isl_affine_hull.c

   1 #include "isl_ctx.h"
   2 #include "isl_seq.h"
   3 #include "isl_set.h"
   4 #include "isl_lp.h"
   5 #include "isl_map.h"
   6 #include "isl_map_private.h"
   7 #include "isl_equalities.h"
   8 #include "isl_sample.h"
   9 #include "isl_tab.h"
  10
  11 struct isl_basic_map *isl_basic_map_implicit_equalities(
  12                                                 struct isl_basic_map *bmap)
  13 {
  14         struct isl_tab *tab;
  15
  16         if (!bmap)
  17                 return bmap;
  18
  19         bmap = isl_basic_map_gauss(bmap, NULL);
  20         if (ISL_F_ISSET(bmap, ISL_BASIC_MAP_EMPTY))
  21                 return bmap;
  22         if (ISL_F_ISSET(bmap, ISL_BASIC_MAP_NO_IMPLICIT))
  23                 return bmap;
  24         if (bmap->n_ineq <= 1)
  25                 return bmap;
  26
  27         tab = isl_tab_from_basic_map(bmap);
  28         tab = isl_tab_detect_implicit_equalities(tab);
  29         bmap = isl_basic_map_update_from_tab(bmap, tab);
  30         isl_tab_free(tab);
  31         bmap = isl_basic_map_gauss(bmap, NULL);
  32         ISL_F_SET(bmap, ISL_BASIC_MAP_NO_IMPLICIT);
  33         return bmap;
  34 }
  35
  36 struct isl_basic_set *isl_basic_set_implicit_equalities(
  37                                                 struct isl_basic_set *bset)
  38 {
  39         return (struct isl_basic_set *)
  40                 isl_basic_map_implicit_equalities((struct isl_basic_map*)bset);
  41 }
  42
  43 struct isl_map *isl_map_implicit_equalities(struct isl_map *map)
  44 {
  45         int i;
  46
  47         if (!map)
  48                 return map;
  49
  50         for (i = 0; i < map->n; ++i) {
  51                 map->p[i] = isl_basic_map_implicit_equalities(map->p[i]);
  52                 if (!map->p[i])
  53                         goto error;
  54         }
  55
  56         return map;
  57 error:
  58         isl_map_free(map);
  59         return NULL;
  60 }
  61
  62 /* Make eq[row][col] of both bmaps equal so we can add the row
  63  * add the column to the common matrix.
  64  * Note that because of the echelon form, the columns of row row
  65  * after column col are zero.
  66  */
  67 static void set_common_multiple(
  68         struct isl_basic_set *bset1, struct isl_basic_set *bset2,
  69         unsigned row, unsigned col)
  70 {
  71         isl_int m, c;
  72
  73         if (isl_int_eq(bset1->eq[row][col], bset2->eq[row][col]))
  74                 return;
  75
  76         isl_int_init(c);
  77         isl_int_init(m);
  78         isl_int_lcm(m, bset1->eq[row][col], bset2->eq[row][col]);
  79         isl_int_divexact(c, m, bset1->eq[row][col]);
  80         isl_seq_scale(bset1->eq[row], bset1->eq[row], c, col+1);
  81         isl_int_divexact(c, m, bset2->eq[row][col]);
  82         isl_seq_scale(bset2->eq[row], bset2->eq[row], c, col+1);
  83         isl_int_clear(c);
  84         isl_int_clear(m);
  85 }
  86
  87 /* Delete a given equality, moving all the following equalities one up.
  88  */
  89 static void delete_row(struct isl_basic_set *bset, unsigned row)
  90 {
  91         isl_int *t;
  92         int r;
  93
  94         t = bset->eq[row];
  95         bset->n_eq--;
  96         for (r = row; r < bset->n_eq; ++r)
  97                 bset->eq[r] = bset->eq[r+1];
  98         bset->eq[bset->n_eq] = t;
  99 }
 100
 101 /* Make first row entries in column col of bset1 identical to
 102  * those of bset2, using the fact that entry bset1->eq[row][col]=a
 103  * is non-zero.  Initially, these elements of bset1 are all zero.
