interface/extract_interface.cc: adjust to removal of Job class
[isl.git] / isl_affine_hull.c
blobe7bde3f641e6bcf09cbb361ea0c91e0452243ae5
1 /*
2 * Copyright 2008-2009 Katholieke Universiteit Leuven
3 * Copyright 2010 INRIA Saclay
4 * Copyright 2012 Ecole Normale Superieure
6 * Use of this software is governed by the MIT license
8 * Written by Sven Verdoolaege, K.U.Leuven, Departement
9 * Computerwetenschappen, Celestijnenlaan 200A, B-3001 Leuven, Belgium
10 * and INRIA Saclay - Ile-de-France, Parc Club Orsay Universite,
11 * ZAC des vignes, 4 rue Jacques Monod, 91893 Orsay, France
12 * and Ecole Normale Superieure, 45 rue d'Ulm, 75230 Paris, France
15 #include <isl_ctx_private.h>
16 #include <isl_map_private.h>
17 #include <isl_seq.h>
18 #include <isl/set.h>
19 #include <isl/lp.h>
20 #include <isl/map.h>
21 #include "isl_equalities.h"
22 #include "isl_sample.h"
23 #include "isl_tab.h"
24 #include <isl_mat_private.h>
25 #include <isl_vec_private.h>
27 struct isl_basic_map *isl_basic_map_implicit_equalities(
28 struct isl_basic_map *bmap)
30 struct isl_tab *tab;
32 if (!bmap)
33 return bmap;
35 bmap = isl_basic_map_gauss(bmap, NULL);
36 if (ISL_F_ISSET(bmap, ISL_BASIC_MAP_EMPTY))
37 return bmap;
38 if (ISL_F_ISSET(bmap, ISL_BASIC_MAP_NO_IMPLICIT))
39 return bmap;
40 if (bmap->n_ineq <= 1)
41 return bmap;
43 tab = isl_tab_from_basic_map(bmap, 0);
44 if (isl_tab_detect_implicit_equalities(tab) < 0)
45 goto error;
46 bmap = isl_basic_map_update_from_tab(bmap, tab);
47 isl_tab_free(tab);
48 bmap = isl_basic_map_gauss(bmap, NULL);
49 ISL_F_SET(bmap, ISL_BASIC_MAP_NO_IMPLICIT);
50 return bmap;
51 error:
52 isl_tab_free(tab);
53 isl_basic_map_free(bmap);
54 return NULL;
57 struct isl_basic_set *isl_basic_set_implicit_equalities(
58 struct isl_basic_set *bset)
60 return (struct isl_basic_set *)
61 isl_basic_map_implicit_equalities((struct isl_basic_map*)bset);
64 struct isl_map *isl_map_implicit_equalities(struct isl_map *map)
66 int i;
68 if (!map)
69 return map;
71 for (i = 0; i < map->n; ++i) {
72 map->p[i] = isl_basic_map_implicit_equalities(map->p[i]);
73 if (!map->p[i])
74 goto error;
77 return map;
78 error:
79 isl_map_free(map);
80 return NULL;
83 /* Make eq[row][col] of both bmaps equal so we can add the row
84 * add the column to the common matrix.
85 * Note that because of the echelon form, the columns of row row
86 * after column col are zero.
88 static void set_common_multiple(
89 struct isl_basic_set *bset1, struct isl_basic_set *bset2,
90 unsigned row, unsigned col)
92 isl_int m, c;
94 if (isl_int_eq(bset1->eq[row][col], bset2->eq[row][col]))
95 return;
97 isl_int_init(c);
98 isl_int_init(m);
99 isl_int_lcm(m, bset1->eq[row][col], bset2->eq[row][col]);
100 isl_int_divexact(c, m, bset1->eq[row][col]);
101 isl_seq_scale(bset1->eq[row], bset1->eq[row], c, col+1);
102 isl_int_divexact(c, m, bset2->eq[row][col]);
103 isl_seq_scale(bset2->eq[row], bset2->eq[row], c, col+1);
104 isl_int_clear(c);
105 isl_int_clear(m);
108 /* Delete a given equality, moving all the following equalities one up.
110 static void delete_row(struct isl_basic_set *bset, unsigned row)
112 isl_int *t;
113 int r;
115 t = bset->eq[row];
116 bset->n_eq--;
117 for (r = row; r < bset->n_eq; ++r)
118 bset->eq[r] = bset->eq[r+1];
119 bset->eq[bset->n_eq] = t;
122 /* Make first row entries in column col of bset1 identical to
123 * those of bset2, using the fact that entry bset1->eq[row][col]=a
124 * is non-zero. Initially, these elements of bset1 are all zero.
125 * For each row i < row, we set
126 * A[i] = a * A[i] + B[i][col] * A[row]
127 * B[i] = a * B[i]
128 * so that
129 * A[i][col] = B[i][col] = a * old(B[i][col])
131 static void construct_column(
132 struct isl_basic_set *bset1, struct isl_basic_set *bset2,
133 unsigned row, unsigned col)
135 int r;
136 isl_int a;
137 isl_int b;
138 unsigned total;
140 isl_int_init(a);
141 isl_int_init(b);
142 total = 1 + isl_basic_set_n_dim(bset1);
143 for (r = 0; r < row; ++r) {
144 if (isl_int_is_zero(bset2->eq[r][col]))
145 continue;
146 isl_int_gcd(b, bset2->eq[r][col], bset1->eq[row][col]);
147 isl_int_divexact(a, bset1->eq[row][col], b);
148 isl_int_divexact(b, bset2->eq[r][col], b);
149 isl_seq_combine(bset1->eq[r], a, bset1->eq[r],
150 b, bset1->eq[row], total);
151 isl_seq_scale(bset2->eq[r], bset2->eq[r], a, total);
153 isl_int_clear(a);
154 isl_int_clear(b);
155 delete_row(bset1, row);
158 /* Make first row entries in column col of bset1 identical to
159 * those of bset2, using only these entries of the two matrices.
160 * Let t be the last row with different entries.
