+/*
+ * Copyright 2008-2009 Katholieke Universiteit Leuven
+ * Copyright 2010 INRIA Saclay
+ *
+ * Use of this software is governed by the MIT license
+ *
+ * Written by Sven Verdoolaege, K.U.Leuven, Departement
+ * Computerwetenschappen, Celestijnenlaan 200A, B-3001 Leuven, Belgium
+ * and INRIA Saclay - Ile-de-France, Parc Club Orsay Universite,
+ * ZAC des vignes, 4 rue Jacques Monod, 91893 Orsay, France
+ */
+
+#include <isl_ctx_private.h>
#include "isl_map_private.h"
-#include "isl_seq.h"
+#include <isl/seq.h>
#include "isl_tab.h"
+#include "isl_sample.h"
+#include <isl_mat_private.h>
+#include <isl_aff_private.h>
+#include <isl_options_private.h>
+#include <isl_config.h>
/*
* The implementation of parametric integer linear programming in this file
* The strategy used for obtaining a feasible solution is different
* from the one used in isl_tab.c. In particular, in isl_tab.c,
* upon finding a constraint that is not yet satisfied, we pivot
- * in a row that increases the constant term of row holding the
+ * in a row that increases the constant term of the row holding the
* constraint, making sure the sample solution remains feasible
* for all the constraints it already satisfied.
* Here, we always pivot in the row holding the constraint,
* then the initial sample value may be chosen equal to zero.
* However, we will not make this assumption. Instead, we apply
* the "big parameter" trick. Any variable x is then not directly
- * used in the tableau, but instead it its represented by another
+ * used in the tableau, but instead it is represented by another
* variable x' = M + x, where M is an arbitrarily large (positive)
* value. x' is therefore always non-negative, whatever the value of x.
- * Taking as initial smaple value x' = 0 corresponds to x = -M,
+ * Taking as initial sample value x' = 0 corresponds to x = -M,
* which is always smaller than any possible value of x.
*
- * We use the big parameter trick both in the main tableau and
- * the context tableau, each of course having its own big parameter.
+ * The big parameter trick is used in the main tableau and
+ * also in the context tableau if isl_context_lex is used.
+ * In this case, each tableaus has its own big parameter.
* Before doing any real work, we check if all the parameters
* happen to be non-negative. If so, we drop the column corresponding
* to M from the initial context tableau.
+ * If isl_context_gbr is used, then the big parameter trick is only
+ * used in the main tableau.
+ */
+
+struct isl_context;
+struct isl_context_op {
+ /* detect nonnegative parameters in context and mark them in tab */
+ struct isl_tab *(*detect_nonnegative_parameters)(
+ struct isl_context *context, struct isl_tab *tab);
+ /* return temporary reference to basic set representation of context */
+ struct isl_basic_set *(*peek_basic_set)(struct isl_context *context);
+ /* return temporary reference to tableau representation of context */
+ struct isl_tab *(*peek_tab)(struct isl_context *context);
+ /* add equality; check is 1 if eq may not be valid;
+ * update is 1 if we may want to call ineq_sign on context later.
+ */
+ void (*add_eq)(struct isl_context *context, isl_int *eq,
+ int check, int update);
+ /* add inequality; check is 1 if ineq may not be valid;
+ * update is 1 if we may want to call ineq_sign on context later.
+ */
+ void (*add_ineq)(struct isl_context *context, isl_int *ineq,
+ int check, int update);
+ /* check sign of ineq based on previous information.
+ * strict is 1 if saturation should be treated as a positive sign.
+ */
+ enum isl_tab_row_sign (*ineq_sign)(struct isl_context *context,
+ isl_int *ineq, int strict);
+ /* check if inequality maintains feasibility */
+ int (*test_ineq)(struct isl_context *context, isl_int *ineq);
+ /* return index of a div that corresponds to "div" */
+ int (*get_div)(struct isl_context *context, struct isl_tab *tab,
+ struct isl_vec *div);
+ /* add div "div" to context and return non-negativity */
+ int (*add_div)(struct isl_context *context, struct isl_vec *div);
+ int (*detect_equalities)(struct isl_context *context,
+ struct isl_tab *tab);
+ /* return row index of "best" split */
+ int (*best_split)(struct isl_context *context, struct isl_tab *tab);
+ /* check if context has already been determined to be empty */
+ int (*is_empty)(struct isl_context *context);
+ /* check if context is still usable */
+ int (*is_ok)(struct isl_context *context);
+ /* save a copy/snapshot of context */
+ void *(*save)(struct isl_context *context);
+ /* restore saved context */
+ void (*restore)(struct isl_context *context, void *);
+ /* discard saved context */
+ void (*discard)(void *);
+ /* invalidate context */
+ void (*invalidate)(struct isl_context *context);
+ /* free context */
+ void (*free)(struct isl_context *context);
+};
+
+struct isl_context {
+ struct isl_context_op *op;
+};
+
+struct isl_context_lex {
+ struct isl_context context;
+ struct isl_tab *tab;
+};
+
+/* A stack (linked list) of solutions of subtrees of the search space.
+ *
+ * "M" describes the solution in terms of the dimensions of "dom".
+ * The number of columns of "M" is one more than the total number
+ * of dimensions of "dom".
+ *
+ * If "M" is NULL, then there is no solution on "dom".
*/
+struct isl_partial_sol {
+ int level;
+ struct isl_basic_set *dom;
+ struct isl_mat *M;
+
+ struct isl_partial_sol *next;
+};
+
+struct isl_sol;
+struct isl_sol_callback {
+ struct isl_tab_callback callback;
+ struct isl_sol *sol;
+};
/* isl_sol is an interface for constructing a solution to
* a parametric integer linear programming problem.
* the solution.
*/
struct isl_sol {
- struct isl_tab *context_tab;
- struct isl_sol *(*add)(struct isl_sol *sol, struct isl_tab *tab);
+ int error;
+ int rational;
+ int level;
+ int max;
+ int n_out;
+ struct isl_context *context;
+ struct isl_partial_sol *partial;
+ void (*add)(struct isl_sol *sol,
+ struct isl_basic_set *dom, struct isl_mat *M);
+ void (*add_empty)(struct isl_sol *sol, struct isl_basic_set *bset);
void (*free)(struct isl_sol *sol);
+ struct isl_sol_callback dec_level;
};
static void sol_free(struct isl_sol *sol)
{
+ struct isl_partial_sol *partial, *next;
if (!sol)
return;
+ for (partial = sol->partial; partial; partial = next) {
+ next = partial->next;
+ isl_basic_set_free(partial->dom);
+ isl_mat_free(partial->M);
+ free(partial);
+ }
sol->free(sol);
}
-struct isl_sol_map {
- struct isl_sol sol;
- struct isl_map *map;
- struct isl_set *empty;
- int max;
-};
-
-static void sol_map_free(struct isl_sol_map *sol_map)
+/* Push a partial solution represented by a domain and mapping M
+ * onto the stack of partial solutions.
+ */
+static void sol_push_sol(struct isl_sol *sol,
+ struct isl_basic_set *dom, struct isl_mat *M)
{
- isl_tab_free(sol_map->sol.context_tab);
- isl_map_free(sol_map->map);
- isl_set_free(sol_map->empty);
- free(sol_map);
+ struct isl_partial_sol *partial;
+
+ if (sol->error || !dom)
+ goto error;
+
+ partial = isl_alloc_type(dom->ctx, struct isl_partial_sol);
+ if (!partial)
+ goto error;
+
+ partial->level = sol->level;
+ partial->dom = dom;
+ partial->M = M;
+ partial->next = sol->partial;
+
+ sol->partial = partial;
+
+ return;
+error:
+ isl_basic_set_free(dom);
+ isl_mat_free(M);
+ sol->error = 1;
}
-static void sol_map_free_wrap(struct isl_sol *sol)
+/* Pop one partial solution from the partial solution stack and
+ * pass it on to sol->add or sol->add_empty.
+ */
+static void sol_pop_one(struct isl_sol *sol)
{
- sol_map_free((struct isl_sol_map *)sol);
+ struct isl_partial_sol *partial;
+
+ partial = sol->partial;
+ sol->partial = partial->next;
+
+ if (partial->M)
+ sol->add(sol, partial->dom, partial->M);
+ else
+ sol->add_empty(sol, partial->dom);
+ free(partial);
}
-static struct isl_sol_map *add_empty(struct isl_sol_map *sol)
+/* Return a fresh copy of the domain represented by the context tableau.
+ */
+static struct isl_basic_set *sol_domain(struct isl_sol *sol)
{
struct isl_basic_set *bset;
- if (!sol->empty)
- return sol;
- sol->empty = isl_set_grow(sol->empty, 1);
- bset = isl_basic_set_copy(sol->sol.context_tab->bset);
- bset = isl_basic_set_simplify(bset);
- bset = isl_basic_set_finalize(bset);
- sol->empty = isl_set_add(sol->empty, bset);
- if (!sol->empty)
- goto error;
- return sol;
-error:
- sol_map_free(sol);
- return NULL;
+ if (sol->error)
+ return NULL;
+
+ bset = isl_basic_set_dup(sol->context->op->peek_basic_set(sol->context));
+ bset = isl_basic_set_update_from_tab(bset,
+ sol->context->op->peek_tab(sol->context));
+
+ return bset;
+}
+
+/* Check whether two partial solutions have the same mapping, where n_div
+ * is the number of divs that the two partial solutions have in common.
+ */
+static int same_solution(struct isl_partial_sol *s1, struct isl_partial_sol *s2,
+ unsigned n_div)
+{
+ int i;
+ unsigned dim;
+
+ if (!s1->M != !s2->M)
+ return 0;
+ if (!s1->M)
+ return 1;
+
+ dim = isl_basic_set_total_dim(s1->dom) - s1->dom->n_div;
+
+ for (i = 0; i < s1->M->n_row; ++i) {
+ if (isl_seq_first_non_zero(s1->M->row[i]+1+dim+n_div,
+ s1->M->n_col-1-dim-n_div) != -1)
+ return 0;
+ if (isl_seq_first_non_zero(s2->M->row[i]+1+dim+n_div,
+ s2->M->n_col-1-dim-n_div) != -1)
+ return 0;
+ if (!isl_seq_eq(s1->M->row[i], s2->M->row[i], 1+dim+n_div))
+ return 0;
+ }
+ return 1;
+}
+
+/* Pop all solutions from the partial solution stack that were pushed onto
+ * the stack at levels that are deeper than the current level.
+ * If the two topmost elements on the stack have the same level
+ * and represent the same solution, then their domains are combined.
+ * This combined domain is the same as the current context domain
+ * as sol_pop is called each time we move back to a higher level.
+ */
+static void sol_pop(struct isl_sol *sol)
+{
+ struct isl_partial_sol *partial;
+ unsigned n_div;
+
+ if (sol->error)
+ return;
+
+ if (sol->level == 0) {
+ for (partial = sol->partial; partial; partial = sol->partial)
+ sol_pop_one(sol);
+ return;
+ }
+
+ partial = sol->partial;
+ if (!partial)
+ return;
+
+ if (partial->level <= sol->level)
+ return;
+
+ if (partial->next && partial->next->level == partial->level) {
+ n_div = isl_basic_set_dim(
+ sol->context->op->peek_basic_set(sol->context),
+ isl_dim_div);
+
+ if (!same_solution(partial, partial->next, n_div)) {
+ sol_pop_one(sol);
+ sol_pop_one(sol);
+ } else {
+ struct isl_basic_set *bset;
+ isl_mat *M;
+ unsigned n;
+
+ n = isl_basic_set_dim(partial->next->dom, isl_dim_div);
+ n -= n_div;
+ bset = sol_domain(sol);
+ isl_basic_set_free(partial->next->dom);
+ partial->next->dom = bset;
+ M = partial->next->M;
+ if (M) {
+ M = isl_mat_drop_cols(M, M->n_col - n, n);
+ partial->next->M = M;
+ if (!M)
+ goto error;
+ }
+ partial->next->level = sol->level;
+
+ if (!bset)
+ goto error;
+
+ sol->partial = partial->next;
+ isl_basic_set_free(partial->dom);
+ isl_mat_free(partial->M);
+ free(partial);
+ }
+ } else
+ sol_pop_one(sol);
+
+ if (0)
+error: sol->error = 1;
+}
+
+static void sol_dec_level(struct isl_sol *sol)
+{
+ if (sol->error)
+ return;
+
+ sol->level--;
+
+ sol_pop(sol);
+}
+
+static int sol_dec_level_wrap(struct isl_tab_callback *cb)
+{
+ struct isl_sol_callback *callback = (struct isl_sol_callback *)cb;
+
+ sol_dec_level(callback->sol);
+
+ return callback->sol->error ? -1 : 0;
+}
+
+/* Move down to next level and push callback onto context tableau
+ * to decrease the level again when it gets rolled back across
+ * the current state. That is, dec_level will be called with
+ * the context tableau in the same state as it is when inc_level
+ * is called.
+ */
+static void sol_inc_level(struct isl_sol *sol)
+{
+ struct isl_tab *tab;
+
+ if (sol->error)
+ return;
+
+ sol->level++;
+ tab = sol->context->op->peek_tab(sol->context);
+ if (isl_tab_push_callback(tab, &sol->dec_level.callback) < 0)
+ sol->error = 1;
+}
+
+static void scale_rows(struct isl_mat *mat, isl_int m, int n_row)
+{
+ int i;
+
+ if (isl_int_is_one(m))
+ return;
+
+ for (i = 0; i < n_row; ++i)
+ isl_seq_scale(mat->row[i], mat->row[i], m, mat->n_col);
}
/* Add the solution identified by the tableau and the context tableau.
* dimensions in the input map
* tab->n_div is equal to the number of divs in the context
*
- * If there is no solution, then the basic set corresponding to the
- * context tableau is added to the set "empty".
+ * If there is no solution, then call add_empty with a basic set
+ * that corresponds to the context tableau. (If add_empty is NULL,
+ * then do nothing).
*
- * Otherwise, a basic map is constructed with the same parameters
- * and divs as the context, the dimensions of the context as input
- * dimensions and a number of output dimensions that is equal to
- * the number of output dimensions in the input map.
+ * If there is a solution, then first construct a matrix that maps
+ * all dimensions of the context to the output variables, i.e.,
+ * the output dimensions in the input map.
* The divs in the input map (if any) that do not correspond to any
* div in the context do not appear in the solution.
* The algorithm will make sure that they have an integer value,
* but these values themselves are of no interest.
+ * We have to be careful not to drop or rearrange any divs in the
+ * context because that would change the meaning of the matrix.
*
- * The constraints and divs of the context are simply copied
- * fron context_tab->bset.
* To extract the value of the output variables, it should be noted
- * that we always use a big parameter M and so the variable stored
- * in the tableau is not an output variable x itself, but
+ * that we always use a big parameter M in the main tableau and so
+ * the variable stored in this tableau is not an output variable x itself, but
* x' = M + x (in case of minimization)
* or
* x' = M - x (in case of maximization)
* are bounded, so this cannot occur.
* Similarly, when x' appears in a row, then the coefficient of M in that
* row is necessarily 1.
- * If the row represents
+ * If the row in the tableau represents
* d x' = c + d M + e(y)
- * then, in case of minimization, an equality
- * c + e(y) - d x' = 0
- * is added, and in case of maximization,
- * c + e(y) + d x' = 0
+ * then, in case of minimization, the corresponding row in the matrix
+ * will be
+ * a c + a e(y)
+ * with a d = m, the (updated) common denominator of the matrix.
+ * In case of maximization, the row will be
+ * -a c - a e(y)
*/
-static struct isl_sol_map *sol_map_add(struct isl_sol_map *sol,
- struct isl_tab *tab)
+static void sol_add(struct isl_sol *sol, struct isl_tab *tab)
+{
+ struct isl_basic_set *bset = NULL;
+ struct isl_mat *mat = NULL;
+ unsigned off;
+ int row;
+ isl_int m;
+
+ if (sol->error || !tab)
+ goto error;
+
+ if (tab->empty && !sol->add_empty)
+ return;
+ if (sol->context->op->is_empty(sol->context))
+ return;
+
+ bset = sol_domain(sol);
+
+ if (tab->empty) {
+ sol_push_sol(sol, bset, NULL);
+ return;
+ }
+
+ off = 2 + tab->M;
+
+ mat = isl_mat_alloc(tab->mat->ctx, 1 + sol->n_out,
+ 1 + tab->n_param + tab->n_div);
+ if (!mat)
+ goto error;
+
+ isl_int_init(m);
+
+ isl_seq_clr(mat->row[0] + 1, mat->n_col - 1);
+ isl_int_set_si(mat->row[0][0], 1);
+ for (row = 0; row < sol->n_out; ++row) {
+ int i = tab->n_param + row;
+ int r, j;
+
+ isl_seq_clr(mat->row[1 + row], mat->n_col);
+ if (!tab->var[i].is_row) {
+ if (tab->M)
+ isl_die(mat->ctx, isl_error_invalid,
+ "unbounded optimum", goto error2);
+ continue;
+ }
+
+ r = tab->var[i].index;
+ if (tab->M &&
+ isl_int_ne(tab->mat->row[r][2], tab->mat->row[r][0]))
+ isl_die(mat->ctx, isl_error_invalid,
+ "unbounded optimum", goto error2);
+ isl_int_gcd(m, mat->row[0][0], tab->mat->row[r][0]);
+ isl_int_divexact(m, tab->mat->row[r][0], m);
+ scale_rows(mat, m, 1 + row);
+ isl_int_divexact(m, mat->row[0][0], tab->mat->row[r][0]);
+ isl_int_mul(mat->row[1 + row][0], m, tab->mat->row[r][1]);
+ for (j = 0; j < tab->n_param; ++j) {
+ int col;
+ if (tab->var[j].is_row)
+ continue;
+ col = tab->var[j].index;
+ isl_int_mul(mat->row[1 + row][1 + j], m,
+ tab->mat->row[r][off + col]);
+ }
+ for (j = 0; j < tab->n_div; ++j) {
+ int col;
+ if (tab->var[tab->n_var - tab->n_div+j].is_row)
+ continue;
+ col = tab->var[tab->n_var - tab->n_div+j].index;
+ isl_int_mul(mat->row[1 + row][1 + tab->n_param + j], m,
+ tab->mat->row[r][off + col]);
+ }
+ if (sol->max)
+ isl_seq_neg(mat->row[1 + row], mat->row[1 + row],
+ mat->n_col);
+ }
+
+ isl_int_clear(m);
+
+ sol_push_sol(sol, bset, mat);
+ return;
+error2:
+ isl_int_clear(m);
+error:
+ isl_basic_set_free(bset);
+ isl_mat_free(mat);
+ sol->error = 1;
+}
+
+struct isl_sol_map {
+ struct isl_sol sol;
+ struct isl_map *map;
+ struct isl_set *empty;
+};
+
+static void sol_map_free(struct isl_sol_map *sol_map)
+{
+ if (!sol_map)
+ return;
+ if (sol_map->sol.context)
+ sol_map->sol.context->op->free(sol_map->sol.context);
+ isl_map_free(sol_map->map);
+ isl_set_free(sol_map->empty);
+ free(sol_map);
+}
+
+static void sol_map_free_wrap(struct isl_sol *sol)
+{
+ sol_map_free((struct isl_sol_map *)sol);
+}
+
+/* This function is called for parts of the context where there is
+ * no solution, with "bset" corresponding to the context tableau.
+ * Simply add the basic set to the set "empty".
+ */
+static void sol_map_add_empty(struct isl_sol_map *sol,
+ struct isl_basic_set *bset)
+{
+ if (!bset)
+ goto error;
+ isl_assert(bset->ctx, sol->empty, goto error);
+
+ sol->empty = isl_set_grow(sol->empty, 1);
+ bset = isl_basic_set_simplify(bset);
+ bset = isl_basic_set_finalize(bset);
+ sol->empty = isl_set_add_basic_set(sol->empty, isl_basic_set_copy(bset));
+ if (!sol->empty)
+ goto error;
+ isl_basic_set_free(bset);
+ return;
+error:
+ isl_basic_set_free(bset);
+ sol->sol.error = 1;
+}
+
+static void sol_map_add_empty_wrap(struct isl_sol *sol,
+ struct isl_basic_set *bset)
+{
+ sol_map_add_empty((struct isl_sol_map *)sol, bset);
+}
+
+/* Given a basic map "dom" that represents the context and an affine
+ * matrix "M" that maps the dimensions of the context to the
+ * output variables, construct a basic map with the same parameters
+ * and divs as the context, the dimensions of the context as input
+ * dimensions and a number of output dimensions that is equal to
+ * the number of output dimensions in the input map.
+ *
+ * The constraints and divs of the context are simply copied
+ * from "dom". For each row
+ * x = c + e(y)
+ * an equality
+ * c + e(y) - d x = 0
+ * is added, with d the common denominator of M.
+ */
+static void sol_map_add(struct isl_sol_map *sol,
+ struct isl_basic_set *dom, struct isl_mat *M)
{
int i;
struct isl_basic_map *bmap = NULL;
- struct isl_tab *context_tab;
unsigned n_eq;
unsigned n_ineq;
unsigned nparam;
unsigned total;
unsigned n_div;
unsigned n_out;
- unsigned off;
- if (!sol || !tab)
+ if (sol->sol.error || !dom || !M)
goto error;
- if (tab->empty)
- return add_empty(sol);
-
- context_tab = sol->sol.context_tab;
- off = 2 + tab->M;
- n_out = isl_map_dim(sol->map, isl_dim_out);
- n_eq = context_tab->bset->n_eq + n_out;
- n_ineq = context_tab->bset->n_ineq;
- nparam = tab->n_param;
+ n_out = sol->sol.n_out;
+ n_eq = dom->n_eq + n_out;
+ n_ineq = dom->n_ineq;
+ n_div = dom->n_div;
+ nparam = isl_basic_set_total_dim(dom) - n_div;
total = isl_map_dim(sol->map, isl_dim_all);
- bmap = isl_basic_map_alloc_dim(isl_map_get_dim(sol->map),
- tab->n_div, n_eq, 2 * tab->n_div + n_ineq);
+ bmap = isl_basic_map_alloc_space(isl_map_get_space(sol->map),
+ n_div, n_eq, 2 * n_div + n_ineq);
if (!bmap)
goto error;
- n_div = tab->n_div;
- if (tab->rational)
+ if (sol->sol.rational)
ISL_F_SET(bmap, ISL_BASIC_MAP_RATIONAL);
- for (i = 0; i < context_tab->bset->n_div; ++i) {
+ for (i = 0; i < dom->n_div; ++i) {
int k = isl_basic_map_alloc_div(bmap);
if (k < 0)
goto error;
- isl_seq_cpy(bmap->div[k],
- context_tab->bset->div[i], 1 + 1 + nparam);
+ isl_seq_cpy(bmap->div[k], dom->div[i], 1 + 1 + nparam);
isl_seq_clr(bmap->div[k] + 1 + 1 + nparam, total - nparam);
isl_seq_cpy(bmap->div[k] + 1 + 1 + total,
- context_tab->bset->div[i] + 1 + 1 + nparam, i);
+ dom->div[i] + 1 + 1 + nparam, i);
}
- for (i = 0; i < context_tab->bset->n_eq; ++i) {
+ for (i = 0; i < dom->n_eq; ++i) {
int k = isl_basic_map_alloc_equality(bmap);
if (k < 0)
goto error;
- isl_seq_cpy(bmap->eq[k], context_tab->bset->eq[i], 1 + nparam);
+ isl_seq_cpy(bmap->eq[k], dom->eq[i], 1 + nparam);
isl_seq_clr(bmap->eq[k] + 1 + nparam, total - nparam);
isl_seq_cpy(bmap->eq[k] + 1 + total,
- context_tab->bset->eq[i] + 1 + nparam, n_div);
+ dom->eq[i] + 1 + nparam, n_div);
}
- for (i = 0; i < context_tab->bset->n_ineq; ++i) {
+ for (i = 0; i < dom->n_ineq; ++i) {
int k = isl_basic_map_alloc_inequality(bmap);
if (k < 0)
goto error;
- isl_seq_cpy(bmap->ineq[k],
- context_tab->bset->ineq[i], 1 + nparam);
+ isl_seq_cpy(bmap->ineq[k], dom->ineq[i], 1 + nparam);
isl_seq_clr(bmap->ineq[k] + 1 + nparam, total - nparam);
isl_seq_cpy(bmap->ineq[k] + 1 + total,
- context_tab->bset->ineq[i] + 1 + nparam, n_div);
+ dom->ineq[i] + 1 + nparam, n_div);
}
- for (i = tab->n_param; i < total; ++i) {
+ for (i = 0; i < M->n_row - 1; ++i) {
int k = isl_basic_map_alloc_equality(bmap);
if (k < 0)
goto error;
- isl_seq_clr(bmap->eq[k] + 1, isl_basic_map_total_dim(bmap));
- if (!tab->var[i].is_row) {
- /* no unbounded */
- isl_assert(bmap->ctx, !tab->M, goto error);
- isl_int_set_si(bmap->eq[k][0], 0);
- if (sol->max)
- isl_int_set_si(bmap->eq[k][1 + i], 1);
- else
- isl_int_set_si(bmap->eq[k][1 + i], -1);
- } else {
- int row, j;
- row = tab->var[i].index;
- /* no unbounded */
- if (tab->M)
- isl_assert(bmap->ctx,
- isl_int_eq(tab->mat->row[row][2],
- tab->mat->row[row][0]),
- goto error);
- isl_int_set(bmap->eq[k][0], tab->mat->row[row][1]);
- for (j = 0; j < tab->n_param; ++j) {
- int col;
- if (tab->var[j].is_row)
- continue;
- col = tab->var[j].index;
- isl_int_set(bmap->eq[k][1 + j],
- tab->mat->row[row][off + col]);
- }
- for (j = 0; j < tab->n_div; ++j) {
- int col;
- if (tab->var[tab->n_var - tab->n_div+j].is_row)
- continue;
- col = tab->var[tab->n_var - tab->n_div+j].index;
- isl_int_set(bmap->eq[k][1 + total + j],
- tab->mat->row[row][off + col]);
- }
- if (sol->max)
- isl_int_set(bmap->eq[k][1 + i],
- tab->mat->row[row][0]);
- else
- isl_int_neg(bmap->eq[k][1 + i],
- tab->mat->row[row][0]);
- }
+ isl_seq_cpy(bmap->eq[k], M->row[1 + i], 1 + nparam);
+ isl_seq_clr(bmap->eq[k] + 1 + nparam, n_out);
+ isl_int_neg(bmap->eq[k][1 + nparam + i], M->row[0][0]);
+ isl_seq_cpy(bmap->eq[k] + 1 + nparam + n_out,
+ M->row[1 + i] + 1 + nparam, n_div);
}
- bmap = isl_basic_map_gauss(bmap, NULL);
- bmap = isl_basic_map_normalize_constraints(bmap);
+ bmap = isl_basic_map_simplify(bmap);
bmap = isl_basic_map_finalize(bmap);
sol->map = isl_map_grow(sol->map, 1);
- sol->map = isl_map_add(sol->map, bmap);
+ sol->map = isl_map_add_basic_map(sol->map, bmap);
+ isl_basic_set_free(dom);
+ isl_mat_free(M);
if (!sol->map)
- goto error;
- return sol;
+ sol->sol.error = 1;
+ return;
error:
+ isl_basic_set_free(dom);
+ isl_mat_free(M);
isl_basic_map_free(bmap);
- sol_free(&sol->sol);
- return NULL;
+ sol->sol.error = 1;
}
-static struct isl_sol *sol_map_add_wrap(struct isl_sol *sol,
- struct isl_tab *tab)
+static void sol_map_add_wrap(struct isl_sol *sol,
+ struct isl_basic_set *dom, struct isl_mat *M)
{
- return (struct isl_sol *)sol_map_add((struct isl_sol_map *)sol, tab);
+ sol_map_add((struct isl_sol_map *)sol, dom, M);
}
return ineq;
}
-/* Return a integer division for use in a parametric cut based on the given row.
