2 * Copyright 2008-2009 Katholieke Universiteit Leuven
4 * Use of this software is governed by the GNU LGPLv2.1 license
6 * Written by Sven Verdoolaege, K.U.Leuven, Departement
7 * Computerwetenschappen, Celestijnenlaan 200A, B-3001 Leuven, Belgium
10 #include <isl_map_private.h>
13 #include <isl_mat_private.h>
16 #include "isl_equalities.h"
19 static struct isl_basic_set
*uset_convex_hull_wrap_bounded(struct isl_set
*set
);
21 static void swap_ineq(struct isl_basic_map
*bmap
, unsigned i
, unsigned j
)
27 bmap
->ineq
[i
] = bmap
->ineq
[j
];
32 /* Return 1 if constraint c is redundant with respect to the constraints
33 * in bmap. If c is a lower [upper] bound in some variable and bmap
34 * does not have a lower [upper] bound in that variable, then c cannot
35 * be redundant and we do not need solve any lp.
37 int isl_basic_map_constraint_is_redundant(struct isl_basic_map
**bmap
,
38 isl_int
*c
, isl_int
*opt_n
, isl_int
*opt_d
)
40 enum isl_lp_result res
;
47 total
= isl_basic_map_total_dim(*bmap
);
48 for (i
= 0; i
< total
; ++i
) {
50 if (isl_int_is_zero(c
[1+i
]))
52 sign
= isl_int_sgn(c
[1+i
]);
53 for (j
= 0; j
< (*bmap
)->n_ineq
; ++j
)
54 if (sign
== isl_int_sgn((*bmap
)->ineq
[j
][1+i
]))
56 if (j
== (*bmap
)->n_ineq
)
62 res
= isl_basic_map_solve_lp(*bmap
, 0, c
, (*bmap
)->ctx
->one
,
64 if (res
== isl_lp_unbounded
)
66 if (res
== isl_lp_error
)
68 if (res
== isl_lp_empty
) {
69 *bmap
= isl_basic_map_set_to_empty(*bmap
);
72 return !isl_int_is_neg(*opt_n
);
75 int isl_basic_set_constraint_is_redundant(struct isl_basic_set
**bset
,
76 isl_int
*c
, isl_int
*opt_n
, isl_int
*opt_d
)
78 return isl_basic_map_constraint_is_redundant(
79 (struct isl_basic_map
**)bset
, c
, opt_n
, opt_d
);
83 * constraints. If the minimal value along the normal of a constraint
84 * is the same if the constraint is removed, then the constraint is redundant.
86 * Alternatively, we could have intersected the basic map with the
87 * corresponding equality and the checked if the dimension was that
90 __isl_give isl_basic_map
*isl_basic_map_remove_redundancies(
91 __isl_take isl_basic_map
*bmap
)
98 bmap
= isl_basic_map_gauss(bmap
, NULL
);
99 if (ISL_F_ISSET(bmap
, ISL_BASIC_MAP_EMPTY
))
101 if (ISL_F_ISSET(bmap
, ISL_BASIC_MAP_NO_REDUNDANT
))
103 if (bmap
->n_ineq
<= 1)
106 tab
= isl_tab_from_basic_map(bmap
);
107 if (isl_tab_detect_implicit_equalities(tab
) < 0)
109 if (isl_tab_detect_redundant(tab
) < 0)
111 bmap
= isl_basic_map_update_from_tab(bmap
, tab
);
113 ISL_F_SET(bmap
, ISL_BASIC_MAP_NO_IMPLICIT
);
114 ISL_F_SET(bmap
, ISL_BASIC_MAP_NO_REDUNDANT
);
118 isl_basic_map_free(bmap
);
122 __isl_give isl_basic_set
*isl_basic_set_remove_redundancies(
123 __isl_take isl_basic_set
*bset
)
125 return (struct isl_basic_set
*)
126 isl_basic_map_remove_redundancies((struct isl_basic_map
*)bset
);
129 /* Check if the set set is bound in the direction of the affine
130 * constraint c and if so, set the constant term such that the
131 * resulting constraint is a bounding constraint for the set.
133 static int uset_is_bound(struct isl_set
*set
, isl_int
*c
, unsigned len
)
141 isl_int_init(opt_denom
);
143 for (j
= 0; j
< set
->n
; ++j
) {
144 enum isl_lp_result res
;
146 if (ISL_F_ISSET(set
->p
[j
], ISL_BASIC_SET_EMPTY
))
149 res
= isl_basic_set_solve_lp(set
->p
[j
],
150 0, c
, set
->ctx
->one
, &opt
, &opt_denom
, NULL
);
151 if (res
== isl_lp_unbounded
)
153 if (res
== isl_lp_error
)
155 if (res
== isl_lp_empty
) {
156 set
->p
[j
] = isl_basic_set_set_to_empty(set
->p
[j
]);
161 if (first
|| isl_int_is_neg(opt
)) {
162 if (!isl_int_is_one(opt_denom
))
163 isl_seq_scale(c
, c
, opt_denom
, len
);
164 isl_int_sub(c
[0], c
[0], opt
);
169 isl_int_clear(opt_denom
);
173 isl_int_clear(opt_denom
);
177 struct isl_basic_set
*isl_basic_set_set_rational(struct isl_basic_set
*bset
)
182 if (ISL_F_ISSET(bset
, ISL_BASIC_MAP_RATIONAL
))
185 bset
= isl_basic_set_cow(bset
);
189 ISL_F_SET(bset
, ISL_BASIC_MAP_RATIONAL
);
191 return isl_basic_set_finalize(bset
);
194 static struct isl_set
*isl_set_set_rational(struct isl_set
*set
)
198 set
= isl_set_cow(set
);
201 for (i
= 0; i
< set
->n
; ++i
) {
202 set
->p
[i
] = isl_basic_set_set_rational(set
->p
[i
]);
212 static struct isl_basic_set
*isl_basic_set_add_equality(
213 struct isl_basic_set
*bset
, isl_int
*c
)
221 if (ISL_F_ISSET(bset
, ISL_BASIC_SET_EMPTY
))
224 isl_assert(bset
->ctx
, isl_basic_set_n_param(bset
) == 0, goto error
);
225 isl_assert(bset
->ctx
, bset
->n_div
== 0, goto error
);
226 dim
= isl_basic_set_n_dim(bset
);
227 bset
= isl_basic_set_cow(bset
);
228 bset
= isl_basic_set_extend(bset
, 0, dim
, 0, 1, 0);
229 i
= isl_basic_set_alloc_equality(bset
);
232 isl_seq_cpy(bset
->eq
[i
], c
, 1 + dim
);
235 isl_basic_set_free(bset
);
239 static struct isl_set
*isl_set_add_basic_set_equality(struct isl_set
*set
, isl_int
*c
)
243 set
= isl_set_cow(set
);
246 for (i
= 0; i
< set
->n
; ++i
) {
247 set
->p
[i
] = isl_basic_set_add_equality(set
->p
[i
], c
);
257 /* Given a union of basic sets, construct the constraints for wrapping
258 * a facet around one of its ridges.
259 * In particular, if each of n the d-dimensional basic sets i in "set"
260 * contains the origin, satisfies the constraints x_1 >= 0 and x_2 >= 0
261 * and is defined by the constraints
265 * then the resulting set is of dimension n*(1+d) and has as constraints
274 static struct isl_basic_set
*wrap_constraints(struct isl_set
*set
)
276 struct isl_basic_set
*lp
;
280 unsigned dim
, lp_dim
;
285 dim
= 1 + isl_set_n_dim(set
);
288 for (i
= 0; i
< set
->n
; ++i
) {
289 n_eq
+= set
->p
[i
]->n_eq
;
290 n_ineq
+= set
->p
[i
]->n_ineq
;
292 lp
= isl_basic_set_alloc(set
->ctx
, 0, dim
* set
->n
, 0, n_eq
, n_ineq
);
293 lp
= isl_basic_set_set_rational(lp
);
296 lp_dim
= isl_basic_set_n_dim(lp
);
297 k
= isl_basic_set_alloc_equality(lp
);
298 isl_int_set_si(lp
->eq
[k
][0], -1);
299 for (i
= 0; i
< set
->n
; ++i
) {
300 isl_int_set_si(lp
->eq
[k
][1+dim
*i
], 0);
301 isl_int_set_si(lp
->eq
[k
][1+dim
*i
+1], 1);
302 isl_seq_clr(lp
->eq
[k
]+1+dim
*i
+2, dim
-2);
304 for (i
= 0; i
< set
->n
; ++i
) {
305 k
= isl_basic_set_alloc_inequality(lp
);
306 isl_seq_clr(lp
->ineq
[k
], 1+lp_dim
);
307 isl_int_set_si(lp
->ineq
[k
][1+dim
*i
], 1);
309 for (j
= 0; j
< set
->p
[i
]->n_eq
; ++j
) {
310 k
= isl_basic_set_alloc_equality(lp
);
311 isl_seq_clr(lp
->eq
[k
], 1+dim
*i
);
312 isl_seq_cpy(lp
->eq
[k
]+1+dim
*i
, set
->p
[i
]->eq
[j
], dim
);
313 isl_seq_clr(lp
->eq
[k
]+1+dim
*(i
+1), dim
*(set
->n
-i
-1));
316 for (j
= 0; j
< set
->p
[i
]->n_ineq
; ++j
) {
317 k
= isl_basic_set_alloc_inequality(lp
);
318 isl_seq_clr(lp
->ineq
[k
], 1+dim
*i
);
319 isl_seq_cpy(lp
->ineq
[k
]+1+dim
*i
, set
->p
[i
]->ineq
[j
], dim
);
320 isl_seq_clr(lp
->ineq
[k
]+1+dim
*(i
+1), dim
*(set
->n
-i
-1));
326 /* Given a facet "facet" of the convex hull of "set" and a facet "ridge"
327 * of that facet, compute the other facet of the convex hull that contains
330 * We first transform the set such that the facet constraint becomes
334 * I.e., the facet lies in
338 * and on that facet, the constraint that defines the ridge is
342 * (This transformation is not strictly needed, all that is needed is
343 * that the ridge contains the origin.)