161 * For each row i < t, we set
162 * A[i] = (A[t][col]-B[t][col]) * A[i] + (B[i][col]-A[i][col) * A[t]
163 * B[i] = (A[t][col]-B[t][col]) * B[i] + (B[i][col]-A[i][col) * B[t]
164 * so that
165 * A[i][col] = B[i][col] = old(A[t][col]*B[i][col]-A[i][col]*B[t][col])
167 static int transform_column(
168 struct isl_basic_set *bset1, struct isl_basic_set *bset2,
169 unsigned row, unsigned col)
171 int i, t;
172 isl_int a, b, g;
173 unsigned total;
175 for (t = row-1; t >= 0; --t)
176 if (isl_int_ne(bset1->eq[t][col], bset2->eq[t][col]))
177 break;
178 if (t < 0)
179 return 0;
181 total = 1 + isl_basic_set_n_dim(bset1);
182 isl_int_init(a);
183 isl_int_init(b);
184 isl_int_init(g);
185 isl_int_sub(b, bset1->eq[t][col], bset2->eq[t][col]);
186 for (i = 0; i < t; ++i) {
187 isl_int_sub(a, bset2->eq[i][col], bset1->eq[i][col]);
188 isl_int_gcd(g, a, b);
189 isl_int_divexact(a, a, g);
190 isl_int_divexact(g, b, g);
191 isl_seq_combine(bset1->eq[i], g, bset1->eq[i], a, bset1->eq[t],
192 total);
193 isl_seq_combine(bset2->eq[i], g, bset2->eq[i], a, bset2->eq[t],
194 total);
196 isl_int_clear(a);
197 isl_int_clear(b);
198 isl_int_clear(g);
199 delete_row(bset1, t);
200 delete_row(bset2, t);
201 return 1;
204 /* The implementation is based on Section 5.2 of Michael Karr,
205 * "Affine Relationships Among Variables of a Program",
206 * except that the echelon form we use starts from the last column
207 * and that we are dealing with integer coefficients.
209 static struct isl_basic_set *affine_hull(
210 struct isl_basic_set *bset1, struct isl_basic_set *bset2)
212 unsigned total;
213 int col;
214 int row;
216 if (!bset1 || !bset2)
217 goto error;
219 total = 1 + isl_basic_set_n_dim(bset1);
221 row = 0;
222 for (col = total-1; col >= 0; --col) {
223 int is_zero1 = row >= bset1->n_eq ||
224 isl_int_is_zero(bset1->eq[row][col]);
225 int is_zero2 = row >= bset2->n_eq ||
226 isl_int_is_zero(bset2->eq[row][col]);
227 if (!is_zero1 && !is_zero2) {
228 set_common_multiple(bset1, bset2, row, col);
229 ++row;
230 } else if (!is_zero1 && is_zero2) {
231 construct_column(bset1, bset2, row, col);
232 } else if (is_zero1 && !is_zero2) {
233 construct_column(bset2, bset1, row, col);
234 } else {
235 if (transform_column(bset1, bset2, row, col))
236 --row;
239 isl_assert(bset1->ctx, row == bset1->n_eq, goto error);
240 isl_basic_set_free(bset2);
241 bset1 = isl_basic_set_normalize_constraints(bset1);
242 return bset1;
243 error:
244 isl_basic_set_free(bset1);
245 isl_basic_set_free(bset2);
246 return NULL;
249 /* Find an integer point in the set represented by "tab"
250 * that lies outside of the equality "eq" e(x) = 0.
251 * If "up" is true, look for a point satisfying e(x) - 1 >= 0.
252 * Otherwise, look for a point satisfying -e(x) - 1 >= 0 (i.e., e(x) <= -1).
253 * The point, if found, is returned.
254 * If no point can be found, a zero-length vector is returned.
256 * Before solving an ILP problem, we first check if simply
257 * adding the normal of the constraint to one of the known
258 * integer points in the basic set represented by "tab"
259 * yields another point inside the basic set.
261 * The caller of this function ensures that the tableau is bounded or
262 * that tab->basis and tab->n_unbounded have been set appropriately.
264 static struct isl_vec *outside_point(struct isl_tab *tab, isl_int *eq, int up)
266 struct isl_ctx *ctx;
267 struct isl_vec *sample = NULL;
268 struct isl_tab_undo *snap;
269 unsigned dim;
271 if (!tab)
272 return NULL;
273 ctx = tab->mat->ctx;
275 dim = tab->n_var;
276 sample = isl_vec_alloc(ctx, 1 + dim);
277 if (!sample)
278 return NULL;
279 isl_int_set_si(sample->el[0], 1);
280 isl_seq_combine(sample->el + 1,
281 ctx->one, tab->bmap->sample->el + 1,
282 up ? ctx->one : ctx->negone, eq + 1, dim);
283 if (isl_basic_map_contains(tab->bmap, sample))
284 return sample;
285 isl_vec_free(sample);
286 sample = NULL;
288 snap = isl_tab_snap(tab);
290 if (!up)
291 isl_seq_neg(eq, eq, 1 + dim);
292 isl_int_sub_ui(eq[0], eq[0], 1);
294 if (isl_tab_extend_cons(tab, 1) < 0)
295 goto error;
296 if (isl_tab_add_ineq(tab, eq) < 0)
297 goto error;
299 sample = isl_tab_sample(tab);
301 isl_int_add_ui(eq[0], eq[0], 1);
302 if (!up)
303 isl_seq_neg(eq, eq, 1 + dim);
305 if (sample && isl_tab_rollback(tab, snap) < 0)
306 goto error;
308 return sample;
309 error:
310 isl_vec_free(sample);
311 return NULL;
314 struct isl_basic_set *isl_basic_set_recession_cone(struct isl_basic_set *bset)
316 int i;
318 bset = isl_basic_set_cow(bset);
319 if (!bset)
320 return NULL;
321 isl_assert(bset->ctx, bset->n_div == 0, goto error);
323 for (i = 0; i < bset->n_eq; ++i)
324 isl_int_set_si(bset->eq[i][0], 0);
326 for (i = 0; i < bset->n_ineq; ++i)
327 isl_int_set_si(bset->ineq[i][0], 0);
329 ISL_F_CLR(bset, ISL_BASIC_SET_NO_IMPLICIT);
330 return isl_basic_set_implicit_equalities(bset);
331 error:
332 isl_basic_set_free(bset);
333 return NULL;
336 __isl_give isl_set *isl_set_recession_cone(__isl_take isl_set *set)
338 int i;
340 if (!set)
341 return NULL;
342 if (set->n == 0)
343 return set;
345 set = isl_set_remove_divs(set);
346 set = isl_set_cow(set);
347 if (!set)
348 return NULL;
350 for (i = 0; i < set->n; ++i) {
351 set->p[i] = isl_basic_set_recession_cone(set->p[i]);
352 if (!set->p[i])
353 goto error;
356 return set;
357 error:
358 isl_set_free(set);
359 return NULL;
362 /* Move "sample" to a point that is one up (or down) from the original
363 * point in dimension "pos".
