3 #include "isl_map_private.h"
7 #include "isl_equalities.h"
10 static struct isl_basic_set
*uset_convex_hull_wrap_bounded(struct isl_set
*set
);
12 static void swap_ineq(struct isl_basic_map
*bmap
, unsigned i
, unsigned j
)
18 bmap
->ineq
[i
] = bmap
->ineq
[j
];
23 /* Return 1 if constraint c is redundant with respect to the constraints
24 * in bmap. If c is a lower [upper] bound in some variable and bmap
25 * does not have a lower [upper] bound in that variable, then c cannot
26 * be redundant and we do not need solve any lp.
28 int isl_basic_map_constraint_is_redundant(struct isl_basic_map
**bmap
,
29 isl_int
*c
, isl_int
*opt_n
, isl_int
*opt_d
)
31 enum isl_lp_result res
;
38 total
= isl_basic_map_total_dim(*bmap
);
39 for (i
= 0; i
< total
; ++i
) {
41 if (isl_int_is_zero(c
[1+i
]))
43 sign
= isl_int_sgn(c
[1+i
]);
44 for (j
= 0; j
< (*bmap
)->n_ineq
; ++j
)
45 if (sign
== isl_int_sgn((*bmap
)->ineq
[j
][1+i
]))
47 if (j
== (*bmap
)->n_ineq
)
53 res
= isl_basic_map_solve_lp(*bmap
, 0, c
, (*bmap
)->ctx
->one
,
55 if (res
== isl_lp_unbounded
)
57 if (res
== isl_lp_error
)
59 if (res
== isl_lp_empty
) {
60 *bmap
= isl_basic_map_set_to_empty(*bmap
);
63 return !isl_int_is_neg(*opt_n
);
66 int isl_basic_set_constraint_is_redundant(struct isl_basic_set
**bset
,
67 isl_int
*c
, isl_int
*opt_n
, isl_int
*opt_d
)
69 return isl_basic_map_constraint_is_redundant(
70 (struct isl_basic_map
**)bset
, c
, opt_n
, opt_d
);
73 /* Compute the convex hull of a basic map, by removing the redundant
74 * constraints. If the minimal value along the normal of a constraint
75 * is the same if the constraint is removed, then the constraint is redundant.
77 * Alternatively, we could have intersected the basic map with the
78 * corresponding equality and the checked if the dimension was that
81 struct isl_basic_map
*isl_basic_map_convex_hull(struct isl_basic_map
*bmap
)
88 bmap
= isl_basic_map_gauss(bmap
, NULL
);
89 if (ISL_F_ISSET(bmap
, ISL_BASIC_MAP_EMPTY
))
91 if (ISL_F_ISSET(bmap
, ISL_BASIC_MAP_NO_REDUNDANT
))
93 if (bmap
->n_ineq
<= 1)
96 tab
= isl_tab_from_basic_map(bmap
);
97 tab
= isl_tab_detect_implicit_equalities(tab
);
98 tab
= isl_tab_detect_redundant(tab
);
99 bmap
= isl_basic_map_update_from_tab(bmap
, tab
);
101 ISL_F_SET(bmap
, ISL_BASIC_MAP_NO_IMPLICIT
);
102 ISL_F_SET(bmap
, ISL_BASIC_MAP_NO_REDUNDANT
);
106 struct isl_basic_set
*isl_basic_set_convex_hull(struct isl_basic_set
*bset
)
108 return (struct isl_basic_set
*)
109 isl_basic_map_convex_hull((struct isl_basic_map
*)bset
);
112 /* Check if the set set is bound in the direction of the affine
113 * constraint c and if so, set the constant term such that the
114 * resulting constraint is a bounding constraint for the set.
116 static int uset_is_bound(struct isl_set
*set
, isl_int
*c
, unsigned len
)
124 isl_int_init(opt_denom
);
126 for (j
= 0; j
< set
->n
; ++j
) {
127 enum isl_lp_result res
;
129 if (ISL_F_ISSET(set
->p
[j
], ISL_BASIC_SET_EMPTY
))
132 res
= isl_basic_set_solve_lp(set
->p
[j
],
133 0, c
, set
->ctx
->one
, &opt
, &opt_denom
, NULL
);
134 if (res
== isl_lp_unbounded
)
136 if (res
== isl_lp_error
)
138 if (res
== isl_lp_empty
) {
139 set
->p
[j
] = isl_basic_set_set_to_empty(set
->p
[j
]);
144 if (!isl_int_is_one(opt_denom
))
145 isl_seq_scale(c
, c
, opt_denom
, len
);
146 if (first
|| isl_int_is_neg(opt
))
147 isl_int_sub(c
[0], c
[0], opt
);
151 isl_int_clear(opt_denom
);
155 isl_int_clear(opt_denom
);
159 /* Check if "c" is a direction that is independent of the previously found "n"
161 * If so, add it to the list, with the negative of the lower bound
162 * in the constant position, i.e., such that c corresponds to a bounding
163 * hyperplane (but not necessarily a facet).
164 * Assumes set "set" is bounded.
166 static int is_independent_bound(struct isl_set
*set
, isl_int
*c
,
167 struct isl_mat
*dirs
, int n
)
172 isl_seq_cpy(dirs
->row
[n
]+1, c
+1, dirs
->n_col
-1);
174 int pos
= isl_seq_first_non_zero(dirs
->row
[n
]+1, dirs
->n_col
-1);
177 for (i
= 0; i
< n
; ++i
) {
179 pos_i
= isl_seq_first_non_zero(dirs
->row
[i
]+1, dirs
->n_col
-1);
184 isl_seq_elim(dirs
->row
[n
]+1, dirs
->row
[i
]+1, pos
,
185 dirs
->n_col
-1, NULL
);
186 pos
= isl_seq_first_non_zero(dirs
->row
[n
]+1, dirs
->n_col
-1);
192 is_bound
= uset_is_bound(set
, dirs
->row
[n
], dirs
->n_col
);
197 isl_int
*t
= dirs
->row
[n
];
198 for (k
= n
; k
> i
; --k
)
199 dirs
->row
[k
] = dirs
->row
[k
-1];
205 /* Compute and return a maximal set of linearly independent bounds
206 * on the set "set", based on the constraints of the basic sets
209 static struct isl_mat
*independent_bounds(struct isl_set
*set
)
212 struct isl_mat
*dirs
= NULL
;
213 unsigned dim
= isl_set_n_dim(set
);
215 dirs
= isl_mat_alloc(set
->ctx
, dim
, 1+dim
);
220 for (i
= 0; n
< dim
&& i
< set
->n
; ++i
) {
222 struct isl_basic_set
*bset
= set
->p
[i
];
224 for (j
= 0; n
< dim
&& j
< bset
->n_eq
; ++j
) {
225 f
= is_independent_bound(set
, bset
->eq
[j
], dirs
, n
);
231 for (j
= 0; n
< dim
&& j
< bset
->n_ineq
; ++j
) {
232 f
= is_independent_bound(set
, bset
->ineq
[j
], dirs
, n
);
246 struct isl_basic_set
*isl_basic_set_set_rational(struct isl_basic_set
*bset
)
251 if (ISL_F_ISSET(bset
, ISL_BASIC_MAP_RATIONAL
))
254 bset
= isl_basic_set_cow(bset
);
258 ISL_F_SET(bset
, ISL_BASIC_MAP_RATIONAL
);
260 return isl_basic_set_finalize(bset
);
263 static struct isl_set
*isl_set_set_rational(struct isl_set
*set
)
267 set
= isl_set_cow(set
);
270 for (i
= 0; i
< set
->n
; ++i
) {
271 set
->p
[i
] = isl_basic_set_set_rational(set
->p
[i
]);
281 static struct isl_basic_set
*isl_basic_set_add_equality(
282 struct isl_basic_set
*bset
, isl_int
*c
)
287 if (ISL_F_ISSET(bset
, ISL_BASIC_SET_EMPTY
))
290 isl_assert(bset
->ctx
, isl_basic_set_n_param(bset
) == 0, goto error
);
291 isl_assert(bset
->ctx
, bset
->n_div
== 0, goto error
);
292 dim
= isl_basic_set_n_dim(bset
);
293 bset
= isl_basic_set_cow(bset
);
294 bset
= isl_basic_set_extend(bset
, 0, dim
, 0, 1, 0);
295 i
= isl_basic_set_alloc_equality(bset
);
298 isl_seq_cpy(bset
->eq
[i
], c
, 1 + dim
);
301 isl_basic_set_free(bset
);
305 static struct isl_set
*isl_set_add_equality(struct isl_set
*set
, isl_int
*c
)
309 set
= isl_set_cow(set
);
312 for (i
= 0; i
< set
->n
; ++i
) {
313 set
->p
[i
] = isl_basic_set_add_equality(set
->p
[i
], c
);
323 /* Given a union of basic sets, construct the constraints for wrapping
324 * a facet around one of its ridges.
