2 * Copyright 2008-2009 Katholieke Universiteit Leuven
3 * Copyright 2014 INRIA Rocquencourt
5 * Use of this software is governed by the MIT license
7 * Written by Sven Verdoolaege, K.U.Leuven, Departement
8 * Computerwetenschappen, Celestijnenlaan 200A, B-3001 Leuven, Belgium
9 * and Inria Paris - Rocquencourt, Domaine de Voluceau - Rocquencourt,
10 * B.P. 105 - 78153 Le Chesnay, France
13 #include <isl_ctx_private.h>
14 #include <isl_map_private.h>
15 #include <isl_lp_private.h>
17 #include <isl_mat_private.h>
18 #include <isl_vec_private.h>
21 #include <isl_options_private.h>
22 #include "isl_equalities.h"
26 #include <bset_to_bmap.c>
27 #include <bset_from_bmap.c>
28 #include <set_to_map.c>
30 static __isl_give isl_basic_set
*uset_convex_hull_wrap_bounded(
31 __isl_take isl_set
*set
);
34 * constraints. If the minimal value along the normal of a constraint
35 * is the same if the constraint is removed, then the constraint is redundant.
37 * Since some constraints may be mutually redundant, sort the constraints
38 * first such that constraints that involve existentially quantified
39 * variables are considered for removal before those that do not.
40 * The sorting is also needed for the use in map_simple_hull.
42 * Note that isl_tab_detect_implicit_equalities may also end up
43 * marking some constraints as redundant. Make sure the constraints
44 * are preserved and undo those marking such that isl_tab_detect_redundant
45 * can consider the constraints in the sorted order.
47 * Alternatively, we could have intersected the basic map with the
48 * corresponding equality and then checked if the dimension was that
51 __isl_give isl_basic_map
*isl_basic_map_remove_redundancies(
52 __isl_take isl_basic_map
*bmap
)
59 bmap
= isl_basic_map_gauss(bmap
, NULL
);
60 if (ISL_F_ISSET(bmap
, ISL_BASIC_MAP_EMPTY
))
62 if (ISL_F_ISSET(bmap
, ISL_BASIC_MAP_NO_REDUNDANT
))
64 if (bmap
->n_ineq
<= 1)
67 bmap
= isl_basic_map_sort_constraints(bmap
);
68 tab
= isl_tab_from_basic_map(bmap
, 0);
72 if (isl_tab_detect_implicit_equalities(tab
) < 0)
74 if (isl_tab_restore_redundant(tab
) < 0)
77 if (isl_tab_detect_redundant(tab
) < 0)
79 bmap
= isl_basic_map_update_from_tab(bmap
, tab
);
83 ISL_F_SET(bmap
, ISL_BASIC_MAP_NO_IMPLICIT
);
84 ISL_F_SET(bmap
, ISL_BASIC_MAP_NO_REDUNDANT
);
88 isl_basic_map_free(bmap
);
92 __isl_give isl_basic_set
*isl_basic_set_remove_redundancies(
93 __isl_take isl_basic_set
*bset
)
95 return bset_from_bmap(
96 isl_basic_map_remove_redundancies(bset_to_bmap(bset
)));
99 /* Remove redundant constraints in each of the basic maps.
101 __isl_give isl_map
*isl_map_remove_redundancies(__isl_take isl_map
*map
)
103 return isl_map_inline_foreach_basic_map(map
,
104 &isl_basic_map_remove_redundancies
);
107 __isl_give isl_set
*isl_set_remove_redundancies(__isl_take isl_set
*set
)
109 return isl_map_remove_redundancies(set
);
112 /* Check if the set set is bound in the direction of the affine
113 * constraint c and if so, set the constant term such that the
114 * resulting constraint is a bounding constraint for the set.
116 static isl_bool
uset_is_bound(__isl_keep isl_set
*set
, isl_int
*c
, unsigned len
)
124 isl_int_init(opt_denom
);
126 for (j
= 0; j
< set
->n
; ++j
) {
127 enum isl_lp_result res
;
129 if (ISL_F_ISSET(set
->p
[j
], ISL_BASIC_SET_EMPTY
))
132 res
= isl_basic_set_solve_lp(set
->p
[j
],
133 0, c
, set
->ctx
->one
, &opt
, &opt_denom
, NULL
);
134 if (res
== isl_lp_unbounded
)
136 if (res
== isl_lp_error
)
138 if (res
== isl_lp_empty
) {
139 set
->p
[j
] = isl_basic_set_set_to_empty(set
->p
[j
]);
144 if (first
|| isl_int_is_neg(opt
)) {
145 if (!isl_int_is_one(opt_denom
))
146 isl_seq_scale(c
, c
, opt_denom
, len
);
147 isl_int_sub(c
[0], c
[0], opt
);
152 isl_int_clear(opt_denom
);
153 return isl_bool_ok(j
>= set
->n
);
156 isl_int_clear(opt_denom
);
157 return isl_bool_error
;
160 static __isl_give isl_set
*isl_set_add_basic_set_equality(
161 __isl_take isl_set
*set
, isl_int
*c
)
165 set
= isl_set_cow(set
);
168 for (i
= 0; i
< set
->n
; ++i
) {
169 set
->p
[i
] = isl_basic_set_add_eq(set
->p
[i
], c
);
179 /* Given a union of basic sets, construct the constraints for wrapping
180 * a facet around one of its ridges.
181 * In particular, if each of n the d-dimensional basic sets i in "set"
182 * contains the origin, satisfies the constraints x_1 >= 0 and x_2 >= 0
183 * and is defined by the constraints
187 * then the resulting set is of dimension n*(1+d) and has as constraints
196 static __isl_give isl_basic_set
*wrap_constraints(__isl_keep isl_set
*set
)
198 struct isl_basic_set
*lp
;
202 isl_size dim
, lp_dim
;
204 dim
= isl_set_dim(set
, isl_dim_set
);
211 for (i
= 0; i
< set
->n
; ++i
) {
212 n_eq
+= set
->p
[i
]->n_eq
;
213 n_ineq
+= set
->p
[i
]->n_ineq
;
215 lp
= isl_basic_set_alloc(set
->ctx
, 0, dim
* set
->n
, 0, n_eq
, n_ineq
);
216 lp
= isl_basic_set_set_rational(lp
);
219 lp_dim
= isl_basic_set_dim(lp
, isl_dim_set
);
221 return isl_basic_set_free(lp
);
222 k
= isl_basic_set_alloc_equality(lp
);
223 isl_int_set_si(lp
->eq
[k
][0], -1);
224 for (i
= 0; i
< set
->n
; ++i
) {
225 isl_int_set_si(lp
->eq
[k
][1+dim
*i
], 0);
226 isl_int_set_si(lp
->eq
[k
][1+dim
*i
+1], 1);
227 isl_seq_clr(lp
->eq
[k
]+1+dim
*i
+2, dim
-2);
229 for (i
= 0; i
< set
->n
; ++i
) {
230 k
= isl_basic_set_alloc_inequality(lp
);
231 isl_seq_clr(lp
->ineq
[k
], 1+lp_dim
);
232 isl_int_set_si(lp
->ineq
[k
][1+dim
*i
], 1);
234 for (j
= 0; j
< set
->p
[i
]->n_eq
; ++j
) {
235 k
= isl_basic_set_alloc_equality(lp
);
236 isl_seq_clr(lp
->eq
[k
], 1+dim
*i
);
237 isl_seq_cpy(lp
->eq
[k
]+1+dim
*i
, set
->p
[i
]->eq
[j
], dim
);
238 isl_seq_clr(lp
->eq
[k
]+1+dim
*(i
+1), dim
*(set
->n
-i
-1));
241 for (j
= 0; j
< set
->p
[i
]->n_ineq
; ++j
) {
242 k
= isl_basic_set_alloc_inequality(lp
);
243 isl_seq_clr(lp
->ineq
[k
], 1+dim
*i
);
244 isl_seq_cpy(lp
->ineq
[k
]+1+dim
*i
, set
->p
[i
]->ineq
[j
], dim
);
245 isl_seq_clr(lp
->ineq
[k
]+1+dim
*(i
+1), dim
*(set
->n
-i
-1));
251 /* Given a facet "facet" of the convex hull of "set" and a facet "ridge"
252 * of that facet, compute the other facet of the convex hull that contains
255 * We first transform the set such that the facet constraint becomes
259 * I.e., the facet lies in
263 * and on that facet, the constraint that defines the ridge is
267 * (This transformation is not strictly needed, all that is needed is
268 * that the ridge contains the origin.)
270 * Since the ridge contains the origin, the cone of the convex hull
271 * will be of the form
276 * with this second constraint defining the new facet.
277 * The constant a is obtained by settting x_1 in the cone of the
278 * convex hull to 1 and minimizing x_2.
279 * Now, each element in the cone of the convex hull is the sum
280 * of elements in the cones of the basic sets.
281 * If a_i is the dilation factor of basic set i, then the problem
282 * we need to solve is
295 * the constraints of each (transformed) basic set.
296 * If a = n/d, then the constraint defining the new facet (in the transformed
299 * -n x_1 + d x_2 >= 0
301 * In the original space, we need to take the same combination of the
302 * corresponding constraints "facet" and "ridge".
304 * If a = -infty = "-1/0", then we just return the original facet constraint.
305 * This means that the facet is unbounded, but has a bounded intersection
306 * with the union of sets.
308 isl_int
*isl_set_wrap_facet(__isl_keep isl_set
*set
,
309 isl_int
*facet
, isl_int
*ridge
)
313 struct isl_mat
*T
= NULL
;
314 struct isl_basic_set
*lp
= NULL
;
316 enum isl_lp_result res
;
320 dim
= isl_set_dim(set
, isl_dim_set
);
324 set
= isl_set_copy(set
);
325 set
= isl_set_set_rational(set
);
328 T
= isl_mat_alloc(ctx
, 3, dim
);
331 isl_int_set_si(T
->row
[0][0], 1);
332 isl_seq_clr(T
->row
[0]+1, dim
- 1);
333 isl_seq_cpy(T
->row
[1], facet
, dim
);
334 isl_seq_cpy(T
->row
[2], ridge
, dim
);
335 T
= isl_mat_right_inverse(T
);
336 set
= isl_set_preimage(set
, T
);
340 lp
= wrap_constraints(set
);
341 obj
= isl_vec_alloc(ctx
, 1 + dim
*set
->n
);
344 isl_int_set_si(obj
->block
.data
[0], 0);
345 for (i
= 0; i
< set
->n
; ++i
) {
346 isl_seq_clr(obj
->block
.data
+ 1 + dim
*i
, 2);
347 isl_int_set_si(obj
->block
.data
[1 + dim
*i
+2], 1);
348 isl_seq_clr(obj
->block
.data
+ 1 + dim
*i
+3, dim
-3);
352 res
= isl_basic_set_solve_lp(lp
, 0,
353 obj
->block
.data
, ctx
->one
, &num
, &den
, NULL
);
354 if (res
== isl_lp_ok
) {
355 isl_int_neg(num
, num
);
356 isl_seq_combine(facet
, num
, facet
, den
, ridge
, dim
);
357 isl_seq_normalize(ctx
, facet
, dim
);
362 isl_basic_set_free(lp
);
364 if (res
== isl_lp_error
)
366 isl_assert(ctx
, res
== isl_lp_ok
|| res
== isl_lp_unbounded
,
370 isl_basic_set_free(lp
);
376 /* Compute the constraint of a facet of "set".
378 * We first compute the intersection with a bounding constraint
379 * that is orthogonal to one of the coordinate axes.
380 * If the affine hull of this intersection has only one equality,
381 * we have found a facet.
382 * Otherwise, we wrap the current bounding constraint around
383 * one of the equalities of the face (one that is not equal to
384 * the current bounding constraint).
385 * This process continues until we have found a facet.
386 * The dimension of the intersection increases by at least
387 * one on each iteration, so termination is guaranteed.
389 static __isl_give isl_mat
*initial_facet_constraint(__isl_keep isl_set
*set
)
391 struct isl_set
*slice
= NULL
;
392 struct isl_basic_set
*face
= NULL
;
394 isl_size dim
= isl_set_dim(set
, isl_dim_set
);
396 isl_mat
*bounds
= NULL
;
400 isl_assert(set
->ctx
, set
->n
> 0, goto error
);
401 bounds
= isl_mat_alloc(set
->ctx
, 1, 1 + dim
);
405 isl_seq_clr(bounds
->row
[0], dim
);
406 isl_int_set_si(bounds
->row
[0][1 + dim
- 1], 1);
407 is_bound
= uset_is_bound(set
, bounds
->row
[0], 1 + dim
);
410 isl_assert(set
->ctx
, is_bound
, goto error
);
411 isl_seq_normalize(set
->ctx
, bounds
->row
[0], 1 + dim
);
415 slice
= isl_set_copy(set
);
416 slice
= isl_set_add_basic_set_equality(slice
, bounds
->row
[0]);
417 face
= isl_set_affine_hull(slice
);
420 if (face
->n_eq
== 1) {
421 isl_basic_set_free(face
);
424 for (i
= 0; i
< face
->n_eq
; ++i
)
425 if (!isl_seq_eq(bounds
->row
[0], face
->eq
[i
], 1 + dim
) &&
426 !isl_seq_is_neg(bounds
->row
[0],
427 face
->eq
[i
], 1 + dim
))
429 isl_assert(set
->ctx
, i
< face
->n_eq
, goto error
);
430 if (!isl_set_wrap_facet(set
, bounds
->row
[0], face
->eq
[i
]))
432 isl_seq_normalize(set
->ctx
, bounds
->row
[0], bounds
->n_col
);
433 isl_basic_set_free(face
);
438 isl_basic_set_free(face
);
439 isl_mat_free(bounds
);
443 /* Given the bounding constraint "c" of a facet of the convex hull of "set",
444 * compute a hyperplane description of the facet, i.e., compute the facets
447 * We compute an affine transformation that transforms the constraint
456 * by computing the right inverse U of a matrix that starts with the rows
469 * Since z_1 is zero, we can drop this variable as well as the corresponding
470 * column of U to obtain
478 * with Q' equal to Q, but without the corresponding row.