345 * Since the ridge contains the origin, the cone of the convex hull
346 * will be of the form
351 * with this second constraint defining the new facet.
352 * The constant a is obtained by settting x_1 in the cone of the
353 * convex hull to 1 and minimizing x_2.
354 * Now, each element in the cone of the convex hull is the sum
355 * of elements in the cones of the basic sets.
356 * If a_i is the dilation factor of basic set i, then the problem
357 * we need to solve is
370 * the constraints of each (transformed) basic set.
371 * If a = n/d, then the constraint defining the new facet (in the transformed
374 * -n x_1 + d x_2 >= 0
376 * In the original space, we need to take the same combination of the
377 * corresponding constraints "facet" and "ridge".
379 * If a = -infty = "-1/0", then we just return the original facet constraint.
380 * This means that the facet is unbounded, but has a bounded intersection
381 * with the union of sets.
383 isl_int
*isl_set_wrap_facet(__isl_keep isl_set
*set
,
384 isl_int
*facet
, isl_int
*ridge
)
388 struct isl_mat
*T
= NULL
;
389 struct isl_basic_set
*lp
= NULL
;
391 enum isl_lp_result res
;
398 set
= isl_set_copy(set
);
399 set
= isl_set_set_rational(set
);
401 dim
= 1 + isl_set_n_dim(set
);
402 T
= isl_mat_alloc(ctx
, 3, dim
);
405 isl_int_set_si(T
->row
[0][0], 1);
406 isl_seq_clr(T
->row
[0]+1, dim
- 1);
407 isl_seq_cpy(T
->row
[1], facet
, dim
);
408 isl_seq_cpy(T
->row
[2], ridge
, dim
);
409 T
= isl_mat_right_inverse(T
);
410 set
= isl_set_preimage(set
, T
);
414 lp
= wrap_constraints(set
);
415 obj
= isl_vec_alloc(ctx
, 1 + dim
*set
->n
);
418 isl_int_set_si(obj
->block
.data
[0], 0);
419 for (i
= 0; i
< set
->n
; ++i
) {
420 isl_seq_clr(obj
->block
.data
+ 1 + dim
*i
, 2);
421 isl_int_set_si(obj
->block
.data
[1 + dim
*i
+2], 1);
422 isl_seq_clr(obj
->block
.data
+ 1 + dim
*i
+3, dim
-3);
426 res
= isl_basic_set_solve_lp(lp
, 0,
427 obj
->block
.data
, ctx
->one
, &num
, &den
, NULL
);
428 if (res
== isl_lp_ok
) {
429 isl_int_neg(num
, num
);
430 isl_seq_combine(facet
, num
, facet
, den
, ridge
, dim
);
431 isl_seq_normalize(ctx
, facet
, dim
);
436 isl_basic_set_free(lp
);
438 if (res
== isl_lp_error
)
440 isl_assert(ctx
, res
== isl_lp_ok
|| res
== isl_lp_unbounded
,
444 isl_basic_set_free(lp
);
450 /* Compute the constraint of a facet of "set".
452 * We first compute the intersection with a bounding constraint
453 * that is orthogonal to one of the coordinate axes.
454 * If the affine hull of this intersection has only one equality,
455 * we have found a facet.
456 * Otherwise, we wrap the current bounding constraint around
457 * one of the equalities of the face (one that is not equal to
458 * the current bounding constraint).
459 * This process continues until we have found a facet.
460 * The dimension of the intersection increases by at least
461 * one on each iteration, so termination is guaranteed.
463 static __isl_give isl_mat
*initial_facet_constraint(__isl_keep isl_set
*set
)
465 struct isl_set
*slice
= NULL
;
466 struct isl_basic_set
*face
= NULL
;
468 unsigned dim
= isl_set_n_dim(set
);
472 isl_assert(set
->ctx
, set
->n
> 0, goto error
);
473 bounds
= isl_mat_alloc(set
->ctx
, 1, 1 + dim
);
477 isl_seq_clr(bounds
->row
[0], dim
);
478 isl_int_set_si(bounds
->row
[0][1 + dim
- 1], 1);
479 is_bound
= uset_is_bound(set
, bounds
->row
[0], 1 + dim
);
482 isl_assert(set
->ctx
, is_bound
, goto error
);
483 isl_seq_normalize(set
->ctx
, bounds
->row
[0], 1 + dim
);
487 slice
= isl_set_copy(set
);
488 slice
= isl_set_add_basic_set_equality(slice
, bounds
->row
[0]);
489 face
= isl_set_affine_hull(slice
);
492 if (face
->n_eq
== 1) {
493 isl_basic_set_free(face
);
496 for (i
= 0; i
< face
->n_eq
; ++i
)
497 if (!isl_seq_eq(bounds
->row
[0], face
->eq
[i
], 1 + dim
) &&
498 !isl_seq_is_neg(bounds
->row
[0],
499 face
->eq
[i
], 1 + dim
))
501 isl_assert(set
->ctx
, i
< face
->n_eq
, goto error
);
502 if (!isl_set_wrap_facet(set
, bounds
->row
[0], face
->eq
[i
]))
504 isl_seq_normalize(set
->ctx
, bounds
->row
[0], bounds
->n_col
);
505 isl_basic_set_free(face
);
510 isl_basic_set_free(face
);
511 isl_mat_free(bounds
);
515 /* Given the bounding constraint "c" of a facet of the convex hull of "set",
516 * compute a hyperplane description of the facet, i.e., compute the facets
519 * We compute an affine transformation that transforms the constraint
528 * by computing the right inverse U of a matrix that starts with the rows
541 * Since z_1 is zero, we can drop this variable as well as the corresponding
542 * column of U to obtain
550 * with Q' equal to Q, but without the corresponding row.
551 * After computing the facets of the facet in the z' space,
552 * we convert them back to the x space through Q.
554 static struct isl_basic_set
*compute_facet(struct isl_set
*set
, isl_int
*c
)
556 struct isl_mat
*m
, *U
, *Q
;
557 struct isl_basic_set
*facet
= NULL
;
562 set
= isl_set_copy(set
);
563 dim
= isl_set_n_dim(set
);
564 m
= isl_mat_alloc(set
->ctx
, 2, 1 + dim
);
567 isl_int_set_si(m
->row
[0][0], 1);
568 isl_seq_clr(m
->row
[0]+1, dim
);
569 isl_seq_cpy(m
->row
[1], c
, 1+dim
);
570 U
= isl_mat_right_inverse(m
);
571 Q
= isl_mat_right_inverse(isl_mat_copy(U
));
572 U
= isl_mat_drop_cols(U
, 1, 1);
573 Q
= isl_mat_drop_rows(Q
, 1, 1);
574 set
= isl_set_preimage(set
, U
);
575 facet
= uset_convex_hull_wrap_bounded(set
);
576 facet
= isl_basic_set_preimage(facet
, Q
);
578 isl_assert(ctx
, facet
->n_eq
== 0, goto error
);
581 isl_basic_set_free(facet
);
586 /* Given an initial facet constraint, compute the remaining facets.
587 * We do this by running through all facets found so far and computing
588 * the adjacent facets through wrapping, adding those facets that we
589 * hadn't already found before.
591 * For each facet we have found so far, we first compute its facets
592 * in the resulting convex hull. That is, we compute the ridges
593 * of the resulting convex hull contained in the facet.
594 * We also compute the corresponding facet in the current approximation
595 * of the convex hull. There is no need to wrap around the ridges
596 * in this facet since that would result in a facet that is already
597 * present in the current approximation.
599 * This function can still be significantly optimized by checking which of
600 * the facets of the basic sets are also facets of the convex hull and
601 * using all the facets so far to help in constructing the facets of the
604 * using the technique in section "3.1 Ridge Generation" of
605 * "Extended Convex Hull" by Fukuda et al.
607 static struct isl_basic_set
*extend(struct isl_basic_set
*hull
,
612 struct isl_basic_set
*facet
= NULL
;
613 struct isl_basic_set
*hull_facet
= NULL
;
619 isl_assert(set
->ctx
, set
->n
> 0, goto error
);
621 dim
= isl_set_n_dim(set
);
623 for (i
= 0; i
< hull
->n_ineq
; ++i
) {
624 facet
= compute_facet(set
, hull
->ineq
[i
]);
625 facet
= isl_basic_set_add_equality(facet
, hull
->ineq
[i
]);
626 facet
= isl_basic_set_gauss(facet
, NULL
);
627 facet
= isl_basic_set_normalize_constraints(facet
);
628 hull_facet
= isl_basic_set_copy(hull
);
629 hull_facet
= isl_basic_set_add_equality(hull_facet
, hull
->ineq
[i
]);
630 hull_facet
= isl_basic_set_gauss(hull_facet
, NULL
);
631 hull_facet
= isl_basic_set_normalize_constraints(hull_facet
);
632 if (!facet
|| !hull_facet
)
634 hull
= isl_basic_set_cow(hull
);
635 hull
= isl_basic_set_extend_dim(hull
,
636 isl_dim_copy(hull
->dim
), 0, 0, facet
->n_ineq
);
639 for (j
= 0; j
< facet
->n_ineq
; ++j
) {
640 for (f
= 0; f
< hull_facet
->n_ineq
; ++f
)
641 if (isl_seq_eq(facet
->ineq
[j
],
642 hull_facet
->ineq
[f
], 1 + dim
))
644 if (f
< hull_facet
->n_ineq
)
646 k
= isl_basic_set_alloc_inequality(hull
);
649 isl_seq_cpy(hull
->ineq
[k
], hull
->ineq
[i
], 1+dim
);
650 if (!isl_set_wrap_facet(set
, hull
->ineq
[k
], facet
->ineq
[j
]))
653 isl_basic_set_free(hull_facet
);
654 isl_basic_set_free(facet
);
656 hull
= isl_basic_set_simplify(hull
);
657 hull
= isl_basic_set_finalize(hull
);
660 isl_basic_set_free(hull_facet
);
661 isl_basic_set_free(facet
);
662 isl_basic_set_free(hull
);
666 /* Special case for computing the convex hull of a one dimensional set.
