* Copyright 2008-2009 Katholieke Universiteit Leuven
* Copyright 2010 INRIA Saclay
*
- * Use of this software is governed by the GNU LGPLv2.1 license
+ * 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
#include "isl_sample.h"
#include <isl_mat_private.h>
#include <isl_aff_private.h>
+#include <isl_options_private.h>
#include <isl_config.h>
/*
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 */
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;
return;
error:
isl_basic_set_free(dom);
+ isl_mat_free(M);
sol->error = 1;
}
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);
}
} else
sol_pop_one(sol);
+
+ if (0)
+error: sol->error = 1;
}
static void sol_dec_level(struct isl_sol *sol)
if (tab->empty && !sol->add_empty)
return;
+ if (sol->context->op->is_empty(sol->context))
+ return;
bset = sol_domain(sol);
sol_map_add_empty((struct isl_sol_map *)sol, bset);
}
-/* Add bset to sol's empty, but only if we are actually collecting
- * the empty set.
- */
-static void sol_map_add_empty_if_needed(struct isl_sol_map *sol,
- struct isl_basic_set *bset)
-{
- if (sol->empty)
- sol_map_add_empty(sol, bset);
- else
- isl_basic_set_free(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
return ineq;
}
+/* Normalize a div expression of the form
+ *
+ * [(g*f(x) + c)/(g * m)]
+ *
+ * with c the constant term and f(x) the remaining coefficients, to
+ *
+ * [(f(x) + [c/g])/m]
+ */
+static void normalize_div(__isl_keep 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
*
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;
}
/* 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
*
} else {
int dcol = tab->var[tab->n_var - tab->n_div + div].index;
- isl_int_set_si(tab->mat->row[row][2 + tab->M + dcol], 1);
+ isl_int_add_ui(tab->mat->row[row][2 + tab->M + dcol],
+ tab->mat->row[row][2 + tab->M + dcol], 1);
}
return tab;
/* Given a conflicting row in the tableau, report all constraints
* involved in the row to the caller. That is, the row itself
- * (if represents a constraint) and all constraint columns with
- * non-zero (and therefore negative) coefficient.
+ * (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)
{
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.
* combination of variables/constraints plus a non-integral constant,
* 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;
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;
if (isl_tab_push_basis(tab) < 0)
goto error;
- tab = cut_to_integer_lexmin(tab);
+ tab = cut_to_integer_lexmin(tab, CUT_ALL);
if (!tab)
goto error;
n = tab->n_div;
d = context->op->get_div(context, tab, div);
+ isl_vec_free(div);
if (d < 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;
if (d >= n && context->op->detect_equalities(context, tab) < 0)
}
}
+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;
context_lex_is_ok,
context_lex_save,
context_lex_restore,
+ context_lex_discard,
context_lex_invalidate,
context_lex_free,
};
{
struct isl_tab *tab;
- bset = isl_basic_set_cow(bset);
if (!bset)
return NULL;
tab = tab_for_lexmin((struct isl_basic_map *)bset, NULL, 1, 0);
return NULL;
}
+/* Representation of the context when using generalized basis reduction.
+ *
+ * "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.
