6 #include "isl_map_private.h"
7 #include "isl_equalities.h"
8 #include "isl_sample.h"
11 struct isl_basic_map
*isl_basic_map_implicit_equalities(
12 struct isl_basic_map
*bmap
)
19 bmap
= isl_basic_map_gauss(bmap
, NULL
);
20 if (ISL_F_ISSET(bmap
, ISL_BASIC_MAP_EMPTY
))
22 if (ISL_F_ISSET(bmap
, ISL_BASIC_MAP_NO_IMPLICIT
))
24 if (bmap
->n_ineq
<= 1)
27 tab
= isl_tab_from_basic_map(bmap
);
28 tab
= isl_tab_detect_implicit_equalities(tab
);
29 bmap
= isl_basic_map_update_from_tab(bmap
, tab
);
31 bmap
= isl_basic_map_gauss(bmap
, NULL
);
32 ISL_F_SET(bmap
, ISL_BASIC_MAP_NO_IMPLICIT
);
36 struct isl_basic_set
*isl_basic_set_implicit_equalities(
37 struct isl_basic_set
*bset
)
39 return (struct isl_basic_set
*)
40 isl_basic_map_implicit_equalities((struct isl_basic_map
*)bset
);
43 struct isl_map
*isl_map_implicit_equalities(struct isl_map
*map
)
50 for (i
= 0; i
< map
->n
; ++i
) {
51 map
->p
[i
] = isl_basic_map_implicit_equalities(map
->p
[i
]);
62 /* Make eq[row][col] of both bmaps equal so we can add the row
63 * add the column to the common matrix.
64 * Note that because of the echelon form, the columns of row row
65 * after column col are zero.
67 static void set_common_multiple(
68 struct isl_basic_set
*bset1
, struct isl_basic_set
*bset2
,
69 unsigned row
, unsigned col
)
73 if (isl_int_eq(bset1
->eq
[row
][col
], bset2
->eq
[row
][col
]))
78 isl_int_lcm(m
, bset1
->eq
[row
][col
], bset2
->eq
[row
][col
]);
79 isl_int_divexact(c
, m
, bset1
->eq
[row
][col
]);
80 isl_seq_scale(bset1
->eq
[row
], bset1
->eq
[row
], c
, col
+1);
81 isl_int_divexact(c
, m
, bset2
->eq
[row
][col
]);
82 isl_seq_scale(bset2
->eq
[row
], bset2
->eq
[row
], c
, col
+1);
87 /* Delete a given equality, moving all the following equalities one up.
89 static void delete_row(struct isl_basic_set
*bset
, unsigned row
)
96 for (r
= row
; r
< bset
->n_eq
; ++r
)
97 bset
->eq
[r
] = bset
->eq
[r
+1];
98 bset
->eq
[bset
->n_eq
] = t
;
101 /* Make first row entries in column col of bset1 identical to
102 * those of bset2, using the fact that entry bset1->eq[row][col]=a
103 * is non-zero. Initially, these elements of bset1 are all zero.
104 * For each row i < row, we set
105 * A[i] = a * A[i] + B[i][col] * A[row]
108 * A[i][col] = B[i][col] = a * old(B[i][col])
110 static void construct_column(
111 struct isl_basic_set
*bset1
, struct isl_basic_set
*bset2
,
112 unsigned row
, unsigned col
)
121 total
= 1 + isl_basic_set_n_dim(bset1
);
122 for (r
= 0; r
< row
; ++r
) {
123 if (isl_int_is_zero(bset2
->eq
[r
][col
]))
125 isl_int_gcd(b
, bset2
->eq
[r
][col
], bset1
->eq
[row
][col
]);
126 isl_int_divexact(a
, bset1
->eq
[row
][col
], b
);
127 isl_int_divexact(b
, bset2
->eq
[r
][col
], b
);
128 isl_seq_combine(bset1
->eq
[r
], a
, bset1
->eq
[r
],
129 b
, bset1
->eq
[row
], total
);
130 isl_seq_scale(bset2
->eq
[r
], bset2
->eq
[r
], a
, total
);
134 delete_row(bset1
, row
);
137 /* Make first row entries in column col of bset1 identical to
138 * those of bset2, using only these entries of the two matrices.
139 * Let t be the last row with different entries.