 104  * For each row i < row, we set
 105  *              A[i] = a * A[i] + B[i][col] * A[row]
 106  *              B[i] = a * B[i]
 107  * so that
 108  *              A[i][col] = B[i][col] = a * old(B[i][col])
 109  */
 110 static void construct_column(
 111         struct isl_basic_set *bset1, struct isl_basic_set *bset2,
 112         unsigned row, unsigned col)
 113 {
 114         int r;
 115         isl_int a;
 116         isl_int b;
 117         unsigned total;
 118
 119         isl_int_init(a);
 120         isl_int_init(b);
 121         total = 1 + isl_basic_set_n_dim(bset1);
 122         for (r = 0; r < row; ++r) {
 123                 if (isl_int_is_zero(bset2->eq[r][col]))
 124                         continue;
 125                 isl_int_gcd(b, bset2->eq[r][col], bset1->eq[row][col]);
 126                 isl_int_divexact(a, bset1->eq[row][col], b);
 127                 isl_int_divexact(b, bset2->eq[r][col], b);
 128                 isl_seq_combine(bset1->eq[r], a, bset1->eq[r],
 129                                               b, bset1->eq[row], total);
 130                 isl_seq_scale(bset2->eq[r], bset2->eq[r], a, total);
 131         }
 132         isl_int_clear(a);
 133         isl_int_clear(b);
 134         delete_row(bset1, row);
 135 }
 136
 137 /* Make first row entries in column col of bset1 identical to
 138  * those of bset2, using only these entries of the two matrices.
 139  * Let t be the last row with different entries.
 140  * For each row i < t, we set
 141  *      A[i] = (A[t][col]-B[t][col]) * A[i] + (B[i][col]-A[i][col) * A[t]
 142  *      B[i] = (A[t][col]-B[t][col]) * B[i] + (B[i][col]-A[i][col) * B[t]
 143  * so that
 144  *      A[i][col] = B[i][col] = old(A[t][col]*B[i][col]-A[i][col]*B[t][col])
 145  */
 146 static int transform_column(
 147         struct isl_basic_set *bset1, struct isl_basic_set *bset2,
 148         unsigned row, unsigned col)
 149 {
 150         int i, t;
 151         isl_int a, b, g;
 152         unsigned total;
 153
 154         for (t = row-1; t >= 0; --t)
 155                 if (isl_int_ne(bset1->eq[t][col], bset2->eq[t][col]))
 156                         break;
 157         if (t < 0)
 158                 return 0;
 159
 160         total = 1 + isl_basic_set_n_dim(bset1);
 161         isl_int_init(a);
 162         isl_int_init(b);
 163         isl_int_init(g);
 164         isl_int_sub(b, bset1->eq[t][col], bset2->eq[t][col]);
 165         for (i = 0; i < t; ++i) {
 166                 isl_int_sub(a, bset2->eq[i][col], bset1->eq[i][col]);
 167                 isl_int_gcd(g, a, b);
 168                 isl_int_divexact(a, a, g);
 169                 isl_int_divexact(g, b, g);
 170                 isl_seq_combine(bset1->eq[i], g, bset1->eq[i], a, bset1->eq[t],
 171                                 total);
 172                 isl_seq_combine(bset2->eq[i], g, bset2->eq[i], a, bset2->eq[t],
 173                                 total);
 174         }
 175         isl_int_clear(a);
 176         isl_int_clear(b);
 177         isl_int_clear(g);
 178         delete_row(bset1, t);
 179         delete_row(bset2, t);
 180         return 1;
 181 }
 182
 183 /* The implementation is based on Section 5.2 of Michael Karr,
 184  * "Affine Relationships Among Variables of a Program",
 185  * except that the echelon form we use starts from the last column
 186  * and that we are dealing with integer coefficients.
