-#include "isl_ilp.h"
-#include "isl_map_private.h"
+/*
+ * Copyright 2008-2009 Katholieke Universiteit Leuven
+ *
+ * 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_ctx_private.h>
+#include <isl_map_private.h>
+#include <isl/ilp.h>
#include "isl_sample.h"
-#include "isl_seq.h"
+#include <isl/seq.h>
#include "isl_equalities.h"
+#include <isl_aff_private.h>
+#include <isl_local_space_private.h>
+#include <isl_mat_private.h>
/* Given a basic set "bset", construct a basic set U such that for
* each element x in U, the whole unit box positioned at x is inside
}
total = isl_basic_set_total_dim(bset);
- unit_box = isl_basic_set_alloc_dim(isl_basic_set_get_dim(bset),
+ unit_box = isl_basic_set_alloc_space(isl_basic_set_get_space(bset),
0, 0, bset->n_ineq);
for (i = 0; i < bset->n_ineq; ++i) {
return NULL;
}
-/* Find an integer point in "bset" that minimizes f (if any).
- * If sol_p is not NULL then the integer point is returned in *sol_p.
- * The optimal value of f is returned in *opt.
- *
- * The algorithm maintains a currently best solution and an interval [l, u]
- * of values of f for which integer solutions could potentially still be found.
- * The initial value of the best solution so far is any solution.
- * The initial value of l is minimal value of f over the rationals
- * (rounded up to the nearest integer).
- * The initial value of u is the value of f at the current solution minus 1.
+/* Find an integer point in "bset" that minimizes f (in any) such that
+ * the value of f lies inside the interval [l, u].
+ * Return this integer point if it can be found.
+ * Otherwise, return sol.
*
* We perform a number of steps until l > u.
* In each step, we look for an integer point with value in either
* If no point can be found, we update l to the upper bound of the interval
* we checked (u or l+floor(u-l-1/2)) plus 1.
*/
+static struct isl_vec *solve_ilp_search(struct isl_basic_set *bset,
+ isl_int *f, isl_int *opt, struct isl_vec *sol, isl_int l, isl_int u)
+{
+ isl_int tmp;
+ int divide = 1;
+
+ isl_int_init(tmp);
+
+ while (isl_int_le(l, u)) {
+ struct isl_basic_set *slice;
+ struct isl_vec *sample;
+
+ if (!divide)
+ isl_int_set(tmp, u);
+ else {
+ isl_int_sub(tmp, u, l);
+ isl_int_fdiv_q_ui(tmp, tmp, 2);
+ isl_int_add(tmp, tmp, l);
+ }
+ slice = add_bounds(isl_basic_set_copy(bset), f, l, tmp);
+ sample = isl_basic_set_sample_vec(slice);
+ if (!sample) {
+ isl_vec_free(sol);
+ sol = NULL;
+ break;
+ }
+ if (sample->size > 0) {
+ isl_vec_free(sol);
+ sol = sample;
+ isl_seq_inner_product(f, sol->el, sol->size, opt);
+ isl_int_sub_ui(u, *opt, 1);
+ divide = 1;
+ } else {
+ isl_vec_free(sample);
+ if (!divide)
+ break;
+ isl_int_add_ui(l, tmp, 1);
+ divide = 0;
+ }
+ }
+
+ isl_int_clear(tmp);
+
+ return sol;
+}
+
+/* Find an integer point in "bset" that minimizes f (if any).
+ * If sol_p is not NULL then the integer point is returned in *sol_p.
+ * The optimal value of f is returned in *opt.
+ *
+ * The algorithm maintains a currently best solution and an interval [l, u]
+ * of values of f for which integer solutions could potentially still be found.
+ * The initial value of the best solution so far is any solution.
+ * The initial value of l is minimal value of f over the rationals
+ * (rounded up to the nearest integer).
+ * The initial value of u is the value of f at the initial solution minus 1.
+ *
+ * We then call solve_ilp_search to perform a binary search on the interval.
