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 isl_map *result = NULL;
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);
2918 isl_map_free(result);
2922 static __isl_give isl_map *map_intersect(__isl_take isl_map *map1,
2923 __isl_take isl_map *map2)
2927 if (!isl_space_is_equal(map1->dim, map2->dim))
2928 isl_die(isl_map_get_ctx(map1), isl_error_invalid,
2929 "spaces don't match", goto error);
2930 return map_intersect_internal(map1, map2);
2937 __isl_give isl_map *isl_map_intersect(__isl_take isl_map *map1,
2938 __isl_take isl_map *map2)
2940 return isl_map_align_params_map_map_and(map1, map2, &map_intersect);
2943 struct isl_set *isl_set_intersect(struct isl_set *set1, struct isl_set *set2)
2945 return (struct isl_set *)
2946 isl_map_intersect((struct isl_map *)set1,
2947 (struct isl_map *)set2);
2950 /* map_intersect_internal accepts intersections
2951 * with parameter domains, so we can just call that function.
2953 static __isl_give isl_map *map_intersect_params(__isl_take isl_map *map,
2954 __isl_take isl_set *params)
2956 return map_intersect_internal(map, params);
2959 __isl_give isl_map *isl_map_intersect_params(__isl_take isl_map *map1,
2960 __isl_take isl_map *map2)
2962 return isl_map_align_params_map_map_and(map1, map2, &map_intersect_params);
2965 __isl_give isl_set *isl_set_intersect_params(__isl_take isl_set *set,
2966 __isl_take isl_set *params)
2968 return isl_map_intersect_params(set, params);
2971 struct isl_basic_map *isl_basic_map_reverse(struct isl_basic_map *bmap)
2974 struct isl_basic_set *bset;
2979 bmap = isl_basic_map_cow(bmap);
2982 dim = isl_space_reverse(isl_space_copy(bmap->dim));
2983 in = isl_basic_map_n_in(bmap);
2984 bset = isl_basic_set_from_basic_map(bmap);
2985 bset = isl_basic_set_swap_vars(bset, in);
2986 return isl_basic_map_from_basic_set(bset, dim);
2989 static __isl_give isl_basic_map *basic_map_space_reset(
2990 __isl_take isl_basic_map *bmap, enum isl_dim_type type)
2994 if (!isl_space_is_named_or_nested(bmap->dim, type))
2997 space = isl_basic_map_get_space(bmap);
2998 space = isl_space_reset(space, type);
2999 bmap = isl_basic_map_reset_space(bmap, space);
3003 __isl_give isl_basic_map *isl_basic_map_insert_dims(
3004 __isl_take isl_basic_map *bmap, enum isl_dim_type type,
3005 unsigned pos, unsigned n)
3008 struct isl_basic_map *res;
3009 struct isl_dim_map *dim_map;
3010 unsigned total, off;
3011 enum isl_dim_type t;
3014 return basic_map_space_reset(bmap, type);
3019 res_dim = isl_space_insert_dims(isl_basic_map_get_space(bmap), type, pos, n);
3021 total = isl_basic_map_total_dim(bmap) + n;
3022 dim_map = isl_dim_map_alloc(bmap->ctx, total);
3024 for (t = isl_dim_param; t <= isl_dim_out; ++t) {
3026 isl_dim_map_dim(dim_map, bmap->dim, t, off);
3028 unsigned size = isl_basic_map_dim(bmap, t);
3029 isl_dim_map_dim_range(dim_map, bmap->dim, t,
3031 isl_dim_map_dim_range(dim_map, bmap->dim, t,
3032 pos, size - pos, off + pos + n);
3034 off += isl_space_dim(res_dim, t);
3036 isl_dim_map_div(dim_map, bmap, off);
3038 res = isl_basic_map_alloc_space(res_dim,
3039 bmap->n_div, bmap->n_eq, bmap->n_ineq);
3040 if (isl_basic_map_is_rational(bmap))
3041 res = isl_basic_map_set_rational(res);
3042 if (isl_basic_map_plain_is_empty(bmap)) {
3043 isl_basic_map_free(bmap);
3044 return isl_basic_map_set_to_empty(res);
3046 res = isl_basic_map_add_constraints_dim_map(res, bmap, dim_map);
3047 return isl_basic_map_finalize(res);
3050 __isl_give isl_basic_set *isl_basic_set_insert_dims(
3051 __isl_take isl_basic_set *bset,
3052 enum isl_dim_type type, unsigned pos, unsigned n)
3054 return isl_basic_map_insert_dims(bset, type, pos, n);
3057 __isl_give isl_basic_map *isl_basic_map_add(__isl_take isl_basic_map *bmap,
3058 enum isl_dim_type type, unsigned n)
3062 return isl_basic_map_insert_dims(bmap, type,
3063 isl_basic_map_dim(bmap, type), n);
3066 __isl_give isl_basic_set *isl_basic_set_add_dims(__isl_take isl_basic_set *bset,
3067 enum isl_dim_type type, unsigned n)
3071 isl_assert(bset->ctx, type != isl_dim_in, goto error);
3072 return (isl_basic_set *)isl_basic_map_add((isl_basic_map *)bset, type, n);
3074 isl_basic_set_free(bset);
3078 static __isl_give isl_map *map_space_reset(__isl_take isl_map *map,
3079 enum isl_dim_type type)
3083 if (!map || !isl_space_is_named_or_nested(map->dim, type))
3086 space = isl_map_get_space(map);
3087 space = isl_space_reset(space, type);
3088 map = isl_map_reset_space(map, space);
3092 __isl_give isl_map *isl_map_insert_dims(__isl_take isl_map *map,
3093 enum isl_dim_type type, unsigned pos, unsigned n)
3098 return map_space_reset(map, type);
3100 map = isl_map_cow(map);
3104 map->dim = isl_space_insert_dims(map->dim, type, pos, n);
3108 for (i = 0; i < map->n; ++i) {
3109 map->p[i] = isl_basic_map_insert_dims(map->p[i], type, pos, n);
3120 __isl_give isl_set *isl_set_insert_dims(__isl_take isl_set *set,
3121 enum isl_dim_type type, unsigned pos, unsigned n)
3123 return isl_map_insert_dims(set, type, pos, n);
3126 __isl_give isl_map *isl_map_add_dims(__isl_take isl_map *map,
3127 enum isl_dim_type type, unsigned n)
3131 return isl_map_insert_dims(map, type, isl_map_dim(map, type), n);
3134 __isl_give isl_set *isl_set_add_dims(__isl_take isl_set *set,
3135 enum isl_dim_type type, unsigned n)
3139 isl_assert(set->ctx, type != isl_dim_in, goto error);
3140 return (isl_set *)isl_map_add_dims((isl_map *)set, type, n);
3146 __isl_give isl_basic_map *isl_basic_map_move_dims(
3147 __isl_take isl_basic_map *bmap,
3148 enum isl_dim_type dst_type, unsigned dst_pos,
3149 enum isl_dim_type src_type, unsigned src_pos, unsigned n)
3151 struct isl_dim_map *dim_map;
3152 struct isl_basic_map *res;
3153 enum isl_dim_type t;
3154 unsigned total, off;
3161 isl_assert(bmap->ctx, src_pos + n <= isl_basic_map_dim(bmap, src_type),
3164 if (dst_type == src_type && dst_pos == src_pos)
3167 isl_assert(bmap->ctx, dst_type != src_type, goto error);
3169 if (pos(bmap->dim, dst_type) + dst_pos ==
3170 pos(bmap->dim, src_type) + src_pos +
3171 ((src_type < dst_type) ? n : 0)) {
3172 bmap = isl_basic_map_cow(bmap);
3176 bmap->dim = isl_space_move_dims(bmap->dim, dst_type, dst_pos,
3177 src_type, src_pos, n);
3181 bmap = isl_basic_map_finalize(bmap);
3186 total = isl_basic_map_total_dim(bmap);
3187 dim_map = isl_dim_map_alloc(bmap->ctx, total);
3190 for (t = isl_dim_param; t <= isl_dim_out; ++t) {
3191 unsigned size = isl_space_dim(bmap->dim, t);
3192 if (t == dst_type) {
3193 isl_dim_map_dim_range(dim_map, bmap->dim, t,
3196 isl_dim_map_dim_range(dim_map, bmap->dim, src_type,
3199 isl_dim_map_dim_range(dim_map, bmap->dim, t,
3200 dst_pos, size - dst_pos, off);
3201 off += size - dst_pos;
3202 } else if (t == src_type) {
3203 isl_dim_map_dim_range(dim_map, bmap->dim, t,
3206 isl_dim_map_dim_range(dim_map, bmap->dim, t,
3207 src_pos + n, size - src_pos - n, off);
3208 off += size - src_pos - n;
3210 isl_dim_map_dim(dim_map, bmap->dim, t, off);
3214 isl_dim_map_div(dim_map, bmap, off);
3216 res = isl_basic_map_alloc_space(isl_basic_map_get_space(bmap),
3217 bmap->n_div, bmap->n_eq, bmap->n_ineq);
3218 bmap = isl_basic_map_add_constraints_dim_map(res, bmap, dim_map);
3220 bmap->dim = isl_space_move_dims(bmap->dim, dst_type, dst_pos,
3221 src_type, src_pos, n);
3225 ISL_F_CLR(bmap, ISL_BASIC_MAP_NORMALIZED);
3226 bmap = isl_basic_map_gauss(bmap, NULL);
3227 bmap = isl_basic_map_finalize(bmap);
3231 isl_basic_map_free(bmap);
3235 __isl_give isl_basic_set *isl_basic_set_move_dims(__isl_take isl_basic_set *bset,
3236 enum isl_dim_type dst_type, unsigned dst_pos,
3237 enum isl_dim_type src_type, unsigned src_pos, unsigned n)
3239 return (isl_basic_set *)isl_basic_map_move_dims(
3240 (isl_basic_map *)bset, dst_type, dst_pos, src_type, src_pos, n);
3243 __isl_give isl_set *isl_set_move_dims(__isl_take isl_set *set,
3244 enum isl_dim_type dst_type, unsigned dst_pos,
3245 enum isl_dim_type src_type, unsigned src_pos, unsigned n)
3249 isl_assert(set->ctx, dst_type != isl_dim_in, goto error);
3250 return (isl_set *)isl_map_move_dims((isl_map *)set, dst_type, dst_pos,
3251 src_type, src_pos, n);
3257 __isl_give isl_map *isl_map_move_dims(__isl_take isl_map *map,
3258 enum isl_dim_type dst_type, unsigned dst_pos,
3259 enum isl_dim_type src_type, unsigned src_pos, unsigned n)
3268 isl_assert(map->ctx, src_pos + n <= isl_map_dim(map, src_type),
3271 if (dst_type == src_type && dst_pos == src_pos)
3274 isl_assert(map->ctx, dst_type != src_type, goto error);
3276 map = isl_map_cow(map);
3280 map->dim = isl_space_move_dims(map->dim, dst_type, dst_pos, src_type, src_pos, n);
3284 for (i = 0; i < map->n; ++i) {
3285 map->p[i] = isl_basic_map_move_dims(map->p[i],
3287 src_type, src_pos, n);
3298 /* Move the specified dimensions to the last columns right before
3299 * the divs. Don't change the dimension specification of bmap.
3300 * That's the responsibility of the caller.
3302 static __isl_give isl_basic_map *move_last(__isl_take isl_basic_map *bmap,
3303 enum isl_dim_type type, unsigned first, unsigned n)
3305 struct isl_dim_map *dim_map;
3306 struct isl_basic_map *res;
3307 enum isl_dim_type t;
3308 unsigned total, off;
3312 if (pos(bmap->dim, type) + first + n ==
3313 1 + isl_space_dim(bmap->dim, isl_dim_all))
3316 total = isl_basic_map_total_dim(bmap);
3317 dim_map = isl_dim_map_alloc(bmap->ctx, total);
3320 for (t = isl_dim_param; t <= isl_dim_out; ++t) {
3321 unsigned size = isl_space_dim(bmap->dim, t);
3323 isl_dim_map_dim_range(dim_map, bmap->dim, t,
3326 isl_dim_map_dim_range(dim_map, bmap->dim, t,
3327 first, n, total - bmap->n_div - n);
3328 isl_dim_map_dim_range(dim_map, bmap->dim, t,
3329 first + n, size - (first + n), off);
3330 off += size - (first + n);
3332 isl_dim_map_dim(dim_map, bmap->dim, t, off);
3336 isl_dim_map_div(dim_map, bmap, off + n);
3338 res = isl_basic_map_alloc_space(isl_basic_map_get_space(bmap),
3339 bmap->n_div, bmap->n_eq, bmap->n_ineq);
3340 res = isl_basic_map_add_constraints_dim_map(res, bmap, dim_map);
3344 /* Turn the n dimensions of type type, starting at first
3345 * into existentially quantified variables.
3347 __isl_give isl_basic_map *isl_basic_map_project_out(
3348 __isl_take isl_basic_map *bmap,
3349 enum isl_dim_type type, unsigned first, unsigned n)
3357 return basic_map_space_reset(bmap, type);
3362 if (ISL_F_ISSET(bmap, ISL_BASIC_MAP_RATIONAL))
3363 return isl_basic_map_remove_dims(bmap, type, first, n);
3365 isl_assert(bmap->ctx, first + n <= isl_basic_map_dim(bmap, type),
3368 bmap = move_last(bmap, type, first, n);
3369 bmap = isl_basic_map_cow(bmap);
3373 row_size = 1 + isl_space_dim(bmap->dim, isl_dim_all) + bmap->extra;
3374 old = bmap->block2.data;
3375 bmap->block2 = isl_blk_extend(bmap->ctx, bmap->block2,
3376 (bmap->extra + n) * (1 + row_size));
3377 if (!bmap->block2.data)
3379 new_div = isl_alloc_array(bmap->ctx, isl_int *, bmap->extra + n);
3382 for (i = 0; i < n; ++i) {
3383 new_div[i] = bmap->block2.data +
3384 (bmap->extra + i) * (1 + row_size);
3385 isl_seq_clr(new_div[i], 1 + row_size);
3387 for (i = 0; i < bmap->extra; ++i)
3388 new_div[n + i] = bmap->block2.data + (bmap->div[i] - old);
3390 bmap->div = new_div;
3394 bmap->dim = isl_space_drop_dims(bmap->dim, type, first, n);
3397 bmap = isl_basic_map_simplify(bmap);
3398 bmap = isl_basic_map_drop_redundant_divs(bmap);
3399 return isl_basic_map_finalize(bmap);
3401 isl_basic_map_free(bmap);
3405 /* Turn the n dimensions of type type, starting at first
3406 * into existentially quantified variables.
3408 struct isl_basic_set *isl_basic_set_project_out(struct isl_basic_set *bset,
3409 enum isl_dim_type type, unsigned first, unsigned n)
3411 return (isl_basic_set *)isl_basic_map_project_out(
3412 (isl_basic_map *)bset, type, first, n);
3415 /* Turn the n dimensions of type type, starting at first
3416 * into existentially quantified variables.
3418 __isl_give isl_map *isl_map_project_out(__isl_take isl_map *map,
3419 enum isl_dim_type type, unsigned first, unsigned n)
3427 return map_space_reset(map, type);
3429 isl_assert(map->ctx, first + n <= isl_map_dim(map, type), goto error);
3431 map = isl_map_cow(map);
3435 map->dim = isl_space_drop_dims(map->dim, type, first, n);
3439 for (i = 0; i < map->n; ++i) {
3440 map->p[i] = isl_basic_map_project_out(map->p[i], type, first, n);
3451 /* Turn the n dimensions of type type, starting at first
3452 * into existentially quantified variables.
3454 __isl_give isl_set *isl_set_project_out(__isl_take isl_set *set,
3455 enum isl_dim_type type, unsigned first, unsigned n)
3457 return (isl_set *)isl_map_project_out((isl_map *)set, type, first, n);
3460 static struct isl_basic_map *add_divs(struct isl_basic_map *bmap, unsigned n)
3464 for (i = 0; i < n; ++i) {
3465 j = isl_basic_map_alloc_div(bmap);
3468 isl_seq_clr(bmap->div[j], 1+1+isl_basic_map_total_dim(bmap));
3472 isl_basic_map_free(bmap);
3476 struct isl_basic_map *isl_basic_map_apply_range(
3477 struct isl_basic_map *bmap1, struct isl_basic_map *bmap2)
3479 isl_space *dim_result = NULL;
3480 struct isl_basic_map *bmap;
3481 unsigned n_in, n_out, n, nparam, total, pos;
3482 struct isl_dim_map *dim_map1, *dim_map2;
3484 if (!bmap1 || !bmap2)
3487 dim_result = isl_space_join(isl_space_copy(bmap1->dim),
3488 isl_space_copy(bmap2->dim));
3490 n_in = isl_basic_map_n_in(bmap1);
3491 n_out = isl_basic_map_n_out(bmap2);
3492 n = isl_basic_map_n_out(bmap1);
3493 nparam = isl_basic_map_n_param(bmap1);
3495 total = nparam + n_in + n_out + bmap1->n_div + bmap2->n_div + n;
3496 dim_map1 = isl_dim_map_alloc(bmap1->ctx, total);
3497 dim_map2 = isl_dim_map_alloc(bmap1->ctx, total);
3498 isl_dim_map_dim(dim_map1, bmap1->dim, isl_dim_param, pos = 0);
3499 isl_dim_map_dim(dim_map2, bmap2->dim, isl_dim_param, pos = 0);
3500 isl_dim_map_dim(dim_map1, bmap1->dim, isl_dim_in, pos += nparam);
3501 isl_dim_map_dim(dim_map2, bmap2->dim, isl_dim_out, pos += n_in);
3502 isl_dim_map_div(dim_map1, bmap1, pos += n_out);
3503 isl_dim_map_div(dim_map2, bmap2, pos += bmap1->n_div);
3504 isl_dim_map_dim(dim_map1, bmap1->dim, isl_dim_out, pos += bmap2->n_div);
3505 isl_dim_map_dim(dim_map2, bmap2->dim, isl_dim_in, pos);
3507 bmap = isl_basic_map_alloc_space(dim_result,
3508 bmap1->n_div + bmap2->n_div + n,
3509 bmap1->n_eq + bmap2->n_eq,
3510 bmap1->n_ineq + bmap2->n_ineq);
3511 bmap = isl_basic_map_add_constraints_dim_map(bmap, bmap1, dim_map1);
3512 bmap = isl_basic_map_add_constraints_dim_map(bmap, bmap2, dim_map2);
3513 bmap = add_divs(bmap, n);
3514 bmap = isl_basic_map_simplify(bmap);
3515 bmap = isl_basic_map_drop_redundant_divs(bmap);
3516 return isl_basic_map_finalize(bmap);
3518 isl_basic_map_free(bmap1);
3519 isl_basic_map_free(bmap2);
3523 struct isl_basic_set *isl_basic_set_apply(
3524 struct isl_basic_set *bset, struct isl_basic_map *bmap)
3529 isl_assert(bset->ctx, isl_basic_map_compatible_domain(bmap, bset),
3532 return (struct isl_basic_set *)
3533 isl_basic_map_apply_range((struct isl_basic_map *)bset, bmap);
3535 isl_basic_set_free(bset);
3536 isl_basic_map_free(bmap);
3540 struct isl_basic_map *isl_basic_map_apply_domain(
3541 struct isl_basic_map *bmap1, struct isl_basic_map *bmap2)
3543 if (!bmap1 || !bmap2)
3546 isl_assert(bmap1->ctx,
3547 isl_basic_map_n_in(bmap1) == isl_basic_map_n_in(bmap2), goto error);
3548 isl_assert(bmap1->ctx,
3549 isl_basic_map_n_param(bmap1) == isl_basic_map_n_param(bmap2),
3552 bmap1 = isl_basic_map_reverse(bmap1);
3553 bmap1 = isl_basic_map_apply_range(bmap1, bmap2);
3554 return isl_basic_map_reverse(bmap1);
3556 isl_basic_map_free(bmap1);
3557 isl_basic_map_free(bmap2);
3561 /* Given two basic maps A -> f(A) and B -> g(B), construct a basic map
3562 * A \cap B -> f(A) + f(B)
3564 struct isl_basic_map *isl_basic_map_sum(
3565 struct isl_basic_map *bmap1, struct isl_basic_map *bmap2)
3567 unsigned n_in, n_out, nparam, total, pos;
3568 struct isl_basic_map *bmap = NULL;
3569 struct isl_dim_map *dim_map1, *dim_map2;
3572 if (!bmap1 || !bmap2)
3575 isl_assert(bmap1->ctx, isl_space_is_equal(bmap1->dim, bmap2->dim),
3578 nparam = isl_basic_map_n_param(bmap1);
3579 n_in = isl_basic_map_n_in(bmap1);
3580 n_out = isl_basic_map_n_out(bmap1);
3582 total = nparam + n_in + n_out + bmap1->n_div + bmap2->n_div + 2 * n_out;
3583 dim_map1 = isl_dim_map_alloc(bmap1->ctx, total);
3584 dim_map2 = isl_dim_map_alloc(bmap2->ctx, total);
3585 isl_dim_map_dim(dim_map1, bmap1->dim, isl_dim_param, pos = 0);
3586 isl_dim_map_dim(dim_map2, bmap2->dim, isl_dim_param, pos);
3587 isl_dim_map_dim(dim_map1, bmap1->dim, isl_dim_in, pos += nparam);
3588 isl_dim_map_dim(dim_map2, bmap2->dim, isl_dim_in, pos);
3589 isl_dim_map_div(dim_map1, bmap1, pos += n_in + n_out);
3590 isl_dim_map_div(dim_map2, bmap2, pos += bmap1->n_div);
3591 isl_dim_map_dim(dim_map1, bmap1->dim, isl_dim_out, pos += bmap2->n_div);
3592 isl_dim_map_dim(dim_map2, bmap2->dim, isl_dim_out, pos += n_out);
3594 bmap = isl_basic_map_alloc_space(isl_space_copy(bmap1->dim),
3595 bmap1->n_div + bmap2->n_div + 2 * n_out,
3596 bmap1->n_eq + bmap2->n_eq + n_out,
3597 bmap1->n_ineq + bmap2->n_ineq);
3598 for (i = 0; i < n_out; ++i) {
3599 int j = isl_basic_map_alloc_equality(bmap);
3602 isl_seq_clr(bmap->eq[j], 1+total);
3603 isl_int_set_si(bmap->eq[j][1+nparam+n_in+i], -1);
3604 isl_int_set_si(bmap->eq[j][1+pos+i], 1);
3605 isl_int_set_si(bmap->eq[j][1+pos-n_out+i], 1);
3607 bmap = isl_basic_map_add_constraints_dim_map(bmap, bmap1, dim_map1);
3608 bmap = isl_basic_map_add_constraints_dim_map(bmap, bmap2, dim_map2);
3609 bmap = add_divs(bmap, 2 * n_out);
3611 bmap = isl_basic_map_simplify(bmap);
3612 return isl_basic_map_finalize(bmap);
3614 isl_basic_map_free(bmap);
3615 isl_basic_map_free(bmap1);
3616 isl_basic_map_free(bmap2);
3620 /* Given two maps A -> f(A) and B -> g(B), construct a map
3621 * A \cap B -> f(A) + f(B)
3623 struct isl_map *isl_map_sum(struct isl_map *map1, struct isl_map *map2)
3625 struct isl_map *result;
3631 isl_assert(map1->ctx, isl_space_is_equal(map1->dim, map2->dim), goto error);
3633 result = isl_map_alloc_space(isl_space_copy(map1->dim),
3634 map1->n * map2->n, 0);
3637 for (i = 0; i < map1->n; ++i)
3638 for (j = 0; j < map2->n; ++j) {
3639 struct isl_basic_map *part;
3640 part = isl_basic_map_sum(
3641 isl_basic_map_copy(map1->p[i]),
3642 isl_basic_map_copy(map2->p[j]));
3643 if (isl_basic_map_is_empty(part))
3644 isl_basic_map_free(part);
3646 result = isl_map_add_basic_map(result, part);
3659 __isl_give isl_set *isl_set_sum(__isl_take isl_set *set1,
3660 __isl_take isl_set *set2)
3662 return (isl_set *)isl_map_sum((isl_map *)set1, (isl_map *)set2);
3665 /* Given a basic map A -> f(A), construct A -> -f(A).
3667 struct isl_basic_map *isl_basic_map_neg(struct isl_basic_map *bmap)
3672 bmap = isl_basic_map_cow(bmap);
3676 n = isl_basic_map_dim(bmap, isl_dim_out);
3677 off = isl_basic_map_offset(bmap, isl_dim_out);
3678 for (i = 0; i < bmap->n_eq; ++i)
3679 for (j = 0; j < n; ++j)
3680 isl_int_neg(bmap->eq[i][off+j], bmap->eq[i][off+j]);
3681 for (i = 0; i < bmap->n_ineq; ++i)
3682 for (j = 0; j < n; ++j)
3683 isl_int_neg(bmap->ineq[i][off+j], bmap->ineq[i][off+j]);
3684 for (i = 0; i < bmap->n_div; ++i)
3685 for (j = 0; j < n; ++j)
3686 isl_int_neg(bmap->div[i][1+off+j], bmap->div[i][1+off+j]);
3687 bmap = isl_basic_map_gauss(bmap, NULL);
3688 return isl_basic_map_finalize(bmap);
3691 __isl_give isl_basic_set *isl_basic_set_neg(__isl_take isl_basic_set *bset)
3693 return isl_basic_map_neg(bset);
3696 /* Given a map A -> f(A), construct A -> -f(A).
3698 struct isl_map *isl_map_neg(struct isl_map *map)
3702 map = isl_map_cow(map);
3706 for (i = 0; i < map->n; ++i) {
3707 map->p[i] = isl_basic_map_neg(map->p[i]);
3718 __isl_give isl_set *isl_set_neg(__isl_take isl_set *set)
3720 return (isl_set *)isl_map_neg((isl_map *)set);
3723 /* Given a basic map A -> f(A) and an integer d, construct a basic map
3724 * A -> floor(f(A)/d).
3726 struct isl_basic_map *isl_basic_map_floordiv(struct isl_basic_map *bmap,
3729 unsigned n_in, n_out, nparam, total, pos;
3730 struct isl_basic_map *result = NULL;
3731 struct isl_dim_map *dim_map;
3737 nparam = isl_basic_map_n_param(bmap);
3738 n_in = isl_basic_map_n_in(bmap);
3739 n_out = isl_basic_map_n_out(bmap);
3741 total = nparam + n_in + n_out + bmap->n_div + n_out;
3742 dim_map = isl_dim_map_alloc(bmap->ctx, total);
3743 isl_dim_map_dim(dim_map, bmap->dim, isl_dim_param, pos = 0);
3744 isl_dim_map_dim(dim_map, bmap->dim, isl_dim_in, pos += nparam);
3745 isl_dim_map_div(dim_map, bmap, pos += n_in + n_out);
3746 isl_dim_map_dim(dim_map, bmap->dim, isl_dim_out, pos += bmap->n_div);
3748 result = isl_basic_map_alloc_space(isl_space_copy(bmap->dim),
3749 bmap->n_div + n_out,
3750 bmap->n_eq, bmap->n_ineq + 2 * n_out);
3751 result = isl_basic_map_add_constraints_dim_map(result, bmap, dim_map);
3752 result = add_divs(result, n_out);
3753 for (i = 0; i < n_out; ++i) {
3755 j = isl_basic_map_alloc_inequality(result);
3758 isl_seq_clr(result->ineq[j], 1+total);
3759 isl_int_neg(result->ineq[j][1+nparam+n_in+i], d);
3760 isl_int_set_si(result->ineq[j][1+pos+i], 1);
3761 j = isl_basic_map_alloc_inequality(result);
3764 isl_seq_clr(result->ineq[j], 1+total);
3765 isl_int_set(result->ineq[j][1+nparam+n_in+i], d);
3766 isl_int_set_si(result->ineq[j][1+pos+i], -1);
3767 isl_int_sub_ui(result->ineq[j][0], d, 1);
3770 result = isl_basic_map_simplify(result);
3771 return isl_basic_map_finalize(result);
3773 isl_basic_map_free(result);
3777 /* Given a map A -> f(A) and an integer d, construct a map
3778 * A -> floor(f(A)/d).
