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 if (isl_tab_detect_redundant(tab
) < 0)
100 bmap
= isl_basic_map_update_from_tab(bmap
, tab
);
102 ISL_F_SET(bmap
, ISL_BASIC_MAP_NO_IMPLICIT
);
103 ISL_F_SET(bmap
, ISL_BASIC_MAP_NO_REDUNDANT
);
107 isl_basic_map_free(bmap
);
111 struct isl_basic_set
*isl_basic_set_convex_hull(struct isl_basic_set
*bset
)
113 return (struct isl_basic_set
*)
114 isl_basic_map_convex_hull((struct isl_basic_map
*)bset
);
117 /* Check if the set set is bound in the direction of the affine
118 * constraint c and if so, set the constant term such that the
119 * resulting constraint is a bounding constraint for the set.
121 static int uset_is_bound(struct isl_set
*set
, isl_int
*c
, unsigned len
)
129 isl_int_init(opt_denom
);
131 for (j
= 0; j
< set
->n
; ++j
) {
132 enum isl_lp_result res
;
134 if (ISL_F_ISSET(set
->p
[j
], ISL_BASIC_SET_EMPTY
))
137 res
= isl_basic_set_solve_lp(set
->p
[j
],
138 0, c
, set
->ctx
->one
, &opt
, &opt_denom
, NULL
);
139 if (res
== isl_lp_unbounded
)
141 if (res
== isl_lp_error
)
143 if (res
== isl_lp_empty
) {
144 set
->p
[j
] = isl_basic_set_set_to_empty(set
->p
[j
]);
149 if (!isl_int_is_one(opt_denom
))
150 isl_seq_scale(c
, c
, opt_denom
, len
);
151 if (first
|| isl_int_is_neg(opt
))
152 isl_int_sub(c
[0], c
[0], opt
);
156 isl_int_clear(opt_denom
);
160 isl_int_clear(opt_denom
);
164 /* Check if "c" is a direction that is independent of the previously found "n"
166 * If so, add it to the list, with the negative of the lower bound
167 * in the constant position, i.e., such that c corresponds to a bounding
168 * hyperplane (but not necessarily a facet).
169 * Assumes set "set" is bounded.
171 static int is_independent_bound(struct isl_set
*set
, isl_int
*c
,
172 struct isl_mat
*dirs
, int n
)
177 isl_seq_cpy(dirs
->row
[n
]+1, c
+1, dirs
->n_col
-1);
179 int pos
= isl_seq_first_non_zero(dirs
->row
[n
]+1, dirs
->n_col
-1);
182 for (i
= 0; i
< n
; ++i
) {
184 pos_i
= isl_seq_first_non_zero(dirs
->row
[i
]+1, dirs
->n_col
-1);
189 isl_seq_elim(dirs
->row
[n
]+1, dirs
->row
[i
]+1, pos
,
190 dirs
->n_col
-1, NULL
);
191 pos
= isl_seq_first_non_zero(dirs
->row
[n
]+1, dirs
->n_col
-1);
197 is_bound
= uset_is_bound(set
, dirs
->row
[n
], dirs
->n_col
);
202 isl_int
*t
= dirs
->row
[n
];
203 for (k
= n
; k
> i
; --k
)
204 dirs
->row
[k
] = dirs
->row
[k
-1];
210 /* Compute and return a maximal set of linearly independent bounds
211 * on the set "set", based on the constraints of the basic sets
214 static struct isl_mat
*independent_bounds(struct isl_set
*set
)
217 struct isl_mat
*dirs
= NULL
;
218 unsigned dim
= isl_set_n_dim(set
);
220 dirs
= isl_mat_alloc(set
->ctx
, dim
, 1+dim
);
225 for (i
= 0; n
< dim
&& i
< set
->n
; ++i
) {
227 struct isl_basic_set
*bset
= set
->p
[i
];
229 for (j
= 0; n
< dim
&& j
< bset
->n_eq
; ++j
) {
230 f
= is_independent_bound(set
, bset
->eq
[j
], dirs
, n
);
236 for (j
= 0; n
< dim
&& j
< bset
->n_ineq
; ++j
) {
237 f
= is_independent_bound(set
, bset
->ineq
[j
], dirs
, n
);
251 struct isl_basic_set
*isl_basic_set_set_rational(struct isl_basic_set
*bset
)
256 if (ISL_F_ISSET(bset
, ISL_BASIC_MAP_RATIONAL
))
259 bset
= isl_basic_set_cow(bset
);
263 ISL_F_SET(bset
, ISL_BASIC_MAP_RATIONAL
);
265 return isl_basic_set_finalize(bset
);
268 static struct isl_set
*isl_set_set_rational(struct isl_set
*set
)
272 set
= isl_set_cow(set
);
275 for (i
= 0; i
< set
->n
; ++i
) {
276 set
->p
[i
] = isl_basic_set_set_rational(set
->p
[i
]);
286 static struct isl_basic_set
*isl_basic_set_add_equality(
287 struct isl_basic_set
*bset
, isl_int
*c
)
292 if (ISL_F_ISSET(bset
, ISL_BASIC_SET_EMPTY
))
295 isl_assert(bset
->ctx
, isl_basic_set_n_param(bset
) == 0, goto error
);
296 isl_assert(bset
->ctx
, bset
->n_div
== 0, goto error
);
297 dim
= isl_basic_set_n_dim(bset
);
298 bset
= isl_basic_set_cow(bset
);
299 bset
= isl_basic_set_extend(bset
, 0, dim
, 0, 1, 0);
300 i
= isl_basic_set_alloc_equality(bset
);
303 isl_seq_cpy(bset
->eq
[i
], c
, 1 + dim
);
306 isl_basic_set_free(bset
);
310 static struct isl_set
*isl_set_add_equality(struct isl_set
*set
, isl_int
*c
)
314 set
= isl_set_cow(set
);
317 for (i
= 0; i
< set
->n
; ++i
) {
318 set
->p
[i
] = isl_basic_set_add_equality(set
->p
[i
], c
);
328 /* Given a union of basic sets, construct the constraints for wrapping
329 * a facet around one of its ridges.
330 * In particular, if each of n the d-dimensional basic sets i in "set"
331 * contains the origin, satisfies the constraints x_1 >= 0 and x_2 >= 0
332 * and is defined by the constraints
336 * then the resulting set is of dimension n*(1+d) and has as constraints
345 static struct isl_basic_set
*wrap_constraints(struct isl_set
*set
)
347 struct isl_basic_set
*lp
;
351 unsigned dim
, lp_dim
;
356 dim
= 1 + isl_set_n_dim(set
);
359 for (i
= 0; i
< set
->n
; ++i
) {
360 n_eq
+= set
->p
[i
]->n_eq
;
361 n_ineq
+= set
->p
[i
]->n_ineq
;
363 lp
= isl_basic_set_alloc(set
->ctx
, 0, dim
* set
->n
, 0, n_eq
, n_ineq
);
366 lp_dim
= isl_basic_set_n_dim(lp
);
367 k
= isl_basic_set_alloc_equality(lp
);
368 isl_int_set_si(lp
->eq
[k
][0], -1);
369 for (i
= 0; i
< set
->n
; ++i
) {
370 isl_int_set_si(lp
->eq
[k
][1+dim
*i
], 0);
371 isl_int_set_si(lp
->eq
[k
][1+dim
*i
+1], 1);
372 isl_seq_clr(lp
->eq
[k
]+1+dim
*i
+2, dim
-2);
374 for (i
= 0; i
< set
->n
; ++i
) {
375 k
= isl_basic_set_alloc_inequality(lp
);
376 isl_seq_clr(lp
->ineq
[k
], 1+lp_dim
);
377 isl_int_set_si(lp
->ineq
[k
][1+dim
*i
], 1);
379 for (j
= 0; j
< set
->p
[i
]->n_eq
; ++j
) {
380 k
= isl_basic_set_alloc_equality(lp
);
381 isl_seq_clr(lp
->eq
[k
], 1+dim
*i
);
382 isl_seq_cpy(lp
->eq
[k
]+1+dim
*i
, set
->p
[i
]->eq
[j
], dim
);
383 isl_seq_clr(lp
->eq
[k
]+1+dim
*(i
+1), dim
*(set
->n
-i
-1));
386 for (j
= 0; j
< set
->p
[i
]->n_ineq
; ++j
) {
387 k
= isl_basic_set_alloc_inequality(lp
);
388 isl_seq_clr(lp
->ineq
[k
], 1+dim
*i
);
389 isl_seq_cpy(lp
->ineq
[k
]+1+dim
*i
, set
->p
[i
]->ineq
[j
], dim
);
390 isl_seq_clr(lp
->ineq
[k
]+1+dim
*(i
+1), dim
*(set
->n
-i
-1));
396 /* Given a facet "facet" of the convex hull of "set" and a facet "ridge"
397 * of that facet, compute the other facet of the convex hull that contains
400 * We first transform the set such that the facet constraint becomes
404 * I.e., the facet lies in
408 * and on that facet, the constraint that defines the ridge is
412 * (This transformation is not strictly needed, all that is needed is
413 * that the ridge contains the origin.)
415 * Since the ridge contains the origin, the cone of the convex hull
416 * will be of the form
421 * with this second constraint defining the new facet.
422 * The constant a is obtained by settting x_1 in the cone of the
423 * convex hull to 1 and minimizing x_2.
424 * Now, each element in the cone of the convex hull is the sum
425 * of elements in the cones of the basic sets.
426 * If a_i is the dilation factor of basic set i, then the problem
427 * we need to solve is
440 * the constraints of each (transformed) basic set.