- * In particular, let the parametric constant of the row be
+/* Normalize a div expression of the form
*
- * \sum_i a_i y_i
+ * [(g*f(x) + c)/(g * m)]
*
- * where y_0 = 1, but none of the y_i corresponds to the big parameter M.
- * The div returned is equal to
+ * with c the constant term and f(x) the remaining coefficients, to
*
- * floor(\sum_i {-a_i} y_i) = floor((\sum_i (-a_i mod d) y_i)/d)
+ * [(f(x) + [c/g])/m]
*/
-static struct isl_vec *get_row_parameter_div(struct isl_tab *tab, int row)
+static void normalize_div(__isl_keep isl_vec *div)
{
- struct isl_vec *div;
+ isl_ctx *ctx = isl_vec_get_ctx(div);
+ int len = div->size - 2;
+
+ isl_seq_gcd(div->el + 2, len, &ctx->normalize_gcd);
+ isl_int_gcd(ctx->normalize_gcd, ctx->normalize_gcd, div->el[0]);
+
+ if (isl_int_is_one(ctx->normalize_gcd))
+ return;
+
+ isl_int_divexact(div->el[0], div->el[0], ctx->normalize_gcd);
+ isl_int_fdiv_q(div->el[1], div->el[1], ctx->normalize_gcd);
+ isl_seq_scale_down(div->el + 2, div->el + 2, ctx->normalize_gcd, len);
+}
+
+/* Return a integer division for use in a parametric cut based on the given row.
+ * In particular, let the parametric constant of the row be
+ *
+ * \sum_i a_i y_i
+ *
+ * where y_0 = 1, but none of the y_i corresponds to the big parameter M.
+ * The div returned is equal to
+ *
+ * floor(\sum_i {-a_i} y_i) = floor((\sum_i (-a_i mod d) y_i)/d)
+ */
+static struct isl_vec *get_row_parameter_div(struct isl_tab *tab, int row)
+{
+ struct isl_vec *div;
div = isl_vec_alloc(tab->mat->ctx, 1 + 1 + tab->n_param + tab->n_div);
if (!div)
isl_int_set(div->el[0], tab->mat->row[row][0]);
get_row_parameter_line(tab, row, div->el + 1);
- div = isl_vec_normalize(div);
isl_seq_neg(div->el + 1, div->el + 1, div->size - 1);
+ normalize_div(div);
isl_seq_fdiv_r(div->el + 1, div->el + 1, div->el[0], div->size - 1);
return div;
isl_int_set(div->el[0], tab->mat->row[row][0]);
get_row_parameter_line(tab, row, div->el + 1);
- div = isl_vec_normalize(div);
+ normalize_div(div);
isl_seq_fdiv_r(div->el + 1, div->el + 1, div->el[0], div->size - 1);
return div;
unsigned div_pos;
struct isl_vec *ineq;
+ if (!bset)
+ return NULL;
+
total = isl_basic_set_total_dim(bset);
div_pos = 1 + total - bset->n_div + div;
}
/* Given a row in the tableau and a div that was created
- * using get_row_split_div and that been constrained to equality, i.e.,
+ * using get_row_split_div and that has been constrained to equality, i.e.,
*
* d = floor(\sum_i {a_i} y_i) = \sum_i {a_i} y_i
*
*/
static struct isl_tab *set_row_cst_to_div(struct isl_tab *tab, int row, int div)
{
- int col;
- unsigned off = 2 + tab->M;
-
isl_seq_fdiv_q(tab->mat->row[row] + 1, tab->mat->row[row] + 1,
tab->mat->row[row][0], 1 + tab->M + tab->n_col);
isl_int_set_si(tab->mat->row[row][0], 1);
- isl_assert(tab->mat->ctx,
- !tab->var[tab->n_var - tab->n_div + div].is_row, goto error);
+ if (tab->var[tab->n_var - tab->n_div + div].is_row) {
+ int drow = tab->var[tab->n_var - tab->n_div + div].index;
+
+ isl_assert(tab->mat->ctx,
+ isl_int_is_one(tab->mat->row[drow][0]), goto error);
+ isl_seq_combine(tab->mat->row[row] + 1,
+ tab->mat->ctx->one, tab->mat->row[row] + 1,
+ tab->mat->ctx->one, tab->mat->row[drow] + 1,
+ 1 + tab->M + tab->n_col);
+ } else {
+ int dcol = tab->var[tab->n_var - tab->n_div + div].index;
- col = tab->var[tab->n_var - tab->n_div + div].index;
- isl_int_set_si(tab->mat->row[row][off + col], 1);
+ isl_int_add_ui(tab->mat->row[row][2 + tab->M + dcol],
+ tab->mat->row[row][2 + tab->M + dcol], 1);
+ }
return tab;
error:
}
/* Return the first known violated constraint, i.e., a non-negative
- * contraint that currently has an either obviously negative value
+ * constraint that currently has an either obviously negative value
* or a previously determined to be negative value.
*
* If any constraint has a negative coefficient for the big parameter,
for (row = tab->n_redundant; row < tab->n_row; ++row) {
if (!isl_tab_var_from_row(tab, row)->is_nonneg)
continue;
- if (isl_int_is_neg(tab->mat->row[row][2]))
- return row;
+ if (!isl_int_is_neg(tab->mat->row[row][2]))
+ continue;
+ if (tab->row_sign)
+ tab->row_sign[row] = isl_tab_row_neg;
+ return row;
}
for (row = tab->n_redundant; row < tab->n_row; ++row) {
if (!isl_tab_var_from_row(tab, row)->is_nonneg)
return -1;
}
+/* Check whether the invariant that all columns are lexico-positive
+ * is satisfied. This function is not called from the current code
+ * but is useful during debugging.
+ */
+static void check_lexpos(struct isl_tab *tab) __attribute__ ((unused));
+static void check_lexpos(struct isl_tab *tab)
+{
+ unsigned off = 2 + tab->M;
+ int col;
+ int var;
+ int row;
+
+ for (col = tab->n_dead; col < tab->n_col; ++col) {
+ if (tab->col_var[col] >= 0 &&
+ (tab->col_var[col] < tab->n_param ||
+ tab->col_var[col] >= tab->n_var - tab->n_div))
+ continue;
+ for (var = tab->n_param; var < tab->n_var - tab->n_div; ++var) {
+ if (!tab->var[var].is_row) {
+ if (tab->var[var].index == col)
+ break;
+ else
+ continue;
+ }
+ row = tab->var[var].index;
+ if (isl_int_is_zero(tab->mat->row[row][off + col]))
+ continue;
+ if (isl_int_is_pos(tab->mat->row[row][off + col]))
+ break;
+ fprintf(stderr, "lexneg column %d (row %d)\n",
+ col, row);
+ }
+ if (var >= tab->n_var - tab->n_div)
+ fprintf(stderr, "zero column %d\n", col);
+ }
+}
+
+/* Report to the caller that the given constraint is part of an encountered
+ * conflict.
+ */
+static int report_conflicting_constraint(struct isl_tab *tab, int con)
+{
+ return tab->conflict(con, tab->conflict_user);
+}
+
+/* Given a conflicting row in the tableau, report all constraints
+ * involved in the row to the caller. That is, the row itself
+ * (if it represents a constraint) and all constraint columns with
+ * non-zero (and therefore negative) coefficients.
+ */
+static int report_conflict(struct isl_tab *tab, int row)
+{
+ int j;
+ isl_int *tr;
+
+ if (!tab->conflict)
+ return 0;
+
+ if (tab->row_var[row] < 0 &&
+ report_conflicting_constraint(tab, ~tab->row_var[row]) < 0)
+ return -1;
+
+ tr = tab->mat->row[row] + 2 + tab->M;
+
+ for (j = tab->n_dead; j < tab->n_col; ++j) {
+ if (tab->col_var[j] >= 0 &&
+ (tab->col_var[j] < tab->n_param ||
+ tab->col_var[j] >= tab->n_var - tab->n_div))
+ continue;
+
+ if (!isl_int_is_neg(tr[j]))
+ continue;
+
+ if (tab->col_var[j] < 0 &&
+ report_conflicting_constraint(tab, ~tab->col_var[j]) < 0)
+ return -1;
+ }
+
+ return 0;
+}
+
/* Resolve all known or obviously violated constraints through pivoting.
* In particular, as long as we can find any violated constraint, we
- * look for a pivoting column that would result in the lexicographicallly
+ * look for a pivoting column that would result in the lexicographically
* smallest increment in the sample point. If there is no such column
* then the tableau is infeasible.
*/
-static struct isl_tab *restore_lexmin(struct isl_tab *tab)
+static int restore_lexmin(struct isl_tab *tab) WARN_UNUSED;
+static int restore_lexmin(struct isl_tab *tab)
{
int row, col;
if (!tab)
- return NULL;
+ return -1;
if (tab->empty)
- return tab;
+ return 0;
while ((row = first_neg(tab)) != -1) {
col = lexmin_pivot_col(tab, row);
- if (col >= tab->n_col)
- return isl_tab_mark_empty(tab);
+ if (col >= tab->n_col) {
+ if (report_conflict(tab, row) < 0)
+ return -1;
+ if (isl_tab_mark_empty(tab) < 0)
+ return -1;
+ return 0;
+ }
if (col < 0)
- goto error;
- isl_tab_pivot(tab, row, col);
+ return -1;
+ if (isl_tab_pivot(tab, row, col) < 0)
+ return -1;
}
- return tab;
-error:
- isl_tab_free(tab);
- return NULL;
+ return 0;
}
/* Given a row that represents an equality, look for an appropriate
i = last_var_col_or_int_par_col(tab, r);
if (i < 0) {
tab->con[r].is_nonneg = 1;
- isl_tab_push_var(tab, isl_tab_undo_nonneg, &tab->con[r]);
+ if (isl_tab_push_var(tab, isl_tab_undo_nonneg, &tab->con[r]) < 0)
+ goto error;
isl_seq_neg(eq, eq, 1 + tab->n_var);
r = isl_tab_add_row(tab, eq);
if (r < 0)
goto error;
tab->con[r].is_nonneg = 1;
- isl_tab_push_var(tab, isl_tab_undo_nonneg, &tab->con[r]);
+ if (isl_tab_push_var(tab, isl_tab_undo_nonneg, &tab->con[r]) < 0)
+ goto error;
} else {
- isl_tab_pivot(tab, r, i);
- isl_tab_kill_col(tab, i);
+ if (isl_tab_pivot(tab, r, i) < 0)
+ goto error;
+ if (isl_tab_kill_col(tab, i) < 0)
+ goto error;
tab->n_eq++;
-
- tab = restore_lexmin(tab);
}
return tab;
* In the end we try to use one of the two constraints to eliminate
* a column.
*/
-static struct isl_tab *add_lexmin_eq(struct isl_tab *tab, isl_int *eq)
+static int add_lexmin_eq(struct isl_tab *tab, isl_int *eq) WARN_UNUSED;
+static int add_lexmin_eq(struct isl_tab *tab, isl_int *eq)
{
int r1, r2;
int row;
+ struct isl_tab_undo *snap;
if (!tab)
- return NULL;
- if (tab->bset) {
- tab->bset = isl_basic_set_add_eq(tab->bset, eq);
- isl_tab_push(tab, isl_tab_undo_bset_eq);
- if (!tab->bset)
- goto error;
- }
+ return -1;
+ snap = isl_tab_snap(tab);
r1 = isl_tab_add_row(tab, eq);
if (r1 < 0)
- goto error;
+ return -1;
tab->con[r1].is_nonneg = 1;
- isl_tab_push_var(tab, isl_tab_undo_nonneg, &tab->con[r1]);
+ if (isl_tab_push_var(tab, isl_tab_undo_nonneg, &tab->con[r1]) < 0)
+ return -1;
row = tab->con[r1].index;
if (is_constant(tab, row)) {
if (!isl_int_is_zero(tab->mat->row[row][1]) ||
- (tab->M && !isl_int_is_zero(tab->mat->row[row][2])))
- return isl_tab_mark_empty(tab);
- return tab;
+ (tab->M && !isl_int_is_zero(tab->mat->row[row][2]))) {
+ if (isl_tab_mark_empty(tab) < 0)
+ return -1;
+ return 0;
+ }
+ if (isl_tab_rollback(tab, snap) < 0)
+ return -1;
+ return 0;
}
- tab = restore_lexmin(tab);
- if (!tab || tab->empty)
- return tab;
+ if (restore_lexmin(tab) < 0)
+ return -1;
+ if (tab->empty)
+ return 0;
isl_seq_neg(eq, eq, 1 + tab->n_var);
r2 = isl_tab_add_row(tab, eq);
if (r2 < 0)
- goto error;
+ return -1;
tab->con[r2].is_nonneg = 1;
- isl_tab_push_var(tab, isl_tab_undo_nonneg, &tab->con[r2]);
+ if (isl_tab_push_var(tab, isl_tab_undo_nonneg, &tab->con[r2]) < 0)
+ return -1;
- tab = restore_lexmin(tab);
- if (!tab || tab->empty)
- return tab;
+ if (restore_lexmin(tab) < 0)
+ return -1;
+ if (tab->empty)
+ return 0;
- if (!tab->con[r1].is_row)
- isl_tab_kill_col(tab, tab->con[r1].index);
- else if (!tab->con[r2].is_row)
- isl_tab_kill_col(tab, tab->con[r2].index);
- else if (isl_int_is_zero(tab->mat->row[tab->con[r1].index][1])) {
- unsigned off = 2 + tab->M;
- int i;
- int row = tab->con[r1].index;
- i = isl_seq_first_non_zero(tab->mat->row[row]+off+tab->n_dead,
- tab->n_col - tab->n_dead);
- if (i != -1) {
- isl_tab_pivot(tab, row, tab->n_dead + i);
- isl_tab_kill_col(tab, tab->n_dead + i);
- }
+ if (!tab->con[r1].is_row) {
+ if (isl_tab_kill_col(tab, tab->con[r1].index) < 0)
+ return -1;
+ } else if (!tab->con[r2].is_row) {
+ if (isl_tab_kill_col(tab, tab->con[r2].index) < 0)
+ return -1;
}
- return tab;
-error:
- isl_tab_free(tab);
- return NULL;
+ if (tab->bmap) {
+ tab->bmap = isl_basic_map_add_ineq(tab->bmap, eq);
+ if (isl_tab_push(tab, isl_tab_undo_bmap_ineq) < 0)
+ return -1;
+ isl_seq_neg(eq, eq, 1 + tab->n_var);
+ tab->bmap = isl_basic_map_add_ineq(tab->bmap, eq);
+ isl_seq_neg(eq, eq, 1 + tab->n_var);
+ if (isl_tab_push(tab, isl_tab_undo_bmap_ineq) < 0)
+ return -1;
+ if (!tab->bmap)
+ return -1;
+ }
+
+ return 0;
}
/* Add an inequality to the tableau, resolving violations using
if (!tab)
return NULL;
- if (tab->bset) {
- tab->bset = isl_basic_set_add_ineq(tab->bset, ineq);
- isl_tab_push(tab, isl_tab_undo_bset_ineq);
- if (!tab->bset)
+ if (tab->bmap) {
+ tab->bmap = isl_basic_map_add_ineq(tab->bmap, ineq);
+ if (isl_tab_push(tab, isl_tab_undo_bmap_ineq) < 0)
+ goto error;
+ if (!tab->bmap)
goto error;
}
r = isl_tab_add_row(tab, ineq);
if (r < 0)
goto error;
tab->con[r].is_nonneg = 1;
- isl_tab_push_var(tab, isl_tab_undo_nonneg, &tab->con[r]);
+ if (isl_tab_push_var(tab, isl_tab_undo_nonneg, &tab->con[r]) < 0)
+ goto error;
if (isl_tab_row_is_redundant(tab, tab->con[r].index)) {
- isl_tab_mark_redundant(tab, tab->con[r].index);
+ if (isl_tab_mark_redundant(tab, tab->con[r].index) < 0)
+ goto error;
return tab;
}
- tab = restore_lexmin(tab);
- if (tab && !tab->empty && tab->con[r].is_row &&
+ if (restore_lexmin(tab) < 0)
+ goto error;
+ if (!tab->empty && tab->con[r].is_row &&
isl_tab_row_is_redundant(tab, tab->con[r].index))
- isl_tab_mark_redundant(tab, tab->con[r].index);
+ if (isl_tab_mark_redundant(tab, tab->con[r].index) < 0)
+ goto error;
return tab;
error:
isl_tab_free(tab);
int i;
unsigned off = 2 + tab->M;
- for (i = 0; i < tab->n_col; ++i) {
+ for (i = tab->n_dead; i < tab->n_col; ++i) {
if (tab->col_var[i] >= 0 &&
(tab->col_var[i] < tab->n_param ||
tab->col_var[i] >= tab->n_var - tab->n_div))
#define I_PAR 1 << 1
#define I_VAR 1 << 2
-/* Check for first (non-parameter) variable that is non-integer and
- * therefore requires a cut.
+/* Check for next (non-parameter) variable after "var" (first if var == -1)
+ * that is non-integer and therefore requires a cut and return
+ * the index of the variable.
* For parametric tableaus, there are three parts in a row,
* the constant, the coefficients of the parameters and the rest.
* For each part, we check whether the coefficients in that part
* current sample value is integral and no cut is required
* (irrespective of whether the variable part is integral).
*/
-static int first_non_integer(struct isl_tab *tab, int *f)
+static int next_non_integer_var(struct isl_tab *tab, int var, int *f)
{
- int i;
+ var = var < 0 ? tab->n_param : var + 1;
- for (i = tab->n_param; i < tab->n_var - tab->n_div; ++i) {
+ for (; var < tab->n_var - tab->n_div; ++var) {
int flags = 0;
int row;
- if (!tab->var[i].is_row)
+ if (!tab->var[var].is_row)
continue;
- row = tab->var[i].index;
+ row = tab->var[var].index;
if (integer_constant(tab, row))
ISL_FL_SET(flags, I_CST);
if (integer_parameter(tab, row))
if (integer_variable(tab, row))
ISL_FL_SET(flags, I_VAR);
*f = flags;
- return row;
+ return var;
}
return -1;
}
+/* Check for first (non-parameter) variable that is non-integer and
+ * therefore requires a cut and return the corresponding row.
+ * For parametric tableaus, there are three parts in a row,
+ * the constant, the coefficients of the parameters and the rest.
+ * For each part, we check whether the coefficients in that part
+ * are all integral and if so, set the corresponding flag in *f.
+ * If the constant and the parameter part are integral, then the
+ * current sample value is integral and no cut is required
+ * (irrespective of whether the variable part is integral).
+ */
+static int first_non_integer_row(struct isl_tab *tab, int *f)
+{
+ int var = next_non_integer_var(tab, -1, f);
+
+ return var < 0 ? -1 : tab->var[var].index;
+}
+
/* Add a (non-parametric) cut to cut away the non-integral sample
* value of the given row.
*
tab->mat->row[row][off + i], tab->mat->row[row][0]);
tab->con[r].is_nonneg = 1;
- isl_tab_push_var(tab, isl_tab_undo_nonneg, &tab->con[r]);
+ if (isl_tab_push_var(tab, isl_tab_undo_nonneg, &tab->con[r]) < 0)
+ return -1;
if (tab->row_sign)
tab->row_sign[tab->con[r].index] = isl_tab_row_neg;
return tab->con[r].index;
}
+#define CUT_ALL 1
+#define CUT_ONE 0
+
/* Given a non-parametric tableau, add cuts until an integer
* sample point is obtained or until the tableau is determined
* to be integer infeasible.
* As long as there is any non-integer value in the sample point,
- * we add an appropriate cut, if possible and resolve the violated
- * cut constraint using restore_lexmin.
+ * we add appropriate cuts, if possible, for each of these
+ * non-integer values and then resolve the violated
+ * cut constraints using restore_lexmin.
* If one of the corresponding rows is equal to an integral
* combination of variables/constraints plus a non-integral constant,
- * then there is no way to obtain an integer point an we return
+ * then there is no way to obtain an integer point and we return
* a tableau that is marked empty.
+ * The parameter cutting_strategy controls the strategy used when adding cuts
+ * to remove non-integer points. CUT_ALL adds all possible cuts
+ * before continuing the search. CUT_ONE adds only one cut at a time.
*/
-static struct isl_tab *cut_to_integer_lexmin(struct isl_tab *tab)
+static struct isl_tab *cut_to_integer_lexmin(struct isl_tab *tab,
+ int cutting_strategy)
{
+ int var;
int row;
int flags;
if (tab->empty)
return tab;
- while ((row = first_non_integer(tab, &flags)) != -1) {
- if (ISL_FL_ISSET(flags, I_VAR))
- return isl_tab_mark_empty(tab);
- row = add_cut(tab, row);
- if (row < 0)
+ while ((var = next_non_integer_var(tab, -1, &flags)) != -1) {
+ do {
+ if (ISL_FL_ISSET(flags, I_VAR)) {
+ if (isl_tab_mark_empty(tab) < 0)
+ goto error;
+ return tab;
+ }
+ row = tab->var[var].index;
+ row = add_cut(tab, row);
+ if (row < 0)
+ goto error;
+ if (cutting_strategy == CUT_ONE)
+ break;
+ } while ((var = next_non_integer_var(tab, var, &flags)) != -1);
+ if (restore_lexmin(tab) < 0)
goto error;
- tab = restore_lexmin(tab);
- if (!tab || tab->empty)
+ if (tab->empty)
break;
}
return tab;
return NULL;
}
-static struct isl_tab *drop_sample(struct isl_tab *tab, int s)
-{
- if (s != tab->n_outside)
- isl_mat_swap_rows(tab->samples, tab->n_outside, s);
- tab->n_outside++;
- isl_tab_push(tab, isl_tab_undo_drop_sample);
-
- return tab;
-}
-
/* Check whether all the currently active samples also satisfy the inequality
* "ineq" (treated as an equality if eq is set).
* Remove those samples that do not.
if (!tab)
return NULL;
- isl_assert(tab->mat->ctx, tab->bset, goto error);
+ isl_assert(tab->mat->ctx, tab->bmap, goto error);
isl_assert(tab->mat->ctx, tab->samples, goto error);
isl_assert(tab->mat->ctx, tab->samples->n_col == 1 + tab->n_var, goto error);
sgn = isl_int_sgn(v);
if (eq ? (sgn == 0) : (sgn >= 0))
continue;
- tab = drop_sample(tab, i);
+ tab = isl_tab_drop_sample(tab, i);
if (!tab)
break;
}
}
/* Check if the context tableau of sol has any integer points.
- * Returns -1 if an error occurred.
+ * Leave tab in empty state if no integer point can be found.
* If an integer point can be found and if moreover it is finite,
* then it is added to the list of sample values.
*
* This function is only called when none of the currently active sample
* values satisfies the most recently added constraint.
*/
-static int context_is_feasible(struct isl_sol *sol)
+static struct isl_tab *check_integer_feasible(struct isl_tab *tab)
{
struct isl_tab_undo *snap;
- struct isl_tab *tab;
- int feasible;
- if (!sol || !sol->context_tab)
- return -1;
+ if (!tab)
+ return NULL;
- snap = isl_tab_snap(sol->context_tab);
- isl_tab_push_basis(sol->context_tab);
+ snap = isl_tab_snap(tab);
+ if (isl_tab_push_basis(tab) < 0)
+ goto error;
- sol->context_tab = cut_to_integer_lexmin(sol->context_tab);
- if (!sol->context_tab)
+ tab = cut_to_integer_lexmin(tab, CUT_ALL);
+ if (!tab)
goto error;
- tab = sol->context_tab;
if (!tab->empty && sample_is_finite(tab)) {
struct isl_vec *sample;
- tab->samples = isl_mat_extend(tab->samples,
- tab->n_sample + 1, tab->samples->n_col);
- if (!tab->samples)
- goto error;
-
sample = isl_tab_get_sample_value(tab);
- if (!sample)
- goto error;
- isl_seq_cpy(tab->samples->row[tab->n_sample],
- sample->el, sample->size);
- isl_vec_free(sample);
- tab->n_sample++;
+
+ tab = isl_tab_add_sample(tab, sample);
}
- feasible = !sol->context_tab->empty;
- if (isl_tab_rollback(sol->context_tab, snap) < 0)
+ if (!tab->empty && isl_tab_rollback(tab, snap) < 0)
goto error;
- return feasible;
+ return tab;
error:
- isl_tab_free(sol->context_tab);
- sol->context_tab = NULL;
- return -1;
+ isl_tab_free(tab);
+ return NULL;
}
-/* First check if any of the currently active sample values satisfies
+/* Check if any of the currently active sample values satisfies
* the inequality "ineq" (an equality if eq is set).
- * If not, continue with check_integer_feasible.
*/
-static int context_valid_sample_or_feasible(struct isl_sol *sol,
- isl_int *ineq, int eq)
+static int tab_has_valid_sample(struct isl_tab *tab, isl_int *ineq, int eq)
{
int i;
isl_int v;
- struct isl_tab *tab;
- if (!sol || !sol->context_tab)
+ if (!tab)
return -1;
- tab = sol->context_tab;
- isl_assert(tab->mat->ctx, tab->bset, return -1);
+ isl_assert(tab->mat->ctx, tab->bmap, return -1);
isl_assert(tab->mat->ctx, tab->samples, return -1);
isl_assert(tab->mat->ctx, tab->samples->n_col == 1 + tab->n_var, return -1);
}
isl_int_clear(v);
- if (i < tab->n_sample)
- return 1;
-
- return context_is_feasible(sol);
+ return i < tab->n_sample;
}
-/* For a div d = floor(f/m), add the constraints
- *
- * f - m d >= 0
- * -(f-(m-1)) + m d >= 0
- *
- * Note that the second constraint is the negation of
- *
- * f - m d >= m
+/* Add a div specified by "div" to the tableau "tab" and return
+ * 1 if the div is obviously non-negative.
*/
-static struct isl_tab *add_div_constraints(struct isl_tab *tab, unsigned div)
+static int context_tab_add_div(struct isl_tab *tab, struct isl_vec *div,
+ int (*add_ineq)(void *user, isl_int *), void *user)
{
- unsigned total;
- unsigned div_pos;
- struct isl_vec *ineq;
-
- if (!tab)
- return NULL;
-
- total = isl_basic_set_total_dim(tab->bset);
- div_pos = 1 + total - tab->bset->n_div + div;
-
- ineq = ineq_for_div(tab->bset, div);
- if (!ineq)
- goto error;
-
- tab = add_lexmin_ineq(tab, ineq->el);
+ int i;
+ int r;
+ struct isl_mat *samples;
+ int nonneg;
- isl_seq_neg(ineq->el, tab->bset->div[div] + 1, 1 + total);
- isl_int_set(ineq->el[div_pos], tab->bset->div[div][0]);
- isl_int_add(ineq->el[0], ineq->el[0], ineq->el[div_pos]);
- isl_int_sub_ui(ineq->el[0], ineq->el[0], 1);
- tab = add_lexmin_ineq(tab, ineq->el);
+ r = isl_tab_add_div(tab, div, add_ineq, user);
+ if (r < 0)
+ return -1;
+ nonneg = tab->var[r].is_nonneg;
+ tab->var[r].frozen = 1;
- isl_vec_free(ineq);
+ samples = isl_mat_extend(tab->samples,
+ tab->n_sample, 1 + tab->n_var);
+ tab->samples = samples;
+ if (!samples)
+ return -1;
+ for (i = tab->n_outside; i < samples->n_row; ++i) {
+ isl_seq_inner_product(div->el + 1, samples->row[i],
+ div->size - 1, &samples->row[i][samples->n_col - 1]);
+ isl_int_fdiv_q(samples->row[i][samples->n_col - 1],
+ samples->row[i][samples->n_col - 1], div->el[0]);
+ }
- return tab;
-error:
- isl_tab_free(tab);
- return NULL;
+ return nonneg;
}
/* Add a div specified by "div" to both the main tableau and
* need to express the meaning of the div.
