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 __isl_give isl_basic_map
*isl_basic_map_set_rational(
178 __isl_take isl_basic_set
*bmap
)
183 if (ISL_F_ISSET(bmap
, ISL_BASIC_MAP_RATIONAL
))
186 bmap
= isl_basic_map_cow(bmap
);
190 ISL_F_SET(bmap
, ISL_BASIC_MAP_RATIONAL
);
192 return isl_basic_map_finalize(bmap
);
195 __isl_give isl_basic_set
*isl_basic_set_set_rational(
196 __isl_take isl_basic_set
*bset
)
198 return isl_basic_map_set_rational(bset
);
201 static struct isl_set
*isl_set_set_rational(struct isl_set
*set
)
205 set
= isl_set_cow(set
);
208 for (i
= 0; i
< set
->n
; ++i
) {
209 set
->p
[i
] = isl_basic_set_set_rational(set
->p
[i
]);
219 static struct isl_basic_set
*isl_basic_set_add_equality(
220 struct isl_basic_set
*bset
, isl_int
*c
)
228 if (ISL_F_ISSET(bset
, ISL_BASIC_SET_EMPTY
))
231 isl_assert(bset
->ctx
, isl_basic_set_n_param(bset
) == 0, goto error
);
232 isl_assert(bset
->ctx
, bset
->n_div
== 0, goto error
);
233 dim
= isl_basic_set_n_dim(bset
);
234 bset
= isl_basic_set_cow(bset
);
235 bset
= isl_basic_set_extend(bset
, 0, dim
, 0, 1, 0);
236 i
= isl_basic_set_alloc_equality(bset
);
239 isl_seq_cpy(bset
->eq
[i
], c
, 1 + dim
);
242 isl_basic_set_free(bset
);
246 static struct isl_set
*isl_set_add_basic_set_equality(struct isl_set
*set
, isl_int
*c
)
250 set
= isl_set_cow(set
);
253 for (i
= 0; i
< set
->n
; ++i
) {
254 set
->p
[i
] = isl_basic_set_add_equality(set
->p
[i
], c
);
264 /* Given a union of basic sets, construct the constraints for wrapping
265 * a facet around one of its ridges.
266 * In particular, if each of n the d-dimensional basic sets i in "set"
267 * contains the origin, satisfies the constraints x_1 >= 0 and x_2 >= 0
268 * and is defined by the constraints
272 * then the resulting set is of dimension n*(1+d) and has as constraints
281 static struct isl_basic_set
*wrap_constraints(struct isl_set
*set
)
283 struct isl_basic_set
*lp
;
287 unsigned dim
, lp_dim
;
292 dim
= 1 + isl_set_n_dim(set
);
295 for (i
= 0; i
< set
->n
; ++i
) {
296 n_eq
+= set
->p
[i
]->n_eq
;
297 n_ineq
+= set
->p
[i
]->n_ineq
;
299 lp
= isl_basic_set_alloc(set
->ctx
, 0, dim
* set
->n
, 0, n_eq
, n_ineq
);
300 lp
= isl_basic_set_set_rational(lp
);
303 lp_dim
= isl_basic_set_n_dim(lp
);
304 k
= isl_basic_set_alloc_equality(lp
);
305 isl_int_set_si(lp
->eq
[k
][0], -1);
306 for (i
= 0; i
< set
->n
; ++i
) {
307 isl_int_set_si(lp
->eq
[k
][1+dim
*i
], 0);
308 isl_int_set_si(lp
->eq
[k
][1+dim
*i
+1], 1);
309 isl_seq_clr(lp
->eq
[k
]+1+dim
*i
+2, dim
-2);
311 for (i
= 0; i
< set
->n
; ++i
) {
312 k
= isl_basic_set_alloc_inequality(lp
);
313 isl_seq_clr(lp
->ineq
[k
], 1+lp_dim
);
314 isl_int_set_si(lp
->ineq
[k
][1+dim
*i
], 1);
316 for (j
= 0; j
< set
->p
[i
]->n_eq
; ++j
) {
317 k
= isl_basic_set_alloc_equality(lp
);
318 isl_seq_clr(lp
->eq
[k
], 1+dim
*i
);
319 isl_seq_cpy(lp
->eq
[k
]+1+dim
*i
, set
->p
[i
]->eq
[j
], dim
);
320 isl_seq_clr(lp
->eq
[k
]+1+dim
*(i
+1), dim
*(set
->n
-i
-1));
323 for (j
= 0; j
< set
->p
[i
]->n_ineq
; ++j
) {
324 k
= isl_basic_set_alloc_inequality(lp
);
325 isl_seq_clr(lp
->ineq
[k
], 1+dim
*i
);
326 isl_seq_cpy(lp
->ineq
[k
]+1+dim
*i
, set
->p
[i
]->ineq
[j
], dim
);
327 isl_seq_clr(lp
->ineq
[k
]+1+dim
*(i
+1), dim
*(set
->n
-i
-1));
333 /* Given a facet "facet" of the convex hull of "set" and a facet "ridge"
334 * of that facet, compute the other facet of the convex hull that contains
337 * We first transform the set such that the facet constraint becomes
341 * I.e., the facet lies in
345 * and on that facet, the constraint that defines the ridge is
349 * (This transformation is not strictly needed, all that is needed is
350 * that the ridge contains the origin.)
352 * Since the ridge contains the origin, the cone of the convex hull
353 * will be of the form
358 * with this second constraint defining the new facet.
359 * The constant a is obtained by settting x_1 in the cone of the
360 * convex hull to 1 and minimizing x_2.
361 * Now, each element in the cone of the convex hull is the sum
362 * of elements in the cones of the basic sets.
363 * If a_i is the dilation factor of basic set i, then the problem
364 * we need to solve is
377 * the constraints of each (transformed) basic set.
378 * If a = n/d, then the constraint defining the new facet (in the transformed
381 * -n x_1 + d x_2 >= 0
383 * In the original space, we need to take the same combination of the
384 * corresponding constraints "facet" and "ridge".
386 * If a = -infty = "-1/0", then we just return the original facet constraint.
387 * This means that the facet is unbounded, but has a bounded intersection
388 * with the union of sets.
390 isl_int
*isl_set_wrap_facet(__isl_keep isl_set
*set
,
391 isl_int
*facet
, isl_int
*ridge
)
395 struct isl_mat
*T
= NULL
;
396 struct isl_basic_set
*lp
= NULL
;
398 enum isl_lp_result res
;
405 set
= isl_set_copy(set
);
406 set
= isl_set_set_rational(set
);
408 dim
= 1 + isl_set_n_dim(set
);
409 T
= isl_mat_alloc(ctx
, 3, dim
);
412 isl_int_set_si(T
->row
[0][0], 1);
413 isl_seq_clr(T
->row
[0]+1, dim
- 1);
414 isl_seq_cpy(T
->row
[1], facet
, dim
);
415 isl_seq_cpy(T
->row
[2], ridge
, dim
);
416 T
= isl_mat_right_inverse(T
);
417 set
= isl_set_preimage(set
, T
);
421 lp
= wrap_constraints(set
);
422 obj
= isl_vec_alloc(ctx
, 1 + dim
*set
->n
);
425 isl_int_set_si(obj
->block
.data
[0], 0);
426 for (i
= 0; i
< set
->n
; ++i
) {
427 isl_seq_clr(obj
->block
.data
+ 1 + dim
*i
, 2);
428 isl_int_set_si(obj
->block
.data
[1 + dim
*i
+2], 1);
429 isl_seq_clr(obj
->block
.data
+ 1 + dim
*i
+3, dim
-3);
433 res
= isl_basic_set_solve_lp(lp
, 0,
434 obj
->block
.data
, ctx
->one
, &num
, &den
, NULL
);
435 if (res
== isl_lp_ok
) {
436 isl_int_neg(num
, num
);
437 isl_seq_combine(facet
, num
, facet
, den
, ridge
, dim
);
438 isl_seq_normalize(ctx
, facet
, dim
);
443 isl_basic_set_free(lp
);
445 if (res
== isl_lp_error
)
447 isl_assert(ctx
, res
== isl_lp_ok
|| res
== isl_lp_unbounded
,
451 isl_basic_set_free(lp
);
457 /* Compute the constraint of a facet of "set".
459 * We first compute the intersection with a bounding constraint
460 * that is orthogonal to one of the coordinate axes.
461 * If the affine hull of this intersection has only one equality,
462 * we have found a facet.
463 * Otherwise, we wrap the current bounding constraint around
464 * one of the equalities of the face (one that is not equal to
465 * the current bounding constraint).
466 * This process continues until we have found a facet.
467 * The dimension of the intersection increases by at least
468 * one on each iteration, so termination is guaranteed.