+ */
struct isl_context_gbr {
struct isl_context context;
struct isl_tab *tab;
}
}
- cgbr->shifted = isl_tab_from_basic_set(bset);
+ cgbr->shifted = isl_tab_from_basic_set(bset, 0);
for (i = 0; i < bset->n_ineq; ++i)
isl_int_set(bset->ineq[i][0], cst->el[i]);
cgbr->cone = isl_tab_from_recession_cone(bset, 0);
if (!cgbr->cone)
return NULL;
- if (isl_tab_track_bset(cgbr->cone, isl_basic_set_dup(bset)) < 0)
+ 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;
}
+/* 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)
{
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;
cgbr->cone = isl_tab_from_recession_cone(bset, 0);
if (!cgbr->cone)
goto error;
- if (isl_tab_track_bset(cgbr->cone, isl_basic_set_dup(bset)) < 0)
+ if (isl_tab_track_bset(cgbr->cone,
+ isl_basic_set_copy(bset)) < 0)
goto error;
}
if (isl_tab_detect_implicit_equalities(cgbr->cone) < 0)
n_ineq = cgbr->tab->bmap->n_ineq;
cgbr->tab = isl_tab_detect_equalities(cgbr->tab, cgbr->cone);
- if (cgbr->tab && cgbr->tab->bmap->n_ineq > n_ineq)
+ if (!cgbr->tab)
+ return -1;
+ if (cgbr->tab->bmap->n_ineq > n_ineq)
propagate_equalities(cgbr, tab, n_ineq);
return 0;
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;
context_gbr_is_ok,
context_gbr_save,
context_gbr_restore,
+ context_gbr_discard,
context_gbr_invalidate,
context_gbr_free,
};
cgbr->shifted = NULL;
cgbr->cone = NULL;
- cgbr->tab = isl_tab_from_basic_set(dom);
+ cgbr->tab = isl_tab_from_basic_set(dom, 1);
cgbr->tab = isl_tab_init_samples(cgbr->tab);
if (!cgbr->tab)
goto error;
- if (isl_tab_track_bset(cgbr->tab,
- isl_basic_set_cow(isl_basic_set_copy(dom))) < 0)
- goto error;
check_gbr_integer_feasible(cgbr);
return &cgbr->context;
* a minimization problem, which means that the variables in the
* tableau have value "M - x" rather than "M + x".
*/
-static struct isl_sol_map *sol_map_init(struct isl_basic_map *bmap,
+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;
}
isl_basic_set_free(dom);
- return sol_map;
+ return &sol_map->sol;
error:
isl_basic_set_free(dom);
sol_map_free(sol_map);
if (!sol->error)
sol->context->op->restore(sol->context, saved);
+ else
+ sol->context->op->discard(saved);
return;
error:
sol->error = 1;
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".
*
* 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;
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);
sol->error = 1;
}
-static void sol_map_find_solutions(struct isl_sol_map *sol_map,
- struct isl_tab *tab)
-{
- 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.
* because they will be added one by one in the given order
* during the construction of the solution map.
*/
-static __isl_give isl_map *basic_map_partial_lexopt_base(
+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)
+ __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))
{
- isl_map *result = NULL;
struct isl_tab *tab;
- struct isl_sol_map *sol_map = NULL;
+ 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_map = sol_map_init(bmap, dom, !!empty, max);
- if (!sol_map)
+ sol = init(bmap, dom, !!empty, max);
+ if (!sol)
goto error;
- context = sol_map->sol.context;
+ 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))
- sol_map_add_empty_if_needed(sol_map,
+ 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 {
+ } else {
tab = tab_for_lexmin(bmap,
context->op->peek_basic_set(context), 1, max);
tab = context->op->detect_nonnegative_parameters(context, tab);
- sol_map_find_solutions(sol_map, tab);
+ find_solutions_main(sol, tab);
}
- if (sol_map->sol.error)
+ 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);
- isl_basic_map_free(bmap);
return result;
-error:
- sol_free(&sol_map->sol);
- isl_basic_map_free(bmap);
- return NULL;
}
/* Structure used during detection of parallel constraints.
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
static __isl_give isl_set *set_minimum(__isl_take isl_space *dim,
__isl_take isl_mat *var)
{
- int i, j, k;
+ int i, k;
isl_basic_set *bset = NULL;
isl_ctx *ctx;
isl_set *set = NULL;
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);
- 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);
+ bset = select_minimum(bset, var, i);
set = isl_set_add_basic_set(set, bset);
}
* an upper bound that is different from the upper bounds on which it
* is defined.
