2 * Copyright 2008-2009 Katholieke Universiteit Leuven
4 * Use of this software is governed by the GNU LGPLv2.1 license
6 * Written by Sven Verdoolaege, K.U.Leuven, Departement
7 * Computerwetenschappen, Celestijnenlaan 200A, B-3001 Leuven, Belgium
12 #include "isl_map_private.h"
16 #include "isl_equalities.h"
19 static struct isl_basic_set
*uset_convex_hull_wrap_bounded(struct isl_set
*set
);
21 static void swap_ineq(struct isl_basic_map
*bmap
, unsigned i
, unsigned j
)
27 bmap
->ineq
[i
] = bmap
->ineq
[j
];
32 /* Return 1 if constraint c is redundant with respect to the constraints
33 * in bmap. If c is a lower [upper] bound in some variable and bmap
34 * does not have a lower [upper] bound in that variable, then c cannot
35 * be redundant and we do not need solve any lp.
37 int isl_basic_map_constraint_is_redundant(struct isl_basic_map
**bmap
,
38 isl_int
*c
, isl_int
*opt_n
, isl_int
*opt_d
)
40 enum isl_lp_result res
;
47 total
= isl_basic_map_total_dim(*bmap
);
48 for (i
= 0; i
< total
; ++i
) {
50 if (isl_int_is_zero(c
[1+i
]))
52 sign
= isl_int_sgn(c
[1+i
]);
53 for (j
= 0; j
< (*bmap
)->n_ineq
; ++j
)
54 if (sign
== isl_int_sgn((*bmap
)->ineq
[j
][1+i
]))
56 if (j
== (*bmap
)->n_ineq
)
62 res
= isl_basic_map_solve_lp(*bmap
, 0, c
, (*bmap
)->ctx
->one
,
64 if (res
== isl_lp_unbounded
)
66 if (res
== isl_lp_error
)
68 if (res
== isl_lp_empty
) {
69 *bmap
= isl_basic_map_set_to_empty(*bmap
);
72 return !isl_int_is_neg(*opt_n
);
75 int isl_basic_set_constraint_is_redundant(struct isl_basic_set
**bset
,
76 isl_int
*c
, isl_int
*opt_n
, isl_int
*opt_d
)
78 return isl_basic_map_constraint_is_redundant(
79 (struct isl_basic_map
**)bset
, c
, opt_n
, opt_d
);
82 /* Compute the convex hull of a basic map, by removing the redundant
83 * constraints. If the minimal value along the normal of a constraint
84 * is the same if the constraint is removed, then the constraint is redundant.
86 * Alternatively, we could have intersected the basic map with the
87 * corresponding equality and the checked if the dimension was that
90 struct isl_basic_map
*isl_basic_map_convex_hull(struct isl_basic_map
*bmap
)
97 bmap
= isl_basic_map_gauss(bmap
, NULL
);
98 if (ISL_F_ISSET(bmap
, ISL_BASIC_MAP_EMPTY
))
100 if (ISL_F_ISSET(bmap
, ISL_BASIC_MAP_NO_REDUNDANT
))
102 if (bmap
->n_ineq
<= 1)
105 tab
= isl_tab_from_basic_map(bmap
);
106 tab
= isl_tab_detect_implicit_equalities(tab
);
107 if (isl_tab_detect_redundant(tab
) < 0)
109 bmap
= isl_basic_map_update_from_tab(bmap
, tab
);
111 ISL_F_SET(bmap
, ISL_BASIC_MAP_NO_IMPLICIT
);
112 ISL_F_SET(bmap
, ISL_BASIC_MAP_NO_REDUNDANT
);
116 isl_basic_map_free(bmap
);
120 struct isl_basic_set
*isl_basic_set_convex_hull(struct isl_basic_set
*bset
)
122 return (struct isl_basic_set
*)
123 isl_basic_map_convex_hull((struct isl_basic_map
*)bset
);
126 /* Check if the set set is bound in the direction of the affine
127 * constraint c and if so, set the constant term such that the
128 * resulting constraint is a bounding constraint for the set.
130 static int uset_is_bound(struct isl_set
*set
, isl_int
*c
, unsigned len
)
138 isl_int_init(opt_denom
);
140 for (j
= 0; j
< set
->n
; ++j
) {
141 enum isl_lp_result res
;
143 if (ISL_F_ISSET(set
->p
[j
], ISL_BASIC_SET_EMPTY
))
146 res
= isl_basic_set_solve_lp(set
->p
[j
],
147 0, c
, set
->ctx
->one
, &opt
, &opt_denom
, NULL
);
148 if (res
== isl_lp_unbounded
)
150 if (res
== isl_lp_error
)
152 if (res
== isl_lp_empty
) {
153 set
->p
[j
] = isl_basic_set_set_to_empty(set
->p
[j
]);
158 if (!isl_int_is_one(opt_denom
))
159 isl_seq_scale(c
, c
, opt_denom
, len
);
160 if (first
|| isl_int_is_neg(opt
))
161 isl_int_sub(c
[0], c
[0], opt
);
165 isl_int_clear(opt_denom
);
169 isl_int_clear(opt_denom
);
173 /* Check if "c" is a direction that is independent of the previously found "n"
175 * If so, add it to the list, with the negative of the lower bound
176 * in the constant position, i.e., such that c corresponds to a bounding
177 * hyperplane (but not necessarily a facet).
178 * Assumes set "set" is bounded.
180 static int is_independent_bound(struct isl_set
*set
, isl_int
*c
,
181 struct isl_mat
*dirs
, int n
)
186 isl_seq_cpy(dirs
->row
[n
]+1, c
+1, dirs
->n_col
-1);
188 int pos
= isl_seq_first_non_zero(dirs
->row
[n
]+1, dirs
->n_col
-1);
191 for (i
= 0; i
< n
; ++i
) {
193 pos_i
= isl_seq_first_non_zero(dirs
->row
[i
]+1, dirs
->n_col
-1);
198 isl_seq_elim(dirs
->row
[n
]+1, dirs
->row
[i
]+1, pos
,
199 dirs
->n_col
-1, NULL
);
200 pos
= isl_seq_first_non_zero(dirs
->row
[n
]+1, dirs
->n_col
-1);
206 is_bound
= uset_is_bound(set
, dirs
->row
[n
], dirs
->n_col
);
211 isl_int
*t
= dirs
->row
[n
];
212 for (k
= n
; k
> i
; --k
)
213 dirs
->row
[k
] = dirs
->row
[k
-1];
219 /* Compute and return a maximal set of linearly independent bounds
220 * on the set "set", based on the constraints of the basic sets
223 static struct isl_mat
*independent_bounds(struct isl_set
*set
)
226 struct isl_mat
*dirs
= NULL
;
227 unsigned dim
= isl_set_n_dim(set
);
229 dirs
= isl_mat_alloc(set
->ctx
, dim
, 1+dim
);
234 for (i
= 0; n
< dim
&& i
< set
->n
; ++i
) {
236 struct isl_basic_set
*bset
= set
->p
[i
];
238 for (j
= 0; n
< dim
&& j
< bset
->n_eq
; ++j
) {
239 f
= is_independent_bound(set
, bset
->eq
[j
], dirs
, n
);
245 for (j
= 0; n
< dim
&& j
< bset
->n_ineq
; ++j
) {
246 f
= is_independent_bound(set
, bset
->ineq
[j
], dirs
, n
);
260 struct isl_basic_set
*isl_basic_set_set_rational(struct isl_basic_set
*bset
)
265 if (ISL_F_ISSET(bset
, ISL_BASIC_MAP_RATIONAL
))
268 bset
= isl_basic_set_cow(bset
);
272 ISL_F_SET(bset
, ISL_BASIC_MAP_RATIONAL
);
274 return isl_basic_set_finalize(bset
);
277 static struct isl_set
*isl_set_set_rational(struct isl_set
*set
)
281 set
= isl_set_cow(set
);
284 for (i
= 0; i
< set
->n
; ++i
) {
285 set
->p
[i
] = isl_basic_set_set_rational(set
->p
[i
]);
295 static struct isl_basic_set
*isl_basic_set_add_equality(
296 struct isl_basic_set
*bset
, isl_int
*c
)
301 if (ISL_F_ISSET(bset
, ISL_BASIC_SET_EMPTY
))
304 isl_assert(bset
->ctx
, isl_basic_set_n_param(bset
) == 0, goto error
);
305 isl_assert(bset
->ctx
, bset
->n_div
== 0, goto error
);
306 dim
= isl_basic_set_n_dim(bset
);
307 bset
= isl_basic_set_cow(bset
);
308 bset
= isl_basic_set_extend(bset
, 0, dim
, 0, 1, 0);
309 i
= isl_basic_set_alloc_equality(bset
);
312 isl_seq_cpy(bset
->eq
[i
], c
, 1 + dim
);
315 isl_basic_set_free(bset
);
319 static struct isl_set
*isl_set_add_equality(struct isl_set
*set
, isl_int
*c
)
323 set
= isl_set_cow(set
);
326 for (i
= 0; i
< set
->n
; ++i
) {
327 set
->p
[i
] = isl_basic_set_add_equality(set
->p
[i
], c
);
337 /* Given a union of basic sets, construct the constraints for wrapping
338 * a facet around one of its ridges.