470 static __isl_give isl_mat
*initial_facet_constraint(__isl_keep isl_set
*set
)
472 struct isl_set
*slice
= NULL
;
473 struct isl_basic_set
*face
= NULL
;
475 unsigned dim
= isl_set_n_dim(set
);
479 isl_assert(set
->ctx
, set
->n
> 0, goto error
);
480 bounds
= isl_mat_alloc(set
->ctx
, 1, 1 + dim
);
484 isl_seq_clr(bounds
->row
[0], dim
);
485 isl_int_set_si(bounds
->row
[0][1 + dim
- 1], 1);
486 is_bound
= uset_is_bound(set
, bounds
->row
[0], 1 + dim
);
489 isl_assert(set
->ctx
, is_bound
, goto error
);
490 isl_seq_normalize(set
->ctx
, bounds
->row
[0], 1 + dim
);
494 slice
= isl_set_copy(set
);
495 slice
= isl_set_add_basic_set_equality(slice
, bounds
->row
[0]);
496 face
= isl_set_affine_hull(slice
);
499 if (face
->n_eq
== 1) {
500 isl_basic_set_free(face
);
503 for (i
= 0; i
< face
->n_eq
; ++i
)
504 if (!isl_seq_eq(bounds
->row
[0], face
->eq
[i
], 1 + dim
) &&
505 !isl_seq_is_neg(bounds
->row
[0],
506 face
->eq
[i
], 1 + dim
))
508 isl_assert(set
->ctx
, i
< face
->n_eq
, goto error
);
509 if (!isl_set_wrap_facet(set
, bounds
->row
[0], face
->eq
[i
]))
511 isl_seq_normalize(set
->ctx
, bounds
->row
[0], bounds
->n_col
);
512 isl_basic_set_free(face
);
517 isl_basic_set_free(face
);
518 isl_mat_free(bounds
);
522 /* Given the bounding constraint "c" of a facet of the convex hull of "set",
523 * compute a hyperplane description of the facet, i.e., compute the facets
526 * We compute an affine transformation that transforms the constraint
535 * by computing the right inverse U of a matrix that starts with the rows
548 * Since z_1 is zero, we can drop this variable as well as the corresponding
549 * column of U to obtain
557 * with Q' equal to Q, but without the corresponding row.
558 * After computing the facets of the facet in the z' space,
559 * we convert them back to the x space through Q.
561 static struct isl_basic_set
*compute_facet(struct isl_set
*set
, isl_int
*c
)
563 struct isl_mat
*m
, *U
, *Q
;
564 struct isl_basic_set
*facet
= NULL
;
569 set
= isl_set_copy(set
);
570 dim
= isl_set_n_dim(set
);
571 m
= isl_mat_alloc(set
->ctx
, 2, 1 + dim
);
574 isl_int_set_si(m
->row
[0][0], 1);
575 isl_seq_clr(m
->row
[0]+1, dim
);
576 isl_seq_cpy(m
->row
[1], c
, 1+dim
);
577 U
= isl_mat_right_inverse(m
);
578 Q
= isl_mat_right_inverse(isl_mat_copy(U
));
579 U
= isl_mat_drop_cols(U
, 1, 1);
580 Q
= isl_mat_drop_rows(Q
, 1, 1);
581 set
= isl_set_preimage(set
, U
);
582 facet
= uset_convex_hull_wrap_bounded(set
);
583 facet
= isl_basic_set_preimage(facet
, Q
);
585 isl_assert(ctx
, facet
->n_eq
== 0, goto error
);
588 isl_basic_set_free(facet
);
593 /* Given an initial facet constraint, compute the remaining facets.
594 * We do this by running through all facets found so far and computing
595 * the adjacent facets through wrapping, adding those facets that we
596 * hadn't already found before.
598 * For each facet we have found so far, we first compute its facets
599 * in the resulting convex hull. That is, we compute the ridges
600 * of the resulting convex hull contained in the facet.
601 * We also compute the corresponding facet in the current approximation
602 * of the convex hull. There is no need to wrap around the ridges
603 * in this facet since that would result in a facet that is already
604 * present in the current approximation.
606 * This function can still be significantly optimized by checking which of
607 * the facets of the basic sets are also facets of the convex hull and
608 * using all the facets so far to help in constructing the facets of the
611 * using the technique in section "3.1 Ridge Generation" of
612 * "Extended Convex Hull" by Fukuda et al.
614 static struct isl_basic_set
*extend(struct isl_basic_set
*hull
,
619 struct isl_basic_set
*facet
= NULL
;
620 struct isl_basic_set
*hull_facet
= NULL
;
626 isl_assert(set
->ctx
, set
->n
> 0, goto error
);
628 dim
= isl_set_n_dim(set
);
630 for (i
= 0; i
< hull
->n_ineq
; ++i
) {
631 facet
= compute_facet(set
, hull
->ineq
[i
]);
632 facet
= isl_basic_set_add_equality(facet
, hull
->ineq
[i
]);
633 facet
= isl_basic_set_gauss(facet
, NULL
);
634 facet
= isl_basic_set_normalize_constraints(facet
);
635 hull_facet
= isl_basic_set_copy(hull
);
636 hull_facet
= isl_basic_set_add_equality(hull_facet
, hull
->ineq
[i
]);
637 hull_facet
= isl_basic_set_gauss(hull_facet
, NULL
);
638 hull_facet
= isl_basic_set_normalize_constraints(hull_facet
);
639 if (!facet
|| !hull_facet
)
641 hull
= isl_basic_set_cow(hull
);
642 hull
= isl_basic_set_extend_dim(hull
,
643 isl_dim_copy(hull
->dim
), 0, 0, facet
->n_ineq
);
646 for (j
= 0; j
< facet
->n_ineq
; ++j
) {
647 for (f
= 0; f
< hull_facet
->n_ineq
; ++f
)
648 if (isl_seq_eq(facet
->ineq
[j
],
649 hull_facet
->ineq
[f
], 1 + dim
))
651 if (f
< hull_facet
->n_ineq
)
653 k
= isl_basic_set_alloc_inequality(hull
);
656 isl_seq_cpy(hull
->ineq
[k
], hull
->ineq
[i
], 1+dim
);
657 if (!isl_set_wrap_facet(set
, hull
->ineq
[k
], facet
->ineq
[j
]))
660 isl_basic_set_free(hull_facet
);
661 isl_basic_set_free(facet
);
663 hull
= isl_basic_set_simplify(hull
);
664 hull
= isl_basic_set_finalize(hull
);
667 isl_basic_set_free(hull_facet
);
668 isl_basic_set_free(facet
);
669 isl_basic_set_free(hull
);
673 /* Special case for computing the convex hull of a one dimensional set.
674 * We simply collect the lower and upper bounds of each basic set
675 * and the biggest of those.
677 static struct isl_basic_set
*convex_hull_1d(struct isl_set
*set
)
679 struct isl_mat
*c
= NULL
;
680 isl_int
*lower
= NULL
;
681 isl_int
*upper
= NULL
;
684 struct isl_basic_set
*hull
;
686 for (i
= 0; i
< set
->n
; ++i
) {
687 set
->p
[i
] = isl_basic_set_simplify(set
->p
[i
]);
691 set
= isl_set_remove_empty_parts(set
);
694 isl_assert(set
->ctx
, set
->n
> 0, goto error
);
695 c
= isl_mat_alloc(set
->ctx
, 2, 2);
699 if (set
->p
[0]->n_eq
> 0) {
700 isl_assert(set
->ctx
, set
->p
[0]->n_eq
== 1, goto error
);
703 if (isl_int_is_pos(set
->p
[0]->eq
[0][1])) {
704 isl_seq_cpy(lower
, set
->p
[0]->eq
[0], 2);
705 isl_seq_neg(upper
, set
->p
[0]->eq
[0], 2);
707 isl_seq_neg(lower
, set
->p
[0]->eq
[0], 2);
708 isl_seq_cpy(upper
, set
->p
[0]->eq
[0], 2);
711 for (j
= 0; j
< set
->p
[0]->n_ineq
; ++j
) {
712 if (isl_int_is_pos(set
->p
[0]->ineq
[j
][1])) {
714 isl_seq_cpy(lower
, set
->p
[0]->ineq
[j
], 2);
717 isl_seq_cpy(upper
, set
->p
[0]->ineq
[j
], 2);
724 for (i
= 0; i
< set
->n
; ++i
) {
725 struct isl_basic_set
*bset
= set
->p
[i
];
729 for (j
= 0; j
< bset
->n_eq
; ++j
) {
733 isl_int_mul(a
, lower
[0], bset
->eq
[j
][1]);
734 isl_int_mul(b
, lower
[1], bset
->eq
[j
][0]);
735 if (isl_int_lt(a
, b
) && isl_int_is_pos(bset
->eq
[j
][1]))
736 isl_seq_cpy(lower
, bset
->eq
[j
], 2);
737 if (isl_int_gt(a
, b
) && isl_int_is_neg(bset
->eq
[j
][1]))
738 isl_seq_neg(lower
, bset
->eq
[j
], 2);
741 isl_int_mul(a
, upper
[0], bset
->eq
[j
][1]);
742 isl_int_mul(b
, upper
[1], bset
->eq
[j
][0]);
743 if (isl_int_lt(a
, b
) && isl_int_is_pos(bset
->eq
[j
][1]))
744 isl_seq_neg(upper
, bset
->eq
[j
], 2);
745 if (isl_int_gt(a
, b
) && isl_int_is_neg(bset
->eq
[j
][1]))
746 isl_seq_cpy(upper
, bset
->eq
[j
], 2);
749 for (j
= 0; j
< bset
->n_ineq
; ++j
) {
750 if (isl_int_is_pos(bset
->ineq
[j
][1]))
752 if (isl_int_is_neg(bset
->ineq
[j
][1]))
754 if (lower
&& isl_int_is_pos(bset
->ineq
[j
][1])) {
755 isl_int_mul(a
, lower
[0], bset
->ineq
[j
][1]);
756 isl_int_mul(b
, lower
[1], bset
->ineq
[j
][0]);
757 if (isl_int_lt(a
, b
))
758 isl_seq_cpy(lower
, bset
->ineq
[j
], 2);
760 if (upper
&& isl_int_is_neg(bset
->ineq
[j
][1])) {
761 isl_int_mul(a
, upper
[0], bset
->ineq
[j
][1]);
762 isl_int_mul(b
, upper
[1], bset
->ineq
[j
][0]);
763 if (isl_int_gt(a
, b
))
764 isl_seq_cpy(upper
, bset
->ineq
[j
], 2);
775 hull
= isl_basic_set_alloc(set
->ctx
, 0, 1, 0, 0, 2);
776 hull
= isl_basic_set_set_rational(hull
);
780 k
= isl_basic_set_alloc_inequality(hull
);
781 isl_seq_cpy(hull
->ineq
[k
], lower
, 2);
784 k
= isl_basic_set_alloc_inequality(hull
);
785 isl_seq_cpy(hull
->ineq
[k
], upper
, 2);
787 hull
= isl_basic_set_finalize(hull
);
797 /* Project out final n dimensions using Fourier-Motzkin */
798 static struct isl_set
*set_project_out(struct isl_ctx
*ctx
,
799 struct isl_set
*set
, unsigned n
)
801 return isl_set_remove_dims(set
, isl_dim_set
, isl_set_n_dim(set
) - n
, n
);
804 static struct isl_basic_set
*convex_hull_0d(struct isl_set
*set
)
806 struct isl_basic_set
*convex_hull
;
811 if (isl_set_is_empty(set
))
812 convex_hull
= isl_basic_set_empty(isl_dim_copy(set
->dim
));
814 convex_hull
= isl_basic_set_universe(isl_dim_copy(set
->dim
));
819 /* Compute the convex hull of a pair of basic sets without any parameters or
820 * integer divisions using Fourier-Motzkin elimination.