140 * For each row i < t, we set
141 * A[i] = (A[t][col]-B[t][col]) * A[i] + (B[i][col]-A[i][col) * A[t]
142 * B[i] = (A[t][col]-B[t][col]) * B[i] + (B[i][col]-A[i][col) * B[t]
144 * A[i][col] = B[i][col] = old(A[t][col]*B[i][col]-A[i][col]*B[t][col])
146 static int transform_column(
147 struct isl_basic_set
*bset1
, struct isl_basic_set
*bset2
,
148 unsigned row
, unsigned col
)
154 for (t
= row
-1; t
>= 0; --t
)
155 if (isl_int_ne(bset1
->eq
[t
][col
], bset2
->eq
[t
][col
]))
160 total
= 1 + isl_basic_set_n_dim(bset1
);
164 isl_int_sub(b
, bset1
->eq
[t
][col
], bset2
->eq
[t
][col
]);
165 for (i
= 0; i
< t
; ++i
) {
166 isl_int_sub(a
, bset2
->eq
[i
][col
], bset1
->eq
[i
][col
]);
167 isl_int_gcd(g
, a
, b
);
168 isl_int_divexact(a
, a
, g
);
169 isl_int_divexact(g
, b
, g
);
170 isl_seq_combine(bset1
->eq
[i
], g
, bset1
->eq
[i
], a
, bset1
->eq
[t
],
172 isl_seq_combine(bset2
->eq
[i
], g
, bset2
->eq
[i
], a
, bset2
->eq
[t
],
178 delete_row(bset1
, t
);
179 delete_row(bset2
, t
);
183 /* The implementation is based on Section 5.2 of Michael Karr,
184 * "Affine Relationships Among Variables of a Program",
185 * except that the echelon form we use starts from the last column
186 * and that we are dealing with integer coefficients.
188 static struct isl_basic_set
*affine_hull(
189 struct isl_basic_set
*bset1
, struct isl_basic_set
*bset2
)
195 total
= 1 + isl_basic_set_n_dim(bset1
);
198 for (col
= total
-1; col
>= 0; --col
) {
199 int is_zero1
= row
>= bset1
->n_eq
||
200 isl_int_is_zero(bset1
->eq
[row
][col
]);
201 int is_zero2
= row
>= bset2
->n_eq
||
202 isl_int_is_zero(bset2
->eq
[row
][col
]);
203 if (!is_zero1
&& !is_zero2
) {
204 set_common_multiple(bset1
, bset2
, row
, col
);
206 } else if (!is_zero1
&& is_zero2
) {
207 construct_column(bset1
, bset2
, row
, col
);
208 } else if (is_zero1
&& !is_zero2
) {
209 construct_column(bset2
, bset1
, row
, col
);
211 if (transform_column(bset1
, bset2
, row
, col
))
215 isl_basic_set_free(bset2
);
216 isl_assert(bset1
->ctx
, row
== bset1
->n_eq
, goto error
);
217 bset1
= isl_basic_set_normalize_constraints(bset1
);
220 isl_basic_set_free(bset1
);
224 /* Find an integer point in the set represented by "tab"
225 * that lies outside of the equality "eq" e(x) = 0.
226 * If "up" is true, look for a point satisfying e(x) - 1 >= 0.
227 * Otherwise, look for a point satisfying -e(x) - 1 >= 0 (i.e., e(x) <= -1).
228 * The point, if found, is returned.
229 * If no point can be found, a zero-length vector is returned.
231 * Before solving an ILP problem, we first check if simply
232 * adding the normal of the constraint to one of the known
233 * integer points in the basic set represented by "tab"
234 * yields another point inside the basic set.
236 * The caller of this function ensures that the tableau is bounded or
237 * that tab->basis and tab->n_unbounded have been set appropriately.