325 * In particular, if each of n the d-dimensional basic sets i in "set"
326 * contains the origin, satisfies the constraints x_1 >= 0 and x_2 >= 0
327 * and is defined by the constraints
331 * then the resulting set is of dimension n*(1+d) and has as constraints
340 static struct isl_basic_set
*wrap_constraints(struct isl_set
*set
)
342 struct isl_basic_set
*lp
;
346 unsigned dim
, lp_dim
;
351 dim
= 1 + isl_set_n_dim(set
);
354 for (i
= 0; i
< set
->n
; ++i
) {
355 n_eq
+= set
->p
[i
]->n_eq
;
356 n_ineq
+= set
->p
[i
]->n_ineq
;
358 lp
= isl_basic_set_alloc(set
->ctx
, 0, dim
* set
->n
, 0, n_eq
, n_ineq
);
361 lp_dim
= isl_basic_set_n_dim(lp
);
362 k
= isl_basic_set_alloc_equality(lp
);
363 isl_int_set_si(lp
->eq
[k
][0], -1);
364 for (i
= 0; i
< set
->n
; ++i
) {
365 isl_int_set_si(lp
->eq
[k
][1+dim
*i
], 0);
366 isl_int_set_si(lp
->eq
[k
][1+dim
*i
+1], 1);
367 isl_seq_clr(lp
->eq
[k
]+1+dim
*i
+2, dim
-2);
369 for (i
= 0; i
< set
->n
; ++i
) {
370 k
= isl_basic_set_alloc_inequality(lp
);
371 isl_seq_clr(lp
->ineq
[k
], 1+lp_dim
);
372 isl_int_set_si(lp
->ineq
[k
][1+dim
*i
], 1);
374 for (j
= 0; j
< set
->p
[i
]->n_eq
; ++j
) {
375 k
= isl_basic_set_alloc_equality(lp
);
376 isl_seq_clr(lp
->eq
[k
], 1+dim
*i
);
377 isl_seq_cpy(lp
->eq
[k
]+1+dim
*i
, set
->p
[i
]->eq
[j
], dim
);
378 isl_seq_clr(lp
->eq
[k
]+1+dim
*(i
+1), dim
*(set
->n
-i
-1));
381 for (j
= 0; j
< set
->p
[i
]->n_ineq
; ++j
) {
382 k
= isl_basic_set_alloc_inequality(lp
);
383 isl_seq_clr(lp
->ineq
[k
], 1+dim
*i
);
384 isl_seq_cpy(lp
->ineq
[k
]+1+dim
*i
, set
->p
[i
]->ineq
[j
], dim
);
385 isl_seq_clr(lp
->ineq
[k
]+1+dim
*(i
+1), dim
*(set
->n
-i
-1));
391 /* Given a facet "facet" of the convex hull of "set" and a facet "ridge"
392 * of that facet, compute the other facet of the convex hull that contains
395 * We first transform the set such that the facet constraint becomes
399 * I.e., the facet lies in
403 * and on that facet, the constraint that defines the ridge is
407 * (This transformation is not strictly needed, all that is needed is
408 * that the ridge contains the origin.)
410 * Since the ridge contains the origin, the cone of the convex hull
411 * will be of the form
416 * with this second constraint defining the new facet.
417 * The constant a is obtained by settting x_1 in the cone of the
418 * convex hull to 1 and minimizing x_2.
419 * Now, each element in the cone of the convex hull is the sum
420 * of elements in the cones of the basic sets.
421 * If a_i is the dilation factor of basic set i, then the problem
422 * we need to solve is
435 * the constraints of each (transformed) basic set.
436 * If a = n/d, then the constraint defining the new facet (in the transformed
439 * -n x_1 + d x_2 >= 0
441 * In the original space, we need to take the same combination of the
442 * corresponding constraints "facet" and "ridge".
444 * Note that a is always finite, since we only apply the wrapping
445 * technique to a union of polytopes.
447 static isl_int
*wrap_facet(struct isl_set
*set
, isl_int
*facet
, isl_int
*ridge
)
450 struct isl_mat
*T
= NULL
;
451 struct isl_basic_set
*lp
= NULL
;
453 enum isl_lp_result res
;
457 set
= isl_set_copy(set
);
459 dim
= 1 + isl_set_n_dim(set
);
460 T
= isl_mat_alloc(set
->ctx
, 3, dim
);
463 isl_int_set_si(T
->row
[0][0], 1);
464 isl_seq_clr(T
->row
[0]+1, dim
- 1);
465 isl_seq_cpy(T
->row
[1], facet
, dim
);
466 isl_seq_cpy(T
->row
[2], ridge
, dim
);
467 T
= isl_mat_right_inverse(T
);
468 set
= isl_set_preimage(set
, T
);
472 lp
= wrap_constraints(set
);
473 obj
= isl_vec_alloc(set
->ctx
, 1 + dim
*set
->n
);
476 isl_int_set_si(obj
->block
.data
[0], 0);
477 for (i
= 0; i
< set
->n
; ++i
) {
478 isl_seq_clr(obj
->block
.data
+ 1 + dim
*i
, 2);
479 isl_int_set_si(obj
->block
.data
[1 + dim
*i
+2], 1);
480 isl_seq_clr(obj
->block
.data
+ 1 + dim
*i
+3, dim
-3);
484 res
= isl_basic_set_solve_lp(lp
, 0,
485 obj
->block
.data
, set
->ctx
->one
, &num
, &den
, NULL
);
486 if (res
== isl_lp_ok
) {
487 isl_int_neg(num
, num
);
488 isl_seq_combine(facet
, num
, facet
, den
, ridge
, dim
);
493 isl_basic_set_free(lp
);
495 isl_assert(set
->ctx
, res
== isl_lp_ok
, return NULL
);
498 isl_basic_set_free(lp
);
504 /* Given a set of d linearly independent bounding constraints of the
505 * convex hull of "set", compute the constraint of a facet of "set".
507 * We first compute the intersection with the first bounding hyperplane
508 * and remove the component corresponding to this hyperplane from
509 * other bounds (in homogeneous space).
510 * We then wrap around one of the remaining bounding constraints
511 * and continue the process until all bounding constraints have been
512 * taken into account.
513 * The resulting linear combination of the bounding constraints will
514 * correspond to a facet of the convex hull.
516 static struct isl_mat
*initial_facet_constraint(struct isl_set
*set
,
517 struct isl_mat
*bounds
)
519 struct isl_set
*slice
= NULL
;
520 struct isl_basic_set
*face
= NULL
;
521 struct isl_mat
*m
, *U
, *Q
;
523 unsigned dim
= isl_set_n_dim(set
);
525 isl_assert(set
->ctx
, set
->n
> 0, goto error
);
526 isl_assert(set
->ctx
, bounds
->n_row
== dim
, goto error
);
528 while (bounds
->n_row
> 1) {
529 slice
= isl_set_copy(set
);
530 slice
= isl_set_add_equality(slice
, bounds
->row
[0]);
531 face
= isl_set_affine_hull(slice
);
534 if (face
->n_eq
== 1) {
535 isl_basic_set_free(face
);
538 m
= isl_mat_alloc(set
->ctx
, 1 + face
->n_eq
, 1 + dim
);
541 isl_int_set_si(m
->row
[0][0], 1);
542 isl_seq_clr(m
->row
[0]+1, dim
);
543 for (i
= 0; i
< face
->n_eq
; ++i
)
544 isl_seq_cpy(m
->row
[1 + i
], face
->eq
[i
], 1 + dim
);
545 U
= isl_mat_right_inverse(m
);
546 Q
= isl_mat_right_inverse(isl_mat_copy(U
));
547 U
= isl_mat_drop_cols(U
, 1 + face
->n_eq
, dim
- face
->n_eq
);
548 Q
= isl_mat_drop_rows(Q
, 1 + face
->n_eq
, dim
- face
->n_eq
);
549 U
= isl_mat_drop_cols(U
, 0, 1);
550 Q
= isl_mat_drop_rows(Q
, 0, 1);
551 bounds
= isl_mat_product(bounds
, U
);
552 bounds
= isl_mat_product(bounds
, Q
);
553 while (isl_seq_first_non_zero(bounds
->row
[bounds
->n_row
-1],
554 bounds
->n_col
) == -1) {
556 isl_assert(set
->ctx
, bounds
->n_row
> 1, goto error
);
558 if (!wrap_facet(set
, bounds
->row
[0],
559 bounds
->row
[bounds
->n_row
-1]))
561 isl_basic_set_free(face
);
566 isl_basic_set_free(face
);
567 isl_mat_free(bounds
);
571 /* Given the bounding constraint "c" of a facet of the convex hull of "set",
572 * compute a hyperplane description of the facet, i.e., compute the facets
575 * We compute an affine transformation that transforms the constraint
584 * by computing the right inverse U of a matrix that starts with the rows
597 * Since z_1 is zero, we can drop this variable as well as the corresponding
598 * column of U to obtain
606 * with Q' equal to Q, but without the corresponding row.
607 * After computing the facets of the facet in the z' space,
608 * we convert them back to the x space through Q.
610 static struct isl_basic_set
*compute_facet(struct isl_set
*set
, isl_int
*c
)
612 struct isl_mat
*m
, *U
, *Q
;
613 struct isl_basic_set
*facet
= NULL
;
618 set
= isl_set_copy(set
);
619 dim
= isl_set_n_dim(set
);
620 m
= isl_mat_alloc(set
->ctx
, 2, 1 + dim
);
623 isl_int_set_si(m
->row
[0][0], 1);
624 isl_seq_clr(m
->row
[0]+1, dim
);
625 isl_seq_cpy(m
->row
[1], c
, 1+dim
);
626 U
= isl_mat_right_inverse(m
);
627 Q
= isl_mat_right_inverse(isl_mat_copy(U
));
628 U
= isl_mat_drop_cols(U
, 1, 1);
629 Q
= isl_mat_drop_rows(Q
, 1, 1);
630 set
= isl_set_preimage(set
, U
);
631 facet
= uset_convex_hull_wrap_bounded(set
);
632 facet
= isl_basic_set_preimage(facet
, Q
);
633 isl_assert(ctx
, facet
->n_eq
== 0, goto error
);
636 isl_basic_set_free(facet
);
641 /* Given an initial facet constraint, compute the remaining facets.
642 * We do this by running through all facets found so far and computing
643 * the adjacent facets through wrapping, adding those facets that we
644 * hadn't already found before.
646 * For each facet we have found so far, we first compute its facets
647 * in the resulting convex hull. That is, we compute the ridges
648 * of the resulting convex hull contained in the facet.
649 * We also compute the corresponding facet in the current approximation
650 * of the convex hull. There is no need to wrap around the ridges
651 * in this facet since that would result in a facet that is already
652 * present in the current approximation.
654 * This function can still be significantly optimized by checking which of
655 * the facets of the basic sets are also facets of the convex hull and
656 * using all the facets so far to help in constructing the facets of the
659 * using the technique in section "3.1 Ridge Generation" of
660 * "Extended Convex Hull" by Fukuda et al.