 187  */
 188 static struct isl_basic_set *affine_hull(
 189         struct isl_basic_set *bset1, struct isl_basic_set *bset2)
 190 {
 191         unsigned total;
 192         int col;
 193         int row;
 194
 195         total = 1 + isl_basic_set_n_dim(bset1);
 196
 197         row = 0;
 198         for (col = total-1; col >= 0; --col) {
 199                 int is_zero1 = row >= bset1->n_eq ||
 200                         isl_int_is_zero(bset1->eq[row][col]);
 201                 int is_zero2 = row >= bset2->n_eq ||
 202                         isl_int_is_zero(bset2->eq[row][col]);
 203                 if (!is_zero1 && !is_zero2) {
 204                         set_common_multiple(bset1, bset2, row, col);
 205                         ++row;
 206                 } else if (!is_zero1 && is_zero2) {
 207                         construct_column(bset1, bset2, row, col);
 208                 } else if (is_zero1 && !is_zero2) {
 209                         construct_column(bset2, bset1, row, col);
 210                 } else {
 211                         if (transform_column(bset1, bset2, row, col))
 212                                 --row;
 213                 }
 214         }
 215         isl_basic_set_free(bset2);
 216         isl_assert(bset1->ctx, row == bset1->n_eq, goto error);
 217         bset1 = isl_basic_set_normalize_constraints(bset1);
 218         return bset1;
 219 error:
 220         isl_basic_set_free(bset1);
 221         return NULL;
 222 }
 223
 224 /* Find an integer point in "bset" that lies outside of the equality
 225  * "eq" e(x) = 0.
 226  * If "up" is true, look for a point satisfying e(x) - 1 >= 0.
 227  * Otherwise, look for a point satisfying -e(x) - 1 >= 0 (i.e., e(x) <= -1).
 228  * The point, if found, is returned as a singleton set.
 229  * If no point can be found, the empty set is returned.
 230  *
 231  * Before solving an ILP problem, we first check if simply
 232  * adding the normal of the constraint to one of the known
 233  * integer points in the basic set yields another point
 234  * inside the basic set.
 235  *
 236  * The caller of this function ensures that "bset" is bounded.
 237  */
 238 static struct isl_basic_set *outside_point(struct isl_ctx *ctx,
 239         struct isl_basic_set *bset, isl_int *eq, int up)
 240 {
 241         struct isl_basic_set *slice = NULL;
 242         struct isl_vec *sample;
 243         struct isl_basic_set *point;
 244         unsigned dim;
 245         int k;
 246
 247         dim = isl_basic_set_n_dim(bset);
 248         sample = isl_vec_alloc(ctx, 1 + dim);
 249         if (!sample)
 250                 return NULL;
 251         isl_int_set_si(sample->block.data[0], 1);
 252         isl_seq_combine(sample->block.data + 1,
 253                 ctx->one, bset->sample->block.data + 1,
 254                 up ? ctx->one : ctx->negone, eq + 1, dim);
 255         if (isl_basic_set_contains(bset, sample))
 256                 return isl_basic_set_from_vec(sample);
 257         isl_vec_free(sample);
 258         sample = NULL;
 259
 260         slice = isl_basic_set_copy(bset);
 261         if (!slice)
 262                 goto error;
 263         slice = isl_basic_set_cow(slice);
 264         slice = isl_basic_set_extend(slice, 0, dim, 0, 0, 1);
 265         k = isl_basic_set_alloc_inequality(slice);
 266         if (k < 0)
 267                 goto error;
 268         if (up)
 269                 isl_seq_cpy(slice->ineq[k], eq, 1 + dim);
 270         else
 271                 isl_seq_neg(slice->ineq[k], eq, 1 + dim);
 272         isl_int_sub_ui(slice->ineq[k][0], slice->ineq[k][0], 1);
 273
 274         sample = isl_basic_set_sample_bounded(slice);
 275         if (!sample)
 276                 goto error;
 277         if (sample->size == 0) {
 278                 isl_vec_free(sample);
 279                 point = isl_basic_set_empty_like(bset);
 280         } else
 281                 point = isl_basic_set_from_vec(sample);
 282
 283         return point;
 284 error:
 285         isl_basic_set_free(slice);
 286         return NULL;
 287 }
 288