239 static struct isl_vec
*outside_point(struct isl_tab
*tab
, isl_int
*eq
, int up
)
242 struct isl_vec
*sample
;
243 struct isl_tab_undo
*snap
;
252 sample
= isl_vec_alloc(ctx
, 1 + dim
);
255 isl_int_set_si(sample
->el
[0], 1);
256 isl_seq_combine(sample
->el
+ 1,
257 ctx
->one
, tab
->bset
->sample
->el
+ 1,
258 up
? ctx
->one
: ctx
->negone
, eq
+ 1, dim
);
259 if (isl_basic_set_contains(tab
->bset
, sample
))
261 isl_vec_free(sample
);
264 snap
= isl_tab_snap(tab
);
267 isl_seq_neg(eq
, eq
, 1 + dim
);
268 isl_int_sub_ui(eq
[0], eq
[0], 1);
270 if (isl_tab_extend_cons(tab
, 1) < 0)
272 tab
= isl_tab_add_ineq(tab
, eq
);
274 sample
= isl_tab_sample(tab
);
276 isl_int_add_ui(eq
[0], eq
[0], 1);
278 isl_seq_neg(eq
, eq
, 1 + dim
);
280 if (isl_tab_rollback(tab
, snap
) < 0)
285 isl_vec_free(sample
);
289 struct isl_basic_set
*isl_basic_set_recession_cone(struct isl_basic_set
*bset
)
293 bset
= isl_basic_set_cow(bset
);
296 isl_assert(bset
->ctx
, bset
->n_div
== 0, goto error
);
298 for (i
= 0; i
< bset
->n_eq
; ++i
)
299 isl_int_set_si(bset
->eq
[i
][0], 0);
301 for (i
= 0; i
< bset
->n_ineq
; ++i
)
302 isl_int_set_si(bset
->ineq
[i
][0], 0);
304 ISL_F_CLR(bset
, ISL_BASIC_SET_NO_IMPLICIT
);
305 return isl_basic_set_implicit_equalities(bset
);
307 isl_basic_set_free(bset
);
311 /* Extend an initial (under-)approximation of the affine hull of basic
312 * set represented by the tableau "tab"
313 * by looking for points that do not satisfy one of the equalities
314 * in the current approximation and adding them to that approximation
315 * until no such points can be found any more.
317 * The caller of this function ensures that "tab" is bounded or
318 * that tab->basis and tab->n_unbounded have been set appropriately.
320 static struct isl_basic_set
*extend_affine_hull(struct isl_tab
*tab
,
321 struct isl_basic_set
*hull
)
331 if (isl_tab_extend_cons(tab
, 2 * dim
+ 1) < 0)
334 for (i
= 0; i
< dim
; ++i
) {
335 struct isl_vec
*sample
;
336 struct isl_basic_set
*point
;
337 for (j
= 0; j
< hull
->n_eq
; ++j
) {
338 sample
= outside_point(tab
, hull
->eq
[j
], 1);
341 if (sample
->size
> 0)
343 isl_vec_free(sample
);
344 sample
= outside_point(tab
, hull
->eq
[j
], 0);
347 if (sample
->size
> 0)
349 isl_vec_free(sample
);
351 tab
= isl_tab_add_eq(tab
, hull
->eq
[j
]);
358 tab
= isl_tab_add_sample(tab
, isl_vec_copy(sample
));
361 point
= isl_basic_set_from_vec(sample
);
362 hull
= affine_hull(hull
, point
);
367 isl_basic_set_free(hull
);
371 /* Drop all constraints in bset that involve any of the dimensions
372 * first to first+n-1.
374 static struct isl_basic_set
*drop_constraints_involving
375 (struct isl_basic_set
*bset
, unsigned first
, unsigned n
)
382 bset
= isl_basic_set_cow(bset
);
384 for (i
= bset
->n_eq
- 1; i
>= 0; --i
) {
385 if (isl_seq_first_non_zero(bset
->eq
[i
] + 1 + first
, n
) == -1)
387 isl_basic_set_drop_equality(bset
, i
);
390 for (i
= bset
->n_ineq
- 1; i
>= 0; --i
) {
391 if (isl_seq_first_non_zero(bset
->ineq
[i
] + 1 + first
, n
) == -1)
393 isl_basic_set_drop_inequality(bset
, i
);
399 /* Look for all equalities satisfied by the integer points in bset,
400 * which is assumed to be bounded.
402 * The equalities are obtained by successively looking for
403 * a point that is affinely independent of the points found so far.
404 * In particular, for each equality satisfied by the points so far,
405 * we check if there is any point on a hyperplane parallel to the
406 * corresponding hyperplane shifted by at least one (in either direction).