479 * After computing the facets of the facet in the z' space,
480 * we convert them back to the x space through Q.
482 static __isl_give isl_basic_set
*compute_facet(__isl_keep isl_set
*set
,
485 struct isl_mat
*m
, *U
, *Q
;
486 struct isl_basic_set
*facet
= NULL
;
490 dim
= isl_set_dim(set
, isl_dim_set
);
494 set
= isl_set_copy(set
);
495 m
= isl_mat_alloc(set
->ctx
, 2, 1 + dim
);
498 isl_int_set_si(m
->row
[0][0], 1);
499 isl_seq_clr(m
->row
[0]+1, dim
);
500 isl_seq_cpy(m
->row
[1], c
, 1+dim
);
501 U
= isl_mat_right_inverse(m
);
502 Q
= isl_mat_right_inverse(isl_mat_copy(U
));
503 U
= isl_mat_drop_cols(U
, 1, 1);
504 Q
= isl_mat_drop_rows(Q
, 1, 1);
505 set
= isl_set_preimage(set
, U
);
506 facet
= uset_convex_hull_wrap_bounded(set
);
507 facet
= isl_basic_set_preimage(facet
, Q
);
508 if (facet
&& facet
->n_eq
!= 0)
509 isl_die(ctx
, isl_error_internal
, "unexpected equality",
510 return isl_basic_set_free(facet
));
513 isl_basic_set_free(facet
);
518 /* Given an initial facet constraint, compute the remaining facets.
519 * We do this by running through all facets found so far and computing
520 * the adjacent facets through wrapping, adding those facets that we
521 * hadn't already found before.
523 * For each facet we have found so far, we first compute its facets
524 * in the resulting convex hull. That is, we compute the ridges
525 * of the resulting convex hull contained in the facet.
526 * We also compute the corresponding facet in the current approximation
527 * of the convex hull. There is no need to wrap around the ridges
528 * in this facet since that would result in a facet that is already
529 * present in the current approximation.
531 * This function can still be significantly optimized by checking which of
532 * the facets of the basic sets are also facets of the convex hull and
533 * using all the facets so far to help in constructing the facets of the
536 * using the technique in section "3.1 Ridge Generation" of
537 * "Extended Convex Hull" by Fukuda et al.
539 static __isl_give isl_basic_set
*extend(__isl_take isl_basic_set
*hull
,
540 __isl_keep isl_set
*set
)
544 struct isl_basic_set
*facet
= NULL
;
545 struct isl_basic_set
*hull_facet
= NULL
;
548 dim
= isl_set_dim(set
, isl_dim_set
);
549 if (dim
< 0 || !hull
)
550 return isl_basic_set_free(hull
);
552 isl_assert(set
->ctx
, set
->n
> 0, goto error
);
554 for (i
= 0; i
< hull
->n_ineq
; ++i
) {
555 facet
= compute_facet(set
, hull
->ineq
[i
]);
556 facet
= isl_basic_set_add_eq(facet
, hull
->ineq
[i
]);
557 facet
= isl_basic_set_gauss(facet
, NULL
);
558 facet
= isl_basic_set_normalize_constraints(facet
);
559 hull_facet
= isl_basic_set_copy(hull
);
560 hull_facet
= isl_basic_set_add_eq(hull_facet
, hull
->ineq
[i
]);
561 hull_facet
= isl_basic_set_gauss(hull_facet
, NULL
);
562 hull_facet
= isl_basic_set_normalize_constraints(hull_facet
);
563 if (!facet
|| !hull_facet
)
565 hull
= isl_basic_set_cow(hull
);
566 hull
= isl_basic_set_extend_space(hull
,
567 isl_space_copy(hull
->dim
), 0, 0, facet
->n_ineq
);
570 for (j
= 0; j
< facet
->n_ineq
; ++j
) {
571 for (f
= 0; f
< hull_facet
->n_ineq
; ++f
)
572 if (isl_seq_eq(facet
->ineq
[j
],
573 hull_facet
->ineq
[f
], 1 + dim
))
575 if (f
< hull_facet
->n_ineq
)
577 k
= isl_basic_set_alloc_inequality(hull
);
580 isl_seq_cpy(hull
->ineq
[k
], hull
->ineq
[i
], 1+dim
);
581 if (!isl_set_wrap_facet(set
, hull
->ineq
[k
], facet
->ineq
[j
]))
584 isl_basic_set_free(hull_facet
);
585 isl_basic_set_free(facet
);
587 hull
= isl_basic_set_simplify(hull
);
588 hull
= isl_basic_set_finalize(hull
);
591 isl_basic_set_free(hull_facet
);
592 isl_basic_set_free(facet
);
593 isl_basic_set_free(hull
);
597 /* Special case for computing the convex hull of a one dimensional set.
598 * We simply collect the lower and upper bounds of each basic set
599 * and the biggest of those.
601 static __isl_give isl_basic_set
*convex_hull_1d(__isl_take isl_set
*set
)
603 struct isl_mat
*c
= NULL
;
604 isl_int
*lower
= NULL
;
605 isl_int
*upper
= NULL
;
608 struct isl_basic_set
*hull
;
610 for (i
= 0; i
< set
->n
; ++i
) {
611 set
->p
[i
] = isl_basic_set_simplify(set
->p
[i
]);
615 set
= isl_set_remove_empty_parts(set
);
618 isl_assert(set
->ctx
, set
->n
> 0, goto error
);
619 c
= isl_mat_alloc(set
->ctx
, 2, 2);
623 if (set
->p
[0]->n_eq
> 0) {
624 isl_assert(set
->ctx
, set
->p
[0]->n_eq
== 1, goto error
);
627 if (isl_int_is_pos(set
->p
[0]->eq
[0][1])) {
628 isl_seq_cpy(lower
, set
->p
[0]->eq
[0], 2);
629 isl_seq_neg(upper
, set
->p
[0]->eq
[0], 2);
631 isl_seq_neg(lower
, set
->p
[0]->eq
[0], 2);
632 isl_seq_cpy(upper
, set
->p
[0]->eq
[0], 2);
635 for (j
= 0; j
< set
->p
[0]->n_ineq
; ++j
) {
636 if (isl_int_is_pos(set
->p
[0]->ineq
[j
][1])) {
638 isl_seq_cpy(lower
, set
->p
[0]->ineq
[j
], 2);
641 isl_seq_cpy(upper
, set
->p
[0]->ineq
[j
], 2);
648 for (i
= 0; i
< set
->n
; ++i
) {
649 struct isl_basic_set
*bset
= set
->p
[i
];
653 for (j
= 0; j
< bset
->n_eq
; ++j
) {
657 isl_int_mul(a
, lower
[0], bset
->eq
[j
][1]);
658 isl_int_mul(b
, lower
[1], bset
->eq
[j
][0]);
659 if (isl_int_lt(a
, b
) && isl_int_is_pos(bset
->eq
[j
][1]))
660 isl_seq_cpy(lower
, bset
->eq
[j
], 2);
661 if (isl_int_gt(a
, b
) && isl_int_is_neg(bset
->eq
[j
][1]))
662 isl_seq_neg(lower
, bset
->eq
[j
], 2);
665 isl_int_mul(a
, upper
[0], bset
->eq
[j
][1]);
666 isl_int_mul(b
, upper
[1], bset
->eq
[j
][0]);
667 if (isl_int_lt(a
, b
) && isl_int_is_pos(bset
->eq
[j
][1]))
668 isl_seq_neg(upper
, bset
->eq
[j
], 2);
669 if (isl_int_gt(a
, b
) && isl_int_is_neg(bset
->eq
[j
][1]))
670 isl_seq_cpy(upper
, bset
->eq
[j
], 2);
673 for (j
= 0; j
< bset
->n_ineq
; ++j
) {
674 if (isl_int_is_pos(bset
->ineq
[j
][1]))
676 if (isl_int_is_neg(bset
->ineq
[j
][1]))
678 if (lower
&& isl_int_is_pos(bset
->ineq
[j
][1])) {
679 isl_int_mul(a
, lower
[0], bset
->ineq
[j
][1]);
680 isl_int_mul(b
, lower
[1], bset
->ineq
[j
][0]);
681 if (isl_int_lt(a
, b
))
682 isl_seq_cpy(lower
, bset
->ineq
[j
], 2);
684 if (upper
&& isl_int_is_neg(bset
->ineq
[j
][1])) {
685 isl_int_mul(a
, upper
[0], bset
->ineq
[j
][1]);
686 isl_int_mul(b
, upper
[1], bset
->ineq
[j
][0]);
687 if (isl_int_gt(a
, b
))
688 isl_seq_cpy(upper
, bset
->ineq
[j
], 2);
699 hull
= isl_basic_set_alloc(set
->ctx
, 0, 1, 0, 0, 2);
700 hull
= isl_basic_set_set_rational(hull
);
704 k
= isl_basic_set_alloc_inequality(hull
);
705 isl_seq_cpy(hull
->ineq
[k
], lower
, 2);
708 k
= isl_basic_set_alloc_inequality(hull
);
709 isl_seq_cpy(hull
->ineq
[k
], upper
, 2);
711 hull
= isl_basic_set_finalize(hull
);
721 static __isl_give isl_basic_set
*convex_hull_0d(__isl_take isl_set
*set
)
723 struct isl_basic_set
*convex_hull
;
728 if (isl_set_is_empty(set
))
729 convex_hull
= isl_basic_set_empty(isl_space_copy(set
->dim
));
731 convex_hull
= isl_basic_set_universe(isl_space_copy(set
->dim
));
736 /* Compute the convex hull of a pair of basic sets without any parameters or
737 * integer divisions using Fourier-Motzkin elimination.
738 * The convex hull is the set of all points that can be written as
739 * the sum of points from both basic sets (in homogeneous coordinates).
740 * We set up the constraints in a space with dimensions for each of
741 * the three sets and then project out the dimensions corresponding
742 * to the two original basic sets, retaining only those corresponding
743 * to the convex hull.
745 static __isl_give isl_basic_set
*convex_hull_pair_elim(
746 __isl_take isl_basic_set
*bset1
, __isl_take isl_basic_set
*bset2
)
749 struct isl_basic_set
*bset
[2];
750 struct isl_basic_set
*hull
= NULL
;
753 dim
= isl_basic_set_dim(bset1
, isl_dim_set
);
754 if (dim
< 0 || !bset2
)
757 hull
= isl_basic_set_alloc(bset1
->ctx
, 0, 2 + 3 * dim
, 0,
758 1 + dim
+ bset1
->n_eq
+ bset2
->n_eq
,
759 2 + bset1
->n_ineq
+ bset2
->n_ineq
);
762 for (i
= 0; i
< 2; ++i
) {
763 for (j
= 0; j
< bset
[i
]->n_eq
; ++j
) {
764 k
= isl_basic_set_alloc_equality(hull
);
767 isl_seq_clr(hull
->eq
[k
], (i
+1) * (1+dim
));
768 isl_seq_clr(hull
->eq
[k
]+(i
+2)*(1+dim
), (1-i
)*(1+dim
));
769 isl_seq_cpy(hull
->eq
[k
]+(i
+1)*(1+dim
), bset
[i
]->eq
[j
],
772 for (j
= 0; j
< bset
[i
]->n_ineq
; ++j
) {
773 k
= isl_basic_set_alloc_inequality(hull
);
776 isl_seq_clr(hull
->ineq
[k
], (i
+1) * (1+dim
));
777 isl_seq_clr(hull
->ineq
[k
]+(i
+2)*(1+dim
), (1-i
)*(1+dim
));
778 isl_seq_cpy(hull
->ineq
[k
]+(i
+1)*(1+dim
),
779 bset
[i
]->ineq
[j
], 1+dim
);
781 k
= isl_basic_set_alloc_inequality(hull
);
784 isl_seq_clr(hull
->ineq
[k
], 1+2+3*dim
);
785 isl_int_set_si(hull
->ineq
[k
][(i
+1)*(1+dim
)], 1);
787 for (j
= 0; j
< 1+dim
; ++j
) {
788 k
= isl_basic_set_alloc_equality(hull
);
791 isl_seq_clr(hull
->eq
[k
], 1+2+3*dim
);
792 isl_int_set_si(hull
->eq
[k
][j
], -1);
793 isl_int_set_si(hull
->eq
[k
][1+dim
+j
], 1);
794 isl_int_set_si(hull
->eq
[k
][2*(1+dim
)+j
], 1);
796 hull
= isl_basic_set_set_rational(hull
);
797 hull
= isl_basic_set_remove_dims(hull
, isl_dim_set
, dim
, 2*(1+dim
));
798 hull
= isl_basic_set_remove_redundancies(hull
);
799 isl_basic_set_free(bset1
);
800 isl_basic_set_free(bset2
);
803 isl_basic_set_free(bset1
);
804 isl_basic_set_free(bset2
);
805 isl_basic_set_free(hull
);
809 /* Is the set bounded for each value of the parameters?