*/
-static int need_split_map(__isl_keep isl_basic_map *bmap,
+static int need_split_basic_map(__isl_keep isl_basic_map *bmap,
__isl_keep isl_mat *cst)
{
int i, j;
return 0;
}
-static int need_split_set(__isl_keep isl_basic_set *bset,
+/* 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_map((isl_basic_map *)bset, 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
isl_set *set;
set = isl_set_from_basic_set(isl_basic_set_copy(empty->p[i]));
- if (need_split_set(empty->p[i], cst))
+ 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);
isl_map *map;
map = isl_map_from_basic_map(isl_basic_map_copy(opt->p[i]));
- if (need_split_map(opt->p[i], cst))
+ 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);
__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
* Moreover, m = min_i(b_i(p)) satisfies the constraints on u and can
* therefore be plugged into the solution.
*/
-static __isl_give isl_map *basic_map_partial_lexopt_symm(
+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 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;
isl_ctx *ctx;
isl_vec *var = NULL;
isl_mat *cst = NULL;
- isl_map *opt;
- isl_set *min_expr;
- isl_space *map_dim, *set_dim;
+ isl_space *map_space, *set_space;
+ union isl_lex_res res;
- map_dim = isl_basic_map_get_space(bmap);
- set_dim = empty ? isl_basic_set_get_space(dom) : NULL;
+ 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);
bmap = isl_basic_map_finalize(bmap);
n_div = isl_basic_set_dim(dom, isl_dim_div);
- dom = isl_basic_set_add(dom, isl_dim_set, 1);
+ 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);
isl_seq_clr(dom->ineq[k] + 1 + n_in + 1, n_div);
}
- min_expr = set_minimum(isl_basic_set_get_space(dom), isl_mat_copy(cst));
-
isl_vec_free(var);
free(list);
- 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_dim);
- }
-
- opt = split_domain(opt, min_expr, cst);
- opt = isl_map_reset_space(opt, map_dim);
-
- return opt;
+ return core(bmap, dom, empty, max, cst, map_space, set_space);
error:
- isl_space_free(map_dim);
- isl_space_free(set_dim);
+ 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);
- return NULL;
+ 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
if (par < 0)
goto error;
if (!par)
- return basic_map_partial_lexopt_base(bmap, dom, empty, max);
+ return basic_map_partial_lexopt_base_map(bmap, dom, empty, max);
- return basic_map_partial_lexopt_symm(bmap, dom, empty, max,
- first, second);
+ return basic_map_partial_lexopt_symm_map(bmap, dom, empty, max,
+ first, second);
error:
isl_basic_set_free(dom);
isl_basic_map_free(bmap);
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);
struct isl_sol_for *sol_for = NULL;
bmap = isl_basic_map_copy(bmap);
+ bmap = isl_basic_map_detect_equalities(bmap);
if (!bmap)
return -1;
- bmap = isl_basic_map_detect_equalities(bmap);
sol_for = sol_for_init(bmap, max, fn, user);
+ if (!sol_for)
+ goto error;
if (isl_basic_map_plain_is_empty(bmap))
/* nothing */;
return isl_basic_map_foreach_lexopt(bset, max, fn, user);
}
-int isl_basic_map_foreach_lexmin(__isl_keep isl_basic_map *bmap,
- int (*fn)(__isl_take isl_basic_set *dom, __isl_take isl_aff_list *list,
- void *user),
- void *user)
-{
- return isl_basic_map_foreach_lexopt(bmap, 0, fn, user);
-}
-
-int isl_basic_map_foreach_lexmax(__isl_keep isl_basic_map *bmap,
- int (*fn)(__isl_take isl_basic_set *dom, __isl_take isl_aff_list *list,
- void *user),
- void *user)
-{
- return isl_basic_map_foreach_lexopt(bmap, 1, fn, user);
-}
-
-int isl_basic_set_foreach_lexmax(__isl_keep isl_basic_set *bset,
- int (*fn)(__isl_take isl_basic_set *dom, __isl_take isl_aff_list *list,
- void *user),
- void *user)
-{
- return isl_basic_map_foreach_lexmax(bset, 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,
{
int i, j;
int r;
- isl_ctx *ctx = isl_basic_set_get_ctx(bset);
