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 #include <bset_to_bmap.c>
  23 #include <set_to_map.c>
  24
  25 enum isl_lp_result isl_tab_solve_lp(__isl_keep isl_basic_map *bmap,
  26         int maximize, isl_int *f, isl_int denom, isl_int *opt,
  27         isl_int *opt_denom, __isl_give isl_vec **sol)
  28 {
  29         struct isl_tab *tab;
  30         enum isl_lp_result res;
  31         unsigned dim = isl_basic_map_total_dim(bmap);
  32
  33         if (maximize)
  34                 isl_seq_neg(f, f, 1 + dim);
  35
  36         bmap = isl_basic_map_gauss(bmap, NULL);
  37         tab = isl_tab_from_basic_map(bmap, 0);
  38         res = isl_tab_min(tab, f, denom, opt, opt_denom, 0);
  39         if (res == isl_lp_ok && sol) {
  40                 *sol = isl_tab_get_sample_value(tab);
  41                 if (!*sol)
  42                         res = isl_lp_error;
  43         }
  44         isl_tab_free(tab);
  45
  46         if (maximize)
  47                 isl_seq_neg(f, f, 1 + dim);
  48         if (maximize && opt)
  49                 isl_int_neg(*opt, *opt);
  50
  51         return res;
  52 }
  53
  54 /* Given a basic map "bmap" and an affine combination of the variables "f"
  55  * with denominator "denom", set *opt / *opt_denom to the minimal
  56  * (or maximal if "maximize" is true) value attained by f/d over "bmap",
  57  * assuming the basic map is not empty and the expression cannot attain
  58  * arbitrarily small (or large) values.
  59  * If opt_denom is NULL, then *opt is rounded up (or down)
  60  * to the nearest integer.
  61  * The return value reflects the nature of the result (empty, unbounded,
  62  * minimal or maximal value returned in *opt).
  63  */
  64 enum isl_lp_result isl_basic_map_solve_lp(struct isl_basic_map *bmap, int max,
  65                                       isl_int *f, isl_int d, isl_int *opt,
  66                                       isl_int *opt_denom,
  67                                       struct isl_vec **sol)
  68 {
  69         if (sol)
  70                 *sol = NULL;
  71
  72         if (!bmap)
  73                 return isl_lp_error;
  74
  75         return isl_tab_solve_lp(bmap, max, f, d, opt, opt_denom, sol);
  76 }
  77
  78 enum isl_lp_result isl_basic_set_solve_lp(struct isl_basic_set *bset, int max,
  79                                       isl_int *f, isl_int d, isl_int *opt,
  80                                       isl_int *opt_denom,
  81                                       struct isl_vec **sol)
  82 {
  83         return isl_basic_map_solve_lp(bset_to_bmap(bset), max,
  84                                         f, d, opt, opt_denom, sol);
  85 }
  86
  87 enum isl_lp_result isl_map_solve_lp(__isl_keep isl_map *map, int max,
  88                                       isl_int *f, isl_int d, isl_int *opt,
  89                                       isl_int *opt_denom,
  90                                       struct isl_vec **sol)
  91 {
  92         int i;
  93         isl_int o;
  94         isl_int t;
  95         isl_int opt_i;
  96         isl_int opt_denom_i;
  97         enum isl_lp_result res;
  98         int max_div;
  99         isl_vec *v = NULL;
 100
 101         if (!map)
 102                 return isl_lp_error;
 103         if (map->n == 0)
 104                 return isl_lp_empty;
 105
 106         max_div = 0;
 107         for (i = 0; i < map->n; ++i)
 108                 if (map->p[i]->n_div > max_div)
 109                         max_div = map->p[i]->n_div;
 110         if (max_div > 0) {
 111                 unsigned total = isl_space_dim(map->dim, isl_dim_all);
 112                 v = isl_vec_alloc(map->ctx, 1 + total + max_div);
 113                 if (!v)
 114                         return isl_lp_error;
 115                 isl_seq_cpy(v->el, f, 1 + total);
 116                 isl_seq_clr(v->el + 1 + total, max_div);
 117                 f = v->el;
 118         }
 119
 120         if (!opt && map->n > 1 && sol) {
 121                 isl_int_init(o);
 122                 opt = &o;
 123         }
 124         if (map->n > 0)
 125                 isl_int_init(opt_i);
 126         if (map->n > 0 && opt_denom) {
 127                 isl_int_init(opt_denom_i);
 128                 isl_int_init(t);
 129         }
 130
 131         res = isl_basic_map_solve_lp(map->p[0], max, f, d,
 132                                         opt, opt_denom, sol);
 133         if (res == isl_lp_error || res == isl_lp_unbounded)
 134                 goto done;
 135
 136         if (sol)
 137                 *sol = NULL;
 138
 139         for (i = 1; i < map->n; ++i) {
 140                 isl_vec *sol_i = NULL;
