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 static 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(__isl_keep isl_basic_set *bset,
  80         int max, isl_int *f, isl_int d, isl_int *opt, isl_int *opt_denom,
  81         __isl_give 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                                       __isl_give 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                 isl_size total = isl_map_dim(map, isl_dim_all);
 112                 if (total < 0)
 113                         return isl_lp_error;
 114                 v = isl_vec_alloc(map->ctx, 1 + total + max_div);
 115                 if (!v)
 116                         return isl_lp_error;
 117                 isl_seq_cpy(v->el, f, 1 + total);
 118                 isl_seq_clr(v->el + 1 + total, max_div);
 119                 f = v->el;
 120         }
 121
 122         if (!opt && map->n > 1 && sol) {
 123                 isl_int_init(o);
 124                 opt = &o;
 125         }
 126         if (map->n > 0)
 127                 isl_int_init(opt_i);
 128         if (map->n > 0 && opt_denom) {
 129                 isl_int_init(opt_denom_i);
 130                 isl_int_init(t);
 131         }
 132
 133         res = isl_basic_map_solve_lp(map->p[0], max, f, d,
 134                                         opt, opt_denom, sol);
 135         if (res == isl_lp_error || res == isl_lp_unbounded)
 136                 goto done;
 137
 138         if (sol)
 139                 *sol = NULL;
 140
 141         for (i = 1; i < map->n; ++i) {
 142                 isl_vec *sol_i = NULL;
 143                 enum isl_lp_result res_i;
 144                 int better;
 145
 146                 res_i = isl_basic_map_solve_lp(map->p[i], max, f, d,
 147                                             &opt_i,
 148                                             opt_denom ? &opt_denom_i : NULL,
 149                                             sol ? &sol_i : NULL);
 150                 if (res_i == isl_lp_error || res_i == isl_lp_unbounded) {
 151                         res = res_i;
 152                         goto done;
 153                 }
 154                 if (res_i == isl_lp_empty)
 155                         continue;
 156                 if (res == isl_lp_empty) {
 157                         better = 1;
 158                 } else if (!opt_denom) {
 159                         if (max)
 160                                 better = isl_int_gt(opt_i, *opt);
 161                         else
 162                                 better = isl_int_lt(opt_i, *opt);
 163                 } else {
 164                         isl_int_mul(t, opt_i, *opt_denom);
 165                         isl_int_submul(t, *opt, opt_denom_i);
 166                         if (max)
 167                                 better = isl_int_is_pos(t);
 168                         else
 169                                 better = isl_int_is_neg(t);
 170                 }
 171                 if (better) {
 172                         res = res_i;
 173                         if (opt)
 174                                 isl_int_set(*opt, opt_i);
 175                         if (opt_denom)
 176                                 isl_int_set(*opt_denom, opt_denom_i);
 177                         if (sol) {
 178                                 isl_vec_free(*sol);
 179                                 *sol = sol_i;
 180                         }
 181                 } else
 182                         isl_vec_free(sol_i);
 183         }
 184
 185 done:
 186         isl_vec_free(v);
 187         if (map->n > 0 && opt_denom) {
 188                 isl_int_clear(opt_denom_i);
 189                 isl_int_clear(t);
 190         }
 191         if (map->n > 0)
 192                 isl_int_clear(opt_i);
 193         if (opt == &o)
 194                 isl_int_clear(o);
 195         return res;
 196 }
 197
 198 enum isl_lp_result isl_set_solve_lp(__isl_keep isl_set *set, int max,
 199                                       isl_int *f, isl_int d, isl_int *opt,
 200                                       isl_int *opt_denom,
 201                                       __isl_give isl_vec **sol)
 202 {
 203         return isl_map_solve_lp(set_to_map(set), max,
 204                                         f, d, opt, opt_denom, sol);
 205 }
 206
 207 /* Return the optimal (rational) value of "obj" over "bset", assuming
 208  * that "obj" and "bset" have aligned parameters and divs.
 209  * If "max" is set, then the maximal value is computed.
 210  * Otherwise, the minimal value is computed.
 211  *
 212  * Return infinity or negative infinity if the optimal value is unbounded and
 213  * NaN if "bset" is empty.
 214  *
 215  * Call isl_basic_set_solve_lp and translate the results.
 216  */
 217 static __isl_give isl_val *basic_set_opt_lp(
 218         __isl_keep isl_basic_set *bset, int max, __isl_keep isl_aff *obj)
 219 {
 220         isl_ctx *ctx;
 221         isl_val *res;
 222         enum isl_lp_result lp_res;
 223
 224         if (!bset || !obj)
 225                 return NULL;
 226
 227         ctx = isl_aff_get_ctx(obj);
 228         res = isl_val_alloc(ctx);
 229         if (!res)
 230                 return NULL;
 231         lp_res = isl_basic_set_solve_lp(bset, max, obj->v->el + 1,
 232                                         obj->v->el[0], &res->n, &res->d, NULL);
 233         if (lp_res == isl_lp_ok)
 234                 return isl_val_normalize(res);
 235         isl_val_free(res);
 236         if (lp_res == isl_lp_error)
 237                 return NULL;
 238         if (lp_res == isl_lp_empty)
 239                 return isl_val_nan(ctx);
 240         if (max)
 241                 return isl_val_infty(ctx);
 242         else
 243                 return isl_val_neginfty(ctx);
 244 }
 245
 246 /* Return the optimal (rational) value of "obj" over "bset", assuming
 247  * that "obj" and "bset" have aligned parameters.
