))
10778 isl_die(map->ctx, isl_error_invalid,
10779 "index out of bounds", goto error);
10781 if (type1 == type2 && pos1 == pos2) {
10782 isl_space *space = isl_map_get_space(map);
10784 return isl_map_empty(space);
10787 bmap = isl_basic_map_alloc_space(isl_map_get_space(map), 0, 0, 1);
10788 i = isl_basic_map_alloc_inequality(bmap);
10791 isl_seq_clr(bmap->ineq[i], 1 + isl_basic_map_total_dim(bmap));
10792 pos1 += isl_basic_map_offset(bmap, type1);
10793 pos2 += isl_basic_map_offset(bmap, type2);
10794 isl_int_set_si(bmap->ineq[i][pos1], 1);
10795 isl_int_set_si(bmap->ineq[i][pos2], -1);
10796 isl_int_set_si(bmap->ineq[i][0], -1);
10797 bmap = isl_basic_map_finalize(bmap);
10799 map = isl_map_intersect(map, isl_map_from_basic_map(bmap));
10803 isl_basic_map_free(bmap);
10808 /* Add a constraint imposing that the value of the first dimension is
10809 * smaller than that of the second.
10811 __isl_give isl_map *isl_map_order_lt(__isl_take isl_map *map,
10812 enum isl_dim_type type1, int pos1, enum isl_dim_type type2, int pos2)
10814 return isl_map_order_gt(map, type2, pos2, type1, pos1);
10817 __isl_give isl_aff *isl_basic_map_get_div(__isl_keep isl_basic_map *bmap,
10821 isl_local_space *ls;
10826 if (!isl_basic_map_divs_known(bmap))
10827 isl_die(isl_basic_map_get_ctx(bmap), isl_error_invalid,
10828 "some divs are unknown", return NULL);
10830 ls = isl_basic_map_get_local_space(bmap);
10831 div = isl_local_space_get_div(ls, pos);
10832 isl_local_space_free(ls);
10837 __isl_give isl_aff *isl_basic_set_get_div(__isl_keep isl_basic_set *bset,
10840 return isl_basic_map_get_div(bset, pos);
10843 /* Plug in "subs" for dimension "type", "pos" of "bset".
10845 * Let i be the dimension to replace and let "subs" be of the form
10849 * Any integer division with a non-zero coefficient for i,
10851 * floor((a i + g)/m)
10855 * floor((a f + d g)/(m d))
10857 * Constraints of the form
10865 * We currently require that "subs" is an integral expression.
10866 * Handling rational expressions may require us to add stride constraints
10867 * as we do in isl_basic_set_preimage_multi_aff.
10869 __isl_give isl_basic_set *isl_basic_set_substitute(
10870 __isl_take isl_basic_set *bset,
10871 enum isl_dim_type type, unsigned pos, __isl_keep isl_aff *subs)
10877 if (bset && isl_basic_set_plain_is_empty(bset))
10880 bset = isl_basic_set_cow(bset);
10881 if (!bset || !subs)
10884 ctx = isl_basic_set_get_ctx(bset);
10885 if (!isl_space_is_equal(bset->dim, subs->ls->dim))
10886 isl_die(ctx, isl_error_invalid,
10887 "spaces don't match", goto error);
10888 if (isl_local_space_dim(subs->ls, isl_dim_div) != 0)
10889 isl_die(ctx, isl_error_unsupported,
10890 "cannot handle divs yet", goto error);
10891 if (!isl_int_is_one(subs->v->el[0]))
10892 isl_die(ctx, isl_error_invalid,
10893 "can only substitute integer expressions", goto error);
10895 pos += isl_basic_set_offset(bset, type);
10899 for (i = 0; i < bset->n_eq; ++i) {
10900 if (isl_int_is_zero(bset->eq[i][pos]))
10902 isl_int_set(v, bset->eq[i][pos]);
10903 isl_int_set_si(bset->eq[i][pos], 0);
10904 isl_seq_combine(bset->eq[i], subs->v->el[0], bset->eq[i],
10905 v, subs->v->el + 1, subs->v->size - 1);
10908 for (i = 0; i < bset->n_ineq; ++i) {
10909 if (isl_int_is_zero(bset->ineq[i][pos]))
10911 isl_int_set(v, bset->ineq[i][pos]);
10912 isl_int_set_si(bset->ineq[i][pos], 0);
10913 isl_seq_combine(bset->ineq[i], subs->v->el[0], bset->ineq[i],
10914 v, subs->v->el + 1, subs->v->size - 1);
10917 for (i = 0; i < bset->n_div; ++i) {
10918 if (isl_int_is_zero(bset->div[i][1 + pos]))
10920 isl_int_set(v, bset->div[i][1 + pos]);
10921 isl_int_set_si(bset->div[i][1 + pos], 0);
10922 isl_seq_combine(bset->div[i] + 1,
10923 subs->v->el[0], bset->div[i] + 1,
10924 v, subs->v->el + 1, subs->v->size - 1);
10925 isl_int_mul(bset->div[i][0], bset->div[i][0], subs->v->el[0]);
10930 bset = isl_basic_set_simplify(bset);
10931 return isl_basic_set_finalize(bset);
10933 isl_basic_set_free(bset);
10937 /* Plug in "subs" for dimension "type", "pos" of "set".
