2 * Copyright 2008-2009 Katholieke Universiteit Leuven
3 * Copyright 2010 INRIA Saclay
4 * Copyright 2012-2013 Ecole Normale Superieure
6 * Use of this software is governed by the MIT license
8 * Written by Sven Verdoolaege, K.U.Leuven, Departement
9 * Computerwetenschappen, Celestijnenlaan 200A, B-3001 Leuven, Belgium
10 * and INRIA Saclay - Ile-de-France, Parc Club Orsay Universite,
11 * ZAC des vignes, 4 rue Jacques Monod, 91893 Orsay, France
12 * and Ecole Normale Superieure, 45 rue d’Ulm, 75230 Paris, France
16 #include <isl_ctx_private.h>
17 #include <isl_map_private.h>
19 #include "isl_space_private.h"
20 #include "isl_equalities.h"
25 #include "isl_map_piplib.h"
26 #include <isl_reordering.h>
27 #include "isl_sample.h"
30 #include <isl_mat_private.h>
31 #include <isl_dim_map.h>
32 #include <isl_local_space_private.h>
33 #include <isl_aff_private.h>
34 #include <isl_options_private.h>
35 #include <isl_morph.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 /* Extract the divs in "bset" as a matrix.
290 __isl_give isl_mat *isl_basic_set_get_divs(__isl_keep isl_basic_set *bset)
292 return isl_basic_map_get_divs(bset);
295 __isl_give isl_local_space *isl_basic_map_get_local_space(
296 __isl_keep isl_basic_map *bmap)
303 div = isl_basic_map_get_divs(bmap);
304 return isl_local_space_alloc_div(isl_space_copy(bmap->dim), div);
307 __isl_give isl_local_space *isl_basic_set_get_local_space(
308 __isl_keep isl_basic_set *bset)
310 return isl_basic_map_get_local_space(bset);
313 __isl_give isl_basic_map *isl_basic_map_from_local_space(
314 __isl_take isl_local_space *ls)
323 n_div = isl_local_space_dim(ls, isl_dim_div);
324 bmap = isl_basic_map_alloc_space(isl_local_space_get_space(ls),
325 n_div, 0, 2 * n_div);
327 for (i = 0; i < n_div; ++i)
328 if (isl_basic_map_alloc_div(bmap) < 0)
331 for (i = 0; i < n_div; ++i) {
332 isl_seq_cpy(bmap->div[i], ls->div->row[i], ls->div->n_col);
333 if (isl_basic_map_add_div_constraints(bmap, i) < 0)
337 isl_local_space_free(ls);
340 isl_local_space_free(ls);
341 isl_basic_map_free(bmap);
345 __isl_give isl_basic_set *isl_basic_set_from_local_space(
346 __isl_take isl_local_space *ls)
348 return isl_basic_map_from_local_space(ls);
351 __isl_give isl_space *isl_map_get_space(__isl_keep isl_map *map)
355 return isl_space_copy(map->dim);
358 __isl_give isl_space *isl_set_get_space(__isl_keep isl_set *set)
362 return isl_space_copy(set->dim);
365 __isl_give isl_basic_map *isl_basic_map_set_tuple_name(
366 __isl_take isl_basic_map *bmap, enum isl_dim_type type, const char *s)
368 bmap = isl_basic_map_cow(bmap);
371 bmap->dim = isl_space_set_tuple_name(bmap->dim, type, s);
374 bmap = isl_basic_map_finalize(bmap);
377 isl_basic_map_free(bmap);
381 __isl_give isl_basic_set *isl_basic_set_set_tuple_name(
382 __isl_take isl_basic_set *bset, const char *s)
384 return isl_basic_map_set_tuple_name(bset, isl_dim_set, s);
387 const char *isl_basic_map_get_tuple_name(__isl_keep isl_basic_map *bmap,
388 enum isl_dim_type type)
390 return bmap ? isl_space_get_tuple_name(bmap->dim, type) : NULL;
393 __isl_give isl_map *isl_map_set_tuple_name(__isl_take isl_map *map,
394 enum isl_dim_type type, const char *s)
398 map = isl_map_cow(map);
402 map->dim = isl_space_set_tuple_name(map->dim, type, s);
406 for (i = 0; i < map->n; ++i) {
407 map->p[i] = isl_basic_map_set_tuple_name(map->p[i], type, s);
418 /* Does the input or output tuple have a name?
420 int isl_map_has_tuple_name(__isl_keep isl_map *map, enum isl_dim_type type)
422 return map ? isl_space_has_tuple_name(map->dim, type) : -1;
425 const char *isl_map_get_tuple_name(__isl_keep isl_map *map,
426 enum isl_dim_type type)
428 return map ? isl_space_get_tuple_name(map->dim, type) : NULL;
431 __isl_give isl_set *isl_set_set_tuple_name(__isl_take isl_set *set,
434 return (isl_set *)isl_map_set_tuple_name((isl_map *)set, isl_dim_set, s);
437 __isl_give isl_map *isl_map_set_tuple_id(__isl_take isl_map *map,
438 enum isl_dim_type type, __isl_take isl_id *id)
440 map = isl_map_cow(map);
442 return isl_id_free(id);
444 map->dim = isl_space_set_tuple_id(map->dim, type, id);
446 return isl_map_reset_space(map, isl_space_copy(map->dim));
449 __isl_give isl_set *isl_set_set_tuple_id(__isl_take isl_set *set,
450 __isl_take isl_id *id)
452 return isl_map_set_tuple_id(set, isl_dim_set, id);
455 __isl_give isl_map *isl_map_reset_tuple_id(__isl_take isl_map *map,
456 enum isl_dim_type type)
458 map = isl_map_cow(map);
462 map->dim = isl_space_reset_tuple_id(map->dim, type);
464 return isl_map_reset_space(map, isl_space_copy(map->dim));
467 __isl_give isl_set *isl_set_reset_tuple_id(__isl_take isl_set *set)
469 return isl_map_reset_tuple_id(set, isl_dim_set);
472 int isl_map_has_tuple_id(__isl_keep isl_map *map, enum isl_dim_type type)
474 return map ? isl_space_has_tuple_id(map->dim, type) : -1;
477 __isl_give isl_id *isl_map_get_tuple_id(__isl_keep isl_map *map,
478 enum isl_dim_type type)
480 return map ? isl_space_get_tuple_id(map->dim, type) : NULL;
483 int isl_set_has_tuple_id(__isl_keep isl_set *set)
485 return isl_map_has_tuple_id(set, isl_dim_set);
488 __isl_give isl_id *isl_set_get_tuple_id(__isl_keep isl_set *set)
490 return isl_map_get_tuple_id(set, isl_dim_set);
493 /* Does the set tuple have a name?
495 int isl_set_has_tuple_name(__isl_keep isl_set *set)
497 return set ? isl_space_has_tuple_name(set->dim, isl_dim_set) : -1;
501 const char *isl_basic_set_get_tuple_name(__isl_keep isl_basic_set *bset)
503 return bset ? isl_space_get_tuple_name(bset->dim, isl_dim_set) : NULL;
506 const char *isl_set_get_tuple_name(__isl_keep isl_set *set)
508 return set ? isl_space_get_tuple_name(set->dim, isl_dim_set) : NULL;
511 const char *isl_basic_map_get_dim_name(__isl_keep isl_basic_map *bmap,
512 enum isl_dim_type type, unsigned pos)
514 return bmap ? isl_space_get_dim_name(bmap->dim, type, pos) : NULL;
517 const char *isl_basic_set_get_dim_name(__isl_keep isl_basic_set *bset,
518 enum isl_dim_type type, unsigned pos)
520 return bset ? isl_space_get_dim_name(bset->dim, type, pos) : NULL;
523 /* Does the given dimension have a name?
525 int isl_map_has_dim_name(__isl_keep isl_map *map,
526 enum isl_dim_type type, unsigned pos)
528 return map ? isl_space_has_dim_name(map->dim, type, pos) : -1;
531 const char *isl_map_get_dim_name(__isl_keep isl_map *map,
532 enum isl_dim_type type, unsigned pos)
534 return map ? isl_space_get_dim_name(map->dim, type, pos) : NULL;
537 const char *isl_set_get_dim_name(__isl_keep isl_set *set,
538 enum isl_dim_type type, unsigned pos)
540 return set ? isl_space_get_dim_name(set->dim, type, pos) : NULL;
543 /* Does the given dimension have a name?
545 int isl_set_has_dim_name(__isl_keep isl_set *set,
546 enum isl_dim_type type, unsigned pos)
548 return set ? isl_space_has_dim_name(set->dim, type, pos) : -1;
551 __isl_give isl_basic_map *isl_basic_map_set_dim_name(
552 __isl_take isl_basic_map *bmap,
553 enum isl_dim_type type, unsigned pos, const char *s)
555 bmap = isl_basic_map_cow(bmap);
558 bmap->dim = isl_space_set_dim_name(bmap->dim, type, pos, s);
561 return isl_basic_map_finalize(bmap);
563 isl_basic_map_free(bmap);
567 __isl_give isl_map *isl_map_set_dim_name(__isl_take isl_map *map,
568 enum isl_dim_type type, unsigned pos, const char *s)
572 map = isl_map_cow(map);
576 map->dim = isl_space_set_dim_name(map->dim, type, pos, s);
580 for (i = 0; i < map->n; ++i) {
581 map->p[i] = isl_basic_map_set_dim_name(map->p[i], type, pos, s);
592 __isl_give isl_basic_set *isl_basic_set_set_dim_name(
593 __isl_take isl_basic_set *bset,
594 enum isl_dim_type type, unsigned pos, const char *s)
596 return (isl_basic_set *)isl_basic_map_set_dim_name(
597 (isl_basic_map *)bset, type, pos, s);
600 __isl_give isl_set *isl_set_set_dim_name(__isl_take isl_set *set,
601 enum isl_dim_type type, unsigned pos, const char *s)
603 return (isl_set *)isl_map_set_dim_name((isl_map *)set, type, pos, s);
606 int isl_basic_map_has_dim_id(__isl_keep isl_basic_map *bmap,
607 enum isl_dim_type type, unsigned pos)
609 return bmap ? isl_space_has_dim_id(bmap->dim, type, pos) : -1;
612 __isl_give isl_id *isl_basic_set_get_dim_id(__isl_keep isl_basic_set *bset,
613 enum isl_dim_type type, unsigned pos)
615 return bset ? isl_space_get_dim_id(bset->dim, type, pos) : NULL;
618 int isl_map_has_dim_id(__isl_keep isl_map *map,
619 enum isl_dim_type type, unsigned pos)
621 return map ? isl_space_has_dim_id(map->dim, type, pos) : -1;
624 __isl_give isl_id *isl_map_get_dim_id(__isl_keep isl_map *map,
625 enum isl_dim_type type, unsigned pos)
627 return map ? isl_space_get_dim_id(map->dim, type, pos) : NULL;
630 int isl_set_has_dim_id(__isl_keep isl_set *set,
631 enum isl_dim_type type, unsigned pos)
633 return isl_map_has_dim_id(set, type, pos);
636 __isl_give isl_id *isl_set_get_dim_id(__isl_keep isl_set *set,
637 enum isl_dim_type type, unsigned pos)
639 return isl_map_get_dim_id(set, type, pos);
642 __isl_give isl_map *isl_map_set_dim_id(__isl_take isl_map *map,
643 enum isl_dim_type type, unsigned pos, __isl_take isl_id *id)
645 map = isl_map_cow(map);
647 return isl_id_free(id);
649 map->dim = isl_space_set_dim_id(map->dim, type, pos, id);
651 return isl_map_reset_space(map, isl_space_copy(map->dim));
654 __isl_give isl_set *isl_set_set_dim_id(__isl_take isl_set *set,
655 enum isl_dim_type type, unsigned pos, __isl_take isl_id *id)
657 return isl_map_set_dim_id(set, type, pos, id);
660 int isl_map_find_dim_by_id(__isl_keep isl_map *map, enum isl_dim_type type,
661 __isl_keep isl_id *id)
665 return isl_space_find_dim_by_id(map->dim, type, id);
668 int isl_set_find_dim_by_id(__isl_keep isl_set *set, enum isl_dim_type type,
669 __isl_keep isl_id *id)
671 return isl_map_find_dim_by_id(set, type, id);
674 int isl_map_find_dim_by_name(__isl_keep isl_map *map, enum isl_dim_type type,
679 return isl_space_find_dim_by_name(map->dim, type, name);
682 int isl_set_find_dim_by_name(__isl_keep isl_set *set, enum isl_dim_type type,
685 return isl_map_find_dim_by_name(set, type, name);
688 int isl_basic_map_is_rational(__isl_keep isl_basic_map *bmap)
692 return ISL_F_ISSET(bmap, ISL_BASIC_MAP_RATIONAL);
695 int isl_basic_set_is_rational(__isl_keep isl_basic_set *bset)
697 return isl_basic_map_is_rational(bset);
700 /* Does "bmap" contain any rational points?
702 * If "bmap" has an equality for each dimension, equating the dimension
703 * to an integer constant, then it has no rational points, even if it
704 * is marked as rational.
706 int isl_basic_map_has_rational(__isl_keep isl_basic_map *bmap)
708 int has_rational = 1;
713 if (isl_basic_map_plain_is_empty(bmap))
715 if (!isl_basic_map_is_rational(bmap))
717 bmap = isl_basic_map_copy(bmap);
718 bmap = isl_basic_map_implicit_equalities(bmap);
721 total = isl_basic_map_total_dim(bmap);
722 if (bmap->n_eq == total) {
724 for (i = 0; i < bmap->n_eq; ++i) {
725 j = isl_seq_first_non_zero(bmap->eq[i] + 1, total);
728 if (!isl_int_is_one(bmap->eq[i][1 + j]) &&
729 !isl_int_is_negone(bmap->eq[i][1 + j]))
731 j = isl_seq_first_non_zero(bmap->eq[i] + 1 + j + 1,
739 isl_basic_map_free(bmap);
744 /* Does "map" contain any rational points?
746 int isl_map_has_rational(__isl_keep isl_map *map)
753 for (i = 0; i < map->n; ++i) {
754 has_rational = isl_basic_map_has_rational(map->p[i]);
755 if (has_rational < 0)
763 /* Does "set" contain any rational points?
765 int isl_set_has_rational(__isl_keep isl_set *set)
767 return isl_map_has_rational(set);
770 /* Is this basic set a parameter domain?
772 int isl_basic_set_is_params(__isl_keep isl_basic_set *bset)
776 return isl_space_is_params(bset->dim);
779 /* Is this set a parameter domain?
781 int isl_set_is_params(__isl_keep isl_set *set)
785 return isl_space_is_params(set->dim);
788 /* Is this map actually a parameter domain?
789 * Users should never call this function. Outside of isl,
790 * a map can never be a parameter domain.
792 int isl_map_is_params(__isl_keep isl_map *map)
796 return isl_space_is_params(map->dim);
799 static struct isl_basic_map *basic_map_init(struct isl_ctx *ctx,
800 struct isl_basic_map *bmap, unsigned extra,
801 unsigned n_eq, unsigned n_ineq)
804 size_t row_size = 1 + isl_space_dim(bmap->dim, isl_dim_all) + extra;
809 bmap->block = isl_blk_alloc(ctx, (n_ineq + n_eq) * row_size);
810 if (isl_blk_is_error(bmap->block))
813 bmap->ineq = isl_alloc_array(ctx, isl_int *, n_ineq + n_eq);
818 bmap->block2 = isl_blk_empty();
821 bmap->block2 = isl_blk_alloc(ctx, extra * (1 + row_size));
822 if (isl_blk_is_error(bmap->block2))
825 bmap->div = isl_alloc_array(ctx, isl_int *, extra);
830 for (i = 0; i < n_ineq + n_eq; ++i)
831 bmap->ineq[i] = bmap->block.data + i * row_size;
833 for (i = 0; i < extra; ++i)
834 bmap->div[i] = bmap->block2.data + i * (1 + row_size);
838 bmap->c_size = n_eq + n_ineq;
839 bmap->eq = bmap->ineq + n_ineq;
848 isl_basic_map_free(bmap);
852 struct isl_basic_set *isl_basic_set_alloc(struct isl_ctx *ctx,
853 unsigned nparam, unsigned dim, unsigned extra,
854 unsigned n_eq, unsigned n_ineq)
856 struct isl_basic_map *bmap;
859 space = isl_space_set_alloc(ctx, nparam, dim);
863 bmap = isl_basic_map_alloc_space(space, extra, n_eq, n_ineq);
864 return (struct isl_basic_set *)bmap;
867 struct isl_basic_set *isl_basic_set_alloc_space(__isl_take isl_space *dim,
868 unsigned extra, unsigned n_eq, unsigned n_ineq)
870 struct isl_basic_map *bmap;
873 isl_assert(dim->ctx, dim->n_in == 0, goto error);
874 bmap = isl_basic_map_alloc_space(dim, extra, n_eq, n_ineq);
875 return (struct isl_basic_set *)bmap;
881 struct isl_basic_map *isl_basic_map_alloc_space(__isl_take isl_space *dim,
882 unsigned extra, unsigned n_eq, unsigned n_ineq)
884 struct isl_basic_map *bmap;
888 bmap = isl_calloc_type(dim->ctx, struct isl_basic_map);
893 return basic_map_init(dim->ctx, bmap, extra, n_eq, n_ineq);
899 struct isl_basic_map *isl_basic_map_alloc(struct isl_ctx *ctx,
900 unsigned nparam, unsigned in, unsigned out, unsigned extra,
901 unsigned n_eq, unsigned n_ineq)
903 struct isl_basic_map *bmap;
906 dim = isl_space_alloc(ctx, nparam, in, out);
910 bmap = isl_basic_map_alloc_space(dim, extra, n_eq, n_ineq);
914 static void dup_constraints(
915 struct isl_basic_map *dst, struct isl_basic_map *src)
918 unsigned total = isl_basic_map_total_dim(src);
920 for (i = 0; i < src->n_eq; ++i) {
921 int j = isl_basic_map_alloc_equality(dst);
922 isl_seq_cpy(dst->eq[j], src->eq[i], 1+total);
925 for (i = 0; i < src->n_ineq; ++i) {
926 int j = isl_basic_map_alloc_inequality(dst);
927 isl_seq_cpy(dst->ineq[j], src->ineq[i], 1+total);
930 for (i = 0; i < src->n_div; ++i) {
931 int j = isl_basic_map_alloc_div(dst);
932 isl_seq_cpy(dst->div[j], src->div[i], 1+1+total);
934 ISL_F_SET(dst, ISL_BASIC_SET_FINAL);
937 struct isl_basic_map *isl_basic_map_dup(struct isl_basic_map *bmap)
939 struct isl_basic_map *dup;
943 dup = isl_basic_map_alloc_space(isl_space_copy(bmap->dim),
944 bmap->n_div, bmap->n_eq, bmap->n_ineq);
947 dup_constraints(dup, bmap);
948 dup->flags = bmap->flags;
949 dup->sample = isl_vec_copy(bmap->sample);
953 struct isl_basic_set *isl_basic_set_dup(struct isl_basic_set *bset)
955 struct isl_basic_map *dup;
957 dup = isl_basic_map_dup((struct isl_basic_map *)bset);
958 return (struct isl_basic_set *)dup;
961 struct isl_basic_set *isl_basic_set_copy(struct isl_basic_set *bset)
966 if (ISL_F_ISSET(bset, ISL_BASIC_SET_FINAL)) {
970 return isl_basic_set_dup(bset);
973 struct isl_set *isl_set_copy(struct isl_set *set)
982 struct isl_basic_map *isl_basic_map_copy(struct isl_basic_map *bmap)
987 if (ISL_F_ISSET(bmap, ISL_BASIC_SET_FINAL)) {
991 bmap = isl_basic_map_dup(bmap);
993 ISL_F_SET(bmap, ISL_BASIC_SET_FINAL);
997 struct isl_map *isl_map_copy(struct isl_map *map)
1006 void *isl_basic_map_free(__isl_take isl_basic_map *bmap)
1011 if (--bmap->ref > 0)
1014 isl_ctx_deref(bmap->ctx);
1016 isl_blk_free(bmap->ctx, bmap->block2);
1018 isl_blk_free(bmap->ctx, bmap->block);
1019 isl_vec_free(bmap->sample);
1020 isl_space_free(bmap->dim);
1026 void *isl_basic_set_free(struct isl_basic_set *bset)
1028 return isl_basic_map_free((struct isl_basic_map *)bset);
1031 static int room_for_con(struct isl_basic_map *bmap, unsigned n)
1033 return bmap->n_eq + bmap->n_ineq + n <= bmap->c_size;
1036 __isl_give isl_map *isl_map_align_params_map_map_and(
1037 __isl_take isl_map *map1, __isl_take isl_map *map2,
1038 __isl_give isl_map *(*fn)(__isl_take isl_map *map1,
1039 __isl_take isl_map *map2))
1043 if (isl_space_match(map1->dim, isl_dim_param, map2->dim, isl_dim_param))
1044 return fn(map1, map2);
1045 if (!isl_space_has_named_params(map1->dim) ||
1046 !isl_space_has_named_params(map2->dim))
1047 isl_die(map1->ctx, isl_error_invalid,
1048 "unaligned unnamed parameters", goto error);
1049 map1 = isl_map_align_params(map1, isl_map_get_space(map2));
1050 map2 = isl_map_align_params(map2, isl_map_get_space(map1));
1051 return fn(map1, map2);
1058 int isl_map_align_params_map_map_and_test(__isl_keep isl_map *map1,
1059 __isl_keep isl_map *map2,
1060 int (*fn)(__isl_keep isl_map *map1, __isl_keep isl_map *map2))
1066 if (isl_space_match(map1->dim, isl_dim_param, map2->dim, isl_dim_param))
1067 return fn(map1, map2);
1068 if (!isl_space_has_named_params(map1->dim) ||
1069 !isl_space_has_named_params(map2->dim))
1070 isl_die(map1->ctx, isl_error_invalid,
1071 "unaligned unnamed parameters", return -1);
1072 map1 = isl_map_copy(map1);
1073 map2 = isl_map_copy(map2);
1074 map1 = isl_map_align_params(map1, isl_map_get_space(map2));
1075 map2 = isl_map_align_params(map2, isl_map_get_space(map1));
1082 int isl_basic_map_alloc_equality(struct isl_basic_map *bmap)
1084 struct isl_ctx *ctx;
1088 isl_assert(ctx, room_for_con(bmap, 1), return -1);
1089 isl_assert(ctx, (bmap->eq - bmap->ineq) + bmap->n_eq <= bmap->c_size,
1091 ISL_F_CLR(bmap, ISL_BASIC_MAP_NORMALIZED);
1092 ISL_F_CLR(bmap, ISL_BASIC_MAP_NO_REDUNDANT);
1093 ISL_F_CLR(bmap, ISL_BASIC_MAP_NO_IMPLICIT);
1094 ISL_F_CLR(bmap, ISL_BASIC_MAP_ALL_EQUALITIES);
1095 ISL_F_CLR(bmap, ISL_BASIC_MAP_NORMALIZED_DIVS);
1096 if ((bmap->eq - bmap->ineq) + bmap->n_eq == bmap->c_size) {
1098 int j = isl_basic_map_alloc_inequality(bmap);
1102 bmap->ineq[j] = bmap->ineq[bmap->n_ineq - 1];
1103 bmap->ineq[bmap->n_ineq - 1] = bmap->eq[-1];
1110 isl_seq_clr(bmap->eq[bmap->n_eq] + 1 + isl_basic_map_total_dim(bmap),
1111 bmap->extra - bmap->n_div);
1112 return bmap->n_eq++;
1115 int isl_basic_set_alloc_equality(struct isl_basic_set *bset)
1117 return isl_basic_map_alloc_equality((struct isl_basic_map *)bset);
1120 int isl_basic_map_free_equality(struct isl_basic_map *bmap, unsigned n)
1124 isl_assert(bmap->ctx, n <= bmap->n_eq, return -1);
1129 int isl_basic_set_free_equality(struct isl_basic_set *bset, unsigned n)
1131 return isl_basic_map_free_equality((struct isl_basic_map *)bset, n);
1134 int isl_basic_map_drop_equality(struct isl_basic_map *bmap, unsigned pos)
1139 isl_assert(bmap->ctx, pos < bmap->n_eq, return -1);
1141 if (pos != bmap->n_eq - 1) {
1143 bmap->eq[pos] = bmap->eq[bmap->n_eq - 1];
1144 bmap->eq[bmap->n_eq - 1] = t;
1150 int isl_basic_set_drop_equality(struct isl_basic_set *bset, unsigned pos)
1152 return isl_basic_map_drop_equality((struct isl_basic_map *)bset, pos);
1155 /* Turn inequality "pos" of "bmap" into an equality.
1157 * In particular, we move the inequality in front of the equalities
1158 * and move the last inequality in the position of the moved inequality.
1159 * Note that isl_tab_make_equalities_explicit depends on this particular
1160 * change in the ordering of the constraints.
1162 void isl_basic_map_inequality_to_equality(
1163 struct isl_basic_map *bmap, unsigned pos)
1167 t = bmap->ineq[pos];
1168 bmap->ineq[pos] = bmap->ineq[bmap->n_ineq - 1];
1169 bmap->ineq[bmap->n_ineq - 1] = bmap->eq[-1];
1174 ISL_F_CLR(bmap, ISL_BASIC_MAP_NO_REDUNDANT);
1175 ISL_F_CLR(bmap, ISL_BASIC_MAP_NORMALIZED);
1176 ISL_F_CLR(bmap, ISL_BASIC_MAP_NORMALIZED_DIVS);
1177 ISL_F_CLR(bmap, ISL_BASIC_MAP_ALL_EQUALITIES);
1180 static int room_for_ineq(struct isl_basic_map *bmap, unsigned n)
1182 return bmap->n_ineq + n <= bmap->eq - bmap->ineq;
1185 int isl_basic_map_alloc_inequality(struct isl_basic_map *bmap)
1187 struct isl_ctx *ctx;
1191 isl_assert(ctx, room_for_ineq(bmap, 1), return -1);
1192 ISL_F_CLR(bmap, ISL_BASIC_MAP_NO_IMPLICIT);
1193 ISL_F_CLR(bmap, ISL_BASIC_MAP_NO_REDUNDANT);
1194 ISL_F_CLR(bmap, ISL_BASIC_MAP_NORMALIZED);
1195 ISL_F_CLR(bmap, ISL_BASIC_MAP_ALL_EQUALITIES);
1196 isl_seq_clr(bmap->ineq[bmap->n_ineq] +
1197 1 + isl_basic_map_total_dim(bmap),
1198 bmap->extra - bmap->n_div);
1199 return bmap->n_ineq++;
1202 int isl_basic_set_alloc_inequality(struct isl_basic_set *bset)
1204 return isl_basic_map_alloc_inequality((struct isl_basic_map *)bset);
1207 int isl_basic_map_free_inequality(struct isl_basic_map *bmap, unsigned n)
1211 isl_assert(bmap->ctx, n <= bmap->n_ineq, return -1);
1216 int isl_basic_set_free_inequality(struct isl_basic_set *bset, unsigned n)
1218 return isl_basic_map_free_inequality((struct isl_basic_map *)bset, n);
1221 int isl_basic_map_drop_inequality(struct isl_basic_map *bmap, unsigned pos)
1226 isl_assert(bmap->ctx, pos < bmap->n_ineq, return -1);
1228 if (pos != bmap->n_ineq - 1) {
1229 t = bmap->ineq[pos];
1230 bmap->ineq[pos] = bmap->ineq[bmap->n_ineq - 1];
1231 bmap->ineq[bmap->n_ineq - 1] = t;
1232 ISL_F_CLR(bmap, ISL_BASIC_MAP_NORMALIZED);
1238 int isl_basic_set_drop_inequality(struct isl_basic_set *bset, unsigned pos)
1240 return isl_basic_map_drop_inequality((struct isl_basic_map *)bset, pos);
1243 __isl_give isl_basic_map *isl_basic_map_add_eq(__isl_take isl_basic_map *bmap,
1248 bmap = isl_basic_map_extend_constraints(bmap, 1, 0);
1251 k = isl_basic_map_alloc_equality(bmap);
1254 isl_seq_cpy(bmap->eq[k], eq, 1 + isl_basic_map_total_dim(bmap));
1257 isl_basic_map_free(bmap);
1261 __isl_give isl_basic_set *isl_basic_set_add_eq(__isl_take isl_basic_set *bset,
1264 return (isl_basic_set *)
1265 isl_basic_map_add_eq((isl_basic_map *)bset, eq);
1268 __isl_give isl_basic_map *isl_basic_map_add_ineq(__isl_take isl_basic_map *bmap,
1273 bmap = isl_basic_map_extend_constraints(bmap, 0, 1);
1276 k = isl_basic_map_alloc_inequality(bmap);
1279 isl_seq_cpy(bmap->ineq[k], ineq, 1 + isl_basic_map_total_dim(bmap));
1282 isl_basic_map_free(bmap);
1286 __isl_give isl_basic_set *isl_basic_set_add_ineq(__isl_take isl_basic_set *bset,
1289 return (isl_basic_set *)
1290 isl_basic_map_add_ineq((isl_basic_map *)bset, ineq);
1293 int isl_basic_map_alloc_div(struct isl_basic_map *bmap)
1297 isl_assert(bmap->ctx, bmap->n_div < bmap->extra, return -1);
1298 isl_seq_clr(bmap->div[bmap->n_div] +
1299 1 + 1 + isl_basic_map_total_dim(bmap),
1300 bmap->extra - bmap->n_div);
1301 ISL_F_CLR(bmap, ISL_BASIC_MAP_NORMALIZED_DIVS);
1302 return bmap->n_div++;
1305 int isl_basic_set_alloc_div(struct isl_basic_set *bset)
1307 return isl_basic_map_alloc_div((struct isl_basic_map *)bset);
1310 int isl_basic_map_free_div(struct isl_basic_map *bmap, unsigned n)
1314 isl_assert(bmap->ctx, n <= bmap->n_div, return -1);
1319 int isl_basic_set_free_div(struct isl_basic_set *bset, unsigned n)
1321 return isl_basic_map_free_div((struct isl_basic_map *)bset, n);
1324 /* Copy constraint from src to dst, putting the vars of src at offset
1325 * dim_off in dst and the divs of src at offset div_off in dst.
1326 * If both sets are actually map, then dim_off applies to the input
1329 static void copy_constraint(struct isl_basic_map *dst_map, isl_int *dst,
1330 struct isl_basic_map *src_map, isl_int *src,
1331 unsigned in_off, unsigned out_off, unsigned div_off)
1333 unsigned src_nparam = isl_basic_map_n_param(src_map);
1334 unsigned dst_nparam = isl_basic_map_n_param(dst_map);
1335 unsigned src_in = isl_basic_map_n_in(src_map);
1336 unsigned dst_in = isl_basic_map_n_in(dst_map);
1337 unsigned src_out = isl_basic_map_n_out(src_map);
1338 unsigned dst_out = isl_basic_map_n_out(dst_map);
1339 isl_int_set(dst[0], src[0]);
1340 isl_seq_cpy(dst+1, src+1, isl_min(dst_nparam, src_nparam));
1341 if (dst_nparam > src_nparam)
1342 isl_seq_clr(dst+1+src_nparam,
1343 dst_nparam - src_nparam);
1344 isl_seq_clr(dst+1+dst_nparam, in_off);
1345 isl_seq_cpy(dst+1+dst_nparam+in_off,
1347 isl_min(dst_in-in_off, src_in));
1348 if (dst_in-in_off > src_in)
1349 isl_seq_clr(dst+1+dst_nparam+in_off+src_in,
1350 dst_in - in_off - src_in);
1351 isl_seq_clr(dst+1+dst_nparam+dst_in, out_off);
1352 isl_seq_cpy(dst+1+dst_nparam+dst_in+out_off,
1353 src+1+src_nparam+src_in,
1354 isl_min(dst_out-out_off, src_out));
1355 if (dst_out-out_off > src_out)
1356 isl_seq_clr(dst+1+dst_nparam+dst_in+out_off+src_out,
1357 dst_out - out_off - src_out);
1358 isl_seq_clr(dst+1+dst_nparam+dst_in+dst_out, div_off);
1359 isl_seq_cpy(dst+1+dst_nparam+dst_in+dst_out+div_off,
1360 src+1+src_nparam+src_in+src_out,
1361 isl_min(dst_map->extra-div_off, src_map->n_div));
1362 if (dst_map->n_div-div_off > src_map->n_div)
1363 isl_seq_clr(dst+1+dst_nparam+dst_in+dst_out+
1364 div_off+src_map->n_div,
1365 dst_map->n_div - div_off - src_map->n_div);
1368 static void copy_div(struct isl_basic_map *dst_map, isl_int *dst,
1369 struct isl_basic_map *src_map, isl_int *src,
1370 unsigned in_off, unsigned out_off, unsigned div_off)
1372 isl_int_set(dst[0], src[0]);
1373 copy_constraint(dst_map, dst+1, src_map, src+1, in_off, out_off, div_off);
1376 static struct isl_basic_map *add_constraints(struct isl_basic_map *bmap1,
1377 struct isl_basic_map *bmap2, unsigned i_pos, unsigned o_pos)
1382 if (!bmap1 || !bmap2)
1385 div_off = bmap1->n_div;
1387 for (i = 0; i < bmap2->n_eq; ++i) {
1388 int i1 = isl_basic_map_alloc_equality(bmap1);
1391 copy_constraint(bmap1, bmap1->eq[i1], bmap2, bmap2->eq[i],
1392 i_pos, o_pos, div_off);
1395 for (i = 0; i < bmap2->n_ineq; ++i) {
1396 int i1 = isl_basic_map_alloc_inequality(bmap1);
1399 copy_constraint(bmap1, bmap1->ineq[i1], bmap2, bmap2->ineq[i],
1400 i_pos, o_pos, div_off);
1403 for (i = 0; i < bmap2->n_div; ++i) {
1404 int i1 = isl_basic_map_alloc_div(bmap1);
1407 copy_div(bmap1, bmap1->div[i1], bmap2, bmap2->div[i],
1408 i_pos, o_pos, div_off);
1411 isl_basic_map_free(bmap2);
1416 isl_basic_map_free(bmap1);
1417 isl_basic_map_free(bmap2);
1421 struct isl_basic_set *isl_basic_set_add_constraints(struct isl_basic_set *bset1,
1422 struct isl_basic_set *bset2, unsigned pos)
1424 return (struct isl_basic_set *)
1425 add_constraints((struct isl_basic_map *)bset1,
1426 (struct isl_basic_map *)bset2, 0, pos);
1429 struct isl_basic_map *isl_basic_map_extend_space(struct isl_basic_map *base,
1430 __isl_take isl_space *dim, unsigned extra,
1431 unsigned n_eq, unsigned n_ineq)
1433 struct isl_basic_map *ext;
1443 dims_ok = isl_space_is_equal(base->dim, dim) &&
1444 base->extra >= base->n_div + extra;
1446 if (dims_ok && room_for_con(base, n_eq + n_ineq) &&
1447 room_for_ineq(base, n_ineq)) {
1448 isl_space_free(dim);
1452 isl_assert(base->ctx, base->dim->nparam <= dim->nparam, goto error);
1453 isl_assert(base->ctx, base->dim->n_in <= dim->n_in, goto error);
1454 isl_assert(base->ctx, base->dim->n_out <= dim->n_out, goto error);
1455 extra += base->extra;
1457 n_ineq += base->n_ineq;
1459 ext = isl_basic_map_alloc_space(dim, extra, n_eq, n_ineq);
1465 ext->sample = isl_vec_copy(base->sample);
1466 flags = base->flags;
1467 ext = add_constraints(ext, base, 0, 0);
1470 ISL_F_CLR(ext, ISL_BASIC_SET_FINAL);
1476 isl_space_free(dim);
1477 isl_basic_map_free(base);
1481 struct isl_basic_set *isl_basic_set_extend_space(struct isl_basic_set *base,
1482 __isl_take isl_space *dim, unsigned extra,
1483 unsigned n_eq, unsigned n_ineq)
1485 return (struct isl_basic_set *)
1486 isl_basic_map_extend_space((struct isl_basic_map *)base, dim,
1487 extra, n_eq, n_ineq);
1490 struct isl_basic_map *isl_basic_map_extend_constraints(
1491 struct isl_basic_map *base, unsigned n_eq, unsigned n_ineq)
1495 return isl_basic_map_extend_space(base, isl_space_copy(base->dim),
1499 struct isl_basic_map *isl_basic_map_extend(struct isl_basic_map *base,
1500 unsigned nparam, unsigned n_in, unsigned n_out, unsigned extra,
1501 unsigned n_eq, unsigned n_ineq)
1503 struct isl_basic_map *bmap;
1508 dim = isl_space_alloc(base->ctx, nparam, n_in, n_out);
1512 bmap = isl_basic_map_extend_space(base, dim, extra, n_eq, n_ineq);
1515 isl_basic_map_free(base);
1519 struct isl_basic_set *isl_basic_set_extend(struct isl_basic_set *base,
1520 unsigned nparam, unsigned dim, unsigned extra,
1521 unsigned n_eq, unsigned n_ineq)
1523 return (struct isl_basic_set *)
1524 isl_basic_map_extend((struct isl_basic_map *)base,
1525 nparam, 0, dim, extra, n_eq, n_ineq);
1528 struct isl_basic_set *isl_basic_set_extend_constraints(
1529 struct isl_basic_set *base, unsigned n_eq, unsigned n_ineq)
1531 return (struct isl_basic_set *)
1532 isl_basic_map_extend_constraints((struct isl_basic_map *)base,
1536 struct isl_basic_set *isl_basic_set_cow(struct isl_basic_set *bset)
1538 return (struct isl_basic_set *)
1539 isl_basic_map_cow((struct isl_basic_map *)bset);
1542 struct isl_basic_map *isl_basic_map_cow(struct isl_basic_map *bmap)
1547 if (bmap->ref > 1) {
1549 bmap = isl_basic_map_dup(bmap);
1552 ISL_F_CLR(bmap, ISL_BASIC_SET_FINAL);
1556 struct isl_set *isl_set_cow(struct isl_set *set)
1564 return isl_set_dup(set);
1567 struct isl_map *isl_map_cow(struct isl_map *map)
1575 return isl_map_dup(map);
1578 static void swap_vars(struct isl_blk blk, isl_int *a,
1579 unsigned a_len, unsigned b_len)
1581 isl_seq_cpy(blk.data, a+a_len, b_len);
1582 isl_seq_cpy(blk.data+b_len, a, a_len);
1583 isl_seq_cpy(a, blk.data, b_len+a_len);
1586 static __isl_give isl_basic_map *isl_basic_map_swap_vars(
1587 __isl_take isl_basic_map *bmap, unsigned pos, unsigned n1, unsigned n2)
1595 isl_assert(bmap->ctx,
1596 pos + n1 + n2 <= 1 + isl_basic_map_total_dim(bmap), goto error);
1598 if (n1 == 0 || n2 == 0)
1601 bmap = isl_basic_map_cow(bmap);
1605 blk = isl_blk_alloc(bmap->ctx, n1 + n2);
1606 if (isl_blk_is_error(blk))
1609 for (i = 0; i < bmap->n_eq; ++i)
1611 bmap->eq[i] + pos, n1, n2);
1613 for (i = 0; i < bmap->n_ineq; ++i)
1615 bmap->ineq[i] + pos, n1, n2);
1617 for (i = 0; i < bmap->n_div; ++i)
1619 bmap->div[i]+1 + pos, n1, n2);
1621 isl_blk_free(bmap->ctx, blk);
1623 ISL_F_CLR(bmap, ISL_BASIC_SET_NORMALIZED);
1624 bmap = isl_basic_map_gauss(bmap, NULL);
1625 return isl_basic_map_finalize(bmap);
1627 isl_basic_map_free(bmap);
1631 static __isl_give isl_basic_set *isl_basic_set_swap_vars(
1632 __isl_take isl_basic_set *bset, unsigned n)
1640 nparam = isl_basic_set_n_param(bset);
1641 dim = isl_basic_set_n_dim(bset);
1642 isl_assert(bset->ctx, n <= dim, goto error);
1644 return isl_basic_map_swap_vars(bset, 1 + nparam, n, dim - n);
1646 isl_basic_set_free(bset);
1650 struct isl_basic_map *isl_basic_map_set_to_empty(struct isl_basic_map *bmap)
1656 total = isl_basic_map_total_dim(bmap);
1657 isl_basic_map_free_div(bmap, bmap->n_div);
1658 isl_basic_map_free_inequality(bmap, bmap->n_ineq);
1660 isl_basic_map_free_equality(bmap, bmap->n_eq-1);
1662 i = isl_basic_map_alloc_equality(bmap);
1666 isl_int_set_si(bmap->eq[i][0], 1);
1667 isl_seq_clr(bmap->eq[i]+1, total);
1668 ISL_F_SET(bmap, ISL_BASIC_MAP_EMPTY);
1669 isl_vec_free(bmap->sample);
1670 bmap->sample = NULL;
1671 return isl_basic_map_finalize(bmap);
1673 isl_basic_map_free(bmap);
1677 struct isl_basic_set *isl_basic_set_set_to_empty(struct isl_basic_set *bset)
1679 return (struct isl_basic_set *)
1680 isl_basic_map_set_to_empty((struct isl_basic_map *)bset);
1683 /* Swap divs "a" and "b" in "bmap" (without modifying any of the constraints
1686 static void swap_div(__isl_keep isl_basic_map *bmap, int a, int b)
1688 isl_int *t = bmap->div[a];
1689 bmap->div[a] = bmap->div[b];
1693 /* Swap divs "a" and "b" in "bmap" and adjust the constraints and
1694 * div definitions accordingly.