 141                 enum isl_lp_result res_i;
 142                 int better;
 143
 144                 res_i = isl_basic_map_solve_lp(map->p[i], max, f, d,
 145                                             &opt_i,
 146                                             opt_denom ? &opt_denom_i : NULL,
 147                                             sol ? &sol_i : NULL);
 148                 if (res_i == isl_lp_error || res_i == isl_lp_unbounded) {
 149                         res = res_i;
 150                         goto done;
 151                 }
 152                 if (res_i == isl_lp_empty)
 153                         continue;
 154                 if (res == isl_lp_empty) {
 155                         better = 1;
 156                 } else if (!opt_denom) {
 157                         if (max)
 158                                 better = isl_int_gt(opt_i, *opt);
 159                         else
 160                                 better = isl_int_lt(opt_i, *opt);
 161                 } else {
 162                         isl_int_mul(t, opt_i, *opt_denom);
 163                         isl_int_submul(t, *opt, opt_denom_i);
 164                         if (max)
 165                                 better = isl_int_is_pos(t);
 166                         else
 167                                 better = isl_int_is_neg(t);
 168                 }
 169                 if (better) {
 170                         res = res_i;
 171                         if (opt)
 172                                 isl_int_set(*opt, opt_i);
 173                         if (opt_denom)
 174                                 isl_int_set(*opt_denom, opt_denom_i);
 175                         if (sol) {
 176                                 isl_vec_free(*sol);
 177                                 *sol = sol_i;
 178                         }
 179                 } else
 180                         isl_vec_free(sol_i);
 181         }
 182
 183 done:
 184         isl_vec_free(v);
 185         if (map->n > 0 && opt_denom) {
 186                 isl_int_clear(opt_denom_i);
 187                 isl_int_clear(t);
 188         }
 189         if (map->n > 0)
 190                 isl_int_clear(opt_i);
 191         if (opt == &o)
 192                 isl_int_clear(o);
 193         return res;
 194 }
 195
 196 enum isl_lp_result isl_set_solve_lp(__isl_keep isl_set *set, int max,
 197                                       isl_int *f, isl_int d, isl_int *opt,
 198                                       isl_int *opt_denom,
 199                                       struct isl_vec **sol)
 200 {
 201         return isl_map_solve_lp(set_to_map(set), max,
 202                                         f, d, opt, opt_denom, sol);
 203 }
 204
 205 /* Return the optimal (rational) value of "obj" over "bset", assuming
 206  * that "obj" and "bset" have aligned parameters and divs.
 207  * If "max" is set, then the maximal value is computed.
 208  * Otherwise, the minimal value is computed.
 209  *
 210  * Return infinity or negative infinity if the optimal value is unbounded and
 211  * NaN if "bset" is empty.
 212  *
 213  * Call isl_basic_set_solve_lp and translate the results.
 214  */
 215 static __isl_give isl_val *basic_set_opt_lp(
 216         __isl_keep isl_basic_set *bset, int max, __isl_keep isl_aff *obj)
 217 {
 218         isl_ctx *ctx;
 219         isl_val *res;
 220         enum isl_lp_result lp_res;
 221
 222         if (!bset || !obj)
 223                 return NULL;
 224
 225         ctx = isl_aff_get_ctx(obj);
 226         res = isl_val_alloc(ctx);
 227         if (!res)
 228                 return NULL;
 229         lp_res = isl_basic_set_solve_lp(bset, max, obj->v->el + 1,
 230                                         obj->v->el[0], &res->n, &res->d, NULL);
 231         if (lp_res == isl_lp_ok)
 232                 return isl_val_normalize(res);
 233         isl_val_free(res);
 234         if (lp_res == isl_lp_error)
 235                 return NULL;
 236         if (lp_res == isl_lp_empty)
 237                 return isl_val_nan(ctx);
 238         if (max)
 239                 return isl_val_infty(ctx);
 240         else
 241                 return isl_val_neginfty(ctx);
 242 }
 243
 244 /* Return the optimal (rational) value of "obj" over "bset", assuming
 245  * that "obj" and "bset" have aligned parameters.
 246  * If "max" is set, then the maximal value is computed.
 247  * Otherwise, the minimal value is computed.
 248  *
 249  * Return infinity or negative infinity if the optimal value is unbounded and
 250  * NaN if "bset" is empty.
 251  *
 252  * Align the divs of "bset" and "obj" and call basic_set_opt_lp.