339 * In particular, if each of n the d-dimensional basic sets i in "set"
340 * contains the origin, satisfies the constraints x_1 >= 0 and x_2 >= 0
341 * and is defined by the constraints
345 * then the resulting set is of dimension n*(1+d) and has as constraints
354 static struct isl_basic_set
*wrap_constraints(struct isl_set
*set
)
356 struct isl_basic_set
*lp
;
360 unsigned dim
, lp_dim
;
365 dim
= 1 + isl_set_n_dim(set
);
368 for (i
= 0; i
< set
->n
; ++i
) {
369 n_eq
+= set
->p
[i
]->n_eq
;
370 n_ineq
+= set
->p
[i
]->n_ineq
;
372 lp
= isl_basic_set_alloc(set
->ctx
, 0, dim
* set
->n
, 0, n_eq
, n_ineq
);
375 lp_dim
= isl_basic_set_n_dim(lp
);
376 k
= isl_basic_set_alloc_equality(lp
);
377 isl_int_set_si(lp
->eq
[k
][0], -1);
378 for (i
= 0; i
< set
->n
; ++i
) {
379 isl_int_set_si(lp
->eq
[k
][1+dim
*i
], 0);
380 isl_int_set_si(lp
->eq
[k
][1+dim
*i
+1], 1);
381 isl_seq_clr(lp
->eq
[k
]+1+dim
*i
+2, dim
-2);
383 for (i
= 0; i
< set
->n
; ++i
) {
384 k
= isl_basic_set_alloc_inequality(lp
);
385 isl_seq_clr(lp
->ineq
[k
], 1+lp_dim
);
386 isl_int_set_si(lp
->ineq
[k
][1+dim
*i
], 1);
388 for (j
= 0; j
< set
->p
[i
]->n_eq
; ++j
) {
389 k
= isl_basic_set_alloc_equality(lp
);
390 isl_seq_clr(lp
->eq
[k
], 1+dim
*i
);
391 isl_seq_cpy(lp
->eq
[k
]+1+dim
*i
, set
->p
[i
]->eq
[j
], dim
);
392 isl_seq_clr(lp
->eq
[k
]+1+dim
*(i
+1), dim
*(set
->n
-i
-1));
395 for (j
= 0; j
< set
->p
[i
]->n_ineq
; ++j
) {
396 k
= isl_basic_set_alloc_inequality(lp
);
397 isl_seq_clr(lp
->ineq
[k
], 1+dim
*i
);
398 isl_seq_cpy(lp
->ineq
[k
]+1+dim
*i
, set
->p
[i
]->ineq
[j
], dim
);
399 isl_seq_clr(lp
->ineq
[k
]+1+dim
*(i
+1), dim
*(set
->n
-i
-1));
405 /* Given a facet "facet" of the convex hull of "set" and a facet "ridge"
406 * of that facet, compute the other facet of the convex hull that contains
409 * We first transform the set such that the facet constraint becomes
413 * I.e., the facet lies in
417 * and on that facet, the constraint that defines the ridge is
421 * (This transformation is not strictly needed, all that is needed is
422 * that the ridge contains the origin.)
424 * Since the ridge contains the origin, the cone of the convex hull
425 * will be of the form
430 * with this second constraint defining the new facet.
431 * The constant a is obtained by settting x_1 in the cone of the
432 * convex hull to 1 and minimizing x_2.
433 * Now, each element in the cone of the convex hull is the sum
434 * of elements in the cones of the basic sets.
435 * If a_i is the dilation factor of basic set i, then the problem
436 * we need to solve is
449 * the constraints of each (transformed) basic set.
450 * If a = n/d, then the constraint defining the new facet (in the transformed
453 * -n x_1 + d x_2 >= 0
455 * In the original space, we need to take the same combination of the
456 * corresponding constraints "facet" and "ridge".
458 * Note that a is always finite, since we only apply the wrapping
459 * technique to a union of polytopes.
461 static isl_int
*wrap_facet(struct isl_set
*set
, isl_int
*facet
, isl_int
*ridge
)
464 struct isl_mat
*T
= NULL
;
465 struct isl_basic_set
*lp
= NULL
;
467 enum isl_lp_result res
;
471 set
= isl_set_copy(set
);
473 dim
= 1 + isl_set_n_dim(set
);
474 T
= isl_mat_alloc(set
->ctx
, 3, dim
);
477 isl_int_set_si(T
->row
[0][0], 1);
478 isl_seq_clr(T
->row
[0]+1, dim
- 1);
479 isl_seq_cpy(T
->row
[1], facet
, dim
);
480 isl_seq_cpy(T
->row
[2], ridge
, dim
);
481 T
= isl_mat_right_inverse(T
);
482 set
= isl_set_preimage(set
, T
);
486 lp
= wrap_constraints(set
);
487 obj
= isl_vec_alloc(set
->ctx
, 1 + dim
*set
->n
);
490 isl_int_set_si(obj
->block
.data
[0], 0);
491 for (i
= 0; i
< set
->n
; ++i
) {
492 isl_seq_clr(obj
->block
.data
+ 1 + dim
*i
, 2);
493 isl_int_set_si(obj
->block
.data
[1 + dim
*i
+2], 1);
494 isl_seq_clr(obj
->block
.data
+ 1 + dim
*i
+3, dim
-3);
498 res
= isl_basic_set_solve_lp(lp
, 0,
499 obj
->block
.data
, set
->ctx
->one
, &num
, &den
, NULL
);
500 if (res
== isl_lp_ok
) {
501 isl_int_neg(num
, num
);
502 isl_seq_combine(facet
, num
, facet
, den
, ridge
, dim
);
507 isl_basic_set_free(lp
);
509 isl_assert(set
->ctx
, res
== isl_lp_ok
, return NULL
);
512 isl_basic_set_free(lp
);
518 /* Given a set of d linearly independent bounding constraints of the
519 * convex hull of "set", compute the constraint of a facet of "set".
521 * We first compute the intersection with the first bounding hyperplane
522 * and remove the component corresponding to this hyperplane from
523 * other bounds (in homogeneous space).
524 * We then wrap around one of the remaining bounding constraints
525 * and continue the process until all bounding constraints have been
526 * taken into account.
527 * The resulting linear combination of the bounding constraints will
528 * correspond to a facet of the convex hull.
530 static struct isl_mat
*initial_facet_constraint(struct isl_set
*set
,
531 struct isl_mat
*bounds
)
533 struct isl_set
*slice
= NULL
;
534 struct isl_basic_set
*face
= NULL
;
535 struct isl_mat
*m
, *U
, *Q
;
537 unsigned dim
= isl_set_n_dim(set
);
539 isl_assert(set
->ctx
, set
->n
> 0, goto error
);
540 isl_assert(set
->ctx
, bounds
->n_row
== dim
, goto error
);
542 while (bounds
->n_row
> 1) {
543 slice
= isl_set_copy(set
);
544 slice
= isl_set_add_equality(slice
, bounds
->row
[0]);
545 face
= isl_set_affine_hull(slice
);
548 if (face
->n_eq
== 1) {
549 isl_basic_set_free(face
);
552 m
= isl_mat_alloc(set
->ctx
, 1 + face
->n_eq
, 1 + dim
);
555 isl_int_set_si(m
->row
[0][0], 1);
556 isl_seq_clr(m
->row
[0]+1, dim
);
557 for (i
= 0; i
< face
->n_eq
; ++i
)
558 isl_seq_cpy(m
->row
[1 + i
], face
->eq
[i
], 1 + dim
);
559 U
= isl_mat_right_inverse(m
);
560 Q
= isl_mat_right_inverse(isl_mat_copy(U
));
561 U
= isl_mat_drop_cols(U
, 1 + face
->n_eq
, dim
- face
->n_eq
);
562 Q
= isl_mat_drop_rows(Q
, 1 + face
->n_eq
, dim
- face
->n_eq
);
563 U
= isl_mat_drop_cols(U
, 0, 1);
564 Q
= isl_mat_drop_rows(Q
, 0, 1);
565 bounds
= isl_mat_product(bounds
, U
);
566 bounds
= isl_mat_product(bounds
, Q
);
567 while (isl_seq_first_non_zero(bounds
->row
[bounds
->n_row
-1],
568 bounds
->n_col
) == -1) {
570 isl_assert(set
->ctx
, bounds
->n_row
> 1, goto error
);
572 if (!wrap_facet(set
, bounds
->row
[0],
573 bounds
->row
[bounds
->n_row
-1]))
575 isl_basic_set_free(face
);
580 isl_basic_set_free(face
);
581 isl_mat_free(bounds
);
585 /* Given the bounding constraint "c" of a facet of the convex hull of "set",
586 * compute a hyperplane description of the facet, i.e., compute the facets
589 * We compute an affine transformation that transforms the constraint
598 * by computing the right inverse U of a matrix that starts with the rows
611 * Since z_1 is zero, we can drop this variable as well as the corresponding
612 * column of U to obtain
620 * with Q' equal to Q, but without the corresponding row.
621 * After computing the facets of the facet in the z' space,
622 * we convert them back to the x space through Q.
624 static struct isl_basic_set
*compute_facet(struct isl_set
*set
, isl_int
*c
)
626 struct isl_mat
*m
, *U
, *Q
;
627 struct isl_basic_set
*facet
= NULL
;
632 set
= isl_set_copy(set
);
633 dim
= isl_set_n_dim(set
);
634 m
= isl_mat_alloc(set
->ctx
, 2, 1 + dim
);
637 isl_int_set_si(m
->row
[0][0], 1);
638 isl_seq_clr(m
->row
[0]+1, dim
);
639 isl_seq_cpy(m
->row
[1], c
, 1+dim
);
640 U
= isl_mat_right_inverse(m
);
641 Q
= isl_mat_right_inverse(isl_mat_copy(U
));
642 U
= isl_mat_drop_cols(U
, 1, 1);
643 Q
= isl_mat_drop_rows(Q
, 1, 1);
644 set
= isl_set_preimage(set
, U
);
645 facet
= uset_convex_hull_wrap_bounded(set
);
646 facet
= isl_basic_set_preimage(facet
, Q
);
647 isl_assert(ctx
, facet
->n_eq
== 0, goto error
);
650 isl_basic_set_free(facet
);
655 /* Given an initial facet constraint, compute the remaining facets.
656 * We do this by running through all facets found so far and computing
657 * the adjacent facets through wrapping, adding those facets that we
658 * hadn't already found before.
660 * For each facet we have found so far, we first compute its facets
661 * in the resulting convex hull. That is, we compute the ridges
662 * of the resulting convex hull contained in the facet.
663 * We also compute the corresponding facet in the current approximation
664 * of the convex hull. There is no need to wrap around the ridges
665 * in this facet since that would result in a facet that is already
666 * present in the current approximation.