667 * We simply collect the lower and upper bounds of each basic set
668 * and the biggest of those.
670 static struct isl_basic_set
*convex_hull_1d(struct isl_set
*set
)
672 struct isl_mat
*c
= NULL
;
673 isl_int
*lower
= NULL
;
674 isl_int
*upper
= NULL
;
677 struct isl_basic_set
*hull
;
679 for (i
= 0; i
< set
->n
; ++i
) {
680 set
->p
[i
] = isl_basic_set_simplify(set
->p
[i
]);
684 set
= isl_set_remove_empty_parts(set
);
687 isl_assert(set
->ctx
, set
->n
> 0, goto error
);
688 c
= isl_mat_alloc(set
->ctx
, 2, 2);
692 if (set
->p
[0]->n_eq
> 0) {
693 isl_assert(set
->ctx
, set
->p
[0]->n_eq
== 1, goto error
);
696 if (isl_int_is_pos(set
->p
[0]->eq
[0][1])) {
697 isl_seq_cpy(lower
, set
->p
[0]->eq
[0], 2);
698 isl_seq_neg(upper
, set
->p
[0]->eq
[0], 2);
700 isl_seq_neg(lower
, set
->p
[0]->eq
[0], 2);
701 isl_seq_cpy(upper
, set
->p
[0]->eq
[0], 2);
704 for (j
= 0; j
< set
->p
[0]->n_ineq
; ++j
) {
705 if (isl_int_is_pos(set
->p
[0]->ineq
[j
][1])) {
707 isl_seq_cpy(lower
, set
->p
[0]->ineq
[j
], 2);
710 isl_seq_cpy(upper
, set
->p
[0]->ineq
[j
], 2);
717 for (i
= 0; i
< set
->n
; ++i
) {
718 struct isl_basic_set
*bset
= set
->p
[i
];
722 for (j
= 0; j
< bset
->n_eq
; ++j
) {
726 isl_int_mul(a
, lower
[0], bset
->eq
[j
][1]);
727 isl_int_mul(b
, lower
[1], bset
->eq
[j
][0]);
728 if (isl_int_lt(a
, b
) && isl_int_is_pos(bset
->eq
[j
][1]))
729 isl_seq_cpy(lower
, bset
->eq
[j
], 2);
730 if (isl_int_gt(a
, b
) && isl_int_is_neg(bset
->eq
[j
][1]))
731 isl_seq_neg(lower
, bset
->eq
[j
], 2);
734 isl_int_mul(a
, upper
[0], bset
->eq
[j
][1]);
735 isl_int_mul(b
, upper
[1], bset
->eq
[j
][0]);
736 if (isl_int_lt(a
, b
) && isl_int_is_pos(bset
->eq
[j
][1]))
737 isl_seq_neg(upper
, bset
->eq
[j
], 2);
738 if (isl_int_gt(a
, b
) && isl_int_is_neg(bset
->eq
[j
][1]))
739 isl_seq_cpy(upper
, bset
->eq
[j
], 2);
742 for (j
= 0; j
< bset
->n_ineq
; ++j
) {
743 if (isl_int_is_pos(bset
->ineq
[j
][1]))
745 if (isl_int_is_neg(bset
->ineq
[j
][1]))
747 if (lower
&& isl_int_is_pos(bset
->ineq
[j
][1])) {
748 isl_int_mul(a
, lower
[0], bset
->ineq
[j
][1]);
749 isl_int_mul(b
, lower
[1], bset
->ineq
[j
][0]);
750 if (isl_int_lt(a
, b
))
751 isl_seq_cpy(lower
, bset
->ineq
[j
], 2);
753 if (upper
&& isl_int_is_neg(bset
->ineq
[j
][1])) {
754 isl_int_mul(a
, upper
[0], bset
->ineq
[j
][1]);
755 isl_int_mul(b
, upper
[1], bset
->ineq
[j
][0]);
756 if (isl_int_gt(a
, b
))
757 isl_seq_cpy(upper
, bset
->ineq
[j
], 2);
768 hull
= isl_basic_set_alloc(set
->ctx
, 0, 1, 0, 0, 2);
769 hull
= isl_basic_set_set_rational(hull
);
773 k
= isl_basic_set_alloc_inequality(hull
);
774 isl_seq_cpy(hull
->ineq
[k
], lower
, 2);
777 k
= isl_basic_set_alloc_inequality(hull
);
778 isl_seq_cpy(hull
->ineq
[k
], upper
, 2);
780 hull
= isl_basic_set_finalize(hull
);
790 /* Project out final n dimensions using Fourier-Motzkin */
791 static struct isl_set
*set_project_out(struct isl_ctx
*ctx
,
792 struct isl_set
*set
, unsigned n
)
794 return isl_set_remove_dims(set
, isl_dim_set
, isl_set_n_dim(set
) - n
, n
);
797 static struct isl_basic_set
*convex_hull_0d(struct isl_set
*set
)
799 struct isl_basic_set
*convex_hull
;
804 if (isl_set_is_empty(set
))
805 convex_hull
= isl_basic_set_empty(isl_dim_copy(set
->dim
));
807 convex_hull
= isl_basic_set_universe(isl_dim_copy(set
->dim
));
812 /* Compute the convex hull of a pair of basic sets without any parameters or
813 * integer divisions using Fourier-Motzkin elimination.
814 * The convex hull is the set of all points that can be written as
815 * the sum of points from both basic sets (in homogeneous coordinates).
816 * We set up the constraints in a space with dimensions for each of
817 * the three sets and then project out the dimensions corresponding
818 * to the two original basic sets, retaining only those corresponding
819 * to the convex hull.
821 static struct isl_basic_set
*convex_hull_pair_elim(struct isl_basic_set
*bset1
,
822 struct isl_basic_set
*bset2
)
825 struct isl_basic_set
*bset
[2];
826 struct isl_basic_set
*hull
= NULL
;
829 if (!bset1
|| !bset2
)
832 dim
= isl_basic_set_n_dim(bset1
);
833 hull
= isl_basic_set_alloc(bset1
->ctx
, 0, 2 + 3 * dim
, 0,
834 1 + dim
+ bset1
->n_eq
+ bset2
->n_eq
,
835 2 + bset1
->n_ineq
+ bset2
->n_ineq
);
838 for (i
= 0; i
< 2; ++i
) {
839 for (j
= 0; j
< bset
[i
]->n_eq
; ++j
) {
840 k
= isl_basic_set_alloc_equality(hull
);
843 isl_seq_clr(hull
->eq
[k
], (i
+1) * (1+dim
));
844 isl_seq_clr(hull
->eq
[k
]+(i
+2)*(1+dim
), (1-i
)*(1+dim
));
845 isl_seq_cpy(hull
->eq
[k
]+(i
+1)*(1+dim
), bset
[i
]->eq
[j
],
848 for (j
= 0; j
< bset
[i
]->n_ineq
; ++j
) {
849 k
= isl_basic_set_alloc_inequality(hull
);
852 isl_seq_clr(hull
->ineq
[k
], (i
+1) * (1+dim
));
853 isl_seq_clr(hull
->ineq
[k
]+(i
+2)*(1+dim
), (1-i
)*(1+dim
));
854 isl_seq_cpy(hull
->ineq
[k
]+(i
+1)*(1+dim
),
855 bset
[i
]->ineq
[j
], 1+dim
);
857 k
= isl_basic_set_alloc_inequality(hull
);
860 isl_seq_clr(hull
->ineq
[k
], 1+2+3*dim
);
861 isl_int_set_si(hull
->ineq
[k
][(i
+1)*(1+dim
)], 1);
863 for (j
= 0; j
< 1+dim
; ++j
) {
864 k
= isl_basic_set_alloc_equality(hull
);
867 isl_seq_clr(hull
->eq
[k
], 1+2+3*dim
);
868 isl_int_set_si(hull
->eq
[k
][j
], -1);
869 isl_int_set_si(hull
->eq
[k
][1+dim
+j
], 1);
870 isl_int_set_si(hull
->eq
[k
][2*(1+dim
)+j
], 1);
872 hull
= isl_basic_set_set_rational(hull
);
873 hull
= isl_basic_set_remove_dims(hull
, isl_dim_set
, dim
, 2*(1+dim
));
874 hull
= isl_basic_set_remove_redundancies(hull
);
875 isl_basic_set_free(bset1
);
876 isl_basic_set_free(bset2
);
879 isl_basic_set_free(bset1
);
880 isl_basic_set_free(bset2
);
881 isl_basic_set_free(hull
);
885 /* Is the set bounded for each value of the parameters?
887 int isl_basic_set_is_bounded(__isl_keep isl_basic_set
*bset
)
894 if (isl_basic_set_fast_is_empty(bset
))
897 tab
= isl_tab_from_recession_cone(bset
, 1);
898 bounded
= isl_tab_cone_is_bounded(tab
);
903 /* Is the image bounded for each value of the parameters and
904 * the domain variables?
906 int isl_basic_map_image_is_bounded(__isl_keep isl_basic_map
*bmap
)
908 unsigned nparam
= isl_basic_map_dim(bmap
, isl_dim_param
);
909 unsigned n_in
= isl_basic_map_dim(bmap
, isl_dim_in
);
912 bmap
= isl_basic_map_copy(bmap
);
913 bmap
= isl_basic_map_cow(bmap
);
914 bmap
= isl_basic_map_move_dims(bmap
, isl_dim_param
, nparam
,
915 isl_dim_in
, 0, n_in
);
916 bounded
= isl_basic_set_is_bounded((isl_basic_set
*)bmap
);
917 isl_basic_map_free(bmap
);
922 /* Is the set bounded for each value of the parameters?
924 int isl_set_is_bounded(__isl_keep isl_set
*set
)
931 for (i
= 0; i
< set
->n
; ++i
) {
932 int bounded
= isl_basic_set_is_bounded(set
->p
[i
]);
933 if (!bounded
|| bounded
< 0)
939 /* Compute the lineality space of the convex hull of bset1 and bset2.
