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_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 static struct isl_basic_set *isl_basic_set_from_vec(struct isl_vec *vec)
 225 {
 226         int i;
 227         int k;
 228         struct isl_basic_set *bset = NULL;
 229         struct isl_ctx *ctx;
 230         unsigned dim;
 231
 232         if (!vec)
 233                 return NULL;
 234         ctx = vec->ctx;
 235         isl_assert(ctx, vec->size != 0, goto error);
 236
 237         bset = isl_basic_set_alloc(ctx, 0, vec->size - 1, 0, vec->size - 1, 0);
 238         if (!bset)
 239                 goto error;
 240         dim = isl_basic_set_n_dim(bset);
 241         for (i = dim - 1; i >= 0; --i) {
 242                 k = isl_basic_set_alloc_equality(bset);
 243                 if (k < 0)
 244                         goto error;
 245                 isl_seq_clr(bset->eq[k], 1 + dim);
 246                 isl_int_neg(bset->eq[k][0], vec->el[1 + i]);
 247                 isl_int_set(bset->eq[k][1 + i], vec->el[0]);
 248         }
 249         isl_vec_free(vec);
 250
 251         return bset;
 252 error:
 253         isl_basic_set_free(bset);
 254         isl_vec_free(vec);
 255         return NULL;
 256 }
 257
 258 /* Find an integer point in "bset" that lies outside of the equality
 259  * "eq" e(x) = 0.
 260  * If "up" is true, look for a point satisfying e(x) - 1 >= 0.
 261  * Otherwise, look for a point satisfying -e(x) - 1 >= 0 (i.e., e(x) <= -1).
 262  * The point, if found, is returned as a singleton set.
 263  * If no point can be found, the empty set is returned.
 264  *
 265  * Before solving an ILP problem, we first check if simply
 266  * adding the normal of the constraint to one of the known
 267  * integer points in the basic set yields another point
 268  * inside the basic set.
 269  *
 270  * The caller of this function ensures that "bset" is bounded.
 271  */
 272 static struct isl_basic_set *outside_point(struct isl_ctx *ctx,
 273         struct isl_basic_set *bset, isl_int *eq, int up)
 274 {
 275         struct isl_basic_set *slice = NULL;
 276         struct isl_vec *sample;
 277         struct isl_basic_set *point;
 278         unsigned dim;
 279         int k;
 280
 281         dim = isl_basic_set_n_dim(bset);
 282         sample = isl_vec_alloc(ctx, 1 + dim);
 283         if (!sample)
 284                 return NULL;
 285         isl_int_set_si(sample->block.data[0], 1);
 286         isl_seq_combine(sample->block.data + 1,
 287                 ctx->one, bset->sample->block.data + 1,
 288                 up ? ctx->one : ctx->negone, eq + 1, dim);
 289         if (isl_basic_set_contains(bset, sample))
 290                 return isl_basic_set_from_vec(sample);
 291         isl_vec_free(sample);
 292         sample = NULL;
 293
 294         slice = isl_basic_set_copy(bset);
 295         if (!slice)
 296                 goto error;
 297         slice = isl_basic_set_cow(slice);
 298         slice = isl_basic_set_extend(slice, 0, dim, 0, 0, 1);
 299         k = isl_basic_set_alloc_inequality(slice);
 300         if (k < 0)
 301                 goto error;
 302         if (up)
 303                 isl_seq_cpy(slice->ineq[k], eq, 1 + dim);
 304         else
 305                 isl_seq_neg(slice->ineq[k], eq, 1 + dim);
 306         isl_int_sub_ui(slice->ineq[k][0], slice->ineq[k][0], 1);
 307
 308         sample = isl_basic_set_sample_bounded(slice);
 309         if (!sample)
 310                 goto error;
 311         if (sample->size == 0) {
 312                 isl_vec_free(sample);
 313                 point = isl_basic_set_empty_like(bset);
 314         } else
 315                 point = isl_basic_set_from_vec(sample);
 316
 317         return point;
 318 error:
 319         isl_basic_set_free(slice);
 320         return NULL;
 321 }
 322
 323 struct isl_basic_set *isl_basic_set_recession_cone(struct isl_basic_set *bset)
 324 {
 325         int i;
 326
 327         bset = isl_basic_set_cow(bset);
 328         if (!bset)
 329                 return NULL;
 330         isl_assert(bset->ctx, bset->n_div == 0, goto error);
 331
 332         for (i = 0; i < bset->n_eq; ++i)
 333                 isl_int_set_si(bset->eq[i][0], 0);
 334
 335         for (i = 0; i < bset->n_ineq; ++i)
 336                 isl_int_set_si(bset->ineq[i][0], 0);
 337
 338         ISL_F_CLR(bset, ISL_BASIC_SET_NO_IMPLICIT);
 339         return isl_basic_set_implicit_equalities(bset);
 340 error:
 341         isl_basic_set_free(bset);
 342         return NULL;
 343 }
 344
 345 /* Extend an initial (under-)approximation of the affine hull of "bset"
 346  * by looking for points that do not satisfy one of the equalities
 347  * in the current approximation and adding them to that approximation
 348  * until no such points can be found any more.
