1 #include "isl_map_private.h"
4 #include "isl_sample.h"
7 * The implementation of parametric integer linear programming in this file
8 * was inspired by the paper "Parametric Integer Programming" and the
9 * report "Solving systems of affine (in)equalities" by Paul Feautrier
12 * The strategy used for obtaining a feasible solution is different
13 * from the one used in isl_tab.c. In particular, in isl_tab.c,
14 * upon finding a constraint that is not yet satisfied, we pivot
15 * in a row that increases the constant term of row holding the
16 * constraint, making sure the sample solution remains feasible
17 * for all the constraints it already satisfied.
18 * Here, we always pivot in the row holding the constraint,
19 * choosing a column that induces the lexicographically smallest
20 * increment to the sample solution.
22 * By starting out from a sample value that is lexicographically
23 * smaller than any integer point in the problem space, the first
24 * feasible integer sample point we find will also be the lexicographically
25 * smallest. If all variables can be assumed to be non-negative,
26 * then the initial sample value may be chosen equal to zero.
27 * However, we will not make this assumption. Instead, we apply
28 * the "big parameter" trick. Any variable x is then not directly
29 * used in the tableau, but instead it its represented by another
30 * variable x' = M + x, where M is an arbitrarily large (positive)
31 * value. x' is therefore always non-negative, whatever the value of x.
32 * Taking as initial smaple value x' = 0 corresponds to x = -M,
33 * which is always smaller than any possible value of x.
35 * The big parameter trick is used in the main tableau and
36 * also in the context tableau if isl_context_lex is used.
37 * In this case, each tableaus has its own big parameter.
38 * Before doing any real work, we check if all the parameters
39 * happen to be non-negative. If so, we drop the column corresponding
40 * to M from the initial context tableau.
41 * If isl_context_gbr is used, then the big parameter trick is only
42 * used in the main tableau.
46 struct isl_context_op {
47 /* detect nonnegative parameters in context and mark them in tab */
48 struct isl_tab *(*detect_nonnegative_parameters)(
49 struct isl_context *context, struct isl_tab *tab);
50 /* return temporary reference to basic set representation of context */
51 struct isl_basic_set *(*peek_basic_set)(struct isl_context *context);
52 /* return temporary reference to tableau representation of context */
53 struct isl_tab *(*peek_tab)(struct isl_context *context);
54 /* add equality; check is 1 if eq may not be valid;
55 * update is 1 if we may want to call ineq_sign on context later.
57 void (*add_eq)(struct isl_context *context, isl_int *eq,
58 int check, int update);
59 /* add inequality; check is 1 if ineq may not be valid;
60 * update is 1 if we may want to call ineq_sign on context later.
62 void (*add_ineq)(struct isl_context *context, isl_int *ineq,
63 int check, int update);
64 /* check sign of ineq based on previous information.
65 * strict is 1 if saturation should be treated as a positive sign.
67 enum isl_tab_row_sign (*ineq_sign)(struct isl_context *context,
68 isl_int *ineq, int strict);
69 /* check if inequality maintains feasibility */
70 int (*test_ineq)(struct isl_context *context, isl_int *ineq);
71 /* return index of a div that corresponds to "div" */
72 int (*get_div)(struct isl_context *context, struct isl_tab *tab,
74 /* add div "div" to context and return index and non-negativity */
75 int (*add_div)(struct isl_context *context, struct isl_vec *div,
77 int (*detect_equalities)(struct isl_context *context,
79 /* return row index of "best" split */
80 int (*best_split)(struct isl_context *context, struct isl_tab *tab);
81 /* check if context has already been determined to be empty */
82 int (*is_empty)(struct isl_context *context);
83 /* check if context is still usable */
84 int (*is_ok)(struct isl_context *context);
85 /* save a copy/snapshot of context */
86 void *(*save)(struct isl_context *context);
87 /* restore saved context */
88 void (*restore)(struct isl_context *context, void *);
89 /* invalidate context */
90 void (*invalidate)(struct isl_context *context);
92 void (*free)(struct isl_context *context);
96 struct isl_context_op *op;
99 struct isl_context_lex {
100 struct isl_context context;
104 /* isl_sol is an interface for constructing a solution to
105 * a parametric integer linear programming problem.
106 * Every time the algorithm reaches a state where a solution
107 * can be read off from the tableau (including cases where the tableau
108 * is empty), the function "add" is called on the isl_sol passed
109 * to find_solutions_main.
111 * The context tableau is owned by isl_sol and is updated incrementally.
113 * There are currently two implementations of this interface,
114 * isl_sol_map, which simply collects the solutions in an isl_map
115 * and (optionally) the parts of the context where there is no solution
117 * isl_sol_for, which calls a user-defined function for each part of
121 struct isl_context *context;
122 struct isl_sol *(*add)(struct isl_sol *sol, struct isl_tab *tab);
123 void (*free)(struct isl_sol *sol);
126 static void sol_free(struct isl_sol *sol)
136 struct isl_set *empty;
140 static void sol_map_free(struct isl_sol_map *sol_map)
142 if (sol_map->sol.context)
143 sol_map->sol.context->op->free(sol_map->sol.context);
144 isl_map_free(sol_map->map);
145 isl_set_free(sol_map->empty);
149 static void sol_map_free_wrap(struct isl_sol *sol)
151 sol_map_free((struct isl_sol_map *)sol);
154 static struct isl_sol_map *add_empty(struct isl_sol_map *sol)
156 struct isl_basic_set *bset;
160 sol->empty = isl_set_grow(sol->empty, 1);
161 bset = sol->sol.context->op->peek_basic_set(sol->sol.context);
162 bset = isl_basic_set_copy(bset);
163 bset = isl_basic_set_simplify(bset);
164 bset = isl_basic_set_finalize(bset);
165 sol->empty = isl_set_add(sol->empty, bset);
174 /* Add the solution identified by the tableau and the context tableau.
176 * The layout of the variables is as follows.
177 * tab->n_var is equal to the total number of variables in the input
178 * map (including divs that were copied from the context)
179 * + the number of extra divs constructed
180 * Of these, the first tab->n_param and the last tab->n_div variables
181 * correspond to the variables in the context, i.e.,
182 * tab->n_param + tab->n_div = context_tab->n_var
183 * tab->n_param is equal to the number of parameters and input
184 * dimensions in the input map
185 * tab->n_div is equal to the number of divs in the context
187 * If there is no solution, then the basic set corresponding to the
188 * context tableau is added to the set "empty".
190 * Otherwise, a basic map is constructed with the same parameters
191 * and divs as the context, the dimensions of the context as input
192 * dimensions and a number of output dimensions that is equal to
193 * the number of output dimensions in the input map.
194 * The divs in the input map (if any) that do not correspond to any
195 * div in the context do not appear in the solution.
196 * The algorithm will make sure that they have an integer value,
197 * but these values themselves are of no interest.
199 * The constraints and divs of the context are simply copied
200 * fron context_tab->bset.
201 * To extract the value of the output variables, it should be noted
202 * that we always use a big parameter M and so the variable stored
203 * in the tableau is not an output variable x itself, but
204 * x' = M + x (in case of minimization)
206 * x' = M - x (in case of maximization)
207 * If x' appears in a column, then its optimal value is zero,
208 * which means that the optimal value of x is an unbounded number
209 * (-M for minimization and M for maximization).
210 * We currently assume that the output dimensions in the original map
211 * are bounded, so this cannot occur.
212 * Similarly, when x' appears in a row, then the coefficient of M in that
213 * row is necessarily 1.
214 * If the row represents
215 * d x' = c + d M + e(y)
216 * then, in case of minimization, an equality
217 * c + e(y) - d x' = 0
218 * is added, and in case of maximization,
219 * c + e(y) + d x' = 0
221 static struct isl_sol_map *sol_map_add(struct isl_sol_map *sol,
225 struct isl_basic_map *bmap = NULL;
226 isl_basic_set *context_bset;
239 return add_empty(sol);
241 context_bset = sol->sol.context->op->peek_basic_set(sol->sol.context);
243 n_out = isl_map_dim(sol->map, isl_dim_out);
244 n_eq = context_bset->n_eq + n_out;
245 n_ineq = context_bset->n_ineq;
246 nparam = tab->n_param;
247 total = isl_map_dim(sol->map, isl_dim_all);
248 bmap = isl_basic_map_alloc_dim(isl_map_get_dim(sol->map),
249 tab->n_div, n_eq, 2 * tab->n_div + n_ineq);
254 ISL_F_SET(bmap, ISL_BASIC_MAP_RATIONAL);
255 for (i = 0; i < context_bset->n_div; ++i) {
256 int k = isl_basic_map_alloc_div(bmap);
259 isl_seq_cpy(bmap->div[k],
260 context_bset->div[i], 1 + 1 + nparam);
261 isl_seq_clr(bmap->div[k] + 1 + 1 + nparam, total - nparam);
262 isl_seq_cpy(bmap->div[k] + 1 + 1 + total,
263 context_bset->div[i] + 1 + 1 + nparam, i);
265 for (i = 0; i < context_bset->n_eq; ++i) {
266 int k = isl_basic_map_alloc_equality(bmap);
269 isl_seq_cpy(bmap->eq[k], context_bset->eq[i], 1 + nparam);
270 isl_seq_clr(bmap->eq[k] + 1 + nparam, total - nparam);
271 isl_seq_cpy(bmap->eq[k] + 1 + total,
272 context_bset->eq[i] + 1 + nparam, n_div);
274 for (i = 0; i < context_bset->n_ineq; ++i) {
275 int k = isl_basic_map_alloc_inequality(bmap);
278 isl_seq_cpy(bmap->ineq[k],
279 context_bset->ineq[i], 1 + nparam);
280 isl_seq_clr(bmap->ineq[k] + 1 + nparam, total - nparam);
281 isl_seq_cpy(bmap->ineq[k] + 1 + total,
282 context_bset->ineq[i] + 1 + nparam, n_div);
284 for (i = tab->n_param; i < total; ++i) {
285 int k = isl_basic_map_alloc_equality(bmap);
288 isl_seq_clr(bmap->eq[k] + 1, isl_basic_map_total_dim(bmap));
289 if (!tab->var[i].is_row) {
291 isl_assert(bmap->ctx, !tab->M, goto error);
292 isl_int_set_si(bmap->eq[k][0], 0);
294 isl_int_set_si(bmap->eq[k][1 + i], 1);
296 isl_int_set_si(bmap->eq[k][1 + i], -1);
299 row = tab->var[i].index;
302 isl_assert(bmap->ctx,
303 isl_int_eq(tab->mat->row[row][2],
304 tab->mat->row[row][0]),
306 isl_int_set(bmap->eq[k][0], tab->mat->row[row][1]);
307 for (j = 0; j < tab->n_param; ++j) {
309 if (tab->var[j].is_row)
311 col = tab->var[j].index;
312 isl_int_set(bmap->eq[k][1 + j],
313 tab->mat->row[row][off + col]);
315 for (j = 0; j < tab->n_div; ++j) {
317 if (tab->var[tab->n_var - tab->n_div+j].is_row)
319 col = tab->var[tab->n_var - tab->n_div+j].index;
320 isl_int_set(bmap->eq[k][1 + total + j],
321 tab->mat->row[row][off + col]);
324 isl_int_set(bmap->eq[k][1 + i],
325 tab->mat->row[row][0]);
327 isl_int_neg(bmap->eq[k][1 + i],
328 tab->mat->row[row][0]);
331 bmap = isl_basic_map_simplify(bmap);
332 bmap = isl_basic_map_finalize(bmap);
333 sol->map = isl_map_grow(sol->map, 1);
334 sol->map = isl_map_add(sol->map, bmap);
339 isl_basic_map_free(bmap);
344 static struct isl_sol *sol_map_add_wrap(struct isl_sol *sol,
347 return (struct isl_sol *)sol_map_add((struct isl_sol_map *)sol, tab);
351 /* Store the "parametric constant" of row "row" of tableau "tab" in "line",
352 * i.e., the constant term and the coefficients of all variables that
353 * appear in the context tableau.
354 * Note that the coefficient of the big parameter M is NOT copied.
355 * The context tableau may not have a big parameter and even when it
356 * does, it is a different big parameter.
358 static void get_row_parameter_line(struct isl_tab *tab, int row, isl_int *line)
361 unsigned off = 2 + tab->M;
363 isl_int_set(line[0], tab->mat->row[row][1]);
364 for (i = 0; i < tab->n_param; ++i) {
365 if (tab->var[i].is_row)
366 isl_int_set_si(line[1 + i], 0);
368 int col = tab->var[i].index;
369 isl_int_set(line[1 + i], tab->mat->row[row][off + col]);
372 for (i = 0; i < tab->n_div; ++i) {
373 if (tab->var[tab->n_var - tab->n_div + i].is_row)
374 isl_int_set_si(line[1 + tab->n_param + i], 0);
376 int col = tab->var[tab->n_var - tab->n_div + i].index;
377 isl_int_set(line[1 + tab->n_param + i],
378 tab->mat->row[row][off + col]);
383 /* Check if rows "row1" and "row2" have identical "parametric constants",
384 * as explained above.
385 * In this case, we also insist that the coefficients of the big parameter
386 * be the same as the values of the constants will only be the same
387 * if these coefficients are also the same.
389 static int identical_parameter_line(struct isl_tab *tab, int row1, int row2)
392 unsigned off = 2 + tab->M;
394 if (isl_int_ne(tab->mat->row[row1][1], tab->mat->row[row2][1]))
397 if (tab->M && isl_int_ne(tab->mat->row[row1][2],
398 tab->mat->row[row2][2]))
401 for (i = 0; i < tab->n_param + tab->n_div; ++i) {
402 int pos = i < tab->n_param ? i :
403 tab->n_var - tab->n_div + i - tab->n_param;
406 if (tab->var[pos].is_row)
408 col = tab->var[pos].index;
409 if (isl_int_ne(tab->mat->row[row1][off + col],
410 tab->mat->row[row2][off + col]))
416 /* Return an inequality that expresses that the "parametric constant"
417 * should be non-negative.