811 isl_bool
isl_basic_set_is_bounded(__isl_keep isl_basic_set
*bset
)
817 return isl_bool_error
;
818 if (isl_basic_set_plain_is_empty(bset
))
819 return isl_bool_true
;
821 tab
= isl_tab_from_recession_cone(bset
, 1);
822 bounded
= isl_tab_cone_is_bounded(tab
);
827 /* Is the image bounded for each value of the parameters and
828 * the domain variables?
830 isl_bool
isl_basic_map_image_is_bounded(__isl_keep isl_basic_map
*bmap
)
832 isl_size nparam
= isl_basic_map_dim(bmap
, isl_dim_param
);
833 isl_size n_in
= isl_basic_map_dim(bmap
, isl_dim_in
);
836 if (nparam
< 0 || n_in
< 0)
837 return isl_bool_error
;
839 bmap
= isl_basic_map_copy(bmap
);
840 bmap
= isl_basic_map_cow(bmap
);
841 bmap
= isl_basic_map_move_dims(bmap
, isl_dim_param
, nparam
,
842 isl_dim_in
, 0, n_in
);
843 bounded
= isl_basic_set_is_bounded(bset_from_bmap(bmap
));
844 isl_basic_map_free(bmap
);
849 /* Is the set bounded for each value of the parameters?
851 isl_bool
isl_set_is_bounded(__isl_keep isl_set
*set
)
856 return isl_bool_error
;
858 for (i
= 0; i
< set
->n
; ++i
) {
859 isl_bool bounded
= isl_basic_set_is_bounded(set
->p
[i
]);
860 if (!bounded
|| bounded
< 0)
863 return isl_bool_true
;
866 /* Compute the lineality space of the convex hull of bset1 and bset2.
868 * We first compute the intersection of the recession cone of bset1
869 * with the negative of the recession cone of bset2 and then compute
870 * the linear hull of the resulting cone.
872 static __isl_give isl_basic_set
*induced_lineality_space(
873 __isl_take isl_basic_set
*bset1
, __isl_take isl_basic_set
*bset2
)
876 struct isl_basic_set
*lin
= NULL
;
879 dim
= isl_basic_set_dim(bset1
, isl_dim_all
);
880 if (dim
< 0 || !bset2
)
883 lin
= isl_basic_set_alloc_space(isl_basic_set_get_space(bset1
), 0,
884 bset1
->n_eq
+ bset2
->n_eq
,
885 bset1
->n_ineq
+ bset2
->n_ineq
);
886 lin
= isl_basic_set_set_rational(lin
);
889 for (i
= 0; i
< bset1
->n_eq
; ++i
) {
890 k
= isl_basic_set_alloc_equality(lin
);
893 isl_int_set_si(lin
->eq
[k
][0], 0);
894 isl_seq_cpy(lin
->eq
[k
] + 1, bset1
->eq
[i
] + 1, dim
);
896 for (i
= 0; i
< bset1
->n_ineq
; ++i
) {
897 k
= isl_basic_set_alloc_inequality(lin
);
900 isl_int_set_si(lin
->ineq
[k
][0], 0);
901 isl_seq_cpy(lin
->ineq
[k
] + 1, bset1
->ineq
[i
] + 1, dim
);
903 for (i
= 0; i
< bset2
->n_eq
; ++i
) {
904 k
= isl_basic_set_alloc_equality(lin
);
907 isl_int_set_si(lin
->eq
[k
][0], 0);
908 isl_seq_neg(lin
->eq
[k
] + 1, bset2
->eq
[i
] + 1, dim
);
910 for (i
= 0; i
< bset2
->n_ineq
; ++i
) {
911 k
= isl_basic_set_alloc_inequality(lin
);
914 isl_int_set_si(lin
->ineq
[k
][0], 0);
915 isl_seq_neg(lin
->ineq
[k
] + 1, bset2
->ineq
[i
] + 1, dim
);
918 isl_basic_set_free(bset1
);
919 isl_basic_set_free(bset2
);
920 return isl_basic_set_affine_hull(lin
);
922 isl_basic_set_free(lin
);
923 isl_basic_set_free(bset1
);
924 isl_basic_set_free(bset2
);
928 static __isl_give isl_basic_set
*uset_convex_hull(__isl_take isl_set
*set
);
930 /* Given a set and a linear space "lin" of dimension n > 0,
931 * project the linear space from the set, compute the convex hull
932 * and then map the set back to the original space.
938 * describe the linear space. We first compute the Hermite normal
939 * form H = M U of M = H Q, to obtain
943 * The last n rows of H will be zero, so the last n variables of x' = Q x
944 * are the one we want to project out. We do this by transforming each
945 * basic set A x >= b to A U x' >= b and then removing the last n dimensions.
946 * After computing the convex hull in x'_1, i.e., A' x'_1 >= b',
947 * we transform the hull back to the original space as A' Q_1 x >= b',
948 * with Q_1 all but the last n rows of Q.
950 static __isl_give isl_basic_set
*modulo_lineality(__isl_take isl_set
*set
,
951 __isl_take isl_basic_set
*lin
)
953 isl_size total
= isl_basic_set_dim(lin
, isl_dim_all
);
955 struct isl_basic_set
*hull
;
956 struct isl_mat
*M
, *U
, *Q
;
958 if (!set
|| total
< 0)
960 lin_dim
= total
- lin
->n_eq
;
961 M
= isl_mat_sub_alloc6(set
->ctx
, lin
->eq
, 0, lin
->n_eq
, 1, total
);
962 M
= isl_mat_left_hermite(M
, 0, &U
, &Q
);
966 isl_basic_set_free(lin
);
968 Q
= isl_mat_drop_rows(Q
, Q
->n_row
- lin_dim
, lin_dim
);
970 U
= isl_mat_lin_to_aff(U
);
971 Q
= isl_mat_lin_to_aff(Q
);
973 set
= isl_set_preimage(set
, U
);
974 set
= isl_set_remove_dims(set
, isl_dim_set
, total
- lin_dim
, lin_dim
);
975 hull
= uset_convex_hull(set
);
976 hull
= isl_basic_set_preimage(hull
, Q
);
980 isl_basic_set_free(lin
);
985 /* Given two polyhedra with as constraints h_{ij} x >= 0 in homegeneous space,
986 * set up an LP for solving
988 * \sum_j \alpha_{1j} h_{1j} = \sum_j \alpha_{2j} h_{2j}
990 * \alpha{i0} corresponds to the (implicit) positivity constraint 1 >= 0
991 * The next \alpha{ij} correspond to the equalities and come in pairs.
992 * The final \alpha{ij} correspond to the inequalities.
994 static __isl_give isl_basic_set
*valid_direction_lp(
995 __isl_take isl_basic_set
*bset1
, __isl_take isl_basic_set
*bset2
)
998 struct isl_basic_set
*lp
;
1004 total
= isl_basic_set_dim(bset1
, isl_dim_all
);
1005 if (total
< 0 || !bset2
)
1009 2 * bset1
->n_eq
+ bset1
->n_ineq
+ 2 * bset2
->n_eq
+ bset2
->n_ineq
;
1010 dim
= isl_space_set_alloc(bset1
->ctx
, 0, n
);
1011 lp
= isl_basic_set_alloc_space(dim
, 0, d
, n
);
1014 for (i
= 0; i
< n
; ++i
) {
1015 k
= isl_basic_set_alloc_inequality(lp
);
1018 isl_seq_clr(lp
->ineq
[k
] + 1, n
);
1019 isl_int_set_si(lp
->ineq
[k
][0], -1);
1020 isl_int_set_si(lp
->ineq
[k
][1 + i
], 1);
1022 for (i
= 0; i
< d
; ++i
) {
1023 k
= isl_basic_set_alloc_equality(lp
);
1027 isl_int_set_si(lp
->eq
[k
][n
], 0); n
++;
1028 /* positivity constraint 1 >= 0 */
1029 isl_int_set_si(lp
->eq
[k
][n
], i
== 0); n
++;
1030 for (j
= 0; j
< bset1
->n_eq
; ++j
) {
1031 isl_int_set(lp
->eq
[k
][n
], bset1
->eq
[j
][i
]); n
++;
1032 isl_int_neg(lp
->eq
[k
][n
], bset1
->eq
[j
][i
]); n
++;
1034 for (j
= 0; j
< bset1
->n_ineq
; ++j
) {
1035 isl_int_set(lp
->eq
[k
][n
], bset1
->ineq
[j
][i
]); n
++;
1037 /* positivity constraint 1 >= 0 */
1038 isl_int_set_si(lp
->eq
[k
][n
], -(i
== 0)); n
++;
1039 for (j
= 0; j
< bset2
->n_eq
; ++j
) {
1040 isl_int_neg(lp
->eq
[k
][n
], bset2
->eq
[j
][i
]); n
++;
1041 isl_int_set(lp
->eq
[k
][n
], bset2
->eq
[j
][i
]); n
++;
1043 for (j
= 0; j
< bset2
->n_ineq
; ++j
) {
1044 isl_int_neg(lp
->eq
[k
][n
], bset2
->ineq
[j
][i
]); n
++;
1047 lp
= isl_basic_set_gauss(lp
, NULL
);
1048 isl_basic_set_free(bset1
);
1049 isl_basic_set_free(bset2
);
1052 isl_basic_set_free(bset1
);
1053 isl_basic_set_free(bset2
);
1057 /* Compute a vector s in the homogeneous space such that <s, r> > 0
1058 * for all rays in the homogeneous space of the two cones that correspond
1059 * to the input polyhedra bset1 and bset2.
1061 * We compute s as a vector that satisfies
1063 * s = \sum_j \alpha_{ij} h_{ij} for i = 1,2 (*)
1065 * with h_{ij} the normals of the facets of polyhedron i
1066 * (including the "positivity constraint" 1 >= 0) and \alpha_{ij}
1067 * strictly positive numbers. For simplicity we impose \alpha_{ij} >= 1.
1068 * We first set up an LP with as variables the \alpha{ij}.
1069 * In this formulation, for each polyhedron i,
1070 * the first constraint is the positivity constraint, followed by pairs
1071 * of variables for the equalities, followed by variables for the inequalities.
1072 * We then simply pick a feasible solution and compute s using (*).
1074 * Note that we simply pick any valid direction and make no attempt
1075 * to pick a "good" or even the "best" valid direction.
1077 static __isl_give isl_vec
*valid_direction(
1078 __isl_take isl_basic_set
*bset1
, __isl_take isl_basic_set
*bset2
)
1080 struct isl_basic_set
*lp
;
1081 struct isl_tab
*tab
;
1082 struct isl_vec
*sample
= NULL
;
1083 struct isl_vec
*dir
;
1088 if (!bset1
|| !bset2
)
1090 lp
= valid_direction_lp(isl_basic_set_copy(bset1
),
1091 isl_basic_set_copy(bset2
));
1092 tab
= isl_tab_from_basic_set(lp
, 0);
1093 sample
= isl_tab_get_sample_value(tab
);
1095 isl_basic_set_free(lp
);
1098 d
= isl_basic_set_dim(bset1
, isl_dim_all
);
1101 dir
= isl_vec_alloc(bset1
->ctx
, 1 + d
);
1104 isl_seq_clr(dir
->block
.data
+ 1, dir
->size
- 1);
1106 /* positivity constraint 1 >= 0 */
1107 isl_int_set(dir
->block
.data
[0], sample
->block
.data
[n
]); n
++;
1108 for (i
= 0; i
< bset1
->n_eq
; ++i
) {
1109 isl_int_sub(sample
->block
.data
[n
],
1110 sample
->block
.data
[n
], sample
->block
.data
[n
+1]);
1111 isl_seq_combine(dir
->block
.data
,
1112 bset1
->ctx
->one
, dir
->block
.data
,
1113 sample
->block
.data
[n
], bset1
->eq
[i
], 1 + d
);
1117 for (i
= 0; i
< bset1
->n_ineq
; ++i
)
1118 isl_seq_combine(dir
->block
.data
,
1119 bset1
->ctx
->one
, dir
->block
.data
,
1120 sample
->block
.data
[n
++], bset1
->ineq
[i
], 1 + d
);
1121 isl_vec_free(sample
);
1122 isl_seq_normalize(bset1
->ctx
, dir
->el
, dir
->size
);
1123 isl_basic_set_free(bset1
);
1124 isl_basic_set_free(bset2
);
1127 isl_vec_free(sample
);
1128 isl_basic_set_free(bset1
);
1129 isl_basic_set_free(bset2
);
1133 /* Given a polyhedron b_i + A_i x >= 0 and a map T = S^{-1},
1134 * compute b_i' + A_i' x' >= 0, with
1136 * [ b_i A_i ] [ y' ] [ y' ]
1137 * [ 1 0 ] S^{-1} [ x' ] >= 0 or [ b_i' A_i' ] [ x' ] >= 0
1139 * In particular, add the "positivity constraint" and then perform
1142 static __isl_give isl_basic_set
*homogeneous_map(__isl_take isl_basic_set
*bset
,
1143 __isl_take isl_mat
*T
)
1148 total
= isl_basic_set_dim(bset
, isl_dim_all
);
1151 bset
= isl_basic_set_extend_constraints(bset
, 0, 1);
1152 k
= isl_basic_set_alloc_inequality(bset
);
1155 isl_seq_clr(bset
->ineq
[k
] + 1, total
);
1156 isl_int_set_si(bset
->ineq
[k
][0], 1);
1157 bset
= isl_basic_set_preimage(bset
, T
);
1161 isl_basic_set_free(bset
);
1165 /* Compute the convex hull of a pair of basic sets without any parameters or
1166 * integer divisions, where the convex hull is known to be pointed,
1167 * but the basic sets may be unbounded.