441 * If a = n/d, then the constraint defining the new facet (in the transformed
444 * -n x_1 + d x_2 >= 0
446 * In the original space, we need to take the same combination of the
447 * corresponding constraints "facet" and "ridge".
449 * Note that a is always finite, since we only apply the wrapping
450 * technique to a union of polytopes.
452 static isl_int
*wrap_facet(struct isl_set
*set
, isl_int
*facet
, isl_int
*ridge
)
455 struct isl_mat
*T
= NULL
;
456 struct isl_basic_set
*lp
= NULL
;
458 enum isl_lp_result res
;
462 set
= isl_set_copy(set
);
464 dim
= 1 + isl_set_n_dim(set
);
465 T
= isl_mat_alloc(set
->ctx
, 3, dim
);
468 isl_int_set_si(T
->row
[0][0], 1);
469 isl_seq_clr(T
->row
[0]+1, dim
- 1);
470 isl_seq_cpy(T
->row
[1], facet
, dim
);
471 isl_seq_cpy(T
->row
[2], ridge
, dim
);
472 T
= isl_mat_right_inverse(T
);
473 set
= isl_set_preimage(set
, T
);
477 lp
= wrap_constraints(set
);
478 obj
= isl_vec_alloc(set
->ctx
, 1 + dim
*set
->n
);
481 isl_int_set_si(obj
->block
.data
[0], 0);
482 for (i
= 0; i
< set
->n
; ++i
) {
483 isl_seq_clr(obj
->block
.data
+ 1 + dim
*i
, 2);
484 isl_int_set_si(obj
->block
.data
[1 + dim
*i
+2], 1);
485 isl_seq_clr(obj
->block
.data
+ 1 + dim
*i
+3, dim
-3);
489 res
= isl_basic_set_solve_lp(lp
, 0,
490 obj
->block
.data
, set
->ctx
->one
, &num
, &den
, NULL
);
491 if (res
== isl_lp_ok
) {
492 isl_int_neg(num
, num
);
493 isl_seq_combine(facet
, num
, facet
, den
, ridge
, dim
);
498 isl_basic_set_free(lp
);
500 isl_assert(set
->ctx
, res
== isl_lp_ok
, return NULL
);
503 isl_basic_set_free(lp
);
509 /* Given a set of d linearly independent bounding constraints of the
510 * convex hull of "set", compute the constraint of a facet of "set".
512 * We first compute the intersection with the first bounding hyperplane
513 * and remove the component corresponding to this hyperplane from
514 * other bounds (in homogeneous space).
515 * We then wrap around one of the remaining bounding constraints
516 * and continue the process until all bounding constraints have been
517 * taken into account.
518 * The resulting linear combination of the bounding constraints will
519 * correspond to a facet of the convex hull.
521 static struct isl_mat
*initial_facet_constraint(struct isl_set
*set
,
522 struct isl_mat
*bounds
)
524 struct isl_set
*slice
= NULL
;
525 struct isl_basic_set
*face
= NULL
;
526 struct isl_mat
*m
, *U
, *Q
;
528 unsigned dim
= isl_set_n_dim(set
);
530 isl_assert(set
->ctx
, set
->n
> 0, goto error
);
531 isl_assert(set
->ctx
, bounds
->n_row
== dim
, goto error
);
533 while (bounds
->n_row
> 1) {
534 slice
= isl_set_copy(set
);
535 slice
= isl_set_add_equality(slice
, bounds
->row
[0]);
536 face
= isl_set_affine_hull(slice
);
539 if (face
->n_eq
== 1) {
540 isl_basic_set_free(face
);
543 m
= isl_mat_alloc(set
->ctx
, 1 + face
->n_eq
, 1 + dim
);
546 isl_int_set_si(m
->row
[0][0], 1);
547 isl_seq_clr(m
->row
[0]+1, dim
);
548 for (i
= 0; i
< face
->n_eq
; ++i
)
549 isl_seq_cpy(m
->row
[1 + i
], face
->eq
[i
], 1 + dim
);
550 U
= isl_mat_right_inverse(m
);
551 Q
= isl_mat_right_inverse(isl_mat_copy(U
));
552 U
= isl_mat_drop_cols(U
, 1 + face
->n_eq
, dim
- face
->n_eq
);
553 Q
= isl_mat_drop_rows(Q
, 1 + face
->n_eq
, dim
- face
->n_eq
);
554 U
= isl_mat_drop_cols(U
, 0, 1);
555 Q
= isl_mat_drop_rows(Q
, 0, 1);
556 bounds
= isl_mat_product(bounds
, U
);
557 bounds
= isl_mat_product(bounds
, Q
);
558 while (isl_seq_first_non_zero(bounds
->row
[bounds
->n_row
-1],
559 bounds
->n_col
) == -1) {
561 isl_assert(set
->ctx
, bounds
->n_row
> 1, goto error
);
563 if (!wrap_facet(set
, bounds
->row
[0],
564 bounds
->row
[bounds
->n_row
-1]))
566 isl_basic_set_free(face
);
571 isl_basic_set_free(face
);
572 isl_mat_free(bounds
);
576 /* Given the bounding constraint "c" of a facet of the convex hull of "set",
577 * compute a hyperplane description of the facet, i.e., compute the facets
580 * We compute an affine transformation that transforms the constraint
589 * by computing the right inverse U of a matrix that starts with the rows
602 * Since z_1 is zero, we can drop this variable as well as the corresponding
603 * column of U to obtain
611 * with Q' equal to Q, but without the corresponding row.
612 * After computing the facets of the facet in the z' space,
613 * we convert them back to the x space through Q.
615 static struct isl_basic_set
*compute_facet(struct isl_set
*set
, isl_int
*c
)
617 struct isl_mat
*m
, *U
, *Q
;
618 struct isl_basic_set
*facet
= NULL
;
623 set
= isl_set_copy(set
);
624 dim
= isl_set_n_dim(set
);
625 m
= isl_mat_alloc(set
->ctx
, 2, 1 + dim
);
628 isl_int_set_si(m
->row
[0][0], 1);
629 isl_seq_clr(m
->row
[0]+1, dim
);
630 isl_seq_cpy(m
->row
[1], c
, 1+dim
);
631 U
= isl_mat_right_inverse(m
);
632 Q
= isl_mat_right_inverse(isl_mat_copy(U
));
633 U
= isl_mat_drop_cols(U
, 1, 1);
634 Q
= isl_mat_drop_rows(Q
, 1, 1);
635 set
= isl_set_preimage(set
, U
);
636 facet
= uset_convex_hull_wrap_bounded(set
);
637 facet
= isl_basic_set_preimage(facet
, Q
);
638 isl_assert(ctx
, facet
->n_eq
== 0, goto error
);
641 isl_basic_set_free(facet
);
646 /* Given an initial facet constraint, compute the remaining facets.
647 * We do this by running through all facets found so far and computing
648 * the adjacent facets through wrapping, adding those facets that we
649 * hadn't already found before.
651 * For each facet we have found so far, we first compute its facets
652 * in the resulting convex hull. That is, we compute the ridges
653 * of the resulting convex hull contained in the facet.
654 * We also compute the corresponding facet in the current approximation
655 * of the convex hull. There is no need to wrap around the ridges
656 * in this facet since that would result in a facet that is already
657 * present in the current approximation.
659 * This function can still be significantly optimized by checking which of
660 * the facets of the basic sets are also facets of the convex hull and
661 * using all the facets so far to help in constructing the facets of the
664 * using the technique in section "3.1 Ridge Generation" of
665 * "Extended Convex Hull" by Fukuda et al.
667 static struct isl_basic_set
*extend(struct isl_basic_set
*hull
,
672 struct isl_basic_set
*facet
= NULL
;
673 struct isl_basic_set
*hull_facet
= NULL
;
676 isl_assert(set
->ctx
, set
->n
> 0, goto error
);
678 dim
= isl_set_n_dim(set
);
680 for (i
= 0; i
< hull
->n_ineq
; ++i
) {
681 facet
= compute_facet(set
, hull
->ineq
[i
]);
682 facet
= isl_basic_set_add_equality(facet
, hull
->ineq
[i
]);
683 facet
= isl_basic_set_gauss(facet
, NULL
);
684 facet
= isl_basic_set_normalize_constraints(facet
);
685 hull_facet
= isl_basic_set_copy(hull
);
686 hull_facet
= isl_basic_set_add_equality(hull_facet
, hull
->ineq
[i
]);
687 hull_facet
= isl_basic_set_gauss(hull_facet
, NULL
);
688 hull_facet
= isl_basic_set_normalize_constraints(hull_facet
);
691 hull
= isl_basic_set_cow(hull
);
692 hull
= isl_basic_set_extend_dim(hull
,
693 isl_dim_copy(hull
->dim
), 0, 0, facet
->n_ineq
);
694 for (j
= 0; j
< facet
->n_ineq
; ++j
) {
695 for (f
= 0; f
< hull_facet
->n_ineq
; ++f
)
696 if (isl_seq_eq(facet
->ineq
[j
],
697 hull_facet
->ineq
[f
], 1 + dim
))
699 if (f
< hull_facet
->n_ineq
)
701 k
= isl_basic_set_alloc_inequality(hull
);
704 isl_seq_cpy(hull
->ineq
[k
], hull
->ineq
[i
], 1+dim
);
705 if (!wrap_facet(set
, hull
->ineq
[k
], facet
->ineq
[j
]))
708 isl_basic_set_free(hull_facet
);
709 isl_basic_set_free(facet
);
711 hull
= isl_basic_set_simplify(hull
);
712 hull
= isl_basic_set_finalize(hull
);
715 isl_basic_set_free(hull_facet
);
716 isl_basic_set_free(facet
);
717 isl_basic_set_free(hull
);
721 /* Special case for computing the convex hull of a one dimensional set.