 248  * If "max" is set, then the maximal value is computed.
 249  * Otherwise, the minimal value is computed.
 250  *
 251  * Return infinity or negative infinity if the optimal value is unbounded and
 252  * NaN if "bset" is empty.
 253  *
 254  * Align the divs of "bset" and "obj" and call basic_set_opt_lp.
 255  */
 256 static __isl_give isl_val *isl_basic_set_opt_lp_val_aligned(
 257         __isl_keep isl_basic_set *bset, int max, __isl_keep isl_aff *obj)
 258 {
 259         int *exp1 = NULL;
 260         int *exp2 = NULL;
 261         isl_ctx *ctx;
 262         isl_mat *bset_div = NULL;
 263         isl_mat *div = NULL;
 264         isl_val *res;
 265         isl_size bset_n_div, obj_n_div;
 266
 267         if (!bset || !obj)
 268                 return NULL;
 269
 270         ctx = isl_aff_get_ctx(obj);
 271         if (!isl_space_is_equal(bset->dim, obj->ls->dim))
 272                 isl_die(ctx, isl_error_invalid,
 273                         "spaces don't match", return NULL);
 274
 275         bset_n_div = isl_basic_set_dim(bset, isl_dim_div);
 276         obj_n_div = isl_aff_dim(obj, isl_dim_div);
 277         if (bset_n_div < 0 || obj_n_div < 0)
 278                 return NULL;
 279         if (bset_n_div == 0 && obj_n_div == 0)
 280                 return basic_set_opt_lp(bset, max, obj);
 281
 282         bset = isl_basic_set_copy(bset);
 283         obj = isl_aff_copy(obj);
 284
 285         bset_div = isl_basic_set_get_divs(bset);
 286         exp1 = isl_alloc_array(ctx, int, bset_n_div);
 287         exp2 = isl_alloc_array(ctx, int, obj_n_div);
 288         if (!bset_div || (bset_n_div && !exp1) || (obj_n_div && !exp2))
 289                 goto error;
 290
 291         div = isl_merge_divs(bset_div, obj->ls->div, exp1, exp2);
 292
 293         bset = isl_basic_set_expand_divs(bset, isl_mat_copy(div), exp1);
 294         obj = isl_aff_expand_divs(obj, isl_mat_copy(div), exp2);
 295
 296         res = basic_set_opt_lp(bset, max, obj);
 297
 298         isl_mat_free(bset_div);
 299         isl_mat_free(div);
 300         free(exp1);
 301         free(exp2);
 302         isl_basic_set_free(bset);
 303         isl_aff_free(obj);
 304
 305         return res;
 306 error:
 307         isl_mat_free(div);
 308         isl_mat_free(bset_div);
 309         free(exp1);
 310         free(exp2);
 311         isl_basic_set_free(bset);
 312         isl_aff_free(obj);
 313         return NULL;
 314 }
 315
 316 /* Return the optimal (rational) value of "obj" over "bset".
 317  * If "max" is set, then the maximal value is computed.
 318  * Otherwise, the minimal value is computed.
 319  *
 320  * Return infinity or negative infinity if the optimal value is unbounded and
 321  * NaN if "bset" is empty.
 322  */
 323 static __isl_give isl_val *isl_basic_set_opt_lp_val(
 324         __isl_keep isl_basic_set *bset, int max, __isl_keep isl_aff *obj)
 325 {
 326         isl_bool equal;
 327         isl_val *res;
 328
 329         if (!bset || !obj)
 330                 return NULL;
 331
 332         equal = isl_basic_set_space_has_equal_params(bset, obj->ls->dim);
 333         if (equal < 0)
 334                 return NULL;
 335         if (equal)
 336                 return isl_basic_set_opt_lp_val_aligned(bset, max, obj);
 337
 338         bset = isl_basic_set_copy(bset);
 339         obj = isl_aff_copy(obj);
 340         bset = isl_basic_set_align_params(bset, isl_aff_get_domain_space(obj));
 341         obj = isl_aff_align_params(obj, isl_basic_set_get_space(bset));
 342
 343         res = isl_basic_set_opt_lp_val_aligned(bset, max, obj);
 344
 345         isl_basic_set_free(bset);
 346         isl_aff_free(obj);
 347
 348         return res;
 349 }
 350
 351 /* Return the minimal (rational) value of "obj" over "bset".
 352  *
 353  * Return negative infinity if the minimal value is unbounded and
 354  * NaN if "bset" is empty.
 355  */
 356 __isl_give isl_val *isl_basic_set_min_lp_val(__isl_keep isl_basic_set *bset,
 357         __isl_keep isl_aff *obj)
 358 {
 359         return isl_basic_set_opt_lp_val(bset, 0, obj);
 360 }
 361
 362 /* Return the maximal (rational) value of "obj" over "bset".
 363  *
 364  * Return infinity if the maximal value is unbounded and
 365  * NaN if "bset" is empty.
 366  */
 367 __isl_give isl_val *isl_basic_set_max_lp_val(__isl_keep isl_basic_set *bset,
 368         __isl_keep isl_aff *obj)
 369 {
 370         return isl_basic_set_opt_lp_val(bset, 1, obj);
 371 }