1169 * We turn this problem into the computation of a convex hull of a pair
1170 * _bounded_ polyhedra by "changing the direction of the homogeneous
1171 * dimension". This idea is due to Matthias Koeppe.
1173 * Consider the cones in homogeneous space that correspond to the
1174 * input polyhedra. The rays of these cones are also rays of the
1175 * polyhedra if the coordinate that corresponds to the homogeneous
1176 * dimension is zero. That is, if the inner product of the rays
1177 * with the homogeneous direction is zero.
1178 * The cones in the homogeneous space can also be considered to
1179 * correspond to other pairs of polyhedra by chosing a different
1180 * homogeneous direction. To ensure that both of these polyhedra
1181 * are bounded, we need to make sure that all rays of the cones
1182 * correspond to vertices and not to rays.
1183 * Let s be a direction such that <s, r> > 0 for all rays r of both cones.
1184 * Then using s as a homogeneous direction, we obtain a pair of polytopes.
1185 * The vector s is computed in valid_direction.
1187 * Note that we need to consider _all_ rays of the cones and not just
1188 * the rays that correspond to rays in the polyhedra. If we were to
1189 * only consider those rays and turn them into vertices, then we
1190 * may inadvertently turn some vertices into rays.
1192 * The standard homogeneous direction is the unit vector in the 0th coordinate.
1193 * We therefore transform the two polyhedra such that the selected
1194 * direction is mapped onto this standard direction and then proceed
1195 * with the normal computation.
1196 * Let S be a non-singular square matrix with s as its first row,
1197 * then we want to map the polyhedra to the space
1199 * [ y' ] [ y ] [ y ] [ y' ]
1200 * [ x' ] = S [ x ] i.e., [ x ] = S^{-1} [ x' ]
1202 * We take S to be the unimodular completion of s to limit the growth
1203 * of the coefficients in the following computations.
1205 * Let b_i + A_i x >= 0 be the constraints of polyhedron i.
1206 * We first move to the homogeneous dimension
1208 * b_i y + A_i x >= 0 [ b_i A_i ] [ y ] [ 0 ]
1209 * y >= 0 or [ 1 0 ] [ x ] >= [ 0 ]
1211 * Then we change directoin
1213 * [ b_i A_i ] [ y' ] [ y' ]
1214 * [ 1 0 ] S^{-1} [ x' ] >= 0 or [ b_i' A_i' ] [ x' ] >= 0
1216 * Then we compute the convex hull of the polytopes b_i' + A_i' x' >= 0
1217 * resulting in b' + A' x' >= 0, which we then convert back
1220 * [ b' A' ] S [ x ] >= 0 or [ b A ] [ x ] >= 0
1222 * The polyhedron b + A x >= 0 is then the convex hull of the input polyhedra.
1224 static __isl_give isl_basic_set
*convex_hull_pair_pointed(
1225 __isl_take isl_basic_set
*bset1
, __isl_take isl_basic_set
*bset2
)
1227 struct isl_ctx
*ctx
= NULL
;
1228 struct isl_vec
*dir
= NULL
;
1229 struct isl_mat
*T
= NULL
;
1230 struct isl_mat
*T2
= NULL
;
1231 struct isl_basic_set
*hull
;
1232 struct isl_set
*set
;
1234 if (!bset1
|| !bset2
)
1236 ctx
= isl_basic_set_get_ctx(bset1
);
1237 dir
= valid_direction(isl_basic_set_copy(bset1
),
1238 isl_basic_set_copy(bset2
));
1241 T
= isl_mat_alloc(ctx
, dir
->size
, dir
->size
);
1244 isl_seq_cpy(T
->row
[0], dir
->block
.data
, dir
->size
);
1245 T
= isl_mat_unimodular_complete(T
, 1);
1246 T2
= isl_mat_right_inverse(isl_mat_copy(T
));
1248 bset1
= homogeneous_map(bset1
, isl_mat_copy(T2
));
1249 bset2
= homogeneous_map(bset2
, T2
);
1250 set
= isl_set_alloc_space(isl_basic_set_get_space(bset1
), 2, 0);
1251 set
= isl_set_add_basic_set(set
, bset1
);
1252 set
= isl_set_add_basic_set(set
, bset2
);
1253 hull
= uset_convex_hull(set
);
1254 hull
= isl_basic_set_preimage(hull
, T
);
1261 isl_basic_set_free(bset1
);
1262 isl_basic_set_free(bset2
);
1266 static __isl_give isl_basic_set
*uset_convex_hull_wrap(__isl_take isl_set
*set
);
1267 static __isl_give isl_basic_set
*modulo_affine_hull(
1268 __isl_take isl_set
*set
, __isl_take isl_basic_set
*affine_hull
);
1270 /* Compute the convex hull of a pair of basic sets without any parameters or
1271 * integer divisions.
1273 * This function is called from uset_convex_hull_unbounded, which
1274 * means that the complete convex hull is unbounded. Some pairs
1275 * of basic sets may still be bounded, though.
1276 * They may even lie inside a lower dimensional space, in which
1277 * case they need to be handled inside their affine hull since
1278 * the main algorithm assumes that the result is full-dimensional.
1280 * If the convex hull of the two basic sets would have a non-trivial
1281 * lineality space, we first project out this lineality space.
1283 static __isl_give isl_basic_set
*convex_hull_pair(
1284 __isl_take isl_basic_set
*bset1
, __isl_take isl_basic_set
*bset2
)
1286 isl_basic_set
*lin
, *aff
;
1287 isl_bool bounded1
, bounded2
;
1290 if (bset1
->ctx
->opt
->convex
== ISL_CONVEX_HULL_FM
)
1291 return convex_hull_pair_elim(bset1
, bset2
);
1293 aff
= isl_set_affine_hull(isl_basic_set_union(isl_basic_set_copy(bset1
),
1294 isl_basic_set_copy(bset2
)));
1298 return modulo_affine_hull(isl_basic_set_union(bset1
, bset2
), aff
);
1299 isl_basic_set_free(aff
);
1301 bounded1
= isl_basic_set_is_bounded(bset1
);
1302 bounded2
= isl_basic_set_is_bounded(bset2
);
1304 if (bounded1
< 0 || bounded2
< 0)
1307 if (bounded1
&& bounded2
)
1308 return uset_convex_hull_wrap(isl_basic_set_union(bset1
, bset2
));
1310 if (bounded1
|| bounded2
)
1311 return convex_hull_pair_pointed(bset1
, bset2
);
1313 lin
= induced_lineality_space(isl_basic_set_copy(bset1
),
1314 isl_basic_set_copy(bset2
));
1317 if (isl_basic_set_plain_is_universe(lin
)) {
1318 isl_basic_set_free(bset1
);
1319 isl_basic_set_free(bset2
);
1322 total
= isl_basic_set_dim(lin
, isl_dim_all
);
1323 if (lin
->n_eq
< total
) {
1324 struct isl_set
*set
;
1325 set
= isl_set_alloc_space(isl_basic_set_get_space(bset1
), 2, 0);
1326 set
= isl_set_add_basic_set(set
, bset1
);
1327 set
= isl_set_add_basic_set(set
, bset2
);
1328 return modulo_lineality(set
, lin
);
1330 isl_basic_set_free(lin
);
1334 return convex_hull_pair_pointed(bset1
, bset2
);
1336 isl_basic_set_free(bset1
);
1337 isl_basic_set_free(bset2
);
1341 /* Compute the lineality space of a basic set.
1342 * We basically just drop the constants and turn every inequality
1344 * Any explicit representations of local variables are removed
1345 * because they may no longer be valid representations
1346 * in the lineality space.
1348 __isl_give isl_basic_set
*isl_basic_set_lineality_space(
1349 __isl_take isl_basic_set
*bset
)
1352 struct isl_basic_set
*lin
= NULL
;
1353 isl_size n_div
, dim
;
1355 n_div
= isl_basic_set_dim(bset
, isl_dim_div
);
1356 dim
= isl_basic_set_dim(bset
, isl_dim_all
);
1357 if (n_div
< 0 || dim
< 0)
1358 return isl_basic_set_free(bset
);
1360 lin
= isl_basic_set_alloc_space(isl_basic_set_get_space(bset
),
1362 for (i
= 0; i
< n_div
; ++i
)
1363 if (isl_basic_set_alloc_div(lin
) < 0)
1367 for (i
= 0; i
< bset
->n_eq
; ++i
) {
1368 k
= isl_basic_set_alloc_equality(lin
);
1371 isl_int_set_si(lin
->eq
[k
][0], 0);
1372 isl_seq_cpy(lin
->eq
[k
] + 1, bset
->eq
[i
] + 1, dim
);
1374 lin
= isl_basic_set_gauss(lin
, NULL
);
1377 for (i
= 0; i
< bset
->n_ineq
&& lin
->n_eq
< dim
; ++i
) {
1378 k
= isl_basic_set_alloc_equality(lin
);
1381 isl_int_set_si(lin
->eq
[k
][0], 0);
1382 isl_seq_cpy(lin
->eq
[k
] + 1, bset
->ineq
[i
] + 1, dim
);
1383 lin
= isl_basic_set_gauss(lin
, NULL
);
1387 isl_basic_set_free(bset
);
1390 isl_basic_set_free(lin
);
1391 isl_basic_set_free(bset
);
1395 /* Compute the (linear) hull of the lineality spaces of the basic sets in the
1398 __isl_give isl_basic_set
*isl_set_combined_lineality_space(
1399 __isl_take isl_set
*set
)
1402 struct isl_set
*lin
= NULL
;
1407 isl_space
*space
= isl_set_get_space(set
);
1409 return isl_basic_set_empty(space
);
1412 lin
= isl_set_alloc_space(isl_set_get_space(set
), set
->n
, 0);
1413 for (i
= 0; i
< set
->n
; ++i
)
1414 lin
= isl_set_add_basic_set(lin
,
1415 isl_basic_set_lineality_space(isl_basic_set_copy(set
->p
[i
])));
1417 return isl_set_affine_hull(lin
);
1420 /* Compute the convex hull of a set without any parameters or
1421 * integer divisions.
1422 * In each step, we combined two basic sets until only one
1423 * basic set is left.
1424 * The input basic sets are assumed not to have a non-trivial
1425 * lineality space. If any of the intermediate results has
1426 * a non-trivial lineality space, it is projected out.
1428 static __isl_give isl_basic_set
*uset_convex_hull_unbounded(
1429 __isl_take isl_set
*set
)
1431 isl_basic_set_list
*list
;
1433 list
= isl_set_get_basic_set_list(set
);
1438 struct isl_basic_set
*t
;
1439 isl_basic_set
*bset1
, *bset2
;
1441 n
= isl_basic_set_list_n_basic_set(list
);
1445 isl_die(isl_basic_set_list_get_ctx(list
),
1447 "expecting at least two elements", goto error
);
1448 bset1
= isl_basic_set_list_get_basic_set(list
, n
- 1);
1449 bset2
= isl_basic_set_list_get_basic_set(list
, n
- 2);
1450 bset1
= convex_hull_pair(bset1
, bset2
);
1452 isl_basic_set_list_free(list
);
1455 bset1
= isl_basic_set_underlying_set(bset1
);
1456 list
= isl_basic_set_list_drop(list
, n
- 2, 2);
1457 list
= isl_basic_set_list_add(list
, bset1
);
1459 t
= isl_basic_set_list_get_basic_set(list
, n
- 2);
1460 t
= isl_basic_set_lineality_space(t
);
1463 if (isl_basic_set_plain_is_universe(t
)) {
1464 isl_basic_set_list_free(list
);
1467 total
= isl_basic_set_dim(t
, isl_dim_all
);
1468 if (t
->n_eq
< total
) {
1469 set
= isl_basic_set_list_union(list
);
1470 return modulo_lineality(set
, t
);
1472 isl_basic_set_free(t
);
1479 isl_basic_set_list_free(list
);
1483 /* Compute an initial hull for wrapping containing a single initial
1485 * This function assumes that the given set is bounded.