722 * We simply collect the lower and upper bounds of each basic set
723 * and the biggest of those.
725 static struct isl_basic_set
*convex_hull_1d(struct isl_set
*set
)
727 struct isl_mat
*c
= NULL
;
728 isl_int
*lower
= NULL
;
729 isl_int
*upper
= NULL
;
732 struct isl_basic_set
*hull
;
734 for (i
= 0; i
< set
->n
; ++i
) {
735 set
->p
[i
] = isl_basic_set_simplify(set
->p
[i
]);
739 set
= isl_set_remove_empty_parts(set
);
742 isl_assert(set
->ctx
, set
->n
> 0, goto error
);
743 c
= isl_mat_alloc(set
->ctx
, 2, 2);
747 if (set
->p
[0]->n_eq
> 0) {
748 isl_assert(set
->ctx
, set
->p
[0]->n_eq
== 1, goto error
);
751 if (isl_int_is_pos(set
->p
[0]->eq
[0][1])) {
752 isl_seq_cpy(lower
, set
->p
[0]->eq
[0], 2);
753 isl_seq_neg(upper
, set
->p
[0]->eq
[0], 2);
755 isl_seq_neg(lower
, set
->p
[0]->eq
[0], 2);
756 isl_seq_cpy(upper
, set
->p
[0]->eq
[0], 2);
759 for (j
= 0; j
< set
->p
[0]->n_ineq
; ++j
) {
760 if (isl_int_is_pos(set
->p
[0]->ineq
[j
][1])) {
762 isl_seq_cpy(lower
, set
->p
[0]->ineq
[j
], 2);
765 isl_seq_cpy(upper
, set
->p
[0]->ineq
[j
], 2);
772 for (i
= 0; i
< set
->n
; ++i
) {
773 struct isl_basic_set
*bset
= set
->p
[i
];
777 for (j
= 0; j
< bset
->n_eq
; ++j
) {
781 isl_int_mul(a
, lower
[0], bset
->eq
[j
][1]);
782 isl_int_mul(b
, lower
[1], bset
->eq
[j
][0]);
783 if (isl_int_lt(a
, b
) && isl_int_is_pos(bset
->eq
[j
][1]))
784 isl_seq_cpy(lower
, bset
->eq
[j
], 2);
785 if (isl_int_gt(a
, b
) && isl_int_is_neg(bset
->eq
[j
][1]))
786 isl_seq_neg(lower
, bset
->eq
[j
], 2);
789 isl_int_mul(a
, upper
[0], bset
->eq
[j
][1]);
790 isl_int_mul(b
, upper
[1], bset
->eq
[j
][0]);
791 if (isl_int_lt(a
, b
) && isl_int_is_pos(bset
->eq
[j
][1]))
792 isl_seq_neg(upper
, bset
->eq
[j
], 2);
793 if (isl_int_gt(a
, b
) && isl_int_is_neg(bset
->eq
[j
][1]))
794 isl_seq_cpy(upper
, bset
->eq
[j
], 2);
797 for (j
= 0; j
< bset
->n_ineq
; ++j
) {
798 if (isl_int_is_pos(bset
->ineq
[j
][1]))
800 if (isl_int_is_neg(bset
->ineq
[j
][1]))
802 if (lower
&& isl_int_is_pos(bset
->ineq
[j
][1])) {
803 isl_int_mul(a
, lower
[0], bset
->ineq
[j
][1]);
804 isl_int_mul(b
, lower
[1], bset
->ineq
[j
][0]);
805 if (isl_int_lt(a
, b
))
806 isl_seq_cpy(lower
, bset
->ineq
[j
], 2);
808 if (upper
&& isl_int_is_neg(bset
->ineq
[j
][1])) {
809 isl_int_mul(a
, upper
[0], bset
->ineq
[j
][1]);
810 isl_int_mul(b
, upper
[1], bset
->ineq
[j
][0]);
811 if (isl_int_gt(a
, b
))
812 isl_seq_cpy(upper
, bset
->ineq
[j
], 2);
823 hull
= isl_basic_set_alloc(set
->ctx
, 0, 1, 0, 0, 2);
824 hull
= isl_basic_set_set_rational(hull
);
828 k
= isl_basic_set_alloc_inequality(hull
);
829 isl_seq_cpy(hull
->ineq
[k
], lower
, 2);
832 k
= isl_basic_set_alloc_inequality(hull
);
833 isl_seq_cpy(hull
->ineq
[k
], upper
, 2);
835 hull
= isl_basic_set_finalize(hull
);
845 /* Project out final n dimensions using Fourier-Motzkin */
846 static struct isl_set
*set_project_out(struct isl_ctx
*ctx
,
847 struct isl_set
*set
, unsigned n
)
849 return isl_set_remove_dims(set
, isl_set_n_dim(set
) - n
, n
);
852 static struct isl_basic_set
*convex_hull_0d(struct isl_set
*set
)
854 struct isl_basic_set
*convex_hull
;
859 if (isl_set_is_empty(set
))
860 convex_hull
= isl_basic_set_empty(isl_dim_copy(set
->dim
));
862 convex_hull
= isl_basic_set_universe(isl_dim_copy(set
->dim
));
867 /* Compute the convex hull of a pair of basic sets without any parameters or
868 * integer divisions using Fourier-Motzkin elimination.
869 * The convex hull is the set of all points that can be written as
870 * the sum of points from both basic sets (in homogeneous coordinates).
871 * We set up the constraints in a space with dimensions for each of
872 * the three sets and then project out the dimensions corresponding
873 * to the two original basic sets, retaining only those corresponding
874 * to the convex hull.
876 static struct isl_basic_set
*convex_hull_pair_elim(struct isl_basic_set
*bset1
,
877 struct isl_basic_set
*bset2
)
880 struct isl_basic_set
*bset
[2];
881 struct isl_basic_set
*hull
= NULL
;
884 if (!bset1
|| !bset2
)
887 dim
= isl_basic_set_n_dim(bset1
);
888 hull
= isl_basic_set_alloc(bset1
->ctx
, 0, 2 + 3 * dim
, 0,
889 1 + dim
+ bset1
->n_eq
+ bset2
->n_eq
,
890 2 + bset1
->n_ineq
+ bset2
->n_ineq
);
893 for (i
= 0; i
< 2; ++i
) {
894 for (j
= 0; j
< bset
[i
]->n_eq
; ++j
) {
895 k
= isl_basic_set_alloc_equality(hull
);
898 isl_seq_clr(hull
->eq
[k
], (i
+1) * (1+dim
));
899 isl_seq_clr(hull
->eq
[k
]+(i
+2)*(1+dim
), (1-i
)*(1+dim
));
900 isl_seq_cpy(hull
->eq
[k
]+(i
+1)*(1+dim
), bset
[i
]->eq
[j
],
903 for (j
= 0; j
< bset
[i
]->n_ineq
; ++j
) {
904 k
= isl_basic_set_alloc_inequality(hull
);
907 isl_seq_clr(hull
->ineq
[k
], (i
+1) * (1+dim
));
908 isl_seq_clr(hull
->ineq
[k
]+(i
+2)*(1+dim
), (1-i
)*(1+dim
));
909 isl_seq_cpy(hull
->ineq
[k
]+(i
+1)*(1+dim
),
910 bset
[i
]->ineq
[j
], 1+dim
);
912 k
= isl_basic_set_alloc_inequality(hull
);
915 isl_seq_clr(hull
->ineq
[k
], 1+2+3*dim
);
916 isl_int_set_si(hull
->ineq
[k
][(i
+1)*(1+dim
)], 1);
918 for (j
= 0; j
< 1+dim
; ++j
) {
919 k
= isl_basic_set_alloc_equality(hull
);
922 isl_seq_clr(hull
->eq
[k
], 1+2+3*dim
);
923 isl_int_set_si(hull
->eq
[k
][j
], -1);
924 isl_int_set_si(hull
->eq
[k
][1+dim
+j
], 1);
925 isl_int_set_si(hull
->eq
[k
][2*(1+dim
)+j
], 1);
927 hull
= isl_basic_set_set_rational(hull
);
928 hull
= isl_basic_set_remove_dims(hull
, dim
, 2*(1+dim
));
929 hull
= isl_basic_set_convex_hull(hull
);
930 isl_basic_set_free(bset1
);
931 isl_basic_set_free(bset2
);
934 isl_basic_set_free(bset1
);
935 isl_basic_set_free(bset2
);
936 isl_basic_set_free(hull
);
940 static int isl_basic_set_is_bounded(struct isl_basic_set
*bset
)
945 tab
= isl_tab_from_recession_cone(bset
);
946 bounded
= isl_tab_cone_is_bounded(tab
);
951 static int isl_set_is_bounded(struct isl_set
*set
)
955 for (i
= 0; i
< set
->n
; ++i
) {
956 int bounded
= isl_basic_set_is_bounded(set
->p
[i
]);
957 if (!bounded
|| bounded
< 0)
963 /* Compute the lineality space of the convex hull of bset1 and bset2.
965 * We first compute the intersection of the recession cone of bset1
966 * with the negative of the recession cone of bset2 and then compute
967 * the linear hull of the resulting cone.