668 * This function can still be significantly optimized by checking which of
669 * the facets of the basic sets are also facets of the convex hull and
670 * using all the facets so far to help in constructing the facets of the
673 * using the technique in section "3.1 Ridge Generation" of
674 * "Extended Convex Hull" by Fukuda et al.
676 static struct isl_basic_set
*extend(struct isl_basic_set
*hull
,
681 struct isl_basic_set
*facet
= NULL
;
682 struct isl_basic_set
*hull_facet
= NULL
;
685 isl_assert(set
->ctx
, set
->n
> 0, goto error
);
687 dim
= isl_set_n_dim(set
);
689 for (i
= 0; i
< hull
->n_ineq
; ++i
) {
690 facet
= compute_facet(set
, hull
->ineq
[i
]);
691 facet
= isl_basic_set_add_equality(facet
, hull
->ineq
[i
]);
692 facet
= isl_basic_set_gauss(facet
, NULL
);
693 facet
= isl_basic_set_normalize_constraints(facet
);
694 hull_facet
= isl_basic_set_copy(hull
);
695 hull_facet
= isl_basic_set_add_equality(hull_facet
, hull
->ineq
[i
]);
696 hull_facet
= isl_basic_set_gauss(hull_facet
, NULL
);
697 hull_facet
= isl_basic_set_normalize_constraints(hull_facet
);
700 hull
= isl_basic_set_cow(hull
);
701 hull
= isl_basic_set_extend_dim(hull
,
702 isl_dim_copy(hull
->dim
), 0, 0, facet
->n_ineq
);
703 for (j
= 0; j
< facet
->n_ineq
; ++j
) {
704 for (f
= 0; f
< hull_facet
->n_ineq
; ++f
)
705 if (isl_seq_eq(facet
->ineq
[j
],
706 hull_facet
->ineq
[f
], 1 + dim
))
708 if (f
< hull_facet
->n_ineq
)
710 k
= isl_basic_set_alloc_inequality(hull
);
713 isl_seq_cpy(hull
->ineq
[k
], hull
->ineq
[i
], 1+dim
);
714 if (!wrap_facet(set
, hull
->ineq
[k
], facet
->ineq
[j
]))
717 isl_basic_set_free(hull_facet
);
718 isl_basic_set_free(facet
);
720 hull
= isl_basic_set_simplify(hull
);
721 hull
= isl_basic_set_finalize(hull
);
724 isl_basic_set_free(hull_facet
);
725 isl_basic_set_free(facet
);
726 isl_basic_set_free(hull
);
730 /* Special case for computing the convex hull of a one dimensional set.
731 * We simply collect the lower and upper bounds of each basic set
732 * and the biggest of those.
734 static struct isl_basic_set
*convex_hull_1d(struct isl_set
*set
)
736 struct isl_mat
*c
= NULL
;
737 isl_int
*lower
= NULL
;
738 isl_int
*upper
= NULL
;
741 struct isl_basic_set
*hull
;
743 for (i
= 0; i
< set
->n
; ++i
) {
744 set
->p
[i
] = isl_basic_set_simplify(set
->p
[i
]);
748 set
= isl_set_remove_empty_parts(set
);
751 isl_assert(set
->ctx
, set
->n
> 0, goto error
);
752 c
= isl_mat_alloc(set
->ctx
, 2, 2);
756 if (set
->p
[0]->n_eq
> 0) {
757 isl_assert(set
->ctx
, set
->p
[0]->n_eq
== 1, goto error
);
760 if (isl_int_is_pos(set
->p
[0]->eq
[0][1])) {
761 isl_seq_cpy(lower
, set
->p
[0]->eq
[0], 2);
762 isl_seq_neg(upper
, set
->p
[0]->eq
[0], 2);
764 isl_seq_neg(lower
, set
->p
[0]->eq
[0], 2);
765 isl_seq_cpy(upper
, set
->p
[0]->eq
[0], 2);
768 for (j
= 0; j
< set
->p
[0]->n_ineq
; ++j
) {
769 if (isl_int_is_pos(set
->p
[0]->ineq
[j
][1])) {
771 isl_seq_cpy(lower
, set
->p
[0]->ineq
[j
], 2);
774 isl_seq_cpy(upper
, set
->p
[0]->ineq
[j
], 2);
781 for (i
= 0; i
< set
->n
; ++i
) {
782 struct isl_basic_set
*bset
= set
->p
[i
];
786 for (j
= 0; j
< bset
->n_eq
; ++j
) {
790 isl_int_mul(a
, lower
[0], bset
->eq
[j
][1]);
791 isl_int_mul(b
, lower
[1], bset
->eq
[j
][0]);
792 if (isl_int_lt(a
, b
) && isl_int_is_pos(bset
->eq
[j
][1]))
793 isl_seq_cpy(lower
, bset
->eq
[j
], 2);
794 if (isl_int_gt(a
, b
) && isl_int_is_neg(bset
->eq
[j
][1]))
795 isl_seq_neg(lower
, bset
->eq
[j
], 2);
798 isl_int_mul(a
, upper
[0], bset
->eq
[j
][1]);
799 isl_int_mul(b
, upper
[1], bset
->eq
[j
][0]);
800 if (isl_int_lt(a
, b
) && isl_int_is_pos(bset
->eq
[j
][1]))
801 isl_seq_neg(upper
, bset
->eq
[j
], 2);
802 if (isl_int_gt(a
, b
) && isl_int_is_neg(bset
->eq
[j
][1]))
803 isl_seq_cpy(upper
, bset
->eq
[j
], 2);
806 for (j
= 0; j
< bset
->n_ineq
; ++j
) {
807 if (isl_int_is_pos(bset
->ineq
[j
][1]))
809 if (isl_int_is_neg(bset
->ineq
[j
][1]))
811 if (lower
&& isl_int_is_pos(bset
->ineq
[j
][1])) {
812 isl_int_mul(a
, lower
[0], bset
->ineq
[j
][1]);
813 isl_int_mul(b
, lower
[1], bset
->ineq
[j
][0]);
814 if (isl_int_lt(a
, b
))
815 isl_seq_cpy(lower
, bset
->ineq
[j
], 2);
817 if (upper
&& isl_int_is_neg(bset
->ineq
[j
][1])) {
818 isl_int_mul(a
, upper
[0], bset
->ineq
[j
][1]);
819 isl_int_mul(b
, upper
[1], bset
->ineq
[j
][0]);
820 if (isl_int_gt(a
, b
))
821 isl_seq_cpy(upper
, bset
->ineq
[j
], 2);
832 hull
= isl_basic_set_alloc(set
->ctx
, 0, 1, 0, 0, 2);
833 hull
= isl_basic_set_set_rational(hull
);
837 k
= isl_basic_set_alloc_inequality(hull
);
838 isl_seq_cpy(hull
->ineq
[k
], lower
, 2);
841 k
= isl_basic_set_alloc_inequality(hull
);
842 isl_seq_cpy(hull
->ineq
[k
], upper
, 2);
844 hull
= isl_basic_set_finalize(hull
);
854 /* Project out final n dimensions using Fourier-Motzkin */
855 static struct isl_set
*set_project_out(struct isl_ctx
*ctx
,
856 struct isl_set
*set
, unsigned n
)
858 return isl_set_remove_dims(set
, isl_set_n_dim(set
) - n
, n
);
861 static struct isl_basic_set
*convex_hull_0d(struct isl_set
*set
)
863 struct isl_basic_set
*convex_hull
;
868 if (isl_set_is_empty(set
))
869 convex_hull
= isl_basic_set_empty(isl_dim_copy(set
->dim
));
871 convex_hull
= isl_basic_set_universe(isl_dim_copy(set
->dim
));
876 /* Compute the convex hull of a pair of basic sets without any parameters or
877 * integer divisions using Fourier-Motzkin elimination.
878 * The convex hull is the set of all points that can be written as
879 * the sum of points from both basic sets (in homogeneous coordinates).
880 * We set up the constraints in a space with dimensions for each of
881 * the three sets and then project out the dimensions corresponding
882 * to the two original basic sets, retaining only those corresponding
883 * to the convex hull.
885 static struct isl_basic_set
*convex_hull_pair_elim(struct isl_basic_set
*bset1
,
886 struct isl_basic_set
*bset2
)
889 struct isl_basic_set
*bset
[2];
890 struct isl_basic_set
*hull
= NULL
;
893 if (!bset1
|| !bset2
)
896 dim
= isl_basic_set_n_dim(bset1
);
897 hull
= isl_basic_set_alloc(bset1
->ctx
, 0, 2 + 3 * dim
, 0,
898 1 + dim
+ bset1
->n_eq
+ bset2
->n_eq
,
899 2 + bset1
->n_ineq
+ bset2
->n_ineq
);
902 for (i
= 0; i
< 2; ++i
) {
903 for (j
= 0; j
< bset
[i
]->n_eq
; ++j
) {
904 k
= isl_basic_set_alloc_equality(hull
);
907 isl_seq_clr(hull
->eq
[k
], (i
+1) * (1+dim
));
908 isl_seq_clr(hull
->eq
[k
]+(i
+2)*(1+dim
), (1-i
)*(1+dim
));
909 isl_seq_cpy(hull
->eq
[k
]+(i
+1)*(1+dim
), bset
[i
]->eq
[j
],
912 for (j
= 0; j
< bset
[i
]->n_ineq
; ++j
) {
913 k
= isl_basic_set_alloc_inequality(hull
);
916 isl_seq_clr(hull
->ineq
[k
], (i
+1) * (1+dim
));
917 isl_seq_clr(hull
->ineq
[k
]+(i
+2)*(1+dim
), (1-i
)*(1+dim
));
918 isl_seq_cpy(hull
->ineq
[k
]+(i
+1)*(1+dim
),
919 bset
[i
]->ineq
[j
], 1+dim
);
921 k
= isl_basic_set_alloc_inequality(hull
);
924 isl_seq_clr(hull
->ineq
[k
], 1+2+3*dim
);
925 isl_int_set_si(hull
->ineq
[k
][(i
+1)*(1+dim
)], 1);
927 for (j
= 0; j
< 1+dim
; ++j
) {
928 k
= isl_basic_set_alloc_equality(hull
);
931 isl_seq_clr(hull
->eq
[k
], 1+2+3*dim
);
932 isl_int_set_si(hull
->eq
[k
][j
], -1);
933 isl_int_set_si(hull
->eq
[k
][1+dim
+j
], 1);
934 isl_int_set_si(hull
->eq
[k
][2*(1+dim
)+j
], 1);
936 hull
= isl_basic_set_set_rational(hull
);
937 hull
= isl_basic_set_remove_dims(hull
, dim
, 2*(1+dim
));
938 hull
= isl_basic_set_convex_hull(hull
);
939 isl_basic_set_free(bset1
);
940 isl_basic_set_free(bset2
);
943 isl_basic_set_free(bset1
);
944 isl_basic_set_free(bset2
);
945 isl_basic_set_free(hull
);
949 static int isl_basic_set_is_bounded(struct isl_basic_set
*bset
)
954 tab
= isl_tab_from_recession_cone(bset
);
955 bounded
= isl_tab_cone_is_bounded(tab
);
960 static int isl_set_is_bounded(struct isl_set
*set
)
964 for (i
= 0; i
< set
->n
; ++i
) {
965 int bounded
= isl_basic_set_is_bounded(set
->p
[i
]);
966 if (!bounded
|| bounded
< 0)
972 /* Compute the lineality space of the convex hull of bset1 and bset2.
