isl_lp.c

   1 /*
   2  * Copyright 2008-2009 Katholieke Universiteit Leuven
   3  *
   4  * Use of this software is governed by the MIT license
   5  *
   6  * Written by Sven Verdoolaege, K.U.Leuven, Departement
   7  * Computerwetenschappen, Celestijnenlaan 200A, B-3001 Leuven, Belgium
   8  */
   9
  10 #include <isl_ctx_private.h>
  11 #include <isl_map_private.h>
  12 #include <isl/lp.h>
  13 #include <isl_seq.h>
  14 #include "isl_tab.h"
  15 #include <isl_options_private.h>
  16 #include <isl_local_space_private.h>
  17 #include <isl_aff_private.h>
  18 #include <isl_mat_private.h>
  19 #include <isl_val_private.h>
  20 #include <isl_vec_private.h>
  21
  22 enum isl_lp_result isl_tab_solve_lp(struct isl_basic_map *bmap, int maximize,
  23                                       isl_int *f, isl_int denom, isl_int *opt,
  24                                       isl_int *opt_denom,
  25                                       struct isl_vec **sol)
  26 {
  27         struct isl_tab *tab;
  28         enum isl_lp_result res;
  29         unsigned dim = isl_basic_map_total_dim(bmap);
  30
  31         if (maximize)
  32                 isl_seq_neg(f, f, 1 + dim);
  33
  34         bmap = isl_basic_map_gauss(bmap, NULL);
  35         tab = isl_tab_from_basic_map(bmap, 0);
  36         res = isl_tab_min(tab, f, denom, opt, opt_denom, 0);
  37         if (res == isl_lp_ok && sol) {
  38                 *sol = isl_tab_get_sample_value(tab);
  39                 if (!*sol)
  40                         res = isl_lp_error;
  41         }
  42         isl_tab_free(tab);
  43
  44         if (maximize)
  45                 isl_seq_neg(f, f, 1 + dim);
  46         if (maximize && opt)
  47                 isl_int_neg(*opt, *opt);
  48
  49         return res;
  50 }
  51
  52 /* Given a basic map "bmap" and an affine combination of the variables "f"
  53  * with denominator "denom", set *opt / *opt_denom to the minimal
  54  * (or maximal if "maximize" is true) value attained by f/d over "bmap",
  55  * assuming the basic map is not empty and the expression cannot attain
  56  * arbitrarily small (or large) values.
  57  * If opt_denom is NULL, then *opt is rounded up (or down)
  58  * to the nearest integer.
  59  * The return value reflects the nature of the result (empty, unbounded,
  60  * minmimal or maximal value returned in *opt).
  61  */
  62 enum isl_lp_result isl_basic_map_solve_lp(struct isl_basic_map *bmap, int max,
  63                                       isl_int *f, isl_int d, isl_int *opt,
  64                                       isl_int *opt_denom,
  65                                       struct isl_vec **sol)
  66 {
  67         if (sol)
  68                 *sol = NULL;
  69
  70         if (!bmap)
  71                 return isl_lp_error;
  72
  73         return isl_tab_solve_lp(bmap, max, f, d, opt, opt_denom, sol);
  74 }
  75
  76 enum isl_lp_result isl_basic_set_solve_lp(struct isl_basic_set *bset, int max,
  77                                       isl_int *f, isl_int d, isl_int *opt,
  78                                       isl_int *opt_denom,
  79                                       struct isl_vec **sol)
  80 {
  81         return isl_basic_map_solve_lp((struct isl_basic_map *)bset, max,
  82                                         f, d, opt, opt_denom, sol);
  83 }
  84
  85 enum isl_lp_result isl_map_solve_lp(__isl_keep isl_map *map, int max,
  86                                       isl_int *f, isl_int d, isl_int *opt,
  87                                       isl_int *opt_denom,
  88                                       struct isl_vec **sol)
  89 {
  90         int i;
  91         isl_int o;
  92         isl_int t;
  93         isl_int opt_i;
  94         isl_int opt_denom_i;
  95         enum isl_lp_result res;
  96         int max_div;
  97         isl_vec *v = NULL;
  98
  99         if (!map)
 100                 return isl_lp_error;
 101         if (map->n == 0)
 102                 return isl_lp_empty;
 103
 104         max_div = 0;
 105         for (i = 0; i < map->n; ++i)
 106                 if (map->p[i]->n_div > max_div)
 107                         max_div = map->p[i]->n_div;
 108         if (max_div > 0) {
 109                 unsigned total = isl_space_dim(map->dim, isl_dim_all);
 110                 v = isl_vec_alloc(map->ctx, 1 + total + max_div);
 111                 if (!v)
 112                         return isl_lp_error;
 113                 isl_seq_cpy(v->el, f, 1 + total);
 114                 isl_seq_clr(v->el + 1 + total, max_div);
 115                 f = v->el;
 116         }
 117
 118         if (!opt && map->n > 1 && sol) {
 119                 isl_int_init(o);
 120                 opt = &o;
 121         }
 122         if (map->n > 0)
 123                 isl_int_init(opt_i);
 124         if (map->n > 0 && opt_denom) {
 125                 isl_int_init(opt_denom_i);