* Return the index of the div or -1 if anything went wrong.
*/
-static int add_div(struct isl_tab *tab, struct isl_tab **context_tab,
+static int add_div(struct isl_tab *tab, struct isl_context *context,
struct isl_vec *div)
{
- int i;
int r;
- int k;
- struct isl_mat *samples;
+ int nonneg;
- if (isl_tab_extend_vars(*context_tab, 1) < 0)
+ if ((nonneg = context->op->add_div(context, div)) < 0)
goto error;
- r = isl_tab_allocate_var(*context_tab);
- if (r < 0)
- goto error;
- (*context_tab)->var[r].is_nonneg = 1;
- (*context_tab)->var[r].frozen = 1;
-
- samples = isl_mat_extend((*context_tab)->samples,
- (*context_tab)->n_sample, 1 + (*context_tab)->n_var);
- (*context_tab)->samples = samples;
- if (!samples)
- goto error;
- for (i = (*context_tab)->n_outside; i < samples->n_row; ++i) {
- isl_seq_inner_product(div->el + 1, samples->row[i],
- div->size - 1, &samples->row[i][samples->n_col - 1]);
- isl_int_fdiv_q(samples->row[i][samples->n_col - 1],
- samples->row[i][samples->n_col - 1], div->el[0]);
- }
- (*context_tab)->bset = isl_basic_set_extend_dim((*context_tab)->bset,
- isl_basic_set_get_dim((*context_tab)->bset), 1, 0, 2);
- k = isl_basic_set_alloc_div((*context_tab)->bset);
- if (k < 0)
- goto error;
- isl_seq_cpy((*context_tab)->bset->div[k], div->el, div->size);
- isl_tab_push((*context_tab), isl_tab_undo_bset_div);
- *context_tab = add_div_constraints(*context_tab, k);
- if (!*context_tab)
+ if (!context->op->is_ok(context))
goto error;
if (isl_tab_extend_vars(tab, 1) < 0)
r = isl_tab_allocate_var(tab);
if (r < 0)
goto error;
- if (!(*context_tab)->M)
+ if (nonneg)
tab->var[r].is_nonneg = 1;
tab->var[r].frozen = 1;
tab->n_div++;
return tab->n_div - 1;
error:
- isl_tab_free(*context_tab);
- *context_tab = NULL;
+ context->op->invalidate(context);
return -1;
}
static int find_div(struct isl_tab *tab, isl_int *div, isl_int denom)
{
int i;
- unsigned total = isl_basic_set_total_dim(tab->bset);
+ unsigned total = isl_basic_map_total_dim(tab->bmap);
- for (i = 0; i < tab->bset->n_div; ++i) {
- if (isl_int_ne(tab->bset->div[i][0], denom))
+ for (i = 0; i < tab->bmap->n_div; ++i) {
+ if (isl_int_ne(tab->bmap->div[i][0], denom))
continue;
- if (!isl_seq_eq(tab->bset->div[i] + 1, div, total))
+ if (!isl_seq_eq(tab->bmap->div[i] + 1, div, 1 + total))
continue;
return i;
}
/* Return the index of a div that corresponds to "div".
* We first check if we already have such a div and if not, we create one.
*/
-static int get_div(struct isl_tab *tab, struct isl_tab **context_tab,
+static int get_div(struct isl_tab *tab, struct isl_context *context,
struct isl_vec *div)
{
int d;
+ struct isl_tab *context_tab = context->op->peek_tab(context);
- d = find_div(*context_tab, div->el + 1, div->el[0]);
+ if (!context_tab)
+ return -1;
+
+ d = find_div(context_tab, div->el + 1, div->el[0]);
if (d != -1)
return d;
- return add_div(tab, context_tab, div);
+ return add_div(tab, context, div);
}
/* Add a parametric cut to cut away the non-integral sample value
* Return the row of the cut or -1.
*/
static int add_parametric_cut(struct isl_tab *tab, int row,
- struct isl_tab **context_tab)
+ struct isl_context *context)
{
struct isl_vec *div;
int d;
int r;
isl_int *r_row;
int col;
+ int n;
unsigned off = 2 + tab->M;
- if (!*context_tab)
- goto error;
-
- if (isl_tab_extend_cons(*context_tab, 3) < 0)
- goto error;
+ if (!context)
+ return -1;
div = get_row_parameter_div(tab, row);
if (!div)
return -1;
- d = get_div(tab, context_tab, div);
+ n = tab->n_div;
+ d = context->op->get_div(context, tab, div);
+ isl_vec_free(div);
if (d < 0)
- goto error;
+ return -1;
if (isl_tab_extend_cons(tab, 1) < 0)
return -1;
}
tab->con[r].is_nonneg = 1;
- isl_tab_push_var(tab, isl_tab_undo_nonneg, &tab->con[r]);
+ if (isl_tab_push_var(tab, isl_tab_undo_nonneg, &tab->con[r]) < 0)
+ return -1;
if (tab->row_sign)
tab->row_sign[tab->con[r].index] = isl_tab_row_neg;
- isl_vec_free(div);
+ row = tab->con[r].index;
- return tab->con[r].index;
-error:
- isl_tab_free(*context_tab);
- *context_tab = NULL;
- return -1;
+ if (d >= n && context->op->detect_equalities(context, tab) < 0)
+ return -1;
+
+ return row;
}
/* Construct a tableau for bmap that can be used for computing
if (!tab->row_sign)
goto error;
}
- if (ISL_F_ISSET(bmap, ISL_BASIC_MAP_EMPTY))
- return isl_tab_mark_empty(tab);
+ if (ISL_F_ISSET(bmap, ISL_BASIC_MAP_EMPTY)) {
+ if (isl_tab_mark_empty(tab) < 0)
+ goto error;
+ return tab;
+ }
for (i = tab->n_param; i < tab->n_var - tab->n_div; ++i) {
tab->var[i].is_nonneg = 1;
if (!tab || tab->empty)
return tab;
}
+ if (bmap->n_eq && restore_lexmin(tab) < 0)
+ goto error;
for (i = 0; i < bmap->n_ineq; ++i) {
if (max)
isl_seq_neg(bmap->ineq[i] + 1 + tab->n_param,
return NULL;
}
-static struct isl_tab *context_tab_for_lexmin(struct isl_basic_set *bset)
+/* Given a main tableau where more than one row requires a split,
+ * determine and return the "best" row to split on.
+ *
+ * Given two rows in the main tableau, if the inequality corresponding
+ * to the first row is redundant with respect to that of the second row
+ * in the current tableau, then it is better to split on the second row,
+ * since in the positive part, both row will be positive.
+ * (In the negative part a pivot will have to be performed and just about
+ * anything can happen to the sign of the other row.)
+ *
+ * As a simple heuristic, we therefore select the row that makes the most
+ * of the other rows redundant.
+ *
+ * Perhaps it would also be useful to look at the number of constraints
+ * that conflict with any given constraint.
+ */
+static int best_split(struct isl_tab *tab, struct isl_tab *context_tab)
{
- struct isl_tab *tab;
+ struct isl_tab_undo *snap;
+ int split;
+ int row;
+ int best = -1;
+ int best_r;
- bset = isl_basic_set_cow(bset);
- if (!bset)
+ if (isl_tab_extend_cons(context_tab, 2) < 0)
+ return -1;
+
+ snap = isl_tab_snap(context_tab);
+
+ for (split = tab->n_redundant; split < tab->n_row; ++split) {
+ struct isl_tab_undo *snap2;
+ struct isl_vec *ineq = NULL;
+ int r = 0;
+ int ok;
+
+ if (!isl_tab_var_from_row(tab, split)->is_nonneg)
+ continue;
+ if (tab->row_sign[split] != isl_tab_row_any)
+ continue;
+
+ ineq = get_row_parameter_ineq(tab, split);
+ if (!ineq)
+ return -1;
+ ok = isl_tab_add_ineq(context_tab, ineq->el) >= 0;
+ isl_vec_free(ineq);
+ if (!ok)
+ return -1;
+
+ snap2 = isl_tab_snap(context_tab);
+
+ for (row = tab->n_redundant; row < tab->n_row; ++row) {
+ struct isl_tab_var *var;
+
+ if (row == split)
+ continue;
+ if (!isl_tab_var_from_row(tab, row)->is_nonneg)
+ continue;
+ if (tab->row_sign[row] != isl_tab_row_any)
+ continue;
+
+ ineq = get_row_parameter_ineq(tab, row);
+ if (!ineq)
+ return -1;
+ ok = isl_tab_add_ineq(context_tab, ineq->el) >= 0;
+ isl_vec_free(ineq);
+ if (!ok)
+ return -1;
+ var = &context_tab->con[context_tab->n_con - 1];
+ if (!context_tab->empty &&
+ !isl_tab_min_at_most_neg_one(context_tab, var))
+ r++;
+ if (isl_tab_rollback(context_tab, snap2) < 0)
+ return -1;
+ }
+ if (best == -1 || r > best_r) {
+ best = split;
+ best_r = r;
+ }
+ if (isl_tab_rollback(context_tab, snap) < 0)
+ return -1;
+ }
+
+ return best;
+}
+
+static struct isl_basic_set *context_lex_peek_basic_set(
+ struct isl_context *context)
+{
+ struct isl_context_lex *clex = (struct isl_context_lex *)context;
+ if (!clex->tab)
return NULL;
- tab = tab_for_lexmin((struct isl_basic_map *)bset, NULL, 1, 0);
- if (!tab)
+ return isl_tab_peek_bset(clex->tab);
+}
+
+static struct isl_tab *context_lex_peek_tab(struct isl_context *context)
+{
+ struct isl_context_lex *clex = (struct isl_context_lex *)context;
+ return clex->tab;
+}
+
+static void context_lex_add_eq(struct isl_context *context, isl_int *eq,
+ int check, int update)
+{
+ struct isl_context_lex *clex = (struct isl_context_lex *)context;
+ if (isl_tab_extend_cons(clex->tab, 2) < 0)
goto error;
- tab->bset = bset;
- tab->n_sample = 0;
- tab->n_outside = 0;
- tab->samples = isl_mat_alloc(bset->ctx, 1, 1 + tab->n_var);
- if (!tab->samples)
+ if (add_lexmin_eq(clex->tab, eq) < 0)
goto error;
- return tab;
+ if (check) {
+ int v = tab_has_valid_sample(clex->tab, eq, 1);
+ if (v < 0)
+ goto error;
+ if (!v)
+ clex->tab = check_integer_feasible(clex->tab);
+ }
+ if (update)
+ clex->tab = check_samples(clex->tab, eq, 1);
+ return;
error:
- isl_basic_set_free(bset);
- return NULL;
+ isl_tab_free(clex->tab);
+ clex->tab = NULL;
}
-/* Construct an isl_sol_map structure for accumulating the solution.
- * If track_empty is set, then we also keep track of the parts
- * of the context where there is no solution.
- * If max is set, then we are solving a maximization, rather than
- * a minimization problem, which means that the variables in the
- * tableau have value "M - x" rather than "M + x".
+static void context_lex_add_ineq(struct isl_context *context, isl_int *ineq,
+ int check, int update)
+{
+ struct isl_context_lex *clex = (struct isl_context_lex *)context;
+ if (isl_tab_extend_cons(clex->tab, 1) < 0)
+ goto error;
+ clex->tab = add_lexmin_ineq(clex->tab, ineq);
+ if (check) {
+ int v = tab_has_valid_sample(clex->tab, ineq, 0);
+ if (v < 0)
+ goto error;
+ if (!v)
+ clex->tab = check_integer_feasible(clex->tab);
+ }
+ if (update)
+ clex->tab = check_samples(clex->tab, ineq, 0);
+ return;
+error:
+ isl_tab_free(clex->tab);
+ clex->tab = NULL;
+}
+
+static int context_lex_add_ineq_wrap(void *user, isl_int *ineq)
+{
+ struct isl_context *context = (struct isl_context *)user;
+ context_lex_add_ineq(context, ineq, 0, 0);
+ return context->op->is_ok(context) ? 0 : -1;
+}
+
+/* Check which signs can be obtained by "ineq" on all the currently
+ * active sample values. See row_sign for more information.
*/
-static struct isl_sol_map *sol_map_init(struct isl_basic_map *bmap,
- struct isl_basic_set *dom, int track_empty, int max)
+static enum isl_tab_row_sign tab_ineq_sign(struct isl_tab *tab, isl_int *ineq,
+ int strict)
{
- struct isl_sol_map *sol_map;
- struct isl_tab *context_tab;
- int f;
+ int i;
+ int sgn;
+ isl_int tmp;
+ enum isl_tab_row_sign res = isl_tab_row_unknown;
- sol_map = isl_calloc_type(bset->ctx, struct isl_sol_map);
- if (!sol_map)
- goto error;
+ isl_assert(tab->mat->ctx, tab->samples, return isl_tab_row_unknown);
+ isl_assert(tab->mat->ctx, tab->samples->n_col == 1 + tab->n_var,
+ return isl_tab_row_unknown);
- sol_map->max = max;
- sol_map->sol.add = &sol_map_add_wrap;
- sol_map->sol.free = &sol_map_free_wrap;
- sol_map->map = isl_map_alloc_dim(isl_basic_map_get_dim(bmap), 1,
- ISL_MAP_DISJOINT);
- if (!sol_map->map)
- goto error;
+ isl_int_init(tmp);
+ for (i = tab->n_outside; i < tab->n_sample; ++i) {
+ isl_seq_inner_product(tab->samples->row[i], ineq,
+ 1 + tab->n_var, &tmp);
+ sgn = isl_int_sgn(tmp);
+ if (sgn > 0 || (sgn == 0 && strict)) {
+ if (res == isl_tab_row_unknown)
+ res = isl_tab_row_pos;
+ if (res == isl_tab_row_neg)
+ res = isl_tab_row_any;
+ }
+ if (sgn < 0) {
+ if (res == isl_tab_row_unknown)
+ res = isl_tab_row_neg;
+ if (res == isl_tab_row_pos)
+ res = isl_tab_row_any;
+ }
+ if (res == isl_tab_row_any)
+ break;
+ }
+ isl_int_clear(tmp);
- context_tab = context_tab_for_lexmin(isl_basic_set_copy(dom));
- context_tab = restore_lexmin(context_tab);
- sol_map->sol.context_tab = context_tab;
- f = context_is_feasible(&sol_map->sol);
- if (f < 0)
- goto error;
+ return res;
+}
- if (track_empty) {
- sol_map->empty = isl_set_alloc_dim(isl_basic_set_get_dim(dom),
- 1, ISL_SET_DISJOINT);
- if (!sol_map->empty)
- goto error;
+static enum isl_tab_row_sign context_lex_ineq_sign(struct isl_context *context,
+ isl_int *ineq, int strict)
+{
+ struct isl_context_lex *clex = (struct isl_context_lex *)context;
+ return tab_ineq_sign(clex->tab, ineq, strict);
+}
+
+/* Check whether "ineq" can be added to the tableau without rendering
+ * it infeasible.
+ */
+static int context_lex_test_ineq(struct isl_context *context, isl_int *ineq)
+{
+ struct isl_context_lex *clex = (struct isl_context_lex *)context;
+ struct isl_tab_undo *snap;
+ int feasible;
+
+ if (!clex->tab)
+ return -1;
+
+ if (isl_tab_extend_cons(clex->tab, 1) < 0)
+ return -1;
+
+ snap = isl_tab_snap(clex->tab);
+ if (isl_tab_push_basis(clex->tab) < 0)
+ return -1;
+ clex->tab = add_lexmin_ineq(clex->tab, ineq);
+ clex->tab = check_integer_feasible(clex->tab);
+ if (!clex->tab)
+ return -1;
+ feasible = !clex->tab->empty;
+ if (isl_tab_rollback(clex->tab, snap) < 0)
+ return -1;
+
+ return feasible;
+}
+
+static int context_lex_get_div(struct isl_context *context, struct isl_tab *tab,
+ struct isl_vec *div)
+{
+ return get_div(tab, context, div);
+}
+
+/* Add a div specified by "div" to the context tableau and return
+ * 1 if the div is obviously non-negative.
+ * context_tab_add_div will always return 1, because all variables
+ * in a isl_context_lex tableau are non-negative.
+ * However, if we are using a big parameter in the context, then this only
+ * reflects the non-negativity of the variable used to _encode_ the
+ * div, i.e., div' = M + div, so we can't draw any conclusions.
+ */
+static int context_lex_add_div(struct isl_context *context, struct isl_vec *div)
+{
+ struct isl_context_lex *clex = (struct isl_context_lex *)context;
+ int nonneg;
+ nonneg = context_tab_add_div(clex->tab, div,
+ context_lex_add_ineq_wrap, context);
+ if (nonneg < 0)
+ return -1;
+ if (clex->tab->M)
+ return 0;
+ return nonneg;
+}
+
+static int context_lex_detect_equalities(struct isl_context *context,
+ struct isl_tab *tab)
+{
+ return 0;
+}
+
+static int context_lex_best_split(struct isl_context *context,
+ struct isl_tab *tab)
+{
+ struct isl_context_lex *clex = (struct isl_context_lex *)context;
+ struct isl_tab_undo *snap;
+ int r;
+
+ snap = isl_tab_snap(clex->tab);
+ if (isl_tab_push_basis(clex->tab) < 0)
+ return -1;
+ r = best_split(tab, clex->tab);
+
+ if (r >= 0 && isl_tab_rollback(clex->tab, snap) < 0)
+ return -1;
+
+ return r;
+}
+
+static int context_lex_is_empty(struct isl_context *context)
+{
+ struct isl_context_lex *clex = (struct isl_context_lex *)context;
+ if (!clex->tab)
+ return -1;
+ return clex->tab->empty;
+}
+
+static void *context_lex_save(struct isl_context *context)
+{
+ struct isl_context_lex *clex = (struct isl_context_lex *)context;
+ struct isl_tab_undo *snap;
+
+ snap = isl_tab_snap(clex->tab);
+ if (isl_tab_push_basis(clex->tab) < 0)
+ return NULL;
+ if (isl_tab_save_samples(clex->tab) < 0)
+ return NULL;
+
+ return snap;
+}
+
+static void context_lex_restore(struct isl_context *context, void *save)
+{
+ struct isl_context_lex *clex = (struct isl_context_lex *)context;
+ if (isl_tab_rollback(clex->tab, (struct isl_tab_undo *)save) < 0) {
+ isl_tab_free(clex->tab);
+ clex->tab = NULL;
}
+}
- isl_basic_set_free(dom);
- return sol_map;
-error:
- isl_basic_set_free(dom);
- sol_map_free(sol_map);
- return NULL;
+static void context_lex_discard(void *save)
+{
+}
+
+static int context_lex_is_ok(struct isl_context *context)
+{
+ struct isl_context_lex *clex = (struct isl_context_lex *)context;
+ return !!clex->tab;
}
/* For each variable in the context tableau, check if the variable can
struct isl_tab *context_tab)
{
int i;
- struct isl_tab_undo *snap, *snap2;
+ struct isl_tab_undo *snap;
struct isl_vec *ineq = NULL;
struct isl_tab_var *var;
int n;
goto error;
snap = isl_tab_snap(context_tab);
- isl_tab_push_basis(context_tab);
-
- snap2 = isl_tab_snap(context_tab);
n = 0;
isl_seq_clr(ineq->el, ineq->size);
for (i = 0; i < context_tab->n_var; ++i) {
isl_int_set_si(ineq->el[1 + i], 1);
- context_tab = isl_tab_add_ineq(context_tab, ineq->el);
+ if (isl_tab_add_ineq(context_tab, ineq->el) < 0)
+ goto error;
var = &context_tab->con[context_tab->n_con - 1];
if (!context_tab->empty &&
!isl_tab_min_at_most_neg_one(context_tab, var)) {
n++;
}
isl_int_set_si(ineq->el[1 + i], 0);
- if (isl_tab_rollback(context_tab, snap2) < 0)
+ if (isl_tab_rollback(context_tab, snap) < 0)
goto error;
}
- if (isl_tab_rollback(context_tab, snap) < 0)
- goto error;
-
- if (n == context_tab->n_var) {
+ if (context_tab->M && n == context_tab->n_var) {
context_tab->mat = isl_mat_drop_cols(context_tab->mat, 2, 1);
context_tab->M = 0;
}
return NULL;
}
-/* Check whether all coefficients of (non-parameter) variables
- * are non-positive, meaning that no pivots can be performed on the row.
- */
-static int is_critical(struct isl_tab *tab, int row)
+static struct isl_tab *context_lex_detect_nonnegative_parameters(
+ struct isl_context *context, struct isl_tab *tab)
{
- int j;
- unsigned off = 2 + tab->M;
+ struct isl_context_lex *clex = (struct isl_context_lex *)context;
+ struct isl_tab_undo *snap;
- for (j = tab->n_dead; j < tab->n_col; ++j) {
- if (tab->col_var[j] >= 0 &&
- (tab->col_var[j] < tab->n_param ||
- tab->col_var[j] >= tab->n_var - tab->n_div))
- continue;
+ if (!tab)
+ return NULL;
- if (isl_int_is_pos(tab->mat->row[row][off + j]))
- return 0;
- }
+ snap = isl_tab_snap(clex->tab);
+ if (isl_tab_push_basis(clex->tab) < 0)
+ goto error;
- return 1;
-}
+ tab = tab_detect_nonnegative_parameters(tab, clex->tab);
-/* Check whether the inequality represented by vec is strict over the integers,
- * i.e., there are no integer values satisfying the constraint with
- * equality. This happens if the gcd of the coefficients is not a divisor
- * of the constant term. If so, scale the constraint down by the gcd
- * of the coefficients.
- */
-static int is_strict(struct isl_vec *vec)
-{
- isl_int gcd;
- int strict = 0;
+ if (isl_tab_rollback(clex->tab, snap) < 0)
+ goto error;
- isl_int_init(gcd);
- isl_seq_gcd(vec->el + 1, vec->size - 1, &gcd);
- if (!isl_int_is_one(gcd)) {
- strict = !isl_int_is_divisible_by(vec->el[0], gcd);
- isl_int_fdiv_q(vec->el[0], vec->el[0], gcd);
- isl_seq_scale_down(vec->el + 1, vec->el + 1, gcd, vec->size-1);
- }
- isl_int_clear(gcd);
-
- return strict;
+ return tab;
+error:
+ isl_tab_free(tab);
+ return NULL;
}
-/* Determine the sign of the given row of the main tableau.
- * The result is one of
- * isl_tab_row_pos: always non-negative; no pivot needed
- * isl_tab_row_neg: always non-positive; pivot
- * isl_tab_row_any: can be both positive and negative; split
- *
- * We first handle some simple cases
- * - the row sign may be known already
- * - the row may be obviously non-negative
- * - the parametric constant may be equal to that of another row
- * for which we know the sign. This sign will be either "pos" or
- * "any". If it had been "neg" then we would have pivoted before.
- *
- * If none of these cases hold, we check the value of the row for each
- * of the currently active samples. Based on the signs of these values
- * we make an initial determination of the sign of the row.
- *
- * all zero -> unk(nown)
- * all non-negative -> pos
- * all non-positive -> neg
- * both negative and positive -> all
- *
- * If we end up with "all", we are done.
- * Otherwise, we perform a check for positive and/or negative
- * values as follows.
- *
- * samples neg unk pos
- * <0 ? Y N Y N
- * pos any pos
- * >0 ? Y N Y N
- * any neg any neg
- *
- * There is no special sign for "zero", because we can usually treat zero
- * as either non-negative or non-positive, whatever works out best.
- * However, if the row is "critical", meaning that pivoting is impossible
- * then we don't want to limp zero with the non-positive case, because
- * then we we would lose the solution for those values of the parameters
- * where the value of the row is zero. Instead, we treat 0 as non-negative
- * ensuring a split if the row can attain both zero and negative values.
- * The same happens when the original constraint was one that could not
- * be satisfied with equality by any integer values of the parameters.
- * In this case, we normalize the constraint, but then a value of zero
- * for the normalized constraint is actually a positive value for the
- * original constraint, so again we need to treat zero as non-negative.
