isl_factorization.c

   1 /*
   2  * Copyright 2005-2007 Universiteit Leiden
   3  * Copyright 2008-2009 Katholieke Universiteit Leuven
   4  * Copyright 2010      INRIA Saclay
   5  *
   6  * Use of this software is governed by the GNU LGPLv2.1 license
   7  *
   8  * Written by Sven Verdoolaege, Leiden Institute of Advanced Computer Science,
   9  * Universiteit Leiden, Niels Bohrweg 1, 2333 CA Leiden, The Netherlands
  10  * and K.U.Leuven, Departement Computerwetenschappen, Celestijnenlaan 200A,
  11  * B-3001 Leuven, Belgium
  12  * and INRIA Saclay - Ile-de-France, Parc Club Orsay Universite,
  13  * ZAC des vignes, 4 rue Jacques Monod, 91893 Orsay, France
  14  */
  15
  16 #include <isl_factorization.h>
  17 #include <isl_dim_private.h>
  18 #include <isl_mat_private.h>
  19
  20 static __isl_give isl_factorizer *isl_factorizer_alloc(
  21         __isl_take isl_morph *morph, int n_group)
  22 {
  23         isl_factorizer *f = NULL;
  24         int *len = NULL;
  25
  26         if (!morph)
  27                 return NULL;
  28
  29         if (n_group > 0) {
  30                 len = isl_alloc_array(morph->dom->ctx, int, n_group);
  31                 if (!len)
  32                         goto error;
  33         }
  34
  35         f = isl_alloc_type(morph->dom->ctx, struct isl_factorizer);
  36         if (!f)
  37                 goto error;
  38
  39         f->morph = morph;
  40         f->n_group = n_group;
  41         f->len = len;
  42
  43         return f;
  44 error:
  45         free(len);
  46         isl_morph_free(morph);
  47         return NULL;
  48 }
  49
  50 void isl_factorizer_free(__isl_take isl_factorizer *f)
  51 {
  52         if (!f)
  53                 return;
  54
  55         isl_morph_free(f->morph);
  56         free(f->len);
  57         free(f);
  58 }
  59
  60 void isl_factorizer_dump(__isl_take isl_factorizer *f, FILE *out)
  61 {
  62         int i;
  63
  64         if (!f)
  65                 return;
  66
  67         isl_morph_dump(f->morph, out);
  68         fprintf(out, "[");
  69         for (i = 0; i < f->n_group; ++i) {
  70                 if (i)
  71                         fprintf(out, ", ");
  72                 fprintf(out, "%d", f->len[i]);
  73         }
  74         fprintf(out, "]\n");
  75 }
  76
  77 __isl_give isl_factorizer *isl_factorizer_identity(__isl_keep isl_basic_set *bset)
  78 {
  79         return isl_factorizer_alloc(isl_morph_identity(bset), 0);
  80 }
  81
  82 __isl_give isl_factorizer *isl_factorizer_groups(__isl_keep isl_basic_set *bset,
  83         __isl_take isl_mat *Q, __isl_take isl_mat *U, int n, int *len)
  84 {
  85         int i;
  86         unsigned nvar;
  87         unsigned ovar;
  88         isl_dim *dim;
  89         isl_basic_set *dom;
  90         isl_basic_set *ran;
  91         isl_morph *morph;
  92         isl_factorizer *f;
  93         isl_mat *id;
  94
  95         if (!bset || !Q || !U)
  96                 goto error;
  97
  98         ovar = 1 + isl_dim_offset(bset->dim, isl_dim_set);
  99         id = isl_mat_identity(bset->ctx, ovar);
 100         Q = isl_mat_diagonal(isl_mat_copy(id), Q);
 101         U = isl_mat_diagonal(id, U);
 102
 103         nvar = isl_basic_set_dim(bset, isl_dim_set);
 104         dim = isl_basic_set_get_dim(bset);
 105         dom = isl_basic_set_universe(isl_dim_copy(dim));
 106         dim = isl_dim_drop(dim, isl_dim_set, 0, nvar);
 107         dim = isl_dim_add(dim, isl_dim_set, nvar);
 108         ran = isl_basic_set_universe(dim);
 109         morph = isl_morph_alloc(dom, ran, Q, U);
 110         f = isl_factorizer_alloc(morph, n);
 111         if (!f)
 112                 return NULL;
 113         for (i = 0; i < n; ++i)
 114                 f->len[i] = len[i];
 115         return f;
 116 error:
 117         isl_mat_free(Q);
 118         isl_mat_free(U);
 119         return NULL;
 120 }
 121
 122 struct isl_factor_groups {
 123         int *pos;               /* for each column: row position of pivot */
 124         int *group;             /* group to which a column belongs */
 125         int *cnt;               /* number of columns in the group */
 126         int *rowgroup;          /* group to which a constraint belongs */
 127 };
 128
 129 /* Initialize isl_factor_groups structure: find pivot row positions,
 130  * each column initially belongs to its own group and the groups
 131  * of the constraints are still unknown.