662 static struct isl_basic_set
*extend(struct isl_basic_set
*hull
,
667 struct isl_basic_set
*facet
= NULL
;
668 struct isl_basic_set
*hull_facet
= NULL
;
671 isl_assert(set
->ctx
, set
->n
> 0, goto error
);
673 dim
= isl_set_n_dim(set
);
675 for (i
= 0; i
< hull
->n_ineq
; ++i
) {
676 facet
= compute_facet(set
, hull
->ineq
[i
]);
677 facet
= isl_basic_set_add_equality(facet
, hull
->ineq
[i
]);
678 facet
= isl_basic_set_gauss(facet
, NULL
);
679 facet
= isl_basic_set_normalize_constraints(facet
);
680 hull_facet
= isl_basic_set_copy(hull
);
681 hull_facet
= isl_basic_set_add_equality(hull_facet
, hull
->ineq
[i
]);
682 hull_facet
= isl_basic_set_gauss(hull_facet
, NULL
);
683 hull_facet
= isl_basic_set_normalize_constraints(hull_facet
);
686 hull
= isl_basic_set_cow(hull
);
687 hull
= isl_basic_set_extend_dim(hull
,
688 isl_dim_copy(hull
->dim
), 0, 0, facet
->n_ineq
);
689 for (j
= 0; j
< facet
->n_ineq
; ++j
) {
690 for (f
= 0; f
< hull_facet
->n_ineq
; ++f
)
691 if (isl_seq_eq(facet
->ineq
[j
],
692 hull_facet
->ineq
[f
], 1 + dim
))
694 if (f
< hull_facet
->n_ineq
)
696 k
= isl_basic_set_alloc_inequality(hull
);
699 isl_seq_cpy(hull
->ineq
[k
], hull
->ineq
[i
], 1+dim
);
700 if (!wrap_facet(set
, hull
->ineq
[k
], facet
->ineq
[j
]))
703 isl_basic_set_free(hull_facet
);
704 isl_basic_set_free(facet
);
706 hull
= isl_basic_set_simplify(hull
);
707 hull
= isl_basic_set_finalize(hull
);
710 isl_basic_set_free(hull_facet
);
711 isl_basic_set_free(facet
);
712 isl_basic_set_free(hull
);
716 /* Special case for computing the convex hull of a one dimensional set.
717 * We simply collect the lower and upper bounds of each basic set
718 * and the biggest of those.
720 static struct isl_basic_set
*convex_hull_1d(struct isl_set
*set
)
722 struct isl_mat
*c
= NULL
;
723 isl_int
*lower
= NULL
;
724 isl_int
*upper
= NULL
;
727 struct isl_basic_set
*hull
;
729 for (i
= 0; i
< set
->n
; ++i
) {
730 set
->p
[i
] = isl_basic_set_simplify(set
->p
[i
]);
734 set
= isl_set_remove_empty_parts(set
);
737 isl_assert(set
->ctx
, set
->n
> 0, goto error
);
738 c
= isl_mat_alloc(set
->ctx
, 2, 2);
742 if (set
->p
[0]->n_eq
> 0) {
743 isl_assert(set
->ctx
, set
->p
[0]->n_eq
== 1, goto error
);
746 if (isl_int_is_pos(set
->p
[0]->eq
[0][1])) {
747 isl_seq_cpy(lower
, set
->p
[0]->eq
[0], 2);
748 isl_seq_neg(upper
, set
->p
[0]->eq
[0], 2);
750 isl_seq_neg(lower
, set
->p
[0]->eq
[0], 2);
751 isl_seq_cpy(upper
, set
->p
[0]->eq
[0], 2);
754 for (j
= 0; j
< set
->p
[0]->n_ineq
; ++j
) {
755 if (isl_int_is_pos(set
->p
[0]->ineq
[j
][1])) {
757 isl_seq_cpy(lower
, set
->p
[0]->ineq
[j
], 2);
760 isl_seq_cpy(upper
, set
->p
[0]->ineq
[j
], 2);
767 for (i
= 0; i
< set
->n
; ++i
) {
768 struct isl_basic_set
*bset
= set
->p
[i
];
772 for (j
= 0; j
< bset
->n_eq
; ++j
) {
776 isl_int_mul(a
, lower
[0], bset
->eq
[j
][1]);
777 isl_int_mul(b
, lower
[1], bset
->eq
[j
][0]);
778 if (isl_int_lt(a
, b
) && isl_int_is_pos(bset
->eq
[j
][1]))
779 isl_seq_cpy(lower
, bset
->eq
[j
], 2);
780 if (isl_int_gt(a
, b
) && isl_int_is_neg(bset
->eq
[j
][1]))
781 isl_seq_neg(lower
, bset
->eq
[j
], 2);
784 isl_int_mul(a
, upper
[0], bset
->eq
[j
][1]);
785 isl_int_mul(b
, upper
[1], bset
->eq
[j
][0]);
786 if (isl_int_lt(a
, b
) && isl_int_is_pos(bset
->eq
[j
][1]))
787 isl_seq_neg(upper
, bset
->eq
[j
], 2);
788 if (isl_int_gt(a
, b
) && isl_int_is_neg(bset
->eq
[j
][1]))
789 isl_seq_cpy(upper
, bset
->eq
[j
], 2);
792 for (j
= 0; j
< bset
->n_ineq
; ++j
) {
793 if (isl_int_is_pos(bset
->ineq
[j
][1]))
795 if (isl_int_is_neg(bset
->ineq
[j
][1]))
797 if (lower
&& isl_int_is_pos(bset
->ineq
[j
][1])) {
798 isl_int_mul(a
, lower
[0], bset
->ineq
[j
][1]);
799 isl_int_mul(b
, lower
[1], bset
->ineq
[j
][0]);
800 if (isl_int_lt(a
, b
))
801 isl_seq_cpy(lower
, bset
->ineq
[j
], 2);
803 if (upper
&& isl_int_is_neg(bset
->ineq
[j
][1])) {
804 isl_int_mul(a
, upper
[0], bset
->ineq
[j
][1]);
805 isl_int_mul(b
, upper
[1], bset
->ineq
[j
][0]);
806 if (isl_int_gt(a
, b
))
807 isl_seq_cpy(upper
, bset
->ineq
[j
], 2);
818 hull
= isl_basic_set_alloc(set
->ctx
, 0, 1, 0, 0, 2);
819 hull
= isl_basic_set_set_rational(hull
);
823 k
= isl_basic_set_alloc_inequality(hull
);
824 isl_seq_cpy(hull
->ineq
[k
], lower
, 2);
827 k
= isl_basic_set_alloc_inequality(hull
);
828 isl_seq_cpy(hull
->ineq
[k
], upper
, 2);
830 hull
= isl_basic_set_finalize(hull
);
840 /* Project out final n dimensions using Fourier-Motzkin */
841 static struct isl_set
*set_project_out(struct isl_ctx
*ctx
,
842 struct isl_set
*set
, unsigned n
)
844 return isl_set_remove_dims(set
, isl_set_n_dim(set
) - n
, n
);
847 static struct isl_basic_set
*convex_hull_0d(struct isl_set
*set
)
849 struct isl_basic_set
*convex_hull
;
854 if (isl_set_is_empty(set
))
855 convex_hull
= isl_basic_set_empty(isl_dim_copy(set
->dim
));
857 convex_hull
= isl_basic_set_universe(isl_dim_copy(set
->dim
));
862 /* Compute the convex hull of a pair of basic sets without any parameters or
863 * integer divisions using Fourier-Motzkin elimination.
864 * The convex hull is the set of all points that can be written as
865 * the sum of points from both basic sets (in homogeneous coordinates).
866 * We set up the constraints in a space with dimensions for each of
867 * the three sets and then project out the dimensions corresponding
868 * to the two original basic sets, retaining only those corresponding
869 * to the convex hull.
871 static struct isl_basic_set
*convex_hull_pair_elim(struct isl_basic_set
*bset1
,
872 struct isl_basic_set
*bset2
)
875 struct isl_basic_set
*bset
[2];
876 struct isl_basic_set
*hull
= NULL
;
879 if (!bset1
|| !bset2
)
882 dim
= isl_basic_set_n_dim(bset1
);
883 hull
= isl_basic_set_alloc(bset1
->ctx
, 0, 2 + 3 * dim
, 0,
884 1 + dim
+ bset1
->n_eq
+ bset2
->n_eq
,
885 2 + bset1
->n_ineq
+ bset2
->n_ineq
);
888 for (i
= 0; i
< 2; ++i
) {
889 for (j
= 0; j
< bset
[i
]->n_eq
; ++j
) {
890 k
= isl_basic_set_alloc_equality(hull
);
893 isl_seq_clr(hull
->eq
[k
], (i
+1) * (1+dim
));
894 isl_seq_clr(hull
->eq
[k
]+(i
+2)*(1+dim
), (1-i
)*(1+dim
));
895 isl_seq_cpy(hull
->eq
[k
]+(i
+1)*(1+dim
), bset
[i
]->eq
[j
],
898 for (j
= 0; j
< bset
[i
]->n_ineq
; ++j
) {
899 k
= isl_basic_set_alloc_inequality(hull
);
902 isl_seq_clr(hull
->ineq
[k
], (i
+1) * (1+dim
));
903 isl_seq_clr(hull
->ineq
[k
]+(i
+2)*(1+dim
), (1-i
)*(1+dim
));
904 isl_seq_cpy(hull
->ineq
[k
]+(i
+1)*(1+dim
),
905 bset
[i
]->ineq
[j
], 1+dim
);
907 k
= isl_basic_set_alloc_inequality(hull
);
910 isl_seq_clr(hull
->ineq
[k
], 1+2+3*dim
);
911 isl_int_set_si(hull
->ineq
[k
][(i
+1)*(1+dim
)], 1);
913 for (j
= 0; j
< 1+dim
; ++j
) {
914 k
= isl_basic_set_alloc_equality(hull
);
917 isl_seq_clr(hull
->eq
[k
], 1+2+3*dim
);
918 isl_int_set_si(hull
->eq
[k
][j
], -1);
919 isl_int_set_si(hull
->eq
[k
][1+dim
+j
], 1);
920 isl_int_set_si(hull
->eq
[k
][2*(1+dim
)+j
], 1);
922 hull
= isl_basic_set_set_rational(hull
);
923 hull
= isl_basic_set_remove_dims(hull
, dim
, 2*(1+dim
));
924 hull
= isl_basic_set_convex_hull(hull
);
925 isl_basic_set_free(bset1
);
926 isl_basic_set_free(bset2
);
929 isl_basic_set_free(bset1
);
930 isl_basic_set_free(bset2
);
931 isl_basic_set_free(hull
);
935 static int isl_basic_set_is_bounded(struct isl_basic_set
*bset
)
940 tab
= isl_tab_from_recession_cone(bset
);
941 bounded
= isl_tab_cone_is_bounded(tab
);
946 static int isl_set_is_bounded(struct isl_set
*set
)
950 for (i
= 0; i
< set
->n
; ++i
) {
951 int bounded
= isl_basic_set_is_bounded(set
->p
[i
]);
952 if (!bounded
|| bounded
< 0)
958 /* Compute the lineality space of the convex hull of bset1 and bset2.