418 * This function is only called when the coefficient of the big parameter
421 static struct isl_vec *get_row_parameter_ineq(struct isl_tab *tab, int row)
423 struct isl_vec *ineq;
425 ineq = isl_vec_alloc(tab->mat->ctx, 1 + tab->n_param + tab->n_div);
429 get_row_parameter_line(tab, row, ineq->el);
431 ineq = isl_vec_normalize(ineq);
436 /* Return a integer division for use in a parametric cut based on the given row.
437 * In particular, let the parametric constant of the row be
441 * where y_0 = 1, but none of the y_i corresponds to the big parameter M.
442 * The div returned is equal to
444 * floor(\sum_i {-a_i} y_i) = floor((\sum_i (-a_i mod d) y_i)/d)
446 static struct isl_vec *get_row_parameter_div(struct isl_tab *tab, int row)
450 div = isl_vec_alloc(tab->mat->ctx, 1 + 1 + tab->n_param + tab->n_div);
454 isl_int_set(div->el[0], tab->mat->row[row][0]);
455 get_row_parameter_line(tab, row, div->el + 1);
456 div = isl_vec_normalize(div);
457 isl_seq_neg(div->el + 1, div->el + 1, div->size - 1);
458 isl_seq_fdiv_r(div->el + 1, div->el + 1, div->el[0], div->size - 1);
463 /* Return a integer division for use in transferring an integrality constraint
465 * In particular, let the parametric constant of the row be
469 * where y_0 = 1, but none of the y_i corresponds to the big parameter M.
470 * The the returned div is equal to
472 * floor(\sum_i {a_i} y_i) = floor((\sum_i (a_i mod d) y_i)/d)
474 static struct isl_vec *get_row_split_div(struct isl_tab *tab, int row)
478 div = isl_vec_alloc(tab->mat->ctx, 1 + 1 + tab->n_param + tab->n_div);
482 isl_int_set(div->el[0], tab->mat->row[row][0]);
483 get_row_parameter_line(tab, row, div->el + 1);
484 div = isl_vec_normalize(div);
485 isl_seq_fdiv_r(div->el + 1, div->el + 1, div->el[0], div->size - 1);
490 /* Construct and return an inequality that expresses an upper bound
492 * In particular, if the div is given by
496 * then the inequality expresses
500 static struct isl_vec *ineq_for_div(struct isl_basic_set *bset, unsigned div)
504 struct isl_vec *ineq;
509 total = isl_basic_set_total_dim(bset);
510 div_pos = 1 + total - bset->n_div + div;
512 ineq = isl_vec_alloc(bset->ctx, 1 + total);
516 isl_seq_cpy(ineq->el, bset->div[div] + 1, 1 + total);
517 isl_int_neg(ineq->el[div_pos], bset->div[div][0]);
521 /* Given a row in the tableau and a div that was created
522 * using get_row_split_div and that been constrained to equality, i.e.,
524 * d = floor(\sum_i {a_i} y_i) = \sum_i {a_i} y_i
526 * replace the expression "\sum_i {a_i} y_i" in the row by d,
527 * i.e., we subtract "\sum_i {a_i} y_i" and add 1 d.
528 * The coefficients of the non-parameters in the tableau have been
529 * verified to be integral. We can therefore simply replace coefficient b
530 * by floor(b). For the coefficients of the parameters we have
531 * floor(a_i) = a_i - {a_i}, while for the other coefficients, we have
534 static struct isl_tab *set_row_cst_to_div(struct isl_tab *tab, int row, int div)
536 isl_seq_fdiv_q(tab->mat->row[row] + 1, tab->mat->row[row] + 1,
537 tab->mat->row[row][0], 1 + tab->M + tab->n_col);
539 isl_int_set_si(tab->mat->row[row][0], 1);
541 if (tab->var[tab->n_var - tab->n_div + div].is_row) {
542 int drow = tab->var[tab->n_var - tab->n_div + div].index;
544 isl_assert(tab->mat->ctx,
545 isl_int_is_one(tab->mat->row[drow][0]), goto error);
546 isl_seq_combine(tab->mat->row[row] + 1,
547 tab->mat->ctx->one, tab->mat->row[row] + 1,
548 tab->mat->ctx->one, tab->mat->row[drow] + 1,
549 1 + tab->M + tab->n_col);
551 int dcol = tab->var[tab->n_var - tab->n_div + div].index;
553 isl_int_set_si(tab->mat->row[row][2 + tab->M + dcol], 1);
562 /* Check if the (parametric) constant of the given row is obviously
563 * negative, meaning that we don't need to consult the context tableau.
564 * If there is a big parameter and its coefficient is non-zero,
565 * then this coefficient determines the outcome.
566 * Otherwise, we check whether the constant is negative and
567 * all non-zero coefficients of parameters are negative and
568 * belong to non-negative parameters.
570 static int is_obviously_neg(struct isl_tab *tab, int row)
574 unsigned off = 2 + tab->M;
577 if (isl_int_is_pos(tab->mat->row[row][2]))
579 if (isl_int_is_neg(tab->mat->row[row][2]))
583 if (isl_int_is_nonneg(tab->mat->row[row][1]))
585 for (i = 0; i < tab->n_param; ++i) {
586 /* Eliminated parameter */
587 if (tab->var[i].is_row)
589 col = tab->var[i].index;
590 if (isl_int_is_zero(tab->mat->row[row][off + col]))
592 if (!tab->var[i].is_nonneg)
594 if (isl_int_is_pos(tab->mat->row[row][off + col]))
597 for (i = 0; i < tab->n_div; ++i) {
598 if (tab->var[tab->n_var - tab->n_div + i].is_row)
600 col = tab->var[tab->n_var - tab->n_div + i].index;
601 if (isl_int_is_zero(tab->mat->row[row][off + col]))
603 if (!tab->var[tab->n_var - tab->n_div + i].is_nonneg)
605 if (isl_int_is_pos(tab->mat->row[row][off + col]))
611 /* Check if the (parametric) constant of the given row is obviously
612 * non-negative, meaning that we don't need to consult the context tableau.
613 * If there is a big parameter and its coefficient is non-zero,
614 * then this coefficient determines the outcome.
615 * Otherwise, we check whether the constant is non-negative and
616 * all non-zero coefficients of parameters are positive and
617 * belong to non-negative parameters.
619 static int is_obviously_nonneg(struct isl_tab *tab, int row)
623 unsigned off = 2 + tab->M;
626 if (isl_int_is_pos(tab->mat->row[row][2]))
628 if (isl_int_is_neg(tab->mat->row[row][2]))
632 if (isl_int_is_neg(tab->mat->row[row][1]))
634 for (i = 0; i < tab->n_param; ++i) {
635 /* Eliminated parameter */
636 if (tab->var[i].is_row)
638 col = tab->var[i].index;
639 if (isl_int_is_zero(tab->mat->row[row][off + col]))
641 if (!tab->var[i].is_nonneg)
643 if (isl_int_is_neg(tab->mat->row[row][off + col]))
646 for (i = 0; i < tab->n_div; ++i) {
647 if (tab->var[tab->n_var - tab->n_div + i].is_row)
649 col = tab->var[tab->n_var - tab->n_div + i].index;
650 if (isl_int_is_zero(tab->mat->row[row][off + col]))
652 if (!tab->var[tab->n_var - tab->n_div + i].is_nonneg)
654 if (isl_int_is_neg(tab->mat->row[row][off + col]))
660 /* Given a row r and two columns, return the column that would
661 * lead to the lexicographically smallest increment in the sample
662 * solution when leaving the basis in favor of the row.
663 * Pivoting with column c will increment the sample value by a non-negative
664 * constant times a_{V,c}/a_{r,c}, with a_{V,c} the elements of column c
665 * corresponding to the non-parametric variables.
666 * If variable v appears in a column c_v, the a_{v,c} = 1 iff c = c_v,
667 * with all other entries in this virtual row equal to zero.
668 * If variable v appears in a row, then a_{v,c} is the element in column c
671 * Let v be the first variable with a_{v,c1}/a_{r,c1} != a_{v,c2}/a_{r,c2}.
672 * Then if a_{v,c1}/a_{r,c1} < a_{v,c2}/a_{r,c2}, i.e.,
673 * a_{v,c2} a_{r,c1} - a_{v,c1} a_{r,c2} > 0, c1 results in the minimal
674 * increment. Otherwise, it's c2.
676 static int lexmin_col_pair(struct isl_tab *tab,
677 int row, int col1, int col2, isl_int tmp)
682 tr = tab->mat->row[row] + 2 + tab->M;
684 for (i = tab->n_param; i < tab->n_var - tab->n_div; ++i) {
688 if (!tab->var[i].is_row) {
689 if (tab->var[i].index == col1)
691 if (tab->var[i].index == col2)
696 if (tab->var[i].index == row)
699 r = tab->mat->row[tab->var[i].index] + 2 + tab->M;
700 s1 = isl_int_sgn(r[col1]);
701 s2 = isl_int_sgn(r[col2]);
702 if (s1 == 0 && s2 == 0)
709 isl_int_mul(tmp, r[col2], tr[col1]);
710 isl_int_submul(tmp, r[col1], tr[col2]);
711 if (isl_int_is_pos(tmp))
713 if (isl_int_is_neg(tmp))
719 /* Given a row in the tableau, find and return the column that would
720 * result in the lexicographically smallest, but positive, increment
721 * in the sample point.
722 * If there is no such column, then return tab->n_col.
723 * If anything goes wrong, return -1.
725 static int lexmin_pivot_col(struct isl_tab *tab, int row)
728 int col = tab->n_col;
732 tr = tab->mat->row[row] + 2 + tab->M;
736 for (j = tab->n_dead; j < tab->n_col; ++j) {
737 if (tab->col_var[j] >= 0 &&
738 (tab->col_var[j] < tab->n_param ||
739 tab->col_var[j] >= tab->n_var - tab->n_div))
742 if (!isl_int_is_pos(tr[j]))
745 if (col == tab->n_col)
748 col = lexmin_col_pair(tab, row, col, j, tmp);
749 isl_assert(tab->mat->ctx, col >= 0, goto error);
759 /* Return the first known violated constraint, i.e., a non-negative
760 * contraint that currently has an either obviously negative value
761 * or a previously determined to be negative value.
763 * If any constraint has a negative coefficient for the big parameter,
764 * if any, then we return one of these first.
766 static int first_neg(struct isl_tab *tab)
771 for (row = tab->n_redundant; row < tab->n_row; ++row) {
772 if (!isl_tab_var_from_row(tab, row)->is_nonneg)
774 if (isl_int_is_neg(tab->mat->row[row][2]))
777 for (row = tab->n_redundant; row < tab->n_row; ++row) {
778 if (!isl_tab_var_from_row(tab, row)->is_nonneg)
781 if (tab->row_sign[row] == 0 &&
782 is_obviously_neg(tab, row))
783 tab->row_sign[row] = isl_tab_row_neg;
784 if (tab->row_sign[row] != isl_tab_row_neg)
786 } else if (!is_obviously_neg(tab, row))
793 /* Resolve all known or obviously violated constraints through pivoting.
794 * In particular, as long as we can find any violated constraint, we
795 * look for a pivoting column that would result in the lexicographicallly
796 * smallest increment in the sample point. If there is no such column
797 * then the tableau is infeasible.
799 static struct isl_tab *restore_lexmin(struct isl_tab *tab)
807 while ((row = first_neg(tab)) != -1) {
808 col = lexmin_pivot_col(tab, row);
809 if (col >= tab->n_col)
810 return isl_tab_mark_empty(tab);
813 isl_tab_pivot(tab, row, col);
821 /* Given a row that represents an equality, look for an appropriate
823 * In particular, if there are any non-zero coefficients among
824 * the non-parameter variables, then we take the last of these
825 * variables. Eliminating this variable in terms of the other
826 * variables and/or parameters does not influence the property
827 * that all column in the initial tableau are lexicographically
828 * positive. The row corresponding to the eliminated variable
829 * will only have non-zero entries below the diagonal of the
830 * initial tableau. That is, we transform
836 * If there is no such non-parameter variable, then we are dealing with
837 * pure parameter equality and we pick any parameter with coefficient 1 or -1
838 * for elimination. This will ensure that the eliminated parameter
839 * always has an integer value whenever all the other parameters are integral.
840 * If there is no such parameter then we return -1.
842 static int last_var_col_or_int_par_col(struct isl_tab *tab, int row)
844 unsigned off = 2 + tab->M;
847 for (i = tab->n_var - tab->n_div - 1; i >= 0 && i >= tab->n_param; --i) {
849 if (tab->var[i].is_row)
851 col = tab->var[i].index;
852 if (col <= tab->n_dead)
854 if (!isl_int_is_zero(tab->mat->row[row][off + col]))
857 for (i = tab->n_dead; i < tab->n_col; ++i) {
858 if (isl_int_is_one(tab->mat->row[row][off + i]))
860 if (isl_int_is_negone(tab->mat->row[row][off + i]))
866 /* Add an equality that is known to be valid to the tableau.
867 * We first check if we can eliminate a variable or a parameter.
868 * If not, we add the equality as two inequalities.
869 * In this case, the equality was a pure parameter equality and there
870 * is no need to resolve any constraint violations.
872 static struct isl_tab *add_lexmin_valid_eq(struct isl_tab *tab, isl_int *eq)
879 r = isl_tab_add_row(tab, eq);
883 r = tab->con[r].index;
884 i = last_var_col_or_int_par_col(tab, r);
886 tab->con[r].is_nonneg = 1;
887 isl_tab_push_var(tab, isl_tab_undo_nonneg, &tab->con[r]);
888 isl_seq_neg(eq, eq, 1 + tab->n_var);
889 r = isl_tab_add_row(tab, eq);
892 tab->con[r].is_nonneg = 1;
893 isl_tab_push_var(tab, isl_tab_undo_nonneg, &tab->con[r]);
895 isl_tab_pivot(tab, r, i);
896 isl_tab_kill_col(tab, i);
899 tab = restore_lexmin(tab);
908 /* Check if the given row is a pure constant.
