isl_transitive_closure.c

   1 /*
   2  * Copyright 2010      INRIA Saclay
   3  *
   4  * Use of this software is governed by the GNU LGPLv2.1 license
   5  *
   6  * Written by Sven Verdoolaege, INRIA Saclay - Ile-de-France,
   7  * Parc Club Orsay Universite, ZAC des vignes, 4 rue Jacques Monod,
   8  * 91893 Orsay, France
   9  */
  10
  11 #include "isl_map.h"
  12 #include "isl_map_private.h"
  13
  14 /*
  15  * The transitive closure implementation is based on the paper
  16  * "Computing the Transitive Closure of a Union of Affine Integer
  17  * Tuple Relations" by Anna Beletska, Denis Barthou, Wlodzimierz Bielecki and
  18  * Albert Cohen.
  19  */
  20
  21 /* Given a union of translations (uniform dependences), return a matrix
  22  * with as many rows as there are disjuncts in the union and as many
  23  * columns as there are input dimensions (which should be equal to
  24  * the number of output dimensions).
  25  * Each row contains the translation performed by the corresponding disjunct.
  26  * If "map" turns out not to be a union of translations, then the contents
  27  * of the returned matrix are undefined and *ok is set to 0.
  28  */
  29 static __isl_give isl_mat *extract_steps(__isl_keep isl_map *map, int *ok)
  30 {
  31         int i, j;
  32         struct isl_mat *steps;
  33         unsigned dim = isl_map_dim(map, isl_dim_in);
  34
  35         *ok = 1;
  36
  37         steps = isl_mat_alloc(map->ctx, map->n, dim);
  38         if (!steps)
  39                 return NULL;
  40
  41         for (i = 0; i < map->n; ++i) {
  42                 struct isl_basic_set *delta;
  43
  44                 delta = isl_basic_map_deltas(isl_basic_map_copy(map->p[i]));
  45
  46                 for (j = 0; j < dim; ++j) {
  47                         int fixed;
  48
  49                         fixed = isl_basic_set_fast_dim_is_fixed(delta, j,
  50                                                             &steps->row[i][j]);
  51                         if (fixed < 0) {
  52                                 isl_basic_set_free(delta);
  53                                 goto error;
  54                         }
  55                         if (!fixed)
  56                                 break;
  57                 }
  58
  59                 isl_basic_set_free(delta);
  60
  61                 if (j < dim)
  62                         break;
  63         }
  64
  65         if (i < map->n)
  66                 *ok = 0;
  67
  68         return steps;
  69 error:
  70         isl_mat_free(steps);
  71         return NULL;
  72 }
  73
  74 /* Given a set of n offsets v_i (the rows of "steps"), construct a relation
  75  * of the given dimension specification that maps a element x to any
  76  * element that can be reached by taking a positive number of steps
  77  * along any of the offsets, where the number of steps k is equal to
  78  * parameter "param".  That is, construct
  79  *
  80  * { [x] -> [y] : exists k_i >= 0, y = x + \sum_i k_i v_i, k = \sum_i k_i > 0 }
  81  *
  82  * If strict is non-negative, then at least one step should be taken
  83  * along the given offset v_strict, i.e., k_strict > 0.