960 * We first compute the intersection of the recession cone of bset1
961 * with the negative of the recession cone of bset2 and then compute
962 * the linear hull of the resulting cone.
964 static struct isl_basic_set
*induced_lineality_space(
965 struct isl_basic_set
*bset1
, struct isl_basic_set
*bset2
)
968 struct isl_basic_set
*lin
= NULL
;
971 if (!bset1
|| !bset2
)
974 dim
= isl_basic_set_total_dim(bset1
);
975 lin
= isl_basic_set_alloc_dim(isl_basic_set_get_dim(bset1
), 0,
976 bset1
->n_eq
+ bset2
->n_eq
,
977 bset1
->n_ineq
+ bset2
->n_ineq
);
978 lin
= isl_basic_set_set_rational(lin
);
981 for (i
= 0; i
< bset1
->n_eq
; ++i
) {
982 k
= isl_basic_set_alloc_equality(lin
);
985 isl_int_set_si(lin
->eq
[k
][0], 0);
986 isl_seq_cpy(lin
->eq
[k
] + 1, bset1
->eq
[i
] + 1, dim
);
988 for (i
= 0; i
< bset1
->n_ineq
; ++i
) {
989 k
= isl_basic_set_alloc_inequality(lin
);
992 isl_int_set_si(lin
->ineq
[k
][0], 0);
993 isl_seq_cpy(lin
->ineq
[k
] + 1, bset1
->ineq
[i
] + 1, dim
);
995 for (i
= 0; i
< bset2
->n_eq
; ++i
) {
996 k
= isl_basic_set_alloc_equality(lin
);
999 isl_int_set_si(lin
->eq
[k
][0], 0);
1000 isl_seq_neg(lin
->eq
[k
] + 1, bset2
->eq
[i
] + 1, dim
);
1002 for (i
= 0; i
< bset2
->n_ineq
; ++i
) {
1003 k
= isl_basic_set_alloc_inequality(lin
);
1006 isl_int_set_si(lin
->ineq
[k
][0], 0);
1007 isl_seq_neg(lin
->ineq
[k
] + 1, bset2
->ineq
[i
] + 1, dim
);
1010 isl_basic_set_free(bset1
);
1011 isl_basic_set_free(bset2
);
1012 return isl_basic_set_affine_hull(lin
);
1014 isl_basic_set_free(lin
);
1015 isl_basic_set_free(bset1
);
1016 isl_basic_set_free(bset2
);
1020 static struct isl_basic_set
*uset_convex_hull(struct isl_set
*set
);
1022 /* Given a set and a linear space "lin" of dimension n > 0,
1023 * project the linear space from the set, compute the convex hull
1024 * and then map the set back to the original space.
1030 * describe the linear space. We first compute the Hermite normal
1031 * form H = M U of M = H Q, to obtain
1035 * The last n rows of H will be zero, so the last n variables of x' = Q x
1036 * are the one we want to project out. We do this by transforming each
1037 * basic set A x >= b to A U x' >= b and then removing the last n dimensions.
1038 * After computing the convex hull in x'_1, i.e., A' x'_1 >= b',
1039 * we transform the hull back to the original space as A' Q_1 x >= b',
1040 * with Q_1 all but the last n rows of Q.
1042 static struct isl_basic_set
*modulo_lineality(struct isl_set
*set
,
1043 struct isl_basic_set
*lin
)
1045 unsigned total
= isl_basic_set_total_dim(lin
);
1047 struct isl_basic_set
*hull
;
1048 struct isl_mat
*M
, *U
, *Q
;
1052 lin_dim
= total
- lin
->n_eq
;
1053 M
= isl_mat_sub_alloc(set
->ctx
, lin
->eq
, 0, lin
->n_eq
, 1, total
);
1054 M
= isl_mat_left_hermite(M
, 0, &U
, &Q
);
1058 isl_basic_set_free(lin
);
1060 Q
= isl_mat_drop_rows(Q
, Q
->n_row
- lin_dim
, lin_dim
);
1062 U
= isl_mat_lin_to_aff(U
);
1063 Q
= isl_mat_lin_to_aff(Q
);
1065 set
= isl_set_preimage(set
, U
);
1066 set
= isl_set_remove_dims(set
, total
- lin_dim
, lin_dim
);
1067 hull
= uset_convex_hull(set
);
1068 hull
= isl_basic_set_preimage(hull
, Q
);
1072 isl_basic_set_free(lin
);
1077 /* Given two polyhedra with as constraints h_{ij} x >= 0 in homegeneous space,
1078 * set up an LP for solving
1080 * \sum_j \alpha_{1j} h_{1j} = \sum_j \alpha_{2j} h_{2j}
1082 * \alpha{i0} corresponds to the (implicit) positivity constraint 1 >= 0
1083 * The next \alpha{ij} correspond to the equalities and come in pairs.
1084 * The final \alpha{ij} correspond to the inequalities.
1086 static struct isl_basic_set
*valid_direction_lp(
1087 struct isl_basic_set
*bset1
, struct isl_basic_set
*bset2
)
1089 struct isl_dim
*dim
;
1090 struct isl_basic_set
*lp
;
1095 if (!bset1
|| !bset2
)
1097 d
= 1 + isl_basic_set_total_dim(bset1
);
1099 2 * bset1
->n_eq
+ bset1
->n_ineq
+ 2 * bset2
->n_eq
+ bset2
->n_ineq
;
1100 dim
= isl_dim_set_alloc(bset1
->ctx
, 0, n
);
1101 lp
= isl_basic_set_alloc_dim(dim
, 0, d
, n
);
1104 for (i
= 0; i
< n
; ++i
) {
1105 k
= isl_basic_set_alloc_inequality(lp
);
1108 isl_seq_clr(lp
->ineq
[k
] + 1, n
);
1109 isl_int_set_si(lp
->ineq
[k
][0], -1);
1110 isl_int_set_si(lp
->ineq
[k
][1 + i
], 1);
1112 for (i
= 0; i
< d
; ++i
) {
1113 k
= isl_basic_set_alloc_equality(lp
);
1117 isl_int_set_si(lp
->eq
[k
][n
++], 0);
1118 /* positivity constraint 1 >= 0 */
1119 isl_int_set_si(lp
->eq
[k
][n
++], i
== 0);
1120 for (j
= 0; j
< bset1
->n_eq
; ++j
) {
1121 isl_int_set(lp
->eq
[k
][n
++], bset1
->eq
[j
][i
]);
1122 isl_int_neg(lp
->eq
[k
][n
++], bset1
->eq
[j
][i
]);
1124 for (j
= 0; j
< bset1
->n_ineq
; ++j
)
1125 isl_int_set(lp
->eq
[k
][n
++], bset1
->ineq
[j
][i
]);
1126 /* positivity constraint 1 >= 0 */
1127 isl_int_set_si(lp
->eq
[k
][n
++], -(i
== 0));
1128 for (j
= 0; j
< bset2
->n_eq
; ++j
) {
1129 isl_int_neg(lp
->eq
[k
][n
++], bset2
->eq
[j
][i
]);
1130 isl_int_set(lp
->eq
[k
][n
++], bset2
->eq
[j
][i
]);
1132 for (j
= 0; j
< bset2
->n_ineq
; ++j
)
1133 isl_int_neg(lp
->eq
[k
][n
++], bset2
->ineq
[j
][i
]);
1135 lp
= isl_basic_set_gauss(lp
, NULL
);
1136 isl_basic_set_free(bset1
);
1137 isl_basic_set_free(bset2
);
1140 isl_basic_set_free(bset1
);
1141 isl_basic_set_free(bset2
);
1145 /* Compute a vector s in the homogeneous space such that <s, r> > 0
1146 * for all rays in the homogeneous space of the two cones that correspond
1147 * to the input polyhedra bset1 and bset2.
1149 * We compute s as a vector that satisfies
1151 * s = \sum_j \alpha_{ij} h_{ij} for i = 1,2 (*)
1153 * with h_{ij} the normals of the facets of polyhedron i
1154 * (including the "positivity constraint" 1 >= 0) and \alpha_{ij}
1155 * strictly positive numbers. For simplicity we impose \alpha_{ij} >= 1.
1156 * We first set up an LP with as variables the \alpha{ij}.
1157 * In this formulateion, for each polyhedron i,
1158 * the first constraint is the positivity constraint, followed by pairs
1159 * of variables for the equalities, followed by variables for the inequalities.
1160 * We then simply pick a feasible solution and compute s using (*).
1162 * Note that we simply pick any valid direction and make no attempt
1163 * to pick a "good" or even the "best" valid direction.