821 * The convex hull is the set of all points that can be written as
822 * the sum of points from both basic sets (in homogeneous coordinates).
823 * We set up the constraints in a space with dimensions for each of
824 * the three sets and then project out the dimensions corresponding
825 * to the two original basic sets, retaining only those corresponding
826 * to the convex hull.
828 static struct isl_basic_set
*convex_hull_pair_elim(struct isl_basic_set
*bset1
,
829 struct isl_basic_set
*bset2
)
832 struct isl_basic_set
*bset
[2];
833 struct isl_basic_set
*hull
= NULL
;
836 if (!bset1
|| !bset2
)
839 dim
= isl_basic_set_n_dim(bset1
);
840 hull
= isl_basic_set_alloc(bset1
->ctx
, 0, 2 + 3 * dim
, 0,
841 1 + dim
+ bset1
->n_eq
+ bset2
->n_eq
,
842 2 + bset1
->n_ineq
+ bset2
->n_ineq
);
845 for (i
= 0; i
< 2; ++i
) {
846 for (j
= 0; j
< bset
[i
]->n_eq
; ++j
) {
847 k
= isl_basic_set_alloc_equality(hull
);
850 isl_seq_clr(hull
->eq
[k
], (i
+1) * (1+dim
));
851 isl_seq_clr(hull
->eq
[k
]+(i
+2)*(1+dim
), (1-i
)*(1+dim
));
852 isl_seq_cpy(hull
->eq
[k
]+(i
+1)*(1+dim
), bset
[i
]->eq
[j
],
855 for (j
= 0; j
< bset
[i
]->n_ineq
; ++j
) {
856 k
= isl_basic_set_alloc_inequality(hull
);
859 isl_seq_clr(hull
->ineq
[k
], (i
+1) * (1+dim
));
860 isl_seq_clr(hull
->ineq
[k
]+(i
+2)*(1+dim
), (1-i
)*(1+dim
));
861 isl_seq_cpy(hull
->ineq
[k
]+(i
+1)*(1+dim
),
862 bset
[i
]->ineq
[j
], 1+dim
);
864 k
= isl_basic_set_alloc_inequality(hull
);
867 isl_seq_clr(hull
->ineq
[k
], 1+2+3*dim
);
868 isl_int_set_si(hull
->ineq
[k
][(i
+1)*(1+dim
)], 1);
870 for (j
= 0; j
< 1+dim
; ++j
) {
871 k
= isl_basic_set_alloc_equality(hull
);
874 isl_seq_clr(hull
->eq
[k
], 1+2+3*dim
);
875 isl_int_set_si(hull
->eq
[k
][j
], -1);
876 isl_int_set_si(hull
->eq
[k
][1+dim
+j
], 1);
877 isl_int_set_si(hull
->eq
[k
][2*(1+dim
)+j
], 1);
879 hull
= isl_basic_set_set_rational(hull
);
880 hull
= isl_basic_set_remove_dims(hull
, isl_dim_set
, dim
, 2*(1+dim
));
881 hull
= isl_basic_set_remove_redundancies(hull
);
882 isl_basic_set_free(bset1
);
883 isl_basic_set_free(bset2
);
886 isl_basic_set_free(bset1
);
887 isl_basic_set_free(bset2
);
888 isl_basic_set_free(hull
);
892 /* Is the set bounded for each value of the parameters?
894 int isl_basic_set_is_bounded(__isl_keep isl_basic_set
*bset
)
901 if (isl_basic_set_fast_is_empty(bset
))
904 tab
= isl_tab_from_recession_cone(bset
, 1);
905 bounded
= isl_tab_cone_is_bounded(tab
);
910 /* Is the image bounded for each value of the parameters and
911 * the domain variables?
913 int isl_basic_map_image_is_bounded(__isl_keep isl_basic_map
*bmap
)
915 unsigned nparam
= isl_basic_map_dim(bmap
, isl_dim_param
);
916 unsigned n_in
= isl_basic_map_dim(bmap
, isl_dim_in
);
919 bmap
= isl_basic_map_copy(bmap
);
920 bmap
= isl_basic_map_cow(bmap
);
921 bmap
= isl_basic_map_move_dims(bmap
, isl_dim_param
, nparam
,
922 isl_dim_in
, 0, n_in
);
923 bounded
= isl_basic_set_is_bounded((isl_basic_set
*)bmap
);
924 isl_basic_map_free(bmap
);
929 /* Is the set bounded for each value of the parameters?
931 int isl_set_is_bounded(__isl_keep isl_set
*set
)
938 for (i
= 0; i
< set
->n
; ++i
) {
939 int bounded
= isl_basic_set_is_bounded(set
->p
[i
]);
940 if (!bounded
|| bounded
< 0)
946 /* Compute the lineality space of the convex hull of bset1 and bset2.
948 * We first compute the intersection of the recession cone of bset1
949 * with the negative of the recession cone of bset2 and then compute
950 * the linear hull of the resulting cone.
952 static struct isl_basic_set
*induced_lineality_space(
953 struct isl_basic_set
*bset1
, struct isl_basic_set
*bset2
)
956 struct isl_basic_set
*lin
= NULL
;
959 if (!bset1
|| !bset2
)
962 dim
= isl_basic_set_total_dim(bset1
);
963 lin
= isl_basic_set_alloc_dim(isl_basic_set_get_dim(bset1
), 0,
964 bset1
->n_eq
+ bset2
->n_eq
,
965 bset1
->n_ineq
+ bset2
->n_ineq
);
966 lin
= isl_basic_set_set_rational(lin
);
969 for (i
= 0; i
< bset1
->n_eq
; ++i
) {
970 k
= isl_basic_set_alloc_equality(lin
);
973 isl_int_set_si(lin
->eq
[k
][0], 0);
974 isl_seq_cpy(lin
->eq
[k
] + 1, bset1
->eq
[i
] + 1, dim
);
976 for (i
= 0; i
< bset1
->n_ineq
; ++i
) {
977 k
= isl_basic_set_alloc_inequality(lin
);
980 isl_int_set_si(lin
->ineq
[k
][0], 0);
981 isl_seq_cpy(lin
->ineq
[k
] + 1, bset1
->ineq
[i
] + 1, dim
);
983 for (i
= 0; i
< bset2
->n_eq
; ++i
) {
984 k
= isl_basic_set_alloc_equality(lin
);
987 isl_int_set_si(lin
->eq
[k
][0], 0);
988 isl_seq_neg(lin
->eq
[k
] + 1, bset2
->eq
[i
] + 1, dim
);
990 for (i
= 0; i
< bset2
->n_ineq
; ++i
) {
991 k
= isl_basic_set_alloc_inequality(lin
);
994 isl_int_set_si(lin
->ineq
[k
][0], 0);
995 isl_seq_neg(lin
->ineq
[k
] + 1, bset2
->ineq
[i
] + 1, dim
);
998 isl_basic_set_free(bset1
);
999 isl_basic_set_free(bset2
);
1000 return isl_basic_set_affine_hull(lin
);
1002 isl_basic_set_free(lin
);
1003 isl_basic_set_free(bset1
);
1004 isl_basic_set_free(bset2
);
1008 static struct isl_basic_set
*uset_convex_hull(struct isl_set
*set
);
1010 /* Given a set and a linear space "lin" of dimension n > 0,
1011 * project the linear space from the set, compute the convex hull
1012 * and then map the set back to the original space.
1018 * describe the linear space. We first compute the Hermite normal
1019 * form H = M U of M = H Q, to obtain
1023 * The last n rows of H will be zero, so the last n variables of x' = Q x
1024 * are the one we want to project out. We do this by transforming each
1025 * basic set A x >= b to A U x' >= b and then removing the last n dimensions.