941 * We first compute the intersection of the recession cone of bset1
942 * with the negative of the recession cone of bset2 and then compute
943 * the linear hull of the resulting cone.
945 static struct isl_basic_set
*induced_lineality_space(
946 struct isl_basic_set
*bset1
, struct isl_basic_set
*bset2
)
949 struct isl_basic_set
*lin
= NULL
;
952 if (!bset1
|| !bset2
)
955 dim
= isl_basic_set_total_dim(bset1
);
956 lin
= isl_basic_set_alloc_dim(isl_basic_set_get_dim(bset1
), 0,
957 bset1
->n_eq
+ bset2
->n_eq
,
958 bset1
->n_ineq
+ bset2
->n_ineq
);
959 lin
= isl_basic_set_set_rational(lin
);
962 for (i
= 0; i
< bset1
->n_eq
; ++i
) {
963 k
= isl_basic_set_alloc_equality(lin
);
966 isl_int_set_si(lin
->eq
[k
][0], 0);
967 isl_seq_cpy(lin
->eq
[k
] + 1, bset1
->eq
[i
] + 1, dim
);
969 for (i
= 0; i
< bset1
->n_ineq
; ++i
) {
970 k
= isl_basic_set_alloc_inequality(lin
);
973 isl_int_set_si(lin
->ineq
[k
][0], 0);
974 isl_seq_cpy(lin
->ineq
[k
] + 1, bset1
->ineq
[i
] + 1, dim
);
976 for (i
= 0; i
< bset2
->n_eq
; ++i
) {
977 k
= isl_basic_set_alloc_equality(lin
);
980 isl_int_set_si(lin
->eq
[k
][0], 0);
981 isl_seq_neg(lin
->eq
[k
] + 1, bset2
->eq
[i
] + 1, dim
);
983 for (i
= 0; i
< bset2
->n_ineq
; ++i
) {
984 k
= isl_basic_set_alloc_inequality(lin
);
987 isl_int_set_si(lin
->ineq
[k
][0], 0);
988 isl_seq_neg(lin
->ineq
[k
] + 1, bset2
->ineq
[i
] + 1, dim
);
991 isl_basic_set_free(bset1
);
992 isl_basic_set_free(bset2
);
993 return isl_basic_set_affine_hull(lin
);
995 isl_basic_set_free(lin
);
996 isl_basic_set_free(bset1
);
997 isl_basic_set_free(bset2
);
1001 static struct isl_basic_set
*uset_convex_hull(struct isl_set
*set
);
1003 /* Given a set and a linear space "lin" of dimension n > 0,
1004 * project the linear space from the set, compute the convex hull
1005 * and then map the set back to the original space.
1011 * describe the linear space. We first compute the Hermite normal
1012 * form H = M U of M = H Q, to obtain
1016 * The last n rows of H will be zero, so the last n variables of x' = Q x
1017 * are the one we want to project out. We do this by transforming each
1018 * basic set A x >= b to A U x' >= b and then removing the last n dimensions.
1019 * After computing the convex hull in x'_1, i.e., A' x'_1 >= b',
1020 * we transform the hull back to the original space as A' Q_1 x >= b',
1021 * with Q_1 all but the last n rows of Q.
1023 static struct isl_basic_set
*modulo_lineality(struct isl_set
*set
,
1024 struct isl_basic_set
*lin
)
1026 unsigned total
= isl_basic_set_total_dim(lin
);
1028 struct isl_basic_set
*hull
;
1029 struct isl_mat
*M
, *U
, *Q
;
1033 lin_dim
= total
- lin
->n_eq
;
1034 M
= isl_mat_sub_alloc(set
->ctx
, lin
->eq
, 0, lin
->n_eq
, 1, total
);
1035 M
= isl_mat_left_hermite(M
, 0, &U
, &Q
);
1039 isl_basic_set_free(lin
);
1041 Q
= isl_mat_drop_rows(Q
, Q
->n_row
- lin_dim
, lin_dim
);
1043 U
= isl_mat_lin_to_aff(U
);
1044 Q
= isl_mat_lin_to_aff(Q
);
1046 set
= isl_set_preimage(set
, U
);
1047 set
= isl_set_remove_dims(set
, isl_dim_set
, total
- lin_dim
, lin_dim
);
1048 hull
= uset_convex_hull(set
);
1049 hull
= isl_basic_set_preimage(hull
, Q
);
1053 isl_basic_set_free(lin
);
1058 /* Given two polyhedra with as constraints h_{ij} x >= 0 in homegeneous space,
1059 * set up an LP for solving
1061 * \sum_j \alpha_{1j} h_{1j} = \sum_j \alpha_{2j} h_{2j}
1063 * \alpha{i0} corresponds to the (implicit) positivity constraint 1 >= 0
1064 * The next \alpha{ij} correspond to the equalities and come in pairs.
1065 * The final \alpha{ij} correspond to the inequalities.
1067 static struct isl_basic_set
*valid_direction_lp(
1068 struct isl_basic_set
*bset1
, struct isl_basic_set
*bset2
)
1070 struct isl_dim
*dim
;
1071 struct isl_basic_set
*lp
;
1076 if (!bset1
|| !bset2
)
1078 d
= 1 + isl_basic_set_total_dim(bset1
);
1080 2 * bset1
->n_eq
+ bset1
->n_ineq
+ 2 * bset2
->n_eq
+ bset2
->n_ineq
;
1081 dim
= isl_dim_set_alloc(bset1
->ctx
, 0, n
);
1082 lp
= isl_basic_set_alloc_dim(dim
, 0, d
, n
);
1085 for (i
= 0; i
< n
; ++i
) {
1086 k
= isl_basic_set_alloc_inequality(lp
);
1089 isl_seq_clr(lp
->ineq
[k
] + 1, n
);
1090 isl_int_set_si(lp
->ineq
[k
][0], -1);
1091 isl_int_set_si(lp
->ineq
[k
][1 + i
], 1);
1093 for (i
= 0; i
< d
; ++i
) {
1094 k
= isl_basic_set_alloc_equality(lp
);
1098 isl_int_set_si(lp
->eq
[k
][n
], 0); n
++;
1099 /* positivity constraint 1 >= 0 */
1100 isl_int_set_si(lp
->eq
[k
][n
], i
== 0); n
++;
1101 for (j
= 0; j
< bset1
->n_eq
; ++j
) {
1102 isl_int_set(lp
->eq
[k
][n
], bset1
->eq
[j
][i
]); n
++;
1103 isl_int_neg(lp
->eq
[k
][n
], bset1
->eq
[j
][i
]); n
++;
1105 for (j
= 0; j
< bset1
->n_ineq
; ++j
) {
1106 isl_int_set(lp
->eq
[k
][n
], bset1
->ineq
[j
][i
]); n
++;
1108 /* positivity constraint 1 >= 0 */
1109 isl_int_set_si(lp
->eq
[k
][n
], -(i
== 0)); n
++;
1110 for (j
= 0; j
< bset2
->n_eq
; ++j
) {
1111 isl_int_neg(lp
->eq
[k
][n
], bset2
->eq
[j
][i
]); n
++;
1112 isl_int_set(lp
->eq
[k
][n
], bset2
->eq
[j
][i
]); n
++;
1114 for (j
= 0; j
< bset2
->n_ineq
; ++j
) {
1115 isl_int_neg(lp
->eq
[k
][n
], bset2
->ineq
[j
][i
]); n
++;
1118 lp
= isl_basic_set_gauss(lp
, NULL
);
1119 isl_basic_set_free(bset1
);
1120 isl_basic_set_free(bset2
);
1123 isl_basic_set_free(bset1
);
1124 isl_basic_set_free(bset2
);
1128 /* Compute a vector s in the homogeneous space such that <s, r> > 0
1129 * for all rays in the homogeneous space of the two cones that correspond
1130 * to the input polyhedra bset1 and bset2.
1132 * We compute s as a vector that satisfies
1134 * s = \sum_j \alpha_{ij} h_{ij} for i = 1,2 (*)
1136 * with h_{ij} the normals of the facets of polyhedron i
1137 * (including the "positivity constraint" 1 >= 0) and \alpha_{ij}
1138 * strictly positive numbers. For simplicity we impose \alpha_{ij} >= 1.
1139 * We first set up an LP with as variables the \alpha{ij}.
1140 * In this formulation, for each polyhedron i,
1141 * the first constraint is the positivity constraint, followed by pairs
1142 * of variables for the equalities, followed by variables for the inequalities.
1143 * We then simply pick a feasible solution and compute s using (*).
1145 * Note that we simply pick any valid direction and make no attempt
1146 * to pick a "good" or even the "best" valid direction.