3780 struct isl_map *isl_map_floordiv(struct isl_map *map, isl_int d)
3784 map = isl_map_cow(map);
3788 ISL_F_CLR(map, ISL_MAP_DISJOINT);
3789 ISL_F_CLR(map, ISL_MAP_NORMALIZED);
3790 for (i = 0; i < map->n; ++i) {
3791 map->p[i] = isl_basic_map_floordiv(map->p[i], d);
3802 static struct isl_basic_map *var_equal(struct isl_basic_map *bmap, unsigned pos)
3808 i = isl_basic_map_alloc_equality(bmap);
3811 nparam = isl_basic_map_n_param(bmap);
3812 n_in = isl_basic_map_n_in(bmap);
3813 isl_seq_clr(bmap->eq[i], 1 + isl_basic_map_total_dim(bmap));
3814 isl_int_set_si(bmap->eq[i][1+nparam+pos], -1);
3815 isl_int_set_si(bmap->eq[i][1+nparam+n_in+pos], 1);
3816 return isl_basic_map_finalize(bmap);
3818 isl_basic_map_free(bmap);
3822 /* Add a constraints to "bmap" expressing i_pos < o_pos
3824 static struct isl_basic_map *var_less(struct isl_basic_map *bmap, unsigned pos)
3830 i = isl_basic_map_alloc_inequality(bmap);
3833 nparam = isl_basic_map_n_param(bmap);
3834 n_in = isl_basic_map_n_in(bmap);
3835 isl_seq_clr(bmap->ineq[i], 1 + isl_basic_map_total_dim(bmap));
3836 isl_int_set_si(bmap->ineq[i][0], -1);
3837 isl_int_set_si(bmap->ineq[i][1+nparam+pos], -1);
3838 isl_int_set_si(bmap->ineq[i][1+nparam+n_in+pos], 1);
3839 return isl_basic_map_finalize(bmap);
3841 isl_basic_map_free(bmap);
3845 /* Add a constraint to "bmap" expressing i_pos <= o_pos
3847 static __isl_give isl_basic_map *var_less_or_equal(
3848 __isl_take isl_basic_map *bmap, unsigned pos)
3854 i = isl_basic_map_alloc_inequality(bmap);
3857 nparam = isl_basic_map_n_param(bmap);
3858 n_in = isl_basic_map_n_in(bmap);
3859 isl_seq_clr(bmap->ineq[i], 1 + isl_basic_map_total_dim(bmap));
3860 isl_int_set_si(bmap->ineq[i][1+nparam+pos], -1);
3861 isl_int_set_si(bmap->ineq[i][1+nparam+n_in+pos], 1);
3862 return isl_basic_map_finalize(bmap);
3864 isl_basic_map_free(bmap);
3868 /* Add a constraints to "bmap" expressing i_pos > o_pos
3870 static struct isl_basic_map *var_more(struct isl_basic_map *bmap, unsigned pos)
3876 i = isl_basic_map_alloc_inequality(bmap);
3879 nparam = isl_basic_map_n_param(bmap);
3880 n_in = isl_basic_map_n_in(bmap);
3881 isl_seq_clr(bmap->ineq[i], 1 + isl_basic_map_total_dim(bmap));
3882 isl_int_set_si(bmap->ineq[i][0], -1);
3883 isl_int_set_si(bmap->ineq[i][1+nparam+pos], 1);
3884 isl_int_set_si(bmap->ineq[i][1+nparam+n_in+pos], -1);
3885 return isl_basic_map_finalize(bmap);
3887 isl_basic_map_free(bmap);
3891 /* Add a constraint to "bmap" expressing i_pos >= o_pos
3893 static __isl_give isl_basic_map *var_more_or_equal(
3894 __isl_take isl_basic_map *bmap, unsigned pos)
3900 i = isl_basic_map_alloc_inequality(bmap);
3903 nparam = isl_basic_map_n_param(bmap);
3904 n_in = isl_basic_map_n_in(bmap);
3905 isl_seq_clr(bmap->ineq[i], 1 + isl_basic_map_total_dim(bmap));
3906 isl_int_set_si(bmap->ineq[i][1+nparam+pos], 1);
3907 isl_int_set_si(bmap->ineq[i][1+nparam+n_in+pos], -1);
3908 return isl_basic_map_finalize(bmap);
3910 isl_basic_map_free(bmap);
3914 __isl_give isl_basic_map *isl_basic_map_equal(
3915 __isl_take isl_space *dim, unsigned n_equal)
3918 struct isl_basic_map *bmap;
3919 bmap = isl_basic_map_alloc_space(dim, 0, n_equal, 0);
3922 for (i = 0; i < n_equal && bmap; ++i)
3923 bmap = var_equal(bmap, i);
3924 return isl_basic_map_finalize(bmap);
3927 /* Return a relation on of dimension "dim" expressing i_[0..pos] << o_[0..pos]
3929 __isl_give isl_basic_map *isl_basic_map_less_at(__isl_take isl_space *dim,
3933 struct isl_basic_map *bmap;
3934 bmap = isl_basic_map_alloc_space(dim, 0, pos, 1);
3937 for (i = 0; i < pos && bmap; ++i)
3938 bmap = var_equal(bmap, i);
3940 bmap = var_less(bmap, pos);
3941 return isl_basic_map_finalize(bmap);
3944 /* Return a relation on of dimension "dim" expressing i_[0..pos] <<= o_[0..pos]
3946 __isl_give isl_basic_map *isl_basic_map_less_or_equal_at(
3947 __isl_take isl_space *dim, unsigned pos)
3950 isl_basic_map *bmap;
3952 bmap = isl_basic_map_alloc_space(dim, 0, pos, 1);
3953 for (i = 0; i < pos; ++i)
3954 bmap = var_equal(bmap, i);
3955 bmap = var_less_or_equal(bmap, pos);
3956 return isl_basic_map_finalize(bmap);
3959 /* Return a relation on pairs of sets of dimension "dim" expressing i_pos > o_pos
3961 __isl_give isl_basic_map *isl_basic_map_more_at(__isl_take isl_space *dim,
3965 struct isl_basic_map *bmap;
3966 bmap = isl_basic_map_alloc_space(dim, 0, pos, 1);
3969 for (i = 0; i < pos && bmap; ++i)
3970 bmap = var_equal(bmap, i);
3972 bmap = var_more(bmap, pos);
3973 return isl_basic_map_finalize(bmap);
3976 /* Return a relation on of dimension "dim" expressing i_[0..pos] >>= o_[0..pos]
3978 __isl_give isl_basic_map *isl_basic_map_more_or_equal_at(
3979 __isl_take isl_space *dim, unsigned pos)
3982 isl_basic_map *bmap;
3984 bmap = isl_basic_map_alloc_space(dim, 0, pos, 1);
3985 for (i = 0; i < pos; ++i)
3986 bmap = var_equal(bmap, i);
3987 bmap = var_more_or_equal(bmap, pos);
3988 return isl_basic_map_finalize(bmap);
3991 static __isl_give isl_map *map_lex_lte_first(__isl_take isl_space *dims,
3992 unsigned n, int equal)
3994 struct isl_map *map;
3997 if (n == 0 && equal)
3998 return isl_map_universe(dims);
4000 map = isl_map_alloc_space(isl_space_copy(dims), n, ISL_MAP_DISJOINT);
4002 for (i = 0; i + 1 < n; ++i)
4003 map = isl_map_add_basic_map(map,
4004 isl_basic_map_less_at(isl_space_copy(dims), i));
4007 map = isl_map_add_basic_map(map,
4008 isl_basic_map_less_or_equal_at(dims, n - 1));
4010 map = isl_map_add_basic_map(map,
4011 isl_basic_map_less_at(dims, n - 1));
4013 isl_space_free(dims);
4018 static __isl_give isl_map *map_lex_lte(__isl_take isl_space *dims, int equal)
4022 return map_lex_lte_first(dims, dims->n_out, equal);
4025 __isl_give isl_map *isl_map_lex_lt_first(__isl_take isl_space *dim, unsigned n)
4027 return map_lex_lte_first(dim, n, 0);
4030 __isl_give isl_map *isl_map_lex_le_first(__isl_take isl_space *dim, unsigned n)
4032 return map_lex_lte_first(dim, n, 1);
4035 __isl_give isl_map *isl_map_lex_lt(__isl_take isl_space *set_dim)
4037 return map_lex_lte(isl_space_map_from_set(set_dim), 0);
4040 __isl_give isl_map *isl_map_lex_le(__isl_take isl_space *set_dim)
4042 return map_lex_lte(isl_space_map_from_set(set_dim), 1);
4045 static __isl_give isl_map *map_lex_gte_first(__isl_take isl_space *dims,
4046 unsigned n, int equal)
4048 struct isl_map *map;
4051 if (n == 0 && equal)
4052 return isl_map_universe(dims);
4054 map = isl_map_alloc_space(isl_space_copy(dims), n, ISL_MAP_DISJOINT);
4056 for (i = 0; i + 1 < n; ++i)
4057 map = isl_map_add_basic_map(map,
4058 isl_basic_map_more_at(isl_space_copy(dims), i));
4061 map = isl_map_add_basic_map(map,
4062 isl_basic_map_more_or_equal_at(dims, n - 1));
4064 map = isl_map_add_basic_map(map,
4065 isl_basic_map_more_at(dims, n - 1));
4067 isl_space_free(dims);
4072 static __isl_give isl_map *map_lex_gte(__isl_take isl_space *dims, int equal)
4076 return map_lex_gte_first(dims, dims->n_out, equal);
4079 __isl_give isl_map *isl_map_lex_gt_first(__isl_take isl_space *dim, unsigned n)
4081 return map_lex_gte_first(dim, n, 0);
4084 __isl_give isl_map *isl_map_lex_ge_first(__isl_take isl_space *dim, unsigned n)
4086 return map_lex_gte_first(dim, n, 1);
4089 __isl_give isl_map *isl_map_lex_gt(__isl_take isl_space *set_dim)
4091 return map_lex_gte(isl_space_map_from_set(set_dim), 0);
4094 __isl_give isl_map *isl_map_lex_ge(__isl_take isl_space *set_dim)
4096 return map_lex_gte(isl_space_map_from_set(set_dim), 1);
4099 __isl_give isl_map *isl_set_lex_le_set(__isl_take isl_set *set1,
4100 __isl_take isl_set *set2)
4103 map = isl_map_lex_le(isl_set_get_space(set1));
4104 map = isl_map_intersect_domain(map, set1);
4105 map = isl_map_intersect_range(map, set2);
4109 __isl_give isl_map *isl_set_lex_lt_set(__isl_take isl_set *set1,
4110 __isl_take isl_set *set2)
4113 map = isl_map_lex_lt(isl_set_get_space(set1));
4114 map = isl_map_intersect_domain(map, set1);
4115 map = isl_map_intersect_range(map, set2);
4119 __isl_give isl_map *isl_set_lex_ge_set(__isl_take isl_set *set1,
4120 __isl_take isl_set *set2)
4123 map = isl_map_lex_ge(isl_set_get_space(set1));
4124 map = isl_map_intersect_domain(map, set1);
4125 map = isl_map_intersect_range(map, set2);
4129 __isl_give isl_map *isl_set_lex_gt_set(__isl_take isl_set *set1,
4130 __isl_take isl_set *set2)
4133 map = isl_map_lex_gt(isl_set_get_space(set1));
4134 map = isl_map_intersect_domain(map, set1);
4135 map = isl_map_intersect_range(map, set2);
4139 __isl_give isl_map *isl_map_lex_le_map(__isl_take isl_map *map1,
4140 __isl_take isl_map *map2)
4143 map = isl_map_lex_le(isl_space_range(isl_map_get_space(map1)));
4144 map = isl_map_apply_domain(map, isl_map_reverse(map1));
4145 map = isl_map_apply_range(map, isl_map_reverse(map2));
4149 __isl_give isl_map *isl_map_lex_lt_map(__isl_take isl_map *map1,
4150 __isl_take isl_map *map2)
4153 map = isl_map_lex_lt(isl_space_range(isl_map_get_space(map1)));
4154 map = isl_map_apply_domain(map, isl_map_reverse(map1));
4155 map = isl_map_apply_range(map, isl_map_reverse(map2));
4159 __isl_give isl_map *isl_map_lex_ge_map(__isl_take isl_map *map1,
4160 __isl_take isl_map *map2)
4163 map = isl_map_lex_ge(isl_space_range(isl_map_get_space(map1)));
4164 map = isl_map_apply_domain(map, isl_map_reverse(map1));
4165 map = isl_map_apply_range(map, isl_map_reverse(map2));
4169 __isl_give isl_map *isl_map_lex_gt_map(__isl_take isl_map *map1,
4170 __isl_take isl_map *map2)
4173 map = isl_map_lex_gt(isl_space_range(isl_map_get_space(map1)));
4174 map = isl_map_apply_domain(map, isl_map_reverse(map1));
4175 map = isl_map_apply_range(map, isl_map_reverse(map2));
4179 __isl_give isl_basic_map *isl_basic_map_from_basic_set(
4180 __isl_take isl_basic_set *bset, __isl_take isl_space *dim)
4182 struct isl_basic_map *bmap;
4184 bset = isl_basic_set_cow(bset);
4188 isl_assert(bset->ctx, isl_space_compatible(bset->dim, dim), goto error);
4189 isl_space_free(bset->dim);
4190 bmap = (struct isl_basic_map *) bset;
4192 return isl_basic_map_finalize(bmap);
4194 isl_basic_set_free(bset);
4195 isl_space_free(dim);
4199 struct isl_basic_set *isl_basic_set_from_basic_map(struct isl_basic_map *bmap)
4203 if (bmap->dim->n_in == 0)
4204 return (struct isl_basic_set *)bmap;
4205 bmap = isl_basic_map_cow(bmap);
4208 bmap->dim = isl_space_as_set_space(bmap->dim);
4211 bmap = isl_basic_map_finalize(bmap);
4212 return (struct isl_basic_set *)bmap;
4214 isl_basic_map_free(bmap);
4218 /* For a div d = floor(f/m), add the constraints
4221 * -(f-(n-1)) + m d >= 0
4223 * Note that the second constraint is the negation of
4227 int isl_basic_map_add_div_constraints_var(__isl_keep isl_basic_map *bmap,
4228 unsigned pos, isl_int *div)
4231 unsigned total = isl_basic_map_total_dim(bmap);
4233 i = isl_basic_map_alloc_inequality(bmap);
4236 isl_seq_cpy(bmap->ineq[i], div + 1, 1 + total);
4237 isl_int_neg(bmap->ineq[i][1 + pos], div[0]);
4239 j = isl_basic_map_alloc_inequality(bmap);
4242 isl_seq_neg(bmap->ineq[j], bmap->ineq[i], 1 + total);
4243 isl_int_add(bmap->ineq[j][0], bmap->ineq[j][0], bmap->ineq[j][1 + pos]);
4244 isl_int_sub_ui(bmap->ineq[j][0], bmap->ineq[j][0], 1);
4248 int isl_basic_set_add_div_constraints_var(__isl_keep isl_basic_set *bset,
4249 unsigned pos, isl_int *div)
4251 return isl_basic_map_add_div_constraints_var((isl_basic_map *)bset,
4255 int isl_basic_map_add_div_constraints(struct isl_basic_map *bmap, unsigned div)
4257 unsigned total = isl_basic_map_total_dim(bmap);
4258 unsigned div_pos = total - bmap->n_div + div;
4260 return isl_basic_map_add_div_constraints_var(bmap, div_pos,
4264 int isl_basic_set_add_div_constraints(struct isl_basic_set *bset, unsigned div)
4266 return isl_basic_map_add_div_constraints(bset, div);
4269 struct isl_basic_set *isl_basic_map_underlying_set(
4270 struct isl_basic_map *bmap)
4274 if (bmap->dim->nparam == 0 && bmap->dim->n_in == 0 &&
4276 !isl_space_is_named_or_nested(bmap->dim, isl_dim_in) &&
4277 !isl_space_is_named_or_nested(bmap->dim, isl_dim_out))
4278 return (struct isl_basic_set *)bmap;
4279 bmap = isl_basic_map_cow(bmap);
4282 bmap->dim = isl_space_underlying(bmap->dim, bmap->n_div);
4285 bmap->extra -= bmap->n_div;
4287 bmap = isl_basic_map_finalize(bmap);
4288 return (struct isl_basic_set *)bmap;
4293 __isl_give isl_basic_set *isl_basic_set_underlying_set(
4294 __isl_take isl_basic_set *bset)
4296 return isl_basic_map_underlying_set((isl_basic_map *)bset);
4299 struct isl_basic_map *isl_basic_map_overlying_set(
4300 struct isl_basic_set *bset, struct isl_basic_map *like)
4302 struct isl_basic_map *bmap;
4303 struct isl_ctx *ctx;
4310 isl_assert(ctx, bset->n_div == 0, goto error);
4311 isl_assert(ctx, isl_basic_set_n_param(bset) == 0, goto error);
4312 isl_assert(ctx, bset->dim->n_out == isl_basic_map_total_dim(like),
4314 if (isl_space_is_equal(bset->dim, like->dim) && like->n_div == 0) {
4315 isl_basic_map_free(like);
4316 return (struct isl_basic_map *)bset;
4318 bset = isl_basic_set_cow(bset);
4321 total = bset->dim->n_out + bset->extra;
4322 bmap = (struct isl_basic_map *)bset;
4323 isl_space_free(bmap->dim);
4324 bmap->dim = isl_space_copy(like->dim);
4327 bmap->n_div = like->n_div;
4328 bmap->extra += like->n_div;
4332 ltotal = total - bmap->extra + like->extra;
4335 bmap->block2 = isl_blk_extend(ctx, bmap->block2,
4336 bmap->extra * (1 + 1 + total));
4337 if (isl_blk_is_error(bmap->block2))
4339 div = isl_realloc_array(ctx, bmap->div, isl_int *, bmap->extra);
4343 for (i = 0; i < bmap->extra; ++i)
4344 bmap->div[i] = bmap->block2.data + i * (1 + 1 + total);
4345 for (i = 0; i < like->n_div; ++i) {
4346 isl_seq_cpy(bmap->div[i], like->div[i], 1 + 1 + ltotal);
4347 isl_seq_clr(bmap->div[i]+1+1+ltotal, total - ltotal);
4349 bmap = isl_basic_map_extend_constraints(bmap,
4350 0, 2 * like->n_div);
4351 for (i = 0; i < like->n_div; ++i) {
4352 if (isl_int_is_zero(bmap->div[i][0]))
4354 if (isl_basic_map_add_div_constraints(bmap, i) < 0)
4358 isl_basic_map_free(like);
4359 bmap = isl_basic_map_simplify(bmap);
4360 bmap = isl_basic_map_finalize(bmap);
4363 isl_basic_map_free(like);
4364 isl_basic_set_free(bset);
4368 struct isl_basic_set *isl_basic_set_from_underlying_set(
4369 struct isl_basic_set *bset, struct isl_basic_set *like)
4371 return (struct isl_basic_set *)
4372 isl_basic_map_overlying_set(bset, (struct isl_basic_map *)like);
4375 struct isl_set *isl_set_from_underlying_set(
4376 struct isl_set *set, struct isl_basic_set *like)
4382 isl_assert(set->ctx, set->dim->n_out == isl_basic_set_total_dim(like),
4384 if (isl_space_is_equal(set->dim, like->dim) && like->n_div == 0) {
4385 isl_basic_set_free(like);
4388 set = isl_set_cow(set);
4391 for (i = 0; i < set->n; ++i) {
4392 set->p[i] = isl_basic_set_from_underlying_set(set->p[i],
4393 isl_basic_set_copy(like));
4397 isl_space_free(set->dim);
4398 set->dim = isl_space_copy(like->dim);
4401 isl_basic_set_free(like);
4404 isl_basic_set_free(like);
4409 struct isl_set *isl_map_underlying_set(struct isl_map *map)
4413 map = isl_map_cow(map);
4416 map->dim = isl_space_cow(map->dim);
4420 for (i = 1; i < map->n; ++i)
4421 isl_assert(map->ctx, map->p[0]->n_div == map->p[i]->n_div,
4423 for (i = 0; i < map->n; ++i) {
4424 map->p[i] = (struct isl_basic_map *)
4425 isl_basic_map_underlying_set(map->p[i]);
4430 map->dim = isl_space_underlying(map->dim, 0);
4432 isl_space_free(map->dim);
4433 map->dim = isl_space_copy(map->p[0]->dim);
4437 return (struct isl_set *)map;
4443 struct isl_set *isl_set_to_underlying_set(struct isl_set *set)
4445 return (struct isl_set *)isl_map_underlying_set((struct isl_map *)set);
4448 __isl_give isl_basic_map *isl_basic_map_reset_space(
4449 __isl_take isl_basic_map *bmap, __isl_take isl_space *dim)
4451 bmap = isl_basic_map_cow(bmap);
4455 isl_space_free(bmap->dim);
4458 bmap = isl_basic_map_finalize(bmap);
4462 isl_basic_map_free(bmap);
4463 isl_space_free(dim);
4467 __isl_give isl_basic_set *isl_basic_set_reset_space(
4468 __isl_take isl_basic_set *bset, __isl_take isl_space *dim)
4470 return (isl_basic_set *)isl_basic_map_reset_space((isl_basic_map *)bset,
4474 __isl_give isl_map *isl_map_reset_space(__isl_take isl_map *map,
4475 __isl_take isl_space *dim)
4479 map = isl_map_cow(map);
4483 for (i = 0; i < map->n; ++i) {
4484 map->p[i] = isl_basic_map_reset_space(map->p[i],
4485 isl_space_copy(dim));
4489 isl_space_free(map->dim);
4495 isl_space_free(dim);
4499 __isl_give isl_set *isl_set_reset_space(__isl_take isl_set *set,
4500 __isl_take isl_space *dim)
4502 return (struct isl_set *) isl_map_reset_space((struct isl_map *)set, dim);
4505 /* Compute the parameter domain of the given basic set.
4507 __isl_give isl_basic_set *isl_basic_set_params(__isl_take isl_basic_set *bset)
4512 if (isl_basic_set_is_params(bset))
4515 n = isl_basic_set_dim(bset, isl_dim_set);
4516 bset = isl_basic_set_project_out(bset, isl_dim_set, 0, n);
4517 space = isl_basic_set_get_space(bset);
4518 space = isl_space_params(space);
4519 bset = isl_basic_set_reset_space(bset, space);
4523 /* Construct a zero-dimensional basic set with the given parameter domain.
4525 __isl_give isl_basic_set *isl_basic_set_from_params(
4526 __isl_take isl_basic_set *bset)
4529 space = isl_basic_set_get_space(bset);
4530 space = isl_space_set_from_params(space);
4531 bset = isl_basic_set_reset_space(bset, space);
4535 /* Compute the parameter domain of the given set.
4537 __isl_give isl_set *isl_set_params(__isl_take isl_set *set)
4542 if (isl_set_is_params(set))
4545 n = isl_set_dim(set, isl_dim_set);
4546 set = isl_set_project_out(set, isl_dim_set, 0, n);
4547 space = isl_set_get_space(set);
4548 space = isl_space_params(space);
4549 set = isl_set_reset_space(set, space);
4553 /* Construct a zero-dimensional set with the given parameter domain.
4555 __isl_give isl_set *isl_set_from_params(__isl_take isl_set *set)
4558 space = isl_set_get_space(set);
4559 space = isl_space_set_from_params(space);
4560 set = isl_set_reset_space(set, space);
4564 /* Compute the parameter domain of the given map.
4566 __isl_give isl_set *isl_map_params(__isl_take isl_map *map)
4571 n = isl_map_dim(map, isl_dim_in);
4572 map = isl_map_project_out(map, isl_dim_in, 0, n);
4573 n = isl_map_dim(map, isl_dim_out);
4574 map = isl_map_project_out(map, isl_dim_out, 0, n);
4575 space = isl_map_get_space(map);
4576 space = isl_space_params(space);
4577 map = isl_map_reset_space(map, space);
4581 struct isl_basic_set *isl_basic_map_domain(struct isl_basic_map *bmap)
4584 struct isl_basic_set *domain;
4590 dim = isl_space_domain(isl_basic_map_get_space(bmap));
4592 n_in = isl_basic_map_n_in(bmap);
4593 n_out = isl_basic_map_n_out(bmap);
4594 domain = isl_basic_set_from_basic_map(bmap);
4595 domain = isl_basic_set_project_out(domain, isl_dim_set, n_in, n_out);
4597 domain = isl_basic_set_reset_space(domain, dim);
4602 int isl_basic_map_may_be_set(__isl_keep isl_basic_map *bmap)
4606 return isl_space_may_be_set(bmap->dim);
4609 /* Is this basic map actually a set?
4610 * Users should never call this function. Outside of isl,
4611 * the type should indicate whether something is a set or a map.
4613 int isl_basic_map_is_set(__isl_keep isl_basic_map *bmap)
4617 return isl_space_is_set(bmap->dim);
4620 struct isl_basic_set *isl_basic_map_range(struct isl_basic_map *bmap)
4624 if (isl_basic_map_is_set(bmap))
4626 return isl_basic_map_domain(isl_basic_map_reverse(bmap));
4629 __isl_give isl_basic_map *isl_basic_map_domain_map(
4630 __isl_take isl_basic_map *bmap)
4634 isl_basic_map *domain;
4635 int nparam, n_in, n_out;
4638 nparam = isl_basic_map_dim(bmap, isl_dim_param);
4639 n_in = isl_basic_map_dim(bmap, isl_dim_in);
4640 n_out = isl_basic_map_dim(bmap, isl_dim_out);
4642 dim = isl_space_from_range(isl_space_domain(isl_basic_map_get_space(bmap)));
4643 domain = isl_basic_map_universe(dim);
4645 bmap = isl_basic_map_from_domain(isl_basic_map_wrap(bmap));
4646 bmap = isl_basic_map_apply_range(bmap, domain);
4647 bmap = isl_basic_map_extend_constraints(bmap, n_in, 0);
4649 total = isl_basic_map_total_dim(bmap);
4651 for (i = 0; i < n_in; ++i) {
4652 k = isl_basic_map_alloc_equality(bmap);
4655 isl_seq_clr(bmap->eq[k], 1 + total);
4656 isl_int_set_si(bmap->eq[k][1 + nparam + i], -1);
4657 isl_int_set_si(bmap->eq[k][1 + nparam + n_in + n_out + i], 1);
4660 bmap = isl_basic_map_gauss(bmap, NULL);
4661 return isl_basic_map_finalize(bmap);
4663 isl_basic_map_free(bmap);
4667 __isl_give isl_basic_map *isl_basic_map_range_map(
4668 __isl_take isl_basic_map *bmap)
4672 isl_basic_map *range;
4673 int nparam, n_in, n_out;
4676 nparam = isl_basic_map_dim(bmap, isl_dim_param);
4677 n_in = isl_basic_map_dim(bmap, isl_dim_in);
4678 n_out = isl_basic_map_dim(bmap, isl_dim_out);
4680 dim = isl_space_from_range(isl_space_range(isl_basic_map_get_space(bmap)));
4681 range = isl_basic_map_universe(dim);
4683 bmap = isl_basic_map_from_domain(isl_basic_map_wrap(bmap));
4684 bmap = isl_basic_map_apply_range(bmap, range);
4685 bmap = isl_basic_map_extend_constraints(bmap, n_out, 0);
4687 total = isl_basic_map_total_dim(bmap);
4689 for (i = 0; i < n_out; ++i) {
4690 k = isl_basic_map_alloc_equality(bmap);
4693 isl_seq_clr(bmap->eq[k], 1 + total);
4694 isl_int_set_si(bmap->eq[k][1 + nparam + n_in + i], -1);
4695 isl_int_set_si(bmap->eq[k][1 + nparam + n_in + n_out + i], 1);
4698 bmap = isl_basic_map_gauss(bmap, NULL);
4699 return isl_basic_map_finalize(bmap);
4701 isl_basic_map_free(bmap);
4705 int isl_map_may_be_set(__isl_keep isl_map *map)
4709 return isl_space_may_be_set(map->dim);
4712 /* Is this map actually a set?
4713 * Users should never call this function. Outside of isl,
4714 * the type should indicate whether something is a set or a map.