910 static int is_constant(struct isl_tab *tab, int row)
912 unsigned off = 2 + tab->M;
914 return isl_seq_first_non_zero(tab->mat->row[row] + off + tab->n_dead,
915 tab->n_col - tab->n_dead) == -1;
918 /* Add an equality that may or may not be valid to the tableau.
919 * If the resulting row is a pure constant, then it must be zero.
920 * Otherwise, the resulting tableau is empty.
922 * If the row is not a pure constant, then we add two inequalities,
923 * each time checking that they can be satisfied.
924 * In the end we try to use one of the two constraints to eliminate
927 static struct isl_tab *add_lexmin_eq(struct isl_tab *tab, isl_int *eq)
931 struct isl_tab_undo *snap;
935 snap = isl_tab_snap(tab);
936 r1 = isl_tab_add_row(tab, eq);
939 tab->con[r1].is_nonneg = 1;
940 isl_tab_push_var(tab, isl_tab_undo_nonneg, &tab->con[r1]);
942 row = tab->con[r1].index;
943 if (is_constant(tab, row)) {
944 if (!isl_int_is_zero(tab->mat->row[row][1]) ||
945 (tab->M && !isl_int_is_zero(tab->mat->row[row][2])))
946 return isl_tab_mark_empty(tab);
947 if (isl_tab_rollback(tab, snap) < 0)
952 tab = restore_lexmin(tab);
953 if (!tab || tab->empty)
956 isl_seq_neg(eq, eq, 1 + tab->n_var);
958 r2 = isl_tab_add_row(tab, eq);
961 tab->con[r2].is_nonneg = 1;
962 isl_tab_push_var(tab, isl_tab_undo_nonneg, &tab->con[r2]);
964 tab = restore_lexmin(tab);
965 if (!tab || tab->empty)
968 if (!tab->con[r1].is_row)
969 isl_tab_kill_col(tab, tab->con[r1].index);
970 else if (!tab->con[r2].is_row)
971 isl_tab_kill_col(tab, tab->con[r2].index);
972 else if (isl_int_is_zero(tab->mat->row[tab->con[r1].index][1])) {
973 unsigned off = 2 + tab->M;
975 int row = tab->con[r1].index;
976 i = isl_seq_first_non_zero(tab->mat->row[row]+off+tab->n_dead,
977 tab->n_col - tab->n_dead);
979 isl_tab_pivot(tab, row, tab->n_dead + i);
980 isl_tab_kill_col(tab, tab->n_dead + i);
985 tab->bset = isl_basic_set_add_ineq(tab->bset, eq);
986 isl_tab_push(tab, isl_tab_undo_bset_ineq);
987 isl_seq_neg(eq, eq, 1 + tab->n_var);
988 tab->bset = isl_basic_set_add_ineq(tab->bset, eq);
989 isl_seq_neg(eq, eq, 1 + tab->n_var);
990 isl_tab_push(tab, isl_tab_undo_bset_ineq);
1001 /* Add an inequality to the tableau, resolving violations using
1004 static struct isl_tab *add_lexmin_ineq(struct isl_tab *tab, isl_int *ineq)
1011 tab->bset = isl_basic_set_add_ineq(tab->bset, ineq);
1012 isl_tab_push(tab, isl_tab_undo_bset_ineq);
1016 r = isl_tab_add_row(tab, ineq);
1019 tab->con[r].is_nonneg = 1;
1020 isl_tab_push_var(tab, isl_tab_undo_nonneg, &tab->con[r]);
1021 if (isl_tab_row_is_redundant(tab, tab->con[r].index)) {
1022 isl_tab_mark_redundant(tab, tab->con[r].index);
1026 tab = restore_lexmin(tab);
1027 if (tab && !tab->empty && tab->con[r].is_row &&
1028 isl_tab_row_is_redundant(tab, tab->con[r].index))
1029 isl_tab_mark_redundant(tab, tab->con[r].index);
1036 /* Check if the coefficients of the parameters are all integral.
1038 static int integer_parameter(struct isl_tab *tab, int row)
1042 unsigned off = 2 + tab->M;
1044 for (i = 0; i < tab->n_param; ++i) {
1045 /* Eliminated parameter */
1046 if (tab->var[i].is_row)
1048 col = tab->var[i].index;
1049 if (!isl_int_is_divisible_by(tab->mat->row[row][off + col],
1050 tab->mat->row[row][0]))
1053 for (i = 0; i < tab->n_div; ++i) {
1054 if (tab->var[tab->n_var - tab->n_div + i].is_row)
1056 col = tab->var[tab->n_var - tab->n_div + i].index;
1057 if (!isl_int_is_divisible_by(tab->mat->row[row][off + col],
1058 tab->mat->row[row][0]))
1064 /* Check if the coefficients of the non-parameter variables are all integral.
1066 static int integer_variable(struct isl_tab *tab, int row)
1069 unsigned off = 2 + tab->M;
1071 for (i = 0; i < tab->n_col; ++i) {
1072 if (tab->col_var[i] >= 0 &&
1073 (tab->col_var[i] < tab->n_param ||
1074 tab->col_var[i] >= tab->n_var - tab->n_div))
1076 if (!isl_int_is_divisible_by(tab->mat->row[row][off + i],
1077 tab->mat->row[row][0]))
1083 /* Check if the constant term is integral.
1085 static int integer_constant(struct isl_tab *tab, int row)
1087 return isl_int_is_divisible_by(tab->mat->row[row][1],
1088 tab->mat->row[row][0]);
1091 #define I_CST 1 << 0
1092 #define I_PAR 1 << 1
1093 #define I_VAR 1 << 2
1095 /* Check for first (non-parameter) variable that is non-integer and
1096 * therefore requires a cut.
1097 * For parametric tableaus, there are three parts in a row,
1098 * the constant, the coefficients of the parameters and the rest.
1099 * For each part, we check whether the coefficients in that part
1100 * are all integral and if so, set the corresponding flag in *f.
1101 * If the constant and the parameter part are integral, then the
1102 * current sample value is integral and no cut is required
1103 * (irrespective of whether the variable part is integral).
1105 static int first_non_integer(struct isl_tab *tab, int *f)
1109 for (i = tab->n_param; i < tab->n_var - tab->n_div; ++i) {
1112 if (!tab->var[i].is_row)
1114 row = tab->var[i].index;
1115 if (integer_constant(tab, row))
1116 ISL_FL_SET(flags, I_CST);
1117 if (integer_parameter(tab, row))
1118 ISL_FL_SET(flags, I_PAR);
1119 if (ISL_FL_ISSET(flags, I_CST) && ISL_FL_ISSET(flags, I_PAR))
1121 if (integer_variable(tab, row))
1122 ISL_FL_SET(flags, I_VAR);
1129 /* Add a (non-parametric) cut to cut away the non-integral sample
1130 * value of the given row.
1132 * If the row is given by
1134 * m r = f + \sum_i a_i y_i
1138 * c = - {-f/m} + \sum_i {a_i/m} y_i >= 0
1140 * The big parameter, if any, is ignored, since it is assumed to be big
1141 * enough to be divisible by any integer.
1142 * If the tableau is actually a parametric tableau, then this function
1143 * is only called when all coefficients of the parameters are integral.
1144 * The cut therefore has zero coefficients for the parameters.
1146 * The current value is known to be negative, so row_sign, if it
1147 * exists, is set accordingly.
1149 * Return the row of the cut or -1.
1151 static int add_cut(struct isl_tab *tab, int row)
1156 unsigned off = 2 + tab->M;
1158 if (isl_tab_extend_cons(tab, 1) < 0)
1160 r = isl_tab_allocate_con(tab);
1164 r_row = tab->mat->row[tab->con[r].index];
1165 isl_int_set(r_row[0], tab->mat->row[row][0]);
1166 isl_int_neg(r_row[1], tab->mat->row[row][1]);
1167 isl_int_fdiv_r(r_row[1], r_row[1], tab->mat->row[row][0]);
1168 isl_int_neg(r_row[1], r_row[1]);
1170 isl_int_set_si(r_row[2], 0);
1171 for (i = 0; i < tab->n_col; ++i)
1172 isl_int_fdiv_r(r_row[off + i],
1173 tab->mat->row[row][off + i], tab->mat->row[row][0]);
1175 tab->con[r].is_nonneg = 1;
1176 isl_tab_push_var(tab, isl_tab_undo_nonneg, &tab->con[r]);
1178 tab->row_sign[tab->con[r].index] = isl_tab_row_neg;
1180 return tab->con[r].index;
1183 /* Given a non-parametric tableau, add cuts until an integer
1184 * sample point is obtained or until the tableau is determined
1185 * to be integer infeasible.
1186 * As long as there is any non-integer value in the sample point,
1187 * we add an appropriate cut, if possible and resolve the violated
1188 * cut constraint using restore_lexmin.
1189 * If one of the corresponding rows is equal to an integral
1190 * combination of variables/constraints plus a non-integral constant,
1191 * then there is no way to obtain an integer point an we return
1192 * a tableau that is marked empty.
1194 static struct isl_tab *cut_to_integer_lexmin(struct isl_tab *tab)
1204 while ((row = first_non_integer(tab, &flags)) != -1) {
1205 if (ISL_FL_ISSET(flags, I_VAR))
1206 return isl_tab_mark_empty(tab);
1207 row = add_cut(tab, row);
1210 tab = restore_lexmin(tab);
1211 if (!tab || tab->empty)
1220 /* Check whether all the currently active samples also satisfy the inequality
1221 * "ineq" (treated as an equality if eq is set).
1222 * Remove those samples that do not.
1224 static struct isl_tab *check_samples(struct isl_tab *tab, isl_int *ineq, int eq)
1232 isl_assert(tab->mat->ctx, tab->bset, goto error);
1233 isl_assert(tab->mat->ctx, tab->samples, goto error);
1234 isl_assert(tab->mat->ctx, tab->samples->n_col == 1 + tab->n_var, goto error);
1237 for (i = tab->n_outside; i < tab->n_sample; ++i) {
1239 isl_seq_inner_product(ineq, tab->samples->row[i],
1240 1 + tab->n_var, &v);
1241 sgn = isl_int_sgn(v);
1242 if (eq ? (sgn == 0) : (sgn >= 0))
1244 tab = isl_tab_drop_sample(tab, i);
1256 /* Check whether the sample value of the tableau is finite,
1257 * i.e., either the tableau does not use a big parameter, or
1258 * all values of the variables are equal to the big parameter plus
1259 * some constant. This constant is the actual sample value.
1261 static int sample_is_finite(struct isl_tab *tab)
1268 for (i = 0; i < tab->n_var; ++i) {
1270 if (!tab->var[i].is_row)
1272 row = tab->var[i].index;
1273 if (isl_int_ne(tab->mat->row[row][0], tab->mat->row[row][2]))
1279 /* Check if the context tableau of sol has any integer points.
1280 * Leave tab in empty state if no integer point can be found.
1281 * If an integer point can be found and if moreover it is finite,
1282 * then it is added to the list of sample values.
1284 * This function is only called when none of the currently active sample
1285 * values satisfies the most recently added constraint.
1287 static struct isl_tab *check_integer_feasible(struct isl_tab *tab)
1289 struct isl_tab_undo *snap;
1295 snap = isl_tab_snap(tab);
1296 isl_tab_push_basis(tab);
1298 tab = cut_to_integer_lexmin(tab);
1302 if (!tab->empty && sample_is_finite(tab)) {
1303 struct isl_vec *sample;
1305 sample = isl_tab_get_sample_value(tab);
1307 tab = isl_tab_add_sample(tab, sample);
1310 if (!tab->empty && isl_tab_rollback(tab, snap) < 0)
1319 /* Check if any of the currently active sample values satisfies
1320 * the inequality "ineq" (an equality if eq is set).
1322 static int tab_has_valid_sample(struct isl_tab *tab, isl_int *ineq, int eq)
1330 isl_assert(tab->mat->ctx, tab->bset, return -1);
1331 isl_assert(tab->mat->ctx, tab->samples, return -1);
1332 isl_assert(tab->mat->ctx, tab->samples->n_col == 1 + tab->n_var, return -1);
1335 for (i = tab->n_outside; i < tab->n_sample; ++i) {
1337 isl_seq_inner_product(ineq, tab->samples->row[i],
1338 1 + tab->n_var, &v);
1339 sgn = isl_int_sgn(v);
1340 if (eq ? (sgn == 0) : (sgn >= 0))
1345 return i < tab->n_sample;
1348 /* For a div d = floor(f/m), add the constraints
1351 * -(f-(m-1)) + m d >= 0
1353 * Note that the second constraint is the negation of
1357 static void add_div_constraints(struct isl_context *context, unsigned div)
1361 struct isl_vec *ineq;
1362 struct isl_basic_set *bset;
1364 bset = context->op->peek_basic_set(context);
1368 total = isl_basic_set_total_dim(bset);
1369 div_pos = 1 + total - bset->n_div + div;
1371 ineq = ineq_for_div(bset, div);
1375 context->op->add_ineq(context, ineq->el, 0, 0);
1377 isl_seq_neg(ineq->el, bset->div[div] + 1, 1 + total);
1378 isl_int_set(ineq->el[div_pos], bset->div[div][0]);
1379 isl_int_add(ineq->el[0], ineq->el[0], ineq->el[div_pos]);
1380 isl_int_sub_ui(ineq->el[0], ineq->el[0], 1);
1382 context->op->add_ineq(context, ineq->el, 0, 0);
1388 context->op->invalidate(context);
1391 /* Add a div specifed by "div" to the tableau "tab" and return
1392 * the index of the new div. *nonneg is set to 1 if the div
1393 * is obviously non-negative.