1148 static struct isl_vec
*valid_direction(
1149 struct isl_basic_set
*bset1
, struct isl_basic_set
*bset2
)
1151 struct isl_basic_set
*lp
;
1152 struct isl_tab
*tab
;
1153 struct isl_vec
*sample
= NULL
;
1154 struct isl_vec
*dir
;
1159 if (!bset1
|| !bset2
)
1161 lp
= valid_direction_lp(isl_basic_set_copy(bset1
),
1162 isl_basic_set_copy(bset2
));
1163 tab
= isl_tab_from_basic_set(lp
);
1164 sample
= isl_tab_get_sample_value(tab
);
1166 isl_basic_set_free(lp
);
1169 d
= isl_basic_set_total_dim(bset1
);
1170 dir
= isl_vec_alloc(bset1
->ctx
, 1 + d
);
1173 isl_seq_clr(dir
->block
.data
+ 1, dir
->size
- 1);
1175 /* positivity constraint 1 >= 0 */
1176 isl_int_set(dir
->block
.data
[0], sample
->block
.data
[n
]); n
++;
1177 for (i
= 0; i
< bset1
->n_eq
; ++i
) {
1178 isl_int_sub(sample
->block
.data
[n
],
1179 sample
->block
.data
[n
], sample
->block
.data
[n
+1]);
1180 isl_seq_combine(dir
->block
.data
,
1181 bset1
->ctx
->one
, dir
->block
.data
,
1182 sample
->block
.data
[n
], bset1
->eq
[i
], 1 + d
);
1186 for (i
= 0; i
< bset1
->n_ineq
; ++i
)
1187 isl_seq_combine(dir
->block
.data
,
1188 bset1
->ctx
->one
, dir
->block
.data
,
1189 sample
->block
.data
[n
++], bset1
->ineq
[i
], 1 + d
);
1190 isl_vec_free(sample
);
1191 isl_seq_normalize(bset1
->ctx
, dir
->el
, dir
->size
);
1192 isl_basic_set_free(bset1
);
1193 isl_basic_set_free(bset2
);
1196 isl_vec_free(sample
);
1197 isl_basic_set_free(bset1
);
1198 isl_basic_set_free(bset2
);
1202 /* Given a polyhedron b_i + A_i x >= 0 and a map T = S^{-1},
1203 * compute b_i' + A_i' x' >= 0, with
1205 * [ b_i A_i ] [ y' ] [ y' ]
1206 * [ 1 0 ] S^{-1} [ x' ] >= 0 or [ b_i' A_i' ] [ x' ] >= 0
1208 * In particular, add the "positivity constraint" and then perform
1211 static struct isl_basic_set
*homogeneous_map(struct isl_basic_set
*bset
,
1218 bset
= isl_basic_set_extend_constraints(bset
, 0, 1);
1219 k
= isl_basic_set_alloc_inequality(bset
);
1222 isl_seq_clr(bset
->ineq
[k
] + 1, isl_basic_set_total_dim(bset
));
1223 isl_int_set_si(bset
->ineq
[k
][0], 1);
1224 bset
= isl_basic_set_preimage(bset
, T
);
1228 isl_basic_set_free(bset
);
1232 /* Compute the convex hull of a pair of basic sets without any parameters or
1233 * integer divisions, where the convex hull is known to be pointed,
1234 * but the basic sets may be unbounded.
1236 * We turn this problem into the computation of a convex hull of a pair
1237 * _bounded_ polyhedra by "changing the direction of the homogeneous
1238 * dimension". This idea is due to Matthias Koeppe.
1240 * Consider the cones in homogeneous space that correspond to the
1241 * input polyhedra. The rays of these cones are also rays of the
1242 * polyhedra if the coordinate that corresponds to the homogeneous
1243 * dimension is zero. That is, if the inner product of the rays
1244 * with the homogeneous direction is zero.
1245 * The cones in the homogeneous space can also be considered to
1246 * correspond to other pairs of polyhedra by chosing a different
1247 * homogeneous direction. To ensure that both of these polyhedra
1248 * are bounded, we need to make sure that all rays of the cones
1249 * correspond to vertices and not to rays.
1250 * Let s be a direction such that <s, r> > 0 for all rays r of both cones.
1251 * Then using s as a homogeneous direction, we obtain a pair of polytopes.
1252 * The vector s is computed in valid_direction.
1254 * Note that we need to consider _all_ rays of the cones and not just
1255 * the rays that correspond to rays in the polyhedra. If we were to
1256 * only consider those rays and turn them into vertices, then we
1257 * may inadvertently turn some vertices into rays.
1259 * The standard homogeneous direction is the unit vector in the 0th coordinate.
1260 * We therefore transform the two polyhedra such that the selected
1261 * direction is mapped onto this standard direction and then proceed
1262 * with the normal computation.
1263 * Let S be a non-singular square matrix with s as its first row,
1264 * then we want to map the polyhedra to the space
1266 * [ y' ] [ y ] [ y ] [ y' ]
1267 * [ x' ] = S [ x ] i.e., [ x ] = S^{-1} [ x' ]
1269 * We take S to be the unimodular completion of s to limit the growth
1270 * of the coefficients in the following computations.
1272 * Let b_i + A_i x >= 0 be the constraints of polyhedron i.
1273 * We first move to the homogeneous dimension
1275 * b_i y + A_i x >= 0 [ b_i A_i ] [ y ] [ 0 ]
1276 * y >= 0 or [ 1 0 ] [ x ] >= [ 0 ]
1278 * Then we change directoin
1280 * [ b_i A_i ] [ y' ] [ y' ]
1281 * [ 1 0 ] S^{-1} [ x' ] >= 0 or [ b_i' A_i' ] [ x' ] >= 0
1283 * Then we compute the convex hull of the polytopes b_i' + A_i' x' >= 0
1284 * resulting in b' + A' x' >= 0, which we then convert back
1287 * [ b' A' ] S [ x ] >= 0 or [ b A ] [ x ] >= 0
1289 * The polyhedron b + A x >= 0 is then the convex hull of the input polyhedra.
1291 static struct isl_basic_set
*convex_hull_pair_pointed(
1292 struct isl_basic_set
*bset1
, struct isl_basic_set
*bset2
)
1294 struct isl_ctx
*ctx
= NULL
;
1295 struct isl_vec
*dir
= NULL
;
1296 struct isl_mat
*T
= NULL
;
1297 struct isl_mat
*T2
= NULL
;
1298 struct isl_basic_set
*hull
;
1299 struct isl_set
*set
;
1301 if (!bset1
|| !bset2
)
1304 dir
= valid_direction(isl_basic_set_copy(bset1
),
1305 isl_basic_set_copy(bset2
));
1308 T
= isl_mat_alloc(bset1
->ctx
, dir
->size
, dir
->size
);
1311 isl_seq_cpy(T
->row
[0], dir
->block
.data
, dir
->size
);
1312 T
= isl_mat_unimodular_complete(T
, 1);
1313 T2
= isl_mat_right_inverse(isl_mat_copy(T
));
1315 bset1
= homogeneous_map(bset1
, isl_mat_copy(T2
));
1316 bset2
= homogeneous_map(bset2
, T2
);
1317 set
= isl_set_alloc_dim(isl_basic_set_get_dim(bset1
), 2, 0);
1318 set
= isl_set_add_basic_set(set
, bset1
);
1319 set
= isl_set_add_basic_set(set
, bset2
);
1320 hull
= uset_convex_hull(set
);
1321 hull
= isl_basic_set_preimage(hull
, T
);
1328 isl_basic_set_free(bset1
);
1329 isl_basic_set_free(bset2
);
1333 static struct isl_basic_set
*uset_convex_hull_wrap(struct isl_set
*set
);
1334 static struct isl_basic_set
*modulo_affine_hull(
1335 struct isl_set
*set
, struct isl_basic_set
*affine_hull
);
1337 /* Compute the convex hull of a pair of basic sets without any parameters or
1338 * integer divisions.
1340 * This function is called from uset_convex_hull_unbounded, which
1341 * means that the complete convex hull is unbounded. Some pairs
1342 * of basic sets may still be bounded, though.
1343 * They may even lie inside a lower dimensional space, in which
1344 * case they need to be handled inside their affine hull since
1345 * the main algorithm assumes that the result is full-dimensional.
1347 * If the convex hull of the two basic sets would have a non-trivial
1348 * lineality space, we first project out this lineality space.
1350 static struct isl_basic_set
*convex_hull_pair(struct isl_basic_set
*bset1
,
1351 struct isl_basic_set
*bset2
)
1353 isl_basic_set
*lin
, *aff
;
1354 int bounded1
, bounded2
;
1356 if (bset1
->ctx
->opt
->convex
== ISL_CONVEX_HULL_FM
)
1357 return convex_hull_pair_elim(bset1
, bset2
);
1359 aff
= isl_set_affine_hull(isl_basic_set_union(isl_basic_set_copy(bset1
),
1360 isl_basic_set_copy(bset2
)));
1364 return modulo_affine_hull(isl_basic_set_union(bset1
, bset2
), aff
);
1365 isl_basic_set_free(aff
);
1367 bounded1
= isl_basic_set_is_bounded(bset1
);
1368 bounded2
= isl_basic_set_is_bounded(bset2
);
1370 if (bounded1
< 0 || bounded2
< 0)
1373 if (bounded1
&& bounded2
)
1374 uset_convex_hull_wrap(isl_basic_set_union(bset1
, bset2
));
1376 if (bounded1
|| bounded2
)
1377 return convex_hull_pair_pointed(bset1
, bset2
);
1379 lin
= induced_lineality_space(isl_basic_set_copy(bset1
),
1380 isl_basic_set_copy(bset2
));
1383 if (isl_basic_set_is_universe(lin
)) {
1384 isl_basic_set_free(bset1
);
1385 isl_basic_set_free(bset2
);
1388 if (lin
->n_eq
< isl_basic_set_total_dim(lin
)) {
1389 struct isl_set
*set
;
1390 set
= isl_set_alloc_dim(isl_basic_set_get_dim(bset1
), 2, 0);
1391 set
= isl_set_add_basic_set(set
, bset1
);
1392 set
= isl_set_add_basic_set(set
, bset2
);
1393 return modulo_lineality(set
, lin
);
1395 isl_basic_set_free(lin
);
1397 return convex_hull_pair_pointed(bset1
, bset2
);
1399 isl_basic_set_free(bset1
);
1400 isl_basic_set_free(bset2
);
1404 /* Compute the lineality space of a basic set.
1405 * We currently do not allow the basic set to have any divs.
1406 * We basically just drop the constants and turn every inequality
1409 struct isl_basic_set
*isl_basic_set_lineality_space(struct isl_basic_set
*bset
)
1412 struct isl_basic_set
*lin
= NULL
;
1417 isl_assert(bset
->ctx
, bset
->n_div
== 0, goto error
);
1418 dim
= isl_basic_set_total_dim(bset
);
1420 lin
= isl_basic_set_alloc_dim(isl_basic_set_get_dim(bset
), 0, dim
, 0);
1423 for (i
= 0; i
< bset
->n_eq
; ++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
->eq
[i
] + 1, dim
);
1430 lin
= isl_basic_set_gauss(lin
, NULL
);
1433 for (i
= 0; i
< bset
->n_ineq
&& lin
->n_eq
< dim
; ++i
) {
1434 k
= isl_basic_set_alloc_equality(lin
);
1437 isl_int_set_si(lin
->eq
[k
][0], 0);
1438 isl_seq_cpy(lin
->eq
[k
] + 1, bset
->ineq
[i
] + 1, dim
);
1439 lin
= isl_basic_set_gauss(lin
, NULL
);
1443 isl_basic_set_free(bset
);
1446 isl_basic_set_free(lin
);
1447 isl_basic_set_free(bset
);
1451 /* Compute the (linear) hull of the lineality spaces of the basic sets in the
1452 * "underlying" set "set".