4716 int isl_map_is_set(__isl_keep isl_map *map)
4720 return isl_space_is_set(map->dim);
4723 struct isl_set *isl_map_range(struct isl_map *map)
4726 struct isl_set *set;
4730 if (isl_map_is_set(map))
4731 return (isl_set *)map;
4733 map = isl_map_cow(map);
4737 set = (struct isl_set *) map;
4738 set->dim = isl_space_range(set->dim);
4741 for (i = 0; i < map->n; ++i) {
4742 set->p[i] = isl_basic_map_range(map->p[i]);
4746 ISL_F_CLR(set, ISL_MAP_DISJOINT);
4747 ISL_F_CLR(set, ISL_SET_NORMALIZED);
4754 __isl_give isl_map *isl_map_domain_map(__isl_take isl_map *map)
4757 isl_space *domain_dim;
4759 map = isl_map_cow(map);
4763 domain_dim = isl_space_from_range(isl_space_domain(isl_map_get_space(map)));
4764 map->dim = isl_space_from_domain(isl_space_wrap(map->dim));
4765 map->dim = isl_space_join(map->dim, domain_dim);
4768 for (i = 0; i < map->n; ++i) {
4769 map->p[i] = isl_basic_map_domain_map(map->p[i]);
4773 ISL_F_CLR(map, ISL_MAP_DISJOINT);
4774 ISL_F_CLR(map, ISL_MAP_NORMALIZED);
4781 __isl_give isl_map *isl_map_range_map(__isl_take isl_map *map)
4784 isl_space *range_dim;
4786 map = isl_map_cow(map);
4790 range_dim = isl_space_range(isl_map_get_space(map));
4791 range_dim = isl_space_from_range(range_dim);
4792 map->dim = isl_space_from_domain(isl_space_wrap(map->dim));
4793 map->dim = isl_space_join(map->dim, range_dim);
4796 for (i = 0; i < map->n; ++i) {
4797 map->p[i] = isl_basic_map_range_map(map->p[i]);
4801 ISL_F_CLR(map, ISL_MAP_DISJOINT);
4802 ISL_F_CLR(map, ISL_MAP_NORMALIZED);
4809 __isl_give isl_map *isl_map_from_set(__isl_take isl_set *set,
4810 __isl_take isl_space *dim)
4813 struct isl_map *map = NULL;
4815 set = isl_set_cow(set);
4818 isl_assert(set->ctx, isl_space_compatible(set->dim, dim), goto error);
4819 map = (struct isl_map *)set;
4820 for (i = 0; i < set->n; ++i) {
4821 map->p[i] = isl_basic_map_from_basic_set(
4822 set->p[i], isl_space_copy(dim));
4826 isl_space_free(map->dim);
4830 isl_space_free(dim);
4835 __isl_give isl_basic_map *isl_basic_map_from_domain(
4836 __isl_take isl_basic_set *bset)
4838 return isl_basic_map_reverse(isl_basic_map_from_range(bset));
4841 __isl_give isl_basic_map *isl_basic_map_from_range(
4842 __isl_take isl_basic_set *bset)
4845 space = isl_basic_set_get_space(bset);
4846 space = isl_space_from_range(space);
4847 bset = isl_basic_set_reset_space(bset, space);
4848 return (isl_basic_map *)bset;
4851 struct isl_map *isl_map_from_range(struct isl_set *set)
4854 space = isl_set_get_space(set);
4855 space = isl_space_from_range(space);
4856 set = isl_set_reset_space(set, space);
4857 return (struct isl_map *)set;
4860 __isl_give isl_map *isl_map_from_domain(__isl_take isl_set *set)
4862 return isl_map_reverse(isl_map_from_range(set));
4865 __isl_give isl_basic_map *isl_basic_map_from_domain_and_range(
4866 __isl_take isl_basic_set *domain, __isl_take isl_basic_set *range)
4868 return isl_basic_map_apply_range(isl_basic_map_reverse(domain), range);
4871 __isl_give isl_map *isl_map_from_domain_and_range(__isl_take isl_set *domain,
4872 __isl_take isl_set *range)
4874 return isl_map_apply_range(isl_map_reverse(domain), range);
4877 struct isl_set *isl_set_from_map(struct isl_map *map)
4880 struct isl_set *set = NULL;
4884 map = isl_map_cow(map);
4887 map->dim = isl_space_as_set_space(map->dim);
4890 set = (struct isl_set *)map;
4891 for (i = 0; i < map->n; ++i) {
4892 set->p[i] = isl_basic_set_from_basic_map(map->p[i]);
4902 __isl_give isl_map *isl_map_alloc_space(__isl_take isl_space *dim, int n,
4905 struct isl_map *map;
4910 isl_die(dim->ctx, isl_error_internal,
4911 "negative number of basic maps", goto error);
4912 map = isl_alloc(dim->ctx, struct isl_map,
4913 sizeof(struct isl_map) +
4914 (n - 1) * sizeof(struct isl_basic_map *));
4918 map->ctx = dim->ctx;
4919 isl_ctx_ref(map->ctx);
4927 isl_space_free(dim);
4931 struct isl_map *isl_map_alloc(struct isl_ctx *ctx,
4932 unsigned nparam, unsigned in, unsigned out, int n,
4935 struct isl_map *map;
4938 dims = isl_space_alloc(ctx, nparam, in, out);
4942 map = isl_map_alloc_space(dims, n, flags);
4946 __isl_give isl_basic_map *isl_basic_map_empty(__isl_take isl_space *dim)
4948 struct isl_basic_map *bmap;
4949 bmap = isl_basic_map_alloc_space(dim, 0, 1, 0);
4950 bmap = isl_basic_map_set_to_empty(bmap);
4954 __isl_give isl_basic_set *isl_basic_set_empty(__isl_take isl_space *dim)
4956 struct isl_basic_set *bset;
4957 bset = isl_basic_set_alloc_space(dim, 0, 1, 0);
4958 bset = isl_basic_set_set_to_empty(bset);
4962 struct isl_basic_map *isl_basic_map_empty_like(struct isl_basic_map *model)
4964 struct isl_basic_map *bmap;
4967 bmap = isl_basic_map_alloc_space(isl_space_copy(model->dim), 0, 1, 0);
4968 bmap = isl_basic_map_set_to_empty(bmap);
4972 struct isl_basic_map *isl_basic_map_empty_like_map(struct isl_map *model)
4974 struct isl_basic_map *bmap;
4977 bmap = isl_basic_map_alloc_space(isl_space_copy(model->dim), 0, 1, 0);
4978 bmap = isl_basic_map_set_to_empty(bmap);
4982 struct isl_basic_set *isl_basic_set_empty_like(struct isl_basic_set *model)
4984 struct isl_basic_set *bset;
4987 bset = isl_basic_set_alloc_space(isl_space_copy(model->dim), 0, 1, 0);
4988 bset = isl_basic_set_set_to_empty(bset);
4992 __isl_give isl_basic_map *isl_basic_map_universe(__isl_take isl_space *dim)
4994 struct isl_basic_map *bmap;
4995 bmap = isl_basic_map_alloc_space(dim, 0, 0, 0);
4996 bmap = isl_basic_map_finalize(bmap);
5000 __isl_give isl_basic_set *isl_basic_set_universe(__isl_take isl_space *dim)
5002 struct isl_basic_set *bset;
5003 bset = isl_basic_set_alloc_space(dim, 0, 0, 0);
5004 bset = isl_basic_set_finalize(bset);
5008 __isl_give isl_basic_map *isl_basic_map_nat_universe(__isl_take isl_space *dim)
5011 unsigned total = isl_space_dim(dim, isl_dim_all);
5012 isl_basic_map *bmap;
5014 bmap= isl_basic_map_alloc_space(dim, 0, 0, total);
5015 for (i = 0; i < total; ++i) {
5016 int k = isl_basic_map_alloc_inequality(bmap);
5019 isl_seq_clr(bmap->ineq[k], 1 + total);
5020 isl_int_set_si(bmap->ineq[k][1 + i], 1);
5024 isl_basic_map_free(bmap);
5028 __isl_give isl_basic_set *isl_basic_set_nat_universe(__isl_take isl_space *dim)
5030 return isl_basic_map_nat_universe(dim);
5033 __isl_give isl_map *isl_map_nat_universe(__isl_take isl_space *dim)
5035 return isl_map_from_basic_map(isl_basic_map_nat_universe(dim));
5038 __isl_give isl_set *isl_set_nat_universe(__isl_take isl_space *dim)
5040 return isl_map_nat_universe(dim);
5043 __isl_give isl_basic_map *isl_basic_map_universe_like(
5044 __isl_keep isl_basic_map *model)
5048 return isl_basic_map_alloc_space(isl_space_copy(model->dim), 0, 0, 0);
5051 struct isl_basic_set *isl_basic_set_universe_like(struct isl_basic_set *model)
5055 return isl_basic_set_alloc_space(isl_space_copy(model->dim), 0, 0, 0);
5058 __isl_give isl_basic_set *isl_basic_set_universe_like_set(
5059 __isl_keep isl_set *model)
5063 return isl_basic_set_alloc_space(isl_space_copy(model->dim), 0, 0, 0);
5066 __isl_give isl_map *isl_map_empty(__isl_take isl_space *dim)
5068 return isl_map_alloc_space(dim, 0, ISL_MAP_DISJOINT);
5071 struct isl_map *isl_map_empty_like(struct isl_map *model)
5075 return isl_map_alloc_space(isl_space_copy(model->dim), 0, ISL_MAP_DISJOINT);
5078 struct isl_map *isl_map_empty_like_basic_map(struct isl_basic_map *model)
5082 return isl_map_alloc_space(isl_space_copy(model->dim), 0, ISL_MAP_DISJOINT);
5085 __isl_give isl_set *isl_set_empty(__isl_take isl_space *dim)
5087 return isl_set_alloc_space(dim, 0, ISL_MAP_DISJOINT);
5090 struct isl_set *isl_set_empty_like(struct isl_set *model)
5094 return isl_set_empty(isl_space_copy(model->dim));
5097 __isl_give isl_map *isl_map_universe(__isl_take isl_space *dim)
5099 struct isl_map *map;
5102 map = isl_map_alloc_space(isl_space_copy(dim), 1, ISL_MAP_DISJOINT);
5103 map = isl_map_add_basic_map(map, isl_basic_map_universe(dim));
5107 __isl_give isl_set *isl_set_universe(__isl_take isl_space *dim)
5109 struct isl_set *set;
5112 set = isl_set_alloc_space(isl_space_copy(dim), 1, ISL_MAP_DISJOINT);
5113 set = isl_set_add_basic_set(set, isl_basic_set_universe(dim));
5117 __isl_give isl_set *isl_set_universe_like(__isl_keep isl_set *model)
5121 return isl_set_universe(isl_space_copy(model->dim));
5124 struct isl_map *isl_map_dup(struct isl_map *map)
5127 struct isl_map *dup;
5131 dup = isl_map_alloc_space(isl_space_copy(map->dim), map->n, map->flags);
5132 for (i = 0; i < map->n; ++i)
5133 dup = isl_map_add_basic_map(dup, isl_basic_map_copy(map->p[i]));
5137 __isl_give isl_map *isl_map_add_basic_map(__isl_take isl_map *map,
5138 __isl_take isl_basic_map *bmap)
5142 if (isl_basic_map_plain_is_empty(bmap)) {
5143 isl_basic_map_free(bmap);
5146 isl_assert(map->ctx, isl_space_is_equal(map->dim, bmap->dim), goto error);
5147 isl_assert(map->ctx, map->n < map->size, goto error);
5148 map->p[map->n] = bmap;
5150 ISL_F_CLR(map, ISL_MAP_NORMALIZED);
5156 isl_basic_map_free(bmap);
5160 void *isl_map_free(struct isl_map *map)
5170 isl_ctx_deref(map->ctx);
5171 for (i = 0; i < map->n; ++i)
5172 isl_basic_map_free(map->p[i]);
5173 isl_space_free(map->dim);
5179 struct isl_map *isl_map_extend(struct isl_map *base,
5180 unsigned nparam, unsigned n_in, unsigned n_out)
5184 base = isl_map_cow(base);
5188 base->dim = isl_space_extend(base->dim, nparam, n_in, n_out);
5191 for (i = 0; i < base->n; ++i) {
5192 base->p[i] = isl_basic_map_extend_space(base->p[i],
5193 isl_space_copy(base->dim), 0, 0, 0);
5203 struct isl_set *isl_set_extend(struct isl_set *base,
5204 unsigned nparam, unsigned dim)
5206 return (struct isl_set *)isl_map_extend((struct isl_map *)base,
5210 static struct isl_basic_map *isl_basic_map_fix_pos_si(
5211 struct isl_basic_map *bmap, unsigned pos, int value)
5215 bmap = isl_basic_map_cow(bmap);
5216 bmap = isl_basic_map_extend_constraints(bmap, 1, 0);
5217 j = isl_basic_map_alloc_equality(bmap);
5220 isl_seq_clr(bmap->eq[j] + 1, isl_basic_map_total_dim(bmap));
5221 isl_int_set_si(bmap->eq[j][pos], -1);
5222 isl_int_set_si(bmap->eq[j][0], value);
5223 bmap = isl_basic_map_simplify(bmap);
5224 return isl_basic_map_finalize(bmap);
5226 isl_basic_map_free(bmap);
5230 static __isl_give isl_basic_map *isl_basic_map_fix_pos(
5231 __isl_take isl_basic_map *bmap, unsigned pos, isl_int value)
5235 bmap = isl_basic_map_cow(bmap);
5236 bmap = isl_basic_map_extend_constraints(bmap, 1, 0);
5237 j = isl_basic_map_alloc_equality(bmap);
5240 isl_seq_clr(bmap->eq[j] + 1, isl_basic_map_total_dim(bmap));
5241 isl_int_set_si(bmap->eq[j][pos], -1);
5242 isl_int_set(bmap->eq[j][0], value);
5243 bmap = isl_basic_map_simplify(bmap);
5244 return isl_basic_map_finalize(bmap);
5246 isl_basic_map_free(bmap);
5250 struct isl_basic_map *isl_basic_map_fix_si(struct isl_basic_map *bmap,
5251 enum isl_dim_type type, unsigned pos, int value)
5255 isl_assert(bmap->ctx, pos < isl_basic_map_dim(bmap, type), goto error);
5256 return isl_basic_map_fix_pos_si(bmap,
5257 isl_basic_map_offset(bmap, type) + pos, value);
5259 isl_basic_map_free(bmap);
5263 __isl_give isl_basic_map *isl_basic_map_fix(__isl_take isl_basic_map *bmap,
5264 enum isl_dim_type type, unsigned pos, isl_int value)
5268 isl_assert(bmap->ctx, pos < isl_basic_map_dim(bmap, type), goto error);
5269 return isl_basic_map_fix_pos(bmap,
5270 isl_basic_map_offset(bmap, type) + pos, value);
5272 isl_basic_map_free(bmap);
5276 struct isl_basic_set *isl_basic_set_fix_si(struct isl_basic_set *bset,
5277 enum isl_dim_type type, unsigned pos, int value)
5279 return (struct isl_basic_set *)
5280 isl_basic_map_fix_si((struct isl_basic_map *)bset,
5284 __isl_give isl_basic_set *isl_basic_set_fix(__isl_take isl_basic_set *bset,
5285 enum isl_dim_type type, unsigned pos, isl_int value)
5287 return (struct isl_basic_set *)
5288 isl_basic_map_fix((struct isl_basic_map *)bset,
5292 struct isl_basic_map *isl_basic_map_fix_input_si(struct isl_basic_map *bmap,
5293 unsigned input, int value)
5295 return isl_basic_map_fix_si(bmap, isl_dim_in, input, value);
5298 struct isl_basic_set *isl_basic_set_fix_dim_si(struct isl_basic_set *bset,
5299 unsigned dim, int value)
5301 return (struct isl_basic_set *)
5302 isl_basic_map_fix_si((struct isl_basic_map *)bset,
5303 isl_dim_set, dim, value);
5306 static int remove_if_empty(__isl_keep isl_map *map, int i)
5308 int empty = isl_basic_map_plain_is_empty(map->p[i]);
5315 isl_basic_map_free(map->p[i]);
5316 if (i != map->n - 1) {
5317 ISL_F_CLR(map, ISL_MAP_NORMALIZED);
5318 map->p[i] = map->p[map->n - 1];
5325 struct isl_map *isl_map_fix_si(struct isl_map *map,
5326 enum isl_dim_type type, unsigned pos, int value)
5330 map = isl_map_cow(map);
5334 isl_assert(map->ctx, pos < isl_map_dim(map, type), goto error);
5335 for (i = map->n - 1; i >= 0; --i) {
5336 map->p[i] = isl_basic_map_fix_si(map->p[i], type, pos, value);
5337 if (remove_if_empty(map, i) < 0)
5340 ISL_F_CLR(map, ISL_MAP_NORMALIZED);
5347 __isl_give isl_set *isl_set_fix_si(__isl_take isl_set *set,
5348 enum isl_dim_type type, unsigned pos, int value)
5350 return (struct isl_set *)
5351 isl_map_fix_si((struct isl_map *)set, type, pos, value);
5354 __isl_give isl_map *isl_map_fix(__isl_take isl_map *map,
5355 enum isl_dim_type type, unsigned pos, isl_int value)
5359 map = isl_map_cow(map);
5363 isl_assert(map->ctx, pos < isl_map_dim(map, type), goto error);
5364 for (i = 0; i < map->n; ++i) {
5365 map->p[i] = isl_basic_map_fix(map->p[i], type, pos, value);
5369 ISL_F_CLR(map, ISL_MAP_NORMALIZED);
5376 __isl_give isl_set *isl_set_fix(__isl_take isl_set *set,
5377 enum isl_dim_type type, unsigned pos, isl_int value)
5379 return (struct isl_set *)isl_map_fix((isl_map *)set, type, pos, value);
5382 struct isl_map *isl_map_fix_input_si(struct isl_map *map,
5383 unsigned input, int value)
5385 return isl_map_fix_si(map, isl_dim_in, input, value);
5388 struct isl_set *isl_set_fix_dim_si(struct isl_set *set, unsigned dim, int value)
5390 return (struct isl_set *)
5391 isl_map_fix_si((struct isl_map *)set, isl_dim_set, dim, value);
5394 static __isl_give isl_basic_map *basic_map_bound_si(
5395 __isl_take isl_basic_map *bmap,
5396 enum isl_dim_type type, unsigned pos, int value, int upper)
5402 isl_assert(bmap->ctx, pos < isl_basic_map_dim(bmap, type), goto error);
5403 pos += isl_basic_map_offset(bmap, type);
5404 bmap = isl_basic_map_cow(bmap);
5405 bmap = isl_basic_map_extend_constraints(bmap, 0, 1);
5406 j = isl_basic_map_alloc_inequality(bmap);
5409 isl_seq_clr(bmap->ineq[j], 1 + isl_basic_map_total_dim(bmap));
5411 isl_int_set_si(bmap->ineq[j][pos], -1);
5412 isl_int_set_si(bmap->ineq[j][0], value);
5414 isl_int_set_si(bmap->ineq[j][pos], 1);
5415 isl_int_set_si(bmap->ineq[j][0], -value);
5417 bmap = isl_basic_map_simplify(bmap);
5418 return isl_basic_map_finalize(bmap);
5420 isl_basic_map_free(bmap);
5424 __isl_give isl_basic_map *isl_basic_map_lower_bound_si(
5425 __isl_take isl_basic_map *bmap,
5426 enum isl_dim_type type, unsigned pos, int value)
5428 return basic_map_bound_si(bmap, type, pos, value, 0);
5431 /* Constrain the values of the given dimension to be no greater than "value".
5433 __isl_give isl_basic_map *isl_basic_map_upper_bound_si(
5434 __isl_take isl_basic_map *bmap,
5435 enum isl_dim_type type, unsigned pos, int value)
5437 return basic_map_bound_si(bmap, type, pos, value, 1);
5440 struct isl_basic_set *isl_basic_set_lower_bound_dim(struct isl_basic_set *bset,
5441 unsigned dim, isl_int value)
5445 bset = isl_basic_set_cow(bset);
5446 bset = isl_basic_set_extend_constraints(bset, 0, 1);
5447 j = isl_basic_set_alloc_inequality(bset);
5450 isl_seq_clr(bset->ineq[j], 1 + isl_basic_set_total_dim(bset));
5451 isl_int_set_si(bset->ineq[j][1 + isl_basic_set_n_param(bset) + dim], 1);
5452 isl_int_neg(bset->ineq[j][0], value);
5453 bset = isl_basic_set_simplify(bset);
5454 return isl_basic_set_finalize(bset);
5456 isl_basic_set_free(bset);
5460 static __isl_give isl_map *map_bound_si(__isl_take isl_map *map,
5461 enum isl_dim_type type, unsigned pos, int value, int upper)
5465 map = isl_map_cow(map);
5469 isl_assert(map->ctx, pos < isl_map_dim(map, type), goto error);
5470 for (i = 0; i < map->n; ++i) {
5471 map->p[i] = basic_map_bound_si(map->p[i],
5472 type, pos, value, upper);
5476 ISL_F_CLR(map, ISL_MAP_NORMALIZED);
5483 __isl_give isl_map *isl_map_lower_bound_si(__isl_take isl_map *map,
5484 enum isl_dim_type type, unsigned pos, int value)
5486 return map_bound_si(map, type, pos, value, 0);
5489 __isl_give isl_map *isl_map_upper_bound_si(__isl_take isl_map *map,
5490 enum isl_dim_type type, unsigned pos, int value)
5492 return map_bound_si(map, type, pos, value, 1);
5495 __isl_give isl_set *isl_set_lower_bound_si(__isl_take isl_set *set,
5496 enum isl_dim_type type, unsigned pos, int value)
5498 return (struct isl_set *)
5499 isl_map_lower_bound_si((struct isl_map *)set, type, pos, value);
5502 __isl_give isl_set *isl_set_upper_bound_si(__isl_take isl_set *set,
5503 enum isl_dim_type type, unsigned pos, int value)
5505 return isl_map_upper_bound_si(set, type, pos, value);
5508 /* Bound the given variable of "bmap" from below (or above is "upper"
5509 * is set) to "value".
5511 static __isl_give isl_basic_map *basic_map_bound(
5512 __isl_take isl_basic_map *bmap,
5513 enum isl_dim_type type, unsigned pos, isl_int value, int upper)
5519 if (pos >= isl_basic_map_dim(bmap, type))
5520 isl_die(bmap->ctx, isl_error_invalid,
5521 "index out of bounds", goto error);
5522 pos += isl_basic_map_offset(bmap, type);
5523 bmap = isl_basic_map_cow(bmap);
5524 bmap = isl_basic_map_extend_constraints(bmap, 0, 1);
5525 j = isl_basic_map_alloc_inequality(bmap);
5528 isl_seq_clr(bmap->ineq[j], 1 + isl_basic_map_total_dim(bmap));
5530 isl_int_set_si(bmap->ineq[j][pos], -1);
5531 isl_int_set(bmap->ineq[j][0], value);
5533 isl_int_set_si(bmap->ineq[j][pos], 1);
5534 isl_int_neg(bmap->ineq[j][0], value);
5536 bmap = isl_basic_map_simplify(bmap);
5537 return isl_basic_map_finalize(bmap);
5539 isl_basic_map_free(bmap);
5543 /* Bound the given variable of "map" from below (or above is "upper"
5544 * is set) to "value".
5546 static __isl_give isl_map *map_bound(__isl_take isl_map *map,
5547 enum isl_dim_type type, unsigned pos, isl_int value, int upper)
5551 map = isl_map_cow(map);
5555 if (pos >= isl_map_dim(map, type))
5556 isl_die(map->ctx, isl_error_invalid,
5557 "index out of bounds", goto error);
5558 for (i = map->n - 1; i >= 0; --i) {
5559 map->p[i] = basic_map_bound(map->p[i], type, pos, value, upper);
5560 if (remove_if_empty(map, i) < 0)
5563 ISL_F_CLR(map, ISL_MAP_NORMALIZED);
5570 __isl_give isl_map *isl_map_lower_bound(__isl_take isl_map *map,
5571 enum isl_dim_type type, unsigned pos, isl_int value)
5573 return map_bound(map, type, pos, value, 0);
5576 __isl_give isl_map *isl_map_upper_bound(__isl_take isl_map *map,
5577 enum isl_dim_type type, unsigned pos, isl_int value)
5579 return map_bound(map, type, pos, value, 1);
5582 __isl_give isl_set *isl_set_lower_bound(__isl_take isl_set *set,
5583 enum isl_dim_type type, unsigned pos, isl_int value)
5585 return isl_map_lower_bound(set, type, pos, value);
5588 __isl_give isl_set *isl_set_upper_bound(__isl_take isl_set *set,
5589 enum isl_dim_type type, unsigned pos, isl_int value)
5591 return isl_map_upper_bound(set, type, pos, value);
5594 struct isl_set *isl_set_lower_bound_dim(struct isl_set *set, unsigned dim,
5599 set = isl_set_cow(set);
5603 isl_assert(set->ctx, dim < isl_set_n_dim(set), goto error);
5604 for (i = 0; i < set->n; ++i) {
5605 set->p[i] = isl_basic_set_lower_bound_dim(set->p[i], dim, value);
5615 struct isl_map *isl_map_reverse(struct isl_map *map)
5619 map = isl_map_cow(map);
5623 map->dim = isl_space_reverse(map->dim);
5626 for (i = 0; i < map->n; ++i) {
5627 map->p[i] = isl_basic_map_reverse(map->p[i]);
5631 ISL_F_CLR(map, ISL_MAP_NORMALIZED);
5638 static struct isl_map *isl_basic_map_partial_lexopt(
5639 struct isl_basic_map *bmap, struct isl_basic_set *dom,
5640 struct isl_set **empty, int max)
5644 if (bmap->ctx->opt->pip == ISL_PIP_PIP)
5645 return isl_pip_basic_map_lexopt(bmap, dom, empty, max);
5647 return isl_tab_basic_map_partial_lexopt(bmap, dom, empty, max);
5649 isl_basic_map_free(bmap);
5650 isl_basic_set_free(dom);
5656 struct isl_map *isl_basic_map_partial_lexmax(
5657 struct isl_basic_map *bmap, struct isl_basic_set *dom,
5658 struct isl_set **empty)
5660 return isl_basic_map_partial_lexopt(bmap, dom, empty, 1);
5663 struct isl_map *isl_basic_map_partial_lexmin(
5664 struct isl_basic_map *bmap, struct isl_basic_set *dom,
5665 struct isl_set **empty)
5667 return isl_basic_map_partial_lexopt(bmap, dom, empty, 0);
5670 struct isl_set *isl_basic_set_partial_lexmin(
5671 struct isl_basic_set *bset, struct isl_basic_set *dom,
5672 struct isl_set **empty)
5674 return (struct isl_set *)
5675 isl_basic_map_partial_lexmin((struct isl_basic_map *)bset,
5679 struct isl_set *isl_basic_set_partial_lexmax(
5680 struct isl_basic_set *bset, struct isl_basic_set *dom,
5681 struct isl_set **empty)
5683 return (struct isl_set *)
5684 isl_basic_map_partial_lexmax((struct isl_basic_map *)bset,
5688 __isl_give isl_pw_multi_aff *isl_basic_map_partial_lexmin_pw_multi_aff(
5689 __isl_take isl_basic_map *bmap, __isl_take isl_basic_set *dom,
5690 __isl_give isl_set **empty)
5692 return isl_basic_map_partial_lexopt_pw_multi_aff(bmap, dom, empty, 0);
5695 __isl_give isl_pw_multi_aff *isl_basic_map_partial_lexmax_pw_multi_aff(
5696 __isl_take isl_basic_map *bmap, __isl_take isl_basic_set *dom,
5697 __isl_give isl_set **empty)
5699 return isl_basic_map_partial_lexopt_pw_multi_aff(bmap, dom, empty, 1);
5702 __isl_give isl_pw_multi_aff *isl_basic_set_partial_lexmin_pw_multi_aff(
5703 __isl_take isl_basic_set *bset, __isl_take isl_basic_set *dom,
5704 __isl_give isl_set **empty)
5706 return isl_basic_map_partial_lexmin_pw_multi_aff(bset, dom, empty);
5709 __isl_give isl_pw_multi_aff *isl_basic_set_partial_lexmax_pw_multi_aff(
5710 __isl_take isl_basic_set *bset, __isl_take isl_basic_set *dom,
5711 __isl_give isl_set **empty)
5713 return isl_basic_map_partial_lexmax_pw_multi_aff(bset, dom, empty);
5716 __isl_give isl_pw_multi_aff *isl_basic_map_lexopt_pw_multi_aff(
5717 __isl_take isl_basic_map *bmap, int max)
5719 isl_basic_set *dom = NULL;
5720 isl_space *dom_space;
5724 dom_space = isl_space_domain(isl_space_copy(bmap->dim));
5725 dom = isl_basic_set_universe(dom_space);
5726 return isl_basic_map_partial_lexopt_pw_multi_aff(bmap, dom, NULL, max);
5728 isl_basic_map_free(bmap);
5732 __isl_give isl_pw_multi_aff *isl_basic_map_lexmin_pw_multi_aff(
5733 __isl_take isl_basic_map *bmap)
5735 return isl_basic_map_lexopt_pw_multi_aff(bmap, 0);
5739 #define TYPE isl_pw_multi_aff
5741 #define SUFFIX _pw_multi_aff
5743 #define EMPTY isl_pw_multi_aff_empty
5745 #define ADD isl_pw_multi_aff_union_add
5746 #include "isl_map_lexopt_templ.c"
5748 /* Given a map "map", compute the lexicographically minimal
5749 * (or maximal) image element for each domain element in dom,
5750 * in the form of an isl_pw_multi_aff.
5751 * Set *empty to those elements in dom that do not have an image element.
5753 * We first compute the lexicographically minimal or maximal element
5754 * in the first basic map. This results in a partial solution "res"
5755 * and a subset "todo" of dom that still need to be handled.
5756 * We then consider each of the remaining maps in "map" and successively
5757 * update both "res" and "todo".
5759 static __isl_give isl_pw_multi_aff *isl_map_partial_lexopt_aligned_pw_multi_aff(
5760 __isl_take isl_map *map, __isl_take isl_set *dom,
5761 __isl_give isl_set **empty, int max)
5764 isl_pw_multi_aff *res;
5770 if (isl_map_plain_is_empty(map)) {
5775 return isl_pw_multi_aff_from_map(map);
5778 res = basic_map_partial_lexopt_pw_multi_aff(
5779 isl_basic_map_copy(map->p[0]),
5780 isl_set_copy(dom), &todo, max);
5782 for (i = 1; i < map->n; ++i) {
5783 isl_pw_multi_aff *res_i;
5786 res_i = basic_map_partial_lexopt_pw_multi_aff(
5787 isl_basic_map_copy(map->p[i]),
5788 isl_set_copy(dom), &todo_i, max);
5791 res = isl_pw_multi_aff_union_lexmax(res, res_i);
5793 res = isl_pw_multi_aff_union_lexmin(res, res_i);
5795 todo = isl_set_intersect(todo, todo_i);
5816 #define TYPE isl_map
5820 #define EMPTY isl_map_empty
5822 #define ADD isl_map_union_disjoint
5823 #include "isl_map_lexopt_templ.c"
5825 /* Given a map "map", compute the lexicographically minimal
5826 * (or maximal) image element for each domain element in dom.
5827 * Set *empty to those elements in dom that do not have an image element.
5829 * We first compute the lexicographically minimal or maximal element
5830 * in the first basic map. This results in a partial solution "res"
5831 * and a subset "todo" of dom that still need to be handled.
5832 * We then consider each of the remaining maps in "map" and successively
5833 * update both "res" and "todo".
5835 * Let res^k and todo^k be the results after k steps and let i = k + 1.
5836 * Assume we are computing the lexicographical maximum.
5837 * We first compute the lexicographically maximal element in basic map i.
5838 * This results in a partial solution res_i and a subset todo_i.
5839 * Then we combine these results with those obtain for the first k basic maps
5840 * to obtain a result that is valid for the first k+1 basic maps.
5841 * In particular, the set where there is no solution is the set where
5842 * there is no solution for the first k basic maps and also no solution
5843 * for the ith basic map, i.e.,
5845 * todo^i = todo^k * todo_i
5847 * On dom(res^k) * dom(res_i), we need to pick the larger of the two
5848 * solutions, arbitrarily breaking ties in favor of res^k.
5849 * That is, when res^k(a) >= res_i(a), we pick res^k and
5850 * when res^k(a) < res_i(a), we pick res_i. (Here, ">=" and "<" denote
5851 * the lexicographic order.)
5852 * In practice, we compute
5854 * res^k * (res_i . "<=")
5858 * res_i * (res^k . "<")
5860 * Finally, we consider the symmetric difference of dom(res^k) and dom(res_i),
5861 * where only one of res^k and res_i provides a solution and we simply pick
5868 * Note that we only compute these intersections when dom(res^k) intersects
5869 * dom(res_i). Otherwise, the only effect of these intersections is to
5870 * potentially break up res^k and res_i into smaller pieces.
5871 * We want to avoid such splintering as much as possible.
5872 * In fact, an earlier implementation of this function would look for
5873 * better results in the domain of res^k and for extra results in todo^k,
5874 * but this would always result in a splintering according to todo^k,
5875 * even when the domain of basic map i is disjoint from the domains of
5876 * the previous basic maps.