1026 * After computing the convex hull in x'_1, i.e., A' x'_1 >= b',
1027 * we transform the hull back to the original space as A' Q_1 x >= b',
1028 * with Q_1 all but the last n rows of Q.
1030 static struct isl_basic_set
*modulo_lineality(struct isl_set
*set
,
1031 struct isl_basic_set
*lin
)
1033 unsigned total
= isl_basic_set_total_dim(lin
);
1035 struct isl_basic_set
*hull
;
1036 struct isl_mat
*M
, *U
, *Q
;
1040 lin_dim
= total
- lin
->n_eq
;
1041 M
= isl_mat_sub_alloc(set
->ctx
, lin
->eq
, 0, lin
->n_eq
, 1, total
);
1042 M
= isl_mat_left_hermite(M
, 0, &U
, &Q
);
1046 isl_basic_set_free(lin
);
1048 Q
= isl_mat_drop_rows(Q
, Q
->n_row
- lin_dim
, lin_dim
);
1050 U
= isl_mat_lin_to_aff(U
);
1051 Q
= isl_mat_lin_to_aff(Q
);
1053 set
= isl_set_preimage(set
, U
);
1054 set
= isl_set_remove_dims(set
, isl_dim_set
, total
- lin_dim
, lin_dim
);
1055 hull
= uset_convex_hull(set
);
1056 hull
= isl_basic_set_preimage(hull
, Q
);
1060 isl_basic_set_free(lin
);
1065 /* Given two polyhedra with as constraints h_{ij} x >= 0 in homegeneous space,
1066 * set up an LP for solving
1068 * \sum_j \alpha_{1j} h_{1j} = \sum_j \alpha_{2j} h_{2j}
1070 * \alpha{i0} corresponds to the (implicit) positivity constraint 1 >= 0
1071 * The next \alpha{ij} correspond to the equalities and come in pairs.
1072 * The final \alpha{ij} correspond to the inequalities.
1074 static struct isl_basic_set
*valid_direction_lp(
1075 struct isl_basic_set
*bset1
, struct isl_basic_set
*bset2
)
1077 struct isl_dim
*dim
;
1078 struct isl_basic_set
*lp
;
1083 if (!bset1
|| !bset2
)
1085 d
= 1 + isl_basic_set_total_dim(bset1
);
1087 2 * bset1
->n_eq
+ bset1
->n_ineq
+ 2 * bset2
->n_eq
+ bset2
->n_ineq
;
1088 dim
= isl_dim_set_alloc(bset1
->ctx
, 0, n
);
1089 lp
= isl_basic_set_alloc_dim(dim
, 0, d
, n
);
1092 for (i
= 0; i
< n
; ++i
) {
1093 k
= isl_basic_set_alloc_inequality(lp
);
1096 isl_seq_clr(lp
->ineq
[k
] + 1, n
);
1097 isl_int_set_si(lp
->ineq
[k
][0], -1);
1098 isl_int_set_si(lp
->ineq
[k
][1 + i
], 1);
1100 for (i
= 0; i
< d
; ++i
) {
1101 k
= isl_basic_set_alloc_equality(lp
);
1105 isl_int_set_si(lp
->eq
[k
][n
], 0); n
++;
1106 /* positivity constraint 1 >= 0 */
1107 isl_int_set_si(lp
->eq
[k
][n
], i
== 0); n
++;
1108 for (j
= 0; j
< bset1
->n_eq
; ++j
) {
1109 isl_int_set(lp
->eq
[k
][n
], bset1
->eq
[j
][i
]); n
++;
1110 isl_int_neg(lp
->eq
[k
][n
], bset1
->eq
[j
][i
]); n
++;
1112 for (j
= 0; j
< bset1
->n_ineq
; ++j
) {
1113 isl_int_set(lp
->eq
[k
][n
], bset1
->ineq
[j
][i
]); n
++;
1115 /* positivity constraint 1 >= 0 */
1116 isl_int_set_si(lp
->eq
[k
][n
], -(i
== 0)); n
++;
1117 for (j
= 0; j
< bset2
->n_eq
; ++j
) {
1118 isl_int_neg(lp
->eq
[k
][n
], bset2
->eq
[j
][i
]); n
++;
1119 isl_int_set(lp
->eq
[k
][n
], bset2
->eq
[j
][i
]); n
++;
1121 for (j
= 0; j
< bset2
->n_ineq
; ++j
) {
1122 isl_int_neg(lp
->eq
[k
][n
], bset2
->ineq
[j
][i
]); n
++;
1125 lp
= isl_basic_set_gauss(lp
, NULL
);
1126 isl_basic_set_free(bset1
);
1127 isl_basic_set_free(bset2
);
1130 isl_basic_set_free(bset1
);
1131 isl_basic_set_free(bset2
);
1135 /* Compute a vector s in the homogeneous space such that <s, r> > 0
1136 * for all rays in the homogeneous space of the two cones that correspond
1137 * to the input polyhedra bset1 and bset2.
1139 * We compute s as a vector that satisfies
1141 * s = \sum_j \alpha_{ij} h_{ij} for i = 1,2 (*)
1143 * with h_{ij} the normals of the facets of polyhedron i
1144 * (including the "positivity constraint" 1 >= 0) and \alpha_{ij}
1145 * strictly positive numbers. For simplicity we impose \alpha_{ij} >= 1.
1146 * We first set up an LP with as variables the \alpha{ij}.
1147 * In this formulation, for each polyhedron i,
1148 * the first constraint is the positivity constraint, followed by pairs
1149 * of variables for the equalities, followed by variables for the inequalities.
1150 * We then simply pick a feasible solution and compute s using (*).
1152 * Note that we simply pick any valid direction and make no attempt
1153 * to pick a "good" or even the "best" valid direction.
1155 static struct isl_vec
*valid_direction(
1156 struct isl_basic_set
*bset1
, struct isl_basic_set
*bset2
)
1158 struct isl_basic_set
*lp
;
1159 struct isl_tab
*tab
;
1160 struct isl_vec
*sample
= NULL
;
1161 struct isl_vec
*dir
;
1166 if (!bset1
|| !bset2
)
1168 lp
= valid_direction_lp(isl_basic_set_copy(bset1
),
1169 isl_basic_set_copy(bset2
));
1170 tab
= isl_tab_from_basic_set(lp
);
1171 sample
= isl_tab_get_sample_value(tab
);
1173 isl_basic_set_free(lp
);
1176 d
= isl_basic_set_total_dim(bset1
);
1177 dir
= isl_vec_alloc(bset1
->ctx
, 1 + d
);
1180 isl_seq_clr(dir
->block
.data
+ 1, dir
->size
- 1);
1182 /* positivity constraint 1 >= 0 */
1183 isl_int_set(dir
->block
.data
[0], sample
->block
.data
[n
]); n
++;
1184 for (i
= 0; i
< bset1
->n_eq
; ++i
) {
1185 isl_int_sub(sample
->block
.data
[n
],
1186 sample
->block
.data
[n
], sample
->block
.data
[n
+1]);
1187 isl_seq_combine(dir
->block
.data
,
1188 bset1
->ctx
->one
, dir
->block
.data
,
1189 sample
->block
.data
[n
], bset1
->eq
[i
], 1 + d
);
1193 for (i
= 0; i
< bset1
->n_ineq
; ++i
)
1194 isl_seq_combine(dir
->block
.data
,
1195 bset1
->ctx
->one
, dir
->block
.data
,
1196 sample
->block
.data
[n
++], bset1
->ineq
[i
], 1 + d
);
1197 isl_vec_free(sample
);
1198 isl_seq_normalize(bset1
->ctx
, dir
->el
, dir
->size
);
1199 isl_basic_set_free(bset1
);
1200 isl_basic_set_free(bset2
);
1203 isl_vec_free(sample
);
1204 isl_basic_set_free(bset1
);
1205 isl_basic_set_free(bset2
);
1209 /* Given a polyhedron b_i + A_i x >= 0 and a map T = S^{-1},
1210 * compute b_i' + A_i' x' >= 0, with
1212 * [ b_i A_i ] [ y' ] [ y' ]
1213 * [ 1 0 ] S^{-1} [ x' ] >= 0 or [ b_i' A_i' ] [ x' ] >= 0
1215 * In particular, add the "positivity constraint" and then perform
1218 static struct isl_basic_set
*homogeneous_map(struct isl_basic_set
*bset
,
1225 bset
= isl_basic_set_extend_constraints(bset
, 0, 1);
1226 k
= isl_basic_set_alloc_inequality(bset
);
1229 isl_seq_clr(bset
->ineq
[k
] + 1, isl_basic_set_total_dim(bset
));
1230 isl_int_set_si(bset
->ineq
[k
][0], 1);
1231 bset
= isl_basic_set_preimage(bset
, T
);
1235 isl_basic_set_free(bset
);
1239 /* Compute the convex hull of a pair of basic sets without any parameters or
1240 * integer divisions, where the convex hull is known to be pointed,
1241 * but the basic sets may be unbounded.
1243 * We turn this problem into the computation of a convex hull of a pair
1244 * _bounded_ polyhedra by "changing the direction of the homogeneous
1245 * dimension". This idea is due to Matthias Koeppe.
1247 * Consider the cones in homogeneous space that correspond to the
1248 * input polyhedra. The rays of these cones are also rays of the
1249 * polyhedra if the coordinate that corresponds to the homogeneous
1250 * dimension is zero. That is, if the inner product of the rays
1251 * with the homogeneous direction is zero.