 253  */
 254 static __isl_give isl_val *isl_basic_set_opt_lp_val_aligned(
 255         __isl_keep isl_basic_set *bset, int max, __isl_keep isl_aff *obj)
 256 {
 257         int *exp1 = NULL;
 258         int *exp2 = NULL;
 259         isl_ctx *ctx;
 260         isl_mat *bset_div = NULL;
 261         isl_mat *div = NULL;
 262         isl_val *res;
 263         int bset_n_div, obj_n_div;
 264
 265         if (!bset || !obj)
 266                 return NULL;
 267
 268         ctx = isl_aff_get_ctx(obj);
 269         if (!isl_space_is_equal(bset->dim, obj->ls->dim))
 270                 isl_die(ctx, isl_error_invalid,
 271                         "spaces don't match", return NULL);
 272
 273         bset_n_div = isl_basic_set_dim(bset, isl_dim_div);
 274         obj_n_div = isl_aff_dim(obj, isl_dim_div);
 275         if (bset_n_div == 0 && obj_n_div == 0)
 276                 return basic_set_opt_lp(bset, max, obj);
 277
 278         bset = isl_basic_set_copy(bset);
 279         obj = isl_aff_copy(obj);
 280
 281         bset_div = isl_basic_set_get_divs(bset);
 282         exp1 = isl_alloc_array(ctx, int, bset_n_div);
 283         exp2 = isl_alloc_array(ctx, int, obj_n_div);
 284         if (!bset_div || (bset_n_div && !exp1) || (obj_n_div && !exp2))
 285                 goto error;
 286
 287         div = isl_merge_divs(bset_div, obj->ls->div, exp1, exp2);
 288
 289         bset = isl_basic_set_expand_divs(bset, isl_mat_copy(div), exp1);
 290         obj = isl_aff_expand_divs(obj, isl_mat_copy(div), exp2);
 291
 292         res = basic_set_opt_lp(bset, max, obj);
 293
 294         isl_mat_free(bset_div);
 295         isl_mat_free(div);
 296         free(exp1);
 297         free(exp2);
 298         isl_basic_set_free(bset);
 299         isl_aff_free(obj);
 300
 301         return res;
 302 error:
 303         isl_mat_free(div);
 304         isl_mat_free(bset_div);
 305         free(exp1);
 306         free(exp2);
 307         isl_basic_set_free(bset);
 308         isl_aff_free(obj);
 309         return NULL;
 310 }
 311
 312 /* Return the optimal (rational) value of "obj" over "bset".
 313  * If "max" is set, then the maximal value is computed.
 314  * Otherwise, the minimal value is computed.
 315  *
 316  * Return infinity or negative infinity if the optimal value is unbounded and
 317  * NaN if "bset" is empty.
 318  */
 319 static __isl_give isl_val *isl_basic_set_opt_lp_val(
 320         __isl_keep isl_basic_set *bset, int max, __isl_keep isl_aff *obj)
 321 {
 322         isl_bool equal;
 323         isl_val *res;
 324
 325         if (!bset || !obj)
 326                 return NULL;
 327
 328         equal = isl_basic_set_space_has_equal_params(bset, obj->ls->dim);
 329         if (equal < 0)
 330                 return NULL;
 331         if (equal)
 332                 return isl_basic_set_opt_lp_val_aligned(bset, max, obj);
 333
 334         bset = isl_basic_set_copy(bset);
 335         obj = isl_aff_copy(obj);
 336         bset = isl_basic_set_align_params(bset, isl_aff_get_domain_space(obj));
 337         obj = isl_aff_align_params(obj, isl_basic_set_get_space(bset));
 338
 339         res = isl_basic_set_opt_lp_val_aligned(bset, max, obj);
 340
 341         isl_basic_set_free(bset);
 342         isl_aff_free(obj);
 343
 344         return res;
 345 }
 346
 347 /* Return the minimal (rational) value of "obj" over "bset".
 348  *
 349  * Return negative infinity if the minimal value is unbounded and
 350  * NaN if "bset" is empty.
 351  */
 352 __isl_give isl_val *isl_basic_set_min_lp_val(__isl_keep isl_basic_set *bset,
 353         __isl_keep isl_aff *obj)
 354 {
 355         return isl_basic_set_opt_lp_val(bset, 0, obj);
 356 }
 357
 358 /* Return the maximal (rational) value of "obj" over "bset".
 359  *
 360  * Return infinity if the maximal value is unbounded and
 361  * NaN if "bset" is empty.
 362  */
 363 __isl_give isl_val *isl_basic_set_max_lp_val(__isl_keep isl_basic_set *bset,
 364         __isl_keep isl_aff *obj)
 365 {
 366         return isl_basic_set_opt_lp_val(bset, 1, obj);
 367 }