365 static void adjacent_point(__isl_keep isl_vec *sample, int pos, int up)
367 if (up)
368 isl_int_add_ui(sample->el[1 + pos], sample->el[1 + pos], 1);
369 else
370 isl_int_sub_ui(sample->el[1 + pos], sample->el[1 + pos], 1);
373 /* Check if any points that are adjacent to "sample" also belong to "bset".
374 * If so, add them to "hull" and return the updated hull.
376 * Before checking whether and adjacent point belongs to "bset", we first
377 * check whether it already belongs to "hull" as this test is typically
378 * much cheaper.
380 static __isl_give isl_basic_set *add_adjacent_points(
381 __isl_take isl_basic_set *hull, __isl_take isl_vec *sample,
382 __isl_keep isl_basic_set *bset)
384 int i, up;
385 int dim;
387 if (!sample)
388 goto error;
390 dim = isl_basic_set_dim(hull, isl_dim_set);
392 for (i = 0; i < dim; ++i) {
393 for (up = 0; up <= 1; ++up) {
394 int contains;
395 isl_basic_set *point;
397 adjacent_point(sample, i, up);
398 contains = isl_basic_set_contains(hull, sample);
399 if (contains < 0)
400 goto error;
401 if (contains) {
402 adjacent_point(sample, i, !up);
403 continue;
405 contains = isl_basic_set_contains(bset, sample);
406 if (contains < 0)
407 goto error;
408 if (contains) {
409 point = isl_basic_set_from_vec(
410 isl_vec_copy(sample));
411 hull = affine_hull(hull, point);
413 adjacent_point(sample, i, !up);
414 if (contains)
415 break;
419 isl_vec_free(sample);
421 return hull;
422 error:
423 isl_vec_free(sample);
424 isl_basic_set_free(hull);
425 return NULL;
428 /* Extend an initial (under-)approximation of the affine hull of basic
429 * set represented by the tableau "tab"
430 * by looking for points that do not satisfy one of the equalities
431 * in the current approximation and adding them to that approximation
432 * until no such points can be found any more.
434 * The caller of this function ensures that "tab" is bounded or
435 * that tab->basis and tab->n_unbounded have been set appropriately.
437 * "bset" may be either NULL or the basic set represented by "tab".
438 * If "bset" is not NULL, we check for any point we find if any
439 * of its adjacent points also belong to "bset".
441 static __isl_give isl_basic_set *extend_affine_hull(struct isl_tab *tab,
442 __isl_take isl_basic_set *hull, __isl_keep isl_basic_set *bset)
444 int i, j;
445 unsigned dim;
447 if (!tab || !hull)
448 goto error;
450 dim = tab->n_var;
452 if (isl_tab_extend_cons(tab, 2 * dim + 1) < 0)
453 goto error;
455 for (i = 0; i < dim; ++i) {
456 struct isl_vec *sample;
457 struct isl_basic_set *point;
458 for (j = 0; j < hull->n_eq; ++j) {
459 sample = outside_point(tab, hull->eq[j], 1);
460 if (!sample)
461 goto error;
462 if (sample->size > 0)
463 break;
464 isl_vec_free(sample);
465 sample = outside_point(tab, hull->eq[j], 0);
466 if (!sample)
467 goto error;
468 if (sample->size > 0)
469 break;
470 isl_vec_free(sample);
472 if (isl_tab_add_eq(tab, hull->eq[j]) < 0)
473 goto error;
475 if (j == hull->n_eq)
476 break;
477 if (tab->samples &&
478 isl_tab_add_sample(tab, isl_vec_copy(sample)) < 0)
479 hull = isl_basic_set_free(hull);
480 if (bset)
481 hull = add_adjacent_points(hull, isl_vec_copy(sample),
482 bset);
483 point = isl_basic_set_from_vec(sample);
484 hull = affine_hull(hull, point);
485 if (!hull)
486 return NULL;
489 return hull;
490 error:
491 isl_basic_set_free(hull);
492 return NULL;
495 /* Drop all constraints in bmap that involve any of the dimensions
496 * first to first+n-1.
498 static __isl_give isl_basic_map *isl_basic_map_drop_constraints_involving(
499 __isl_take isl_basic_map *bmap, unsigned first, unsigned n)
501 int i;
503 if (n == 0)
504 return bmap;
506 bmap = isl_basic_map_cow(bmap);
508 if (!bmap)
509 return NULL;
511 for (i = bmap->n_eq - 1; i >= 0; --i) {
512 if (isl_seq_first_non_zero(bmap->eq[i] + 1 + first, n) == -1)
513 continue;
514 isl_basic_map_drop_equality(bmap, i);
517 for (i = bmap->n_ineq - 1; i >= 0; --i) {
518 if (isl_seq_first_non_zero(bmap->ineq[i] + 1 + first, n) == -1)
519 continue;
520 isl_basic_map_drop_inequality(bmap, i);
523 bmap = isl_basic_map_add_known_div_constraints(bmap);
524 return bmap;
527 /* Drop all constraints in bset that involve any of the dimensions
528 * first to first+n-1.
530 __isl_give isl_basic_set *isl_basic_set_drop_constraints_involving(
531 __isl_take isl_basic_set *bset, unsigned first, unsigned n)
533 return isl_basic_map_drop_constraints_involving(bset, first, n);
536 /* Drop all constraints in bmap that do not involve any of the dimensions
537 * first to first + n - 1 of the given type.
