--- /dev/null
+#include "isl_ilp.h"
+#include "isl_map_private.h"
+#include "isl_sample.h"
+#include "isl_seq.h"
+#include "isl_equalities.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
+ * the given basic set.
+ * Note that U may not contain all points that satisfy this property.
+ *
+ * We simply add the sum of all negative coefficients to the constant
+ * term. This ensures that if x satisfies the resulting constraints,
+ * then x plus any sum of unit vectors satisfies the original constraints.
+ */
+static struct isl_basic_set *unit_box_base_points(struct isl_basic_set *bset)
+{
+ int i, j, k;
+ struct isl_basic_set *unit_box = NULL;
+ unsigned total;
+
+ if (!bset)
+ goto error;
+
+ if (bset->n_eq != 0) {
+ unit_box = isl_basic_set_empty_like(bset);
+ isl_basic_set_free(bset);
+ return unit_box;
+ }
+
+ total = isl_basic_set_total_dim(bset);
+ unit_box = isl_basic_set_alloc_dim(isl_basic_set_get_dim(bset),
+ 0, 0, bset->n_ineq);
+
+ for (i = 0; i < bset->n_ineq; ++i) {
+ k = isl_basic_set_alloc_inequality(unit_box);
+ if (k < 0)
+ goto error;
+ isl_seq_cpy(unit_box->ineq[k], bset->ineq[i], 1 + total);
+ for (j = 0; j < total; ++j) {
+ if (isl_int_is_nonneg(unit_box->ineq[k][1 + j]))
+ continue;
+ isl_int_add(unit_box->ineq[k][0],
+ unit_box->ineq[k][0], unit_box->ineq[k][1 + j]);
+ }
+ }
+
+ isl_basic_set_free(bset);
+ return unit_box;
+error:
+ isl_basic_set_free(bset);
+ isl_basic_set_free(unit_box);
+ return NULL;
+}
+
+/* Find an integer point in "bset", preferably one that is
+ * close to minimizing "f".
+ *
+ * We first check if we can easily put unit boxes inside bset.
+ * If so, we take the best base point of any of the unit boxes we can find
+ * and round it up to the nearest integer.
+ * If not, we simply pick any integer point in "bset".
+ */
+static struct isl_vec *initial_solution(struct isl_basic_set *bset, isl_int *f)
+{
+ enum isl_lp_result res;
+ struct isl_basic_set *unit_box;
+ struct isl_vec *sol;
+
+ unit_box = unit_box_base_points(isl_basic_set_copy(bset));
+
+ res = isl_basic_set_solve_lp(unit_box, 0, f, bset->ctx->one,
+ NULL, NULL, &sol);
+ if (res == isl_lp_ok) {
+ isl_basic_set_free(unit_box);
+ return isl_vec_ceil(sol);
+ }
+
+ isl_basic_set_free(unit_box);
+
+ return isl_basic_set_sample(isl_basic_set_copy(bset));
+}
+
+/* Restrict "bset" to those points with values for f in the interval [l, u].
+ */
+static struct isl_basic_set *add_bounds(struct isl_basic_set *bset,
+ isl_int *f, isl_int l, isl_int u)
+{
+ int k;
+ unsigned total;
+
+ total = isl_basic_set_total_dim(bset);
+ bset = isl_basic_set_extend_constraints(bset, 0, 2);
+
+ k = isl_basic_set_alloc_inequality(bset);
+ if (k < 0)
+ goto error;
+ isl_seq_cpy(bset->ineq[k], f, 1 + total);
+ isl_int_sub(bset->ineq[k][0], bset->ineq[k][0], l);
+
+ k = isl_basic_set_alloc_inequality(bset);
+ if (k < 0)
+ goto error;
+ isl_seq_neg(bset->ineq[k], f, 1 + total);
+ isl_int_add(bset->ineq[k][0], bset->ineq[k][0], u);
+
+ return bset;
+error:
+ isl_basic_set_free(bset);
+ 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.
