isl_scan.c

   1 /*
   2  * Copyright 2008-2009 Katholieke Universiteit Leuven
   3  *
   4  * Use of this software is governed by the GNU LGPLv2.1 license
   5  *
   6  * Written by Sven Verdoolaege, K.U.Leuven, Departement
   7  * Computerwetenschappen, Celestijnenlaan 200A, B-3001 Leuven, Belgium
   8  */
   9
  10 #include "isl_basis_reduction.h"
  11 #include "isl_scan.h"
  12 #include "isl_seq.h"
  13 #include "isl_tab.h"
  14 #include <isl_map_private.h>
  15
  16 struct isl_counter {
  17         struct isl_scan_callback callback;
  18         isl_int count;
  19         isl_int max;
  20 };
  21
  22 static int increment_counter(struct isl_scan_callback *cb,
  23         __isl_take isl_vec *sample)
  24 {
  25         struct isl_counter *cnt = (struct isl_counter *)cb;
  26
  27         isl_int_add_ui(cnt->count, cnt->count, 1);
  28
  29         isl_vec_free(sample);
  30
  31         if (isl_int_is_zero(cnt->max) || isl_int_lt(cnt->count, cnt->max))
  32                 return 0;
  33         return -1;
  34 }
  35
  36 static int increment_range(struct isl_scan_callback *cb, isl_int min, isl_int max)
  37 {
  38         struct isl_counter *cnt = (struct isl_counter *)cb;
  39
  40         isl_int_add(cnt->count, cnt->count, max);
  41         isl_int_sub(cnt->count, cnt->count, min);
  42         isl_int_add_ui(cnt->count, cnt->count, 1);
  43
  44         if (isl_int_is_zero(cnt->max) || isl_int_lt(cnt->count, cnt->max))
  45                 return 0;
  46         isl_int_set(cnt->count, cnt->max);
  47         return -1;
  48 }
  49
  50 /* Call callback->add with the current sample value of the tableau "tab".
  51  */
  52 static int add_solution(struct isl_tab *tab, struct isl_scan_callback *callback)
  53 {
  54         struct isl_vec *sample;
  55
  56         if (!tab)
  57                 return -1;
  58         sample = isl_tab_get_sample_value(tab);
  59         if (!sample)
  60                 return -1;
  61
  62         return callback->add(callback, sample);
  63 }
  64
  65 static int scan_0D(struct isl_basic_set *bset,
  66         struct isl_scan_callback *callback)
  67 {
  68         struct isl_vec *sample;
  69
  70         sample = isl_vec_alloc(bset->ctx, 1);
  71         isl_basic_set_free(bset);
  72
  73         if (!sample)
  74                 return -1;
  75
  76         isl_int_set_si(sample->el[0], 1);
  77
  78         return callback->add(callback, sample);
  79 }
  80
  81 /* Look for all integer points in "bset", which is assumed to be unbounded,
  82  * and call callback->add on each of them.
  83  *
  84  * We first compute a reduced basis for the set and then scan
  85  * the set in the directions of this basis.
  86  * We basically perform a depth first search, where in each level i
  87  * we compute the range in the i-th basis vector direction, given
  88  * fixed values in the directions of the previous basis vector.
  89  * We then add an equality to the tableau fixing the value in the
  90  * direction of the current basis vector to each value in the range
  91  * in turn and then continue to the next level.
  92  *
  93  * The search is implemented iteratively.  "level" identifies the current
  94  * basis vector.  "init" is true if we want the first value at the current
  95  * level and false if we want the next value.
  96  * Solutions are added in the leaves of the search tree, i.e., after
  97  * we have fixed a value in each direction of the basis.