1487 static __isl_give isl_basic_set
*initial_hull(__isl_take isl_basic_set
*hull
,
1488 __isl_keep isl_set
*set
)
1490 struct isl_mat
*bounds
= NULL
;
1496 bounds
= initial_facet_constraint(set
);
1499 k
= isl_basic_set_alloc_inequality(hull
);
1502 dim
= isl_set_dim(set
, isl_dim_set
);
1505 isl_assert(set
->ctx
, 1 + dim
== bounds
->n_col
, goto error
);
1506 isl_seq_cpy(hull
->ineq
[k
], bounds
->row
[0], bounds
->n_col
);
1507 isl_mat_free(bounds
);
1511 isl_basic_set_free(hull
);
1512 isl_mat_free(bounds
);
1516 struct max_constraint
{
1522 static isl_bool
max_constraint_equal(const void *entry
, const void *val
)
1524 struct max_constraint
*a
= (struct max_constraint
*)entry
;
1525 isl_int
*b
= (isl_int
*)val
;
1527 return isl_bool_ok(isl_seq_eq(a
->c
->row
[0] + 1, b
, a
->c
->n_col
- 1));
1530 static isl_stat
update_constraint(struct isl_ctx
*ctx
,
1531 struct isl_hash_table
*table
,
1532 isl_int
*con
, unsigned len
, int n
, int ineq
)
1534 struct isl_hash_table_entry
*entry
;
1535 struct max_constraint
*c
;
1538 c_hash
= isl_seq_get_hash(con
+ 1, len
);
1539 entry
= isl_hash_table_find(ctx
, table
, c_hash
, max_constraint_equal
,
1542 return isl_stat_error
;
1543 if (entry
== isl_hash_table_entry_none
)
1547 isl_hash_table_remove(ctx
, table
, entry
);
1551 if (isl_int_gt(c
->c
->row
[0][0], con
[0]))
1553 if (isl_int_eq(c
->c
->row
[0][0], con
[0])) {
1558 c
->c
= isl_mat_cow(c
->c
);
1559 isl_int_set(c
->c
->row
[0][0], con
[0]);
1565 /* Check whether the constraint hash table "table" contains the constraint
1568 static isl_bool
has_constraint(struct isl_ctx
*ctx
,
1569 struct isl_hash_table
*table
, isl_int
*con
, unsigned len
, int n
)
1571 struct isl_hash_table_entry
*entry
;
1572 struct max_constraint
*c
;
1575 c_hash
= isl_seq_get_hash(con
+ 1, len
);
1576 entry
= isl_hash_table_find(ctx
, table
, c_hash
, max_constraint_equal
,
1579 return isl_bool_error
;
1580 if (entry
== isl_hash_table_entry_none
)
1581 return isl_bool_false
;
1584 return isl_bool_false
;
1585 return isl_bool_ok(isl_int_eq(c
->c
->row
[0][0], con
[0]));
1588 /* Are the constraints of "bset" known to be facets?
1589 * If there are any equality constraints, then they are not.
1590 * If there may be redundant constraints, then those
1591 * redundant constraints are not facets.
1593 static isl_bool
has_facets(__isl_keep isl_basic_set
*bset
)
1597 n_eq
= isl_basic_set_n_equality(bset
);
1599 return isl_bool_error
;
1601 return isl_bool_false
;
1602 return ISL_F_ISSET(bset
, ISL_BASIC_SET_NO_REDUNDANT
);
1605 /* Check for inequality constraints of a basic set without equalities
1606 * or redundant constraints
1607 * such that the same or more stringent copies of the constraint appear
1608 * in all of the basic sets. Such constraints are necessarily facet
1609 * constraints of the convex hull.
1611 * If the resulting basic set is by chance identical to one of
1612 * the basic sets in "set", then we know that this basic set contains
1613 * all other basic sets and is therefore the convex hull of set.
1614 * In this case we set *is_hull to 1.
1616 static __isl_give isl_basic_set
*common_constraints(
1617 __isl_take isl_basic_set
*hull
, __isl_keep isl_set
*set
, int *is_hull
)
1620 int min_constraints
;
1622 struct max_constraint
*constraints
= NULL
;
1623 struct isl_hash_table
*table
= NULL
;
1628 for (i
= 0; i
< set
->n
; ++i
) {
1629 isl_bool facets
= has_facets(set
->p
[i
]);
1631 return isl_basic_set_free(hull
);
1637 min_constraints
= set
->p
[i
]->n_ineq
;
1639 for (i
= best
+ 1; i
< set
->n
; ++i
) {
1640 isl_bool facets
= has_facets(set
->p
[i
]);
1642 return isl_basic_set_free(hull
);
1645 if (set
->p
[i
]->n_ineq
>= min_constraints
)
1647 min_constraints
= set
->p
[i
]->n_ineq
;
1650 constraints
= isl_calloc_array(hull
->ctx
, struct max_constraint
,
1654 table
= isl_alloc_type(hull
->ctx
, struct isl_hash_table
);
1655 if (isl_hash_table_init(hull
->ctx
, table
, min_constraints
))
1658 total
= isl_set_dim(set
, isl_dim_all
);
1661 for (i
= 0; i
< set
->p
[best
]->n_ineq
; ++i
) {
1662 constraints
[i
].c
= isl_mat_sub_alloc6(hull
->ctx
,
1663 set
->p
[best
]->ineq
+ i
, 0, 1, 0, 1 + total
);
1664 if (!constraints
[i
].c
)
1666 constraints
[i
].ineq
= 1;
1668 for (i
= 0; i
< min_constraints
; ++i
) {
1669 struct isl_hash_table_entry
*entry
;
1671 c_hash
= isl_seq_get_hash(constraints
[i
].c
->row
[0] + 1, total
);
1672 entry
= isl_hash_table_find(hull
->ctx
, table
, c_hash
,
1673 max_constraint_equal
, constraints
[i
].c
->row
[0] + 1, 1);
1676 isl_assert(hull
->ctx
, !entry
->data
, goto error
);
1677 entry
->data
= &constraints
[i
];
1681 for (s
= 0; s
< set
->n
; ++s
) {
1685 for (i
= 0; i
< set
->p
[s
]->n_eq
; ++i
) {
1686 isl_int
*eq
= set
->p
[s
]->eq
[i
];
1687 for (j
= 0; j
< 2; ++j
) {
1688 isl_seq_neg(eq
, eq
, 1 + total
);
1689 if (update_constraint(hull
->ctx
, table
,
1690 eq
, total
, n
, 0) < 0)
1694 for (i
= 0; i
< set
->p
[s
]->n_ineq
; ++i
) {
1695 isl_int
*ineq
= set
->p
[s
]->ineq
[i
];
1696 if (update_constraint(hull
->ctx
, table
, ineq
, total
, n
,
1697 set
->p
[s
]->n_eq
== 0) < 0)
1703 for (i
= 0; i
< min_constraints
; ++i
) {
1704 if (constraints
[i
].count
< n
)
1706 if (!constraints
[i
].ineq
)
1708 j
= isl_basic_set_alloc_inequality(hull
);
1711 isl_seq_cpy(hull
->ineq
[j
], constraints
[i
].c
->row
[0], 1 + total
);
1714 for (s
= 0; s
< set
->n
; ++s
) {
1715 if (set
->p
[s
]->n_eq
)
1717 if (set
->p
[s
]->n_ineq
!= hull
->n_ineq
)
1719 for (i
= 0; i
< set
->p
[s
]->n_ineq
; ++i
) {
1721 isl_int
*ineq
= set
->p
[s
]->ineq
[i
];
1722 has
= has_constraint(hull
->ctx
, table
, ineq
, total
, n
);
1728 if (i
== set
->p
[s
]->n_ineq
)
1732 isl_hash_table_clear(table
);
1733 for (i
= 0; i
< min_constraints
; ++i
)
1734 isl_mat_free(constraints
[i
].c
);
1739 isl_hash_table_clear(table
);
1742 for (i
= 0; i
< min_constraints
; ++i
)
1743 isl_mat_free(constraints
[i
].c
);
1748 /* Create a template for the convex hull of "set" and fill it up
1749 * obvious facet constraints, if any. If the result happens to
1750 * be the convex hull of "set" then *is_hull is set to 1.
1752 static __isl_give isl_basic_set
*proto_hull(__isl_keep isl_set
*set
,
1755 struct isl_basic_set
*hull
;
1760 for (i
= 0; i
< set
->n
; ++i
) {
1761 n_ineq
+= set
->p
[i
]->n_eq
;
1762 n_ineq
+= set
->p
[i
]->n_ineq
;
1764 hull
= isl_basic_set_alloc_space(isl_space_copy(set
->dim
), 0, 0, n_ineq
);
1765 hull
= isl_basic_set_set_rational(hull
);
1768 return common_constraints(hull
, set
, is_hull
);
1771 static __isl_give isl_basic_set
*uset_convex_hull_wrap(__isl_take isl_set
*set
)
1773 struct isl_basic_set
*hull
;
1776 hull
= proto_hull(set
, &is_hull
);
1777 if (hull
&& !is_hull
) {
1778 if (hull
->n_ineq
== 0)
1779 hull
= initial_hull(hull
, set
);
1780 hull
= extend(hull
, set
);
1787 /* Compute the convex hull of a set without any parameters or
1788 * integer divisions. Depending on whether the set is bounded,
1789 * we pass control to the wrapping based convex hull or
1790 * the Fourier-Motzkin elimination based convex hull.
1791 * We also handle a few special cases before checking the boundedness.
1793 static __isl_give isl_basic_set
*uset_convex_hull(__isl_take isl_set
*set
)
1797 struct isl_basic_set
*convex_hull
= NULL
;
1798 struct isl_basic_set
*lin
;
1800 dim
= isl_set_dim(set
, isl_dim_all
);
1804 return convex_hull_0d(set
);
1806 set
= isl_set_coalesce(set
);
1807 set
= isl_set_set_rational(set
);
1812 convex_hull
= isl_basic_set_copy(set
->p
[0]);
1817 return convex_hull_1d(set
);
1819 bounded
= isl_set_is_bounded(set
);
1822 if (bounded
&& set
->ctx
->opt
->convex
== ISL_CONVEX_HULL_WRAP
)
1823 return uset_convex_hull_wrap(set
);
1825 lin
= isl_set_combined_lineality_space(isl_set_copy(set
));
1828 if (isl_basic_set_plain_is_universe(lin
)) {
1832 if (lin
->n_eq
< dim
)
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 __isl_give isl_basic_set
*uset_convex_hull_wrap_bounded(
1848 __isl_take isl_set
*set
)
1850 struct isl_basic_set
*convex_hull
= NULL
;
1853 dim
= isl_set_dim(set
, isl_dim_all
);
1858 convex_hull
= isl_basic_set_universe(isl_space_copy(set
->dim
));
1860 convex_hull
= isl_basic_set_set_rational(convex_hull
);
1864 set
= isl_set_set_rational(set
);
1865 set
= isl_set_coalesce(set
);
1869 convex_hull
= isl_basic_set_copy(set
->p
[0]);
1871 convex_hull
= isl_basic_map_remove_redundancies(convex_hull
);
1875 return convex_hull_1d(set
);
1877 return uset_convex_hull_wrap(set
);
1883 /* Compute the convex hull of set "set" with affine hull "affine_hull",
1884 * We first remove the equalities (transforming the set), compute the
1885 * convex hull of the transformed set and then add the equalities back
1886 * (after performing the inverse transformation.
1888 static __isl_give isl_basic_set
*modulo_affine_hull(
1889 __isl_take isl_set
*set
, __isl_take isl_basic_set
*affine_hull
)
1893 struct isl_basic_set
*dummy
;
1894 struct isl_basic_set
*convex_hull
;
1896 dummy
= isl_basic_set_remove_equalities(
1897 isl_basic_set_copy(affine_hull
), &T
, &T2
);
1900 isl_basic_set_free(dummy
);
1901 set
= isl_set_preimage(set
, T
);
1902 convex_hull
= uset_convex_hull(set
);
1903 convex_hull
= isl_basic_set_preimage(convex_hull
, T2
);
1904 convex_hull
= isl_basic_set_intersect(convex_hull
, affine_hull
);
1909 isl_basic_set_free(affine_hull
);
1914 /* Return an empty basic map living in the same space as "map".
1916 static __isl_give isl_basic_map
*replace_map_by_empty_basic_map(
1917 __isl_take isl_map
*map
)
1921 space
= isl_map_get_space(map
);
1923 return isl_basic_map_empty(space
);
1926 /* Compute the convex hull of a map.
1928 * The implementation was inspired by "Extended Convex Hull" by Fukuda et al.,
1929 * specifically, the wrapping of facets to obtain new facets.