 126                 isl_int_init(t);
 127         }
 128
 129         res = isl_basic_map_solve_lp(map->p[0], max, f, d,
 130                                         opt, opt_denom, sol);
 131         if (res == isl_lp_error || res == isl_lp_unbounded)
 132                 goto done;
 133
 134         if (sol)
 135                 *sol = NULL;
 136
 137         for (i = 1; i < map->n; ++i) {
 138                 isl_vec *sol_i = NULL;
 139                 enum isl_lp_result res_i;
 140                 int better;
 141
 142                 res_i = isl_basic_map_solve_lp(map->p[i], max, f, d,
 143                                             &opt_i,
 144                                             opt_denom ? &opt_denom_i : NULL,
 145                                             sol ? &sol_i : NULL);
 146                 if (res_i == isl_lp_error || res_i == isl_lp_unbounded) {
 147                         res = res_i;
 148                         goto done;
 149                 }
 150                 if (res_i == isl_lp_empty)
 151                         continue;
 152                 if (res == isl_lp_empty) {
 153                         better = 1;
 154                 } else if (!opt_denom) {
 155                         if (max)
 156                                 better = isl_int_gt(opt_i, *opt);
 157                         else
 158                                 better = isl_int_lt(opt_i, *opt);
 159                 } else {
 160                         isl_int_mul(t, opt_i, *opt_denom);
 161                         isl_int_submul(t, *opt, opt_denom_i);
 162                         if (max)
 163                                 better = isl_int_is_pos(t);
 164                         else
 165                                 better = isl_int_is_neg(t);
 166                 }
 167                 if (better) {
 168                         res = res_i;
 169                         if (opt)
 170                                 isl_int_set(*opt, opt_i);
 171                         if (opt_denom)
 172                                 isl_int_set(*opt_denom, opt_denom_i);
 173                         if (sol) {
 174                                 isl_vec_free(*sol);
 175                                 *sol = sol_i;
 176                         }
 177                 } else
 178                         isl_vec_free(sol_i);
 179         }
 180
 181 done:
 182         isl_vec_free(v);
 183         if (map->n > 0 && opt_denom) {
 184                 isl_int_clear(opt_denom_i);
 185                 isl_int_clear(t);
 186         }
 187         if (map->n > 0)
 188                 isl_int_clear(opt_i);
 189         if (opt == &o)
 190                 isl_int_clear(o);
 191         return res;
 192 }
 193
 194 enum isl_lp_result isl_set_solve_lp(__isl_keep isl_set *set, int max,
 195                                       isl_int *f, isl_int d, isl_int *opt,
 196                                       isl_int *opt_denom,
 197                                       struct isl_vec **sol)
 198 {
 199         return isl_map_solve_lp((struct isl_map *)set, max,
 200                                         f, d, opt, opt_denom, sol);
 201 }
 202
 203 /* Return the optimal (rational) value of "obj" over "bset", assuming
 204  * that "obj" and "bset" have aligned parameters and divs.
 205  * If "max" is set, then the maximal value is computed.
 206  * Otherwise, the minimal value is computed.
 207  *
 208  * Return infinity or negative infinity if the optimal value is unbounded and
 209  * NaN if "bset" is empty.
 210  *
 211  * Call isl_basic_set_solve_lp and translate the results.
 212  */
 213 static __isl_give isl_val *basic_set_opt_lp(
 214         __isl_keep isl_basic_set *bset, int max, __isl_keep isl_aff *obj)
 215 {
 216         isl_ctx *ctx;
 217         isl_val *res;
 218         enum isl_lp_result lp_res;
 219
 220         if (!bset || !obj)
 221                 return NULL;
 222
 223         ctx = isl_aff_get_ctx(obj);
 224         res = isl_val_alloc(ctx);
 225         if (!res)
 226                 return NULL;
 227         lp_res = isl_basic_set_solve_lp(bset, max, obj->v->el + 1,
 228                                         obj->v->el[0], &res->n, &res->d, NULL);
 229         if (lp_res == isl_lp_ok)
 230                 return isl_val_normalize(res);
 231         isl_val_free(res);
 232         if (lp_res == isl_lp_error)
 233                 return NULL;
 234         if (lp_res == isl_lp_empty)
 235                 return isl_val_nan(ctx);
 236         if (max)
 237                 return isl_val_infty(ctx);
 238         else
 239                 return isl_val_neginfty(ctx);
 240 }
 241
 242 /* Return the optimal (rational) value of "obj" over "bset", assuming
 243  * that "obj" and "bset" have aligned parameters.
 244  * If "max" is set, then the maximal value is computed.
 245  * Otherwise, the minimal value is computed.