408 static struct isl_basic_set
*uset_affine_hull_bounded(struct isl_basic_set
*bset
)
410 struct isl_vec
*sample
= NULL
;
411 struct isl_basic_set
*hull
;
412 struct isl_tab
*tab
= NULL
;
415 if (isl_basic_set_fast_is_empty(bset
))
418 dim
= isl_basic_set_n_dim(bset
);
420 if (bset
->sample
&& bset
->sample
->size
== 1 + dim
) {
421 int contains
= isl_basic_set_contains(bset
, bset
->sample
);
427 sample
= isl_vec_copy(bset
->sample
);
429 isl_vec_free(bset
->sample
);
434 tab
= isl_tab_from_basic_set(bset
);
437 tab
->bset
= isl_basic_set_copy(bset
);
440 struct isl_tab_undo
*snap
;
441 snap
= isl_tab_snap(tab
);
442 sample
= isl_tab_sample(tab
);
443 if (isl_tab_rollback(tab
, snap
) < 0)
445 isl_vec_free(tab
->bset
->sample
);
446 tab
->bset
->sample
= isl_vec_copy(sample
);
451 if (sample
->size
== 0) {
453 isl_vec_free(sample
);
454 return isl_basic_set_set_to_empty(bset
);
457 hull
= isl_basic_set_from_vec(sample
);
459 isl_basic_set_free(bset
);
460 hull
= extend_affine_hull(tab
, hull
);
465 isl_vec_free(sample
);
467 isl_basic_set_free(bset
);
471 /* Given an unbounded tableau and an integer point satisfying the tableau,
472 * construct an intial affine hull containing the recession cone
473 * shifted to the given point.
475 * The unbounded directions are taken from the last rows of the basis,
476 * which is assumed to have been initialized appropriately.
478 static __isl_give isl_basic_set
*initial_hull(struct isl_tab
*tab
,
479 __isl_take isl_vec
*vec
)
483 struct isl_basic_set
*bset
= NULL
;
490 isl_assert(ctx
, vec
->size
!= 0, goto error
);
492 bset
= isl_basic_set_alloc(ctx
, 0, vec
->size
- 1, 0, vec
->size
- 1, 0);
495 dim
= isl_basic_set_n_dim(bset
) - tab
->n_unbounded
;
496 for (i
= 0; i
< dim
; ++i
) {
497 k
= isl_basic_set_alloc_equality(bset
);
500 isl_seq_cpy(bset
->eq
[k
] + 1, tab
->basis
->row
[1 + i
] + 1,
502 isl_seq_inner_product(bset
->eq
[k
] + 1, vec
->el
+1,
503 vec
->size
- 1, &bset
->eq
[k
][0]);
504 isl_int_neg(bset
->eq
[k
][0], bset
->eq
[k
][0]);
507 bset
= isl_basic_set_gauss(bset
, NULL
);
511 isl_basic_set_free(bset
);
516 /* Given a tableau of a set and a tableau of the corresponding
517 * recession cone, detect and add all equalities to the tableau.
518 * If the tableau is bounded, then we can simply keep the
519 * tableau in its state after the return from extend_affine_hull.
520 * However, if the tableau is unbounded, then
521 * isl_tab_set_initial_basis_with_cone will add some additional
522 * constraints to the tableau that have to be removed again.
523 * In this case, we therefore rollback to the state before
524 * any constraints were added and then add the eqaulities back in.