1395 static int context_tab_add_div(struct isl_tab *tab, struct isl_vec *div,
1401 struct isl_mat *samples;
1403 for (i = 0; i < tab->n_var; ++i) {
1404 if (isl_int_is_zero(div->el[2 + i]))
1406 if (!tab->var[i].is_nonneg)
1409 *nonneg = i == tab->n_var;
1411 if (isl_tab_extend_cons(tab, 3) < 0)
1413 if (isl_tab_extend_vars(tab, 1) < 0)
1415 r = isl_tab_allocate_var(tab);
1419 tab->var[r].is_nonneg = 1;
1420 tab->var[r].frozen = 1;
1422 samples = isl_mat_extend(tab->samples,
1423 tab->n_sample, 1 + tab->n_var);
1424 tab->samples = samples;
1427 for (i = tab->n_outside; i < samples->n_row; ++i) {
1428 isl_seq_inner_product(div->el + 1, samples->row[i],
1429 div->size - 1, &samples->row[i][samples->n_col - 1]);
1430 isl_int_fdiv_q(samples->row[i][samples->n_col - 1],
1431 samples->row[i][samples->n_col - 1], div->el[0]);
1434 tab->bset = isl_basic_set_extend_dim(tab->bset,
1435 isl_basic_set_get_dim(tab->bset), 1, 0, 2);
1436 k = isl_basic_set_alloc_div(tab->bset);
1439 isl_seq_cpy(tab->bset->div[k], div->el, div->size);
1440 isl_tab_push(tab, isl_tab_undo_bset_div);
1445 /* Add a div specified by "div" to both the main tableau and
1446 * the context tableau. In case of the main tableau, we only
1447 * need to add an extra div. In the context tableau, we also
1448 * need to express the meaning of the div.
1449 * Return the index of the div or -1 if anything went wrong.
1451 static int add_div(struct isl_tab *tab, struct isl_context *context,
1452 struct isl_vec *div)
1458 k = context->op->add_div(context, div, &nonneg);
1462 add_div_constraints(context, k);
1463 if (!context->op->is_ok(context))
1466 if (isl_tab_extend_vars(tab, 1) < 0)
1468 r = isl_tab_allocate_var(tab);
1472 tab->var[r].is_nonneg = 1;
1473 tab->var[r].frozen = 1;
1476 return tab->n_div - 1;
1478 context->op->invalidate(context);
1482 static int find_div(struct isl_tab *tab, isl_int *div, isl_int denom)
1485 unsigned total = isl_basic_set_total_dim(tab->bset);
1487 for (i = 0; i < tab->bset->n_div; ++i) {
1488 if (isl_int_ne(tab->bset->div[i][0], denom))
1490 if (!isl_seq_eq(tab->bset->div[i] + 1, div, total))
1497 /* Return the index of a div that corresponds to "div".
1498 * We first check if we already have such a div and if not, we create one.
1500 static int get_div(struct isl_tab *tab, struct isl_context *context,
1501 struct isl_vec *div)
1504 struct isl_tab *context_tab = context->op->peek_tab(context);
1509 d = find_div(context_tab, div->el + 1, div->el[0]);
1513 return add_div(tab, context, div);
1516 /* Add a parametric cut to cut away the non-integral sample value
1518 * Let a_i be the coefficients of the constant term and the parameters
1519 * and let b_i be the coefficients of the variables or constraints
1520 * in basis of the tableau.
1521 * Let q be the div q = floor(\sum_i {-a_i} y_i).
1523 * The cut is expressed as
1525 * c = \sum_i -{-a_i} y_i + \sum_i {b_i} x_i + q >= 0
1527 * If q did not already exist in the context tableau, then it is added first.
1528 * If q is in a column of the main tableau then the "+ q" can be accomplished
1529 * by setting the corresponding entry to the denominator of the constraint.
1530 * If q happens to be in a row of the main tableau, then the corresponding
1531 * row needs to be added instead (taking care of the denominators).
1532 * Note that this is very unlikely, but perhaps not entirely impossible.
1534 * The current value of the cut is known to be negative (or at least
1535 * non-positive), so row_sign is set accordingly.
1537 * Return the row of the cut or -1.
1539 static int add_parametric_cut(struct isl_tab *tab, int row,
1540 struct isl_context *context)
1542 struct isl_vec *div;
1549 unsigned off = 2 + tab->M;
1554 div = get_row_parameter_div(tab, row);
1559 d = context->op->get_div(context, tab, div);
1563 if (isl_tab_extend_cons(tab, 1) < 0)
1565 r = isl_tab_allocate_con(tab);
1569 r_row = tab->mat->row[tab->con[r].index];
1570 isl_int_set(r_row[0], tab->mat->row[row][0]);
1571 isl_int_neg(r_row[1], tab->mat->row[row][1]);
1572 isl_int_fdiv_r(r_row[1], r_row[1], tab->mat->row[row][0]);
1573 isl_int_neg(r_row[1], r_row[1]);
1575 isl_int_set_si(r_row[2], 0);
1576 for (i = 0; i < tab->n_param; ++i) {
1577 if (tab->var[i].is_row)
1579 col = tab->var[i].index;
1580 isl_int_neg(r_row[off + col], tab->mat->row[row][off + col]);
1581 isl_int_fdiv_r(r_row[off + col], r_row[off + col],
1582 tab->mat->row[row][0]);
1583 isl_int_neg(r_row[off + col], r_row[off + col]);
1585 for (i = 0; i < tab->n_div; ++i) {
1586 if (tab->var[tab->n_var - tab->n_div + i].is_row)
1588 col = tab->var[tab->n_var - tab->n_div + i].index;
1589 isl_int_neg(r_row[off + col], tab->mat->row[row][off + col]);
1590 isl_int_fdiv_r(r_row[off + col], r_row[off + col],
1591 tab->mat->row[row][0]);
1592 isl_int_neg(r_row[off + col], r_row[off + col]);
1594 for (i = 0; i < tab->n_col; ++i) {
1595 if (tab->col_var[i] >= 0 &&
1596 (tab->col_var[i] < tab->n_param ||
1597 tab->col_var[i] >= tab->n_var - tab->n_div))
1599 isl_int_fdiv_r(r_row[off + i],
1600 tab->mat->row[row][off + i], tab->mat->row[row][0]);
1602 if (tab->var[tab->n_var - tab->n_div + d].is_row) {
1604 int d_row = tab->var[tab->n_var - tab->n_div + d].index;
1606 isl_int_gcd(gcd, tab->mat->row[d_row][0], r_row[0]);
1607 isl_int_divexact(r_row[0], r_row[0], gcd);
1608 isl_int_divexact(gcd, tab->mat->row[d_row][0], gcd);
1609 isl_seq_combine(r_row + 1, gcd, r_row + 1,
1610 r_row[0], tab->mat->row[d_row] + 1,
1611 off - 1 + tab->n_col);
1612 isl_int_mul(r_row[0], r_row[0], tab->mat->row[d_row][0]);
1615 col = tab->var[tab->n_var - tab->n_div + d].index;
1616 isl_int_set(r_row[off + col], tab->mat->row[row][0]);
1619 tab->con[r].is_nonneg = 1;
1620 isl_tab_push_var(tab, isl_tab_undo_nonneg, &tab->con[r]);
1622 tab->row_sign[tab->con[r].index] = isl_tab_row_neg;
1626 row = tab->con[r].index;
1628 if (d >= n && context->op->detect_equalities(context, tab) < 0)
1634 /* Construct a tableau for bmap that can be used for computing
1635 * the lexicographic minimum (or maximum) of bmap.
1636 * If not NULL, then dom is the domain where the minimum
1637 * should be computed. In this case, we set up a parametric
1638 * tableau with row signs (initialized to "unknown").
1639 * If M is set, then the tableau will use a big parameter.
1640 * If max is set, then a maximum should be computed instead of a minimum.
1641 * This means that for each variable x, the tableau will contain the variable
1642 * x' = M - x, rather than x' = M + x. This in turn means that the coefficient
1643 * of the variables in all constraints are negated prior to adding them
1646 static struct isl_tab *tab_for_lexmin(struct isl_basic_map *bmap,
1647 struct isl_basic_set *dom, unsigned M, int max)
1650 struct isl_tab *tab;
1652 tab = isl_tab_alloc(bmap->ctx, 2 * bmap->n_eq + bmap->n_ineq + 1,
1653 isl_basic_map_total_dim(bmap), M);
1657 tab->rational = ISL_F_ISSET(bmap, ISL_BASIC_MAP_RATIONAL);
1659 tab->n_param = isl_basic_set_total_dim(dom) - dom->n_div;
1660 tab->n_div = dom->n_div;
1661 tab->row_sign = isl_calloc_array(bmap->ctx,
1662 enum isl_tab_row_sign, tab->mat->n_row);
1666 if (ISL_F_ISSET(bmap, ISL_BASIC_MAP_EMPTY))
1667 return isl_tab_mark_empty(tab);
1669 for (i = tab->n_param; i < tab->n_var - tab->n_div; ++i) {
1670 tab->var[i].is_nonneg = 1;
1671 tab->var[i].frozen = 1;
1673 for (i = 0; i < bmap->n_eq; ++i) {
1675 isl_seq_neg(bmap->eq[i] + 1 + tab->n_param,
1676 bmap->eq[i] + 1 + tab->n_param,
1677 tab->n_var - tab->n_param - tab->n_div);
1678 tab = add_lexmin_valid_eq(tab, bmap->eq[i]);
1680 isl_seq_neg(bmap->eq[i] + 1 + tab->n_param,
1681 bmap->eq[i] + 1 + tab->n_param,
1682 tab->n_var - tab->n_param - tab->n_div);
1683 if (!tab || tab->empty)
1686 for (i = 0; i < bmap->n_ineq; ++i) {
1688 isl_seq_neg(bmap->ineq[i] + 1 + tab->n_param,
1689 bmap->ineq[i] + 1 + tab->n_param,
1690 tab->n_var - tab->n_param - tab->n_div);
1691 tab = add_lexmin_ineq(tab, bmap->ineq[i]);
1693 isl_seq_neg(bmap->ineq[i] + 1 + tab->n_param,
1694 bmap->ineq[i] + 1 + tab->n_param,
1695 tab->n_var - tab->n_param - tab->n_div);
1696 if (!tab || tab->empty)
1705 /* Given a main tableau where more than one row requires a split,
1706 * determine and return the "best" row to split on.
1708 * Given two rows in the main tableau, if the inequality corresponding
1709 * to the first row is redundant with respect to that of the second row
1710 * in the current tableau, then it is better to split on the second row,
1711 * since in the positive part, both row will be positive.
1712 * (In the negative part a pivot will have to be performed and just about
1713 * anything can happen to the sign of the other row.)
1715 * As a simple heuristic, we therefore select the row that makes the most
1716 * of the other rows redundant.
1718 * Perhaps it would also be useful to look at the number of constraints
1719 * that conflict with any given constraint.
1721 static int best_split(struct isl_tab *tab, struct isl_tab *context_tab)
1723 struct isl_tab_undo *snap;
1729 if (isl_tab_extend_cons(context_tab, 2) < 0)
1732 snap = isl_tab_snap(context_tab);
1734 for (split = tab->n_redundant; split < tab->n_row; ++split) {
1735 struct isl_tab_undo *snap2;
1736 struct isl_vec *ineq = NULL;
1739 if (!isl_tab_var_from_row(tab, split)->is_nonneg)
1741 if (tab->row_sign[split] != isl_tab_row_any)
1744 ineq = get_row_parameter_ineq(tab, split);
1747 context_tab = isl_tab_add_ineq(context_tab, ineq->el);
1750 snap2 = isl_tab_snap(context_tab);
1752 for (row = tab->n_redundant; row < tab->n_row; ++row) {
1753 struct isl_tab_var *var;
1757 if (!isl_tab_var_from_row(tab, row)->is_nonneg)
1759 if (tab->row_sign[row] != isl_tab_row_any)
1762 ineq = get_row_parameter_ineq(tab, row);
1765 context_tab = isl_tab_add_ineq(context_tab, ineq->el);
1767 var = &context_tab->con[context_tab->n_con - 1];
1768 if (!context_tab->empty &&
1769 !isl_tab_min_at_most_neg_one(context_tab, var))
1771 if (isl_tab_rollback(context_tab, snap2) < 0)
1774 if (best == -1 || r > best_r) {
1778 if (isl_tab_rollback(context_tab, snap) < 0)
1785 static struct isl_basic_set *context_lex_peek_basic_set(
1786 struct isl_context *context)
1788 struct isl_context_lex *clex = (struct isl_context_lex *)context;
1791 return clex->tab->bset;
1794 static struct isl_tab *context_lex_peek_tab(struct isl_context *context)
1796 struct isl_context_lex *clex = (struct isl_context_lex *)context;
1800 static void context_lex_extend(struct isl_context *context, int n)
1802 struct isl_context_lex *clex = (struct isl_context_lex *)context;
1805 if (isl_tab_extend_cons(clex->tab, n) >= 0)
1807 isl_tab_free(clex->tab);
1811 static void context_lex_add_eq(struct isl_context *context, isl_int *eq,
1812 int check, int update)
1814 struct isl_context_lex *clex = (struct isl_context_lex *)context;
1815 if (isl_tab_extend_cons(clex->tab, 2) < 0)
1817 clex->tab = add_lexmin_eq(clex->tab, eq);
1819 int v = tab_has_valid_sample(clex->tab, eq, 1);
1823 clex->tab = check_integer_feasible(clex->tab);
1826 clex->tab = check_samples(clex->tab, eq, 1);
1829 isl_tab_free(clex->tab);
1833 static void context_lex_add_ineq(struct isl_context *context, isl_int *ineq,
1834 int check, int update)
1836 struct isl_context_lex *clex = (struct isl_context_lex *)context;
1837 if (isl_tab_extend_cons(clex->tab, 1) < 0)
1839 clex->tab = add_lexmin_ineq(clex->tab, ineq);
1841 int v = tab_has_valid_sample(clex->tab, ineq, 0);
1845 clex->tab = check_integer_feasible(clex->tab);
1848 clex->tab = check_samples(clex->tab, ineq, 0);
1851 isl_tab_free(clex->tab);
1855 /* Check which signs can be obtained by "ineq" on all the currently
1856 * active sample values. See row_sign for more information.