 246  *
 247  * Return infinity or negative infinity if the optimal value is unbounded and
 248  * NaN if "bset" is empty.
 249  *
 250  * Align the divs of "bset" and "obj" and call basic_set_opt_lp.
 251  */
 252 static __isl_give isl_val *isl_basic_set_opt_lp_val_aligned(
 253         __isl_keep isl_basic_set *bset, int max, __isl_keep isl_aff *obj)
 254 {
 255         int *exp1 = NULL;
 256         int *exp2 = NULL;
 257         isl_ctx *ctx;
 258         isl_mat *bset_div = NULL;
 259         isl_mat *div = NULL;
 260         isl_val *res;
 261         int bset_n_div, obj_n_div;
 262
 263         if (!bset || !obj)
 264                 return NULL;
 265
 266         ctx = isl_aff_get_ctx(obj);
 267         if (!isl_space_is_equal(bset->dim, obj->ls->dim))
 268                 isl_die(ctx, isl_error_invalid,
 269                         "spaces don't match", return NULL);
 270
 271         bset_n_div = isl_basic_set_dim(bset, isl_dim_div);
 272         obj_n_div = isl_aff_dim(obj, isl_dim_div);
 273         if (bset_n_div == 0 && obj_n_div == 0)
 274                 return basic_set_opt_lp(bset, max, obj);
 275
 276         bset = isl_basic_set_copy(bset);
 277         obj = isl_aff_copy(obj);
 278
 279         bset_div = isl_basic_set_get_divs(bset);
 280         exp1 = isl_alloc_array(ctx, int, bset_n_div);
 281         exp2 = isl_alloc_array(ctx, int, obj_n_div);
 282         if (!bset_div || (bset_n_div && !exp1) || (obj_n_div && !exp2))
 283                 goto error;
 284
 285         div = isl_merge_divs(bset_div, obj->ls->div, exp1, exp2);
 286
 287         bset = isl_basic_set_expand_divs(bset, isl_mat_copy(div), exp1);
 288         obj = isl_aff_expand_divs(obj, isl_mat_copy(div), exp2);
 289
 290         res = basic_set_opt_lp(bset, max, obj);
 291
 292         isl_mat_free(bset_div);
 293         isl_mat_free(div);
 294         free(exp1);
 295         free(exp2);
 296         isl_basic_set_free(bset);
 297         isl_aff_free(obj);
 298
 299         return res;
 300 error:
 301         isl_mat_free(div);
 302         isl_mat_free(bset_div);
 303         free(exp1);
 304         free(exp2);
 305         isl_basic_set_free(bset);
 306         isl_aff_free(obj);
 307         return NULL;
 308 }
 309
 310 /* Return the optimal (rational) value of "obj" over "bset".
 311  * If "max" is set, then the maximal value is computed.
 312  * Otherwise, the minimal value is computed.
 313  *
 314  * Return infinity or negative infinity if the optimal value is unbounded and
 315  * NaN if "bset" is empty.
 316  */
 317 static __isl_give isl_val *isl_basic_set_opt_lp_val(
 318         __isl_keep isl_basic_set *bset, int max, __isl_keep isl_aff *obj)
 319 {
 320         isl_val *res;
 321
 322         if (!bset || !obj)
 323                 return NULL;
 324
 325         if (isl_space_match(bset->dim, isl_dim_param,
 326                             obj->ls->dim, isl_dim_param))
 327                 return isl_basic_set_opt_lp_val_aligned(bset, max, obj);
 328
 329         bset = isl_basic_set_copy(bset);
 330         obj = isl_aff_copy(obj);
 331         bset = isl_basic_set_align_params(bset, isl_aff_get_domain_space(obj));
 332         obj = isl_aff_align_params(obj, isl_basic_set_get_space(bset));
 333
 334         res = isl_basic_set_opt_lp_val_aligned(bset, max, obj);
 335
 336         isl_basic_set_free(bset);
 337         isl_aff_free(obj);
 338
 339         return res;
 340 }
 341
 342 /* Return the minimal (rational) value of "obj" over "bset".
 343  *
 344  * Return negative infinity if the minimal value is unbounded and
 345  * NaN if "bset" is empty.
 346  */
 347 __isl_give isl_val *isl_basic_set_min_lp_val(__isl_keep isl_basic_set *bset,
 348         __isl_keep isl_aff *obj)
 349 {
 350         return isl_basic_set_opt_lp_val(bset, 0, obj);
 351 }
 352
 353 /* Return the maximal (rational) value of "obj" over "bset".
 354  *
 355  * Return infinity if the maximal value is unbounded and
 356  * NaN if "bset" is empty.
 357  */
 358 __isl_give isl_val *isl_basic_set_max_lp_val(__isl_keep isl_basic_set *bset,
 359         __isl_keep isl_aff *obj)
 360 {
 361         return isl_basic_set_opt_lp_val(bset, 1, obj);
 362 }