 289 struct isl_basic_set *isl_basic_set_recession_cone(struct isl_basic_set *bset)
 290 {
 291         int i;
 292
 293         bset = isl_basic_set_cow(bset);
 294         if (!bset)
 295                 return NULL;
 296         isl_assert(bset->ctx, bset->n_div == 0, goto error);
 297
 298         for (i = 0; i < bset->n_eq; ++i)
 299                 isl_int_set_si(bset->eq[i][0], 0);
 300
 301         for (i = 0; i < bset->n_ineq; ++i)
 302                 isl_int_set_si(bset->ineq[i][0], 0);
 303
 304         ISL_F_CLR(bset, ISL_BASIC_SET_NO_IMPLICIT);
 305         return isl_basic_set_implicit_equalities(bset);
 306 error:
 307         isl_basic_set_free(bset);
 308         return NULL;
 309 }
 310
 311 /* Extend an initial (under-)approximation of the affine hull of "bset"
 312  * by looking for points that do not satisfy one of the equalities
 313  * in the current approximation and adding them to that approximation
 314  * until no such points can be found any more.
 315  *
 316  * The caller of this function ensures that "bset" is bounded.
 317  */
 318 static struct isl_basic_set *extend_affine_hull(struct isl_basic_set *bset,
 319         struct isl_basic_set *hull)
 320 {
 321         int i, j, k;
 322         struct isl_ctx *ctx;
 323         unsigned dim;
 324
 325         ctx = bset->ctx;
 326         dim = isl_basic_set_n_dim(bset);
 327         for (i = 0; i < dim; ++i) {
 328                 struct isl_basic_set *point;
 329                 for (j = 0; j < hull->n_eq; ++j) {
 330                         point = outside_point(ctx, bset, hull->eq[j], 1);
 331                         if (!point)
 332                                 goto error;
 333                         if (!ISL_F_ISSET(point, ISL_BASIC_SET_EMPTY))
 334                                 break;
 335                         isl_basic_set_free(point);
 336                         point = outside_point(ctx, bset, hull->eq[j], 0);
 337                         if (!point)
 338                                 goto error;
 339                         if (!ISL_F_ISSET(point, ISL_BASIC_SET_EMPTY))
 340                                 break;
 341                         isl_basic_set_free(point);
 342
 343                         bset = isl_basic_set_extend_constraints(bset, 1, 0);
 344                         k = isl_basic_set_alloc_equality(bset);
 345                         if (k < 0)
 346                                 goto error;
 347                         isl_seq_cpy(bset->eq[k], hull->eq[j],
 348                                         1 + isl_basic_set_total_dim(hull));
 349                         bset = isl_basic_set_gauss(bset, NULL);
 350                         if (!bset)
 351                                 goto error;
 352                 }
 353                 if (j == hull->n_eq)
 354                         break;
 355                 hull = affine_hull(hull, point);
 356         }
 357         isl_basic_set_free(bset);
 358
 359         return hull;
 360 error:
 361         isl_basic_set_free(bset);
 362         isl_basic_set_free(hull);
 363         return NULL;
 364 }
 365
 366 /* Drop all constraints in bset that involve any of the dimensions
 367  * first to first+n-1.
 368  */
 369 static struct isl_basic_set *drop_constraints_involving
 370         (struct isl_basic_set *bset, unsigned first, unsigned n)
 371 {
 372         int i;
 373
 374         if (!bset)
 375                 return NULL;
 376
 377         bset = isl_basic_set_cow(bset);
 378
 379         for (i = bset->n_eq - 1; i >= 0; --i) {
 380                 if (isl_seq_first_non_zero(bset->eq[i] + 1 + first, n) == -1)
 381                         continue;
 382                 isl_basic_set_drop_equality(bset, i);
 383         }
 384
 385         for (i = bset->n_ineq - 1; i >= 0; --i) {
 386                 if (isl_seq_first_non_zero(bset->ineq[i] + 1 + first, n) == -1)
 387                         continue;
 388                 isl_basic_set_drop_inequality(bset, i);
 389         }
 390
 391         return bset;
 392 }
 393
 394 /* Look for all equalities satisfied by the integer points in bset,
 395  * which is assumed to be bounded.