+ *
+ * We perform a number of steps until l > u.
+ * In each step, we look for an integer point with value in either
+ * the whole interval [l, u] or half of the interval [l, l+floor(u-l-1/2)].
+ * The choice depends on whether we have found an integer point in the
+ * previous step. If so, we look for the next point in half of the remaining
+ * interval.
+ * If we find a point, the current solution is updated and u is set
+ * to its value minus 1.
+ * 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 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;
+ struct isl_vec *sol;
+ int divide = 1;
+
+ res = isl_basic_set_solve_lp(bset, 0, f, bset->ctx->one,
+ opt, NULL, &sol);
+ if (res == isl_lp_ok && isl_int_is_one(sol->el[0])) {
+ if (sol_p)
+ *sol_p = sol;
+ else
+ isl_vec_free(sol);
+ return isl_lp_ok;
+ }
+ isl_vec_free(sol);
+ if (res == isl_lp_error || res == isl_lp_empty)
+ return res;
+
+ sol = initial_solution(bset, f);
+ if (!sol)
+ return isl_lp_error;
+ if (sol->size == 0) {
+ isl_vec_free(sol);
+ return isl_lp_empty;
+ }
+ if (res == isl_lp_unbounded) {
+ isl_vec_free(sol);
+ return isl_lp_unbounded;
+ }
+
+ 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(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;
+ }
+ }
+
+ isl_int_clear(l);
+ isl_int_clear(u);
+ isl_int_clear(tmp);
+
+ if (sol_p)
+ *sol_p = sol;
+ else
+ isl_vec_free(sol);
+
+ return res;
+}
+
+enum isl_lp_result solve_ilp_with_eq(struct isl_basic_set *bset, int max,
+ isl_int *f, isl_int *opt,
+ struct isl_vec **sol_p)
+{
+ unsigned dim;
+ enum isl_lp_result res;
+ struct isl_mat *T = NULL;
+ struct isl_vec *v;
+
+ dim = isl_basic_set_total_dim(bset);
+ v = isl_vec_alloc(bset->ctx, 1 + dim);
+ if (!v)
+ goto error;
+ isl_seq_cpy(v->el, f, 1 + dim);
+ bset = isl_basic_set_remove_equalities(bset, &T, NULL);
+ v = isl_vec_mat_product(v, isl_mat_copy(T));
+ 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) {
+ *sol_p = isl_mat_vec_product(T, *sol_p);
+ if (!*sol_p)
+ res = isl_lp_error;
+ } else
+ isl_mat_free(T);
+ return res;
+error:
+ isl_mat_free(T);
+ isl_basic_set_free(bset);
+ return isl_lp_error;
+}
+
+/* Find an integer point in "bset" that minimizes (or maximizes if max is set)
+ * 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.
+ *
+ * If there is any equality among the points in "bset", then we first
+ * project it out. Otherwise, we continue with solve_ilp above.
+ */
+enum isl_lp_result isl_basic_set_solve_ilp(struct isl_basic_set *bset, int max,
+ isl_int *f, isl_int *opt,
+ struct isl_vec **sol_p)
+{
+ unsigned dim;
+ enum isl_lp_result res;
+
+ if (!bset)
+ return isl_lp_error;
+ if (sol_p)
+ *sol_p = NULL;
+
+ isl_assert(bset->ctx, isl_basic_set_n_param(bset) == 0, goto error);
+
+ if (bset->n_eq)
+ return solve_ilp_with_eq(bset, max, f, opt, sol_p);
+
+ dim = isl_basic_set_total_dim(bset);
+
+ if (max)
+ isl_seq_neg(f, f, 1 + dim);
+
+ res = solve_ilp(bset, f, opt, sol_p);
+
+ if (max) {
+ isl_seq_neg(f, f, 1 + dim);
+ isl_int_neg(*opt, *opt);
+ }
+
+ return res;
+error:
+ isl_basic_set_free(bset);
+ return isl_lp_error;
+}
projects / platform / upstream / isl.git / commitdiff