- * In both these cases, we have the following decision tree instead:
- *
- * all non-negative -> pos
- * all negative -> neg
- * both negative and non-negative -> all
- *
- * samples neg pos
- * <0 ? Y N
- * any pos
- * >=0 ? Y N
- * any neg
- */
-static int row_sign(struct isl_tab *tab, struct isl_sol *sol, int row)
+static void context_lex_invalidate(struct isl_context *context)
{
- int i;
- struct isl_tab_undo *snap = NULL;
- struct isl_vec *ineq = NULL;
- int res = isl_tab_row_unknown;
- int critical;
- int strict;
- int sgn;
- int row2;
- isl_int tmp;
- struct isl_tab *context_tab = sol->context_tab;
+ struct isl_context_lex *clex = (struct isl_context_lex *)context;
+ isl_tab_free(clex->tab);
+ clex->tab = NULL;
+}
- if (tab->row_sign[row] != isl_tab_row_unknown)
- return tab->row_sign[row];
- if (is_obviously_nonneg(tab, row))
- return isl_tab_row_pos;
- for (row2 = tab->n_redundant; row2 < tab->n_row; ++row2) {
- if (tab->row_sign[row2] == isl_tab_row_unknown)
- continue;
- if (identical_parameter_line(tab, row, row2))
- return tab->row_sign[row2];
- }
+static void context_lex_free(struct isl_context *context)
+{
+ struct isl_context_lex *clex = (struct isl_context_lex *)context;
+ isl_tab_free(clex->tab);
+ free(clex);
+}
- critical = is_critical(tab, row);
+struct isl_context_op isl_context_lex_op = {
+ context_lex_detect_nonnegative_parameters,
+ context_lex_peek_basic_set,
+ context_lex_peek_tab,
+ context_lex_add_eq,
+ context_lex_add_ineq,
+ context_lex_ineq_sign,
+ context_lex_test_ineq,
+ context_lex_get_div,
+ context_lex_add_div,
+ context_lex_detect_equalities,
+ context_lex_best_split,
+ context_lex_is_empty,
+ context_lex_is_ok,
+ context_lex_save,
+ context_lex_restore,
+ context_lex_discard,
+ context_lex_invalidate,
+ context_lex_free,
+};
- isl_assert(tab->mat->ctx, context_tab->samples, goto error);
- isl_assert(tab->mat->ctx, context_tab->samples->n_col == 1 + context_tab->n_var, goto error);
+static struct isl_tab *context_tab_for_lexmin(struct isl_basic_set *bset)
+{
+ struct isl_tab *tab;
- ineq = get_row_parameter_ineq(tab, row);
- if (!ineq)
+ if (!bset)
+ return NULL;
+ tab = tab_for_lexmin((struct isl_basic_map *)bset, NULL, 1, 0);
+ if (!tab)
goto error;
+ if (isl_tab_track_bset(tab, bset) < 0)
+ goto error;
+ tab = isl_tab_init_samples(tab);
+ return tab;
+error:
+ isl_basic_set_free(bset);
+ return NULL;
+}
- strict = is_strict(ineq);
-
- isl_int_init(tmp);
- for (i = context_tab->n_outside; i < context_tab->n_sample; ++i) {
- isl_seq_inner_product(context_tab->samples->row[i], ineq->el,
- ineq->size, &tmp);
- sgn = isl_int_sgn(tmp);
- if (sgn > 0 || (sgn == 0 && (critical || strict))) {
- if (res == isl_tab_row_unknown)
- res = isl_tab_row_pos;
- if (res == isl_tab_row_neg)
- res = isl_tab_row_any;
- }
- if (sgn < 0) {
- if (res == isl_tab_row_unknown)
- res = isl_tab_row_neg;
- if (res == isl_tab_row_pos)
- res = isl_tab_row_any;
- }
- if (res == isl_tab_row_any)
- break;
- }
- isl_int_clear(tmp);
-
- if (res != isl_tab_row_any) {
- if (isl_tab_extend_cons(context_tab, 1) < 0)
- goto error;
-
- snap = isl_tab_snap(context_tab);
- isl_tab_push_basis(context_tab);
- }
-
- if (res == isl_tab_row_unknown || res == isl_tab_row_pos) {
- /* test for negative values */
- int feasible;
- isl_seq_neg(ineq->el, ineq->el, ineq->size);
- isl_int_sub_ui(ineq->el[0], ineq->el[0], 1);
+static struct isl_context *isl_context_lex_alloc(struct isl_basic_set *dom)
+{
+ struct isl_context_lex *clex;
- isl_tab_push_basis(context_tab);
- sol->context_tab = add_lexmin_ineq(sol->context_tab, ineq->el);
- feasible = context_is_feasible(sol);
- if (feasible < 0)
- goto error;
- context_tab = sol->context_tab;
- if (!feasible)
- res = isl_tab_row_pos;
- else
- res = (res == isl_tab_row_unknown) ? isl_tab_row_neg
- : isl_tab_row_any;
- if (isl_tab_rollback(context_tab, snap) < 0)
- goto error;
+ if (!dom)
+ return NULL;
- if (res == isl_tab_row_neg) {
- isl_seq_neg(ineq->el, ineq->el, ineq->size);
- isl_int_sub_ui(ineq->el[0], ineq->el[0], 1);
- }
- }
+ clex = isl_alloc_type(dom->ctx, struct isl_context_lex);
+ if (!clex)
+ return NULL;
- if (res == isl_tab_row_neg) {
- /* test for positive values */
- int feasible;
- if (!critical && !strict)
- isl_int_sub_ui(ineq->el[0], ineq->el[0], 1);
+ clex->context.op = &isl_context_lex_op;
- isl_tab_push_basis(context_tab);
- sol->context_tab = add_lexmin_ineq(sol->context_tab, ineq->el);
- feasible = context_is_feasible(sol);
- if (feasible < 0)
- goto error;
- context_tab = sol->context_tab;
- if (feasible)
- res = isl_tab_row_any;
- if (isl_tab_rollback(context_tab, snap) < 0)
- goto error;
- }
+ clex->tab = context_tab_for_lexmin(isl_basic_set_copy(dom));
+ if (restore_lexmin(clex->tab) < 0)
+ goto error;
+ clex->tab = check_integer_feasible(clex->tab);
+ if (!clex->tab)
+ goto error;
- isl_vec_free(ineq);
- return res;
+ return &clex->context;
error:
- isl_vec_free(ineq);
- return 0;
+ clex->context.op->free(&clex->context);
+ return NULL;
}
-static struct isl_sol *find_solutions(struct isl_sol *sol, struct isl_tab *tab);
-
-/* Find solutions for values of the parameters that satisfy the given
- * inequality.
+/* Representation of the context when using generalized basis reduction.
*
- * We currently take a snapshot of the context tableau that is reset
- * when we return from this function, while we make a copy of the main
- * tableau, leaving the original main tableau untouched.
- * These are fairly arbitrary choices. Making a copy also of the context
- * tableau would obviate the need to undo any changes made to it later,
- * while taking a snapshot of the main tableau could reduce memory usage.
- * If we were to switch to taking a snapshot of the main tableau,
- * we would have to keep in mind that we need to save the row signs
- * and that we need to do this before saving the current basis
- * such that the basis has been restore before we restore the row signs.
+ * "shifted" contains the offsets of the unit hypercubes that lie inside the
+ * context. Any rational point in "shifted" can therefore be rounded
+ * up to an integer point in the context.
+ * If the context is constrained by any equality, then "shifted" is not used
+ * as it would be empty.
*/
-static struct isl_sol *find_in_pos(struct isl_sol *sol,
- struct isl_tab *tab, isl_int *ineq)
-{
- struct isl_tab_undo *snap;
-
- snap = isl_tab_snap(sol->context_tab);
- isl_tab_push_basis(sol->context_tab);
- if (isl_tab_extend_cons(sol->context_tab, 1) < 0)
- goto error;
+struct isl_context_gbr {
+ struct isl_context context;
+ struct isl_tab *tab;
+ struct isl_tab *shifted;
+ struct isl_tab *cone;
+};
- tab = isl_tab_dup(tab);
+static struct isl_tab *context_gbr_detect_nonnegative_parameters(
+ struct isl_context *context, struct isl_tab *tab)
+{
+ struct isl_context_gbr *cgbr = (struct isl_context_gbr *)context;
if (!tab)
- goto error;
-
- sol->context_tab = add_lexmin_ineq(sol->context_tab, ineq);
- sol->context_tab = check_samples(sol->context_tab, ineq, 0);
+ return NULL;
+ return tab_detect_nonnegative_parameters(tab, cgbr->tab);
+}
- sol = find_solutions(sol, tab);
+static struct isl_basic_set *context_gbr_peek_basic_set(
+ struct isl_context *context)
+{
+ struct isl_context_gbr *cgbr = (struct isl_context_gbr *)context;
+ if (!cgbr->tab)
+ return NULL;
+ return isl_tab_peek_bset(cgbr->tab);
+}
- isl_tab_rollback(sol->context_tab, snap);
- return sol;
-error:
- isl_tab_rollback(sol->context_tab, snap);
- sol_free(sol);
- return NULL;
+static struct isl_tab *context_gbr_peek_tab(struct isl_context *context)
+{
+ struct isl_context_gbr *cgbr = (struct isl_context_gbr *)context;
+ return cgbr->tab;
}
-/* Record the absence of solutions for those values of the parameters
- * that do not satisfy the given inequality with equality.
+/* Initialize the "shifted" tableau of the context, which
+ * contains the constraints of the original tableau shifted
+ * by the sum of all negative coefficients. This ensures
+ * that any rational point in the shifted tableau can
+ * be rounded up to yield an integer point in the original tableau.
*/
-static struct isl_sol *no_sol_in_strict(struct isl_sol *sol,
- struct isl_tab *tab, struct isl_vec *ineq)
+static void gbr_init_shifted(struct isl_context_gbr *cgbr)
{
- int empty;
- int f;
- struct isl_tab_undo *snap;
- snap = isl_tab_snap(sol->context_tab);
- isl_tab_push_basis(sol->context_tab);
- if (isl_tab_extend_cons(sol->context_tab, 1) < 0)
- goto error;
+ int i, j;
+ struct isl_vec *cst;
+ struct isl_basic_set *bset = isl_tab_peek_bset(cgbr->tab);
+ unsigned dim = isl_basic_set_total_dim(bset);
- isl_int_sub_ui(ineq->el[0], ineq->el[0], 1);
+ cst = isl_vec_alloc(cgbr->tab->mat->ctx, bset->n_ineq);
+ if (!cst)
+ return;
- sol->context_tab = add_lexmin_ineq(sol->context_tab, ineq->el);
- f = context_valid_sample_or_feasible(sol, ineq->el, 0);
- if (f < 0)
- goto error;
+ for (i = 0; i < bset->n_ineq; ++i) {
+ isl_int_set(cst->el[i], bset->ineq[i][0]);
+ for (j = 0; j < dim; ++j) {
+ if (!isl_int_is_neg(bset->ineq[i][1 + j]))
+ continue;
+ isl_int_add(bset->ineq[i][0], bset->ineq[i][0],
+ bset->ineq[i][1 + j]);
+ }
+ }
- empty = tab->empty;
- tab->empty = 1;
- sol = sol->add(sol, tab);
- tab->empty = empty;
+ cgbr->shifted = isl_tab_from_basic_set(bset, 0);
- isl_int_add_ui(ineq->el[0], ineq->el[0], 1);
+ for (i = 0; i < bset->n_ineq; ++i)
+ isl_int_set(bset->ineq[i][0], cst->el[i]);
- if (isl_tab_rollback(sol->context_tab, snap) < 0)
- goto error;
- return sol;
-error:
- sol_free(sol);
- return NULL;
+ isl_vec_free(cst);
}
-/* Given a main tableau where more than one row requires a split,
- * determine and return the "best" row to split on.
- *
- * Given two rows in the main tableau, if the inequality corresponding
- * to the first row is redundant with respect to that of the second row
- * in the current tableau, then it is better to split on the second row,
- * since in the positive part, both row will be positive.
- * (In the negative part a pivot will have to be performed and just about
- * anything can happen to the sign of the other row.)
- *
- * As a simple heuristic, we therefore select the row that makes the most
- * of the other rows redundant.
- *
- * Perhaps it would also be useful to look at the number of constraints
- * that conflict with any given constraint.
+/* Check if the shifted tableau is non-empty, and if so
+ * use the sample point to construct an integer point
+ * of the context tableau.
*/
-static int best_split(struct isl_tab *tab, struct isl_tab *context_tab)
+static struct isl_vec *gbr_get_shifted_sample(struct isl_context_gbr *cgbr)
{
- struct isl_tab_undo *snap, *snap2;
- int split;
- int row;
- int best = -1;
- int best_r;
+ struct isl_vec *sample;
- if (isl_tab_extend_cons(context_tab, 2) < 0)
- return -1;
+ if (!cgbr->shifted)
+ gbr_init_shifted(cgbr);
+ if (!cgbr->shifted)
+ return NULL;
+ if (cgbr->shifted->empty)
+ return isl_vec_alloc(cgbr->tab->mat->ctx, 0);
- snap = isl_tab_snap(context_tab);
- isl_tab_push_basis(context_tab);
- snap2 = isl_tab_snap(context_tab);
+ sample = isl_tab_get_sample_value(cgbr->shifted);
+ sample = isl_vec_ceil(sample);
- for (split = tab->n_redundant; split < tab->n_row; ++split) {
- struct isl_tab_undo *snap3;
- struct isl_vec *ineq = NULL;
- int r = 0;
+ return sample;
+}
- if (!isl_tab_var_from_row(tab, split)->is_nonneg)
- continue;
- if (tab->row_sign[split] != isl_tab_row_any)
- continue;
+static struct isl_basic_set *drop_constant_terms(struct isl_basic_set *bset)
+{
+ int i;
- ineq = get_row_parameter_ineq(tab, split);
- if (!ineq)
- return -1;
- context_tab = isl_tab_add_ineq(context_tab, ineq->el);
- isl_vec_free(ineq);
+ if (!bset)
+ return NULL;
- snap3 = isl_tab_snap(context_tab);
+ for (i = 0; i < bset->n_eq; ++i)
+ isl_int_set_si(bset->eq[i][0], 0);
- for (row = tab->n_redundant; row < tab->n_row; ++row) {
- struct isl_tab_var *var;
+ for (i = 0; i < bset->n_ineq; ++i)
+ isl_int_set_si(bset->ineq[i][0], 0);
- if (row == split)
- continue;
- if (!isl_tab_var_from_row(tab, row)->is_nonneg)
- continue;
- if (tab->row_sign[row] != isl_tab_row_any)
- continue;
+ return bset;
+}
- ineq = get_row_parameter_ineq(tab, row);
- if (!ineq)
- return -1;
- context_tab = isl_tab_add_ineq(context_tab, ineq->el);
- isl_vec_free(ineq);
- var = &context_tab->con[context_tab->n_con - 1];
- if (!context_tab->empty &&
- !isl_tab_min_at_most_neg_one(context_tab, var))
- r++;
- if (isl_tab_rollback(context_tab, snap3) < 0)
- return -1;
+static int use_shifted(struct isl_context_gbr *cgbr)
+{
+ return cgbr->tab->bmap->n_eq == 0 && cgbr->tab->bmap->n_div == 0;
+}
+
+static struct isl_vec *gbr_get_sample(struct isl_context_gbr *cgbr)
+{
+ struct isl_basic_set *bset;
+ struct isl_basic_set *cone;
+
+ if (isl_tab_sample_is_integer(cgbr->tab))
+ return isl_tab_get_sample_value(cgbr->tab);
+
+ if (use_shifted(cgbr)) {
+ struct isl_vec *sample;
+
+ sample = gbr_get_shifted_sample(cgbr);
+ if (!sample || sample->size > 0)
+ return sample;
+
+ isl_vec_free(sample);
+ }
+
+ if (!cgbr->cone) {
+ bset = isl_tab_peek_bset(cgbr->tab);
+ cgbr->cone = isl_tab_from_recession_cone(bset, 0);
+ if (!cgbr->cone)
+ return NULL;
+ if (isl_tab_track_bset(cgbr->cone,
+ isl_basic_set_copy(bset)) < 0)
+ return NULL;
+ }
+ if (isl_tab_detect_implicit_equalities(cgbr->cone) < 0)
+ return NULL;
+
+ if (cgbr->cone->n_dead == cgbr->cone->n_col) {
+ struct isl_vec *sample;
+ struct isl_tab_undo *snap;
+
+ if (cgbr->tab->basis) {
+ if (cgbr->tab->basis->n_col != 1 + cgbr->tab->n_var) {
+ isl_mat_free(cgbr->tab->basis);
+ cgbr->tab->basis = NULL;
+ }
+ cgbr->tab->n_zero = 0;
+ cgbr->tab->n_unbounded = 0;
}
- if (best == -1 || r > best_r) {
- best = split;
- best_r = r;
+
+ snap = isl_tab_snap(cgbr->tab);
+
+ sample = isl_tab_sample(cgbr->tab);
+
+ if (isl_tab_rollback(cgbr->tab, snap) < 0) {
+ isl_vec_free(sample);
+ return NULL;
+ }
+
+ return sample;
+ }
+
+ cone = isl_basic_set_dup(isl_tab_peek_bset(cgbr->cone));
+ cone = drop_constant_terms(cone);
+ cone = isl_basic_set_update_from_tab(cone, cgbr->cone);
+ cone = isl_basic_set_underlying_set(cone);
+ cone = isl_basic_set_gauss(cone, NULL);
+
+ bset = isl_basic_set_dup(isl_tab_peek_bset(cgbr->tab));
+ bset = isl_basic_set_update_from_tab(bset, cgbr->tab);
+ bset = isl_basic_set_underlying_set(bset);
+ bset = isl_basic_set_gauss(bset, NULL);
+
+ return isl_basic_set_sample_with_cone(bset, cone);
+}
+
+static void check_gbr_integer_feasible(struct isl_context_gbr *cgbr)
+{
+ struct isl_vec *sample;
+
+ if (!cgbr->tab)
+ return;
+
+ if (cgbr->tab->empty)
+ return;
+
+ sample = gbr_get_sample(cgbr);
+ if (!sample)
+ goto error;
+
+ if (sample->size == 0) {
+ isl_vec_free(sample);
+ if (isl_tab_mark_empty(cgbr->tab) < 0)
+ goto error;
+ return;
+ }
+
+ cgbr->tab = isl_tab_add_sample(cgbr->tab, sample);
+
+ return;
+error:
+ isl_tab_free(cgbr->tab);
+ cgbr->tab = NULL;
+}
+
+static struct isl_tab *add_gbr_eq(struct isl_tab *tab, isl_int *eq)
+{
+ if (!tab)
+ return NULL;
+
+ if (isl_tab_extend_cons(tab, 2) < 0)
+ goto error;
+
+ if (isl_tab_add_eq(tab, eq) < 0)
+ goto error;
+
+ return tab;
+error:
+ isl_tab_free(tab);
+ return NULL;
+}
+
+/* Add the equality described by "eq" to the context.
+ * If "check" is set, then we check if the context is empty after
+ * adding the equality.
+ * If "update" is set, then we check if the samples are still valid.
+ *
+ * We do not explicitly add shifted copies of the equality to
+ * cgbr->shifted since they would conflict with each other.
+ * Instead, we directly mark cgbr->shifted empty.
+ */
+static void context_gbr_add_eq(struct isl_context *context, isl_int *eq,
+ int check, int update)
+{
+ struct isl_context_gbr *cgbr = (struct isl_context_gbr *)context;
+
+ cgbr->tab = add_gbr_eq(cgbr->tab, eq);
+
+ if (cgbr->shifted && !cgbr->shifted->empty && use_shifted(cgbr)) {
+ if (isl_tab_mark_empty(cgbr->shifted) < 0)
+ goto error;
+ }
+
+ if (cgbr->cone && cgbr->cone->n_col != cgbr->cone->n_dead) {
+ if (isl_tab_extend_cons(cgbr->cone, 2) < 0)
+ goto error;
+ if (isl_tab_add_eq(cgbr->cone, eq) < 0)
+ goto error;
+ }
+
+ if (check) {
+ int v = tab_has_valid_sample(cgbr->tab, eq, 1);
+ if (v < 0)
+ goto error;
+ if (!v)
+ check_gbr_integer_feasible(cgbr);
+ }
+ if (update)
+ cgbr->tab = check_samples(cgbr->tab, eq, 1);
+ return;
+error:
+ isl_tab_free(cgbr->tab);
+ cgbr->tab = NULL;
+}
+
+static void add_gbr_ineq(struct isl_context_gbr *cgbr, isl_int *ineq)
+{
+ if (!cgbr->tab)
+ return;
+
+ if (isl_tab_extend_cons(cgbr->tab, 1) < 0)
+ goto error;
+
+ if (isl_tab_add_ineq(cgbr->tab, ineq) < 0)
+ goto error;
+
+ if (cgbr->shifted && !cgbr->shifted->empty && use_shifted(cgbr)) {
+ int i;
+ unsigned dim;
+ dim = isl_basic_map_total_dim(cgbr->tab->bmap);
+
+ if (isl_tab_extend_cons(cgbr->shifted, 1) < 0)
+ goto error;
+
+ for (i = 0; i < dim; ++i) {
+ if (!isl_int_is_neg(ineq[1 + i]))
+ continue;
+ isl_int_add(ineq[0], ineq[0], ineq[1 + i]);
+ }
+
+ if (isl_tab_add_ineq(cgbr->shifted, ineq) < 0)
+ goto error;
+
+ for (i = 0; i < dim; ++i) {
+ if (!isl_int_is_neg(ineq[1 + i]))
+ continue;
+ isl_int_sub(ineq[0], ineq[0], ineq[1 + i]);
}
- if (isl_tab_rollback(context_tab, snap2) < 0)
+ }
+
+ if (cgbr->cone && cgbr->cone->n_col != cgbr->cone->n_dead) {
+ if (isl_tab_extend_cons(cgbr->cone, 1) < 0)
+ goto error;
+ if (isl_tab_add_ineq(cgbr->cone, ineq) < 0)
+ goto error;
+ }
+
+ return;
+error:
+ isl_tab_free(cgbr->tab);
+ cgbr->tab = NULL;
+}
+
+static void context_gbr_add_ineq(struct isl_context *context, isl_int *ineq,
+ int check, int update)
+{
+ struct isl_context_gbr *cgbr = (struct isl_context_gbr *)context;
+
+ add_gbr_ineq(cgbr, ineq);
+ if (!cgbr->tab)
+ return;
+
+ if (check) {
+ int v = tab_has_valid_sample(cgbr->tab, ineq, 0);
+ if (v < 0)
+ goto error;
+ if (!v)
+ check_gbr_integer_feasible(cgbr);
+ }
+ if (update)
+ cgbr->tab = check_samples(cgbr->tab, ineq, 0);
+ return;
+error:
+ isl_tab_free(cgbr->tab);
+ cgbr->tab = NULL;
+}
+
+static int context_gbr_add_ineq_wrap(void *user, isl_int *ineq)
+{
+ struct isl_context *context = (struct isl_context *)user;
+ context_gbr_add_ineq(context, ineq, 0, 0);
+ return context->op->is_ok(context) ? 0 : -1;
+}
+
+static enum isl_tab_row_sign context_gbr_ineq_sign(struct isl_context *context,
+ isl_int *ineq, int strict)
+{
+ struct isl_context_gbr *cgbr = (struct isl_context_gbr *)context;
+ return tab_ineq_sign(cgbr->tab, ineq, strict);
+}
+
+/* Check whether "ineq" can be added to the tableau without rendering
+ * it infeasible.
+ */
+static int context_gbr_test_ineq(struct isl_context *context, isl_int *ineq)
+{
+ struct isl_context_gbr *cgbr = (struct isl_context_gbr *)context;
+ struct isl_tab_undo *snap;
+ struct isl_tab_undo *shifted_snap = NULL;
+ struct isl_tab_undo *cone_snap = NULL;
+ int feasible;
+
+ if (!cgbr->tab)
+ return -1;
+
+ if (isl_tab_extend_cons(cgbr->tab, 1) < 0)
+ return -1;
+
+ snap = isl_tab_snap(cgbr->tab);
+ if (cgbr->shifted)
+ shifted_snap = isl_tab_snap(cgbr->shifted);
+ if (cgbr->cone)
+ cone_snap = isl_tab_snap(cgbr->cone);
+ add_gbr_ineq(cgbr, ineq);
+ check_gbr_integer_feasible(cgbr);
+ if (!cgbr->tab)
+ return -1;
+ feasible = !cgbr->tab->empty;
+ if (isl_tab_rollback(cgbr->tab, snap) < 0)
+ return -1;
+ if (shifted_snap) {
+ if (isl_tab_rollback(cgbr->shifted, shifted_snap))
return -1;
+ } else if (cgbr->shifted) {
+ isl_tab_free(cgbr->shifted);
+ cgbr->shifted = NULL;
}
+ if (cone_snap) {
+ if (isl_tab_rollback(cgbr->cone, cone_snap))
+ return -1;
+ } else if (cgbr->cone) {
+ isl_tab_free(cgbr->cone);
+ cgbr->cone = NULL;
+ }
+
+ return feasible;
+}
+
+/* Return the column of the last of the variables associated to
+ * a column that has a non-zero coefficient.
+ * This function is called in a context where only coefficients
+ * of parameters or divs can be non-zero.
+ */
+static int last_non_zero_var_col(struct isl_tab *tab, isl_int *p)
+{
+ int i;
+ int col;
- if (isl_tab_rollback(context_tab, snap) < 0)
+ if (tab->n_var == 0)
return -1;
- return best;
+ for (i = tab->n_var - 1; i >= 0; --i) {
+ if (i >= tab->n_param && i < tab->n_var - tab->n_div)
+ continue;
+ if (tab->var[i].is_row)
+ continue;
+ col = tab->var[i].index;
+ if (!isl_int_is_zero(p[col]))
+ return col;
+ }
+
+ return -1;
}
-/* Compute the lexicographic minimum of the set represented by the main
- * tableau "tab" within the context "sol->context_tab".
- * On entry the sample value of the main tableau is lexicographically
- * less than or equal to this lexicographic minimum.
- * Pivots are performed until a feasible point is found, which is then
- * necessarily equal to the minimum, or until the tableau is found to
- * be infeasible. Some pivots may need to be performed for only some
- * feasible values of the context tableau. If so, the context tableau
- * is split into a part where the pivot is needed and a part where it is not.
+/* Look through all the recently added equalities in the context
+ * to see if we can propagate any of them to the main tableau.
*
- * Whenever we enter the main loop, the main tableau is such that no
- * "obvious" pivots need to be performed on it, where "obvious" means
- * that the given row can be seen to be negative without looking at
- * the context tableau. In particular, for non-parametric problems,
- * no pivots need to be performed on the main tableau.
- * The caller of find_solutions is responsible for making this property
- * hold prior to the first iteration of the loop, while restore_lexmin
- * is called before every other iteration.
- *
- * Inside the main loop, we first examine the signs of the rows of
- * the main tableau within the context of the context tableau.
- * If we find a row that is always non-positive for all values of
- * the parameters satisfying the context tableau and negative for at
- * least one value of the parameters, we perform the appropriate pivot
- * and start over. An exception is the case where no pivot can be
- * performed on the row. In this case, we require that the sign of
- * the row is negative for all values of the parameters (rather than just
- * non-positive). This special case is handled inside row_sign, which
- * will say that the row can have any sign if it determines that it can
- * attain both negative and zero values.
- *
- * If we can't find a row that always requires a pivot, but we can find
- * one or more rows that require a pivot for some values of the parameters
- * (i.e., the row can attain both positive and negative signs), then we split
- * the context tableau into two parts, one where we force the sign to be
- * non-negative and one where we force is to be negative.
- * The non-negative part is handled by a recursive call (through find_in_pos).
- * Upon returning from this call, we continue with the negative part and
- * perform the required pivot.
- *
- * If no such rows can be found, all rows are non-negative and we have
- * found a (rational) feasible point. If we only wanted a rational point
- * then we are done.
- * Otherwise, we check if all values of the sample point of the tableau
- * are integral for the variables. If so, we have found the minimal
- * integral point and we are done.
- * If the sample point is not integral, then we need to make a distinction
- * based on whether the constant term is non-integral or the coefficients
- * of the parameters. Furthermore, in order to decide how to handle
- * the non-integrality, we also need to know whether the coefficients
- * of the other columns in the tableau are integral. This leads
- * to the following table. The first two rows do not correspond
- * to a non-integral sample point and are only mentioned for completeness.
- *
- * constant parameters other
- *
- * int int int |
- * int int rat | -> no problem
+ * The newly added equalities in the context are encoded as pairs
+ * of inequalities starting at inequality "first".
*
- * rat int int -> fail
- *
- * rat int rat -> cut
- *
- * int rat rat |
- * rat rat rat | -> parametric cut
- *
- * int rat int |
- * rat rat int | -> split context
- *
- * If the parametric constant is completely integral, then there is nothing
- * to be done. If the constant term is non-integral, but all the other
- * coefficient are integral, then there is nothing that can be done
- * and the tableau has no integral solution.
- * If, on the other hand, one or more of the other columns have rational
- * coeffcients, but the parameter coefficients are all integral, then
- * we can perform a regular (non-parametric) cut.
+ * We tentatively add each of these equalities to the main tableau
+ * and if this happens to result in a row with a final coefficient
+ * that is one or negative one, we use it to kill a column
+ * in the main tableau. Otherwise, we discard the tentatively
+ * added row.