1252 * The cones in the homogeneous space can also be considered to
1253 * correspond to other pairs of polyhedra by chosing a different
1254 * homogeneous direction. To ensure that both of these polyhedra
1255 * are bounded, we need to make sure that all rays of the cones
1256 * correspond to vertices and not to rays.
1257 * Let s be a direction such that <s, r> > 0 for all rays r of both cones.
1258 * Then using s as a homogeneous direction, we obtain a pair of polytopes.
1259 * The vector s is computed in valid_direction.
1261 * Note that we need to consider _all_ rays of the cones and not just
1262 * the rays that correspond to rays in the polyhedra. If we were to
1263 * only consider those rays and turn them into vertices, then we
1264 * may inadvertently turn some vertices into rays.
1266 * The standard homogeneous direction is the unit vector in the 0th coordinate.
1267 * We therefore transform the two polyhedra such that the selected
1268 * direction is mapped onto this standard direction and then proceed
1269 * with the normal computation.
1270 * Let S be a non-singular square matrix with s as its first row,
1271 * then we want to map the polyhedra to the space
1273 * [ y' ] [ y ] [ y ] [ y' ]
1274 * [ x' ] = S [ x ] i.e., [ x ] = S^{-1} [ x' ]
1276 * We take S to be the unimodular completion of s to limit the growth
1277 * of the coefficients in the following computations.
1279 * Let b_i + A_i x >= 0 be the constraints of polyhedron i.
1280 * We first move to the homogeneous dimension
1282 * b_i y + A_i x >= 0 [ b_i A_i ] [ y ] [ 0 ]
1283 * y >= 0 or [ 1 0 ] [ x ] >= [ 0 ]
1285 * Then we change directoin
1287 * [ b_i A_i ] [ y' ] [ y' ]
1288 * [ 1 0 ] S^{-1} [ x' ] >= 0 or [ b_i' A_i' ] [ x' ] >= 0
1290 * Then we compute the convex hull of the polytopes b_i' + A_i' x' >= 0
1291 * resulting in b' + A' x' >= 0, which we then convert back
1294 * [ b' A' ] S [ x ] >= 0 or [ b A ] [ x ] >= 0
1296 * The polyhedron b + A x >= 0 is then the convex hull of the input polyhedra.
1298 static struct isl_basic_set
*convex_hull_pair_pointed(
1299 struct isl_basic_set
*bset1
, struct isl_basic_set
*bset2
)
1301 struct isl_ctx
*ctx
= NULL
;
1302 struct isl_vec
*dir
= NULL
;
1303 struct isl_mat
*T
= NULL
;
1304 struct isl_mat
*T2
= NULL
;
1305 struct isl_basic_set
*hull
;
1306 struct isl_set
*set
;
1308 if (!bset1
|| !bset2
)
1311 dir
= valid_direction(isl_basic_set_copy(bset1
),
1312 isl_basic_set_copy(bset2
));
1315 T
= isl_mat_alloc(bset1
->ctx
, dir
->size
, dir
->size
);
1318 isl_seq_cpy(T
->row
[0], dir
->block
.data
, dir
->size
);
1319 T
= isl_mat_unimodular_complete(T
, 1);
1320 T2
= isl_mat_right_inverse(isl_mat_copy(T
));
1322 bset1
= homogeneous_map(bset1
, isl_mat_copy(T2
));
1323 bset2
= homogeneous_map(bset2
, T2
);
1324 set
= isl_set_alloc_dim(isl_basic_set_get_dim(bset1
), 2, 0);
1325 set
= isl_set_add_basic_set(set
, bset1
);
1326 set
= isl_set_add_basic_set(set
, bset2
);
1327 hull
= uset_convex_hull(set
);
1328 hull
= isl_basic_set_preimage(hull
, T
);
1335 isl_basic_set_free(bset1
);
1336 isl_basic_set_free(bset2
);
1340 static struct isl_basic_set
*uset_convex_hull_wrap(struct isl_set
*set
);
1341 static struct isl_basic_set
*modulo_affine_hull(
1342 struct isl_set
*set
, struct isl_basic_set
*affine_hull
);
1344 /* Compute the convex hull of a pair of basic sets without any parameters or
1345 * integer divisions.
1347 * This function is called from uset_convex_hull_unbounded, which
1348 * means that the complete convex hull is unbounded. Some pairs
1349 * of basic sets may still be bounded, though.
1350 * They may even lie inside a lower dimensional space, in which
1351 * case they need to be handled inside their affine hull since
1352 * the main algorithm assumes that the result is full-dimensional.
1354 * If the convex hull of the two basic sets would have a non-trivial
1355 * lineality space, we first project out this lineality space.
1357 static struct isl_basic_set
*convex_hull_pair(struct isl_basic_set
*bset1
,
1358 struct isl_basic_set
*bset2
)
1360 isl_basic_set
*lin
, *aff
;
1361 int bounded1
, bounded2
;
1363 if (bset1
->ctx
->opt
->convex
== ISL_CONVEX_HULL_FM
)
1364 return convex_hull_pair_elim(bset1
, bset2
);
1366 aff
= isl_set_affine_hull(isl_basic_set_union(isl_basic_set_copy(bset1
),
1367 isl_basic_set_copy(bset2
)));
1371 return modulo_affine_hull(isl_basic_set_union(bset1
, bset2
), aff
);
1372 isl_basic_set_free(aff
);
1374 bounded1
= isl_basic_set_is_bounded(bset1
);
1375 bounded2
= isl_basic_set_is_bounded(bset2
);
1377 if (bounded1
< 0 || bounded2
< 0)
1380 if (bounded1
&& bounded2
)
1381 uset_convex_hull_wrap(isl_basic_set_union(bset1
, bset2
));
1383 if (bounded1
|| bounded2
)
1384 return convex_hull_pair_pointed(bset1
, bset2
);
1386 lin
= induced_lineality_space(isl_basic_set_copy(bset1
),
1387 isl_basic_set_copy(bset2
));
1390 if (isl_basic_set_is_universe(lin
)) {
1391 isl_basic_set_free(bset1
);
1392 isl_basic_set_free(bset2
);
1395 if (lin
->n_eq
< isl_basic_set_total_dim(lin
)) {
1396 struct isl_set
*set
;
1397 set
= isl_set_alloc_dim(isl_basic_set_get_dim(bset1
), 2, 0);
1398 set
= isl_set_add_basic_set(set
, bset1
);
1399 set
= isl_set_add_basic_set(set
, bset2
);
1400 return modulo_lineality(set
, lin
);
1402 isl_basic_set_free(lin
);
1404 return convex_hull_pair_pointed(bset1
, bset2
);
1406 isl_basic_set_free(bset1
);
1407 isl_basic_set_free(bset2
);
1411 /* Compute the lineality space of a basic set.
1412 * We currently do not allow the basic set to have any divs.
1413 * We basically just drop the constants and turn every inequality
1416 struct isl_basic_set
*isl_basic_set_lineality_space(struct isl_basic_set
*bset
)
1419 struct isl_basic_set
*lin
= NULL
;
1424 isl_assert(bset
->ctx
, bset
->n_div
== 0, goto error
);
1425 dim
= isl_basic_set_total_dim(bset
);
1427 lin
= isl_basic_set_alloc_dim(isl_basic_set_get_dim(bset
), 0, dim
, 0);
1430 for (i
= 0; i
< bset
->n_eq
; ++i
) {
1431 k
= isl_basic_set_alloc_equality(lin
);
1434 isl_int_set_si(lin
->eq
[k
][0], 0);
1435 isl_seq_cpy(lin
->eq
[k
] + 1, bset
->eq
[i
] + 1, dim
);
1437 lin
= isl_basic_set_gauss(lin
, NULL
);
1440 for (i
= 0; i
< bset
->n_ineq
&& lin
->n_eq
< dim
; ++i
) {
1441 k
= isl_basic_set_alloc_equality(lin
);
1444 isl_int_set_si(lin
->eq
[k
][0], 0);
1445 isl_seq_cpy(lin
->eq
[k
] + 1, bset
->ineq
[i
] + 1, dim
);
1446 lin
= isl_basic_set_gauss(lin
, NULL
);
1450 isl_basic_set_free(bset
);
1453 isl_basic_set_free(lin
);
1454 isl_basic_set_free(bset
);
1458 /* Compute the (linear) hull of the lineality spaces of the basic sets in the
1459 * "underlying" set "set".
1461 static struct isl_basic_set
*uset_combined_lineality_space(struct isl_set
*set
)
1464 struct isl_set
*lin
= NULL
;
1469 struct isl_dim
*dim
= isl_set_get_dim(set
);
1471 return isl_basic_set_empty(dim
);
1474 lin
= isl_set_alloc_dim(isl_set_get_dim(set
), set
->n
, 0);
1475 for (i
= 0; i
< set
->n
; ++i
)
1476 lin
= isl_set_add_basic_set(lin
,
1477 isl_basic_set_lineality_space(isl_basic_set_copy(set
->p
[i
])));
1479 return isl_set_affine_hull(lin
);
1482 /* Compute the convex hull of a set without any parameters or
1483 * integer divisions.
1484 * In each step, we combined two basic sets until only one
1485 * basic set is left.
1486 * The input basic sets are assumed not to have a non-trivial
1487 * lineality space. If any of the intermediate results has
1488 * a non-trivial lineality space, it is projected out.