 396  *
 397  * The equalities are obtained by successively looking for
 398  * a point that is affinely independent of the points found so far.
 399  * In particular, for each equality satisfied by the points so far,
 400  * we check if there is any point on a hyperplane parallel to the
 401  * corresponding hyperplane shifted by at least one (in either direction).
 402  */
 403 static struct isl_basic_set *uset_affine_hull_bounded(struct isl_basic_set *bset)
 404 {
 405         struct isl_vec *sample = NULL;
 406         struct isl_basic_set *hull;
 407
 408         if (isl_basic_set_is_empty(bset))
 409                 return bset;
 410
 411         sample = isl_basic_set_sample_vec(isl_basic_set_copy(bset));
 412         if (!sample)
 413                 goto error;
 414         if (sample->size == 0) {
 415                 struct isl_basic_set *hull;
 416                 isl_vec_free(sample);
 417                 hull = isl_basic_set_empty_like(bset);
 418                 isl_basic_set_free(bset);
 419                 return hull;
 420         }
 421         if (sample->size == 1) {
 422                 isl_vec_free(sample);
 423                 return bset;
 424         }
 425
 426         hull = isl_basic_set_from_vec(sample);
 427
 428         return extend_affine_hull(bset, hull);
 429 error:
 430         isl_basic_set_free(bset);
 431         return NULL;
 432 }
 433
 434 /* Compute the affine hull of "bset", where "cone" is the recession cone
 435  * of "bset".
 436  *
 437  * We first compute a unimodular transformation that puts the unbounded
 438  * directions in the last dimensions.  In particular, we take a transformation
 439  * that maps all equalities to equalities (in HNF) on the first dimensions.
 440  * Let x be the original dimensions and y the transformed, with y_1 bounded
 441  * and y_2 unbounded.
 442  *
 443  *             [ y_1 ]                  [ y_1 ]   [ Q_1 ]
 444  *      x = U  [ y_2 ]                  [ y_2 ] = [ Q_2 ] x
 445  *
 446  * Let's call the input basic set S.  We compute S' = preimage(S, U)
 447  * and drop the final dimensions including any constraints involving them.
 448  * This results in set S''.
 449  * Then we compute the affine hull A'' of S''.
 450  * Let F y_1 >= g be the constraint system of A''.  In the transformed
 451  * space the y_2 are unbounded, so we can add them back without any constraints,
 452  * resulting in
 453  *
 454  *                      [ y_1 ]
 455  *              [ F 0 ] [ y_2 ] >= g
 456  * or
 457  *                      [ Q_1 ]
 458  *              [ F 0 ] [ Q_2 ] x >= g
 459  * or
 460  *              F Q_1 x >= g
 461  *
 462  * The affine hull in the original space is then obtained as
 463  * A = preimage(A'', Q_1).