526 struct isl_tab
*isl_tab_detect_equalities(struct isl_tab
*tab
,
527 struct isl_tab
*tab_cone
)
530 struct isl_vec
*sample
;
531 struct isl_basic_set
*hull
;
532 struct isl_tab_undo
*snap
;
534 if (!tab
|| !tab_cone
)
537 snap
= isl_tab_snap(tab
);
539 isl_mat_free(tab
->basis
);
542 isl_assert(tab
->mat
->ctx
, tab
->bset
, goto error
);
543 isl_assert(tab
->mat
->ctx
, tab
->samples
, goto error
);
544 isl_assert(tab
->mat
->ctx
, tab
->samples
->n_col
== 1 + tab
->n_var
, goto error
);
545 isl_assert(tab
->mat
->ctx
, tab
->n_sample
> tab
->n_outside
, goto error
);
547 if (isl_tab_set_initial_basis_with_cone(tab
, tab_cone
) < 0)
550 sample
= isl_vec_alloc(tab
->mat
->ctx
, 1 + tab
->n_var
);
554 isl_seq_cpy(sample
->el
, tab
->samples
->row
[tab
->n_outside
], sample
->size
);
556 isl_vec_free(tab
->bset
->sample
);
557 tab
->bset
->sample
= isl_vec_copy(sample
);
559 if (tab
->n_unbounded
== 0)
560 hull
= isl_basic_set_from_vec(isl_vec_copy(sample
));
562 hull
= initial_hull(tab
, isl_vec_copy(sample
));
564 for (j
= tab
->n_outside
+ 1; j
< tab
->n_sample
; ++j
) {
565 isl_seq_cpy(sample
->el
, tab
->samples
->row
[j
], sample
->size
);
566 hull
= affine_hull(hull
,
567 isl_basic_set_from_vec(isl_vec_copy(sample
)));
570 isl_vec_free(sample
);
572 hull
= extend_affine_hull(tab
, hull
);
576 if (tab
->n_unbounded
== 0) {
577 isl_basic_set_free(hull
);
581 if (isl_tab_rollback(tab
, snap
) < 0)
584 if (hull
->n_eq
> tab
->n_zero
) {
585 for (j
= 0; j
< hull
->n_eq
; ++j
) {
586 isl_seq_normalize(tab
->mat
->ctx
, hull
->eq
[j
], 1 + tab
->n_var
);
587 tab
= isl_tab_add_eq(tab
, hull
->eq
[j
]);
591 isl_basic_set_free(hull
);
599 /* Compute the affine hull of "bset", where "cone" is the recession cone
602 * We first compute a unimodular transformation that puts the unbounded
603 * directions in the last dimensions. In particular, we take a transformation
604 * that maps all equalities to equalities (in HNF) on the first dimensions.
605 * Let x be the original dimensions and y the transformed, with y_1 bounded
608 * [ y_1 ] [ y_1 ] [ Q_1 ]
609 * x = U [ y_2 ] [ y_2 ] = [ Q_2 ] x
611 * Let's call the input basic set S. We compute S' = preimage(S, U)
612 * and drop the final dimensions including any constraints involving them.
613 * This results in set S''.
614 * Then we compute the affine hull A'' of S''.
615 * Let F y_1 >= g be the constraint system of A''. In the transformed
616 * space the y_2 are unbounded, so we can add them back without any constraints,
620 * [ F 0 ] [ y_2 ] >= g
623 * [ F 0 ] [ Q_2 ] x >= g
627 * The affine hull in the original space is then obtained as
628 * A = preimage(A'', Q_1).
630 static struct isl_basic_set
*affine_hull_with_cone(struct isl_basic_set
*bset
,
631 struct isl_basic_set
*cone
)
635 struct isl_basic_set
*hull
;
636 struct isl_mat
*M
, *U
, *Q
;
641 total
= isl_basic_set_total_dim(cone
);
642 cone_dim
= total
- cone
->n_eq
;
644 M
= isl_mat_sub_alloc(bset
->ctx
, cone
->eq
, 0, cone
->n_eq
, 1, total
);
645 M
= isl_mat_left_hermite(M
, 0, &U
, &Q
);
650 U
= isl_mat_lin_to_aff(U
);
651 bset
= isl_basic_set_preimage(bset
, isl_mat_copy(U
));
653 bset
= drop_constraints_involving(bset
, total
- cone_dim
, cone_dim
);
654 bset
= isl_basic_set_drop_dims(bset
, total
- cone_dim
, cone_dim
);
656 Q
= isl_mat_lin_to_aff(Q
);
657 Q
= isl_mat_drop_rows(Q
, 1 + total
- cone_dim
, cone_dim
);
659 if (bset
&& bset
->sample
&& bset
->sample
->size
== 1 + total
)
660 bset
->sample
= isl_mat_vec_product(isl_mat_copy(Q
), bset
->sample
);
662 hull
= uset_affine_hull_bounded(bset
);
667 struct isl_vec
*sample
= isl_vec_copy(hull
->sample
);
668 U
= isl_mat_drop_cols(U
, 1 + total
- cone_dim
, cone_dim
);
669 if (sample
&& sample
->size
> 0)
670 sample
= isl_mat_vec_product(U
, sample
);
673 hull
= isl_basic_set_preimage(hull
, Q
);
674 isl_vec_free(hull
->sample
);
675 hull
->sample
= sample
;
678 isl_basic_set_free(cone
);
682 isl_basic_set_free(bset
);
683 isl_basic_set_free(cone
);
687 /* Look for all equalities satisfied by the integer points in bset,
688 * which is assumed not to have any explicit equalities.