1165 static struct isl_vec
*valid_direction(
1166 struct isl_basic_set
*bset1
, struct isl_basic_set
*bset2
)
1168 struct isl_basic_set
*lp
;
1169 struct isl_tab
*tab
;
1170 struct isl_vec
*sample
= NULL
;
1171 struct isl_vec
*dir
;
1176 if (!bset1
|| !bset2
)
1178 lp
= valid_direction_lp(isl_basic_set_copy(bset1
),
1179 isl_basic_set_copy(bset2
));
1180 tab
= isl_tab_from_basic_set(lp
);
1181 sample
= isl_tab_get_sample_value(tab
);
1183 isl_basic_set_free(lp
);
1186 d
= isl_basic_set_total_dim(bset1
);
1187 dir
= isl_vec_alloc(bset1
->ctx
, 1 + d
);
1190 isl_seq_clr(dir
->block
.data
+ 1, dir
->size
- 1);
1192 /* positivity constraint 1 >= 0 */
1193 isl_int_set(dir
->block
.data
[0], sample
->block
.data
[n
++]);
1194 for (i
= 0; i
< bset1
->n_eq
; ++i
) {
1195 isl_int_sub(sample
->block
.data
[n
],
1196 sample
->block
.data
[n
], sample
->block
.data
[n
+1]);
1197 isl_seq_combine(dir
->block
.data
,
1198 bset1
->ctx
->one
, dir
->block
.data
,
1199 sample
->block
.data
[n
], bset1
->eq
[i
], 1 + d
);
1203 for (i
= 0; i
< bset1
->n_ineq
; ++i
)
1204 isl_seq_combine(dir
->block
.data
,
1205 bset1
->ctx
->one
, dir
->block
.data
,
1206 sample
->block
.data
[n
++], bset1
->ineq
[i
], 1 + d
);
1207 isl_vec_free(sample
);
1208 isl_seq_normalize(bset1
->ctx
, dir
->block
.data
+ 1, dir
->size
- 1);
1209 isl_basic_set_free(bset1
);
1210 isl_basic_set_free(bset2
);
1213 isl_vec_free(sample
);
1214 isl_basic_set_free(bset1
);
1215 isl_basic_set_free(bset2
);
1219 /* Given a polyhedron b_i + A_i x >= 0 and a map T = S^{-1},
1220 * compute b_i' + A_i' x' >= 0, with
1222 * [ b_i A_i ] [ y' ] [ y' ]
1223 * [ 1 0 ] S^{-1} [ x' ] >= 0 or [ b_i' A_i' ] [ x' ] >= 0
1225 * In particular, add the "positivity constraint" and then perform
1228 static struct isl_basic_set
*homogeneous_map(struct isl_basic_set
*bset
,
1235 bset
= isl_basic_set_extend_constraints(bset
, 0, 1);
1236 k
= isl_basic_set_alloc_inequality(bset
);
1239 isl_seq_clr(bset
->ineq
[k
] + 1, isl_basic_set_total_dim(bset
));
1240 isl_int_set_si(bset
->ineq
[k
][0], 1);
1241 bset
= isl_basic_set_preimage(bset
, T
);
1245 isl_basic_set_free(bset
);
1249 /* Compute the convex hull of a pair of basic sets without any parameters or
1250 * integer divisions, where the convex hull is known to be pointed,
1251 * but the basic sets may be unbounded.
1253 * We turn this problem into the computation of a convex hull of a pair
1254 * _bounded_ polyhedra by "changing the direction of the homogeneous
1255 * dimension". This idea is due to Matthias Koeppe.
1257 * Consider the cones in homogeneous space that correspond to the
1258 * input polyhedra. The rays of these cones are also rays of the
1259 * polyhedra if the coordinate that corresponds to the homogeneous
1260 * dimension is zero. That is, if the inner product of the rays
1261 * with the homogeneous direction is zero.
1262 * The cones in the homogeneous space can also be considered to
1263 * correspond to other pairs of polyhedra by chosing a different
1264 * homogeneous direction. To ensure that both of these polyhedra
1265 * are bounded, we need to make sure that all rays of the cones
1266 * correspond to vertices and not to rays.
1267 * Let s be a direction such that <s, r> > 0 for all rays r of both cones.
1268 * Then using s as a homogeneous direction, we obtain a pair of polytopes.
1269 * The vector s is computed in valid_direction.
1271 * Note that we need to consider _all_ rays of the cones and not just
1272 * the rays that correspond to rays in the polyhedra. If we were to
1273 * only consider those rays and turn them into vertices, then we
1274 * may inadvertently turn some vertices into rays.
1276 * The standard homogeneous direction is the unit vector in the 0th coordinate.
1277 * We therefore transform the two polyhedra such that the selected
1278 * direction is mapped onto this standard direction and then proceed
1279 * with the normal computation.
1280 * Let S be a non-singular square matrix with s as its first row,
1281 * then we want to map the polyhedra to the space
1283 * [ y' ] [ y ] [ y ] [ y' ]
1284 * [ x' ] = S [ x ] i.e., [ x ] = S^{-1} [ x' ]
1286 * We take S to be the unimodular completion of s to limit the growth
1287 * of the coefficients in the following computations.
1289 * Let b_i + A_i x >= 0 be the constraints of polyhedron i.
1290 * We first move to the homogeneous dimension
1292 * b_i y + A_i x >= 0 [ b_i A_i ] [ y ] [ 0 ]
1293 * y >= 0 or [ 1 0 ] [ x ] >= [ 0 ]
1295 * Then we change directoin
1297 * [ b_i A_i ] [ y' ] [ y' ]
1298 * [ 1 0 ] S^{-1} [ x' ] >= 0 or [ b_i' A_i' ] [ x' ] >= 0
1300 * Then we compute the convex hull of the polytopes b_i' + A_i' x' >= 0
1301 * resulting in b' + A' x' >= 0, which we then convert back
1304 * [ b' A' ] S [ x ] >= 0 or [ b A ] [ x ] >= 0
1306 * The polyhedron b + A x >= 0 is then the convex hull of the input polyhedra.
1308 static struct isl_basic_set
*convex_hull_pair_pointed(
1309 struct isl_basic_set
*bset1
, struct isl_basic_set
*bset2
)
1311 struct isl_ctx
*ctx
= NULL
;
1312 struct isl_vec
*dir
= NULL
;
1313 struct isl_mat
*T
= NULL
;
1314 struct isl_mat
*T2
= NULL
;
1315 struct isl_basic_set
*hull
;
1316 struct isl_set
*set
;
1318 if (!bset1
|| !bset2
)
1321 dir
= valid_direction(isl_basic_set_copy(bset1
),
1322 isl_basic_set_copy(bset2
));
1325 T
= isl_mat_alloc(bset1
->ctx
, dir
->size
, dir
->size
);
1328 isl_seq_cpy(T
->row
[0], dir
->block
.data
, dir
->size
);
1329 T
= isl_mat_unimodular_complete(T
, 1);
1330 T2
= isl_mat_right_inverse(isl_mat_copy(T
));
1332 bset1
= homogeneous_map(bset1
, isl_mat_copy(T2
));
1333 bset2
= homogeneous_map(bset2
, T2
);
1334 set
= isl_set_alloc_dim(isl_basic_set_get_dim(bset1
), 2, 0);
1335 set
= isl_set_add(set
, bset1
);
1336 set
= isl_set_add(set
, bset2
);
1337 hull
= uset_convex_hull(set
);
1338 hull
= isl_basic_set_preimage(hull
, T
);
1345 isl_basic_set_free(bset1
);
1346 isl_basic_set_free(bset2
);
1350 /* Compute the convex hull of a pair of basic sets without any parameters or
1351 * integer divisions.
1353 * If the convex hull of the two basic sets would have a non-trivial
1354 * lineality space, we first project out this lineality space.
1356 static struct isl_basic_set
*convex_hull_pair(struct isl_basic_set
*bset1
,
1357 struct isl_basic_set
*bset2
)
1359 struct isl_basic_set
*lin
;
1361 if (isl_basic_set_is_bounded(bset1
) || isl_basic_set_is_bounded(bset2
))
1362 return convex_hull_pair_pointed(bset1
, bset2
);
1364 lin
= induced_lineality_space(isl_basic_set_copy(bset1
),
1365 isl_basic_set_copy(bset2
));
1368 if (isl_basic_set_is_universe(lin
)) {
1369 isl_basic_set_free(bset1
);
1370 isl_basic_set_free(bset2
);
1373 if (lin
->n_eq
< isl_basic_set_total_dim(lin
)) {
1374 struct isl_set
*set
;
1375 set
= isl_set_alloc_dim(isl_basic_set_get_dim(bset1
), 2, 0);
1376 set
= isl_set_add(set
, bset1
);
1377 set
= isl_set_add(set
, bset2
);
1378 return modulo_lineality(set
, lin
);
1380 isl_basic_set_free(lin
);
1382 return convex_hull_pair_pointed(bset1
, bset2
);
1384 isl_basic_set_free(bset1
);
1385 isl_basic_set_free(bset2
);
1389 /* Compute the lineality space of a basic set.
1390 * We currently do not allow the basic set to have any divs.
1391 * We basically just drop the constants and turn every inequality
1394 struct isl_basic_set
*isl_basic_set_lineality_space(struct isl_basic_set
*bset
)
1397 struct isl_basic_set
*lin
= NULL
;
1402 isl_assert(bset
->ctx
, bset
->n_div
== 0, goto error
);
1403 dim
= isl_basic_set_total_dim(bset
);
1405 lin
= isl_basic_set_alloc_dim(isl_basic_set_get_dim(bset
), 0, dim
, 0);
1408 for (i
= 0; i
< bset
->n_eq
; ++i
) {
1409 k
= isl_basic_set_alloc_equality(lin
);
1412 isl_int_set_si(lin
->eq
[k
][0], 0);
1413 isl_seq_cpy(lin
->eq
[k
] + 1, bset
->eq
[i
] + 1, dim
);
1415 lin
= isl_basic_set_gauss(lin
, NULL
);
1418 for (i
= 0; i
< bset
->n_ineq
&& lin
->n_eq
< dim
; ++i
) {
1419 k
= isl_basic_set_alloc_equality(lin
);
1422 isl_int_set_si(lin
->eq
[k
][0], 0);
1423 isl_seq_cpy(lin
->eq
[k
] + 1, bset
->ineq
[i
] + 1, dim
);
1424 lin
= isl_basic_set_gauss(lin
, NULL
);
1428 isl_basic_set_free(bset
);
1431 isl_basic_set_free(lin
);
1432 isl_basic_set_free(bset
);
1436 /* Compute the (linear) hull of the lineality spaces of the basic sets in the
1437 * "underlying" set "set".