+ isl_ctx *ctx;
isl_vec *v = NULL;
- isl_vec *sol = isl_vec_alloc(ctx, 0);
+ isl_vec *sol = NULL;
struct isl_tab *tab;
struct isl_trivial *triv = NULL;
int level, init;
+ if (!bset)
+ return NULL;
+
+ ctx = isl_basic_set_get_ctx(bset);
+ sol = isl_vec_alloc(ctx, 0);
+
tab = tab_for_lexmin(bset, NULL, 0, 0);
if (!tab)
goto error;
int side, base;
if (init) {
- tab = cut_to_integer_lexmin(tab);
+ tab = cut_to_integer_lexmin(tab, CUT_ONE);
if (!tab)
goto error;
if (tab->empty)
isl_ctx *ctx = isl_basic_set_get_ctx(bset);
isl_vec *sol;
+ if (!bset)
+ return NULL;
+
tab = tab_for_lexmin(bset, NULL, 0, 0);
if (!tab)
goto error;
isl_basic_set_free(bset);
return NULL;
}
+
+struct isl_sol_pma {
+ struct isl_sol sol;
+ isl_pw_multi_aff *pma;
+ isl_set *empty;
+};
+
+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);
+ }
+ aff = isl_aff_normalize(aff);
+ maff = isl_multi_aff_set_aff(maff, i - 1, aff);
+ }
+ 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;
+}
+
+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".
+ */
+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_sol_pma *sol_pma = NULL;
+
+ if (!bmap)
+ goto error;
+
+ sol_pma = isl_calloc_type(bmap->ctx, struct isl_sol_pma);
+ if (!sol_pma)
+ goto error;
+
+ 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;
+
+ sol_pma->sol.context = isl_context_alloc(dom);
+ if (!sol_pma->sol.context)
+ goto error;
+
+ 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;
+ }
+
+ isl_basic_set_free(dom);
+ return &sol_pma->sol;
+error:
+ isl_basic_set_free(dom);
+ sol_pma_free(sol_pma);
+ 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_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_pw_multi_aff *result = NULL;
+ struct isl_sol *sol;
+ struct isl_sol_pma *sol_pma;
+
+ 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;
+}
+
+/* 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.
+ *
+ * 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)
+{
+ int i;
+ unsigned pos;
+
+ pos = isl_multi_aff_dim(maff, isl_dim_in) - 1;
+
+ for (i = 0; i < maff->n; ++i)
+ if (isl_aff_involves_dims(maff->p[i], isl_dim_in, pos, 1))
+ return 1;
+
+ return 0;
+}
+
+/* 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;
+
+ 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);
+
+ for (i = 0; i < var->n_row; ++i) {
+ isl_pw_aff *paff_i;
+
+ 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);
+ }
+
+ 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 (!opt || !min_expr || !cst)
+ goto error;
+
+ 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_pw_multi_aff_free(opt);
+ isl_pw_aff_free(min_expr_pa);
+ isl_set_free(min_expr);
+ isl_mat_free(cst);
+ return NULL;
+}
+
+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);
+
+/* 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)
+{
+ isl_pw_multi_aff *opt;
+ isl_pw_aff *min_expr_pa;
+ isl_set *min_expr;
+ union isl_lex_res res;
+
+ 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));
+
+ opt = basic_map_partial_lexopt_pma(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_pma(opt, min_expr_pa, min_expr, cst);
+ opt = isl_pw_multi_aff_reset_space(opt, map_space);
+
+ res.pma = opt;
+ return res;
+}
+
+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 basic_map_partial_lexopt_symm(bmap, dom, empty, max,
+ first, second, &basic_map_partial_lexopt_symm_pma_core).pma;
+}
+
+/* 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)
+{
+ 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_pma(bmap, dom, empty, max);
+
+ return basic_map_partial_lexopt_symm_pma(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 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)
+{
+ 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_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