 464  */
 465 static struct isl_basic_set *affine_hull_with_cone(struct isl_basic_set *bset,
 466         struct isl_basic_set *cone)
 467 {
 468         unsigned total;
 469         unsigned cone_dim;
 470         struct isl_basic_set *hull;
 471         struct isl_mat *M, *U, *Q;
 472
 473         if (!bset || !cone)
 474                 goto error;
 475
 476         total = isl_basic_set_total_dim(cone);
 477         cone_dim = total - cone->n_eq;
 478
 479         M = isl_mat_sub_alloc(bset->ctx, cone->eq, 0, cone->n_eq, 1, total);
 480         M = isl_mat_left_hermite(M, 0, &U, &Q);
 481         if (!M)
 482                 goto error;
 483         isl_mat_free(M);
 484
 485         U = isl_mat_lin_to_aff(U);
 486         bset = isl_basic_set_preimage(bset, isl_mat_copy(U));
 487
 488         bset = drop_constraints_involving(bset, total - cone_dim, cone_dim);
 489         bset = isl_basic_set_drop_dims(bset, total - cone_dim, cone_dim);
 490
 491         Q = isl_mat_lin_to_aff(Q);
 492         Q = isl_mat_drop_rows(Q, 1 + total - cone_dim, cone_dim);
 493
 494         if (bset && bset->sample && bset->sample->size == 1 + total)
 495                 bset->sample = isl_mat_vec_product(isl_mat_copy(Q), bset->sample);
 496
 497         hull = uset_affine_hull_bounded(bset);
 498
 499         if (!hull)
 500                 isl_mat_free(U);
 501         else {
 502                 struct isl_vec *sample = isl_vec_copy(hull->sample);
 503                 U = isl_mat_drop_cols(U, 1 + total - cone_dim, cone_dim);
 504                 if (sample && sample->size > 0)
 505                         sample = isl_mat_vec_product(U, sample);
 506                 else
 507                         isl_mat_free(U);
 508                 hull = isl_basic_set_preimage(hull, Q);
 509                 isl_vec_free(hull->sample);
 510                 hull->sample = sample;
 511         }
 512
 513         isl_basic_set_free(cone);
 514
 515         return hull;
 516 error:
 517         isl_basic_set_free(bset);
 518         isl_basic_set_free(cone);
 519         return NULL;
 520 }
 521
 522 /* Look for all equalities satisfied by the integer points in bset,
 523  * which is assumed not to have any explicit equalities.
 524  *
 525  * The equalities are obtained by successively looking for
 526  * a point that is affinely independent of the points found so far.
 527  * In particular, for each equality satisfied by the points so far,
 528  * we check if there is any point on a hyperplane parallel to the
 529  * corresponding hyperplane shifted by at least one (in either direction).
 530  *
 531  * Before looking for any outside points, we first compute the recession
 532  * cone.  The directions of this recession cone will always be part
 533  * of the affine hull, so there is no need for looking for any points
 534  * in these directions.
 535  * In particular, if the recession cone is full-dimensional, then
 536  * the affine hull is simply the whole universe.
 537  */
 538 static struct isl_basic_set *uset_affine_hull(struct isl_basic_set *bset)
 539 {
 540         struct isl_basic_set *cone;
 541
 542         if (isl_basic_set_fast_is_empty(bset))
 543                 return bset;
 544
 545         cone = isl_basic_set_recession_cone(isl_basic_set_copy(bset));
 546         if (!cone)
 547                 goto error;
 548         if (cone->n_eq == 0) {
 549                 struct isl_basic_set *hull;
 550                 isl_basic_set_free(cone);
 551                 hull = isl_basic_set_universe_like(bset);
 552                 isl_basic_set_free(bset);
 553                 return hull;
 554         }
 555
 556         if (cone->n_eq < isl_basic_set_total_dim(cone))
 557                 return affine_hull_with_cone(bset, cone);
 558
 559         isl_basic_set_free(cone);
 560         return uset_affine_hull_bounded(bset);
 561 error:
 562         isl_basic_set_free(bset);
 563         return NULL;
 564 }
 565
 566 /* Look for all equalities satisfied by the integer points in bmap
 567  * that are independent of the equalities already explicitly available
 568  * in bmap.
 569  *
 570  * We first remove all equalities already explicitly available,
 571  * then look for additional equalities in the reduced space
 572  * and then transform the result to the original space.
 573  * The original equalities are _not_ added to this set.  This is
 574  * the responsibility of the calling function.
 575  * The resulting basic set has all meaning about the dimensions removed.
 576  * In particular, dimensions that correspond to existential variables
 577  * in bmap and that are found to be fixed are not removed.
