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         isl_size dim = isl_basic_map_dim(bmap, isl_dim_all);
  32
  33         if (dim < 0)
  34                 return isl_lp_error;
  35         if (maximize)
  36                 isl_seq_neg(f, f, 1 + dim);
  37
  38         bmap = isl_basic_map_gauss(bmap, NULL);
  39         tab = isl_tab_from_basic_map(bmap, 0);
  40         res = isl_tab_min(tab, f, denom, opt, opt_denom, 0);
  41         if (res == isl_lp_ok && sol) {
  42                 *sol = isl_tab_get_sample_value(tab);
  43                 if (!*sol)
  44                         res = isl_lp_error;
  45         }
  46         isl_tab_free(tab);
  47
  48         if (maximize)
  49                 isl_seq_neg(f, f, 1 + dim);
  50         if (maximize && opt)
  51                 isl_int_neg(*opt, *opt);
  52
  53         return res;
  54 }
  55
  56 /* Given a basic map "bmap" and an affine combination of the variables "f"
  57  * with denominator "denom", set *opt / *opt_denom to the minimal
  58  * (or maximal if "maximize" is true) value attained by f/d over "bmap",
  59  * assuming the basic map is not empty and the expression cannot attain
  60  * arbitrarily small (or large) values.
  61  * If opt_denom is NULL, then *opt is rounded up (or down)
  62  * to the nearest integer.
  63  * The return value reflects the nature of the result (empty, unbounded,
  64  * minimal or maximal value returned in *opt).
  65  */
  66 enum isl_lp_result isl_basic_map_solve_lp(__isl_keep isl_basic_map *bmap,
  67         int max, isl_int *f, isl_int d, isl_int *opt, isl_int *opt_denom,
  68         __isl_give isl_vec **sol)
  69 {
  70         if (sol)
  71                 *sol = NULL;
  72
  73         if (!bmap)
  74                 return isl_lp_error;
  75
  76         return isl_tab_solve_lp(bmap, max, f, d, opt, opt_denom, sol);
  77 }
  78
  79 enum isl_lp_result isl_basic_set_solve_lp(struct isl_basic_set *bset, int max,
  80                                       isl_int *f, isl_int d, isl_int *opt,
  81                                       isl_int *opt_denom,
  82                                       struct isl_vec **sol)
  83 {
  84         return isl_basic_map_solve_lp(bset_to_bmap(bset), max,
  85                                         f, d, opt, opt_denom, sol);
  86 }
  87
  88 enum isl_lp_result isl_map_solve_lp(__isl_keep isl_map *map, int max,
  89                                       isl_int *f, isl_int d, isl_int *opt,
  90                                       isl_int *opt_denom,
  91                                       struct isl_vec **sol)
  92 {
  93         int i;
  94         isl_int o;
  95         isl_int t;
  96         isl_int opt_i;
  97         isl_int opt_denom_i;
  98         enum isl_lp_result res;
  99         int max_div;
 100         isl_vec *v = NULL;
 101
 102         if (!map)
 103                 return isl_lp_error;
 104         if (map->n == 0)
 105                 return isl_lp_empty;
 106
 107         max_div = 0;
 108         for (i = 0; i < map->n; ++i)
 109                 if (map->p[i]->n_div > max_div)
 110                         max_div = map->p[i]->n_div;
 111         if (max_div > 0) {
 112                 isl_size total = isl_map_dim(map, isl_dim_all);
 113                 if (total < 0)
 114                         return isl_lp_error;
 115                 v = isl_vec_alloc(map->ctx, 1 + total + max_div);
 116                 if (!v)
 117                         return isl_lp_error;
 118                 isl_seq_cpy(v->el, f, 1 + total);
 119                 isl_seq_clr(v->el + 1 + total, max_div);
 120                 f = v->el;
 121         }
 122
 123         if (!opt && map->n > 1 && sol) {
 124                 isl_int_init(o);
 125                 opt = &o;
 126         }
 127         if (map->n > 0)
 128                 isl_int_init(opt_i);
 129         if (map->n > 0 && opt_denom) {
 130                 isl_int_init(opt_denom_i);
 131                 isl_int_init(t);
 132         }
 133
 134         res = isl_basic_map_solve_lp(map->p[0], max, f, d,
 135                                         opt, opt_denom, sol);
 136         if (res == isl_lp_error || res == isl_lp_unbounded)
 137                 goto done;
 138
 139         if (sol)
 140                 *sol = NULL;
 141
 142         for (i = 1; i < map->n; ++i) {
 143                 isl_vec *sol_i = NULL;
 144                 enum isl_lp_result res_i;
 145                 int better;
 146
 147                 res_i = isl_basic_map_solve_lp(map->p[i], max, f, d,