1858 static enum isl_tab_row_sign tab_ineq_sign(struct isl_tab *tab, isl_int *ineq,
1864 int res = isl_tab_row_unknown;
1866 isl_assert(tab->mat->ctx, tab->samples, return 0);
1867 isl_assert(tab->mat->ctx, tab->samples->n_col == 1 + tab->n_var, return 0);
1870 for (i = tab->n_outside; i < tab->n_sample; ++i) {
1871 isl_seq_inner_product(tab->samples->row[i], ineq,
1872 1 + tab->n_var, &tmp);
1873 sgn = isl_int_sgn(tmp);
1874 if (sgn > 0 || (sgn == 0 && strict)) {
1875 if (res == isl_tab_row_unknown)
1876 res = isl_tab_row_pos;
1877 if (res == isl_tab_row_neg)
1878 res = isl_tab_row_any;
1881 if (res == isl_tab_row_unknown)
1882 res = isl_tab_row_neg;
1883 if (res == isl_tab_row_pos)
1884 res = isl_tab_row_any;
1886 if (res == isl_tab_row_any)
1894 static enum isl_tab_row_sign context_lex_ineq_sign(struct isl_context *context,
1895 isl_int *ineq, int strict)
1897 struct isl_context_lex *clex = (struct isl_context_lex *)context;
1898 return tab_ineq_sign(clex->tab, ineq, strict);
1901 /* Check whether "ineq" can be added to the tableau without rendering
1904 static int context_lex_test_ineq(struct isl_context *context, isl_int *ineq)
1906 struct isl_context_lex *clex = (struct isl_context_lex *)context;
1907 struct isl_tab_undo *snap;
1913 if (isl_tab_extend_cons(clex->tab, 1) < 0)
1916 snap = isl_tab_snap(clex->tab);
1917 isl_tab_push_basis(clex->tab);
1918 clex->tab = add_lexmin_ineq(clex->tab, ineq);
1919 clex->tab = check_integer_feasible(clex->tab);
1922 feasible = !clex->tab->empty;
1923 if (isl_tab_rollback(clex->tab, snap) < 0)
1929 static int context_lex_get_div(struct isl_context *context, struct isl_tab *tab,
1930 struct isl_vec *div)
1932 return get_div(tab, context, div);
1935 static int context_lex_add_div(struct isl_context *context, struct isl_vec *div,
1938 struct isl_context_lex *clex = (struct isl_context_lex *)context;
1939 return context_tab_add_div(clex->tab, div, nonneg);
1942 static int context_lex_detect_equalities(struct isl_context *context,
1943 struct isl_tab *tab)
1948 static int context_lex_best_split(struct isl_context *context,
1949 struct isl_tab *tab)
1951 struct isl_context_lex *clex = (struct isl_context_lex *)context;
1952 struct isl_tab_undo *snap;
1955 snap = isl_tab_snap(clex->tab);
1956 isl_tab_push_basis(clex->tab);
1957 r = best_split(tab, clex->tab);
1959 if (isl_tab_rollback(clex->tab, snap) < 0)
1965 static int context_lex_is_empty(struct isl_context *context)
1967 struct isl_context_lex *clex = (struct isl_context_lex *)context;
1970 return clex->tab->empty;
1973 static void *context_lex_save(struct isl_context *context)
1975 struct isl_context_lex *clex = (struct isl_context_lex *)context;
1976 struct isl_tab_undo *snap;
1978 snap = isl_tab_snap(clex->tab);
1979 isl_tab_push_basis(clex->tab);
1980 isl_tab_save_samples(clex->tab);
1985 static void context_lex_restore(struct isl_context *context, void *save)
1987 struct isl_context_lex *clex = (struct isl_context_lex *)context;
1988 if (isl_tab_rollback(clex->tab, (struct isl_tab_undo *)save) < 0) {
1989 isl_tab_free(clex->tab);
1994 static int context_lex_is_ok(struct isl_context *context)
1996 struct isl_context_lex *clex = (struct isl_context_lex *)context;
2000 /* For each variable in the context tableau, check if the variable can
2001 * only attain non-negative values. If so, mark the parameter as non-negative
2002 * in the main tableau. This allows for a more direct identification of some
2003 * cases of violated constraints.
2005 static struct isl_tab *tab_detect_nonnegative_parameters(struct isl_tab *tab,
2006 struct isl_tab *context_tab)
2009 struct isl_tab_undo *snap;
2010 struct isl_vec *ineq = NULL;
2011 struct isl_tab_var *var;
2014 if (context_tab->n_var == 0)
2017 ineq = isl_vec_alloc(tab->mat->ctx, 1 + context_tab->n_var);
2021 if (isl_tab_extend_cons(context_tab, 1) < 0)
2024 snap = isl_tab_snap(context_tab);
2027 isl_seq_clr(ineq->el, ineq->size);
2028 for (i = 0; i < context_tab->n_var; ++i) {
2029 isl_int_set_si(ineq->el[1 + i], 1);
2030 context_tab = isl_tab_add_ineq(context_tab, ineq->el);
2031 var = &context_tab->con[context_tab->n_con - 1];
2032 if (!context_tab->empty &&
2033 !isl_tab_min_at_most_neg_one(context_tab, var)) {
2035 if (i >= tab->n_param)
2036 j = i - tab->n_param + tab->n_var - tab->n_div;
2037 tab->var[j].is_nonneg = 1;
2040 isl_int_set_si(ineq->el[1 + i], 0);
2041 if (isl_tab_rollback(context_tab, snap) < 0)
2045 if (context_tab->M && n == context_tab->n_var) {
2046 context_tab->mat = isl_mat_drop_cols(context_tab->mat, 2, 1);
2058 static struct isl_tab *context_lex_detect_nonnegative_parameters(
2059 struct isl_context *context, struct isl_tab *tab)
2061 struct isl_context_lex *clex = (struct isl_context_lex *)context;
2062 struct isl_tab_undo *snap;
2064 snap = isl_tab_snap(clex->tab);
2065 isl_tab_push_basis(clex->tab);
2067 tab = tab_detect_nonnegative_parameters(tab, clex->tab);
2069 if (isl_tab_rollback(clex->tab, snap) < 0)
2078 static void context_lex_invalidate(struct isl_context *context)
2080 struct isl_context_lex *clex = (struct isl_context_lex *)context;
2081 isl_tab_free(clex->tab);
2085 static void context_lex_free(struct isl_context *context)
2087 struct isl_context_lex *clex = (struct isl_context_lex *)context;
2088 isl_tab_free(clex->tab);
2092 struct isl_context_op isl_context_lex_op = {
2093 context_lex_detect_nonnegative_parameters,
2094 context_lex_peek_basic_set,
2095 context_lex_peek_tab,
2097 context_lex_add_ineq,
2098 context_lex_ineq_sign,
2099 context_lex_test_ineq,
2100 context_lex_get_div,
2101 context_lex_add_div,
2102 context_lex_detect_equalities,
2103 context_lex_best_split,
2104 context_lex_is_empty,
2107 context_lex_restore,
2108 context_lex_invalidate,
2112 static struct isl_tab *context_tab_for_lexmin(struct isl_basic_set *bset)
2114 struct isl_tab *tab;
2116 bset = isl_basic_set_cow(bset);
2119 tab = tab_for_lexmin((struct isl_basic_map *)bset, NULL, 1, 0);
2123 tab = isl_tab_init_samples(tab);
2126 isl_basic_set_free(bset);
2130 static struct isl_context *isl_context_lex_alloc(struct isl_basic_set *dom)
2132 struct isl_context_lex *clex;
2137 clex = isl_alloc_type(dom->ctx, struct isl_context_lex);
2141 clex->context.op = &isl_context_lex_op;
2143 clex->tab = context_tab_for_lexmin(isl_basic_set_copy(dom));
2144 clex->tab = restore_lexmin(clex->tab);
2145 clex->tab = check_integer_feasible(clex->tab);
2149 return &clex->context;
2151 clex->context.op->free(&clex->context);
2155 struct isl_context_gbr {
2156 struct isl_context context;
2157 struct isl_tab *tab;
2158 struct isl_tab *shifted;
2159 struct isl_tab *cone;
2162 static struct isl_tab *context_gbr_detect_nonnegative_parameters(
2163 struct isl_context *context, struct isl_tab *tab)
2165 struct isl_context_gbr *cgbr = (struct isl_context_gbr *)context;
2166 return tab_detect_nonnegative_parameters(tab, cgbr->tab);
2169 static struct isl_basic_set *context_gbr_peek_basic_set(
2170 struct isl_context *context)
2172 struct isl_context_gbr *cgbr = (struct isl_context_gbr *)context;
2175 return cgbr->tab->bset;
2178 static struct isl_tab *context_gbr_peek_tab(struct isl_context *context)
2180 struct isl_context_gbr *cgbr = (struct isl_context_gbr *)context;
2184 /* Initialize the "shifted" tableau of the context, which
2185 * contains the constraints of the original tableau shifted
2186 * by the sum of all negative coefficients. This ensures
2187 * that any rational point in the shifted tableau can
2188 * be rounded up to yield an integer point in the original tableau.
2190 static void gbr_init_shifted(struct isl_context_gbr *cgbr)
2193 struct isl_vec *cst;
2194 struct isl_basic_set *bset = cgbr->tab->bset;
2195 unsigned dim = isl_basic_set_total_dim(bset);
2197 cst = isl_vec_alloc(cgbr->tab->mat->ctx, bset->n_ineq);
2201 for (i = 0; i < bset->n_ineq; ++i) {
2202 isl_int_set(cst->el[i], bset->ineq[i][0]);
2203 for (j = 0; j < dim; ++j) {
2204 if (!isl_int_is_neg(bset->ineq[i][1 + j]))
2206 isl_int_add(bset->ineq[i][0], bset->ineq[i][0],
2207 bset->ineq[i][1 + j]);
2211 cgbr->shifted = isl_tab_from_basic_set(bset);
2213 for (i = 0; i < bset->n_ineq; ++i)
2214 isl_int_set(bset->ineq[i][0], cst->el[i]);
2219 /* Check if the shifted tableau is non-empty, and if so
2220 * use the sample point to construct an integer point
2221 * of the context tableau.