5878 static __isl_give isl_map *isl_map_partial_lexopt_aligned(
5879 __isl_take isl_map *map, __isl_take isl_set *dom,
5880 __isl_give isl_set **empty, int max)
5883 struct isl_map *res;
5884 struct isl_set *todo;
5889 if (isl_map_plain_is_empty(map)) {
5897 res = basic_map_partial_lexopt(isl_basic_map_copy(map->p[0]),
5898 isl_set_copy(dom), &todo, max);
5900 for (i = 1; i < map->n; ++i) {
5904 isl_space *dim = isl_space_range(isl_map_get_space(res));
5906 res_i = basic_map_partial_lexopt(isl_basic_map_copy(map->p[i]),
5907 isl_set_copy(dom), &todo_i, max);
5910 lt = isl_map_lex_lt(isl_space_copy(dim));
5911 le = isl_map_lex_le(dim);
5913 lt = isl_map_lex_gt(isl_space_copy(dim));
5914 le = isl_map_lex_ge(dim);
5916 lt = isl_map_apply_range(isl_map_copy(res), lt);
5917 lt = isl_map_intersect(lt, isl_map_copy(res_i));
5918 le = isl_map_apply_range(isl_map_copy(res_i), le);
5919 le = isl_map_intersect(le, isl_map_copy(res));
5921 if (!isl_map_is_empty(lt) || !isl_map_is_empty(le)) {
5922 res = isl_map_intersect_domain(res,
5923 isl_set_copy(todo_i));
5924 res_i = isl_map_intersect_domain(res_i,
5925 isl_set_copy(todo));
5928 res = isl_map_union_disjoint(res, res_i);
5929 res = isl_map_union_disjoint(res, lt);
5930 res = isl_map_union_disjoint(res, le);
5932 todo = isl_set_intersect(todo, todo_i);
5952 __isl_give isl_map *isl_map_partial_lexmax(
5953 __isl_take isl_map *map, __isl_take isl_set *dom,
5954 __isl_give isl_set **empty)
5956 return isl_map_partial_lexopt(map, dom, empty, 1);
5959 __isl_give isl_map *isl_map_partial_lexmin(
5960 __isl_take isl_map *map, __isl_take isl_set *dom,
5961 __isl_give isl_set **empty)
5963 return isl_map_partial_lexopt(map, dom, empty, 0);
5966 __isl_give isl_set *isl_set_partial_lexmin(
5967 __isl_take isl_set *set, __isl_take isl_set *dom,
5968 __isl_give isl_set **empty)
5970 return (struct isl_set *)
5971 isl_map_partial_lexmin((struct isl_map *)set,
5975 __isl_give isl_set *isl_set_partial_lexmax(
5976 __isl_take isl_set *set, __isl_take isl_set *dom,
5977 __isl_give isl_set **empty)
5979 return (struct isl_set *)
5980 isl_map_partial_lexmax((struct isl_map *)set,
5984 __isl_give isl_map *isl_basic_map_lexopt(__isl_take isl_basic_map *bmap, int max)
5986 struct isl_basic_set *dom = NULL;
5991 dom_dim = isl_space_domain(isl_space_copy(bmap->dim));
5992 dom = isl_basic_set_universe(dom_dim);
5993 return isl_basic_map_partial_lexopt(bmap, dom, NULL, max);
5995 isl_basic_map_free(bmap);
5999 __isl_give isl_map *isl_basic_map_lexmin(__isl_take isl_basic_map *bmap)
6001 return isl_basic_map_lexopt(bmap, 0);
6004 __isl_give isl_map *isl_basic_map_lexmax(__isl_take isl_basic_map *bmap)
6006 return isl_basic_map_lexopt(bmap, 1);
6009 __isl_give isl_set *isl_basic_set_lexmin(__isl_take isl_basic_set *bset)
6011 return (isl_set *)isl_basic_map_lexmin((isl_basic_map *)bset);
6014 __isl_give isl_set *isl_basic_set_lexmax(__isl_take isl_basic_set *bset)
6016 return (isl_set *)isl_basic_map_lexmax((isl_basic_map *)bset);
6019 __isl_give isl_set *isl_set_lexmin(__isl_take isl_set *set)
6021 return (isl_set *)isl_map_lexmin((isl_map *)set);
6024 __isl_give isl_set *isl_set_lexmax(__isl_take isl_set *set)
6026 return (isl_set *)isl_map_lexmax((isl_map *)set);
6029 /* Extract the first and only affine expression from list
6030 * and then add it to *pwaff with the given dom.
6031 * This domain is known to be disjoint from other domains
6032 * because of the way isl_basic_map_foreach_lexmax works.
6034 static int update_dim_opt(__isl_take isl_basic_set *dom,
6035 __isl_take isl_aff_list *list, void *user)
6037 isl_ctx *ctx = isl_basic_set_get_ctx(dom);
6039 isl_pw_aff **pwaff = user;
6040 isl_pw_aff *pwaff_i;
6042 if (isl_aff_list_n_aff(list) != 1)
6043 isl_die(ctx, isl_error_internal,
6044 "expecting single element list", goto error);
6046 aff = isl_aff_list_get_aff(list, 0);
6047 pwaff_i = isl_pw_aff_alloc(isl_set_from_basic_set(dom), aff);
6049 *pwaff = isl_pw_aff_add_disjoint(*pwaff, pwaff_i);
6051 isl_aff_list_free(list);
6055 isl_basic_set_free(dom);
6056 isl_aff_list_free(list);
6060 /* Given a basic map with one output dimension, compute the minimum or
6061 * maximum of that dimension as an isl_pw_aff.
6063 * The isl_pw_aff is constructed by having isl_basic_map_foreach_lexopt
6064 * call update_dim_opt on each leaf of the result.
6066 static __isl_give isl_pw_aff *basic_map_dim_opt(__isl_keep isl_basic_map *bmap,
6069 isl_space *dim = isl_basic_map_get_space(bmap);
6073 dim = isl_space_from_domain(isl_space_domain(dim));
6074 dim = isl_space_add_dims(dim, isl_dim_out, 1);
6075 pwaff = isl_pw_aff_empty(dim);
6077 r = isl_basic_map_foreach_lexopt(bmap, max, &update_dim_opt, &pwaff);
6079 return isl_pw_aff_free(pwaff);
6084 /* Compute the minimum or maximum of the given output dimension
6085 * as a function of the parameters and the input dimensions,
6086 * but independently of the other output dimensions.
6088 * We first project out the other output dimension and then compute
6089 * the "lexicographic" maximum in each basic map, combining the results
6090 * using isl_pw_aff_union_max.
6092 static __isl_give isl_pw_aff *map_dim_opt(__isl_take isl_map *map, int pos,
6099 n_out = isl_map_dim(map, isl_dim_out);
6100 map = isl_map_project_out(map, isl_dim_out, pos + 1, n_out - (pos + 1));
6101 map = isl_map_project_out(map, isl_dim_out, 0, pos);
6106 isl_space *dim = isl_map_get_space(map);
6107 dim = isl_space_domain(isl_space_from_range(dim));
6109 return isl_pw_aff_empty(dim);
6112 pwaff = basic_map_dim_opt(map->p[0], max);
6113 for (i = 1; i < map->n; ++i) {
6114 isl_pw_aff *pwaff_i;
6116 pwaff_i = basic_map_dim_opt(map->p[i], max);
6117 pwaff = isl_pw_aff_union_opt(pwaff, pwaff_i, max);
6125 /* Compute the maximum of the given output dimension as a function of the
6126 * parameters and input dimensions, but independently of
6127 * the other output dimensions.
6129 __isl_give isl_pw_aff *isl_map_dim_max(__isl_take isl_map *map, int pos)
6131 return map_dim_opt(map, pos, 1);
6134 /* Compute the minimum or maximum of the given set dimension
6135 * as a function of the parameters,
6136 * but independently of the other set dimensions.
6138 static __isl_give isl_pw_aff *set_dim_opt(__isl_take isl_set *set, int pos,
6141 return map_dim_opt(set, pos, max);
6144 /* Compute the maximum of the given set dimension as a function of the
6145 * parameters, but independently of the other set dimensions.
6147 __isl_give isl_pw_aff *isl_set_dim_max(__isl_take isl_set *set, int pos)
6149 return set_dim_opt(set, pos, 1);
6152 /* Compute the minimum of the given set dimension as a function of the
6153 * parameters, but independently of the other set dimensions.
6155 __isl_give isl_pw_aff *isl_set_dim_min(__isl_take isl_set *set, int pos)
6157 return set_dim_opt(set, pos, 0);
6160 /* Apply a preimage specified by "mat" on the parameters of "bset".
6161 * bset is assumed to have only parameters and divs.
6163 static struct isl_basic_set *basic_set_parameter_preimage(
6164 struct isl_basic_set *bset, struct isl_mat *mat)
6171 bset->dim = isl_space_cow(bset->dim);
6175 nparam = isl_basic_set_dim(bset, isl_dim_param);
6177 isl_assert(bset->ctx, mat->n_row == 1 + nparam, goto error);
6179 bset->dim->nparam = 0;
6180 bset->dim->n_out = nparam;
6181 bset = isl_basic_set_preimage(bset, mat);
6183 bset->dim->nparam = bset->dim->n_out;
6184 bset->dim->n_out = 0;
6189 isl_basic_set_free(bset);
6193 /* Apply a preimage specified by "mat" on the parameters of "set".
6194 * set is assumed to have only parameters and divs.
6196 static struct isl_set *set_parameter_preimage(
6197 struct isl_set *set, struct isl_mat *mat)
6199 isl_space *dim = NULL;
6205 dim = isl_space_copy(set->dim);
6206 dim = isl_space_cow(dim);
6210 nparam = isl_set_dim(set, isl_dim_param);
6212 isl_assert(set->ctx, mat->n_row == 1 + nparam, goto error);
6215 dim->n_out = nparam;
6216 isl_set_reset_space(set, dim);
6217 set = isl_set_preimage(set, mat);
6220 dim = isl_space_copy(set->dim);
6221 dim = isl_space_cow(dim);
6224 dim->nparam = dim->n_out;
6226 isl_set_reset_space(set, dim);
6229 isl_space_free(dim);
6236 /* Intersect the basic set "bset" with the affine space specified by the
6237 * equalities in "eq".
6239 static struct isl_basic_set *basic_set_append_equalities(
6240 struct isl_basic_set *bset, struct isl_mat *eq)
6248 bset = isl_basic_set_extend_space(bset, isl_space_copy(bset->dim), 0,
6253 len = 1 + isl_space_dim(bset->dim, isl_dim_all) + bset->extra;
6254 for (i = 0; i < eq->n_row; ++i) {
6255 k = isl_basic_set_alloc_equality(bset);
6258 isl_seq_cpy(bset->eq[k], eq->row[i], eq->n_col);
6259 isl_seq_clr(bset->eq[k] + eq->n_col, len - eq->n_col);
6263 bset = isl_basic_set_gauss(bset, NULL);
6264 bset = isl_basic_set_finalize(bset);
6269 isl_basic_set_free(bset);
6273 /* Intersect the set "set" with the affine space specified by the
6274 * equalities in "eq".
6276 static struct isl_set *set_append_equalities(struct isl_set *set,
6284 for (i = 0; i < set->n; ++i) {
6285 set->p[i] = basic_set_append_equalities(set->p[i],
6298 /* Project the given basic set onto its parameter domain, possibly introducing
6299 * new, explicit, existential variables in the constraints.
6300 * The input has parameters and (possibly implicit) existential variables.
6301 * The output has the same parameters, but only
6302 * explicit existentially quantified variables.
6304 * The actual projection is performed by pip, but pip doesn't seem
6305 * to like equalities very much, so we first remove the equalities
6306 * among the parameters by performing a variable compression on
6307 * the parameters. Afterward, an inverse transformation is performed
6308 * and the equalities among the parameters are inserted back in.
6310 static struct isl_set *parameter_compute_divs(struct isl_basic_set *bset)
6314 struct isl_mat *T, *T2;
6315 struct isl_set *set;
6316 unsigned nparam, n_div;
6318 bset = isl_basic_set_cow(bset);
6322 if (bset->n_eq == 0)
6323 return isl_basic_set_lexmin(bset);
6325 isl_basic_set_gauss(bset, NULL);
6327 nparam = isl_basic_set_dim(bset, isl_dim_param);
6328 n_div = isl_basic_set_dim(bset, isl_dim_div);
6330 for (i = 0, j = n_div - 1; i < bset->n_eq && j >= 0; --j) {
6331 if (!isl_int_is_zero(bset->eq[i][1 + nparam + j]))
6334 if (i == bset->n_eq)
6335 return isl_basic_set_lexmin(bset);
6337 eq = isl_mat_sub_alloc6(bset->ctx, bset->eq, i, bset->n_eq - i,
6339 eq = isl_mat_cow(eq);
6340 T = isl_mat_variable_compression(isl_mat_copy(eq), &T2);
6341 if (T && T->n_col == 0) {
6345 bset = isl_basic_set_set_to_empty(bset);
6346 return isl_set_from_basic_set(bset);
6348 bset = basic_set_parameter_preimage(bset, T);
6350 set = isl_basic_set_lexmin(bset);
6351 set = set_parameter_preimage(set, T2);
6352 set = set_append_equalities(set, eq);
6356 /* Compute an explicit representation for all the existentially
6357 * quantified variables.
6358 * The input and output dimensions are first turned into parameters.
6359 * compute_divs then returns a map with the same parameters and
6360 * no input or output dimensions and the dimension specification
6361 * is reset to that of the input.
6363 static struct isl_map *compute_divs(struct isl_basic_map *bmap)
6365 struct isl_basic_set *bset;
6366 struct isl_set *set;
6367 struct isl_map *map;
6368 isl_space *dim, *orig_dim = NULL;
6373 bmap = isl_basic_map_cow(bmap);
6377 nparam = isl_basic_map_dim(bmap, isl_dim_param);
6378 n_in = isl_basic_map_dim(bmap, isl_dim_in);
6379 n_out = isl_basic_map_dim(bmap, isl_dim_out);
6380 dim = isl_space_set_alloc(bmap->ctx, nparam + n_in + n_out, 0);
6384 orig_dim = bmap->dim;
6386 bset = (struct isl_basic_set *)bmap;
6388 set = parameter_compute_divs(bset);
6389 map = (struct isl_map *)set;
6390 map = isl_map_reset_space(map, orig_dim);
6394 isl_basic_map_free(bmap);
6398 int isl_basic_map_divs_known(__isl_keep isl_basic_map *bmap)
6406 off = isl_space_dim(bmap->dim, isl_dim_all);
6407 for (i = 0; i < bmap->n_div; ++i) {
6408 if (isl_int_is_zero(bmap->div[i][0]))
6410 isl_assert(bmap->ctx, isl_int_is_zero(bmap->div[i][1+1+off+i]),
6416 static int map_divs_known(__isl_keep isl_map *map)
6423 for (i = 0; i < map->n; ++i) {
6424 int known = isl_basic_map_divs_known(map->p[i]);
6432 /* If bmap contains any unknown divs, then compute explicit
6433 * expressions for them. However, this computation may be
6434 * quite expensive, so first try to remove divs that aren't
6437 struct isl_map *isl_basic_map_compute_divs(struct isl_basic_map *bmap)
6440 struct isl_map *map;
6442 known = isl_basic_map_divs_known(bmap);
6446 return isl_map_from_basic_map(bmap);
6448 bmap = isl_basic_map_drop_redundant_divs(bmap);
6450 known = isl_basic_map_divs_known(bmap);
6454 return isl_map_from_basic_map(bmap);
6456 map = compute_divs(bmap);
6459 isl_basic_map_free(bmap);
6463 struct isl_map *isl_map_compute_divs(struct isl_map *map)
6467 struct isl_map *res;
6474 known = map_divs_known(map);
6482 res = isl_basic_map_compute_divs(isl_basic_map_copy(map->p[0]));
6483 for (i = 1 ; i < map->n; ++i) {
6485 r2 = isl_basic_map_compute_divs(isl_basic_map_copy(map->p[i]));
6486 if (ISL_F_ISSET(map, ISL_MAP_DISJOINT))
6487 res = isl_map_union_disjoint(res, r2);
6489 res = isl_map_union(res, r2);
6496 struct isl_set *isl_basic_set_compute_divs(struct isl_basic_set *bset)
6498 return (struct isl_set *)
6499 isl_basic_map_compute_divs((struct isl_basic_map *)bset);
6502 struct isl_set *isl_set_compute_divs(struct isl_set *set)
6504 return (struct isl_set *)
6505 isl_map_compute_divs((struct isl_map *)set);
6508 struct isl_set *isl_map_domain(struct isl_map *map)
6511 struct isl_set *set;
6516 map = isl_map_cow(map);
6520 set = (struct isl_set *)map;
6521 set->dim = isl_space_domain(set->dim);
6524 for (i = 0; i < map->n; ++i) {
6525 set->p[i] = isl_basic_map_domain(map->p[i]);
6529 ISL_F_CLR(set, ISL_MAP_DISJOINT);
6530 ISL_F_CLR(set, ISL_SET_NORMALIZED);
6537 /* Return the union of "map1" and "map2", where we assume for now that
6538 * "map1" and "map2" are disjoint. Note that the basic maps inside
6539 * "map1" or "map2" may not be disjoint from each other.
6540 * Also note that this function is also called from isl_map_union,
6541 * which takes care of handling the situation where "map1" and "map2"
6542 * may not be disjoint.
6544 * If one of the inputs is empty, we can simply return the other input.
6545 * Similarly, if one of the inputs is universal, then it is equal to the union.
6547 static __isl_give isl_map *map_union_disjoint(__isl_take isl_map *map1,
6548 __isl_take isl_map *map2)
6552 struct isl_map *map = NULL;
6567 is_universe = isl_map_plain_is_universe(map1);
6568 if (is_universe < 0)
6575 is_universe = isl_map_plain_is_universe(map2);
6576 if (is_universe < 0)
6583 isl_assert(map1->ctx, isl_space_is_equal(map1->dim, map2->dim), goto error);
6585 if (ISL_F_ISSET(map1, ISL_MAP_DISJOINT) &&
6586 ISL_F_ISSET(map2, ISL_MAP_DISJOINT))
6587 ISL_FL_SET(flags, ISL_MAP_DISJOINT);
6589 map = isl_map_alloc_space(isl_space_copy(map1->dim),
6590 map1->n + map2->n, flags);
6593 for (i = 0; i < map1->n; ++i) {
6594 map = isl_map_add_basic_map(map,
6595 isl_basic_map_copy(map1->p[i]));
6599 for (i = 0; i < map2->n; ++i) {
6600 map = isl_map_add_basic_map(map,
6601 isl_basic_map_copy(map2->p[i]));
6615 __isl_give isl_map *isl_map_union_disjoint(__isl_take isl_map *map1,
6616 __isl_take isl_map *map2)
6618 return isl_map_align_params_map_map_and(map1, map2, &map_union_disjoint);
6621 struct isl_map *isl_map_union(struct isl_map *map1, struct isl_map *map2)
6623 map1 = isl_map_union_disjoint(map1, map2);
6627 ISL_F_CLR(map1, ISL_MAP_DISJOINT);
6631 struct isl_set *isl_set_union_disjoint(
6632 struct isl_set *set1, struct isl_set *set2)
6634 return (struct isl_set *)
6635 isl_map_union_disjoint(
6636 (struct isl_map *)set1, (struct isl_map *)set2);
6639 struct isl_set *isl_set_union(struct isl_set *set1, struct isl_set *set2)
6641 return (struct isl_set *)
6642 isl_map_union((struct isl_map *)set1, (struct isl_map *)set2);
6645 /* Apply "fn" to pairs of elements from "map" and "set" and collect
6648 * "map" and "set" are assumed to be compatible and non-NULL.
6650 static __isl_give isl_map *map_intersect_set(__isl_take isl_map *map,
6651 __isl_take isl_set *set,
6652 __isl_give isl_basic_map *fn(__isl_take isl_basic_map *bmap,
6653 __isl_take isl_basic_set *bset))
6656 struct isl_map *result;
6659 if (isl_set_plain_is_universe(set)) {
6664 if (ISL_F_ISSET(map, ISL_MAP_DISJOINT) &&
6665 ISL_F_ISSET(set, ISL_MAP_DISJOINT))
6666 ISL_FL_SET(flags, ISL_MAP_DISJOINT);
6668 result = isl_map_alloc_space(isl_space_copy(map->dim),
6669 map->n * set->n, flags);
6670 for (i = 0; result && i < map->n; ++i)
6671 for (j = 0; j < set->n; ++j) {
6672 result = isl_map_add_basic_map(result,
6673 fn(isl_basic_map_copy(map->p[i]),
6674 isl_basic_set_copy(set->p[j])));
6684 static __isl_give isl_map *map_intersect_range(__isl_take isl_map *map,
6685 __isl_take isl_set *set)
6690 if (!isl_map_compatible_range(map, set))
6691 isl_die(set->ctx, isl_error_invalid,
6692 "incompatible spaces", goto error);
6694 return map_intersect_set(map, set, &isl_basic_map_intersect_range);
6701 __isl_give isl_map *isl_map_intersect_range(__isl_take isl_map *map,
6702 __isl_take isl_set *set)
6704 return isl_map_align_params_map_map_and(map, set, &map_intersect_range);
6707 static __isl_give isl_map *map_intersect_domain(__isl_take isl_map *map,
6708 __isl_take isl_set *set)
6713 if (!isl_map_compatible_domain(map, set))
6714 isl_die(set->ctx, isl_error_invalid,
6715 "incompatible spaces", goto error);
6717 return map_intersect_set(map, set, &isl_basic_map_intersect_domain);
6724 __isl_give isl_map *isl_map_intersect_domain(__isl_take isl_map *map,
6725 __isl_take isl_set *set)
6727 return isl_map_align_params_map_map_and(map, set,
6728 &map_intersect_domain);
6731 static __isl_give isl_map *map_apply_domain(__isl_take isl_map *map1,
6732 __isl_take isl_map *map2)
6736 map1 = isl_map_reverse(map1);
6737 map1 = isl_map_apply_range(map1, map2);
6738 return isl_map_reverse(map1);
6745 __isl_give isl_map *isl_map_apply_domain(__isl_take isl_map *map1,
6746 __isl_take isl_map *map2)
6748 return isl_map_align_params_map_map_and(map1, map2, &map_apply_domain);
6751 static __isl_give isl_map *map_apply_range(__isl_take isl_map *map1,
6752 __isl_take isl_map *map2)
6754 isl_space *dim_result;
6755 struct isl_map *result;
6761 dim_result = isl_space_join(isl_space_copy(map1->dim),
6762 isl_space_copy(map2->dim));
6764 result = isl_map_alloc_space(dim_result, map1->n * map2->n, 0);
6767 for (i = 0; i < map1->n; ++i)
6768 for (j = 0; j < map2->n; ++j) {
6769 result = isl_map_add_basic_map(result,
6770 isl_basic_map_apply_range(
6771 isl_basic_map_copy(map1->p[i]),
6772 isl_basic_map_copy(map2->p[j])));
6778 if (result && result->n <= 1)
6779 ISL_F_SET(result, ISL_MAP_DISJOINT);
6787 __isl_give isl_map *isl_map_apply_range(__isl_take isl_map *map1,
6788 __isl_take isl_map *map2)
6790 return isl_map_align_params_map_map_and(map1, map2, &map_apply_range);
6794 * returns range - domain
6796 struct isl_basic_set *isl_basic_map_deltas(struct isl_basic_map *bmap)
6798 isl_space *dims, *target_dim;
6799 struct isl_basic_set *bset;
6806 isl_assert(bmap->ctx, isl_space_tuple_match(bmap->dim, isl_dim_in,
6807 bmap->dim, isl_dim_out),
6809 target_dim = isl_space_domain(isl_basic_map_get_space(bmap));
6810 dim = isl_basic_map_n_in(bmap);
6811 nparam = isl_basic_map_n_param(bmap);
6812 bset = isl_basic_set_from_basic_map(bmap);
6813 bset = isl_basic_set_cow(bset);
6814 dims = isl_basic_set_get_space(bset);
6815 dims = isl_space_add_dims(dims, isl_dim_set, dim);
6816 bset = isl_basic_set_extend_space(bset, dims, 0, dim, 0);
6817 bset = isl_basic_set_swap_vars(bset, 2*dim);
6818 for (i = 0; i < dim; ++i) {
6819 int j = isl_basic_map_alloc_equality(
6820 (struct isl_basic_map *)bset);
6823 isl_seq_clr(bset->eq[j], 1 + isl_basic_set_total_dim(bset));
6824 isl_int_set_si(bset->eq[j][1+nparam+i], 1);
6825 isl_int_set_si(bset->eq[j][1+nparam+dim+i], 1);
6826 isl_int_set_si(bset->eq[j][1+nparam+2*dim+i], -1);
6828 bset = isl_basic_set_project_out(bset, isl_dim_set, dim, 2*dim);
6829 bset = isl_basic_set_reset_space(bset, target_dim);
6832 isl_basic_map_free(bmap);
6837 * returns range - domain
6839 __isl_give isl_set *isl_map_deltas(__isl_take isl_map *map)
6843 struct isl_set *result;
6848 isl_assert(map->ctx, isl_space_tuple_match(map->dim, isl_dim_in,
6849 map->dim, isl_dim_out),
6851 dim = isl_map_get_space(map);
6852 dim = isl_space_domain(dim);
6853 result = isl_set_alloc_space(dim, map->n, 0);
6856 for (i = 0; i < map->n; ++i)
6857 result = isl_set_add_basic_set(result,
6858 isl_basic_map_deltas(isl_basic_map_copy(map->p[i])));
6867 * returns [domain -> range] -> range - domain
6869 __isl_give isl_basic_map *isl_basic_map_deltas_map(
6870 __isl_take isl_basic_map *bmap)
6874 isl_basic_map *domain;
6878 if (!isl_space_tuple_match(bmap->dim, isl_dim_in, bmap->dim, isl_dim_out))
6879 isl_die(bmap->ctx, isl_error_invalid,
6880 "domain and range don't match", goto error);
6882 nparam = isl_basic_map_dim(bmap, isl_dim_param);
6883 n = isl_basic_map_dim(bmap, isl_dim_in);
6885 dim = isl_space_from_range(isl_space_domain(isl_basic_map_get_space(bmap)));
6886 domain = isl_basic_map_universe(dim);
6888 bmap = isl_basic_map_from_domain(isl_basic_map_wrap(bmap));
6889 bmap = isl_basic_map_apply_range(bmap, domain);
6890 bmap = isl_basic_map_extend_constraints(bmap, n, 0);
6892 total = isl_basic_map_total_dim(bmap);
6894 for (i = 0; i < n; ++i) {
6895 k = isl_basic_map_alloc_equality(bmap);
6898 isl_seq_clr(bmap->eq[k], 1 + total);
6899 isl_int_set_si(bmap->eq[k][1 + nparam + i], 1);
6900 isl_int_set_si(bmap->eq[k][1 + nparam + n + i], -1);
6901 isl_int_set_si(bmap->eq[k][1 + nparam + n + n + i], 1);
6904 bmap = isl_basic_map_gauss(bmap, NULL);
6905 return isl_basic_map_finalize(bmap);
6907 isl_basic_map_free(bmap);
6912 * returns [domain -> range] -> range - domain
6914 __isl_give isl_map *isl_map_deltas_map(__isl_take isl_map *map)
6917 isl_space *domain_dim;
6922 if (!isl_space_tuple_match(map->dim, isl_dim_in, map->dim, isl_dim_out))
6923 isl_die(map->ctx, isl_error_invalid,
6924 "domain and range don't match", goto error);
6926 map = isl_map_cow(map);
6930 domain_dim = isl_space_from_range(isl_space_domain(isl_map_get_space(map)));
6931 map->dim = isl_space_from_domain(isl_space_wrap(map->dim));
6932 map->dim = isl_space_join(map->dim, domain_dim);
6935 for (i = 0; i < map->n; ++i) {
6936 map->p[i] = isl_basic_map_deltas_map(map->p[i]);
6940 ISL_F_CLR(map, ISL_MAP_NORMALIZED);
6947 static __isl_give isl_basic_map *basic_map_identity(__isl_take isl_space *dims)
6949 struct isl_basic_map *bmap;
6957 nparam = dims->nparam;
6959 bmap = isl_basic_map_alloc_space(dims, 0, dim, 0);
6963 for (i = 0; i < dim; ++i) {
6964 int j = isl_basic_map_alloc_equality(bmap);
6967 isl_seq_clr(bmap->eq[j], 1 + isl_basic_map_total_dim(bmap));
6968 isl_int_set_si(bmap->eq[j][1+nparam+i], 1);
6969 isl_int_set_si(bmap->eq[j][1+nparam+dim+i], -1);
6971 return isl_basic_map_finalize(bmap);
6973 isl_basic_map_free(bmap);
6977 __isl_give isl_basic_map *isl_basic_map_identity(__isl_take isl_space *dim)
6981 if (dim->n_in != dim->n_out)
6982 isl_die(dim->ctx, isl_error_invalid,
6983 "number of input and output dimensions needs to be "
6984 "the same", goto error);
6985 return basic_map_identity(dim);
6987 isl_space_free(dim);
6991 struct isl_basic_map *isl_basic_map_identity_like(struct isl_basic_map *model)
6993 if (!model || !model->dim)
6995 return isl_basic_map_identity(isl_space_copy(model->dim));
6998 __isl_give isl_map *isl_map_identity(__isl_take isl_space *dim)
7000 return isl_map_from_basic_map(isl_basic_map_identity(dim));
7003 struct isl_map *isl_map_identity_like(struct isl_map *model)
7005 if (!model || !model->dim)
7007 return isl_map_identity(isl_space_copy(model->dim));
7010 struct isl_map *isl_map_identity_like_basic_map(struct isl_basic_map *model)
7012 if (!model || !model->dim)
7014 return isl_map_identity(isl_space_copy(model->dim));
7017 __isl_give isl_map *isl_set_identity(__isl_take isl_set *set)
7019 isl_space *dim = isl_set_get_space(set);
7021 id = isl_map_identity(isl_space_map_from_set(dim));
7022 return isl_map_intersect_range(id, set);
7025 /* Construct a basic set with all set dimensions having only non-negative
7028 __isl_give isl_basic_set *isl_basic_set_positive_orthant(
7029 __isl_take isl_space *space)
7034 struct isl_basic_set *bset;
7038 nparam = space->nparam;
7040 bset = isl_basic_set_alloc_space(space, 0, 0, dim);
7043 for (i = 0; i < dim; ++i) {
7044 int k = isl_basic_set_alloc_inequality(bset);
7047 isl_seq_clr(bset->ineq[k], 1 + isl_basic_set_total_dim(bset));
7048 isl_int_set_si(bset->ineq[k][1 + nparam + i], 1);
7052 isl_basic_set_free(bset);
7056 /* Construct the half-space x_pos >= 0.