974 * We first compute the intersection of the recession cone of bset1
975 * with the negative of the recession cone of bset2 and then compute
976 * the linear hull of the resulting cone.
978 static struct isl_basic_set
*induced_lineality_space(
979 struct isl_basic_set
*bset1
, struct isl_basic_set
*bset2
)
982 struct isl_basic_set
*lin
= NULL
;
985 if (!bset1
|| !bset2
)
988 dim
= isl_basic_set_total_dim(bset1
);
989 lin
= isl_basic_set_alloc_dim(isl_basic_set_get_dim(bset1
), 0,
990 bset1
->n_eq
+ bset2
->n_eq
,
991 bset1
->n_ineq
+ bset2
->n_ineq
);
992 lin
= isl_basic_set_set_rational(lin
);
995 for (i
= 0; i
< bset1
->n_eq
; ++i
) {
996 k
= isl_basic_set_alloc_equality(lin
);
999 isl_int_set_si(lin
->eq
[k
][0], 0);
1000 isl_seq_cpy(lin
->eq
[k
] + 1, bset1
->eq
[i
] + 1, dim
);
1002 for (i
= 0; i
< bset1
->n_ineq
; ++i
) {
1003 k
= isl_basic_set_alloc_inequality(lin
);
1006 isl_int_set_si(lin
->ineq
[k
][0], 0);
1007 isl_seq_cpy(lin
->ineq
[k
] + 1, bset1
->ineq
[i
] + 1, dim
);
1009 for (i
= 0; i
< bset2
->n_eq
; ++i
) {
1010 k
= isl_basic_set_alloc_equality(lin
);
1013 isl_int_set_si(lin
->eq
[k
][0], 0);
1014 isl_seq_neg(lin
->eq
[k
] + 1, bset2
->eq
[i
] + 1, dim
);
1016 for (i
= 0; i
< bset2
->n_ineq
; ++i
) {
1017 k
= isl_basic_set_alloc_inequality(lin
);
1020 isl_int_set_si(lin
->ineq
[k
][0], 0);
1021 isl_seq_neg(lin
->ineq
[k
] + 1, bset2
->ineq
[i
] + 1, dim
);
1024 isl_basic_set_free(bset1
);
1025 isl_basic_set_free(bset2
);
1026 return isl_basic_set_affine_hull(lin
);
1028 isl_basic_set_free(lin
);
1029 isl_basic_set_free(bset1
);
1030 isl_basic_set_free(bset2
);
1034 static struct isl_basic_set
*uset_convex_hull(struct isl_set
*set
);
1036 /* Given a set and a linear space "lin" of dimension n > 0,
1037 * project the linear space from the set, compute the convex hull
1038 * and then map the set back to the original space.
1044 * describe the linear space. We first compute the Hermite normal
1045 * form H = M U of M = H Q, to obtain
1049 * The last n rows of H will be zero, so the last n variables of x' = Q x
1050 * are the one we want to project out. We do this by transforming each
1051 * basic set A x >= b to A U x' >= b and then removing the last n dimensions.
1052 * After computing the convex hull in x'_1, i.e., A' x'_1 >= b',
1053 * we transform the hull back to the original space as A' Q_1 x >= b',
1054 * with Q_1 all but the last n rows of Q.
1056 static struct isl_basic_set
*modulo_lineality(struct isl_set
*set
,
1057 struct isl_basic_set
*lin
)
1059 unsigned total
= isl_basic_set_total_dim(lin
);
1061 struct isl_basic_set
*hull
;
1062 struct isl_mat
*M
, *U
, *Q
;
1066 lin_dim
= total
- lin
->n_eq
;
1067 M
= isl_mat_sub_alloc(set
->ctx
, lin
->eq
, 0, lin
->n_eq
, 1, total
);
1068 M
= isl_mat_left_hermite(M
, 0, &U
, &Q
);
1072 isl_basic_set_free(lin
);
1074 Q
= isl_mat_drop_rows(Q
, Q
->n_row
- lin_dim
, lin_dim
);
1076 U
= isl_mat_lin_to_aff(U
);
1077 Q
= isl_mat_lin_to_aff(Q
);
1079 set
= isl_set_preimage(set
, U
);
1080 set
= isl_set_remove_dims(set
, total
- lin_dim
, lin_dim
);
1081 hull
= uset_convex_hull(set
);
1082 hull
= isl_basic_set_preimage(hull
, Q
);
1086 isl_basic_set_free(lin
);
1091 /* Given two polyhedra with as constraints h_{ij} x >= 0 in homegeneous space,
1092 * set up an LP for solving
1094 * \sum_j \alpha_{1j} h_{1j} = \sum_j \alpha_{2j} h_{2j}
1096 * \alpha{i0} corresponds to the (implicit) positivity constraint 1 >= 0
1097 * The next \alpha{ij} correspond to the equalities and come in pairs.
1098 * The final \alpha{ij} correspond to the inequalities.
1100 static struct isl_basic_set
*valid_direction_lp(
1101 struct isl_basic_set
*bset1
, struct isl_basic_set
*bset2
)
1103 struct isl_dim
*dim
;
1104 struct isl_basic_set
*lp
;
1109 if (!bset1
|| !bset2
)
1111 d
= 1 + isl_basic_set_total_dim(bset1
);
1113 2 * bset1
->n_eq
+ bset1
->n_ineq
+ 2 * bset2
->n_eq
+ bset2
->n_ineq
;
1114 dim
= isl_dim_set_alloc(bset1
->ctx
, 0, n
);
1115 lp
= isl_basic_set_alloc_dim(dim
, 0, d
, n
);
1118 for (i
= 0; i
< n
; ++i
) {
1119 k
= isl_basic_set_alloc_inequality(lp
);
1122 isl_seq_clr(lp
->ineq
[k
] + 1, n
);
1123 isl_int_set_si(lp
->ineq
[k
][0], -1);
1124 isl_int_set_si(lp
->ineq
[k
][1 + i
], 1);
1126 for (i
= 0; i
< d
; ++i
) {
1127 k
= isl_basic_set_alloc_equality(lp
);
1131 isl_int_set_si(lp
->eq
[k
][n
++], 0);
1132 /* positivity constraint 1 >= 0 */
1133 isl_int_set_si(lp
->eq
[k
][n
++], i
== 0);
1134 for (j
= 0; j
< bset1
->n_eq
; ++j
) {
1135 isl_int_set(lp
->eq
[k
][n
++], bset1
->eq
[j
][i
]);
1136 isl_int_neg(lp
->eq
[k
][n
++], bset1
->eq
[j
][i
]);
1138 for (j
= 0; j
< bset1
->n_ineq
; ++j
)
1139 isl_int_set(lp
->eq
[k
][n
++], bset1
->ineq
[j
][i
]);
1140 /* positivity constraint 1 >= 0 */
1141 isl_int_set_si(lp
->eq
[k
][n
++], -(i
== 0));
1142 for (j
= 0; j
< bset2
->n_eq
; ++j
) {
1143 isl_int_neg(lp
->eq
[k
][n
++], bset2
->eq
[j
][i
]);
1144 isl_int_set(lp
->eq
[k
][n
++], bset2
->eq
[j
][i
]);
1146 for (j
= 0; j
< bset2
->n_ineq
; ++j
)
1147 isl_int_neg(lp
->eq
[k
][n
++], bset2
->ineq
[j
][i
]);
1149 lp
= isl_basic_set_gauss(lp
, NULL
);
1150 isl_basic_set_free(bset1
);
1151 isl_basic_set_free(bset2
);
1154 isl_basic_set_free(bset1
);
1155 isl_basic_set_free(bset2
);
1159 /* Compute a vector s in the homogeneous space such that <s, r> > 0
1160 * for all rays in the homogeneous space of the two cones that correspond
1161 * to the input polyhedra bset1 and bset2.
1163 * We compute s as a vector that satisfies
1165 * s = \sum_j \alpha_{ij} h_{ij} for i = 1,2 (*)
1167 * with h_{ij} the normals of the facets of polyhedron i
1168 * (including the "positivity constraint" 1 >= 0) and \alpha_{ij}
1169 * strictly positive numbers. For simplicity we impose \alpha_{ij} >= 1.
1170 * We first set up an LP with as variables the \alpha{ij}.
1171 * In this formulateion, for each polyhedron i,
1172 * the first constraint is the positivity constraint, followed by pairs
1173 * of variables for the equalities, followed by variables for the inequalities.
1174 * We then simply pick a feasible solution and compute s using (*).
1176 * Note that we simply pick any valid direction and make no attempt
1177 * to pick a "good" or even the "best" valid direction.