1931 __isl_give isl_basic_map
*isl_map_convex_hull(__isl_take isl_map
*map
)
1933 struct isl_basic_set
*bset
;
1934 struct isl_basic_map
*model
= NULL
;
1935 struct isl_basic_set
*affine_hull
= NULL
;
1936 struct isl_basic_map
*convex_hull
= NULL
;
1937 struct isl_set
*set
= NULL
;
1939 map
= isl_map_detect_equalities(map
);
1940 map
= isl_map_align_divs_internal(map
);
1945 return replace_map_by_empty_basic_map(map
);
1947 model
= isl_basic_map_copy(map
->p
[0]);
1948 set
= isl_map_underlying_set(map
);
1952 affine_hull
= isl_set_affine_hull(isl_set_copy(set
));
1955 if (affine_hull
->n_eq
!= 0)
1956 bset
= modulo_affine_hull(set
, affine_hull
);
1958 isl_basic_set_free(affine_hull
);
1959 bset
= uset_convex_hull(set
);
1962 convex_hull
= isl_basic_map_overlying_set(bset
, model
);
1966 ISL_F_SET(convex_hull
, ISL_BASIC_MAP_NO_IMPLICIT
);
1967 ISL_F_SET(convex_hull
, ISL_BASIC_MAP_ALL_EQUALITIES
);
1968 ISL_F_CLR(convex_hull
, ISL_BASIC_MAP_RATIONAL
);
1972 isl_basic_map_free(model
);
1976 struct isl_basic_set
*isl_set_convex_hull(struct isl_set
*set
)
1978 return bset_from_bmap(isl_map_convex_hull(set_to_map(set
)));
1981 __isl_give isl_basic_map
*isl_map_polyhedral_hull(__isl_take isl_map
*map
)
1983 isl_basic_map
*hull
;
1985 hull
= isl_map_convex_hull(map
);
1986 return isl_basic_map_remove_divs(hull
);
1989 __isl_give isl_basic_set
*isl_set_polyhedral_hull(__isl_take isl_set
*set
)
1991 return bset_from_bmap(isl_map_polyhedral_hull(set_to_map(set
)));
1994 struct sh_data_entry
{
1995 struct isl_hash_table
*table
;
1996 struct isl_tab
*tab
;
1999 /* Holds the data needed during the simple hull computation.
2001 * n the number of basic sets in the original set
2002 * hull_table a hash table of already computed constraints
2003 * in the simple hull
2004 * p for each basic set,
2005 * table a hash table of the constraints
2006 * tab the tableau corresponding to the basic set
2009 struct isl_ctx
*ctx
;
2011 struct isl_hash_table
*hull_table
;
2012 struct sh_data_entry p
[1];
2015 static void sh_data_free(struct sh_data
*data
)
2021 isl_hash_table_free(data
->ctx
, data
->hull_table
);
2022 for (i
= 0; i
< data
->n
; ++i
) {
2023 isl_hash_table_free(data
->ctx
, data
->p
[i
].table
);
2024 isl_tab_free(data
->p
[i
].tab
);
2029 struct ineq_cmp_data
{
2034 static isl_bool
has_ineq(const void *entry
, const void *val
)
2036 isl_int
*row
= (isl_int
*)entry
;
2037 struct ineq_cmp_data
*v
= (struct ineq_cmp_data
*)val
;
2039 return isl_bool_ok(isl_seq_eq(row
+ 1, v
->p
+ 1, v
->len
) ||
2040 isl_seq_is_neg(row
+ 1, v
->p
+ 1, v
->len
));
2043 static int hash_ineq(struct isl_ctx
*ctx
, struct isl_hash_table
*table
,
2044 isl_int
*ineq
, unsigned len
)
2047 struct ineq_cmp_data v
;
2048 struct isl_hash_table_entry
*entry
;
2052 c_hash
= isl_seq_get_hash(ineq
+ 1, len
);
2053 entry
= isl_hash_table_find(ctx
, table
, c_hash
, has_ineq
, &v
, 1);
2060 /* Fill hash table "table" with the constraints of "bset".
2061 * Equalities are added as two inequalities.
2062 * The value in the hash table is a pointer to the (in)equality of "bset".
2064 static isl_stat
hash_basic_set(struct isl_hash_table
*table
,
2065 __isl_keep isl_basic_set
*bset
)
2068 isl_size dim
= isl_basic_set_dim(bset
, isl_dim_all
);
2071 return isl_stat_error
;
2072 for (i
= 0; i
< bset
->n_eq
; ++i
) {
2073 for (j
= 0; j
< 2; ++j
) {
2074 isl_seq_neg(bset
->eq
[i
], bset
->eq
[i
], 1 + dim
);
2075 if (hash_ineq(bset
->ctx
, table
, bset
->eq
[i
], dim
) < 0)
2076 return isl_stat_error
;
2079 for (i
= 0; i
< bset
->n_ineq
; ++i
) {
2080 if (hash_ineq(bset
->ctx
, table
, bset
->ineq
[i
], dim
) < 0)
2081 return isl_stat_error
;
2086 static struct sh_data
*sh_data_alloc(__isl_keep isl_set
*set
, unsigned n_ineq
)
2088 struct sh_data
*data
;
2091 data
= isl_calloc(set
->ctx
, struct sh_data
,
2092 sizeof(struct sh_data
) +
2093 (set
->n
- 1) * sizeof(struct sh_data_entry
));
2096 data
->ctx
= set
->ctx
;
2098 data
->hull_table
= isl_hash_table_alloc(set
->ctx
, n_ineq
);
2099 if (!data
->hull_table
)
2101 for (i
= 0; i
< set
->n
; ++i
) {
2102 data
->p
[i
].table
= isl_hash_table_alloc(set
->ctx
,
2103 2 * set
->p
[i
]->n_eq
+ set
->p
[i
]->n_ineq
);
2104 if (!data
->p
[i
].table
)
2106 if (hash_basic_set(data
->p
[i
].table
, set
->p
[i
]) < 0)
2115 /* Check if inequality "ineq" is a bound for basic set "j" or if
2116 * it can be relaxed (by increasing the constant term) to become
2117 * a bound for that basic set. In the latter case, the constant
2119 * Relaxation of the constant term is only allowed if "shift" is set.
2121 * Return 1 if "ineq" is a bound
2122 * 0 if "ineq" may attain arbitrarily small values on basic set "j"
2123 * -1 if some error occurred
2125 static int is_bound(struct sh_data
*data
, __isl_keep isl_set
*set
, int j
,
2126 isl_int
*ineq
, int shift
)
2128 enum isl_lp_result res
;
2131 if (!data
->p
[j
].tab
) {
2132 data
->p
[j
].tab
= isl_tab_from_basic_set(set
->p
[j
], 0);
2133 if (!data
->p
[j
].tab
)
2139 res
= isl_tab_min(data
->p
[j
].tab
, ineq
, data
->ctx
->one
,
2141 if (res
== isl_lp_ok
&& isl_int_is_neg(opt
)) {
2143 isl_int_sub(ineq
[0], ineq
[0], opt
);
2145 res
= isl_lp_unbounded
;
2150 return (res
== isl_lp_ok
|| res
== isl_lp_empty
) ? 1 :
2151 res
== isl_lp_unbounded
? 0 : -1;
2154 /* Set the constant term of "ineq" to the maximum of those of the constraints
2155 * in the basic sets of "set" following "i" that are parallel to "ineq".
2156 * That is, if any of the basic sets of "set" following "i" have a more
2157 * relaxed copy of "ineq", then replace "ineq" by the most relaxed copy.
2158 * "c_hash" is the hash value of the linear part of "ineq".
2159 * "v" has been set up for use by has_ineq.
2161 * Note that the two inequality constraints corresponding to an equality are
2162 * represented by the same inequality constraint in data->p[j].table
2163 * (but with different hash values). This means the constraint (or at
2164 * least its constant term) may need to be temporarily negated to get
2165 * the actually hashed constraint.
2167 static isl_stat
set_max_constant_term(struct sh_data
*data
,
2168 __isl_keep isl_set
*set
,
2169 int i
, isl_int
*ineq
, uint32_t c_hash
, struct ineq_cmp_data
*v
)
2173 struct isl_hash_table_entry
*entry
;
2175 ctx
= isl_set_get_ctx(set
);
2176 for (j
= i
+ 1; j
< set
->n
; ++j
) {
2180 entry
= isl_hash_table_find(ctx
, data
->p
[j
].table
,
2181 c_hash
, &has_ineq
, v
, 0);
2183 return isl_stat_error
;
2184 if (entry
== isl_hash_table_entry_none
)
2187 ineq_j
= entry
->data
;
2188 neg
= isl_seq_is_neg(ineq_j
+ 1, ineq
+ 1, v
->len
);
2190 isl_int_neg(ineq_j
[0], ineq_j
[0]);
2191 if (isl_int_gt(ineq_j
[0], ineq
[0]))
2192 isl_int_set(ineq
[0], ineq_j
[0]);
2194 isl_int_neg(ineq_j
[0], ineq_j
[0]);
2200 /* Check if inequality "ineq" from basic set "i" is or can be relaxed to
2201 * become a bound on the whole set. If so, add the (relaxed) inequality
2202 * to "hull". Relaxation is only allowed if "shift" is set.
2204 * We first check if "hull" already contains a translate of the inequality.
2205 * If so, we are done.
2206 * Then, we check if any of the previous basic sets contains a translate
2207 * of the inequality. If so, then we have already considered this
2208 * inequality and we are done.
2209 * Otherwise, for each basic set other than "i", we check if the inequality
2210 * is a bound on the basic set, but first replace the constant term
2211 * by the maximal value of any translate of the inequality in any
2212 * of the following basic sets.
2213 * For previous basic sets, we know that they do not contain a translate
2214 * of the inequality, so we directly call is_bound.
2215 * For following basic sets, we first check if a translate of the
2216 * inequality appears in its description. If so, the constant term
2217 * of the inequality has already been updated with respect to this
2218 * translate and the inequality is therefore known to be a bound
2219 * of this basic set.
2221 static __isl_give isl_basic_set
*add_bound(__isl_take isl_basic_set
*hull
,
2222 struct sh_data
*data
, __isl_keep isl_set
*set
, int i
, isl_int
*ineq
,
2226 struct ineq_cmp_data v
;
2227 struct isl_hash_table_entry
*entry
;
2231 total
= isl_basic_set_dim(hull
, isl_dim_all
);
2233 return isl_basic_set_free(hull
);
2237 c_hash
= isl_seq_get_hash(ineq
+ 1, v
.len
);
2239 entry
= isl_hash_table_find(hull
->ctx
, data
->hull_table
, c_hash
,
2242 return isl_basic_set_free(hull
);
2243 if (entry
!= isl_hash_table_entry_none
)
2246 for (j
= 0; j
< i
; ++j
) {
2247 entry
= isl_hash_table_find(hull
->ctx
, data
->p
[j
].table
,
2248 c_hash
, has_ineq
, &v
, 0);
2250 return isl_basic_set_free(hull
);
2251 if (entry
!= isl_hash_table_entry_none
)
2257 k
= isl_basic_set_alloc_inequality(hull
);
2260 isl_seq_cpy(hull
->ineq
[k
], ineq
, 1 + v
.len
);
2262 if (set_max_constant_term(data
, set
, i
, hull
->ineq
[k
], c_hash
, &v
) < 0)
2264 for (j
= 0; j
< i
; ++j
) {
2266 bound
= is_bound(data
, set
, j
, hull
->ineq
[k
], shift
);
2273 return isl_basic_set_free_inequality(hull
, 1);
2275 for (j
= i
+ 1; j
< set
->n
; ++j
) {
2277 entry
= isl_hash_table_find(hull
->ctx
, data
->p
[j
].table
,
2278 c_hash
, has_ineq
, &v
, 0);
2280 return isl_basic_set_free(hull
);
2281 if (entry
!= isl_hash_table_entry_none
)
2283 bound
= is_bound(data
, set
, j
, hull
->ineq
[k
], shift
);
2290 return isl_basic_set_free_inequality(hull
, 1);
2292 entry
= isl_hash_table_find(hull
->ctx
, data
->hull_table
, c_hash
,
2296 entry
->data
= hull
->ineq
[k
];
2300 isl_basic_set_free(hull
);
2304 /* Check if any inequality from basic set "i" is or can be relaxed to
2305 * become a bound on the whole set. If so, add the (relaxed) inequality
2306 * to "hull". Relaxation is only allowed if "shift" is set.
2308 static __isl_give isl_basic_set
*add_bounds(__isl_take isl_basic_set
*bset
,
2309 struct sh_data
*data
, __isl_keep isl_set
*set
, int i
, int shift
)
2312 isl_size dim
= isl_basic_set_dim(bset
, isl_dim_all
);
2315 return isl_basic_set_free(bset
);
2317 for (j
= 0; j
< set
->p
[i
]->n_eq
; ++j
) {
2318 for (k
= 0; k
< 2; ++k
) {
2319 isl_seq_neg(set
->p
[i
]->eq
[j
], set
->p
[i
]->eq
[j
], 1+dim
);
2320 bset
= add_bound(bset
, data
, set
, i
, set
->p
[i
]->eq
[j
],
2324 for (j
= 0; j
< set
->p
[i
]->n_ineq
; ++j
)
2325 bset
= add_bound(bset
, data
, set
, i
, set
->p
[i
]->ineq
[j
], shift
);
2329 /* Compute a superset of the convex hull of set that is described
2330 * by only (translates of) the constraints in the constituents of set.
2331 * Translation is only allowed if "shift" is set.