1696 void isl_basic_map_swap_div(struct isl_basic_map *bmap, int a, int b)
1699 unsigned off = isl_space_dim(bmap->dim, isl_dim_all);
1701 swap_div(bmap, a, b);
1703 for (i = 0; i < bmap->n_eq; ++i)
1704 isl_int_swap(bmap->eq[i][1+off+a], bmap->eq[i][1+off+b]);
1706 for (i = 0; i < bmap->n_ineq; ++i)
1707 isl_int_swap(bmap->ineq[i][1+off+a], bmap->ineq[i][1+off+b]);
1709 for (i = 0; i < bmap->n_div; ++i)
1710 isl_int_swap(bmap->div[i][1+1+off+a], bmap->div[i][1+1+off+b]);
1711 ISL_F_CLR(bmap, ISL_BASIC_MAP_NORMALIZED);
1714 /* Eliminate the specified n dimensions starting at first from the
1715 * constraints, without removing the dimensions from the space.
1716 * If the set is rational, the dimensions are eliminated using Fourier-Motzkin.
1718 __isl_give isl_map *isl_map_eliminate(__isl_take isl_map *map,
1719 enum isl_dim_type type, unsigned first, unsigned n)
1728 if (first + n > isl_map_dim(map, type) || first + n < first)
1729 isl_die(map->ctx, isl_error_invalid,
1730 "index out of bounds", goto error);
1732 map = isl_map_cow(map);
1736 for (i = 0; i < map->n; ++i) {
1737 map->p[i] = isl_basic_map_eliminate(map->p[i], type, first, n);
1747 /* Eliminate the specified n dimensions starting at first from the
1748 * constraints, without removing the dimensions from the space.
1749 * If the set is rational, the dimensions are eliminated using Fourier-Motzkin.
1751 __isl_give isl_set *isl_set_eliminate(__isl_take isl_set *set,
1752 enum isl_dim_type type, unsigned first, unsigned n)
1754 return (isl_set *)isl_map_eliminate((isl_map *)set, type, first, n);
1757 /* Eliminate the specified n dimensions starting at first from the
1758 * constraints, without removing the dimensions from the space.
1759 * If the set is rational, the dimensions are eliminated using Fourier-Motzkin.
1761 __isl_give isl_set *isl_set_eliminate_dims(__isl_take isl_set *set,
1762 unsigned first, unsigned n)
1764 return isl_set_eliminate(set, isl_dim_set, first, n);
1767 __isl_give isl_basic_map *isl_basic_map_remove_divs(
1768 __isl_take isl_basic_map *bmap)
1772 bmap = isl_basic_map_eliminate_vars(bmap,
1773 isl_space_dim(bmap->dim, isl_dim_all), bmap->n_div);
1777 return isl_basic_map_finalize(bmap);
1780 __isl_give isl_basic_set *isl_basic_set_remove_divs(
1781 __isl_take isl_basic_set *bset)
1783 return (struct isl_basic_set *)isl_basic_map_remove_divs(
1784 (struct isl_basic_map *)bset);
1787 __isl_give isl_map *isl_map_remove_divs(__isl_take isl_map *map)
1796 map = isl_map_cow(map);
1800 for (i = 0; i < map->n; ++i) {
1801 map->p[i] = isl_basic_map_remove_divs(map->p[i]);
1811 __isl_give isl_set *isl_set_remove_divs(__isl_take isl_set *set)
1813 return isl_map_remove_divs(set);
1816 struct isl_basic_map *isl_basic_map_remove_dims(struct isl_basic_map *bmap,
1817 enum isl_dim_type type, unsigned first, unsigned n)
1821 isl_assert(bmap->ctx, first + n <= isl_basic_map_dim(bmap, type),
1823 if (n == 0 && !isl_space_is_named_or_nested(bmap->dim, type))
1825 bmap = isl_basic_map_eliminate_vars(bmap,
1826 isl_basic_map_offset(bmap, type) - 1 + first, n);
1829 if (ISL_F_ISSET(bmap, ISL_BASIC_MAP_EMPTY) && type == isl_dim_div)
1831 bmap = isl_basic_map_drop(bmap, type, first, n);
1834 isl_basic_map_free(bmap);
1838 /* Return true if the definition of the given div (recursively) involves
1839 * any of the given variables.
1841 static int div_involves_vars(__isl_keep isl_basic_map *bmap, int div,
1842 unsigned first, unsigned n)
1845 unsigned div_offset = isl_basic_map_offset(bmap, isl_dim_div);
1847 if (isl_int_is_zero(bmap->div[div][0]))
1849 if (isl_seq_first_non_zero(bmap->div[div] + 1 + first, n) >= 0)
1852 for (i = bmap->n_div - 1; i >= 0; --i) {
1853 if (isl_int_is_zero(bmap->div[div][1 + div_offset + i]))
1855 if (div_involves_vars(bmap, i, first, n))
1862 /* Try and add a lower and/or upper bound on "div" to "bmap"
1863 * based on inequality "i".
1864 * "total" is the total number of variables (excluding the divs).
1865 * "v" is a temporary object that can be used during the calculations.
1866 * If "lb" is set, then a lower bound should be constructed.
1867 * If "ub" is set, then an upper bound should be constructed.
1869 * The calling function has already checked that the inequality does not
1870 * reference "div", but we still need to check that the inequality is
1871 * of the right form. We'll consider the case where we want to construct
1872 * a lower bound. The construction of upper bounds is similar.
1874 * Let "div" be of the form
1876 * q = floor((a + f(x))/d)
1878 * We essentially check if constraint "i" is of the form
1882 * so that we can use it to derive a lower bound on "div".
1883 * However, we allow a slightly more general form
1887 * with the condition that the coefficients of g(x) - f(x) are all
1889 * Rewriting this constraint as
1893 * adding a + f(x) to both sides and dividing by d, we obtain
1895 * (a + f(x))/d >= (a-b)/d + (f(x)-g(x))/d
1897 * Taking the floor on both sides, we obtain
1899 * q >= floor((a-b)/d) + (f(x)-g(x))/d
1903 * (g(x)-f(x))/d + ceil((b-a)/d) + q >= 0
1905 * In the case of an upper bound, we construct the constraint
1907 * (g(x)+f(x))/d + floor((b+a)/d) - q >= 0
1910 static __isl_give isl_basic_map *insert_bounds_on_div_from_ineq(
1911 __isl_take isl_basic_map *bmap, int div, int i,
1912 unsigned total, isl_int v, int lb, int ub)
1916 for (j = 0; (lb || ub) && j < total + bmap->n_div; ++j) {
1918 isl_int_sub(v, bmap->ineq[i][1 + j],
1919 bmap->div[div][1 + 1 + j]);
1920 lb = isl_int_is_divisible_by(v, bmap->div[div][0]);
1923 isl_int_add(v, bmap->ineq[i][1 + j],
1924 bmap->div[div][1 + 1 + j]);
1925 ub = isl_int_is_divisible_by(v, bmap->div[div][0]);
1931 bmap = isl_basic_map_extend_constraints(bmap, 0, lb + ub);
1933 int k = isl_basic_map_alloc_inequality(bmap);
1936 for (j = 0; j < 1 + total + bmap->n_div; ++j) {
1937 isl_int_sub(bmap->ineq[k][j], bmap->ineq[i][j],
1938 bmap->div[div][1 + j]);
1939 isl_int_cdiv_q(bmap->ineq[k][j],
1940 bmap->ineq[k][j], bmap->div[div][0]);
1942 isl_int_set_si(bmap->ineq[k][1 + total + div], 1);
1945 int k = isl_basic_map_alloc_inequality(bmap);
1948 for (j = 0; j < 1 + total + bmap->n_div; ++j) {
1949 isl_int_add(bmap->ineq[k][j], bmap->ineq[i][j],
1950 bmap->div[div][1 + j]);
1951 isl_int_fdiv_q(bmap->ineq[k][j],
1952 bmap->ineq[k][j], bmap->div[div][0]);
1954 isl_int_set_si(bmap->ineq[k][1 + total + div], -1);
1959 isl_basic_map_free(bmap);
1963 /* This function is called right before "div" is eliminated from "bmap"
1964 * using Fourier-Motzkin.
1965 * Look through the constraints of "bmap" for constraints on the argument
1966 * of the integer division and use them to construct constraints on the
1967 * integer division itself. These constraints can then be combined
1968 * during the Fourier-Motzkin elimination.
1969 * Note that it is only useful to introduce lower bounds on "div"
1970 * if "bmap" already contains upper bounds on "div" as the newly
1971 * introduce lower bounds can then be combined with the pre-existing
1972 * upper bounds. Similarly for upper bounds.
1973 * We therefore first check if "bmap" contains any lower and/or upper bounds
1976 * It is interesting to note that the introduction of these constraints
1977 * can indeed lead to more accurate results, even when compared to
1978 * deriving constraints on the argument of "div" from constraints on "div".
1979 * Consider, for example, the set
1981 * { [i,j,k] : 3 + i + 2j >= 0 and 2 * [(i+2j)/4] <= k }
1983 * The second constraint can be rewritten as
1985 * 2 * [(-i-2j+3)/4] + k >= 0
1987 * from which we can derive
1989 * -i - 2j + 3 >= -2k
1995 * Combined with the first constraint, we obtain
1997 * -3 <= 3 + 2k or k >= -3
1999 * If, on the other hand we derive a constraint on [(i+2j)/4] from
2000 * the first constraint, we obtain
2002 * [(i + 2j)/4] >= [-3/4] = -1
2004 * Combining this constraint with the second constraint, we obtain
2008 static __isl_give isl_basic_map *insert_bounds_on_div(
2009 __isl_take isl_basic_map *bmap, int div)
2012 int check_lb, check_ub;
2019 if (isl_int_is_zero(bmap->div[div][0]))
2022 total = isl_space_dim(bmap->dim, isl_dim_all);
2026 for (i = 0; (!check_lb || !check_ub) && i < bmap->n_ineq; ++i) {
2027 int s = isl_int_sgn(bmap->ineq[i][1 + total + div]);
2034 if (!check_lb && !check_ub)
2039 for (i = 0; bmap && i < bmap->n_ineq; ++i) {
2040 if (!isl_int_is_zero(bmap->ineq[i][1 + total + div]))
2043 bmap = insert_bounds_on_div_from_ineq(bmap, div, i, total, v,
2044 check_lb, check_ub);
2052 /* Remove all divs (recursively) involving any of the given dimensions
2053 * in their definitions.
2055 __isl_give isl_basic_map *isl_basic_map_remove_divs_involving_dims(
2056 __isl_take isl_basic_map *bmap,
2057 enum isl_dim_type type, unsigned first, unsigned n)
2063 isl_assert(bmap->ctx, first + n <= isl_basic_map_dim(bmap, type),
2065 first += isl_basic_map_offset(bmap, type);
2067 for (i = bmap->n_div - 1; i >= 0; --i) {
2068 if (!div_involves_vars(bmap, i, first, n))
2070 bmap = insert_bounds_on_div(bmap, i);
2071 bmap = isl_basic_map_remove_dims(bmap, isl_dim_div, i, 1);
2079 isl_basic_map_free(bmap);
2083 __isl_give isl_basic_set *isl_basic_set_remove_divs_involving_dims(
2084 __isl_take isl_basic_set *bset,
2085 enum isl_dim_type type, unsigned first, unsigned n)
2087 return isl_basic_map_remove_divs_involving_dims(bset, type, first, n);
2090 __isl_give isl_map *isl_map_remove_divs_involving_dims(__isl_take isl_map *map,
2091 enum isl_dim_type type, unsigned first, unsigned n)
2100 map = isl_map_cow(map);
2104 for (i = 0; i < map->n; ++i) {
2105 map->p[i] = isl_basic_map_remove_divs_involving_dims(map->p[i],
2116 __isl_give isl_set *isl_set_remove_divs_involving_dims(__isl_take isl_set *set,
2117 enum isl_dim_type type, unsigned first, unsigned n)
2119 return (isl_set *)isl_map_remove_divs_involving_dims((isl_map *)set,
2123 /* Does the desciption of "bmap" depend on the specified dimensions?
2124 * We also check whether the dimensions appear in any of the div definitions.
2125 * In principle there is no need for this check. If the dimensions appear
2126 * in a div definition, they also appear in the defining constraints of that
2129 int isl_basic_map_involves_dims(__isl_keep isl_basic_map *bmap,
2130 enum isl_dim_type type, unsigned first, unsigned n)
2137 if (first + n > isl_basic_map_dim(bmap, type))
2138 isl_die(bmap->ctx, isl_error_invalid,
2139 "index out of bounds", return -1);
2141 first += isl_basic_map_offset(bmap, type);
2142 for (i = 0; i < bmap->n_eq; ++i)
2143 if (isl_seq_first_non_zero(bmap->eq[i] + first, n) >= 0)
2145 for (i = 0; i < bmap->n_ineq; ++i)
2146 if (isl_seq_first_non_zero(bmap->ineq[i] + first, n) >= 0)
2148 for (i = 0; i < bmap->n_div; ++i) {
2149 if (isl_int_is_zero(bmap->div[i][0]))
2151 if (isl_seq_first_non_zero(bmap->div[i] + 1 + first, n) >= 0)
2158 int isl_map_involves_dims(__isl_keep isl_map *map,
2159 enum isl_dim_type type, unsigned first, unsigned n)
2166 if (first + n > isl_map_dim(map, type))
2167 isl_die(map->ctx, isl_error_invalid,
2168 "index out of bounds", return -1);
2170 for (i = 0; i < map->n; ++i) {
2171 int involves = isl_basic_map_involves_dims(map->p[i],
2173 if (involves < 0 || involves)
2180 int isl_basic_set_involves_dims(__isl_keep isl_basic_set *bset,
2181 enum isl_dim_type type, unsigned first, unsigned n)
2183 return isl_basic_map_involves_dims(bset, type, first, n);
2186 int isl_set_involves_dims(__isl_keep isl_set *set,
2187 enum isl_dim_type type, unsigned first, unsigned n)
2189 return isl_map_involves_dims(set, type, first, n);
2192 /* Return true if the definition of the given div is unknown or depends
2195 static int div_is_unknown(__isl_keep isl_basic_map *bmap, int div)
2198 unsigned div_offset = isl_basic_map_offset(bmap, isl_dim_div);
2200 if (isl_int_is_zero(bmap->div[div][0]))
2203 for (i = bmap->n_div - 1; i >= 0; --i) {
2204 if (isl_int_is_zero(bmap->div[div][1 + div_offset + i]))
2206 if (div_is_unknown(bmap, i))
2213 /* Remove all divs that are unknown or defined in terms of unknown divs.
2215 __isl_give isl_basic_map *isl_basic_map_remove_unknown_divs(
2216 __isl_take isl_basic_map *bmap)
2223 for (i = bmap->n_div - 1; i >= 0; --i) {
2224 if (!div_is_unknown(bmap, i))
2226 bmap = isl_basic_map_remove_dims(bmap, isl_dim_div, i, 1);
2235 /* Remove all divs that are unknown or defined in terms of unknown divs.
2237 __isl_give isl_basic_set *isl_basic_set_remove_unknown_divs(
2238 __isl_take isl_basic_set *bset)
2240 return isl_basic_map_remove_unknown_divs(bset);
2243 __isl_give isl_map *isl_map_remove_unknown_divs(__isl_take isl_map *map)
2252 map = isl_map_cow(map);
2256 for (i = 0; i < map->n; ++i) {
2257 map->p[i] = isl_basic_map_remove_unknown_divs(map->p[i]);
2267 __isl_give isl_set *isl_set_remove_unknown_divs(__isl_take isl_set *set)
2269 return (isl_set *)isl_map_remove_unknown_divs((isl_map *)set);
2272 __isl_give isl_basic_set *isl_basic_set_remove_dims(
2273 __isl_take isl_basic_set *bset,
2274 enum isl_dim_type type, unsigned first, unsigned n)
2276 return (isl_basic_set *)
2277 isl_basic_map_remove_dims((isl_basic_map *)bset, type, first, n);
2280 struct isl_map *isl_map_remove_dims(struct isl_map *map,
2281 enum isl_dim_type type, unsigned first, unsigned n)
2288 map = isl_map_cow(map);
2291 isl_assert(map->ctx, first + n <= isl_map_dim(map, type), goto error);
2293 for (i = 0; i < map->n; ++i) {
2294 map->p[i] = isl_basic_map_eliminate_vars(map->p[i],
2295 isl_basic_map_offset(map->p[i], type) - 1 + first, n);
2299 map = isl_map_drop(map, type, first, n);
2306 __isl_give isl_set *isl_set_remove_dims(__isl_take isl_set *bset,
2307 enum isl_dim_type type, unsigned first, unsigned n)
2309 return (isl_set *)isl_map_remove_dims((isl_map *)bset, type, first, n);
2312 /* Project out n inputs starting at first using Fourier-Motzkin */
2313 struct isl_map *isl_map_remove_inputs(struct isl_map *map,
2314 unsigned first, unsigned n)
2316 return isl_map_remove_dims(map, isl_dim_in, first, n);
2319 static void dump_term(struct isl_basic_map *bmap,
2320 isl_int c, int pos, FILE *out)
2323 unsigned in = isl_basic_map_n_in(bmap);
2324 unsigned dim = in + isl_basic_map_n_out(bmap);
2325 unsigned nparam = isl_basic_map_n_param(bmap);
2327 isl_int_print(out, c, 0);
2329 if (!isl_int_is_one(c))
2330 isl_int_print(out, c, 0);
2331 if (pos < 1 + nparam) {
2332 name = isl_space_get_dim_name(bmap->dim,
2333 isl_dim_param, pos - 1);
2335 fprintf(out, "%s", name);
2337 fprintf(out, "p%d", pos - 1);
2338 } else if (pos < 1 + nparam + in)
2339 fprintf(out, "i%d", pos - 1 - nparam);
2340 else if (pos < 1 + nparam + dim)
2341 fprintf(out, "o%d", pos - 1 - nparam - in);
2343 fprintf(out, "e%d", pos - 1 - nparam - dim);
2347 static void dump_constraint_sign(struct isl_basic_map *bmap, isl_int *c,
2348 int sign, FILE *out)
2352 unsigned len = 1 + isl_basic_map_total_dim(bmap);
2356 for (i = 0, first = 1; i < len; ++i) {
2357 if (isl_int_sgn(c[i]) * sign <= 0)
2360 fprintf(out, " + ");
2362 isl_int_abs(v, c[i]);
2363 dump_term(bmap, v, i, out);
2370 static void dump_constraint(struct isl_basic_map *bmap, isl_int *c,
2371 const char *op, FILE *out, int indent)
2375 fprintf(out, "%*s", indent, "");
2377 dump_constraint_sign(bmap, c, 1, out);
2378 fprintf(out, " %s ", op);
2379 dump_constraint_sign(bmap, c, -1, out);
2383 for (i = bmap->n_div; i < bmap->extra; ++i) {
2384 if (isl_int_is_zero(c[1+isl_space_dim(bmap->dim, isl_dim_all)+i]))
2386 fprintf(out, "%*s", indent, "");
2387 fprintf(out, "ERROR: unused div coefficient not zero\n");
2392 static void dump_constraints(struct isl_basic_map *bmap,
2393 isl_int **c, unsigned n,
2394 const char *op, FILE *out, int indent)
2398 for (i = 0; i < n; ++i)
2399 dump_constraint(bmap, c[i], op, out, indent);
2402 static void dump_affine(struct isl_basic_map *bmap, isl_int *exp, FILE *out)
2406 unsigned total = isl_basic_map_total_dim(bmap);
2408 for (j = 0; j < 1 + total; ++j) {
2409 if (isl_int_is_zero(exp[j]))
2411 if (!first && isl_int_is_pos(exp[j]))
2413 dump_term(bmap, exp[j], j, out);
2418 static void dump(struct isl_basic_map *bmap, FILE *out, int indent)
2422 dump_constraints(bmap, bmap->eq, bmap->n_eq, "=", out, indent);
2423 dump_constraints(bmap, bmap->ineq, bmap->n_ineq, ">=", out, indent);
2425 for (i = 0; i < bmap->n_div; ++i) {
2426 fprintf(out, "%*s", indent, "");
2427 fprintf(out, "e%d = [(", i);
2428 dump_affine(bmap, bmap->div[i]+1, out);
2430 isl_int_print(out, bmap->div[i][0], 0);
2431 fprintf(out, "]\n");
2435 void isl_basic_set_print_internal(struct isl_basic_set *bset,
2436 FILE *out, int indent)
2439 fprintf(out, "null basic set\n");
2443 fprintf(out, "%*s", indent, "");
2444 fprintf(out, "ref: %d, nparam: %d, dim: %d, extra: %d, flags: %x\n",
2445 bset->ref, bset->dim->nparam, bset->dim->n_out,
2446 bset->extra, bset->flags);
2447 dump((struct isl_basic_map *)bset, out, indent);
2450 void isl_basic_map_print_internal(struct isl_basic_map *bmap,
2451 FILE *out, int indent)
2454 fprintf(out, "null basic map\n");
2458 fprintf(out, "%*s", indent, "");
2459 fprintf(out, "ref: %d, nparam: %d, in: %d, out: %d, extra: %d, "
2460 "flags: %x, n_name: %d\n",
2462 bmap->dim->nparam, bmap->dim->n_in, bmap->dim->n_out,
2463 bmap->extra, bmap->flags, bmap->dim->n_id);
2464 dump(bmap, out, indent);
2467 int isl_inequality_negate(struct isl_basic_map *bmap, unsigned pos)
2472 total = isl_basic_map_total_dim(bmap);
2473 isl_assert(bmap->ctx, pos < bmap->n_ineq, return -1);
2474 isl_seq_neg(bmap->ineq[pos], bmap->ineq[pos], 1 + total);
2475 isl_int_sub_ui(bmap->ineq[pos][0], bmap->ineq[pos][0], 1);
2476 ISL_F_CLR(bmap, ISL_BASIC_MAP_NORMALIZED);
2480 __isl_give isl_set *isl_set_alloc_space(__isl_take isl_space *dim, int n,
2483 struct isl_set *set;
2487 isl_assert(dim->ctx, dim->n_in == 0, goto error);
2488 isl_assert(dim->ctx, n >= 0, goto error);
2489 set = isl_alloc(dim->ctx, struct isl_set,
2490 sizeof(struct isl_set) +
2491 (n - 1) * sizeof(struct isl_basic_set *));
2495 set->ctx = dim->ctx;
2496 isl_ctx_ref(set->ctx);
2504 isl_space_free(dim);
2508 struct isl_set *isl_set_alloc(struct isl_ctx *ctx,
2509 unsigned nparam, unsigned dim, int n, unsigned flags)
2511 struct isl_set *set;
2514 dims = isl_space_alloc(ctx, nparam, 0, dim);
2518 set = isl_set_alloc_space(dims, n, flags);
2522 /* Make sure "map" has room for at least "n" more basic maps.
2524 struct isl_map *isl_map_grow(struct isl_map *map, int n)
2527 struct isl_map *grown = NULL;
2531 isl_assert(map->ctx, n >= 0, goto error);
2532 if (map->n + n <= map->size)
2534 grown = isl_map_alloc_space(isl_map_get_space(map), map->n + n, map->flags);
2537 for (i = 0; i < map->n; ++i) {
2538 grown->p[i] = isl_basic_map_copy(map->p[i]);
2546 isl_map_free(grown);
2551 /* Make sure "set" has room for at least "n" more basic sets.
2553 struct isl_set *isl_set_grow(struct isl_set *set, int n)
2555 return (struct isl_set *)isl_map_grow((struct isl_map *)set, n);
2558 struct isl_set *isl_set_dup(struct isl_set *set)
2561 struct isl_set *dup;
2566 dup = isl_set_alloc_space(isl_space_copy(set->dim), set->n, set->flags);
2569 for (i = 0; i < set->n; ++i)
2570 dup = isl_set_add_basic_set(dup, isl_basic_set_copy(set->p[i]));
2574 struct isl_set *isl_set_from_basic_set(struct isl_basic_set *bset)
2576 return isl_map_from_basic_map(bset);
2579 struct isl_map *isl_map_from_basic_map(struct isl_basic_map *bmap)
2581 struct isl_map *map;
2586 map = isl_map_alloc_space(isl_space_copy(bmap->dim), 1, ISL_MAP_DISJOINT);
2587 return isl_map_add_basic_map(map, bmap);
2590 __isl_give isl_set *isl_set_add_basic_set(__isl_take isl_set *set,
2591 __isl_take isl_basic_set *bset)
2593 return (struct isl_set *)isl_map_add_basic_map((struct isl_map *)set,
2594 (struct isl_basic_map *)bset);
2597 void *isl_set_free(__isl_take isl_set *set)
2607 isl_ctx_deref(set->ctx);
2608 for (i = 0; i < set->n; ++i)
2609 isl_basic_set_free(set->p[i]);
2610 isl_space_free(set->dim);
2616 void isl_set_print_internal(struct isl_set *set, FILE *out, int indent)
2621 fprintf(out, "null set\n");
2625 fprintf(out, "%*s", indent, "");
2626 fprintf(out, "ref: %d, n: %d, nparam: %d, dim: %d, flags: %x\n",
2627 set->ref, set->n, set->dim->nparam, set->dim->n_out,
2629 for (i = 0; i < set->n; ++i) {
2630 fprintf(out, "%*s", indent, "");
2631 fprintf(out, "basic set %d:\n", i);
2632 isl_basic_set_print_internal(set->p[i], out, indent+4);
2636 void isl_map_print_internal(struct isl_map *map, FILE *out, int indent)
2641 fprintf(out, "null map\n");
2645 fprintf(out, "%*s", indent, "");
2646 fprintf(out, "ref: %d, n: %d, nparam: %d, in: %d, out: %d, "
2647 "flags: %x, n_name: %d\n",
2648 map->ref, map->n, map->dim->nparam, map->dim->n_in,
2649 map->dim->n_out, map->flags, map->dim->n_id);
2650 for (i = 0; i < map->n; ++i) {
2651 fprintf(out, "%*s", indent, "");
2652 fprintf(out, "basic map %d:\n", i);
2653 isl_basic_map_print_internal(map->p[i], out, indent+4);
2657 struct isl_basic_map *isl_basic_map_intersect_domain(
2658 struct isl_basic_map *bmap, struct isl_basic_set *bset)
2660 struct isl_basic_map *bmap_domain;
2665 isl_assert(bset->ctx, isl_space_match(bmap->dim, isl_dim_param,
2666 bset->dim, isl_dim_param), goto error);
2668 if (isl_space_dim(bset->dim, isl_dim_set) != 0)
2669 isl_assert(bset->ctx,
2670 isl_basic_map_compatible_domain(bmap, bset), goto error);
2672 bmap = isl_basic_map_cow(bmap);
2675 bmap = isl_basic_map_extend_space(bmap, isl_space_copy(bmap->dim),
2676 bset->n_div, bset->n_eq, bset->n_ineq);
2677 bmap_domain = isl_basic_map_from_domain(bset);
2678 bmap = add_constraints(bmap, bmap_domain, 0, 0);
2680 bmap = isl_basic_map_simplify(bmap);
2681 return isl_basic_map_finalize(bmap);
2683 isl_basic_map_free(bmap);
2684 isl_basic_set_free(bset);
2688 struct isl_basic_map *isl_basic_map_intersect_range(
2689 struct isl_basic_map *bmap, struct isl_basic_set *bset)
2691 struct isl_basic_map *bmap_range;
2696 isl_assert(bset->ctx, isl_space_match(bmap->dim, isl_dim_param,
2697 bset->dim, isl_dim_param), goto error);
2699 if (isl_space_dim(bset->dim, isl_dim_set) != 0)
2700 isl_assert(bset->ctx,
2701 isl_basic_map_compatible_range(bmap, bset), goto error);
2703 if (isl_basic_set_is_universe(bset)) {
2704 isl_basic_set_free(bset);
2708 bmap = isl_basic_map_cow(bmap);
2711 bmap = isl_basic_map_extend_space(bmap, isl_space_copy(bmap->dim),
2712 bset->n_div, bset->n_eq, bset->n_ineq);
2713 bmap_range = isl_basic_map_from_basic_set(bset, isl_space_copy(bset->dim));
2714 bmap = add_constraints(bmap, bmap_range, 0, 0);
2716 bmap = isl_basic_map_simplify(bmap);
2717 return isl_basic_map_finalize(bmap);
2719 isl_basic_map_free(bmap);
2720 isl_basic_set_free(bset);
2724 int isl_basic_map_contains(struct isl_basic_map *bmap, struct isl_vec *vec)
2730 total = 1 + isl_basic_map_total_dim(bmap);
2731 if (total != vec->size)
2736 for (i = 0; i < bmap->n_eq; ++i) {
2737 isl_seq_inner_product(vec->el, bmap->eq[i], total, &s);
2738 if (!isl_int_is_zero(s)) {
2744 for (i = 0; i < bmap->n_ineq; ++i) {
2745 isl_seq_inner_product(vec->el, bmap->ineq[i], total, &s);
2746 if (isl_int_is_neg(s)) {
2757 int isl_basic_set_contains(struct isl_basic_set *bset, struct isl_vec *vec)
2759 return isl_basic_map_contains((struct isl_basic_map *)bset, vec);
2762 struct isl_basic_map *isl_basic_map_intersect(
2763 struct isl_basic_map *bmap1, struct isl_basic_map *bmap2)
2765 struct isl_vec *sample = NULL;
2767 if (!bmap1 || !bmap2)
2770 isl_assert(bmap1->ctx, isl_space_match(bmap1->dim, isl_dim_param,
2771 bmap2->dim, isl_dim_param), goto error);
2772 if (isl_space_dim(bmap1->dim, isl_dim_all) ==
2773 isl_space_dim(bmap1->dim, isl_dim_param) &&
2774 isl_space_dim(bmap2->dim, isl_dim_all) !=
2775 isl_space_dim(bmap2->dim, isl_dim_param))
2776 return isl_basic_map_intersect(bmap2, bmap1);
2778 if (isl_space_dim(bmap2->dim, isl_dim_all) !=
2779 isl_space_dim(bmap2->dim, isl_dim_param))
2780 isl_assert(bmap1->ctx,
2781 isl_space_is_equal(bmap1->dim, bmap2->dim), goto error);
2783 if (bmap1->sample &&
2784 isl_basic_map_contains(bmap1, bmap1->sample) > 0 &&
2785 isl_basic_map_contains(bmap2, bmap1->sample) > 0)
2786 sample = isl_vec_copy(bmap1->sample);
2787 else if (bmap2->sample &&
2788 isl_basic_map_contains(bmap1, bmap2->sample) > 0 &&
2789 isl_basic_map_contains(bmap2, bmap2->sample) > 0)
2790 sample = isl_vec_copy(bmap2->sample);
2792 bmap1 = isl_basic_map_cow(bmap1);
2795 bmap1 = isl_basic_map_extend_space(bmap1, isl_space_copy(bmap1->dim),
2796 bmap2->n_div, bmap2->n_eq, bmap2->n_ineq);
2797 bmap1 = add_constraints(bmap1, bmap2, 0, 0);
2800 isl_vec_free(sample);
2802 isl_vec_free(bmap1->sample);
2803 bmap1->sample = sample;
2806 bmap1 = isl_basic_map_simplify(bmap1);
2807 return isl_basic_map_finalize(bmap1);
2810 isl_vec_free(sample);
2811 isl_basic_map_free(bmap1);
2812 isl_basic_map_free(bmap2);
2816 struct isl_basic_set *isl_basic_set_intersect(
2817 struct isl_basic_set *bset1, struct isl_basic_set *bset2)
2819 return (struct isl_basic_set *)
2820 isl_basic_map_intersect(
2821 (struct isl_basic_map *)bset1,
2822 (struct isl_basic_map *)bset2);
2825 __isl_give isl_basic_set *isl_basic_set_intersect_params(
2826 __isl_take isl_basic_set *bset1, __isl_take isl_basic_set *bset2)
2828 return isl_basic_set_intersect(bset1, bset2);
2831 /* Special case of isl_map_intersect, where both map1 and map2
2832 * are convex, without any divs and such that either map1 or map2
2833 * contains a single constraint. This constraint is then simply
2834 * added to the other map.
2836 static __isl_give isl_map *map_intersect_add_constraint(
2837 __isl_take isl_map *map1, __isl_take isl_map *map2)
2839 isl_assert(map1->ctx, map1->n == 1, goto error);
2840 isl_assert(map2->ctx, map1->n == 1, goto error);
2841 isl_assert(map1->ctx, map1->p[0]->n_div == 0, goto error);
2842 isl_assert(map2->ctx, map1->p[0]->n_div == 0, goto error);
2844 if (map2->p[0]->n_eq + map2->p[0]->n_ineq != 1)
2845 return isl_map_intersect(map2, map1);
2847 isl_assert(map2->ctx,
2848 map2->p[0]->n_eq + map2->p[0]->n_ineq == 1, goto error);
2850 map1 = isl_map_cow(map1);
2853 if (isl_map_plain_is_empty(map1)) {
2857 map1->p[0] = isl_basic_map_cow(map1->p[0]);
2858 if (map2->p[0]->n_eq == 1)
2859 map1->p[0] = isl_basic_map_add_eq(map1->p[0], map2->p[0]->eq[0]);
2861 map1->p[0] = isl_basic_map_add_ineq(map1->p[0],
2862 map2->p[0]->ineq[0]);
2864 map1->p[0] = isl_basic_map_simplify(map1->p[0]);
2865 map1->p[0] = isl_basic_map_finalize(map1->p[0]);
2869 if (isl_basic_map_plain_is_empty(map1->p[0])) {
2870 isl_basic_map_free(map1->p[0]);
2883 /* map2 may be either a parameter domain or a map living in the same
2886 static __isl_give isl_map *map_intersect_internal(__isl_take isl_map *map1,
2887 __isl_take isl_map *map2)
2896 if ((isl_map_plain_is_empty(map1) ||
2897 isl_map_plain_is_universe(map2)) &&
2898 isl_space_is_equal(map1->dim, map2->dim)) {
2902 if ((isl_map_plain_is_empty(map2) ||
2903 isl_map_plain_is_universe(map1)) &&
2904 isl_space_is_equal(map1->dim, map2->dim)) {
2909 if (map1->n == 1 && map2->n == 1 &&
2910 map1->p[0]->n_div == 0 && map2->p[0]->n_div == 0 &&
2911 isl_space_is_equal(map1->dim, map2->dim) &&
2912 (map1->p[0]->n_eq + map1->p[0]->n_ineq == 1 ||
2913 map2->p[0]->n_eq + map2->p[0]->n_ineq == 1))
2914 return map_intersect_add_constraint(map1, map2);
2916 if (isl_space_dim(map2->dim, isl_dim_all) !=
2917 isl_space_dim(map2->dim, isl_dim_param))
2918 isl_assert(map1->ctx,
2919 isl_space_is_equal(map1->dim, map2->dim), goto error);
2921 if (ISL_F_ISSET(map1, ISL_MAP_DISJOINT) &&
2922 ISL_F_ISSET(map2, ISL_MAP_DISJOINT))
2923 ISL_FL_SET(flags, ISL_MAP_DISJOINT);
2925 result = isl_map_alloc_space(isl_space_copy(map1->dim),
2926 map1->n * map2->n, flags);
2929 for (i = 0; i < map1->n; ++i)
2930 for (j = 0; j < map2->n; ++j) {
2931 struct isl_basic_map *part;
2932 part = isl_basic_map_intersect(
2933 isl_basic_map_copy(map1->p[i]),
2934 isl_basic_map_copy(map2->p[j]));
2935 if (isl_basic_map_is_empty(part) < 0)
2936 part = isl_basic_map_free(part);
2937 result = isl_map_add_basic_map(result, part);
2950 static __isl_give isl_map *map_intersect(__isl_take isl_map *map1,
2951 __isl_take isl_map *map2)
2955 if (!isl_space_is_equal(map1->dim, map2->dim))
2956 isl_die(isl_map_get_ctx(map1), isl_error_invalid,
2957 "spaces don't match", goto error);
2958 return map_intersect_internal(map1, map2);
2965 __isl_give isl_map *isl_map_intersect(__isl_take isl_map *map1,
2966 __isl_take isl_map *map2)
2968 return isl_map_align_params_map_map_and(map1, map2, &map_intersect);
2971 struct isl_set *isl_set_intersect(struct isl_set *set1, struct isl_set *set2)
2973 return (struct isl_set *)
2974 isl_map_intersect((struct isl_map *)set1,
2975 (struct isl_map *)set2);
2978 /* map_intersect_internal accepts intersections
2979 * with parameter domains, so we can just call that function.