1454 static struct isl_basic_set
*uset_combined_lineality_space(struct isl_set
*set
)
1457 struct isl_set
*lin
= NULL
;
1462 struct isl_dim
*dim
= isl_set_get_dim(set
);
1464 return isl_basic_set_empty(dim
);
1467 lin
= isl_set_alloc_dim(isl_set_get_dim(set
), set
->n
, 0);
1468 for (i
= 0; i
< set
->n
; ++i
)
1469 lin
= isl_set_add_basic_set(lin
,
1470 isl_basic_set_lineality_space(isl_basic_set_copy(set
->p
[i
])));
1472 return isl_set_affine_hull(lin
);
1475 /* Compute the convex hull of a set without any parameters or
1476 * integer divisions.
1477 * In each step, we combined two basic sets until only one
1478 * basic set is left.
1479 * The input basic sets are assumed not to have a non-trivial
1480 * lineality space. If any of the intermediate results has
1481 * a non-trivial lineality space, it is projected out.
1483 static struct isl_basic_set
*uset_convex_hull_unbounded(struct isl_set
*set
)
1485 struct isl_basic_set
*convex_hull
= NULL
;
1487 convex_hull
= isl_set_copy_basic_set(set
);
1488 set
= isl_set_drop_basic_set(set
, convex_hull
);
1491 while (set
->n
> 0) {
1492 struct isl_basic_set
*t
;
1493 t
= isl_set_copy_basic_set(set
);
1496 set
= isl_set_drop_basic_set(set
, t
);
1499 convex_hull
= convex_hull_pair(convex_hull
, t
);
1502 t
= isl_basic_set_lineality_space(isl_basic_set_copy(convex_hull
));
1505 if (isl_basic_set_is_universe(t
)) {
1506 isl_basic_set_free(convex_hull
);
1510 if (t
->n_eq
< isl_basic_set_total_dim(t
)) {
1511 set
= isl_set_add_basic_set(set
, convex_hull
);
1512 return modulo_lineality(set
, t
);
1514 isl_basic_set_free(t
);
1520 isl_basic_set_free(convex_hull
);
1524 /* Compute an initial hull for wrapping containing a single initial
1526 * This function assumes that the given set is bounded.
1528 static struct isl_basic_set
*initial_hull(struct isl_basic_set
*hull
,
1529 struct isl_set
*set
)
1531 struct isl_mat
*bounds
= NULL
;
1537 bounds
= initial_facet_constraint(set
);
1540 k
= isl_basic_set_alloc_inequality(hull
);
1543 dim
= isl_set_n_dim(set
);
1544 isl_assert(set
->ctx
, 1 + dim
== bounds
->n_col
, goto error
);
1545 isl_seq_cpy(hull
->ineq
[k
], bounds
->row
[0], bounds
->n_col
);
1546 isl_mat_free(bounds
);
1550 isl_basic_set_free(hull
);
1551 isl_mat_free(bounds
);
1555 struct max_constraint
{
1561 static int max_constraint_equal(const void *entry
, const void *val
)
1563 struct max_constraint
*a
= (struct max_constraint
*)entry
;
1564 isl_int
*b
= (isl_int
*)val
;
1566 return isl_seq_eq(a
->c
->row
[0] + 1, b
, a
->c
->n_col
- 1);
1569 static void update_constraint(struct isl_ctx
*ctx
, struct isl_hash_table
*table
,
1570 isl_int
*con
, unsigned len
, int n
, int ineq
)
1572 struct isl_hash_table_entry
*entry
;
1573 struct max_constraint
*c
;
1576 c_hash
= isl_seq_get_hash(con
+ 1, len
);
1577 entry
= isl_hash_table_find(ctx
, table
, c_hash
, max_constraint_equal
,
1583 isl_hash_table_remove(ctx
, table
, entry
);
1587 if (isl_int_gt(c
->c
->row
[0][0], con
[0]))
1589 if (isl_int_eq(c
->c
->row
[0][0], con
[0])) {
1594 c
->c
= isl_mat_cow(c
->c
);
1595 isl_int_set(c
->c
->row
[0][0], con
[0]);
1599 /* Check whether the constraint hash table "table" constains the constraint
1602 static int has_constraint(struct isl_ctx
*ctx
, struct isl_hash_table
*table
,
1603 isl_int
*con
, unsigned len
, int n
)
1605 struct isl_hash_table_entry
*entry
;
1606 struct max_constraint
*c
;
1609 c_hash
= isl_seq_get_hash(con
+ 1, len
);
1610 entry
= isl_hash_table_find(ctx
, table
, c_hash
, max_constraint_equal
,
1617 return isl_int_eq(c
->c
->row
[0][0], con
[0]);
1620 /* Check for inequality constraints of a basic set without equalities
1621 * such that the same or more stringent copies of the constraint appear
1622 * in all of the basic sets. Such constraints are necessarily facet
1623 * constraints of the convex hull.
1625 * If the resulting basic set is by chance identical to one of
1626 * the basic sets in "set", then we know that this basic set contains
1627 * all other basic sets and is therefore the convex hull of set.
1628 * In this case we set *is_hull to 1.
1630 static struct isl_basic_set
*common_constraints(struct isl_basic_set
*hull
,
1631 struct isl_set
*set
, int *is_hull
)
1634 int min_constraints
;
1636 struct max_constraint
*constraints
= NULL
;
1637 struct isl_hash_table
*table
= NULL
;
1642 for (i
= 0; i
< set
->n
; ++i
)
1643 if (set
->p
[i
]->n_eq
== 0)
1647 min_constraints
= set
->p
[i
]->n_ineq
;
1649 for (i
= best
+ 1; i
< set
->n
; ++i
) {
1650 if (set
->p
[i
]->n_eq
!= 0)
1652 if (set
->p
[i
]->n_ineq
>= min_constraints
)
1654 min_constraints
= set
->p
[i
]->n_ineq
;
1657 constraints
= isl_calloc_array(hull
->ctx
, struct max_constraint
,
1661 table
= isl_alloc_type(hull
->ctx
, struct isl_hash_table
);
1662 if (isl_hash_table_init(hull
->ctx
, table
, min_constraints
))
1665 total
= isl_dim_total(set
->dim
);
1666 for (i
= 0; i
< set
->p
[best
]->n_ineq
; ++i
) {
1667 constraints
[i
].c
= isl_mat_sub_alloc(hull
->ctx
,
1668 set
->p
[best
]->ineq
+ i
, 0, 1, 0, 1 + total
);
1669 if (!constraints
[i
].c
)
1671 constraints
[i
].ineq
= 1;
1673 for (i
= 0; i
< min_constraints
; ++i
) {
1674 struct isl_hash_table_entry
*entry
;
1676 c_hash
= isl_seq_get_hash(constraints
[i
].c
->row
[0] + 1, total
);
1677 entry
= isl_hash_table_find(hull
->ctx
, table
, c_hash
,
1678 max_constraint_equal
, constraints
[i
].c
->row
[0] + 1, 1);
1681 isl_assert(hull
->ctx
, !entry
->data
, goto error
);
1682 entry
->data
= &constraints
[i
];
1686 for (s
= 0; s
< set
->n
; ++s
) {
1690 for (i
= 0; i
< set
->p
[s
]->n_eq
; ++i
) {
1691 isl_int
*eq
= set
->p
[s
]->eq
[i
];
1692 for (j
= 0; j
< 2; ++j
) {
1693 isl_seq_neg(eq
, eq
, 1 + total
);
1694 update_constraint(hull
->ctx
, table
,
1698 for (i
= 0; i
< set
->p
[s
]->n_ineq
; ++i
) {
1699 isl_int
*ineq
= set
->p
[s
]->ineq
[i
];
1700 update_constraint(hull
->ctx
, table
, ineq
, total
, n
,
1701 set
->p
[s
]->n_eq
== 0);
1706 for (i
= 0; i
< min_constraints
; ++i
) {
1707 if (constraints
[i
].count
< n
)
1709 if (!constraints
[i
].ineq
)
1711 j
= isl_basic_set_alloc_inequality(hull
);
1714 isl_seq_cpy(hull
->ineq
[j
], constraints
[i
].c
->row
[0], 1 + total
);
1717 for (s
= 0; s
< set
->n
; ++s
) {
1718 if (set
->p
[s
]->n_eq
)
1720 if (set
->p
[s
]->n_ineq
!= hull
->n_ineq
)
1722 for (i
= 0; i
< set
->p
[s
]->n_ineq
; ++i
) {
1723 isl_int
*ineq
= set
->p
[s
]->ineq
[i
];
1724 if (!has_constraint(hull
->ctx
, table
, ineq
, total
, n
))
1727 if (i
== set
->p
[s
]->n_ineq
)
1731 isl_hash_table_clear(table
);
1732 for (i
= 0; i
< min_constraints
; ++i
)
1733 isl_mat_free(constraints
[i
].c
);
1738 isl_hash_table_clear(table
);
1741 for (i
= 0; i
< min_constraints
; ++i
)
1742 isl_mat_free(constraints
[i
].c
);
1747 /* Create a template for the convex hull of "set" and fill it up
1748 * obvious facet constraints, if any. If the result happens to
1749 * be the convex hull of "set" then *is_hull is set to 1.