690 * The equalities are obtained by successively looking for
691 * a point that is affinely independent of the points found so far.
692 * In particular, for each equality satisfied by the points so far,
693 * we check if there is any point on a hyperplane parallel to the
694 * corresponding hyperplane shifted by at least one (in either direction).
696 * Before looking for any outside points, we first compute the recession
697 * cone. The directions of this recession cone will always be part
698 * of the affine hull, so there is no need for looking for any points
699 * in these directions.
700 * In particular, if the recession cone is full-dimensional, then
701 * the affine hull is simply the whole universe.
703 static struct isl_basic_set
*uset_affine_hull(struct isl_basic_set
*bset
)
705 struct isl_basic_set
*cone
;
707 if (isl_basic_set_fast_is_empty(bset
))
710 cone
= isl_basic_set_recession_cone(isl_basic_set_copy(bset
));
713 if (cone
->n_eq
== 0) {
714 struct isl_basic_set
*hull
;
715 isl_basic_set_free(cone
);
716 hull
= isl_basic_set_universe_like(bset
);
717 isl_basic_set_free(bset
);
721 if (cone
->n_eq
< isl_basic_set_total_dim(cone
))
722 return affine_hull_with_cone(bset
, cone
);
724 isl_basic_set_free(cone
);
725 return uset_affine_hull_bounded(bset
);
727 isl_basic_set_free(bset
);
731 /* Look for all equalities satisfied by the integer points in bmap
732 * that are independent of the equalities already explicitly available
735 * We first remove all equalities already explicitly available,
736 * then look for additional equalities in the reduced space
737 * and then transform the result to the original space.
738 * The original equalities are _not_ added to this set. This is
739 * the responsibility of the calling function.
740 * The resulting basic set has all meaning about the dimensions removed.
741 * In particular, dimensions that correspond to existential variables
742 * in bmap and that are found to be fixed are not removed.
744 static struct isl_basic_set
*equalities_in_underlying_set(
745 struct isl_basic_map
*bmap
)
747 struct isl_mat
*T1
= NULL
;
748 struct isl_mat
*T2
= NULL
;
749 struct isl_basic_set
*bset
= NULL
;
750 struct isl_basic_set
*hull
= NULL
;
752 bset
= isl_basic_map_underlying_set(bmap
);
756 bset
= isl_basic_set_remove_equalities(bset
, &T1
, &T2
);
760 hull
= uset_affine_hull(bset
);
767 struct isl_vec
*sample
= isl_vec_copy(hull
->sample
);
768 if (sample
&& sample
->size
> 0)
769 sample
= isl_mat_vec_product(T1
, sample
);
772 hull
= isl_basic_set_preimage(hull
, T2
);
773 isl_vec_free(hull
->sample
);
774 hull
->sample
= sample
;
780 isl_basic_set_free(bset
);
781 isl_basic_set_free(hull
);
785 /* Detect and make explicit all equalities satisfied by the (integer)
788 struct isl_basic_map
*isl_basic_map_detect_equalities(
789 struct isl_basic_map
*bmap
)
792 struct isl_basic_set
*hull
= NULL
;
796 if (bmap
->n_ineq
== 0)
798 if (ISL_F_ISSET(bmap
, ISL_BASIC_MAP_EMPTY
))
800 if (ISL_F_ISSET(bmap
, ISL_BASIC_MAP_ALL_EQUALITIES
))
802 if (ISL_F_ISSET(bmap
, ISL_BASIC_MAP_RATIONAL
))
803 return isl_basic_map_implicit_equalities(bmap
);
805 hull