  84  */
  85 static __isl_give isl_map *path_along_steps(__isl_take isl_dim *dim,
  86         __isl_keep isl_mat *steps, unsigned param, int strict)
  87 {
  88         int i, j, k;
  89         struct isl_basic_map *path = NULL;
  90         unsigned d;
  91         unsigned n;
  92         unsigned nparam;
  93
  94         if (!dim || !steps)
  95                 goto error;
  96
  97         d = isl_dim_size(dim, isl_dim_in);
  98         n = steps->n_row;
  99         nparam = isl_dim_size(dim, isl_dim_param);
 100
 101         path = isl_basic_map_alloc_dim(isl_dim_copy(dim), n, d + 1, n + 1);
 102
 103         for (i = 0; i < n; ++i) {
 104                 k = isl_basic_map_alloc_div(path);
 105                 if (k < 0)
 106                         goto error;
 107                 isl_assert(steps->ctx, i == k, goto error);
 108                 isl_int_set_si(path->div[k][0], 0);
 109         }
 110
 111         for (i = 0; i < d; ++i) {
 112                 k = isl_basic_map_alloc_equality(path);
 113                 if (k < 0)
 114                         goto error;
 115                 isl_seq_clr(path->eq[k], 1 + isl_basic_map_total_dim(path));
 116                 isl_int_set_si(path->eq[k][1 + nparam + i], 1);
 117                 isl_int_set_si(path->eq[k][1 + nparam + d + i], -1);
 118                 for (j = 0; j < n; ++j)
 119                         isl_int_set(path->eq[k][1 + nparam + 2 * d + j],
 120                                     steps->row[j][i]);
 121         }
 122
 123         k = isl_basic_map_alloc_equality(path);
 124         if (k < 0)
 125                 goto error;
 126         isl_seq_clr(path->eq[k], 1 + isl_basic_map_total_dim(path));
 127         isl_int_set_si(path->eq[k][1 + param], -1);
 128         for (j = 0; j < n; ++j)
 129                 isl_int_set_si(path->eq[k][1 + nparam + 2 * d + j], 1);
 130
 131         for (i = 0; i < n; ++i) {
 132                 k = isl_basic_map_alloc_inequality(path);
 133                 if (k < 0)
 134                         goto error;
 135                 isl_seq_clr(path->ineq[k], 1 + isl_basic_map_total_dim(path));
 136                 isl_int_set_si(path->ineq[k][1 + nparam + 2 * d + i], 1);
 137                 if (i == strict)
 138                         isl_int_set_si(path->ineq[k][0], -1);
 139         }
 140
 141         k = isl_basic_map_alloc_inequality(path);
 142         if (k < 0)
 143                 goto error;
 144         isl_seq_clr(path->ineq[k], 1 + isl_basic_map_total_dim(path));
 145         isl_int_set_si(path->ineq[k][1 + param], 1);
 146         isl_int_set_si(path->ineq[k][0], -1);
 147
 148         isl_dim_free(dim);
 149
 150         path = isl_basic_map_simplify(path);
 151         path = isl_basic_map_finalize(path);
 152         return isl_map_from_basic_map(path);
 153 error:
 154         isl_dim_free(dim);
 155         isl_basic_map_free(path);
 156         return NULL;
 157 }
 158
 159 /* Check whether the overapproximation of the power of "map" is exactly
 160  * the power of "map".  In particular, for each path of a given length
 161  * that starts of in domain or range and ends up in the range,
 162  * check whether there is at least one path of the same length
 163  * with a valid first segment, i.e., one in "map".
 164  *
 165  * "domain" and "range" are the domain and range of "map"
 166  * "steps" represents the translations of "map"
 167  * "path" is a path along "steps"
 168  *
 169  * "domain", "range", "steps" and "path" have been precomputed by the calling
 170  * function.
 171  */
 172 static int check_exactness(__isl_take isl_map *map, __isl_take isl_set *domain,
 173         __isl_take isl_set *range, __isl_take isl_map *path,
 174         __isl_keep isl_mat *steps, unsigned param)
 175 {
 176         isl_map *test;
 177         int ok;
 178         int i;
 179
 180         if (!map)
 181                 goto error;
 182
 183         test = isl_map_empty(isl_map_get_dim(map));
 184         for (i = 0; i < map->n; ++i) {
 185                 struct isl_map *path_i;
 186                 struct isl_set *dom_i;
 187                 path_i = path_along_steps(isl_map_get_dim(map), steps, param, i);
 188                 dom_i = isl_set_from_basic_set(
 189                         isl_basic_map_domain(isl_basic_map_copy(map->p[i])));
 190                 path_i = isl_map_intersect_domain(path_i, dom_i);
 191                 test = isl_map_union(test, path_i);
 192         }
 193         isl_map_free(map);
 194         test = isl_map_intersect_range(test, isl_set_copy(range));
 195
 196         domain = isl_set_union(domain, isl_set_copy(range));
 197         path = isl_map_intersect_domain(path, domain);
 198         path = isl_map_intersect_range(path, range);
 199
 200         ok = isl_map_is_subset(path, test);
 201
 202         isl_map_free(path);
 203         isl_map_free(test);
 204
 205         return ok;
 206 error:
 207         isl_map_free(map);
 208         isl_set_free(domain);
 209         isl_set_free(range);
 210         isl_map_free(path);
 211         return -1;
 212 }
 213
 214 /* Compute the positive powers of "map", or an overapproximation.