7058 static __isl_give isl_basic_set *nonneg_halfspace(__isl_take isl_space *dim,
7062 isl_basic_set *nonneg;
7064 nonneg = isl_basic_set_alloc_space(dim, 0, 0, 1);
7065 k = isl_basic_set_alloc_inequality(nonneg);
7068 isl_seq_clr(nonneg->ineq[k], 1 + isl_basic_set_total_dim(nonneg));
7069 isl_int_set_si(nonneg->ineq[k][pos], 1);
7071 return isl_basic_set_finalize(nonneg);
7073 isl_basic_set_free(nonneg);
7077 /* Construct the half-space x_pos <= -1.
7079 static __isl_give isl_basic_set *neg_halfspace(__isl_take isl_space *dim, int pos)
7084 neg = isl_basic_set_alloc_space(dim, 0, 0, 1);
7085 k = isl_basic_set_alloc_inequality(neg);
7088 isl_seq_clr(neg->ineq[k], 1 + isl_basic_set_total_dim(neg));
7089 isl_int_set_si(neg->ineq[k][0], -1);
7090 isl_int_set_si(neg->ineq[k][pos], -1);
7092 return isl_basic_set_finalize(neg);
7094 isl_basic_set_free(neg);
7098 __isl_give isl_set *isl_set_split_dims(__isl_take isl_set *set,
7099 enum isl_dim_type type, unsigned first, unsigned n)
7102 isl_basic_set *nonneg;
7110 isl_assert(set->ctx, first + n <= isl_set_dim(set, type), goto error);
7112 for (i = 0; i < n; ++i) {
7113 nonneg = nonneg_halfspace(isl_set_get_space(set),
7114 pos(set->dim, type) + first + i);
7115 neg = neg_halfspace(isl_set_get_space(set),
7116 pos(set->dim, type) + first + i);
7118 set = isl_set_intersect(set, isl_basic_set_union(nonneg, neg));
7127 static int foreach_orthant(__isl_take isl_set *set, int *signs, int first,
7128 int len, int (*fn)(__isl_take isl_set *orthant, int *signs, void *user),
7135 if (isl_set_plain_is_empty(set)) {
7140 return fn(set, signs, user);
7143 half = isl_set_from_basic_set(nonneg_halfspace(isl_set_get_space(set),
7145 half = isl_set_intersect(half, isl_set_copy(set));
7146 if (foreach_orthant(half, signs, first + 1, len, fn, user) < 0)
7150 half = isl_set_from_basic_set(neg_halfspace(isl_set_get_space(set),
7152 half = isl_set_intersect(half, set);
7153 return foreach_orthant(half, signs, first + 1, len, fn, user);
7159 /* Call "fn" on the intersections of "set" with each of the orthants
7160 * (except for obviously empty intersections). The orthant is identified
7161 * by the signs array, with each entry having value 1 or -1 according
7162 * to the sign of the corresponding variable.
7164 int isl_set_foreach_orthant(__isl_keep isl_set *set,
7165 int (*fn)(__isl_take isl_set *orthant, int *signs, void *user),
7175 if (isl_set_plain_is_empty(set))
7178 nparam = isl_set_dim(set, isl_dim_param);
7179 nvar = isl_set_dim(set, isl_dim_set);
7181 signs = isl_alloc_array(set->ctx, int, nparam + nvar);
7183 r = foreach_orthant(isl_set_copy(set), signs, 0, nparam + nvar,
7191 int isl_set_is_equal(struct isl_set *set1, struct isl_set *set2)
7193 return isl_map_is_equal((struct isl_map *)set1, (struct isl_map *)set2);
7196 int isl_basic_map_is_subset(
7197 struct isl_basic_map *bmap1, struct isl_basic_map *bmap2)
7200 struct isl_map *map1;
7201 struct isl_map *map2;
7203 if (!bmap1 || !bmap2)
7206 map1 = isl_map_from_basic_map(isl_basic_map_copy(bmap1));
7207 map2 = isl_map_from_basic_map(isl_basic_map_copy(bmap2));
7209 is_subset = isl_map_is_subset(map1, map2);
7217 int isl_basic_set_is_subset(__isl_keep isl_basic_set *bset1,
7218 __isl_keep isl_basic_set *bset2)
7220 return isl_basic_map_is_subset(bset1, bset2);
7223 int isl_basic_map_is_equal(
7224 struct isl_basic_map *bmap1, struct isl_basic_map *bmap2)
7228 if (!bmap1 || !bmap2)
7230 is_subset = isl_basic_map_is_subset(bmap1, bmap2);
7233 is_subset = isl_basic_map_is_subset(bmap2, bmap1);
7237 int isl_basic_set_is_equal(
7238 struct isl_basic_set *bset1, struct isl_basic_set *bset2)
7240 return isl_basic_map_is_equal(
7241 (struct isl_basic_map *)bset1, (struct isl_basic_map *)bset2);
7244 int isl_map_is_empty(struct isl_map *map)
7251 for (i = 0; i < map->n; ++i) {
7252 is_empty = isl_basic_map_is_empty(map->p[i]);
7261 int isl_map_plain_is_empty(__isl_keep isl_map *map)
7263 return map ? map->n == 0 : -1;
7266 int isl_map_fast_is_empty(__isl_keep isl_map *map)
7268 return isl_map_plain_is_empty(map);
7271 int isl_set_plain_is_empty(struct isl_set *set)
7273 return set ? set->n == 0 : -1;
7276 int isl_set_fast_is_empty(__isl_keep isl_set *set)
7278 return isl_set_plain_is_empty(set);
7281 int isl_set_is_empty(struct isl_set *set)
7283 return isl_map_is_empty((struct isl_map *)set);
7286 int isl_map_has_equal_space(__isl_keep isl_map *map1, __isl_keep isl_map *map2)
7291 return isl_space_is_equal(map1->dim, map2->dim);
7294 int isl_set_has_equal_space(__isl_keep isl_set *set1, __isl_keep isl_set *set2)
7299 return isl_space_is_equal(set1->dim, set2->dim);
7302 static int map_is_equal(__isl_keep isl_map *map1, __isl_keep isl_map *map2)
7308 is_subset = isl_map_is_subset(map1, map2);
7311 is_subset = isl_map_is_subset(map2, map1);
7315 int isl_map_is_equal(__isl_keep isl_map *map1, __isl_keep isl_map *map2)
7317 return isl_map_align_params_map_map_and_test(map1, map2, &map_is_equal);
7320 int isl_basic_map_is_strict_subset(
7321 struct isl_basic_map *bmap1, struct isl_basic_map *bmap2)
7325 if (!bmap1 || !bmap2)
7327 is_subset = isl_basic_map_is_subset(bmap1, bmap2);
7330 is_subset = isl_basic_map_is_subset(bmap2, bmap1);
7331 if (is_subset == -1)
7336 int isl_map_is_strict_subset(struct isl_map *map1, struct isl_map *map2)
7342 is_subset = isl_map_is_subset(map1, map2);
7345 is_subset = isl_map_is_subset(map2, map1);
7346 if (is_subset == -1)
7351 int isl_set_is_strict_subset(__isl_keep isl_set *set1, __isl_keep isl_set *set2)
7353 return isl_map_is_strict_subset((isl_map *)set1, (isl_map *)set2);
7356 int isl_basic_map_is_universe(struct isl_basic_map *bmap)
7360 return bmap->n_eq == 0 && bmap->n_ineq == 0;
7363 int isl_basic_set_is_universe(struct isl_basic_set *bset)
7367 return bset->n_eq == 0 && bset->n_ineq == 0;
7370 int isl_map_plain_is_universe(__isl_keep isl_map *map)
7377 for (i = 0; i < map->n; ++i) {
7378 int r = isl_basic_map_is_universe(map->p[i]);
7386 int isl_set_plain_is_universe(__isl_keep isl_set *set)
7388 return isl_map_plain_is_universe((isl_map *) set);
7391 int isl_set_fast_is_universe(__isl_keep isl_set *set)
7393 return isl_set_plain_is_universe(set);
7396 int isl_basic_map_is_empty(struct isl_basic_map *bmap)
7398 struct isl_basic_set *bset = NULL;
7399 struct isl_vec *sample = NULL;
7406 if (ISL_F_ISSET(bmap, ISL_BASIC_MAP_EMPTY))
7409 if (isl_basic_map_is_universe(bmap))
7412 if (ISL_F_ISSET(bmap, ISL_BASIC_MAP_RATIONAL)) {
7413 struct isl_basic_map *copy = isl_basic_map_copy(bmap);
7414 copy = isl_basic_map_remove_redundancies(copy);
7415 empty = ISL_F_ISSET(copy, ISL_BASIC_MAP_EMPTY);
7416 isl_basic_map_free(copy);
7420 total = 1 + isl_basic_map_total_dim(bmap);
7421 if (bmap->sample && bmap->sample->size == total) {
7422 int contains = isl_basic_map_contains(bmap, bmap->sample);
7428 isl_vec_free(bmap->sample);
7429 bmap->sample = NULL;
7430 bset = isl_basic_map_underlying_set(isl_basic_map_copy(bmap));
7433 sample = isl_basic_set_sample_vec(bset);
7436 empty = sample->size == 0;
7437 isl_vec_free(bmap->sample);
7438 bmap->sample = sample;
7440 ISL_F_SET(bmap, ISL_BASIC_MAP_EMPTY);
7445 int isl_basic_map_plain_is_empty(__isl_keep isl_basic_map *bmap)
7449 return ISL_F_ISSET(bmap, ISL_BASIC_MAP_EMPTY);
7452 int isl_basic_map_fast_is_empty(__isl_keep isl_basic_map *bmap)
7454 return isl_basic_map_plain_is_empty(bmap);
7457 int isl_basic_set_plain_is_empty(__isl_keep isl_basic_set *bset)
7461 return ISL_F_ISSET(bset, ISL_BASIC_SET_EMPTY);
7464 int isl_basic_set_fast_is_empty(__isl_keep isl_basic_set *bset)
7466 return isl_basic_set_plain_is_empty(bset);
7469 int isl_basic_set_is_empty(struct isl_basic_set *bset)
7471 return isl_basic_map_is_empty((struct isl_basic_map *)bset);
7474 struct isl_map *isl_basic_map_union(
7475 struct isl_basic_map *bmap1, struct isl_basic_map *bmap2)
7477 struct isl_map *map;
7478 if (!bmap1 || !bmap2)
7481 isl_assert(bmap1->ctx, isl_space_is_equal(bmap1->dim, bmap2->dim), goto error);
7483 map = isl_map_alloc_space(isl_space_copy(bmap1->dim), 2, 0);
7486 map = isl_map_add_basic_map(map, bmap1);
7487 map = isl_map_add_basic_map(map, bmap2);
7490 isl_basic_map_free(bmap1);
7491 isl_basic_map_free(bmap2);
7495 struct isl_set *isl_basic_set_union(
7496 struct isl_basic_set *bset1, struct isl_basic_set *bset2)
7498 return (struct isl_set *)isl_basic_map_union(
7499 (struct isl_basic_map *)bset1,
7500 (struct isl_basic_map *)bset2);
7503 /* Order divs such that any div only depends on previous divs */
7504 struct isl_basic_map *isl_basic_map_order_divs(struct isl_basic_map *bmap)
7512 off = isl_space_dim(bmap->dim, isl_dim_all);
7514 for (i = 0; i < bmap->n_div; ++i) {
7516 if (isl_int_is_zero(bmap->div[i][0]))
7518 pos = isl_seq_first_non_zero(bmap->div[i]+1+1+off+i,
7522 isl_basic_map_swap_div(bmap, i, i + pos);
7528 struct isl_basic_set *isl_basic_set_order_divs(struct isl_basic_set *bset)
7530 return (struct isl_basic_set *)
7531 isl_basic_map_order_divs((struct isl_basic_map *)bset);
7534 __isl_give isl_map *isl_map_order_divs(__isl_take isl_map *map)
7541 for (i = 0; i < map->n; ++i) {
7542 map->p[i] = isl_basic_map_order_divs(map->p[i]);
7553 /* Apply the expansion computed by isl_merge_divs.
7554 * The expansion itself is given by "exp" while the resulting
7555 * list of divs is given by "div".
7557 __isl_give isl_basic_set *isl_basic_set_expand_divs(
7558 __isl_take isl_basic_set *bset, __isl_take isl_mat *div, int *exp)
7563 bset = isl_basic_set_cow(bset);
7567 if (div->n_row < bset->n_div)
7568 isl_die(isl_mat_get_ctx(div), isl_error_invalid,
7569 "not an expansion", goto error);
7571 bset = isl_basic_map_extend_space(bset, isl_space_copy(bset->dim),
7572 div->n_row - bset->n_div, 0,
7573 2 * (div->n_row - bset->n_div));
7575 n_div = bset->n_div;
7576 for (i = n_div; i < div->n_row; ++i)
7577 if (isl_basic_set_alloc_div(bset) < 0)
7581 for (i = div->n_row - 1; i >= 0; --i) {
7582 if (j >= 0 && exp[j] == i) {
7584 isl_basic_map_swap_div(bset, i, j);
7587 isl_seq_cpy(bset->div[i], div->row[i], div->n_col);
7588 if (isl_basic_map_add_div_constraints(bset, i) < 0)
7596 isl_basic_set_free(bset);
7601 /* Look for a div in dst that corresponds to the div "div" in src.
7602 * The divs before "div" in src and dst are assumed to be the same.
7604 * Returns -1 if no corresponding div was found and the position
7605 * of the corresponding div in dst otherwise.
7607 static int find_div(struct isl_basic_map *dst,
7608 struct isl_basic_map *src, unsigned div)
7612 unsigned total = isl_space_dim(src->dim, isl_dim_all);
7614 isl_assert(dst->ctx, div <= dst->n_div, return -1);
7615 for (i = div; i < dst->n_div; ++i)
7616 if (isl_seq_eq(dst->div[i], src->div[div], 1+1+total+div) &&
7617 isl_seq_first_non_zero(dst->div[i]+1+1+total+div,
7618 dst->n_div - div) == -1)
7623 struct isl_basic_map *isl_basic_map_align_divs(
7624 struct isl_basic_map *dst, struct isl_basic_map *src)
7632 if (src->n_div == 0)
7635 for (i = 0; i < src->n_div; ++i)
7636 isl_assert(src->ctx, !isl_int_is_zero(src->div[i][0]), goto error);
7638 src = isl_basic_map_order_divs(src);
7639 dst = isl_basic_map_cow(dst);
7640 dst = isl_basic_map_extend_space(dst, isl_space_copy(dst->dim),
7641 src->n_div, 0, 2 * src->n_div);
7644 total = isl_space_dim(src->dim, isl_dim_all);
7645 for (i = 0; i < src->n_div; ++i) {
7646 int j = find_div(dst, src, i);
7648 j = isl_basic_map_alloc_div(dst);
7651 isl_seq_cpy(dst->div[j], src->div[i], 1+1+total+i);
7652 isl_seq_clr(dst->div[j]+1+1+total+i, dst->n_div - i);
7653 if (isl_basic_map_add_div_constraints(dst, j) < 0)
7657 isl_basic_map_swap_div(dst, i, j);
7661 isl_basic_map_free(dst);
7665 struct isl_basic_set *isl_basic_set_align_divs(
7666 struct isl_basic_set *dst, struct isl_basic_set *src)
7668 return (struct isl_basic_set *)isl_basic_map_align_divs(
7669 (struct isl_basic_map *)dst, (struct isl_basic_map *)src);
7672 struct isl_map *isl_map_align_divs(struct isl_map *map)
7680 map = isl_map_compute_divs(map);
7681 map = isl_map_cow(map);
7685 for (i = 1; i < map->n; ++i)
7686 map->p[0] = isl_basic_map_align_divs(map->p[0], map->p[i]);
7687 for (i = 1; i < map->n; ++i)
7688 map->p[i] = isl_basic_map_align_divs(map->p[i], map->p[0]);
7690 ISL_F_CLR(map, ISL_MAP_NORMALIZED);
7694 struct isl_set *isl_set_align_divs(struct isl_set *set)
7696 return (struct isl_set *)isl_map_align_divs((struct isl_map *)set);
7699 static __isl_give isl_set *set_apply( __isl_take isl_set *set,
7700 __isl_take isl_map *map)
7704 isl_assert(set->ctx, isl_map_compatible_domain(map, set), goto error);
7705 map = isl_map_intersect_domain(map, set);
7706 set = isl_map_range(map);
7714 __isl_give isl_set *isl_set_apply( __isl_take isl_set *set,
7715 __isl_take isl_map *map)
7717 return isl_map_align_params_map_map_and(set, map, &set_apply);
7720 /* There is no need to cow as removing empty parts doesn't change
7721 * the meaning of the set.
7723 struct isl_map *isl_map_remove_empty_parts(struct isl_map *map)
7730 for (i = map->n - 1; i >= 0; --i)
7731 remove_if_empty(map, i);
7736 struct isl_set *isl_set_remove_empty_parts(struct isl_set *set)
7738 return (struct isl_set *)
7739 isl_map_remove_empty_parts((struct isl_map *)set);
7742 struct isl_basic_map *isl_map_copy_basic_map(struct isl_map *map)
7744 struct isl_basic_map *bmap;
7745 if (!map || map->n == 0)
7747 bmap = map->p[map->n-1];
7748 isl_assert(map->ctx, ISL_F_ISSET(bmap, ISL_BASIC_SET_FINAL), return NULL);
7749 return isl_basic_map_copy(bmap);
7752 struct isl_basic_set *isl_set_copy_basic_set(struct isl_set *set)
7754 return (struct isl_basic_set *)
7755 isl_map_copy_basic_map((struct isl_map *)set);
7758 __isl_give isl_map *isl_map_drop_basic_map(__isl_take isl_map *map,
7759 __isl_keep isl_basic_map *bmap)
7765 for (i = map->n-1; i >= 0; --i) {
7766 if (map->p[i] != bmap)
7768 map = isl_map_cow(map);
7771 isl_basic_map_free(map->p[i]);
7772 if (i != map->n-1) {
7773 ISL_F_CLR(map, ISL_SET_NORMALIZED);
7774 map->p[i] = map->p[map->n-1];
7785 struct isl_set *isl_set_drop_basic_set(struct isl_set *set,
7786 struct isl_basic_set *bset)
7788 return (struct isl_set *)isl_map_drop_basic_map((struct isl_map *)set,
7789 (struct isl_basic_map *)bset);
7792 /* Given two basic sets bset1 and bset2, compute the maximal difference
7793 * between the values of dimension pos in bset1 and those in bset2
7794 * for any common value of the parameters and dimensions preceding pos.
7796 static enum isl_lp_result basic_set_maximal_difference_at(
7797 __isl_keep isl_basic_set *bset1, __isl_keep isl_basic_set *bset2,
7798 int pos, isl_int *opt)
7801 struct isl_basic_map *bmap1 = NULL;
7802 struct isl_basic_map *bmap2 = NULL;
7803 struct isl_ctx *ctx;
7804 struct isl_vec *obj;
7807 unsigned dim1, dim2;
7808 enum isl_lp_result res;
7810 if (!bset1 || !bset2)
7811 return isl_lp_error;
7813 nparam = isl_basic_set_n_param(bset1);
7814 dim1 = isl_basic_set_n_dim(bset1);
7815 dim2 = isl_basic_set_n_dim(bset2);
7816 dims = isl_space_alloc(bset1->ctx, nparam, pos, dim1 - pos);
7817 bmap1 = isl_basic_map_from_basic_set(isl_basic_set_copy(bset1), dims);
7818 dims = isl_space_alloc(bset2->ctx, nparam, pos, dim2 - pos);
7819 bmap2 = isl_basic_map_from_basic_set(isl_basic_set_copy(bset2), dims);
7820 if (!bmap1 || !bmap2)
7822 bmap1 = isl_basic_map_cow(bmap1);
7823 bmap1 = isl_basic_map_extend(bmap1, nparam,
7824 pos, (dim1 - pos) + (dim2 - pos),
7825 bmap2->n_div, bmap2->n_eq, bmap2->n_ineq);
7826 bmap1 = add_constraints(bmap1, bmap2, 0, dim1 - pos);
7829 total = isl_basic_map_total_dim(bmap1);
7831 obj = isl_vec_alloc(ctx, 1 + total);
7832 isl_seq_clr(obj->block.data, 1 + total);
7833 isl_int_set_si(obj->block.data[1+nparam+pos], 1);
7834 isl_int_set_si(obj->block.data[1+nparam+pos+(dim1-pos)], -1);
7837 res = isl_basic_map_solve_lp(bmap1, 1, obj->block.data, ctx->one,
7839 isl_basic_map_free(bmap1);
7843 isl_basic_map_free(bmap1);
7844 isl_basic_map_free(bmap2);
7845 return isl_lp_error;
7848 /* Given two _disjoint_ basic sets bset1 and bset2, check whether
7849 * for any common value of the parameters and dimensions preceding pos
7850 * in both basic sets, the values of dimension pos in bset1 are
7851 * smaller or larger than those in bset2.
7854 * 1 if bset1 follows bset2
7855 * -1 if bset1 precedes bset2
7856 * 0 if bset1 and bset2 are incomparable
7857 * -2 if some error occurred.
7859 int isl_basic_set_compare_at(struct isl_basic_set *bset1,
7860 struct isl_basic_set *bset2, int pos)
7863 enum isl_lp_result res;
7868 res = basic_set_maximal_difference_at(bset1, bset2, pos, &opt);
7870 if (res == isl_lp_empty)
7872 else if ((res == isl_lp_ok && isl_int_is_pos(opt)) ||
7873 res == isl_lp_unbounded)
7875 else if (res == isl_lp_ok && isl_int_is_neg(opt))
7884 /* Given two basic sets bset1 and bset2, check whether
7885 * for any common value of the parameters and dimensions preceding pos
7886 * there is a value of dimension pos in bset1 that is larger
7887 * than a value of the same dimension in bset2.
7890 * 1 if there exists such a pair
7891 * 0 if there is no such pair, but there is a pair of equal values
7893 * -2 if some error occurred.
7895 int isl_basic_set_follows_at(__isl_keep isl_basic_set *bset1,
7896 __isl_keep isl_basic_set *bset2, int pos)
7899 enum isl_lp_result res;
7904 res = basic_set_maximal_difference_at(bset1, bset2, pos, &opt);
7906 if (res == isl_lp_empty)
7908 else if ((res == isl_lp_ok && isl_int_is_pos(opt)) ||
7909 res == isl_lp_unbounded)
7911 else if (res == isl_lp_ok && isl_int_is_neg(opt))
7913 else if (res == isl_lp_ok)
7922 /* Given two sets set1 and set2, check whether
7923 * for any common value of the parameters and dimensions preceding pos
7924 * there is a value of dimension pos in set1 that is larger
7925 * than a value of the same dimension in set2.
7928 * 1 if there exists such a pair
7929 * 0 if there is no such pair, but there is a pair of equal values
7931 * -2 if some error occurred.
7933 int isl_set_follows_at(__isl_keep isl_set *set1,
7934 __isl_keep isl_set *set2, int pos)
7942 for (i = 0; i < set1->n; ++i)
7943 for (j = 0; j < set2->n; ++j) {
7945 f = isl_basic_set_follows_at(set1->p[i], set2->p[j], pos);
7946 if (f == 1 || f == -2)
7955 static int isl_basic_map_plain_has_fixed_var(__isl_keep isl_basic_map *bmap,
7956 unsigned pos, isl_int *val)
7964 total = isl_basic_map_total_dim(bmap);
7965 for (i = 0, d = total-1; i < bmap->n_eq && d+1 > pos; ++i) {
7966 for (; d+1 > pos; --d)
7967 if (!isl_int_is_zero(bmap->eq[i][1+d]))
7971 if (isl_seq_first_non_zero(bmap->eq[i]+1, d) != -1)
7973 if (isl_seq_first_non_zero(bmap->eq[i]+1+d+1, total-d-1) != -1)
7975 if (!isl_int_is_one(bmap->eq[i][1+d]))
7978 isl_int_neg(*val, bmap->eq[i][0]);
7984 static int isl_map_plain_has_fixed_var(__isl_keep isl_map *map,
7985 unsigned pos, isl_int *val)
7997 return isl_basic_map_plain_has_fixed_var(map->p[0], pos, val);
8000 fixed = isl_basic_map_plain_has_fixed_var(map->p[0], pos, &v);
8001 for (i = 1; fixed == 1 && i < map->n; ++i) {
8002 fixed = isl_basic_map_plain_has_fixed_var(map->p[i], pos, &tmp);
8003 if (fixed == 1 && isl_int_ne(tmp, v))
8007 isl_int_set(*val, v);
8013 static int isl_basic_set_plain_has_fixed_var(__isl_keep isl_basic_set *bset,
8014 unsigned pos, isl_int *val)
8016 return isl_basic_map_plain_has_fixed_var((struct isl_basic_map *)bset,
8020 static int isl_set_plain_has_fixed_var(__isl_keep isl_set *set, unsigned pos,
8023 return isl_map_plain_has_fixed_var((struct isl_map *)set, pos, val);
8026 int isl_basic_map_plain_is_fixed(__isl_keep isl_basic_map *bmap,
8027 enum isl_dim_type type, unsigned pos, isl_int *val)
8029 if (pos >= isl_basic_map_dim(bmap, type))
8031 return isl_basic_map_plain_has_fixed_var(bmap,
8032 isl_basic_map_offset(bmap, type) - 1 + pos, val);
8035 int isl_map_plain_is_fixed(__isl_keep isl_map *map,
8036 enum isl_dim_type type, unsigned pos, isl_int *val)
8038 if (pos >= isl_map_dim(map, type))
8040 return isl_map_plain_has_fixed_var(map,
8041 map_offset(map, type) - 1 + pos, val);
8044 int isl_set_plain_is_fixed(__isl_keep isl_set *set,
8045 enum isl_dim_type type, unsigned pos, isl_int *val)
8047 return isl_map_plain_is_fixed(set, type, pos, val);
8050 int isl_map_fast_is_fixed(__isl_keep isl_map *map,
8051 enum isl_dim_type type, unsigned pos, isl_int *val)
8053 return isl_map_plain_is_fixed(map, type, pos, val);
8056 /* Check if dimension dim has fixed value and if so and if val is not NULL,
8057 * then return this fixed value in *val.
8059 int isl_basic_set_plain_dim_is_fixed(__isl_keep isl_basic_set *bset,
8060 unsigned dim, isl_int *val)
8062 return isl_basic_set_plain_has_fixed_var(bset,
8063 isl_basic_set_n_param(bset) + dim, val);
8066 /* Check if dimension dim has fixed value and if so and if val is not NULL,
8067 * then return this fixed value in *val.
8069 int isl_set_plain_dim_is_fixed(__isl_keep isl_set *set,
8070 unsigned dim, isl_int *val)
8072 return isl_set_plain_has_fixed_var(set, isl_set_n_param(set) + dim, val);
8075 int isl_set_fast_dim_is_fixed(__isl_keep isl_set *set,
8076 unsigned dim, isl_int *val)
8078 return isl_set_plain_dim_is_fixed(set, dim, val);
8081 /* Check if input variable in has fixed value and if so and if val is not NULL,
8082 * then return this fixed value in *val.
8084 int isl_map_plain_input_is_fixed(__isl_keep isl_map *map,
8085 unsigned in, isl_int *val)
8087 return isl_map_plain_has_fixed_var(map, isl_map_n_param(map) + in, val);
8090 /* Check if dimension dim has an (obvious) fixed lower bound and if so
8091 * and if val is not NULL, then return this lower bound in *val.
8093 int isl_basic_set_plain_dim_has_fixed_lower_bound(
8094 __isl_keep isl_basic_set *bset, unsigned dim, isl_int *val)
8096 int i, i_eq = -1, i_ineq = -1;
8103 total = isl_basic_set_total_dim(bset);
8104 nparam = isl_basic_set_n_param(bset);
8105 for (i = 0; i < bset->n_eq; ++i) {
8106 if (isl_int_is_zero(bset->eq[i][1+nparam+dim]))
8112 for (i = 0; i < bset->n_ineq; ++i) {
8113 if (!isl_int_is_pos(bset->ineq[i][1+nparam+dim]))
8115 if (i_eq != -1 || i_ineq != -1)
8119 if (i_eq == -1 && i_ineq == -1)
8121 c = i_eq != -1 ? bset->eq[i_eq] : bset->ineq[i_ineq];
8122 /* The coefficient should always be one due to normalization. */
8123 if (!isl_int_is_one(c[1+nparam+dim]))
8125 if (isl_seq_first_non_zero(c+1, nparam+dim) != -1)
8127 if (isl_seq_first_non_zero(c+1+nparam+dim+1,
8128 total - nparam - dim - 1) != -1)
8131 isl_int_neg(*val, c[0]);
8135 int isl_set_plain_dim_has_fixed_lower_bound(__isl_keep isl_set *set,
8136 unsigned dim, isl_int *val)
8148 return isl_basic_set_plain_dim_has_fixed_lower_bound(set->p[0],
8152 fixed = isl_basic_set_plain_dim_has_fixed_lower_bound(set->p[0],
8154 for (i = 1; fixed == 1 && i < set->n; ++i) {
8155 fixed = isl_basic_set_plain_dim_has_fixed_lower_bound(set->p[i],
8157 if (fixed == 1 && isl_int_ne(tmp, v))
8161 isl_int_set(*val, v);
8172 /* uset_gist depends on constraints without existentially quantified
8173 * variables sorting first.