539 __isl_give isl_basic_map *isl_basic_map_drop_constraints_not_involving_dims(
540 __isl_take isl_basic_map *bmap,
541 enum isl_dim_type type, unsigned first, unsigned n)
543 int i;
544 unsigned dim;
546 if (n == 0) {
547 isl_space *space = isl_basic_map_get_space(bmap);
548 isl_basic_map_free(bmap);
549 return isl_basic_map_universe(space);
551 bmap = isl_basic_map_cow(bmap);
552 if (!bmap)
553 return NULL;
555 dim = isl_basic_map_dim(bmap, type);
556 if (first + n > dim || first + n < first)
557 isl_die(isl_basic_map_get_ctx(bmap), isl_error_invalid,
558 "index out of bounds", return isl_basic_map_free(bmap));
560 first += isl_basic_map_offset(bmap, type) - 1;
562 for (i = bmap->n_eq - 1; i >= 0; --i) {
563 if (isl_seq_first_non_zero(bmap->eq[i] + 1 + first, n) != -1)
564 continue;
565 isl_basic_map_drop_equality(bmap, i);
568 for (i = bmap->n_ineq - 1; i >= 0; --i) {
569 if (isl_seq_first_non_zero(bmap->ineq[i] + 1 + first, n) != -1)
570 continue;
571 isl_basic_map_drop_inequality(bmap, i);
574 bmap = isl_basic_map_add_known_div_constraints(bmap);
575 return bmap;
578 /* Drop all constraints in bset that do not involve any of the dimensions
579 * first to first + n - 1 of the given type.
581 __isl_give isl_basic_set *isl_basic_set_drop_constraints_not_involving_dims(
582 __isl_take isl_basic_set *bset,
583 enum isl_dim_type type, unsigned first, unsigned n)
585 return isl_basic_map_drop_constraints_not_involving_dims(bset,
586 type, first, n);
589 /* Drop all constraints in bmap that involve any of the dimensions
590 * first to first + n - 1 of the given type.
592 __isl_give isl_basic_map *isl_basic_map_drop_constraints_involving_dims(
593 __isl_take isl_basic_map *bmap,
594 enum isl_dim_type type, unsigned first, unsigned n)
596 unsigned dim;
598 if (!bmap)
599 return NULL;
600 if (n == 0)
601 return bmap;
603 dim = isl_basic_map_dim(bmap, type);
604 if (first + n > dim || first + n < first)
605 isl_die(isl_basic_map_get_ctx(bmap), isl_error_invalid,
606 "index out of bounds", return isl_basic_map_free(bmap));
608 bmap = isl_basic_map_remove_divs_involving_dims(bmap, type, first, n);
609 first += isl_basic_map_offset(bmap, type) - 1;
610 return isl_basic_map_drop_constraints_involving(bmap, first, n);
613 /* Drop all constraints in bset that involve any of the dimensions
614 * first to first + n - 1 of the given type.
616 __isl_give isl_basic_set *isl_basic_set_drop_constraints_involving_dims(
617 __isl_take isl_basic_set *bset,
618 enum isl_dim_type type, unsigned first, unsigned n)
620 return isl_basic_map_drop_constraints_involving_dims(bset,
621 type, first, n);
624 /* Drop all constraints in map that involve any of the dimensions
625 * first to first + n - 1 of the given type.
627 __isl_give isl_map *isl_map_drop_constraints_involving_dims(
628 __isl_take isl_map *map,
629 enum isl_dim_type type, unsigned first, unsigned n)
631 int i;
632 unsigned dim;
634 if (!map)
635 return NULL;
636 if (n == 0)
637 return map;
639 dim = isl_map_dim(map, type);
640 if (first + n > dim || first + n < first)
641 isl_die(isl_map_get_ctx(map), isl_error_invalid,
642 "index out of bounds", return isl_map_free(map));
644 map = isl_map_cow(map);
645 if (!map)
646 return NULL;
648 for (i = 0; i < map->n; ++i) {
649 map->p[i] = isl_basic_map_drop_constraints_involving_dims(
650 map->p[i], type, first, n);
651 if (!map->p[i])
652 return isl_map_free(map);
655 return map;
658 /* Drop all constraints in set that involve any of the dimensions
659 * first to first + n - 1 of the given type.
661 __isl_give isl_set *isl_set_drop_constraints_involving_dims(
662 __isl_take isl_set *set,
663 enum isl_dim_type type, unsigned first, unsigned n)
665 return isl_map_drop_constraints_involving_dims(set, type, first, n);
668 /* Construct an initial underapproximatino of the hull of "bset"
669 * from "sample" and any of its adjacent points that also belong to "bset".
671 static __isl_give isl_basic_set *initialize_hull(__isl_keep isl_basic_set *bset,
672 __isl_take isl_vec *sample)
674 isl_basic_set *hull;
676 hull = isl_basic_set_from_vec(isl_vec_copy(sample));
677 hull = add_adjacent_points(hull, sample, bset);
679 return hull;
682 /* Look for all equalities satisfied by the integer points in bset,
683 * which is assumed to be bounded.
685 * The equalities are obtained by successively looking for
686 * a point that is affinely independent of the points found so far.
687 * In particular, for each equality satisfied by the points so far,
688 * we check if there is any point on a hyperplane parallel to the
689 * corresponding hyperplane shifted by at least one (in either direction).
691 static struct isl_basic_set *uset_affine_hull_bounded(struct isl_basic_set *bset)
693 struct isl_vec *sample = NULL;
694 struct isl_basic_set *hull;
695 struct isl_tab *tab = NULL;
696 unsigned dim;
698 if (isl_basic_set_plain_is_empty(bset))
699 return bset;
701 dim = isl_basic_set_n_dim(bset);
703 if (bset->sample && bset->sample->size == 1 + dim) {
704 int contains = isl_basic_set_contains(bset, bset->sample);
705 if (contains < 0)
706 goto error;
707 if (contains) {
708 if (dim == 0)
709 return bset;
710 sample = isl_vec_copy(bset->sample);
711 } else {
712 isl_vec_free(bset->sample);
713 bset->sample = NULL;
717 tab = isl_tab_from_basic_set(bset, 1);
718 if (!tab)
719 goto error;
720 if (tab->empty) {
721 isl_tab_free(tab);
722 isl_vec_free(sample);
723 return isl_basic_set_set_to_empty(bset);
726 if (!sample) {
727 struct isl_tab_undo *snap;
728 snap = isl_tab_snap(tab);
729 sample = isl_tab_sample(tab);
730 if (isl_tab_rollback(tab, snap) < 0)
731 goto error;
732 isl_vec_free(tab->bmap->sample);
733 tab->bmap->sample = isl_vec_copy(sample);
736 if (!sample)
737 goto error;
738 if (sample->size == 0) {
739 isl_tab_free(tab);
740 isl_vec_free(sample);
741 return isl_basic_set_set_to_empty(bset);
744 hull = initialize_hull(bset, sample);
746 hull = extend_affine_hull(tab, hull, bset);
747 isl_basic_set_free(bset);
748 isl_tab_free(tab);
750 return hull;
751 error:
752 isl_vec_free(sample);
753 isl_tab_free(tab);
754 isl_basic_set_free(bset);
755 return NULL;
758 /* Given an unbounded tableau and an integer point satisfying the tableau,
759 * construct an initial affine hull containing the recession cone
760 * shifted to the given point.