1490 static struct isl_basic_set
*uset_convex_hull_unbounded(struct isl_set
*set
)
1492 struct isl_basic_set
*convex_hull
= NULL
;
1494 convex_hull
= isl_set_copy_basic_set(set
);
1495 set
= isl_set_drop_basic_set(set
, convex_hull
);
1498 while (set
->n
> 0) {
1499 struct isl_basic_set
*t
;
1500 t
= isl_set_copy_basic_set(set
);
1503 set
= isl_set_drop_basic_set(set
, t
);
1506 convex_hull
= convex_hull_pair(convex_hull
, t
);
1509 t
= isl_basic_set_lineality_space(isl_basic_set_copy(convex_hull
));
1512 if (isl_basic_set_is_universe(t
)) {
1513 isl_basic_set_free(convex_hull
);
1517 if (t
->n_eq
< isl_basic_set_total_dim(t
)) {
1518 set
= isl_set_add_basic_set(set
, convex_hull
);
1519 return modulo_lineality(set
, t
);
1521 isl_basic_set_free(t
);
1527 isl_basic_set_free(convex_hull
);
1531 /* Compute an initial hull for wrapping containing a single initial
1533 * This function assumes that the given set is bounded.
1535 static struct isl_basic_set
*initial_hull(struct isl_basic_set
*hull
,
1536 struct isl_set
*set
)
1538 struct isl_mat
*bounds
= NULL
;
1544 bounds
= initial_facet_constraint(set
);
1547 k
= isl_basic_set_alloc_inequality(hull
);
1550 dim
= isl_set_n_dim(set
);
1551 isl_assert(set
->ctx
, 1 + dim
== bounds
->n_col
, goto error
);
1552 isl_seq_cpy(hull
->ineq
[k
], bounds
->row
[0], bounds
->n_col
);
1553 isl_mat_free(bounds
);
1557 isl_basic_set_free(hull
);
1558 isl_mat_free(bounds
);
1562 struct max_constraint
{
1568 static int max_constraint_equal(const void *entry
, const void *val
)
1570 struct max_constraint
*a
= (struct max_constraint
*)entry
;
1571 isl_int
*b
= (isl_int
*)val
;
1573 return isl_seq_eq(a
->c
->row
[0] + 1, b
, a
->c
->n_col
- 1);
1576 static void update_constraint(struct isl_ctx
*ctx
, struct isl_hash_table
*table
,
1577 isl_int
*con
, unsigned len
, int n
, int ineq
)
1579 struct isl_hash_table_entry
*entry
;
1580 struct max_constraint
*c
;
1583 c_hash
= isl_seq_get_hash(con
+ 1, len
);
1584 entry
= isl_hash_table_find(ctx
, table
, c_hash
, max_constraint_equal
,
1590 isl_hash_table_remove(ctx
, table
, entry
);
1594 if (isl_int_gt(c
->c
->row
[0][0], con
[0]))
1596 if (isl_int_eq(c
->c
->row
[0][0], con
[0])) {
1601 c
->c
= isl_mat_cow(c
->c
);
1602 isl_int_set(c
->c
->row
[0][0], con
[0]);
1606 /* Check whether the constraint hash table "table" constains the constraint
1609 static int has_constraint(struct isl_ctx
*ctx
, struct isl_hash_table
*table
,
1610 isl_int
*con
, unsigned len
, int n
)
1612 struct isl_hash_table_entry
*entry
;
1613 struct max_constraint
*c
;
1616 c_hash
= isl_seq_get_hash(con
+ 1, len
);
1617 entry
= isl_hash_table_find(ctx
, table
, c_hash
, max_constraint_equal
,
1624 return isl_int_eq(c
->c
->row
[0][0], con
[0]);
1627 /* Check for inequality constraints of a basic set without equalities
1628 * such that the same or more stringent copies of the constraint appear
1629 * in all of the basic sets. Such constraints are necessarily facet
1630 * constraints of the convex hull.
1632 * If the resulting basic set is by chance identical to one of
1633 * the basic sets in "set", then we know that this basic set contains
1634 * all other basic sets and is therefore the convex hull of set.
1635 * In this case we set *is_hull to 1.
1637 static struct isl_basic_set
*common_constraints(struct isl_basic_set
*hull
,
1638 struct isl_set
*set
, int *is_hull
)
1641 int min_constraints
;
1643 struct max_constraint
*constraints
= NULL
;
1644 struct isl_hash_table
*table
= NULL
;
1649 for (i
= 0; i
< set
->n
; ++i
)
1650 if (set
->p
[i
]->n_eq
== 0)
1654 min_constraints
= set
->p
[i
]->n_ineq
;
1656 for (i
= best
+ 1; i
< set
->n
; ++i
) {
1657 if (set
->p
[i
]->n_eq
!= 0)
1659 if (set
->p
[i
]->n_ineq
>= min_constraints
)
1661 min_constraints
= set
->p
[i
]->n_ineq
;
1664 constraints
= isl_calloc_array(hull
->ctx
, struct max_constraint
,
1668 table
= isl_alloc_type(hull
->ctx
, struct isl_hash_table
);
1669 if (isl_hash_table_init(hull
->ctx
, table
, min_constraints
))
1672 total
= isl_dim_total(set
->dim
);
1673 for (i
= 0; i
< set
->p
[best
]->n_ineq
; ++i
) {
1674 constraints
[i
].c
= isl_mat_sub_alloc(hull
->ctx
,
1675 set
->p
[best
]->ineq
+ i
, 0, 1, 0, 1 + total
);
1676 if (!constraints
[i
].c
)
1678 constraints
[i
].ineq
= 1;
1680 for (i
= 0; i
< min_constraints
; ++i
) {
1681 struct isl_hash_table_entry
*entry
;
1683 c_hash
= isl_seq_get_hash(constraints
[i
].c
->row
[0] + 1, total
);
1684 entry
= isl_hash_table_find(hull
->ctx
, table
, c_hash
,
1685 max_constraint_equal
, constraints
[i
].c
->row
[0] + 1, 1);
1688 isl_assert(hull
->ctx
, !entry
->data
, goto error
);
1689 entry
->data
= &constraints
[i
];
1693 for (s
= 0; s
< set
->n
; ++s
) {
1697 for (i
= 0; i
< set
->p
[s
]->n_eq
; ++i
) {
1698 isl_int
*eq
= set
->p
[s
]->eq
[i
];
1699 for (j
= 0; j
< 2; ++j
) {
1700 isl_seq_neg(eq
, eq
, 1 + total
);
1701 update_constraint(hull
->ctx
, table
,
1705 for (i
= 0; i
< set
->p
[s
]->n_ineq
; ++i
) {
1706 isl_int
*ineq
= set
->p
[s
]->ineq
[i
];
1707 update_constraint(hull
->ctx
, table
, ineq
, total
, n
,
1708 set
->p
[s
]->n_eq
== 0);
1713 for (i
= 0; i
< min_constraints
; ++i
) {
1714 if (constraints
[i
].count
< n
)
1716 if (!constraints
[i
].ineq
)
1718 j
= isl_basic_set_alloc_inequality(hull
);
1721 isl_seq_cpy(hull
->ineq
[j
], constraints
[i
].c
->row
[0], 1 + total
);
1724 for (s
= 0; s
< set
->n
; ++s
) {
1725 if (set
->p
[s
]->n_eq
)
1727 if (set
->p
[s
]->n_ineq
!= hull
->n_ineq
)
1729 for (i
= 0; i
< set
->p
[s
]->n_ineq
; ++i
) {
1730 isl_int
*ineq
= set
->p
[s
]->ineq
[i
];
1731 if (!has_constraint(hull
->ctx
, table
, ineq
, total
, n
))
1734 if (i
== set
->p
[s
]->n_ineq
)
1738 isl_hash_table_clear(table
);
1739 for (i
= 0; i
< min_constraints
; ++i
)
1740 isl_mat_free(constraints
[i
].c
);
1745 isl_hash_table_clear(table
);
1748 for (i
= 0; i
< min_constraints
; ++i
)
1749 isl_mat_free(constraints
[i
].c
);
1754 /* Create a template for the convex hull of "set" and fill it up
1755 * obvious facet constraints, if any. If the result happens to
1756 * be the convex hull of "set" then *is_hull is set to 1.
1758 static struct isl_basic_set
*proto_hull(struct isl_set
*set
, int *is_hull
)
1760 struct isl_basic_set
*hull
;
1765 for (i
= 0; i
< set
->n
; ++i
) {
1766 n_ineq
+= set
->p
[i
]->n_eq
;
1767 n_ineq
+= set
->p
[i
]->n_ineq
;
1769 hull
= isl_basic_set_alloc_dim(isl_dim_copy(set
->dim
), 0, 0, n_ineq
);
1770 hull
= isl_basic_set_set_rational(hull
);
1773 return common_constraints(hull
, set
, is_hull
);
1776 static struct isl_basic_set
*uset_convex_hull_wrap(struct isl_set
*set
)
1778 struct isl_basic_set
*hull
;
1781 hull
= proto_hull(set
, &is_hull
);
1782 if (hull
&& !is_hull
) {
1783 if (hull
->n_ineq
== 0)
1784 hull
= initial_hull(hull
, set
);
1785 hull
= extend(hull
, set
);
1792 /* Compute the convex hull of a set without any parameters or
1793 * integer divisions. Depending on whether the set is bounded,
1794 * we pass control to the wrapping based convex hull or
1795 * the Fourier-Motzkin elimination based convex hull.
1796 * We also handle a few special cases before checking the boundedness.