8175 static int qsort_constraint_cmp(const void *p1, const void *p2)
8177 const struct constraint *c1 = (const struct constraint *)p1;
8178 const struct constraint *c2 = (const struct constraint *)p2;
8180 unsigned size = isl_min(c1->size, c2->size);
8182 l1 = isl_seq_last_non_zero(c1->c, size);
8183 l2 = isl_seq_last_non_zero(c2->c, size);
8188 return isl_seq_cmp(c1->c, c2->c, size);
8191 static struct isl_basic_map *isl_basic_map_sort_constraints(
8192 struct isl_basic_map *bmap)
8195 struct constraint *c;
8200 total = isl_basic_map_total_dim(bmap);
8201 c = isl_alloc_array(bmap->ctx, struct constraint, bmap->n_ineq);
8204 for (i = 0; i < bmap->n_ineq; ++i) {
8206 c[i].c = bmap->ineq[i];
8208 qsort(c, bmap->n_ineq, sizeof(struct constraint), qsort_constraint_cmp);
8209 for (i = 0; i < bmap->n_ineq; ++i)
8210 bmap->ineq[i] = c[i].c;
8214 isl_basic_map_free(bmap);
8218 __isl_give isl_basic_set *isl_basic_set_sort_constraints(
8219 __isl_take isl_basic_set *bset)
8221 return (struct isl_basic_set *)isl_basic_map_sort_constraints(
8222 (struct isl_basic_map *)bset);
8225 struct isl_basic_map *isl_basic_map_normalize(struct isl_basic_map *bmap)
8229 if (ISL_F_ISSET(bmap, ISL_BASIC_MAP_NORMALIZED))
8231 bmap = isl_basic_map_remove_redundancies(bmap);
8232 bmap = isl_basic_map_sort_constraints(bmap);
8233 ISL_F_SET(bmap, ISL_BASIC_MAP_NORMALIZED);
8237 struct isl_basic_set *isl_basic_set_normalize(struct isl_basic_set *bset)
8239 return (struct isl_basic_set *)isl_basic_map_normalize(
8240 (struct isl_basic_map *)bset);
8243 int isl_basic_map_plain_cmp(const __isl_keep isl_basic_map *bmap1,
8244 const __isl_keep isl_basic_map *bmap2)
8251 if (ISL_F_ISSET(bmap1, ISL_BASIC_MAP_RATIONAL) !=
8252 ISL_F_ISSET(bmap2, ISL_BASIC_MAP_RATIONAL))
8253 return ISL_F_ISSET(bmap1, ISL_BASIC_MAP_RATIONAL) ? -1 : 1;
8254 if (isl_basic_map_n_param(bmap1) != isl_basic_map_n_param(bmap2))
8255 return isl_basic_map_n_param(bmap1) - isl_basic_map_n_param(bmap2);
8256 if (isl_basic_map_n_in(bmap1) != isl_basic_map_n_in(bmap2))
8257 return isl_basic_map_n_out(bmap1) - isl_basic_map_n_out(bmap2);
8258 if (isl_basic_map_n_out(bmap1) != isl_basic_map_n_out(bmap2))
8259 return isl_basic_map_n_out(bmap1) - isl_basic_map_n_out(bmap2);
8260 if (ISL_F_ISSET(bmap1, ISL_BASIC_MAP_EMPTY) &&
8261 ISL_F_ISSET(bmap2, ISL_BASIC_MAP_EMPTY))
8263 if (ISL_F_ISSET(bmap1, ISL_BASIC_MAP_EMPTY))
8265 if (ISL_F_ISSET(bmap2, ISL_BASIC_MAP_EMPTY))
8267 if (bmap1->n_eq != bmap2->n_eq)
8268 return bmap1->n_eq - bmap2->n_eq;
8269 if (bmap1->n_ineq != bmap2->n_ineq)
8270 return bmap1->n_ineq - bmap2->n_ineq;
8271 if (bmap1->n_div != bmap2->n_div)
8272 return bmap1->n_div - bmap2->n_div;
8273 total = isl_basic_map_total_dim(bmap1);
8274 for (i = 0; i < bmap1->n_eq; ++i) {
8275 cmp = isl_seq_cmp(bmap1->eq[i], bmap2->eq[i], 1+total);
8279 for (i = 0; i < bmap1->n_ineq; ++i) {
8280 cmp = isl_seq_cmp(bmap1->ineq[i], bmap2->ineq[i], 1+total);
8284 for (i = 0; i < bmap1->n_div; ++i) {
8285 cmp = isl_seq_cmp(bmap1->div[i], bmap2->div[i], 1+1+total);
8292 int isl_basic_set_plain_cmp(const __isl_keep isl_basic_set *bset1,
8293 const __isl_keep isl_basic_set *bset2)
8295 return isl_basic_map_plain_cmp(bset1, bset2);
8298 int isl_set_plain_cmp(__isl_keep isl_set *set1, __isl_keep isl_set *set2)
8304 if (set1->n != set2->n)
8305 return set1->n - set2->n;
8307 for (i = 0; i < set1->n; ++i) {
8308 cmp = isl_basic_set_plain_cmp(set1->p[i], set2->p[i]);
8316 int isl_basic_map_plain_is_equal(__isl_keep isl_basic_map *bmap1,
8317 __isl_keep isl_basic_map *bmap2)
8319 return isl_basic_map_plain_cmp(bmap1, bmap2) == 0;
8322 int isl_basic_set_plain_is_equal(__isl_keep isl_basic_set *bset1,
8323 __isl_keep isl_basic_set *bset2)
8325 return isl_basic_map_plain_is_equal((isl_basic_map *)bset1,
8326 (isl_basic_map *)bset2);
8329 static int qsort_bmap_cmp(const void *p1, const void *p2)
8331 const struct isl_basic_map *bmap1 = *(const struct isl_basic_map **)p1;
8332 const struct isl_basic_map *bmap2 = *(const struct isl_basic_map **)p2;
8334 return isl_basic_map_plain_cmp(bmap1, bmap2);
8337 /* We normalize in place, but if anything goes wrong we need
8338 * to return NULL, so we need to make sure we don't change the
8339 * meaning of any possible other copies of map.
8341 struct isl_map *isl_map_normalize(struct isl_map *map)
8344 struct isl_basic_map *bmap;
8348 if (ISL_F_ISSET(map, ISL_MAP_NORMALIZED))
8350 for (i = 0; i < map->n; ++i) {
8351 bmap = isl_basic_map_normalize(isl_basic_map_copy(map->p[i]));
8354 isl_basic_map_free(map->p[i]);
8357 qsort(map->p, map->n, sizeof(struct isl_basic_map *), qsort_bmap_cmp);
8358 ISL_F_SET(map, ISL_MAP_NORMALIZED);
8359 map = isl_map_remove_empty_parts(map);
8362 for (i = map->n - 1; i >= 1; --i) {
8363 if (!isl_basic_map_plain_is_equal(map->p[i-1], map->p[i]))
8365 isl_basic_map_free(map->p[i-1]);
8366 for (j = i; j < map->n; ++j)
8367 map->p[j-1] = map->p[j];
8377 struct isl_set *isl_set_normalize(struct isl_set *set)
8379 return (struct isl_set *)isl_map_normalize((struct isl_map *)set);
8382 int isl_map_plain_is_equal(__isl_keep isl_map *map1, __isl_keep isl_map *map2)
8392 if (!isl_space_is_equal(map1->dim, map2->dim))
8395 map1 = isl_map_copy(map1);
8396 map2 = isl_map_copy(map2);
8397 map1 = isl_map_normalize(map1);
8398 map2 = isl_map_normalize(map2);
8401 equal = map1->n == map2->n;
8402 for (i = 0; equal && i < map1->n; ++i) {
8403 equal = isl_basic_map_plain_is_equal(map1->p[i], map2->p[i]);
8416 int isl_map_fast_is_equal(__isl_keep isl_map *map1, __isl_keep isl_map *map2)
8418 return isl_map_plain_is_equal(map1, map2);
8421 int isl_set_plain_is_equal(__isl_keep isl_set *set1, __isl_keep isl_set *set2)
8423 return isl_map_plain_is_equal((struct isl_map *)set1,
8424 (struct isl_map *)set2);
8427 int isl_set_fast_is_equal(__isl_keep isl_set *set1, __isl_keep isl_set *set2)
8429 return isl_set_plain_is_equal(set1, set2);
8432 /* Return an interval that ranges from min to max (inclusive)
8434 struct isl_basic_set *isl_basic_set_interval(struct isl_ctx *ctx,
8435 isl_int min, isl_int max)
8438 struct isl_basic_set *bset = NULL;
8440 bset = isl_basic_set_alloc(ctx, 0, 1, 0, 0, 2);
8444 k = isl_basic_set_alloc_inequality(bset);
8447 isl_int_set_si(bset->ineq[k][1], 1);
8448 isl_int_neg(bset->ineq[k][0], min);
8450 k = isl_basic_set_alloc_inequality(bset);
8453 isl_int_set_si(bset->ineq[k][1], -1);
8454 isl_int_set(bset->ineq[k][0], max);
8458 isl_basic_set_free(bset);
8462 /* Return the Cartesian product of the basic sets in list (in the given order).
8464 __isl_give isl_basic_set *isl_basic_set_list_product(
8465 __isl_take struct isl_basic_set_list *list)
8473 struct isl_basic_set *product = NULL;
8477 isl_assert(list->ctx, list->n > 0, goto error);
8478 isl_assert(list->ctx, list->p[0], goto error);
8479 nparam = isl_basic_set_n_param(list->p[0]);
8480 dim = isl_basic_set_n_dim(list->p[0]);
8481 extra = list->p[0]->n_div;
8482 n_eq = list->p[0]->n_eq;
8483 n_ineq = list->p[0]->n_ineq;
8484 for (i = 1; i < list->n; ++i) {
8485 isl_assert(list->ctx, list->p[i], goto error);
8486 isl_assert(list->ctx,
8487 nparam == isl_basic_set_n_param(list->p[i]), goto error);
8488 dim += isl_basic_set_n_dim(list->p[i]);
8489 extra += list->p[i]->n_div;
8490 n_eq += list->p[i]->n_eq;
8491 n_ineq += list->p[i]->n_ineq;
8493 product = isl_basic_set_alloc(list->ctx, nparam, dim, extra,
8498 for (i = 0; i < list->n; ++i) {
8499 isl_basic_set_add_constraints(product,
8500 isl_basic_set_copy(list->p[i]), dim);
8501 dim += isl_basic_set_n_dim(list->p[i]);
8503 isl_basic_set_list_free(list);
8506 isl_basic_set_free(product);
8507 isl_basic_set_list_free(list);
8511 struct isl_basic_map *isl_basic_map_product(
8512 struct isl_basic_map *bmap1, struct isl_basic_map *bmap2)
8514 isl_space *dim_result = NULL;
8515 struct isl_basic_map *bmap;
8516 unsigned in1, in2, out1, out2, nparam, total, pos;
8517 struct isl_dim_map *dim_map1, *dim_map2;
8519 if (!bmap1 || !bmap2)
8522 isl_assert(bmap1->ctx, isl_space_match(bmap1->dim, isl_dim_param,
8523 bmap2->dim, isl_dim_param), goto error);
8524 dim_result = isl_space_product(isl_space_copy(bmap1->dim),
8525 isl_space_copy(bmap2->dim));
8527 in1 = isl_basic_map_n_in(bmap1);
8528 in2 = isl_basic_map_n_in(bmap2);
8529 out1 = isl_basic_map_n_out(bmap1);
8530 out2 = isl_basic_map_n_out(bmap2);
8531 nparam = isl_basic_map_n_param(bmap1);
8533 total = nparam + in1 + in2 + out1 + out2 + bmap1->n_div + bmap2->n_div;
8534 dim_map1 = isl_dim_map_alloc(bmap1->ctx, total);
8535 dim_map2 = isl_dim_map_alloc(bmap1->ctx, total);
8536 isl_dim_map_dim(dim_map1, bmap1->dim, isl_dim_param, pos = 0);
8537 isl_dim_map_dim(dim_map2, bmap2->dim, isl_dim_param, pos = 0);
8538 isl_dim_map_dim(dim_map1, bmap1->dim, isl_dim_in, pos += nparam);
8539 isl_dim_map_dim(dim_map2, bmap2->dim, isl_dim_in, pos += in1);
8540 isl_dim_map_dim(dim_map1, bmap1->dim, isl_dim_out, pos += in2);
8541 isl_dim_map_dim(dim_map2, bmap2->dim, isl_dim_out, pos += out1);
8542 isl_dim_map_div(dim_map1, bmap1, pos += out2);
8543 isl_dim_map_div(dim_map2, bmap2, pos += bmap1->n_div);
8545 bmap = isl_basic_map_alloc_space(dim_result,
8546 bmap1->n_div + bmap2->n_div,
8547 bmap1->n_eq + bmap2->n_eq,
8548 bmap1->n_ineq + bmap2->n_ineq);
8549 bmap = isl_basic_map_add_constraints_dim_map(bmap, bmap1, dim_map1);
8550 bmap = isl_basic_map_add_constraints_dim_map(bmap, bmap2, dim_map2);
8551 bmap = isl_basic_map_simplify(bmap);
8552 return isl_basic_map_finalize(bmap);
8554 isl_basic_map_free(bmap1);
8555 isl_basic_map_free(bmap2);
8559 __isl_give isl_basic_map *isl_basic_map_flat_product(
8560 __isl_take isl_basic_map *bmap1, __isl_take isl_basic_map *bmap2)
8562 isl_basic_map *prod;
8564 prod = isl_basic_map_product(bmap1, bmap2);
8565 prod = isl_basic_map_flatten(prod);
8569 __isl_give isl_basic_set *isl_basic_set_flat_product(
8570 __isl_take isl_basic_set *bset1, __isl_take isl_basic_set *bset2)
8572 return isl_basic_map_flat_range_product(bset1, bset2);
8575 __isl_give isl_basic_map *isl_basic_map_domain_product(
8576 __isl_take isl_basic_map *bmap1, __isl_take isl_basic_map *bmap2)
8578 isl_space *space_result = NULL;
8579 isl_basic_map *bmap;
8580 unsigned in1, in2, out, nparam, total, pos;
8581 struct isl_dim_map *dim_map1, *dim_map2;
8583 if (!bmap1 || !bmap2)
8586 space_result = isl_space_domain_product(isl_space_copy(bmap1->dim),
8587 isl_space_copy(bmap2->dim));
8589 in1 = isl_basic_map_dim(bmap1, isl_dim_in);
8590 in2 = isl_basic_map_dim(bmap2, isl_dim_in);
8591 out = isl_basic_map_dim(bmap1, isl_dim_out);
8592 nparam = isl_basic_map_dim(bmap1, isl_dim_param);
8594 total = nparam + in1 + in2 + out + bmap1->n_div + bmap2->n_div;
8595 dim_map1 = isl_dim_map_alloc(bmap1->ctx, total);
8596 dim_map2 = isl_dim_map_alloc(bmap1->ctx, total);
8597 isl_dim_map_dim(dim_map1, bmap1->dim, isl_dim_param, pos = 0);
8598 isl_dim_map_dim(dim_map2, bmap2->dim, isl_dim_param, pos = 0);
8599 isl_dim_map_dim(dim_map1, bmap1->dim, isl_dim_in, pos += nparam);
8600 isl_dim_map_dim(dim_map2, bmap2->dim, isl_dim_in, pos += in1);
8601 isl_dim_map_dim(dim_map1, bmap1->dim, isl_dim_out, pos += in2);
8602 isl_dim_map_dim(dim_map2, bmap2->dim, isl_dim_out, pos);
8603 isl_dim_map_div(dim_map1, bmap1, pos += out);
8604 isl_dim_map_div(dim_map2, bmap2, pos += bmap1->n_div);
8606 bmap = isl_basic_map_alloc_space(space_result,
8607 bmap1->n_div + bmap2->n_div,
8608 bmap1->n_eq + bmap2->n_eq,
8609 bmap1->n_ineq + bmap2->n_ineq);
8610 bmap = isl_basic_map_add_constraints_dim_map(bmap, bmap1, dim_map1);
8611 bmap = isl_basic_map_add_constraints_dim_map(bmap, bmap2, dim_map2);
8612 bmap = isl_basic_map_simplify(bmap);
8613 return isl_basic_map_finalize(bmap);
8615 isl_basic_map_free(bmap1);
8616 isl_basic_map_free(bmap2);
8620 __isl_give isl_basic_map *isl_basic_map_range_product(
8621 __isl_take isl_basic_map *bmap1, __isl_take isl_basic_map *bmap2)
8623 isl_space *dim_result = NULL;
8624 isl_basic_map *bmap;
8625 unsigned in, out1, out2, nparam, total, pos;
8626 struct isl_dim_map *dim_map1, *dim_map2;
8628 if (!bmap1 || !bmap2)
8631 if (!isl_space_match(bmap1->dim, isl_dim_param,
8632 bmap2->dim, isl_dim_param))
8633 isl_die(isl_basic_map_get_ctx(bmap1), isl_error_invalid,
8634 "parameters don't match", goto error);
8636 dim_result = isl_space_range_product(isl_space_copy(bmap1->dim),
8637 isl_space_copy(bmap2->dim));
8639 in = isl_basic_map_dim(bmap1, isl_dim_in);
8640 out1 = isl_basic_map_n_out(bmap1);
8641 out2 = isl_basic_map_n_out(bmap2);
8642 nparam = isl_basic_map_n_param(bmap1);
8644 total = nparam + in + out1 + out2 + bmap1->n_div + bmap2->n_div;
8645 dim_map1 = isl_dim_map_alloc(bmap1->ctx, total);
8646 dim_map2 = isl_dim_map_alloc(bmap1->ctx, total);
8647 isl_dim_map_dim(dim_map1, bmap1->dim, isl_dim_param, pos = 0);
8648 isl_dim_map_dim(dim_map2, bmap2->dim, isl_dim_param, pos = 0);
8649 isl_dim_map_dim(dim_map1, bmap1->dim, isl_dim_in, pos += nparam);
8650 isl_dim_map_dim(dim_map2, bmap2->dim, isl_dim_in, pos);
8651 isl_dim_map_dim(dim_map1, bmap1->dim, isl_dim_out, pos += in);
8652 isl_dim_map_dim(dim_map2, bmap2->dim, isl_dim_out, pos += out1);
8653 isl_dim_map_div(dim_map1, bmap1, pos += out2);
8654 isl_dim_map_div(dim_map2, bmap2, pos += bmap1->n_div);
8656 bmap = isl_basic_map_alloc_space(dim_result,
8657 bmap1->n_div + bmap2->n_div,
8658 bmap1->n_eq + bmap2->n_eq,
8659 bmap1->n_ineq + bmap2->n_ineq);
8660 bmap = isl_basic_map_add_constraints_dim_map(bmap, bmap1, dim_map1);
8661 bmap = isl_basic_map_add_constraints_dim_map(bmap, bmap2, dim_map2);
8662 bmap = isl_basic_map_simplify(bmap);
8663 return isl_basic_map_finalize(bmap);
8665 isl_basic_map_free(bmap1);
8666 isl_basic_map_free(bmap2);
8670 __isl_give isl_basic_map *isl_basic_map_flat_range_product(
8671 __isl_take isl_basic_map *bmap1, __isl_take isl_basic_map *bmap2)
8673 isl_basic_map *prod;
8675 prod = isl_basic_map_range_product(bmap1, bmap2);
8676 prod = isl_basic_map_flatten_range(prod);
8680 static __isl_give isl_map *map_product(__isl_take isl_map *map1,
8681 __isl_take isl_map *map2,
8682 __isl_give isl_space *(*dim_product)(__isl_take isl_space *left,
8683 __isl_take isl_space *right),
8684 __isl_give isl_basic_map *(*basic_map_product)(
8685 __isl_take isl_basic_map *left, __isl_take isl_basic_map *right))
8688 struct isl_map *result;
8694 isl_assert(map1->ctx, isl_space_match(map1->dim, isl_dim_param,
8695 map2->dim, isl_dim_param), goto error);
8697 if (ISL_F_ISSET(map1, ISL_MAP_DISJOINT) &&
8698 ISL_F_ISSET(map2, ISL_MAP_DISJOINT))
8699 ISL_FL_SET(flags, ISL_MAP_DISJOINT);
8701 result = isl_map_alloc_space(dim_product(isl_space_copy(map1->dim),
8702 isl_space_copy(map2->dim)),
8703 map1->n * map2->n, flags);
8706 for (i = 0; i < map1->n; ++i)
8707 for (j = 0; j < map2->n; ++j) {
8708 struct isl_basic_map *part;
8709 part = basic_map_product(isl_basic_map_copy(map1->p[i]),
8710 isl_basic_map_copy(map2->p[j]));
8711 if (isl_basic_map_is_empty(part))
8712 isl_basic_map_free(part);
8714 result = isl_map_add_basic_map(result, part);
8727 /* Given two maps A -> B and C -> D, construct a map [A -> C] -> [B -> D]
8729 static __isl_give isl_map *map_product_aligned(__isl_take isl_map *map1,
8730 __isl_take isl_map *map2)
8732 return map_product(map1, map2, &isl_space_product, &isl_basic_map_product);
8735 __isl_give isl_map *isl_map_product(__isl_take isl_map *map1,
8736 __isl_take isl_map *map2)
8738 return isl_map_align_params_map_map_and(map1, map2, &map_product_aligned);
8741 /* Given two maps A -> B and C -> D, construct a map (A, C) -> (B, D)
8743 __isl_give isl_map *isl_map_flat_product(__isl_take isl_map *map1,
8744 __isl_take isl_map *map2)
8748 prod = isl_map_product(map1, map2);
8749 prod = isl_map_flatten(prod);
8753 /* Given two set A and B, construct its Cartesian product A x B.
8755 struct isl_set *isl_set_product(struct isl_set *set1, struct isl_set *set2)
8757 return isl_map_range_product(set1, set2);
8760 __isl_give isl_set *isl_set_flat_product(__isl_take isl_set *set1,
8761 __isl_take isl_set *set2)
8763 return isl_map_flat_range_product(set1, set2);
8766 /* Given two maps A -> B and C -> D, construct a map [A -> C] -> (B * D)
8768 static __isl_give isl_map *map_domain_product_aligned(__isl_take isl_map *map1,
8769 __isl_take isl_map *map2)
8771 return map_product(map1, map2, &isl_space_domain_product,
8772 &isl_basic_map_domain_product);
8775 /* Given two maps A -> B and C -> D, construct a map (A * C) -> [B -> D]
8777 static __isl_give isl_map *map_range_product_aligned(__isl_take isl_map *map1,
8778 __isl_take isl_map *map2)
8780 return map_product(map1, map2, &isl_space_range_product,
8781 &isl_basic_map_range_product);
8784 __isl_give isl_map *isl_map_domain_product(__isl_take isl_map *map1,
8785 __isl_take isl_map *map2)
8787 return isl_map_align_params_map_map_and(map1, map2,
8788 &map_domain_product_aligned);
8791 __isl_give isl_map *isl_map_range_product(__isl_take isl_map *map1,
8792 __isl_take isl_map *map2)
8794 return isl_map_align_params_map_map_and(map1, map2,
8795 &map_range_product_aligned);
8798 /* Given two maps A -> B and C -> D, construct a map (A, C) -> (B * D)
8800 __isl_give isl_map *isl_map_flat_domain_product(__isl_take isl_map *map1,
8801 __isl_take isl_map *map2)
8805 prod = isl_map_domain_product(map1, map2);
8806 prod = isl_map_flatten_domain(prod);
8810 /* Given two maps A -> B and C -> D, construct a map (A * C) -> (B, D)
8812 __isl_give isl_map *isl_map_flat_range_product(__isl_take isl_map *map1,
8813 __isl_take isl_map *map2)
8817 prod = isl_map_range_product(map1, map2);
8818 prod = isl_map_flatten_range(prod);
8822 uint32_t isl_basic_map_get_hash(__isl_keep isl_basic_map *bmap)
8825 uint32_t hash = isl_hash_init();
8830 bmap = isl_basic_map_copy(bmap);
8831 bmap = isl_basic_map_normalize(bmap);
8834 total = isl_basic_map_total_dim(bmap);
8835 isl_hash_byte(hash, bmap->n_eq & 0xFF);
8836 for (i = 0; i < bmap->n_eq; ++i) {
8838 c_hash = isl_seq_get_hash(bmap->eq[i], 1 + total);
8839 isl_hash_hash(hash, c_hash);
8841 isl_hash_byte(hash, bmap->n_ineq & 0xFF);
8842 for (i = 0; i < bmap->n_ineq; ++i) {
8844 c_hash = isl_seq_get_hash(bmap->ineq[i], 1 + total);
8845 isl_hash_hash(hash, c_hash);
8847 isl_hash_byte(hash, bmap->n_div & 0xFF);
8848 for (i = 0; i < bmap->n_div; ++i) {
8850 if (isl_int_is_zero(bmap->div[i][0]))
8852 isl_hash_byte(hash, i & 0xFF);
8853 c_hash = isl_seq_get_hash(bmap->div[i], 1 + 1 + total);
8854 isl_hash_hash(hash, c_hash);
8856 isl_basic_map_free(bmap);
8860 uint32_t isl_basic_set_get_hash(__isl_keep isl_basic_set *bset)
8862 return isl_basic_map_get_hash((isl_basic_map *)bset);
8865 uint32_t isl_map_get_hash(__isl_keep isl_map *map)
8872 map = isl_map_copy(map);
8873 map = isl_map_normalize(map);
8877 hash = isl_hash_init();
8878 for (i = 0; i < map->n; ++i) {
8880 bmap_hash = isl_basic_map_get_hash(map->p[i]);
8881 isl_hash_hash(hash, bmap_hash);
8889 uint32_t isl_set_get_hash(__isl_keep isl_set *set)
8891 return isl_map_get_hash((isl_map *)set);
8894 /* Check if the value for dimension dim is completely determined
8895 * by the values of the other parameters and variables.
8896 * That is, check if dimension dim is involved in an equality.
8898 int isl_basic_set_dim_is_unique(struct isl_basic_set *bset, unsigned dim)
8905 nparam = isl_basic_set_n_param(bset);
8906 for (i = 0; i < bset->n_eq; ++i)
8907 if (!isl_int_is_zero(bset->eq[i][1 + nparam + dim]))
8912 /* Check if the value for dimension dim is completely determined
8913 * by the values of the other parameters and variables.
8914 * That is, check if dimension dim is involved in an equality
8915 * for each of the subsets.
8917 int isl_set_dim_is_unique(struct isl_set *set, unsigned dim)
8923 for (i = 0; i < set->n; ++i) {
8925 unique = isl_basic_set_dim_is_unique(set->p[i], dim);
8932 int isl_set_n_basic_set(__isl_keep isl_set *set)
8934 return set ? set->n : 0;
8937 int isl_map_foreach_basic_map(__isl_keep isl_map *map,
8938 int (*fn)(__isl_take isl_basic_map *bmap, void *user), void *user)
8945 for (i = 0; i < map->n; ++i)
8946 if (fn(isl_basic_map_copy(map->p[i]), user) < 0)
8952 int isl_set_foreach_basic_set(__isl_keep isl_set *set,
8953 int (*fn)(__isl_take isl_basic_set *bset, void *user), void *user)
8960 for (i = 0; i < set->n; ++i)
8961 if (fn(isl_basic_set_copy(set->p[i]), user) < 0)
8967 __isl_give isl_basic_set *isl_basic_set_lift(__isl_take isl_basic_set *bset)
8974 bset = isl_basic_set_cow(bset);
8978 dim = isl_basic_set_get_space(bset);
8979 dim = isl_space_lift(dim, bset->n_div);
8982 isl_space_free(bset->dim);
8984 bset->extra -= bset->n_div;
8987 bset = isl_basic_set_finalize(bset);
8991 isl_basic_set_free(bset);
8995 __isl_give isl_set *isl_set_lift(__isl_take isl_set *set)
9001 set = isl_set_align_divs(set);
9006 set = isl_set_cow(set);
9010 n_div = set->p[0]->n_div;
9011 dim = isl_set_get_space(set);
9012 dim = isl_space_lift(dim, n_div);
9015 isl_space_free(set->dim);
9018 for (i = 0; i < set->n; ++i) {
9019 set->p[i] = isl_basic_set_lift(set->p[i]);
9030 __isl_give isl_map *isl_set_lifting(__isl_take isl_set *set)
9033 struct isl_basic_map *bmap;
9040 set = isl_set_align_divs(set);
9045 dim = isl_set_get_space(set);
9046 if (set->n == 0 || set->p[0]->n_div == 0) {
9048 return isl_map_identity(isl_space_map_from_set(dim));
9051 n_div = set->p[0]->n_div;
9052 dim = isl_space_map_from_set(dim);
9053 n_param = isl_space_dim(dim, isl_dim_param);
9054 n_set = isl_space_dim(dim, isl_dim_in);
9055 dim = isl_space_extend(dim, n_param, n_set, n_set + n_div);
9056 bmap = isl_basic_map_alloc_space(dim, 0, n_set, 2 * n_div);
9057 for (i = 0; i < n_set; ++i)
9058 bmap = var_equal(bmap, i);
9060 total = n_param + n_set + n_set + n_div;
9061 for (i = 0; i < n_div; ++i) {
9062 k = isl_basic_map_alloc_inequality(bmap);
9065 isl_seq_cpy(bmap->ineq[k], set->p[0]->div[i]+1, 1+n_param);
9066 isl_seq_clr(bmap->ineq[k]+1+n_param, n_set);
9067 isl_seq_cpy(bmap->ineq[k]+1+n_param+n_set,
9068 set->p[0]->div[i]+1+1+n_param, n_set + n_div);
9069 isl_int_neg(bmap->ineq[k][1+n_param+n_set+n_set+i],
9070 set->p[0]->div[i][0]);
9072 l = isl_basic_map_alloc_inequality(bmap);
9075 isl_seq_neg(bmap->ineq[l], bmap->ineq[k], 1 + total);
9076 isl_int_add(bmap->ineq[l][0], bmap->ineq[l][0],
9077 set->p[0]->div[i][0]);
9078 isl_int_sub_ui(bmap->ineq[l][0], bmap->ineq[l][0], 1);
9082 bmap = isl_basic_map_simplify(bmap);
9083 bmap = isl_basic_map_finalize(bmap);
9084 return isl_map_from_basic_map(bmap);
9087 isl_basic_map_free(bmap);
9091 int isl_basic_set_size(__isl_keep isl_basic_set *bset)
9099 dim = isl_basic_set_total_dim(bset);
9100 size += bset->n_eq * (1 + dim);
9101 size += bset->n_ineq * (1 + dim);
9102 size += bset->n_div * (2 + dim);
9107 int isl_set_size(__isl_keep isl_set *set)
9115 for (i = 0; i < set->n; ++i)
9116 size += isl_basic_set_size(set->p[i]);
9121 /* Check if there is any lower bound (if lower == 0) and/or upper
9122 * bound (if upper == 0) on the specified dim.