2333 static __isl_give isl_basic_set
*uset_simple_hull(__isl_take isl_set
*set
,
2336 struct sh_data
*data
= NULL
;
2337 struct isl_basic_set
*hull
= NULL
;
2345 for (i
= 0; i
< set
->n
; ++i
) {
2348 n_ineq
+= 2 * set
->p
[i
]->n_eq
+ set
->p
[i
]->n_ineq
;
2351 hull
= isl_basic_set_alloc_space(isl_space_copy(set
->dim
), 0, 0, n_ineq
);
2355 data
= sh_data_alloc(set
, n_ineq
);
2359 for (i
= 0; i
< set
->n
; ++i
)
2360 hull
= add_bounds(hull
, data
, set
, i
, shift
);
2368 isl_basic_set_free(hull
);
2373 /* Compute a superset of the convex hull of map that is described
2374 * by only (translates of) the constraints in the constituents of map.
2375 * Handle trivial cases where map is NULL or contains at most one disjunct.
2377 static __isl_give isl_basic_map
*map_simple_hull_trivial(
2378 __isl_take isl_map
*map
)
2380 isl_basic_map
*hull
;
2385 return replace_map_by_empty_basic_map(map
);
2387 hull
= isl_basic_map_copy(map
->p
[0]);
2392 /* Return a copy of the simple hull cached inside "map".
2393 * "shift" determines whether to return the cached unshifted or shifted
2396 static __isl_give isl_basic_map
*cached_simple_hull(__isl_take isl_map
*map
,
2399 isl_basic_map
*hull
;
2401 hull
= isl_basic_map_copy(map
->cached_simple_hull
[shift
]);
2407 /* Compute a superset of the convex hull of map that is described
2408 * by only (translates of) the constraints in the constituents of map.
2409 * Translation is only allowed if "shift" is set.
2411 * The constraints are sorted while removing redundant constraints
2412 * in order to indicate a preference of which constraints should
2413 * be preserved. In particular, pairs of constraints that are
2414 * sorted together are preferred to either both be preserved
2415 * or both be removed. The sorting is performed inside
2416 * isl_basic_map_remove_redundancies.
2418 * The result of the computation is stored in map->cached_simple_hull[shift]
2419 * such that it can be reused in subsequent calls. The cache is cleared
2420 * whenever the map is modified (in isl_map_cow).
2421 * Note that the results need to be stored in the input map for there
2422 * to be any chance that they may get reused. In particular, they
2423 * are stored in a copy of the input map that is saved before
2424 * the integer division alignment.
2426 static __isl_give isl_basic_map
*map_simple_hull(__isl_take isl_map
*map
,
2429 struct isl_set
*set
= NULL
;
2430 struct isl_basic_map
*model
= NULL
;
2431 struct isl_basic_map
*hull
;
2432 struct isl_basic_map
*affine_hull
;
2433 struct isl_basic_set
*bset
= NULL
;
2436 if (!map
|| map
->n
<= 1)
2437 return map_simple_hull_trivial(map
);
2439 if (map
->cached_simple_hull
[shift
])
2440 return cached_simple_hull(map
, shift
);
2442 map
= isl_map_detect_equalities(map
);
2443 if (!map
|| map
->n
<= 1)
2444 return map_simple_hull_trivial(map
);
2445 affine_hull
= isl_map_affine_hull(isl_map_copy(map
));
2446 input
= isl_map_copy(map
);
2447 map
= isl_map_align_divs_internal(map
);
2448 model
= map
? isl_basic_map_copy(map
->p
[0]) : NULL
;
2450 set
= isl_map_underlying_set(map
);
2452 bset
= uset_simple_hull(set
, shift
);
2454 hull
= isl_basic_map_overlying_set(bset
, model
);
2456 hull
= isl_basic_map_intersect(hull
, affine_hull
);
2457 hull
= isl_basic_map_remove_redundancies(hull
);
2460 ISL_F_SET(hull
, ISL_BASIC_MAP_NO_IMPLICIT
);
2461 ISL_F_SET(hull
, ISL_BASIC_MAP_ALL_EQUALITIES
);
2464 hull
= isl_basic_map_finalize(hull
);
2466 input
->cached_simple_hull
[shift
] = isl_basic_map_copy(hull
);
2467 isl_map_free(input
);
2472 /* Compute a superset of the convex hull of map that is described
2473 * by only translates of the constraints in the constituents of map.
2475 __isl_give isl_basic_map
*isl_map_simple_hull(__isl_take isl_map
*map
)
2477 return map_simple_hull(map
, 1);
2480 struct isl_basic_set
*isl_set_simple_hull(struct isl_set
*set
)
2482 return bset_from_bmap(isl_map_simple_hull(set_to_map(set
)));
2485 /* Compute a superset of the convex hull of map that is described
2486 * by only the constraints in the constituents of map.
2488 __isl_give isl_basic_map
*isl_map_unshifted_simple_hull(
2489 __isl_take isl_map
*map
)
2491 return map_simple_hull(map
, 0);
2494 __isl_give isl_basic_set
*isl_set_unshifted_simple_hull(
2495 __isl_take isl_set
*set
)
2497 return isl_map_unshifted_simple_hull(set
);
2500 /* Drop all inequalities from "bmap1" that do not also appear in "bmap2".
2501 * A constraint that appears with different constant terms
2502 * in "bmap1" and "bmap2" is also kept, with the least restrictive
2503 * (i.e., greatest) constant term.
2504 * "bmap1" and "bmap2" are assumed to have the same (known)
2505 * integer divisions.
2506 * The constraints of both "bmap1" and "bmap2" are assumed
2507 * to have been sorted using isl_basic_map_sort_constraints.
2509 * Run through the inequality constraints of "bmap1" and "bmap2"
2511 * Each constraint of "bmap1" without a matching constraint in "bmap2"
2513 * If a match is found, the constraint is kept. If needed, the constant
2514 * term of the constraint is adjusted.
2516 static __isl_give isl_basic_map
*select_shared_inequalities(
2517 __isl_take isl_basic_map
*bmap1
, __isl_keep isl_basic_map
*bmap2
)
2521 bmap1
= isl_basic_map_cow(bmap1
);
2522 if (!bmap1
|| !bmap2
)
2523 return isl_basic_map_free(bmap1
);
2525 i1
= bmap1
->n_ineq
- 1;
2526 i2
= bmap2
->n_ineq
- 1;
2527 while (bmap1
&& i1
>= 0 && i2
>= 0) {
2530 cmp
= isl_basic_map_constraint_cmp(bmap1
, bmap1
->ineq
[i1
],
2537 if (isl_basic_map_drop_inequality(bmap1
, i1
) < 0)
2538 bmap1
= isl_basic_map_free(bmap1
);
2542 if (isl_int_lt(bmap1
->ineq
[i1
][0], bmap2
->ineq
[i2
][0]))
2543 isl_int_set(bmap1
->ineq
[i1
][0], bmap2
->ineq
[i2
][0]);
2547 for (; i1
>= 0; --i1
)
2548 if (isl_basic_map_drop_inequality(bmap1
, i1
) < 0)
2549 bmap1
= isl_basic_map_free(bmap1
);
2554 /* Drop all equalities from "bmap1" that do not also appear in "bmap2".
2555 * "bmap1" and "bmap2" are assumed to have the same (known)
2556 * integer divisions.
2558 * Run through the equality constraints of "bmap1" and "bmap2".
2559 * Each constraint of "bmap1" without a matching constraint in "bmap2"
2562 static __isl_give isl_basic_map
*select_shared_equalities(
2563 __isl_take isl_basic_map
*bmap1
, __isl_keep isl_basic_map
*bmap2
)
2568 bmap1
= isl_basic_map_cow(bmap1
);
2569 total
= isl_basic_map_dim(bmap1
, isl_dim_all
);
2570 if (total
< 0 || !bmap2
)
2571 return isl_basic_map_free(bmap1
);
2573 i1
= bmap1
->n_eq
- 1;
2574 i2
= bmap2
->n_eq
- 1;
2575 while (bmap1
&& i1
>= 0 && i2
>= 0) {
2578 last1
= isl_seq_last_non_zero(bmap1
->eq
[i1
] + 1, total
);
2579 last2
= isl_seq_last_non_zero(bmap2
->eq
[i2
] + 1, total
);
2580 if (last1
> last2
) {
2584 if (last1
< last2
) {
2585 if (isl_basic_map_drop_equality(bmap1
, i1
) < 0)
2586 bmap1
= isl_basic_map_free(bmap1
);
2590 if (!isl_seq_eq(bmap1
->eq
[i1
], bmap2
->eq
[i2
], 1 + total
)) {
2591 if (isl_basic_map_drop_equality(bmap1
, i1
) < 0)
2592 bmap1
= isl_basic_map_free(bmap1
);
2597 for (; i1
>= 0; --i1
)
2598 if (isl_basic_map_drop_equality(bmap1
, i1
) < 0)
2599 bmap1
= isl_basic_map_free(bmap1
);
2604 /* Compute a superset of "bmap1" and "bmap2" that is described
2605 * by only the constraints that appear in both "bmap1" and "bmap2".
2607 * First drop constraints that involve unknown integer divisions
2608 * since it is not trivial to check whether two such integer divisions
2609 * in different basic maps are the same.
2610 * Then align the remaining (known) divs and sort the constraints.
2611 * Finally drop all inequalities and equalities from "bmap1" that
2612 * do not also appear in "bmap2".
2614 __isl_give isl_basic_map
*isl_basic_map_plain_unshifted_simple_hull(
2615 __isl_take isl_basic_map
*bmap1
, __isl_take isl_basic_map
*bmap2
)
2617 bmap1
= isl_basic_map_drop_constraint_involving_unknown_divs(bmap1
);
2618 bmap2
= isl_basic_map_drop_constraint_involving_unknown_divs(bmap2
);
2619 bmap2
= isl_basic_map_align_divs(bmap2
, bmap1
);
2620 bmap1
= isl_basic_map_align_divs(bmap1
, bmap2
);
2621 bmap1
= isl_basic_map_gauss(bmap1
, NULL
);
2622 bmap2
= isl_basic_map_gauss(bmap2
, NULL
);
2623 bmap1
= isl_basic_map_sort_constraints(bmap1
);
2624 bmap2
= isl_basic_map_sort_constraints(bmap2
);
2626 bmap1
= select_shared_inequalities(bmap1
, bmap2
);
2627 bmap1
= select_shared_equalities(bmap1
, bmap2
);
2629 isl_basic_map_free(bmap2
);
2630 bmap1
= isl_basic_map_finalize(bmap1
);
2634 /* Compute a superset of the convex hull of "map" that is described
2635 * by only the constraints in the constituents of "map".
2636 * In particular, the result is composed of constraints that appear
2637 * in each of the basic maps of "map"
2639 * Constraints that involve unknown integer divisions are dropped
2640 * since it is not trivial to check whether two such integer divisions
2641 * in different basic maps are the same.
2643 * The hull is initialized from the first basic map and then
2644 * updated with respect to the other basic maps in turn.
2646 __isl_give isl_basic_map
*isl_map_plain_unshifted_simple_hull(
2647 __isl_take isl_map
*map
)
2650 isl_basic_map
*hull
;
2655 return map_simple_hull_trivial(map
);
2656 map
= isl_map_drop_constraint_involving_unknown_divs(map
);
2657 hull
= isl_basic_map_copy(map
->p
[0]);
2658 for (i
= 1; i
< map
->n
; ++i
) {
2659 isl_basic_map
*bmap_i
;
2661 bmap_i
= isl_basic_map_copy(map
->p
[i
]);
2662 hull
= isl_basic_map_plain_unshifted_simple_hull(hull
, bmap_i
);
2669 /* Compute a superset of the convex hull of "set" that is described
2670 * by only the constraints in the constituents of "set".
2671 * In particular, the result is composed of constraints that appear
2672 * in each of the basic sets of "set"
2674 __isl_give isl_basic_set
*isl_set_plain_unshifted_simple_hull(
2675 __isl_take isl_set
*set
)
2677 return isl_map_plain_unshifted_simple_hull(set
);
2680 /* Check if "ineq" is a bound on "set" and, if so, add it to "hull".
2682 * For each basic set in "set", we first check if the basic set
2683 * contains a translate of "ineq". If this translate is more relaxed,
2684 * then we assume that "ineq" is not a bound on this basic set.
2685 * Otherwise, we know that it is a bound.
2686 * If the basic set does not contain a translate of "ineq", then
2687 * we call is_bound to perform the test.
2689 static __isl_give isl_basic_set
*add_bound_from_constraint(
2690 __isl_take isl_basic_set
*hull
, struct sh_data
*data
,
2691 __isl_keep isl_set
*set
, isl_int
*ineq
)
2696 struct ineq_cmp_data v
;
2699 total
= isl_basic_set_dim(hull
, isl_dim_all
);
2700 if (total
< 0 || !set
)
2701 return isl_basic_set_free(hull
);
2705 c_hash
= isl_seq_get_hash(ineq
+ 1, v
.len
);
2707 ctx
= isl_basic_set_get_ctx(hull
);
2708 for (i
= 0; i
< set
->n
; ++i
) {
2710 struct isl_hash_table_entry
*entry
;
2712 entry
= isl_hash_table_find(ctx
, data
->p
[i
].table
,
2713 c_hash
, &has_ineq
, &v
, 0);
2715 return isl_basic_set_free(hull
);
2716 if (entry
!= isl_hash_table_entry_none
) {
2717 isl_int
*ineq_i
= entry
->data
;
2718 int neg
, more_relaxed
;
2720 neg
= isl_seq_is_neg(ineq_i
+ 1, ineq
+ 1, v
.len
);
2722 isl_int_neg(ineq_i
[0], ineq_i
[0]);
2723 more_relaxed
= isl_int_gt(ineq_i
[0], ineq
[0]);
2725 isl_int_neg(ineq_i
[0], ineq_i
[0]);
2731 bound
= is_bound(data
, set
, i
, ineq
, 0);
2733 return isl_basic_set_free(hull
);
2740 k
= isl_basic_set_alloc_inequality(hull
);
2742 return isl_basic_set_free(hull
);
2743 isl_seq_cpy(hull
->ineq
[k
], ineq
, 1 + v
.len
);
2748 /* Compute a superset of the convex hull of "set" that is described
2749 * by only some of the "n_ineq" constraints in the list "ineq", where "set"
2750 * has no parameters or integer divisions.