969 static struct isl_basic_set
*induced_lineality_space(
970 struct isl_basic_set
*bset1
, struct isl_basic_set
*bset2
)
973 struct isl_basic_set
*lin
= NULL
;
976 if (!bset1
|| !bset2
)
979 dim
= isl_basic_set_total_dim(bset1
);
980 lin
= isl_basic_set_alloc_dim(isl_basic_set_get_dim(bset1
), 0,
981 bset1
->n_eq
+ bset2
->n_eq
,
982 bset1
->n_ineq
+ bset2
->n_ineq
);
983 lin
= isl_basic_set_set_rational(lin
);
986 for (i
= 0; i
< bset1
->n_eq
; ++i
) {
987 k
= isl_basic_set_alloc_equality(lin
);
990 isl_int_set_si(lin
->eq
[k
][0], 0);
991 isl_seq_cpy(lin
->eq
[k
] + 1, bset1
->eq
[i
] + 1, dim
);
993 for (i
= 0; i
< bset1
->n_ineq
; ++i
) {
994 k
= isl_basic_set_alloc_inequality(lin
);
997 isl_int_set_si(lin
->ineq
[k
][0], 0);
998 isl_seq_cpy(lin
->ineq
[k
] + 1, bset1
->ineq
[i
] + 1, dim
);
1000 for (i
= 0; i
< bset2
->n_eq
; ++i
) {
1001 k
= isl_basic_set_alloc_equality(lin
);
1004 isl_int_set_si(lin
->eq
[k
][0], 0);
1005 isl_seq_neg(lin
->eq
[k
] + 1, bset2
->eq
[i
] + 1, dim
);
1007 for (i
= 0; i
< bset2
->n_ineq
; ++i
) {
1008 k
= isl_basic_set_alloc_inequality(lin
);
1011 isl_int_set_si(lin
->ineq
[k
][0], 0);
1012 isl_seq_neg(lin
->ineq
[k
] + 1, bset2
->ineq
[i
] + 1, dim
);
1015 isl_basic_set_free(bset1
);
1016 isl_basic_set_free(bset2
);
1017 return isl_basic_set_affine_hull(lin
);
1019 isl_basic_set_free(lin
);
1020 isl_basic_set_free(bset1
);
1021 isl_basic_set_free(bset2
);
1025 static struct isl_basic_set
*uset_convex_hull(struct isl_set
*set
);
1027 /* Given a set and a linear space "lin" of dimension n > 0,
1028 * project the linear space from the set, compute the convex hull
1029 * and then map the set back to the original space.
1035 * describe the linear space. We first compute the Hermite normal
1036 * form H = M U of M = H Q, to obtain
1040 * The last n rows of H will be zero, so the last n variables of x' = Q x
1041 * are the one we want to project out. We do this by transforming each
1042 * basic set A x >= b to A U x' >= b and then removing the last n dimensions.
1043 * After computing the convex hull in x'_1, i.e., A' x'_1 >= b',
1044 * we transform the hull back to the original space as A' Q_1 x >= b',
1045 * with Q_1 all but the last n rows of Q.
1047 static struct isl_basic_set
*modulo_lineality(struct isl_set
*set
,
1048 struct isl_basic_set
*lin
)
1050 unsigned total
= isl_basic_set_total_dim(lin
);
1052 struct isl_basic_set
*hull
;
1053 struct isl_mat
*M
, *U
, *Q
;
1057 lin_dim
= total
- lin
->n_eq
;
1058 M
= isl_mat_sub_alloc(set
->ctx
, lin
->eq
, 0, lin
->n_eq
, 1, total
);
1059 M
= isl_mat_left_hermite(M
, 0, &U
, &Q
);
1063 isl_basic_set_free(lin
);
1065 Q
= isl_mat_drop_rows(Q
, Q
->n_row
- lin_dim
, lin_dim
);
1067 U
= isl_mat_lin_to_aff(U
);
1068 Q
= isl_mat_lin_to_aff(Q
);
1070 set
= isl_set_preimage(set
, U
);
1071 set
= isl_set_remove_dims(set
, total
- lin_dim
, lin_dim
);
1072 hull
= uset_convex_hull(set
);
1073 hull
= isl_basic_set_preimage(hull
, Q
);
1077 isl_basic_set_free(lin
);
1082 /* Given two polyhedra with as constraints h_{ij} x >= 0 in homegeneous space,
1083 * set up an LP for solving
1085 * \sum_j \alpha_{1j} h_{1j} = \sum_j \alpha_{2j} h_{2j}
1087 * \alpha{i0} corresponds to the (implicit) positivity constraint 1 >= 0
1088 * The next \alpha{ij} correspond to the equalities and come in pairs.
1089 * The final \alpha{ij} correspond to the inequalities.
1091 static struct isl_basic_set
*valid_direction_lp(
1092 struct isl_basic_set
*bset1
, struct isl_basic_set
*bset2
)
1094 struct isl_dim
*dim
;
1095 struct isl_basic_set
*lp
;
1100 if (!bset1
|| !bset2
)
1102 d
= 1 + isl_basic_set_total_dim(bset1
);
1104 2 * bset1
->n_eq
+ bset1
->n_ineq
+ 2 * bset2
->n_eq
+ bset2
->n_ineq
;
1105 dim
= isl_dim_set_alloc(bset1
->ctx
, 0, n
);
1106 lp
= isl_basic_set_alloc_dim(dim
, 0, d
, n
);
1109 for (i
= 0; i
< n
; ++i
) {
1110 k
= isl_basic_set_alloc_inequality(lp
);
1113 isl_seq_clr(lp
->ineq
[k
] + 1, n
);
1114 isl_int_set_si(lp
->ineq
[k
][0], -1);
1115 isl_int_set_si(lp
->ineq
[k
][1 + i
], 1);
1117 for (i
= 0; i
< d
; ++i
) {
1118 k
= isl_basic_set_alloc_equality(lp
);
1122 isl_int_set_si(lp
->eq
[k
][n
++], 0);
1123 /* positivity constraint 1 >= 0 */
1124 isl_int_set_si(lp
->eq
[k
][n
++], i
== 0);
1125 for (j
= 0; j
< bset1
->n_eq
; ++j
) {
1126 isl_int_set(lp
->eq
[k
][n
++], bset1
->eq
[j
][i
]);
1127 isl_int_neg(lp
->eq
[k
][n
++], bset1
->eq
[j
][i
]);
1129 for (j
= 0; j
< bset1
->n_ineq
; ++j
)
1130 isl_int_set(lp
->eq
[k
][n
++], bset1
->ineq
[j
][i
]);
1131 /* positivity constraint 1 >= 0 */
1132 isl_int_set_si(lp
->eq
[k
][n
++], -(i
== 0));
1133 for (j
= 0; j
< bset2
->n_eq
; ++j
) {
1134 isl_int_neg(lp
->eq
[k
][n
++], bset2
->eq
[j
][i
]);
1135 isl_int_set(lp
->eq
[k
][n
++], bset2
->eq
[j
][i
]);
1137 for (j
= 0; j
< bset2
->n_ineq
; ++j
)
1138 isl_int_neg(lp
->eq
[k
][n
++], bset2
->ineq
[j
][i
]);
1140 lp
= isl_basic_set_gauss(lp
, NULL
);
1141 isl_basic_set_free(bset1
);
1142 isl_basic_set_free(bset2
);
1145 isl_basic_set_free(bset1
);
1146 isl_basic_set_free(bset2
);
1150 /* Compute a vector s in the homogeneous space such that <s, r> > 0
1151 * for all rays in the homogeneous space of the two cones that correspond
1152 * to the input polyhedra bset1 and bset2.
1154 * We compute s as a vector that satisfies
1156 * s = \sum_j \alpha_{ij} h_{ij} for i = 1,2 (*)
1158 * with h_{ij} the normals of the facets of polyhedron i
1159 * (including the "positivity constraint" 1 >= 0) and \alpha_{ij}
1160 * strictly positive numbers. For simplicity we impose \alpha_{ij} >= 1.
1161 * We first set up an LP with as variables the \alpha{ij}.
1162 * In this formulateion, for each polyhedron i,
1163 * the first constraint is the positivity constraint, followed by pairs
1164 * of variables for the equalities, followed by variables for the inequalities.
1165 * We then simply pick a feasible solution and compute s using (*).
1167 * Note that we simply pick any valid direction and make no attempt
1168 * to pick a "good" or even the "best" valid direction.