= equalities_in_underlying_set(isl_basic_map_copy(bmap
));
808 if (ISL_F_ISSET(hull
, ISL_BASIC_SET_EMPTY
)) {
809 isl_basic_set_free(hull
);
810 return isl_basic_map_set_to_empty(bmap
);
812 bmap
= isl_basic_map_extend_dim(bmap
, isl_dim_copy(bmap
->dim
), 0,
814 for (i
= 0; i
< hull
->n_eq
; ++i
) {
815 j
= isl_basic_map_alloc_equality(bmap
);
818 isl_seq_cpy(bmap
->eq
[j
], hull
->eq
[i
],
819 1 + isl_basic_set_total_dim(hull
));
821 isl_vec_free(bmap
->sample
);
822 bmap
->sample
= isl_vec_copy(hull
->sample
);
823 isl_basic_set_free(hull
);
824 ISL_F_SET(bmap
, ISL_BASIC_MAP_NO_IMPLICIT
| ISL_BASIC_MAP_ALL_EQUALITIES
);
825 bmap
= isl_basic_map_simplify(bmap
);
826 return isl_basic_map_finalize(bmap
);
828 isl_basic_set_free(hull
);
829 isl_basic_map_free(bmap
);
833 __isl_give isl_basic_set
*isl_basic_set_detect_equalities(
834 __isl_take isl_basic_set
*bset
)
836 return (isl_basic_set
*)
837 isl_basic_map_detect_equalities((isl_basic_map
*)bset
);
840 struct isl_map
*isl_map_detect_equalities(struct isl_map
*map
)
842 struct isl_basic_map
*bmap
;
848 for (i
= 0; i
< map
->n
; ++i
) {
849 bmap
= isl_basic_map_copy(map
->p
[i
]);
850 bmap
= isl_basic_map_detect_equalities(bmap
);
853 isl_basic_map_free(map
->p
[i
]);
863 __isl_give isl_set
*isl_set_detect_equalities(__isl_take isl_set
*set
)
865 return (isl_set
*)isl_map_detect_equalities((isl_map
*)set
);
868 /* After computing the rational affine hull (by detecting the implicit
869 * equalities), we compute the additional equalities satisfied by
870 * the integer points (if any) and add the original equalities back in.
872 struct isl_basic_map
*isl_basic_map_affine_hull(struct isl_basic_map
*bmap
)
874 bmap
= isl_basic_map_detect_equalities(bmap
);
875 bmap
= isl_basic_map_cow(bmap
);
876 isl_basic_map_free_inequality(bmap
, bmap
->n_ineq
);
880 struct isl_basic_set
*isl_basic_set_affine_hull(struct isl_basic_set
*bset
)
882 return (struct isl_basic_set
*)
883 isl_basic_map_affine_hull((struct isl_basic_map
*)bset
);
886 struct isl_basic_map
*isl_map_affine_hull(struct isl_map
*map
)
889 struct isl_basic_map
*model
= NULL
;
890 struct isl_basic_map
*hull
= NULL
;
897 hull
= isl_basic_map_empty_like_map(map
);
902 map
= isl_map_detect_equalities(map
);
903 map
= isl_map_align_divs(map
);
906 model
= isl_basic_map_copy(map
->p
[0]);
907 set
= isl_map_underlying_set(map
);
908 set
= isl_set_cow(set
);
912 for (i
= 0; i
< set
->n
; ++i
) {
913 set
->p
[i
] = isl_basic_set_cow(set
->p
[i
]);
914 set
->p
[i
] = isl_basic_set_affine_hull(set
->p
[i
]);
915 set
->p
[i
] = isl_basic_set_gauss(set
->p
[i
], NULL
);
919 set
= isl_set_remove_empty_parts(set
);
921 hull
= isl_basic_map_empty_like(model
);
922 isl_basic_map_free(model
);
924 struct isl_basic_set
*bset
;
926 set
->p
[0] = affine_hull(set
->p
[0], set
->p
[--set
->n
]);
930 bset
= isl_basic_set_copy(set
->p
[0]);
931 hull
= isl_basic_map_overlying_set(bset
, model
);
934 hull
= isl_basic_map_simplify(hull
);
935 return isl_basic_map_finalize(hull
);
937 isl_basic_map_free(model
);
942 struct isl_basic_set
*isl_set_affine_hull(struct isl_set
*set
)
944 return (struct isl_basic_set
*)
945 isl_map_affine_hull((struct isl_map
*)set
);