 578  */
 579 static struct isl_basic_set *equalities_in_underlying_set(
 580                                                 struct isl_basic_map *bmap)
 581 {
 582         struct isl_mat *T1 = NULL;
 583         struct isl_mat *T2 = NULL;
 584         struct isl_basic_set *bset = NULL;
 585         struct isl_basic_set *hull = NULL;
 586
 587         bset = isl_basic_map_underlying_set(bmap);
 588         if (!bset)
 589                 return NULL;
 590         if (bset->n_eq)
 591                 bset = isl_basic_set_remove_equalities(bset, &T1, &T2);
 592         if (!bset)
 593                 goto error;
 594
 595         hull = uset_affine_hull(bset);
 596         if (!T2)
 597                 return hull;
 598
 599         if (!hull)
 600                 isl_mat_free(T1);
 601         else {
 602                 struct isl_vec *sample = isl_vec_copy(hull->sample);
 603                 if (sample && sample->size > 0)
 604                         sample = isl_mat_vec_product(T1, sample);
 605                 else
 606                         isl_mat_free(T1);
 607                 hull = isl_basic_set_preimage(hull, T2);
 608                 isl_vec_free(hull->sample);
 609                 hull->sample = sample;
 610         }
 611
 612         return hull;
 613 error:
 614         isl_mat_free(T2);
 615         isl_basic_set_free(bset);
 616         isl_basic_set_free(hull);
 617         return NULL;
 618 }
 619
 620 /* Detect and make explicit all equalities satisfied by the (integer)
 621  * points in bmap.
 622  */
 623 struct isl_basic_map *isl_basic_map_detect_equalities(
 624                                                 struct isl_basic_map *bmap)
 625 {
 626         int i, j;
 627         struct isl_basic_set *hull = NULL;
 628
 629         if (!bmap)
 630                 return NULL;
 631         if (bmap->n_ineq == 0)
 632                 return bmap;
 633         if (ISL_F_ISSET(bmap, ISL_BASIC_MAP_EMPTY))
 634                 return bmap;
 635         if (ISL_F_ISSET(bmap, ISL_BASIC_MAP_ALL_EQUALITIES))
 636                 return bmap;
 637         if (ISL_F_ISSET(bmap, ISL_BASIC_MAP_RATIONAL))
 638                 return isl_basic_map_implicit_equalities(bmap);
 639
 640         hull = equalities_in_underlying_set(isl_basic_map_copy(bmap));
 641         if (!hull)
 642                 goto error;
 643         if (ISL_F_ISSET(hull, ISL_BASIC_SET_EMPTY)) {
 644                 isl_basic_set_free(hull);
 645                 return isl_basic_map_set_to_empty(bmap);
 646         }
 647         bmap = isl_basic_map_extend_dim(bmap, isl_dim_copy(bmap->dim), 0,
 648                                         hull->n_eq, 0);
 649         for (i = 0; i < hull->n_eq; ++i) {
 650                 j = isl_basic_map_alloc_equality(bmap);
 651                 if (j < 0)
 652                         goto error;
 653                 isl_seq_cpy(bmap->eq[j], hull->eq[i],
 654                                 1 + isl_basic_set_total_dim(hull));
 655         }
 656         isl_vec_free(bmap->sample);
 657         bmap->sample = isl_vec_copy(hull->sample);
 658         isl_basic_set_free(hull);
 659         ISL_F_SET(bmap, ISL_BASIC_MAP_NO_IMPLICIT | ISL_BASIC_MAP_ALL_EQUALITIES);
 660         bmap = isl_basic_map_simplify(bmap);
 661         return isl_basic_map_finalize(bmap);
 662 error:
 663         isl_basic_set_free(hull);
 664         isl_basic_map_free(bmap);
 665         return NULL;
 666 }
 667
 668 __isl_give isl_basic_set *isl_basic_set_detect_equalities(
 669                                                 __isl_take isl_basic_set *bset)
 670 {
 671         return (isl_basic_set *)
 672                 isl_basic_map_detect_equalities((isl_basic_map *)bset);
 673 }
 674
 675 struct isl_map *isl_map_detect_equalities(struct isl_map *map)
 676 {
 677         struct isl_basic_map *bmap;
 678         int i;
 679
 680         if (!map)
 681                 return NULL;
 682
 683         for (i = 0; i < map->n; ++i) {
 684                 bmap = isl_basic_map_copy(map->p[i]);
 685                 bmap = isl_basic_map_detect_equalities(bmap);
 686                 if (!bmap)
 687                         goto error;
 688                 isl_basic_map_free(map->p[i]);
 689                 map->p[i] = bmap;
 690         }
 691
 692         return map;
 693 error:
 694         isl_map_free(map);
 695         return NULL;
 696 }
 697
 698 __isl_give isl_set *isl_set_detect_equalities(__isl_take isl_set *set)
 699 {
 700         return (isl_set *)isl_map_detect_equalities((isl_map *)set);
 701 }
 702
 703 /* After computing the rational affine hull (by detecting the implicit
 704  * equalities), we compute the additional equalities satisfied by
 705  * the integer points (if any) and add the original equalities back in.