1751 static struct isl_basic_set
*proto_hull(struct isl_set
*set
, int *is_hull
)
1753 struct isl_basic_set
*hull
;
1758 for (i
= 0; i
< set
->n
; ++i
) {
1759 n_ineq
+= set
->p
[i
]->n_eq
;
1760 n_ineq
+= set
->p
[i
]->n_ineq
;
1762 hull
= isl_basic_set_alloc_dim(isl_dim_copy(set
->dim
), 0, 0, n_ineq
);
1763 hull
= isl_basic_set_set_rational(hull
);
1766 return common_constraints(hull
, set
, is_hull
);
1769 static struct isl_basic_set
*uset_convex_hull_wrap(struct isl_set
*set
)
1771 struct isl_basic_set
*hull
;
1774 hull
= proto_hull(set
, &is_hull
);
1775 if (hull
&& !is_hull
) {
1776 if (hull
->n_ineq
== 0)
1777 hull
= initial_hull(hull
, set
);
1778 hull
= extend(hull
, set
);
1785 /* Compute the convex hull of a set without any parameters or
1786 * integer divisions. Depending on whether the set is bounded,
1787 * we pass control to the wrapping based convex hull or
1788 * the Fourier-Motzkin elimination based convex hull.
1789 * We also handle a few special cases before checking the boundedness.
1791 static struct isl_basic_set
*uset_convex_hull(struct isl_set
*set
)
1793 struct isl_basic_set
*convex_hull
= NULL
;
1794 struct isl_basic_set
*lin
;
1796 if (isl_set_n_dim(set
) == 0)
1797 return convex_hull_0d(set
);
1799 set
= isl_set_coalesce(set
);
1800 set
= isl_set_set_rational(set
);
1807 convex_hull
= isl_basic_set_copy(set
->p
[0]);
1811 if (isl_set_n_dim(set
) == 1)
1812 return convex_hull_1d(set
);
1814 if (isl_set_is_bounded(set
) &&
1815 set
->ctx
->opt
->convex
== ISL_CONVEX_HULL_WRAP
)
1816 return uset_convex_hull_wrap(set
);
1818 lin
= uset_combined_lineality_space(isl_set_copy(set
));
1821 if (isl_basic_set_is_universe(lin
)) {
1825 if (lin
->n_eq
< isl_basic_set_total_dim(lin
))
1826 return modulo_lineality(set
, lin
);
1827 isl_basic_set_free(lin
);
1829 return uset_convex_hull_unbounded(set
);
1832 isl_basic_set_free(convex_hull
);
1836 /* This is the core procedure, where "set" is a "pure" set, i.e.,
1837 * without parameters or divs and where the convex hull of set is
1838 * known to be full-dimensional.
1840 static struct isl_basic_set
*uset_convex_hull_wrap_bounded(struct isl_set
*set
)
1842 struct isl_basic_set
*convex_hull
= NULL
;
1847 if (isl_set_n_dim(set
) == 0) {
1848 convex_hull
= isl_basic_set_universe(isl_dim_copy(set
->dim
));
1850 convex_hull
= isl_basic_set_set_rational(convex_hull
);
1854 set
= isl_set_set_rational(set
);
1855 set
= isl_set_coalesce(set
);
1859 convex_hull
= isl_basic_set_copy(set
->p
[0]);
1863 if (isl_set_n_dim(set
) == 1)
1864 return convex_hull_1d(set
);
1866 return uset_convex_hull_wrap(set
);
1872 /* Compute the convex hull of set "set" with affine hull "affine_hull",
1873 * We first remove the equalities (transforming the set), compute the
1874 * convex hull of the transformed set and then add the equalities back
1875 * (after performing the inverse transformation.
1877 static struct isl_basic_set
*modulo_affine_hull(
1878 struct isl_set
*set
, struct isl_basic_set
*affine_hull
)
1882 struct isl_basic_set
*dummy
;
1883 struct isl_basic_set
*convex_hull
;
1885 dummy
= isl_basic_set_remove_equalities(
1886 isl_basic_set_copy(affine_hull
), &T
, &T2
);
1889 isl_basic_set_free(dummy
);
1890 set
= isl_set_preimage(set
, T
);
1891 convex_hull
= uset_convex_hull(set
);
1892 convex_hull
= isl_basic_set_preimage(convex_hull
, T2
);
1893 convex_hull
= isl_basic_set_intersect(convex_hull
, affine_hull
);
1896 isl_basic_set_free(affine_hull
);
1901 /* Compute the convex hull of a map.
1903 * The implementation was inspired by "Extended Convex Hull" by Fukuda et al.,
1904 * specifically, the wrapping of facets to obtain new facets.
1906 struct isl_basic_map
*isl_map_convex_hull(struct isl_map
*map
)
1908 struct isl_basic_set
*bset
;
1909 struct isl_basic_map
*model
= NULL
;
1910 struct isl_basic_set
*affine_hull
= NULL
;
1911 struct isl_basic_map
*convex_hull
= NULL
;
1912 struct isl_set
*set
= NULL
;
1913 struct isl_ctx
*ctx
;
1920 convex_hull
= isl_basic_map_empty_like_map(map
);
1925 map
= isl_map_detect_equalities(map
);
1926 map
= isl_map_align_divs(map
);
1929 model
= isl_basic_map_copy(map
->p
[0]);
1930 set
= isl_map_underlying_set(map
);
1934 affine_hull
= isl_set_affine_hull(isl_set_copy(set
));
1937 if (affine_hull
->n_eq
!= 0)
1938 bset
= modulo_affine_hull(set
, affine_hull
);
1940 isl_basic_set_free(affine_hull
);
1941 bset
= uset_convex_hull(set
);
1944 convex_hull
= isl_basic_map_overlying_set(bset
, model
);
1948 ISL_F_SET(convex_hull
, ISL_BASIC_MAP_NO_IMPLICIT
);
1949 ISL_F_SET(convex_hull
, ISL_BASIC_MAP_ALL_EQUALITIES
);
1950 ISL_F_CLR(convex_hull
, ISL_BASIC_MAP_RATIONAL
);
1954 isl_basic_map_free(model
);
1958 struct isl_basic_set
*isl_set_convex_hull(struct isl_set
*set
)
1960 return (struct isl_basic_set
*)
1961 isl_map_convex_hull((struct isl_map
*)set
);
1964 __isl_give isl_basic_map
*isl_map_polyhedral_hull(__isl_take isl_map
*map
)
1966 isl_basic_map
*hull
;
1968 hull
= isl_map_convex_hull(map
);
1969 return isl_basic_map_remove_divs(hull
);
1972 __isl_give isl_basic_set
*isl_set_polyhedral_hull(__isl_take isl_set
*set
)
1974 return (isl_basic_set
*)isl_map_polyhedral_hull((isl_map
*)set
);
1977 struct sh_data_entry
{
1978 struct isl_hash_table
*table
;
1979 struct isl_tab
*tab
;
1982 /* Holds the data needed during the simple hull computation.
1984 * n the number of basic sets in the original set
1985 * hull_table a hash table of already computed constraints
1986 * in the simple hull
1987 * p for each basic set,
1988 * table a hash table of the constraints
1989 * tab the tableau corresponding to the basic set
1992 struct isl_ctx
*ctx
;
1994 struct isl_hash_table
*hull_table
;
1995 struct sh_data_entry p
[1];
1998 static void sh_data_free(struct sh_data
*data
)
2004 isl_hash_table_free(data
->ctx
, data
->hull_table
);
2005 for (i
= 0; i
< data
->n
; ++i
) {
2006 isl_hash_table_free(data
->ctx
, data
->p
[i
].table
);
2007 isl_tab_free(data
->p
[i
].tab
);
2012 struct ineq_cmp_data
{
2017 static int has_ineq(const void *entry
, const void *val
)
2019 isl_int
*row
= (isl_int
*)entry
;
2020 struct ineq_cmp_data
*v
= (struct ineq_cmp_data
*)val
;
2022 return isl_seq_eq(row
+ 1, v
->p
+ 1, v
->len
) ||
2023 isl_seq_is_neg(row
+ 1, v
->p
+ 1, v
->len
);
2026 static int hash_ineq(struct isl_ctx
*ctx
, struct isl_hash_table
*table
,
2027 isl_int
*ineq
, unsigned len
)
2030 struct ineq_cmp_data v
;
2031 struct isl_hash_table_entry
*entry
;
2035 c_hash
= isl_seq_get_hash(ineq
+ 1, len
);
2036 entry
= isl_hash_table_find(ctx
, table
, c_hash
, has_ineq
, &v
, 1);
2043 /* Fill hash table "table" with the constraints of "bset".
2044 * Equalities are added as two inequalities.
2045 * The value in the hash table is a pointer to the (in)equality of "bset".
2047 static int hash_basic_set(struct isl_hash_table
*table
,
2048 struct isl_basic_set
*bset
)
2051 unsigned dim
= isl_basic_set_total_dim(bset
);
2053 for (i
= 0; i
< bset
->n_eq
; ++i
) {
2054 for (j
= 0; j
< 2; ++j
) {
2055 isl_seq_neg(bset
->eq
[i
], bset
->eq
[i
], 1 + dim
);
2056 if (hash_ineq(bset
->ctx
, table
, bset
->eq
[i
], dim
) < 0)
2060 for (i
= 0; i
< bset
->n_ineq
; ++i
) {
2061 if (hash_ineq(bset
->ctx
, table
, bset
->ineq
[i
], dim
) < 0)
2067 static struct sh_data
*sh_data_alloc(struct isl_set
*set
, unsigned n_ineq
)
2069 struct sh_data
*data
;
2072 data
= isl_calloc(set
->ctx
, struct sh_data
,
2073 sizeof(struct sh_data
) +
2074 (set
->n
- 1) * sizeof(struct sh_data_entry
));
2077 data
->ctx
= set
->ctx
;
2079 data
->hull_table
= isl_hash_table_alloc(set
->ctx
, n_ineq
);
2080 if (!data
->hull_table
)
2082 for (i
= 0; i
< set
->n
; ++i
) {
2083 data
->p
[i
].table
= isl_hash_table_alloc(set
->ctx
,
2084 2 * set
->p
[i
]->n_eq
+ set
->p
[i
]->n_ineq
);
2085 if (!data
->p
[i
].table
)
2087 if (hash_basic_set(data
->p
[i
].table
, set
->p
[i
]) < 0)
2096 /* Check if inequality "ineq" is a bound for basic set "j" or if
2097 * it can be relaxed (by increasing the constant term) to become
2098 * a bound for that basic set. In the latter case, the constant
2100 * Return 1 if "ineq" is a bound
2101 * 0 if "ineq" may attain arbitrarily small values on basic set "j"
2102 * -1 if some error occurred
2104 static int is_bound(struct sh_data
*data
, struct isl_set
*set
, int j
,
2107 enum isl_lp_result res
;
2110 if (!data
->p
[j
].tab
) {
2111 data
->p
[j
].tab
= isl_tab_from_basic_set(set
->p
[j
]);
2112 if (!data
->p
[j
].tab
)
2118 res
= isl_tab_min(data
->p
[j
].tab
, ineq
, data
->ctx
->one
,
2120 if (res
== isl_lp_ok
&& isl_int_is_neg(opt
))
2121 isl_int_sub(ineq
[0], ineq
[0], opt
);
2125 return (res
== isl_lp_ok
|| res
== isl_lp_empty
) ? 1 :
2126 res
== isl_lp_unbounded
? 0 : -1;
2129 /* Check if inequality "ineq" from basic set "i" can be relaxed to
2130 * become a bound on the whole set. If so, add the (relaxed) inequality
2133 * We first check if "hull" already contains a translate of the inequality.