1798 static struct isl_basic_set
*uset_convex_hull(struct isl_set
*set
)
1800 struct isl_basic_set
*convex_hull
= NULL
;
1801 struct isl_basic_set
*lin
;
1803 if (isl_set_n_dim(set
) == 0)
1804 return convex_hull_0d(set
);
1806 set
= isl_set_coalesce(set
);
1807 set
= isl_set_set_rational(set
);
1814 convex_hull
= isl_basic_set_copy(set
->p
[0]);
1818 if (isl_set_n_dim(set
) == 1)
1819 return convex_hull_1d(set
);
1821 if (isl_set_is_bounded(set
) &&
1822 set
->ctx
->opt
->convex
== ISL_CONVEX_HULL_WRAP
)
1823 return uset_convex_hull_wrap(set
);
1825 lin
= uset_combined_lineality_space(isl_set_copy(set
));
1828 if (isl_basic_set_is_universe(lin
)) {
1832 if (lin
->n_eq
< isl_basic_set_total_dim(lin
))
1833 return modulo_lineality(set
, lin
);
1834 isl_basic_set_free(lin
);
1836 return uset_convex_hull_unbounded(set
);
1839 isl_basic_set_free(convex_hull
);
1843 /* This is the core procedure, where "set" is a "pure" set, i.e.,
1844 * without parameters or divs and where the convex hull of set is
1845 * known to be full-dimensional.
1847 static struct isl_basic_set
*uset_convex_hull_wrap_bounded(struct isl_set
*set
)
1849 struct isl_basic_set
*convex_hull
= NULL
;
1854 if (isl_set_n_dim(set
) == 0) {
1855 convex_hull
= isl_basic_set_universe(isl_dim_copy(set
->dim
));
1857 convex_hull
= isl_basic_set_set_rational(convex_hull
);
1861 set
= isl_set_set_rational(set
);
1862 set
= isl_set_coalesce(set
);
1866 convex_hull
= isl_basic_set_copy(set
->p
[0]);
1870 if (isl_set_n_dim(set
) == 1)
1871 return convex_hull_1d(set
);
1873 return uset_convex_hull_wrap(set
);
1879 /* Compute the convex hull of set "set" with affine hull "affine_hull",
1880 * We first remove the equalities (transforming the set), compute the
1881 * convex hull of the transformed set and then add the equalities back
1882 * (after performing the inverse transformation.
1884 static struct isl_basic_set
*modulo_affine_hull(
1885 struct isl_set
*set
, struct isl_basic_set
*affine_hull
)
1889 struct isl_basic_set
*dummy
;
1890 struct isl_basic_set
*convex_hull
;
1892 dummy
= isl_basic_set_remove_equalities(
1893 isl_basic_set_copy(affine_hull
), &T
, &T2
);
1896 isl_basic_set_free(dummy
);
1897 set
= isl_set_preimage(set
, T
);
1898 convex_hull
= uset_convex_hull(set
);
1899 convex_hull
= isl_basic_set_preimage(convex_hull
, T2
);
1900 convex_hull
= isl_basic_set_intersect(convex_hull
, affine_hull
);
1903 isl_basic_set_free(affine_hull
);
1908 /* Compute the convex hull of a map.
1910 * The implementation was inspired by "Extended Convex Hull" by Fukuda et al.,
1911 * specifically, the wrapping of facets to obtain new facets.
1913 struct isl_basic_map
*isl_map_convex_hull(struct isl_map
*map
)
1915 struct isl_basic_set
*bset
;
1916 struct isl_basic_map
*model
= NULL
;
1917 struct isl_basic_set
*affine_hull
= NULL
;
1918 struct isl_basic_map
*convex_hull
= NULL
;
1919 struct isl_set
*set
= NULL
;
1920 struct isl_ctx
*ctx
;
1927 convex_hull
= isl_basic_map_empty_like_map(map
);
1932 map
= isl_map_detect_equalities(map
);
1933 map
= isl_map_align_divs(map
);
1936 model
= isl_basic_map_copy(map
->p
[0]);
1937 set
= isl_map_underlying_set(map
);
1941 affine_hull
= isl_set_affine_hull(isl_set_copy(set
));
1944 if (affine_hull
->n_eq
!= 0)
1945 bset
= modulo_affine_hull(set
, affine_hull
);
1947 isl_basic_set_free(affine_hull
);
1948 bset
= uset_convex_hull(set
);
1951 convex_hull
= isl_basic_map_overlying_set(bset
, model
);
1955 ISL_F_SET(convex_hull
, ISL_BASIC_MAP_NO_IMPLICIT
);
1956 ISL_F_SET(convex_hull
, ISL_BASIC_MAP_ALL_EQUALITIES
);
1957 ISL_F_CLR(convex_hull
, ISL_BASIC_MAP_RATIONAL
);
1961 isl_basic_map_free(model
);
1965 struct isl_basic_set
*isl_set_convex_hull(struct isl_set
*set
)
1967 return (struct isl_basic_set
*)
1968 isl_map_convex_hull((struct isl_map
*)set
);
1971 __isl_give isl_basic_map
*isl_map_polyhedral_hull(__isl_take isl_map
*map
)
1973 isl_basic_map
*hull
;
1975 hull
= isl_map_convex_hull(map
);
1976 return isl_basic_map_remove_divs(hull
);
1979 __isl_give isl_basic_set
*isl_set_polyhedral_hull(__isl_take isl_set
*set
)
1981 return (isl_basic_set
*)isl_map_polyhedral_hull((isl_map
*)set
);
1984 struct sh_data_entry
{
1985 struct isl_hash_table
*table
;
1986 struct isl_tab
*tab
;
1989 /* Holds the data needed during the simple hull computation.
1991 * n the number of basic sets in the original set
1992 * hull_table a hash table of already computed constraints
1993 * in the simple hull
1994 * p for each basic set,
1995 * table a hash table of the constraints
1996 * tab the tableau corresponding to the basic set
1999 struct isl_ctx
*ctx
;
2001 struct isl_hash_table
*hull_table
;
2002 struct sh_data_entry p
[1];
2005 static void sh_data_free(struct sh_data
*data
)
2011 isl_hash_table_free(data
->ctx
, data
->hull_table
);
2012 for (i
= 0; i
< data
->n
; ++i
) {
2013 isl_hash_table_free(data
->ctx
, data
->p
[i
].table
);
2014 isl_tab_free(data
->p
[i
].tab
);
2019 struct ineq_cmp_data
{
2024 static int has_ineq(const void *entry
, const void *val
)
2026 isl_int
*row
= (isl_int
*)entry
;
2027 struct ineq_cmp_data
*v
= (struct ineq_cmp_data
*)val
;
2029 return isl_seq_eq(row
+ 1, v
->p
+ 1, v
->len
) ||
2030 isl_seq_is_neg(row
+ 1, v
->p
+ 1, v
->len
);
2033 static int hash_ineq(struct isl_ctx
*ctx
, struct isl_hash_table
*table
,
2034 isl_int
*ineq
, unsigned len
)
2037 struct ineq_cmp_data v
;
2038 struct isl_hash_table_entry
*entry
;
2042 c_hash
= isl_seq_get_hash(ineq
+ 1, len
);
2043 entry
= isl_hash_table_find(ctx
, table
, c_hash
, has_ineq
, &v
, 1);
2050 /* Fill hash table "table" with the constraints of "bset".
2051 * Equalities are added as two inequalities.
2052 * The value in the hash table is a pointer to the (in)equality of "bset".
2054 static int hash_basic_set(struct isl_hash_table
*table
,
2055 struct isl_basic_set
*bset
)
2058 unsigned dim
= isl_basic_set_total_dim(bset
);
2060 for (i
= 0; i
< bset
->n_eq
; ++i
) {
2061 for (j
= 0; j
< 2; ++j
) {
2062 isl_seq_neg(bset
->eq
[i
], bset
->eq
[i
], 1 + dim
);
2063 if (hash_ineq(bset
->ctx
, table
, bset
->eq
[i
], dim
) < 0)
2067 for (i
= 0; i
< bset
->n_ineq
; ++i
) {
2068 if (hash_ineq(bset
->ctx
, table
, bset
->ineq
[i
], dim
) < 0)
2074 static struct sh_data
*sh_data_alloc(struct isl_set
*set
, unsigned n_ineq
)
2076 struct sh_data
*data
;
2079 data
= isl_calloc(set
->ctx
, struct sh_data
,
2080 sizeof(struct sh_data
) +
2081 (set
->n
- 1) * sizeof(struct sh_data_entry
));
2084 data
->ctx
= set
->ctx
;
2086 data
->hull_table
= isl_hash_table_alloc(set
->ctx
, n_ineq
);
2087 if (!data
->hull_table
)
2089 for (i
= 0; i
< set
->n
; ++i
) {
2090 data
->p
[i
].table
= isl_hash_table_alloc(set
->ctx
,
2091 2 * set
->p
[i
]->n_eq
+ set
->p
[i
]->n_ineq
);
2092 if (!data
->p
[i
].table
)
2094 if (hash_basic_set(data
->p
[i
].table
, set
->p
[i
]) < 0)
2103 /* Check if inequality "ineq" is a bound for basic set "j" or if
2104 * it can be relaxed (by increasing the constant term) to become
2105 * a bound for that basic set. In the latter case, the constant
2107 * Return 1 if "ineq" is a bound
2108 * 0 if "ineq" may attain arbitrarily small values on basic set "j"
2109 * -1 if some error occurred
2111 static int is_bound(struct sh_data
*data
, struct isl_set
*set
, int j
,
2114 enum isl_lp_result res
;
2117 if (!data
->p
[j
].tab
) {
2118 data
->p
[j
].tab
= isl_tab_from_basic_set(set
->p
[j
]);
2119 if (!data
->p
[j
].tab
)
2125 res
= isl_tab_min(data
->p
[j
].tab
, ineq
, data
->ctx
->one
,
2127 if (res
== isl_lp_ok
&& isl_int_is_neg(opt
))
2128 isl_int_sub(ineq
[0], ineq
[0], opt
);
2132 return (res
== isl_lp_ok
|| res
== isl_lp_empty
) ? 1 :
2133 res
== isl_lp_unbounded
? 0 : -1;
2136 /* Check if inequality "ineq" from basic set "i" can be relaxed to
2137 * become a bound on the whole set. If so, add the (relaxed) inequality
2140 * We first check if "hull" already contains a translate of the inequality.