1439 static struct isl_basic_set
*uset_combined_lineality_space(struct isl_set
*set
)
1442 struct isl_set
*lin
= NULL
;
1447 struct isl_dim
*dim
= isl_set_get_dim(set
);
1449 return isl_basic_set_empty(dim
);
1452 lin
= isl_set_alloc_dim(isl_set_get_dim(set
), set
->n
, 0);
1453 for (i
= 0; i
< set
->n
; ++i
)
1454 lin
= isl_set_add(lin
,
1455 isl_basic_set_lineality_space(isl_basic_set_copy(set
->p
[i
])));
1457 return isl_set_affine_hull(lin
);
1460 /* Compute the convex hull of a set without any parameters or
1461 * integer divisions.
1462 * In each step, we combined two basic sets until only one
1463 * basic set is left.
1464 * The input basic sets are assumed not to have a non-trivial
1465 * lineality space. If any of the intermediate results has
1466 * a non-trivial lineality space, it is projected out.
1468 static struct isl_basic_set
*uset_convex_hull_unbounded(struct isl_set
*set
)
1470 struct isl_basic_set
*convex_hull
= NULL
;
1472 convex_hull
= isl_set_copy_basic_set(set
);
1473 set
= isl_set_drop_basic_set(set
, convex_hull
);
1476 while (set
->n
> 0) {
1477 struct isl_basic_set
*t
;
1478 t
= isl_set_copy_basic_set(set
);
1481 set
= isl_set_drop_basic_set(set
, t
);
1484 convex_hull
= convex_hull_pair(convex_hull
, t
);
1487 t
= isl_basic_set_lineality_space(isl_basic_set_copy(convex_hull
));
1490 if (isl_basic_set_is_universe(t
)) {
1491 isl_basic_set_free(convex_hull
);
1495 if (t
->n_eq
< isl_basic_set_total_dim(t
)) {
1496 set
= isl_set_add(set
, convex_hull
);
1497 return modulo_lineality(set
, t
);
1499 isl_basic_set_free(t
);
1505 isl_basic_set_free(convex_hull
);
1509 /* Compute an initial hull for wrapping containing a single initial
1510 * facet by first computing bounds on the set and then using these
1511 * bounds to construct an initial facet.
1512 * This function is a remnant of an older implementation where the
1513 * bounds were also used to check whether the set was bounded.
1514 * Since this function will now only be called when we know the
1515 * set to be bounded, the initial facet should probably be constructed
1516 * by simply using the coordinate directions instead.
1518 static struct isl_basic_set
*initial_hull(struct isl_basic_set
*hull
,
1519 struct isl_set
*set
)
1521 struct isl_mat
*bounds
= NULL
;
1527 bounds
= independent_bounds(set
);
1530 isl_assert(set
->ctx
, bounds
->n_row
== isl_set_n_dim(set
), goto error
);
1531 bounds
= initial_facet_constraint(set
, bounds
);
1534 k
= isl_basic_set_alloc_inequality(hull
);
1537 dim
= isl_set_n_dim(set
);
1538 isl_assert(set
->ctx
, 1 + dim
== bounds
->n_col
, goto error
);
1539 isl_seq_cpy(hull
->ineq
[k
], bounds
->row
[0], bounds
->n_col
);
1540 isl_mat_free(bounds
);
1544 isl_basic_set_free(hull
);
1545 isl_mat_free(bounds
);
1549 struct max_constraint
{
1555 static int max_constraint_equal(const void *entry
, const void *val
)
1557 struct max_constraint
*a
= (struct max_constraint
*)entry
;
1558 isl_int
*b
= (isl_int
*)val
;
1560 return isl_seq_eq(a
->c
->row
[0] + 1, b
, a
->c
->n_col
- 1);
1563 static void update_constraint(struct isl_ctx
*ctx
, struct isl_hash_table
*table
,
1564 isl_int
*con
, unsigned len
, int n
, int ineq
)
1566 struct isl_hash_table_entry
*entry
;
1567 struct max_constraint
*c
;
1570 c_hash
= isl_seq_get_hash(con
+ 1, len
);
1571 entry
= isl_hash_table_find(ctx
, table
, c_hash
, max_constraint_equal
,
1577 isl_hash_table_remove(ctx
, table
, entry
);
1581 if (isl_int_gt(c
->c
->row
[0][0], con
[0]))
1583 if (isl_int_eq(c
->c
->row
[0][0], con
[0])) {
1588 c
->c
= isl_mat_cow(c
->c
);
1589 isl_int_set(c
->c
->row
[0][0], con
[0]);
1593 /* Check whether the constraint hash table "table" constains the constraint
1596 static int has_constraint(struct isl_ctx
*ctx
, struct isl_hash_table
*table
,
1597 isl_int
*con
, unsigned len
, int n
)
1599 struct isl_hash_table_entry
*entry
;
1600 struct max_constraint
*c
;
1603 c_hash
= isl_seq_get_hash(con
+ 1, len
);
1604 entry
= isl_hash_table_find(ctx
, table
, c_hash
, max_constraint_equal
,
1611 return isl_int_eq(c
->c
->row
[0][0], con
[0]);
1614 /* Check for inequality constraints of a basic set without equalities
1615 * such that the same or more stringent copies of the constraint appear
1616 * in all of the basic sets. Such constraints are necessarily facet
1617 * constraints of the convex hull.
1619 * If the resulting basic set is by chance identical to one of
1620 * the basic sets in "set", then we know that this basic set contains
1621 * all other basic sets and is therefore the convex hull of set.
1622 * In this case we set *is_hull to 1.
1624 static struct isl_basic_set
*common_constraints(struct isl_basic_set
*hull
,
1625 struct isl_set
*set
, int *is_hull
)
1628 int min_constraints
;
1630 struct max_constraint
*constraints
= NULL
;
1631 struct isl_hash_table
*table
= NULL
;
1636 for (i
= 0; i
< set
->n
; ++i
)
1637 if (set
->p
[i
]->n_eq
== 0)
1641 min_constraints
= set
->p
[i
]->n_ineq
;
1643 for (i
= best
+ 1; i
< set
->n
; ++i
) {
1644 if (set
->p
[i
]->n_eq
!= 0)
1646 if (set
->p
[i
]->n_ineq
>= min_constraints
)
1648 min_constraints
= set
->p
[i
]->n_ineq
;
1651 constraints
= isl_calloc_array(hull
->ctx
, struct max_constraint
,
1655 table
= isl_alloc_type(hull
->ctx
, struct isl_hash_table
);
1656 if (isl_hash_table_init(hull
->ctx
, table
, min_constraints
))
1659 total
= isl_dim_total(set
->dim
);
1660 for (i
= 0; i
< set
->p
[best
]->n_ineq
; ++i
) {
1661 constraints
[i
].c
= isl_mat_sub_alloc(hull
->ctx
,
1662 set
->p
[best
]->ineq
+ i
, 0, 1, 0, 1 + total
);
1663 if (!constraints
[i
].c
)
1665 constraints
[i
].ineq
= 1;
1667 for (i
= 0; i
< min_constraints
; ++i
) {
1668 struct isl_hash_table_entry
*entry
;
1670 c_hash
= isl_seq_get_hash(constraints
[i
].c
->row
[0] + 1, total
);
1671 entry
= isl_hash_table_find(hull
->ctx
, table
, c_hash
,
1672 max_constraint_equal
, constraints
[i
].c
->row
[0] + 1, 1);
1675 isl_assert(hull
->ctx
, !entry
->data
, goto error
);
1676 entry
->data
= &constraints
[i
];
1680 for (s
= 0; s
< set
->n
; ++s
) {
1684 for (i
= 0; i
< set
->p
[s
]->n_eq
; ++i
) {
1685 isl_int
*eq
= set
->p
[s
]->eq
[i
];
1686 for (j
= 0; j
< 2; ++j
) {
1687 isl_seq_neg(eq
, eq
, 1 + total
);
1688 update_constraint(hull
->ctx
, table
,
1692 for (i
= 0; i
< set
->p
[s
]->n_ineq
; ++i
) {
1693 isl_int
*ineq
= set
->p
[s
]->ineq
[i
];
1694 update_constraint(hull
->ctx
, table
, ineq
, total
, n
,
1695 set
->p
[s
]->n_eq
== 0);
1700 for (i
= 0; i
< min_constraints
; ++i
) {
1701 if (constraints
[i
].count
< n
)
1703 if (!constraints
[i
].ineq
)
1705 j
= isl_basic_set_alloc_inequality(hull
);
1708 isl_seq_cpy(hull
->ineq
[j
], constraints
[i
].c
->row
[0], 1 + total
);
1711 for (s
= 0; s
< set
->n
; ++s
) {
1712 if (set
->p
[s
]->n_eq
)
1714 if (set
->p
[s
]->n_ineq
!= hull
->n_ineq
)
1716 for (i
= 0; i
< set
->p
[s
]->n_ineq
; ++i
) {
1717 isl_int
*ineq
= set
->p
[s
]->ineq
[i
];
1718 if (!has_constraint(hull
->ctx
, table
, ineq
, total
, n
))
1721 if (i
== set
->p
[s
]->n_ineq
)
1725 isl_hash_table_clear(table
);
1726 for (i
= 0; i
< min_constraints
; ++i
)
1727 isl_mat_free(constraints
[i
].c
);
1732 isl_hash_table_clear(table
);
1735 for (i
= 0; i
< min_constraints
; ++i
)
1736 isl_mat_free(constraints
[i
].c
);
1741 /* Create a template for the convex hull of "set" and fill it up
1742 * obvious facet constraints, if any. If the result happens to
1743 * be the convex hull of "set" then *is_hull is set to 1.