2223 static struct isl_vec *gbr_get_shifted_sample(struct isl_context_gbr *cgbr)
2225 struct isl_vec *sample;
2228 gbr_init_shifted(cgbr);
2231 if (cgbr->shifted->empty)
2232 return isl_vec_alloc(cgbr->tab->mat->ctx, 0);
2234 sample = isl_tab_get_sample_value(cgbr->shifted);
2235 sample = isl_vec_ceil(sample);
2240 static struct isl_basic_set *drop_constant_terms(struct isl_basic_set *bset)
2247 for (i = 0; i < bset->n_eq; ++i)
2248 isl_int_set_si(bset->eq[i][0], 0);
2250 for (i = 0; i < bset->n_ineq; ++i)
2251 isl_int_set_si(bset->ineq[i][0], 0);
2256 static int use_shifted(struct isl_context_gbr *cgbr)
2258 return cgbr->tab->bset->n_eq == 0 && cgbr->tab->bset->n_div == 0;
2261 static struct isl_vec *gbr_get_sample(struct isl_context_gbr *cgbr)
2263 struct isl_basic_set *bset;
2264 struct isl_basic_set *cone;
2266 if (isl_tab_sample_is_integer(cgbr->tab))
2267 return isl_tab_get_sample_value(cgbr->tab);
2269 if (use_shifted(cgbr)) {
2270 struct isl_vec *sample;
2272 sample = gbr_get_shifted_sample(cgbr);
2273 if (!sample || sample->size > 0)
2276 isl_vec_free(sample);
2280 cgbr->cone = isl_tab_from_recession_cone(cgbr->tab->bset);
2283 cgbr->cone->bset = isl_basic_set_dup(cgbr->tab->bset);
2285 cgbr->cone = isl_tab_detect_implicit_equalities(cgbr->cone);
2289 if (cgbr->cone->n_dead == cgbr->cone->n_col) {
2290 struct isl_vec *sample;
2291 struct isl_tab_undo *snap;
2293 if (cgbr->tab->basis) {
2294 if (cgbr->tab->basis->n_col != 1 + cgbr->tab->n_var) {
2295 isl_mat_free(cgbr->tab->basis);
2296 cgbr->tab->basis = NULL;
2298 cgbr->tab->n_zero = 0;
2299 cgbr->tab->n_unbounded = 0;
2303 snap = isl_tab_snap(cgbr->tab);
2305 sample = isl_tab_sample(cgbr->tab);
2307 if (isl_tab_rollback(cgbr->tab, snap) < 0) {
2308 isl_vec_free(sample);
2315 cone = isl_basic_set_dup(cgbr->cone->bset);
2316 cone = drop_constant_terms(cone);
2317 cone = isl_basic_set_update_from_tab(cone, cgbr->cone);
2318 cone = isl_basic_set_underlying_set(cone);
2319 cone = isl_basic_set_gauss(cone, NULL);
2321 bset = isl_basic_set_dup(cgbr->tab->bset);
2322 bset = isl_basic_set_update_from_tab(bset, cgbr->tab);
2323 bset = isl_basic_set_underlying_set(bset);
2324 bset = isl_basic_set_gauss(bset, NULL);
2326 return isl_basic_set_sample_with_cone(bset, cone);
2329 static void check_gbr_integer_feasible(struct isl_context_gbr *cgbr)
2331 struct isl_vec *sample;
2336 if (cgbr->tab->empty)
2339 sample = gbr_get_sample(cgbr);
2343 if (sample->size == 0) {
2344 isl_vec_free(sample);
2345 cgbr->tab = isl_tab_mark_empty(cgbr->tab);
2349 cgbr->tab = isl_tab_add_sample(cgbr->tab, sample);
2353 isl_tab_free(cgbr->tab);
2357 static struct isl_tab *add_gbr_eq(struct isl_tab *tab, isl_int *eq)
2364 if (isl_tab_extend_cons(tab, 2) < 0)
2367 tab = isl_tab_add_eq(tab, eq);
2375 static void context_gbr_add_eq(struct isl_context *context, isl_int *eq,
2376 int check, int update)
2378 struct isl_context_gbr *cgbr = (struct isl_context_gbr *)context;
2380 cgbr->tab = add_gbr_eq(cgbr->tab, eq);
2382 if (cgbr->cone && cgbr->cone->n_col != cgbr->cone->n_dead) {
2383 if (isl_tab_extend_cons(cgbr->cone, 2) < 0)
2385 cgbr->cone = isl_tab_add_eq(cgbr->cone, eq);
2389 int v = tab_has_valid_sample(cgbr->tab, eq, 1);
2393 check_gbr_integer_feasible(cgbr);
2396 cgbr->tab = check_samples(cgbr->tab, eq, 1);
2399 isl_tab_free(cgbr->tab);
2403 static void add_gbr_ineq(struct isl_context_gbr *cgbr, isl_int *ineq)
2408 if (isl_tab_extend_cons(cgbr->tab, 1) < 0)
2411 cgbr->tab = isl_tab_add_ineq(cgbr->tab, ineq);
2413 if (cgbr->shifted && !cgbr->shifted->empty && use_shifted(cgbr)) {
2416 dim = isl_basic_set_total_dim(cgbr->tab->bset);
2418 if (isl_tab_extend_cons(cgbr->shifted, 1) < 0)
2421 for (i = 0; i < dim; ++i) {
2422 if (!isl_int_is_neg(ineq[1 + i]))
2424 isl_int_add(ineq[0], ineq[0], ineq[1 + i]);
2427 cgbr->shifted = isl_tab_add_ineq(cgbr->shifted, ineq);
2429 for (i = 0; i < dim; ++i) {
2430 if (!isl_int_is_neg(ineq[1 + i]))
2432 isl_int_sub(ineq[0], ineq[0], ineq[1 + i]);
2436 if (cgbr->cone && cgbr->cone->n_col != cgbr->cone->n_dead) {
2437 if (isl_tab_extend_cons(cgbr->cone, 1) < 0)
2439 cgbr->cone = isl_tab_add_ineq(cgbr->cone, ineq);
2444 isl_tab_free(cgbr->tab);
2448 static void context_gbr_add_ineq(struct isl_context *context, isl_int *ineq,
2449 int check, int update)
2451 struct isl_context_gbr *cgbr = (struct isl_context_gbr *)context;
2453 add_gbr_ineq(cgbr, ineq);
2458 int v = tab_has_valid_sample(cgbr->tab, ineq, 0);
2462 check_gbr_integer_feasible(cgbr);
2465 cgbr->tab = check_samples(cgbr->tab, ineq, 0);
2468 isl_tab_free(cgbr->tab);
2472 static enum isl_tab_row_sign context_gbr_ineq_sign(struct isl_context *context,
2473 isl_int *ineq, int strict)
2475 struct isl_context_gbr *cgbr = (struct isl_context_gbr *)context;
2476 return tab_ineq_sign(cgbr->tab, ineq, strict);
2479 /* Check whether "ineq" can be added to the tableau without rendering
2482 static int context_gbr_test_ineq(struct isl_context *context, isl_int *ineq)
2484 struct isl_context_gbr *cgbr = (struct isl_context_gbr *)context;
2485 struct isl_tab_undo *snap;
2486 struct isl_tab_undo *shifted_snap = NULL;
2487 struct isl_tab_undo *cone_snap = NULL;
2493 if (isl_tab_extend_cons(cgbr->tab, 1) < 0)
2496 snap = isl_tab_snap(cgbr->tab);
2498 shifted_snap = isl_tab_snap(cgbr->shifted);
2500 cone_snap = isl_tab_snap(cgbr->cone);
2501 add_gbr_ineq(cgbr, ineq);
2502 check_gbr_integer_feasible(cgbr);
2505 feasible = !cgbr->tab->empty;
2506 if (isl_tab_rollback(cgbr->tab, snap) < 0)
2509 if (isl_tab_rollback(cgbr->shifted, shifted_snap))
2511 } else if (cgbr->shifted) {
2512 isl_tab_free(cgbr->shifted);
2513 cgbr->shifted = NULL;
2516 if (isl_tab_rollback(cgbr->cone, cone_snap))
2518 } else if (cgbr->cone) {
2519 isl_tab_free(cgbr->cone);
2526 /* Return the column of the last of the variables associated to
2527 * a column that has a non-zero coefficient.
2528 * This function is called in a context where only coefficients
2529 * of parameters or divs can be non-zero.
2531 static int last_non_zero_var_col(struct isl_tab *tab, isl_int *p)
2535 unsigned dim = tab->n_var - tab->n_param - tab->n_div;
2537 if (tab->n_var == 0)
2540 for (i = tab->n_var - 1; i >= 0; --i) {
2541 if (i >= tab->n_param && i < tab->n_var - tab->n_div)
2543 if (tab->var[i].is_row)
2545 col = tab->var[i].index;
2546 if (!isl_int_is_zero(p[col]))
2553 /* Look through all the recently added equalities in the context
2554 * to see if we can propagate any of them to the main tableau.
2556 * The newly added equalities in the context are encoded as pairs
2557 * of inequalities starting at inequality "first".
2559 * We tentatively add each of these equalities to the main tableau
2560 * and if this happens to result in a row with a final coefficient
2561 * that is one or negative one, we use it to kill a column
2562 * in the main tableau. Otherwise, we discard the tentatively
2565 static void propagate_equalities(struct isl_context_gbr *cgbr,
2566 struct isl_tab *tab, unsigned first)
2569 struct isl_vec *eq = NULL;
2571 eq = isl_vec_alloc(tab->mat->ctx, 1 + tab->n_var);
2575 if (isl_tab_extend_cons(tab, (cgbr->tab->bset->n_ineq - first)/2) < 0)
2578 isl_seq_clr(eq->el + 1 + tab->n_param,
2579 tab->n_var - tab->n_param - tab->n_div);
2580 for (i = first; i < cgbr->tab->bset->n_ineq; i += 2) {
2583 struct isl_tab_undo *snap;
2584 snap = isl_tab_snap(tab);
2586 isl_seq_cpy(eq->el, cgbr->tab->bset->ineq[i], 1 + tab->n_param);
2587 isl_seq_cpy(eq->el + 1 + tab->n_var - tab->n_div,
2588 cgbr->tab->bset->ineq[i] + 1 + tab->n_param,
2591 r = isl_tab_add_row(tab, eq->el);
2594 r = tab->con[r].index;
2595 j = last_non_zero_var_col(tab, tab->mat->row[r] + 2 + tab->M);
2596 if (j < 0 || j < tab->n_dead ||
2597 !isl_int_is_one(tab->mat->row[r][0]) ||
2598 (!isl_int_is_one(tab->mat->row[r][2 + tab->M + j]) &&
2599 !isl_int_is_negone(tab->mat->row[r][2 + tab->M + j]))) {
2600 if (isl_tab_rollback(tab, snap) < 0)
2604 isl_tab_pivot(tab, r, j);
2605 isl_tab_kill_col(tab, j);
2607 tab = restore_lexmin(tab);
2615 isl_tab_free(cgbr->tab);
2619 static int context_gbr_detect_equalities(struct isl_context *context,
2620 struct isl_tab *tab)
2622 struct isl_context_gbr *cgbr = (struct isl_context_gbr *)context;
2623 struct isl_ctx *ctx;
2625 enum isl_lp_result res;
2628 ctx = cgbr->tab->mat->ctx;
2631 cgbr->cone = isl_tab_from_recession_cone(cgbr->tab->bset);
2634 cgbr->cone->bset = isl_basic_set_dup(cgbr->tab->bset);
2636 cgbr->cone = isl_tab_detect_implicit_equalities(cgbr->cone);
2638 n_ineq = cgbr->tab->bset->n_ineq;
2639 cgbr->tab = isl_tab_detect_equalities(cgbr->tab, cgbr->cone);
2640 if (cgbr->tab && cgbr->tab->bset->n_ineq > n_ineq)
2641 propagate_equalities(cgbr, tab, n_ineq);
2645 isl_tab_free(cgbr->tab);
2650 static int context_gbr_get_div(struct isl_context *context, struct isl_tab *tab,
2651 struct isl_vec *div)
2653 return get_div(tab, context, div);
2656 static int context_gbr_add_div(struct isl_context *context, struct isl_vec *div,
2659 struct isl_context_gbr *cgbr = (struct isl_context_gbr *)context;
2663 if (isl_tab_extend_cons(cgbr->cone, 3) < 0)
2665 if (isl_tab_extend_vars(cgbr->cone, 1) < 0)
2667 if (isl_tab_allocate_var(cgbr->cone) <0)
2670 cgbr->cone->bset = isl_basic_set_extend_dim(cgbr->cone->bset,
2671 isl_basic_set_get_dim(cgbr->cone->bset), 1, 0, 2);
2672 k = isl_basic_set_alloc_div(cgbr->cone->bset);
2675 isl_seq_cpy(cgbr->cone->bset->div[k], div->el, div->size);
2676 isl_tab_push(cgbr->cone, isl_tab_undo_bset_div);
2678 return context_tab_add_div(cgbr->tab, div, nonneg);
2681 static int context_gbr_best_split(struct isl_context *context,
2682 struct isl_tab *tab)
2684 struct isl_context_gbr *cgbr = (struct isl_context_gbr *)context;
2685 struct isl_tab_undo *snap;
2688 snap = isl_tab_snap(cgbr->tab);
2689 r = best_split(tab, cgbr->tab);
2691 if (isl_tab_rollback(cgbr->tab, snap) < 0)
2697 static int context_gbr_is_empty(struct isl_context *context)
2699 struct isl_context_gbr *cgbr = (struct isl_context_gbr *)context;
2702 return cgbr->tab->empty;
2705 struct isl_gbr_tab_undo {
2706 struct isl_tab_undo *tab_snap;
2707 struct isl_tab_undo *shifted_snap;
2708 struct isl_tab_undo *cone_snap;
2711 static void *context_gbr_save(struct isl_context *context)
2713 struct isl_context_gbr *cgbr = (struct isl_context_gbr *)context;
2714 struct isl_gbr_tab_undo *snap;
2716 snap = isl_alloc_type(cgbr->tab->mat->ctx, struct isl_gbr_tab_undo);
2720 snap->tab_snap = isl_tab_snap(cgbr->tab);
2721 isl_tab_save_samples(cgbr->tab);
2724 snap->shifted_snap = isl_tab_snap(cgbr->shifted);
2726 snap->shifted_snap = NULL;
2729 snap->cone_snap = isl_tab_snap(cgbr->cone);
2731 snap->cone_snap = NULL;
2736 static void context_gbr_restore(struct isl_context *context, void *save)
2738 struct isl_context_gbr *cgbr = (struct isl_context_gbr *)context;
2739 struct isl_gbr_tab_undo *snap = (struct isl_gbr_tab_undo *)save;
2740 if (isl_tab_rollback(cgbr->tab, snap->tab_snap) < 0) {
2741 isl_tab_free(cgbr->tab);
2745 if (snap->shifted_snap)
2746 isl_tab_rollback(cgbr->shifted, snap->shifted_snap);
2747 else if (cgbr->shifted) {
2748 isl_tab_free(cgbr->shifted);
2749 cgbr->shifted = NULL;
2752 if (snap->cone_snap)
2753 isl_tab_rollback(cgbr->cone, snap->cone_snap);
2754 else if (cgbr->cone) {
2755 isl_tab_free(cgbr->cone);
2762 static int context_gbr_is_ok(struct isl_context *context)
2764 struct isl_context_gbr *cgbr = (struct isl_context_gbr *)context;
2768 static void context_gbr_invalidate(struct isl_context *context)
2770 struct isl_context_gbr *cgbr = (struct isl_context_gbr *)context;
2771 isl_tab_free(cgbr->tab);
2775 static void context_gbr_free(struct isl_context *context)
2777 struct isl_context_gbr *cgbr = (struct isl_context_gbr *)context;
2778 isl_tab_free(cgbr->tab);
2779 isl_tab_free(cgbr->shifted);
2780 isl_tab_free(cgbr->cone);
2784 struct isl_context_op isl_context_gbr_op = {
2785 context_gbr_detect_nonnegative_parameters,
2786 context_gbr_peek_basic_set,
2787 context_gbr_peek_tab,
2789 context_gbr_add_ineq,
2790 context_gbr_ineq_sign,
2791 context_gbr_test_ineq,
2792 context_gbr_get_div,
2793 context_gbr_add_div,
2794 context_gbr_detect_equalities,
2795 context_gbr_best_split,
2796 context_gbr_is_empty,
2799 context_gbr_restore,
2800 context_gbr_invalidate,
2804 static struct isl_context *isl_context_gbr_alloc(struct isl_basic_set *dom)
2806 struct isl_context_gbr *cgbr;
2811 cgbr = isl_calloc_type(dom->ctx, struct isl_context_gbr);
2815 cgbr->context.op = &isl_context_gbr_op;
2817 cgbr->shifted = NULL;
2819 cgbr->tab = isl_tab_from_basic_set(dom);
2820 cgbr->tab = isl_tab_init_samples(cgbr->tab);
2823 cgbr->tab->bset = isl_basic_set_cow(isl_basic_set_copy(dom));
2824 if (!cgbr->tab->bset)
2826 check_gbr_integer_feasible(cgbr);
2828 return &cgbr->context;
2830 cgbr->context.op->free(&cgbr->context);
2834 static struct isl_context *isl_context_alloc(struct isl_basic_set *dom)
2839 if (dom->ctx->context == ISL_CONTEXT_LEXMIN)
2840 return isl_context_lex_alloc(dom);
2842 return isl_context_gbr_alloc(dom);
2845 /* Construct an isl_sol_map structure for accumulating the solution.
2846 * If track_empty is set, then we also keep track of the parts
2847 * of the context where there is no solution.
2848 * If max is set, then we are solving a maximization, rather than
2849 * a minimization problem, which means that the variables in the
2850 * tableau have value "M - x" rather than "M + x".