 215  * The power is given by parameter "param".  If the result is exact,
 216  * then *exact is set to 1.
 217  */
 218 __isl_give isl_map *isl_map_power(__isl_take isl_map *map, unsigned param,
 219         int *exact)
 220 {
 221         struct isl_mat *steps = NULL;
 222         struct isl_set *domain = NULL;
 223         struct isl_set *range = NULL;
 224         struct isl_map *app = NULL;
 225         struct isl_map *path = NULL;
 226         int ok;
 227
 228         if (exact)
 229                 *exact = 1;
 230
 231         map = isl_map_remove_empty_parts(map);
 232         if (!map)
 233                 return NULL;
 234
 235         if (isl_map_fast_is_empty(map))
 236                 return map;
 237
 238         isl_assert(map->ctx, param < isl_map_dim(map, isl_dim_param), goto error);
 239         isl_assert(map->ctx,
 240                 isl_map_dim(map, isl_dim_in) == isl_map_dim(map, isl_dim_out),
 241                 goto error);
 242
 243         domain = isl_map_domain(isl_map_copy(map));
 244         range = isl_map_range(isl_map_copy(map));
 245         app = isl_map_from_domain_and_range(isl_set_copy(domain),
 246                                             isl_set_copy(range));
 247
 248         steps = extract_steps(map, &ok);
 249         if (!ok)
 250                 goto not_exact;
 251
 252         path = path_along_steps(isl_map_get_dim(map), steps, param, -1);
 253         app = isl_map_intersect(app, isl_map_copy(path));
 254
 255         if (exact &&
 256             (*exact = check_exactness(isl_map_copy(map), isl_set_copy(domain),
 257                                   isl_set_copy(range), isl_map_copy(path),
 258                                   steps, param)) < 0)
 259                 goto error;
 260
 261         if (0) {
 262 not_exact:
 263                 if (exact)
 264                         *exact = 0;
 265         }
 266         isl_set_free(domain);
 267         isl_set_free(range);
 268         isl_mat_free(steps);
 269         isl_map_free(path);
 270         isl_map_free(map);
 271         return app;
 272 error:
 273         isl_set_free(domain);
 274         isl_set_free(range);
 275         isl_mat_free(steps);
 276         isl_map_free(path);
 277         isl_map_free(map);
 278         isl_map_free(app);
 279         return NULL;
 280 }
 281
 282 /* Compute the transitive closure  of "map", or an overapproximation.
 283  * If the result is exact, then *exact is set to 1.
 284  * Simply compute the powers of map and then project out the parameter
 285  * describing the power.
 286  */
 287 __isl_give isl_map *isl_map_transitive_closure(__isl_take isl_map *map,
 288         int *exact)
 289 {
 290         unsigned param;
 291
 292         if (!map)
 293                 goto error;
 294
 295         param = isl_map_dim(map, isl_dim_param);
 296         map = isl_map_add(map, isl_dim_param, 1);
 297         map = isl_map_power(map, param, exact);
 298         map = isl_map_project_out(map, isl_dim_param, param, 1);
 299
 300         return map;
 301 error:
 302         isl_map_free(map);
 303         return NULL;
 304 }