+ */
static enum isl_lp_result solve_ilp(struct isl_basic_set *bset,
isl_int *f, isl_int *opt,
struct isl_vec **sol_p)
{
enum isl_lp_result res;
- isl_int l, u, tmp;
+ isl_int l, u;
struct isl_vec *sol;
- int divide = 1;
res = isl_basic_set_solve_lp(bset, 0, f, bset->ctx->one,
opt, NULL, &sol);
isl_int_init(l);
isl_int_init(u);
- isl_int_init(tmp);
isl_int_set(l, *opt);
isl_seq_inner_product(f, sol->el, sol->size, opt);
isl_int_sub_ui(u, *opt, 1);
- while (isl_int_le(l, u)) {
- struct isl_basic_set *slice;
- struct isl_vec *sample;
-
- if (!divide)
- isl_int_set(tmp, u);
- else {
- isl_int_sub(tmp, u, l);
- isl_int_fdiv_q_ui(tmp, tmp, 2);
- isl_int_add(tmp, tmp, l);
- }
- slice = add_bounds(isl_basic_set_copy(bset), f, l, tmp);
- sample = isl_basic_set_sample_vec(slice);
- if (!sample) {
- isl_vec_free(sol);
- sol = NULL;
- res = isl_lp_error;
- break;
- }
- if (sample->size > 0) {
- isl_vec_free(sol);
- sol = sample;
- isl_seq_inner_product(f, sol->el, sol->size, opt);
- isl_int_sub_ui(u, *opt, 1);
- divide = 1;
- } else {
- isl_vec_free(sample);
- if (!divide)
- break;
- isl_int_add_ui(l, tmp, 1);
- divide = 0;
- }
- }
+ sol = solve_ilp_search(bset, f, opt, sol, l, u);
+ if (!sol)
+ res = isl_lp_error;
isl_int_clear(l);
isl_int_clear(u);
- isl_int_clear(tmp);
if (sol_p)
*sol_p = sol;
struct isl_mat *T = NULL;
struct isl_vec *v;
+ bset = isl_basic_set_copy(bset);
dim = isl_basic_set_total_dim(bset);
v = isl_vec_alloc(bset->ctx, 1 + dim);
if (!v)
goto error;
res = isl_basic_set_solve_ilp(bset, max, v->el, opt, sol_p);
isl_vec_free(v);
- if (res == isl_lp_ok && *sol_p) {
+ if (res == isl_lp_ok && sol_p) {
*sol_p = isl_mat_vec_product(T, *sol_p);
if (!*sol_p)
res = isl_lp_error;
} else
isl_mat_free(T);
+ isl_basic_set_free(bset);
return res;
error:
isl_mat_free(T);
isl_assert(bset->ctx, isl_basic_set_n_param(bset) == 0, goto error);
+ if (isl_basic_set_plain_is_empty(bset))
+ return isl_lp_empty;
+
if (bset->n_eq)
return solve_ilp_with_eq(bset, max, f, opt, sol_p);
isl_basic_set_free(bset);
return isl_lp_error;
}
+
+static enum isl_lp_result basic_set_opt(__isl_keep isl_basic_set *bset, int max,
+ __isl_keep isl_aff *obj, isl_int *opt)
+{
+ enum isl_lp_result res;
+
+ if (!obj)
+ return isl_lp_error;
+ bset = isl_basic_set_copy(bset);
+ bset = isl_basic_set_underlying_set(bset);
+ res = isl_basic_set_solve_ilp(bset, max, obj->v->el + 1, opt, NULL);
+ isl_basic_set_free(bset);
+ return res;
+}
+
+static __isl_give isl_mat *extract_divs(__isl_keep isl_basic_set *bset)
+{
+ int i;
+ isl_ctx *ctx = isl_basic_set_get_ctx(bset);
+ isl_mat *div;
+
+ div = isl_mat_alloc(ctx, bset->n_div,
+ 1 + 1 + isl_basic_set_total_dim(bset));
+ if (!div)
+ return NULL;
+
+ for (i = 0; i < bset->n_div; ++i)
+ isl_seq_cpy(div->row[i], bset->div[i], div->n_col);
+
+ return div;
+}
+
+enum isl_lp_result isl_basic_set_opt(__isl_keep isl_basic_set *bset, int max,
+ __isl_keep isl_aff *obj, isl_int *opt)
+{
+ int *exp1 = NULL;
+ int *exp2 = NULL;
+ isl_ctx *ctx;
+ isl_mat *bset_div = NULL;
+ isl_mat *div = NULL;
+ enum isl_lp_result res;
+
+ if (!bset || !obj)
+ return isl_lp_error;
+
+ ctx = isl_aff_get_ctx(obj);
+ if (!isl_space_is_equal(bset->dim, obj->ls->dim))
+ isl_die(ctx, isl_error_invalid,
+ "spaces don't match", return isl_lp_error);
+ if (!isl_int_is_one(obj->v->el[0]))