2852 static struct isl_sol_map *sol_map_init(struct isl_basic_map *bmap,
2853 struct isl_basic_set *dom, int track_empty, int max)
2855 struct isl_sol_map *sol_map;
2857 sol_map = isl_calloc_type(bset->ctx, struct isl_sol_map);
2862 sol_map->sol.add = &sol_map_add_wrap;
2863 sol_map->sol.free = &sol_map_free_wrap;
2864 sol_map->map = isl_map_alloc_dim(isl_basic_map_get_dim(bmap), 1,
2869 sol_map->sol.context = isl_context_alloc(dom);
2870 if (!sol_map->sol.context)
2874 sol_map->empty = isl_set_alloc_dim(isl_basic_set_get_dim(dom),
2875 1, ISL_SET_DISJOINT);
2876 if (!sol_map->empty)
2880 isl_basic_set_free(dom);
2883 isl_basic_set_free(dom);
2884 sol_map_free(sol_map);
2888 /* Check whether all coefficients of (non-parameter) variables
2889 * are non-positive, meaning that no pivots can be performed on the row.
2891 static int is_critical(struct isl_tab *tab, int row)
2894 unsigned off = 2 + tab->M;
2896 for (j = tab->n_dead; j < tab->n_col; ++j) {
2897 if (tab->col_var[j] >= 0 &&
2898 (tab->col_var[j] < tab->n_param ||
2899 tab->col_var[j] >= tab->n_var - tab->n_div))
2902 if (isl_int_is_pos(tab->mat->row[row][off + j]))
2909 /* Check whether the inequality represented by vec is strict over the integers,
2910 * i.e., there are no integer values satisfying the constraint with
2911 * equality. This happens if the gcd of the coefficients is not a divisor
2912 * of the constant term. If so, scale the constraint down by the gcd
2913 * of the coefficients.
2915 static int is_strict(struct isl_vec *vec)
2921 isl_seq_gcd(vec->el + 1, vec->size - 1, &gcd);
2922 if (!isl_int_is_one(gcd)) {
2923 strict = !isl_int_is_divisible_by(vec->el[0], gcd);
2924 isl_int_fdiv_q(vec->el[0], vec->el[0], gcd);
2925 isl_seq_scale_down(vec->el + 1, vec->el + 1, gcd, vec->size-1);
2932 /* Determine the sign of the given row of the main tableau.
2933 * The result is one of
2934 * isl_tab_row_pos: always non-negative; no pivot needed
2935 * isl_tab_row_neg: always non-positive; pivot
2936 * isl_tab_row_any: can be both positive and negative; split
2938 * We first handle some simple cases
2939 * - the row sign may be known already
2940 * - the row may be obviously non-negative
2941 * - the parametric constant may be equal to that of another row
2942 * for which we know the sign. This sign will be either "pos" or
2943 * "any". If it had been "neg" then we would have pivoted before.
2945 * If none of these cases hold, we check the value of the row for each
2946 * of the currently active samples. Based on the signs of these values
2947 * we make an initial determination of the sign of the row.
2949 * all zero -> unk(nown)
2950 * all non-negative -> pos
2951 * all non-positive -> neg
2952 * both negative and positive -> all
2954 * If we end up with "all", we are done.
2955 * Otherwise, we perform a check for positive and/or negative
2956 * values as follows.
2958 * samples neg unk pos
2964 * There is no special sign for "zero", because we can usually treat zero
2965 * as either non-negative or non-positive, whatever works out best.
2966 * However, if the row is "critical", meaning that pivoting is impossible
2967 * then we don't want to limp zero with the non-positive case, because
2968 * then we we would lose the solution for those values of the parameters
2969 * where the value of the row is zero. Instead, we treat 0 as non-negative
2970 * ensuring a split if the row can attain both zero and negative values.
2971 * The same happens when the original constraint was one that could not
2972 * be satisfied with equality by any integer values of the parameters.
2973 * In this case, we normalize the constraint, but then a value of zero
2974 * for the normalized constraint is actually a positive value for the
2975 * original constraint, so again we need to treat zero as non-negative.
2976 * In both these cases, we have the following decision tree instead:
2978 * all non-negative -> pos
2979 * all negative -> neg
2980 * both negative and non-negative -> all
2988 static enum isl_tab_row_sign row_sign(struct isl_tab *tab,
2989 struct isl_sol *sol, int row)
2991 struct isl_vec *ineq = NULL;
2992 int res = isl_tab_row_unknown;
2997 if (tab->row_sign[row] != isl_tab_row_unknown)
2998 return tab->row_sign[row];
2999 if (is_obviously_nonneg(tab, row))
3000 return isl_tab_row_pos;
3001 for (row2 = tab->n_redundant; row2 < tab->n_row; ++row2) {
3002 if (tab->row_sign[row2] == isl_tab_row_unknown)
3004 if (identical_parameter_line(tab, row, row2))
3005 return tab->row_sign[row2];
3008 critical = is_critical(tab, row);
3010 ineq = get_row_parameter_ineq(tab, row);
3014 strict = is_strict(ineq);
3016 res = sol->context->op->ineq_sign(sol->context, ineq->el,
3017 critical || strict);
3019 if (res == isl_tab_row_unknown || res == isl_tab_row_pos) {
3020 /* test for negative values */
3022 isl_seq_neg(ineq->el, ineq->el, ineq->size);
3023 isl_int_sub_ui(ineq->el[0], ineq->el[0], 1);
3025 feasible = sol->context->op->test_ineq(sol->context, ineq->el);
3029 res = isl_tab_row_pos;
3031 res = (res == isl_tab_row_unknown) ? isl_tab_row_neg
3033 if (res == isl_tab_row_neg) {
3034 isl_seq_neg(ineq->el, ineq->el, ineq->size);
3035 isl_int_sub_ui(ineq->el[0], ineq->el[0], 1);
3039 if (res == isl_tab_row_neg) {
3040 /* test for positive values */
3042 if (!critical && !strict)
3043 isl_int_sub_ui(ineq->el[0], ineq->el[0], 1);
3045 feasible = sol->context->op->test_ineq(sol->context, ineq->el);
3049 res = isl_tab_row_any;
3059 static struct isl_sol *find_solutions(struct isl_sol *sol, struct isl_tab *tab);
3061 /* Find solutions for values of the parameters that satisfy the given
3064 * We currently take a snapshot of the context tableau that is reset
3065 * when we return from this function, while we make a copy of the main
3066 * tableau, leaving the original main tableau untouched.
3067 * These are fairly arbitrary choices. Making a copy also of the context
3068 * tableau would obviate the need to undo any changes made to it later,
3069 * while taking a snapshot of the main tableau could reduce memory usage.
3070 * If we were to switch to taking a snapshot of the main tableau,
3071 * we would have to keep in mind that we need to save the row signs
3072 * and that we need to do this before saving the current basis
3073 * such that the basis has been restore before we restore the row signs.
3075 static struct isl_sol *find_in_pos(struct isl_sol *sol,
3076 struct isl_tab *tab, isl_int *ineq)
3082 saved = sol->context->op->save(sol->context);
3084 tab = isl_tab_dup(tab);
3088 sol->context->op->add_ineq(sol->context, ineq, 0, 1);
3090 sol = find_solutions(sol, tab);
3092 sol->context->op->restore(sol->context, saved);
3099 /* Record the absence of solutions for those values of the parameters
3100 * that do not satisfy the given inequality with equality.
3102 static struct isl_sol *no_sol_in_strict(struct isl_sol *sol,
3103 struct isl_tab *tab, struct isl_vec *ineq)
3110 saved = sol->context->op->save(sol->context);
3112 isl_int_sub_ui(ineq->el[0], ineq->el[0], 1);
3114 sol->context->op->add_ineq(sol->context, ineq->el, 1, 0);
3120 sol = sol->add(sol, tab);
3123 isl_int_add_ui(ineq->el[0], ineq->el[0], 1);
3125 sol->context->op->restore(sol->context, saved);
3132 /* Compute the lexicographic minimum of the set represented by the main
3133 * tableau "tab" within the context "sol->context_tab".
3134 * On entry the sample value of the main tableau is lexicographically
3135 * less than or equal to this lexicographic minimum.
3136 * Pivots are performed until a feasible point is found, which is then
3137 * necessarily equal to the minimum, or until the tableau is found to
3138 * be infeasible. Some pivots may need to be performed for only some
3139 * feasible values of the context tableau. If so, the context tableau
3140 * is split into a part where the pivot is needed and a part where it is not.
3142 * Whenever we enter the main loop, the main tableau is such that no
3143 * "obvious" pivots need to be performed on it, where "obvious" means
3144 * that the given row can be seen to be negative without looking at
3145 * the context tableau. In particular, for non-parametric problems,
3146 * no pivots need to be performed on the main tableau.
3147 * The caller of find_solutions is responsible for making this property
3148 * hold prior to the first iteration of the loop, while restore_lexmin
3149 * is called before every other iteration.
3151 * Inside the main loop, we first examine the signs of the rows of
3152 * the main tableau within the context of the context tableau.
3153 * If we find a row that is always non-positive for all values of
3154 * the parameters satisfying the context tableau and negative for at
3155 * least one value of the parameters, we perform the appropriate pivot
3156 * and start over. An exception is the case where no pivot can be
3157 * performed on the row. In this case, we require that the sign of
3158 * the row is negative for all values of the parameters (rather than just
3159 * non-positive). This special case is handled inside row_sign, which
3160 * will say that the row can have any sign if it determines that it can
3161 * attain both negative and zero values.
3163 * If we can't find a row that always requires a pivot, but we can find
3164 * one or more rows that require a pivot for some values of the parameters
3165 * (i.e., the row can attain both positive and negative signs), then we split
3166 * the context tableau into two parts, one where we force the sign to be
3167 * non-negative and one where we force is to be negative.
3168 * The non-negative part is handled by a recursive call (through find_in_pos).
3169 * Upon returning from this call, we continue with the negative part and
3170 * perform the required pivot.
3172 * If no such rows can be found, all rows are non-negative and we have
3173 * found a (rational) feasible point. If we only wanted a rational point
3175 * Otherwise, we check if all values of the sample point of the tableau
3176 * are integral for the variables. If so, we have found the minimal
3177 * integral point and we are done.
3178 * If the sample point is not integral, then we need to make a distinction
3179 * based on whether the constant term is non-integral or the coefficients
3180 * of the parameters. Furthermore, in order to decide how to handle
3181 * the non-integrality, we also need to know whether the coefficients
3182 * of the other columns in the tableau are integral. This leads
3183 * to the following table. The first two rows do not correspond
3184 * to a non-integral sample point and are only mentioned for completeness.
3186 * constant parameters other
3189 * int int rat | -> no problem
3191 * rat int int -> fail
3193 * rat int rat -> cut
3196 * rat rat rat | -> parametric cut
3199 * rat rat int | -> split context
3201 * If the parametric constant is completely integral, then there is nothing
3202 * to be done. If the constant term is non-integral, but all the other
3203 * coefficient are integral, then there is nothing that can be done
3204 * and the tableau has no integral solution.
3205 * If, on the other hand, one or more of the other columns have rational
3206 * coeffcients, but the parameter coefficients are all integral, then
3207 * we can perform a regular (non-parametric) cut.
3208 * Finally, if there is any parameter coefficient that is non-integral,
3209 * then we need to involve the context tableau. There are two cases here.
3210 * If at least one other column has a rational coefficient, then we
3211 * can perform a parametric cut in the main tableau by adding a new
3212 * integer division in the context tableau.
3213 * If all other columns have integral coefficients, then we need to
3214 * enforce that the rational combination of parameters (c + \sum a_i y_i)/m
3215 * is always integral. We do this by introducing an integer division
3216 * q = floor((c + \sum a_i y_i)/m) and stipulating that its argument should
3217 * always be integral in the context tableau, i.e., m q = c + \sum a_i y_i.
3218 * Since q is expressed in the tableau as
3219 * c + \sum a_i y_i - m q >= 0
3220 * -c - \sum a_i y_i + m q + m - 1 >= 0
3221 * it is sufficient to add the inequality
3222 * -c - \sum a_i y_i + m q >= 0
3223 * In the part of the context where this inequality does not hold, the
3224 * main tableau is marked as being empty.
3226 static struct isl_sol *find_solutions(struct isl_sol *sol, struct isl_tab *tab)
3228 struct isl_context *context;
3233 context = sol->context;
3237 if (context->op->is_empty(context))
3240 for (; tab && !tab->empty; tab = restore_lexmin(tab)) {
3247 for (row = tab->n_redundant; row < tab->n_row; ++row) {
3248 if (!isl_tab_var_from_row(tab, row)->is_nonneg)
3250 sgn = row_sign(tab, sol, row);
3253 tab->row_sign[row] = sgn;
3254 if (sgn == isl_tab_row_any)
3256 if (sgn == isl_tab_row_any && split == -1)
3258 if (sgn == isl_tab_row_neg)
3261 if (row < tab->n_row)
3264 struct isl_vec *ineq;
3266 split = context->op->best_split(context, tab);
3269 ineq = get_row_parameter_ineq(tab, split);
3273 for (row = tab->n_redundant; row < tab->n_row; ++row) {
3274 if (!isl_tab_var_from_row(tab, row)->is_nonneg)
3276 if (tab->row_sign[row] == isl_tab_row_any)
3277 tab->row_sign[row] = isl_tab_row_unknown;
3279 tab->row_sign[split] = isl_tab_row_pos;
3280 sol = find_in_pos(sol, tab, ineq->el);
3281 tab->row_sign[split] = isl_tab_row_neg;
3283 isl_seq_neg(ineq->el, ineq->el, ineq->size);
3284 isl_int_sub_ui(ineq->el[0], ineq->el[0], 1);
3285 context->op->add_ineq(context, ineq->el, 0, 1);
3293 row = first_non_integer(tab, &flags);
3296 if (ISL_FL_ISSET(flags, I_PAR)) {
3297 if (ISL_FL_ISSET(flags, I_VAR)) {
3298 tab = isl_tab_mark_empty(tab);
3301 row = add_cut(tab, row);
3302 } else if (ISL_FL_ISSET(flags, I_VAR)) {
3303 struct isl_vec *div;
3304 struct isl_vec *ineq;
3306 div = get_row_split_div(tab, row);
3309 d = context->op->get_div(context, tab, div);
3313 ineq = ineq_for_div(context->op->peek_basic_set(context), d);
3314 sol = no_sol_in_strict(sol, tab, ineq);
3315 isl_seq_neg(ineq->el, ineq->el, ineq->size);
3316 context->op->add_ineq(context, ineq->el, 1, 1);
3318 if (!sol || !context->op->is_ok(context))
3320 tab = set_row_cst_to_div(tab, row, d);
3322 row = add_parametric_cut(tab, row, context);
3327 sol = sol->add(sol, tab);
3336 /* Compute the lexicographic minimum of the set represented by the main
3337 * tableau "tab" within the context "sol->context_tab".