2981 static __isl_give isl_map *map_intersect_params(__isl_take isl_map *map,
2982 __isl_take isl_set *params)
2984 return map_intersect_internal(map, params);
2987 __isl_give isl_map *isl_map_intersect_params(__isl_take isl_map *map1,
2988 __isl_take isl_map *map2)
2990 return isl_map_align_params_map_map_and(map1, map2, &map_intersect_params);
2993 __isl_give isl_set *isl_set_intersect_params(__isl_take isl_set *set,
2994 __isl_take isl_set *params)
2996 return isl_map_intersect_params(set, params);
2999 struct isl_basic_map *isl_basic_map_reverse(struct isl_basic_map *bmap)
3002 struct isl_basic_set *bset;
3007 bmap = isl_basic_map_cow(bmap);
3010 dim = isl_space_reverse(isl_space_copy(bmap->dim));
3011 in = isl_basic_map_n_in(bmap);
3012 bset = isl_basic_set_from_basic_map(bmap);
3013 bset = isl_basic_set_swap_vars(bset, in);
3014 return isl_basic_map_from_basic_set(bset, dim);
3017 static __isl_give isl_basic_map *basic_map_space_reset(
3018 __isl_take isl_basic_map *bmap, enum isl_dim_type type)
3024 if (!isl_space_is_named_or_nested(bmap->dim, type))
3027 space = isl_basic_map_get_space(bmap);
3028 space = isl_space_reset(space, type);
3029 bmap = isl_basic_map_reset_space(bmap, space);
3033 __isl_give isl_basic_map *isl_basic_map_insert_dims(
3034 __isl_take isl_basic_map *bmap, enum isl_dim_type type,
3035 unsigned pos, unsigned n)
3038 struct isl_basic_map *res;
3039 struct isl_dim_map *dim_map;
3040 unsigned total, off;
3041 enum isl_dim_type t;
3044 return basic_map_space_reset(bmap, type);
3049 res_dim = isl_space_insert_dims(isl_basic_map_get_space(bmap), type, pos, n);
3051 total = isl_basic_map_total_dim(bmap) + n;
3052 dim_map = isl_dim_map_alloc(bmap->ctx, total);
3054 for (t = isl_dim_param; t <= isl_dim_out; ++t) {
3056 isl_dim_map_dim(dim_map, bmap->dim, t, off);
3058 unsigned size = isl_basic_map_dim(bmap, t);
3059 isl_dim_map_dim_range(dim_map, bmap->dim, t,
3061 isl_dim_map_dim_range(dim_map, bmap->dim, t,
3062 pos, size - pos, off + pos + n);
3064 off += isl_space_dim(res_dim, t);
3066 isl_dim_map_div(dim_map, bmap, off);
3068 res = isl_basic_map_alloc_space(res_dim,
3069 bmap->n_div, bmap->n_eq, bmap->n_ineq);
3070 if (isl_basic_map_is_rational(bmap))
3071 res = isl_basic_map_set_rational(res);
3072 if (isl_basic_map_plain_is_empty(bmap)) {
3073 isl_basic_map_free(bmap);
3075 return isl_basic_map_set_to_empty(res);
3077 res = isl_basic_map_add_constraints_dim_map(res, bmap, dim_map);
3078 return isl_basic_map_finalize(res);
3081 __isl_give isl_basic_set *isl_basic_set_insert_dims(
3082 __isl_take isl_basic_set *bset,
3083 enum isl_dim_type type, unsigned pos, unsigned n)
3085 return isl_basic_map_insert_dims(bset, type, pos, n);
3088 __isl_give isl_basic_map *isl_basic_map_add(__isl_take isl_basic_map *bmap,
3089 enum isl_dim_type type, unsigned n)
3093 return isl_basic_map_insert_dims(bmap, type,
3094 isl_basic_map_dim(bmap, type), n);
3097 __isl_give isl_basic_set *isl_basic_set_add_dims(__isl_take isl_basic_set *bset,
3098 enum isl_dim_type type, unsigned n)
3102 isl_assert(bset->ctx, type != isl_dim_in, goto error);
3103 return (isl_basic_set *)isl_basic_map_add((isl_basic_map *)bset, type, n);
3105 isl_basic_set_free(bset);
3109 static __isl_give isl_map *map_space_reset(__isl_take isl_map *map,
3110 enum isl_dim_type type)
3114 if (!map || !isl_space_is_named_or_nested(map->dim, type))
3117 space = isl_map_get_space(map);
3118 space = isl_space_reset(space, type);
3119 map = isl_map_reset_space(map, space);
3123 __isl_give isl_map *isl_map_insert_dims(__isl_take isl_map *map,
3124 enum isl_dim_type type, unsigned pos, unsigned n)
3129 return map_space_reset(map, type);
3131 map = isl_map_cow(map);
3135 map->dim = isl_space_insert_dims(map->dim, type, pos, n);
3139 for (i = 0; i < map->n; ++i) {
3140 map->p[i] = isl_basic_map_insert_dims(map->p[i], type, pos, n);
3151 __isl_give isl_set *isl_set_insert_dims(__isl_take isl_set *set,
3152 enum isl_dim_type type, unsigned pos, unsigned n)
3154 return isl_map_insert_dims(set, type, pos, n);
3157 __isl_give isl_map *isl_map_add_dims(__isl_take isl_map *map,
3158 enum isl_dim_type type, unsigned n)
3162 return isl_map_insert_dims(map, type, isl_map_dim(map, type), n);
3165 __isl_give isl_set *isl_set_add_dims(__isl_take isl_set *set,
3166 enum isl_dim_type type, unsigned n)
3170 isl_assert(set->ctx, type != isl_dim_in, goto error);
3171 return (isl_set *)isl_map_add_dims((isl_map *)set, type, n);
3177 __isl_give isl_basic_map *isl_basic_map_move_dims(
3178 __isl_take isl_basic_map *bmap,
3179 enum isl_dim_type dst_type, unsigned dst_pos,
3180 enum isl_dim_type src_type, unsigned src_pos, unsigned n)
3182 struct isl_dim_map *dim_map;
3183 struct isl_basic_map *res;
3184 enum isl_dim_type t;
3185 unsigned total, off;
3192 isl_assert(bmap->ctx, src_pos + n <= isl_basic_map_dim(bmap, src_type),
3195 if (dst_type == src_type && dst_pos == src_pos)
3198 isl_assert(bmap->ctx, dst_type != src_type, goto error);
3200 if (pos(bmap->dim, dst_type) + dst_pos ==
3201 pos(bmap->dim, src_type) + src_pos +
3202 ((src_type < dst_type) ? n : 0)) {
3203 bmap = isl_basic_map_cow(bmap);
3207 bmap->dim = isl_space_move_dims(bmap->dim, dst_type, dst_pos,
3208 src_type, src_pos, n);
3212 bmap = isl_basic_map_finalize(bmap);
3217 total = isl_basic_map_total_dim(bmap);
3218 dim_map = isl_dim_map_alloc(bmap->ctx, total);
3221 for (t = isl_dim_param; t <= isl_dim_out; ++t) {
3222 unsigned size = isl_space_dim(bmap->dim, t);
3223 if (t == dst_type) {
3224 isl_dim_map_dim_range(dim_map, bmap->dim, t,
3227 isl_dim_map_dim_range(dim_map, bmap->dim, src_type,
3230 isl_dim_map_dim_range(dim_map, bmap->dim, t,
3231 dst_pos, size - dst_pos, off);
3232 off += size - dst_pos;
3233 } else if (t == src_type) {
3234 isl_dim_map_dim_range(dim_map, bmap->dim, t,
3237 isl_dim_map_dim_range(dim_map, bmap->dim, t,
3238 src_pos + n, size - src_pos - n, off);
3239 off += size - src_pos - n;
3241 isl_dim_map_dim(dim_map, bmap->dim, t, off);
3245 isl_dim_map_div(dim_map, bmap, off);
3247 res = isl_basic_map_alloc_space(isl_basic_map_get_space(bmap),
3248 bmap->n_div, bmap->n_eq, bmap->n_ineq);
3249 bmap = isl_basic_map_add_constraints_dim_map(res, bmap, dim_map);
3253 bmap->dim = isl_space_move_dims(bmap->dim, dst_type, dst_pos,
3254 src_type, src_pos, n);
3258 ISL_F_CLR(bmap, ISL_BASIC_MAP_NORMALIZED);
3259 bmap = isl_basic_map_gauss(bmap, NULL);
3260 bmap = isl_basic_map_finalize(bmap);
3264 isl_basic_map_free(bmap);
3268 __isl_give isl_basic_set *isl_basic_set_move_dims(__isl_take isl_basic_set *bset,
3269 enum isl_dim_type dst_type, unsigned dst_pos,
3270 enum isl_dim_type src_type, unsigned src_pos, unsigned n)
3272 return (isl_basic_set *)isl_basic_map_move_dims(
3273 (isl_basic_map *)bset, dst_type, dst_pos, src_type, src_pos, n);
3276 __isl_give isl_set *isl_set_move_dims(__isl_take isl_set *set,
3277 enum isl_dim_type dst_type, unsigned dst_pos,
3278 enum isl_dim_type src_type, unsigned src_pos, unsigned n)
3282 isl_assert(set->ctx, dst_type != isl_dim_in, goto error);
3283 return (isl_set *)isl_map_move_dims((isl_map *)set, dst_type, dst_pos,
3284 src_type, src_pos, n);
3290 __isl_give isl_map *isl_map_move_dims(__isl_take isl_map *map,
3291 enum isl_dim_type dst_type, unsigned dst_pos,
3292 enum isl_dim_type src_type, unsigned src_pos, unsigned n)
3301 isl_assert(map->ctx, src_pos + n <= isl_map_dim(map, src_type),
3304 if (dst_type == src_type && dst_pos == src_pos)
3307 isl_assert(map->ctx, dst_type != src_type, goto error);
3309 map = isl_map_cow(map);
3313 map->dim = isl_space_move_dims(map->dim, dst_type, dst_pos, src_type, src_pos, n);
3317 for (i = 0; i < map->n; ++i) {
3318 map->p[i] = isl_basic_map_move_dims(map->p[i],
3320 src_type, src_pos, n);
3331 /* Move the specified dimensions to the last columns right before
3332 * the divs. Don't change the dimension specification of bmap.
3333 * That's the responsibility of the caller.
3335 static __isl_give isl_basic_map *move_last(__isl_take isl_basic_map *bmap,
3336 enum isl_dim_type type, unsigned first, unsigned n)
3338 struct isl_dim_map *dim_map;
3339 struct isl_basic_map *res;
3340 enum isl_dim_type t;
3341 unsigned total, off;
3345 if (pos(bmap->dim, type) + first + n ==
3346 1 + isl_space_dim(bmap->dim, isl_dim_all))
3349 total = isl_basic_map_total_dim(bmap);
3350 dim_map = isl_dim_map_alloc(bmap->ctx, total);
3353 for (t = isl_dim_param; t <= isl_dim_out; ++t) {
3354 unsigned size = isl_space_dim(bmap->dim, t);
3356 isl_dim_map_dim_range(dim_map, bmap->dim, t,
3359 isl_dim_map_dim_range(dim_map, bmap->dim, t,
3360 first, n, total - bmap->n_div - n);
3361 isl_dim_map_dim_range(dim_map, bmap->dim, t,
3362 first + n, size - (first + n), off);
3363 off += size - (first + n);
3365 isl_dim_map_dim(dim_map, bmap->dim, t, off);
3369 isl_dim_map_div(dim_map, bmap, off + n);
3371 res = isl_basic_map_alloc_space(isl_basic_map_get_space(bmap),
3372 bmap->n_div, bmap->n_eq, bmap->n_ineq);
3373 res = isl_basic_map_add_constraints_dim_map(res, bmap, dim_map);
3377 /* Insert "n" rows in the divs of "bmap".
3379 * The number of columns is not changed, which means that the last
3380 * dimensions of "bmap" are being reintepreted as the new divs.
3381 * The space of "bmap" is not adjusted, however, which means
3382 * that "bmap" is left in an inconsistent state. Removing "n" dimensions
3383 * from the space of "bmap" is the responsibility of the caller.
3385 static __isl_give isl_basic_map *insert_div_rows(__isl_take isl_basic_map *bmap,
3393 bmap = isl_basic_map_cow(bmap);
3397 row_size = 1 + isl_space_dim(bmap->dim, isl_dim_all) + bmap->extra;
3398 old = bmap->block2.data;
3399 bmap->block2 = isl_blk_extend(bmap->ctx, bmap->block2,
3400 (bmap->extra + n) * (1 + row_size));
3401 if (!bmap->block2.data)
3402 return isl_basic_map_free(bmap);
3403 new_div = isl_alloc_array(bmap->ctx, isl_int *, bmap->extra + n);
3405 return isl_basic_map_free(bmap);
3406 for (i = 0; i < n; ++i) {
3407 new_div[i] = bmap->block2.data +
3408 (bmap->extra + i) * (1 + row_size);
3409 isl_seq_clr(new_div[i], 1 + row_size);
3411 for (i = 0; i < bmap->extra; ++i)
3412 new_div[n + i] = bmap->block2.data + (bmap->div[i] - old);
3414 bmap->div = new_div;
3421 /* Turn the n dimensions of type type, starting at first
3422 * into existentially quantified variables.
3424 __isl_give isl_basic_map *isl_basic_map_project_out(
3425 __isl_take isl_basic_map *bmap,
3426 enum isl_dim_type type, unsigned first, unsigned n)
3429 return basic_map_space_reset(bmap, type);
3434 if (ISL_F_ISSET(bmap, ISL_BASIC_MAP_RATIONAL))
3435 return isl_basic_map_remove_dims(bmap, type, first, n);
3437 isl_assert(bmap->ctx, first + n <= isl_basic_map_dim(bmap, type),
3440 bmap = move_last(bmap, type, first, n);
3441 bmap = isl_basic_map_cow(bmap);
3442 bmap = insert_div_rows(bmap, n);
3446 bmap->dim = isl_space_drop_dims(bmap->dim, type, first, n);
3449 bmap = isl_basic_map_simplify(bmap);
3450 bmap = isl_basic_map_drop_redundant_divs(bmap);
3451 return isl_basic_map_finalize(bmap);
3453 isl_basic_map_free(bmap);
3457 /* Turn the n dimensions of type type, starting at first
3458 * into existentially quantified variables.
3460 struct isl_basic_set *isl_basic_set_project_out(struct isl_basic_set *bset,
3461 enum isl_dim_type type, unsigned first, unsigned n)
3463 return (isl_basic_set *)isl_basic_map_project_out(
3464 (isl_basic_map *)bset, type, first, n);
3467 /* Turn the n dimensions of type type, starting at first
3468 * into existentially quantified variables.
3470 __isl_give isl_map *isl_map_project_out(__isl_take isl_map *map,
3471 enum isl_dim_type type, unsigned first, unsigned n)
3479 return map_space_reset(map, type);
3481 isl_assert(map->ctx, first + n <= isl_map_dim(map, type), goto error);
3483 map = isl_map_cow(map);
3487 map->dim = isl_space_drop_dims(map->dim, type, first, n);
3491 for (i = 0; i < map->n; ++i) {
3492 map->p[i] = isl_basic_map_project_out(map->p[i], type, first, n);
3503 /* Turn the n dimensions of type type, starting at first
3504 * into existentially quantified variables.
3506 __isl_give isl_set *isl_set_project_out(__isl_take isl_set *set,
3507 enum isl_dim_type type, unsigned first, unsigned n)
3509 return (isl_set *)isl_map_project_out((isl_map *)set, type, first, n);
3512 static struct isl_basic_map *add_divs(struct isl_basic_map *bmap, unsigned n)
3516 for (i = 0; i < n; ++i) {
3517 j = isl_basic_map_alloc_div(bmap);
3520 isl_seq_clr(bmap->div[j], 1+1+isl_basic_map_total_dim(bmap));
3524 isl_basic_map_free(bmap);
3528 struct isl_basic_map *isl_basic_map_apply_range(
3529 struct isl_basic_map *bmap1, struct isl_basic_map *bmap2)
3531 isl_space *dim_result = NULL;
3532 struct isl_basic_map *bmap;
3533 unsigned n_in, n_out, n, nparam, total, pos;
3534 struct isl_dim_map *dim_map1, *dim_map2;
3536 if (!bmap1 || !bmap2)
3539 dim_result = isl_space_join(isl_space_copy(bmap1->dim),
3540 isl_space_copy(bmap2->dim));
3542 n_in = isl_basic_map_n_in(bmap1);
3543 n_out = isl_basic_map_n_out(bmap2);
3544 n = isl_basic_map_n_out(bmap1);
3545 nparam = isl_basic_map_n_param(bmap1);
3547 total = nparam + n_in + n_out + bmap1->n_div + bmap2->n_div + n;
3548 dim_map1 = isl_dim_map_alloc(bmap1->ctx, total);
3549 dim_map2 = isl_dim_map_alloc(bmap1->ctx, total);
3550 isl_dim_map_dim(dim_map1, bmap1->dim, isl_dim_param, pos = 0);
3551 isl_dim_map_dim(dim_map2, bmap2->dim, isl_dim_param, pos = 0);
3552 isl_dim_map_dim(dim_map1, bmap1->dim, isl_dim_in, pos += nparam);
3553 isl_dim_map_dim(dim_map2, bmap2->dim, isl_dim_out, pos += n_in);
3554 isl_dim_map_div(dim_map1, bmap1, pos += n_out);
3555 isl_dim_map_div(dim_map2, bmap2, pos += bmap1->n_div);
3556 isl_dim_map_dim(dim_map1, bmap1->dim, isl_dim_out, pos += bmap2->n_div);
3557 isl_dim_map_dim(dim_map2, bmap2->dim, isl_dim_in, pos);
3559 bmap = isl_basic_map_alloc_space(dim_result,
3560 bmap1->n_div + bmap2->n_div + n,
3561 bmap1->n_eq + bmap2->n_eq,
3562 bmap1->n_ineq + bmap2->n_ineq);
3563 bmap = isl_basic_map_add_constraints_dim_map(bmap, bmap1, dim_map1);
3564 bmap = isl_basic_map_add_constraints_dim_map(bmap, bmap2, dim_map2);
3565 bmap = add_divs(bmap, n);
3566 bmap = isl_basic_map_simplify(bmap);
3567 bmap = isl_basic_map_drop_redundant_divs(bmap);
3568 return isl_basic_map_finalize(bmap);
3570 isl_basic_map_free(bmap1);
3571 isl_basic_map_free(bmap2);
3575 struct isl_basic_set *isl_basic_set_apply(
3576 struct isl_basic_set *bset, struct isl_basic_map *bmap)
3581 isl_assert(bset->ctx, isl_basic_map_compatible_domain(bmap, bset),
3584 return (struct isl_basic_set *)
3585 isl_basic_map_apply_range((struct isl_basic_map *)bset, bmap);
3587 isl_basic_set_free(bset);
3588 isl_basic_map_free(bmap);
3592 struct isl_basic_map *isl_basic_map_apply_domain(
3593 struct isl_basic_map *bmap1, struct isl_basic_map *bmap2)
3595 if (!bmap1 || !bmap2)
3598 isl_assert(bmap1->ctx,
3599 isl_basic_map_n_in(bmap1) == isl_basic_map_n_in(bmap2), goto error);
3600 isl_assert(bmap1->ctx,
3601 isl_basic_map_n_param(bmap1) == isl_basic_map_n_param(bmap2),
3604 bmap1 = isl_basic_map_reverse(bmap1);
3605 bmap1 = isl_basic_map_apply_range(bmap1, bmap2);
3606 return isl_basic_map_reverse(bmap1);
3608 isl_basic_map_free(bmap1);
3609 isl_basic_map_free(bmap2);
3613 /* Given two basic maps A -> f(A) and B -> g(B), construct a basic map
3614 * A \cap B -> f(A) + f(B)
3616 struct isl_basic_map *isl_basic_map_sum(
3617 struct isl_basic_map *bmap1, struct isl_basic_map *bmap2)
3619 unsigned n_in, n_out, nparam, total, pos;
3620 struct isl_basic_map *bmap = NULL;
3621 struct isl_dim_map *dim_map1, *dim_map2;
3624 if (!bmap1 || !bmap2)
3627 isl_assert(bmap1->ctx, isl_space_is_equal(bmap1->dim, bmap2->dim),
3630 nparam = isl_basic_map_n_param(bmap1);
3631 n_in = isl_basic_map_n_in(bmap1);
3632 n_out = isl_basic_map_n_out(bmap1);
3634 total = nparam + n_in + n_out + bmap1->n_div + bmap2->n_div + 2 * n_out;
3635 dim_map1 = isl_dim_map_alloc(bmap1->ctx, total);
3636 dim_map2 = isl_dim_map_alloc(bmap2->ctx, total);
3637 isl_dim_map_dim(dim_map1, bmap1->dim, isl_dim_param, pos = 0);
3638 isl_dim_map_dim(dim_map2, bmap2->dim, isl_dim_param, pos);
3639 isl_dim_map_dim(dim_map1, bmap1->dim, isl_dim_in, pos += nparam);
3640 isl_dim_map_dim(dim_map2, bmap2->dim, isl_dim_in, pos);
3641 isl_dim_map_div(dim_map1, bmap1, pos += n_in + n_out);
3642 isl_dim_map_div(dim_map2, bmap2, pos += bmap1->n_div);
3643 isl_dim_map_dim(dim_map1, bmap1->dim, isl_dim_out, pos += bmap2->n_div);
3644 isl_dim_map_dim(dim_map2, bmap2->dim, isl_dim_out, pos += n_out);
3646 bmap = isl_basic_map_alloc_space(isl_space_copy(bmap1->dim),
3647 bmap1->n_div + bmap2->n_div + 2 * n_out,
3648 bmap1->n_eq + bmap2->n_eq + n_out,
3649 bmap1->n_ineq + bmap2->n_ineq);
3650 for (i = 0; i < n_out; ++i) {
3651 int j = isl_basic_map_alloc_equality(bmap);
3654 isl_seq_clr(bmap->eq[j], 1+total);
3655 isl_int_set_si(bmap->eq[j][1+nparam+n_in+i], -1);
3656 isl_int_set_si(bmap->eq[j][1+pos+i], 1);
3657 isl_int_set_si(bmap->eq[j][1+pos-n_out+i], 1);
3659 bmap = isl_basic_map_add_constraints_dim_map(bmap, bmap1, dim_map1);
3660 bmap = isl_basic_map_add_constraints_dim_map(bmap, bmap2, dim_map2);
3661 bmap = add_divs(bmap, 2 * n_out);
3663 bmap = isl_basic_map_simplify(bmap);
3664 return isl_basic_map_finalize(bmap);
3666 isl_basic_map_free(bmap);
3667 isl_basic_map_free(bmap1);
3668 isl_basic_map_free(bmap2);
3672 /* Given two maps A -> f(A) and B -> g(B), construct a map
3673 * A \cap B -> f(A) + f(B)
3675 struct isl_map *isl_map_sum(struct isl_map *map1, struct isl_map *map2)
3677 struct isl_map *result;
3683 isl_assert(map1->ctx, isl_space_is_equal(map1->dim, map2->dim), goto error);
3685 result = isl_map_alloc_space(isl_space_copy(map1->dim),
3686 map1->n * map2->n, 0);
3689 for (i = 0; i < map1->n; ++i)
3690 for (j = 0; j < map2->n; ++j) {
3691 struct isl_basic_map *part;
3692 part = isl_basic_map_sum(
3693 isl_basic_map_copy(map1->p[i]),
3694 isl_basic_map_copy(map2->p[j]));
3695 if (isl_basic_map_is_empty(part))
3696 isl_basic_map_free(part);
3698 result = isl_map_add_basic_map(result, part);
3711 __isl_give isl_set *isl_set_sum(__isl_take isl_set *set1,
3712 __isl_take isl_set *set2)
3714 return (isl_set *)isl_map_sum((isl_map *)set1, (isl_map *)set2);
3717 /* Given a basic map A -> f(A), construct A -> -f(A).
3719 struct isl_basic_map *isl_basic_map_neg(struct isl_basic_map *bmap)
3724 bmap = isl_basic_map_cow(bmap);
3728 n = isl_basic_map_dim(bmap, isl_dim_out);
3729 off = isl_basic_map_offset(bmap, isl_dim_out);
3730 for (i = 0; i < bmap->n_eq; ++i)
3731 for (j = 0; j < n; ++j)
3732 isl_int_neg(bmap->eq[i][off+j], bmap->eq[i][off+j]);
3733 for (i = 0; i < bmap->n_ineq; ++i)
3734 for (j = 0; j < n; ++j)
3735 isl_int_neg(bmap->ineq[i][off+j], bmap->ineq[i][off+j]);
3736 for (i = 0; i < bmap->n_div; ++i)
3737 for (j = 0; j < n; ++j)
3738 isl_int_neg(bmap->div[i][1+off+j], bmap->div[i][1+off+j]);
3739 bmap = isl_basic_map_gauss(bmap, NULL);
3740 return isl_basic_map_finalize(bmap);
3743 __isl_give isl_basic_set *isl_basic_set_neg(__isl_take isl_basic_set *bset)
3745 return isl_basic_map_neg(bset);
3748 /* Given a map A -> f(A), construct A -> -f(A).
3750 struct isl_map *isl_map_neg(struct isl_map *map)
3754 map = isl_map_cow(map);
3758 for (i = 0; i < map->n; ++i) {
3759 map->p[i] = isl_basic_map_neg(map->p[i]);
3770 __isl_give isl_set *isl_set_neg(__isl_take isl_set *set)
3772 return (isl_set *)isl_map_neg((isl_map *)set);
3775 /* Given a basic map A -> f(A) and an integer d, construct a basic map
3776 * A -> floor(f(A)/d).
3778 struct isl_basic_map *isl_basic_map_floordiv(struct isl_basic_map *bmap,
3781 unsigned n_in, n_out, nparam, total, pos;
3782 struct isl_basic_map *result = NULL;
3783 struct isl_dim_map *dim_map;
3789 nparam = isl_basic_map_n_param(bmap);
3790 n_in = isl_basic_map_n_in(bmap);
3791 n_out = isl_basic_map_n_out(bmap);
3793 total = nparam + n_in + n_out + bmap->n_div + n_out;
3794 dim_map = isl_dim_map_alloc(bmap->ctx, total);
3795 isl_dim_map_dim(dim_map, bmap->dim, isl_dim_param, pos = 0);
3796 isl_dim_map_dim(dim_map, bmap->dim, isl_dim_in, pos += nparam);
3797 isl_dim_map_div(dim_map, bmap, pos += n_in + n_out);
3798 isl_dim_map_dim(dim_map, bmap->dim, isl_dim_out, pos += bmap->n_div);
3800 result = isl_basic_map_alloc_space(isl_space_copy(bmap->dim),
3801 bmap->n_div + n_out,
3802 bmap->n_eq, bmap->n_ineq + 2 * n_out);
3803 result = isl_basic_map_add_constraints_dim_map(result, bmap, dim_map);
3804 result = add_divs(result, n_out);
3805 for (i = 0; i < n_out; ++i) {
3807 j = isl_basic_map_alloc_inequality(result);
3810 isl_seq_clr(result->ineq[j], 1+total);
3811 isl_int_neg(result->ineq[j][1+nparam+n_in+i], d);
3812 isl_int_set_si(result->ineq[j][1+pos+i], 1);
3813 j = isl_basic_map_alloc_inequality(result);
3816 isl_seq_clr(result->ineq[j], 1+total);
3817 isl_int_set(result->ineq[j][1+nparam+n_in+i], d);
3818 isl_int_set_si(result->ineq[j][1+pos+i], -1);
3819 isl_int_sub_ui(result->ineq[j][0], d, 1);
3822 result = isl_basic_map_simplify(result);
3823 return isl_basic_map_finalize(result);
3825 isl_basic_map_free(result);
3829 /* Given a map A -> f(A) and an integer d, construct a map
3830 * A -> floor(f(A)/d).
3832 struct isl_map *isl_map_floordiv(struct isl_map *map, isl_int d)
3836 map = isl_map_cow(map);
3840 ISL_F_CLR(map, ISL_MAP_DISJOINT);
3841 ISL_F_CLR(map, ISL_MAP_NORMALIZED);
3842 for (i = 0; i < map->n; ++i) {
3843 map->p[i] = isl_basic_map_floordiv(map->p[i], d);
3854 static struct isl_basic_map *var_equal(struct isl_basic_map *bmap, unsigned pos)
3860 i = isl_basic_map_alloc_equality(bmap);
3863 nparam = isl_basic_map_n_param(bmap);
3864 n_in = isl_basic_map_n_in(bmap);
3865 isl_seq_clr(bmap->eq[i], 1 + isl_basic_map_total_dim(bmap));
3866 isl_int_set_si(bmap->eq[i][1+nparam+pos], -1);
3867 isl_int_set_si(bmap->eq[i][1+nparam+n_in+pos], 1);
3868 return isl_basic_map_finalize(bmap);
3870 isl_basic_map_free(bmap);
3874 /* Add a constraints to "bmap" expressing i_pos < o_pos
3876 static struct isl_basic_map *var_less(struct isl_basic_map *bmap, unsigned pos)
3882 i = isl_basic_map_alloc_inequality(bmap);
3885 nparam = isl_basic_map_n_param(bmap);
3886 n_in = isl_basic_map_n_in(bmap);
3887 isl_seq_clr(bmap->ineq[i], 1 + isl_basic_map_total_dim(bmap));
3888 isl_int_set_si(bmap->ineq[i][0], -1);
3889 isl_int_set_si(bmap->ineq[i][1+nparam+pos], -1);
3890 isl_int_set_si(bmap->ineq[i][1+nparam+n_in+pos], 1);
3891 return isl_basic_map_finalize(bmap);
3893 isl_basic_map_free(bmap);
3897 /* Add a constraint to "bmap" expressing i_pos <= o_pos
3899 static __isl_give isl_basic_map *var_less_or_equal(
3900 __isl_take isl_basic_map *bmap, unsigned pos)
3906 i = isl_basic_map_alloc_inequality(bmap);
3909 nparam = isl_basic_map_n_param(bmap);
3910 n_in = isl_basic_map_n_in(bmap);
3911 isl_seq_clr(bmap->ineq[i], 1 + isl_basic_map_total_dim(bmap));
3912 isl_int_set_si(bmap->ineq[i][1+nparam+pos], -1);
3913 isl_int_set_si(bmap->ineq[i][1+nparam+n_in+pos], 1);
3914 return isl_basic_map_finalize(bmap);
3916 isl_basic_map_free(bmap);
3920 /* Add a constraints to "bmap" expressing i_pos > o_pos
3922 static struct isl_basic_map *var_more(struct isl_basic_map *bmap, unsigned pos)
3928 i = isl_basic_map_alloc_inequality(bmap);
3931 nparam = isl_basic_map_n_param(bmap);
3932 n_in = isl_basic_map_n_in(bmap);
3933 isl_seq_clr(bmap->ineq[i], 1 + isl_basic_map_total_dim(bmap));
3934 isl_int_set_si(bmap->ineq[i][0], -1);
3935 isl_int_set_si(bmap->ineq[i][1+nparam+pos], 1);
3936 isl_int_set_si(bmap->ineq[i][1+nparam+n_in+pos], -1);
3937 return isl_basic_map_finalize(bmap);
3939 isl_basic_map_free(bmap);
3943 /* Add a constraint to "bmap" expressing i_pos >= o_pos
3945 static __isl_give isl_basic_map *var_more_or_equal(
3946 __isl_take isl_basic_map *bmap, unsigned pos)
3952 i = isl_basic_map_alloc_inequality(bmap);
3955 nparam = isl_basic_map_n_param(bmap);
3956 n_in = isl_basic_map_n_in(bmap);
3957 isl_seq_clr(bmap->ineq[i], 1 + isl_basic_map_total_dim(bmap));
3958 isl_int_set_si(bmap->ineq[i][1+nparam+pos], 1);
3959 isl_int_set_si(bmap->ineq[i][1+nparam+n_in+pos], -1);
3960 return isl_basic_map_finalize(bmap);
3962 isl_basic_map_free(bmap);
3966 __isl_give isl_basic_map *isl_basic_map_equal(
3967 __isl_take isl_space *dim, unsigned n_equal)
3970 struct isl_basic_map *bmap;
3971 bmap = isl_basic_map_alloc_space(dim, 0, n_equal, 0);
3974 for (i = 0; i < n_equal && bmap; ++i)
3975 bmap = var_equal(bmap, i);
3976 return isl_basic_map_finalize(bmap);
3979 /* Return a relation on of dimension "dim" expressing i_[0..pos] << o_[0..pos]
3981 __isl_give isl_basic_map *isl_basic_map_less_at(__isl_take isl_space *dim,
3985 struct isl_basic_map *bmap;
3986 bmap = isl_basic_map_alloc_space(dim, 0, pos, 1);
3989 for (i = 0; i < pos && bmap; ++i)
3990 bmap = var_equal(bmap, i);
3992 bmap = var_less(bmap, pos);
3993 return isl_basic_map_finalize(bmap);
3996 /* Return a relation on of dimension "dim" expressing i_[0..pos] <<= o_[0..pos]
3998 __isl_give isl_basic_map *isl_basic_map_less_or_equal_at(
3999 __isl_take isl_space *dim, unsigned pos)
4002 isl_basic_map *bmap;
4004 bmap = isl_basic_map_alloc_space(dim, 0, pos, 1);
4005 for (i = 0; i < pos; ++i)
4006 bmap = var_equal(bmap, i);
4007 bmap = var_less_or_equal(bmap, pos);
4008 return isl_basic_map_finalize(bmap);
4011 /* Return a relation on pairs of sets of dimension "dim" expressing i_pos > o_pos
4013 __isl_give isl_basic_map *isl_basic_map_more_at(__isl_take isl_space *dim,
4017 struct isl_basic_map *bmap;
4018 bmap = isl_basic_map_alloc_space(dim, 0, pos, 1);
4021 for (i = 0; i < pos && bmap; ++i)
4022 bmap = var_equal(bmap, i);
4024 bmap = var_more(bmap, pos);
4025 return isl_basic_map_finalize(bmap);
4028 /* Return a relation on of dimension "dim" expressing i_[0..pos] >>= o_[0..pos]
4030 __isl_give isl_basic_map *isl_basic_map_more_or_equal_at(
4031 __isl_take isl_space *dim, unsigned pos)
4034 isl_basic_map *bmap;
4036 bmap = isl_basic_map_alloc_space(dim, 0, pos, 1);
4037 for (i = 0; i < pos; ++i)
4038 bmap = var_equal(bmap, i);
4039 bmap = var_more_or_equal(bmap, pos);
4040 return isl_basic_map_finalize(bmap);
4043 static __isl_give isl_map *map_lex_lte_first(__isl_take isl_space *dims,
4044 unsigned n, int equal)
4046 struct isl_map *map;
4049 if (n == 0 && equal)
4050 return isl_map_universe(dims);
4052 map = isl_map_alloc_space(isl_space_copy(dims), n, ISL_MAP_DISJOINT);
4054 for (i = 0; i + 1 < n; ++i)
4055 map = isl_map_add_basic_map(map,
4056 isl_basic_map_less_at(isl_space_copy(dims), i));
4059 map = isl_map_add_basic_map(map,
4060 isl_basic_map_less_or_equal_at(dims, n - 1));
4062 map = isl_map_add_basic_map(map,
4063 isl_basic_map_less_at(dims, n - 1));
4065 isl_space_free(dims);
4070 static __isl_give isl_map *map_lex_lte(__isl_take isl_space *dims, int equal)
4074 return map_lex_lte_first(dims, dims->n_out, equal);
4077 __isl_give isl_map *isl_map_lex_lt_first(__isl_take isl_space *dim, unsigned n)
4079 return map_lex_lte_first(dim, n, 0);
4082 __isl_give isl_map *isl_map_lex_le_first(__isl_take isl_space *dim, unsigned n)
4084 return map_lex_lte_first(dim, n, 1);
4087 __isl_give isl_map *isl_map_lex_lt(__isl_take isl_space *set_dim)
4089 return map_lex_lte(isl_space_map_from_set(set_dim), 0);
4092 __isl_give isl_map *isl_map_lex_le(__isl_take isl_space *set_dim)
4094 return map_lex_lte(isl_space_map_from_set(set_dim), 1);
4097 static __isl_give isl_map *map_lex_gte_first(__isl_take isl_space *dims,
4098 unsigned n, int equal)
4100 struct isl_map *map;
4103 if (n == 0 && equal)
4104 return isl_map_universe(dims);
4106 map = isl_map_alloc_space(isl_space_copy(dims), n, ISL_MAP_DISJOINT);
4108 for (i = 0; i + 1 < n; ++i)
4109 map = isl_map_add_basic_map(map,
4110 isl_basic_map_more_at(isl_space_copy(dims), i));
4113 map = isl_map_add_basic_map(map,
4114 isl_basic_map_more_or_equal_at(dims, n - 1));
4116 map = isl_map_add_basic_map(map,
4117 isl_basic_map_more_at(dims, n - 1));
4119 isl_space_free(dims);
4124 static __isl_give isl_map *map_lex_gte(__isl_take isl_space *dims, int equal)
4128 return map_lex_gte_first(dims, dims->n_out, equal);
4131 __isl_give isl_map *isl_map_lex_gt_first(__isl_take isl_space *dim, unsigned n)
4133 return map_lex_gte_first(dim, n, 0);
4136 __isl_give isl_map *isl_map_lex_ge_first(__isl_take isl_space *dim, unsigned n)
4138 return map_lex_gte_first(dim, n, 1);
4141 __isl_give isl_map *isl_map_lex_gt(__isl_take isl_space *set_dim)
4143 return map_lex_gte(isl_space_map_from_set(set_dim), 0);
4146 __isl_give isl_map *isl_map_lex_ge(__isl_take isl_space *set_dim)
4148 return map_lex_gte(isl_space_map_from_set(set_dim), 1);
4151 __isl_give isl_map *isl_set_lex_le_set(__isl_take isl_set *set1,
4152 __isl_take isl_set *set2)
4155 map = isl_map_lex_le(isl_set_get_space(set1));
4156 map = isl_map_intersect_domain(map, set1);
4157 map = isl_map_intersect_range(map, set2);
4161 __isl_give isl_map *isl_set_lex_lt_set(__isl_take isl_set *set1,
4162 __isl_take isl_set *set2)
4165 map = isl_map_lex_lt(isl_set_get_space(set1));
4166 map = isl_map_intersect_domain(map, set1);
4167 map = isl_map_intersect_range(map, set2);
4171 __isl_give isl_map *isl_set_lex_ge_set(__isl_take isl_set *set1,
4172 __isl_take isl_set *set2)
4175 map = isl_map_lex_ge(isl_set_get_space(set1));
4176 map = isl_map_intersect_domain(map, set1);
4177 map = isl_map_intersect_range(map, set2);
4181 __isl_give isl_map *isl_set_lex_gt_set(__isl_take isl_set *set1,
4182 __isl_take isl_set *set2)
4185 map = isl_map_lex_gt(isl_set_get_space(set1));
4186 map = isl_map_intersect_domain(map, set1);
4187 map = isl_map_intersect_range(map, set2);
4191 __isl_give isl_map *isl_map_lex_le_map(__isl_take isl_map *map1,
4192 __isl_take isl_map *map2)
4195 map = isl_map_lex_le(isl_space_range(isl_map_get_space(map1)));
4196 map = isl_map_apply_domain(map, isl_map_reverse(map1));
4197 map = isl_map_apply_range(map, isl_map_reverse(map2));
4201 __isl_give isl_map *isl_map_lex_lt_map(__isl_take isl_map *map1,
4202 __isl_take isl_map *map2)
4205 map = isl_map_lex_lt(isl_space_range(isl_map_get_space(map1)));
4206 map = isl_map_apply_domain(map, isl_map_reverse(map1));
4207 map = isl_map_apply_range(map, isl_map_reverse(map2));
4211 __isl_give isl_map *isl_map_lex_ge_map(__isl_take isl_map *map1,
4212 __isl_take isl_map *map2)
4215 map = isl_map_lex_ge(isl_space_range(isl_map_get_space(map1)));
4216 map = isl_map_apply_domain(map, isl_map_reverse(map1));
4217 map = isl_map_apply_range(map, isl_map_reverse(map2));
4221 __isl_give isl_map *isl_map_lex_gt_map(__isl_take isl_map *map1,
4222 __isl_take isl_map *map2)
4225 map = isl_map_lex_gt(isl_space_range(isl_map_get_space(map1)));
4226 map = isl_map_apply_domain(map, isl_map_reverse(map1));
4227 map = isl_map_apply_range(map, isl_map_reverse(map2));
4231 __isl_give isl_basic_map *isl_basic_map_from_basic_set(
4232 __isl_take isl_basic_set *bset, __isl_take isl_space *dim)
4234 struct isl_basic_map *bmap;
4236 bset = isl_basic_set_cow(bset);
4240 isl_assert(bset->ctx, isl_space_compatible(bset->dim, dim), goto error);
4241 isl_space_free(bset->dim);
4242 bmap = (struct isl_basic_map *) bset;
4244 return isl_basic_map_finalize(bmap);
4246 isl_basic_set_free(bset);
4247 isl_space_free(dim);
4251 struct isl_basic_set *isl_basic_set_from_basic_map(struct isl_basic_map *bmap)
4255 if (bmap->dim->n_in == 0)
4256 return (struct isl_basic_set *)bmap;
4257 bmap = isl_basic_map_cow(bmap);
4260 bmap->dim = isl_space_as_set_space(bmap->dim);
4263 bmap = isl_basic_map_finalize(bmap);
4264 return (struct isl_basic_set *)bmap;
4266 isl_basic_map_free(bmap);
4270 /* For a div d = floor(f/m), add the constraints
4273 * -(f-(n-1)) + m d >= 0
4275 * Note that the second constraint is the negation of
4279 int isl_basic_map_add_div_constraints_var(__isl_keep isl_basic_map *bmap,
4280 unsigned pos, isl_int *div)
4283 unsigned total = isl_basic_map_total_dim(bmap);
4285 i = isl_basic_map_alloc_inequality(bmap);
4288 isl_seq_cpy(bmap->ineq[i], div + 1, 1 + total);
4289 isl_int_neg(bmap->ineq[i][1 + pos], div[0]);
4291 j = isl_basic_map_alloc_inequality(bmap);
4294 isl_seq_neg(bmap->ineq[j], bmap->ineq[i], 1 + total);
4295 isl_int_add(bmap->ineq[j][0], bmap->ineq[j][0], bmap->ineq[j][1 + pos]);
4296 isl_int_sub_ui(bmap->ineq[j][0], bmap->ineq[j][0], 1);
4300 int isl_basic_set_add_div_constraints_var(__isl_keep isl_basic_set *bset,
4301 unsigned pos, isl_int *div)
4303 return isl_basic_map_add_div_constraints_var((isl_basic_map *)bset,
4307 int isl_basic_map_add_div_constraints(struct isl_basic_map *bmap, unsigned div)
4309 unsigned total = isl_basic_map_total_dim(bmap);
4310 unsigned div_pos = total - bmap->n_div + div;
4312 return isl_basic_map_add_div_constraints_var(bmap, div_pos,
4316 int isl_basic_set_add_div_constraints(struct isl_basic_set *bset, unsigned div)
4318 return isl_basic_map_add_div_constraints(bset, div);
4321 struct isl_basic_set *isl_basic_map_underlying_set(
4322 struct isl_basic_map *bmap)
4326 if (bmap->dim->nparam == 0 && bmap->dim->n_in == 0 &&
4328 !isl_space_is_named_or_nested(bmap->dim, isl_dim_in) &&
4329 !isl_space_is_named_or_nested(bmap->dim, isl_dim_out))
4330 return (struct isl_basic_set *)bmap;
4331 bmap = isl_basic_map_cow(bmap);
4334 bmap->dim = isl_space_underlying(bmap->dim, bmap->n_div);
4337 bmap->extra -= bmap->n_div;
4339 bmap = isl_basic_map_finalize(bmap);
4340 return (struct isl_basic_set *)bmap;
4342 isl_basic_map_free(bmap);
4346 __isl_give isl_basic_set *isl_basic_set_underlying_set(
4347 __isl_take isl_basic_set *bset)
4349 return isl_basic_map_underlying_set((isl_basic_map *)bset);
4352 struct isl_basic_map *isl_basic_map_overlying_set(
4353 struct isl_basic_set *bset, struct isl_basic_map *like)
4355 struct isl_basic_map *bmap;
4356 struct isl_ctx *ctx;
4363 isl_assert(ctx, bset->n_div == 0, goto error);
4364 isl_assert(ctx, isl_basic_set_n_param(bset) == 0, goto error);
4365 isl_assert(ctx, bset->dim->n_out == isl_basic_map_total_dim(like),
4367 if (isl_space_is_equal(bset->dim, like->dim) && like->n_div == 0) {
4368 isl_basic_map_free(like);
4369 return (struct isl_basic_map *)bset;
4371 bset = isl_basic_set_cow(bset);
4374 total = bset->dim->n_out + bset->extra;
4375 bmap = (struct isl_basic_map *)bset;
4376 isl_space_free(bmap->dim);
4377 bmap->dim = isl_space_copy(like->dim);
4380 bmap->n_div = like->n_div;
4381 bmap->extra += like->n_div;
4385 ltotal = total - bmap->extra + like->extra;
4388 bmap->block2 = isl_blk_extend(ctx, bmap->block2,
4389 bmap->extra * (1 + 1 + total));
4390 if (isl_blk_is_error(bmap->block2))
4392 div = isl_realloc_array(ctx, bmap->div, isl_int *, bmap->extra);
4396 for (i = 0; i < bmap->extra; ++i)
4397 bmap->div[i] = bmap->block2.data + i * (1 + 1 + total);
4398 for (i = 0; i < like->n_div; ++i) {
4399 isl_seq_cpy(bmap->div[i], like->div[i], 1 + 1 + ltotal);
4400 isl_seq_clr(bmap->div[i]+1+1+ltotal, total - ltotal);
4402 bmap = isl_basic_map_extend_constraints(bmap,
4403 0, 2 * like->n_div);
4404 for (i = 0; i < like->n_div; ++i) {
4407 if (isl_int_is_zero(bmap->div[i][0]))
4409 if (isl_basic_map_add_div_constraints(bmap, i) < 0)
4410 bmap = isl_basic_map_free(bmap);
4413 isl_basic_map_free(like);
4414 bmap = isl_basic_map_simplify(bmap);
4415 bmap = isl_basic_map_finalize(bmap);
4418 isl_basic_map_free(like);
4419 isl_basic_set_free(bset);
4423 struct isl_basic_set *isl_basic_set_from_underlying_set(
4424 struct isl_basic_set *bset, struct isl_basic_set *like)
4426 return (struct isl_basic_set *)
4427 isl_basic_map_overlying_set(bset, (struct isl_basic_map *)like);
4430 struct isl_set *isl_set_from_underlying_set(
4431 struct isl_set *set, struct isl_basic_set *like)
4437 isl_assert(set->ctx, set->dim->n_out == isl_basic_set_total_dim(like),
4439 if (isl_space_is_equal(set->dim, like->dim) && like->n_div == 0) {
4440 isl_basic_set_free(like);
4443 set = isl_set_cow(set);
4446 for (i = 0; i < set->n; ++i) {
4447 set->p[i] = isl_basic_set_from_underlying_set(set->p[i],
4448 isl_basic_set_copy(like));
4452 isl_space_free(set->dim);
4453 set->dim = isl_space_copy(like->dim);
4456 isl_basic_set_free(like);
4459 isl_basic_set_free(like);
4464 struct isl_set *isl_map_underlying_set(struct isl_map *map)
4468 map = isl_map_cow(map);
4471 map->dim = isl_space_cow(map->dim);
4475 for (i = 1; i < map->n; ++i)
4476 isl_assert(map->ctx, map->p[0]->n_div == map->p[i]->n_div,
4478 for (i = 0; i < map->n; ++i) {
4479 map->p[i] = (struct isl_basic_map *)
4480 isl_basic_map_underlying_set(map->p[i]);
4485 map->dim = isl_space_underlying(map->dim, 0);
4487 isl_space_free(map->dim);
4488 map->dim = isl_space_copy(map->p[0]->dim);
4492 return (struct isl_set *)map;
4498 struct isl_set *isl_set_to_underlying_set(struct isl_set *set)
4500 return (struct isl_set *)isl_map_underlying_set((struct isl_map *)set);
4503 __isl_give isl_basic_map *isl_basic_map_reset_space(
4504 __isl_take isl_basic_map *bmap, __isl_take isl_space *dim)
4506 bmap = isl_basic_map_cow(bmap);
4510 isl_space_free(bmap->dim);
4513 bmap = isl_basic_map_finalize(bmap);
4517 isl_basic_map_free(bmap);
4518 isl_space_free(dim);
4522 __isl_give isl_basic_set *isl_basic_set_reset_space(
4523 __isl_take isl_basic_set *bset, __isl_take isl_space *dim)
4525 return (isl_basic_set *)isl_basic_map_reset_space((isl_basic_map *)bset,
4529 __isl_give isl_map *isl_map_reset_space(__isl_take isl_map *map,
4530 __isl_take isl_space *dim)
4534 map = isl_map_cow(map);
4538 for (i = 0; i < map->n; ++i) {
4539 map->p[i] = isl_basic_map_reset_space(map->p[i],
4540 isl_space_copy(dim));
4544 isl_space_free(map->dim);
4550 isl_space_free(dim);
4554 __isl_give isl_set *isl_set_reset_space(__isl_take isl_set *set,
4555 __isl_take isl_space *dim)
4557 return (struct isl_set *) isl_map_reset_space((struct isl_map *)set, dim);
4560 /* Compute the parameter domain of the given basic set.