 706  */
 707 struct isl_basic_map *isl_basic_map_affine_hull(struct isl_basic_map *bmap)
 708 {
 709         bmap = isl_basic_map_detect_equalities(bmap);
 710         bmap = isl_basic_map_cow(bmap);
 711         isl_basic_map_free_inequality(bmap, bmap->n_ineq);
 712         return bmap;
 713 }
 714
 715 struct isl_basic_set *isl_basic_set_affine_hull(struct isl_basic_set *bset)
 716 {
 717         return (struct isl_basic_set *)
 718                 isl_basic_map_affine_hull((struct isl_basic_map *)bset);
 719 }
 720
 721 struct isl_basic_map *isl_map_affine_hull(struct isl_map *map)
 722 {
 723         int i;
 724         struct isl_basic_map *model = NULL;
 725         struct isl_basic_map *hull = NULL;
 726         struct isl_set *set;
 727
 728         if (!map)
 729                 return NULL;
 730
 731         if (map->n == 0) {
 732                 hull = isl_basic_map_empty_like_map(map);
 733                 isl_map_free(map);
 734                 return hull;
 735         }
 736
 737         map = isl_map_detect_equalities(map);
 738         map = isl_map_align_divs(map);
 739         if (!map)
 740                 return NULL;
 741         model = isl_basic_map_copy(map->p[0]);
 742         set = isl_map_underlying_set(map);
 743         set = isl_set_cow(set);
 744         if (!set)
 745                 goto error;
 746
 747         for (i = 0; i < set->n; ++i) {
 748                 set->p[i] = isl_basic_set_cow(set->p[i]);
 749                 set->p[i] = isl_basic_set_affine_hull(set->p[i]);
 750                 set->p[i] = isl_basic_set_gauss(set->p[i], NULL);
 751                 if (!set->p[i])
 752                         goto error;
 753         }
 754         set = isl_set_remove_empty_parts(set);
 755         if (set->n == 0) {
 756                 hull = isl_basic_map_empty_like(model);
 757                 isl_basic_map_free(model);
 758         } else {
 759                 struct isl_basic_set *bset;
 760                 while (set->n > 1) {
 761                         set->p[0] = affine_hull(set->p[0], set->p[--set->n]);
 762                         if (!set->p[0])
 763                                 goto error;
 764                 }
 765                 bset = isl_basic_set_copy(set->p[0]);
 766                 hull = isl_basic_map_overlying_set(bset, model);
 767         }
 768         isl_set_free(set);
 769         hull = isl_basic_map_simplify(hull);
 770         return isl_basic_map_finalize(hull);
 771 error:
 772         isl_basic_map_free(model);
 773         isl_set_free(set);
 774         return NULL;
 775 }
 776
 777 struct isl_basic_set *isl_set_affine_hull(struct isl_set *set)
 778 {
 779         return (struct isl_basic_set *)
 780                 isl_map_affine_hull((struct isl_map *)set);
 781 }