1179 static struct isl_vec
*valid_direction(
1180 struct isl_basic_set
*bset1
, struct isl_basic_set
*bset2
)
1182 struct isl_basic_set
*lp
;
1183 struct isl_tab
*tab
;
1184 struct isl_vec
*sample
= NULL
;
1185 struct isl_vec
*dir
;
1190 if (!bset1
|| !bset2
)
1192 lp
= valid_direction_lp(isl_basic_set_copy(bset1
),
1193 isl_basic_set_copy(bset2
));
1194 tab
= isl_tab_from_basic_set(lp
);
1195 sample
= isl_tab_get_sample_value(tab
);
1197 isl_basic_set_free(lp
);
1200 d
= isl_basic_set_total_dim(bset1
);
1201 dir
= isl_vec_alloc(bset1
->ctx
, 1 + d
);
1204 isl_seq_clr(dir
->block
.data
+ 1, dir
->size
- 1);
1206 /* positivity constraint 1 >= 0 */
1207 isl_int_set(dir
->block
.data
[0], sample
->block
.data
[n
++]);
1208 for (i
= 0; i
< bset1
->n_eq
; ++i
) {
1209 isl_int_sub(sample
->block
.data
[n
],
1210 sample
->block
.data
[n
], sample
->block
.data
[n
+1]);
1211 isl_seq_combine(dir
->block
.data
,
1212 bset1
->ctx
->one
, dir
->block
.data
,
1213 sample
->block
.data
[n
], bset1
->eq
[i
], 1 + d
);
1217 for (i
= 0; i
< bset1
->n_ineq
; ++i
)
1218 isl_seq_combine(dir
->block
.data
,
1219 bset1
->ctx
->one
, dir
->block
.data
,
1220 sample
->block
.data
[n
++], bset1
->ineq
[i
], 1 + d
);
1221 isl_vec_free(sample
);
1222 isl_seq_normalize(bset1
->ctx
, dir
->block
.data
+ 1, dir
->size
- 1);
1223 isl_basic_set_free(bset1
);
1224 isl_basic_set_free(bset2
);
1227 isl_vec_free(sample
);
1228 isl_basic_set_free(bset1
);
1229 isl_basic_set_free(bset2
);
1233 /* Given a polyhedron b_i + A_i x >= 0 and a map T = S^{-1},
1234 * compute b_i' + A_i' x' >= 0, with
1236 * [ b_i A_i ] [ y' ] [ y' ]
1237 * [ 1 0 ] S^{-1} [ x' ] >= 0 or [ b_i' A_i' ] [ x' ] >= 0
1239 * In particular, add the "positivity constraint" and then perform
1242 static struct isl_basic_set
*homogeneous_map(struct isl_basic_set
*bset
,
1249 bset
= isl_basic_set_extend_constraints(bset
, 0, 1);
1250 k
= isl_basic_set_alloc_inequality(bset
);
1253 isl_seq_clr(bset
->ineq
[k
] + 1, isl_basic_set_total_dim(bset
));
1254 isl_int_set_si(bset
->ineq
[k
][0], 1);
1255 bset
= isl_basic_set_preimage(bset
, T
);
1259 isl_basic_set_free(bset
);
1263 /* Compute the convex hull of a pair of basic sets without any parameters or
1264 * integer divisions, where the convex hull is known to be pointed,
1265 * but the basic sets may be unbounded.
1267 * We turn this problem into the computation of a convex hull of a pair
1268 * _bounded_ polyhedra by "changing the direction of the homogeneous
1269 * dimension". This idea is due to Matthias Koeppe.
1271 * Consider the cones in homogeneous space that correspond to the
1272 * input polyhedra. The rays of these cones are also rays of the
1273 * polyhedra if the coordinate that corresponds to the homogeneous
1274 * dimension is zero. That is, if the inner product of the rays
1275 * with the homogeneous direction is zero.
1276 * The cones in the homogeneous space can also be considered to
1277 * correspond to other pairs of polyhedra by chosing a different
1278 * homogeneous direction. To ensure that both of these polyhedra
1279 * are bounded, we need to make sure that all rays of the cones
1280 * correspond to vertices and not to rays.
1281 * Let s be a direction such that <s, r> > 0 for all rays r of both cones.
1282 * Then using s as a homogeneous direction, we obtain a pair of polytopes.
1283 * The vector s is computed in valid_direction.
1285 * Note that we need to consider _all_ rays of the cones and not just
1286 * the rays that correspond to rays in the polyhedra. If we were to
1287 * only consider those rays and turn them into vertices, then we
1288 * may inadvertently turn some vertices into rays.
1290 * The standard homogeneous direction is the unit vector in the 0th coordinate.
1291 * We therefore transform the two polyhedra such that the selected
1292 * direction is mapped onto this standard direction and then proceed
1293 * with the normal computation.
1294 * Let S be a non-singular square matrix with s as its first row,
1295 * then we want to map the polyhedra to the space
1297 * [ y' ] [ y ] [ y ] [ y' ]
1298 * [ x' ] = S [ x ] i.e., [ x ] = S^{-1} [ x' ]
1300 * We take S to be the unimodular completion of s to limit the growth
1301 * of the coefficients in the following computations.
1303 * Let b_i + A_i x >= 0 be the constraints of polyhedron i.
1304 * We first move to the homogeneous dimension
1306 * b_i y + A_i x >= 0 [ b_i A_i ] [ y ] [ 0 ]
1307 * y >= 0 or [ 1 0 ] [ x ] >= [ 0 ]
1309 * Then we change directoin
1311 * [ b_i A_i ] [ y' ] [ y' ]
1312 * [ 1 0 ] S^{-1} [ x' ] >= 0 or [ b_i' A_i' ] [ x' ] >= 0
1314 * Then we compute the convex hull of the polytopes b_i' + A_i' x' >= 0
1315 * resulting in b' + A' x' >= 0, which we then convert back
1318 * [ b' A' ] S [ x ] >= 0 or [ b A ] [ x ] >= 0
1320 * The polyhedron b + A x >= 0 is then the convex hull of the input polyhedra.
1322 static struct isl_basic_set
*convex_hull_pair_pointed(
1323 struct isl_basic_set
*bset1
, struct isl_basic_set
*bset2
)
1325 struct isl_ctx
*ctx
= NULL
;
1326 struct isl_vec
*dir
= NULL
;
1327 struct isl_mat
*T
= NULL
;
1328 struct isl_mat
*T2
= NULL
;
1329 struct isl_basic_set
*hull
;
1330 struct isl_set
*set
;
1332 if (!bset1
|| !bset2
)
1335 dir
= valid_direction(isl_basic_set_copy(bset1
),
1336 isl_basic_set_copy(bset2
));
1339 T
= isl_mat_alloc(bset1
->ctx
, dir
->size
, dir
->size
);
1342 isl_seq_cpy(T
->row
[0], dir
->block
.data
, dir
->size
);
1343 T
= isl_mat_unimodular_complete(T
, 1);
1344 T2
= isl_mat_right_inverse(isl_mat_copy(T
));
1346 bset1
= homogeneous_map(bset1
, isl_mat_copy(T2
));
1347 bset2
= homogeneous_map(bset2
, T2
);
1348 set
= isl_set_alloc_dim(isl_basic_set_get_dim(bset1
), 2, 0);
1349 set
= isl_set_add(set
, bset1
);
1350 set
= isl_set_add(set
, bset2
);
1351 hull
= uset_convex_hull(set
);
1352 hull
= isl_basic_set_preimage(hull
, T
);
1359 isl_basic_set_free(bset1
);
1360 isl_basic_set_free(bset2
);
1364 /* Compute the convex hull of a pair of basic sets without any parameters or
1365 * integer divisions.
1367 * If the convex hull of the two basic sets would have a non-trivial
1368 * lineality space, we first project out this lineality space.
1370 static struct isl_basic_set
*convex_hull_pair(struct isl_basic_set
*bset1
,
1371 struct isl_basic_set
*bset2
)
1373 struct isl_basic_set
*lin
;
1375 if (isl_basic_set_is_bounded(bset1
) || isl_basic_set_is_bounded(bset2
))
1376 return convex_hull_pair_pointed(bset1
, bset2
);
1378 lin
= induced_lineality_space(isl_basic_set_copy(bset1
),
1379 isl_basic_set_copy(bset2
));
1382 if (isl_basic_set_is_universe(lin
)) {
1383 isl_basic_set_free(bset1
);
1384 isl_basic_set_free(bset2
);
1387 if (lin
->n_eq
< isl_basic_set_total_dim(lin
)) {
1388 struct isl_set
*set
;
1389 set
= isl_set_alloc_dim(isl_basic_set_get_dim(bset1
), 2, 0);
1390 set
= isl_set_add(set
, bset1
);
1391 set
= isl_set_add(set
, bset2
);
1392 return modulo_lineality(set
, lin
);
1394 isl_basic_set_free(lin
);
1396 return convex_hull_pair_pointed(bset1
, bset2
);
1398 isl_basic_set_free(bset1
);
1399 isl_basic_set_free(bset2
);
1403 /* Compute the lineality space of a basic set.
1404 * We currently do not allow the basic set to have any divs.
1405 * We basically just drop the constants and turn every inequality
1408 struct isl_basic_set
*isl_basic_set_lineality_space(struct isl_basic_set
*bset
)
1411 struct isl_basic_set
*lin
= NULL
;
1416 isl_assert(bset
->ctx
, bset
->n_div
== 0, goto error
);
1417 dim
= isl_basic_set_total_dim(bset
);
1419 lin
= isl_basic_set_alloc_dim(isl_basic_set_get_dim(bset
), 0, dim
, 0);
1422 for (i
= 0; i
< bset
->n_eq
; ++i
) {
1423 k
= isl_basic_set_alloc_equality(lin
);
1426 isl_int_set_si(lin
->eq
[k
][0], 0);
1427 isl_seq_cpy(lin
->eq
[k
] + 1, bset
->eq
[i
] + 1, dim
);
1429 lin
= isl_basic_set_gauss(lin
, NULL
);
1432 for (i
= 0; i
< bset
->n_ineq
&& lin
->n_eq
< dim
; ++i
) {
1433 k
= isl_basic_set_alloc_equality(lin
);
1436 isl_int_set_si(lin
->eq
[k
][0], 0);
1437 isl_seq_cpy(lin
->eq
[k
] + 1, bset
->ineq
[i
] + 1, dim
);
1438 lin
= isl_basic_set_gauss(lin
, NULL
);
1442 isl_basic_set_free(bset
);
1445 isl_basic_set_free(lin
);
1446 isl_basic_set_free(bset
);
1450 /* Compute the (linear) hull of the lineality spaces of the basic sets in the
1451 * "underlying" set "set".
