| /* |
| * Copyright 2008-2009 Katholieke Universiteit Leuven |
| * |
| * Use of this software is governed by the GNU LGPLv2.1 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_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 |
| * 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_vec(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 (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 |
| * 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 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; |
| struct isl_vec *sol; |
| |
| 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_set(l, *opt); |
| |
| isl_seq_inner_product(f, sol->el, sol->size, opt); |
| isl_int_sub_ui(u, *opt, 1); |
| |
| sol = solve_ilp_search(bset, f, opt, sol, l, u); |
| if (!sol) |
| res = isl_lp_error; |
| |
| isl_int_clear(l); |
| isl_int_clear(u); |
| |
| if (sol_p) |
| *sol_p = sol; |
| else |
| isl_vec_free(sol); |
| |
| return res; |
| } |
| |
| static 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; |
| |
| 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; |
| 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); |
| isl_basic_set_free(bset); |
| 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 (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); |
| |
| 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; |
| } |
| |
| 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_dim_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. |
| */ |
| enum isl_lp_result isl_set_opt(__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; |
| } |
| |
| 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); |
| } |