4562 __isl_give isl_basic_set *isl_basic_set_params(__isl_take isl_basic_set *bset)
4567 if (isl_basic_set_is_params(bset))
4570 n = isl_basic_set_dim(bset, isl_dim_set);
4571 bset = isl_basic_set_project_out(bset, isl_dim_set, 0, n);
4572 space = isl_basic_set_get_space(bset);
4573 space = isl_space_params(space);
4574 bset = isl_basic_set_reset_space(bset, space);
4578 /* Construct a zero-dimensional basic set with the given parameter domain.
4580 __isl_give isl_basic_set *isl_basic_set_from_params(
4581 __isl_take isl_basic_set *bset)
4584 space = isl_basic_set_get_space(bset);
4585 space = isl_space_set_from_params(space);
4586 bset = isl_basic_set_reset_space(bset, space);
4590 /* Compute the parameter domain of the given set.
4592 __isl_give isl_set *isl_set_params(__isl_take isl_set *set)
4597 if (isl_set_is_params(set))
4600 n = isl_set_dim(set, isl_dim_set);
4601 set = isl_set_project_out(set, isl_dim_set, 0, n);
4602 space = isl_set_get_space(set);
4603 space = isl_space_params(space);
4604 set = isl_set_reset_space(set, space);
4608 /* Construct a zero-dimensional set with the given parameter domain.
4610 __isl_give isl_set *isl_set_from_params(__isl_take isl_set *set)
4613 space = isl_set_get_space(set);
4614 space = isl_space_set_from_params(space);
4615 set = isl_set_reset_space(set, space);
4619 /* Compute the parameter domain of the given map.
4621 __isl_give isl_set *isl_map_params(__isl_take isl_map *map)
4626 n = isl_map_dim(map, isl_dim_in);
4627 map = isl_map_project_out(map, isl_dim_in, 0, n);
4628 n = isl_map_dim(map, isl_dim_out);
4629 map = isl_map_project_out(map, isl_dim_out, 0, n);
4630 space = isl_map_get_space(map);
4631 space = isl_space_params(space);
4632 map = isl_map_reset_space(map, space);
4636 struct isl_basic_set *isl_basic_map_domain(struct isl_basic_map *bmap)
4639 struct isl_basic_set *domain;
4645 dim = isl_space_domain(isl_basic_map_get_space(bmap));
4647 n_in = isl_basic_map_n_in(bmap);
4648 n_out = isl_basic_map_n_out(bmap);
4649 domain = isl_basic_set_from_basic_map(bmap);
4650 domain = isl_basic_set_project_out(domain, isl_dim_set, n_in, n_out);
4652 domain = isl_basic_set_reset_space(domain, dim);
4657 int isl_basic_map_may_be_set(__isl_keep isl_basic_map *bmap)
4661 return isl_space_may_be_set(bmap->dim);
4664 /* Is this basic map actually a set?
4665 * Users should never call this function. Outside of isl,
4666 * the type should indicate whether something is a set or a map.
4668 int isl_basic_map_is_set(__isl_keep isl_basic_map *bmap)
4672 return isl_space_is_set(bmap->dim);
4675 struct isl_basic_set *isl_basic_map_range(struct isl_basic_map *bmap)
4679 if (isl_basic_map_is_set(bmap))
4681 return isl_basic_map_domain(isl_basic_map_reverse(bmap));
4684 __isl_give isl_basic_map *isl_basic_map_domain_map(
4685 __isl_take isl_basic_map *bmap)
4689 isl_basic_map *domain;
4690 int nparam, n_in, n_out;
4693 nparam = isl_basic_map_dim(bmap, isl_dim_param);
4694 n_in = isl_basic_map_dim(bmap, isl_dim_in);
4695 n_out = isl_basic_map_dim(bmap, isl_dim_out);
4697 dim = isl_space_from_range(isl_space_domain(isl_basic_map_get_space(bmap)));
4698 domain = isl_basic_map_universe(dim);
4700 bmap = isl_basic_map_from_domain(isl_basic_map_wrap(bmap));
4701 bmap = isl_basic_map_apply_range(bmap, domain);
4702 bmap = isl_basic_map_extend_constraints(bmap, n_in, 0);
4704 total = isl_basic_map_total_dim(bmap);
4706 for (i = 0; i < n_in; ++i) {
4707 k = isl_basic_map_alloc_equality(bmap);
4710 isl_seq_clr(bmap->eq[k], 1 + total);
4711 isl_int_set_si(bmap->eq[k][1 + nparam + i], -1);
4712 isl_int_set_si(bmap->eq[k][1 + nparam + n_in + n_out + i], 1);
4715 bmap = isl_basic_map_gauss(bmap, NULL);
4716 return isl_basic_map_finalize(bmap);
4718 isl_basic_map_free(bmap);
4722 __isl_give isl_basic_map *isl_basic_map_range_map(
4723 __isl_take isl_basic_map *bmap)
4727 isl_basic_map *range;
4728 int nparam, n_in, n_out;
4731 nparam = isl_basic_map_dim(bmap, isl_dim_param);
4732 n_in = isl_basic_map_dim(bmap, isl_dim_in);
4733 n_out = isl_basic_map_dim(bmap, isl_dim_out);
4735 dim = isl_space_from_range(isl_space_range(isl_basic_map_get_space(bmap)));
4736 range = isl_basic_map_universe(dim);
4738 bmap = isl_basic_map_from_domain(isl_basic_map_wrap(bmap));
4739 bmap = isl_basic_map_apply_range(bmap, range);
4740 bmap = isl_basic_map_extend_constraints(bmap, n_out, 0);
4742 total = isl_basic_map_total_dim(bmap);
4744 for (i = 0; i < n_out; ++i) {
4745 k = isl_basic_map_alloc_equality(bmap);
4748 isl_seq_clr(bmap->eq[k], 1 + total);
4749 isl_int_set_si(bmap->eq[k][1 + nparam + n_in + i], -1);
4750 isl_int_set_si(bmap->eq[k][1 + nparam + n_in + n_out + i], 1);
4753 bmap = isl_basic_map_gauss(bmap, NULL);
4754 return isl_basic_map_finalize(bmap);
4756 isl_basic_map_free(bmap);
4760 int isl_map_may_be_set(__isl_keep isl_map *map)
4764 return isl_space_may_be_set(map->dim);
4767 /* Is this map actually a set?
4768 * Users should never call this function. Outside of isl,
4769 * the type should indicate whether something is a set or a map.
4771 int isl_map_is_set(__isl_keep isl_map *map)
4775 return isl_space_is_set(map->dim);
4778 struct isl_set *isl_map_range(struct isl_map *map)
4781 struct isl_set *set;
4785 if (isl_map_is_set(map))
4786 return (isl_set *)map;
4788 map = isl_map_cow(map);
4792 set = (struct isl_set *) map;
4793 set->dim = isl_space_range(set->dim);
4796 for (i = 0; i < map->n; ++i) {
4797 set->p[i] = isl_basic_map_range(map->p[i]);
4801 ISL_F_CLR(set, ISL_MAP_DISJOINT);
4802 ISL_F_CLR(set, ISL_SET_NORMALIZED);
4809 __isl_give isl_map *isl_map_domain_map(__isl_take isl_map *map)
4812 isl_space *domain_dim;
4814 map = isl_map_cow(map);
4818 domain_dim = isl_space_from_range(isl_space_domain(isl_map_get_space(map)));
4819 map->dim = isl_space_from_domain(isl_space_wrap(map->dim));
4820 map->dim = isl_space_join(map->dim, domain_dim);
4823 for (i = 0; i < map->n; ++i) {
4824 map->p[i] = isl_basic_map_domain_map(map->p[i]);
4828 ISL_F_CLR(map, ISL_MAP_DISJOINT);
4829 ISL_F_CLR(map, ISL_MAP_NORMALIZED);
4836 __isl_give isl_map *isl_map_range_map(__isl_take isl_map *map)
4839 isl_space *range_dim;
4841 map = isl_map_cow(map);
4845 range_dim = isl_space_range(isl_map_get_space(map));
4846 range_dim = isl_space_from_range(range_dim);
4847 map->dim = isl_space_from_domain(isl_space_wrap(map->dim));
4848 map->dim = isl_space_join(map->dim, range_dim);
4851 for (i = 0; i < map->n; ++i) {
4852 map->p[i] = isl_basic_map_range_map(map->p[i]);
4856 ISL_F_CLR(map, ISL_MAP_DISJOINT);
4857 ISL_F_CLR(map, ISL_MAP_NORMALIZED);
4864 __isl_give isl_map *isl_map_from_set(__isl_take isl_set *set,
4865 __isl_take isl_space *dim)
4868 struct isl_map *map = NULL;
4870 set = isl_set_cow(set);
4873 isl_assert(set->ctx, isl_space_compatible(set->dim, dim), goto error);
4874 map = (struct isl_map *)set;
4875 for (i = 0; i < set->n; ++i) {
4876 map->p[i] = isl_basic_map_from_basic_set(
4877 set->p[i], isl_space_copy(dim));
4881 isl_space_free(map->dim);
4885 isl_space_free(dim);
4890 __isl_give isl_basic_map *isl_basic_map_from_domain(
4891 __isl_take isl_basic_set *bset)
4893 return isl_basic_map_reverse(isl_basic_map_from_range(bset));
4896 __isl_give isl_basic_map *isl_basic_map_from_range(
4897 __isl_take isl_basic_set *bset)
4900 space = isl_basic_set_get_space(bset);
4901 space = isl_space_from_range(space);
4902 bset = isl_basic_set_reset_space(bset, space);
4903 return (isl_basic_map *)bset;
4906 struct isl_map *isl_map_from_range(struct isl_set *set)
4909 space = isl_set_get_space(set);
4910 space = isl_space_from_range(space);
4911 set = isl_set_reset_space(set, space);
4912 return (struct isl_map *)set;
4915 __isl_give isl_map *isl_map_from_domain(__isl_take isl_set *set)
4917 return isl_map_reverse(isl_map_from_range(set));
4920 __isl_give isl_basic_map *isl_basic_map_from_domain_and_range(
4921 __isl_take isl_basic_set *domain, __isl_take isl_basic_set *range)
4923 return isl_basic_map_apply_range(isl_basic_map_reverse(domain), range);
4926 __isl_give isl_map *isl_map_from_domain_and_range(__isl_take isl_set *domain,
4927 __isl_take isl_set *range)
4929 return isl_map_apply_range(isl_map_reverse(domain), range);
4932 struct isl_set *isl_set_from_map(struct isl_map *map)
4935 struct isl_set *set = NULL;
4939 map = isl_map_cow(map);
4942 map->dim = isl_space_as_set_space(map->dim);
4945 set = (struct isl_set *)map;
4946 for (i = 0; i < map->n; ++i) {
4947 set->p[i] = isl_basic_set_from_basic_map(map->p[i]);
4957 __isl_give isl_map *isl_map_alloc_space(__isl_take isl_space *dim, int n,
4960 struct isl_map *map;
4965 isl_die(dim->ctx, isl_error_internal,
4966 "negative number of basic maps", goto error);
4967 map = isl_alloc(dim->ctx, struct isl_map,
4968 sizeof(struct isl_map) +
4969 (n - 1) * sizeof(struct isl_basic_map *));
4973 map->ctx = dim->ctx;
4974 isl_ctx_ref(map->ctx);
4982 isl_space_free(dim);
4986 struct isl_map *isl_map_alloc(struct isl_ctx *ctx,
4987 unsigned nparam, unsigned in, unsigned out, int n,
4990 struct isl_map *map;
4993 dims = isl_space_alloc(ctx, nparam, in, out);
4997 map = isl_map_alloc_space(dims, n, flags);
5001 __isl_give isl_basic_map *isl_basic_map_empty(__isl_take isl_space *dim)
5003 struct isl_basic_map *bmap;
5004 bmap = isl_basic_map_alloc_space(dim, 0, 1, 0);
5005 bmap = isl_basic_map_set_to_empty(bmap);
5009 __isl_give isl_basic_set *isl_basic_set_empty(__isl_take isl_space *dim)
5011 struct isl_basic_set *bset;
5012 bset = isl_basic_set_alloc_space(dim, 0, 1, 0);
5013 bset = isl_basic_set_set_to_empty(bset);
5017 struct isl_basic_map *isl_basic_map_empty_like(struct isl_basic_map *model)
5019 struct isl_basic_map *bmap;
5022 bmap = isl_basic_map_alloc_space(isl_space_copy(model->dim), 0, 1, 0);
5023 bmap = isl_basic_map_set_to_empty(bmap);
5027 struct isl_basic_map *isl_basic_map_empty_like_map(struct isl_map *model)
5029 struct isl_basic_map *bmap;
5032 bmap = isl_basic_map_alloc_space(isl_space_copy(model->dim), 0, 1, 0);
5033 bmap = isl_basic_map_set_to_empty(bmap);
5037 struct isl_basic_set *isl_basic_set_empty_like(struct isl_basic_set *model)
5039 struct isl_basic_set *bset;
5042 bset = isl_basic_set_alloc_space(isl_space_copy(model->dim), 0, 1, 0);
5043 bset = isl_basic_set_set_to_empty(bset);
5047 __isl_give isl_basic_map *isl_basic_map_universe(__isl_take isl_space *dim)
5049 struct isl_basic_map *bmap;
5050 bmap = isl_basic_map_alloc_space(dim, 0, 0, 0);
5051 bmap = isl_basic_map_finalize(bmap);
5055 __isl_give isl_basic_set *isl_basic_set_universe(__isl_take isl_space *dim)
5057 struct isl_basic_set *bset;
5058 bset = isl_basic_set_alloc_space(dim, 0, 0, 0);
5059 bset = isl_basic_set_finalize(bset);
5063 __isl_give isl_basic_map *isl_basic_map_nat_universe(__isl_take isl_space *dim)
5066 unsigned total = isl_space_dim(dim, isl_dim_all);
5067 isl_basic_map *bmap;
5069 bmap= isl_basic_map_alloc_space(dim, 0, 0, total);
5070 for (i = 0; i < total; ++i) {
5071 int k = isl_basic_map_alloc_inequality(bmap);
5074 isl_seq_clr(bmap->ineq[k], 1 + total);
5075 isl_int_set_si(bmap->ineq[k][1 + i], 1);
5079 isl_basic_map_free(bmap);
5083 __isl_give isl_basic_set *isl_basic_set_nat_universe(__isl_take isl_space *dim)
5085 return isl_basic_map_nat_universe(dim);
5088 __isl_give isl_map *isl_map_nat_universe(__isl_take isl_space *dim)
5090 return isl_map_from_basic_map(isl_basic_map_nat_universe(dim));
5093 __isl_give isl_set *isl_set_nat_universe(__isl_take isl_space *dim)
5095 return isl_map_nat_universe(dim);
5098 __isl_give isl_basic_map *isl_basic_map_universe_like(
5099 __isl_keep isl_basic_map *model)
5103 return isl_basic_map_alloc_space(isl_space_copy(model->dim), 0, 0, 0);
5106 struct isl_basic_set *isl_basic_set_universe_like(struct isl_basic_set *model)
5110 return isl_basic_set_alloc_space(isl_space_copy(model->dim), 0, 0, 0);
5113 __isl_give isl_basic_set *isl_basic_set_universe_like_set(
5114 __isl_keep isl_set *model)
5118 return isl_basic_set_alloc_space(isl_space_copy(model->dim), 0, 0, 0);
5121 __isl_give isl_map *isl_map_empty(__isl_take isl_space *dim)
5123 return isl_map_alloc_space(dim, 0, ISL_MAP_DISJOINT);
5126 struct isl_map *isl_map_empty_like(struct isl_map *model)
5130 return isl_map_alloc_space(isl_space_copy(model->dim), 0, ISL_MAP_DISJOINT);
5133 struct isl_map *isl_map_empty_like_basic_map(struct isl_basic_map *model)
5137 return isl_map_alloc_space(isl_space_copy(model->dim), 0, ISL_MAP_DISJOINT);
5140 __isl_give isl_set *isl_set_empty(__isl_take isl_space *dim)
5142 return isl_set_alloc_space(dim, 0, ISL_MAP_DISJOINT);
5145 struct isl_set *isl_set_empty_like(struct isl_set *model)
5149 return isl_set_empty(isl_space_copy(model->dim));
5152 __isl_give isl_map *isl_map_universe(__isl_take isl_space *dim)
5154 struct isl_map *map;
5157 map = isl_map_alloc_space(isl_space_copy(dim), 1, ISL_MAP_DISJOINT);
5158 map = isl_map_add_basic_map(map, isl_basic_map_universe(dim));
5162 __isl_give isl_set *isl_set_universe(__isl_take isl_space *dim)
5164 struct isl_set *set;
5167 set = isl_set_alloc_space(isl_space_copy(dim), 1, ISL_MAP_DISJOINT);
5168 set = isl_set_add_basic_set(set, isl_basic_set_universe(dim));
5172 __isl_give isl_set *isl_set_universe_like(__isl_keep isl_set *model)
5176 return isl_set_universe(isl_space_copy(model->dim));
5179 struct isl_map *isl_map_dup(struct isl_map *map)
5182 struct isl_map *dup;
5186 dup = isl_map_alloc_space(isl_space_copy(map->dim), map->n, map->flags);
5187 for (i = 0; i < map->n; ++i)
5188 dup = isl_map_add_basic_map(dup, isl_basic_map_copy(map->p[i]));
5192 __isl_give isl_map *isl_map_add_basic_map(__isl_take isl_map *map,
5193 __isl_take isl_basic_map *bmap)
5197 if (isl_basic_map_plain_is_empty(bmap)) {
5198 isl_basic_map_free(bmap);
5201 isl_assert(map->ctx, isl_space_is_equal(map->dim, bmap->dim), goto error);
5202 isl_assert(map->ctx, map->n < map->size, goto error);
5203 map->p[map->n] = bmap;
5205 ISL_F_CLR(map, ISL_MAP_NORMALIZED);
5211 isl_basic_map_free(bmap);
5215 void *isl_map_free(struct isl_map *map)
5225 isl_ctx_deref(map->ctx);
5226 for (i = 0; i < map->n; ++i)
5227 isl_basic_map_free(map->p[i]);
5228 isl_space_free(map->dim);
5234 struct isl_map *isl_map_extend(struct isl_map *base,
5235 unsigned nparam, unsigned n_in, unsigned n_out)
5239 base = isl_map_cow(base);
5243 base->dim = isl_space_extend(base->dim, nparam, n_in, n_out);
5246 for (i = 0; i < base->n; ++i) {
5247 base->p[i] = isl_basic_map_extend_space(base->p[i],
5248 isl_space_copy(base->dim), 0, 0, 0);
5258 struct isl_set *isl_set_extend(struct isl_set *base,
5259 unsigned nparam, unsigned dim)
5261 return (struct isl_set *)isl_map_extend((struct isl_map *)base,
5265 static struct isl_basic_map *isl_basic_map_fix_pos_si(
5266 struct isl_basic_map *bmap, unsigned pos, int value)
5270 bmap = isl_basic_map_cow(bmap);
5271 bmap = isl_basic_map_extend_constraints(bmap, 1, 0);
5272 j = isl_basic_map_alloc_equality(bmap);
5275 isl_seq_clr(bmap->eq[j] + 1, isl_basic_map_total_dim(bmap));
5276 isl_int_set_si(bmap->eq[j][pos], -1);
5277 isl_int_set_si(bmap->eq[j][0], value);
5278 bmap = isl_basic_map_simplify(bmap);
5279 return isl_basic_map_finalize(bmap);
5281 isl_basic_map_free(bmap);
5285 static __isl_give isl_basic_map *isl_basic_map_fix_pos(
5286 __isl_take isl_basic_map *bmap, unsigned pos, isl_int value)
5290 bmap = isl_basic_map_cow(bmap);
5291 bmap = isl_basic_map_extend_constraints(bmap, 1, 0);
5292 j = isl_basic_map_alloc_equality(bmap);
5295 isl_seq_clr(bmap->eq[j] + 1, isl_basic_map_total_dim(bmap));
5296 isl_int_set_si(bmap->eq[j][pos], -1);
5297 isl_int_set(bmap->eq[j][0], value);
5298 bmap = isl_basic_map_simplify(bmap);
5299 return isl_basic_map_finalize(bmap);
5301 isl_basic_map_free(bmap);
5305 struct isl_basic_map *isl_basic_map_fix_si(struct isl_basic_map *bmap,
5306 enum isl_dim_type type, unsigned pos, int value)
5310 isl_assert(bmap->ctx, pos < isl_basic_map_dim(bmap, type), goto error);
5311 return isl_basic_map_fix_pos_si(bmap,
5312 isl_basic_map_offset(bmap, type) + pos, value);
5314 isl_basic_map_free(bmap);
5318 __isl_give isl_basic_map *isl_basic_map_fix(__isl_take isl_basic_map *bmap,
5319 enum isl_dim_type type, unsigned pos, isl_int value)
5323 isl_assert(bmap->ctx, pos < isl_basic_map_dim(bmap, type), goto error);
5324 return isl_basic_map_fix_pos(bmap,
5325 isl_basic_map_offset(bmap, type) + pos, value);
5327 isl_basic_map_free(bmap);
5331 struct isl_basic_set *isl_basic_set_fix_si(struct isl_basic_set *bset,
5332 enum isl_dim_type type, unsigned pos, int value)
5334 return (struct isl_basic_set *)
5335 isl_basic_map_fix_si((struct isl_basic_map *)bset,
5339 __isl_give isl_basic_set *isl_basic_set_fix(__isl_take isl_basic_set *bset,
5340 enum isl_dim_type type, unsigned pos, isl_int value)
5342 return (struct isl_basic_set *)
5343 isl_basic_map_fix((struct isl_basic_map *)bset,
5347 struct isl_basic_map *isl_basic_map_fix_input_si(struct isl_basic_map *bmap,
5348 unsigned input, int value)
5350 return isl_basic_map_fix_si(bmap, isl_dim_in, input, value);
5353 struct isl_basic_set *isl_basic_set_fix_dim_si(struct isl_basic_set *bset,
5354 unsigned dim, int value)
5356 return (struct isl_basic_set *)
5357 isl_basic_map_fix_si((struct isl_basic_map *)bset,
5358 isl_dim_set, dim, value);
5361 static int remove_if_empty(__isl_keep isl_map *map, int i)
5363 int empty = isl_basic_map_plain_is_empty(map->p[i]);
5370 isl_basic_map_free(map->p[i]);
5371 if (i != map->n - 1) {
5372 ISL_F_CLR(map, ISL_MAP_NORMALIZED);
5373 map->p[i] = map->p[map->n - 1];
5380 /* Perform "fn" on each basic map of "map", where we may not be holding
5381 * the only reference to "map".
5382 * In particular, "fn" should be a semantics preserving operation
5383 * that we want to apply to all copies of "map". We therefore need
5384 * to be careful not to modify "map" in a way that breaks "map"
5385 * in case anything goes wrong.
5387 __isl_give isl_map *isl_map_inline_foreach_basic_map(__isl_take isl_map *map,
5388 __isl_give isl_basic_map *(*fn)(__isl_take isl_basic_map *bmap))
5390 struct isl_basic_map *bmap;
5396 for (i = map->n - 1; i >= 0; --i) {
5397 bmap = isl_basic_map_copy(map->p[i]);
5401 isl_basic_map_free(map->p[i]);
5403 if (remove_if_empty(map, i) < 0)
5413 struct isl_map *isl_map_fix_si(struct isl_map *map,
5414 enum isl_dim_type type, unsigned pos, int value)
5418 map = isl_map_cow(map);
5422 isl_assert(map->ctx, pos < isl_map_dim(map, type), goto error);
5423 for (i = map->n - 1; i >= 0; --i) {
5424 map->p[i] = isl_basic_map_fix_si(map->p[i], type, pos, value);
5425 if (remove_if_empty(map, i) < 0)
5428 ISL_F_CLR(map, ISL_MAP_NORMALIZED);
5435 __isl_give isl_set *isl_set_fix_si(__isl_take isl_set *set,
5436 enum isl_dim_type type, unsigned pos, int value)
5438 return (struct isl_set *)
5439 isl_map_fix_si((struct isl_map *)set, type, pos, value);
5442 __isl_give isl_map *isl_map_fix(__isl_take isl_map *map,
5443 enum isl_dim_type type, unsigned pos, isl_int value)
5447 map = isl_map_cow(map);
5451 isl_assert(map->ctx, pos < isl_map_dim(map, type), goto error);
5452 for (i = 0; i < map->n; ++i) {
5453 map->p[i] = isl_basic_map_fix(map->p[i], type, pos, value);
5457 ISL_F_CLR(map, ISL_MAP_NORMALIZED);
5464 __isl_give isl_set *isl_set_fix(__isl_take isl_set *set,
5465 enum isl_dim_type type, unsigned pos, isl_int value)
5467 return (struct isl_set *)isl_map_fix((isl_map *)set, type, pos, value);
5470 struct isl_map *isl_map_fix_input_si(struct isl_map *map,
5471 unsigned input, int value)
5473 return isl_map_fix_si(map, isl_dim_in, input, value);
5476 struct isl_set *isl_set_fix_dim_si(struct isl_set *set, unsigned dim, int value)
5478 return (struct isl_set *)
5479 isl_map_fix_si((struct isl_map *)set, isl_dim_set, dim, value);
5482 static __isl_give isl_basic_map *basic_map_bound_si(
5483 __isl_take isl_basic_map *bmap,
5484 enum isl_dim_type type, unsigned pos, int value, int upper)
5490 isl_assert(bmap->ctx, pos < isl_basic_map_dim(bmap, type), goto error);
5491 pos += isl_basic_map_offset(bmap, type);
5492 bmap = isl_basic_map_cow(bmap);
5493 bmap = isl_basic_map_extend_constraints(bmap, 0, 1);
5494 j = isl_basic_map_alloc_inequality(bmap);
5497 isl_seq_clr(bmap->ineq[j], 1 + isl_basic_map_total_dim(bmap));
5499 isl_int_set_si(bmap->ineq[j][pos], -1);
5500 isl_int_set_si(bmap->ineq[j][0], value);
5502 isl_int_set_si(bmap->ineq[j][pos], 1);
5503 isl_int_set_si(bmap->ineq[j][0], -value);
5505 bmap = isl_basic_map_simplify(bmap);
5506 return isl_basic_map_finalize(bmap);
5508 isl_basic_map_free(bmap);
5512 __isl_give isl_basic_map *isl_basic_map_lower_bound_si(
5513 __isl_take isl_basic_map *bmap,
5514 enum isl_dim_type type, unsigned pos, int value)
5516 return basic_map_bound_si(bmap, type, pos, value, 0);
5519 /* Constrain the values of the given dimension to be no greater than "value".
5521 __isl_give isl_basic_map *isl_basic_map_upper_bound_si(
5522 __isl_take isl_basic_map *bmap,
5523 enum isl_dim_type type, unsigned pos, int value)
5525 return basic_map_bound_si(bmap, type, pos, value, 1);
5528 struct isl_basic_set *isl_basic_set_lower_bound_dim(struct isl_basic_set *bset,
5529 unsigned dim, isl_int value)
5533 bset = isl_basic_set_cow(bset);
5534 bset = isl_basic_set_extend_constraints(bset, 0, 1);
5535 j = isl_basic_set_alloc_inequality(bset);
5538 isl_seq_clr(bset->ineq[j], 1 + isl_basic_set_total_dim(bset));
5539 isl_int_set_si(bset->ineq[j][1 + isl_basic_set_n_param(bset) + dim], 1);
5540 isl_int_neg(bset->ineq[j][0], value);
5541 bset = isl_basic_set_simplify(bset);
5542 return isl_basic_set_finalize(bset);
5544 isl_basic_set_free(bset);
5548 static __isl_give isl_map *map_bound_si(__isl_take isl_map *map,
5549 enum isl_dim_type type, unsigned pos, int value, int upper)
5553 map = isl_map_cow(map);
5557 isl_assert(map->ctx, pos < isl_map_dim(map, type), goto error);
5558 for (i = 0; i < map->n; ++i) {
5559 map->p[i] = basic_map_bound_si(map->p[i],
5560 type, pos, value, upper);
5564 ISL_F_CLR(map, ISL_MAP_NORMALIZED);
5571 __isl_give isl_map *isl_map_lower_bound_si(__isl_take isl_map *map,
5572 enum isl_dim_type type, unsigned pos, int value)
5574 return map_bound_si(map, type, pos, value, 0);
5577 __isl_give isl_map *isl_map_upper_bound_si(__isl_take isl_map *map,
5578 enum isl_dim_type type, unsigned pos, int value)
5580 return map_bound_si(map, type, pos, value, 1);
5583 __isl_give isl_set *isl_set_lower_bound_si(__isl_take isl_set *set,
5584 enum isl_dim_type type, unsigned pos, int value)
5586 return (struct isl_set *)
5587 isl_map_lower_bound_si((struct isl_map *)set, type, pos, value);
5590 __isl_give isl_set *isl_set_upper_bound_si(__isl_take isl_set *set,
5591 enum isl_dim_type type, unsigned pos, int value)
5593 return isl_map_upper_bound_si(set, type, pos, value);
5596 /* Bound the given variable of "bmap" from below (or above is "upper"
5597 * is set) to "value".
5599 static __isl_give isl_basic_map *basic_map_bound(
5600 __isl_take isl_basic_map *bmap,
5601 enum isl_dim_type type, unsigned pos, isl_int value, int upper)
5607 if (pos >= isl_basic_map_dim(bmap, type))
5608 isl_die(bmap->ctx, isl_error_invalid,
5609 "index out of bounds", goto error);
5610 pos += isl_basic_map_offset(bmap, type);
5611 bmap = isl_basic_map_cow(bmap);
5612 bmap = isl_basic_map_extend_constraints(bmap, 0, 1);
5613 j = isl_basic_map_alloc_inequality(bmap);
5616 isl_seq_clr(bmap->ineq[j], 1 + isl_basic_map_total_dim(bmap));
5618 isl_int_set_si(bmap->ineq[j][pos], -1);
5619 isl_int_set(bmap->ineq[j][0], value);
5621 isl_int_set_si(bmap->ineq[j][pos], 1);
5622 isl_int_neg(bmap->ineq[j][0], value);
5624 bmap = isl_basic_map_simplify(bmap);
5625 return isl_basic_map_finalize(bmap);
5627 isl_basic_map_free(bmap);
5631 /* Bound the given variable of "map" from below (or above is "upper"
5632 * is set) to "value".
5634 static __isl_give isl_map *map_bound(__isl_take isl_map *map,
5635 enum isl_dim_type type, unsigned pos, isl_int value, int upper)
5639 map = isl_map_cow(map);
5643 if (pos >= isl_map_dim(map, type))
5644 isl_die(map->ctx, isl_error_invalid,
5645 "index out of bounds", goto error);
5646 for (i = map->n - 1; i >= 0; --i) {
5647 map->p[i] = basic_map_bound(map->p[i], type, pos, value, upper);
5648 if (remove_if_empty(map, i) < 0)
5651 ISL_F_CLR(map, ISL_MAP_NORMALIZED);
5658 __isl_give isl_map *isl_map_lower_bound(__isl_take isl_map *map,
5659 enum isl_dim_type type, unsigned pos, isl_int value)
5661 return map_bound(map, type, pos, value, 0);
5664 __isl_give isl_map *isl_map_upper_bound(__isl_take isl_map *map,
5665 enum isl_dim_type type, unsigned pos, isl_int value)
5667 return map_bound(map, type, pos, value, 1);
5670 __isl_give isl_set *isl_set_lower_bound(__isl_take isl_set *set,
5671 enum isl_dim_type type, unsigned pos, isl_int value)
5673 return isl_map_lower_bound(set, type, pos, value);
5676 __isl_give isl_set *isl_set_upper_bound(__isl_take isl_set *set,
5677 enum isl_dim_type type, unsigned pos, isl_int value)
5679 return isl_map_upper_bound(set, type, pos, value);
5682 struct isl_set *isl_set_lower_bound_dim(struct isl_set *set, unsigned dim,
5687 set = isl_set_cow(set);
5691 isl_assert(set->ctx, dim < isl_set_n_dim(set), goto error);
5692 for (i = 0; i < set->n; ++i) {
5693 set->p[i] = isl_basic_set_lower_bound_dim(set->p[i], dim, value);
5703 struct isl_map *isl_map_reverse(struct isl_map *map)
5707 map = isl_map_cow(map);
5711 map->dim = isl_space_reverse(map->dim);
5714 for (i = 0; i < map->n; ++i) {
5715 map->p[i] = isl_basic_map_reverse(map->p[i]);
5719 ISL_F_CLR(map, ISL_MAP_NORMALIZED);
5726 static struct isl_map *isl_basic_map_partial_lexopt(
5727 struct isl_basic_map *bmap, struct isl_basic_set *dom,
5728 struct isl_set **empty, int max)
5732 if (bmap->ctx->opt->pip == ISL_PIP_PIP)
5733 return isl_pip_basic_map_lexopt(bmap, dom, empty, max);
5735 return isl_tab_basic_map_partial_lexopt(bmap, dom, empty, max);
5737 isl_basic_map_free(bmap);
5738 isl_basic_set_free(dom);
5744 struct isl_map *isl_basic_map_partial_lexmax(
5745 struct isl_basic_map *bmap, struct isl_basic_set *dom,
5746 struct isl_set **empty)
5748 return isl_basic_map_partial_lexopt(bmap, dom, empty, 1);
5751 struct isl_map *isl_basic_map_partial_lexmin(
5752 struct isl_basic_map *bmap, struct isl_basic_set *dom,
5753 struct isl_set **empty)
5755 return isl_basic_map_partial_lexopt(bmap, dom, empty, 0);
5758 struct isl_set *isl_basic_set_partial_lexmin(
5759 struct isl_basic_set *bset, struct isl_basic_set *dom,
5760 struct isl_set **empty)
5762 return (struct isl_set *)
5763 isl_basic_map_partial_lexmin((struct isl_basic_map *)bset,
5767 struct isl_set *isl_basic_set_partial_lexmax(
5768 struct isl_basic_set *bset, struct isl_basic_set *dom,
5769 struct isl_set **empty)
5771 return (struct isl_set *)
5772 isl_basic_map_partial_lexmax((struct isl_basic_map *)bset,
5776 __isl_give isl_pw_multi_aff *isl_basic_map_partial_lexmin_pw_multi_aff(
5777 __isl_take isl_basic_map *bmap, __isl_take isl_basic_set *dom,
5778 __isl_give isl_set **empty)
5780 return isl_basic_map_partial_lexopt_pw_multi_aff(bmap, dom, empty, 0);
5783 __isl_give isl_pw_multi_aff *isl_basic_map_partial_lexmax_pw_multi_aff(
5784 __isl_take isl_basic_map *bmap, __isl_take isl_basic_set *dom,
5785 __isl_give isl_set **empty)
5787 return isl_basic_map_partial_lexopt_pw_multi_aff(bmap, dom, empty, 1);
5790 __isl_give isl_pw_multi_aff *isl_basic_set_partial_lexmin_pw_multi_aff(
5791 __isl_take isl_basic_set *bset, __isl_take isl_basic_set *dom,
5792 __isl_give isl_set **empty)
5794 return isl_basic_map_partial_lexmin_pw_multi_aff(bset, dom, empty);
5797 __isl_give isl_pw_multi_aff *isl_basic_set_partial_lexmax_pw_multi_aff(
5798 __isl_take isl_basic_set *bset, __isl_take isl_basic_set *dom,
5799 __isl_give isl_set **empty)
5801 return isl_basic_map_partial_lexmax_pw_multi_aff(bset, dom, empty);
5804 __isl_give isl_pw_multi_aff *isl_basic_map_lexopt_pw_multi_aff(
5805 __isl_take isl_basic_map *bmap, int max)
5807 isl_basic_set *dom = NULL;
5808 isl_space *dom_space;
5812 dom_space = isl_space_domain(isl_space_copy(bmap->dim));
5813 dom = isl_basic_set_universe(dom_space);
5814 return isl_basic_map_partial_lexopt_pw_multi_aff(bmap, dom, NULL, max);
5816 isl_basic_map_free(bmap);
5820 __isl_give isl_pw_multi_aff *isl_basic_map_lexmin_pw_multi_aff(
5821 __isl_take isl_basic_map *bmap)
5823 return isl_basic_map_lexopt_pw_multi_aff(bmap, 0);
5827 #define TYPE isl_pw_multi_aff
5829 #define SUFFIX _pw_multi_aff
5831 #define EMPTY isl_pw_multi_aff_empty
5833 #define ADD isl_pw_multi_aff_union_add
5834 #include "isl_map_lexopt_templ.c"
5836 /* Given a map "map", compute the lexicographically minimal
5837 * (or maximal) image element for each domain element in dom,
5838 * in the form of an isl_pw_multi_aff.
5839 * Set *empty to those elements in dom that do not have an image element.
5841 * We first compute the lexicographically minimal or maximal element
5842 * in the first basic map. This results in a partial solution "res"
5843 * and a subset "todo" of dom that still need to be handled.
5844 * We then consider each of the remaining maps in "map" and successively
5845 * update both "res" and "todo".