10939 __isl_give isl_set *isl_set_substitute(__isl_take isl_set *set,
10940 enum isl_dim_type type, unsigned pos, __isl_keep isl_aff *subs)
10944 if (set && isl_set_plain_is_empty(set))
10947 set = isl_set_cow(set);
10951 for (i = set->n - 1; i >= 0; --i) {
10952 set->p[i] = isl_basic_set_substitute(set->p[i], type, pos, subs);
10953 if (remove_if_empty(set, i) < 0)
10963 /* Check if the range of "ma" is compatible with "space".
10964 * Return -1 if anything is wrong.
10966 static int check_space_compatible_range_multi_aff(
10967 __isl_keep isl_space *space, __isl_keep isl_multi_aff *ma)
10970 isl_space *ma_space;
10972 ma_space = isl_multi_aff_get_space(ma);
10973 m = isl_space_is_range_internal(space, ma_space);
10974 isl_space_free(ma_space);
10976 isl_die(isl_space_get_ctx(space), isl_error_invalid,
10977 "spaces don't match", return -1);
10981 /* Check if the range of "ma" is compatible with "bset".
10982 * Return -1 if anything is wrong.
10984 static int check_basic_set_compatible_range_multi_aff(
10985 __isl_keep isl_basic_set *bset, __isl_keep isl_multi_aff *ma)
10987 return check_space_compatible_range_multi_aff(bset->dim, ma);
10990 /* Copy the divs from "ma" to "bset", adding zeros for the coefficients
10991 * of the other divs in "bset".
10993 static int set_ma_divs(__isl_keep isl_basic_set *bset,
10994 __isl_keep isl_multi_aff *ma, int n_div)
10997 isl_local_space *ls;
11002 ls = isl_aff_get_domain_local_space(ma->p[0]);
11006 for (i = 0; i < n_div; ++i) {
11007 isl_seq_cpy(bset->div[i], ls->div->row[i], ls->div->n_col);
11008 isl_seq_clr(bset->div[i] + ls->div->n_col, bset->n_div - n_div);
11009 if (isl_basic_set_add_div_constraints(bset, i) < 0)
11013 isl_local_space_free(ls);
11016 isl_local_space_free(ls);
11020 /* How many stride constraints does "ma" enforce?
11021 * That is, how many of the affine expressions have a denominator
11022 * different from one?
11024 static int multi_aff_strides(__isl_keep isl_multi_aff *ma)
11029 for (i = 0; i < ma->n; ++i)
11030 if (!isl_int_is_one(ma->p[i]->v->el[0]))
11036 /* For each affine expression in ma of the form
11038 * x_i = (f_i y + h_i)/m_i
11040 * with m_i different from one, add a constraint to "bset"
11043 * f_i y + h_i = m_i alpha_i
11045 * with alpha_i an additional existentially quantified variable.