3339 * As a preprocessing step, we first transfer all the purely parametric
3340 * equalities from the main tableau to the context tableau, i.e.,
3341 * parameters that have been pivoted to a row.
3342 * These equalities are ignored by the main algorithm, because the
3343 * corresponding rows may not be marked as being non-negative.
3344 * In parts of the context where the added equality does not hold,
3345 * the main tableau is marked as being empty.
3347 static struct isl_sol *find_solutions_main(struct isl_sol *sol,
3348 struct isl_tab *tab)
3352 for (row = tab->n_redundant; row < tab->n_row; ++row) {
3356 if (tab->row_var[row] < 0)
3358 if (tab->row_var[row] >= tab->n_param &&
3359 tab->row_var[row] < tab->n_var - tab->n_div)
3361 if (tab->row_var[row] < tab->n_param)
3362 p = tab->row_var[row];
3364 p = tab->row_var[row]
3365 + tab->n_param - (tab->n_var - tab->n_div);
3367 eq = isl_vec_alloc(tab->mat->ctx, 1+tab->n_param+tab->n_div);
3368 get_row_parameter_line(tab, row, eq->el);
3369 isl_int_neg(eq->el[1 + p], tab->mat->row[row][0]);
3370 eq = isl_vec_normalize(eq);
3372 sol = no_sol_in_strict(sol, tab, eq);
3374 isl_seq_neg(eq->el, eq->el, eq->size);
3375 sol = no_sol_in_strict(sol, tab, eq);
3376 isl_seq_neg(eq->el, eq->el, eq->size);
3378 sol->context->op->add_eq(sol->context, eq->el, 1, 1);
3382 isl_tab_mark_redundant(tab, row);
3384 if (sol->context->op->is_empty(sol->context))
3387 row = tab->n_redundant - 1;
3390 return find_solutions(sol, tab);
3397 static struct isl_sol_map *sol_map_find_solutions(struct isl_sol_map *sol_map,
3398 struct isl_tab *tab)
3400 return (struct isl_sol_map *)find_solutions_main(&sol_map->sol, tab);
3403 /* Check if integer division "div" of "dom" also occurs in "bmap".
3404 * If so, return its position within the divs.
3405 * If not, return -1.
3407 static int find_context_div(struct isl_basic_map *bmap,
3408 struct isl_basic_set *dom, unsigned div)
3411 unsigned b_dim = isl_dim_total(bmap->dim);
3412 unsigned d_dim = isl_dim_total(dom->dim);
3414 if (isl_int_is_zero(dom->div[div][0]))
3416 if (isl_seq_first_non_zero(dom->div[div] + 2 + d_dim, dom->n_div) != -1)
3419 for (i = 0; i < bmap->n_div; ++i) {
3420 if (isl_int_is_zero(bmap->div[i][0]))
3422 if (isl_seq_first_non_zero(bmap->div[i] + 2 + d_dim,
3423 (b_dim - d_dim) + bmap->n_div) != -1)
3425 if (isl_seq_eq(bmap->div[i], dom->div[div], 2 + d_dim))
3431 /* The correspondence between the variables in the main tableau,
3432 * the context tableau, and the input map and domain is as follows.
3433 * The first n_param and the last n_div variables of the main tableau
3434 * form the variables of the context tableau.
3435 * In the basic map, these n_param variables correspond to the
3436 * parameters and the input dimensions. In the domain, they correspond
3437 * to the parameters and the set dimensions.
3438 * The n_div variables correspond to the integer divisions in the domain.
3439 * To ensure that everything lines up, we may need to copy some of the
3440 * integer divisions of the domain to the map. These have to be placed
3441 * in the same order as those in the context and they have to be placed
3442 * after any other integer divisions that the map may have.
3443 * This function performs the required reordering.
3445 static struct isl_basic_map *align_context_divs(struct isl_basic_map *bmap,
3446 struct isl_basic_set *dom)
3452 for (i = 0; i < dom->n_div; ++i)
3453 if (find_context_div(bmap, dom, i) != -1)
3455 other = bmap->n_div - common;
3456 if (dom->n_div - common > 0) {
3457 bmap = isl_basic_map_extend_dim(bmap, isl_dim_copy(bmap->dim),
3458 dom->n_div - common, 0, 0);
3462 for (i = 0; i < dom->n_div; ++i) {
3463 int pos = find_context_div(bmap, dom, i);
3465 pos = isl_basic_map_alloc_div(bmap);
3468 isl_int_set_si(bmap->div[pos][0], 0);
3470 if (pos != other + i)
3471 isl_basic_map_swap_div(bmap, pos, other + i);
3475 isl_basic_map_free(bmap);
3479 /* Compute the lexicographic minimum (or maximum if "max" is set)
3480 * of "bmap" over the domain "dom" and return the result as a map.
3481 * If "empty" is not NULL, then *empty is assigned a set that
3482 * contains those parts of the domain where there is no solution.
3483 * If "bmap" is marked as rational (ISL_BASIC_MAP_RATIONAL),
3484 * then we compute the rational optimum. Otherwise, we compute
3485 * the integral optimum.
3487 * We perform some preprocessing. As the PILP solver does not
3488 * handle implicit equalities very well, we first make sure all
3489 * the equalities are explicitly available.
3490 * We also make sure the divs in the domain are properly order,
3491 * because they will be added one by one in the given order
3492 * during the construction of the solution map.
3494 struct isl_map *isl_tab_basic_map_partial_lexopt(
3495 struct isl_basic_map *bmap, struct isl_basic_set *dom,
3496 struct isl_set **empty, int max)
3498 struct isl_tab *tab;
3499 struct isl_map *result = NULL;
3500 struct isl_sol_map *sol_map = NULL;
3501 struct isl_context *context;
3508 isl_assert(bmap->ctx,
3509 isl_basic_map_compatible_domain(bmap, dom), goto error);
3511 bmap = isl_basic_map_detect_equalities(bmap);
3514 dom = isl_basic_set_order_divs(dom);
3515 bmap = align_context_divs(bmap, dom);
3517 sol_map = sol_map_init(bmap, dom, !!empty, max);
3521 context = sol_map->sol.context;
3522 if (isl_basic_set_fast_is_empty(context->op->peek_basic_set(context)))
3524 else if (isl_basic_map_fast_is_empty(bmap))
3525 sol_map = add_empty(sol_map);
3527 tab = tab_for_lexmin(bmap,
3528 context->op->peek_basic_set(context), 1, max);
3529 tab = context->op->detect_nonnegative_parameters(context, tab);
3530 sol_map = sol_map_find_solutions(sol_map, tab);
3535 result = isl_map_copy(sol_map->map);
3537 *empty = isl_set_copy(sol_map->empty);
3538 sol_map_free(sol_map);
3539 isl_basic_map_free(bmap);
3542 sol_map_free(sol_map);
3543 isl_basic_map_free(bmap);
3547 struct isl_sol_for {
3549 int (*fn)(__isl_take isl_basic_set *dom,
3550 __isl_take isl_mat *map, void *user);
3555 static void sol_for_free(struct isl_sol_for *sol_for)
3557 if (sol_for->sol.context)
3558 sol_for->sol.context->op->free(sol_for->sol.context);
3562 static void sol_for_free_wrap(struct isl_sol *sol)
3564 sol_for_free((struct isl_sol_for *)sol);
3567 /* Add the solution identified by the tableau and the context tableau.
3569 * See documentation of sol_map_add for more details.
3571 * Instead of constructing a basic map, this function calls a user
3572 * defined function with the current context as a basic set and
3573 * an affine matrix reprenting the relation between the input and output.
3574 * The number of rows in this matrix is equal to one plus the number
3575 * of output variables. The number of columns is equal to one plus
3576 * the total dimension of the context, i.e., the number of parameters,
3577 * input variables and divs. Since some of the columns in the matrix
3578 * may refer to the divs, the basic set is not simplified.
3579 * (Simplification may reorder or remove divs.)
3581 static struct isl_sol_for *sol_for_add(struct isl_sol_for *sol,
3582 struct isl_tab *tab)
3584 struct isl_basic_set *bset;
3585 struct isl_mat *mat = NULL;
3598 n_out = tab->n_var - tab->n_param - tab->n_div;
3599 mat = isl_mat_alloc(tab->mat->ctx, 1 + n_out, 1 + tab->n_param + tab->n_div);
3603 isl_seq_clr(mat->row[0] + 1, mat->n_col - 1);
3604 isl_int_set_si(mat->row[0][0], 1);
3605 for (row = 0; row < n_out; ++row) {
3606 int i = tab->n_param + row;
3609 isl_seq_clr(mat->row[1 + row], mat->n_col);
3610 if (!tab->var[i].is_row)
3613 r = tab->var[i].index;
3616 isl_assert(mat->ctx, isl_int_eq(tab->mat->row[r][2],
3617 tab->mat->row[r][0]),
3619 isl_int_set(mat->row[1 + row][0], tab->mat->row[r][1]);
3620 for (j = 0; j < tab->n_param; ++j) {
3622 if (tab->var[j].is_row)
3624 col = tab->var[j].index;
3625 isl_int_set(mat->row[1 + row][1 + j],
3626 tab->mat->row[r][off + col]);
3628 for (j = 0; j < tab->n_div; ++j) {
3630 if (tab->var[tab->n_var - tab->n_div+j].is_row)
3632 col = tab->var[tab->n_var - tab->n_div+j].index;
3633 isl_int_set(mat->row[1 + row][1 + tab->n_param + j],
3634 tab->mat->row[r][off + col]);
3636 if (!isl_int_is_one(tab->mat->row[r][0]))
3637 isl_seq_scale_down(mat->row[1 + row], mat->row[1 + row],
3638 tab->mat->row[r][0], mat->n_col);
3640 isl_seq_neg(mat->row[1 + row], mat->row[1 + row],
3644 bset = sol->sol.context->op->peek_basic_set(sol->sol.context);
3645 bset = isl_basic_set_dup(bset);
3646 bset = isl_basic_set_finalize(bset);
3648 if (sol->fn(bset, isl_mat_copy(mat), sol->user) < 0)
3655 sol_free(&sol->sol);
3659 static struct isl_sol *sol_for_add_wrap(struct isl_sol *sol,
3660 struct isl_tab *tab)
3662 return (struct isl_sol *)sol_for_add((struct isl_sol_for *)sol, tab);
3665 static struct isl_sol_for *sol_for_init(struct isl_basic_map *bmap, int max,
3666 int (*fn)(__isl_take isl_basic_set *dom, __isl_take isl_mat *map,
3670 struct isl_sol_for *sol_for = NULL;
3671 struct isl_dim *dom_dim;
3672 struct isl_basic_set *dom = NULL;
3674 sol_for = isl_calloc_type(bset->ctx, struct isl_sol_for);
3678 dom_dim = isl_dim_domain(isl_dim_copy(bmap->dim));
3679 dom = isl_basic_set_universe(dom_dim);
3682 sol_for->user = user;
3684 sol_for->sol.add = &sol_for_add_wrap;
3685 sol_for->sol.free = &sol_for_free_wrap;
3687 sol_for->sol.context = isl_context_alloc(dom);
3688 if (!sol_for->sol.context)
3691 isl_basic_set_free(dom);
3694 isl_basic_set_free(dom);
3695 sol_for_free(sol_for);
3699 static struct isl_sol_for *sol_for_find_solutions(struct isl_sol_for *sol_for,
3700 struct isl_tab *tab)
3702 return (struct isl_sol_for *)find_solutions_main(&sol_for->sol, tab);
3705 int isl_basic_map_foreach_lexopt(__isl_keep isl_basic_map *bmap, int max,
3706 int (*fn)(__isl_take isl_basic_set *dom, __isl_take isl_mat *map,
3710 struct isl_sol_for *sol_for = NULL;
3712 bmap = isl_basic_map_copy(bmap);
3716 bmap = isl_basic_map_detect_equalities(bmap);
3717 sol_for = sol_for_init(bmap, max, fn, user);
3719 if (isl_basic_map_fast_is_empty(bmap))
3722 struct isl_tab *tab;
3723 struct isl_context *context = sol_for->sol.context;
3724 tab = tab_for_lexmin(bmap,
3725 context->op->peek_basic_set(context), 1, max);
3726 tab = context->op->detect_nonnegative_parameters(context, tab);
3727 sol_for = sol_for_find_solutions(sol_for, tab);
3732 sol_for_free(sol_for);
3733 isl_basic_map_free(bmap);
3736 sol_for_free(sol_for);
3737 isl_basic_map_free(bmap);
3741 int isl_basic_map_foreach_lexmin(__isl_keep isl_basic_map *bmap,
3742 int (*fn)(__isl_take isl_basic_set *dom, __isl_take isl_mat *map,
3746 return isl_basic_map_foreach_lexopt(bmap, 0, fn, user);
3749 int isl_basic_map_foreach_lexmax(__isl_keep isl_basic_map *bmap,
3750 int (*fn)(__isl_take isl_basic_set *dom, __isl_take isl_mat *map,
3754 return isl_basic_map_foreach_lexopt(bmap, 1, fn, user);