5847 static __isl_give isl_pw_multi_aff *isl_map_partial_lexopt_aligned_pw_multi_aff(
5848 __isl_take isl_map *map, __isl_take isl_set *dom,
5849 __isl_give isl_set **empty, int max)
5852 isl_pw_multi_aff *res;
5858 if (isl_map_plain_is_empty(map)) {
5863 return isl_pw_multi_aff_from_map(map);
5866 res = basic_map_partial_lexopt_pw_multi_aff(
5867 isl_basic_map_copy(map->p[0]),
5868 isl_set_copy(dom), &todo, max);
5870 for (i = 1; i < map->n; ++i) {
5871 isl_pw_multi_aff *res_i;
5874 res_i = basic_map_partial_lexopt_pw_multi_aff(
5875 isl_basic_map_copy(map->p[i]),
5876 isl_set_copy(dom), &todo_i, max);
5879 res = isl_pw_multi_aff_union_lexmax(res, res_i);
5881 res = isl_pw_multi_aff_union_lexmin(res, res_i);
5883 todo = isl_set_intersect(todo, todo_i);
5904 #define TYPE isl_map
5908 #define EMPTY isl_map_empty
5910 #define ADD isl_map_union_disjoint
5911 #include "isl_map_lexopt_templ.c"
5913 /* Given a map "map", compute the lexicographically minimal
5914 * (or maximal) image element for each domain element in dom.
5915 * Set *empty to those elements in dom that do not have an image element.
5917 * We first compute the lexicographically minimal or maximal element
5918 * in the first basic map. This results in a partial solution "res"
5919 * and a subset "todo" of dom that still need to be handled.
5920 * We then consider each of the remaining maps in "map" and successively
5921 * update both "res" and "todo".
5923 * Let res^k and todo^k be the results after k steps and let i = k + 1.
5924 * Assume we are computing the lexicographical maximum.
5925 * We first compute the lexicographically maximal element in basic map i.
5926 * This results in a partial solution res_i and a subset todo_i.
5927 * Then we combine these results with those obtain for the first k basic maps
5928 * to obtain a result that is valid for the first k+1 basic maps.
5929 * In particular, the set where there is no solution is the set where
5930 * there is no solution for the first k basic maps and also no solution
5931 * for the ith basic map, i.e.,
5933 * todo^i = todo^k * todo_i
5935 * On dom(res^k) * dom(res_i), we need to pick the larger of the two
5936 * solutions, arbitrarily breaking ties in favor of res^k.
5937 * That is, when res^k(a) >= res_i(a), we pick res^k and
5938 * when res^k(a) < res_i(a), we pick res_i. (Here, ">=" and "<" denote
5939 * the lexicographic order.)
5940 * In practice, we compute
5942 * res^k * (res_i . "<=")
5946 * res_i * (res^k . "<")
5948 * Finally, we consider the symmetric difference of dom(res^k) and dom(res_i),
5949 * where only one of res^k and res_i provides a solution and we simply pick
5956 * Note that we only compute these intersections when dom(res^k) intersects
5957 * dom(res_i). Otherwise, the only effect of these intersections is to
5958 * potentially break up res^k and res_i into smaller pieces.
5959 * We want to avoid such splintering as much as possible.
5960 * In fact, an earlier implementation of this function would look for
5961 * better results in the domain of res^k and for extra results in todo^k,
5962 * but this would always result in a splintering according to todo^k,
5963 * even when the domain of basic map i is disjoint from the domains of
5964 * the previous basic maps.
5966 static __isl_give isl_map *isl_map_partial_lexopt_aligned(
5967 __isl_take isl_map *map, __isl_take isl_set *dom,
5968 __isl_give isl_set **empty, int max)
5971 struct isl_map *res;
5972 struct isl_set *todo;
5977 if (isl_map_plain_is_empty(map)) {
5985 res = basic_map_partial_lexopt(isl_basic_map_copy(map->p[0]),
5986 isl_set_copy(dom), &todo, max);
5988 for (i = 1; i < map->n; ++i) {
5992 isl_space *dim = isl_space_range(isl_map_get_space(res));
5994 res_i = basic_map_partial_lexopt(isl_basic_map_copy(map->p[i]),
5995 isl_set_copy(dom), &todo_i, max);
5998 lt = isl_map_lex_lt(isl_space_copy(dim));
5999 le = isl_map_lex_le(dim);
6001 lt = isl_map_lex_gt(isl_space_copy(dim));
6002 le = isl_map_lex_ge(dim);
6004 lt = isl_map_apply_range(isl_map_copy(res), lt);
6005 lt = isl_map_intersect(lt, isl_map_copy(res_i));
6006 le = isl_map_apply_range(isl_map_copy(res_i), le);
6007 le = isl_map_intersect(le, isl_map_copy(res));
6009 if (!isl_map_is_empty(lt) || !isl_map_is_empty(le)) {
6010 res = isl_map_intersect_domain(res,
6011 isl_set_copy(todo_i));
6012 res_i = isl_map_intersect_domain(res_i,
6013 isl_set_copy(todo));
6016 res = isl_map_union_disjoint(res, res_i);
6017 res = isl_map_union_disjoint(res, lt);
6018 res = isl_map_union_disjoint(res, le);
6020 todo = isl_set_intersect(todo, todo_i);
6040 __isl_give isl_map *isl_map_partial_lexmax(
6041 __isl_take isl_map *map, __isl_take isl_set *dom,
6042 __isl_give isl_set **empty)
6044 return isl_map_partial_lexopt(map, dom, empty, 1);
6047 __isl_give isl_map *isl_map_partial_lexmin(
6048 __isl_take isl_map *map, __isl_take isl_set *dom,
6049 __isl_give isl_set **empty)
6051 return isl_map_partial_lexopt(map, dom, empty, 0);
6054 __isl_give isl_set *isl_set_partial_lexmin(
6055 __isl_take isl_set *set, __isl_take isl_set *dom,
6056 __isl_give isl_set **empty)
6058 return (struct isl_set *)
6059 isl_map_partial_lexmin((struct isl_map *)set,
6063 __isl_give isl_set *isl_set_partial_lexmax(
6064 __isl_take isl_set *set, __isl_take isl_set *dom,
6065 __isl_give isl_set **empty)
6067 return (struct isl_set *)
6068 isl_map_partial_lexmax((struct isl_map *)set,
6072 /* Compute the lexicographic minimum (or maximum if "max" is set)
6073 * of "bmap" over its domain.
6075 * Since we are not interested in the part of the domain space where
6076 * there is no solution, we initialize the domain to those constraints
6077 * of "bmap" that only involve the parameters and the input dimensions.
6078 * This relieves the parametric programming engine from detecting those
6079 * inequalities and transferring them to the context. More importantly,
6080 * it ensures that those inequalities are transferred first and not
6081 * intermixed with inequalities that actually split the domain.
6083 __isl_give isl_map *isl_basic_map_lexopt(__isl_take isl_basic_map *bmap, int max)
6087 isl_basic_map *copy;
6090 n_div = isl_basic_map_dim(bmap, isl_dim_div);
6091 n_out = isl_basic_map_dim(bmap, isl_dim_out);
6092 copy = isl_basic_map_copy(bmap);
6093 copy = isl_basic_map_drop_constraints_involving_dims(copy,
6094 isl_dim_div, 0, n_div);
6095 copy = isl_basic_map_drop_constraints_involving_dims(copy,
6096 isl_dim_out, 0, n_out);
6097 dom = isl_basic_map_domain(copy);
6098 return isl_basic_map_partial_lexopt(bmap, dom, NULL, max);
6101 __isl_give isl_map *isl_basic_map_lexmin(__isl_take isl_basic_map *bmap)
6103 return isl_basic_map_lexopt(bmap, 0);
6106 __isl_give isl_map *isl_basic_map_lexmax(__isl_take isl_basic_map *bmap)
6108 return isl_basic_map_lexopt(bmap, 1);
6111 __isl_give isl_set *isl_basic_set_lexmin(__isl_take isl_basic_set *bset)
6113 return (isl_set *)isl_basic_map_lexmin((isl_basic_map *)bset);
6116 __isl_give isl_set *isl_basic_set_lexmax(__isl_take isl_basic_set *bset)
6118 return (isl_set *)isl_basic_map_lexmax((isl_basic_map *)bset);
6121 /* Extract the first and only affine expression from list
6122 * and then add it to *pwaff with the given dom.
6123 * This domain is known to be disjoint from other domains
6124 * because of the way isl_basic_map_foreach_lexmax works.
6126 static int update_dim_opt(__isl_take isl_basic_set *dom,
6127 __isl_take isl_aff_list *list, void *user)
6129 isl_ctx *ctx = isl_basic_set_get_ctx(dom);
6131 isl_pw_aff **pwaff = user;
6132 isl_pw_aff *pwaff_i;
6136 if (isl_aff_list_n_aff(list) != 1)
6137 isl_die(ctx, isl_error_internal,
6138 "expecting single element list", goto error);
6140 aff = isl_aff_list_get_aff(list, 0);
6141 pwaff_i = isl_pw_aff_alloc(isl_set_from_basic_set(dom), aff);
6143 *pwaff = isl_pw_aff_add_disjoint(*pwaff, pwaff_i);
6145 isl_aff_list_free(list);
6149 isl_basic_set_free(dom);
6150 isl_aff_list_free(list);
6154 /* Given a basic map with one output dimension, compute the minimum or
6155 * maximum of that dimension as an isl_pw_aff.
6157 * The isl_pw_aff is constructed by having isl_basic_map_foreach_lexopt
6158 * call update_dim_opt on each leaf of the result.
6160 static __isl_give isl_pw_aff *basic_map_dim_opt(__isl_keep isl_basic_map *bmap,
6163 isl_space *dim = isl_basic_map_get_space(bmap);
6167 dim = isl_space_from_domain(isl_space_domain(dim));
6168 dim = isl_space_add_dims(dim, isl_dim_out, 1);
6169 pwaff = isl_pw_aff_empty(dim);
6171 r = isl_basic_map_foreach_lexopt(bmap, max, &update_dim_opt, &pwaff);
6173 return isl_pw_aff_free(pwaff);
6178 /* Compute the minimum or maximum of the given output dimension
6179 * as a function of the parameters and the input dimensions,
6180 * but independently of the other output dimensions.
6182 * We first project out the other output dimension and then compute
6183 * the "lexicographic" maximum in each basic map, combining the results
6184 * using isl_pw_aff_union_max.
6186 static __isl_give isl_pw_aff *map_dim_opt(__isl_take isl_map *map, int pos,
6193 n_out = isl_map_dim(map, isl_dim_out);
6194 map = isl_map_project_out(map, isl_dim_out, pos + 1, n_out - (pos + 1));
6195 map = isl_map_project_out(map, isl_dim_out, 0, pos);
6200 isl_space *dim = isl_map_get_space(map);
6201 dim = isl_space_domain(isl_space_from_range(dim));
6203 return isl_pw_aff_empty(dim);
6206 pwaff = basic_map_dim_opt(map->p[0], max);
6207 for (i = 1; i < map->n; ++i) {
6208 isl_pw_aff *pwaff_i;
6210 pwaff_i = basic_map_dim_opt(map->p[i], max);
6211 pwaff = isl_pw_aff_union_opt(pwaff, pwaff_i, max);
6219 /* Compute the maximum of the given output dimension as a function of the
6220 * parameters and input dimensions, but independently of
6221 * the other output dimensions.
6223 __isl_give isl_pw_aff *isl_map_dim_max(__isl_take isl_map *map, int pos)
6225 return map_dim_opt(map, pos, 1);
6228 /* Compute the minimum or maximum of the given set dimension
6229 * as a function of the parameters,
6230 * but independently of the other set dimensions.
6232 static __isl_give isl_pw_aff *set_dim_opt(__isl_take isl_set *set, int pos,
6235 return map_dim_opt(set, pos, max);
6238 /* Compute the maximum of the given set dimension as a function of the
6239 * parameters, but independently of the other set dimensions.
6241 __isl_give isl_pw_aff *isl_set_dim_max(__isl_take isl_set *set, int pos)
6243 return set_dim_opt(set, pos, 1);
6246 /* Compute the minimum of the given set dimension as a function of the
6247 * parameters, but independently of the other set dimensions.
6249 __isl_give isl_pw_aff *isl_set_dim_min(__isl_take isl_set *set, int pos)
6251 return set_dim_opt(set, pos, 0);
6254 /* Apply a preimage specified by "mat" on the parameters of "bset".
6255 * bset is assumed to have only parameters and divs.
6257 static struct isl_basic_set *basic_set_parameter_preimage(
6258 struct isl_basic_set *bset, struct isl_mat *mat)
6265 bset->dim = isl_space_cow(bset->dim);
6269 nparam = isl_basic_set_dim(bset, isl_dim_param);
6271 isl_assert(bset->ctx, mat->n_row == 1 + nparam, goto error);
6273 bset->dim->nparam = 0;
6274 bset->dim->n_out = nparam;
6275 bset = isl_basic_set_preimage(bset, mat);
6277 bset->dim->nparam = bset->dim->n_out;
6278 bset->dim->n_out = 0;
6283 isl_basic_set_free(bset);
6287 /* Apply a preimage specified by "mat" on the parameters of "set".
6288 * set is assumed to have only parameters and divs.
6290 static struct isl_set *set_parameter_preimage(
6291 struct isl_set *set, struct isl_mat *mat)
6293 isl_space *dim = NULL;
6299 dim = isl_space_copy(set->dim);
6300 dim = isl_space_cow(dim);
6304 nparam = isl_set_dim(set, isl_dim_param);
6306 isl_assert(set->ctx, mat->n_row == 1 + nparam, goto error);
6309 dim->n_out = nparam;
6310 isl_set_reset_space(set, dim);
6311 set = isl_set_preimage(set, mat);
6314 dim = isl_space_copy(set->dim);
6315 dim = isl_space_cow(dim);
6318 dim->nparam = dim->n_out;
6320 isl_set_reset_space(set, dim);
6323 isl_space_free(dim);
6330 /* Intersect the basic set "bset" with the affine space specified by the
6331 * equalities in "eq".
6333 static struct isl_basic_set *basic_set_append_equalities(
6334 struct isl_basic_set *bset, struct isl_mat *eq)
6342 bset = isl_basic_set_extend_space(bset, isl_space_copy(bset->dim), 0,
6347 len = 1 + isl_space_dim(bset->dim, isl_dim_all) + bset->extra;
6348 for (i = 0; i < eq->n_row; ++i) {
6349 k = isl_basic_set_alloc_equality(bset);
6352 isl_seq_cpy(bset->eq[k], eq->row[i], eq->n_col);
6353 isl_seq_clr(bset->eq[k] + eq->n_col, len - eq->n_col);
6357 bset = isl_basic_set_gauss(bset, NULL);
6358 bset = isl_basic_set_finalize(bset);
6363 isl_basic_set_free(bset);
6367 /* Intersect the set "set" with the affine space specified by the
6368 * equalities in "eq".
6370 static struct isl_set *set_append_equalities(struct isl_set *set,
6378 for (i = 0; i < set->n; ++i) {
6379 set->p[i] = basic_set_append_equalities(set->p[i],
6392 /* Given a basic set "bset" that only involves parameters and existentially
6393 * quantified variables, return the index of the first equality
6394 * that only involves parameters. If there is no such equality then
6395 * return bset->n_eq.
6397 * This function assumes that isl_basic_set_gauss has been called on "bset".
6399 static int first_parameter_equality(__isl_keep isl_basic_set *bset)
6402 unsigned nparam, n_div;
6407 nparam = isl_basic_set_dim(bset, isl_dim_param);
6408 n_div = isl_basic_set_dim(bset, isl_dim_div);
6410 for (i = 0, j = n_div - 1; i < bset->n_eq && j >= 0; --j) {
6411 if (!isl_int_is_zero(bset->eq[i][1 + nparam + j]))
6418 /* Compute an explicit representation for the existentially quantified
6419 * variables in "bset" by computing the "minimal value" of the set
6420 * variables. Since there are no set variables, the computation of
6421 * the minimal value essentially computes an explicit representation
6422 * of the non-empty part(s) of "bset".
6424 * The input only involves parameters and existentially quantified variables.
6425 * All equalities among parameters have been removed.
6427 * Since the existentially quantified variables in the result are in general
6428 * going to be different from those in the input, we first replace
6429 * them by the minimal number of variables based on their equalities.
6430 * This should simplify the parametric integer programming.
6432 static __isl_give isl_set *base_compute_divs(__isl_take isl_basic_set *bset)
6434 isl_morph *morph1, *morph2;
6440 if (bset->n_eq == 0)
6441 return isl_basic_set_lexmin(bset);
6443 morph1 = isl_basic_set_parameter_compression(bset);
6444 bset = isl_morph_basic_set(isl_morph_copy(morph1), bset);
6445 bset = isl_basic_set_lift(bset);
6446 morph2 = isl_basic_set_variable_compression(bset, isl_dim_set);
6447 bset = isl_morph_basic_set(morph2, bset);
6448 n = isl_basic_set_dim(bset, isl_dim_set);
6449 bset = isl_basic_set_project_out(bset, isl_dim_set, 0, n);
6451 set = isl_basic_set_lexmin(bset);
6453 set = isl_morph_set(isl_morph_inverse(morph1), set);
6458 /* Project the given basic set onto its parameter domain, possibly introducing
6459 * new, explicit, existential variables in the constraints.
6460 * The input has parameters and (possibly implicit) existential variables.
6461 * The output has the same parameters, but only
6462 * explicit existentially quantified variables.
6464 * The actual projection is performed by pip, but pip doesn't seem
6465 * to like equalities very much, so we first remove the equalities
6466 * among the parameters by performing a variable compression on
6467 * the parameters. Afterward, an inverse transformation is performed
6468 * and the equalities among the parameters are inserted back in.
6470 * The variable compression on the parameters may uncover additional
6471 * equalities that were only implicit before. We therefore check
6472 * if there are any new parameter equalities in the result and
6473 * if so recurse. The removal of parameter equalities is required
6474 * for the parameter compression performed by base_compute_divs.
6476 static struct isl_set *parameter_compute_divs(struct isl_basic_set *bset)
6480 struct isl_mat *T, *T2;
6481 struct isl_set *set;
6484 bset = isl_basic_set_cow(bset);
6488 if (bset->n_eq == 0)
6489 return base_compute_divs(bset);
6491 bset = isl_basic_set_gauss(bset, NULL);
6494 if (isl_basic_set_plain_is_empty(bset))
6495 return isl_set_from_basic_set(bset);
6497 i = first_parameter_equality(bset);
6498 if (i == bset->n_eq)
6499 return base_compute_divs(bset);
6501 nparam = isl_basic_set_dim(bset, isl_dim_param);
6502 eq = isl_mat_sub_alloc6(bset->ctx, bset->eq, i, bset->n_eq - i,
6504 eq = isl_mat_cow(eq);
6505 T = isl_mat_variable_compression(isl_mat_copy(eq), &T2);
6506 if (T && T->n_col == 0) {
6510 bset = isl_basic_set_set_to_empty(bset);
6511 return isl_set_from_basic_set(bset);
6513 bset = basic_set_parameter_preimage(bset, T);
6515 i = first_parameter_equality(bset);
6518 else if (i == bset->n_eq)
6519 set = base_compute_divs(bset);
6521 set = parameter_compute_divs(bset);
6522 set = set_parameter_preimage(set, T2);
6523 set = set_append_equalities(set, eq);
6527 /* Insert the divs from "ls" before those of "bmap".
6529 * The number of columns is not changed, which means that the last
6530 * dimensions of "bmap" are being reintepreted as the divs from "ls".
6531 * The caller is responsible for removing the same number of dimensions
6532 * from the space of "bmap".
6534 static __isl_give isl_basic_map *insert_divs_from_local_space(
6535 __isl_take isl_basic_map *bmap, __isl_keep isl_local_space *ls)
6541 n_div = isl_local_space_dim(ls, isl_dim_div);
6545 old_n_div = bmap->n_div;
6546 bmap = insert_div_rows(bmap, n_div);
6550 for (i = 0; i < n_div; ++i) {
6551 isl_seq_cpy(bmap->div[i], ls->div->row[i], ls->div->n_col);
6552 isl_seq_clr(bmap->div[i] + ls->div->n_col, old_n_div);
6558 /* Replace the space of "bmap" by the space and divs of "ls".
6560 * If "ls" has any divs, then we simplify the result since we may
6561 * have discovered some additional equalities that could simplify
6562 * the div expressions.
6564 static __isl_give isl_basic_map *basic_replace_space_by_local_space(
6565 __isl_take isl_basic_map *bmap, __isl_take isl_local_space *ls)
6569 bmap = isl_basic_map_cow(bmap);
6573 n_div = isl_local_space_dim(ls, isl_dim_div);
6574 bmap = insert_divs_from_local_space(bmap, ls);
6578 isl_space_free(bmap->dim);
6579 bmap->dim = isl_local_space_get_space(ls);
6583 isl_local_space_free(ls);
6585 bmap = isl_basic_map_simplify(bmap);
6586 bmap = isl_basic_map_finalize(bmap);
6589 isl_basic_map_free(bmap);
6590 isl_local_space_free(ls);
6594 /* Replace the space of "map" by the space and divs of "ls".
6596 static __isl_give isl_map *replace_space_by_local_space(__isl_take isl_map *map,
6597 __isl_take isl_local_space *ls)
6601 map = isl_map_cow(map);
6605 for (i = 0; i < map->n; ++i) {
6606 map->p[i] = basic_replace_space_by_local_space(map->p[i],
6607 isl_local_space_copy(ls));
6611 isl_space_free(map->dim);
6612 map->dim = isl_local_space_get_space(ls);
6616 isl_local_space_free(ls);
6619 isl_local_space_free(ls);
6624 /* Compute an explicit representation for the existentially
6625 * quantified variables for which do not know any explicit representation yet.
6627 * We first sort the existentially quantified variables so that the
6628 * existentially quantified variables for which we already have an explicit
6629 * representation are placed before those for which we do not.
6630 * The input dimensions, the output dimensions and the existentially
6631 * quantified variables for which we already have an explicit
6632 * representation are then turned into parameters.
6633 * compute_divs returns a map with the same parameters and
6634 * no input or output dimensions and the dimension specification
6635 * is reset to that of the input, including the existentially quantified
6636 * variables for which we already had an explicit representation.
6638 static struct isl_map *compute_divs(struct isl_basic_map *bmap)
6640 struct isl_basic_set *bset;
6641 struct isl_set *set;
6642 struct isl_map *map;
6644 isl_local_space *ls;
6651 bmap = isl_basic_map_sort_divs(bmap);
6652 bmap = isl_basic_map_cow(bmap);
6656 for (n_known = 0; n_known < bmap->n_div; ++n_known)
6657 if (isl_int_is_zero(bmap->div[n_known][0]))
6660 nparam = isl_basic_map_dim(bmap, isl_dim_param);
6661 n_in = isl_basic_map_dim(bmap, isl_dim_in);
6662 n_out = isl_basic_map_dim(bmap, isl_dim_out);
6663 dim = isl_space_set_alloc(bmap->ctx,
6664 nparam + n_in + n_out + n_known, 0);
6668 ls = isl_basic_map_get_local_space(bmap);
6669 ls = isl_local_space_drop_dims(ls, isl_dim_div,
6670 n_known, bmap->n_div - n_known);
6672 for (i = n_known; i < bmap->n_div; ++i)
6673 swap_div(bmap, i - n_known, i);
6674 bmap->n_div -= n_known;
6675 bmap->extra -= n_known;
6677 bmap = isl_basic_map_reset_space(bmap, dim);
6678 bset = (struct isl_basic_set *)bmap;
6680 set = parameter_compute_divs(bset);
6681 map = (struct isl_map *)set;
6682 map = replace_space_by_local_space(map, ls);
6686 isl_basic_map_free(bmap);
6690 int isl_basic_map_divs_known(__isl_keep isl_basic_map *bmap)
6698 off = isl_space_dim(bmap->dim, isl_dim_all);
6699 for (i = 0; i < bmap->n_div; ++i) {
6700 if (isl_int_is_zero(bmap->div[i][0]))
6702 isl_assert(bmap->ctx, isl_int_is_zero(bmap->div[i][1+1+off+i]),
6708 static int map_divs_known(__isl_keep isl_map *map)
6715 for (i = 0; i < map->n; ++i) {
6716 int known = isl_basic_map_divs_known(map->p[i]);
6724 /* If bmap contains any unknown divs, then compute explicit
6725 * expressions for them. However, this computation may be
6726 * quite expensive, so first try to remove divs that aren't
6729 struct isl_map *isl_basic_map_compute_divs(struct isl_basic_map *bmap)
6732 struct isl_map *map;
6734 known = isl_basic_map_divs_known(bmap);
6738 return isl_map_from_basic_map(bmap);
6740 bmap = isl_basic_map_drop_redundant_divs(bmap);
6742 known = isl_basic_map_divs_known(bmap);
6746 return isl_map_from_basic_map(bmap);
6748 map = compute_divs(bmap);
6751 isl_basic_map_free(bmap);
6755 struct isl_map *isl_map_compute_divs(struct isl_map *map)
6759 struct isl_map *res;
6766 known = map_divs_known(map);
6774 res = isl_basic_map_compute_divs(isl_basic_map_copy(map->p[0]));
6775 for (i = 1 ; i < map->n; ++i) {
6777 r2 = isl_basic_map_compute_divs(isl_basic_map_copy(map->p[i]));
6778 if (ISL_F_ISSET(map, ISL_MAP_DISJOINT))
6779 res = isl_map_union_disjoint(res, r2);
6781 res = isl_map_union(res, r2);
6788 struct isl_set *isl_basic_set_compute_divs(struct isl_basic_set *bset)
6790 return (struct isl_set *)
6791 isl_basic_map_compute_divs((struct isl_basic_map *)bset);
6794 struct isl_set *isl_set_compute_divs(struct isl_set *set)
6796 return (struct isl_set *)
6797 isl_map_compute_divs((struct isl_map *)set);
6800 struct isl_set *isl_map_domain(struct isl_map *map)
6803 struct isl_set *set;
6808 map = isl_map_cow(map);
6812 set = (struct isl_set *)map;
6813 set->dim = isl_space_domain(set->dim);
6816 for (i = 0; i < map->n; ++i) {
6817 set->p[i] = isl_basic_map_domain(map->p[i]);
6821 ISL_F_CLR(set, ISL_MAP_DISJOINT);
6822 ISL_F_CLR(set, ISL_SET_NORMALIZED);
6829 /* Return the union of "map1" and "map2", where we assume for now that
6830 * "map1" and "map2" are disjoint. Note that the basic maps inside
6831 * "map1" or "map2" may not be disjoint from each other.
6832 * Also note that this function is also called from isl_map_union,
6833 * which takes care of handling the situation where "map1" and "map2"
6834 * may not be disjoint.
6836 * If one of the inputs is empty, we can simply return the other input.
6837 * Similarly, if one of the inputs is universal, then it is equal to the union.
6839 static __isl_give isl_map *map_union_disjoint(__isl_take isl_map *map1,
6840 __isl_take isl_map *map2)
6844 struct isl_map *map = NULL;
6859 is_universe = isl_map_plain_is_universe(map1);
6860 if (is_universe < 0)
6867 is_universe = isl_map_plain_is_universe(map2);
6868 if (is_universe < 0)
6875 isl_assert(map1->ctx, isl_space_is_equal(map1->dim, map2->dim), goto error);
6877 if (ISL_F_ISSET(map1, ISL_MAP_DISJOINT) &&
6878 ISL_F_ISSET(map2, ISL_MAP_DISJOINT))
6879 ISL_FL_SET(flags, ISL_MAP_DISJOINT);
6881 map = isl_map_alloc_space(isl_space_copy(map1->dim),
6882 map1->n + map2->n, flags);
6885 for (i = 0; i < map1->n; ++i) {
6886 map = isl_map_add_basic_map(map,
6887 isl_basic_map_copy(map1->p[i]));
6891 for (i = 0; i < map2->n; ++i) {
6892 map = isl_map_add_basic_map(map,
6893 isl_basic_map_copy(map2->p[i]));
6907 __isl_give isl_map *isl_map_union_disjoint(__isl_take isl_map *map1,
6908 __isl_take isl_map *map2)
6910 return isl_map_align_params_map_map_and(map1, map2, &map_union_disjoint);
6913 struct isl_map *isl_map_union(struct isl_map *map1, struct isl_map *map2)
6915 map1 = isl_map_union_disjoint(map1, map2);
6919 ISL_F_CLR(map1, ISL_MAP_DISJOINT);
6923 struct isl_set *isl_set_union_disjoint(
6924 struct isl_set *set1, struct isl_set *set2)
6926 return (struct isl_set *)
6927 isl_map_union_disjoint(
6928 (struct isl_map *)set1, (struct isl_map *)set2);
6931 struct isl_set *isl_set_union(struct isl_set *set1, struct isl_set *set2)
6933 return (struct isl_set *)
6934 isl_map_union((struct isl_map *)set1, (struct isl_map *)set2);
6937 /* Apply "fn" to pairs of elements from "map" and "set" and collect
6940 * "map" and "set" are assumed to be compatible and non-NULL.
6942 static __isl_give isl_map *map_intersect_set(__isl_take isl_map *map,
6943 __isl_take isl_set *set,
6944 __isl_give isl_basic_map *fn(__isl_take isl_basic_map *bmap,
6945 __isl_take isl_basic_set *bset))
6948 struct isl_map *result;
6951 if (isl_set_plain_is_universe(set)) {
6956 if (ISL_F_ISSET(map, ISL_MAP_DISJOINT) &&
6957 ISL_F_ISSET(set, ISL_MAP_DISJOINT))
6958 ISL_FL_SET(flags, ISL_MAP_DISJOINT);
6960 result = isl_map_alloc_space(isl_space_copy(map->dim),
6961 map->n * set->n, flags);
6962 for (i = 0; result && i < map->n; ++i)
6963 for (j = 0; j < set->n; ++j) {
6964 result = isl_map_add_basic_map(result,
6965 fn(isl_basic_map_copy(map->p[i]),
6966 isl_basic_set_copy(set->p[j])));
6976 static __isl_give isl_map *map_intersect_range(__isl_take isl_map *map,
6977 __isl_take isl_set *set)
6982 if (!isl_map_compatible_range(map, set))
6983 isl_die(set->ctx, isl_error_invalid,
6984 "incompatible spaces", goto error);
6986 return map_intersect_set(map, set, &isl_basic_map_intersect_range);
6993 __isl_give isl_map *isl_map_intersect_range(__isl_take isl_map *map,
6994 __isl_take isl_set *set)
6996 return isl_map_align_params_map_map_and(map, set, &map_intersect_range);
6999 static __isl_give isl_map *map_intersect_domain(__isl_take isl_map *map,
7000 __isl_take isl_set *set)
7005 if (!isl_map_compatible_domain(map, set))
7006 isl_die(set->ctx, isl_error_invalid,
7007 "incompatible spaces", goto error);
7009 return map_intersect_set(map, set, &isl_basic_map_intersect_domain);
7016 __isl_give isl_map *isl_map_intersect_domain(__isl_take isl_map *map,
7017 __isl_take isl_set *set)
7019 return isl_map_align_params_map_map_and(map, set,
7020 &map_intersect_domain);
7023 static __isl_give isl_map *map_apply_domain(__isl_take isl_map *map1,
7024 __isl_take isl_map *map2)
7028 map1 = isl_map_reverse(map1);
7029 map1 = isl_map_apply_range(map1, map2);
7030 return isl_map_reverse(map1);
7037 __isl_give isl_map *isl_map_apply_domain(__isl_take isl_map *map1,
7038 __isl_take isl_map *map2)
7040 return isl_map_align_params_map_map_and(map1, map2, &map_apply_domain);
7043 static __isl_give isl_map *map_apply_range(__isl_take isl_map *map1,
7044 __isl_take isl_map *map2)
7046 isl_space *dim_result;
7047 struct isl_map *result;
7053 dim_result = isl_space_join(isl_space_copy(map1->dim),
7054 isl_space_copy(map2->dim));
7056 result = isl_map_alloc_space(dim_result, map1->n * map2->n, 0);
7059 for (i = 0; i < map1->n; ++i)
7060 for (j = 0; j < map2->n; ++j) {
7061 result = isl_map_add_basic_map(result,
7062 isl_basic_map_apply_range(
7063 isl_basic_map_copy(map1->p[i]),
7064 isl_basic_map_copy(map2->p[j])));
7070 if (result && result->n <= 1)
7071 ISL_F_SET(result, ISL_MAP_DISJOINT);
7079 __isl_give isl_map *isl_map_apply_range(__isl_take isl_map *map1,
7080 __isl_take isl_map *map2)
7082 return isl_map_align_params_map_map_and(map1, map2, &map_apply_range);
7086 * returns range - domain
7088 struct isl_basic_set *isl_basic_map_deltas(struct isl_basic_map *bmap)
7090 isl_space *dims, *target_dim;
7091 struct isl_basic_set *bset;
7098 isl_assert(bmap->ctx, isl_space_tuple_match(bmap->dim, isl_dim_in,
7099 bmap->dim, isl_dim_out),
7101 target_dim = isl_space_domain(isl_basic_map_get_space(bmap));
7102 dim = isl_basic_map_n_in(bmap);
7103 nparam = isl_basic_map_n_param(bmap);
7104 bset = isl_basic_set_from_basic_map(bmap);
7105 bset = isl_basic_set_cow(bset);
7106 dims = isl_basic_set_get_space(bset);
7107 dims = isl_space_add_dims(dims, isl_dim_set, dim);
7108 bset = isl_basic_set_extend_space(bset, dims, 0, dim, 0);
7109 bset = isl_basic_set_swap_vars(bset, 2*dim);
7110 for (i = 0; i < dim; ++i) {
7111 int j = isl_basic_map_alloc_equality(
7112 (struct isl_basic_map *)bset);
7114 bset = isl_basic_set_free(bset);
7117 isl_seq_clr(bset->eq[j], 1 + isl_basic_set_total_dim(bset));
7118 isl_int_set_si(bset->eq[j][1+nparam+i], 1);
7119 isl_int_set_si(bset->eq[j][1+nparam+dim+i], 1);
7120 isl_int_set_si(bset->eq[j][1+nparam+2*dim+i], -1);
7122 bset = isl_basic_set_project_out(bset, isl_dim_set, dim, 2*dim);
7123 bset = isl_basic_set_reset_space(bset, target_dim);
7126 isl_basic_map_free(bmap);
7131 * returns range - domain
7133 __isl_give isl_set *isl_map_deltas(__isl_take isl_map *map)
7137 struct isl_set *result;
7142 isl_assert(map->ctx, isl_space_tuple_match(map->dim, isl_dim_in,
7143 map->dim, isl_dim_out),
7145 dim = isl_map_get_space(map);
7146 dim = isl_space_domain(dim);
7147 result = isl_set_alloc_space(dim, map->n, 0);
7150 for (i = 0; i < map->n; ++i)
7151 result = isl_set_add_basic_set(result,
7152 isl_basic_map_deltas(isl_basic_map_copy(map->p[i])));
7161 * returns [domain -> range] -> range - domain
7163 __isl_give isl_basic_map *isl_basic_map_deltas_map(
7164 __isl_take isl_basic_map *bmap)
7168 isl_basic_map *domain;
7172 if (!isl_space_tuple_match(bmap->dim, isl_dim_in, bmap->dim, isl_dim_out))
7173 isl_die(bmap->ctx, isl_error_invalid,
7174 "domain and range don't match", goto error);
7176 nparam = isl_basic_map_dim(bmap, isl_dim_param);
7177 n = isl_basic_map_dim(bmap, isl_dim_in);
7179 dim = isl_space_from_range(isl_space_domain(isl_basic_map_get_space(bmap)));
7180 domain = isl_basic_map_universe(dim);
7182 bmap = isl_basic_map_from_domain(isl_basic_map_wrap(bmap));
7183 bmap = isl_basic_map_apply_range(bmap, domain);
7184 bmap = isl_basic_map_extend_constraints(bmap, n, 0);
7186 total = isl_basic_map_total_dim(bmap);
7188 for (i = 0; i < n; ++i) {
7189 k = isl_basic_map_alloc_equality(bmap);
7192 isl_seq_clr(bmap->eq[k], 1 + total);
7193 isl_int_set_si(bmap->eq[k][1 + nparam + i], 1);
7194 isl_int_set_si(bmap->eq[k][1 + nparam + n + i], -1);
7195 isl_int_set_si(bmap->eq[k][1 + nparam + n + n + i], 1);
7198 bmap = isl_basic_map_gauss(bmap, NULL);
7199 return isl_basic_map_finalize(bmap);
7201 isl_basic_map_free(bmap);
7206 * returns [domain -> range] -> range - domain
7208 __isl_give isl_map *isl_map_deltas_map(__isl_take isl_map *map)
7211 isl_space *domain_dim;
7216 if (!isl_space_tuple_match(map->dim, isl_dim_in, map->dim, isl_dim_out))
7217 isl_die(map->ctx, isl_error_invalid,
7218 "domain and range don't match", goto error);
7220 map = isl_map_cow(map);
7224 domain_dim = isl_space_from_range(isl_space_domain(isl_map_get_space(map)));
7225 map->dim = isl_space_from_domain(isl_space_wrap(map->dim));
7226 map->dim = isl_space_join(map->dim, domain_dim);
7229 for (i = 0; i < map->n; ++i) {
7230 map->p[i] = isl_basic_map_deltas_map(map->p[i]);
7234 ISL_F_CLR(map, ISL_MAP_NORMALIZED);
7241 static __isl_give isl_basic_map *basic_map_identity(__isl_take isl_space *dims)
7243 struct isl_basic_map *bmap;
7251 nparam = dims->nparam;
7253 bmap = isl_basic_map_alloc_space(dims, 0, dim, 0);
7257 for (i = 0; i < dim; ++i) {
7258 int j = isl_basic_map_alloc_equality(bmap);
7261 isl_seq_clr(bmap->eq[j], 1 + isl_basic_map_total_dim(bmap));
7262 isl_int_set_si(bmap->eq[j][1+nparam+i], 1);
7263 isl_int_set_si(bmap->eq[j][1+nparam+dim+i], -1);
7265 return isl_basic_map_finalize(bmap);
7267 isl_basic_map_free(bmap);
7271 __isl_give isl_basic_map *isl_basic_map_identity(__isl_take isl_space *dim)
7275 if (dim->n_in != dim->n_out)
7276 isl_die(dim->ctx, isl_error_invalid,
7277 "number of input and output dimensions needs to be "
7278 "the same", goto error);
7279 return basic_map_identity(dim);
7281 isl_space_free(dim);
7285 struct isl_basic_map *isl_basic_map_identity_like(struct isl_basic_map *model)
7287 if (!model || !model->dim)
7289 return isl_basic_map_identity(isl_space_copy(model->dim));
7292 __isl_give isl_map *isl_map_identity(__isl_take isl_space *dim)
7294 return isl_map_from_basic_map(isl_basic_map_identity(dim));
7297 struct isl_map *isl_map_identity_like(struct isl_map *model)
7299 if (!model || !model->dim)
7301 return isl_map_identity(isl_space_copy(model->dim));
7304 struct isl_map *isl_map_identity_like_basic_map(struct isl_basic_map *model)
7306 if (!model || !model->dim)
7308 return isl_map_identity(isl_space_copy(model->dim));
7311 __isl_give isl_map *isl_set_identity(__isl_take isl_set *set)
7313 isl_space *dim = isl_set_get_space(set);
7315 id = isl_map_identity(isl_space_map_from_set(dim));
7316 return isl_map_intersect_range(id, set);
7319 /* Construct a basic set with all set dimensions having only non-negative
7322 __isl_give isl_basic_set *isl_basic_set_positive_orthant(
7323 __isl_take isl_space *space)
7328 struct isl_basic_set *bset;
7332 nparam = space->nparam;
7334 bset = isl_basic_set_alloc_space(space, 0, 0, dim);
7337 for (i = 0; i < dim; ++i) {
7338 int k = isl_basic_set_alloc_inequality(bset);
7341 isl_seq_clr(bset->ineq[k], 1 + isl_basic_set_total_dim(bset));
7342 isl_int_set_si(bset->ineq[k][1 + nparam + i], 1);
7346 isl_basic_set_free(bset);
7350 /* Construct the half-space x_pos >= 0.
7352 static __isl_give isl_basic_set *nonneg_halfspace(__isl_take isl_space *dim,
7356 isl_basic_set *nonneg;
7358 nonneg = isl_basic_set_alloc_space(dim, 0, 0, 1);
7359 k = isl_basic_set_alloc_inequality(nonneg);
7362 isl_seq_clr(nonneg->ineq[k], 1 + isl_basic_set_total_dim(nonneg));
7363 isl_int_set_si(nonneg->ineq[k][pos], 1);
7365 return isl_basic_set_finalize(nonneg);
7367 isl_basic_set_free(nonneg);
7371 /* Construct the half-space x_pos <= -1.