 132  */
 133 static int init_groups(struct isl_factor_groups *g, __isl_keep isl_mat *H)
 134 {
 135         int i, j;
 136
 137         if (!H)
 138                 return -1;
 139
 140         g->pos = isl_alloc_array(H->ctx, int, H->n_col);
 141         g->group = isl_alloc_array(H->ctx, int, H->n_col);
 142         g->cnt = isl_alloc_array(H->ctx, int, H->n_col);
 143         g->rowgroup = isl_alloc_array(H->ctx, int, H->n_row);
 144
 145         if (!g->pos || !g->group || !g->cnt || !g->rowgroup)
 146                 return -1;
 147
 148         for (i = 0; i < H->n_row; ++i)
 149                 g->rowgroup[i] = -1;
 150         for (i = 0, j = 0; i < H->n_col; ++i) {
 151                 for ( ; j < H->n_row; ++j)
 152                         if (!isl_int_is_zero(H->row[j][i]))
 153                                 break;
 154                 g->pos[i] = j;
 155         }
 156         for (i = 0; i < H->n_col; ++i) {
 157                 g->group[i] = i;
 158                 g->cnt[i] = 1;
 159         }
 160
 161         return 0;
 162 }
 163
 164 /* Update group[k] to the group column k belongs to.
 165  * When merging two groups, only the group of the current
 166  * group leader is changed.  Here we change the group of
 167  * the other members to also point to the group that the
 168  * old group leader now points to.
 169  */
 170 static void update_group(struct isl_factor_groups *g, int k)
 171 {
 172         int p = g->group[k];
 173         while (g->cnt[p] == 0)
 174                 p = g->group[p];
 175         g->group[k] = p;
 176 }
 177
 178 /* Merge group i with all groups of the subsequent columns
 179  * with non-zero coefficients in row j of H.
 180  * (The previous columns are all zero; otherwise we would have handled
 181  * the row before.)
 182  */
 183 static int update_group_i_with_row_j(struct isl_factor_groups *g, int i, int j,
 184         __isl_keep isl_mat *H)
 185 {
 186         int k;
 187
 188         g->rowgroup[j] = g->group[i];
 189         for (k = i + 1; k < H->n_col && j >= g->pos[k]; ++k) {
 190                 update_group(g, k);
 191                 update_group(g, i);
 192                 if (g->group[k] != g->group[i] &&
 193                     !isl_int_is_zero(H->row[j][k])) {
 194                         isl_assert(H->ctx, g->cnt[g->group[k]] != 0, return -1);
 195                         isl_assert(H->ctx, g->cnt[g->group[i]] != 0, return -1);
 196                         if (g->group[i] < g->group[k]) {
 197                                 g->cnt[g->group[i]] += g->cnt[g->group[k]];
 198                                 g->cnt[g->group[k]] = 0;
 199                                 g->group[g->group[k]] = g->group[i];
 200                         } else {
 201                                 g->cnt[g->group[k]] += g->cnt[g->group[i]];
 202                                 g->cnt[g->group[i]] = 0;
 203                                 g->group[g->group[i]] = g->group[k];
 204                         }
 205                 }
 206         }
 207
 208         return 0;
 209 }
 210
 211 /* Update the group information based on the constraint matrix.