 148                                             &opt_i,
 149                                             opt_denom ? &opt_denom_i : NULL,
 150                                             sol ? &sol_i : NULL);
 151                 if (res_i == isl_lp_error || res_i == isl_lp_unbounded) {
 152                         res = res_i;
 153                         goto done;
 154                 }
 155                 if (res_i == isl_lp_empty)
 156                         continue;
 157                 if (res == isl_lp_empty) {
 158                         better = 1;
 159                 } else if (!opt_denom) {
 160                         if (max)
 161                                 better = isl_int_gt(opt_i, *opt);
 162                         else
 163                                 better = isl_int_lt(opt_i, *opt);
 164                 } else {
 165                         isl_int_mul(t, opt_i, *opt_denom);
 166                         isl_int_submul(t, *opt, opt_denom_i);
 167                         if (max)
 168                                 better = isl_int_is_pos(t);
 169                         else
 170                                 better = isl_int_is_neg(t);
 171                 }
 172                 if (better) {
 173                         res = res_i;
 174                         if (opt)
 175                                 isl_int_set(*opt, opt_i);
 176                         if (opt_denom)
 177                                 isl_int_set(*opt_denom, opt_denom_i);
 178                         if (sol) {
 179                                 isl_vec_free(*sol);
 180                                 *sol = sol_i;
 181                         }
 182                 } else
 183                         isl_vec_free(sol_i);
 184         }
 185
 186 done:
 187         isl_vec_free(v);
 188         if (map->n > 0 && opt_denom) {
 189                 isl_int_clear(opt_denom_i);
 190                 isl_int_clear(t);
 191         }
 192         if (map->n > 0)
 193                 isl_int_clear(opt_i);
 194         if (opt == &o)
 195                 isl_int_clear(o);
 196         return res;
 197 }
 198
 199 enum isl_lp_result isl_set_solve_lp(__isl_keep isl_set *set, int max,
 200                                       isl_int *f, isl_int d, isl_int *opt,
 201                                       isl_int *opt_denom,
 202                                       struct isl_vec **sol)
 203 {
 204         return isl_map_solve_lp(set_to_map(set), max,
 205                                         f, d, opt, opt_denom, sol);
 206 }
 207
 208 /* Return the optimal (rational) value of "obj" over "bset", assuming
 209  * that "obj" and "bset" have aligned parameters and divs.
 210  * If "max" is set, then the maximal value is computed.
 211  * Otherwise, the minimal value is computed.
 212  *
 213  * Return infinity or negative infinity if the optimal value is unbounded and
 214  * NaN if "bset" is empty.
 215  *
 216  * Call isl_basic_set_solve_lp and translate the results.
 217  */
 218 static __isl_give isl_val *basic_set_opt_lp(
 219         __isl_keep isl_basic_set *bset, int max, __isl_keep isl_aff *obj)
 220 {
 221         isl_ctx *ctx;
 222         isl_val *res;
 223         enum isl_lp_result lp_res;
 224
 225         if (!bset || !obj)
 226                 return NULL;
 227
 228         ctx = isl_aff_get_ctx(obj);
 229         res = isl_val_alloc(ctx);
 230         if (!res)
 231                 return NULL;
 232         lp_res = isl_basic_set_solve_lp(bset, max, obj->v->el + 1,
 233                                         obj->v->el[0], &res->n, &res->d, NULL);
 234         if (lp_res == isl_lp_ok)
 235                 return isl_val_normalize(res);
 236         isl_val_free(res);
 237         if (lp_res == isl_lp_error)
 238                 return NULL;
 239         if (lp_res == isl_lp_empty)
 240                 return isl_val_nan(ctx);
 241         if (max)
 242                 return isl_val_infty(ctx);
 243         else
 244                 return isl_val_neginfty(ctx);
 245 }
 246
 247 /* Return the optimal (rational) value of "obj" over "bset", assuming
 248  * that "obj" and "bset" have aligned parameters.
 249  * If "max" is set, then the maximal value is computed.
 250  * Otherwise, the minimal value is computed.
 251  *
 252  * Return infinity or negative infinity if the optimal value is unbounded and
 253  * NaN if "bset" is empty.
 254  *
 255  * Align the divs of "bset" and "obj" and call basic_set_opt_lp.