 349  *
 350  * The caller of this function ensures that "bset" is bounded.
 351  */
 352 static struct isl_basic_set *extend_affine_hull(struct isl_basic_set *bset,
 353         struct isl_basic_set *hull)
 354 {
 355         int i, j, k;
 356         struct isl_ctx *ctx;
 357         unsigned dim;
 358
 359         ctx = bset->ctx;
 360         dim = isl_basic_set_n_dim(bset);
 361         for (i = 0; i < dim; ++i) {
 362                 struct isl_basic_set *point;
 363                 for (j = 0; j < hull->n_eq; ++j) {
 364                         point = outside_point(ctx, bset, hull->eq[j], 1);
 365                         if (!point)
 366                                 goto error;
 367                         if (!ISL_F_ISSET(point, ISL_BASIC_SET_EMPTY))
 368                                 break;
 369                         isl_basic_set_free(point);
 370                         point = outside_point(ctx, bset, hull->eq[j], 0);
 371                         if (!point)
 372                                 goto error;
 373                         if (!ISL_F_ISSET(point, ISL_BASIC_SET_EMPTY))
 374                                 break;
 375                         isl_basic_set_free(point);
 376
 377                         bset = isl_basic_set_extend_constraints(bset, 1, 0);
 378                         k = isl_basic_set_alloc_equality(bset);
 379                         if (k < 0)
 380                                 goto error;
 381                         isl_seq_cpy(bset->eq[k], hull->eq[j],
 382                                         1 + isl_basic_set_total_dim(hull));
 383                         bset = isl_basic_set_gauss(bset, NULL);
 384                         if (!bset)
 385                                 goto error;
 386                 }
 387                 if (j == hull->n_eq)
 388                         break;
 389                 hull = affine_hull(hull, point);
 390         }
 391         isl_basic_set_free(bset);
 392
 393         return hull;
 394 error:
 395         isl_basic_set_free(bset);
 396         isl_basic_set_free(hull);
 397         return NULL;
 398 }
 399
 400 /* Drop all constraints in bset that involve any of the dimensions
 401  * first to first+n-1.
 402  */
 403 static struct isl_basic_set *drop_constraints_involving
 404         (struct isl_basic_set *bset, unsigned first, unsigned n)
 405 {
 406         int i;
 407
 408         if (!bset)
 409                 return NULL;
 410
 411         bset = isl_basic_set_cow(bset);
 412
 413         for (i = bset->n_eq - 1; i >= 0; --i) {
 414                 if (isl_seq_first_non_zero(bset->eq[i] + 1 + first, n) == -1)
 415                         continue;
 416                 isl_basic_set_drop_equality(bset, i);
 417         }
 418
 419         for (i = bset->n_ineq - 1; i >= 0; --i) {
 420                 if (isl_seq_first_non_zero(bset->ineq[i] + 1 + first, n) == -1)
 421                         continue;
 422                 isl_basic_set_drop_inequality(bset, i);
 423         }
 424
 425         return bset;
 426 }
 427
 428 /* Compute the affine hull of "bset", where "hull" is an initial approximation
 429  * with only a single point of "bset" and "cone" is the recession cone
 430  * of "bset".
 431  *
 432  * We first compute a unimodular transformation that puts the unbounded
 433  * directions in the last dimensions.  In particular, we take a transformation
 434  * that maps all equalities to equalities (in HNF) on the first dimensions.
 435  * Let x be the original dimensions and y the transformed, with y_1 bounded
 436  * and y_2 unbounded.