1745 static struct isl_basic_set
*proto_hull(struct isl_set
*set
, int *is_hull
)
1747 struct isl_basic_set
*hull
;
1752 for (i
= 0; i
< set
->n
; ++i
) {
1753 n_ineq
+= set
->p
[i
]->n_eq
;
1754 n_ineq
+= set
->p
[i
]->n_ineq
;
1756 hull
= isl_basic_set_alloc_dim(isl_dim_copy(set
->dim
), 0, 0, n_ineq
);
1757 hull
= isl_basic_set_set_rational(hull
);
1760 return common_constraints(hull
, set
, is_hull
);
1763 static struct isl_basic_set
*uset_convex_hull_wrap(struct isl_set
*set
)
1765 struct isl_basic_set
*hull
;
1768 hull
= proto_hull(set
, &is_hull
);
1769 if (hull
&& !is_hull
) {
1770 if (hull
->n_ineq
== 0)
1771 hull
= initial_hull(hull
, set
);
1772 hull
= extend(hull
, set
);
1779 /* Compute the convex hull of a set without any parameters or
1780 * integer divisions. Depending on whether the set is bounded,
1781 * we pass control to the wrapping based convex hull or
1782 * the Fourier-Motzkin elimination based convex hull.
1783 * We also handle a few special cases before checking the boundedness.
1785 static struct isl_basic_set
*uset_convex_hull(struct isl_set
*set
)
1787 struct isl_basic_set
*convex_hull
= NULL
;
1788 struct isl_basic_set
*lin
;
1790 if (isl_set_n_dim(set
) == 0)
1791 return convex_hull_0d(set
);
1793 set
= isl_set_coalesce(set
);
1794 set
= isl_set_set_rational(set
);
1801 convex_hull
= isl_basic_set_copy(set
->p
[0]);
1805 if (isl_set_n_dim(set
) == 1)
1806 return convex_hull_1d(set
);
1808 if (isl_set_is_bounded(set
))
1809 return uset_convex_hull_wrap(set
);
1811 lin
= uset_combined_lineality_space(isl_set_copy(set
));
1814 if (isl_basic_set_is_universe(lin
)) {
1818 if (lin
->n_eq
< isl_basic_set_total_dim(lin
))
1819 return modulo_lineality(set
, lin
);
1820 isl_basic_set_free(lin
);
1822 return uset_convex_hull_unbounded(set
);
1825 isl_basic_set_free(convex_hull
);
1829 /* This is the core procedure, where "set" is a "pure" set, i.e.,
1830 * without parameters or divs and where the convex hull of set is
1831 * known to be full-dimensional.
1833 static struct isl_basic_set
*uset_convex_hull_wrap_bounded(struct isl_set
*set
)
1835 struct isl_basic_set
*convex_hull
= NULL
;
1837 if (isl_set_n_dim(set
) == 0) {
1838 convex_hull
= isl_basic_set_universe(isl_dim_copy(set
->dim
));
1840 convex_hull
= isl_basic_set_set_rational(convex_hull
);
1844 set
= isl_set_set_rational(set
);
1848 set
= isl_set_coalesce(set
);
1852 convex_hull
= isl_basic_set_copy(set
->p
[0]);
1856 if (isl_set_n_dim(set
) == 1)
1857 return convex_hull_1d(set
);
1859 return uset_convex_hull_wrap(set
);
1865 /* Compute the convex hull of set "set" with affine hull "affine_hull",
1866 * We first remove the equalities (transforming the set), compute the
1867 * convex hull of the transformed set and then add the equalities back
1868 * (after performing the inverse transformation.
1870 static struct isl_basic_set
*modulo_affine_hull(struct isl_ctx
*ctx
,
1871 struct isl_set
*set
, struct isl_basic_set
*affine_hull
)
1875 struct isl_basic_set
*dummy
;
1876 struct isl_basic_set
*convex_hull
;
1878 dummy
= isl_basic_set_remove_equalities(
1879 isl_basic_set_copy(affine_hull
), &T
, &T2
);
1882 isl_basic_set_free(dummy
);
1883 set
= isl_set_preimage(set
, T
);
1884 convex_hull
= uset_convex_hull(set
);
1885 convex_hull
= isl_basic_set_preimage(convex_hull
, T2
);
1886 convex_hull
= isl_basic_set_intersect(convex_hull
, affine_hull
);
1889 isl_basic_set_free(affine_hull
);
1894 /* Compute the convex hull of a map.
1896 * The implementation was inspired by "Extended Convex Hull" by Fukuda et al.,
1897 * specifically, the wrapping of facets to obtain new facets.
1899 struct isl_basic_map
*isl_map_convex_hull(struct isl_map
*map
)
1901 struct isl_basic_set
*bset
;
1902 struct isl_basic_map
*model
= NULL
;
1903 struct isl_basic_set
*affine_hull
= NULL
;
1904 struct isl_basic_map
*convex_hull
= NULL
;
1905 struct isl_set
*set
= NULL
;
1906 struct isl_ctx
*ctx
;
1913 convex_hull
= isl_basic_map_empty_like_map(map
);
1918 map
= isl_map_detect_equalities(map
);
1919 map
= isl_map_align_divs(map
);
1920 model
= isl_basic_map_copy(map
->p
[0]);
1921 set
= isl_map_underlying_set(map
);
1925 affine_hull
= isl_set_affine_hull(isl_set_copy(set
));
1928 if (affine_hull
->n_eq
!= 0)
1929 bset
= modulo_affine_hull(ctx
, set
, affine_hull
);
1931 isl_basic_set_free(affine_hull
);
1932 bset
= uset_convex_hull(set
);
1935 convex_hull
= isl_basic_map_overlying_set(bset
, model
);
1937 ISL_F_SET(convex_hull
, ISL_BASIC_MAP_NO_IMPLICIT
);
1938 ISL_F_SET(convex_hull
, ISL_BASIC_MAP_ALL_EQUALITIES
);
1939 ISL_F_CLR(convex_hull
, ISL_BASIC_MAP_RATIONAL
);
1943 isl_basic_map_free(model
);
1947 struct isl_basic_set
*isl_set_convex_hull(struct isl_set
*set
)
1949 return (struct isl_basic_set
*)
1950 isl_map_convex_hull((struct isl_map
*)set
);
1953 struct sh_data_entry
{
1954 struct isl_hash_table
*table
;
1955 struct isl_tab
*tab
;
1958 /* Holds the data needed during the simple hull computation.
1960 * n the number of basic sets in the original set
1961 * hull_table a hash table of already computed constraints
1962 * in the simple hull
1963 * p for each basic set,
1964 * table a hash table of the constraints
1965 * tab the tableau corresponding to the basic set
1968 struct isl_ctx
*ctx
;
1970 struct isl_hash_table
*hull_table
;
1971 struct sh_data_entry p
[1];
1974 static void sh_data_free(struct sh_data
*data
)
1980 isl_hash_table_free(data
->ctx
, data
->hull_table
);
1981 for (i
= 0; i
< data
->n
; ++i
) {
1982 isl_hash_table_free(data
->ctx
, data
->p
[i
].table
);
1983 isl_tab_free(data
->p
[i
].tab
);
1988 struct ineq_cmp_data
{
1993 static int has_ineq(const void *entry
, const void *val
)
1995 isl_int
*row
= (isl_int
*)entry
;
1996 struct ineq_cmp_data
*v
= (struct ineq_cmp_data
*)val
;
1998 return isl_seq_eq(row
+ 1, v
->p
+ 1, v
->len
) ||
1999 isl_seq_is_neg(row
+ 1, v
->p
+ 1, v
->len
);
2002 static int hash_ineq(struct isl_ctx
*ctx
, struct isl_hash_table
*table
,
2003 isl_int
*ineq
, unsigned len
)
2006 struct ineq_cmp_data v
;
2007 struct isl_hash_table_entry
*entry
;
2011 c_hash
= isl_seq_get_hash(ineq
+ 1, len
);
2012 entry
= isl_hash_table_find(ctx
, table
, c_hash
, has_ineq
, &v
, 1);
2019 /* Fill hash table "table" with the constraints of "bset".
2020 * Equalities are added as two inequalities.
2021 * The value in the hash table is a pointer to the (in)equality of "bset".
2023 static int hash_basic_set(struct isl_hash_table
*table
,
2024 struct isl_basic_set
*bset
)
2027 unsigned dim
= isl_basic_set_total_dim(bset
);
2029 for (i
= 0; i
< bset
->n_eq
; ++i
) {
2030 for (j
= 0; j
< 2; ++j
) {
2031 isl_seq_neg(bset
->eq
[i
], bset
->eq
[i
], 1 + dim
);
2032 if (hash_ineq(bset
->ctx
, table
, bset
->eq
[i
], dim
) < 0)
2036 for (i
= 0; i
< bset
->n_ineq
; ++i
) {
2037 if (hash_ineq(bset
->ctx
, table
, bset
->ineq
[i
], dim
) < 0)
2043 static struct sh_data
*sh_data_alloc(struct isl_set
*set
, unsigned n_ineq
)
2045 struct sh_data
*data
;
2048 data
= isl_calloc(set
->ctx
, struct sh_data
,
2049 sizeof(struct sh_data
) +
2050 (set
->n
- 1) * sizeof(struct sh_data_entry
));
2053 data
->ctx
= set
->ctx
;
2055 data
->hull_table
= isl_hash_table_alloc(set
->ctx
, n_ineq
);
2056 if (!data
->hull_table
)
2058 for (i
= 0; i
< set
->n
; ++i
) {
2059 data
->p
[i
].table
= isl_hash_table_alloc(set
->ctx
,
2060 2 * set
->p
[i
]->n_eq
+ set
->p
[i
]->n_ineq
);
2061 if (!data
->p
[i
].table
)
2063 if (hash_basic_set(data
->p
[i
].table
, set
->p
[i
]) < 0)
2072 /* Check if inequality "ineq" is a bound for basic set "j" or if
2073 * it can be relaxed (by increasing the constant term) to become
2074 * a bound for that basic set. In the latter case, the constant
2076 * Return 1 if "ineq" is a bound
2077 * 0 if "ineq" may attain arbitrarily small values on basic set "j"
2078 * -1 if some error occurred
2080 static int is_bound(struct sh_data
*data
, struct isl_set
*set
, int j
,
2083 enum isl_lp_result res
;
2086 if (!data
->p
[j
].tab
) {
2087 data
->p
[j
].tab
= isl_tab_from_basic_set(set
->p
[j
]);
2088 if (!data
->p
[j
].tab
)
2094 res
= isl_tab_min(data
->p
[j
].tab
, ineq
, data
->ctx
->one
,
2096 if (res
== isl_lp_ok
&& isl_int_is_neg(opt
))
2097 isl_int_sub(ineq
[0], ineq
[0], opt
);
2101 return res
== isl_lp_ok
? 1 :
2102 res
== isl_lp_unbounded
? 0 : -1;
2105 /* Check if inequality "ineq" from basic set "i" can be relaxed to
2106 * become a bound on the whole set. If so, add the (relaxed) inequality
2109 * We first check if "hull" already contains a translate of the inequality.