762 * The unbounded directions are taken from the last rows of the basis,
763 * which is assumed to have been initialized appropriately.
765 static __isl_give isl_basic_set *initial_hull(struct isl_tab *tab,
766 __isl_take isl_vec *vec)
768 int i;
769 int k;
770 struct isl_basic_set *bset = NULL;
771 struct isl_ctx *ctx;
772 unsigned dim;
774 if (!vec || !tab)
775 return NULL;
776 ctx = vec->ctx;
777 isl_assert(ctx, vec->size != 0, goto error);
779 bset = isl_basic_set_alloc(ctx, 0, vec->size - 1, 0, vec->size - 1, 0);
780 if (!bset)
781 goto error;
782 dim = isl_basic_set_n_dim(bset) - tab->n_unbounded;
783 for (i = 0; i < dim; ++i) {
784 k = isl_basic_set_alloc_equality(bset);
785 if (k < 0)
786 goto error;
787 isl_seq_cpy(bset->eq[k] + 1, tab->basis->row[1 + i] + 1,
788 vec->size - 1);
789 isl_seq_inner_product(bset->eq[k] + 1, vec->el +1,
790 vec->size - 1, &bset->eq[k][0]);
791 isl_int_neg(bset->eq[k][0], bset->eq[k][0]);
793 bset->sample = vec;
794 bset = isl_basic_set_gauss(bset, NULL);
796 return bset;
797 error:
798 isl_basic_set_free(bset);
799 isl_vec_free(vec);
800 return NULL;
803 /* Given a tableau of a set and a tableau of the corresponding
804 * recession cone, detect and add all equalities to the tableau.
805 * If the tableau is bounded, then we can simply keep the
806 * tableau in its state after the return from extend_affine_hull.
807 * However, if the tableau is unbounded, then
808 * isl_tab_set_initial_basis_with_cone will add some additional
809 * constraints to the tableau that have to be removed again.
810 * In this case, we therefore rollback to the state before
811 * any constraints were added and then add the equalities back in.
813 struct isl_tab *isl_tab_detect_equalities(struct isl_tab *tab,
814 struct isl_tab *tab_cone)
816 int j;
817 struct isl_vec *sample;
818 struct isl_basic_set *hull = NULL;
819 struct isl_tab_undo *snap;
821 if (!tab || !tab_cone)
822 goto error;
824 snap = isl_tab_snap(tab);
826 isl_mat_free(tab->basis);
827 tab->basis = NULL;
829 isl_assert(tab->mat->ctx, tab->bmap, goto error);
830 isl_assert(tab->mat->ctx, tab->samples, goto error);
831 isl_assert(tab->mat->ctx, tab->samples->n_col == 1 + tab->n_var, goto error);
832 isl_assert(tab->mat->ctx, tab->n_sample > tab->n_outside, goto error);
834 if (isl_tab_set_initial_basis_with_cone(tab, tab_cone) < 0)
835 goto error;
837 sample = isl_vec_alloc(tab->mat->ctx, 1 + tab->n_var);
838 if (!sample)
839 goto error;
841 isl_seq_cpy(sample->el, tab->samples->row[tab->n_outside], sample->size);
843 isl_vec_free(tab->bmap->sample);
844 tab->bmap->sample = isl_vec_copy(sample);
846 if (tab->n_unbounded == 0)
847 hull = isl_basic_set_from_vec(isl_vec_copy(sample));
848 else
849 hull = initial_hull(tab, isl_vec_copy(sample));
851 for (j = tab->n_outside + 1; j < tab->n_sample; ++j) {
852 isl_seq_cpy(sample->el, tab->samples->row[j], sample->size);
853 hull = affine_hull(hull,
854 isl_basic_set_from_vec(isl_vec_copy(sample)));
857 isl_vec_free(sample);
859 hull = extend_affine_hull(tab, hull, NULL);
860 if (!hull)
861 goto error;
863 if (tab->n_unbounded == 0) {
864 isl_basic_set_free(hull);
865 return tab;
868 if (isl_tab_rollback(tab, snap) < 0)
869 goto error;
871 if (hull->n_eq > tab->n_zero) {
872 for (j = 0; j < hull->n_eq; ++j) {
873 isl_seq_normalize(tab->mat->ctx, hull->eq[j], 1 + tab->n_var);
874 if (isl_tab_add_eq(tab, hull->eq[j]) < 0)
875 goto error;
879 isl_basic_set_free(hull);
881 return tab;
882 error:
883 isl_basic_set_free(hull);
884 isl_tab_free(tab);
885 return NULL;
888 /* Compute the affine hull of "bset", where "cone" is the recession cone
889 * of "bset".
891 * We first compute a unimodular transformation that puts the unbounded
892 * directions in the last dimensions. In particular, we take a transformation
893 * that maps all equalities to equalities (in HNF) on the first dimensions.
894 * Let x be the original dimensions and y the transformed, with y_1 bounded
895 * and y_2 unbounded.
897 * [ y_1 ] [ y_1 ] [ Q_1 ]
898 * x = U [ y_2 ] [ y_2 ] = [ Q_2 ] x
900 * Let's call the input basic set S. We compute S' = preimage(S, U)
901 * and drop the final dimensions including any constraints involving them.
902 * This results in set S''.
903 * Then we compute the affine hull A'' of S''.
904 * Let F y_1 >= g be the constraint system of A''. In the transformed
905 * space the y_2 are unbounded, so we can add them back without any constraints,
906 * resulting in
908 * [ y_1 ]
909 * [ F 0 ] [ y_2 ] >= g
910 * or
911 * [ Q_1 ]
912 * [ F 0 ] [ Q_2 ] x >= g
913 * or
914 * F Q_1 x >= g
916 * The affine hull in the original space is then obtained as
917 * A = preimage(A'', Q_1).