9124 static int basic_map_dim_is_bounded(__isl_keep isl_basic_map *bmap,
9125 enum isl_dim_type type, unsigned pos, int lower, int upper)
9132 isl_assert(bmap->ctx, pos < isl_basic_map_dim(bmap, type), return -1);
9134 pos += isl_basic_map_offset(bmap, type);
9136 for (i = 0; i < bmap->n_div; ++i) {
9137 if (isl_int_is_zero(bmap->div[i][0]))
9139 if (!isl_int_is_zero(bmap->div[i][1 + pos]))
9143 for (i = 0; i < bmap->n_eq; ++i)
9144 if (!isl_int_is_zero(bmap->eq[i][pos]))
9147 for (i = 0; i < bmap->n_ineq; ++i) {
9148 int sgn = isl_int_sgn(bmap->ineq[i][pos]);
9155 return lower && upper;
9158 int isl_basic_map_dim_is_bounded(__isl_keep isl_basic_map *bmap,
9159 enum isl_dim_type type, unsigned pos)
9161 return basic_map_dim_is_bounded(bmap, type, pos, 0, 0);
9164 int isl_basic_map_dim_has_lower_bound(__isl_keep isl_basic_map *bmap,
9165 enum isl_dim_type type, unsigned pos)
9167 return basic_map_dim_is_bounded(bmap, type, pos, 0, 1);
9170 int isl_basic_map_dim_has_upper_bound(__isl_keep isl_basic_map *bmap,
9171 enum isl_dim_type type, unsigned pos)
9173 return basic_map_dim_is_bounded(bmap, type, pos, 1, 0);
9176 int isl_map_dim_is_bounded(__isl_keep isl_map *map,
9177 enum isl_dim_type type, unsigned pos)
9184 for (i = 0; i < map->n; ++i) {
9186 bounded = isl_basic_map_dim_is_bounded(map->p[i], type, pos);
9187 if (bounded < 0 || !bounded)
9194 /* Return 1 if the specified dim is involved in both an upper bound
9195 * and a lower bound.
9197 int isl_set_dim_is_bounded(__isl_keep isl_set *set,
9198 enum isl_dim_type type, unsigned pos)
9200 return isl_map_dim_is_bounded((isl_map *)set, type, pos);
9203 /* Does "map" have a bound (according to "fn") for any of its basic maps?
9205 static int has_any_bound(__isl_keep isl_map *map,
9206 enum isl_dim_type type, unsigned pos,
9207 int (*fn)(__isl_keep isl_basic_map *bmap,
9208 enum isl_dim_type type, unsigned pos))
9215 for (i = 0; i < map->n; ++i) {
9217 bounded = fn(map->p[i], type, pos);
9218 if (bounded < 0 || bounded)
9225 /* Return 1 if the specified dim is involved in any lower bound.
9227 int isl_set_dim_has_any_lower_bound(__isl_keep isl_set *set,
9228 enum isl_dim_type type, unsigned pos)
9230 return has_any_bound(set, type, pos,
9231 &isl_basic_map_dim_has_lower_bound);
9234 /* Return 1 if the specified dim is involved in any upper bound.
9236 int isl_set_dim_has_any_upper_bound(__isl_keep isl_set *set,
9237 enum isl_dim_type type, unsigned pos)
9239 return has_any_bound(set, type, pos,
9240 &isl_basic_map_dim_has_upper_bound);
9243 /* Does "map" have a bound (according to "fn") for all of its basic maps?
9245 static int has_bound(__isl_keep isl_map *map,
9246 enum isl_dim_type type, unsigned pos,
9247 int (*fn)(__isl_keep isl_basic_map *bmap,
9248 enum isl_dim_type type, unsigned pos))
9255 for (i = 0; i < map->n; ++i) {
9257 bounded = fn(map->p[i], type, pos);
9258 if (bounded < 0 || !bounded)
9265 /* Return 1 if the specified dim has a lower bound (in each of its basic sets).
9267 int isl_set_dim_has_lower_bound(__isl_keep isl_set *set,
9268 enum isl_dim_type type, unsigned pos)
9270 return has_bound(set, type, pos, &isl_basic_map_dim_has_lower_bound);
9273 /* Return 1 if the specified dim has an upper bound (in each of its basic sets).
9275 int isl_set_dim_has_upper_bound(__isl_keep isl_set *set,
9276 enum isl_dim_type type, unsigned pos)
9278 return has_bound(set, type, pos, &isl_basic_map_dim_has_upper_bound);
9281 /* For each of the "n" variables starting at "first", determine
9282 * the sign of the variable and put the results in the first "n"
9283 * elements of the array "signs".
9285 * 1 means that the variable is non-negative
9286 * -1 means that the variable is non-positive
9287 * 0 means the variable attains both positive and negative values.
9289 int isl_basic_set_vars_get_sign(__isl_keep isl_basic_set *bset,
9290 unsigned first, unsigned n, int *signs)
9292 isl_vec *bound = NULL;
9293 struct isl_tab *tab = NULL;
9294 struct isl_tab_undo *snap;
9297 if (!bset || !signs)
9300 bound = isl_vec_alloc(bset->ctx, 1 + isl_basic_set_total_dim(bset));
9301 tab = isl_tab_from_basic_set(bset, 0);
9305 isl_seq_clr(bound->el, bound->size);
9306 isl_int_set_si(bound->el[0], -1);
9308 snap = isl_tab_snap(tab);
9309 for (i = 0; i < n; ++i) {
9312 isl_int_set_si(bound->el[1 + first + i], -1);
9313 if (isl_tab_add_ineq(tab, bound->el) < 0)
9316 isl_int_set_si(bound->el[1 + first + i], 0);
9317 if (isl_tab_rollback(tab, snap) < 0)
9325 isl_int_set_si(bound->el[1 + first + i], 1);
9326 if (isl_tab_add_ineq(tab, bound->el) < 0)
9329 isl_int_set_si(bound->el[1 + first + i], 0);
9330 if (isl_tab_rollback(tab, snap) < 0)
9333 signs[i] = empty ? -1 : 0;
9337 isl_vec_free(bound);
9341 isl_vec_free(bound);
9345 int isl_basic_set_dims_get_sign(__isl_keep isl_basic_set *bset,
9346 enum isl_dim_type type, unsigned first, unsigned n, int *signs)
9348 if (!bset || !signs)
9350 isl_assert(bset->ctx, first + n <= isl_basic_set_dim(bset, type),
9353 first += pos(bset->dim, type) - 1;
9354 return isl_basic_set_vars_get_sign(bset, first, n, signs);
9357 /* Check if the given basic map is obviously single-valued.
9358 * In particular, for each output dimension, check that there is
9359 * an equality that defines the output dimension in terms of
9360 * earlier dimensions.
9362 int isl_basic_map_plain_is_single_valued(__isl_keep isl_basic_map *bmap)
9372 total = 1 + isl_basic_map_total_dim(bmap);
9373 n_out = isl_basic_map_dim(bmap, isl_dim_out);
9374 o_out = isl_basic_map_offset(bmap, isl_dim_out);
9376 for (i = 0; i < n_out; ++i) {
9377 for (j = 0; j < bmap->n_eq; ++j) {
9378 if (isl_int_is_zero(bmap->eq[j][o_out + i]))
9380 if (isl_seq_first_non_zero(bmap->eq[j] + o_out + i + 1,
9381 total - (o_out + i + 1)) == -1)
9384 if (j >= bmap->n_eq)
9391 /* Check if the given basic map is single-valued.
9396 * and check if the result is a subset of the identity mapping.
9398 int isl_basic_map_is_single_valued(__isl_keep isl_basic_map *bmap)
9401 isl_basic_map *test;
9405 sv = isl_basic_map_plain_is_single_valued(bmap);
9409 test = isl_basic_map_reverse(isl_basic_map_copy(bmap));
9410 test = isl_basic_map_apply_range(test, isl_basic_map_copy(bmap));
9412 space = isl_basic_map_get_space(bmap);
9413 space = isl_space_map_from_set(isl_space_range(space));
9414 id = isl_basic_map_identity(space);
9416 sv = isl_basic_map_is_subset(test, id);
9418 isl_basic_map_free(test);
9419 isl_basic_map_free(id);
9424 /* Check if the given map is obviously single-valued.
9426 int isl_map_plain_is_single_valued(__isl_keep isl_map *map)
9435 return isl_basic_map_plain_is_single_valued(map->p[0]);
9438 /* Check if the given map is single-valued.
9443 * and check if the result is a subset of the identity mapping.
9445 int isl_map_is_single_valued(__isl_keep isl_map *map)
9452 sv = isl_map_plain_is_single_valued(map);
9456 test = isl_map_reverse(isl_map_copy(map));
9457 test = isl_map_apply_range(test, isl_map_copy(map));
9459 dim = isl_space_map_from_set(isl_space_range(isl_map_get_space(map)));
9460 id = isl_map_identity(dim);
9462 sv = isl_map_is_subset(test, id);
9470 int isl_map_is_injective(__isl_keep isl_map *map)
9474 map = isl_map_copy(map);
9475 map = isl_map_reverse(map);
9476 in = isl_map_is_single_valued(map);
9482 /* Check if the given map is obviously injective.
9484 int isl_map_plain_is_injective(__isl_keep isl_map *map)
9488 map = isl_map_copy(map);
9489 map = isl_map_reverse(map);
9490 in = isl_map_plain_is_single_valued(map);
9496 int isl_map_is_bijective(__isl_keep isl_map *map)
9500 sv = isl_map_is_single_valued(map);
9504 return isl_map_is_injective(map);
9507 int isl_set_is_singleton(__isl_keep isl_set *set)
9509 return isl_map_is_single_valued((isl_map *)set);
9512 int isl_map_is_translation(__isl_keep isl_map *map)
9517 delta = isl_map_deltas(isl_map_copy(map));
9518 ok = isl_set_is_singleton(delta);
9519 isl_set_free(delta);
9524 static int unique(isl_int *p, unsigned pos, unsigned len)
9526 if (isl_seq_first_non_zero(p, pos) != -1)
9528 if (isl_seq_first_non_zero(p + pos + 1, len - pos - 1) != -1)
9533 int isl_basic_set_is_box(__isl_keep isl_basic_set *bset)
9542 if (isl_basic_set_dim(bset, isl_dim_div) != 0)
9545 nvar = isl_basic_set_dim(bset, isl_dim_set);
9546 ovar = isl_space_offset(bset->dim, isl_dim_set);
9547 for (j = 0; j < nvar; ++j) {
9548 int lower = 0, upper = 0;
9549 for (i = 0; i < bset->n_eq; ++i) {
9550 if (isl_int_is_zero(bset->eq[i][1 + ovar + j]))
9552 if (!unique(bset->eq[i] + 1 + ovar, j, nvar))
9558 for (i = 0; i < bset->n_ineq; ++i) {
9559 if (isl_int_is_zero(bset->ineq[i][1 + ovar + j]))
9561 if (!unique(bset->ineq[i] + 1 + ovar, j, nvar))
9563 if (isl_int_is_pos(bset->ineq[i][1 + ovar + j]))
9568 if (!lower || !upper)
9575 int isl_set_is_box(__isl_keep isl_set *set)
9582 return isl_basic_set_is_box(set->p[0]);
9585 int isl_basic_set_is_wrapping(__isl_keep isl_basic_set *bset)
9590 return isl_space_is_wrapping(bset->dim);
9593 int isl_set_is_wrapping(__isl_keep isl_set *set)
9598 return isl_space_is_wrapping(set->dim);
9601 __isl_give isl_basic_set *isl_basic_map_wrap(__isl_take isl_basic_map *bmap)
9603 bmap = isl_basic_map_cow(bmap);
9607 bmap->dim = isl_space_wrap(bmap->dim);
9611 bmap = isl_basic_map_finalize(bmap);
9613 return (isl_basic_set *)bmap;
9615 isl_basic_map_free(bmap);
9619 __isl_give isl_set *isl_map_wrap(__isl_take isl_map *map)
9623 map = isl_map_cow(map);
9627 for (i = 0; i < map->n; ++i) {
9628 map->p[i] = (isl_basic_map *)isl_basic_map_wrap(map->p[i]);
9632 map->dim = isl_space_wrap(map->dim);
9636 return (isl_set *)map;
9642 __isl_give isl_basic_map *isl_basic_set_unwrap(__isl_take isl_basic_set *bset)
9644 bset = isl_basic_set_cow(bset);
9648 bset->dim = isl_space_unwrap(bset->dim);
9652 bset = isl_basic_set_finalize(bset);
9654 return (isl_basic_map *)bset;
9656 isl_basic_set_free(bset);
9660 __isl_give isl_map *isl_set_unwrap(__isl_take isl_set *set)
9667 if (!isl_set_is_wrapping(set))
9668 isl_die(set->ctx, isl_error_invalid, "not a wrapping set",
9671 set = isl_set_cow(set);
9675 for (i = 0; i < set->n; ++i) {
9676 set->p[i] = (isl_basic_set *)isl_basic_set_unwrap(set->p[i]);
9681 set->dim = isl_space_unwrap(set->dim);
9685 return (isl_map *)set;
9691 __isl_give isl_basic_map *isl_basic_map_reset(__isl_take isl_basic_map *bmap,
9692 enum isl_dim_type type)
9697 if (!isl_space_is_named_or_nested(bmap->dim, type))
9700 bmap = isl_basic_map_cow(bmap);
9704 bmap->dim = isl_space_reset(bmap->dim, type);
9708 bmap = isl_basic_map_finalize(bmap);
9712 isl_basic_map_free(bmap);
9716 __isl_give isl_map *isl_map_reset(__isl_take isl_map *map,
9717 enum isl_dim_type type)
9724 if (!isl_space_is_named_or_nested(map->dim, type))
9727 map = isl_map_cow(map);
9731 for (i = 0; i < map->n; ++i) {
9732 map->p[i] = isl_basic_map_reset(map->p[i], type);
9736 map->dim = isl_space_reset(map->dim, type);
9746 __isl_give isl_basic_map *isl_basic_map_flatten(__isl_take isl_basic_map *bmap)
9751 if (!bmap->dim->nested[0] && !bmap->dim->nested[1])
9754 bmap = isl_basic_map_cow(bmap);
9758 bmap->dim = isl_space_flatten(bmap->dim);
9762 bmap = isl_basic_map_finalize(bmap);
9766 isl_basic_map_free(bmap);
9770 __isl_give isl_basic_set *isl_basic_set_flatten(__isl_take isl_basic_set *bset)
9772 return (isl_basic_set *)isl_basic_map_flatten((isl_basic_map *)bset);
9775 __isl_give isl_basic_map *isl_basic_map_flatten_domain(
9776 __isl_take isl_basic_map *bmap)
9781 if (!bmap->dim->nested[0])
9784 bmap = isl_basic_map_cow(bmap);
9788 bmap->dim = isl_space_flatten_domain(bmap->dim);
9792 bmap = isl_basic_map_finalize(bmap);
9796 isl_basic_map_free(bmap);
9800 __isl_give isl_basic_map *isl_basic_map_flatten_range(
9801 __isl_take isl_basic_map *bmap)
9806 if (!bmap->dim->nested[1])
9809 bmap = isl_basic_map_cow(bmap);
9813 bmap->dim = isl_space_flatten_range(bmap->dim);
9817 bmap = isl_basic_map_finalize(bmap);
9821 isl_basic_map_free(bmap);
9825 __isl_give isl_map *isl_map_flatten(__isl_take isl_map *map)
9832 if (!map->dim->nested[0] && !map->dim->nested[1])
9835 map = isl_map_cow(map);
9839 for (i = 0; i < map->n; ++i) {
9840 map->p[i] = isl_basic_map_flatten(map->p[i]);
9844 map->dim = isl_space_flatten(map->dim);
9854 __isl_give isl_set *isl_set_flatten(__isl_take isl_set *set)
9856 return (isl_set *)isl_map_flatten((isl_map *)set);
9859 __isl_give isl_map *isl_set_flatten_map(__isl_take isl_set *set)
9861 isl_space *dim, *flat_dim;
9864 dim = isl_set_get_space(set);
9865 flat_dim = isl_space_flatten(isl_space_copy(dim));
9866 map = isl_map_identity(isl_space_join(isl_space_reverse(dim), flat_dim));
9867 map = isl_map_intersect_domain(map, set);
9872 __isl_give isl_map *isl_map_flatten_domain(__isl_take isl_map *map)
9879 if (!map->dim->nested[0])
9882 map = isl_map_cow(map);
9886 for (i = 0; i < map->n; ++i) {
9887 map->p[i] = isl_basic_map_flatten_domain(map->p[i]);
9891 map->dim = isl_space_flatten_domain(map->dim);
9901 __isl_give isl_map *isl_map_flatten_range(__isl_take isl_map *map)
9908 if (!map->dim->nested[1])
9911 map = isl_map_cow(map);
9915 for (i = 0; i < map->n; ++i) {
9916 map->p[i] = isl_basic_map_flatten_range(map->p[i]);
9920 map->dim = isl_space_flatten_range(map->dim);
9930 /* Reorder the dimensions of "bmap" according to the given dim_map
9931 * and set the dimension specification to "dim".
9933 __isl_give isl_basic_map *isl_basic_map_realign(__isl_take isl_basic_map *bmap,
9934 __isl_take isl_space *dim, __isl_take struct isl_dim_map *dim_map)
9939 bmap = isl_basic_map_cow(bmap);
9940 if (!bmap || !dim || !dim_map)
9943 flags = bmap->flags;
9944 ISL_FL_CLR(flags, ISL_BASIC_MAP_FINAL);
9945 ISL_FL_CLR(flags, ISL_BASIC_MAP_NORMALIZED);
9946 ISL_FL_CLR(flags, ISL_BASIC_MAP_NORMALIZED_DIVS);
9947 res = isl_basic_map_alloc_space(dim,
9948 bmap->n_div, bmap->n_eq, bmap->n_ineq);
9949 res = isl_basic_map_add_constraints_dim_map(res, bmap, dim_map);
9952 res = isl_basic_map_finalize(res);
9956 isl_basic_map_free(bmap);
9957 isl_space_free(dim);
9961 /* Reorder the dimensions of "map" according to given reordering.
9963 __isl_give isl_map *isl_map_realign(__isl_take isl_map *map,
9964 __isl_take isl_reordering *r)
9967 struct isl_dim_map *dim_map;
9969 map = isl_map_cow(map);
9970 dim_map = isl_dim_map_from_reordering(r);
9971 if (!map || !r || !dim_map)
9974 for (i = 0; i < map->n; ++i) {
9975 struct isl_dim_map *dim_map_i;
9977 dim_map_i = isl_dim_map_extend(dim_map, map->p[i]);
9979 map->p[i] = isl_basic_map_realign(map->p[i],
9980 isl_space_copy(r->dim), dim_map_i);
9986 map = isl_map_reset_space(map, isl_space_copy(r->dim));
9988 isl_reordering_free(r);
9994 isl_reordering_free(r);
9998 __isl_give isl_set *isl_set_realign(__isl_take isl_set *set,
9999 __isl_take isl_reordering *r)
10001 return (isl_set *)isl_map_realign((isl_map *)set, r);
10004 __isl_give isl_map *isl_map_align_params(__isl_take isl_map *map,
10005 __isl_take isl_space *model)
10009 if (!map || !model)
10012 ctx = isl_space_get_ctx(model);
10013 if (!isl_space_has_named_params(model))
10014 isl_die(ctx, isl_error_invalid,
10015 "model has unnamed parameters", goto error);
10016 if (!isl_space_has_named_params(map->dim))
10017 isl_die(ctx, isl_error_invalid,
10018 "relation has unnamed parameters", goto error);
10019 if (!isl_space_match(map->dim, isl_dim_param, model, isl_dim_param)) {
10020 isl_reordering *exp;
10022 model = isl_space_drop_dims(model, isl_dim_in,
10023 0, isl_space_dim(model, isl_dim_in));
10024 model = isl_space_drop_dims(model, isl_dim_out,
10025 0, isl_space_dim(model, isl_dim_out));
10026 exp = isl_parameter_alignment_reordering(map->dim, model);
10027 exp = isl_reordering_extend_space(exp, isl_map_get_space(map));
10028 map = isl_map_realign(map, exp);
10031 isl_space_free(model);
10034 isl_space_free(model);
10039 __isl_give isl_set *isl_set_align_params(__isl_take isl_set *set,
10040 __isl_take isl_space *model)
10042 return isl_map_align_params(set, model);
10045 /* Align the parameters of "bmap" to those of "model", introducing
10046 * additional parameters if needed.
10048 __isl_give isl_basic_map *isl_basic_map_align_params(
10049 __isl_take isl_basic_map *bmap, __isl_take isl_space *model)
10053 if (!bmap || !model)
10056 ctx = isl_space_get_ctx(model);
10057 if (!isl_space_has_named_params(model))
10058 isl_die(ctx, isl_error_invalid,
10059 "model has unnamed parameters", goto error);
10060 if (!isl_space_has_named_params(bmap->dim))
10061 isl_die(ctx, isl_error_invalid,
10062 "relation has unnamed parameters", goto error);
10063 if (!isl_space_match(bmap->dim, isl_dim_param, model, isl_dim_param)) {
10064 isl_reordering *exp;
10065 struct isl_dim_map *dim_map;
10067 model = isl_space_drop_dims(model, isl_dim_in,
10068 0, isl_space_dim(model, isl_dim_in));
10069 model = isl_space_drop_dims(model, isl_dim_out,
10070 0, isl_space_dim(model, isl_dim_out));
10071 exp = isl_parameter_alignment_reordering(bmap->dim, model);
10072 exp = isl_reordering_extend_space(exp,
10073 isl_basic_map_get_space(bmap));
10074 dim_map = isl_dim_map_from_reordering(exp);
10075 bmap = isl_basic_map_realign(bmap,
10076 exp ? isl_space_copy(exp->dim) : NULL,
10077 isl_dim_map_extend(dim_map, bmap));
10078 isl_reordering_free(exp);
10082 isl_space_free(model);
10085 isl_space_free(model);
10086 isl_basic_map_free(bmap);
10090 /* Align the parameters of "bset" to those of "model", introducing
10091 * additional parameters if needed.
10093 __isl_give isl_basic_set *isl_basic_set_align_params(
10094 __isl_take isl_basic_set *bset, __isl_take isl_space *model)
10096 return isl_basic_map_align_params(bset, model);
10099 __isl_give isl_mat *isl_basic_map_equalities_matrix(
10100 __isl_keep isl_basic_map *bmap, enum isl_dim_type c1,
10101 enum isl_dim_type c2, enum isl_dim_type c3,
10102 enum isl_dim_type c4, enum isl_dim_type c5)
10104 enum isl_dim_type c[5] = { c1, c2, c3, c4, c5 };
10105 struct isl_mat *mat;
10111 mat = isl_mat_alloc(bmap->ctx, bmap->n_eq,
10112 isl_basic_map_total_dim(bmap) + 1);
10115 for (i = 0; i < bmap->n_eq; ++i)
10116 for (j = 0, pos = 0; j < 5; ++j) {
10117 int off = isl_basic_map_offset(bmap, c[j]);
10118 for (k = 0; k < isl_basic_map_dim(bmap, c[j]); ++k) {
10119 isl_int_set(mat->row[i][pos],
10120 bmap->eq[i][off + k]);
10128 __isl_give isl_mat *isl_basic_map_inequalities_matrix(
10129 __isl_keep isl_basic_map *bmap, enum isl_dim_type c1,
10130 enum isl_dim_type c2, enum isl_dim_type c3,
10131 enum isl_dim_type c4, enum isl_dim_type c5)
10133 enum isl_dim_type c[5] = { c1, c2, c3, c4, c5 };
10134 struct isl_mat *mat;
10140 mat = isl_mat_alloc(bmap->ctx, bmap->n_ineq,
10141 isl_basic_map_total_dim(bmap) + 1);
10144 for (i = 0; i < bmap->n_ineq; ++i)
10145 for (j = 0, pos = 0; j < 5; ++j) {
10146 int off = isl_basic_map_offset(bmap, c[j]);
10147 for (k = 0; k < isl_basic_map_dim(bmap, c[j]); ++k) {
10148 isl_int_set(mat->row[i][pos],
10149 bmap->ineq[i][off + k]);
10157 __isl_give isl_basic_map *isl_basic_map_from_constraint_matrices(
10158 __isl_take isl_space *dim,
10159 __isl_take isl_mat *eq, __isl_take isl_mat *ineq, enum isl_dim_type c1,
10160 enum isl_dim_type c2, enum isl_dim_type c3,
10161 enum isl_dim_type c4, enum isl_dim_type c5)
10163 enum isl_dim_type c[5] = { c1, c2, c3, c4, c5 };
10164 isl_basic_map *bmap;
10170 if (!dim || !eq || !ineq)
10173 if (eq->n_col != ineq->n_col)
10174 isl_die(dim->ctx, isl_error_invalid,
10175 "equalities and inequalities matrices should have "
10176 "same number of columns", goto error);
10178 total = 1 + isl_space_dim(dim, isl_dim_all);
10180 if (eq->n_col < total)
10181 isl_die(dim->ctx, isl_error_invalid,
10182 "number of columns too small", goto error);
10184 extra = eq->n_col - total;
10186 bmap = isl_basic_map_alloc_space(isl_space_copy(dim), extra,
10187 eq->n_row, ineq->n_row);
10190 for (i = 0; i < extra; ++i) {
10191 k = isl_basic_map_alloc_div(bmap);
10194 isl_int_set_si(bmap->div[k][0], 0);
10196 for (i = 0; i < eq->n_row; ++i) {
10197 l = isl_basic_map_alloc_equality(bmap);
10200 for (j = 0, pos = 0; j < 5; ++j) {
10201 int off = isl_basic_map_offset(bmap, c[j]);
10202 for (k = 0; k < isl_basic_map_dim(bmap, c[j]); ++k) {
10203 isl_int_set(bmap->eq[l][off + k],
10209 for (i = 0; i < ineq->n_row; ++i) {
10210 l = isl_basic_map_alloc_inequality(bmap);
10213 for (j = 0, pos = 0; j < 5; ++j) {
10214 int off = isl_basic_map_offset(bmap, c[j]);
10215 for (k = 0; k < isl_basic_map_dim(bmap, c[j]); ++k) {
10216 isl_int_set(bmap->ineq[l][off + k],
10217 ineq->row[i][pos]);
10223 isl_space_free(dim);
10225 isl_mat_free(ineq);
10229 isl_space_free(dim);
10231 isl_mat_free(ineq);
10235 __isl_give isl_mat *isl_basic_set_equalities_matrix(
10236 __isl_keep isl_basic_set *bset, enum isl_dim_type c1,
10237 enum isl_dim_type c2, enum isl_dim_type c3, enum isl_dim_type c4)
10239 return isl_basic_map_equalities_matrix((isl_basic_map *)bset,
10240 c1, c2, c3, c4, isl_dim_in);
10243 __isl_give isl_mat *isl_basic_set_inequalities_matrix(
10244 __isl_keep isl_basic_set *bset, enum isl_dim_type c1,
10245 enum isl_dim_type c2, enum isl_dim_type c3, enum isl_dim_type c4)
10247 return isl_basic_map_inequalities_matrix((isl_basic_map *)bset,
10248 c1, c2, c3, c4, isl_dim_in);
10251 __isl_give isl_basic_set *isl_basic_set_from_constraint_matrices(
10252 __isl_take isl_space *dim,
10253 __isl_take isl_mat *eq, __isl_take isl_mat *ineq, enum isl_dim_type c1,
10254 enum isl_dim_type c2, enum isl_dim_type c3, enum isl_dim_type c4)
10256 return (isl_basic_set*)
10257 isl_basic_map_from_constraint_matrices(dim, eq, ineq,
10258 c1, c2, c3, c4, isl_dim_in);
10261 int isl_basic_map_can_zip(__isl_keep isl_basic_map *bmap)
10266 return isl_space_can_zip(bmap->dim);
10269 int isl_map_can_zip(__isl_keep isl_map *map)
10274 return isl_space_can_zip(map->dim);
10277 /* Given a basic map (A -> B) -> (C -> D), return the corresponding basic map
10278 * (A -> C) -> (B -> D).
10280 __isl_give isl_basic_map *isl_basic_map_zip(__isl_take isl_basic_map *bmap)
10289 if (!isl_basic_map_can_zip(bmap))
10290 isl_die(bmap->ctx, isl_error_invalid,
10291 "basic map cannot be zipped", goto error);
10292 pos = isl_basic_map_offset(bmap, isl_dim_in) +
10293 isl_space_dim(bmap->dim->nested[0], isl_dim_in);
10294 n1 = isl_space_dim(bmap->dim->nested[0], isl_dim_out);
10295 n2 = isl_space_dim(bmap->dim->nested[1], isl_dim_in);
10296 bmap = isl_basic_map_cow(bmap);
10297 bmap = isl_basic_map_swap_vars(bmap, pos, n1, n2);
10300 bmap->dim = isl_space_zip(bmap->dim);
10305 isl_basic_map_free(bmap);
10309 /* Given a map (A -> B) -> (C -> D), return the corresponding map
10310 * (A -> C) -> (B -> D).