2110 * If so, we are done.
2111 * Then, we check if any of the previous basic sets contains a translate
2112 * of the inequality. If so, then we have already considered this
2113 * inequality and we are done.
2114 * Otherwise, for each basic set other than "i", we check if the inequality
2115 * is a bound on the basic set.
2116 * For previous basic sets, we know that they do not contain a translate
2117 * of the inequality, so we directly call is_bound.
2118 * For following basic sets, we first check if a translate of the
2119 * inequality appears in its description and if so directly update
2120 * the inequality accordingly.
2122 static struct isl_basic_set
*add_bound(struct isl_basic_set
*hull
,
2123 struct sh_data
*data
, struct isl_set
*set
, int i
, isl_int
*ineq
)
2126 struct ineq_cmp_data v
;
2127 struct isl_hash_table_entry
*entry
;
2133 v
.len
= isl_basic_set_total_dim(hull
);
2135 c_hash
= isl_seq_get_hash(ineq
+ 1, v
.len
);
2137 entry
= isl_hash_table_find(hull
->ctx
, data
->hull_table
, c_hash
,
2142 for (j
= 0; j
< i
; ++j
) {
2143 entry
= isl_hash_table_find(hull
->ctx
, data
->p
[j
].table
,
2144 c_hash
, has_ineq
, &v
, 0);
2151 k
= isl_basic_set_alloc_inequality(hull
);
2152 isl_seq_cpy(hull
->ineq
[k
], ineq
, 1 + v
.len
);
2156 for (j
= 0; j
< i
; ++j
) {
2158 bound
= is_bound(data
, set
, j
, hull
->ineq
[k
]);
2165 isl_basic_set_free_inequality(hull
, 1);
2169 for (j
= i
+ 1; j
< set
->n
; ++j
) {
2172 entry
= isl_hash_table_find(hull
->ctx
, data
->p
[j
].table
,
2173 c_hash
, has_ineq
, &v
, 0);
2175 ineq_j
= entry
->data
;
2176 neg
= isl_seq_is_neg(ineq_j
+ 1,
2177 hull
->ineq
[k
] + 1, v
.len
);
2179 isl_int_neg(ineq_j
[0], ineq_j
[0]);
2180 if (isl_int_gt(ineq_j
[0], hull
->ineq
[k
][0]))
2181 isl_int_set(hull
->ineq
[k
][0], ineq_j
[0]);
2183 isl_int_neg(ineq_j
[0], ineq_j
[0]);
2186 bound
= is_bound(data
, set
, j
, hull
->ineq
[k
]);
2193 isl_basic_set_free_inequality(hull
, 1);
2197 entry
= isl_hash_table_find(hull
->ctx
, data
->hull_table
, c_hash
,
2201 entry
->data
= hull
->ineq
[k
];
2205 isl_basic_set_free(hull
);
2209 /* Check if any inequality from basic set "i" can be relaxed to
2210 * become a bound on the whole set. If so, add the (relaxed) inequality
2213 static struct isl_basic_set
*add_bounds(struct isl_basic_set
*bset
,
2214 struct sh_data
*data
, struct isl_set
*set
, int i
)
2217 unsigned dim
= isl_basic_set_total_dim(bset
);
2219 for (j
= 0; j
< set
->p
[i
]->n_eq
; ++j
) {
2220 for (k
= 0; k
< 2; ++k
) {
2221 isl_seq_neg(set
->p
[i
]->eq
[j
], set
->p
[i
]->eq
[j
], 1+dim
);
2222 add_bound(bset
, data
, set
, i
, set
->p
[i
]->eq
[j
]);
2225 for (j
= 0; j
< set
->p
[i
]->n_ineq
; ++j
)
2226 add_bound(bset
, data
, set
, i
, set
->p
[i
]->ineq
[j
]);
2230 /* Compute a superset of the convex hull of set that is described
2231 * by only translates of the constraints in the constituents of set.
2233 static struct isl_basic_set
*uset_simple_hull(struct isl_set
*set
)
2235 struct sh_data
*data
= NULL
;
2236 struct isl_basic_set
*hull
= NULL
;
2244 for (i
= 0; i
< set
->n
; ++i
) {
2247 n_ineq
+= 2 * set
->p
[i
]->n_eq
+ set
->p
[i
]->n_ineq
;
2250 hull
= isl_basic_set_alloc_dim(isl_dim_copy(set
->dim
), 0, 0, n_ineq
);
2254 data
= sh_data_alloc(set
, n_ineq
);
2258 for (i
= 0; i
< set
->n
; ++i
)
2259 hull
= add_bounds(hull
, data
, set
, i
);
2267 isl_basic_set_free(hull
);
2272 /* Compute a superset of the convex hull of map that is described
2273 * by only translates of the constraints in the constituents of map.
2275 struct isl_basic_map
*isl_map_simple_hull(struct isl_map
*map
)
2277 struct isl_set
*set
= NULL
;
2278 struct isl_basic_map
*model
= NULL
;
2279 struct isl_basic_map
*hull
;
2280 struct isl_basic_map
*affine_hull
;
2281 struct isl_basic_set
*bset
= NULL
;
2286 hull
= isl_basic_map_empty_like_map(map
);
2291 hull
= isl_basic_map_copy(map
->p
[0]);
2296 map
= isl_map_detect_equalities(map
);
2297 affine_hull
= isl_map_affine_hull(isl_map_copy(map
));
2298 map
= isl_map_align_divs(map
);
2299 model
= isl_basic_map_copy(map
->p
[0]);
2301 set
= isl_map_underlying_set(map
);
2303 bset
= uset_simple_hull(set
);
2305 hull
= isl_basic_map_overlying_set(bset
, model
);
2307 hull
= isl_basic_map_intersect(hull
, affine_hull
);
2308 hull
= isl_basic_map_convex_hull(hull
);
2309 ISL_F_SET(hull
, ISL_BASIC_MAP_NO_IMPLICIT
);
2310 ISL_F_SET(hull
, ISL_BASIC_MAP_ALL_EQUALITIES
);
2315 struct isl_basic_set
*isl_set_simple_hull(struct isl_set
*set
)
2317 return (struct isl_basic_set
*)
2318 isl_map_simple_hull((struct isl_map
*)set
);
2321 /* Given a set "set", return parametric bounds on the dimension "dim".
2323 static struct isl_basic_set
*set_bounds(struct isl_set
*set
, int dim
)
2325 unsigned set_dim
= isl_set_dim(set
, isl_dim_set
);
2326 set
= isl_set_copy(set
);
2327 set
= isl_set_eliminate_dims(set
, dim
+ 1, set_dim
- (dim
+ 1));
2328 set
= isl_set_eliminate_dims(set
, 0, dim
);
2329 return isl_set_convex_hull(set
);
2332 /* Computes a "simple hull" and then check if each dimension in the
2333 * resulting hull is bounded by a symbolic constant. If not, the
2334 * hull is intersected with the corresponding bounds on the whole set.
2336 struct isl_basic_set
*isl_set_bounded_simple_hull(struct isl_set
*set
)
2339 struct isl_basic_set
*hull
;
2340 unsigned nparam
, left
;
2341 int removed_divs
= 0;
2343 hull
= isl_set_simple_hull(isl_set_copy(set
));
2347 nparam
= isl_basic_set_dim(hull
, isl_dim_param
);
2348 for (i
= 0; i
< isl_basic_set_dim(hull
, isl_dim_set
); ++i
) {
2349 int lower
= 0, upper
= 0;
2350 struct isl_basic_set
*bounds
;
2352 left
= isl_basic_set_total_dim(hull
) - nparam
- i
- 1;
2353 for (j
= 0; j
< hull
->n_eq
; ++j
) {
2354 if (isl_int_is_zero(hull
->eq
[j
][1 + nparam
+ i
]))
2356 if (isl_seq_first_non_zero(hull
->eq
[j
]+1+nparam
+i
+1,
2363 for (j
= 0; j
< hull
->n_ineq
; ++j
) {
2364 if (isl_int_is_zero(hull
->ineq
[j
][1 + nparam
+ i
]))
2366 if (isl_seq_first_non_zero(hull
->ineq
[j
]+1+nparam
+i
+1,
2368 isl_seq_first_non_zero(hull
->ineq
[j
]+1+nparam
,
2371 if (isl_int_is_pos(hull
->ineq
[j
][1 + nparam
+ i
]))
2382 if (!removed_divs
) {
2383 set
= isl_set_remove_divs(set
);
2388 bounds
= set_bounds(set
, i
);
2389 hull
= isl_basic_set_intersect(hull
, bounds
);