7373 static __isl_give isl_basic_set *neg_halfspace(__isl_take isl_space *dim, int pos)
7378 neg = isl_basic_set_alloc_space(dim, 0, 0, 1);
7379 k = isl_basic_set_alloc_inequality(neg);
7382 isl_seq_clr(neg->ineq[k], 1 + isl_basic_set_total_dim(neg));
7383 isl_int_set_si(neg->ineq[k][0], -1);
7384 isl_int_set_si(neg->ineq[k][pos], -1);
7386 return isl_basic_set_finalize(neg);
7388 isl_basic_set_free(neg);
7392 __isl_give isl_set *isl_set_split_dims(__isl_take isl_set *set,
7393 enum isl_dim_type type, unsigned first, unsigned n)
7396 isl_basic_set *nonneg;
7404 isl_assert(set->ctx, first + n <= isl_set_dim(set, type), goto error);
7406 for (i = 0; i < n; ++i) {
7407 nonneg = nonneg_halfspace(isl_set_get_space(set),
7408 pos(set->dim, type) + first + i);
7409 neg = neg_halfspace(isl_set_get_space(set),
7410 pos(set->dim, type) + first + i);
7412 set = isl_set_intersect(set, isl_basic_set_union(nonneg, neg));
7421 static int foreach_orthant(__isl_take isl_set *set, int *signs, int first,
7422 int len, int (*fn)(__isl_take isl_set *orthant, int *signs, void *user),
7429 if (isl_set_plain_is_empty(set)) {
7434 return fn(set, signs, user);
7437 half = isl_set_from_basic_set(nonneg_halfspace(isl_set_get_space(set),
7439 half = isl_set_intersect(half, isl_set_copy(set));
7440 if (foreach_orthant(half, signs, first + 1, len, fn, user) < 0)
7444 half = isl_set_from_basic_set(neg_halfspace(isl_set_get_space(set),
7446 half = isl_set_intersect(half, set);
7447 return foreach_orthant(half, signs, first + 1, len, fn, user);
7453 /* Call "fn" on the intersections of "set" with each of the orthants
7454 * (except for obviously empty intersections). The orthant is identified
7455 * by the signs array, with each entry having value 1 or -1 according
7456 * to the sign of the corresponding variable.
7458 int isl_set_foreach_orthant(__isl_keep isl_set *set,
7459 int (*fn)(__isl_take isl_set *orthant, int *signs, void *user),
7469 if (isl_set_plain_is_empty(set))
7472 nparam = isl_set_dim(set, isl_dim_param);
7473 nvar = isl_set_dim(set, isl_dim_set);
7475 signs = isl_alloc_array(set->ctx, int, nparam + nvar);
7477 r = foreach_orthant(isl_set_copy(set), signs, 0, nparam + nvar,
7485 int isl_set_is_equal(struct isl_set *set1, struct isl_set *set2)
7487 return isl_map_is_equal((struct isl_map *)set1, (struct isl_map *)set2);
7490 int isl_basic_map_is_subset(
7491 struct isl_basic_map *bmap1, struct isl_basic_map *bmap2)
7494 struct isl_map *map1;
7495 struct isl_map *map2;
7497 if (!bmap1 || !bmap2)
7500 map1 = isl_map_from_basic_map(isl_basic_map_copy(bmap1));
7501 map2 = isl_map_from_basic_map(isl_basic_map_copy(bmap2));
7503 is_subset = isl_map_is_subset(map1, map2);
7511 int isl_basic_set_is_subset(__isl_keep isl_basic_set *bset1,
7512 __isl_keep isl_basic_set *bset2)
7514 return isl_basic_map_is_subset(bset1, bset2);
7517 int isl_basic_map_is_equal(
7518 struct isl_basic_map *bmap1, struct isl_basic_map *bmap2)
7522 if (!bmap1 || !bmap2)
7524 is_subset = isl_basic_map_is_subset(bmap1, bmap2);
7527 is_subset = isl_basic_map_is_subset(bmap2, bmap1);
7531 int isl_basic_set_is_equal(
7532 struct isl_basic_set *bset1, struct isl_basic_set *bset2)
7534 return isl_basic_map_is_equal(
7535 (struct isl_basic_map *)bset1, (struct isl_basic_map *)bset2);
7538 int isl_map_is_empty(struct isl_map *map)
7545 for (i = 0; i < map->n; ++i) {
7546 is_empty = isl_basic_map_is_empty(map->p[i]);
7555 int isl_map_plain_is_empty(__isl_keep isl_map *map)
7557 return map ? map->n == 0 : -1;
7560 int isl_map_fast_is_empty(__isl_keep isl_map *map)
7562 return isl_map_plain_is_empty(map);
7565 int isl_set_plain_is_empty(struct isl_set *set)
7567 return set ? set->n == 0 : -1;
7570 int isl_set_fast_is_empty(__isl_keep isl_set *set)
7572 return isl_set_plain_is_empty(set);
7575 int isl_set_is_empty(struct isl_set *set)
7577 return isl_map_is_empty((struct isl_map *)set);
7580 int isl_map_has_equal_space(__isl_keep isl_map *map1, __isl_keep isl_map *map2)
7585 return isl_space_is_equal(map1->dim, map2->dim);
7588 int isl_set_has_equal_space(__isl_keep isl_set *set1, __isl_keep isl_set *set2)
7593 return isl_space_is_equal(set1->dim, set2->dim);
7596 static int map_is_equal(__isl_keep isl_map *map1, __isl_keep isl_map *map2)
7602 is_subset = isl_map_is_subset(map1, map2);
7605 is_subset = isl_map_is_subset(map2, map1);
7609 int isl_map_is_equal(__isl_keep isl_map *map1, __isl_keep isl_map *map2)
7611 return isl_map_align_params_map_map_and_test(map1, map2, &map_is_equal);
7614 int isl_basic_map_is_strict_subset(
7615 struct isl_basic_map *bmap1, struct isl_basic_map *bmap2)
7619 if (!bmap1 || !bmap2)
7621 is_subset = isl_basic_map_is_subset(bmap1, bmap2);
7624 is_subset = isl_basic_map_is_subset(bmap2, bmap1);
7625 if (is_subset == -1)
7630 int isl_map_is_strict_subset(struct isl_map *map1, struct isl_map *map2)
7636 is_subset = isl_map_is_subset(map1, map2);
7639 is_subset = isl_map_is_subset(map2, map1);
7640 if (is_subset == -1)
7645 int isl_set_is_strict_subset(__isl_keep isl_set *set1, __isl_keep isl_set *set2)
7647 return isl_map_is_strict_subset((isl_map *)set1, (isl_map *)set2);
7650 int isl_basic_map_is_universe(struct isl_basic_map *bmap)
7654 return bmap->n_eq == 0 && bmap->n_ineq == 0;
7657 int isl_basic_set_is_universe(struct isl_basic_set *bset)
7661 return bset->n_eq == 0 && bset->n_ineq == 0;
7664 int isl_map_plain_is_universe(__isl_keep isl_map *map)
7671 for (i = 0; i < map->n; ++i) {
7672 int r = isl_basic_map_is_universe(map->p[i]);
7680 int isl_set_plain_is_universe(__isl_keep isl_set *set)
7682 return isl_map_plain_is_universe((isl_map *) set);
7685 int isl_set_fast_is_universe(__isl_keep isl_set *set)
7687 return isl_set_plain_is_universe(set);
7690 int isl_basic_map_is_empty(struct isl_basic_map *bmap)
7692 struct isl_basic_set *bset = NULL;
7693 struct isl_vec *sample = NULL;
7700 if (ISL_F_ISSET(bmap, ISL_BASIC_MAP_EMPTY))
7703 if (isl_basic_map_is_universe(bmap))
7706 if (ISL_F_ISSET(bmap, ISL_BASIC_MAP_RATIONAL)) {
7707 struct isl_basic_map *copy = isl_basic_map_copy(bmap);
7708 copy = isl_basic_map_remove_redundancies(copy);
7709 empty = isl_basic_map_plain_is_empty(copy);
7710 isl_basic_map_free(copy);
7714 total = 1 + isl_basic_map_total_dim(bmap);
7715 if (bmap->sample && bmap->sample->size == total) {
7716 int contains = isl_basic_map_contains(bmap, bmap->sample);
7722 isl_vec_free(bmap->sample);
7723 bmap->sample = NULL;
7724 bset = isl_basic_map_underlying_set(isl_basic_map_copy(bmap));
7727 sample = isl_basic_set_sample_vec(bset);
7730 empty = sample->size == 0;
7731 isl_vec_free(bmap->sample);
7732 bmap->sample = sample;
7734 ISL_F_SET(bmap, ISL_BASIC_MAP_EMPTY);
7739 int isl_basic_map_plain_is_empty(__isl_keep isl_basic_map *bmap)
7743 return ISL_F_ISSET(bmap, ISL_BASIC_MAP_EMPTY);
7746 int isl_basic_map_fast_is_empty(__isl_keep isl_basic_map *bmap)
7748 return isl_basic_map_plain_is_empty(bmap);
7751 int isl_basic_set_plain_is_empty(__isl_keep isl_basic_set *bset)
7755 return ISL_F_ISSET(bset, ISL_BASIC_SET_EMPTY);
7758 int isl_basic_set_fast_is_empty(__isl_keep isl_basic_set *bset)
7760 return isl_basic_set_plain_is_empty(bset);
7763 int isl_basic_set_is_empty(struct isl_basic_set *bset)
7765 return isl_basic_map_is_empty((struct isl_basic_map *)bset);
7768 struct isl_map *isl_basic_map_union(
7769 struct isl_basic_map *bmap1, struct isl_basic_map *bmap2)
7771 struct isl_map *map;
7772 if (!bmap1 || !bmap2)
7775 isl_assert(bmap1->ctx, isl_space_is_equal(bmap1->dim, bmap2->dim), goto error);
7777 map = isl_map_alloc_space(isl_space_copy(bmap1->dim), 2, 0);
7780 map = isl_map_add_basic_map(map, bmap1);
7781 map = isl_map_add_basic_map(map, bmap2);
7784 isl_basic_map_free(bmap1);
7785 isl_basic_map_free(bmap2);
7789 struct isl_set *isl_basic_set_union(
7790 struct isl_basic_set *bset1, struct isl_basic_set *bset2)
7792 return (struct isl_set *)isl_basic_map_union(
7793 (struct isl_basic_map *)bset1,
7794 (struct isl_basic_map *)bset2);
7797 /* Order divs such that any div only depends on previous divs */
7798 struct isl_basic_map *isl_basic_map_order_divs(struct isl_basic_map *bmap)
7806 off = isl_space_dim(bmap->dim, isl_dim_all);
7808 for (i = 0; i < bmap->n_div; ++i) {
7810 if (isl_int_is_zero(bmap->div[i][0]))
7812 pos = isl_seq_first_non_zero(bmap->div[i]+1+1+off+i,
7816 isl_basic_map_swap_div(bmap, i, i + pos);
7822 struct isl_basic_set *isl_basic_set_order_divs(struct isl_basic_set *bset)
7824 return (struct isl_basic_set *)
7825 isl_basic_map_order_divs((struct isl_basic_map *)bset);
7828 __isl_give isl_map *isl_map_order_divs(__isl_take isl_map *map)
7835 for (i = 0; i < map->n; ++i) {
7836 map->p[i] = isl_basic_map_order_divs(map->p[i]);
7847 /* Apply the expansion computed by isl_merge_divs.
7848 * The expansion itself is given by "exp" while the resulting
7849 * list of divs is given by "div".
7851 __isl_give isl_basic_set *isl_basic_set_expand_divs(
7852 __isl_take isl_basic_set *bset, __isl_take isl_mat *div, int *exp)
7857 bset = isl_basic_set_cow(bset);
7861 if (div->n_row < bset->n_div)
7862 isl_die(isl_mat_get_ctx(div), isl_error_invalid,
7863 "not an expansion", goto error);
7865 n_div = bset->n_div;
7866 bset = isl_basic_map_extend_space(bset, isl_space_copy(bset->dim),
7867 div->n_row - n_div, 0,
7868 2 * (div->n_row - n_div));
7870 for (i = n_div; i < div->n_row; ++i)
7871 if (isl_basic_set_alloc_div(bset) < 0)
7875 for (i = div->n_row - 1; i >= 0; --i) {
7876 if (j >= 0 && exp[j] == i) {
7878 isl_basic_map_swap_div(bset, i, j);
7881 isl_seq_cpy(bset->div[i], div->row[i], div->n_col);
7882 if (isl_basic_map_add_div_constraints(bset, i) < 0)
7890 isl_basic_set_free(bset);
7895 /* Look for a div in dst that corresponds to the div "div" in src.
7896 * The divs before "div" in src and dst are assumed to be the same.
7898 * Returns -1 if no corresponding div was found and the position
7899 * of the corresponding div in dst otherwise.
7901 static int find_div(struct isl_basic_map *dst,
7902 struct isl_basic_map *src, unsigned div)
7906 unsigned total = isl_space_dim(src->dim, isl_dim_all);
7908 isl_assert(dst->ctx, div <= dst->n_div, return -1);
7909 for (i = div; i < dst->n_div; ++i)
7910 if (isl_seq_eq(dst->div[i], src->div[div], 1+1+total+div) &&
7911 isl_seq_first_non_zero(dst->div[i]+1+1+total+div,
7912 dst->n_div - div) == -1)
7917 struct isl_basic_map *isl_basic_map_align_divs(
7918 struct isl_basic_map *dst, struct isl_basic_map *src)
7926 if (src->n_div == 0)
7929 for (i = 0; i < src->n_div; ++i)
7930 isl_assert(src->ctx, !isl_int_is_zero(src->div[i][0]), goto error);
7932 src = isl_basic_map_order_divs(src);
7933 dst = isl_basic_map_cow(dst);
7934 dst = isl_basic_map_extend_space(dst, isl_space_copy(dst->dim),
7935 src->n_div, 0, 2 * src->n_div);
7938 total = isl_space_dim(src->dim, isl_dim_all);
7939 for (i = 0; i < src->n_div; ++i) {
7940 int j = find_div(dst, src, i);
7942 j = isl_basic_map_alloc_div(dst);
7945 isl_seq_cpy(dst->div[j], src->div[i], 1+1+total+i);
7946 isl_seq_clr(dst->div[j]+1+1+total+i, dst->n_div - i);
7947 if (isl_basic_map_add_div_constraints(dst, j) < 0)
7951 isl_basic_map_swap_div(dst, i, j);
7955 isl_basic_map_free(dst);
7959 struct isl_basic_set *isl_basic_set_align_divs(
7960 struct isl_basic_set *dst, struct isl_basic_set *src)
7962 return (struct isl_basic_set *)isl_basic_map_align_divs(
7963 (struct isl_basic_map *)dst, (struct isl_basic_map *)src);
7966 struct isl_map *isl_map_align_divs(struct isl_map *map)
7974 map = isl_map_compute_divs(map);
7975 map = isl_map_cow(map);
7979 for (i = 1; i < map->n; ++i)
7980 map->p[0] = isl_basic_map_align_divs(map->p[0], map->p[i]);
7981 for (i = 1; i < map->n; ++i)
7982 map->p[i] = isl_basic_map_align_divs(map->p[i], map->p[0]);
7984 ISL_F_CLR(map, ISL_MAP_NORMALIZED);
7988 struct isl_set *isl_set_align_divs(struct isl_set *set)
7990 return (struct isl_set *)isl_map_align_divs((struct isl_map *)set);
7993 static __isl_give isl_set *set_apply( __isl_take isl_set *set,
7994 __isl_take isl_map *map)
7998 isl_assert(set->ctx, isl_map_compatible_domain(map, set), goto error);
7999 map = isl_map_intersect_domain(map, set);
8000 set = isl_map_range(map);
8008 __isl_give isl_set *isl_set_apply( __isl_take isl_set *set,
8009 __isl_take isl_map *map)
8011 return isl_map_align_params_map_map_and(set, map, &set_apply);
8014 /* There is no need to cow as removing empty parts doesn't change
8015 * the meaning of the set.
8017 struct isl_map *isl_map_remove_empty_parts(struct isl_map *map)
8024 for (i = map->n - 1; i >= 0; --i)
8025 remove_if_empty(map, i);
8030 struct isl_set *isl_set_remove_empty_parts(struct isl_set *set)
8032 return (struct isl_set *)
8033 isl_map_remove_empty_parts((struct isl_map *)set);
8036 struct isl_basic_map *isl_map_copy_basic_map(struct isl_map *map)
8038 struct isl_basic_map *bmap;
8039 if (!map || map->n == 0)
8041 bmap = map->p[map->n-1];
8042 isl_assert(map->ctx, ISL_F_ISSET(bmap, ISL_BASIC_SET_FINAL), return NULL);
8043 return isl_basic_map_copy(bmap);
8046 struct isl_basic_set *isl_set_copy_basic_set(struct isl_set *set)
8048 return (struct isl_basic_set *)
8049 isl_map_copy_basic_map((struct isl_map *)set);
8052 __isl_give isl_map *isl_map_drop_basic_map(__isl_take isl_map *map,
8053 __isl_keep isl_basic_map *bmap)
8059 for (i = map->n-1; i >= 0; --i) {
8060 if (map->p[i] != bmap)
8062 map = isl_map_cow(map);
8065 isl_basic_map_free(map->p[i]);
8066 if (i != map->n-1) {
8067 ISL_F_CLR(map, ISL_SET_NORMALIZED);
8068 map->p[i] = map->p[map->n-1];
8079 struct isl_set *isl_set_drop_basic_set(struct isl_set *set,
8080 struct isl_basic_set *bset)
8082 return (struct isl_set *)isl_map_drop_basic_map((struct isl_map *)set,
8083 (struct isl_basic_map *)bset);
8086 /* Given two basic sets bset1 and bset2, compute the maximal difference
8087 * between the values of dimension pos in bset1 and those in bset2
8088 * for any common value of the parameters and dimensions preceding pos.
8090 static enum isl_lp_result basic_set_maximal_difference_at(
8091 __isl_keep isl_basic_set *bset1, __isl_keep isl_basic_set *bset2,
8092 int pos, isl_int *opt)
8095 struct isl_basic_map *bmap1 = NULL;
8096 struct isl_basic_map *bmap2 = NULL;
8097 struct isl_ctx *ctx;
8098 struct isl_vec *obj;
8101 unsigned dim1, dim2;
8102 enum isl_lp_result res;
8104 if (!bset1 || !bset2)
8105 return isl_lp_error;
8107 nparam = isl_basic_set_n_param(bset1);
8108 dim1 = isl_basic_set_n_dim(bset1);
8109 dim2 = isl_basic_set_n_dim(bset2);
8110 dims = isl_space_alloc(bset1->ctx, nparam, pos, dim1 - pos);
8111 bmap1 = isl_basic_map_from_basic_set(isl_basic_set_copy(bset1), dims);
8112 dims = isl_space_alloc(bset2->ctx, nparam, pos, dim2 - pos);
8113 bmap2 = isl_basic_map_from_basic_set(isl_basic_set_copy(bset2), dims);
8114 if (!bmap1 || !bmap2)
8116 bmap1 = isl_basic_map_cow(bmap1);
8117 bmap1 = isl_basic_map_extend(bmap1, nparam,
8118 pos, (dim1 - pos) + (dim2 - pos),
8119 bmap2->n_div, bmap2->n_eq, bmap2->n_ineq);
8120 bmap1 = add_constraints(bmap1, bmap2, 0, dim1 - pos);
8123 total = isl_basic_map_total_dim(bmap1);
8125 obj = isl_vec_alloc(ctx, 1 + total);
8128 isl_seq_clr(obj->block.data, 1 + total);
8129 isl_int_set_si(obj->block.data[1+nparam+pos], 1);
8130 isl_int_set_si(obj->block.data[1+nparam+pos+(dim1-pos)], -1);
8131 res = isl_basic_map_solve_lp(bmap1, 1, obj->block.data, ctx->one,
8133 isl_basic_map_free(bmap1);
8137 isl_basic_map_free(bmap2);
8139 isl_basic_map_free(bmap1);
8140 return isl_lp_error;
8143 /* Given two _disjoint_ basic sets bset1 and bset2, check whether
8144 * for any common value of the parameters and dimensions preceding pos
8145 * in both basic sets, the values of dimension pos in bset1 are
8146 * smaller or larger than those in bset2.
8149 * 1 if bset1 follows bset2
8150 * -1 if bset1 precedes bset2
8151 * 0 if bset1 and bset2 are incomparable
8152 * -2 if some error occurred.
8154 int isl_basic_set_compare_at(struct isl_basic_set *bset1,
8155 struct isl_basic_set *bset2, int pos)
8158 enum isl_lp_result res;
8163 res = basic_set_maximal_difference_at(bset1, bset2, pos, &opt);
8165 if (res == isl_lp_empty)
8167 else if ((res == isl_lp_ok && isl_int_is_pos(opt)) ||
8168 res == isl_lp_unbounded)
8170 else if (res == isl_lp_ok && isl_int_is_neg(opt))
8179 /* Given two basic sets bset1 and bset2, check whether
8180 * for any common value of the parameters and dimensions preceding pos
8181 * there is a value of dimension pos in bset1 that is larger
8182 * than a value of the same dimension in bset2.
8185 * 1 if there exists such a pair
8186 * 0 if there is no such pair, but there is a pair of equal values
8188 * -2 if some error occurred.
8190 int isl_basic_set_follows_at(__isl_keep isl_basic_set *bset1,
8191 __isl_keep isl_basic_set *bset2, int pos)
8194 enum isl_lp_result res;
8199 res = basic_set_maximal_difference_at(bset1, bset2, pos, &opt);
8201 if (res == isl_lp_empty)
8203 else if ((res == isl_lp_ok && isl_int_is_pos(opt)) ||
8204 res == isl_lp_unbounded)
8206 else if (res == isl_lp_ok && isl_int_is_neg(opt))
8208 else if (res == isl_lp_ok)
8217 /* Given two sets set1 and set2, check whether
8218 * for any common value of the parameters and dimensions preceding pos
8219 * there is a value of dimension pos in set1 that is larger
8220 * than a value of the same dimension in set2.
8223 * 1 if there exists such a pair
8224 * 0 if there is no such pair, but there is a pair of equal values
8226 * -2 if some error occurred.
8228 int isl_set_follows_at(__isl_keep isl_set *set1,
8229 __isl_keep isl_set *set2, int pos)
8237 for (i = 0; i < set1->n; ++i)
8238 for (j = 0; j < set2->n; ++j) {
8240 f = isl_basic_set_follows_at(set1->p[i], set2->p[j], pos);
8241 if (f == 1 || f == -2)
8250 static int isl_basic_map_plain_has_fixed_var(__isl_keep isl_basic_map *bmap,
8251 unsigned pos, isl_int *val)
8259 total = isl_basic_map_total_dim(bmap);
8260 for (i = 0, d = total-1; i < bmap->n_eq && d+1 > pos; ++i) {
8261 for (; d+1 > pos; --d)
8262 if (!isl_int_is_zero(bmap->eq[i][1+d]))
8266 if (isl_seq_first_non_zero(bmap->eq[i]+1, d) != -1)
8268 if (isl_seq_first_non_zero(bmap->eq[i]+1+d+1, total-d-1) != -1)
8270 if (!isl_int_is_one(bmap->eq[i][1+d]))
8273 isl_int_neg(*val, bmap->eq[i][0]);
8279 static int isl_map_plain_has_fixed_var(__isl_keep isl_map *map,
8280 unsigned pos, isl_int *val)
8292 return isl_basic_map_plain_has_fixed_var(map->p[0], pos, val);
8295 fixed = isl_basic_map_plain_has_fixed_var(map->p[0], pos, &v);
8296 for (i = 1; fixed == 1 && i < map->n; ++i) {
8297 fixed = isl_basic_map_plain_has_fixed_var(map->p[i], pos, &tmp);
8298 if (fixed == 1 && isl_int_ne(tmp, v))
8302 isl_int_set(*val, v);
8308 static int isl_basic_set_plain_has_fixed_var(__isl_keep isl_basic_set *bset,
8309 unsigned pos, isl_int *val)
8311 return isl_basic_map_plain_has_fixed_var((struct isl_basic_map *)bset,
8315 static int isl_set_plain_has_fixed_var(__isl_keep isl_set *set, unsigned pos,
8318 return isl_map_plain_has_fixed_var((struct isl_map *)set, pos, val);
8321 int isl_basic_map_plain_is_fixed(__isl_keep isl_basic_map *bmap,
8322 enum isl_dim_type type, unsigned pos, isl_int *val)
8324 if (pos >= isl_basic_map_dim(bmap, type))
8326 return isl_basic_map_plain_has_fixed_var(bmap,
8327 isl_basic_map_offset(bmap, type) - 1 + pos, val);
8330 int isl_map_plain_is_fixed(__isl_keep isl_map *map,
8331 enum isl_dim_type type, unsigned pos, isl_int *val)
8333 if (pos >= isl_map_dim(map, type))
8335 return isl_map_plain_has_fixed_var(map,
8336 map_offset(map, type) - 1 + pos, val);
8339 int isl_set_plain_is_fixed(__isl_keep isl_set *set,
8340 enum isl_dim_type type, unsigned pos, isl_int *val)
8342 return isl_map_plain_is_fixed(set, type, pos, val);
8345 int isl_map_fast_is_fixed(__isl_keep isl_map *map,
8346 enum isl_dim_type type, unsigned pos, isl_int *val)
8348 return isl_map_plain_is_fixed(map, type, pos, val);
8351 /* Check if dimension dim has fixed value and if so and if val is not NULL,
8352 * then return this fixed value in *val.
8354 int isl_basic_set_plain_dim_is_fixed(__isl_keep isl_basic_set *bset,
8355 unsigned dim, isl_int *val)
8357 return isl_basic_set_plain_has_fixed_var(bset,
8358 isl_basic_set_n_param(bset) + dim, val);
8361 /* Check if dimension dim has fixed value and if so and if val is not NULL,
8362 * then return this fixed value in *val.
8364 int isl_set_plain_dim_is_fixed(__isl_keep isl_set *set,
8365 unsigned dim, isl_int *val)
8367 return isl_set_plain_has_fixed_var(set, isl_set_n_param(set) + dim, val);
8370 int isl_set_fast_dim_is_fixed(__isl_keep isl_set *set,
8371 unsigned dim, isl_int *val)
8373 return isl_set_plain_dim_is_fixed(set, dim, val);
8376 /* Check if input variable in has fixed value and if so and if val is not NULL,
8377 * then return this fixed value in *val.
8379 int isl_map_plain_input_is_fixed(__isl_keep isl_map *map,
8380 unsigned in, isl_int *val)
8382 return isl_map_plain_has_fixed_var(map, isl_map_n_param(map) + in, val);
8385 /* Check if dimension dim has an (obvious) fixed lower bound and if so
8386 * and if val is not NULL, then return this lower bound in *val.
8388 int isl_basic_set_plain_dim_has_fixed_lower_bound(
8389 __isl_keep isl_basic_set *bset, unsigned dim, isl_int *val)
8391 int i, i_eq = -1, i_ineq = -1;
8398 total = isl_basic_set_total_dim(bset);
8399 nparam = isl_basic_set_n_param(bset);
8400 for (i = 0; i < bset->n_eq; ++i) {
8401 if (isl_int_is_zero(bset->eq[i][1+nparam+dim]))
8407 for (i = 0; i < bset->n_ineq; ++i) {
8408 if (!isl_int_is_pos(bset->ineq[i][1+nparam+dim]))
8410 if (i_eq != -1 || i_ineq != -1)
8414 if (i_eq == -1 && i_ineq == -1)
8416 c = i_eq != -1 ? bset->eq[i_eq] : bset->ineq[i_ineq];
8417 /* The coefficient should always be one due to normalization. */
8418 if (!isl_int_is_one(c[1+nparam+dim]))
8420 if (isl_seq_first_non_zero(c+1, nparam+dim) != -1)
8422 if (isl_seq_first_non_zero(c+1+nparam+dim+1,
8423 total - nparam - dim - 1) != -1)
8426 isl_int_neg(*val, c[0]);
8430 int isl_set_plain_dim_has_fixed_lower_bound(__isl_keep isl_set *set,
8431 unsigned dim, isl_int *val)
8443 return isl_basic_set_plain_dim_has_fixed_lower_bound(set->p[0],
8447 fixed = isl_basic_set_plain_dim_has_fixed_lower_bound(set->p[0],
8449 for (i = 1; fixed == 1 && i < set->n; ++i) {
8450 fixed = isl_basic_set_plain_dim_has_fixed_lower_bound(set->p[i],
8452 if (fixed == 1 && isl_int_ne(tmp, v))
8456 isl_int_set(*val, v);
8467 /* uset_gist depends on constraints without existentially quantified
8468 * variables sorting first.
8470 static int qsort_constraint_cmp(const void *p1, const void *p2)
8472 const struct constraint *c1 = (const struct constraint *)p1;
8473 const struct constraint *c2 = (const struct constraint *)p2;
8475 unsigned size = isl_min(c1->size, c2->size);
8477 l1 = isl_seq_last_non_zero(c1->c + 1, size);
8478 l2 = isl_seq_last_non_zero(c2->c + 1, size);
8483 return isl_seq_cmp(c1->c + 1, c2->c + 1, size);
8486 static struct isl_basic_map *isl_basic_map_sort_constraints(
8487 struct isl_basic_map *bmap)
8490 struct constraint *c;
8495 total = isl_basic_map_total_dim(bmap);
8496 c = isl_alloc_array(bmap->ctx, struct constraint, bmap->n_ineq);
8499 for (i = 0; i < bmap->n_ineq; ++i) {
8501 c[i].c = bmap->ineq[i];
8503 qsort(c, bmap->n_ineq, sizeof(struct constraint), qsort_constraint_cmp);
8504 for (i = 0; i < bmap->n_ineq; ++i)
8505 bmap->ineq[i] = c[i].c;
8509 isl_basic_map_free(bmap);
8513 __isl_give isl_basic_set *isl_basic_set_sort_constraints(
8514 __isl_take isl_basic_set *bset)
8516 return (struct isl_basic_set *)isl_basic_map_sort_constraints(
8517 (struct isl_basic_map *)bset);
8520 struct isl_basic_map *isl_basic_map_normalize(struct isl_basic_map *bmap)
8524 if (ISL_F_ISSET(bmap, ISL_BASIC_MAP_NORMALIZED))
8526 bmap = isl_basic_map_remove_redundancies(bmap);
8527 bmap = isl_basic_map_sort_constraints(bmap);
8529 ISL_F_SET(bmap, ISL_BASIC_MAP_NORMALIZED);
8533 struct isl_basic_set *isl_basic_set_normalize(struct isl_basic_set *bset)
8535 return (struct isl_basic_set *)isl_basic_map_normalize(
8536 (struct isl_basic_map *)bset);
8539 int isl_basic_map_plain_cmp(const __isl_keep isl_basic_map *bmap1,
8540 const __isl_keep isl_basic_map *bmap2)
8547 if (ISL_F_ISSET(bmap1, ISL_BASIC_MAP_RATIONAL) !=
8548 ISL_F_ISSET(bmap2, ISL_BASIC_MAP_RATIONAL))
8549 return ISL_F_ISSET(bmap1, ISL_BASIC_MAP_RATIONAL) ? -1 : 1;
8550 if (isl_basic_map_n_param(bmap1) != isl_basic_map_n_param(bmap2))
8551 return isl_basic_map_n_param(bmap1) - isl_basic_map_n_param(bmap2);
8552 if (isl_basic_map_n_in(bmap1) != isl_basic_map_n_in(bmap2))
8553 return isl_basic_map_n_out(bmap1) - isl_basic_map_n_out(bmap2);
8554 if (isl_basic_map_n_out(bmap1) != isl_basic_map_n_out(bmap2))
8555 return isl_basic_map_n_out(bmap1) - isl_basic_map_n_out(bmap2);
8556 if (ISL_F_ISSET(bmap1, ISL_BASIC_MAP_EMPTY) &&
8557 ISL_F_ISSET(bmap2, ISL_BASIC_MAP_EMPTY))
8559 if (ISL_F_ISSET(bmap1, ISL_BASIC_MAP_EMPTY))
8561 if (ISL_F_ISSET(bmap2, ISL_BASIC_MAP_EMPTY))
8563 if (bmap1->n_eq != bmap2->n_eq)
8564 return bmap1->n_eq - bmap2->n_eq;
8565 if (bmap1->n_ineq != bmap2->n_ineq)
8566 return bmap1->n_ineq - bmap2->n_ineq;
8567 if (bmap1->n_div != bmap2->n_div)
8568 return bmap1->n_div - bmap2->n_div;
8569 total = isl_basic_map_total_dim(bmap1);
8570 for (i = 0; i < bmap1->n_eq; ++i) {
8571 cmp = isl_seq_cmp(bmap1->eq[i], bmap2->eq[i], 1+total);
8575 for (i = 0; i < bmap1->n_ineq; ++i) {
8576 cmp = isl_seq_cmp(bmap1->ineq[i], bmap2->ineq[i], 1+total);
8580 for (i = 0; i < bmap1->n_div; ++i) {
8581 cmp = isl_seq_cmp(bmap1->div[i], bmap2->div[i], 1+1+total);
8588 int isl_basic_set_plain_cmp(const __isl_keep isl_basic_set *bset1,
8589 const __isl_keep isl_basic_set *bset2)
8591 return isl_basic_map_plain_cmp(bset1, bset2);
8594 int isl_set_plain_cmp(__isl_keep isl_set *set1, __isl_keep isl_set *set2)
8600 if (set1->n != set2->n)
8601 return set1->n - set2->n;
8603 for (i = 0; i < set1->n; ++i) {
8604 cmp = isl_basic_set_plain_cmp(set1->p[i], set2->p[i]);
8612 int isl_basic_map_plain_is_equal(__isl_keep isl_basic_map *bmap1,
8613 __isl_keep isl_basic_map *bmap2)
8615 return isl_basic_map_plain_cmp(bmap1, bmap2) == 0;
8618 int isl_basic_set_plain_is_equal(__isl_keep isl_basic_set *bset1,
8619 __isl_keep isl_basic_set *bset2)
8621 return isl_basic_map_plain_is_equal((isl_basic_map *)bset1,
8622 (isl_basic_map *)bset2);
8625 static int qsort_bmap_cmp(const void *p1, const void *p2)
8627 const struct isl_basic_map *bmap1 = *(const struct isl_basic_map **)p1;
8628 const struct isl_basic_map *bmap2 = *(const struct isl_basic_map **)p2;
8630 return isl_basic_map_plain_cmp(bmap1, bmap2);
8633 /* We normalize in place, but if anything goes wrong we need
8634 * to return NULL, so we need to make sure we don't change the
8635 * meaning of any possible other copies of map.
8637 struct isl_map *isl_map_normalize(struct isl_map *map)
8640 struct isl_basic_map *bmap;
8644 if (ISL_F_ISSET(map, ISL_MAP_NORMALIZED))
8646 for (i = 0; i < map->n; ++i) {
8647 bmap = isl_basic_map_normalize(isl_basic_map_copy(map->p[i]));
8650 isl_basic_map_free(map->p[i]);
8653 qsort(map->p, map->n, sizeof(struct isl_basic_map *), qsort_bmap_cmp);
8654 ISL_F_SET(map, ISL_MAP_NORMALIZED);
8655 map = isl_map_remove_empty_parts(map);
8658 for (i = map->n - 1; i >= 1; --i) {
8659 if (!isl_basic_map_plain_is_equal(map->p[i-1], map->p[i]))
8661 isl_basic_map_free(map->p[i-1]);
8662 for (j = i; j < map->n; ++j)
8663 map->p[j-1] = map->p[j];
8673 struct isl_set *isl_set_normalize(struct isl_set *set)
8675 return (struct isl_set *)isl_map_normalize((struct isl_map *)set);
8678 int isl_map_plain_is_equal(__isl_keep isl_map *map1, __isl_keep isl_map *map2)
8688 if (!isl_space_is_equal(map1->dim, map2->dim))
8691 map1 = isl_map_copy(map1);
8692 map2 = isl_map_copy(map2);
8693 map1 = isl_map_normalize(map1);
8694 map2 = isl_map_normalize(map2);
8697 equal = map1->n == map2->n;
8698 for (i = 0; equal && i < map1->n; ++i) {
8699 equal = isl_basic_map_plain_is_equal(map1->p[i], map2->p[i]);
8712 int isl_map_fast_is_equal(__isl_keep isl_map *map1, __isl_keep isl_map *map2)
8714 return isl_map_plain_is_equal(map1, map2);
8717 int isl_set_plain_is_equal(__isl_keep isl_set *set1, __isl_keep isl_set *set2)
8719 return isl_map_plain_is_equal((struct isl_map *)set1,
8720 (struct isl_map *)set2);
8723 int isl_set_fast_is_equal(__isl_keep isl_set *set1, __isl_keep isl_set *set2)
8725 return isl_set_plain_is_equal(set1, set2);
8728 /* Return an interval that ranges from min to max (inclusive)
8730 struct isl_basic_set *isl_basic_set_interval(struct isl_ctx *ctx,
8731 isl_int min, isl_int max)
8734 struct isl_basic_set *bset = NULL;
8736 bset = isl_basic_set_alloc(ctx, 0, 1, 0, 0, 2);
8740 k = isl_basic_set_alloc_inequality(bset);
8743 isl_int_set_si(bset->ineq[k][1], 1);
8744 isl_int_neg(bset->ineq[k][0], min);
8746 k = isl_basic_set_alloc_inequality(bset);
8749 isl_int_set_si(bset->ineq[k][1], -1);
8750 isl_int_set(bset->ineq[k][0], max);
8754 isl_basic_set_free(bset);
8758 /* Return the Cartesian product of the basic sets in list (in the given order).