919 static struct isl_basic_set *affine_hull_with_cone(struct isl_basic_set *bset,
920 struct isl_basic_set *cone)
922 unsigned total;
923 unsigned cone_dim;
924 struct isl_basic_set *hull;
925 struct isl_mat *M, *U, *Q;
927 if (!bset || !cone)
928 goto error;
930 total = isl_basic_set_total_dim(cone);
931 cone_dim = total - cone->n_eq;
933 M = isl_mat_sub_alloc6(bset->ctx, cone->eq, 0, cone->n_eq, 1, total);
934 M = isl_mat_left_hermite(M, 0, &U, &Q);
935 if (!M)
936 goto error;
937 isl_mat_free(M);
939 U = isl_mat_lin_to_aff(U);
940 bset = isl_basic_set_preimage(bset, isl_mat_copy(U));
942 bset = isl_basic_set_drop_constraints_involving(bset, total - cone_dim,
943 cone_dim);
944 bset = isl_basic_set_drop_dims(bset, total - cone_dim, cone_dim);
946 Q = isl_mat_lin_to_aff(Q);
947 Q = isl_mat_drop_rows(Q, 1 + total - cone_dim, cone_dim);
949 if (bset && bset->sample && bset->sample->size == 1 + total)
950 bset->sample = isl_mat_vec_product(isl_mat_copy(Q), bset->sample);
952 hull = uset_affine_hull_bounded(bset);
954 if (!hull) {
955 isl_mat_free(Q);
956 isl_mat_free(U);
957 } else {
958 struct isl_vec *sample = isl_vec_copy(hull->sample);
959 U = isl_mat_drop_cols(U, 1 + total - cone_dim, cone_dim);
960 if (sample && sample->size > 0)
961 sample = isl_mat_vec_product(U, sample);
962 else
963 isl_mat_free(U);
964 hull = isl_basic_set_preimage(hull, Q);
965 if (hull) {
966 isl_vec_free(hull->sample);
967 hull->sample = sample;
968 } else
969 isl_vec_free(sample);
972 isl_basic_set_free(cone);
974 return hull;
975 error:
976 isl_basic_set_free(bset);
977 isl_basic_set_free(cone);
978 return NULL;
981 /* Look for all equalities satisfied by the integer points in bset,
982 * which is assumed not to have any explicit equalities.
984 * The equalities are obtained by successively looking for
985 * a point that is affinely independent of the points found so far.
986 * In particular, for each equality satisfied by the points so far,
987 * we check if there is any point on a hyperplane parallel to the
988 * corresponding hyperplane shifted by at least one (in either direction).
990 * Before looking for any outside points, we first compute the recession
991 * cone. The directions of this recession cone will always be part
992 * of the affine hull, so there is no need for looking for any points
993 * in these directions.
994 * In particular, if the recession cone is full-dimensional, then
995 * the affine hull is simply the whole universe.
997 static struct isl_basic_set *uset_affine_hull(struct isl_basic_set *bset)
999 struct isl_basic_set *cone;
1001 if (isl_basic_set_plain_is_empty(bset))
1002 return bset;
1004 cone = isl_basic_set_recession_cone(isl_basic_set_copy(bset));
1005 if (!cone)
1006 goto error;
1007 if (cone->n_eq == 0) {
1008 isl_space *space;
1009 space = isl_basic_set_get_space(bset);
1010 isl_basic_set_free(cone);
1011 isl_basic_set_free(bset);
1012 return isl_basic_set_universe(space);
1015 if (cone->n_eq < isl_basic_set_total_dim(cone))
1016 return affine_hull_with_cone(bset, cone);
1018 isl_basic_set_free(cone);
1019 return uset_affine_hull_bounded(bset);
1020 error:
1021 isl_basic_set_free(bset);
1022 return NULL;
1025 /* Look for all equalities satisfied by the integer points in bmap
1026 * that are independent of the equalities already explicitly available
1027 * in bmap.
1029 * We first remove all equalities already explicitly available,
1030 * then look for additional equalities in the reduced space
1031 * and then transform the result to the original space.
1032 * The original equalities are _not_ added to this set. This is
1033 * the responsibility of the calling function.
1034 * The resulting basic set has all meaning about the dimensions removed.
1035 * In particular, dimensions that correspond to existential variables
1036 * in bmap and that are found to be fixed are not removed.
1038 static struct isl_basic_set *equalities_in_underlying_set(
1039 struct isl_basic_map *bmap)
1041 struct isl_mat *T1 = NULL;
1042 struct isl_mat *T2 = NULL;
1043 struct isl_basic_set *bset = NULL;
1044 struct isl_basic_set *hull = NULL;
1046 bset = isl_basic_map_underlying_set(bmap);
1047 if (!bset)
1048 return NULL;
1049 if (bset->n_eq)
1050 bset = isl_basic_set_remove_equalities(bset, &T1, &T2);
1051 if (!bset)
1052 goto error;
1054 hull = uset_affine_hull(bset);
1055 if (!T2)
1056 return hull;
1058 if (!hull) {
1059 isl_mat_free(T1);
1060 isl_mat_free(T2);
1061 } else {
1062 struct isl_vec *sample = isl_vec_copy(hull->sample);
1063 if (sample && sample->size > 0)
1064 sample = isl_mat_vec_product(T1, sample);
1065 else
1066 isl_mat_free(T1);
1067 hull = isl_basic_set_preimage(hull, T2);
1068 if (hull) {
1069 isl_vec_free(hull->sample);
1070 hull->sample = sample;
1071 } else
1072 isl_vec_free(sample);
1075 return hull;
1076 error:
1077 isl_mat_free(T1);
1078 isl_mat_free(T2);
1079 isl_basic_set_free(bset);
1080 isl_basic_set_free(hull);
1081 return NULL;
1084 /* Detect and make explicit all equalities satisfied by the (integer)
1085 * points in bmap.