1170 static struct isl_vec
*valid_direction(
1171 struct isl_basic_set
*bset1
, struct isl_basic_set
*bset2
)
1173 struct isl_basic_set
*lp
;
1174 struct isl_tab
*tab
;
1175 struct isl_vec
*sample
= NULL
;
1176 struct isl_vec
*dir
;
1181 if (!bset1
|| !bset2
)
1183 lp
= valid_direction_lp(isl_basic_set_copy(bset1
),
1184 isl_basic_set_copy(bset2
));
1185 tab
= isl_tab_from_basic_set(lp
);
1186 sample
= isl_tab_get_sample_value(tab
);
1188 isl_basic_set_free(lp
);
1191 d
= isl_basic_set_total_dim(bset1
);
1192 dir
= isl_vec_alloc(bset1
->ctx
, 1 + d
);
1195 isl_seq_clr(dir
->block
.data
+ 1, dir
->size
- 1);
1197 /* positivity constraint 1 >= 0 */
1198 isl_int_set(dir
->block
.data
[0], sample
->block
.data
[n
++]);
1199 for (i
= 0; i
< bset1
->n_eq
; ++i
) {
1200 isl_int_sub(sample
->block
.data
[n
],
1201 sample
->block
.data
[n
], sample
->block
.data
[n
+1]);
1202 isl_seq_combine(dir
->block
.data
,
1203 bset1
->ctx
->one
, dir
->block
.data
,
1204 sample
->block
.data
[n
], bset1
->eq
[i
], 1 + d
);
1208 for (i
= 0; i
< bset1
->n_ineq
; ++i
)
1209 isl_seq_combine(dir
->block
.data
,
1210 bset1
->ctx
->one
, dir
->block
.data
,
1211 sample
->block
.data
[n
++], bset1
->ineq
[i
], 1 + d
);
1212 isl_vec_free(sample
);
1213 isl_seq_normalize(bset1
->ctx
, dir
->block
.data
+ 1, dir
->size
- 1);
1214 isl_basic_set_free(bset1
);
1215 isl_basic_set_free(bset2
);
1218 isl_vec_free(sample
);
1219 isl_basic_set_free(bset1
);
1220 isl_basic_set_free(bset2
);
1224 /* Given a polyhedron b_i + A_i x >= 0 and a map T = S^{-1},
1225 * compute b_i' + A_i' x' >= 0, with
1227 * [ b_i A_i ] [ y' ] [ y' ]
1228 * [ 1 0 ] S^{-1} [ x' ] >= 0 or [ b_i' A_i' ] [ x' ] >= 0
1230 * In particular, add the "positivity constraint" and then perform
1233 static struct isl_basic_set
*homogeneous_map(struct isl_basic_set
*bset
,
1240 bset
= isl_basic_set_extend_constraints(bset
, 0, 1);
1241 k
= isl_basic_set_alloc_inequality(bset
);
1244 isl_seq_clr(bset
->ineq
[k
] + 1, isl_basic_set_total_dim(bset
));
1245 isl_int_set_si(bset
->ineq
[k
][0], 1);
1246 bset
= isl_basic_set_preimage(bset
, T
);
1250 isl_basic_set_free(bset
);
1254 /* Compute the convex hull of a pair of basic sets without any parameters or
1255 * integer divisions, where the convex hull is known to be pointed,
1256 * but the basic sets may be unbounded.
1258 * We turn this problem into the computation of a convex hull of a pair
1259 * _bounded_ polyhedra by "changing the direction of the homogeneous
1260 * dimension". This idea is due to Matthias Koeppe.
1262 * Consider the cones in homogeneous space that correspond to the
1263 * input polyhedra. The rays of these cones are also rays of the
1264 * polyhedra if the coordinate that corresponds to the homogeneous
1265 * dimension is zero. That is, if the inner product of the rays
1266 * with the homogeneous direction is zero.
1267 * The cones in the homogeneous space can also be considered to
1268 * correspond to other pairs of polyhedra by chosing a different
1269 * homogeneous direction. To ensure that both of these polyhedra
1270 * are bounded, we need to make sure that all rays of the cones
1271 * correspond to vertices and not to rays.
1272 * Let s be a direction such that <s, r> > 0 for all rays r of both cones.
1273 * Then using s as a homogeneous direction, we obtain a pair of polytopes.
1274 * The vector s is computed in valid_direction.
1276 * Note that we need to consider _all_ rays of the cones and not just
1277 * the rays that correspond to rays in the polyhedra. If we were to
1278 * only consider those rays and turn them into vertices, then we
1279 * may inadvertently turn some vertices into rays.
1281 * The standard homogeneous direction is the unit vector in the 0th coordinate.
1282 * We therefore transform the two polyhedra such that the selected
1283 * direction is mapped onto this standard direction and then proceed
1284 * with the normal computation.
1285 * Let S be a non-singular square matrix with s as its first row,
1286 * then we want to map the polyhedra to the space
1288 * [ y' ] [ y ] [ y ] [ y' ]
1289 * [ x' ] = S [ x ] i.e., [ x ] = S^{-1} [ x' ]
1291 * We take S to be the unimodular completion of s to limit the growth
1292 * of the coefficients in the following computations.
1294 * Let b_i + A_i x >= 0 be the constraints of polyhedron i.
1295 * We first move to the homogeneous dimension
1297 * b_i y + A_i x >= 0 [ b_i A_i ] [ y ] [ 0 ]
1298 * y >= 0 or [ 1 0 ] [ x ] >= [ 0 ]
1300 * Then we change directoin
1302 * [ b_i A_i ] [ y' ] [ y' ]
1303 * [ 1 0 ] S^{-1} [ x' ] >= 0 or [ b_i' A_i' ] [ x' ] >= 0
1305 * Then we compute the convex hull of the polytopes b_i' + A_i' x' >= 0
1306 * resulting in b' + A' x' >= 0, which we then convert back
1309 * [ b' A' ] S [ x ] >= 0 or [ b A ] [ x ] >= 0
1311 * The polyhedron b + A x >= 0 is then the convex hull of the input polyhedra.
1313 static struct isl_basic_set
*convex_hull_pair_pointed(
1314 struct isl_basic_set
*bset1
, struct isl_basic_set
*bset2
)
1316 struct isl_ctx
*ctx
= NULL
;
1317 struct isl_vec
*dir
= NULL
;
1318 struct isl_mat
*T
= NULL
;
1319 struct isl_mat
*T2
= NULL
;
1320 struct isl_basic_set
*hull
;
1321 struct isl_set
*set
;
1323 if (!bset1
|| !bset2
)
1326 dir
= valid_direction(isl_basic_set_copy(bset1
),
1327 isl_basic_set_copy(bset2
));
1330 T
= isl_mat_alloc(bset1
->ctx
, dir
->size
, dir
->size
);
1333 isl_seq_cpy(T
->row
[0], dir
->block
.data
, dir
->size
);
1334 T
= isl_mat_unimodular_complete(T
, 1);
1335 T2
= isl_mat_right_inverse(isl_mat_copy(T
));
1337 bset1
= homogeneous_map(bset1
, isl_mat_copy(T2
));
1338 bset2
= homogeneous_map(bset2
, T2
);
1339 set
= isl_set_alloc_dim(isl_basic_set_get_dim(bset1
), 2, 0);
1340 set
= isl_set_add(set
, bset1
);
1341 set
= isl_set_add(set
, bset2
);
1342 hull
= uset_convex_hull(set
);
1343 hull
= isl_basic_set_preimage(hull
, T
);
1350 isl_basic_set_free(bset1
);
1351 isl_basic_set_free(bset2
);
1355 /* Compute the convex hull of a pair of basic sets without any parameters or
1356 * integer divisions.
1358 * If the convex hull of the two basic sets would have a non-trivial
1359 * lineality space, we first project out this lineality space.
1361 static struct isl_basic_set
*convex_hull_pair(struct isl_basic_set
*bset1
,
1362 struct isl_basic_set
*bset2
)
1364 struct isl_basic_set
*lin
;
1366 if (isl_basic_set_is_bounded(bset1
) || isl_basic_set_is_bounded(bset2
))
1367 return convex_hull_pair_pointed(bset1
, bset2
);
1369 lin
= induced_lineality_space(isl_basic_set_copy(bset1
),
1370 isl_basic_set_copy(bset2
));
1373 if (isl_basic_set_is_universe(lin
)) {
1374 isl_basic_set_free(bset1
);
1375 isl_basic_set_free(bset2
);
1378 if (lin
->n_eq
< isl_basic_set_total_dim(lin
)) {
1379 struct isl_set
*set
;
1380 set
= isl_set_alloc_dim(isl_basic_set_get_dim(bset1
), 2, 0);
1381 set
= isl_set_add(set
, bset1
);
1382 set
= isl_set_add(set
, bset2
);
1383 return modulo_lineality(set
, lin
);
1385 isl_basic_set_free(lin
);
1387 return convex_hull_pair_pointed(bset1
, bset2
);
1389 isl_basic_set_free(bset1
);
1390 isl_basic_set_free(bset2
);
1394 /* Compute the lineality space of a basic set.
1395 * We currently do not allow the basic set to have any divs.
1396 * We basically just drop the constants and turn every inequality
1399 struct isl_basic_set
*isl_basic_set_lineality_space(struct isl_basic_set
*bset
)
1402 struct isl_basic_set
*lin
= NULL
;
1407 isl_assert(bset
->ctx
, bset
->n_div
== 0, goto error
);
1408 dim
= isl_basic_set_total_dim(bset
);
1410 lin
= isl_basic_set_alloc_dim(isl_basic_set_get_dim(bset
), 0, dim
, 0);
1413 for (i
= 0; i
< bset
->n_eq
; ++i
) {
1414 k
= isl_basic_set_alloc_equality(lin
);
1417 isl_int_set_si(lin
->eq
[k
][0], 0);
1418 isl_seq_cpy(lin
->eq
[k
] + 1, bset
->eq
[i
] + 1, dim
);
1420 lin
= isl_basic_set_gauss(lin
, NULL
);
1423 for (i
= 0; i
< bset
->n_ineq
&& lin
->n_eq
< dim
; ++i
) {
1424 k
= isl_basic_set_alloc_equality(lin
);
1427 isl_int_set_si(lin
->eq
[k
][0], 0);
1428 isl_seq_cpy(lin
->eq
[k
] + 1, bset
->ineq
[i
] + 1, dim
);
1429 lin
= isl_basic_set_gauss(lin
, NULL
);
1433 isl_basic_set_free(bset
);
1436 isl_basic_set_free(lin
);
1437 isl_basic_set_free(bset
);
1441 /* Compute the (linear) hull of the lineality spaces of the basic sets in the
1442 * "underlying" set "set".
1444 static struct isl_basic_set
*uset_combined_lineality_space(struct isl_set
*set
)
1447 struct isl_set
*lin
= NULL
;
1452 struct isl_dim
*dim
= isl_set_get_dim(set
);
1454 return isl_basic_set_empty(dim
);
1457 lin
= isl_set_alloc_dim(isl_set_get_dim(set
), set
->n
, 0);
1458 for (i
= 0; i
< set
->n
; ++i
)
1459 lin
= isl_set_add(lin
,
1460 isl_basic_set_lineality_space(isl_basic_set_copy(set
->p
[i
])));
1462 return isl_set_affine_hull(lin
);
1465 /* Compute the convex hull of a set without any parameters or
1466 * integer divisions.