+ */
+static void propagate_equalities(struct isl_context_gbr *cgbr,
+ struct isl_tab *tab, unsigned first)
+{
+ int i;
+ struct isl_vec *eq = NULL;
+
+ eq = isl_vec_alloc(tab->mat->ctx, 1 + tab->n_var);
+ if (!eq)
+ goto error;
+
+ if (isl_tab_extend_cons(tab, (cgbr->tab->bmap->n_ineq - first)/2) < 0)
+ goto error;
+
+ isl_seq_clr(eq->el + 1 + tab->n_param,
+ tab->n_var - tab->n_param - tab->n_div);
+ for (i = first; i < cgbr->tab->bmap->n_ineq; i += 2) {
+ int j;
+ int r;
+ struct isl_tab_undo *snap;
+ snap = isl_tab_snap(tab);
+
+ isl_seq_cpy(eq->el, cgbr->tab->bmap->ineq[i], 1 + tab->n_param);
+ isl_seq_cpy(eq->el + 1 + tab->n_var - tab->n_div,
+ cgbr->tab->bmap->ineq[i] + 1 + tab->n_param,
+ tab->n_div);
+
+ r = isl_tab_add_row(tab, eq->el);
+ if (r < 0)
+ goto error;
+ r = tab->con[r].index;
+ j = last_non_zero_var_col(tab, tab->mat->row[r] + 2 + tab->M);
+ if (j < 0 || j < tab->n_dead ||
+ !isl_int_is_one(tab->mat->row[r][0]) ||
+ (!isl_int_is_one(tab->mat->row[r][2 + tab->M + j]) &&
+ !isl_int_is_negone(tab->mat->row[r][2 + tab->M + j]))) {
+ if (isl_tab_rollback(tab, snap) < 0)
+ goto error;
+ continue;
+ }
+ if (isl_tab_pivot(tab, r, j) < 0)
+ goto error;
+ if (isl_tab_kill_col(tab, j) < 0)
+ goto error;
+
+ if (restore_lexmin(tab) < 0)
+ goto error;
+ }
+
+ isl_vec_free(eq);
+
+ return;
+error:
+ isl_vec_free(eq);
+ isl_tab_free(cgbr->tab);
+ cgbr->tab = NULL;
+}
+
+static int context_gbr_detect_equalities(struct isl_context *context,
+ struct isl_tab *tab)
+{
+ struct isl_context_gbr *cgbr = (struct isl_context_gbr *)context;
+ struct isl_ctx *ctx;
+ unsigned n_ineq;
+
+ ctx = cgbr->tab->mat->ctx;
+
+ if (!cgbr->cone) {
+ struct isl_basic_set *bset = isl_tab_peek_bset(cgbr->tab);
+ cgbr->cone = isl_tab_from_recession_cone(bset, 0);
+ if (!cgbr->cone)
+ goto error;
+ if (isl_tab_track_bset(cgbr->cone,
+ isl_basic_set_copy(bset)) < 0)
+ goto error;
+ }
+ if (isl_tab_detect_implicit_equalities(cgbr->cone) < 0)
+ goto error;
+
+ n_ineq = cgbr->tab->bmap->n_ineq;
+ cgbr->tab = isl_tab_detect_equalities(cgbr->tab, cgbr->cone);
+ if (!cgbr->tab)
+ return -1;
+ if (cgbr->tab->bmap->n_ineq > n_ineq)
+ propagate_equalities(cgbr, tab, n_ineq);
+
+ return 0;
+error:
+ isl_tab_free(cgbr->tab);
+ cgbr->tab = NULL;
+ return -1;
+}
+
+static int context_gbr_get_div(struct isl_context *context, struct isl_tab *tab,
+ struct isl_vec *div)
+{
+ return get_div(tab, context, div);
+}
+
+static int context_gbr_add_div(struct isl_context *context, struct isl_vec *div)
+{
+ struct isl_context_gbr *cgbr = (struct isl_context_gbr *)context;
+ if (cgbr->cone) {
+ int k;
+
+ if (isl_tab_extend_cons(cgbr->cone, 3) < 0)
+ return -1;
+ if (isl_tab_extend_vars(cgbr->cone, 1) < 0)
+ return -1;
+ if (isl_tab_allocate_var(cgbr->cone) <0)
+ return -1;
+
+ cgbr->cone->bmap = isl_basic_map_extend_space(cgbr->cone->bmap,
+ isl_basic_map_get_space(cgbr->cone->bmap), 1, 0, 2);
+ k = isl_basic_map_alloc_div(cgbr->cone->bmap);
+ if (k < 0)
+ return -1;
+ isl_seq_cpy(cgbr->cone->bmap->div[k], div->el, div->size);
+ if (isl_tab_push(cgbr->cone, isl_tab_undo_bmap_div) < 0)
+ return -1;
+ }
+ return context_tab_add_div(cgbr->tab, div,
+ context_gbr_add_ineq_wrap, context);
+}
+
+static int context_gbr_best_split(struct isl_context *context,
+ struct isl_tab *tab)
+{
+ struct isl_context_gbr *cgbr = (struct isl_context_gbr *)context;
+ struct isl_tab_undo *snap;
+ int r;
+
+ snap = isl_tab_snap(cgbr->tab);
+ r = best_split(tab, cgbr->tab);
+
+ if (r >= 0 && isl_tab_rollback(cgbr->tab, snap) < 0)
+ return -1;
+
+ return r;
+}
+
+static int context_gbr_is_empty(struct isl_context *context)
+{
+ struct isl_context_gbr *cgbr = (struct isl_context_gbr *)context;
+ if (!cgbr->tab)
+ return -1;
+ return cgbr->tab->empty;
+}
+
+struct isl_gbr_tab_undo {
+ struct isl_tab_undo *tab_snap;
+ struct isl_tab_undo *shifted_snap;
+ struct isl_tab_undo *cone_snap;
+};
+
+static void *context_gbr_save(struct isl_context *context)
+{
+ struct isl_context_gbr *cgbr = (struct isl_context_gbr *)context;
+ struct isl_gbr_tab_undo *snap;
+
+ snap = isl_alloc_type(cgbr->tab->mat->ctx, struct isl_gbr_tab_undo);
+ if (!snap)
+ return NULL;
+
+ snap->tab_snap = isl_tab_snap(cgbr->tab);
+ if (isl_tab_save_samples(cgbr->tab) < 0)
+ goto error;
+
+ if (cgbr->shifted)
+ snap->shifted_snap = isl_tab_snap(cgbr->shifted);
+ else
+ snap->shifted_snap = NULL;
+
+ if (cgbr->cone)
+ snap->cone_snap = isl_tab_snap(cgbr->cone);
+ else
+ snap->cone_snap = NULL;
+
+ return snap;
+error:
+ free(snap);
+ return NULL;
+}
+
+static void context_gbr_restore(struct isl_context *context, void *save)
+{
+ struct isl_context_gbr *cgbr = (struct isl_context_gbr *)context;
+ struct isl_gbr_tab_undo *snap = (struct isl_gbr_tab_undo *)save;
+ if (!snap)
+ goto error;
+ if (isl_tab_rollback(cgbr->tab, snap->tab_snap) < 0) {
+ isl_tab_free(cgbr->tab);
+ cgbr->tab = NULL;
+ }
+
+ if (snap->shifted_snap) {
+ if (isl_tab_rollback(cgbr->shifted, snap->shifted_snap) < 0)
+ goto error;
+ } else if (cgbr->shifted) {
+ isl_tab_free(cgbr->shifted);
+ cgbr->shifted = NULL;
+ }
+
+ if (snap->cone_snap) {
+ if (isl_tab_rollback(cgbr->cone, snap->cone_snap) < 0)
+ goto error;
+ } else if (cgbr->cone) {
+ isl_tab_free(cgbr->cone);
+ cgbr->cone = NULL;
+ }
+
+ free(snap);
+
+ return;
+error:
+ free(snap);
+ isl_tab_free(cgbr->tab);
+ cgbr->tab = NULL;
+}
+
+static void context_gbr_discard(void *save)
+{
+ struct isl_gbr_tab_undo *snap = (struct isl_gbr_tab_undo *)save;
+ free(snap);
+}
+
+static int context_gbr_is_ok(struct isl_context *context)
+{
+ struct isl_context_gbr *cgbr = (struct isl_context_gbr *)context;
+ return !!cgbr->tab;
+}
+
+static void context_gbr_invalidate(struct isl_context *context)
+{
+ struct isl_context_gbr *cgbr = (struct isl_context_gbr *)context;
+ isl_tab_free(cgbr->tab);
+ cgbr->tab = NULL;
+}
+
+static void context_gbr_free(struct isl_context *context)
+{
+ struct isl_context_gbr *cgbr = (struct isl_context_gbr *)context;
+ isl_tab_free(cgbr->tab);
+ isl_tab_free(cgbr->shifted);
+ isl_tab_free(cgbr->cone);
+ free(cgbr);
+}
+
+struct isl_context_op isl_context_gbr_op = {
+ context_gbr_detect_nonnegative_parameters,
+ context_gbr_peek_basic_set,
+ context_gbr_peek_tab,
+ context_gbr_add_eq,
+ context_gbr_add_ineq,
+ context_gbr_ineq_sign,
+ context_gbr_test_ineq,
+ context_gbr_get_div,
+ context_gbr_add_div,
+ context_gbr_detect_equalities,
+ context_gbr_best_split,
+ context_gbr_is_empty,
+ context_gbr_is_ok,
+ context_gbr_save,
+ context_gbr_restore,
+ context_gbr_discard,
+ context_gbr_invalidate,
+ context_gbr_free,
+};
+
+static struct isl_context *isl_context_gbr_alloc(struct isl_basic_set *dom)
+{
+ struct isl_context_gbr *cgbr;
+
+ if (!dom)
+ return NULL;
+
+ cgbr = isl_calloc_type(dom->ctx, struct isl_context_gbr);
+ if (!cgbr)
+ return NULL;
+
+ cgbr->context.op = &isl_context_gbr_op;
+
+ cgbr->shifted = NULL;
+ cgbr->cone = NULL;
+ cgbr->tab = isl_tab_from_basic_set(dom, 1);
+ cgbr->tab = isl_tab_init_samples(cgbr->tab);
+ if (!cgbr->tab)
+ goto error;
+ check_gbr_integer_feasible(cgbr);
+
+ return &cgbr->context;
+error:
+ cgbr->context.op->free(&cgbr->context);
+ return NULL;
+}
+
+static struct isl_context *isl_context_alloc(struct isl_basic_set *dom)
+{
+ if (!dom)
+ return NULL;
+
+ if (dom->ctx->opt->context == ISL_CONTEXT_LEXMIN)
+ return isl_context_lex_alloc(dom);
+ else
+ return isl_context_gbr_alloc(dom);
+}
+
+/* Construct an isl_sol_map structure for accumulating the solution.
+ * If track_empty is set, then we also keep track of the parts
+ * of the context where there is no solution.
+ * If max is set, then we are solving a maximization, rather than
+ * a minimization problem, which means that the variables in the
+ * tableau have value "M - x" rather than "M + x".
+ */
+static struct isl_sol *sol_map_init(struct isl_basic_map *bmap,
+ struct isl_basic_set *dom, int track_empty, int max)
+{
+ struct isl_sol_map *sol_map = NULL;
+
+ if (!bmap)
+ goto error;
+
+ sol_map = isl_calloc_type(bmap->ctx, struct isl_sol_map);
+ if (!sol_map)
+ goto error;
+
+ sol_map->sol.rational = ISL_F_ISSET(bmap, ISL_BASIC_MAP_RATIONAL);
+ sol_map->sol.dec_level.callback.run = &sol_dec_level_wrap;
+ sol_map->sol.dec_level.sol = &sol_map->sol;
+ sol_map->sol.max = max;
+ sol_map->sol.n_out = isl_basic_map_dim(bmap, isl_dim_out);
+ sol_map->sol.add = &sol_map_add_wrap;
+ sol_map->sol.add_empty = track_empty ? &sol_map_add_empty_wrap : NULL;
+ sol_map->sol.free = &sol_map_free_wrap;
+ sol_map->map = isl_map_alloc_space(isl_basic_map_get_space(bmap), 1,
+ ISL_MAP_DISJOINT);
+ if (!sol_map->map)
+ goto error;
+
+ sol_map->sol.context = isl_context_alloc(dom);
+ if (!sol_map->sol.context)
+ goto error;
+
+ if (track_empty) {
+ sol_map->empty = isl_set_alloc_space(isl_basic_set_get_space(dom),
+ 1, ISL_SET_DISJOINT);
+ if (!sol_map->empty)
+ goto error;
+ }
+
+ isl_basic_set_free(dom);
+ return &sol_map->sol;
+error:
+ isl_basic_set_free(dom);
+ sol_map_free(sol_map);
+ return NULL;
+}
+
+/* Check whether all coefficients of (non-parameter) variables
+ * are non-positive, meaning that no pivots can be performed on the row.
+ */
+static int is_critical(struct isl_tab *tab, int row)
+{
+ int j;
+ unsigned off = 2 + tab->M;
+
+ for (j = tab->n_dead; j < tab->n_col; ++j) {
+ if (tab->col_var[j] >= 0 &&
+ (tab->col_var[j] < tab->n_param ||
+ tab->col_var[j] >= tab->n_var - tab->n_div))
+ continue;
+
+ if (isl_int_is_pos(tab->mat->row[row][off + j]))
+ return 0;
+ }
+
+ return 1;
+}
+
+/* Check whether the inequality represented by vec is strict over the integers,
+ * i.e., there are no integer values satisfying the constraint with
+ * equality. This happens if the gcd of the coefficients is not a divisor
+ * of the constant term. If so, scale the constraint down by the gcd
+ * of the coefficients.
+ */
+static int is_strict(struct isl_vec *vec)
+{
+ isl_int gcd;
+ int strict = 0;
+
+ isl_int_init(gcd);
+ isl_seq_gcd(vec->el + 1, vec->size - 1, &gcd);
+ if (!isl_int_is_one(gcd)) {
+ strict = !isl_int_is_divisible_by(vec->el[0], gcd);
+ isl_int_fdiv_q(vec->el[0], vec->el[0], gcd);
+ isl_seq_scale_down(vec->el + 1, vec->el + 1, gcd, vec->size-1);
+ }
+ isl_int_clear(gcd);
+
+ return strict;
+}
+
+/* Determine the sign of the given row of the main tableau.
+ * The result is one of
+ * isl_tab_row_pos: always non-negative; no pivot needed
+ * isl_tab_row_neg: always non-positive; pivot
+ * isl_tab_row_any: can be both positive and negative; split
+ *
+ * We first handle some simple cases
+ * - the row sign may be known already
+ * - the row may be obviously non-negative
+ * - the parametric constant may be equal to that of another row
+ * for which we know the sign. This sign will be either "pos" or
+ * "any". If it had been "neg" then we would have pivoted before.
+ *
+ * If none of these cases hold, we check the value of the row for each
+ * of the currently active samples. Based on the signs of these values
+ * we make an initial determination of the sign of the row.
+ *
+ * all zero -> unk(nown)
+ * all non-negative -> pos
+ * all non-positive -> neg
+ * both negative and positive -> all
+ *
+ * If we end up with "all", we are done.
+ * Otherwise, we perform a check for positive and/or negative
+ * values as follows.
+ *
+ * samples neg unk pos
+ * <0 ? Y N Y N
+ * pos any pos
+ * >0 ? Y N Y N
+ * any neg any neg
+ *
+ * There is no special sign for "zero", because we can usually treat zero
+ * as either non-negative or non-positive, whatever works out best.
+ * However, if the row is "critical", meaning that pivoting is impossible
+ * then we don't want to limp zero with the non-positive case, because
+ * then we we would lose the solution for those values of the parameters
+ * where the value of the row is zero. Instead, we treat 0 as non-negative
+ * ensuring a split if the row can attain both zero and negative values.
+ * The same happens when the original constraint was one that could not
+ * be satisfied with equality by any integer values of the parameters.
+ * In this case, we normalize the constraint, but then a value of zero
+ * for the normalized constraint is actually a positive value for the
+ * original constraint, so again we need to treat zero as non-negative.
+ * In both these cases, we have the following decision tree instead:
+ *
+ * all non-negative -> pos
+ * all negative -> neg
+ * both negative and non-negative -> all
+ *
+ * samples neg pos
+ * <0 ? Y N
+ * any pos
+ * >=0 ? Y N
+ * any neg
+ */
+static enum isl_tab_row_sign row_sign(struct isl_tab *tab,
+ struct isl_sol *sol, int row)
+{
+ struct isl_vec *ineq = NULL;
+ enum isl_tab_row_sign res = isl_tab_row_unknown;
+ int critical;
+ int strict;
+ int row2;
+
+ if (tab->row_sign[row] != isl_tab_row_unknown)
+ return tab->row_sign[row];
+ if (is_obviously_nonneg(tab, row))
+ return isl_tab_row_pos;
+ for (row2 = tab->n_redundant; row2 < tab->n_row; ++row2) {
+ if (tab->row_sign[row2] == isl_tab_row_unknown)
+ continue;
+ if (identical_parameter_line(tab, row, row2))
+ return tab->row_sign[row2];
+ }
+
+ critical = is_critical(tab, row);
+
+ ineq = get_row_parameter_ineq(tab, row);
+ if (!ineq)
+ goto error;
+
+ strict = is_strict(ineq);
+
+ res = sol->context->op->ineq_sign(sol->context, ineq->el,
+ critical || strict);
+
+ if (res == isl_tab_row_unknown || res == isl_tab_row_pos) {
+ /* test for negative values */
+ int feasible;
+ isl_seq_neg(ineq->el, ineq->el, ineq->size);
+ isl_int_sub_ui(ineq->el[0], ineq->el[0], 1);
+
+ feasible = sol->context->op->test_ineq(sol->context, ineq->el);
+ if (feasible < 0)
+ goto error;
+ if (!feasible)
+ res = isl_tab_row_pos;
+ else
+ res = (res == isl_tab_row_unknown) ? isl_tab_row_neg
+ : isl_tab_row_any;
+ if (res == isl_tab_row_neg) {
+ isl_seq_neg(ineq->el, ineq->el, ineq->size);
+ isl_int_sub_ui(ineq->el[0], ineq->el[0], 1);
+ }
+ }
+
+ if (res == isl_tab_row_neg) {
+ /* test for positive values */
+ int feasible;
+ if (!critical && !strict)
+ isl_int_sub_ui(ineq->el[0], ineq->el[0], 1);
+
+ feasible = sol->context->op->test_ineq(sol->context, ineq->el);
+ if (feasible < 0)
+ goto error;
+ if (feasible)
+ res = isl_tab_row_any;
+ }
+
+ isl_vec_free(ineq);
+ return res;
+error:
+ isl_vec_free(ineq);
+ return isl_tab_row_unknown;
+}
+
+static void find_solutions(struct isl_sol *sol, struct isl_tab *tab);
+
+/* Find solutions for values of the parameters that satisfy the given
+ * inequality.
+ *
+ * We currently take a snapshot of the context tableau that is reset
+ * when we return from this function, while we make a copy of the main
+ * tableau, leaving the original main tableau untouched.
+ * These are fairly arbitrary choices. Making a copy also of the context
+ * tableau would obviate the need to undo any changes made to it later,
+ * while taking a snapshot of the main tableau could reduce memory usage.
+ * If we were to switch to taking a snapshot of the main tableau,
+ * we would have to keep in mind that we need to save the row signs
+ * and that we need to do this before saving the current basis
+ * such that the basis has been restore before we restore the row signs.
+ */
+static void find_in_pos(struct isl_sol *sol, struct isl_tab *tab, isl_int *ineq)
+{
+ void *saved;
+
+ if (!sol->context)
+ goto error;
+ saved = sol->context->op->save(sol->context);
+
+ tab = isl_tab_dup(tab);
+ if (!tab)
+ goto error;
+
+ sol->context->op->add_ineq(sol->context, ineq, 0, 1);
+
+ find_solutions(sol, tab);
+
+ if (!sol->error)
+ sol->context->op->restore(sol->context, saved);
+ else
+ sol->context->op->discard(saved);
+ return;
+error:
+ sol->error = 1;
+}
+
+/* Record the absence of solutions for those values of the parameters
+ * that do not satisfy the given inequality with equality.
+ */
+static void no_sol_in_strict(struct isl_sol *sol,
+ struct isl_tab *tab, struct isl_vec *ineq)
+{
+ int empty;
+ void *saved;
+
+ if (!sol->context || sol->error)
+ goto error;
+ saved = sol->context->op->save(sol->context);
+
+ isl_int_sub_ui(ineq->el[0], ineq->el[0], 1);
+
+ sol->context->op->add_ineq(sol->context, ineq->el, 1, 0);
+ if (!sol->context)
+ goto error;
+
+ empty = tab->empty;
+ tab->empty = 1;
+ sol_add(sol, tab);
+ tab->empty = empty;
+
+ isl_int_add_ui(ineq->el[0], ineq->el[0], 1);
+
+ sol->context->op->restore(sol->context, saved);
+ return;
+error:
+ sol->error = 1;
+}
+
+/* Compute the lexicographic minimum of the set represented by the main
+ * tableau "tab" within the context "sol->context_tab".
+ * On entry the sample value of the main tableau is lexicographically
+ * less than or equal to this lexicographic minimum.
+ * Pivots are performed until a feasible point is found, which is then
+ * necessarily equal to the minimum, or until the tableau is found to
+ * be infeasible. Some pivots may need to be performed for only some
+ * feasible values of the context tableau. If so, the context tableau
+ * is split into a part where the pivot is needed and a part where it is not.
+ *
+ * Whenever we enter the main loop, the main tableau is such that no
+ * "obvious" pivots need to be performed on it, where "obvious" means
+ * that the given row can be seen to be negative without looking at
+ * the context tableau. In particular, for non-parametric problems,
+ * no pivots need to be performed on the main tableau.
+ * The caller of find_solutions is responsible for making this property
+ * hold prior to the first iteration of the loop, while restore_lexmin
+ * is called before every other iteration.
+ *
+ * Inside the main loop, we first examine the signs of the rows of
+ * the main tableau within the context of the context tableau.
+ * If we find a row that is always non-positive for all values of
+ * the parameters satisfying the context tableau and negative for at
+ * least one value of the parameters, we perform the appropriate pivot
+ * and start over. An exception is the case where no pivot can be
+ * performed on the row. In this case, we require that the sign of
+ * the row is negative for all values of the parameters (rather than just
+ * non-positive). This special case is handled inside row_sign, which
+ * will say that the row can have any sign if it determines that it can
+ * attain both negative and zero values.
+ *
+ * If we can't find a row that always requires a pivot, but we can find
+ * one or more rows that require a pivot for some values of the parameters
+ * (i.e., the row can attain both positive and negative signs), then we split
+ * the context tableau into two parts, one where we force the sign to be
+ * non-negative and one where we force is to be negative.
+ * The non-negative part is handled by a recursive call (through find_in_pos).
+ * Upon returning from this call, we continue with the negative part and
+ * perform the required pivot.
+ *
+ * If no such rows can be found, all rows are non-negative and we have
+ * found a (rational) feasible point. If we only wanted a rational point
+ * then we are done.
+ * Otherwise, we check if all values of the sample point of the tableau
+ * are integral for the variables. If so, we have found the minimal
+ * integral point and we are done.
+ * If the sample point is not integral, then we need to make a distinction
+ * based on whether the constant term is non-integral or the coefficients
+ * of the parameters. Furthermore, in order to decide how to handle
+ * the non-integrality, we also need to know whether the coefficients
+ * of the other columns in the tableau are integral. This leads
+ * to the following table. The first two rows do not correspond
+ * to a non-integral sample point and are only mentioned for completeness.
+ *
+ * constant parameters other
+ *
+ * int int int |
+ * int int rat | -> no problem
+ *
+ * rat int int -> fail
+ *
+ * rat int rat -> cut
+ *
+ * int rat rat |
+ * rat rat rat | -> parametric cut
+ *
+ * int rat int |
+ * rat rat int | -> split context
+ *
+ * If the parametric constant is completely integral, then there is nothing
+ * to be done. If the constant term is non-integral, but all the other
+ * coefficient are integral, then there is nothing that can be done
+ * and the tableau has no integral solution.
+ * If, on the other hand, one or more of the other columns have rational
+ * coefficients, but the parameter coefficients are all integral, then
+ * we can perform a regular (non-parametric) cut.
* Finally, if there is any parameter coefficient that is non-integral,
* then we need to involve the context tableau. There are two cases here.
* If at least one other column has a rational coefficient, then we
* In the part of the context where this inequality does not hold, the
* main tableau is marked as being empty.
*/
-static struct isl_sol *find_solutions(struct isl_sol *sol, struct isl_tab *tab)
+static void find_solutions(struct isl_sol *sol, struct isl_tab *tab)
+{
+ struct isl_context *context;
+ int r;
+
+ if (!tab || sol->error)
+ goto error;
+
+ context = sol->context;
+
+ if (tab->empty)
+ goto done;
+ if (context->op->is_empty(context))
+ goto done;
+
+ for (r = 0; r >= 0 && tab && !tab->empty; r = restore_lexmin(tab)) {
+ int flags;
+ int row;
+ enum isl_tab_row_sign sgn;
+ int split = -1;
+ int n_split = 0;
+
+ for (row = tab->n_redundant; row < tab->n_row; ++row) {
+ if (!isl_tab_var_from_row(tab, row)->is_nonneg)
+ continue;
+ sgn = row_sign(tab, sol, row);
+ if (!sgn)
+ goto error;
+ tab->row_sign[row] = sgn;
+ if (sgn == isl_tab_row_any)
+ n_split++;
+ if (sgn == isl_tab_row_any && split == -1)
+ split = row;
+ if (sgn == isl_tab_row_neg)
+ break;
+ }
+ if (row < tab->n_row)
+ continue;
+ if (split != -1) {
+ struct isl_vec *ineq;
+ if (n_split != 1)
+ split = context->op->best_split(context, tab);
+ if (split < 0)
+ goto error;
+ ineq = get_row_parameter_ineq(tab, split);
+ if (!ineq)
+ goto error;
+ is_strict(ineq);
+ for (row = tab->n_redundant; row < tab->n_row; ++row) {
+ if (!isl_tab_var_from_row(tab, row)->is_nonneg)
+ continue;
+ if (tab->row_sign[row] == isl_tab_row_any)
+ tab->row_sign[row] = isl_tab_row_unknown;
+ }
+ tab->row_sign[split] = isl_tab_row_pos;
+ sol_inc_level(sol);
+ find_in_pos(sol, tab, ineq->el);
+ tab->row_sign[split] = isl_tab_row_neg;
+ row = split;
+ isl_seq_neg(ineq->el, ineq->el, ineq->size);
+ isl_int_sub_ui(ineq->el[0], ineq->el[0], 1);
+ if (!sol->error)
+ context->op->add_ineq(context, ineq->el, 0, 1);
+ isl_vec_free(ineq);
+ if (sol->error)
+ goto error;
+ continue;
+ }
+ if (tab->rational)
+ break;
+ row = first_non_integer_row(tab, &flags);
+ if (row < 0)
+ break;
+ if (ISL_FL_ISSET(flags, I_PAR)) {
+ if (ISL_FL_ISSET(flags, I_VAR)) {
+ if (isl_tab_mark_empty(tab) < 0)
+ goto error;
+ break;
+ }
+ row = add_cut(tab, row);
+ } else if (ISL_FL_ISSET(flags, I_VAR)) {
+ struct isl_vec *div;
+ struct isl_vec *ineq;
+ int d;
+ div = get_row_split_div(tab, row);
+ if (!div)
+ goto error;
+ d = context->op->get_div(context, tab, div);
+ isl_vec_free(div);
+ if (d < 0)
+ goto error;
+ ineq = ineq_for_div(context->op->peek_basic_set(context), d);
+ if (!ineq)
+ goto error;
+ sol_inc_level(sol);
+ no_sol_in_strict(sol, tab, ineq);
+ isl_seq_neg(ineq->el, ineq->el, ineq->size);
+ context->op->add_ineq(context, ineq->el, 1, 1);
+ isl_vec_free(ineq);
+ if (sol->error || !context->op->is_ok(context))
+ goto error;
+ tab = set_row_cst_to_div(tab, row, d);
+ if (context->op->is_empty(context))
+ break;
+ } else
+ row = add_parametric_cut(tab, row, context);
+ if (row < 0)
+ goto error;
+ }
+ if (r < 0)
+ goto error;
+done:
+ sol_add(sol, tab);
+ isl_tab_free(tab);
+ return;
+error:
+ isl_tab_free(tab);
+ sol->error = 1;
+}
+
+/* Does "sol" contain a pair of partial solutions that could potentially
+ * be merged?