1087 struct isl_basic_map *isl_basic_map_detect_equalities(
1088 struct isl_basic_map *bmap)
1090 int i, j;
1091 struct isl_basic_set *hull = NULL;
1093 if (!bmap)
1094 return NULL;
1095 if (bmap->n_ineq == 0)
1096 return bmap;
1097 if (ISL_F_ISSET(bmap, ISL_BASIC_MAP_EMPTY))
1098 return bmap;
1099 if (ISL_F_ISSET(bmap, ISL_BASIC_MAP_ALL_EQUALITIES))
1100 return bmap;
1101 if (ISL_F_ISSET(bmap, ISL_BASIC_MAP_RATIONAL))
1102 return isl_basic_map_implicit_equalities(bmap);
1104 hull = equalities_in_underlying_set(isl_basic_map_copy(bmap));
1105 if (!hull)
1106 goto error;
1107 if (ISL_F_ISSET(hull, ISL_BASIC_SET_EMPTY)) {
1108 isl_basic_set_free(hull);
1109 return isl_basic_map_set_to_empty(bmap);
1111 bmap = isl_basic_map_extend_space(bmap, isl_space_copy(bmap->dim), 0,
1112 hull->n_eq, 0);
1113 for (i = 0; i < hull->n_eq; ++i) {
1114 j = isl_basic_map_alloc_equality(bmap);
1115 if (j < 0)
1116 goto error;
1117 isl_seq_cpy(bmap->eq[j], hull->eq[i],
1118 1 + isl_basic_set_total_dim(hull));
1120 isl_vec_free(bmap->sample);
1121 bmap->sample = isl_vec_copy(hull->sample);
1122 isl_basic_set_free(hull);
1123 ISL_F_SET(bmap, ISL_BASIC_MAP_NO_IMPLICIT | ISL_BASIC_MAP_ALL_EQUALITIES);
1124 bmap = isl_basic_map_simplify(bmap);
1125 return isl_basic_map_finalize(bmap);
1126 error:
1127 isl_basic_set_free(hull);
1128 isl_basic_map_free(bmap);
1129 return NULL;
1132 __isl_give isl_basic_set *isl_basic_set_detect_equalities(
1133 __isl_take isl_basic_set *bset)
1135 return (isl_basic_set *)
1136 isl_basic_map_detect_equalities((isl_basic_map *)bset);
1139 __isl_give isl_map *isl_map_detect_equalities(__isl_take isl_map *map)
1141 return isl_map_inline_foreach_basic_map(map,
1142 &isl_basic_map_detect_equalities);
1145 __isl_give isl_set *isl_set_detect_equalities(__isl_take isl_set *set)
1147 return (isl_set *)isl_map_detect_equalities((isl_map *)set);
1150 /* Return the superset of "bmap" described by the equalities
1151 * satisfied by "bmap" that are already known.
1153 __isl_give isl_basic_map *isl_basic_map_plain_affine_hull(
1154 __isl_take isl_basic_map *bmap)
1156 bmap = isl_basic_map_cow(bmap);
1157 if (bmap)
1158 isl_basic_map_free_inequality(bmap, bmap->n_ineq);
1159 bmap = isl_basic_map_finalize(bmap);
1160 return bmap;
1163 /* After computing the rational affine hull (by detecting the implicit
1164 * equalities), we compute the additional equalities satisfied by
1165 * the integer points (if any) and add the original equalities back in.
1167 struct isl_basic_map *isl_basic_map_affine_hull(struct isl_basic_map *bmap)
1169 bmap = isl_basic_map_detect_equalities(bmap);
1170 bmap = isl_basic_map_plain_affine_hull(bmap);
1171 return bmap;
1174 struct isl_basic_set *isl_basic_set_affine_hull(struct isl_basic_set *bset)
1176 return (struct isl_basic_set *)
1177 isl_basic_map_affine_hull((struct isl_basic_map *)bset);
1180 /* Given a rational affine matrix "M", add stride constraints to "bmap"
1181 * that ensure that
1183 * M(x)
1185 * is an integer vector. The variables x include all the variables
1186 * of "bmap" except the unknown divs.
1188 * If d is the common denominator of M, then we need to impose that
1190 * d M(x) = 0 mod d
1192 * or
1194 * exists alpha : d M(x) = d alpha
1196 * This function is similar to add_strides in isl_morph.c
1198 static __isl_give isl_basic_map *add_strides(__isl_take isl_basic_map *bmap,
1199 __isl_keep isl_mat *M, int n_known)
1201 int i, div, k;
1202 isl_int gcd;
1204 if (isl_int_is_one(M->row[0][0]))
1205 return bmap;
1207 bmap = isl_basic_map_extend_space(bmap, isl_space_copy(bmap->dim),
1208 M->n_row - 1, M->n_row - 1, 0);
1210 isl_int_init(gcd);
1211 for (i = 1; i < M->n_row; ++i) {
1212 isl_seq_gcd(M->row[i], M->n_col, &gcd);
1213 if (isl_int_is_divisible_by(gcd, M->row[0][0]))
1214 continue;
1215 div = isl_basic_map_alloc_div(bmap);
1216 if (div < 0)
1217 goto error;
1218 isl_int_set_si(bmap->div[div][0], 0);
1219 k = isl_basic_map_alloc_equality(bmap);
1220 if (k < 0)
1221 goto error;
1222 isl_seq_cpy(bmap->eq[k], M->row[i], M->n_col);
1223 isl_seq_clr(bmap->eq[k] + M->n_col, bmap->n_div - n_known);
1224 isl_int_set(bmap->eq[k][M->n_col - n_known + div],
1225 M->row[0][0]);
1227 isl_int_clear(gcd);
1229 return bmap;
1230 error:
1231 isl_int_clear(gcd);
1232 isl_basic_map_free(bmap);
1233 return NULL;
1236 /* If there are any equalities that involve (multiple) unknown divs,
1237 * then extract the stride information encoded by those equalities
1238 * and make it explicitly available in "bmap".
1240 * We first sort the divs so that the unknown divs appear last and
1241 * then we count how many equalities involve these divs.
1243 * Let these equalities be of the form
1245 * A(x) + B y = 0
1247 * where y represents the unknown divs and x the remaining variables.
1248 * Let [H 0] be the Hermite Normal Form of B, i.e.,
1250 * B = [H 0] Q
1252 * Then x is a solution of the equalities iff
1254 * H^-1 A(x) (= - [I 0] Q y)
1256 * is an integer vector. Let d be the common denominator of H^-1.
1257 * We impose
1259 * d H^-1 A(x) = d alpha
1261 * in add_strides, with alpha fresh existentially quantified variables.