1467 * In each step, we combined two basic sets until only one
1468 * basic set is left.
1469 * The input basic sets are assumed not to have a non-trivial
1470 * lineality space. If any of the intermediate results has
1471 * a non-trivial lineality space, it is projected out.
1473 static struct isl_basic_set
*uset_convex_hull_unbounded(struct isl_set
*set
)
1475 struct isl_basic_set
*convex_hull
= NULL
;
1477 convex_hull
= isl_set_copy_basic_set(set
);
1478 set
= isl_set_drop_basic_set(set
, convex_hull
);
1481 while (set
->n
> 0) {
1482 struct isl_basic_set
*t
;
1483 t
= isl_set_copy_basic_set(set
);
1486 set
= isl_set_drop_basic_set(set
, t
);
1489 convex_hull
= convex_hull_pair(convex_hull
, t
);
1492 t
= isl_basic_set_lineality_space(isl_basic_set_copy(convex_hull
));
1495 if (isl_basic_set_is_universe(t
)) {
1496 isl_basic_set_free(convex_hull
);
1500 if (t
->n_eq
< isl_basic_set_total_dim(t
)) {
1501 set
= isl_set_add(set
, convex_hull
);
1502 return modulo_lineality(set
, t
);
1504 isl_basic_set_free(t
);
1510 isl_basic_set_free(convex_hull
);
1514 /* Compute an initial hull for wrapping containing a single initial
1515 * facet by first computing bounds on the set and then using these
1516 * bounds to construct an initial facet.
1517 * This function is a remnant of an older implementation where the
1518 * bounds were also used to check whether the set was bounded.
1519 * Since this function will now only be called when we know the
1520 * set to be bounded, the initial facet should probably be constructed
1521 * by simply using the coordinate directions instead.
1523 static struct isl_basic_set
*initial_hull(struct isl_basic_set
*hull
,
1524 struct isl_set
*set
)
1526 struct isl_mat
*bounds
= NULL
;
1532 bounds
= independent_bounds(set
);
1535 isl_assert(set
->ctx
, bounds
->n_row
== isl_set_n_dim(set
), goto error
);
1536 bounds
= initial_facet_constraint(set
, bounds
);
1539 k
= isl_basic_set_alloc_inequality(hull
);
1542 dim
= isl_set_n_dim(set
);
1543 isl_assert(set
->ctx
, 1 + dim
== bounds
->n_col
, goto error
);
1544 isl_seq_cpy(hull
->ineq
[k
], bounds
->row
[0], bounds
->n_col
);
1545 isl_mat_free(bounds
);
1549 isl_basic_set_free(hull
);
1550 isl_mat_free(bounds
);
1554 struct max_constraint
{
1560 static int max_constraint_equal(const void *entry
, const void *val
)
1562 struct max_constraint
*a
= (struct max_constraint
*)entry
;
1563 isl_int
*b
= (isl_int
*)val
;
1565 return isl_seq_eq(a
->c
->row
[0] + 1, b
, a
->c
->n_col
- 1);
1568 static void update_constraint(struct isl_ctx
*ctx
, struct isl_hash_table
*table
,
1569 isl_int
*con
, unsigned len
, int n
, int ineq
)
1571 struct isl_hash_table_entry
*entry
;
1572 struct max_constraint
*c
;
1575 c_hash
= isl_seq_get_hash(con
+ 1, len
);
1576 entry
= isl_hash_table_find(ctx
, table
, c_hash
, max_constraint_equal
,
1582 isl_hash_table_remove(ctx
, table
, entry
);
1586 if (isl_int_gt(c
->c
->row
[0][0], con
[0]))
1588 if (isl_int_eq(c
->c
->row
[0][0], con
[0])) {
1593 c
->c
= isl_mat_cow(c
->c
);
1594 isl_int_set(c
->c
->row
[0][0], con
[0]);
1598 /* Check whether the constraint hash table "table" constains the constraint
1601 static int has_constraint(struct isl_ctx
*ctx
, struct isl_hash_table
*table
,
1602 isl_int
*con
, unsigned len
, int n
)
1604 struct isl_hash_table_entry
*entry
;
1605 struct max_constraint
*c
;
1608 c_hash
= isl_seq_get_hash(con
+ 1, len
);
1609 entry
= isl_hash_table_find(ctx
, table
, c_hash
, max_constraint_equal
,
1616 return isl_int_eq(c
->c
->row
[0][0], con
[0]);
1619 /* Check for inequality constraints of a basic set without equalities
1620 * such that the same or more stringent copies of the constraint appear
1621 * in all of the basic sets. Such constraints are necessarily facet
1622 * constraints of the convex hull.
1624 * If the resulting basic set is by chance identical to one of
1625 * the basic sets in "set", then we know that this basic set contains
1626 * all other basic sets and is therefore the convex hull of set.
1627 * In this case we set *is_hull to 1.
1629 static struct isl_basic_set
*common_constraints(struct isl_basic_set
*hull
,
1630 struct isl_set
*set
, int *is_hull
)
1633 int min_constraints
;
1635 struct max_constraint
*constraints
= NULL
;
1636 struct isl_hash_table
*table
= NULL
;
1641 for (i
= 0; i
< set
->n
; ++i
)
1642 if (set
->p
[i
]->n_eq
== 0)
1646 min_constraints
= set
->p
[i
]->n_ineq
;
1648 for (i
= best
+ 1; i
< set
->n
; ++i
) {
1649 if (set
->p
[i
]->n_eq
!= 0)
1651 if (set
->p
[i
]->n_ineq
>= min_constraints
)
1653 min_constraints
= set
->p
[i
]->n_ineq
;
1656 constraints
= isl_calloc_array(hull
->ctx
, struct max_constraint
,
1660 table
= isl_alloc_type(hull
->ctx
, struct isl_hash_table
);
1661 if (isl_hash_table_init(hull
->ctx
, table
, min_constraints
))
1664 total
= isl_dim_total(set
->dim
);
1665 for (i
= 0; i
< set
->p
[best
]->n_ineq
; ++i
) {
1666 constraints
[i
].c
= isl_mat_sub_alloc(hull
->ctx
,
1667 set
->p
[best
]->ineq
+ i
, 0, 1, 0, 1 + total
);
1668 if (!constraints
[i
].c
)
1670 constraints
[i
].ineq
= 1;
1672 for (i
= 0; i
< min_constraints
; ++i
) {
1673 struct isl_hash_table_entry
*entry
;
1675 c_hash
= isl_seq_get_hash(constraints
[i
].c
->row
[0] + 1, total
);
1676 entry
= isl_hash_table_find(hull
->ctx
, table
, c_hash
,
1677 max_constraint_equal
, constraints
[i
].c
->row
[0] + 1, 1);
1680 isl_assert(hull
->ctx
, !entry
->data
, goto error
);
1681 entry
->data
= &constraints
[i
];
1685 for (s
= 0; s
< set
->n
; ++s
) {
1689 for (i
= 0; i
< set
->p
[s
]->n_eq
; ++i
) {
1690 isl_int
*eq
= set
->p
[s
]->eq
[i
];
1691 for (j
= 0; j
< 2; ++j
) {
1692 isl_seq_neg(eq
, eq
, 1 + total
);
1693 update_constraint(hull
->ctx
, table
,
1697 for (i
= 0; i
< set
->p
[s
]->n_ineq
; ++i
) {
1698 isl_int
*ineq
= set
->p
[s
]->ineq
[i
];
1699 update_constraint(hull
->ctx
, table
, ineq
, total
, n
,
1700 set
->p
[s
]->n_eq
== 0);
1705 for (i
= 0; i
< min_constraints
; ++i
) {
1706 if (constraints
[i
].count
< n
)
1708 if (!constraints
[i
].ineq
)
1710 j
= isl_basic_set_alloc_inequality(hull
);
1713 isl_seq_cpy(hull
->ineq
[j
], constraints
[i
].c
->row
[0], 1 + total
);
1716 for (s
= 0; s
< set
->n
; ++s
) {
1717 if (set
->p
[s
]->n_eq
)
1719 if (set
->p
[s
]->n_ineq
!= hull
->n_ineq
)
1721 for (i
= 0; i
< set
->p
[s
]->n_ineq
; ++i
) {
1722 isl_int
*ineq
= set
->p
[s
]->ineq
[i
];
1723 if (!has_constraint(hull
->ctx
, table
, ineq
, total
, n
))
1726 if (i
== set
->p
[s
]->n_ineq
)
1730 isl_hash_table_clear(table
);
1731 for (i
= 0; i
< min_constraints
; ++i
)
1732 isl_mat_free(constraints
[i
].c
);
1737 isl_hash_table_clear(table
);
1740 for (i
= 0; i
< min_constraints
; ++i
)
1741 isl_mat_free(constraints
[i
].c
);
1746 /* Create a template for the convex hull of "set" and fill it up
1747 * obvious facet constraints, if any. If the result happens to
1748 * be the convex hull of "set" then *is_hull is set to 1.
