| /* |
| * 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/lp.h> |
| #include <isl_seq.h> |
| #include "isl_tab.h" |
| #include <isl_options_private.h> |
| #include <isl_local_space_private.h> |
| #include <isl_aff_private.h> |
| #include <isl_mat_private.h> |
| #include <isl_val_private.h> |
| #include <isl_vec_private.h> |
| |
| #include <bset_to_bmap.c> |
| #include <set_to_map.c> |
| |
| enum isl_lp_result isl_tab_solve_lp(__isl_keep isl_basic_map *bmap, |
| int maximize, isl_int *f, isl_int denom, isl_int *opt, |
| isl_int *opt_denom, __isl_give isl_vec **sol) |
| { |
| struct isl_tab *tab; |
| enum isl_lp_result res; |
| unsigned dim = isl_basic_map_total_dim(bmap); |
| |
| if (maximize) |
| isl_seq_neg(f, f, 1 + dim); |
| |
| bmap = isl_basic_map_gauss(bmap, NULL); |
| tab = isl_tab_from_basic_map(bmap, 0); |
| res = isl_tab_min(tab, f, denom, opt, opt_denom, 0); |
| if (res == isl_lp_ok && sol) { |
| *sol = isl_tab_get_sample_value(tab); |
| if (!*sol) |
| res = isl_lp_error; |
| } |
| isl_tab_free(tab); |
| |
| if (maximize) |
| isl_seq_neg(f, f, 1 + dim); |
| if (maximize && opt) |
| isl_int_neg(*opt, *opt); |
| |
| return res; |
| } |
| |
| /* Given a basic map "bmap" and an affine combination of the variables "f" |
| * with denominator "denom", set *opt / *opt_denom to the minimal |
| * (or maximal if "maximize" is true) value attained by f/d over "bmap", |
| * assuming the basic map is not empty and the expression cannot attain |
| * arbitrarily small (or large) values. |
| * If opt_denom is NULL, then *opt is rounded up (or down) |
| * to the nearest integer. |
| * The return value reflects the nature of the result (empty, unbounded, |
| * minimal or maximal value returned in *opt). |
| */ |
| enum isl_lp_result isl_basic_map_solve_lp(__isl_keep isl_basic_map *bmap, |
| int max, isl_int *f, isl_int d, isl_int *opt, isl_int *opt_denom, |
| __isl_give isl_vec **sol) |
| { |
| if (sol) |
| *sol = NULL; |
| |
| if (!bmap) |
| return isl_lp_error; |
| |
| return isl_tab_solve_lp(bmap, max, f, d, opt, opt_denom, sol); |
| } |
| |
| enum isl_lp_result isl_basic_set_solve_lp(struct isl_basic_set *bset, int max, |
| isl_int *f, isl_int d, isl_int *opt, |
| isl_int *opt_denom, |
| struct isl_vec **sol) |
| { |
| return isl_basic_map_solve_lp(bset_to_bmap(bset), max, |
| f, d, opt, opt_denom, sol); |
| } |
| |
| enum isl_lp_result isl_map_solve_lp(__isl_keep isl_map *map, int max, |
| isl_int *f, isl_int d, isl_int *opt, |
| isl_int *opt_denom, |
| struct isl_vec **sol) |
| { |
| int i; |
| isl_int o; |
| isl_int t; |
| isl_int opt_i; |
| isl_int opt_denom_i; |
| enum isl_lp_result res; |
| int max_div; |
| isl_vec *v = NULL; |
| |
| if (!map) |
| return isl_lp_error; |
| if (map->n == 0) |
| return isl_lp_empty; |
| |
| max_div = 0; |
| for (i = 0; i < map->n; ++i) |
| if (map->p[i]->n_div > max_div) |
| max_div = map->p[i]->n_div; |
| if (max_div > 0) { |
| unsigned total = isl_space_dim(map->dim, isl_dim_all); |
| v = isl_vec_alloc(map->ctx, 1 + total + max_div); |
| if (!v) |
| return isl_lp_error; |
| isl_seq_cpy(v->el, f, 1 + total); |
| isl_seq_clr(v->el + 1 + total, max_div); |
| f = v->el; |