2134 * If so, we are done.
2135 * Then, we check if any of the previous basic sets contains a translate
2136 * of the inequality. If so, then we have already considered this
2137 * inequality and we are done.
2138 * Otherwise, for each basic set other than "i", we check if the inequality
2139 * is a bound on the basic set.
2140 * For previous basic sets, we know that they do not contain a translate
2141 * of the inequality, so we directly call is_bound.
2142 * For following basic sets, we first check if a translate of the
2143 * inequality appears in its description and if so directly update
2144 * the inequality accordingly.
2146 static struct isl_basic_set
*add_bound(struct isl_basic_set
*hull
,
2147 struct sh_data
*data
, struct isl_set
*set
, int i
, isl_int
*ineq
)
2150 struct ineq_cmp_data v
;
2151 struct isl_hash_table_entry
*entry
;
2157 v
.len
= isl_basic_set_total_dim(hull
);
2159 c_hash
= isl_seq_get_hash(ineq
+ 1, v
.len
);
2161 entry
= isl_hash_table_find(hull
->ctx
, data
->hull_table
, c_hash
,
2166 for (j
= 0; j
< i
; ++j
) {
2167 entry
= isl_hash_table_find(hull
->ctx
, data
->p
[j
].table
,
2168 c_hash
, has_ineq
, &v
, 0);
2175 k
= isl_basic_set_alloc_inequality(hull
);
2176 isl_seq_cpy(hull
->ineq
[k
], ineq
, 1 + v
.len
);
2180 for (j
= 0; j
< i
; ++j
) {
2182 bound
= is_bound(data
, set
, j
, hull
->ineq
[k
]);
2189 isl_basic_set_free_inequality(hull
, 1);
2193 for (j
= i
+ 1; j
< set
->n
; ++j
) {
2196 entry
= isl_hash_table_find(hull
->ctx
, data
->p
[j
].table
,
2197 c_hash
, has_ineq
, &v
, 0);
2199 ineq_j
= entry
->data
;
2200 neg
= isl_seq_is_neg(ineq_j
+ 1,
2201 hull
->ineq
[k
] + 1, v
.len
);
2203 isl_int_neg(ineq_j
[0], ineq_j
[0]);
2204 if (isl_int_gt(ineq_j
[0], hull
->ineq
[k
][0]))
2205 isl_int_set(hull
->ineq
[k
][0], ineq_j
[0]);
2207 isl_int_neg(ineq_j
[0], ineq_j
[0]);
2210 bound
= is_bound(data
, set
, j
, hull
->ineq
[k
]);
2217 isl_basic_set_free_inequality(hull
, 1);
2221 entry
= isl_hash_table_find(hull
->ctx
, data
->hull_table
, c_hash
,
2225 entry
->data
= hull
->ineq
[k
];
2229 isl_basic_set_free(hull
);
2233 /* Check if any inequality from basic set "i" can be relaxed to
2234 * become a bound on the whole set. If so, add the (relaxed) inequality
2237 static struct isl_basic_set
*add_bounds(struct isl_basic_set
*bset
,
2238 struct sh_data
*data
, struct isl_set
*set
, int i
)
2241 unsigned dim
= isl_basic_set_total_dim(bset
);
2243 for (j
= 0; j
< set
->p
[i
]->n_eq
; ++j
) {
2244 for (k
= 0; k
< 2; ++k
) {
2245 isl_seq_neg(set
->p
[i
]->eq
[j
], set
->p
[i
]->eq
[j
], 1+dim
);
2246 bset
= add_bound(bset
, data
, set
, i
, set
->p
[i
]->eq
[j
]);
2249 for (j
= 0; j
< set
->p
[i
]->n_ineq
; ++j
)
2250 bset
= add_bound(bset
, data
, set
, i
, set
->p
[i
]->ineq
[j
]);
2254 /* Compute a superset of the convex hull of set that is described
2255 * by only translates of the constraints in the constituents of set.
2257 static struct isl_basic_set
*uset_simple_hull(struct isl_set
*set
)
2259 struct sh_data
*data
= NULL
;
2260 struct isl_basic_set
*hull
= NULL
;
2268 for (i
= 0; i
< set
->n
; ++i
) {
2271 n_ineq
+= 2 * set
->p
[i
]->n_eq
+ set
->p
[i
]->n_ineq
;
2274 hull
= isl_basic_set_alloc_dim(isl_dim_copy(set
->dim
), 0, 0, n_ineq
);
2278 data
= sh_data_alloc(set
, n_ineq
);
2282 for (i
= 0; i
< set
->n
; ++i
)
2283 hull
= add_bounds(hull
, data
, set
, i
);
2291 isl_basic_set_free(hull
);
2296 /* Compute a superset of the convex hull of map that is described
2297 * by only translates of the constraints in the constituents of map.
2299 struct isl_basic_map
*isl_map_simple_hull(struct isl_map
*map
)
2301 struct isl_set
*set
= NULL
;
2302 struct isl_basic_map
*model
= NULL
;
2303 struct isl_basic_map
*hull
;
2304 struct isl_basic_map
*affine_hull
;
2305 struct isl_basic_set
*bset
= NULL
;
2310 hull
= isl_basic_map_empty_like_map(map
);
2315 hull
= isl_basic_map_copy(map
->p
[0]);
2320 map
= isl_map_detect_equalities(map
);
2321 affine_hull
= isl_map_affine_hull(isl_map_copy(map
));
2322 map
= isl_map_align_divs(map
);
2323 model
= isl_basic_map_copy(map
->p
[0]);
2325 set
= isl_map_underlying_set(map
);
2327 bset
= uset_simple_hull(set
);
2329 hull
= isl_basic_map_overlying_set(bset
, model
);
2331 hull
= isl_basic_map_intersect(hull
, affine_hull
);
2332 hull
= isl_basic_map_remove_redundancies(hull
);
2333 ISL_F_SET(hull
, ISL_BASIC_MAP_NO_IMPLICIT
);
2334 ISL_F_SET(hull
, ISL_BASIC_MAP_ALL_EQUALITIES
);
2339 struct isl_basic_set
*isl_set_simple_hull(struct isl_set
*set
)
2341 return (struct isl_basic_set
*)
2342 isl_map_simple_hull((struct isl_map
*)set
);
2345 /* Given a set "set", return parametric bounds on the dimension "dim".
2347 static struct isl_basic_set
*set_bounds(struct isl_set
*set
, int dim
)
2349 unsigned set_dim
= isl_set_dim(set
, isl_dim_set
);
2350 set
= isl_set_copy(set
);
2351 set
= isl_set_eliminate_dims(set
, dim
+ 1, set_dim
- (dim
+ 1));
2352 set
= isl_set_eliminate_dims(set
, 0, dim
);
2353 return isl_set_convex_hull(set
);
2356 /* Computes a "simple hull" and then check if each dimension in the
2357 * resulting hull is bounded by a symbolic constant. If not, the
2358 * hull is intersected with the corresponding bounds on the whole set.
2360 struct isl_basic_set
*isl_set_bounded_simple_hull(struct isl_set
*set
)
2363 struct isl_basic_set
*hull
;
2364 unsigned nparam
, left
;
2365 int removed_divs
= 0;
2367 hull
= isl_set_simple_hull(isl_set_copy(set
));
2371 nparam
= isl_basic_set_dim(hull
, isl_dim_param
);
2372 for (i
= 0; i
< isl_basic_set_dim(hull
, isl_dim_set
); ++i
) {
2373 int lower
= 0, upper
= 0;
2374 struct isl_basic_set
*bounds
;
2376 left
= isl_basic_set_total_dim(hull
) - nparam
- i
- 1;
2377 for (j
= 0; j
< hull
->n_eq
; ++j
) {
2378 if (isl_int_is_zero(hull
->eq
[j
][1 + nparam
+ i
]))
2380 if (isl_seq_first_non_zero(hull
->eq
[j
]+1+nparam
+i
+1,
2387 for (j
= 0; j
< hull
->n_ineq
; ++j
) {
2388 if (isl_int_is_zero(hull
->ineq
[j
][1 + nparam
+ i
]))
2390 if (isl_seq_first_non_zero(hull
->ineq
[j
]+1+nparam
+i
+1,
2392 isl_seq_first_non_zero(hull
->ineq
[j
]+1+nparam
,
2395 if (isl_int_is_pos(hull
->ineq
[j
][1 + nparam
+ i
]))
2406 if (!removed_divs
) {
2407 set
= isl_set_remove_divs(set
);
2412 bounds
= set_bounds(set
, i
);
2413 hull
= isl_basic_set_intersect(hull
, bounds
);