1750 static struct isl_basic_set
*proto_hull(struct isl_set
*set
, int *is_hull
)
1752 struct isl_basic_set
*hull
;
1757 for (i
= 0; i
< set
->n
; ++i
) {
1758 n_ineq
+= set
->p
[i
]->n_eq
;
1759 n_ineq
+= set
->p
[i
]->n_ineq
;
1761 hull
= isl_basic_set_alloc_dim(isl_dim_copy(set
->dim
), 0, 0, n_ineq
);
1762 hull
= isl_basic_set_set_rational(hull
);
1765 return common_constraints(hull
, set
, is_hull
);
1768 static struct isl_basic_set
*uset_convex_hull_wrap(struct isl_set
*set
)
1770 struct isl_basic_set
*hull
;
1773 hull
= proto_hull(set
, &is_hull
);
1774 if (hull
&& !is_hull
) {
1775 if (hull
->n_ineq
== 0)
1776 hull
= initial_hull(hull
, set
);
1777 hull
= extend(hull
, set
);
1784 /* Compute the convex hull of a set without any parameters or
1785 * integer divisions. Depending on whether the set is bounded,
1786 * we pass control to the wrapping based convex hull or
1787 * the Fourier-Motzkin elimination based convex hull.
1788 * We also handle a few special cases before checking the boundedness.
1790 static struct isl_basic_set
*uset_convex_hull(struct isl_set
*set
)
1792 struct isl_basic_set
*convex_hull
= NULL
;
1793 struct isl_basic_set
*lin
;
1795 if (isl_set_n_dim(set
) == 0)
1796 return convex_hull_0d(set
);
1798 set
= isl_set_coalesce(set
);
1799 set
= isl_set_set_rational(set
);
1806 convex_hull
= isl_basic_set_copy(set
->p
[0]);
1810 if (isl_set_n_dim(set
) == 1)
1811 return convex_hull_1d(set
);
1813 if (isl_set_is_bounded(set
))
1814 return uset_convex_hull_wrap(set
);
1816 lin
= uset_combined_lineality_space(isl_set_copy(set
));
1819 if (isl_basic_set_is_universe(lin
)) {
1823 if (lin
->n_eq
< isl_basic_set_total_dim(lin
))
1824 return modulo_lineality(set
, lin
);
1825 isl_basic_set_free(lin
);
1827 return uset_convex_hull_unbounded(set
);
1830 isl_basic_set_free(convex_hull
);
1834 /* This is the core procedure, where "set" is a "pure" set, i.e.,
1835 * without parameters or divs and where the convex hull of set is
1836 * known to be full-dimensional.
1838 static struct isl_basic_set
*uset_convex_hull_wrap_bounded(struct isl_set
*set
)
1840 struct isl_basic_set
*convex_hull
= NULL
;
1842 if (isl_set_n_dim(set
) == 0) {
1843 convex_hull
= isl_basic_set_universe(isl_dim_copy(set
->dim
));
1845 convex_hull
= isl_basic_set_set_rational(convex_hull
);
1849 set
= isl_set_set_rational(set
);
1853 set
= isl_set_coalesce(set
);
1857 convex_hull
= isl_basic_set_copy(set
->p
[0]);
1861 if (isl_set_n_dim(set
) == 1)
1862 return convex_hull_1d(set
);
1864 return uset_convex_hull_wrap(set
);
1870 /* Compute the convex hull of set "set" with affine hull "affine_hull",
1871 * We first remove the equalities (transforming the set), compute the
1872 * convex hull of the transformed set and then add the equalities back
1873 * (after performing the inverse transformation.
1875 static struct isl_basic_set
*modulo_affine_hull(struct isl_ctx
*ctx
,
1876 struct isl_set
*set
, struct isl_basic_set
*affine_hull
)
1880 struct isl_basic_set
*dummy
;
1881 struct isl_basic_set
*convex_hull
;
1883 dummy
= isl_basic_set_remove_equalities(
1884 isl_basic_set_copy(affine_hull
), &T
, &T2
);
1887 isl_basic_set_free(dummy
);
1888 set
= isl_set_preimage(set
, T
);
1889 convex_hull
= uset_convex_hull(set
);
1890 convex_hull
= isl_basic_set_preimage(convex_hull
, T2
);
1891 convex_hull
= isl_basic_set_intersect(convex_hull
, affine_hull
);
1894 isl_basic_set_free(affine_hull
);
1899 /* Compute the convex hull of a map.
1901 * The implementation was inspired by "Extended Convex Hull" by Fukuda et al.,
1902 * specifically, the wrapping of facets to obtain new facets.
1904 struct isl_basic_map
*isl_map_convex_hull(struct isl_map
*map
)
1906 struct isl_basic_set
*bset
;
1907 struct isl_basic_map
*model
= NULL
;
1908 struct isl_basic_set
*affine_hull
= NULL
;
1909 struct isl_basic_map
*convex_hull
= NULL
;
1910 struct isl_set
*set
= NULL
;
1911 struct isl_ctx
*ctx
;
1918 convex_hull
= isl_basic_map_empty_like_map(map
);
1923 map
= isl_map_detect_equalities(map
);
1924 map
= isl_map_align_divs(map
);
1925 model
= isl_basic_map_copy(map
->p
[0]);
1926 set
= isl_map_underlying_set(map
);
1930 affine_hull
= isl_set_affine_hull(isl_set_copy(set
));
1933 if (affine_hull
->n_eq
!= 0)
1934 bset
= modulo_affine_hull(ctx
, set
, affine_hull
);
1936 isl_basic_set_free(affine_hull
);
1937 bset
= uset_convex_hull(set
);
1940 convex_hull
= isl_basic_map_overlying_set(bset
, model
);
1942 ISL_F_SET(convex_hull
, ISL_BASIC_MAP_NO_IMPLICIT
);
1943 ISL_F_SET(convex_hull
, ISL_BASIC_MAP_ALL_EQUALITIES
);
1944 ISL_F_CLR(convex_hull
, ISL_BASIC_MAP_RATIONAL
);
1948 isl_basic_map_free(model
);
1952 struct isl_basic_set
*isl_set_convex_hull(struct isl_set
*set
)
1954 return (struct isl_basic_set
*)
1955 isl_map_convex_hull((struct isl_map
*)set
);
1958 struct sh_data_entry
{
1959 struct isl_hash_table
*table
;
1960 struct isl_tab
*tab
;
1963 /* Holds the data needed during the simple hull computation.
1965 * n the number of basic sets in the original set
1966 * hull_table a hash table of already computed constraints
1967 * in the simple hull
1968 * p for each basic set,
1969 * table a hash table of the constraints
1970 * tab the tableau corresponding to the basic set
1973 struct isl_ctx
*ctx
;
1975 struct isl_hash_table
*hull_table
;
1976 struct sh_data_entry p
[1];
1979 static void sh_data_free(struct sh_data
*data
)
1985 isl_hash_table_free(data
->ctx
, data
->hull_table
);
1986 for (i
= 0; i
< data
->n
; ++i
) {
1987 isl_hash_table_free(data
->ctx
, data
->p
[i
].table
);
1988 isl_tab_free(data
->p
[i
].tab
);
1993 struct ineq_cmp_data
{
1998 static int has_ineq(const void *entry
, const void *val
)
2000 isl_int
*row
= (isl_int
*)entry
;
2001 struct ineq_cmp_data
*v
= (struct ineq_cmp_data
*)val
;
2003 return isl_seq_eq(row
+ 1, v
->p
+ 1, v
->len
) ||
2004 isl_seq_is_neg(row
+ 1, v
->p
+ 1, v
->len
);
2007 static int hash_ineq(struct isl_ctx
*ctx
, struct isl_hash_table
*table
,
2008 isl_int
*ineq
, unsigned len
)
2011 struct ineq_cmp_data v
;
2012 struct isl_hash_table_entry
*entry
;
2016 c_hash
= isl_seq_get_hash(ineq
+ 1, len
);
2017 entry
= isl_hash_table_find(ctx
, table
, c_hash
, has_ineq
, &v
, 1);
2024 /* Fill hash table "table" with the constraints of "bset".
2025 * Equalities are added as two inequalities.
2026 * The value in the hash table is a pointer to the (in)equality of "bset".
2028 static int hash_basic_set(struct isl_hash_table
*table
,
2029 struct isl_basic_set
*bset
)
2032 unsigned dim
= isl_basic_set_total_dim(bset
);
2034 for (i
= 0; i
< bset
->n_eq
; ++i
) {
2035 for (j
= 0; j
< 2; ++j
) {
2036 isl_seq_neg(bset
->eq
[i
], bset
->eq
[i
], 1 + dim
);
2037 if (hash_ineq(bset
->ctx
, table
, bset
->eq
[i
], dim
) < 0)
2041 for (i
= 0; i
< bset
->n_ineq
; ++i
) {
2042 if (hash_ineq(bset
->ctx
, table
, bset
->ineq
[i
], dim
) < 0)
2048 static struct sh_data
*sh_data_alloc(struct isl_set
*set
, unsigned n_ineq
)
2050 struct sh_data
*data
;
2053 data
= isl_calloc(set
->ctx
, struct sh_data
,
2054 sizeof(struct sh_data
) +
2055 (set
->n
- 1) * sizeof(struct sh_data_entry
));
2058 data
->ctx
= set
->ctx
;
2060 data
->hull_table
= isl_hash_table_alloc(set
->ctx
, n_ineq
);
2061 if (!data
->hull_table
)
2063 for (i
= 0; i
< set
->n
; ++i
) {
2064 data
->p
[i
].table
= isl_hash_table_alloc(set
->ctx
,
2065 2 * set
->p
[i
]->n_eq
+ set
->p
[i
]->n_ineq
);
2066 if (!data
->p
[i
].table
)
2068 if (hash_basic_set(data
->p
[i
].table
, set
->p
[i
]) < 0)
2077 /* Check if inequality "ineq" is a bound for basic set "j" or if
2078 * it can be relaxed (by increasing the constant term) to become
2079 * a bound for that basic set. In the latter case, the constant
2081 * Return 1 if "ineq" is a bound
2082 * 0 if "ineq" may attain arbitrarily small values on basic set "j"
2083 * -1 if some error occurred
2085 static int is_bound(struct sh_data
*data
, struct isl_set
*set
, int j
,
2088 enum isl_lp_result res
;
2091 if (!data
->p
[j
].tab
) {
2092 data
->p
[j
].tab
= isl_tab_from_basic_set(set
->p
[j
]);
2093 if (!data
->p
[j
].tab
)
2099 res
= isl_tab_min(data
->p
[j
].tab
, ineq
, data
->ctx
->one
,
2101 if (res
== isl_lp_ok
&& isl_int_is_neg(opt
))
2102 isl_int_sub(ineq
[0], ineq
[0], opt
);
2106 return res
== isl_lp_ok
? 1 :
2107 res
== isl_lp_unbounded
? 0 : -1;
2110 /* Check if inequality "ineq" from basic set "i" can be relaxed to
2111 * become a bound on the whole set. If so, add the (relaxed) inequality
2114 * We first check if "hull" already contains a translate of the inequality.