8760 __isl_give isl_basic_set *isl_basic_set_list_product(
8761 __isl_take struct isl_basic_set_list *list)
8769 struct isl_basic_set *product = NULL;
8773 isl_assert(list->ctx, list->n > 0, goto error);
8774 isl_assert(list->ctx, list->p[0], goto error);
8775 nparam = isl_basic_set_n_param(list->p[0]);
8776 dim = isl_basic_set_n_dim(list->p[0]);
8777 extra = list->p[0]->n_div;
8778 n_eq = list->p[0]->n_eq;
8779 n_ineq = list->p[0]->n_ineq;
8780 for (i = 1; i < list->n; ++i) {
8781 isl_assert(list->ctx, list->p[i], goto error);
8782 isl_assert(list->ctx,
8783 nparam == isl_basic_set_n_param(list->p[i]), goto error);
8784 dim += isl_basic_set_n_dim(list->p[i]);
8785 extra += list->p[i]->n_div;
8786 n_eq += list->p[i]->n_eq;
8787 n_ineq += list->p[i]->n_ineq;
8789 product = isl_basic_set_alloc(list->ctx, nparam, dim, extra,
8794 for (i = 0; i < list->n; ++i) {
8795 isl_basic_set_add_constraints(product,
8796 isl_basic_set_copy(list->p[i]), dim);
8797 dim += isl_basic_set_n_dim(list->p[i]);
8799 isl_basic_set_list_free(list);
8802 isl_basic_set_free(product);
8803 isl_basic_set_list_free(list);
8807 struct isl_basic_map *isl_basic_map_product(
8808 struct isl_basic_map *bmap1, struct isl_basic_map *bmap2)
8810 isl_space *dim_result = NULL;
8811 struct isl_basic_map *bmap;
8812 unsigned in1, in2, out1, out2, nparam, total, pos;
8813 struct isl_dim_map *dim_map1, *dim_map2;
8815 if (!bmap1 || !bmap2)
8818 isl_assert(bmap1->ctx, isl_space_match(bmap1->dim, isl_dim_param,
8819 bmap2->dim, isl_dim_param), goto error);
8820 dim_result = isl_space_product(isl_space_copy(bmap1->dim),
8821 isl_space_copy(bmap2->dim));
8823 in1 = isl_basic_map_n_in(bmap1);
8824 in2 = isl_basic_map_n_in(bmap2);
8825 out1 = isl_basic_map_n_out(bmap1);
8826 out2 = isl_basic_map_n_out(bmap2);
8827 nparam = isl_basic_map_n_param(bmap1);
8829 total = nparam + in1 + in2 + out1 + out2 + bmap1->n_div + bmap2->n_div;
8830 dim_map1 = isl_dim_map_alloc(bmap1->ctx, total);
8831 dim_map2 = isl_dim_map_alloc(bmap1->ctx, total);
8832 isl_dim_map_dim(dim_map1, bmap1->dim, isl_dim_param, pos = 0);
8833 isl_dim_map_dim(dim_map2, bmap2->dim, isl_dim_param, pos = 0);
8834 isl_dim_map_dim(dim_map1, bmap1->dim, isl_dim_in, pos += nparam);
8835 isl_dim_map_dim(dim_map2, bmap2->dim, isl_dim_in, pos += in1);
8836 isl_dim_map_dim(dim_map1, bmap1->dim, isl_dim_out, pos += in2);
8837 isl_dim_map_dim(dim_map2, bmap2->dim, isl_dim_out, pos += out1);
8838 isl_dim_map_div(dim_map1, bmap1, pos += out2);
8839 isl_dim_map_div(dim_map2, bmap2, pos += bmap1->n_div);
8841 bmap = isl_basic_map_alloc_space(dim_result,
8842 bmap1->n_div + bmap2->n_div,
8843 bmap1->n_eq + bmap2->n_eq,
8844 bmap1->n_ineq + bmap2->n_ineq);
8845 bmap = isl_basic_map_add_constraints_dim_map(bmap, bmap1, dim_map1);
8846 bmap = isl_basic_map_add_constraints_dim_map(bmap, bmap2, dim_map2);
8847 bmap = isl_basic_map_simplify(bmap);
8848 return isl_basic_map_finalize(bmap);
8850 isl_basic_map_free(bmap1);
8851 isl_basic_map_free(bmap2);
8855 __isl_give isl_basic_map *isl_basic_map_flat_product(
8856 __isl_take isl_basic_map *bmap1, __isl_take isl_basic_map *bmap2)
8858 isl_basic_map *prod;
8860 prod = isl_basic_map_product(bmap1, bmap2);
8861 prod = isl_basic_map_flatten(prod);
8865 __isl_give isl_basic_set *isl_basic_set_flat_product(
8866 __isl_take isl_basic_set *bset1, __isl_take isl_basic_set *bset2)
8868 return isl_basic_map_flat_range_product(bset1, bset2);
8871 __isl_give isl_basic_map *isl_basic_map_domain_product(
8872 __isl_take isl_basic_map *bmap1, __isl_take isl_basic_map *bmap2)
8874 isl_space *space_result = NULL;
8875 isl_basic_map *bmap;
8876 unsigned in1, in2, out, nparam, total, pos;
8877 struct isl_dim_map *dim_map1, *dim_map2;
8879 if (!bmap1 || !bmap2)
8882 space_result = isl_space_domain_product(isl_space_copy(bmap1->dim),
8883 isl_space_copy(bmap2->dim));
8885 in1 = isl_basic_map_dim(bmap1, isl_dim_in);
8886 in2 = isl_basic_map_dim(bmap2, isl_dim_in);
8887 out = isl_basic_map_dim(bmap1, isl_dim_out);
8888 nparam = isl_basic_map_dim(bmap1, isl_dim_param);
8890 total = nparam + in1 + in2 + out + bmap1->n_div + bmap2->n_div;
8891 dim_map1 = isl_dim_map_alloc(bmap1->ctx, total);
8892 dim_map2 = isl_dim_map_alloc(bmap1->ctx, total);
8893 isl_dim_map_dim(dim_map1, bmap1->dim, isl_dim_param, pos = 0);
8894 isl_dim_map_dim(dim_map2, bmap2->dim, isl_dim_param, pos = 0);
8895 isl_dim_map_dim(dim_map1, bmap1->dim, isl_dim_in, pos += nparam);
8896 isl_dim_map_dim(dim_map2, bmap2->dim, isl_dim_in, pos += in1);
8897 isl_dim_map_dim(dim_map1, bmap1->dim, isl_dim_out, pos += in2);
8898 isl_dim_map_dim(dim_map2, bmap2->dim, isl_dim_out, pos);
8899 isl_dim_map_div(dim_map1, bmap1, pos += out);
8900 isl_dim_map_div(dim_map2, bmap2, pos += bmap1->n_div);
8902 bmap = isl_basic_map_alloc_space(space_result,
8903 bmap1->n_div + bmap2->n_div,
8904 bmap1->n_eq + bmap2->n_eq,
8905 bmap1->n_ineq + bmap2->n_ineq);
8906 bmap = isl_basic_map_add_constraints_dim_map(bmap, bmap1, dim_map1);
8907 bmap = isl_basic_map_add_constraints_dim_map(bmap, bmap2, dim_map2);
8908 bmap = isl_basic_map_simplify(bmap);
8909 return isl_basic_map_finalize(bmap);
8911 isl_basic_map_free(bmap1);
8912 isl_basic_map_free(bmap2);
8916 __isl_give isl_basic_map *isl_basic_map_range_product(
8917 __isl_take isl_basic_map *bmap1, __isl_take isl_basic_map *bmap2)
8919 isl_space *dim_result = NULL;
8920 isl_basic_map *bmap;
8921 unsigned in, out1, out2, nparam, total, pos;
8922 struct isl_dim_map *dim_map1, *dim_map2;
8924 if (!bmap1 || !bmap2)
8927 if (!isl_space_match(bmap1->dim, isl_dim_param,
8928 bmap2->dim, isl_dim_param))
8929 isl_die(isl_basic_map_get_ctx(bmap1), isl_error_invalid,
8930 "parameters don't match", goto error);
8932 dim_result = isl_space_range_product(isl_space_copy(bmap1->dim),
8933 isl_space_copy(bmap2->dim));
8935 in = isl_basic_map_dim(bmap1, isl_dim_in);
8936 out1 = isl_basic_map_n_out(bmap1);
8937 out2 = isl_basic_map_n_out(bmap2);
8938 nparam = isl_basic_map_n_param(bmap1);
8940 total = nparam + in + out1 + out2 + bmap1->n_div + bmap2->n_div;
8941 dim_map1 = isl_dim_map_alloc(bmap1->ctx, total);
8942 dim_map2 = isl_dim_map_alloc(bmap1->ctx, total);
8943 isl_dim_map_dim(dim_map1, bmap1->dim, isl_dim_param, pos = 0);
8944 isl_dim_map_dim(dim_map2, bmap2->dim, isl_dim_param, pos = 0);
8945 isl_dim_map_dim(dim_map1, bmap1->dim, isl_dim_in, pos += nparam);
8946 isl_dim_map_dim(dim_map2, bmap2->dim, isl_dim_in, pos);
8947 isl_dim_map_dim(dim_map1, bmap1->dim, isl_dim_out, pos += in);
8948 isl_dim_map_dim(dim_map2, bmap2->dim, isl_dim_out, pos += out1);
8949 isl_dim_map_div(dim_map1, bmap1, pos += out2);
8950 isl_dim_map_div(dim_map2, bmap2, pos += bmap1->n_div);
8952 bmap = isl_basic_map_alloc_space(dim_result,
8953 bmap1->n_div + bmap2->n_div,
8954 bmap1->n_eq + bmap2->n_eq,
8955 bmap1->n_ineq + bmap2->n_ineq);
8956 bmap = isl_basic_map_add_constraints_dim_map(bmap, bmap1, dim_map1);
8957 bmap = isl_basic_map_add_constraints_dim_map(bmap, bmap2, dim_map2);
8958 bmap = isl_basic_map_simplify(bmap);
8959 return isl_basic_map_finalize(bmap);
8961 isl_basic_map_free(bmap1);
8962 isl_basic_map_free(bmap2);
8966 __isl_give isl_basic_map *isl_basic_map_flat_range_product(
8967 __isl_take isl_basic_map *bmap1, __isl_take isl_basic_map *bmap2)
8969 isl_basic_map *prod;
8971 prod = isl_basic_map_range_product(bmap1, bmap2);
8972 prod = isl_basic_map_flatten_range(prod);
8976 static __isl_give isl_map *map_product(__isl_take isl_map *map1,
8977 __isl_take isl_map *map2,
8978 __isl_give isl_space *(*dim_product)(__isl_take isl_space *left,
8979 __isl_take isl_space *right),
8980 __isl_give isl_basic_map *(*basic_map_product)(
8981 __isl_take isl_basic_map *left, __isl_take isl_basic_map *right))
8984 struct isl_map *result;
8990 isl_assert(map1->ctx, isl_space_match(map1->dim, isl_dim_param,
8991 map2->dim, isl_dim_param), goto error);
8993 if (ISL_F_ISSET(map1, ISL_MAP_DISJOINT) &&
8994 ISL_F_ISSET(map2, ISL_MAP_DISJOINT))
8995 ISL_FL_SET(flags, ISL_MAP_DISJOINT);
8997 result = isl_map_alloc_space(dim_product(isl_space_copy(map1->dim),
8998 isl_space_copy(map2->dim)),
8999 map1->n * map2->n, flags);
9002 for (i = 0; i < map1->n; ++i)
9003 for (j = 0; j < map2->n; ++j) {
9004 struct isl_basic_map *part;
9005 part = basic_map_product(isl_basic_map_copy(map1->p[i]),
9006 isl_basic_map_copy(map2->p[j]));
9007 if (isl_basic_map_is_empty(part))
9008 isl_basic_map_free(part);
9010 result = isl_map_add_basic_map(result, part);
9023 /* Given two maps A -> B and C -> D, construct a map [A -> C] -> [B -> D]
9025 static __isl_give isl_map *map_product_aligned(__isl_take isl_map *map1,
9026 __isl_take isl_map *map2)
9028 return map_product(map1, map2, &isl_space_product, &isl_basic_map_product);
9031 __isl_give isl_map *isl_map_product(__isl_take isl_map *map1,
9032 __isl_take isl_map *map2)
9034 return isl_map_align_params_map_map_and(map1, map2, &map_product_aligned);
9037 /* Given two maps A -> B and C -> D, construct a map (A, C) -> (B, D)
9039 __isl_give isl_map *isl_map_flat_product(__isl_take isl_map *map1,
9040 __isl_take isl_map *map2)
9044 prod = isl_map_product(map1, map2);
9045 prod = isl_map_flatten(prod);
9049 /* Given two set A and B, construct its Cartesian product A x B.
9051 struct isl_set *isl_set_product(struct isl_set *set1, struct isl_set *set2)
9053 return isl_map_range_product(set1, set2);
9056 __isl_give isl_set *isl_set_flat_product(__isl_take isl_set *set1,
9057 __isl_take isl_set *set2)
9059 return isl_map_flat_range_product(set1, set2);
9062 /* Given two maps A -> B and C -> D, construct a map [A -> C] -> (B * D)
9064 static __isl_give isl_map *map_domain_product_aligned(__isl_take isl_map *map1,
9065 __isl_take isl_map *map2)
9067 return map_product(map1, map2, &isl_space_domain_product,
9068 &isl_basic_map_domain_product);
9071 /* Given two maps A -> B and C -> D, construct a map (A * C) -> [B -> D]
9073 static __isl_give isl_map *map_range_product_aligned(__isl_take isl_map *map1,
9074 __isl_take isl_map *map2)
9076 return map_product(map1, map2, &isl_space_range_product,
9077 &isl_basic_map_range_product);
9080 __isl_give isl_map *isl_map_domain_product(__isl_take isl_map *map1,
9081 __isl_take isl_map *map2)
9083 return isl_map_align_params_map_map_and(map1, map2,
9084 &map_domain_product_aligned);
9087 __isl_give isl_map *isl_map_range_product(__isl_take isl_map *map1,
9088 __isl_take isl_map *map2)
9090 return isl_map_align_params_map_map_and(map1, map2,
9091 &map_range_product_aligned);
9094 /* Given two maps A -> B and C -> D, construct a map (A, C) -> (B * D)
9096 __isl_give isl_map *isl_map_flat_domain_product(__isl_take isl_map *map1,
9097 __isl_take isl_map *map2)
9101 prod = isl_map_domain_product(map1, map2);
9102 prod = isl_map_flatten_domain(prod);
9106 /* Given two maps A -> B and C -> D, construct a map (A * C) -> (B, D)
9108 __isl_give isl_map *isl_map_flat_range_product(__isl_take isl_map *map1,
9109 __isl_take isl_map *map2)
9113 prod = isl_map_range_product(map1, map2);
9114 prod = isl_map_flatten_range(prod);
9118 uint32_t isl_basic_map_get_hash(__isl_keep isl_basic_map *bmap)
9121 uint32_t hash = isl_hash_init();
9126 bmap = isl_basic_map_copy(bmap);
9127 bmap = isl_basic_map_normalize(bmap);
9130 total = isl_basic_map_total_dim(bmap);
9131 isl_hash_byte(hash, bmap->n_eq & 0xFF);
9132 for (i = 0; i < bmap->n_eq; ++i) {
9134 c_hash = isl_seq_get_hash(bmap->eq[i], 1 + total);
9135 isl_hash_hash(hash, c_hash);
9137 isl_hash_byte(hash, bmap->n_ineq & 0xFF);
9138 for (i = 0; i < bmap->n_ineq; ++i) {
9140 c_hash = isl_seq_get_hash(bmap->ineq[i], 1 + total);
9141 isl_hash_hash(hash, c_hash);
9143 isl_hash_byte(hash, bmap->n_div & 0xFF);
9144 for (i = 0; i < bmap->n_div; ++i) {
9146 if (isl_int_is_zero(bmap->div[i][0]))
9148 isl_hash_byte(hash, i & 0xFF);
9149 c_hash = isl_seq_get_hash(bmap->div[i], 1 + 1 + total);
9150 isl_hash_hash(hash, c_hash);
9152 isl_basic_map_free(bmap);
9156 uint32_t isl_basic_set_get_hash(__isl_keep isl_basic_set *bset)
9158 return isl_basic_map_get_hash((isl_basic_map *)bset);
9161 uint32_t isl_map_get_hash(__isl_keep isl_map *map)
9168 map = isl_map_copy(map);
9169 map = isl_map_normalize(map);
9173 hash = isl_hash_init();
9174 for (i = 0; i < map->n; ++i) {
9176 bmap_hash = isl_basic_map_get_hash(map->p[i]);
9177 isl_hash_hash(hash, bmap_hash);
9185 uint32_t isl_set_get_hash(__isl_keep isl_set *set)
9187 return isl_map_get_hash((isl_map *)set);
9190 /* Check if the value for dimension dim is completely determined
9191 * by the values of the other parameters and variables.
9192 * That is, check if dimension dim is involved in an equality.
9194 int isl_basic_set_dim_is_unique(struct isl_basic_set *bset, unsigned dim)
9201 nparam = isl_basic_set_n_param(bset);
9202 for (i = 0; i < bset->n_eq; ++i)
9203 if (!isl_int_is_zero(bset->eq[i][1 + nparam + dim]))
9208 /* Check if the value for dimension dim is completely determined
9209 * by the values of the other parameters and variables.
9210 * That is, check if dimension dim is involved in an equality
9211 * for each of the subsets.
9213 int isl_set_dim_is_unique(struct isl_set *set, unsigned dim)
9219 for (i = 0; i < set->n; ++i) {
9221 unique = isl_basic_set_dim_is_unique(set->p[i], dim);
9228 int isl_set_n_basic_set(__isl_keep isl_set *set)
9230 return set ? set->n : 0;
9233 int isl_map_foreach_basic_map(__isl_keep isl_map *map,
9234 int (*fn)(__isl_take isl_basic_map *bmap, void *user), void *user)
9241 for (i = 0; i < map->n; ++i)
9242 if (fn(isl_basic_map_copy(map->p[i]), user) < 0)
9248 int isl_set_foreach_basic_set(__isl_keep isl_set *set,
9249 int (*fn)(__isl_take isl_basic_set *bset, void *user), void *user)
9256 for (i = 0; i < set->n; ++i)
9257 if (fn(isl_basic_set_copy(set->p[i]), user) < 0)
9263 __isl_give isl_basic_set *isl_basic_set_lift(__isl_take isl_basic_set *bset)
9270 bset = isl_basic_set_cow(bset);
9274 dim = isl_basic_set_get_space(bset);
9275 dim = isl_space_lift(dim, bset->n_div);
9278 isl_space_free(bset->dim);
9280 bset->extra -= bset->n_div;
9283 bset = isl_basic_set_finalize(bset);
9287 isl_basic_set_free(bset);
9291 __isl_give isl_set *isl_set_lift(__isl_take isl_set *set)
9297 set = isl_set_align_divs(set);
9302 set = isl_set_cow(set);
9306 n_div = set->p[0]->n_div;
9307 dim = isl_set_get_space(set);
9308 dim = isl_space_lift(dim, n_div);
9311 isl_space_free(set->dim);
9314 for (i = 0; i < set->n; ++i) {
9315 set->p[i] = isl_basic_set_lift(set->p[i]);
9326 __isl_give isl_map *isl_set_lifting(__isl_take isl_set *set)
9329 struct isl_basic_map *bmap;
9336 set = isl_set_align_divs(set);
9341 dim = isl_set_get_space(set);
9342 if (set->n == 0 || set->p[0]->n_div == 0) {
9344 return isl_map_identity(isl_space_map_from_set(dim));
9347 n_div = set->p[0]->n_div;
9348 dim = isl_space_map_from_set(dim);
9349 n_param = isl_space_dim(dim, isl_dim_param);
9350 n_set = isl_space_dim(dim, isl_dim_in);
9351 dim = isl_space_extend(dim, n_param, n_set, n_set + n_div);
9352 bmap = isl_basic_map_alloc_space(dim, 0, n_set, 2 * n_div);
9353 for (i = 0; i < n_set; ++i)
9354 bmap = var_equal(bmap, i);
9356 total = n_param + n_set + n_set + n_div;
9357 for (i = 0; i < n_div; ++i) {
9358 k = isl_basic_map_alloc_inequality(bmap);
9361 isl_seq_cpy(bmap->ineq[k], set->p[0]->div[i]+1, 1+n_param);
9362 isl_seq_clr(bmap->ineq[k]+1+n_param, n_set);
9363 isl_seq_cpy(bmap->ineq[k]+1+n_param+n_set,
9364 set->p[0]->div[i]+1+1+n_param, n_set + n_div);
9365 isl_int_neg(bmap->ineq[k][1+n_param+n_set+n_set+i],
9366 set->p[0]->div[i][0]);
9368 l = isl_basic_map_alloc_inequality(bmap);
9371 isl_seq_neg(bmap->ineq[l], bmap->ineq[k], 1 + total);
9372 isl_int_add(bmap->ineq[l][0], bmap->ineq[l][0],
9373 set->p[0]->div[i][0]);
9374 isl_int_sub_ui(bmap->ineq[l][0], bmap->ineq[l][0], 1);
9378 bmap = isl_basic_map_simplify(bmap);
9379 bmap = isl_basic_map_finalize(bmap);
9380 return isl_map_from_basic_map(bmap);
9383 isl_basic_map_free(bmap);
9387 int isl_basic_set_size(__isl_keep isl_basic_set *bset)
9395 dim = isl_basic_set_total_dim(bset);
9396 size += bset->n_eq * (1 + dim);
9397 size += bset->n_ineq * (1 + dim);
9398 size += bset->n_div * (2 + dim);
9403 int isl_set_size(__isl_keep isl_set *set)
9411 for (i = 0; i < set->n; ++i)
9412 size += isl_basic_set_size(set->p[i]);
9417 /* Check if there is any lower bound (if lower == 0) and/or upper
9418 * bound (if upper == 0) on the specified dim.
9420 static int basic_map_dim_is_bounded(__isl_keep isl_basic_map *bmap,
9421 enum isl_dim_type type, unsigned pos, int lower, int upper)
9428 isl_assert(bmap->ctx, pos < isl_basic_map_dim(bmap, type), return -1);
9430 pos += isl_basic_map_offset(bmap, type);
9432 for (i = 0; i < bmap->n_div; ++i) {
9433 if (isl_int_is_zero(bmap->div[i][0]))
9435 if (!isl_int_is_zero(bmap->div[i][1 + pos]))
9439 for (i = 0; i < bmap->n_eq; ++i)
9440 if (!isl_int_is_zero(bmap->eq[i][pos]))
9443 for (i = 0; i < bmap->n_ineq; ++i) {
9444 int sgn = isl_int_sgn(bmap->ineq[i][pos]);
9451 return lower && upper;
9454 int isl_basic_map_dim_is_bounded(__isl_keep isl_basic_map *bmap,
9455 enum isl_dim_type type, unsigned pos)
9457 return basic_map_dim_is_bounded(bmap, type, pos, 0, 0);
9460 int isl_basic_map_dim_has_lower_bound(__isl_keep isl_basic_map *bmap,
9461 enum isl_dim_type type, unsigned pos)
9463 return basic_map_dim_is_bounded(bmap, type, pos, 0, 1);
9466 int isl_basic_map_dim_has_upper_bound(__isl_keep isl_basic_map *bmap,
9467 enum isl_dim_type type, unsigned pos)
9469 return basic_map_dim_is_bounded(bmap, type, pos, 1, 0);
9472 int isl_map_dim_is_bounded(__isl_keep isl_map *map,
9473 enum isl_dim_type type, unsigned pos)
9480 for (i = 0; i < map->n; ++i) {
9482 bounded = isl_basic_map_dim_is_bounded(map->p[i], type, pos);
9483 if (bounded < 0 || !bounded)
9490 /* Return 1 if the specified dim is involved in both an upper bound
9491 * and a lower bound.
9493 int isl_set_dim_is_bounded(__isl_keep isl_set *set,
9494 enum isl_dim_type type, unsigned pos)
9496 return isl_map_dim_is_bounded((isl_map *)set, type, pos);
9499 /* Does "map" have a bound (according to "fn") for any of its basic maps?
9501 static int has_any_bound(__isl_keep isl_map *map,
9502 enum isl_dim_type type, unsigned pos,
9503 int (*fn)(__isl_keep isl_basic_map *bmap,
9504 enum isl_dim_type type, unsigned pos))
9511 for (i = 0; i < map->n; ++i) {
9513 bounded = fn(map->p[i], type, pos);
9514 if (bounded < 0 || bounded)
9521 /* Return 1 if the specified dim is involved in any lower bound.
9523 int isl_set_dim_has_any_lower_bound(__isl_keep isl_set *set,
9524 enum isl_dim_type type, unsigned pos)
9526 return has_any_bound(set, type, pos,
9527 &isl_basic_map_dim_has_lower_bound);
9530 /* Return 1 if the specified dim is involved in any upper bound.
9532 int isl_set_dim_has_any_upper_bound(__isl_keep isl_set *set,
9533 enum isl_dim_type type, unsigned pos)
9535 return has_any_bound(set, type, pos,
9536 &isl_basic_map_dim_has_upper_bound);
9539 /* Does "map" have a bound (according to "fn") for all of its basic maps?
9541 static int has_bound(__isl_keep isl_map *map,
9542 enum isl_dim_type type, unsigned pos,
9543 int (*fn)(__isl_keep isl_basic_map *bmap,
9544 enum isl_dim_type type, unsigned pos))
9551 for (i = 0; i < map->n; ++i) {
9553 bounded = fn(map->p[i], type, pos);
9554 if (bounded < 0 || !bounded)
9561 /* Return 1 if the specified dim has a lower bound (in each of its basic sets).
9563 int isl_set_dim_has_lower_bound(__isl_keep isl_set *set,
9564 enum isl_dim_type type, unsigned pos)
9566 return has_bound(set, type, pos, &isl_basic_map_dim_has_lower_bound);
9569 /* Return 1 if the specified dim has an upper bound (in each of its basic sets).
9571 int isl_set_dim_has_upper_bound(__isl_keep isl_set *set,
9572 enum isl_dim_type type, unsigned pos)
9574 return has_bound(set, type, pos, &isl_basic_map_dim_has_upper_bound);
9577 /* For each of the "n" variables starting at "first", determine
9578 * the sign of the variable and put the results in the first "n"
9579 * elements of the array "signs".
9581 * 1 means that the variable is non-negative
9582 * -1 means that the variable is non-positive
9583 * 0 means the variable attains both positive and negative values.
9585 int isl_basic_set_vars_get_sign(__isl_keep isl_basic_set *bset,
9586 unsigned first, unsigned n, int *signs)
9588 isl_vec *bound = NULL;
9589 struct isl_tab *tab = NULL;
9590 struct isl_tab_undo *snap;
9593 if (!bset || !signs)
9596 bound = isl_vec_alloc(bset->ctx, 1 + isl_basic_set_total_dim(bset));
9597 tab = isl_tab_from_basic_set(bset, 0);
9601 isl_seq_clr(bound->el, bound->size);
9602 isl_int_set_si(bound->el[0], -1);
9604 snap = isl_tab_snap(tab);
9605 for (i = 0; i < n; ++i) {
9608 isl_int_set_si(bound->el[1 + first + i], -1);
9609 if (isl_tab_add_ineq(tab, bound->el) < 0)
9612 isl_int_set_si(bound->el[1 + first + i], 0);
9613 if (isl_tab_rollback(tab, snap) < 0)
9621 isl_int_set_si(bound->el[1 + first + i], 1);
9622 if (isl_tab_add_ineq(tab, bound->el) < 0)
9625 isl_int_set_si(bound->el[1 + first + i], 0);
9626 if (isl_tab_rollback(tab, snap) < 0)
9629 signs[i] = empty ? -1 : 0;
9633 isl_vec_free(bound);
9637 isl_vec_free(bound);
9641 int isl_basic_set_dims_get_sign(__isl_keep isl_basic_set *bset,
9642 enum isl_dim_type type, unsigned first, unsigned n, int *signs)
9644 if (!bset || !signs)
9646 isl_assert(bset->ctx, first + n <= isl_basic_set_dim(bset, type),
9649 first += pos(bset->dim, type) - 1;
9650 return isl_basic_set_vars_get_sign(bset, first, n, signs);
9653 /* Check if the given basic map is obviously single-valued.
9654 * In particular, for each output dimension, check that there is
9655 * an equality that defines the output dimension in terms of
9656 * earlier dimensions.
9658 int isl_basic_map_plain_is_single_valued(__isl_keep isl_basic_map *bmap)
9668 total = 1 + isl_basic_map_total_dim(bmap);
9669 n_out = isl_basic_map_dim(bmap, isl_dim_out);
9670 o_out = isl_basic_map_offset(bmap, isl_dim_out);
9672 for (i = 0; i < n_out; ++i) {
9673 for (j = 0; j < bmap->n_eq; ++j) {
9674 if (isl_int_is_zero(bmap->eq[j][o_out + i]))
9676 if (isl_seq_first_non_zero(bmap->eq[j] + o_out + i + 1,
9677 total - (o_out + i + 1)) == -1)
9680 if (j >= bmap->n_eq)
9687 /* Check if the given basic map is single-valued.
9692 * and check if the result is a subset of the identity mapping.
9694 int isl_basic_map_is_single_valued(__isl_keep isl_basic_map *bmap)
9697 isl_basic_map *test;
9701 sv = isl_basic_map_plain_is_single_valued(bmap);
9705 test = isl_basic_map_reverse(isl_basic_map_copy(bmap));
9706 test = isl_basic_map_apply_range(test, isl_basic_map_copy(bmap));
9708 space = isl_basic_map_get_space(bmap);
9709 space = isl_space_map_from_set(isl_space_range(space));
9710 id = isl_basic_map_identity(space);
9712 sv = isl_basic_map_is_subset(test, id);
9714 isl_basic_map_free(test);
9715 isl_basic_map_free(id);
9720 /* Check if the given map is obviously single-valued.
9722 int isl_map_plain_is_single_valued(__isl_keep isl_map *map)
9731 return isl_basic_map_plain_is_single_valued(map->p[0]);
9734 /* Check if the given map is single-valued.
9739 * and check if the result is a subset of the identity mapping.
9741 int isl_map_is_single_valued(__isl_keep isl_map *map)
9748 sv = isl_map_plain_is_single_valued(map);
9752 test = isl_map_reverse(isl_map_copy(map));
9753 test = isl_map_apply_range(test, isl_map_copy(map));
9755 dim = isl_space_map_from_set(isl_space_range(isl_map_get_space(map)));
9756 id = isl_map_identity(dim);
9758 sv = isl_map_is_subset(test, id);
9766 int isl_map_is_injective(__isl_keep isl_map *map)
9770 map = isl_map_copy(map);
9771 map = isl_map_reverse(map);
9772 in = isl_map_is_single_valued(map);
9778 /* Check if the given map is obviously injective.
9780 int isl_map_plain_is_injective(__isl_keep isl_map *map)
9784 map = isl_map_copy(map);
9785 map = isl_map_reverse(map);
9786 in = isl_map_plain_is_single_valued(map);
9792 int isl_map_is_bijective(__isl_keep isl_map *map)
9796 sv = isl_map_is_single_valued(map);
9800 return isl_map_is_injective(map);
9803 int isl_set_is_singleton(__isl_keep isl_set *set)
9805 return isl_map_is_single_valued((isl_map *)set);
9808 int isl_map_is_translation(__isl_keep isl_map *map)
9813 delta = isl_map_deltas(isl_map_copy(map));
9814 ok = isl_set_is_singleton(delta);
9815 isl_set_free(delta);
9820 static int unique(isl_int *p, unsigned pos, unsigned len)
9822 if (isl_seq_first_non_zero(p, pos) != -1)
9824 if (isl_seq_first_non_zero(p + pos + 1, len - pos - 1) != -1)
9829 int isl_basic_set_is_box(__isl_keep isl_basic_set *bset)
9838 if (isl_basic_set_dim(bset, isl_dim_div) != 0)
9841 nvar = isl_basic_set_dim(bset, isl_dim_set);
9842 ovar = isl_space_offset(bset->dim, isl_dim_set);
9843 for (j = 0; j < nvar; ++j) {
9844 int lower = 0, upper = 0;
9845 for (i = 0; i < bset->n_eq; ++i) {
9846 if (isl_int_is_zero(bset->eq[i][1 + ovar + j]))
9848 if (!unique(bset->eq[i] + 1 + ovar, j, nvar))
9854 for (i = 0; i < bset->n_ineq; ++i) {
9855 if (isl_int_is_zero(bset->ineq[i][1 + ovar + j]))
9857 if (!unique(bset->ineq[i] + 1 + ovar, j, nvar))
9859 if (isl_int_is_pos(bset->ineq[i][1 + ovar + j]))
9864 if (!lower || !upper)
9871 int isl_set_is_box(__isl_keep isl_set *set)
9878 return isl_basic_set_is_box(set->p[0]);
9881 int isl_basic_set_is_wrapping(__isl_keep isl_basic_set *bset)
9886 return isl_space_is_wrapping(bset->dim);
9889 int isl_set_is_wrapping(__isl_keep isl_set *set)
9894 return isl_space_is_wrapping(set->dim);
9897 __isl_give isl_basic_set *isl_basic_map_wrap(__isl_take isl_basic_map *bmap)
9899 bmap = isl_basic_map_cow(bmap);
9903 bmap->dim = isl_space_wrap(bmap->dim);
9907 bmap = isl_basic_map_finalize(bmap);
9909 return (isl_basic_set *)bmap;
9911 isl_basic_map_free(bmap);
9915 __isl_give isl_set *isl_map_wrap(__isl_take isl_map *map)
9919 map = isl_map_cow(map);
9923 for (i = 0; i < map->n; ++i) {
9924 map->p[i] = (isl_basic_map *)isl_basic_map_wrap(map->p[i]);
9928 map->dim = isl_space_wrap(map->dim);
9932 return (isl_set *)map;
9938 __isl_give isl_basic_map *isl_basic_set_unwrap(__isl_take isl_basic_set *bset)
9940 bset = isl_basic_set_cow(bset);
9944 bset->dim = isl_space_unwrap(bset->dim);
9948 bset = isl_basic_set_finalize(bset);
9950 return (isl_basic_map *)bset;
9952 isl_basic_set_free(bset);
9956 __isl_give isl_map *isl_set_unwrap(__isl_take isl_set *set)
9963 if (!isl_set_is_wrapping(set))
9964 isl_die(set->ctx, isl_error_invalid, "not a wrapping set",
9967 set = isl_set_cow(set);
9971 for (i = 0; i < set->n; ++i) {
9972 set->p[i] = (isl_basic_set *)isl_basic_set_unwrap(set->p[i]);
9977 set->dim = isl_space_unwrap(set->dim);
9981 return (isl_map *)set;
9987 __isl_give isl_basic_map *isl_basic_map_reset(__isl_take isl_basic_map *bmap,
9988 enum isl_dim_type type)
9993 if (!isl_space_is_named_or_nested(bmap->dim, type))
9996 bmap = isl_basic_map_cow(bmap);
10000 bmap->dim = isl_space_reset(bmap->dim, type);
10004 bmap = isl_basic_map_finalize(bmap);
10008 isl_basic_map_free(bmap);
10012 __isl_give isl_map *isl_map_reset(__isl_take isl_map *map,
10013 enum isl_dim_type type)
10020 if (!isl_space_is_named_or_nested(map->dim, type))
10023 map = isl_map_cow(map);
10027 for (i = 0; i < map->n; ++i) {
10028 map->p[i] = isl_basic_map_reset(map->p[i], type);
10032 map->dim = isl_space_reset(map->dim, type);
10042 __isl_give isl_basic_map *isl_basic_map_flatten(__isl_take isl_basic_map *bmap)
10047 if (!bmap->dim->nested[0] && !bmap->dim->nested[1])
10050 bmap = isl_basic_map_cow(bmap);
10054 bmap->dim = isl_space_flatten(bmap->dim);
10058 bmap = isl_basic_map_finalize(bmap);
10062 isl_basic_map_free(bmap);
10066 __isl_give isl_basic_set *isl_basic_set_flatten(__isl_take isl_basic_set *bset)
10068 return (isl_basic_set *)isl_basic_map_flatten((isl_basic_map *)bset);
10071 __isl_give isl_basic_map *isl_basic_map_flatten_domain(
10072 __isl_take isl_basic_map *bmap)
10077 if (!bmap->dim->nested[0])
10080 bmap = isl_basic_map_cow(bmap);
10084 bmap->dim = isl_space_flatten_domain(bmap->dim);
10088 bmap = isl_basic_map_finalize(bmap);
10092 isl_basic_map_free(bmap);
10096 __isl_give isl_basic_map *isl_basic_map_flatten_range(
10097 __isl_take isl_basic_map *bmap)
10102 if (!bmap->dim->nested[1])
10105 bmap = isl_basic_map_cow(bmap);
10109 bmap->dim = isl_space_flatten_range(bmap->dim);
10113 bmap = isl_basic_map_finalize(bmap);
10117 isl_basic_map_free(bmap);
10121 __isl_give isl_map *isl_map_flatten(__isl_take isl_map *map)
10128 if (!map->dim->nested[0] && !map->dim->nested[1])
10131 map = isl_map_cow(map);
10135 for (i = 0; i < map->n; ++i) {
10136 map->p[i] = isl_basic_map_flatten(map->p[i]);
10140 map->dim = isl_space_flatten(map->dim);
10150 __isl_give isl_set *isl_set_flatten(__isl_take isl_set *set)
10152 return (isl_set *)isl_map_flatten((isl_map *)set);
10155 __isl_give isl_map *isl_set_flatten_map(__isl_take isl_set *set)
10157 isl_space *dim, *flat_dim;
10160 dim = isl_set_get_space(set);
10161 flat_dim = isl_space_flatten(isl_space_copy(dim));
10162 map = isl_map_identity(isl_space_join(isl_space_reverse(dim), flat_dim));
10163 map = isl_map_intersect_domain(map, set);
10168 __isl_give isl_map *isl_map_flatten_domain(__isl_take isl_map *map)
10175 if (!map->dim->nested[0])
10178 map = isl_map_cow(map);
10182 for (i = 0; i < map->n; ++i) {
10183 map->p[i] = isl_basic_map_flatten_domain(map->p[i]);
10187 map->dim = isl_space_flatten_domain(map->dim);
10197 __isl_give isl_map *isl_map_flatten_range(__isl_take isl_map *map)
10204 if (!map->dim->nested[1])
10207 map = isl_map_cow(map);
10211 for (i = 0; i < map->n; ++i) {
10212 map->p[i] = isl_basic_map_flatten_range(map->p[i]);
10216 map->dim = isl_space_flatten_range(map->dim);
10226 /* Reorder the dimensions of "bmap" according to the given dim_map
10227 * and set the dimension specification to "dim".
10229 __isl_give isl_basic_map *isl_basic_map_realign(__isl_take isl_basic_map *bmap,
10230 __isl_take isl_space *dim, __isl_take struct isl_dim_map *dim_map)
10232 isl_basic_map *res;
10235 bmap = isl_basic_map_cow(bmap);
10236 if (!bmap || !dim || !dim_map)
10239 flags = bmap->flags;
10240 ISL_FL_CLR(flags, ISL_BASIC_MAP_FINAL);
10241 ISL_FL_CLR(flags, ISL_BASIC_MAP_NORMALIZED);
10242 ISL_FL_CLR(flags, ISL_BASIC_MAP_NORMALIZED_DIVS);
10243 res = isl_basic_map_alloc_space(dim,
10244 bmap->n_div, bmap->n_eq, bmap->n_ineq);
10245 res = isl_basic_map_add_constraints_dim_map(res, bmap, dim_map);
10247 res->flags = flags;
10248 res = isl_basic_map_finalize(res);
10252 isl_basic_map_free(bmap);
10253 isl_space_free(dim);
10257 /* Reorder the dimensions of "map" according to given reordering.
10259 __isl_give isl_map *isl_map_realign(__isl_take isl_map *map,
10260 __isl_take isl_reordering *r)
10263 struct isl_dim_map *dim_map;
10265 map = isl_map_cow(map);
10266 dim_map = isl_dim_map_from_reordering(r);
10267 if (!map || !r || !dim_map)
10270 for (i = 0; i < map->n; ++i) {
10271 struct isl_dim_map *dim_map_i;
10273 dim_map_i = isl_dim_map_extend(dim_map, map->p[i]);
10275 map->p[i] = isl_basic_map_realign(map->p[i],
10276 isl_space_copy(r->dim), dim_map_i);
10282 map = isl_map_reset_space(map, isl_space_copy(r->dim));
10284 isl_reordering_free(r);
10290 isl_reordering_free(r);
10294 __isl_give isl_set *isl_set_realign(__isl_take isl_set *set,
10295 __isl_take isl_reordering *r)
10297 return (isl_set *)isl_map_realign((isl_map *)set, r);
10300 __isl_give isl_map *isl_map_align_params(__isl_take isl_map *map,
10301 __isl_take isl_space *model)
10305 if (!map || !model)
10308 ctx = isl_space_get_ctx(model);
10309 if (!isl_space_has_named_params(model))
10310 isl_die(ctx, isl_error_invalid,
10311 "model has unnamed parameters", goto error);
10312 if (!isl_space_has_named_params(map->dim))
10313 isl_die(ctx, isl_error_invalid,
10314 "relation has unnamed parameters", goto error);
10315 if (!isl_space_match(map->dim, isl_dim_param, model, isl_dim_param)) {
10316 isl_reordering *exp;
10318 model = isl_space_drop_dims(model, isl_dim_in,
10319 0, isl_space_dim(model, isl_dim_in));
10320 model = isl_space_drop_dims(model, isl_dim_out,
10321 0, isl_space_dim(model, isl_dim_out));
10322 exp = isl_parameter_alignment_reordering(map->dim, model);
10323 exp = isl_reordering_extend_space(exp, isl_map_get_space(map));
10324 map = isl_map_realign(map, exp);
10327 isl_space_free(model);
10330 isl_space_free(model);
10335 __isl_give isl_set *isl_set_align_params(__isl_take isl_set *set,
10336 __isl_take isl_space *model)
10338 return isl_map_align_params(set, model);
10341 /* Align the parameters of "bmap" to those of "model", introducing
10342 * additional parameters if needed.
10344 __isl_give isl_basic_map *isl_basic_map_align_params(
10345 __isl_take isl_basic_map *bmap, __isl_take isl_space *model)
10349 if (!bmap || !model)
10352 ctx = isl_space_get_ctx(model);
10353 if (!isl_space_has_named_params(model))
10354 isl_die(ctx, isl_error_invalid,
10355 "model has unnamed parameters", goto error);
10356 if (!isl_space_has_named_params(bmap->dim))
10357 isl_die(ctx, isl_error_invalid,
10358 "relation has unnamed parameters", goto error);
10359 if (!isl_space_match(bmap->dim, isl_dim_param, model, isl_dim_param)) {
10360 isl_reordering *exp;
10361 struct isl_dim_map *dim_map;
10363 model = isl_space_drop_dims(model, isl_dim_in,
10364 0, isl_space_dim(model, isl_dim_in));
10365 model = isl_space_drop_dims(model, isl_dim_out,
10366 0, isl_space_dim(model, isl_dim_out));
10367 exp = isl_parameter_alignment_reordering(bmap->dim, model);
10368 exp = isl_reordering_extend_space(exp,
10369 isl_basic_map_get_space(bmap));
10370 dim_map = isl_dim_map_from_reordering(exp);
10371 bmap = isl_basic_map_realign(bmap,
10372 exp ? isl_space_copy(exp->dim) : NULL,
10373 isl_dim_map_extend(dim_map, bmap));
10374 isl_reordering_free(exp);
10378 isl_space_free(model);
10381 isl_space_free(model);
10382 isl_basic_map_free(bmap);
10386 /* Align the parameters of "bset" to those of "model", introducing
10387 * additional parameters if needed.