2141 * If so, we are done.
2142 * Then, we check if any of the previous basic sets contains a translate
2143 * of the inequality. If so, then we have already considered this
2144 * inequality and we are done.
2145 * Otherwise, for each basic set other than "i", we check if the inequality
2146 * is a bound on the basic set.
2147 * For previous basic sets, we know that they do not contain a translate
2148 * of the inequality, so we directly call is_bound.
2149 * For following basic sets, we first check if a translate of the
2150 * inequality appears in its description and if so directly update
2151 * the inequality accordingly.
2153 static struct isl_basic_set
*add_bound(struct isl_basic_set
*hull
,
2154 struct sh_data
*data
, struct isl_set
*set
, int i
, isl_int
*ineq
)
2157 struct ineq_cmp_data v
;
2158 struct isl_hash_table_entry
*entry
;
2164 v
.len
= isl_basic_set_total_dim(hull
);
2166 c_hash
= isl_seq_get_hash(ineq
+ 1, v
.len
);
2168 entry
= isl_hash_table_find(hull
->ctx
, data
->hull_table
, c_hash
,
2173 for (j
= 0; j
< i
; ++j
) {
2174 entry
= isl_hash_table_find(hull
->ctx
, data
->p
[j
].table
,
2175 c_hash
, has_ineq
, &v
, 0);
2182 k
= isl_basic_set_alloc_inequality(hull
);
2183 isl_seq_cpy(hull
->ineq
[k
], ineq
, 1 + v
.len
);
2187 for (j
= 0; j
< i
; ++j
) {
2189 bound
= is_bound(data
, set
, j
, hull
->ineq
[k
]);
2196 isl_basic_set_free_inequality(hull
, 1);
2200 for (j
= i
+ 1; j
< set
->n
; ++j
) {
2203 entry
= isl_hash_table_find(hull
->ctx
, data
->p
[j
].table
,
2204 c_hash
, has_ineq
, &v
, 0);
2206 ineq_j
= entry
->data
;
2207 neg
= isl_seq_is_neg(ineq_j
+ 1,
2208 hull
->ineq
[k
] + 1, v
.len
);
2210 isl_int_neg(ineq_j
[0], ineq_j
[0]);
2211 if (isl_int_gt(ineq_j
[0], hull
->ineq
[k
][0]))
2212 isl_int_set(hull
->ineq
[k
][0], ineq_j
[0]);
2214 isl_int_neg(ineq_j
[0], ineq_j
[0]);
2217 bound
= is_bound(data
, set
, j
, hull
->ineq
[k
]);
2224 isl_basic_set_free_inequality(hull
, 1);
2228 entry
= isl_hash_table_find(hull
->ctx
, data
->hull_table
, c_hash
,
2232 entry
->data
= hull
->ineq
[k
];
2236 isl_basic_set_free(hull
);
2240 /* Check if any inequality from basic set "i" can be relaxed to
2241 * become a bound on the whole set. If so, add the (relaxed) inequality
2244 static struct isl_basic_set
*add_bounds(struct isl_basic_set
*bset
,
2245 struct sh_data
*data
, struct isl_set
*set
, int i
)
2248 unsigned dim
= isl_basic_set_total_dim(bset
);
2250 for (j
= 0; j
< set
->p
[i
]->n_eq
; ++j
) {
2251 for (k
= 0; k
< 2; ++k
) {
2252 isl_seq_neg(set
->p
[i
]->eq
[j
], set
->p
[i
]->eq
[j
], 1+dim
);
2253 bset
= add_bound(bset
, data
, set
, i
, set
->p
[i
]->eq
[j
]);
2256 for (j
= 0; j
< set
->p
[i
]->n_ineq
; ++j
)
2257 bset
= add_bound(bset
, data
, set
, i
, set
->p
[i
]->ineq
[j
]);
2261 /* Compute a superset of the convex hull of set that is described
2262 * by only translates of the constraints in the constituents of set.
2264 static struct isl_basic_set
*uset_simple_hull(struct isl_set
*set
)
2266 struct sh_data
*data
= NULL
;
2267 struct isl_basic_set
*hull
= NULL
;
2275 for (i
= 0; i
< set
->n
; ++i
) {
2278 n_ineq
+= 2 * set
->p
[i
]->n_eq
+ set
->p
[i
]->n_ineq
;
2281 hull
= isl_basic_set_alloc_dim(isl_dim_copy(set
->dim
), 0, 0, n_ineq
);
2285 data
= sh_data_alloc(set
, n_ineq
);
2289 for (i
= 0; i
< set
->n
; ++i
)
2290 hull
= add_bounds(hull
, data
, set
, i
);
2298 isl_basic_set_free(hull
);
2303 /* Compute a superset of the convex hull of map that is described
2304 * by only translates of the constraints in the constituents of map.
2306 struct isl_basic_map
*isl_map_simple_hull(struct isl_map
*map
)
2308 struct isl_set
*set
= NULL
;
2309 struct isl_basic_map
*model
= NULL
;
2310 struct isl_basic_map
*hull
;
2311 struct isl_basic_map
*affine_hull
;
2312 struct isl_basic_set
*bset
= NULL
;
2317 hull
= isl_basic_map_empty_like_map(map
);
2322 hull
= isl_basic_map_copy(map
->p
[0]);
2327 map
= isl_map_detect_equalities(map
);
2328 affine_hull
= isl_map_affine_hull(isl_map_copy(map
));
2329 map
= isl_map_align_divs(map
);
2330 model
= isl_basic_map_copy(map
->p
[0]);
2332 set
= isl_map_underlying_set(map
);
2334 bset
= uset_simple_hull(set
);
2336 hull
= isl_basic_map_overlying_set(bset
, model
);
2338 hull
= isl_basic_map_intersect(hull
, affine_hull
);
2339 hull
= isl_basic_map_remove_redundancies(hull
);
2340 ISL_F_SET(hull
, ISL_BASIC_MAP_NO_IMPLICIT
);
2341 ISL_F_SET(hull
, ISL_BASIC_MAP_ALL_EQUALITIES
);
2346 struct isl_basic_set
*isl_set_simple_hull(struct isl_set
*set
)
2348 return (struct isl_basic_set
*)
2349 isl_map_simple_hull((struct isl_map
*)set
);
2352 /* Given a set "set", return parametric bounds on the dimension "dim".
2354 static struct isl_basic_set
*set_bounds(struct isl_set
*set
, int dim
)
2356 unsigned set_dim
= isl_set_dim(set
, isl_dim_set
);
2357 set
= isl_set_copy(set
);
2358 set
= isl_set_eliminate_dims(set
, dim
+ 1, set_dim
- (dim
+ 1));
2359 set
= isl_set_eliminate_dims(set
, 0, dim
);
2360 return isl_set_convex_hull(set
);
2363 /* Computes a "simple hull" and then check if each dimension in the
2364 * resulting hull is bounded by a symbolic constant. If not, the
2365 * hull is intersected with the corresponding bounds on the whole set.
2367 struct isl_basic_set
*isl_set_bounded_simple_hull(struct isl_set
*set
)
2370 struct isl_basic_set
*hull
;
2371 unsigned nparam
, left
;
2372 int removed_divs
= 0;
2374 hull
= isl_set_simple_hull(isl_set_copy(set
));
2378 nparam
= isl_basic_set_dim(hull
, isl_dim_param
);
2379 for (i
= 0; i
< isl_basic_set_dim(hull
, isl_dim_set
); ++i
) {
2380 int lower
= 0, upper
= 0;
2381 struct isl_basic_set
*bounds
;
2383 left
= isl_basic_set_total_dim(hull
) - nparam
- i
- 1;
2384 for (j
= 0; j
< hull
->n_eq
; ++j
) {
2385 if (isl_int_is_zero(hull
->eq
[j
][1 + nparam
+ i
]))
2387 if (isl_seq_first_non_zero(hull
->eq
[j
]+1+nparam
+i
+1,
2394 for (j
= 0; j
< hull
->n_ineq
; ++j
) {
2395 if (isl_int_is_zero(hull
->ineq
[j
][1 + nparam
+ i
]))
2397 if (isl_seq_first_non_zero(hull
->ineq
[j
]+1+nparam
+i
+1,
2399 isl_seq_first_non_zero(hull
->ineq
[j
]+1+nparam
,
2402 if (isl_int_is_pos(hull
->ineq
[j
][1 + nparam
+ i
]))
2413 if (!removed_divs
) {
2414 set
= isl_set_remove_divs(set
);
2419 bounds
= set_bounds(set
, i
);
2420 hull
= isl_basic_set_intersect(hull
, bounds
);