+ *
+ * We currently only check that "sol" is not in an error state
+ * and that there are at least two partial solutions of which the final two
+ * are defined at the same level.
+ */
+static int sol_has_mergeable_solutions(struct isl_sol *sol)
+{
+ if (sol->error)
+ return 0;
+ if (!sol->partial)
+ return 0;
+ if (!sol->partial->next)
+ return 0;
+ return sol->partial->level == sol->partial->next->level;
+}
+
+/* Compute the lexicographic minimum of the set represented by the main
+ * tableau "tab" within the context "sol->context_tab".
+ *
+ * As a preprocessing step, we first transfer all the purely parametric
+ * equalities from the main tableau to the context tableau, i.e.,
+ * parameters that have been pivoted to a row.
+ * These equalities are ignored by the main algorithm, because the
+ * corresponding rows may not be marked as being non-negative.
+ * In parts of the context where the added equality does not hold,
+ * the main tableau is marked as being empty.
+ *
+ * Before we embark on the actual computation, we save a copy
+ * of the context. When we return, we check if there are any
+ * partial solutions that can potentially be merged. If so,
+ * we perform a rollback to the initial state of the context.
+ * The merging of partial solutions happens inside calls to
+ * sol_dec_level that are pushed onto the undo stack of the context.
+ * If there are no partial solutions that can potentially be merged
+ * then the rollback is skipped as it would just be wasted effort.
+ */
+static void find_solutions_main(struct isl_sol *sol, struct isl_tab *tab)
+{
+ int row;
+ void *saved;
+
+ if (!tab)
+ goto error;
+
+ sol->level = 0;
+
+ for (row = tab->n_redundant; row < tab->n_row; ++row) {
+ int p;
+ struct isl_vec *eq;
+
+ if (tab->row_var[row] < 0)
+ continue;
+ if (tab->row_var[row] >= tab->n_param &&
+ tab->row_var[row] < tab->n_var - tab->n_div)
+ continue;
+ if (tab->row_var[row] < tab->n_param)
+ p = tab->row_var[row];
+ else
+ p = tab->row_var[row]
+ + tab->n_param - (tab->n_var - tab->n_div);
+
+ eq = isl_vec_alloc(tab->mat->ctx, 1+tab->n_param+tab->n_div);
+ if (!eq)
+ goto error;
+ get_row_parameter_line(tab, row, eq->el);
+ isl_int_neg(eq->el[1 + p], tab->mat->row[row][0]);
+ eq = isl_vec_normalize(eq);
+
+ sol_inc_level(sol);
+ no_sol_in_strict(sol, tab, eq);
+
+ isl_seq_neg(eq->el, eq->el, eq->size);
+ sol_inc_level(sol);
+ no_sol_in_strict(sol, tab, eq);
+ isl_seq_neg(eq->el, eq->el, eq->size);
+
+ sol->context->op->add_eq(sol->context, eq->el, 1, 1);
+
+ isl_vec_free(eq);
+
+ if (isl_tab_mark_redundant(tab, row) < 0)
+ goto error;
+
+ if (sol->context->op->is_empty(sol->context))
+ break;
+
+ row = tab->n_redundant - 1;
+ }
+
+ saved = sol->context->op->save(sol->context);
+
+ find_solutions(sol, tab);
+
+ if (sol_has_mergeable_solutions(sol))
+ sol->context->op->restore(sol->context, saved);
+ else
+ sol->context->op->discard(saved);
+
+ sol->level = 0;
+ sol_pop(sol);
+
+ return;
+error:
+ isl_tab_free(tab);
+ sol->error = 1;
+}
+
+/* Check if integer division "div" of "dom" also occurs in "bmap".
+ * If so, return its position within the divs.
+ * If not, return -1.
+ */
+static int find_context_div(struct isl_basic_map *bmap,
+ struct isl_basic_set *dom, unsigned div)
+{
+ int i;
+ unsigned b_dim = isl_space_dim(bmap->dim, isl_dim_all);
+ unsigned d_dim = isl_space_dim(dom->dim, isl_dim_all);
+
+ if (isl_int_is_zero(dom->div[div][0]))
+ return -1;
+ if (isl_seq_first_non_zero(dom->div[div] + 2 + d_dim, dom->n_div) != -1)
+ return -1;
+
+ for (i = 0; i < bmap->n_div; ++i) {
+ if (isl_int_is_zero(bmap->div[i][0]))
+ continue;
+ if (isl_seq_first_non_zero(bmap->div[i] + 2 + d_dim,
+ (b_dim - d_dim) + bmap->n_div) != -1)
+ continue;
+ if (isl_seq_eq(bmap->div[i], dom->div[div], 2 + d_dim))
+ return i;
+ }
+ return -1;
+}
+
+/* The correspondence between the variables in the main tableau,
+ * the context tableau, and the input map and domain is as follows.
+ * The first n_param and the last n_div variables of the main tableau
+ * form the variables of the context tableau.
+ * In the basic map, these n_param variables correspond to the
+ * parameters and the input dimensions. In the domain, they correspond
+ * to the parameters and the set dimensions.
+ * The n_div variables correspond to the integer divisions in the domain.
+ * To ensure that everything lines up, we may need to copy some of the
+ * integer divisions of the domain to the map. These have to be placed
+ * in the same order as those in the context and they have to be placed
+ * after any other integer divisions that the map may have.
+ * This function performs the required reordering.
+ */
+static struct isl_basic_map *align_context_divs(struct isl_basic_map *bmap,
+ struct isl_basic_set *dom)
+{
+ int i;
+ int common = 0;
+ int other;
+
+ for (i = 0; i < dom->n_div; ++i)
+ if (find_context_div(bmap, dom, i) != -1)
+ common++;
+ other = bmap->n_div - common;
+ if (dom->n_div - common > 0) {
+ bmap = isl_basic_map_extend_space(bmap, isl_space_copy(bmap->dim),
+ dom->n_div - common, 0, 0);
+ if (!bmap)
+ return NULL;
+ }
+ for (i = 0; i < dom->n_div; ++i) {
+ int pos = find_context_div(bmap, dom, i);
+ if (pos < 0) {
+ pos = isl_basic_map_alloc_div(bmap);
+ if (pos < 0)
+ goto error;
+ isl_int_set_si(bmap->div[pos][0], 0);
+ }
+ if (pos != other + i)
+ isl_basic_map_swap_div(bmap, pos, other + i);
+ }
+ return bmap;
+error:
+ isl_basic_map_free(bmap);
+ return NULL;
+}
+
+/* Base case of isl_tab_basic_map_partial_lexopt, after removing
+ * some obvious symmetries.
+ *
+ * We make sure the divs in the domain are properly ordered,
+ * because they will be added one by one in the given order
+ * during the construction of the solution map.
+ */
+static struct isl_sol *basic_map_partial_lexopt_base(
+ __isl_take isl_basic_map *bmap, __isl_take isl_basic_set *dom,
+ __isl_give isl_set **empty, int max,
+ struct isl_sol *(*init)(__isl_keep isl_basic_map *bmap,
+ __isl_take isl_basic_set *dom, int track_empty, int max))
+{
+ struct isl_tab *tab;
+ struct isl_sol *sol = NULL;
+ struct isl_context *context;
+
+ if (dom->n_div) {
+ dom = isl_basic_set_order_divs(dom);
+ bmap = align_context_divs(bmap, dom);
+ }
+ sol = init(bmap, dom, !!empty, max);
+ if (!sol)
+ goto error;
+
+ context = sol->context;
+ if (isl_basic_set_plain_is_empty(context->op->peek_basic_set(context)))
+ /* nothing */;
+ else if (isl_basic_map_plain_is_empty(bmap)) {
+ if (sol->add_empty)
+ sol->add_empty(sol,
+ isl_basic_set_copy(context->op->peek_basic_set(context)));
+ } else {
+ tab = tab_for_lexmin(bmap,
+ context->op->peek_basic_set(context), 1, max);
+ tab = context->op->detect_nonnegative_parameters(context, tab);
+ find_solutions_main(sol, tab);
+ }
+ if (sol->error)
+ goto error;
+
+ isl_basic_map_free(bmap);
+ return sol;
+error:
+ sol_free(sol);
+ isl_basic_map_free(bmap);
+ return NULL;
+}
+
+/* Base case of isl_tab_basic_map_partial_lexopt, after removing
+ * some obvious symmetries.
+ *
+ * We call basic_map_partial_lexopt_base and extract the results.
+ */
+static __isl_give isl_map *basic_map_partial_lexopt_base_map(
+ __isl_take isl_basic_map *bmap, __isl_take isl_basic_set *dom,
+ __isl_give isl_set **empty, int max)
+{
+ isl_map *result = NULL;
+ struct isl_sol *sol;
+ struct isl_sol_map *sol_map;
+
+ sol = basic_map_partial_lexopt_base(bmap, dom, empty, max,
+ &sol_map_init);
+ if (!sol)
+ return NULL;
+ sol_map = (struct isl_sol_map *) sol;
+
+ result = isl_map_copy(sol_map->map);
+ if (empty)
+ *empty = isl_set_copy(sol_map->empty);
+ sol_free(&sol_map->sol);
+ return result;
+}
+
+/* Structure used during detection of parallel constraints.
+ * n_in: number of "input" variables: isl_dim_param + isl_dim_in
+ * n_out: number of "output" variables: isl_dim_out + isl_dim_div
+ * val: the coefficients of the output variables
+ */
+struct isl_constraint_equal_info {
+ isl_basic_map *bmap;
+ unsigned n_in;
+ unsigned n_out;
+ isl_int *val;
+};
+
+/* Check whether the coefficients of the output variables
+ * of the constraint in "entry" are equal to info->val.
+ */
+static int constraint_equal(const void *entry, const void *val)
+{
+ isl_int **row = (isl_int **)entry;
+ const struct isl_constraint_equal_info *info = val;
+
+ return isl_seq_eq((*row) + 1 + info->n_in, info->val, info->n_out);
+}
+
+/* Check whether "bmap" has a pair of constraints that have
+ * the same coefficients for the output variables.
+ * Note that the coefficients of the existentially quantified
+ * variables need to be zero since the existentially quantified
+ * of the result are usually not the same as those of the input.
+ * the isl_dim_out and isl_dim_div dimensions.
+ * If so, return 1 and return the row indices of the two constraints
+ * in *first and *second.
+ */
+static int parallel_constraints(__isl_keep isl_basic_map *bmap,
+ int *first, int *second)
+{
+ int i;
+ isl_ctx *ctx = isl_basic_map_get_ctx(bmap);
+ struct isl_hash_table *table = NULL;
+ struct isl_hash_table_entry *entry;
+ struct isl_constraint_equal_info info;
+ unsigned n_out;
+ unsigned n_div;
+
+ ctx = isl_basic_map_get_ctx(bmap);
+ table = isl_hash_table_alloc(ctx, bmap->n_ineq);
+ if (!table)
+ goto error;
+
+ info.n_in = isl_basic_map_dim(bmap, isl_dim_param) +
+ isl_basic_map_dim(bmap, isl_dim_in);
+ info.bmap = bmap;
+ n_out = isl_basic_map_dim(bmap, isl_dim_out);
+ n_div = isl_basic_map_dim(bmap, isl_dim_div);
+ info.n_out = n_out + n_div;
+ for (i = 0; i < bmap->n_ineq; ++i) {
+ uint32_t hash;
+
+ info.val = bmap->ineq[i] + 1 + info.n_in;
+ if (isl_seq_first_non_zero(info.val, n_out) < 0)
+ continue;
+ if (isl_seq_first_non_zero(info.val + n_out, n_div) >= 0)
+ continue;
+ hash = isl_seq_get_hash(info.val, info.n_out);
+ entry = isl_hash_table_find(ctx, table, hash,
+ constraint_equal, &info, 1);
+ if (!entry)
+ goto error;
+ if (entry->data)
+ break;
+ entry->data = &bmap->ineq[i];
+ }
+
+ if (i < bmap->n_ineq) {
+ *first = ((isl_int **)entry->data) - bmap->ineq;
+ *second = i;
+ }
+
+ isl_hash_table_free(ctx, table);
+
+ return i < bmap->n_ineq;
+error:
+ isl_hash_table_free(ctx, table);
+ return -1;
+}
+
+/* Given a set of upper bounds in "var", add constraints to "bset"
+ * that make the i-th bound smallest.
+ *
+ * In particular, if there are n bounds b_i, then add the constraints
+ *
+ * b_i <= b_j for j > i
+ * b_i < b_j for j < i
+ */
+static __isl_give isl_basic_set *select_minimum(__isl_take isl_basic_set *bset,
+ __isl_keep isl_mat *var, int i)
+{
+ isl_ctx *ctx;
+ int j, k;
+
+ ctx = isl_mat_get_ctx(var);
+
+ for (j = 0; j < var->n_row; ++j) {
+ if (j == i)
+ continue;
+ k = isl_basic_set_alloc_inequality(bset);
+ if (k < 0)
+ goto error;
+ isl_seq_combine(bset->ineq[k], ctx->one, var->row[j],
+ ctx->negone, var->row[i], var->n_col);
+ isl_int_set_si(bset->ineq[k][var->n_col], 0);
+ if (j < i)
+ isl_int_sub_ui(bset->ineq[k][0], bset->ineq[k][0], 1);
+ }
+
+ bset = isl_basic_set_finalize(bset);
+
+ return bset;
+error:
+ isl_basic_set_free(bset);
+ return NULL;
+}
+
+/* Given a set of upper bounds on the last "input" variable m,
+ * construct a set that assigns the minimal upper bound to m, i.e.,
+ * construct a set that divides the space into cells where one
+ * of the upper bounds is smaller than all the others and assign
+ * this upper bound to m.
+ *
+ * In particular, if there are n bounds b_i, then the result
+ * consists of n basic sets, each one of the form
+ *
+ * m = b_i
+ * b_i <= b_j for j > i
+ * b_i < b_j for j < i
+ */
+static __isl_give isl_set *set_minimum(__isl_take isl_space *dim,
+ __isl_take isl_mat *var)
+{
+ int i, k;
+ isl_basic_set *bset = NULL;
+ isl_ctx *ctx;
+ isl_set *set = NULL;
+
+ if (!dim || !var)
+ goto error;
+
+ ctx = isl_space_get_ctx(dim);
+ set = isl_set_alloc_space(isl_space_copy(dim),
+ var->n_row, ISL_SET_DISJOINT);
+
+ for (i = 0; i < var->n_row; ++i) {
+ bset = isl_basic_set_alloc_space(isl_space_copy(dim), 0,
+ 1, var->n_row - 1);
+ k = isl_basic_set_alloc_equality(bset);
+ if (k < 0)
+ goto error;
+ isl_seq_cpy(bset->eq[k], var->row[i], var->n_col);
+ isl_int_set_si(bset->eq[k][var->n_col], -1);
+ bset = select_minimum(bset, var, i);
+ set = isl_set_add_basic_set(set, bset);
+ }
+
+ isl_space_free(dim);
+ isl_mat_free(var);
+ return set;
+error:
+ isl_basic_set_free(bset);
+ isl_set_free(set);
+ isl_space_free(dim);
+ isl_mat_free(var);
+ return NULL;
+}
+
+/* Given that the last input variable of "bmap" represents the minimum
+ * of the bounds in "cst", check whether we need to split the domain
+ * based on which bound attains the minimum.
+ *
+ * A split is needed when the minimum appears in an integer division
+ * or in an equality. Otherwise, it is only needed if it appears in
+ * an upper bound that is different from the upper bounds on which it
+ * is defined.
+ */
+static int need_split_basic_map(__isl_keep isl_basic_map *bmap,
+ __isl_keep isl_mat *cst)
+{
+ int i, j;
+ unsigned total;
+ unsigned pos;
+
+ pos = cst->n_col - 1;
+ total = isl_basic_map_dim(bmap, isl_dim_all);
+
+ for (i = 0; i < bmap->n_div; ++i)
+ if (!isl_int_is_zero(bmap->div[i][2 + pos]))
+ return 1;
+
+ for (i = 0; i < bmap->n_eq; ++i)
+ if (!isl_int_is_zero(bmap->eq[i][1 + pos]))
+ return 1;
+
+ for (i = 0; i < bmap->n_ineq; ++i) {
+ if (isl_int_is_nonneg(bmap->ineq[i][1 + pos]))
+ continue;
+ if (!isl_int_is_negone(bmap->ineq[i][1 + pos]))
+ return 1;
+ if (isl_seq_first_non_zero(bmap->ineq[i] + 1 + pos + 1,
+ total - pos - 1) >= 0)
+ return 1;
+
+ for (j = 0; j < cst->n_row; ++j)
+ if (isl_seq_eq(bmap->ineq[i], cst->row[j], cst->n_col))
+ break;
+ if (j >= cst->n_row)
+ return 1;
+ }
+
+ return 0;
+}
+
+/* Given that the last set variable of "bset" represents the minimum
+ * of the bounds in "cst", check whether we need to split the domain
+ * based on which bound attains the minimum.
+ *
+ * We simply call need_split_basic_map here. This is safe because
+ * the position of the minimum is computed from "cst" and not
+ * from "bmap".
+ */
+static int need_split_basic_set(__isl_keep isl_basic_set *bset,
+ __isl_keep isl_mat *cst)
+{
+ return need_split_basic_map((isl_basic_map *)bset, cst);
+}
+
+/* Given that the last set variable of "set" represents the minimum
+ * of the bounds in "cst", check whether we need to split the domain
+ * based on which bound attains the minimum.
+ */
+static int need_split_set(__isl_keep isl_set *set, __isl_keep isl_mat *cst)
+{
+ int i;
+
+ for (i = 0; i < set->n; ++i)
+ if (need_split_basic_set(set->p[i], cst))
+ return 1;
+
+ return 0;
+}
+
+/* Given a set of which the last set variable is the minimum
+ * of the bounds in "cst", split each basic set in the set
+ * in pieces where one of the bounds is (strictly) smaller than the others.
+ * This subdivision is given in "min_expr".
+ * The variable is subsequently projected out.
+ *
+ * We only do the split when it is needed.
+ * For example if the last input variable m = min(a,b) and the only
+ * constraints in the given basic set are lower bounds on m,
+ * i.e., l <= m = min(a,b), then we can simply project out m
+ * to obtain l <= a and l <= b, without having to split on whether
+ * m is equal to a or b.
+ */
+static __isl_give isl_set *split(__isl_take isl_set *empty,
+ __isl_take isl_set *min_expr, __isl_take isl_mat *cst)
+{
+ int n_in;
+ int i;
+ isl_space *dim;
+ isl_set *res;
+
+ if (!empty || !min_expr || !cst)
+ goto error;
+
+ n_in = isl_set_dim(empty, isl_dim_set);
+ dim = isl_set_get_space(empty);
+ dim = isl_space_drop_dims(dim, isl_dim_set, n_in - 1, 1);
+ res = isl_set_empty(dim);
+
+ for (i = 0; i < empty->n; ++i) {
+ isl_set *set;
+
+ set = isl_set_from_basic_set(isl_basic_set_copy(empty->p[i]));
+ if (need_split_basic_set(empty->p[i], cst))
+ set = isl_set_intersect(set, isl_set_copy(min_expr));
+ set = isl_set_remove_dims(set, isl_dim_set, n_in - 1, 1);
+
+ res = isl_set_union_disjoint(res, set);
+ }
+
+ isl_set_free(empty);
+ isl_set_free(min_expr);
+ isl_mat_free(cst);
+ return res;
+error:
+ isl_set_free(empty);
+ isl_set_free(min_expr);
+ isl_mat_free(cst);
+ return NULL;
+}
+
+/* Given a map of which the last input variable is the minimum
+ * of the bounds in "cst", split each basic set in the set
+ * in pieces where one of the bounds is (strictly) smaller than the others.
+ * This subdivision is given in "min_expr".
+ * The variable is subsequently projected out.
+ *
+ * The implementation is essentially the same as that of "split".
+ */
+static __isl_give isl_map *split_domain(__isl_take isl_map *opt,
+ __isl_take isl_set *min_expr, __isl_take isl_mat *cst)
+{
+ int n_in;
+ int i;
+ isl_space *dim;
+ isl_map *res;
+
+ if (!opt || !min_expr || !cst)
+ goto error;
+
+ n_in = isl_map_dim(opt, isl_dim_in);
+ dim = isl_map_get_space(opt);
+ dim = isl_space_drop_dims(dim, isl_dim_in, n_in - 1, 1);
+ res = isl_map_empty(dim);
+
+ for (i = 0; i < opt->n; ++i) {
+ isl_map *map;
+
+ map = isl_map_from_basic_map(isl_basic_map_copy(opt->p[i]));
+ if (need_split_basic_map(opt->p[i], cst))
+ map = isl_map_intersect_domain(map,
+ isl_set_copy(min_expr));
+ map = isl_map_remove_dims(map, isl_dim_in, n_in - 1, 1);
+
+ res = isl_map_union_disjoint(res, map);
+ }
+
+ isl_map_free(opt);
+ isl_set_free(min_expr);
+ isl_mat_free(cst);
+ return res;
+error:
+ isl_map_free(opt);
+ isl_set_free(min_expr);
+ isl_mat_free(cst);
+ return NULL;
+}
+
+static __isl_give isl_map *basic_map_partial_lexopt(
+ __isl_take isl_basic_map *bmap, __isl_take isl_basic_set *dom,
+ __isl_give isl_set **empty, int max);
+
+union isl_lex_res {
+ void *p;
+ isl_map *map;
+ isl_pw_multi_aff *pma;
+};
+
+/* This function is called from basic_map_partial_lexopt_symm.
+ * The last variable of "bmap" and "dom" corresponds to the minimum
+ * of the bounds in "cst". "map_space" is the space of the original
+ * input relation (of basic_map_partial_lexopt_symm) and "set_space"
+ * is the space of the original domain.
+ *
+ * We recursively call basic_map_partial_lexopt and then plug in
+ * the definition of the minimum in the result.
+ */
+static __isl_give union isl_lex_res basic_map_partial_lexopt_symm_map_core(
+ __isl_take isl_basic_map *bmap, __isl_take isl_basic_set *dom,
+ __isl_give isl_set **empty, int max, __isl_take isl_mat *cst,
+ __isl_take isl_space *map_space, __isl_take isl_space *set_space)
+{
+ isl_map *opt;
+ isl_set *min_expr;
+ union isl_lex_res res;
+
+ min_expr = set_minimum(isl_basic_set_get_space(dom), isl_mat_copy(cst));
+
+ opt = basic_map_partial_lexopt(bmap, dom, empty, max);
+
+ if (empty) {
+ *empty = split(*empty,
+ isl_set_copy(min_expr), isl_mat_copy(cst));
+ *empty = isl_set_reset_space(*empty, set_space);
+ }
+
+ opt = split_domain(opt, min_expr, cst);
+ opt = isl_map_reset_space(opt, map_space);
+
+ res.map = opt;
+ return res;
+}
+
+/* Given a basic map with at least two parallel constraints (as found
+ * by the function parallel_constraints), first look for more constraints
+ * parallel to the two constraint and replace the found list of parallel
+ * constraints by a single constraint with as "input" part the minimum
+ * of the input parts of the list of constraints. Then, recursively call
+ * basic_map_partial_lexopt (possibly finding more parallel constraints)
+ * and plug in the definition of the minimum in the result.
+ *
+ * More specifically, given a set of constraints
+ *
+ * a x + b_i(p) >= 0
+ *
+ * Replace this set by a single constraint
+ *
+ * a x + u >= 0
+ *
+ * with u a new parameter with constraints
+ *
+ * u <= b_i(p)
+ *
+ * Any solution to the new system is also a solution for the original system
+ * since
+ *
+ * a x >= -u >= -b_i(p)
+ *
+ * Moreover, m = min_i(b_i(p)) satisfies the constraints on u and can
+ * therefore be plugged into the solution.
+ */
+static union isl_lex_res basic_map_partial_lexopt_symm(
+ __isl_take isl_basic_map *bmap, __isl_take isl_basic_set *dom,
+ __isl_give isl_set **empty, int max, int first, int second,
+ __isl_give union isl_lex_res (*core)(__isl_take isl_basic_map *bmap,
+ __isl_take isl_basic_set *dom,
+ __isl_give isl_set **empty,
+ int max, __isl_take isl_mat *cst,
+ __isl_take isl_space *map_space,
+ __isl_take isl_space *set_space))
+{
+ int i, n, k;
+ int *list = NULL;
+ unsigned n_in, n_out, n_div;
+ isl_ctx *ctx;
+ isl_vec *var = NULL;
+ isl_mat *cst = NULL;
+ isl_space *map_space, *set_space;
+ union isl_lex_res res;
+
+ map_space = isl_basic_map_get_space(bmap);
+ set_space = empty ? isl_basic_set_get_space(dom) : NULL;
+
+ n_in = isl_basic_map_dim(bmap, isl_dim_param) +
+ isl_basic_map_dim(bmap, isl_dim_in);
+ n_out = isl_basic_map_dim(bmap, isl_dim_all) - n_in;
+
+ ctx = isl_basic_map_get_ctx(bmap);
+ list = isl_alloc_array(ctx, int, bmap->n_ineq);
+ var = isl_vec_alloc(ctx, n_out);
+ if (!list || !var)
+ goto error;
+
+ list[0] = first;
+ list[1] = second;
+ isl_seq_cpy(var->el, bmap->ineq[first] + 1 + n_in, n_out);
+ for (i = second + 1, n = 2; i < bmap->n_ineq; ++i) {
+ if (isl_seq_eq(var->el, bmap->ineq[i] + 1 + n_in, n_out))
+ list[n++] = i;
+ }
+
+ cst = isl_mat_alloc(ctx, n, 1 + n_in);
+ if (!cst)
+ goto error;
+
+ for (i = 0; i < n; ++i)
+ isl_seq_cpy(cst->row[i], bmap->ineq[list[i]], 1 + n_in);
+
+ bmap = isl_basic_map_cow(bmap);
+ if (!bmap)
+ goto error;
+ for (i = n - 1; i >= 0; --i)
+ if (isl_basic_map_drop_inequality(bmap, list[i]) < 0)
+ goto error;
+
+ bmap = isl_basic_map_add(bmap, isl_dim_in, 1);
+ bmap = isl_basic_map_extend_constraints(bmap, 0, 1);
+ k = isl_basic_map_alloc_inequality(bmap);
+ if (k < 0)
+ goto error;
+ isl_seq_clr(bmap->ineq[k], 1 + n_in);
+ isl_int_set_si(bmap->ineq[k][1 + n_in], 1);
+ isl_seq_cpy(bmap->ineq[k] + 1 + n_in + 1, var->el, n_out);
+ bmap = isl_basic_map_finalize(bmap);
+
+ n_div = isl_basic_set_dim(dom, isl_dim_div);
+ dom = isl_basic_set_add_dims(dom, isl_dim_set, 1);
+ dom = isl_basic_set_extend_constraints(dom, 0, n);
+ for (i = 0; i < n; ++i) {
+ k = isl_basic_set_alloc_inequality(dom);
+ if (k < 0)
+ goto error;
+ isl_seq_cpy(dom->ineq[k], cst->row[i], 1 + n_in);
+ isl_int_set_si(dom->ineq[k][1 + n_in], -1);
+ isl_seq_clr(dom->ineq[k] + 1 + n_in + 1, n_div);
+ }
+
+ isl_vec_free(var);
+ free(list);
+
+ return core(bmap, dom, empty, max, cst, map_space, set_space);
+error:
+ isl_space_free(map_space);
+ isl_space_free(set_space);
+ isl_mat_free(cst);
+ isl_vec_free(var);
+ free(list);
+ isl_basic_set_free(dom);
+ isl_basic_map_free(bmap);
+ res.p = NULL;
+ return res;
+}
+
+static __isl_give isl_map *basic_map_partial_lexopt_symm_map(
+ __isl_take isl_basic_map *bmap, __isl_take isl_basic_set *dom,
+ __isl_give isl_set **empty, int max, int first, int second)
+{
+ return basic_map_partial_lexopt_symm(bmap, dom, empty, max,
+ first, second, &basic_map_partial_lexopt_symm_map_core).map;
+}
+
+/* Recursive part of isl_tab_basic_map_partial_lexopt, after detecting
+ * equalities and removing redundant constraints.