1453 static struct isl_basic_set
*uset_combined_lineality_space(struct isl_set
*set
)
1456 struct isl_set
*lin
= NULL
;
1461 struct isl_dim
*dim
= isl_set_get_dim(set
);
1463 return isl_basic_set_empty(dim
);
1466 lin
= isl_set_alloc_dim(isl_set_get_dim(set
), set
->n
, 0);
1467 for (i
= 0; i
< set
->n
; ++i
)
1468 lin
= isl_set_add(lin
,
1469 isl_basic_set_lineality_space(isl_basic_set_copy(set
->p
[i
])));
1471 return isl_set_affine_hull(lin
);
1474 /* Compute the convex hull of a set without any parameters or
1475 * integer divisions.
1476 * In each step, we combined two basic sets until only one
1477 * basic set is left.
1478 * The input basic sets are assumed not to have a non-trivial
1479 * lineality space. If any of the intermediate results has
1480 * a non-trivial lineality space, it is projected out.
1482 static struct isl_basic_set
*uset_convex_hull_unbounded(struct isl_set
*set
)
1484 struct isl_basic_set
*convex_hull
= NULL
;
1486 convex_hull
= isl_set_copy_basic_set(set
);
1487 set
= isl_set_drop_basic_set(set
, convex_hull
);
1490 while (set
->n
> 0) {
1491 struct isl_basic_set
*t
;
1492 t
= isl_set_copy_basic_set(set
);
1495 set
= isl_set_drop_basic_set(set
, t
);
1498 convex_hull
= convex_hull_pair(convex_hull
, t
);
1501 t
= isl_basic_set_lineality_space(isl_basic_set_copy(convex_hull
));
1504 if (isl_basic_set_is_universe(t
)) {
1505 isl_basic_set_free(convex_hull
);
1509 if (t
->n_eq
< isl_basic_set_total_dim(t
)) {
1510 set
= isl_set_add(set
, convex_hull
);
1511 return modulo_lineality(set
, t
);
1513 isl_basic_set_free(t
);
1519 isl_basic_set_free(convex_hull
);
1523 /* Compute an initial hull for wrapping containing a single initial
1524 * facet by first computing bounds on the set and then using these
1525 * bounds to construct an initial facet.
1526 * This function is a remnant of an older implementation where the
1527 * bounds were also used to check whether the set was bounded.
1528 * Since this function will now only be called when we know the
1529 * set to be bounded, the initial facet should probably be constructed
1530 * by simply using the coordinate directions instead.
1532 static struct isl_basic_set
*initial_hull(struct isl_basic_set
*hull
,
1533 struct isl_set
*set
)
1535 struct isl_mat
*bounds
= NULL
;
1541 bounds
= independent_bounds(set
);
1544 isl_assert(set
->ctx
, bounds
->n_row
== isl_set_n_dim(set
), goto error
);
1545 bounds
= initial_facet_constraint(set
, bounds
);
1548 k
= isl_basic_set_alloc_inequality(hull
);
1551 dim
= isl_set_n_dim(set
);
1552 isl_assert(set
->ctx
, 1 + dim
== bounds
->n_col
, goto error
);
1553 isl_seq_cpy(hull
->ineq
[k
], bounds
->row
[0], bounds
->n_col
);
1554 isl_mat_free(bounds
);
1558 isl_basic_set_free(hull
);
1559 isl_mat_free(bounds
);
1563 struct max_constraint
{
1569 static int max_constraint_equal(const void *entry
, const void *val
)
1571 struct max_constraint
*a
= (struct max_constraint
*)entry
;
1572 isl_int
*b
= (isl_int
*)val
;
1574 return isl_seq_eq(a
->c
->row
[0] + 1, b
, a
->c
->n_col
- 1);
1577 static void update_constraint(struct isl_ctx
*ctx
, struct isl_hash_table
*table
,
1578 isl_int
*con
, unsigned len
, int n
, int ineq
)
1580 struct isl_hash_table_entry
*entry
;
1581 struct max_constraint
*c
;
1584 c_hash
= isl_seq_get_hash(con
+ 1, len
);
1585 entry
= isl_hash_table_find(ctx
, table
, c_hash
, max_constraint_equal
,
1591 isl_hash_table_remove(ctx
, table
, entry
);
1595 if (isl_int_gt(c
->c
->row
[0][0], con
[0]))
1597 if (isl_int_eq(c
->c
->row
[0][0], con
[0])) {
1602 c
->c
= isl_mat_cow(c
->c
);
1603 isl_int_set(c
->c
->row
[0][0], con
[0]);
1607 /* Check whether the constraint hash table "table" constains the constraint
1610 static int has_constraint(struct isl_ctx
*ctx
, struct isl_hash_table
*table
,
1611 isl_int
*con
, unsigned len
, int n
)
1613 struct isl_hash_table_entry
*entry
;
1614 struct max_constraint
*c
;
1617 c_hash
= isl_seq_get_hash(con
+ 1, len
);
1618 entry
= isl_hash_table_find(ctx
, table
, c_hash
, max_constraint_equal
,
1625 return isl_int_eq(c
->c
->row
[0][0], con
[0]);
1628 /* Check for inequality constraints of a basic set without equalities
1629 * such that the same or more stringent copies of the constraint appear
1630 * in all of the basic sets. Such constraints are necessarily facet
1631 * constraints of the convex hull.
1633 * If the resulting basic set is by chance identical to one of
1634 * the basic sets in "set", then we know that this basic set contains
1635 * all other basic sets and is therefore the convex hull of set.
1636 * In this case we set *is_hull to 1.
1638 static struct isl_basic_set
*common_constraints(struct isl_basic_set
*hull
,
1639 struct isl_set
*set
, int *is_hull
)
1642 int min_constraints
;
1644 struct max_constraint
*constraints
= NULL
;
1645 struct isl_hash_table
*table
= NULL
;
1650 for (i
= 0; i
< set
->n
; ++i
)
1651 if (set
->p
[i
]->n_eq
== 0)
1655 min_constraints
= set
->p
[i
]->n_ineq
;
1657 for (i
= best
+ 1; i
< set
->n
; ++i
) {
1658 if (set
->p
[i
]->n_eq
!= 0)
1660 if (set
->p
[i
]->n_ineq
>= min_constraints
)
1662 min_constraints
= set
->p
[i
]->n_ineq
;
1665 constraints
= isl_calloc_array(hull
->ctx
, struct max_constraint
,
1669 table
= isl_alloc_type(hull
->ctx
, struct isl_hash_table
);
1670 if (isl_hash_table_init(hull
->ctx
, table
, min_constraints
))
1673 total
= isl_dim_total(set
->dim
);
1674 for (i
= 0; i
< set
->p
[best
]->n_ineq
; ++i
) {
1675 constraints
[i
].c
= isl_mat_sub_alloc(hull
->ctx
,
1676 set
->p
[best
]->ineq
+ i
, 0, 1, 0, 1 + total
);
1677 if (!constraints
[i
].c
)
1679 constraints
[i
].ineq
= 1;
1681 for (i
= 0; i
< min_constraints
; ++i
) {
1682 struct isl_hash_table_entry
*entry
;
1684 c_hash
= isl_seq_get_hash(constraints
[i
].c
->row
[0] + 1, total
);
1685 entry
= isl_hash_table_find(hull
->ctx
, table
, c_hash
,
1686 max_constraint_equal
, constraints
[i
].c
->row
[0] + 1, 1);
1689 isl_assert(hull
->ctx
, !entry
->data
, goto error
);
1690 entry
->data
= &constraints
[i
];
1694 for (s
= 0; s
< set
->n
; ++s
) {
1698 for (i
= 0; i
< set
->p
[s
]->n_eq
; ++i
) {
1699 isl_int
*eq
= set
->p
[s
]->eq
[i
];
1700 for (j
= 0; j
< 2; ++j
) {
1701 isl_seq_neg(eq
, eq
, 1 + total
);
1702 update_constraint(hull
->ctx
, table
,
1706 for (i
= 0; i
< set
->p
[s
]->n_ineq
; ++i
) {
1707 isl_int
*ineq
= set
->p
[s
]->ineq
[i
];
1708 update_constraint(hull
->ctx
, table
, ineq
, total
, n
,
1709 set
->p
[s
]->n_eq
== 0);
1714 for (i
= 0; i
< min_constraints
; ++i
) {
1715 if (constraints
[i
].count
< n
)
1717 if (!constraints
[i
].ineq
)
1719 j
= isl_basic_set_alloc_inequality(hull
);
1722 isl_seq_cpy(hull
->ineq
[j
], constraints
[i
].c
->row
[0], 1 + total
);
1725 for (s
= 0; s
< set
->n
; ++s
) {
1726 if (set
->p
[s
]->n_eq
)
1728 if (set
->p
[s
]->n_ineq
!= hull
->n_ineq
)
1730 for (i
= 0; i
< set
->p
[s
]->n_ineq
; ++i
) {
1731 isl_int
*ineq
= set
->p
[s
]->ineq
[i
];
1732 if (!has_constraint(hull
->ctx
, table
, ineq
, total
, n
))
1735 if (i
== set
->p
[s
]->n_ineq
)
1739 isl_hash_table_clear(table
);
1740 for (i
= 0; i
< min_constraints
; ++i
)
1741 isl_mat_free(constraints
[i
].c
);
1746 isl_hash_table_clear(table
);
1749 for (i
= 0; i
< min_constraints
; ++i
)
1750 isl_mat_free(constraints
[i
].c
);
1755 /* Create a template for the convex hull of "set" and fill it up
1756 * obvious facet constraints, if any. If the result happens to
1757 * be the convex hull of "set" then *is_hull is set to 1.