2115 * If so, we are done.
2116 * Then, we check if any of the previous basic sets contains a translate
2117 * of the inequality. If so, then we have already considered this
2118 * inequality and we are done.
2119 * Otherwise, for each basic set other than "i", we check if the inequality
2120 * is a bound on the basic set.
2121 * For previous basic sets, we know that they do not contain a translate
2122 * of the inequality, so we directly call is_bound.
2123 * For following basic sets, we first check if a translate of the
2124 * inequality appears in its description and if so directly update
2125 * the inequality accordingly.
2127 static struct isl_basic_set
*add_bound(struct isl_basic_set
*hull
,
2128 struct sh_data
*data
, struct isl_set
*set
, int i
, isl_int
*ineq
)
2131 struct ineq_cmp_data v
;
2132 struct isl_hash_table_entry
*entry
;
2138 v
.len
= isl_basic_set_total_dim(hull
);
2140 c_hash
= isl_seq_get_hash(ineq
+ 1, v
.len
);
2142 entry
= isl_hash_table_find(hull
->ctx
, data
->hull_table
, c_hash
,
2147 for (j
= 0; j
< i
; ++j
) {
2148 entry
= isl_hash_table_find(hull
->ctx
, data
->p
[j
].table
,
2149 c_hash
, has_ineq
, &v
, 0);
2156 k
= isl_basic_set_alloc_inequality(hull
);
2157 isl_seq_cpy(hull
->ineq
[k
], ineq
, 1 + v
.len
);
2161 for (j
= 0; j
< i
; ++j
) {
2163 bound
= is_bound(data
, set
, j
, hull
->ineq
[k
]);
2170 isl_basic_set_free_inequality(hull
, 1);
2174 for (j
= i
+ 1; j
< set
->n
; ++j
) {
2177 entry
= isl_hash_table_find(hull
->ctx
, data
->p
[j
].table
,
2178 c_hash
, has_ineq
, &v
, 0);
2180 ineq_j
= entry
->data
;
2181 neg
= isl_seq_is_neg(ineq_j
+ 1,
2182 hull
->ineq
[k
] + 1, v
.len
);
2184 isl_int_neg(ineq_j
[0], ineq_j
[0]);
2185 if (isl_int_gt(ineq_j
[0], hull
->ineq
[k
][0]))
2186 isl_int_set(hull
->ineq
[k
][0], ineq_j
[0]);
2188 isl_int_neg(ineq_j
[0], ineq_j
[0]);
2191 bound
= is_bound(data
, set
, j
, hull
->ineq
[k
]);
2198 isl_basic_set_free_inequality(hull
, 1);
2202 entry
= isl_hash_table_find(hull
->ctx
, data
->hull_table
, c_hash
,
2206 entry
->data
= hull
->ineq
[k
];
2210 isl_basic_set_free(hull
);
2214 /* Check if any inequality from basic set "i" can be relaxed to
2215 * become a bound on the whole set. If so, add the (relaxed) inequality
2218 static struct isl_basic_set
*add_bounds(struct isl_basic_set
*bset
,
2219 struct sh_data
*data
, struct isl_set
*set
, int i
)
2222 unsigned dim
= isl_basic_set_total_dim(bset
);
2224 for (j
= 0; j
< set
->p
[i
]->n_eq
; ++j
) {
2225 for (k
= 0; k
< 2; ++k
) {
2226 isl_seq_neg(set
->p
[i
]->eq
[j
], set
->p
[i
]->eq
[j
], 1+dim
);
2227 add_bound(bset
, data
, set
, i
, set
->p
[i
]->eq
[j
]);
2230 for (j
= 0; j
< set
->p
[i
]->n_ineq
; ++j
)
2231 add_bound(bset
, data
, set
, i
, set
->p
[i
]->ineq
[j
]);
2235 /* Compute a superset of the convex hull of set that is described
2236 * by only translates of the constraints in the constituents of set.
2238 static struct isl_basic_set
*uset_simple_hull(struct isl_set
*set
)
2240 struct sh_data
*data
= NULL
;
2241 struct isl_basic_set
*hull
= NULL
;
2249 for (i
= 0; i
< set
->n
; ++i
) {
2252 n_ineq
+= 2 * set
->p
[i
]->n_eq
+ set
->p
[i
]->n_ineq
;
2255 hull
= isl_basic_set_alloc_dim(isl_dim_copy(set
->dim
), 0, 0, n_ineq
);
2259 data
= sh_data_alloc(set
, n_ineq
);
2263 for (i
= 0; i
< set
->n
; ++i
)
2264 hull
= add_bounds(hull
, data
, set
, i
);
2272 isl_basic_set_free(hull
);
2277 /* Compute a superset of the convex hull of map that is described
2278 * by only translates of the constraints in the constituents of map.
2280 struct isl_basic_map
*isl_map_simple_hull(struct isl_map
*map
)
2282 struct isl_set
*set
= NULL
;
2283 struct isl_basic_map
*model
= NULL
;
2284 struct isl_basic_map
*hull
;
2285 struct isl_basic_map
*affine_hull
;
2286 struct isl_basic_set
*bset
= NULL
;
2291 hull
= isl_basic_map_empty_like_map(map
);
2296 hull
= isl_basic_map_copy(map
->p
[0]);
2301 map
= isl_map_detect_equalities(map
);
2302 affine_hull
= isl_map_affine_hull(isl_map_copy(map
));
2303 map
= isl_map_align_divs(map
);
2304 model
= isl_basic_map_copy(map
->p
[0]);
2306 set
= isl_map_underlying_set(map
);
2308 bset
= uset_simple_hull(set
);
2310 hull
= isl_basic_map_overlying_set(bset
, model
);
2312 hull
= isl_basic_map_intersect(hull
, affine_hull
);
2313 hull
= isl_basic_map_convex_hull(hull
);
2314 ISL_F_SET(hull
, ISL_BASIC_MAP_NO_IMPLICIT
);
2315 ISL_F_SET(hull
, ISL_BASIC_MAP_ALL_EQUALITIES
);
2320 struct isl_basic_set
*isl_set_simple_hull(struct isl_set
*set
)
2322 return (struct isl_basic_set
*)
2323 isl_map_simple_hull((struct isl_map
*)set
);
2326 /* Given a set "set", return parametric bounds on the dimension "dim".
2328 static struct isl_basic_set
*set_bounds(struct isl_set
*set
, int dim
)
2330 unsigned set_dim
= isl_set_dim(set
, isl_dim_set
);
2331 set
= isl_set_copy(set
);
2332 set
= isl_set_eliminate_dims(set
, dim
+ 1, set_dim
- (dim
+ 1));
2333 set
= isl_set_eliminate_dims(set
, 0, dim
);
2334 return isl_set_convex_hull(set
);
2337 /* Computes a "simple hull" and then check if each dimension in the
2338 * resulting hull is bounded by a symbolic constant. If not, the
2339 * hull is intersected with the corresponding bounds on the whole set.
2341 struct isl_basic_set
*isl_set_bounded_simple_hull(struct isl_set
*set
)
2344 struct isl_basic_set
*hull
;
2345 unsigned nparam
, left
;
2346 int removed_divs
= 0;
2348 hull
= isl_set_simple_hull(isl_set_copy(set
));
2352 nparam
= isl_basic_set_dim(hull
, isl_dim_param
);
2353 for (i
= 0; i
< isl_basic_set_dim(hull
, isl_dim_set
); ++i
) {
2354 int lower
= 0, upper
= 0;
2355 struct isl_basic_set
*bounds
;
2357 left
= isl_basic_set_total_dim(hull
) - nparam
- i
- 1;
2358 for (j
= 0; j
< hull
->n_eq
; ++j
) {
2359 if (isl_int_is_zero(hull
->eq
[j
][1 + nparam
+ i
]))
2361 if (isl_seq_first_non_zero(hull
->eq
[j
]+1+nparam
+i
+1,
2368 for (j
= 0; j
< hull
->n_ineq
; ++j
) {
2369 if (isl_int_is_zero(hull
->ineq
[j
][1 + nparam
+ i
]))
2371 if (isl_seq_first_non_zero(hull
->ineq
[j
]+1+nparam
+i
+1,
2373 isl_seq_first_non_zero(hull
->ineq
[j
]+1+nparam
,
2376 if (isl_int_is_pos(hull
->ineq
[j
][1 + nparam
+ i
]))
2387 if (!removed_divs
) {
2388 set
= isl_set_remove_divs(set
);
2393 bounds
= set_bounds(set
, i
);
2394 hull
= isl_basic_set_intersect(hull
, bounds
);