2752 * The inequalities in "ineq" are assumed to have been sorted such
2753 * that constraints with the same linear part appear together and
2754 * that among constraints with the same linear part, those with
2755 * smaller constant term appear first.
2757 * We reuse the same data structure that is used by uset_simple_hull,
2758 * but we do not need the hull table since we will not consider the
2759 * same constraint more than once. We therefore allocate it with zero size.
2761 * We run through the constraints and try to add them one by one,
2762 * skipping identical constraints. If we have added a constraint and
2763 * the next constraint is a more relaxed translate, then we skip this
2764 * next constraint as well.
2766 static __isl_give isl_basic_set
*uset_unshifted_simple_hull_from_constraints(
2767 __isl_take isl_set
*set
, int n_ineq
, isl_int
**ineq
)
2771 struct sh_data
*data
= NULL
;
2772 isl_basic_set
*hull
= NULL
;
2775 hull
= isl_basic_set_alloc_space(isl_set_get_space(set
), 0, 0, n_ineq
);
2779 data
= sh_data_alloc(set
, 0);
2783 dim
= isl_set_dim(set
, isl_dim_set
);
2786 for (i
= 0; i
< n_ineq
; ++i
) {
2787 int hull_n_ineq
= hull
->n_ineq
;
2790 parallel
= i
> 0 && isl_seq_eq(ineq
[i
- 1] + 1, ineq
[i
] + 1,
2793 (last_added
|| isl_int_eq(ineq
[i
- 1][0], ineq
[i
][0])))
2795 hull
= add_bound_from_constraint(hull
, data
, set
, ineq
[i
]);
2798 last_added
= hull
->n_ineq
> hull_n_ineq
;
2807 isl_basic_set_free(hull
);
2811 /* Collect pointers to all the inequalities in the elements of "list"
2812 * in "ineq". For equalities, store both a pointer to the equality and
2813 * a pointer to its opposite, which is first copied to "mat".
2814 * "ineq" and "mat" are assumed to have been preallocated to the right size
2815 * (the number of inequalities + 2 times the number of equalites and
2816 * the number of equalities, respectively).
2818 static __isl_give isl_mat
*collect_inequalities(__isl_take isl_mat
*mat
,
2819 __isl_keep isl_basic_set_list
*list
, isl_int
**ineq
)
2821 int i
, j
, n_eq
, n_ineq
;
2824 n
= isl_basic_set_list_n_basic_set(list
);
2826 return isl_mat_free(mat
);
2830 for (i
= 0; i
< n
; ++i
) {
2831 isl_basic_set
*bset
;
2832 bset
= isl_basic_set_list_get_basic_set(list
, i
);
2834 return isl_mat_free(mat
);
2835 for (j
= 0; j
< bset
->n_eq
; ++j
) {
2836 ineq
[n_ineq
++] = mat
->row
[n_eq
];
2837 ineq
[n_ineq
++] = bset
->eq
[j
];
2838 isl_seq_neg(mat
->row
[n_eq
++], bset
->eq
[j
], mat
->n_col
);
2840 for (j
= 0; j
< bset
->n_ineq
; ++j
)
2841 ineq
[n_ineq
++] = bset
->ineq
[j
];
2842 isl_basic_set_free(bset
);
2848 /* Comparison routine for use as an isl_sort callback.
2850 * Constraints with the same linear part are sorted together and
2851 * among constraints with the same linear part, those with smaller
2852 * constant term are sorted first.
2854 static int cmp_ineq(const void *a
, const void *b
, void *arg
)
2856 unsigned dim
= *(unsigned *) arg
;
2857 isl_int
* const *ineq1
= a
;
2858 isl_int
* const *ineq2
= b
;
2861 cmp
= isl_seq_cmp((*ineq1
) + 1, (*ineq2
) + 1, dim
);
2864 return isl_int_cmp((*ineq1
)[0], (*ineq2
)[0]);
2867 /* Compute a superset of the convex hull of "set" that is described
2868 * by only constraints in the elements of "list", where "set" has
2869 * no parameters or integer divisions.
2871 * We collect all the constraints in those elements and then
2872 * sort the constraints such that constraints with the same linear part
2873 * are sorted together and that those with smaller constant term are
2876 static __isl_give isl_basic_set
*uset_unshifted_simple_hull_from_basic_set_list(
2877 __isl_take isl_set
*set
, __isl_take isl_basic_set_list
*list
)
2879 int i
, n_eq
, n_ineq
;
2883 isl_mat
*mat
= NULL
;
2884 isl_int
**ineq
= NULL
;
2885 isl_basic_set
*hull
;
2887 n
= isl_basic_set_list_n_basic_set(list
);
2890 ctx
= isl_set_get_ctx(set
);
2894 for (i
= 0; i
< n
; ++i
) {
2895 isl_basic_set
*bset
;
2896 bset
= isl_basic_set_list_get_basic_set(list
, i
);
2900 n_ineq
+= 2 * bset
->n_eq
+ bset
->n_ineq
;
2901 isl_basic_set_free(bset
);
2904 ineq
= isl_alloc_array(ctx
, isl_int
*, n_ineq
);
2905 if (n_ineq
> 0 && !ineq
)
2908 dim
= isl_set_dim(set
, isl_dim_set
);
2911 mat
= isl_mat_alloc(ctx
, n_eq
, 1 + dim
);
2912 mat
= collect_inequalities(mat
, list
, ineq
);
2916 if (isl_sort(ineq
, n_ineq
, sizeof(ineq
[0]), &cmp_ineq
, &dim
) < 0)
2919 hull
= uset_unshifted_simple_hull_from_constraints(set
, n_ineq
, ineq
);
2923 isl_basic_set_list_free(list
);
2929 isl_basic_set_list_free(list
);
2933 /* Compute a superset of the convex hull of "map" that is described
2934 * by only constraints in the elements of "list".
2936 * If the list is empty, then we can only describe the universe set.
2937 * If the input map is empty, then all constraints are valid, so
2938 * we return the intersection of the elements in "list".
2940 * Otherwise, we align all divs and temporarily treat them
2941 * as regular variables, computing the unshifted simple hull in
2942 * uset_unshifted_simple_hull_from_basic_set_list.
2944 static __isl_give isl_basic_map
*map_unshifted_simple_hull_from_basic_map_list(
2945 __isl_take isl_map
*map
, __isl_take isl_basic_map_list
*list
)
2948 isl_basic_map
*model
;
2949 isl_basic_map
*hull
;
2951 isl_basic_set_list
*bset_list
;
2953 n
= isl_basic_map_list_n_basic_map(list
);
2960 space
= isl_map_get_space(map
);
2962 isl_basic_map_list_free(list
);
2963 return isl_basic_map_universe(space
);
2965 if (isl_map_plain_is_empty(map
)) {
2967 return isl_basic_map_list_intersect(list
);
2970 map
= isl_map_align_divs_to_basic_map_list(map
, list
);
2973 list
= isl_basic_map_list_align_divs_to_basic_map(list
, map
->p
[0]);
2975 model
= isl_basic_map_list_get_basic_map(list
, 0);
2977 set
= isl_map_underlying_set(map
);
2978 bset_list
= isl_basic_map_list_underlying_set(list
);
2980 hull
= uset_unshifted_simple_hull_from_basic_set_list(set
, bset_list
);
2981 hull
= isl_basic_map_overlying_set(hull
, model
);
2986 isl_basic_map_list_free(list
);
2990 /* Return a sequence of the basic maps that make up the maps in "list".
2992 static __isl_give isl_basic_map_list
*collect_basic_maps(
2993 __isl_take isl_map_list
*list
)
2998 isl_basic_map_list
*bmap_list
;
3002 n
= isl_map_list_n_map(list
);
3003 ctx
= isl_map_list_get_ctx(list
);
3004 bmap_list
= isl_basic_map_list_alloc(ctx
, 0);
3006 bmap_list
= isl_basic_map_list_free(bmap_list
);
3008 for (i
= 0; i
< n
; ++i
) {
3010 isl_basic_map_list
*list_i
;
3012 map
= isl_map_list_get_map(list
, i
);
3013 map
= isl_map_compute_divs(map
);
3014 list_i
= isl_map_get_basic_map_list(map
);
3016 bmap_list
= isl_basic_map_list_concat(bmap_list
, list_i
);
3019 isl_map_list_free(list
);
3023 /* Compute a superset of the convex hull of "map" that is described
3024 * by only constraints in the elements of "list".
3026 * If "map" is the universe, then the convex hull (and therefore
3027 * any superset of the convexhull) is the universe as well.
3029 * Otherwise, we collect all the basic maps in the map list and
3030 * continue with map_unshifted_simple_hull_from_basic_map_list.
3032 __isl_give isl_basic_map
*isl_map_unshifted_simple_hull_from_map_list(
3033 __isl_take isl_map
*map
, __isl_take isl_map_list
*list
)
3035 isl_basic_map_list
*bmap_list
;
3038 is_universe
= isl_map_plain_is_universe(map
);
3039 if (is_universe
< 0)
3040 map
= isl_map_free(map
);
3041 if (is_universe
< 0 || is_universe
) {
3042 isl_map_list_free(list
);
3043 return isl_map_unshifted_simple_hull(map
);
3046 bmap_list
= collect_basic_maps(list
);
3047 return map_unshifted_simple_hull_from_basic_map_list(map
, bmap_list
);
3050 /* Compute a superset of the convex hull of "set" that is described
3051 * by only constraints in the elements of "list".
3053 __isl_give isl_basic_set
*isl_set_unshifted_simple_hull_from_set_list(
3054 __isl_take isl_set
*set
, __isl_take isl_set_list
*list
)
3056 return isl_map_unshifted_simple_hull_from_map_list(set
, list
);
3059 /* Given a set "set", return parametric bounds on the dimension "dim".
3061 static __isl_give isl_basic_set
*set_bounds(__isl_keep isl_set
*set
, int dim
)
3063 isl_size set_dim
= isl_set_dim(set
, isl_dim_set
);
3066 set
= isl_set_copy(set
);
3067 set
= isl_set_eliminate_dims(set
, dim
+ 1, set_dim
- (dim
+ 1));
3068 set
= isl_set_eliminate_dims(set
, 0, dim
);
3069 return isl_set_convex_hull(set
);
3072 /* Computes a "simple hull" and then check if each dimension in the
3073 * resulting hull is bounded by a symbolic constant. If not, the
3074 * hull is intersected with the corresponding bounds on the whole set.
3076 __isl_give isl_basic_set
*isl_set_bounded_simple_hull(__isl_take isl_set
*set
)
3079 struct isl_basic_set
*hull
;
3080 isl_size nparam
, dim
, total
;
3082 int removed_divs
= 0;
3084 hull
= isl_set_simple_hull(isl_set_copy(set
));
3085 nparam
= isl_basic_set_dim(hull
, isl_dim_param
);
3086 dim
= isl_basic_set_dim(hull
, isl_dim_set
);
3087 total
= isl_basic_set_dim(hull
, isl_dim_all
);
3088 if (nparam
< 0 || dim
< 0 || total
< 0)
3091 for (i
= 0; i
< dim
; ++i
) {
3092 int lower
= 0, upper
= 0;
3093 struct isl_basic_set
*bounds
;
3095 left
= total
- nparam
- i
- 1;
3096 for (j
= 0; j
< hull
->n_eq
; ++j
) {
3097 if (isl_int_is_zero(hull
->eq
[j
][1 + nparam
+ i
]))
3099 if (isl_seq_first_non_zero(hull
->eq
[j
]+1+nparam
+i
+1,
3106 for (j
= 0; j
< hull
->n_ineq
; ++j
) {
3107 if (isl_int_is_zero(hull
->ineq
[j
][1 + nparam
+ i
]))
3109 if (isl_seq_first_non_zero(hull
->ineq
[j
]+1+nparam
+i
+1,
3111 isl_seq_first_non_zero(hull
->ineq
[j
]+1+nparam
,
3114 if (isl_int_is_pos(hull
->ineq
[j
][1 + nparam
+ i
]))
3125 if (!removed_divs
) {
3126 set
= isl_set_remove_divs(set
);
3131 bounds
= set_bounds(set
, i
);
3132 hull
= isl_basic_set_intersect(hull
, bounds
);
3141 isl_basic_set_free(hull
);