 212  */
 213 static int update_groups(struct isl_factor_groups *g, __isl_keep isl_mat *H)
 214 {
 215         int i, j;
 216
 217         for (i = 0; i < H->n_col && g->cnt[0] < H->n_col; ++i) {
 218                 if (g->pos[i] == H->n_row)
 219                         continue; /* A line direction */
 220                 if (g->rowgroup[g->pos[i]] == -1)
 221                         g->rowgroup[g->pos[i]] = i;
 222                 for (j = g->pos[i] + 1; j < H->n_row; ++j) {
 223                         if (isl_int_is_zero(H->row[j][i]))
 224                                 continue;
 225                         if (g->rowgroup[j] != -1)
 226                                 continue;
 227                         if (update_group_i_with_row_j(g, i, j, H) < 0)
 228                                 return -1;
 229                 }
 230         }
 231
 232         return 0;
 233 }
 234
 235 static void clear_groups(struct isl_factor_groups *g)
 236 {
 237         if (!g)
 238                 return;
 239         free(g->pos);
 240         free(g->group);
 241         free(g->cnt);
 242         free(g->rowgroup);
 243 }
 244
 245 /* Determine if the set variables of the basic set can be factorized and
 246  * return the results in an isl_factorizer.
 247  *
 248  * The algorithm works by first computing the Hermite normal form
 249  * and then grouping columns linked by one or more constraints together,
 250  * where a constraints "links" two or more columns if the constraint
 251  * has nonzero coefficients in the columns.
 252  */
 253 __isl_give isl_factorizer *isl_basic_set_factorizer(
 254         __isl_keep isl_basic_set *bset)
 255 {
 256         int i, j, n, done;
 257         isl_mat *H, *U, *Q;
 258         unsigned nvar;
 259         struct isl_factor_groups g = { 0 };
 260         isl_factorizer *f;
 261
 262         if (!bset)
 263                 return NULL;
 264
 265         isl_assert(bset->ctx, isl_basic_set_dim(bset, isl_dim_div) == 0,
 266                 return NULL);
 267
 268         nvar = isl_basic_set_dim(bset, isl_dim_set);
 269         if (nvar <= 1)
 270                 return isl_factorizer_identity(bset);
 271
 272         H = isl_mat_alloc(bset->ctx, bset->n_eq + bset->n_ineq, nvar);
 273         if (!H)
 274                 return NULL;
 275         isl_mat_sub_copy(bset->ctx, H->row, bset->eq, bset->n_eq,
 276                 0, 1 + isl_dim_offset(bset->dim, isl_dim_set), nvar);
 277         isl_mat_sub_copy(bset->ctx, H->row + bset->n_eq, bset->ineq, bset->n_ineq,
 278                 0, 1 + isl_dim_offset(bset->dim, isl_dim_set), nvar);
 279         H = isl_mat_left_hermite(H, 0, &U, &Q);
 280
 281         if (init_groups(&g, H) < 0)
 282                 goto error;
 283         if (update_groups(&g, H) < 0)
 284                 goto error;
 285
 286         if (g.cnt[0] == nvar) {
 287                 isl_mat_free(H);
 288                 isl_mat_free(U);
 289                 isl_mat_free(Q);
 290                 clear_groups(&g);
 291
 292                 return isl_factorizer_identity(bset);
 293         }
 294
 295         done = 0;
 296         n = 0;
 297         while (done != nvar) {
 298                 int group = g.group[done];
 299                 for (i = 1; i < g.cnt[group]; ++i) {
 300                         if (g.group[done + i] == group)
 301                                 continue;
 302                         for (j = done + g.cnt[group]; j < nvar; ++j)
 303                                 if (g.group[j] == group)
 304                                         break;
 305                         g.group[j] = g.group[done + i];
 306                         Q = isl_mat_swap_rows(Q, done + i, j);
 307                         U = isl_mat_swap_cols(U, done + i, j);
 308                 }
 309                 done += g.cnt[group];
 310                 g.pos[n++] = g.cnt[group];
 311         }
 312
 313         f = isl_factorizer_groups(bset, Q, U, n, g.pos);
 314
 315         isl_mat_free(H);
 316         clear_groups(&g);
 317
 318         return f;
 319 error:
 320         isl_mat_free(H);
 321         isl_mat_free(U);
 322         isl_mat_free(Q);
 323         clear_groups(&g);
 324         return NULL;
 325 }