11047 static __isl_give isl_basic_set *add_ma_strides(
11048 __isl_take isl_basic_set *bset, __isl_keep isl_multi_aff *ma)
11054 total = isl_basic_set_total_dim(bset);
11055 for (i = 0; i < ma->n; ++i) {
11058 if (isl_int_is_one(ma->p[i]->v->el[0]))
11060 div = isl_basic_set_alloc_div(bset);
11061 k = isl_basic_set_alloc_equality(bset);
11062 if (div < 0 || k < 0)
11064 isl_int_set_si(bset->div[div][0], 0);
11065 len = ma->p[i]->v->size;
11066 isl_seq_cpy(bset->eq[k], ma->p[i]->v->el + 1, len - 1);
11067 isl_seq_clr(bset->eq[k] + len - 1, 1 + total - (len - 1));
11068 isl_int_neg(bset->eq[k][1 + total], ma->p[i]->v->el[0]);
11074 isl_basic_set_free(bset);
11078 /* Compute the preimage of "bset" under the function represented by "ma".
11079 * In other words, plug in "ma" in "bset". The result is a basic set
11080 * that lives in the domain space of "ma".
11082 * If bset is represented by
11084 * A(p) + B x + C(divs) >= 0
11086 * and ma is represented by
11088 * x = D(p) + F(y) + G(divs')
11090 * then the result is
11092 * A(p) + B D(p) + B F(y) + B G(divs') + C(divs) >= 0
11094 * The divs in the input set are similarly adjusted.
11097 * floor((a_i(p) + b_i x + c_i(divs))/n_i)
11101 * floor((a_i(p) + b_i D(p) + b_i F(y) + B_i G(divs') + c_i(divs))/n_i)
11103 * If bset is not a rational set and if F(y) involves any denominators
11105 * x_i = (f_i y + h_i)/m_i
11107 * the additional constraints are added to ensure that we only
11108 * map back integer points. That is we enforce
11110 * f_i y + h_i = m_i alpha_i
11112 * with alpha_i an additional existentially quantified variable.
11114 * We first copy over the divs from "ma".
11115 * Then we add the modified constraints and divs from "bset".
11116 * Finally, we add the stride constraints, if needed.
11118 __isl_give isl_basic_set *isl_basic_set_preimage_multi_aff(
11119 __isl_take isl_basic_set *bset, __isl_take isl_multi_aff *ma)
11123 isl_basic_set *res = NULL;
11124 int n_div_bset, n_div_ma;
11125 isl_int f, c1, c2, g;
11126 int rational, strides;
11133 ma = isl_multi_aff_align_divs(ma);
11136 if (check_basic_set_compatible_range_multi_aff(bset, ma) < 0)
11139 n_div_bset = isl_basic_set_dim(bset, isl_dim_div);
11140 n_div_ma = ma->n ? isl_aff_dim(ma->p[0], isl_dim_div) : 0;
11142 space = isl_space_domain(isl_multi_aff_get_space(ma));
11143 rational = isl_basic_set_is_rational(bset);
11144 strides = rational ? 0 : multi_aff_strides(ma);
11145 res = isl_basic_set_alloc_space(space, n_div_ma + n_div_bset + strides,
11146 bset->n_eq + strides, bset->n_ineq + 2 * n_div_ma);
11148 res = isl_basic_set_set_rational(res);
11150 for (i = 0; i < n_div_ma + n_div_bset; ++i)
11151 if (isl_basic_set_alloc_div(res) < 0)
11154 if (set_ma_divs(res, ma, n_div_ma) < 0)
11157 for (i = 0; i < bset->n_eq; ++i) {
11158 k = isl_basic_set_alloc_equality(res);
11161 isl_seq_preimage(res->eq[k], bset->eq[i], ma, n_div_ma,
11162 n_div_bset, f, c1, c2, g, 0);
11165 for (i = 0; i < bset->n_ineq; ++i) {
11166 k = isl_basic_set_alloc_inequality(res);
11169 isl_seq_preimage(res->ineq[k], bset->ineq[i], ma, n_div_ma,
11170 n_div_bset, f, c1, c2, g, 0);
11173 for (i = 0; i < bset->n_div; ++i) {
11174 if (isl_int_is_zero(bset->div[i][0])) {
11175 isl_int_set_si(res->div[n_div_ma + i][0], 0);
11178 isl_seq_preimage(res->div[n_div_ma + i], bset->div[i],
11179 ma, n_div_ma, n_div_bset, f, c1, c2, g, 1);
11183 res = add_ma_strides(res, ma);
11189 isl_basic_set_free(bset);
11190 isl_multi_aff_free(ma);
11191 res = isl_basic_set_simplify(res);
11192 return isl_basic_set_finalize(res);
11198 isl_basic_set_free(bset);
11199 isl_multi_aff_free(ma);
11200 isl_basic_set_free(res);
11204 /* Check if the range of "ma" is compatible with "set".