1263 static __isl_give isl_basic_map *isl_basic_map_make_strides_explicit(
1264 __isl_take isl_basic_map *bmap)
1266 int known;
1267 int n_known;
1268 int n, n_col;
1269 int total;
1270 isl_ctx *ctx;
1271 isl_mat *A, *B, *M;
1273 known = isl_basic_map_divs_known(bmap);
1274 if (known < 0)
1275 return isl_basic_map_free(bmap);
1276 if (known)
1277 return bmap;
1278 bmap = isl_basic_map_sort_divs(bmap);
1279 bmap = isl_basic_map_gauss(bmap, NULL);
1280 if (!bmap)
1281 return NULL;
1283 for (n_known = 0; n_known < bmap->n_div; ++n_known)
1284 if (isl_int_is_zero(bmap->div[n_known][0]))
1285 break;
1286 ctx = isl_basic_map_get_ctx(bmap);
1287 total = isl_space_dim(bmap->dim, isl_dim_all);
1288 for (n = 0; n < bmap->n_eq; ++n)
1289 if (isl_seq_first_non_zero(bmap->eq[n] + 1 + total + n_known,
1290 bmap->n_div - n_known) == -1)
1291 break;
1292 if (n == 0)
1293 return bmap;
1294 B = isl_mat_sub_alloc6(ctx, bmap->eq, 0, n, 0, 1 + total + n_known);
1295 n_col = bmap->n_div - n_known;
1296 A = isl_mat_sub_alloc6(ctx, bmap->eq, 0, n, 1 + total + n_known, n_col);
1297 A = isl_mat_left_hermite(A, 0, NULL, NULL);
1298 A = isl_mat_drop_cols(A, n, n_col - n);
1299 A = isl_mat_lin_to_aff(A);
1300 A = isl_mat_right_inverse(A);
1301 B = isl_mat_insert_zero_rows(B, 0, 1);
1302 B = isl_mat_set_element_si(B, 0, 0, 1);
1303 M = isl_mat_product(A, B);
1304 if (!M)
1305 return isl_basic_map_free(bmap);
1306 bmap = add_strides(bmap, M, n_known);
1307 bmap = isl_basic_map_gauss(bmap, NULL);
1308 isl_mat_free(M);
1310 return bmap;
1313 /* Compute the affine hull of each basic map in "map" separately
1314 * and make all stride information explicit so that we can remove
1315 * all unknown divs without losing this information.
1316 * The result is also guaranteed to be gaussed.
1318 * In simple cases where a div is determined by an equality,
1319 * calling isl_basic_map_gauss is enough to make the stride information
1320 * explicit, as it will derive an explicit representation for the div
1321 * from the equality. If, however, the stride information
1322 * is encoded through multiple unknown divs then we need to make
1323 * some extra effort in isl_basic_map_make_strides_explicit.
1325 static __isl_give isl_map *isl_map_local_affine_hull(__isl_take isl_map *map)
1327 int i;
1329 map = isl_map_cow(map);
1330 if (!map)
1331 return NULL;
1333 for (i = 0; i < map->n; ++i) {
1334 map->p[i] = isl_basic_map_affine_hull(map->p[i]);
1335 map->p[i] = isl_basic_map_gauss(map->p[i], NULL);
1336 map->p[i] = isl_basic_map_make_strides_explicit(map->p[i]);
1337 if (!map->p[i])
1338 return isl_map_free(map);
1341 return map;
1344 static __isl_give isl_set *isl_set_local_affine_hull(__isl_take isl_set *set)
1346 return isl_map_local_affine_hull(set);
1349 /* Return an empty basic map living in the same space as "map".
1351 static __isl_give isl_basic_map *replace_map_by_empty_basic_map(
1352 __isl_take isl_map *map)
1354 isl_space *space;
1356 space = isl_map_get_space(map);
1357 isl_map_free(map);
1358 return isl_basic_map_empty(space);
1361 /* Compute the affine hull of "map".
1363 * We first compute the affine hull of each basic map separately.
1364 * Then we align the divs and recompute the affine hulls of the basic
1365 * maps since some of them may now have extra divs.
1366 * In order to avoid performing parametric integer programming to
1367 * compute explicit expressions for the divs, possible leading to
1368 * an explosion in the number of basic maps, we first drop all unknown
1369 * divs before aligning the divs. Note that isl_map_local_affine_hull tries
1370 * to make sure that all stride information is explicitly available
1371 * in terms of known divs. This involves calling isl_basic_set_gauss,
1372 * which is also needed because affine_hull assumes its input has been gaussed,
1373 * while isl_map_affine_hull may be called on input that has not been gaussed,
1374 * in particular from initial_facet_constraint.
1375 * Similarly, align_divs may reorder some divs so that we need to
1376 * gauss the result again.
1377 * Finally, we combine the individual affine hulls into a single
1378 * affine hull.
1380 __isl_give isl_basic_map *isl_map_affine_hull(__isl_take isl_map *map)
1382 struct isl_basic_map *model = NULL;
1383 struct isl_basic_map *hull = NULL;
1384 struct isl_set *set;
1385 isl_basic_set *bset;
1387 map = isl_map_detect_equalities(map);
1388 map = isl_map_local_affine_hull(map);
1389 map = isl_map_remove_empty_parts(map);
1390 map = isl_map_remove_unknown_divs(map);
1391 map = isl_map_align_divs(map);
1393 if (!map)
1394 return NULL;
1396 if (map->n == 0)
1397 return replace_map_by_empty_basic_map(map);
1399 model = isl_basic_map_copy(map->p[0]);
1400 set = isl_map_underlying_set(map);
1401 set = isl_set_cow(set);
1402 set = isl_set_local_affine_hull(set);
1403 if (!set)
1404 goto error;
1406 while (set->n > 1)
1407 set->p[0] = affine_hull(set->p[0], set->p[--set->n]);
1409 bset = isl_basic_set_copy(set->p[0]);
1410 hull = isl_basic_map_overlying_set(bset, model);
1411 isl_set_free(set);
1412 hull = isl_basic_map_simplify(hull);
1413 return isl_basic_map_finalize(hull);
1414 error:
1415 isl_basic_map_free(model);
1416 isl_set_free(set);
1417 return NULL;
1420 struct isl_basic_set *isl_set_affine_hull(struct isl_set *set)
1422 return (struct isl_basic_set *)
1423 isl_map_affine_hull((struct isl_map *)set);