1759 static struct isl_basic_set
*proto_hull(struct isl_set
*set
, int *is_hull
)
1761 struct isl_basic_set
*hull
;
1766 for (i
= 0; i
< set
->n
; ++i
) {
1767 n_ineq
+= set
->p
[i
]->n_eq
;
1768 n_ineq
+= set
->p
[i
]->n_ineq
;
1770 hull
= isl_basic_set_alloc_dim(isl_dim_copy(set
->dim
), 0, 0, n_ineq
);
1771 hull
= isl_basic_set_set_rational(hull
);
1774 return common_constraints(hull
, set
, is_hull
);
1777 static struct isl_basic_set
*uset_convex_hull_wrap(struct isl_set
*set
)
1779 struct isl_basic_set
*hull
;
1782 hull
= proto_hull(set
, &is_hull
);
1783 if (hull
&& !is_hull
) {
1784 if (hull
->n_ineq
== 0)
1785 hull
= initial_hull(hull
, set
);
1786 hull
= extend(hull
, set
);
1793 /* Compute the convex hull of a set without any parameters or
1794 * integer divisions. Depending on whether the set is bounded,
1795 * we pass control to the wrapping based convex hull or
1796 * the Fourier-Motzkin elimination based convex hull.
1797 * We also handle a few special cases before checking the boundedness.
1799 static struct isl_basic_set
*uset_convex_hull(struct isl_set
*set
)
1801 struct isl_basic_set
*convex_hull
= NULL
;
1802 struct isl_basic_set
*lin
;
1804 if (isl_set_n_dim(set
) == 0)
1805 return convex_hull_0d(set
);
1807 set
= isl_set_coalesce(set
);
1808 set
= isl_set_set_rational(set
);
1815 convex_hull
= isl_basic_set_copy(set
->p
[0]);
1819 if (isl_set_n_dim(set
) == 1)
1820 return convex_hull_1d(set
);
1822 if (isl_set_is_bounded(set
))
1823 return uset_convex_hull_wrap(set
);
1825 lin
= uset_combined_lineality_space(isl_set_copy(set
));
1828 if (isl_basic_set_is_universe(lin
)) {
1832 if (lin
->n_eq
< isl_basic_set_total_dim(lin
))
1833 return modulo_lineality(set
, lin
);
1834 isl_basic_set_free(lin
);
1836 return uset_convex_hull_unbounded(set
);
1839 isl_basic_set_free(convex_hull
);
1843 /* This is the core procedure, where "set" is a "pure" set, i.e.,
1844 * without parameters or divs and where the convex hull of set is
1845 * known to be full-dimensional.
1847 static struct isl_basic_set
*uset_convex_hull_wrap_bounded(struct isl_set
*set
)
1849 struct isl_basic_set
*convex_hull
= NULL
;
1851 if (isl_set_n_dim(set
) == 0) {
1852 convex_hull
= isl_basic_set_universe(isl_dim_copy(set
->dim
));
1854 convex_hull
= isl_basic_set_set_rational(convex_hull
);
1858 set
= isl_set_set_rational(set
);
1862 set
= isl_set_coalesce(set
);
1866 convex_hull
= isl_basic_set_copy(set
->p
[0]);
1870 if (isl_set_n_dim(set
) == 1)
1871 return convex_hull_1d(set
);
1873 return uset_convex_hull_wrap(set
);
1879 /* Compute the convex hull of set "set" with affine hull "affine_hull",
1880 * We first remove the equalities (transforming the set), compute the
1881 * convex hull of the transformed set and then add the equalities back
1882 * (after performing the inverse transformation.
1884 static struct isl_basic_set
*modulo_affine_hull(struct isl_ctx
*ctx
,
1885 struct isl_set
*set
, struct isl_basic_set
*affine_hull
)
1889 struct isl_basic_set
*dummy
;
1890 struct isl_basic_set
*convex_hull
;
1892 dummy
= isl_basic_set_remove_equalities(
1893 isl_basic_set_copy(affine_hull
), &T
, &T2
);
1896 isl_basic_set_free(dummy
);
1897 set
= isl_set_preimage(set
, T
);
1898 convex_hull
= uset_convex_hull(set
);
1899 convex_hull
= isl_basic_set_preimage(convex_hull
, T2
);
1900 convex_hull
= isl_basic_set_intersect(convex_hull
, affine_hull
);
1903 isl_basic_set_free(affine_hull
);
1908 /* Compute the convex hull of a map.
1910 * The implementation was inspired by "Extended Convex Hull" by Fukuda et al.,
1911 * specifically, the wrapping of facets to obtain new facets.
1913 struct isl_basic_map
*isl_map_convex_hull(struct isl_map
*map
)
1915 struct isl_basic_set
*bset
;
1916 struct isl_basic_map
*model
= NULL
;
1917 struct isl_basic_set
*affine_hull
= NULL
;
1918 struct isl_basic_map
*convex_hull
= NULL
;
1919 struct isl_set
*set
= NULL
;
1920 struct isl_ctx
*ctx
;
1927 convex_hull
= isl_basic_map_empty_like_map(map
);
1932 map
= isl_map_detect_equalities(map
);
1933 map
= isl_map_align_divs(map
);
1934 model
= isl_basic_map_copy(map
->p
[0]);
1935 set
= isl_map_underlying_set(map
);
1939 affine_hull
= isl_set_affine_hull(isl_set_copy(set
));
1942 if (affine_hull
->n_eq
!= 0)
1943 bset
= modulo_affine_hull(ctx
, set
, affine_hull
);
1945 isl_basic_set_free(affine_hull
);
1946 bset
= uset_convex_hull(set
);
1949 convex_hull
= isl_basic_map_overlying_set(bset
, model
);
1951 ISL_F_SET(convex_hull
, ISL_BASIC_MAP_NO_IMPLICIT
);
1952 ISL_F_SET(convex_hull
, ISL_BASIC_MAP_ALL_EQUALITIES
);
1953 ISL_F_CLR(convex_hull
, ISL_BASIC_MAP_RATIONAL
);
1957 isl_basic_map_free(model
);
1961 struct isl_basic_set
*isl_set_convex_hull(struct isl_set
*set
)
1963 return (struct isl_basic_set
*)
1964 isl_map_convex_hull((struct isl_map
*)set
);
1967 struct sh_data_entry
{
1968 struct isl_hash_table
*table
;
1969 struct isl_tab
*tab
;
1972 /* Holds the data needed during the simple hull computation.
1974 * n the number of basic sets in the original set
1975 * hull_table a hash table of already computed constraints
1976 * in the simple hull
1977 * p for each basic set,
1978 * table a hash table of the constraints
1979 * tab the tableau corresponding to the basic set
1982 struct isl_ctx
*ctx
;
1984 struct isl_hash_table
*hull_table
;
1985 struct sh_data_entry p
[1];
1988 static void sh_data_free(struct sh_data
*data
)
1994 isl_hash_table_free(data
->ctx
, data
->hull_table
);
1995 for (i
= 0; i
< data
->n
; ++i
) {
1996 isl_hash_table_free(data
->ctx
, data
->p
[i
].table
);
1997 isl_tab_free(data
->p
[i
].tab
);
2002 struct ineq_cmp_data
{
2007 static int has_ineq(const void *entry
, const void *val
)
2009 isl_int
*row
= (isl_int
*)entry
;
2010 struct ineq_cmp_data
*v
= (struct ineq_cmp_data
*)val
;
2012 return isl_seq_eq(row
+ 1, v
->p
+ 1, v
->len
) ||
2013 isl_seq_is_neg(row
+ 1, v
->p
+ 1, v
->len
);
2016 static int hash_ineq(struct isl_ctx
*ctx
, struct isl_hash_table
*table
,
2017 isl_int
*ineq
, unsigned len
)
2020 struct ineq_cmp_data v
;
2021 struct isl_hash_table_entry
*entry
;
2025 c_hash
= isl_seq_get_hash(ineq
+ 1, len
);
2026 entry
= isl_hash_table_find(ctx
, table
, c_hash
, has_ineq
, &v
, 1);
2033 /* Fill hash table "table" with the constraints of "bset".
2034 * Equalities are added as two inequalities.
2035 * The value in the hash table is a pointer to the (in)equality of "bset".