11205 * Return -1 if anything is wrong.
11207 static int check_set_compatible_range_multi_aff(
11208 __isl_keep isl_set *set, __isl_keep isl_multi_aff *ma)
11210 return check_space_compatible_range_multi_aff(set->dim, ma);
11213 /* Compute the preimage of "set" under the function represented by "ma".
11214 * In other words, plug in "ma" in "set. The result is a set
11215 * that lives in the domain space of "ma".
11217 static __isl_give isl_set *set_preimage_multi_aff(__isl_take isl_set *set,
11218 __isl_take isl_multi_aff *ma)
11222 set = isl_set_cow(set);
11223 ma = isl_multi_aff_align_divs(ma);
11226 if (check_set_compatible_range_multi_aff(set, ma) < 0)
11229 for (i = 0; i < set->n; ++i) {
11230 set->p[i] = isl_basic_set_preimage_multi_aff(set->p[i],
11231 isl_multi_aff_copy(ma));
11236 isl_space_free(set->dim);
11237 set->dim = isl_multi_aff_get_domain_space(ma);
11241 isl_multi_aff_free(ma);
11243 ISL_F_CLR(set, ISL_MAP_DISJOINT);
11244 ISL_F_CLR(set, ISL_SET_NORMALIZED);
11247 isl_multi_aff_free(ma);
11252 __isl_give isl_set *isl_set_preimage_multi_aff(__isl_take isl_set *set,
11253 __isl_take isl_multi_aff *ma)
11258 if (isl_space_match(set->dim, isl_dim_param, ma->space, isl_dim_param))
11259 return set_preimage_multi_aff(set, ma);
11261 if (!isl_space_has_named_params(set->dim) ||
11262 !isl_space_has_named_params(ma->space))
11263 isl_die(set->ctx, isl_error_invalid,
11264 "unaligned unnamed parameters", goto error);
11265 set = isl_set_align_params(set, isl_multi_aff_get_space(ma));
11266 ma = isl_multi_aff_align_params(ma, isl_set_get_space(set));
11268 return set_preimage_multi_aff(set, ma);
11270 isl_multi_aff_free(ma);
11271 return isl_set_free(set);
11274 /* Compute the preimage of "set" under the function represented by "pma".
11275 * In other words, plug in "pma" in "set. The result is a set
11276 * that lives in the domain space of "pma".
11278 static __isl_give isl_set *set_preimage_pw_multi_aff(__isl_take isl_set *set,
11279 __isl_take isl_pw_multi_aff *pma)
11288 isl_pw_multi_aff_free(pma);
11289 res = isl_set_empty(isl_set_get_space(set));
11294 res = isl_set_preimage_multi_aff(isl_set_copy(set),
11295 isl_multi_aff_copy(pma->p[0].maff));
11296 res = isl_set_intersect(res, isl_set_copy(pma->p[0].set));
11298 for (i = 1; i < pma->n; ++i) {
11301 res_i = isl_set_preimage_multi_aff(isl_set_copy(set),
11302 isl_multi_aff_copy(pma->p[i].maff));
11303 res_i = isl_set_intersect(res_i, isl_set_copy(pma->p[i].set));
11304 res = isl_set_union(res, res_i);
11307 isl_pw_multi_aff_free(pma);
11311 isl_pw_multi_aff_free(pma);
11316 __isl_give isl_set *isl_set_preimage_pw_multi_aff(__isl_take isl_set *set,
11317 __isl_take isl_pw_multi_aff *pma)
11322 if (isl_space_match(set->dim, isl_dim_param, pma->dim, isl_dim_param))
11323 return set_preimage_pw_multi_aff(set, pma);
11325 if (!isl_space_has_named_params(set->dim) ||
11326 !isl_space_has_named_params(pma->dim))
11327 isl_die(set->ctx, isl_error_invalid,
11328 "unaligned unnamed parameters", goto error);
11329 set = isl_set_align_params(set, isl_pw_multi_aff_get_space(pma));
11330 pma = isl_pw_multi_aff_align_params(pma, isl_set_get_space(set));
11332 return set_preimage_pw_multi_aff(set, pma);
11334 isl_pw_multi_aff_free(pma);
11335 return isl_set_free(set);