| } |
| |
| if (!opt && map->n > 1 && sol) { |
| isl_int_init(o); |
| opt = &o; |
| } |
| if (map->n > 0) |
| isl_int_init(opt_i); |
| if (map->n > 0 && opt_denom) { |
| isl_int_init(opt_denom_i); |
| isl_int_init(t); |
| } |
| |
| res = isl_basic_map_solve_lp(map->p[0], max, f, d, |
| opt, opt_denom, sol); |
| if (res == isl_lp_error || res == isl_lp_unbounded) |
| goto done; |
| |
| if (sol) |
| *sol = NULL; |
| |
| for (i = 1; i < map->n; ++i) { |
| isl_vec *sol_i = NULL; |
| enum isl_lp_result res_i; |
| int better; |
| |
| res_i = isl_basic_map_solve_lp(map->p[i], max, f, d, |
| &opt_i, |
| opt_denom ? &opt_denom_i : NULL, |
| sol ? &sol_i : NULL); |
| if (res_i == isl_lp_error || res_i == isl_lp_unbounded) { |
| res = res_i; |
| goto done; |
| } |
| if (res_i == isl_lp_empty) |
| continue; |
| if (res == isl_lp_empty) { |
| better = 1; |
| } else if (!opt_denom) { |
| if (max) |
| better = isl_int_gt(opt_i, *opt); |
| else |
| better = isl_int_lt(opt_i, *opt); |
| } else { |
| isl_int_mul(t, opt_i, *opt_denom); |
| isl_int_submul(t, *opt, opt_denom_i); |
| if (max) |
| better = isl_int_is_pos(t); |
| else |
| better = isl_int_is_neg(t); |
| } |
| if (better) { |
| res = res_i; |
| if (opt) |
| isl_int_set(*opt, opt_i); |
| if (opt_denom) |
| isl_int_set(*opt_denom, opt_denom_i); |
| if (sol) { |
| isl_vec_free(*sol); |
| *sol = sol_i; |
| } |
| } else |
| isl_vec_free(sol_i); |
| } |
| |
| done: |
| isl_vec_free(v); |
| if (map->n > 0 && opt_denom) { |
| isl_int_clear(opt_denom_i); |
| isl_int_clear(t); |
| } |
| if (map->n > 0) |
| isl_int_clear(opt_i); |
| if (opt == &o) |
| isl_int_clear(o); |
| return res; |
| } |
| |
| enum isl_lp_result isl_set_solve_lp(__isl_keep isl_set *set, int max, |
| isl_int *f, isl_int d, isl_int *opt, |
| isl_int *opt_denom, |
| struct isl_vec **sol) |
| { |
| return isl_map_solve_lp(set_to_map(set), max, |
| f, d, opt, opt_denom, sol); |
| } |
| |
| /* Return the optimal (rational) value of "obj" over "bset", assuming |
| * that "obj" and "bset" have aligned parameters and divs. |
| * If "max" is set, then the maximal value is computed. |
| * Otherwise, the minimal value is computed. |
| * |
| * Return infinity or negative infinity if the optimal value is unbounded and |
| * NaN if "bset" is empty. |
| * |
| * Call isl_basic_set_solve_lp and translate the results. |
| */ |
| static __isl_give isl_val *basic_set_opt_lp( |
| __isl_keep isl_basic_set *bset, int max, __isl_keep isl_aff *obj) |
| { |
| isl_ctx *ctx; |
| isl_val *res; |
| enum isl_lp_result lp_res; |
| |
| if (!bset || !obj) |
| return NULL; |
| |
| ctx = isl_aff_get_ctx(obj); |
| res = isl_val_alloc(ctx); |
| if (!res) |
| return NULL; |
| lp_res = isl_basic_set_solve_lp(bset, max, obj->v->el + 1, |
| obj->v->el[0], &res->n, &res->d, NULL); |
| if (lp_res == isl_lp_ok) |
| return isl_val_normalize(res); |
| isl_val_free(res); |
| if (lp_res == isl_lp_error) |
| return NULL; |
| if (lp_res == isl_lp_empty) |
| return isl_val_nan(ctx); |
| if (max) |
| return isl_val_infty(ctx); |
| else |
| return isl_val_neginfty(ctx); |
| } |
| |
| /* Return the optimal (rational) value of "obj" over "bset", assuming |