10389 __isl_give isl_basic_set *isl_basic_set_align_params(
10390 __isl_take isl_basic_set *bset, __isl_take isl_space *model)
10392 return isl_basic_map_align_params(bset, model);
10395 __isl_give isl_mat *isl_basic_map_equalities_matrix(
10396 __isl_keep isl_basic_map *bmap, enum isl_dim_type c1,
10397 enum isl_dim_type c2, enum isl_dim_type c3,
10398 enum isl_dim_type c4, enum isl_dim_type c5)
10400 enum isl_dim_type c[5] = { c1, c2, c3, c4, c5 };
10401 struct isl_mat *mat;
10407 mat = isl_mat_alloc(bmap->ctx, bmap->n_eq,
10408 isl_basic_map_total_dim(bmap) + 1);
10411 for (i = 0; i < bmap->n_eq; ++i)
10412 for (j = 0, pos = 0; j < 5; ++j) {
10413 int off = isl_basic_map_offset(bmap, c[j]);
10414 for (k = 0; k < isl_basic_map_dim(bmap, c[j]); ++k) {
10415 isl_int_set(mat->row[i][pos],
10416 bmap->eq[i][off + k]);
10424 __isl_give isl_mat *isl_basic_map_inequalities_matrix(
10425 __isl_keep isl_basic_map *bmap, enum isl_dim_type c1,
10426 enum isl_dim_type c2, enum isl_dim_type c3,
10427 enum isl_dim_type c4, enum isl_dim_type c5)
10429 enum isl_dim_type c[5] = { c1, c2, c3, c4, c5 };
10430 struct isl_mat *mat;
10436 mat = isl_mat_alloc(bmap->ctx, bmap->n_ineq,
10437 isl_basic_map_total_dim(bmap) + 1);
10440 for (i = 0; i < bmap->n_ineq; ++i)
10441 for (j = 0, pos = 0; j < 5; ++j) {
10442 int off = isl_basic_map_offset(bmap, c[j]);
10443 for (k = 0; k < isl_basic_map_dim(bmap, c[j]); ++k) {
10444 isl_int_set(mat->row[i][pos],
10445 bmap->ineq[i][off + k]);
10453 __isl_give isl_basic_map *isl_basic_map_from_constraint_matrices(
10454 __isl_take isl_space *dim,
10455 __isl_take isl_mat *eq, __isl_take isl_mat *ineq, enum isl_dim_type c1,
10456 enum isl_dim_type c2, enum isl_dim_type c3,
10457 enum isl_dim_type c4, enum isl_dim_type c5)
10459 enum isl_dim_type c[5] = { c1, c2, c3, c4, c5 };
10460 isl_basic_map *bmap;
10466 if (!dim || !eq || !ineq)
10469 if (eq->n_col != ineq->n_col)
10470 isl_die(dim->ctx, isl_error_invalid,
10471 "equalities and inequalities matrices should have "
10472 "same number of columns", goto error);
10474 total = 1 + isl_space_dim(dim, isl_dim_all);
10476 if (eq->n_col < total)
10477 isl_die(dim->ctx, isl_error_invalid,
10478 "number of columns too small", goto error);
10480 extra = eq->n_col - total;
10482 bmap = isl_basic_map_alloc_space(isl_space_copy(dim), extra,
10483 eq->n_row, ineq->n_row);
10486 for (i = 0; i < extra; ++i) {
10487 k = isl_basic_map_alloc_div(bmap);
10490 isl_int_set_si(bmap->div[k][0], 0);
10492 for (i = 0; i < eq->n_row; ++i) {
10493 l = isl_basic_map_alloc_equality(bmap);
10496 for (j = 0, pos = 0; j < 5; ++j) {
10497 int off = isl_basic_map_offset(bmap, c[j]);
10498 for (k = 0; k < isl_basic_map_dim(bmap, c[j]); ++k) {
10499 isl_int_set(bmap->eq[l][off + k],
10505 for (i = 0; i < ineq->n_row; ++i) {
10506 l = isl_basic_map_alloc_inequality(bmap);
10509 for (j = 0, pos = 0; j < 5; ++j) {
10510 int off = isl_basic_map_offset(bmap, c[j]);
10511 for (k = 0; k < isl_basic_map_dim(bmap, c[j]); ++k) {
10512 isl_int_set(bmap->ineq[l][off + k],
10513 ineq->row[i][pos]);
10519 isl_space_free(dim);
10521 isl_mat_free(ineq);
10523 bmap = isl_basic_map_simplify(bmap);
10524 return isl_basic_map_finalize(bmap);
10526 isl_space_free(dim);
10528 isl_mat_free(ineq);
10532 __isl_give isl_mat *isl_basic_set_equalities_matrix(
10533 __isl_keep isl_basic_set *bset, enum isl_dim_type c1,
10534 enum isl_dim_type c2, enum isl_dim_type c3, enum isl_dim_type c4)
10536 return isl_basic_map_equalities_matrix((isl_basic_map *)bset,
10537 c1, c2, c3, c4, isl_dim_in);
10540 __isl_give isl_mat *isl_basic_set_inequalities_matrix(
10541 __isl_keep isl_basic_set *bset, enum isl_dim_type c1,
10542 enum isl_dim_type c2, enum isl_dim_type c3, enum isl_dim_type c4)
10544 return isl_basic_map_inequalities_matrix((isl_basic_map *)bset,
10545 c1, c2, c3, c4, isl_dim_in);
10548 __isl_give isl_basic_set *isl_basic_set_from_constraint_matrices(
10549 __isl_take isl_space *dim,
10550 __isl_take isl_mat *eq, __isl_take isl_mat *ineq, enum isl_dim_type c1,
10551 enum isl_dim_type c2, enum isl_dim_type c3, enum isl_dim_type c4)
10553 return (isl_basic_set*)
10554 isl_basic_map_from_constraint_matrices(dim, eq, ineq,
10555 c1, c2, c3, c4, isl_dim_in);
10558 int isl_basic_map_can_zip(__isl_keep isl_basic_map *bmap)
10563 return isl_space_can_zip(bmap->dim);
10566 int isl_map_can_zip(__isl_keep isl_map *map)
10571 return isl_space_can_zip(map->dim);
10574 /* Given a basic map (A -> B) -> (C -> D), return the corresponding basic map
10575 * (A -> C) -> (B -> D).
10577 __isl_give isl_basic_map *isl_basic_map_zip(__isl_take isl_basic_map *bmap)
10586 if (!isl_basic_map_can_zip(bmap))
10587 isl_die(bmap->ctx, isl_error_invalid,
10588 "basic map cannot be zipped", goto error);
10589 pos = isl_basic_map_offset(bmap, isl_dim_in) +
10590 isl_space_dim(bmap->dim->nested[0], isl_dim_in);
10591 n1 = isl_space_dim(bmap->dim->nested[0], isl_dim_out);
10592 n2 = isl_space_dim(bmap->dim->nested[1], isl_dim_in);
10593 bmap = isl_basic_map_cow(bmap);
10594 bmap = isl_basic_map_swap_vars(bmap, pos, n1, n2);
10597 bmap->dim = isl_space_zip(bmap->dim);
10602 isl_basic_map_free(bmap);
10606 /* Given a map (A -> B) -> (C -> D), return the corresponding map
10607 * (A -> C) -> (B -> D).
10609 __isl_give isl_map *isl_map_zip(__isl_take isl_map *map)
10616 if (!isl_map_can_zip(map))
10617 isl_die(map->ctx, isl_error_invalid, "map cannot be zipped",
10620 map = isl_map_cow(map);
10624 for (i = 0; i < map->n; ++i) {
10625 map->p[i] = isl_basic_map_zip(map->p[i]);
10630 map->dim = isl_space_zip(map->dim);
10640 /* Can we apply isl_basic_map_curry to "bmap"?
10641 * That is, does it have a nested relation in its domain?
10643 int isl_basic_map_can_curry(__isl_keep isl_basic_map *bmap)
10648 return isl_space_can_curry(bmap->dim);
10651 /* Can we apply isl_map_curry to "map"?
10652 * That is, does it have a nested relation in its domain?
10654 int isl_map_can_curry(__isl_keep isl_map *map)
10659 return isl_space_can_curry(map->dim);
10662 /* Given a basic map (A -> B) -> C, return the corresponding basic map
10665 __isl_give isl_basic_map *isl_basic_map_curry(__isl_take isl_basic_map *bmap)
10671 if (!isl_basic_map_can_curry(bmap))
10672 isl_die(bmap->ctx, isl_error_invalid,
10673 "basic map cannot be curried", goto error);
10674 bmap = isl_basic_map_cow(bmap);
10677 bmap->dim = isl_space_curry(bmap->dim);
10682 isl_basic_map_free(bmap);
10686 /* Given a map (A -> B) -> C, return the corresponding map
10689 __isl_give isl_map *isl_map_curry(__isl_take isl_map *map)
10696 if (!isl_map_can_curry(map))
10697 isl_die(map->ctx, isl_error_invalid, "map cannot be curried",
10700 map = isl_map_cow(map);
10704 for (i = 0; i < map->n; ++i) {
10705 map->p[i] = isl_basic_map_curry(map->p[i]);
10710 map->dim = isl_space_curry(map->dim);
10720 /* Can we apply isl_basic_map_uncurry to "bmap"?
10721 * That is, does it have a nested relation in its domain?
10723 int isl_basic_map_can_uncurry(__isl_keep isl_basic_map *bmap)
10728 return isl_space_can_uncurry(bmap->dim);
10731 /* Can we apply isl_map_uncurry to "map"?
10732 * That is, does it have a nested relation in its domain?
10734 int isl_map_can_uncurry(__isl_keep isl_map *map)
10739 return isl_space_can_uncurry(map->dim);
10742 /* Given a basic map A -> (B -> C), return the corresponding basic map
10745 __isl_give isl_basic_map *isl_basic_map_uncurry(__isl_take isl_basic_map *bmap)
10751 if (!isl_basic_map_can_uncurry(bmap))
10752 isl_die(bmap->ctx, isl_error_invalid,
10753 "basic map cannot be uncurried",
10754 return isl_basic_map_free(bmap));
10755 bmap = isl_basic_map_cow(bmap);
10758 bmap->dim = isl_space_uncurry(bmap->dim);
10760 return isl_basic_map_free(bmap);
10764 /* Given a map A -> (B -> C), return the corresponding map
10767 __isl_give isl_map *isl_map_uncurry(__isl_take isl_map *map)
10774 if (!isl_map_can_uncurry(map))
10775 isl_die(map->ctx, isl_error_invalid, "map cannot be uncurried",
10776 return isl_map_free(map));
10778 map = isl_map_cow(map);
10782 for (i = 0; i < map->n; ++i) {
10783 map->p[i] = isl_basic_map_uncurry(map->p[i]);
10785 return isl_map_free(map);
10788 map->dim = isl_space_uncurry(map->dim);
10790 return isl_map_free(map);
10795 /* Construct a basic map mapping the domain of the affine expression
10796 * to a one-dimensional range prescribed by the affine expression.
10798 __isl_give isl_basic_map *isl_basic_map_from_aff(__isl_take isl_aff *aff)
10802 isl_local_space *ls;
10803 isl_basic_map *bmap;
10808 ls = isl_aff_get_local_space(aff);
10809 bmap = isl_basic_map_from_local_space(ls);
10810 bmap = isl_basic_map_extend_constraints(bmap, 1, 0);
10811 k = isl_basic_map_alloc_equality(bmap);
10815 pos = isl_basic_map_offset(bmap, isl_dim_out);
10816 isl_seq_cpy(bmap->eq[k], aff->v->el + 1, pos);
10817 isl_int_neg(bmap->eq[k][pos], aff->v->el[0]);
10818 isl_seq_cpy(bmap->eq[k] + pos + 1, aff->v->el + 1 + pos,
10819 aff->v->size - (pos + 1));
10822 bmap = isl_basic_map_finalize(bmap);
10826 isl_basic_map_free(bmap);
10830 /* Construct a map mapping the domain of the affine expression
10831 * to a one-dimensional range prescribed by the affine expression.
10833 __isl_give isl_map *isl_map_from_aff(__isl_take isl_aff *aff)
10835 isl_basic_map *bmap;
10837 bmap = isl_basic_map_from_aff(aff);
10838 return isl_map_from_basic_map(bmap);
10841 /* Construct a basic map mapping the domain the multi-affine expression
10842 * to its range, with each dimension in the range equated to the
10843 * corresponding affine expression.
10845 __isl_give isl_basic_map *isl_basic_map_from_multi_aff(
10846 __isl_take isl_multi_aff *maff)
10850 isl_basic_map *bmap;
10855 if (isl_space_dim(maff->space, isl_dim_out) != maff->n)
10856 isl_die(isl_multi_aff_get_ctx(maff), isl_error_internal,
10857 "invalid space", return isl_multi_aff_free(maff));
10859 space = isl_space_domain(isl_multi_aff_get_space(maff));
10860 bmap = isl_basic_map_universe(isl_space_from_domain(space));
10862 for (i = 0; i < maff->n; ++i) {
10864 isl_basic_map *bmap_i;
10866 aff = isl_aff_copy(maff->p[i]);
10867 bmap_i = isl_basic_map_from_aff(aff);
10869 bmap = isl_basic_map_flat_range_product(bmap, bmap_i);
10872 bmap = isl_basic_map_reset_space(bmap, isl_multi_aff_get_space(maff));
10874 isl_multi_aff_free(maff);
10878 /* Construct a map mapping the domain the multi-affine expression
10879 * to its range, with each dimension in the range equated to the
10880 * corresponding affine expression.
10882 __isl_give isl_map *isl_map_from_multi_aff(__isl_take isl_multi_aff *maff)
10884 isl_basic_map *bmap;
10886 bmap = isl_basic_map_from_multi_aff(maff);
10887 return isl_map_from_basic_map(bmap);
10890 /* Construct a basic map mapping a domain in the given space to
10891 * to an n-dimensional range, with n the number of elements in the list,
10892 * where each coordinate in the range is prescribed by the
10893 * corresponding affine expression.
10894 * The domains of all affine expressions in the list are assumed to match
10897 __isl_give isl_basic_map *isl_basic_map_from_aff_list(
10898 __isl_take isl_space *domain_dim, __isl_take isl_aff_list *list)
10902 isl_basic_map *bmap;
10907 dim = isl_space_from_domain(domain_dim);
10908 bmap = isl_basic_map_universe(dim);
10910 for (i = 0; i < list->n; ++i) {
10912 isl_basic_map *bmap_i;
10914 aff = isl_aff_copy(list->p[i]);
10915 bmap_i = isl_basic_map_from_aff(aff);
10917 bmap = isl_basic_map_flat_range_product(bmap, bmap_i);
10920 isl_aff_list_free(list);
10924 __isl_give isl_set *isl_set_equate(__isl_take isl_set *set,
10925 enum isl_dim_type type1, int pos1, enum isl_dim_type type2, int pos2)
10927 return isl_map_equate(set, type1, pos1, type2, pos2);
10930 /* Construct a basic map where the given dimensions are equal to each other.
10932 static __isl_give isl_basic_map *equator(__isl_take isl_space *space,
10933 enum isl_dim_type type1, int pos1, enum isl_dim_type type2, int pos2)
10935 isl_basic_map *bmap = NULL;
10941 if (pos1 >= isl_space_dim(space, type1))
10942 isl_die(isl_space_get_ctx(space), isl_error_invalid,
10943 "index out of bounds", goto error);
10944 if (pos2 >= isl_space_dim(space, type2))
10945 isl_die(isl_space_get_ctx(space), isl_error_invalid,
10946 "index out of bounds", goto error);
10948 if (type1 == type2 && pos1 == pos2)
10949 return isl_basic_map_universe(space);
10951 bmap = isl_basic_map_alloc_space(isl_space_copy(space), 0, 1, 0);
10952 i = isl_basic_map_alloc_equality(bmap);
10955 isl_seq_clr(bmap->eq[i], 1 + isl_basic_map_total_dim(bmap));
10956 pos1 += isl_basic_map_offset(bmap, type1);
10957 pos2 += isl_basic_map_offset(bmap, type2);
10958 isl_int_set_si(bmap->eq[i][pos1], -1);
10959 isl_int_set_si(bmap->eq[i][pos2], 1);
10960 bmap = isl_basic_map_finalize(bmap);
10961 isl_space_free(space);
10964 isl_space_free(space);
10965 isl_basic_map_free(bmap);
10969 /* Add a constraint imposing that the given two dimensions are equal.
10971 __isl_give isl_basic_map *isl_basic_map_equate(__isl_take isl_basic_map *bmap,
10972 enum isl_dim_type type1, int pos1, enum isl_dim_type type2, int pos2)
10976 eq = equator(isl_basic_map_get_space(bmap), type1, pos1, type2, pos2);
10978 bmap = isl_basic_map_intersect(bmap, eq);
10983 /* Add a constraint imposing that the given two dimensions are equal.
10985 __isl_give isl_map *isl_map_equate(__isl_take isl_map *map,
10986 enum isl_dim_type type1, int pos1, enum isl_dim_type type2, int pos2)
10988 isl_basic_map *bmap;
10990 bmap = equator(isl_map_get_space(map), type1, pos1, type2, pos2);
10992 map = isl_map_intersect(map, isl_map_from_basic_map(bmap));
10997 /* Add a constraint imposing that the given two dimensions have opposite values.
10999 __isl_give isl_map *isl_map_oppose(__isl_take isl_map *map,
11000 enum isl_dim_type type1, int pos1, enum isl_dim_type type2, int pos2)
11002 isl_basic_map *bmap = NULL;
11008 if (pos1 >= isl_map_dim(map, type1))
11009 isl_die(map->ctx, isl_error_invalid,
11010 "index out of bounds", goto error);
11011 if (pos2 >= isl_map_dim(map, type2))
11012 isl_die(map->ctx, isl_error_invalid,
11013 "index out of bounds", goto error);
11015 bmap = isl_basic_map_alloc_space(isl_map_get_space(map), 0, 1, 0);
11016 i = isl_basic_map_alloc_equality(bmap);
11019 isl_seq_clr(bmap->eq[i], 1 + isl_basic_map_total_dim(bmap));
11020 pos1 += isl_basic_map_offset(bmap, type1);
11021 pos2 += isl_basic_map_offset(bmap, type2);
11022 isl_int_set_si(bmap->eq[i][pos1], 1);
11023 isl_int_set_si(bmap->eq[i][pos2], 1);
11024 bmap = isl_basic_map_finalize(bmap);
11026 map = isl_map_intersect(map, isl_map_from_basic_map(bmap));
11030 isl_basic_map_free(bmap);
11035 /* Add a constraint imposing that the value of the first dimension is
11036 * greater than or equal to that of the second.
11038 __isl_give isl_basic_map *isl_basic_map_order_ge(__isl_take isl_basic_map *bmap,
11039 enum isl_dim_type type1, int pos1, enum isl_dim_type type2, int pos2)
11042 isl_local_space *ls;
11047 if (pos1 >= isl_basic_map_dim(bmap, type1))
11048 isl_die(bmap->ctx, isl_error_invalid,
11049 "index out of bounds", return isl_basic_map_free(bmap));
11050 if (pos2 >= isl_basic_map_dim(bmap, type2))
11051 isl_die(bmap->ctx, isl_error_invalid,
11052 "index out of bounds", return isl_basic_map_free(bmap));
11054 if (type1 == type2 && pos1 == pos2)
11057 ls = isl_local_space_from_space(isl_basic_map_get_space(bmap));
11058 c = isl_inequality_alloc(ls);
11059 c = isl_constraint_set_coefficient_si(c, type1, pos1, 1);
11060 c = isl_constraint_set_coefficient_si(c, type2, pos2, -1);
11061 bmap = isl_basic_map_add_constraint(bmap, c);
11066 /* Construct a basic map where the value of the first dimension is
11067 * greater than that of the second.
11069 static __isl_give isl_basic_map *greator(__isl_take isl_space *space,
11070 enum isl_dim_type type1, int pos1, enum isl_dim_type type2, int pos2)
11072 isl_basic_map *bmap = NULL;
11078 if (pos1 >= isl_space_dim(space, type1))
11079 isl_die(isl_space_get_ctx(space), isl_error_invalid,
11080 "index out of bounds", goto error);
11081 if (pos2 >= isl_space_dim(space, type2))
11082 isl_die(isl_space_get_ctx(space), isl_error_invalid,
11083 "index out of bounds", goto error);
11085 if (type1 == type2 && pos1 == pos2)
11086 return isl_basic_map_empty(space);
11088 bmap = isl_basic_map_alloc_space(space, 0, 0, 1);
11089 i = isl_basic_map_alloc_inequality(bmap);
11092 isl_seq_clr(bmap->ineq[i], 1 + isl_basic_map_total_dim(bmap));
11093 pos1 += isl_basic_map_offset(bmap, type1);
11094 pos2 += isl_basic_map_offset(bmap, type2);
11095 isl_int_set_si(bmap->ineq[i][pos1], 1);
11096 isl_int_set_si(bmap->ineq[i][pos2], -1);
11097 isl_int_set_si(bmap->ineq[i][0], -1);
11098 bmap = isl_basic_map_finalize(bmap);
11102 isl_space_free(space);
11103 isl_basic_map_free(bmap);
11107 /* Add a constraint imposing that the value of the first dimension is
11108 * greater than that of the second.
11110 __isl_give isl_basic_map *isl_basic_map_order_gt(__isl_take isl_basic_map *bmap,
11111 enum isl_dim_type type1, int pos1, enum isl_dim_type type2, int pos2)
11115 gt = greator(isl_basic_map_get_space(bmap), type1, pos1, type2, pos2);
11117 bmap = isl_basic_map_intersect(bmap, gt);
11122 /* Add a constraint imposing that the value of the first dimension is
11123 * greater than that of the second.
11125 __isl_give isl_map *isl_map_order_gt(__isl_take isl_map *map,
11126 enum isl_dim_type type1, int pos1, enum isl_dim_type type2, int pos2)
11128 isl_basic_map *bmap;
11130 bmap = greator(isl_map_get_space(map), type1, pos1, type2, pos2);
11132 map = isl_map_intersect(map, isl_map_from_basic_map(bmap));
11137 /* Add a constraint imposing that the value of the first dimension is
11138 * smaller than that of the second.
11140 __isl_give isl_map *isl_map_order_lt(__isl_take isl_map *map,
11141 enum isl_dim_type type1, int pos1, enum isl_dim_type type2, int pos2)
11143 return isl_map_order_gt(map, type2, pos2, type1, pos1);
11146 __isl_give isl_aff *isl_basic_map_get_div(__isl_keep isl_basic_map *bmap,
11150 isl_local_space *ls;
11155 if (!isl_basic_map_divs_known(bmap))
11156 isl_die(isl_basic_map_get_ctx(bmap), isl_error_invalid,
11157 "some divs are unknown", return NULL);
11159 ls = isl_basic_map_get_local_space(bmap);
11160 div = isl_local_space_get_div(ls, pos);
11161 isl_local_space_free(ls);
11166 __isl_give isl_aff *isl_basic_set_get_div(__isl_keep isl_basic_set *bset,
11169 return isl_basic_map_get_div(bset, pos);
11172 /* Plug in "subs" for dimension "type", "pos" of "bset".
11174 * Let i be the dimension to replace and let "subs" be of the form
11178 * Any integer division with a non-zero coefficient for i,
11180 * floor((a i + g)/m)
11184 * floor((a f + d g)/(m d))
11186 * Constraints of the form
11194 * We currently require that "subs" is an integral expression.
11195 * Handling rational expressions may require us to add stride constraints
11196 * as we do in isl_basic_set_preimage_multi_aff.
11198 __isl_give isl_basic_set *isl_basic_set_substitute(
11199 __isl_take isl_basic_set *bset,
11200 enum isl_dim_type type, unsigned pos, __isl_keep isl_aff *subs)
11206 if (bset && isl_basic_set_plain_is_empty(bset))
11209 bset = isl_basic_set_cow(bset);
11210 if (!bset || !subs)
11213 ctx = isl_basic_set_get_ctx(bset);
11214 if (!isl_space_is_equal(bset->dim, subs->ls->dim))
11215 isl_die(ctx, isl_error_invalid,
11216 "spaces don't match", goto error);
11217 if (isl_local_space_dim(subs->ls, isl_dim_div) != 0)
11218 isl_die(ctx, isl_error_unsupported,
11219 "cannot handle divs yet", goto error);
11220 if (!isl_int_is_one(subs->v->el[0]))
11221 isl_die(ctx, isl_error_invalid,
11222 "can only substitute integer expressions", goto error);
11224 pos += isl_basic_set_offset(bset, type);
11228 for (i = 0; i < bset->n_eq; ++i) {
11229 if (isl_int_is_zero(bset->eq[i][pos]))
11231 isl_int_set(v, bset->eq[i][pos]);
11232 isl_int_set_si(bset->eq[i][pos], 0);
11233 isl_seq_combine(bset->eq[i], subs->v->el[0], bset->eq[i],
11234 v, subs->v->el + 1, subs->v->size - 1);
11237 for (i = 0; i < bset->n_ineq; ++i) {
11238 if (isl_int_is_zero(bset->ineq[i][pos]))
11240 isl_int_set(v, bset->ineq[i][pos]);
11241 isl_int_set_si(bset->ineq[i][pos], 0);
11242 isl_seq_combine(bset->ineq[i], subs->v->el[0], bset->ineq[i],
11243 v, subs->v->el + 1, subs->v->size - 1);
11246 for (i = 0; i < bset->n_div; ++i) {
11247 if (isl_int_is_zero(bset->div[i][1 + pos]))
11249 isl_int_set(v, bset->div[i][1 + pos]);
11250 isl_int_set_si(bset->div[i][1 + pos], 0);
11251 isl_seq_combine(bset->div[i] + 1,
11252 subs->v->el[0], bset->div[i] + 1,
11253 v, subs->v->el + 1, subs->v->size - 1);
11254 isl_int_mul(bset->div[i][0], bset->div[i][0], subs->v->el[0]);
11259 bset = isl_basic_set_simplify(bset);
11260 return isl_basic_set_finalize(bset);
11262 isl_basic_set_free(bset);
11266 /* Plug in "subs" for dimension "type", "pos" of "set".
11268 __isl_give isl_set *isl_set_substitute(__isl_take isl_set *set,
11269 enum isl_dim_type type, unsigned pos, __isl_keep isl_aff *subs)
11273 if (set && isl_set_plain_is_empty(set))
11276 set = isl_set_cow(set);
11280 for (i = set->n - 1; i >= 0; --i) {
11281 set->p[i] = isl_basic_set_substitute(set->p[i], type, pos, subs);
11282 if (remove_if_empty(set, i) < 0)
11292 /* Check if the range of "ma" is compatible with the domain or range
11293 * (depending on "type") of "bmap".
11294 * Return -1 if anything is wrong.
11296 static int check_basic_map_compatible_range_multi_aff(
11297 __isl_keep isl_basic_map *bmap, enum isl_dim_type type,
11298 __isl_keep isl_multi_aff *ma)
11301 isl_space *ma_space;
11303 ma_space = isl_multi_aff_get_space(ma);
11304 m = isl_space_tuple_match(bmap->dim, type, ma_space, isl_dim_out);
11305 isl_space_free(ma_space);
11307 isl_die(isl_basic_map_get_ctx(bmap), isl_error_invalid,
11308 "spaces don't match", return -1);
11312 /* Copy the divs from "ma" to "bmap", adding zeros for the "n_before"
11313 * coefficients before the transformed range of dimensions,
11314 * the "n_after" coefficients after the transformed range of dimensions
11315 * and the coefficients of the other divs in "bmap".
11317 static int set_ma_divs(__isl_keep isl_basic_map *bmap,
11318 __isl_keep isl_multi_aff *ma, int n_before, int n_after, int n_div)
11323 isl_local_space *ls;
11328 ls = isl_aff_get_domain_local_space(ma->p[0]);
11332 n_param = isl_local_space_dim(ls, isl_dim_param);
11333 n_set = isl_local_space_dim(ls, isl_dim_set);
11334 for (i = 0; i < n_div; ++i) {
11335 int o_bmap = 0, o_ls = 0;
11337 isl_seq_cpy(bmap->div[i], ls->div->row[i], 1 + 1 + n_param);
11338 o_bmap += 1 + 1 + n_param;
11339 o_ls += 1 + 1 + n_param;
11340 isl_seq_clr(bmap->div[i] + o_bmap, n_before);
11341 o_bmap += n_before;
11342 isl_seq_cpy(bmap->div[i] + o_bmap,
11343 ls->div->row[i] + o_ls, n_set);
11346 isl_seq_clr(bmap->div[i] + o_bmap, n_after);
11348 isl_seq_cpy(bmap->div[i] + o_bmap,
11349 ls->div->row[i] + o_ls, n_div);
11352 isl_seq_clr(bmap->div[i] + o_bmap, bmap->n_div - n_div);
11353 if (isl_basic_set_add_div_constraints(bmap, i) < 0)
11357 isl_local_space_free(ls);
11360 isl_local_space_free(ls);
11364 /* How many stride constraints does "ma" enforce?
11365 * That is, how many of the affine expressions have a denominator
11366 * different from one?
11368 static int multi_aff_strides(__isl_keep isl_multi_aff *ma)
11373 for (i = 0; i < ma->n; ++i)
11374 if (!isl_int_is_one(ma->p[i]->v->el[0]))
11380 /* For each affine expression in ma of the form
11382 * x_i = (f_i y + h_i)/m_i
11384 * with m_i different from one, add a constraint to "bmap"
11387 * f_i y + h_i = m_i alpha_i
11389 * with alpha_i an additional existentially quantified variable.
11391 static __isl_give isl_basic_map *add_ma_strides(
11392 __isl_take isl_basic_map *bmap, __isl_keep isl_multi_aff *ma,
11393 int n_before, int n_after)
11402 total = isl_basic_map_total_dim(bmap);
11403 n_param = isl_multi_aff_dim(ma, isl_dim_param);
11404 n_in = isl_multi_aff_dim(ma, isl_dim_in);
11405 n_div = isl_multi_aff_dim(ma, isl_dim_div);
11406 for (i = 0; i < ma->n; ++i) {
11407 int o_bmap = 0, o_ma = 1;
11409 if (isl_int_is_one(ma->p[i]->v->el[0]))
11411 div = isl_basic_map_alloc_div(bmap);
11412 k = isl_basic_map_alloc_equality(bmap);
11413 if (div < 0 || k < 0)
11415 isl_int_set_si(bmap->div[div][0], 0);
11416 isl_seq_cpy(bmap->eq[k] + o_bmap,
11417 ma->p[i]->v->el + o_ma, 1 + n_param);
11418 o_bmap += 1 + n_param;
11419 o_ma += 1 + n_param;
11420 isl_seq_clr(bmap->eq[k] + o_bmap, n_before);
11421 o_bmap += n_before;
11422 isl_seq_cpy(bmap->eq[k] + o_bmap,
11423 ma->p[i]->v->el + o_ma, n_in);
11426 isl_seq_clr(bmap->eq[k] + o_bmap, n_after);
11428 isl_seq_cpy(bmap->eq[k] + o_bmap,
11429 ma->p[i]->v->el + o_ma, n_div);
11432 isl_seq_clr(bmap->eq[k] + o_bmap, 1 + total - o_bmap);
11433 isl_int_neg(bmap->eq[k][1 + total], ma->p[i]->v->el[0]);
11439 isl_basic_map_free(bmap);
11443 /* Replace the domain or range space (depending on "type) of "space" by "set".
11445 static __isl_give isl_space *isl_space_set(__isl_take isl_space *space,
11446 enum isl_dim_type type, __isl_take isl_space *set)
11448 if (type == isl_dim_in) {
11449 space = isl_space_range(space);
11450 space = isl_space_map_from_domain_and_range(set, space);
11452 space = isl_space_domain(space);
11453 space = isl_space_map_from_domain_and_range(space, set);
11459 /* Compute the preimage of the domain or range (depending on "type")
11460 * of "bmap" under the function represented by "ma".
11461 * In other words, plug in "ma" in the domain or range of "bmap".
11462 * The result is a basic map that lives in the same space as "bmap"
11463 * except that the domain or range has been replaced by
11464 * the domain space of "ma".
11466 * If bmap is represented by
11468 * A(p) + S u + B x + T v + C(divs) >= 0,
11470 * where u and x are input and output dimensions if type == isl_dim_out
11471 * while x and v are input and output dimensions if type == isl_dim_in,
11472 * and ma is represented by
11474 * x = D(p) + F(y) + G(divs')
11476 * then the result is
11478 * A(p) + B D(p) + S u + B F(y) + T v + B G(divs') + C(divs) >= 0
11480 * The divs in the input set are similarly adjusted.
11483 * floor((a_i(p) + s u + b_i x + t v + c_i(divs))/n_i)
11487 * floor((a_i(p) + b_i D(p) + s u + b_i F(y) + t v +
11488 * B_i G(divs') + c_i(divs))/n_i)
11490 * If bmap is not a rational map and if F(y) involves any denominators
11492 * x_i = (f_i y + h_i)/m_i
11494 * then additional constraints are added to ensure that we only
11495 * map back integer points. That is we enforce
11497 * f_i y + h_i = m_i alpha_i
11499 * with alpha_i an additional existentially quantified variable.
11501 * We first copy over the divs from "ma".
11502 * Then we add the modified constraints and divs from "bmap".
11503 * Finally, we add the stride constraints, if needed.
11505 __isl_give isl_basic_map *isl_basic_map_preimage_multi_aff(
11506 __isl_take isl_basic_map *bmap, enum isl_dim_type type,
11507 __isl_take isl_multi_aff *ma)
11511 isl_basic_map *res = NULL;
11512 int n_before, n_after, n_div_bmap, n_div_ma;
11513 isl_int f, c1, c2, g;
11514 int rational, strides;
11521 ma = isl_multi_aff_align_divs(ma);
11524 if (check_basic_map_compatible_range_multi_aff(bmap, type, ma) < 0)
11527 if (type == isl_dim_in) {
11529 n_after = isl_basic_map_dim(bmap, isl_dim_out);
11531 n_before = isl_basic_map_dim(bmap, isl_dim_in);
11534 n_div_bmap = isl_basic_map_dim(bmap, isl_dim_div);
11535 n_div_ma = ma->n ? isl_aff_dim(ma->p[0], isl_dim_div) : 0;
11537 space = isl_multi_aff_get_domain_space(ma);
11538 space = isl_space_set(isl_basic_map_get_space(bmap), type, space);
11539 rational = isl_basic_map_is_rational(bmap);
11540 strides = rational ? 0 : multi_aff_strides(ma);
11541 res = isl_basic_map_alloc_space(space, n_div_ma + n_div_bmap + strides,
11542 bmap->n_eq + strides, bmap->n_ineq + 2 * n_div_ma);
11544 res = isl_basic_map_set_rational(res);
11546 for (i = 0; i < n_div_ma + n_div_bmap; ++i)
11547 if (isl_basic_map_alloc_div(res) < 0)
11550 if (set_ma_divs(res, ma, n_before, n_after, n_div_ma) < 0)
11553 for (i = 0; i < bmap->n_eq; ++i) {
11554 k = isl_basic_map_alloc_equality(res);
11557 isl_seq_preimage(res->eq[k], bmap->eq[i], ma, n_before,
11558 n_after, n_div_ma, n_div_bmap, f, c1, c2, g, 0);
11561 for (i = 0; i < bmap->n_ineq; ++i) {
11562 k = isl_basic_map_alloc_inequality(res);
11565 isl_seq_preimage(res->ineq[k], bmap->ineq[i], ma, n_before,
11566 n_after, n_div_ma, n_div_bmap, f, c1, c2, g, 0);
11569 for (i = 0; i < bmap->n_div; ++i) {
11570 if (isl_int_is_zero(bmap->div[i][0])) {
11571 isl_int_set_si(res->div[n_div_ma + i][0], 0);
11574 isl_seq_preimage(res->div[n_div_ma + i], bmap->div[i], ma,
11575 n_before, n_after, n_div_ma, n_div_bmap,
11580 res = add_ma_strides(res, ma, n_before, n_after);
11586 isl_basic_map_free(bmap);
11587 isl_multi_aff_free(ma);
11588 res = isl_basic_set_simplify(res);
11589 return isl_basic_map_finalize(res);
11595 isl_basic_map_free(bmap);
11596 isl_multi_aff_free(ma);
11597 isl_basic_map_free(res);
11601 /* Compute the preimage of "bset" under the function represented by "ma".
11602 * In other words, plug in "ma" in "bset". The result is a basic set
11603 * that lives in the domain space of "ma".
11605 __isl_give isl_basic_set *isl_basic_set_preimage_multi_aff(
11606 __isl_take isl_basic_set *bset, __isl_take isl_multi_aff *ma)
11608 return isl_basic_map_preimage_multi_aff(bset, isl_dim_set, ma);
11611 /* Check if the range of "ma" is compatible with the domain or range
11612 * (depending on "type") of "map".
11613 * Return -1 if anything is wrong.
11615 static int check_map_compatible_range_multi_aff(
11616 __isl_keep isl_map *map, enum isl_dim_type type,
11617 __isl_keep isl_multi_aff *ma)
11620 isl_space *ma_space;
11622 ma_space = isl_multi_aff_get_space(ma);
11623 m = isl_space_tuple_match(map->dim, type, ma_space, isl_dim_out);
11624 isl_space_free(ma_space);
11626 isl_die(isl_map_get_ctx(map), isl_error_invalid,
11627 "spaces don't match", return -1);
11631 /* Compute the preimage of the domain or range (depending on "type")
11632 * of "map" under the function represented by "ma".
11633 * In other words, plug in "ma" in the domain or range of "map".
11634 * The result is a map that lives in the same space as "map"
11635 * except that the domain or range has been replaced by
11636 * the domain space of "ma".
11638 * The parameters are assumed to have been aligned.
11640 static __isl_give isl_map *map_preimage_multi_aff(__isl_take isl_map *map,
11641 enum isl_dim_type type, __isl_take isl_multi_aff *ma)
11646 map = isl_map_cow(map);
11647 ma = isl_multi_aff_align_divs(ma);
11650 if (check_map_compatible_range_multi_aff(map, type, ma) < 0)
11653 for (i = 0; i < map->n; ++i) {
11654 map->p[i] = isl_basic_map_preimage_multi_aff(map->p[i], type,
11655 isl_multi_aff_copy(ma));
11660 space = isl_multi_aff_get_domain_space(ma);
11661 space = isl_space_set(isl_map_get_space(map), type, space);
11663 isl_space_free(map->dim);
11668 isl_multi_aff_free(ma);
11670 ISL_F_CLR(map, ISL_MAP_DISJOINT);
11671 ISL_F_CLR(map, ISL_SET_NORMALIZED);
11674 isl_multi_aff_free(ma);
11679 /* Compute the preimage of the domain or range (depending on "type")
11680 * of "map" under the function represented by "ma".
11681 * In other words, plug in "ma" in the domain or range of "map".
11682 * The result is a map that lives in the same space as "map"
11683 * except that the domain or range has been replaced by
11684 * the domain space of "ma".
11686 __isl_give isl_map *isl_map_preimage_multi_aff(__isl_take isl_map *map,
11687 enum isl_dim_type type, __isl_take isl_multi_aff *ma)
11692 if (isl_space_match(map->dim, isl_dim_param, ma->space, isl_dim_param))
11693 return map_preimage_multi_aff(map, type, ma);
11695 if (!isl_space_has_named_params(map->dim) ||
11696 !isl_space_has_named_params(ma->space))
11697 isl_die(map->ctx, isl_error_invalid,
11698 "unaligned unnamed parameters", goto error);
11699 map = isl_map_align_params(map, isl_multi_aff_get_space(ma));
11700 ma = isl_multi_aff_align_params(ma, isl_map_get_space(map));
11702 return map_preimage_multi_aff(map, type, ma);
11704 isl_multi_aff_free(ma);
11705 return isl_map_free(map);
11708 /* Compute the preimage of "set" under the function represented by "ma".
11709 * In other words, plug in "ma" "set". The result is a set
11710 * that lives in the domain space of "ma".
11712 __isl_give isl_set *isl_set_preimage_multi_aff(__isl_take isl_set *set,
11713 __isl_take isl_multi_aff *ma)
11715 return isl_map_preimage_multi_aff(set, isl_dim_set, ma);
11718 /* Compute the preimage of the domain of "map" under the function
11719 * represented by "ma".
11720 * In other words, plug in "ma" in the domain of "map".
11721 * The result is a map that lives in the same space as "map"
11722 * except that the domain has been replaced by the domain space of "ma".
11724 __isl_give isl_map *isl_map_preimage_domain_multi_aff(__isl_take isl_map *map,
11725 __isl_take isl_multi_aff *ma)
11727 return isl_map_preimage_multi_aff(map, isl_dim_in, ma);
11730 /* Compute the preimage of "set" under the function represented by "pma".
11731 * In other words, plug in "pma" in "set. The result is a set
11732 * that lives in the domain space of "pma".
11734 static __isl_give isl_set *set_preimage_pw_multi_aff(__isl_take isl_set *set,
11735 __isl_take isl_pw_multi_aff *pma)
11744 isl_pw_multi_aff_free(pma);
11745 res = isl_set_empty(isl_set_get_space(set));
11750 res = isl_set_preimage_multi_aff(isl_set_copy(set),
11751 isl_multi_aff_copy(pma->p[0].maff));
11752 res = isl_set_intersect(res, isl_set_copy(pma->p[0].set));
11754 for (i = 1; i < pma->n; ++i) {
11757 res_i = isl_set_preimage_multi_aff(isl_set_copy(set),
11758 isl_multi_aff_copy(pma->p[i].maff));
11759 res_i = isl_set_intersect(res_i, isl_set_copy(pma->p[i].set));
11760 res = isl_set_union(res, res_i);
11763 isl_pw_multi_aff_free(pma);
11767 isl_pw_multi_aff_free(pma);
11772 __isl_give isl_set *isl_set_preimage_pw_multi_aff(__isl_take isl_set *set,
11773 __isl_take isl_pw_multi_aff *pma)
11778 if (isl_space_match(set->dim, isl_dim_param, pma->dim, isl_dim_param))
11779 return set_preimage_pw_multi_aff(set, pma);
11781 if (!isl_space_has_named_params(set->dim) ||
11782 !isl_space_has_named_params(pma->dim))
11783 isl_die(set->ctx, isl_error_invalid,
11784 "unaligned unnamed parameters", goto error);
11785 set = isl_set_align_params(set, isl_pw_multi_aff_get_space(pma));
11786 pma = isl_pw_multi_aff_align_params(pma, isl_set_get_space(set));
11788 return set_preimage_pw_multi_aff(set, pma);
11790 isl_pw_multi_aff_free(pma);
11791 return isl_set_free(set);