  98  */
  99 int isl_basic_set_scan(struct isl_basic_set *bset,
 100         struct isl_scan_callback *callback)
 101 {
 102         unsigned dim;
 103         struct isl_mat *B = NULL;
 104         struct isl_tab *tab = NULL;
 105         struct isl_vec *min;
 106         struct isl_vec *max;
 107         struct isl_tab_undo **snap;
 108         int level;
 109         int init;
 110         enum isl_lp_result res;
 111
 112         if (!bset)
 113                 return -1;
 114
 115         dim = isl_basic_set_total_dim(bset);
 116         if (dim == 0)
 117                 return scan_0D(bset, callback);
 118
 119         min = isl_vec_alloc(bset->ctx, dim);
 120         max = isl_vec_alloc(bset->ctx, dim);
 121         snap = isl_alloc_array(bset->ctx, struct isl_tab_undo *, dim);
 122
 123         if (!min || !max || !snap)
 124                 goto error;
 125
 126         tab = isl_tab_from_basic_set(bset);
 127         if (!tab)
 128                 goto error;
 129         if (isl_tab_extend_cons(tab, dim + 1) < 0)
 130                 goto error;
 131
 132         tab->basis = isl_mat_identity(bset->ctx, 1 + dim);
 133         if (1)
 134                 tab = isl_tab_compute_reduced_basis(tab);
 135         if (!tab)
 136                 goto error;
 137         B = isl_mat_copy(tab->basis);
 138         if (!B)
 139                 goto error;
 140
 141         level = 0;
 142         init = 1;
 143
 144         while (level >= 0) {
 145                 int empty = 0;
 146                 if (init) {
 147                         res = isl_tab_min(tab, B->row[1 + level],
 148                                     bset->ctx->one, &min->el[level], NULL, 0);
 149                         if (res == isl_lp_empty)
 150                                 empty = 1;
 151                         if (res == isl_lp_error || res == isl_lp_unbounded)
 152                                 goto error;
 153                         isl_seq_neg(B->row[1 + level] + 1,
 154                                     B->row[1 + level] + 1, dim);
 155                         res = isl_tab_min(tab, B->row[1 + level],
 156                                     bset->ctx->one, &max->el[level], NULL, 0);
 157                         isl_seq_neg(B->row[1 + level] + 1,
 158                                     B->row[1 + level] + 1, dim);
 159                         isl_int_neg(max->el[level], max->el[level]);
 160                         if (res == isl_lp_empty)
 161                                 empty = 1;
 162                         if (res == isl_lp_error || res == isl_lp_unbounded)
 163                                 goto error;
 164                         snap[level] = isl_tab_snap(tab);
 165                 } else
 166                         isl_int_add_ui(min->el[level], min->el[level], 1);
 167
 168                 if (empty || isl_int_gt(min->el[level], max->el[level])) {
 169                         level--;
 170                         init = 0;
 171                         if (level >= 0)
 172                                 if (isl_tab_rollback(tab, snap[level]) < 0)
 173                                         goto error;
 174                         continue;
 175                 }
 176                 if (level == dim - 1 && callback->add == increment_counter) {
 177                         if (increment_range(callback,
 178                                             min->el[level], max->el[level]))
 179                                 goto error;
 180                         level--;
 181                         init = 0;
 182                         if (level >= 0)
 183                                 if (isl_tab_rollback(tab, snap[level]) < 0)
 184                                         goto error;
 185                         continue;
 186                 }
 187                 isl_int_neg(B->row[1 + level][0], min->el[level]);
 188                 if (isl_tab_add_valid_eq(tab, B->row[1 + level]) < 0)
 189                         goto error;
 190                 isl_int_set_si(B->row[1 + level][0], 0);
 191                 if (level < dim - 1) {
 192                         ++level;
 193                         init = 1;
 194                         continue;
 195                 }
 196                 if (add_solution(tab, callback) < 0)
 197                         goto error;
 198                 init = 0;
 199                 if (isl_tab_rollback(tab, snap[level]) < 0)
 200                         goto error;
 201         }
 202
 203         isl_tab_free(tab);
 204         free(snap);
 205         isl_vec_free(min);
 206         isl_vec_free(max);
 207         isl_basic_set_free(bset);
 208         isl_mat_free(B);
 209         return 0;
 210 error:
 211         isl_tab_free(tab);
 212         free(snap);
 213         isl_vec_free(min);
 214         isl_vec_free(max);
 215         isl_basic_set_free(bset);
 216         isl_mat_free(B);
 217         return -1;
 218 }
 219
 220 int isl_set_scan(__isl_take isl_set *set, struct isl_scan_callback *callback)
 221 {
 222         int i;
 223
 224         if (!set || !callback)
 225                 goto error;
 226
 227         set = isl_set_cow(set);
 228         set = isl_set_make_disjoint(set);
 229         set = isl_set_compute_divs(set);
 230         if (!set)
 231                 goto error;
 232
 233         for (i = 0; i < set->n; ++i)
 234                 if (isl_basic_set_scan(isl_basic_set_copy(set->p[i]),
 235                                         callback) < 0)
 236                         goto error;
 237
 238         isl_set_free(set);
 239         return 0;
 240 error:
 241         isl_set_free(set);
 242         return -1;
 243 }
 244
 245 int isl_set_count_upto(__isl_keep isl_set *set, isl_int max, isl_int *count)
 246 {
 247         struct isl_counter cnt = { { &increment_counter } };
 248
 249         if (!set)
 250                 return -1;
 251
 252         isl_int_init(cnt.count);
 253         isl_int_init(cnt.max);
 254
 255         isl_int_set_si(cnt.count, 0);
 256         isl_int_set(cnt.max, max);
 257         if (isl_set_scan(isl_set_copy(set), &cnt.callback) < 0 &&
 258             isl_int_lt(cnt.count, cnt.max))
 259                 goto error;
 260
 261         isl_int_set(*count, cnt.count);
 262         isl_int_clear(cnt.max);
 263         isl_int_clear(cnt.count);
 264
 265         return 0;
 266 error:
 267         isl_int_clear(cnt.count);
 268         return -1;
 269 }
 270
 271 int isl_set_count(__isl_keep isl_set *set, isl_int *count)
 272 {
 273         if (!set)
 274                 return -1;
 275         return isl_set_count_upto(set, set->ctx->zero, count);
 276 }