+ isl_die(ctx, isl_error_unsupported,
+ "expecting integer affine expression",
+ return isl_lp_error);
+
+ if (bset->n_div == 0 && obj->ls->div->n_row == 0)
+ return basic_set_opt(bset, max, obj, opt);
+
+ bset = isl_basic_set_copy(bset);
+ obj = isl_aff_copy(obj);
+
+ bset_div = extract_divs(bset);
+ exp1 = isl_alloc_array(ctx, int, bset_div->n_row);
+ exp2 = isl_alloc_array(ctx, int, obj->ls->div->n_row);
+ if (!bset_div || !exp1 || !exp2)
+ goto error;
+
+ div = isl_merge_divs(bset_div, obj->ls->div, exp1, exp2);
+
+ bset = isl_basic_set_expand_divs(bset, isl_mat_copy(div), exp1);
+ obj = isl_aff_expand_divs(obj, isl_mat_copy(div), exp2);
+
+ res = basic_set_opt(bset, max, obj, opt);
+
+ isl_mat_free(bset_div);
+ isl_mat_free(div);
+ free(exp1);
+ free(exp2);
+ isl_basic_set_free(bset);
+ isl_aff_free(obj);
+
+ return res;
+error:
+ isl_mat_free(div);
+ isl_mat_free(bset_div);
+ free(exp1);
+ free(exp2);
+ isl_basic_set_free(bset);
+ isl_aff_free(obj);
+ return isl_lp_error;
+}
+
+/* Compute the minimum (maximum if max is set) of the integer affine
+ * expression obj over the points in set and put the result in *opt.
+ *
+ * The parameters are assumed to have been aligned.
+ */
+static enum isl_lp_result isl_set_opt_aligned(__isl_keep isl_set *set, int max,
+ __isl_keep isl_aff *obj, isl_int *opt)
+{
+ int i;
+ enum isl_lp_result res;
+ int empty = 1;
+ isl_int opt_i;
+
+ if (!set || !obj)
+ return isl_lp_error;
+ if (set->n == 0)
+ return isl_lp_empty;
+
+ res = isl_basic_set_opt(set->p[0], max, obj, opt);
+ if (res == isl_lp_error || res == isl_lp_unbounded)
+ return res;
+ if (set->n == 1)
+ return res;
+ if (res == isl_lp_ok)
+ empty = 0;
+
+ isl_int_init(opt_i);
+ for (i = 1; i < set->n; ++i) {
+ res = isl_basic_set_opt(set->p[i], max, obj, &opt_i);
+ if (res == isl_lp_error || res == isl_lp_unbounded) {
+ isl_int_clear(opt_i);
+ return res;
+ }
+ if (res == isl_lp_ok)
+ empty = 0;
+ if (isl_int_gt(opt_i, *opt))
+ isl_int_set(*opt, opt_i);
+ }
+ isl_int_clear(opt_i);
+
+ return empty ? isl_lp_empty : isl_lp_ok;
+}
+
+/* Compute the minimum (maximum if max is set) of the integer affine
+ * expression obj over the points in set and put the result in *opt.
+ */
+enum isl_lp_result isl_set_opt(__isl_keep isl_set *set, int max,
+ __isl_keep isl_aff *obj, isl_int *opt)
+{
+ enum isl_lp_result res;
+
+ if (!set || !obj)
+ return isl_lp_error;
+
+ if (isl_space_match(set->dim, isl_dim_param,
+ obj->ls->dim, isl_dim_param))
+ return isl_set_opt_aligned(set, max, obj, opt);
+
+ set = isl_set_copy(set);
+ obj = isl_aff_copy(obj);
+ set = isl_set_align_params(set, isl_aff_get_domain_space(obj));
+ obj = isl_aff_align_params(obj, isl_set_get_space(set));
+
+ res = isl_set_opt_aligned(set, max, obj, opt);
+
+ isl_set_free(set);
+ isl_aff_free(obj);
+
+ return res;
+}
+
+enum isl_lp_result isl_basic_set_max(__isl_keep isl_basic_set *bset,
+ __isl_keep isl_aff *obj, isl_int *opt)
+{
+ return isl_basic_set_opt(bset, 1, obj, opt);
+}
+
+enum isl_lp_result isl_set_max(__isl_keep isl_set *set,
+ __isl_keep isl_aff *obj, isl_int *opt)
+{
+ return isl_set_opt(set, 1, obj, opt);
+}
+
+enum isl_lp_result isl_set_min(__isl_keep isl_set *set,
+ __isl_keep isl_aff *obj, isl_int *opt)
+{
+ return isl_set_opt(set, 0, obj, opt);
+}
projects / platform / upstream / isl.git / blobdiff