+ *
+ * We first check if there are any parallel constraints (left).
+ * If not, we are in the base case.
+ * If there are parallel constraints, we replace them by a single
+ * constraint in basic_map_partial_lexopt_symm and then call
+ * this function recursively to look for more parallel constraints.
+ */
+static __isl_give isl_map *basic_map_partial_lexopt(
+ __isl_take isl_basic_map *bmap, __isl_take isl_basic_set *dom,
+ __isl_give isl_set **empty, int max)
+{
+ int par = 0;
+ int first, second;
+
+ if (!bmap)
+ goto error;
+
+ if (bmap->ctx->opt->pip_symmetry)
+ par = parallel_constraints(bmap, &first, &second);
+ if (par < 0)
+ goto error;
+ if (!par)
+ return basic_map_partial_lexopt_base_map(bmap, dom, empty, max);
+
+ return basic_map_partial_lexopt_symm_map(bmap, dom, empty, max,
+ first, second);
+error:
+ isl_basic_set_free(dom);
+ isl_basic_map_free(bmap);
+ return NULL;
+}
+
+/* Compute the lexicographic minimum (or maximum if "max" is set)
+ * of "bmap" over the domain "dom" and return the result as a map.
+ * If "empty" is not NULL, then *empty is assigned a set that
+ * contains those parts of the domain where there is no solution.
+ * If "bmap" is marked as rational (ISL_BASIC_MAP_RATIONAL),
+ * then we compute the rational optimum. Otherwise, we compute
+ * the integral optimum.
+ *
+ * We perform some preprocessing. As the PILP solver does not
+ * handle implicit equalities very well, we first make sure all
+ * the equalities are explicitly available.
+ *
+ * We also add context constraints to the basic map and remove
+ * redundant constraints. This is only needed because of the
+ * way we handle simple symmetries. In particular, we currently look
+ * for symmetries on the constraints, before we set up the main tableau.
+ * It is then no good to look for symmetries on possibly redundant constraints.
+ */
+struct isl_map *isl_tab_basic_map_partial_lexopt(
+ struct isl_basic_map *bmap, struct isl_basic_set *dom,
+ struct isl_set **empty, int max)
+{
+ if (empty)
+ *empty = NULL;
+ if (!bmap || !dom)
+ goto error;
+
+ isl_assert(bmap->ctx,
+ isl_basic_map_compatible_domain(bmap, dom), goto error);
+
+ if (isl_basic_set_dim(dom, isl_dim_all) == 0)
+ return basic_map_partial_lexopt(bmap, dom, empty, max);
+
+ bmap = isl_basic_map_intersect_domain(bmap, isl_basic_set_copy(dom));
+ bmap = isl_basic_map_detect_equalities(bmap);
+ bmap = isl_basic_map_remove_redundancies(bmap);
+
+ return basic_map_partial_lexopt(bmap, dom, empty, max);
+error:
+ isl_basic_set_free(dom);
+ isl_basic_map_free(bmap);
+ return NULL;
+}
+
+struct isl_sol_for {
+ struct isl_sol sol;
+ int (*fn)(__isl_take isl_basic_set *dom,
+ __isl_take isl_aff_list *list, void *user);
+ void *user;
+};
+
+static void sol_for_free(struct isl_sol_for *sol_for)
+{
+ if (sol_for->sol.context)
+ sol_for->sol.context->op->free(sol_for->sol.context);
+ free(sol_for);
+}
+
+static void sol_for_free_wrap(struct isl_sol *sol)
+{
+ sol_for_free((struct isl_sol_for *)sol);
+}
+
+/* Add the solution identified by the tableau and the context tableau.
+ *
+ * See documentation of sol_add for more details.
+ *
+ * Instead of constructing a basic map, this function calls a user
+ * defined function with the current context as a basic set and
+ * a list of affine expressions representing the relation between
+ * the input and output. The space over which the affine expressions
+ * are defined is the same as that of the domain. The number of
+ * affine expressions in the list is equal to the number of output variables.
+ */
+static void sol_for_add(struct isl_sol_for *sol,
+ struct isl_basic_set *dom, struct isl_mat *M)
+{
+ int i;
+ isl_ctx *ctx;
+ isl_local_space *ls;
+ isl_aff *aff;
+ isl_aff_list *list;
+
+ if (sol->sol.error || !dom || !M)
+ goto error;
+
+ ctx = isl_basic_set_get_ctx(dom);
+ ls = isl_basic_set_get_local_space(dom);
+ list = isl_aff_list_alloc(ctx, M->n_row - 1);
+ for (i = 1; i < M->n_row; ++i) {
+ aff = isl_aff_alloc(isl_local_space_copy(ls));
+ if (aff) {
+ isl_int_set(aff->v->el[0], M->row[0][0]);
+ isl_seq_cpy(aff->v->el + 1, M->row[i], M->n_col);
+ }
+ aff = isl_aff_normalize(aff);
+ list = isl_aff_list_add(list, aff);
+ }
+ isl_local_space_free(ls);
+
+ dom = isl_basic_set_finalize(dom);
+
+ if (sol->fn(isl_basic_set_copy(dom), list, sol->user) < 0)
+ goto error;
+
+ isl_basic_set_free(dom);
+ isl_mat_free(M);
+ return;
+error:
+ isl_basic_set_free(dom);
+ isl_mat_free(M);
+ sol->sol.error = 1;
+}
+
+static void sol_for_add_wrap(struct isl_sol *sol,
+ struct isl_basic_set *dom, struct isl_mat *M)
+{
+ sol_for_add((struct isl_sol_for *)sol, dom, M);
+}
+
+static struct isl_sol_for *sol_for_init(struct isl_basic_map *bmap, int max,
+ int (*fn)(__isl_take isl_basic_set *dom, __isl_take isl_aff_list *list,
+ void *user),
+ void *user)
+{
+ struct isl_sol_for *sol_for = NULL;
+ isl_space *dom_dim;
+ struct isl_basic_set *dom = NULL;
+
+ sol_for = isl_calloc_type(bmap->ctx, struct isl_sol_for);
+ if (!sol_for)
+ goto error;
+
+ dom_dim = isl_space_domain(isl_space_copy(bmap->dim));
+ dom = isl_basic_set_universe(dom_dim);
+
+ sol_for->sol.rational = ISL_F_ISSET(bmap, ISL_BASIC_MAP_RATIONAL);
+ sol_for->sol.dec_level.callback.run = &sol_dec_level_wrap;
+ sol_for->sol.dec_level.sol = &sol_for->sol;
+ sol_for->fn = fn;
+ sol_for->user = user;
+ sol_for->sol.max = max;
+ sol_for->sol.n_out = isl_basic_map_dim(bmap, isl_dim_out);
+ sol_for->sol.add = &sol_for_add_wrap;
+ sol_for->sol.add_empty = NULL;
+ sol_for->sol.free = &sol_for_free_wrap;
+
+ sol_for->sol.context = isl_context_alloc(dom);
+ if (!sol_for->sol.context)
+ goto error;
+
+ isl_basic_set_free(dom);
+ return sol_for;
+error:
+ isl_basic_set_free(dom);
+ sol_for_free(sol_for);
+ return NULL;
+}
+
+static void sol_for_find_solutions(struct isl_sol_for *sol_for,
+ struct isl_tab *tab)
+{
+ find_solutions_main(&sol_for->sol, tab);
+}
+
+int isl_basic_map_foreach_lexopt(__isl_keep isl_basic_map *bmap, int max,
+ int (*fn)(__isl_take isl_basic_set *dom, __isl_take isl_aff_list *list,
+ void *user),
+ void *user)
+{
+ struct isl_sol_for *sol_for = NULL;
+
+ bmap = isl_basic_map_copy(bmap);
+ bmap = isl_basic_map_detect_equalities(bmap);
+ if (!bmap)
+ return -1;
+
+ sol_for = sol_for_init(bmap, max, fn, user);
+ if (!sol_for)
+ goto error;
+
+ if (isl_basic_map_plain_is_empty(bmap))
+ /* nothing */;
+ else {
+ struct isl_tab *tab;
+ struct isl_context *context = sol_for->sol.context;
+ tab = tab_for_lexmin(bmap,
+ context->op->peek_basic_set(context), 1, max);
+ tab = context->op->detect_nonnegative_parameters(context, tab);
+ sol_for_find_solutions(sol_for, tab);
+ if (sol_for->sol.error)
+ goto error;
+ }
+
+ sol_free(&sol_for->sol);
+ isl_basic_map_free(bmap);
+ return 0;
+error:
+ sol_free(&sol_for->sol);
+ isl_basic_map_free(bmap);
+ return -1;
+}
+
+int isl_basic_set_foreach_lexopt(__isl_keep isl_basic_set *bset, int max,
+ int (*fn)(__isl_take isl_basic_set *dom, __isl_take isl_aff_list *list,
+ void *user),
+ void *user)
+{
+ return isl_basic_map_foreach_lexopt(bset, max, fn, user);
+}
+
+/* Check if the given sequence of len variables starting at pos
+ * represents a trivial (i.e., zero) solution.
+ * The variables are assumed to be non-negative and to come in pairs,
+ * with each pair representing a variable of unrestricted sign.
+ * The solution is trivial if each such pair in the sequence consists
+ * of two identical values, meaning that the variable being represented
+ * has value zero.
+ */
+static int region_is_trivial(struct isl_tab *tab, int pos, int len)
+{
+ int i;
+
+ if (len == 0)
+ return 0;
+
+ for (i = 0; i < len; i += 2) {
+ int neg_row;
+ int pos_row;
+
+ neg_row = tab->var[pos + i].is_row ?
+ tab->var[pos + i].index : -1;
+ pos_row = tab->var[pos + i + 1].is_row ?
+ tab->var[pos + i + 1].index : -1;
+
+ if ((neg_row < 0 ||
+ isl_int_is_zero(tab->mat->row[neg_row][1])) &&
+ (pos_row < 0 ||
+ isl_int_is_zero(tab->mat->row[pos_row][1])))
+ continue;
+
+ if (neg_row < 0 || pos_row < 0)
+ return 0;
+ if (isl_int_ne(tab->mat->row[neg_row][1],
+ tab->mat->row[pos_row][1]))
+ return 0;
+ }
+
+ return 1;
+}
+
+/* Return the index of the first trivial region or -1 if all regions
+ * are non-trivial.
+ */
+static int first_trivial_region(struct isl_tab *tab,
+ int n_region, struct isl_region *region)
{
- struct isl_tab **context_tab;
+ int i;
- if (!tab || !sol)
- goto error;
+ for (i = 0; i < n_region; ++i) {
+ if (region_is_trivial(tab, region[i].pos, region[i].len))
+ return i;
+ }
- context_tab = &sol->context_tab;
+ return -1;
+}
- if (tab->empty)
- goto done;
- if ((*context_tab)->empty)
- goto done;
+/* Check if the solution is optimal, i.e., whether the first
+ * n_op entries are zero.
+ */
+static int is_optimal(__isl_keep isl_vec *sol, int n_op)
+{
+ int i;
- for (; tab && !tab->empty; tab = restore_lexmin(tab)) {
- int flags;
- int row;
- int sgn;
- int split = -1;
- int n_split = 0;
+ for (i = 0; i < n_op; ++i)
+ if (!isl_int_is_zero(sol->el[1 + i]))
+ return 0;
+ return 1;
+}
- for (row = tab->n_redundant; row < tab->n_row; ++row) {
- if (!isl_tab_var_from_row(tab, row)->is_nonneg)
- continue;
- sgn = row_sign(tab, sol, row);
- if (!sgn)
- goto error;
- tab->row_sign[row] = sgn;
- if (sgn == isl_tab_row_any)
- n_split++;
- if (sgn == isl_tab_row_any && split == -1)
- split = row;
- if (sgn == isl_tab_row_neg)
- break;
- }
- if (row < tab->n_row)
- continue;
- if (split != -1) {
- struct isl_vec *ineq;
- if (n_split != 1)
- split = best_split(tab, *context_tab);
- if (split < 0)
- goto error;
- ineq = get_row_parameter_ineq(tab, split);
- if (!ineq)
- goto error;
- is_strict(ineq);
- for (row = tab->n_redundant; row < tab->n_row; ++row) {
- if (!isl_tab_var_from_row(tab, row)->is_nonneg)
- continue;
- if (tab->row_sign[row] == isl_tab_row_any)
- tab->row_sign[row] = isl_tab_row_unknown;
- }
- tab->row_sign[split] = isl_tab_row_pos;
- sol = find_in_pos(sol, tab, ineq->el);
- tab->row_sign[split] = isl_tab_row_neg;
- row = split;
- isl_seq_neg(ineq->el, ineq->el, ineq->size);
- isl_int_sub_ui(ineq->el[0], ineq->el[0], 1);
- *context_tab = add_lexmin_ineq(*context_tab, ineq->el);
- *context_tab = check_samples(*context_tab, ineq->el, 0);
- isl_vec_free(ineq);
- if (!sol)
- goto error;
- continue;
- }
- if (tab->rational)
- break;
- row = first_non_integer(tab, &flags);
- if (row < 0)
+/* Add constraints to "tab" that ensure that any solution is significantly
+ * better that that represented by "sol". That is, find the first
+ * relevant (within first n_op) non-zero coefficient and force it (along
+ * with all previous coefficients) to be zero.
+ * If the solution is already optimal (all relevant coefficients are zero),
+ * then just mark the table as empty.
+ */
+static int force_better_solution(struct isl_tab *tab,
+ __isl_keep isl_vec *sol, int n_op)
+{
+ int i;
+ isl_ctx *ctx;
+ isl_vec *v = NULL;
+
+ if (!sol)
+ return -1;
+
+ for (i = 0; i < n_op; ++i)
+ if (!isl_int_is_zero(sol->el[1 + i]))
break;
- if (ISL_FL_ISSET(flags, I_PAR)) {
- if (ISL_FL_ISSET(flags, I_VAR)) {
- tab = isl_tab_mark_empty(tab);
- break;
- }
- row = add_cut(tab, row);
- } else if (ISL_FL_ISSET(flags, I_VAR)) {
- struct isl_vec *div;
- struct isl_vec *ineq;
- int d;
- if (isl_tab_extend_cons(*context_tab, 3) < 0)
- goto error;
- div = get_row_split_div(tab, row);
- if (!div)
- goto error;
- d = get_div(tab, context_tab, div);
- isl_vec_free(div);
- if (d < 0)
- goto error;
- ineq = ineq_for_div((*context_tab)->bset, d);
- sol = no_sol_in_strict(sol, tab, ineq);
- isl_seq_neg(ineq->el, ineq->el, ineq->size);
- *context_tab = add_lexmin_ineq(*context_tab, ineq->el);
- *context_tab = check_samples(*context_tab, ineq->el, 0);
- isl_vec_free(ineq);
- if (!sol)
- goto error;
- tab = set_row_cst_to_div(tab, row, d);
- } else
- row = add_parametric_cut(tab, row, context_tab);
- if (row < 0)
+
+ if (i == n_op) {
+ if (isl_tab_mark_empty(tab) < 0)
+ return -1;
+ return 0;
+ }
+
+ ctx = isl_vec_get_ctx(sol);
+ v = isl_vec_alloc(ctx, 1 + tab->n_var);
+ if (!v)
+ return -1;
+
+ for (; i >= 0; --i) {
+ v = isl_vec_clr(v);
+ isl_int_set_si(v->el[1 + i], -1);
+ if (add_lexmin_eq(tab, v->el) < 0)
goto error;
}
-done:
- sol = sol->add(sol, tab);
- isl_tab_free(tab);
- return sol;
+
+ isl_vec_free(v);
+ return 0;
error:
- isl_tab_free(tab);
- sol_free(sol);
- return NULL;
+ isl_vec_free(v);
+ return -1;
}
-/* Compute the lexicographic minimum of the set represented by the main
- * tableau "tab" within the context "sol->context_tab".
+struct isl_trivial {
+ int update;
+ int region;
+ int side;
+ struct isl_tab_undo *snap;
+};
+
+/* Return the lexicographically smallest non-trivial solution of the
+ * given ILP problem.
*
- * As a preprocessing step, we first transfer all the purely parametric
- * equalities from the main tableau to the context tableau, i.e.,
- * parameters that have been pivoted to a row.
- * These equalities are ignored by the main algorithm, because the
- * corresponding rows may not be marked as being non-negative.
- * In parts of the context where the added equality does not hold,
- * the main tableau is marked as being empty.
+ * All variables are assumed to be non-negative.
+ *
+ * n_op is the number of initial coordinates to optimize.
+ * That is, once a solution has been found, we will only continue looking
+ * for solution that result in significantly better values for those
+ * initial coordinates. That is, we only continue looking for solutions
+ * that increase the number of initial zeros in this sequence.
+ *
+ * A solution is non-trivial, if it is non-trivial on each of the
+ * specified regions. Each region represents a sequence of pairs
+ * of variables. A solution is non-trivial on such a region if
+ * at least one of these pairs consists of different values, i.e.,
+ * such that the non-negative variable represented by the pair is non-zero.
+ *
+ * Whenever a conflict is encountered, all constraints involved are
+ * reported to the caller through a call to "conflict".
+ *
+ * We perform a simple branch-and-bound backtracking search.
+ * Each level in the search represents initially trivial region that is forced
+ * to be non-trivial.
+ * At each level we consider n cases, where n is the length of the region.
+ * In terms of the n/2 variables of unrestricted signs being encoded by
+ * the region, we consider the cases
+ * x_0 >= 1
+ * x_0 <= -1
+ * x_0 = 0 and x_1 >= 1
+ * x_0 = 0 and x_1 <= -1
+ * x_0 = 0 and x_1 = 0 and x_2 >= 1
+ * x_0 = 0 and x_1 = 0 and x_2 <= -1
+ * ...
+ * The cases are considered in this order, assuming that each pair
+ * x_i_a x_i_b represents the value x_i_b - x_i_a.
+ * That is, x_0 >= 1 is enforced by adding the constraint
+ * x_0_b - x_0_a >= 1
*/
-static struct isl_sol *find_solutions_main(struct isl_sol *sol,
- struct isl_tab *tab)
+__isl_give isl_vec *isl_tab_basic_set_non_trivial_lexmin(
+ __isl_take isl_basic_set *bset, int n_op, int n_region,
+ struct isl_region *region,
+ int (*conflict)(int con, void *user), void *user)
{
- int row;
+ int i, j;
+ int r;
+ isl_ctx *ctx;
+ isl_vec *v = NULL;
+ isl_vec *sol = NULL;
+ struct isl_tab *tab;
+ struct isl_trivial *triv = NULL;
+ int level, init;
- for (row = tab->n_redundant; row < tab->n_row; ++row) {
- int p;
- struct isl_vec *eq;
+ if (!bset)
+ return NULL;
- if (tab->row_var[row] < 0)
- continue;
- if (tab->row_var[row] >= tab->n_param &&
- tab->row_var[row] < tab->n_var - tab->n_div)
- continue;
- if (tab->row_var[row] < tab->n_param)
- p = tab->row_var[row];
- else
- p = tab->row_var[row]
- + tab->n_param - (tab->n_var - tab->n_div);
+ ctx = isl_basic_set_get_ctx(bset);
+ sol = isl_vec_alloc(ctx, 0);
- if (isl_tab_extend_cons(sol->context_tab, 2) < 0)
- goto error;
+ tab = tab_for_lexmin(bset, NULL, 0, 0);
+ if (!tab)
+ goto error;
+ tab->conflict = conflict;
+ tab->conflict_user = user;
- eq = isl_vec_alloc(tab->mat->ctx, 1+tab->n_param+tab->n_div);
- get_row_parameter_line(tab, row, eq->el);
- isl_int_neg(eq->el[1 + p], tab->mat->row[row][0]);
- eq = isl_vec_normalize(eq);
+ v = isl_vec_alloc(ctx, 1 + tab->n_var);
+ triv = isl_calloc_array(ctx, struct isl_trivial, n_region);
+ if (!v || !triv)
+ goto error;
- sol = no_sol_in_strict(sol, tab, eq);
+ level = 0;
+ init = 1;
- isl_seq_neg(eq->el, eq->el, eq->size);
- sol = no_sol_in_strict(sol, tab, eq);
- isl_seq_neg(eq->el, eq->el, eq->size);
+ while (level >= 0) {
+ int side, base;
+
+ if (init) {
+ tab = cut_to_integer_lexmin(tab, CUT_ONE);
+ if (!tab)
+ goto error;
+ if (tab->empty)
+ goto backtrack;
+ r = first_trivial_region(tab, n_region, region);
+ if (r < 0) {
+ for (i = 0; i < level; ++i)
+ triv[i].update = 1;
+ isl_vec_free(sol);
+ sol = isl_tab_get_sample_value(tab);
+ if (!sol)
+ goto error;
+ if (is_optimal(sol, n_op))
+ break;
+ goto backtrack;
+ }
+ if (level >= n_region)
+ isl_die(ctx, isl_error_internal,
+ "nesting level too deep", goto error);
+ if (isl_tab_extend_cons(tab,
+ 2 * region[r].len + 2 * n_op) < 0)
+ goto error;
+ triv[level].region = r;
+ triv[level].side = 0;
+ }
- sol->context_tab = add_lexmin_eq(sol->context_tab, eq->el);
- context_valid_sample_or_feasible(sol, eq->el, 1);
- sol->context_tab = check_samples(sol->context_tab, eq->el, 1);
+ r = triv[level].region;
+ side = triv[level].side;
+ base = 2 * (side/2);
+
+ if (side >= region[r].len) {
+backtrack:
+ level--;
+ init = 0;
+ if (level >= 0)
+ if (isl_tab_rollback(tab, triv[level].snap) < 0)
+ goto error;
+ continue;
+ }
- isl_vec_free(eq);
+ if (triv[level].update) {
+ if (force_better_solution(tab, sol, n_op) < 0)
+ goto error;
+ triv[level].update = 0;
+ }
- isl_tab_mark_redundant(tab, row);
+ if (side == base && base >= 2) {
+ for (j = base - 2; j < base; ++j) {
+ v = isl_vec_clr(v);
+ isl_int_set_si(v->el[1 + region[r].pos + j], 1);
+ if (add_lexmin_eq(tab, v->el) < 0)
+ goto error;
+ }
+ }
- if (!sol->context_tab)
+ triv[level].snap = isl_tab_snap(tab);
+ if (isl_tab_push_basis(tab) < 0)
goto error;
- if (sol->context_tab->empty)
- break;
- row = tab->n_redundant - 1;
+ v = isl_vec_clr(v);
+ isl_int_set_si(v->el[0], -1);
+ isl_int_set_si(v->el[1 + region[r].pos + side], -1);
+ isl_int_set_si(v->el[1 + region[r].pos + (side ^ 1)], 1);
+ tab = add_lexmin_ineq(tab, v->el);
+
+ triv[level].side++;
+ level++;
+ init = 1;
}
- return find_solutions(sol, tab);
+ free(triv);
+ isl_vec_free(v);
+ isl_tab_free(tab);
+ isl_basic_set_free(bset);
+
+ return sol;
error:
+ free(triv);
+ isl_vec_free(v);
isl_tab_free(tab);
- sol_free(sol);
+ isl_basic_set_free(bset);
+ isl_vec_free(sol);
return NULL;
}
-static struct isl_sol_map *sol_map_find_solutions(struct isl_sol_map *sol_map,
- struct isl_tab *tab)
-{
- return (struct isl_sol_map *)find_solutions_main(&sol_map->sol, tab);
-}
-
-/* Check if integer division "div" of "dom" also occurs in "bmap".
- * If so, return its position within the divs.
- * If not, return -1.
+/* Return the lexicographically smallest rational point in "bset",
+ * assuming that all variables are non-negative.
+ * If "bset" is empty, then return a zero-length vector.
*/
-static int find_context_div(struct isl_basic_map *bmap,
- struct isl_basic_set *dom, unsigned div)
+__isl_give isl_vec *isl_tab_basic_set_non_neg_lexmin(
+ __isl_take isl_basic_set *bset)
{
- int i;
- unsigned b_dim = isl_dim_total(bmap->dim);
- unsigned d_dim = isl_dim_total(dom->dim);
+ struct isl_tab *tab;
+ isl_ctx *ctx = isl_basic_set_get_ctx(bset);
+ isl_vec *sol;
- if (isl_int_is_zero(dom->div[div][0]))
- return -1;
- if (isl_seq_first_non_zero(dom->div[div] + 2 + d_dim, dom->n_div) != -1)
- return -1;
+ if (!bset)
+ return NULL;
- for (i = 0; i < bmap->n_div; ++i) {
- if (isl_int_is_zero(bmap->div[i][0]))
- continue;
- if (isl_seq_first_non_zero(bmap->div[i] + 2 + d_dim,
- (b_dim - d_dim) + bmap->n_div) != -1)
- continue;
- if (isl_seq_eq(bmap->div[i], dom->div[div], 2 + d_dim))
- return i;
- }
- return -1;
+ tab = tab_for_lexmin(bset, NULL, 0, 0);
+ if (!tab)
+ goto error;
+ if (tab->empty)
+ sol = isl_vec_alloc(ctx, 0);
+ else
+ sol = isl_tab_get_sample_value(tab);
+ isl_tab_free(tab);
+ isl_basic_set_free(bset);
+ return sol;
+error:
+ isl_tab_free(tab);
+ isl_basic_set_free(bset);
+ return NULL;
}
-/* The correspondence between the variables in the main tableau,
- * the context tableau, and the input map and domain is as follows.
- * The first n_param and the last n_div variables of the main tableau
- * form the variables of the context tableau.
- * In the basic map, these n_param variables correspond to the
- * parameters and the input dimensions. In the domain, they correspond
- * to the parameters and the set dimensions.
- * The n_div variables correspond to the integer divisions in the domain.
- * To ensure that everything lines up, we may need to copy some of the
- * integer divisions of the domain to the map. These have to be placed
- * in the same order as those in the context and they have to be placed
- * after any other integer divisions that the map may have.
- * This function performs the required reordering.