 437  *
 438  *             [ y_1 ]                  [ y_1 ]   [ Q_1 ]
 439  *      x = U  [ y_2 ]                  [ y_2 ] = [ Q_2 ] x
 440  *
 441  * Let's call the input basic set S and the initial hull H.
 442  * We compute S' = preimage(S, U) and H' = preimage(H, U)
 443  * and drop the final dimensions including any constraints involving them.
 444  * This results in sets S'' and H''.
 445  * Then we extend H'' to the affine hull A'' of S''.
 446  * Let F y_1 >= g be the constraint system of A''.  In the transformed
 447  * space the y_2 are unbounded, so we can add them back without any constraints,
 448  * resulting in
 449  *
 450  *                      [ y_1 ]
 451  *              [ F 0 ] [ y_2 ] >= g
 452  * or
 453  *                      [ Q_1 ]
 454  *              [ F 0 ] [ Q_2 ] x >= g
 455  * or
 456  *              F Q_1 x >= g
 457  *
 458  * The affine hull in the original space is then obtained as
 459  * A = preimage(A'', Q_1).
 460  */
 461 static struct isl_basic_set *affine_hull_with_cone(struct isl_basic_set *bset,
 462         struct isl_basic_set *hull, struct isl_basic_set *cone)
 463 {
 464         unsigned total;
 465         unsigned cone_dim;
 466         struct isl_mat *M, *U, *Q;
 467
 468         if (!bset || !hull || !cone)
 469                 goto error;
 470
 471         total = isl_basic_set_total_dim(cone);
 472         cone_dim = total - cone->n_eq;
 473
 474         M = isl_mat_sub_alloc(bset->ctx, cone->eq, 0, cone->n_eq, 1, total);
 475         M = isl_mat_left_hermite(M, 0, &U, &Q);
 476         if (!M)
 477                 goto error;
 478         isl_mat_free(M);
 479
 480         U = isl_mat_lin_to_aff(U);
 481         bset = isl_basic_set_preimage(bset, isl_mat_copy(U));
 482         hull = isl_basic_set_preimage(hull, U);
 483
 484         bset = drop_constraints_involving(bset, total - cone_dim, cone_dim);
 485         bset = isl_basic_set_drop_dims(bset, total - cone_dim, cone_dim);
 486         hull = drop_constraints_involving(hull, total - cone_dim, cone_dim);
 487         hull = isl_basic_set_drop_dims(hull, total - cone_dim, cone_dim);
 488
 489         Q = isl_mat_lin_to_aff(Q);
 490         Q = isl_mat_drop_rows(Q, 1 + total - cone_dim, cone_dim);
 491
 492         if (bset && bset->sample)
 493                 bset->sample = isl_mat_vec_product(isl_mat_copy(Q), bset->sample);
 494
 495         hull = extend_affine_hull(bset, hull);
 496
 497         hull = isl_basic_set_preimage(hull, Q);
 498
 499         isl_basic_set_free(cone);
 500
 501         return hull;
 502 error:
 503         isl_basic_set_free(bset);
 504         isl_basic_set_free(hull);
 505         isl_basic_set_free(cone);
 506         return NULL;
 507 }
 508
 509 /* Look for all equalities satisfied by the integer points in bset,
 510  * which is assumed not to have any explicit equalities.
 511  *
 512  * The equalities are obtained by successively looking for
 513  * a point that is affinely independent of the points found so far.
 514  * In particular, for each equality satisfied by the points so far,
 515  * we check if there is any point on a hyperplane parallel to the
 516  * corresponding hyperplane shifted by at least one (in either direction).
 517  *
 518  * Before looking for any outside points, we first compute the recession
 519  * cone.  The directions of this recession cone will always be part
 520  * of the affine hull, so there is no need for looking for any points
 521  * in these directions.
 522  * In particular, if the recession cone is full-dimensional, then
 523  * the affine hull is simply the whole universe.