 256  */
 257 static __isl_give isl_val *isl_basic_set_opt_lp_val_aligned(
 258         __isl_keep isl_basic_set *bset, int max, __isl_keep isl_aff *obj)
 259 {
 260         int *exp1 = NULL;
 261         int *exp2 = NULL;
 262         isl_ctx *ctx;
 263         isl_mat *bset_div = NULL;
 264         isl_mat *div = NULL;
 265         isl_val *res;
 266         isl_size bset_n_div, obj_n_div;
 267
 268         if (!bset || !obj)
 269                 return NULL;
 270
 271         ctx = isl_aff_get_ctx(obj);
 272         if (!isl_space_is_equal(bset->dim, obj->ls->dim))
 273                 isl_die(ctx, isl_error_invalid,
 274                         "spaces don't match", return NULL);
 275
 276         bset_n_div = isl_basic_set_dim(bset, isl_dim_div);
 277         obj_n_div = isl_aff_dim(obj, isl_dim_div);
 278         if (bset_n_div < 0 || obj_n_div < 0)
 279                 return NULL;
 280         if (bset_n_div == 0 && obj_n_div == 0)
 281                 return basic_set_opt_lp(bset, max, obj);
 282
 283         bset = isl_basic_set_copy(bset);
 284         obj = isl_aff_copy(obj);
 285
 286         bset_div = isl_basic_set_get_divs(bset);
 287         exp1 = isl_alloc_array(ctx, int, bset_n_div);
 288         exp2 = isl_alloc_array(ctx, int, obj_n_div);
 289         if (!bset_div || (bset_n_div && !exp1) || (obj_n_div && !exp2))
 290                 goto error;
 291
 292         div = isl_merge_divs(bset_div, obj->ls->div, exp1, exp2);
 293
 294         bset = isl_basic_set_expand_divs(bset, isl_mat_copy(div), exp1);
 295         obj = isl_aff_expand_divs(obj, isl_mat_copy(div), exp2);
 296
 297         res = basic_set_opt_lp(bset, max, obj);
 298
 299         isl_mat_free(bset_div);
 300         isl_mat_free(div);
 301         free(exp1);
 302         free(exp2);
 303         isl_basic_set_free(bset);
 304         isl_aff_free(obj);
 305
 306         return res;
 307 error:
 308         isl_mat_free(div);
 309         isl_mat_free(bset_div);
 310         free(exp1);
 311         free(exp2);
 312         isl_basic_set_free(bset);
 313         isl_aff_free(obj);
 314         return NULL;
 315 }
 316
 317 /* Return the optimal (rational) value of "obj" over "bset".
 318  * If "max" is set, then the maximal value is computed.
 319  * Otherwise, the minimal value is computed.
 320  *
 321  * Return infinity or negative infinity if the optimal value is unbounded and
 322  * NaN if "bset" is empty.
 323  */
 324 static __isl_give isl_val *isl_basic_set_opt_lp_val(
 325         __isl_keep isl_basic_set *bset, int max, __isl_keep isl_aff *obj)
 326 {
 327         isl_bool equal;
 328         isl_val *res;
 329
 330         if (!bset || !obj)
 331                 return NULL;
 332
 333         equal = isl_basic_set_space_has_equal_params(bset, obj->ls->dim);
 334         if (equal < 0)
 335                 return NULL;
 336         if (equal)
 337                 return isl_basic_set_opt_lp_val_aligned(bset, max, obj);
 338
 339         bset = isl_basic_set_copy(bset);
 340         obj = isl_aff_copy(obj);
 341         bset = isl_basic_set_align_params(bset, isl_aff_get_domain_space(obj));
 342         obj = isl_aff_align_params(obj, isl_basic_set_get_space(bset));
 343
 344         res = isl_basic_set_opt_lp_val_aligned(bset, max, obj);
 345
 346         isl_basic_set_free(bset);
 347         isl_aff_free(obj);
 348
 349         return res;
 350 }
 351
 352 /* Return the minimal (rational) value of "obj" over "bset".
 353  *
 354  * Return negative infinity if the minimal value is unbounded and
 355  * NaN if "bset" is empty.
 356  */
 357 __isl_give isl_val *isl_basic_set_min_lp_val(__isl_keep isl_basic_set *bset,
 358         __isl_keep isl_aff *obj)
 359 {
 360         return isl_basic_set_opt_lp_val(bset, 0, obj);
 361 }
 362
 363 /* Return the maximal (rational) value of "obj" over "bset".
 364  *
 365  * Return infinity if the maximal value is unbounded and
 366  * NaN if "bset" is empty.
 367  */
 368 __isl_give isl_val *isl_basic_set_max_lp_val(__isl_keep isl_basic_set *bset,
 369         __isl_keep isl_aff *obj)
 370 {
 371         return isl_basic_set_opt_lp_val(bset, 1, obj);
 372 }