| * that "obj" and "bset" have aligned parameters. |
| * If "max" is set, then the maximal value is computed. |
| * Otherwise, the minimal value is computed. |
| * |
| * Return infinity or negative infinity if the optimal value is unbounded and |
| * NaN if "bset" is empty. |
| * |
| * Align the divs of "bset" and "obj" and call basic_set_opt_lp. |
| */ |
| static __isl_give isl_val *isl_basic_set_opt_lp_val_aligned( |
| __isl_keep isl_basic_set *bset, int max, __isl_keep isl_aff *obj) |
| { |
| int *exp1 = NULL; |
| int *exp2 = NULL; |
| isl_ctx *ctx; |
| isl_mat *bset_div = NULL; |
| isl_mat *div = NULL; |
| isl_val *res; |
| int bset_n_div, obj_n_div; |
| |
| if (!bset || !obj) |
| return NULL; |
| |
| 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 NULL); |
| |
| bset_n_div = isl_basic_set_dim(bset, isl_dim_div); |
| obj_n_div = isl_aff_dim(obj, isl_dim_div); |
| if (bset_n_div == 0 && obj_n_div == 0) |
| return basic_set_opt_lp(bset, max, obj); |
| |
| bset = isl_basic_set_copy(bset); |
| obj = isl_aff_copy(obj); |
| |
| bset_div = isl_basic_set_get_divs(bset); |
| exp1 = isl_alloc_array(ctx, int, bset_n_div); |
| exp2 = isl_alloc_array(ctx, int, obj_n_div); |
| if (!bset_div || (bset_n_div && !exp1) || (obj_n_div && !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_lp(bset, max, obj); |
| |
| 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 NULL; |
| } |
| |
| /* Return the optimal (rational) value of "obj" over "bset". |
| * If "max" is set, then the maximal value is computed. |
| * Otherwise, the minimal value is computed. |
| * |
| * Return infinity or negative infinity if the optimal value is unbounded and |
| * NaN if "bset" is empty. |
| */ |
| static __isl_give isl_val *isl_basic_set_opt_lp_val( |
| __isl_keep isl_basic_set *bset, int max, __isl_keep isl_aff *obj) |
| { |
| isl_bool equal; |
| isl_val *res; |
| |
| if (!bset || !obj) |
| return NULL; |
| |
| equal = isl_basic_set_space_has_equal_params(bset, obj->ls->dim); |
| if (equal < 0) |
| return NULL; |
| if (equal) |
| return isl_basic_set_opt_lp_val_aligned(bset, max, obj); |
| |
| bset = isl_basic_set_copy(bset); |
| obj = isl_aff_copy(obj); |
| bset = isl_basic_set_align_params(bset, isl_aff_get_domain_space(obj)); |
| obj = isl_aff_align_params(obj, isl_basic_set_get_space(bset)); |
| |
| res = isl_basic_set_opt_lp_val_aligned(bset, max, obj); |
| |
| isl_basic_set_free(bset); |
| isl_aff_free(obj); |
| |
| return res; |
| } |
| |
| /* Return the minimal (rational) value of "obj" over "bset". |
| * |
| * Return negative infinity if the minimal value is unbounded and |
| * NaN if "bset" is empty. |
| */ |
| __isl_give isl_val *isl_basic_set_min_lp_val(__isl_keep isl_basic_set *bset, |
| __isl_keep isl_aff *obj) |
| { |
| return isl_basic_set_opt_lp_val(bset, 0, obj); |
| } |
| |
| /* Return the maximal (rational) value of "obj" over "bset". |
| * |
| * Return infinity if the maximal value is unbounded and |
| * NaN if "bset" is empty. |
| */ |
| __isl_give isl_val *isl_basic_set_max_lp_val(__isl_keep isl_basic_set *bset, |
| __isl_keep isl_aff *obj) |
| { |
| return isl_basic_set_opt_lp_val(bset, 1, obj); |
| } |