10312 __isl_give isl_map *isl_map_zip(__isl_take isl_map *map)
10319 if (!isl_map_can_zip(map))
10320 isl_die(map->ctx, isl_error_invalid, "map cannot be zipped",
10323 map = isl_map_cow(map);
10327 for (i = 0; i < map->n; ++i) {
10328 map->p[i] = isl_basic_map_zip(map->p[i]);
10333 map->dim = isl_space_zip(map->dim);
10343 /* Can we apply isl_basic_map_curry to "bmap"?
10344 * That is, does it have a nested relation in its domain?
10346 int isl_basic_map_can_curry(__isl_keep isl_basic_map *bmap)
10351 return isl_space_can_curry(bmap->dim);
10354 /* Can we apply isl_map_curry to "map"?
10355 * That is, does it have a nested relation in its domain?
10357 int isl_map_can_curry(__isl_keep isl_map *map)
10362 return isl_space_can_curry(map->dim);
10365 /* Given a basic map (A -> B) -> C, return the corresponding basic map
10368 __isl_give isl_basic_map *isl_basic_map_curry(__isl_take isl_basic_map *bmap)
10374 if (!isl_basic_map_can_curry(bmap))
10375 isl_die(bmap->ctx, isl_error_invalid,
10376 "basic map cannot be curried", goto error);
10377 bmap->dim = isl_space_curry(bmap->dim);
10382 isl_basic_map_free(bmap);
10386 /* Given a map (A -> B) -> C, return the corresponding map
10389 __isl_give isl_map *isl_map_curry(__isl_take isl_map *map)
10396 if (!isl_map_can_curry(map))
10397 isl_die(map->ctx, isl_error_invalid, "map cannot be curried",
10400 map = isl_map_cow(map);
10404 for (i = 0; i < map->n; ++i) {
10405 map->p[i] = isl_basic_map_curry(map->p[i]);
10410 map->dim = isl_space_curry(map->dim);
10420 /* Can we apply isl_basic_map_uncurry to "bmap"?
10421 * That is, does it have a nested relation in its domain?
10423 int isl_basic_map_can_uncurry(__isl_keep isl_basic_map *bmap)
10428 return isl_space_can_uncurry(bmap->dim);
10431 /* Can we apply isl_map_uncurry to "map"?
10432 * That is, does it have a nested relation in its domain?
10434 int isl_map_can_uncurry(__isl_keep isl_map *map)
10439 return isl_space_can_uncurry(map->dim);
10442 /* Given a basic map A -> (B -> C), return the corresponding basic map
10445 __isl_give isl_basic_map *isl_basic_map_uncurry(__isl_take isl_basic_map *bmap)
10451 if (!isl_basic_map_can_uncurry(bmap))
10452 isl_die(bmap->ctx, isl_error_invalid,
10453 "basic map cannot be uncurried",
10454 return isl_basic_map_free(bmap));
10455 bmap->dim = isl_space_uncurry(bmap->dim);
10457 return isl_basic_map_free(bmap);
10461 /* Given a map A -> (B -> C), return the corresponding map
10464 __isl_give isl_map *isl_map_uncurry(__isl_take isl_map *map)
10471 if (!isl_map_can_uncurry(map))
10472 isl_die(map->ctx, isl_error_invalid, "map cannot be uncurried",
10473 return isl_map_free(map));
10475 map = isl_map_cow(map);
10479 for (i = 0; i < map->n; ++i) {
10480 map->p[i] = isl_basic_map_uncurry(map->p[i]);
10482 return isl_map_free(map);
10485 map->dim = isl_space_uncurry(map->dim);
10487 return isl_map_free(map);
10492 /* Construct a basic map mapping the domain of the affine expression
10493 * to a one-dimensional range prescribed by the affine expression.
10495 __isl_give isl_basic_map *isl_basic_map_from_aff(__isl_take isl_aff *aff)
10499 isl_local_space *ls;
10500 isl_basic_map *bmap;
10505 ls = isl_aff_get_local_space(aff);
10506 bmap = isl_basic_map_from_local_space(ls);
10507 bmap = isl_basic_map_extend_constraints(bmap, 1, 0);
10508 k = isl_basic_map_alloc_equality(bmap);
10512 pos = isl_basic_map_offset(bmap, isl_dim_out);
10513 isl_seq_cpy(bmap->eq[k], aff->v->el + 1, pos);
10514 isl_int_neg(bmap->eq[k][pos], aff->v->el[0]);
10515 isl_seq_cpy(bmap->eq[k] + pos + 1, aff->v->el + 1 + pos,
10516 aff->v->size - (pos + 1));
10519 bmap = isl_basic_map_finalize(bmap);
10523 isl_basic_map_free(bmap);
10527 /* Construct a map mapping the domain of the affine expression
10528 * to a one-dimensional range prescribed by the affine expression.
10530 __isl_give isl_map *isl_map_from_aff(__isl_take isl_aff *aff)
10532 isl_basic_map *bmap;
10534 bmap = isl_basic_map_from_aff(aff);
10535 return isl_map_from_basic_map(bmap);
10538 /* Construct a basic map mapping the domain the multi-affine expression
10539 * to its range, with each dimension in the range equated to the
10540 * corresponding affine expression.
10542 __isl_give isl_basic_map *isl_basic_map_from_multi_aff(
10543 __isl_take isl_multi_aff *maff)
10547 isl_basic_map *bmap;
10552 if (isl_space_dim(maff->space, isl_dim_out) != maff->n)
10553 isl_die(isl_multi_aff_get_ctx(maff), isl_error_internal,
10554 "invalid space", return isl_multi_aff_free(maff));
10556 space = isl_space_domain(isl_multi_aff_get_space(maff));
10557 bmap = isl_basic_map_universe(isl_space_from_domain(space));
10559 for (i = 0; i < maff->n; ++i) {
10561 isl_basic_map *bmap_i;
10563 aff = isl_aff_copy(maff->p[i]);
10564 bmap_i = isl_basic_map_from_aff(aff);
10566 bmap = isl_basic_map_flat_range_product(bmap, bmap_i);
10569 bmap = isl_basic_map_reset_space(bmap, isl_multi_aff_get_space(maff));
10571 isl_multi_aff_free(maff);
10575 /* Construct a map mapping the domain the multi-affine expression
10576 * to its range, with each dimension in the range equated to the
10577 * corresponding affine expression.
10579 __isl_give isl_map *isl_map_from_multi_aff(__isl_take isl_multi_aff *maff)
10581 isl_basic_map *bmap;
10583 bmap = isl_basic_map_from_multi_aff(maff);
10584 return isl_map_from_basic_map(bmap);
10587 /* Construct a basic map mapping a domain in the given space to
10588 * to an n-dimensional range, with n the number of elements in the list,
10589 * where each coordinate in the range is prescribed by the
10590 * corresponding affine expression.
10591 * The domains of all affine expressions in the list are assumed to match
10594 __isl_give isl_basic_map *isl_basic_map_from_aff_list(
10595 __isl_take isl_space *domain_dim, __isl_take isl_aff_list *list)
10599 isl_basic_map *bmap;
10604 dim = isl_space_from_domain(domain_dim);
10605 bmap = isl_basic_map_universe(dim);
10607 for (i = 0; i < list->n; ++i) {
10609 isl_basic_map *bmap_i;
10611 aff = isl_aff_copy(list->p[i]);
10612 bmap_i = isl_basic_map_from_aff(aff);
10614 bmap = isl_basic_map_flat_range_product(bmap, bmap_i);
10617 isl_aff_list_free(list);
10621 __isl_give isl_set *isl_set_equate(__isl_take isl_set *set,
10622 enum isl_dim_type type1, int pos1, enum isl_dim_type type2, int pos2)
10624 return isl_map_equate(set, type1, pos1, type2, pos2);
10627 /* Construct a basic map where the given dimensions are equal to each other.
10629 static __isl_give isl_basic_map *equator(__isl_take isl_space *space,
10630 enum isl_dim_type type1, int pos1, enum isl_dim_type type2, int pos2)
10632 isl_basic_map *bmap = NULL;
10638 if (pos1 >= isl_space_dim(space, type1))
10639 isl_die(isl_space_get_ctx(space), isl_error_invalid,
10640 "index out of bounds", goto error);
10641 if (pos2 >= isl_space_dim(space, type2))
10642 isl_die(isl_space_get_ctx(space), isl_error_invalid,
10643 "index out of bounds", goto error);
10645 if (type1 == type2 && pos1 == pos2)
10646 return isl_basic_map_universe(space);
10648 bmap = isl_basic_map_alloc_space(isl_space_copy(space), 0, 1, 0);
10649 i = isl_basic_map_alloc_equality(bmap);
10652 isl_seq_clr(bmap->eq[i], 1 + isl_basic_map_total_dim(bmap));
10653 pos1 += isl_basic_map_offset(bmap, type1);
10654 pos2 += isl_basic_map_offset(bmap, type2);
10655 isl_int_set_si(bmap->eq[i][pos1], -1);
10656 isl_int_set_si(bmap->eq[i][pos2], 1);
10657 bmap = isl_basic_map_finalize(bmap);
10658 isl_space_free(space);
10661 isl_space_free(space);
10662 isl_basic_map_free(bmap);
10666 /* Add a constraint imposing that the given two dimensions are equal.
10668 __isl_give isl_basic_map *isl_basic_map_equate(__isl_take isl_basic_map *bmap,
10669 enum isl_dim_type type1, int pos1, enum isl_dim_type type2, int pos2)
10673 eq = equator(isl_basic_map_get_space(bmap), type1, pos1, type2, pos2);
10675 bmap = isl_basic_map_intersect(bmap, eq);
10680 /* Add a constraint imposing that the given two dimensions are equal.
10682 __isl_give isl_map *isl_map_equate(__isl_take isl_map *map,
10683 enum isl_dim_type type1, int pos1, enum isl_dim_type type2, int pos2)
10685 isl_basic_map *bmap;
10687 bmap = equator(isl_map_get_space(map), type1, pos1, type2, pos2);
10689 map = isl_map_intersect(map, isl_map_from_basic_map(bmap));
10694 /* Add a constraint imposing that the given two dimensions have opposite values.
10696 __isl_give isl_map *isl_map_oppose(__isl_take isl_map *map,
10697 enum isl_dim_type type1, int pos1, enum isl_dim_type type2, int pos2)
10699 isl_basic_map *bmap = NULL;
10705 if (pos1 >= isl_map_dim(map, type1))
10706 isl_die(map->ctx, isl_error_invalid,
10707 "index out of bounds", goto error);
10708 if (pos2 >= isl_map_dim(map, type2))
10709 isl_die(map->ctx, isl_error_invalid,
10710 "index out of bounds", goto error);
10712 bmap = isl_basic_map_alloc_space(isl_map_get_space(map), 0, 1, 0);
10713 i = isl_basic_map_alloc_equality(bmap);
10716 isl_seq_clr(bmap->eq[i], 1 + isl_basic_map_total_dim(bmap));
10717 pos1 += isl_basic_map_offset(bmap, type1);
10718 pos2 += isl_basic_map_offset(bmap, type2);
10719 isl_int_set_si(bmap->eq[i][pos1], 1);
10720 isl_int_set_si(bmap->eq[i][pos2], 1);
10721 bmap = isl_basic_map_finalize(bmap);
10723 map = isl_map_intersect(map, isl_map_from_basic_map(bmap));
10727 isl_basic_map_free(bmap);
10732 /* Add a constraint imposing that the value of the first dimension is
10733 * greater than or equal to that of the second.
10735 __isl_give isl_basic_map *isl_basic_map_order_ge(__isl_take isl_basic_map *bmap,
10736 enum isl_dim_type type1, int pos1, enum isl_dim_type type2, int pos2)
10739 isl_local_space *ls;
10744 if (pos1 >= isl_basic_map_dim(bmap, type1))
10745 isl_die(bmap->ctx, isl_error_invalid,
10746 "index out of bounds", return isl_basic_map_free(bmap));
10747 if (pos2 >= isl_basic_map_dim(bmap, type2))
10748 isl_die(bmap->ctx, isl_error_invalid,
10749 "index out of bounds", return isl_basic_map_free(bmap));
10751 if (type1 == type2 && pos1 == pos2)
10754 ls = isl_local_space_from_space(isl_basic_map_get_space(bmap));
10755 c = isl_inequality_alloc(ls);
10756 c = isl_constraint_set_coefficient_si(c, type1, pos1, 1);
10757 c = isl_constraint_set_coefficient_si(c, type2, pos2, -1);
10758 bmap = isl_basic_map_add_constraint(bmap, c);
10763 /* Add a constraint imposing that the value of the first dimension is
10764 * greater than that of the second.
10766 __isl_give isl_map *isl_map_order_gt(__isl_take isl_map *map,
10767 enum isl_dim_type type1, int pos1, enum isl_dim_type type2, int pos2)
10769 isl_basic_map *bmap = NULL;
10775 if (pos1 >= isl_map_dim(map, type1))
10776 isl_die(map->ctx, isl_error_invalid,
10777 "index out of bounds", goto error);
10778 if (pos2 >= isl_map_dim(map, type2))
10779 isl_die(map->ctx, isl_error_invalid,
10780 "index out of bounds", goto error);
10782 if (type1 == type2 && pos1 == pos2) {
10783 isl_space *space = isl_map_get_space(map);
10785 return isl_map_empty(space);
10788 bmap = isl_basic_map_alloc_space(isl_map_get_space(map), 0, 0, 1);
10789 i = isl_basic_map_alloc_inequality(bmap);
10792 isl_seq_clr(bmap->ineq[i], 1 + isl_basic_map_total_dim(bmap));
10793 pos1 += isl_basic_map_offset(bmap, type1);
10794 pos2 += isl_basic_map_offset(bmap, type2);
10795 isl_int_set_si(bmap->ineq[i][pos1], 1);
10796 isl_int_set_si(bmap->ineq[i][pos2], -1);
10797 isl_int_set_si(bmap->ineq[i][0], -1);
10798 bmap = isl_basic_map_finalize(bmap);
10800 map = isl_map_intersect(map, isl_map_from_basic_map(bmap));
10804 isl_basic_map_free(bmap);
10809 /* Add a constraint imposing that the value of the first dimension is
10810 * smaller than that of the second.
10812 __isl_give isl_map *isl_map_order_lt(__isl_take isl_map *map,
10813 enum isl_dim_type type1, int pos1, enum isl_dim_type type2, int pos2)
10815 return isl_map_order_gt(map, type2, pos2, type1, pos1);
10818 __isl_give isl_aff *isl_basic_map_get_div(__isl_keep isl_basic_map *bmap,
10822 isl_local_space *ls;
10827 if (!isl_basic_map_divs_known(bmap))
10828 isl_die(isl_basic_map_get_ctx(bmap), isl_error_invalid,
10829 "some divs are unknown", return NULL);
10831 ls = isl_basic_map_get_local_space(bmap);
10832 div = isl_local_space_get_div(ls, pos);
10833 isl_local_space_free(ls);
10838 __isl_give isl_aff *isl_basic_set_get_div(__isl_keep isl_basic_set *bset,
10841 return isl_basic_map_get_div(bset, pos);
10844 /* Plug in "subs" for dimension "type", "pos" of "bset".
10846 * Let i be the dimension to replace and let "subs" be of the form
10850 * Any integer division with a non-zero coefficient for i,
10852 * floor((a i + g)/m)
10856 * floor((a f + d g)/(m d))
10858 * Constraints of the form
10866 * We currently require that "subs" is an integral expression.
10867 * Handling rational expressions may require us to add stride constraints
10868 * as we do in isl_basic_set_preimage_multi_aff.
10870 __isl_give isl_basic_set *isl_basic_set_substitute(
10871 __isl_take isl_basic_set *bset,
10872 enum isl_dim_type type, unsigned pos, __isl_keep isl_aff *subs)
10878 if (bset && isl_basic_set_plain_is_empty(bset))
10881 bset = isl_basic_set_cow(bset);
10882 if (!bset || !subs)
10885 ctx = isl_basic_set_get_ctx(bset);
10886 if (!isl_space_is_equal(bset->dim, subs->ls->dim))
10887 isl_die(ctx, isl_error_invalid,
10888 "spaces don't match", goto error);
10889 if (isl_local_space_dim(subs->ls, isl_dim_div) != 0)
10890 isl_die(ctx, isl_error_unsupported,
10891 "cannot handle divs yet", goto error);
10892 if (!isl_int_is_one(subs->v->el[0]))
10893 isl_die(ctx, isl_error_invalid,
10894 "can only substitute integer expressions", goto error);
10896 pos += isl_basic_set_offset(bset, type);
10900 for (i = 0; i < bset->n_eq; ++i) {
10901 if (isl_int_is_zero(bset->eq[i][pos]))
10903 isl_int_set(v, bset->eq[i][pos]);
10904 isl_int_set_si(bset->eq[i][pos], 0);
10905 isl_seq_combine(bset->eq[i], subs->v->el[0], bset->eq[i],
10906 v, subs->v->el + 1, subs->v->size - 1);
10909 for (i = 0; i < bset->n_ineq; ++i) {
10910 if (isl_int_is_zero(bset->ineq[i][pos]))
10912 isl_int_set(v, bset->ineq[i][pos]);
10913 isl_int_set_si(bset->ineq[i][pos], 0);
10914 isl_seq_combine(bset->ineq[i], subs->v->el[0], bset->ineq[i],
10915 v, subs->v->el + 1, subs->v->size - 1);
10918 for (i = 0; i < bset->n_div; ++i) {
10919 if (isl_int_is_zero(bset->div[i][1 + pos]))
10921 isl_int_set(v, bset->div[i][1 + pos]);
10922 isl_int_set_si(bset->div[i][1 + pos], 0);
10923 isl_seq_combine(bset->div[i] + 1,
10924 subs->v->el[0], bset->div[i] + 1,
10925 v, subs->v->el + 1, subs->v->size - 1);
10926 isl_int_mul(bset->div[i][0], bset->div[i][0], subs->v->el[0]);
10931 bset = isl_basic_set_simplify(bset);
10932 return isl_basic_set_finalize(bset);
10934 isl_basic_set_free(bset);
10938 /* Plug in "subs" for dimension "type", "pos" of "set".
10940 __isl_give isl_set *isl_set_substitute(__isl_take isl_set *set,
10941 enum isl_dim_type type, unsigned pos, __isl_keep isl_aff *subs)
10945 if (set && isl_set_plain_is_empty(set))
10948 set = isl_set_cow(set);
10952 for (i = set->n - 1; i >= 0; --i) {
10953 set->p[i] = isl_basic_set_substitute(set->p[i], type, pos, subs);
10954 if (remove_if_empty(set, i) < 0)
10964 /* Check if the range of "ma" is compatible with "space".
10965 * Return -1 if anything is wrong.
10967 static int check_space_compatible_range_multi_aff(
10968 __isl_keep isl_space *space, __isl_keep isl_multi_aff *ma)
10971 isl_space *ma_space;
10973 ma_space = isl_multi_aff_get_space(ma);
10974 m = isl_space_is_range_internal(space, ma_space);
10975 isl_space_free(ma_space);
10977 isl_die(isl_space_get_ctx(space), isl_error_invalid,
10978 "spaces don't match", return -1);
10982 /* Check if the range of "ma" is compatible with "bset".
10983 * Return -1 if anything is wrong.
10985 static int check_basic_set_compatible_range_multi_aff(
10986 __isl_keep isl_basic_set *bset, __isl_keep isl_multi_aff *ma)
10988 return check_space_compatible_range_multi_aff(bset->dim, ma);
10991 /* Copy the divs from "ma" to "bset", adding zeros for the coefficients
10992 * of the other divs in "bset".
10994 static int set_ma_divs(__isl_keep isl_basic_set *bset,
10995 __isl_keep isl_multi_aff *ma, int n_div)
10998 isl_local_space *ls;
11003 ls = isl_aff_get_domain_local_space(ma->p[0]);
11007 for (i = 0; i < n_div; ++i) {
11008 isl_seq_cpy(bset->div[i], ls->div->row[i], ls->div->n_col);
11009 isl_seq_clr(bset->div[i] + ls->div->n_col, bset->n_div - n_div);
11010 if (isl_basic_set_add_div_constraints(bset, i) < 0)
11014 isl_local_space_free(ls);
11017 isl_local_space_free(ls);
11021 /* How many stride constraints does "ma" enforce?
11022 * That is, how many of the affine expressions have a denominator
11023 * different from one?
11025 static int multi_aff_strides(__isl_keep isl_multi_aff *ma)
11030 for (i = 0; i < ma->n; ++i)
11031 if (!isl_int_is_one(ma->p[i]->v->el[0]))
11037 /* For each affine expression in ma of the form
11039 * x_i = (f_i y + h_i)/m_i
11041 * with m_i different from one, add a constraint to "bset"
11044 * f_i y + h_i = m_i alpha_i
11046 * with alpha_i an additional existentially quantified variable.
11048 static __isl_give isl_basic_set *add_ma_strides(
11049 __isl_take isl_basic_set *bset, __isl_keep isl_multi_aff *ma)
11055 total = isl_basic_set_total_dim(bset);
11056 for (i = 0; i < ma->n; ++i) {
11059 if (isl_int_is_one(ma->p[i]->v->el[0]))
11061 div = isl_basic_set_alloc_div(bset);
11062 k = isl_basic_set_alloc_equality(bset);
11063 if (div < 0 || k < 0)
11065 isl_int_set_si(bset->div[div][0], 0);
11066 len = ma->p[i]->v->size;
11067 isl_seq_cpy(bset->eq[k], ma->p[i]->v->el + 1, len - 1);
11068 isl_seq_clr(bset->eq[k] + len - 1, 1 + total - (len - 1));
11069 isl_int_neg(bset->eq[k][1 + total], ma->p[i]->v->el[0]);
11075 isl_basic_set_free(bset);
11079 /* Compute the preimage of "bset" under the function represented by "ma".
11080 * In other words, plug in "ma" in "bset". The result is a basic set
11081 * that lives in the domain space of "ma".
11083 * If bset is represented by
11085 * A(p) + B x + C(divs) >= 0
11087 * and ma is represented by
11089 * x = D(p) + F(y) + G(divs')
11091 * then the result is
11093 * A(p) + B D(p) + B F(y) + B G(divs') + C(divs) >= 0
11095 * The divs in the input set are similarly adjusted.
11098 * floor((a_i(p) + b_i x + c_i(divs))/n_i)
11102 * floor((a_i(p) + b_i D(p) + b_i F(y) + B_i G(divs') + c_i(divs))/n_i)
11104 * If bset is not a rational set and if F(y) involves any denominators
11106 * x_i = (f_i y + h_i)/m_i
11108 * the additional constraints are added to ensure that we only
11109 * map back integer points. That is we enforce
11111 * f_i y + h_i = m_i alpha_i
11113 * with alpha_i an additional existentially quantified variable.
11115 * We first copy over the divs from "ma".
11116 * Then we add the modified constraints and divs from "bset".
11117 * Finally, we add the stride constraints, if needed.
11119 __isl_give isl_basic_set *isl_basic_set_preimage_multi_aff(
11120 __isl_take isl_basic_set *bset, __isl_take isl_multi_aff *ma)
11124 isl_basic_set *res = NULL;
11125 int n_div_bset, n_div_ma;
11126 isl_int f, c1, c2, g;
11127 int rational, strides;
11134 ma = isl_multi_aff_align_divs(ma);
11137 if (check_basic_set_compatible_range_multi_aff(bset, ma) < 0)
11140 n_div_bset = isl_basic_set_dim(bset, isl_dim_div);
11141 n_div_ma = ma->n ? isl_aff_dim(ma->p[0], isl_dim_div) : 0;
11143 space = isl_space_domain(isl_multi_aff_get_space(ma));
11144 rational = isl_basic_set_is_rational(bset);
11145 strides = rational ? 0 : multi_aff_strides(ma);
11146 res = isl_basic_set_alloc_space(space, n_div_ma + n_div_bset + strides,
11147 bset->n_eq + strides, bset->n_ineq + 2 * n_div_ma);
11149 res = isl_basic_set_set_rational(res);
11151 for (i = 0; i < n_div_ma + n_div_bset; ++i)
11152 if (isl_basic_set_alloc_div(res) < 0)
11155 if (set_ma_divs(res, ma, n_div_ma) < 0)
11158 for (i = 0; i < bset->n_eq; ++i) {
11159 k = isl_basic_set_alloc_equality(res);
11162 isl_seq_preimage(res->eq[k], bset->eq[i], ma, n_div_ma,
11163 n_div_bset, f, c1, c2, g, 0);
11166 for (i = 0; i < bset->n_ineq; ++i) {
11167 k = isl_basic_set_alloc_inequality(res);
11170 isl_seq_preimage(res->ineq[k], bset->ineq[i], ma, n_div_ma,
11171 n_div_bset, f, c1, c2, g, 0);
11174 for (i = 0; i < bset->n_div; ++i) {
11175 if (isl_int_is_zero(bset->div[i][0])) {
11176 isl_int_set_si(res->div[n_div_ma + i][0], 0);
11179 isl_seq_preimage(res->div[n_div_ma + i], bset->div[i],
11180 ma, n_div_ma, n_div_bset, f, c1, c2, g, 1);
11184 res = add_ma_strides(res, ma);
11190 isl_basic_set_free(bset);
11191 isl_multi_aff_free(ma);
11192 res = isl_basic_set_simplify(res);
11193 return isl_basic_set_finalize(res);
11199 isl_basic_set_free(bset);
11200 isl_multi_aff_free(ma);
11201 isl_basic_set_free(res);
11205 /* Check if the range of "ma" is compatible with "set".
11206 * Return -1 if anything is wrong.
11208 static int check_set_compatible_range_multi_aff(
11209 __isl_keep isl_set *set, __isl_keep isl_multi_aff *ma)
11211 return check_space_compatible_range_multi_aff(set->dim, ma);
11214 /* Compute the preimage of "set" under the function represented by "ma".
11215 * In other words, plug in "ma" in "set. The result is a set
11216 * that lives in the domain space of "ma".
11218 static __isl_give isl_set *set_preimage_multi_aff(__isl_take isl_set *set,
11219 __isl_take isl_multi_aff *ma)
11223 set = isl_set_cow(set);
11224 ma = isl_multi_aff_align_divs(ma);
11227 if (check_set_compatible_range_multi_aff(set, ma) < 0)
11230 for (i = 0; i < set->n; ++i) {
11231 set->p[i] = isl_basic_set_preimage_multi_aff(set->p[i],
11232 isl_multi_aff_copy(ma));
11237 isl_space_free(set->dim);
11238 set->dim = isl_multi_aff_get_domain_space(ma);
11242 isl_multi_aff_free(ma);
11244 ISL_F_CLR(set, ISL_MAP_DISJOINT);
11245 ISL_F_CLR(set, ISL_SET_NORMALIZED);
11248 isl_multi_aff_free(ma);
11253 __isl_give isl_set *isl_set_preimage_multi_aff(__isl_take isl_set *set,
11254 __isl_take isl_multi_aff *ma)
11259 if (isl_space_match(set->dim, isl_dim_param, ma->space, isl_dim_param))
11260 return set_preimage_multi_aff(set, ma);
11262 if (!isl_space_has_named_params(set->dim) ||
11263 !isl_space_has_named_params(ma->space))
11264 isl_die(set->ctx, isl_error_invalid,
11265 "unaligned unnamed parameters", goto error);
11266 set = isl_set_align_params(set, isl_multi_aff_get_space(ma));
11267 ma = isl_multi_aff_align_params(ma, isl_set_get_space(set));
11269 return set_preimage_multi_aff(set, ma);
11271 isl_multi_aff_free(ma);
11272 return isl_set_free(set);
11275 /* Compute the preimage of "set" under the function represented by "pma".
11276 * In other words, plug in "pma" in "set. The result is a set
11277 * that lives in the domain space of "pma".
11279 static __isl_give isl_set *set_preimage_pw_multi_aff(__isl_take isl_set *set,
11280 __isl_take isl_pw_multi_aff *pma)
11289 isl_pw_multi_aff_free(pma);
11290 res = isl_set_empty(isl_set_get_space(set));
11295 res = isl_set_preimage_multi_aff(isl_set_copy(set),
11296 isl_multi_aff_copy(pma->p[0].maff));
11297 res = isl_set_intersect(res, isl_set_copy(pma->p[0].set));
11299 for (i = 1; i < pma->n; ++i) {
11302 res_i = isl_set_preimage_multi_aff(isl_set_copy(set),
11303 isl_multi_aff_copy(pma->p[i].maff));
11304 res_i = isl_set_intersect(res_i, isl_set_copy(pma->p[i].set));
11305 res = isl_set_union(res, res_i);
11308 isl_pw_multi_aff_free(pma);
11312 isl_pw_multi_aff_free(pma);
11317 __isl_give isl_set *isl_set_preimage_pw_multi_aff(__isl_take isl_set *set,
11318 __isl_take isl_pw_multi_aff *pma)
11323 if (isl_space_match(set->dim, isl_dim_param, pma->dim, isl_dim_param))
11324 return set_preimage_pw_multi_aff(set, pma);
11326 if (!isl_space_has_named_params(set->dim) ||
11327 !isl_space_has_named_params(pma->dim))
11328 isl_die(set->ctx, isl_error_invalid,
11329 "unaligned unnamed parameters", goto error);
11330 set = isl_set_align_params(set, isl_pw_multi_aff_get_space(pma));
11331 pma = isl_pw_multi_aff_align_params(pma, isl_set_get_space(set));
11333 return set_preimage_pw_multi_aff(set, pma);
11335 isl_pw_multi_aff_free(pma);
11336 return isl_set_free(set);