- */
-static struct isl_basic_map *align_context_divs(struct isl_basic_map *bmap,
- struct isl_basic_set *dom)
-{
- int i;
- int common = 0;
- int other;
+struct isl_sol_pma {
+ struct isl_sol sol;
+ isl_pw_multi_aff *pma;
+ isl_set *empty;
+};
- for (i = 0; i < dom->n_div; ++i)
- if (find_context_div(bmap, dom, i) != -1)
- common++;
- other = bmap->n_div - common;
- if (dom->n_div - common > 0) {
- bmap = isl_basic_map_extend_dim(bmap, isl_dim_copy(bmap->dim),
- dom->n_div - common, 0, 0);
- if (!bmap)
- return NULL;
- }
- for (i = 0; i < dom->n_div; ++i) {
- int pos = find_context_div(bmap, dom, i);
- if (pos < 0) {
- pos = isl_basic_map_alloc_div(bmap);
- if (pos < 0)
- goto error;
- isl_int_set_si(bmap->div[pos][0], 0);
+static void sol_pma_free(struct isl_sol_pma *sol_pma)
+{
+ if (!sol_pma)
+ return;
+ if (sol_pma->sol.context)
+ sol_pma->sol.context->op->free(sol_pma->sol.context);
+ isl_pw_multi_aff_free(sol_pma->pma);
+ isl_set_free(sol_pma->empty);
+ free(sol_pma);
+}
+
+/* This function is called for parts of the context where there is
+ * no solution, with "bset" corresponding to the context tableau.
+ * Simply add the basic set to the set "empty".
+ */
+static void sol_pma_add_empty(struct isl_sol_pma *sol,
+ __isl_take isl_basic_set *bset)
+{
+ if (!bset)
+ goto error;
+ isl_assert(bset->ctx, sol->empty, goto error);
+
+ sol->empty = isl_set_grow(sol->empty, 1);
+ bset = isl_basic_set_simplify(bset);
+ bset = isl_basic_set_finalize(bset);
+ sol->empty = isl_set_add_basic_set(sol->empty, bset);
+ if (!sol->empty)
+ sol->sol.error = 1;
+ return;
+error:
+ isl_basic_set_free(bset);
+ sol->sol.error = 1;
+}
+
+/* Given a basic map "dom" that represents the context and an affine
+ * matrix "M" that maps the dimensions of the context to the
+ * output variables, construct an isl_pw_multi_aff with a single
+ * cell corresponding to "dom" and affine expressions copied from "M".
+ */
+static void sol_pma_add(struct isl_sol_pma *sol,
+ __isl_take isl_basic_set *dom, __isl_take isl_mat *M)
+{
+ int i;
+ isl_local_space *ls;
+ isl_aff *aff;
+ isl_multi_aff *maff;
+ isl_pw_multi_aff *pma;
+
+ maff = isl_multi_aff_alloc(isl_pw_multi_aff_get_space(sol->pma));
+ ls = isl_basic_set_get_local_space(dom);
+ for (i = 1; i < M->n_row; ++i) {
+ aff = isl_aff_alloc(isl_local_space_copy(ls));
+ if (aff) {
+ isl_int_set(aff->v->el[0], M->row[0][0]);
+ isl_seq_cpy(aff->v->el + 1, M->row[i], M->n_col);
}
- if (pos != other + i)
- isl_basic_map_swap_div(bmap, pos, other + i);
+ aff = isl_aff_normalize(aff);
+ maff = isl_multi_aff_set_aff(maff, i - 1, aff);
}
- return bmap;
-error:
- isl_basic_map_free(bmap);
- return NULL;
+ isl_local_space_free(ls);
+ isl_mat_free(M);
+ dom = isl_basic_set_simplify(dom);
+ dom = isl_basic_set_finalize(dom);
+ pma = isl_pw_multi_aff_alloc(isl_set_from_basic_set(dom), maff);
+ sol->pma = isl_pw_multi_aff_add_disjoint(sol->pma, pma);
+ if (!sol->pma)
+ sol->sol.error = 1;
}
-/* Compute the lexicographic minimum (or maximum if "max" is set)
- * of "bmap" over the domain "dom" and return the result as a map.
- * If "empty" is not NULL, then *empty is assigned a set that
- * contains those parts of the domain where there is no solution.
- * If "bmap" is marked as rational (ISL_BASIC_MAP_RATIONAL),
- * then we compute the rational optimum. Otherwise, we compute
- * the integral optimum.
- *
- * We perform some preprocessing. As the PILP solver does not
- * handle implicit equalities very well, we first make sure all
- * the equalities are explicitly available.
- * We also make sure the divs in the domain are properly order,
- * because they will be added one by one in the given order
- * during the construction of the solution map.
+static void sol_pma_free_wrap(struct isl_sol *sol)
+{
+ sol_pma_free((struct isl_sol_pma *)sol);
+}
+
+static void sol_pma_add_empty_wrap(struct isl_sol *sol,
+ __isl_take isl_basic_set *bset)
+{
+ sol_pma_add_empty((struct isl_sol_pma *)sol, bset);
+}
+
+static void sol_pma_add_wrap(struct isl_sol *sol,
+ __isl_take isl_basic_set *dom, __isl_take isl_mat *M)
+{
+ sol_pma_add((struct isl_sol_pma *)sol, dom, M);
+}
+
+/* Construct an isl_sol_pma structure for accumulating the solution.
+ * If track_empty is set, then we also keep track of the parts
+ * of the context where there is no solution.
+ * If max is set, then we are solving a maximization, rather than
+ * a minimization problem, which means that the variables in the
+ * tableau have value "M - x" rather than "M + x".
*/
-struct isl_map *isl_tab_basic_map_partial_lexopt(
- struct isl_basic_map *bmap, struct isl_basic_set *dom,
- struct isl_set **empty, int max)
+static struct isl_sol *sol_pma_init(__isl_keep isl_basic_map *bmap,
+ __isl_take isl_basic_set *dom, int track_empty, int max)
{
- struct isl_tab *tab;
- struct isl_map *result = NULL;
- struct isl_sol_map *sol_map = NULL;
+ struct isl_sol_pma *sol_pma = NULL;
- if (empty)
- *empty = NULL;
- if (!bmap || !dom)
+ if (!bmap)
goto error;
- isl_assert(bmap->ctx,
- isl_basic_map_compatible_domain(bmap, dom), goto error);
+ sol_pma = isl_calloc_type(bmap->ctx, struct isl_sol_pma);
+ if (!sol_pma)
+ goto error;
- bmap = isl_basic_map_detect_equalities(bmap);
+ sol_pma->sol.rational = ISL_F_ISSET(bmap, ISL_BASIC_MAP_RATIONAL);
+ sol_pma->sol.dec_level.callback.run = &sol_dec_level_wrap;
+ sol_pma->sol.dec_level.sol = &sol_pma->sol;
+ sol_pma->sol.max = max;
+ sol_pma->sol.n_out = isl_basic_map_dim(bmap, isl_dim_out);
+ sol_pma->sol.add = &sol_pma_add_wrap;
+ sol_pma->sol.add_empty = track_empty ? &sol_pma_add_empty_wrap : NULL;
+ sol_pma->sol.free = &sol_pma_free_wrap;
+ sol_pma->pma = isl_pw_multi_aff_empty(isl_basic_map_get_space(bmap));
+ if (!sol_pma->pma)
+ goto error;
- if (dom->n_div) {
- dom = isl_basic_set_order_divs(dom);
- bmap = align_context_divs(bmap, dom);
- }
- sol_map = sol_map_init(bmap, dom, !!empty, max);
- if (!sol_map)
+ sol_pma->sol.context = isl_context_alloc(dom);
+ if (!sol_pma->sol.context)
goto error;
- if (isl_basic_set_fast_is_empty(sol_map->sol.context_tab->bset))
- /* nothing */;
- else if (isl_basic_map_fast_is_empty(bmap))
- sol_map = add_empty(sol_map);
- else {
- tab = tab_for_lexmin(bmap,
- sol_map->sol.context_tab->bset, 1, max);
- tab = tab_detect_nonnegative_parameters(tab,
- sol_map->sol.context_tab);
- sol_map = sol_map_find_solutions(sol_map, tab);
- if (!sol_map)
+ if (track_empty) {
+ sol_pma->empty = isl_set_alloc_space(isl_basic_set_get_space(dom),
+ 1, ISL_SET_DISJOINT);
+ if (!sol_pma->empty)
goto error;
}
- result = isl_map_copy(sol_map->map);
- if (empty)
- *empty = isl_set_copy(sol_map->empty);
- sol_map_free(sol_map);
- isl_basic_map_free(bmap);
- return result;
+ isl_basic_set_free(dom);
+ return &sol_pma->sol;
error:
- sol_map_free(sol_map);
- isl_basic_map_free(bmap);
+ isl_basic_set_free(dom);
+ sol_pma_free(sol_pma);
return NULL;
}
-struct isl_sol_for {
- struct isl_sol sol;
- int (*fn)(__isl_take isl_basic_set *dom,
- __isl_take isl_mat *map, void *user);
- void *user;
- int max;
-};
-
-static void sol_for_free(struct isl_sol_for *sol_for)
+/* Base case of isl_tab_basic_map_partial_lexopt, after removing
+ * some obvious symmetries.
+ *
+ * We call basic_map_partial_lexopt_base and extract the results.
+ */
+static __isl_give isl_pw_multi_aff *basic_map_partial_lexopt_base_pma(
+ __isl_take isl_basic_map *bmap, __isl_take isl_basic_set *dom,
+ __isl_give isl_set **empty, int max)
{
- isl_tab_free(sol_for->sol.context_tab);
- free(sol_for);
-}
+ isl_pw_multi_aff *result = NULL;
+ struct isl_sol *sol;
+ struct isl_sol_pma *sol_pma;
-static void sol_for_free_wrap(struct isl_sol *sol)
-{
- sol_for_free((struct isl_sol_for *)sol);
+ sol = basic_map_partial_lexopt_base(bmap, dom, empty, max,
+ &sol_pma_init);
+ if (!sol)
+ return NULL;
+ sol_pma = (struct isl_sol_pma *) sol;
+
+ result = isl_pw_multi_aff_copy(sol_pma->pma);
+ if (empty)
+ *empty = isl_set_copy(sol_pma->empty);
+ sol_free(&sol_pma->sol);
+ return result;
}
-/* Add the solution identified by the tableau and the context tableau.
+/* Given that the last input variable of "maff" represents the minimum
+ * of some bounds, check whether we need to plug in the expression
+ * of the minimum.
*
- * See documentation of sol_map_add for more details.
- *
- * Instead of constructing a basic map, this function calls a user
- * defined function with the current context as a basic set and
- * an affine matrix reprenting the relation between the input and output.
- * The number of rows in this matrix is equal to one plus the number
- * of output variables. The number of columns is equal to one plus
- * the total dimension of the context, i.e., the number of parameters,
- * input variables and divs. Since some of the columns in the matrix
- * may refer to the divs, the basic set is not simplified.
- * (Simplification may reorder or remove divs.)
- */
-static struct isl_sol_for *sol_for_add(struct isl_sol_for *sol,
- struct isl_tab *tab)
+ * In particular, check if the last input variable appears in any
+ * of the expressions in "maff".
+ */
+static int need_substitution(__isl_keep isl_multi_aff *maff)
{
- struct isl_tab *context_tab;
- struct isl_basic_set *bset;
- struct isl_mat *mat = NULL;
- unsigned n_out;
- unsigned off;
- int row, i;
+ int i;
+ unsigned pos;
- if (!sol || !tab)
- goto error;
+ pos = isl_multi_aff_dim(maff, isl_dim_in) - 1;
- if (tab->empty)
- return sol;
+ for (i = 0; i < maff->n; ++i)
+ if (isl_aff_involves_dims(maff->p[i], isl_dim_in, pos, 1))
+ return 1;
- off = 2 + tab->M;
- context_tab = sol->sol.context_tab;
+ return 0;
+}
- n_out = tab->n_var - tab->n_param - tab->n_div;
- mat = isl_mat_alloc(tab->mat->ctx, 1 + n_out, 1 + tab->n_param + tab->n_div);
- if (!mat)
+/* Given a set of upper bounds on the last "input" variable m,
+ * construct a piecewise affine expression that selects
+ * the minimal upper bound to m, i.e.,
+ * divide the space into cells where one
+ * of the upper bounds is smaller than all the others and select
+ * this upper bound on that cell.
+ *
+ * In particular, if there are n bounds b_i, then the result
+ * consists of n cell, each one of the form
+ *
+ * b_i <= b_j for j > i
+ * b_i < b_j for j < i
+ *
+ * The affine expression on this cell is
+ *
+ * b_i
+ */
+static __isl_give isl_pw_aff *set_minimum_pa(__isl_take isl_space *space,
+ __isl_take isl_mat *var)
+{
+ int i;
+ isl_aff *aff = NULL;
+ isl_basic_set *bset = NULL;
+ isl_ctx *ctx;
+ isl_pw_aff *paff = NULL;
+ isl_space *pw_space;
+ isl_local_space *ls = NULL;
+
+ if (!space || !var)
goto error;
- isl_seq_clr(mat->row[0] + 1, mat->n_col - 1);
- isl_int_set_si(mat->row[0][0], 1);
- for (row = 0; row < n_out; ++row) {
- int i = tab->n_param + row;
- int r, j;
+ ctx = isl_space_get_ctx(space);
+ ls = isl_local_space_from_space(isl_space_copy(space));
+ pw_space = isl_space_copy(space);
+ pw_space = isl_space_from_domain(pw_space);
+ pw_space = isl_space_add_dims(pw_space, isl_dim_out, 1);
+ paff = isl_pw_aff_alloc_size(pw_space, var->n_row);
- isl_seq_clr(mat->row[1 + row], mat->n_col);
- if (!tab->var[i].is_row)
- continue;
+ for (i = 0; i < var->n_row; ++i) {
+ isl_pw_aff *paff_i;
- r = tab->var[i].index;
- /* no unbounded */
- if (tab->M)
- isl_assert(mat->ctx, isl_int_eq(tab->mat->row[r][2],
- tab->mat->row[r][0]),
- goto error);
- isl_int_set(mat->row[1 + row][0], tab->mat->row[r][1]);
- for (j = 0; j < tab->n_param; ++j) {
- int col;
- if (tab->var[j].is_row)
- continue;
- col = tab->var[j].index;
- isl_int_set(mat->row[1 + row][1 + j],
- tab->mat->row[r][off + col]);
- }
- for (j = 0; j < tab->n_div; ++j) {
- int col;
- if (tab->var[tab->n_var - tab->n_div+j].is_row)
- continue;
- col = tab->var[tab->n_var - tab->n_div+j].index;
- isl_int_set(mat->row[1 + row][1 + tab->n_param + j],
- tab->mat->row[r][off + col]);
- }
- if (!isl_int_is_one(tab->mat->row[r][0]))
- isl_seq_scale_down(mat->row[1 + row], mat->row[1 + row],
- tab->mat->row[r][0], mat->n_col);
- if (sol->max)
- isl_seq_neg(mat->row[1 + row], mat->row[1 + row],
- mat->n_col);
+ aff = isl_aff_alloc(isl_local_space_copy(ls));
+ bset = isl_basic_set_alloc_space(isl_space_copy(space), 0,
+ 0, var->n_row - 1);
+ if (!aff || !bset)
+ goto error;
+ isl_int_set_si(aff->v->el[0], 1);
+ isl_seq_cpy(aff->v->el + 1, var->row[i], var->n_col);
+ isl_int_set_si(aff->v->el[1 + var->n_col], 0);
+ bset = select_minimum(bset, var, i);
+ paff_i = isl_pw_aff_alloc(isl_set_from_basic_set(bset), aff);
+ paff = isl_pw_aff_add_disjoint(paff, paff_i);
}
- bset = isl_basic_set_dup(context_tab->bset);
- bset = isl_basic_set_finalize(bset);
+ isl_local_space_free(ls);
+ isl_space_free(space);
+ isl_mat_free(var);
+ return paff;
+error:
+ isl_aff_free(aff);
+ isl_basic_set_free(bset);
+ isl_pw_aff_free(paff);
+ isl_local_space_free(ls);
+ isl_space_free(space);
+ isl_mat_free(var);
+ return NULL;
+}
+
+/* Given a piecewise multi-affine expression of which the last input variable
+ * is the minimum of the bounds in "cst", plug in the value of the minimum.
+ * This minimum expression is given in "min_expr_pa".
+ * The set "min_expr" contains the same information, but in the form of a set.
+ * The variable is subsequently projected out.
+ *
+ * The implementation is similar to those of "split" and "split_domain".
+ * If the variable appears in a given expression, then minimum expression
+ * is plugged in. Otherwise, if the variable appears in the constraints
+ * and a split is required, then the domain is split. Otherwise, no split
+ * is performed.
+ */
+static __isl_give isl_pw_multi_aff *split_domain_pma(
+ __isl_take isl_pw_multi_aff *opt, __isl_take isl_pw_aff *min_expr_pa,
+ __isl_take isl_set *min_expr, __isl_take isl_mat *cst)
+{
+ int n_in;
+ int i;
+ isl_space *space;
+ isl_pw_multi_aff *res;
- if (sol->fn(bset, isl_mat_copy(mat), sol->user) < 0)
+ if (!opt || !min_expr || !cst)
goto error;
- isl_mat_free(mat);
- return sol;
+ n_in = isl_pw_multi_aff_dim(opt, isl_dim_in);
+ space = isl_pw_multi_aff_get_space(opt);
+ space = isl_space_drop_dims(space, isl_dim_in, n_in - 1, 1);
+ res = isl_pw_multi_aff_empty(space);
+
+ for (i = 0; i < opt->n; ++i) {
+ isl_pw_multi_aff *pma;
+
+ pma = isl_pw_multi_aff_alloc(isl_set_copy(opt->p[i].set),
+ isl_multi_aff_copy(opt->p[i].maff));
+ if (need_substitution(opt->p[i].maff))
+ pma = isl_pw_multi_aff_substitute(pma,
+ isl_dim_in, n_in - 1, min_expr_pa);
+ else if (need_split_set(opt->p[i].set, cst))
+ pma = isl_pw_multi_aff_intersect_domain(pma,
+ isl_set_copy(min_expr));
+ pma = isl_pw_multi_aff_project_out(pma,
+ isl_dim_in, n_in - 1, 1);
+
+ res = isl_pw_multi_aff_add_disjoint(res, pma);
+ }
+
+ isl_pw_multi_aff_free(opt);
+ isl_pw_aff_free(min_expr_pa);
+ isl_set_free(min_expr);
+ isl_mat_free(cst);
+ return res;
error:
- isl_mat_free(mat);
- sol_free(&sol->sol);
+ isl_pw_multi_aff_free(opt);
+ isl_pw_aff_free(min_expr_pa);
+ isl_set_free(min_expr);
+ isl_mat_free(cst);
return NULL;
}
-static struct isl_sol *sol_for_add_wrap(struct isl_sol *sol,
- struct isl_tab *tab)
-{
- return (struct isl_sol *)sol_for_add((struct isl_sol_for *)sol, tab);
-}
+static __isl_give isl_pw_multi_aff *basic_map_partial_lexopt_pma(
+ __isl_take isl_basic_map *bmap, __isl_take isl_basic_set *dom,
+ __isl_give isl_set **empty, int max);
-static struct isl_sol_for *sol_for_init(struct isl_basic_map *bmap, int max,
- int (*fn)(__isl_take isl_basic_set *dom, __isl_take isl_mat *map,
- void *user),
- void *user)
+/* This function is called from basic_map_partial_lexopt_symm.
+ * The last variable of "bmap" and "dom" corresponds to the minimum
+ * of the bounds in "cst". "map_space" is the space of the original
+ * input relation (of basic_map_partial_lexopt_symm) and "set_space"
+ * is the space of the original domain.
+ *
+ * We recursively call basic_map_partial_lexopt and then plug in
+ * the definition of the minimum in the result.
+ */
+static __isl_give union isl_lex_res basic_map_partial_lexopt_symm_pma_core(
+ __isl_take isl_basic_map *bmap, __isl_take isl_basic_set *dom,
+ __isl_give isl_set **empty, int max, __isl_take isl_mat *cst,
+ __isl_take isl_space *map_space, __isl_take isl_space *set_space)
{
- struct isl_sol_for *sol_for = NULL;
- struct isl_dim *dom_dim;
- struct isl_basic_set *dom = NULL;
- struct isl_tab *context_tab;
- int f;
+ isl_pw_multi_aff *opt;
+ isl_pw_aff *min_expr_pa;
+ isl_set *min_expr;
+ union isl_lex_res res;
- sol_for = isl_calloc_type(bset->ctx, struct isl_sol_for);
- if (!sol_for)
- goto error;
+ min_expr = set_minimum(isl_basic_set_get_space(dom), isl_mat_copy(cst));
+ min_expr_pa = set_minimum_pa(isl_basic_set_get_space(dom),
+ isl_mat_copy(cst));
- dom_dim = isl_dim_domain(isl_dim_copy(bmap->dim));
- dom = isl_basic_set_universe(dom_dim);
+ opt = basic_map_partial_lexopt_pma(bmap, dom, empty, max);
- sol_for->fn = fn;
- sol_for->user = user;
- sol_for->max = max;
- sol_for->sol.add = &sol_for_add_wrap;
- sol_for->sol.free = &sol_for_free_wrap;
+ if (empty) {
+ *empty = split(*empty,
+ isl_set_copy(min_expr), isl_mat_copy(cst));
+ *empty = isl_set_reset_space(*empty, set_space);
+ }
- context_tab = context_tab_for_lexmin(isl_basic_set_copy(dom));
- context_tab = restore_lexmin(context_tab);
- sol_for->sol.context_tab = context_tab;
- f = context_is_feasible(&sol_for->sol);
- if (f < 0)
- goto error;
+ opt = split_domain_pma(opt, min_expr_pa, min_expr, cst);
+ opt = isl_pw_multi_aff_reset_space(opt, map_space);
- isl_basic_set_free(dom);
- return sol_for;
-error:
- isl_basic_set_free(dom);
- sol_for_free(sol_for);
- return NULL;
+ res.pma = opt;
+ return res;
}
-static struct isl_sol_for *sol_for_find_solutions(struct isl_sol_for *sol_for,
- struct isl_tab *tab)
+static __isl_give isl_pw_multi_aff *basic_map_partial_lexopt_symm_pma(
+ __isl_take isl_basic_map *bmap, __isl_take isl_basic_set *dom,
+ __isl_give isl_set **empty, int max, int first, int second)
{
- return (struct isl_sol_for *)find_solutions_main(&sol_for->sol, tab);
+ return basic_map_partial_lexopt_symm(bmap, dom, empty, max,
+ first, second, &basic_map_partial_lexopt_symm_pma_core).pma;
}
-int isl_basic_map_foreach_lexopt(__isl_keep isl_basic_map *bmap, int max,
- int (*fn)(__isl_take isl_basic_set *dom, __isl_take isl_mat *map,
- void *user),
- void *user)
+/* Recursive part of isl_basic_map_partial_lexopt_pw_multi_aff, after detecting
+ * equalities and removing redundant constraints.
+ *
+ * We first check if there are any parallel constraints (left).
+ * If not, we are in the base case.
+ * If there are parallel constraints, we replace them by a single
+ * constraint in basic_map_partial_lexopt_symm_pma and then call
+ * this function recursively to look for more parallel constraints.
+ */
+static __isl_give isl_pw_multi_aff *basic_map_partial_lexopt_pma(
+ __isl_take isl_basic_map *bmap, __isl_take isl_basic_set *dom,
+ __isl_give isl_set **empty, int max)
{
- struct isl_sol_for *sol_for = NULL;
+ int par = 0;
+ int first, second;
- bmap = isl_basic_map_copy(bmap);
if (!bmap)
- return -1;
-
- bmap = isl_basic_map_detect_equalities(bmap);
- sol_for = sol_for_init(bmap, max, fn, user);
-
- if (isl_basic_map_fast_is_empty(bmap))
- /* nothing */;
- else {
- struct isl_tab *tab;
- tab = tab_for_lexmin(bmap,
- sol_for->sol.context_tab->bset, 1, max);
- tab = tab_detect_nonnegative_parameters(tab,
- sol_for->sol.context_tab);
- sol_for = sol_for_find_solutions(sol_for, tab);
- if (!sol_for)
- goto error;
- }
+ goto error;
- sol_for_free(sol_for);
- isl_basic_map_free(bmap);
- return 0;
+ if (bmap->ctx->opt->pip_symmetry)
+ par = parallel_constraints(bmap, &first, &second);
+ if (par < 0)
+ goto error;
+ if (!par)
+ return basic_map_partial_lexopt_base_pma(bmap, dom, empty, max);
+
+ return basic_map_partial_lexopt_symm_pma(bmap, dom, empty, max,
+ first, second);
error:
- sol_for_free(sol_for);
+ isl_basic_set_free(dom);
isl_basic_map_free(bmap);
- return -1;
+ return NULL;
}
-int isl_basic_map_foreach_lexmin(__isl_keep isl_basic_map *bmap,
- int (*fn)(__isl_take isl_basic_set *dom, __isl_take isl_mat *map,
- void *user),
- void *user)
+/* Compute the lexicographic minimum (or maximum if "max" is set)
+ * of "bmap" over the domain "dom" and return the result as a piecewise
+ * multi-affine expression.
+ * If "empty" is not NULL, then *empty is assigned a set that
+ * contains those parts of the domain where there is no solution.
+ * If "bmap" is marked as rational (ISL_BASIC_MAP_RATIONAL),
+ * then we compute the rational optimum. Otherwise, we compute
+ * the integral optimum.
+ *
+ * We perform some preprocessing. As the PILP solver does not
+ * handle implicit equalities very well, we first make sure all
+ * the equalities are explicitly available.
+ *
+ * We also add context constraints to the basic map and remove
+ * redundant constraints. This is only needed because of the
+ * way we handle simple symmetries. In particular, we currently look
+ * for symmetries on the constraints, before we set up the main tableau.
+ * It is then no good to look for symmetries on possibly redundant constraints.
+ */
+__isl_give isl_pw_multi_aff *isl_basic_map_partial_lexopt_pw_multi_aff(
+ __isl_take isl_basic_map *bmap, __isl_take isl_basic_set *dom,
+ __isl_give isl_set **empty, int max)
{
- return isl_basic_map_foreach_lexopt(bmap, 0, fn, user);
-}
+ if (empty)
+ *empty = NULL;
+ if (!bmap || !dom)
+ goto error;
-int isl_basic_map_foreach_lexmax(__isl_keep isl_basic_map *bmap,
- int (*fn)(__isl_take isl_basic_set *dom, __isl_take isl_mat *map,
- void *user),
- void *user)
-{
- return isl_basic_map_foreach_lexopt(bmap, 1, fn, user);
+ isl_assert(bmap->ctx,
+ isl_basic_map_compatible_domain(bmap, dom), goto error);
+
+ if (isl_basic_set_dim(dom, isl_dim_all) == 0)
+ return basic_map_partial_lexopt_pma(bmap, dom, empty, max);
+
+ bmap = isl_basic_map_intersect_domain(bmap, isl_basic_set_copy(dom));
+ bmap = isl_basic_map_detect_equalities(bmap);
+ bmap = isl_basic_map_remove_redundancies(bmap);
+
+ return basic_map_partial_lexopt_pma(bmap, dom, empty, max);
+error:
+ isl_basic_set_free(dom);
+ isl_basic_map_free(bmap);
+ return NULL;
}
projects / platform / upstream / isl.git / blobdiff