2037 static int hash_basic_set(struct isl_hash_table
*table
,
2038 struct isl_basic_set
*bset
)
2041 unsigned dim
= isl_basic_set_total_dim(bset
);
2043 for (i
= 0; i
< bset
->n_eq
; ++i
) {
2044 for (j
= 0; j
< 2; ++j
) {
2045 isl_seq_neg(bset
->eq
[i
], bset
->eq
[i
], 1 + dim
);
2046 if (hash_ineq(bset
->ctx
, table
, bset
->eq
[i
], dim
) < 0)
2050 for (i
= 0; i
< bset
->n_ineq
; ++i
) {
2051 if (hash_ineq(bset
->ctx
, table
, bset
->ineq
[i
], dim
) < 0)
2057 static struct sh_data
*sh_data_alloc(struct isl_set
*set
, unsigned n_ineq
)
2059 struct sh_data
*data
;
2062 data
= isl_calloc(set
->ctx
, struct sh_data
,
2063 sizeof(struct sh_data
) +
2064 (set
->n
- 1) * sizeof(struct sh_data_entry
));
2067 data
->ctx
= set
->ctx
;
2069 data
->hull_table
= isl_hash_table_alloc(set
->ctx
, n_ineq
);
2070 if (!data
->hull_table
)
2072 for (i
= 0; i
< set
->n
; ++i
) {
2073 data
->p
[i
].table
= isl_hash_table_alloc(set
->ctx
,
2074 2 * set
->p
[i
]->n_eq
+ set
->p
[i
]->n_ineq
);
2075 if (!data
->p
[i
].table
)
2077 if (hash_basic_set(data
->p
[i
].table
, set
->p
[i
]) < 0)
2086 /* Check if inequality "ineq" is a bound for basic set "j" or if
2087 * it can be relaxed (by increasing the constant term) to become
2088 * a bound for that basic set. In the latter case, the constant
2090 * Return 1 if "ineq" is a bound
2091 * 0 if "ineq" may attain arbitrarily small values on basic set "j"
2092 * -1 if some error occurred
2094 static int is_bound(struct sh_data
*data
, struct isl_set
*set
, int j
,
2097 enum isl_lp_result res
;
2100 if (!data
->p
[j
].tab
) {
2101 data
->p
[j
].tab
= isl_tab_from_basic_set(set
->p
[j
]);
2102 if (!data
->p
[j
].tab
)
2108 res
= isl_tab_min(data
->p
[j
].tab
, ineq
, data
->ctx
->one
,
2110 if (res
== isl_lp_ok
&& isl_int_is_neg(opt
))
2111 isl_int_sub(ineq
[0], ineq
[0], opt
);
2115 return res
== isl_lp_ok
? 1 :
2116 res
== isl_lp_unbounded
? 0 : -1;
2119 /* Check if inequality "ineq" from basic set "i" can be relaxed to
2120 * become a bound on the whole set. If so, add the (relaxed) inequality
2123 * We first check if "hull" already contains a translate of the inequality.
2124 * If so, we are done.
2125 * Then, we check if any of the previous basic sets contains a translate
2126 * of the inequality. If so, then we have already considered this
2127 * inequality and we are done.
2128 * Otherwise, for each basic set other than "i", we check if the inequality
2129 * is a bound on the basic set.
2130 * For previous basic sets, we know that they do not contain a translate
2131 * of the inequality, so we directly call is_bound.
2132 * For following basic sets, we first check if a translate of the
2133 * inequality appears in its description and if so directly update
2134 * the inequality accordingly.
2136 static struct isl_basic_set
*add_bound(struct isl_basic_set
*hull
,
2137 struct sh_data
*data
, struct isl_set
*set
, int i
, isl_int
*ineq
)
2140 struct ineq_cmp_data v
;
2141 struct isl_hash_table_entry
*entry
;
2147 v
.len
= isl_basic_set_total_dim(hull
);
2149 c_hash
= isl_seq_get_hash(ineq
+ 1, v
.len
);
2151 entry
= isl_hash_table_find(hull
->ctx
, data
->hull_table
, c_hash
,
2156 for (j
= 0; j
< i
; ++j
) {
2157 entry
= isl_hash_table_find(hull
->ctx
, data
->p
[j
].table
,
2158 c_hash
, has_ineq
, &v
, 0);
2165 k
= isl_basic_set_alloc_inequality(hull
);
2166 isl_seq_cpy(hull
->ineq
[k
], ineq
, 1 + v
.len
);
2170 for (j
= 0; j
< i
; ++j
) {
2172 bound
= is_bound(data
, set
, j
, hull
->ineq
[k
]);
2179 isl_basic_set_free_inequality(hull
, 1);
2183 for (j
= i
+ 1; j
< set
->n
; ++j
) {
2186 entry
= isl_hash_table_find(hull
->ctx
, data
->p
[j
].table
,
2187 c_hash
, has_ineq
, &v
, 0);
2189 ineq_j
= entry
->data
;
2190 neg
= isl_seq_is_neg(ineq_j
+ 1,
2191 hull
->ineq
[k
] + 1, v
.len
);
2193 isl_int_neg(ineq_j
[0], ineq_j
[0]);
2194 if (isl_int_gt(ineq_j
[0], hull
->ineq
[k
][0]))
2195 isl_int_set(hull
->ineq
[k
][0], ineq_j
[0]);
2197 isl_int_neg(ineq_j
[0], ineq_j
[0]);
2200 bound
= is_bound(data
, set
, j
, hull
->ineq
[k
]);
2207 isl_basic_set_free_inequality(hull
, 1);
2211 entry
= isl_hash_table_find(hull
->ctx
, data
->hull_table
, c_hash
,
2215 entry
->data
= hull
->ineq
[k
];
2219 isl_basic_set_free(hull
);
2223 /* Check if any inequality from basic set "i" can be relaxed to
2224 * become a bound on the whole set. If so, add the (relaxed) inequality
2227 static struct isl_basic_set
*add_bounds(struct isl_basic_set
*bset
,
2228 struct sh_data
*data
, struct isl_set
*set
, int i
)
2231 unsigned dim
= isl_basic_set_total_dim(bset
);
2233 for (j
= 0; j
< set
->p
[i
]->n_eq
; ++j
) {
2234 for (k
= 0; k
< 2; ++k
) {
2235 isl_seq_neg(set
->p
[i
]->eq
[j
], set
->p
[i
]->eq
[j
], 1+dim
);
2236 add_bound(bset
, data
, set
, i
, set
->p
[i
]->eq
[j
]);
2239 for (j
= 0; j
< set
->p
[i
]->n_ineq
; ++j
)
2240 add_bound(bset
, data
, set
, i
, set
->p
[i
]->ineq
[j
]);
2244 /* Compute a superset of the convex hull of set that is described
2245 * by only translates of the constraints in the constituents of set.
2247 static struct isl_basic_set
*uset_simple_hull(struct isl_set
*set
)
2249 struct sh_data
*data
= NULL
;
2250 struct isl_basic_set
*hull
= NULL
;
2258 for (i
= 0; i
< set
->n
; ++i
) {
2261 n_ineq
+= 2 * set
->p
[i
]->n_eq
+ set
->p
[i
]->n_ineq
;
2264 hull
= isl_basic_set_alloc_dim(isl_dim_copy(set
->dim
), 0, 0, n_ineq
);
2268 data
= sh_data_alloc(set
, n_ineq
);
2272 for (i
= 0; i
< set
->n
; ++i
)
2273 hull
= add_bounds(hull
, data
, set
, i
);
2281 isl_basic_set_free(hull
);
2286 /* Compute a superset of the convex hull of map that is described
2287 * by only translates of the constraints in the constituents of map.
2289 struct isl_basic_map
*isl_map_simple_hull(struct isl_map
*map
)
2291 struct isl_set
*set
= NULL
;
2292 struct isl_basic_map
*model
= NULL
;
2293 struct isl_basic_map
*hull
;
2294 struct isl_basic_map
*affine_hull
;
2295 struct isl_basic_set
*bset
= NULL
;
2300 hull
= isl_basic_map_empty_like_map(map
);
2305 hull
= isl_basic_map_copy(map
->p
[0]);
2310 map
= isl_map_detect_equalities(map
);
2311 affine_hull
= isl_map_affine_hull(isl_map_copy(map
));
2312 map
= isl_map_align_divs(map
);
2313 model
= isl_basic_map_copy(map
->p
[0]);
2315 set
= isl_map_underlying_set(map
);
2317 bset
= uset_simple_hull(set
);
2319 hull
= isl_basic_map_overlying_set(bset
, model
);
2321 hull
= isl_basic_map_intersect(hull
, affine_hull
);
2322 hull
= isl_basic_map_convex_hull(hull
);
2323 ISL_F_SET(hull
, ISL_BASIC_MAP_NO_IMPLICIT
);
2324 ISL_F_SET(hull
, ISL_BASIC_MAP_ALL_EQUALITIES
);
2329 struct isl_basic_set
*isl_set_simple_hull(struct isl_set
*set
)
2331 return (struct isl_basic_set
*)
2332 isl_map_simple_hull((struct isl_map
*)set
);
2335 /* Given a set "set", return parametric bounds on the dimension "dim".
2337 static struct isl_basic_set
*set_bounds(struct isl_set
*set
, int dim
)
2339 unsigned set_dim
= isl_set_dim(set
, isl_dim_set
);
2340 set
= isl_set_copy(set
);
2341 set
= isl_set_eliminate_dims(set
, dim
+ 1, set_dim
- (dim
+ 1));
2342 set
= isl_set_eliminate_dims(set
, 0, dim
);
2343 return isl_set_convex_hull(set
);
2346 /* Computes a "simple hull" and then check if each dimension in the
2347 * resulting hull is bounded by a symbolic constant. If not, the
2348 * hull is intersected with the corresponding bounds on the whole set.
2350 struct isl_basic_set
*isl_set_bounded_simple_hull(struct isl_set
*set
)
2353 struct isl_basic_set
*hull
;
2354 unsigned nparam
, left
;
2355 int removed_divs
= 0;
2357 hull
= isl_set_simple_hull(isl_set_copy(set
));
2361 nparam
= isl_basic_set_dim(hull
, isl_dim_param
);
2362 for (i
= 0; i
< isl_basic_set_dim(hull
, isl_dim_set
); ++i
) {
2363 int lower
= 0, upper
= 0;
2364 struct isl_basic_set
*bounds
;
2366 left
= isl_basic_set_total_dim(hull
) - nparam
- i
- 1;
2367 for (j
= 0; j
< hull
->n_eq
; ++j
) {
2368 if (isl_int_is_zero(hull
->eq
[j
][1 + nparam
+ i
]))
2370 if (isl_seq_first_non_zero(hull
->eq
[j
]+1+nparam
+i
+1,
2377 for (j
= 0; j
< hull
->n_ineq
; ++j
) {
2378 if (isl_int_is_zero(hull
->ineq
[j
][1 + nparam
+ i
]))
2380 if (isl_seq_first_non_zero(hull
->ineq
[j
]+1+nparam
+i
+1,
2382 isl_seq_first_non_zero(hull
->ineq
[j
]+1+nparam
,
2385 if (isl_int_is_pos(hull
->ineq
[j
][1 + nparam
+ i
]))
2396 if (!removed_divs
) {
2397 set
= isl_set_remove_divs(set
);
2402 bounds
= set_bounds(set
, i
);
2403 hull
= isl_basic_set_intersect(hull
, bounds
);