 524  */
 525 static struct isl_basic_set *uset_affine_hull(struct isl_basic_set *bset)
 526 {
 527         struct isl_basic_set *hull = NULL;
 528         struct isl_vec *sample = NULL;
 529         struct isl_basic_set *cone;
 530
 531         if (isl_basic_set_is_empty(bset))
 532                 return bset;
 533
 534         sample = isl_basic_set_sample(isl_basic_set_copy(bset));
 535         if (!sample)
 536                 goto error;
 537         if (sample->size == 0) {
 538                 isl_vec_free(sample);
 539                 hull = isl_basic_set_empty_like(bset);
 540                 isl_basic_set_free(bset);
 541                 return hull;
 542         }
 543         if (sample->size == 1) {
 544                 isl_vec_free(sample);
 545                 return bset;
 546         }
 547
 548         cone = isl_basic_set_recession_cone(isl_basic_set_copy(bset));
 549         if (!cone)
 550                 goto error;
 551         if (cone->n_eq == 0) {
 552                 isl_basic_set_free(cone);
 553                 isl_vec_free(sample);
 554                 hull = isl_basic_set_universe_like(bset);
 555                 isl_basic_set_free(bset);
 556                 return hull;
 557         }
 558
 559         hull = isl_basic_set_from_vec(sample);
 560         if (cone->n_eq < isl_basic_set_total_dim(cone))
 561                 return affine_hull_with_cone(bset, hull, cone);
 562
 563         isl_basic_set_free(cone);
 564         return extend_affine_hull(bset, hull);
 565 error:
 566         isl_vec_free(sample);
 567         isl_basic_set_free(bset);
 568         isl_basic_set_free(hull);
 569         return NULL;
 570 }
 571
 572 /* Look for all equalities satisfied by the integer points in bmap
 573  * that are independent of the equalities already explicitly available
 574  * in bmap.
 575  *
 576  * We first remove all equalities already explicitly available,
 577  * then look for additional equalities in the reduced space
 578  * and then transform the result to the original space.
 579  * The original equalities are _not_ added to this set.  This is
 580  * the responsibility of the calling function.
 581  * The resulting basic set has all meaning about the dimensions removed.
 582  * In particular, dimensions that correspond to existential variables
 583  * in bmap and that are found to be fixed are not removed.
 584  */
 585 static struct isl_basic_set *equalities_in_underlying_set(
 586                                                 struct isl_basic_map *bmap)
 587 {
 588         struct isl_mat *T2 = NULL;
 589         struct isl_basic_set *bset = NULL;
 590         struct isl_basic_set *hull = NULL;
 591
 592         bset = isl_basic_map_underlying_set(bmap);
 593         bset = isl_basic_set_remove_equalities(bset, NULL, &T2);
 594         if (!bset)
 595                 goto error;
 596
 597         hull = uset_affine_hull(bset);
 598         if (T2)
 599                 hull = isl_basic_set_preimage(hull, T2);
 600
 601         return hull;
 602 error:
 603         isl_mat_free(T2);
 604         isl_basic_set_free(bset);
 605         isl_basic_set_free(hull);
 606         return NULL;
 607 }
 608
 609 /* Detect and make explicit all equalities satisfied by the (integer)
 610  * points in bmap.
 611  */
 612 struct isl_basic_map *isl_basic_map_detect_equalities(
 613                                                 struct isl_basic_map *bmap)
 614 {
 615         int i, j;
 616         struct isl_basic_set *hull = NULL;
 617
 618         if (!bmap)
 619                 return NULL;
 620         if (bmap->n_ineq == 0)
 621                 return bmap;
 622         if (ISL_F_ISSET(bmap, ISL_BASIC_MAP_EMPTY))
 623                 return bmap;
 624         if (ISL_F_ISSET(bmap, ISL_BASIC_MAP_ALL_EQUALITIES))
 625                 return bmap;
 626         if (ISL_F_ISSET(bmap, ISL_BASIC_MAP_RATIONAL))
 627                 return isl_basic_map_implicit_equalities(bmap);
 628
 629         hull = equalities_in_underlying_set(isl_basic_map_copy(bmap));
 630         if (!hull)
 631                 goto error;
 632         if (ISL_F_ISSET(hull, ISL_BASIC_SET_EMPTY)) {
 633                 isl_basic_set_free(hull);
 634                 return isl_basic_map_set_to_empty(bmap);
 635         }
 636         bmap = isl_basic_map_extend_dim(bmap, isl_dim_copy(bmap->dim), 0,
 637                                         hull->n_eq, 0);
 638         for (i = 0; i < hull->n_eq; ++i) {
 639                 j = isl_basic_map_alloc_equality(bmap);
 640                 if (j < 0)
 641                         goto error;
 642                 isl_seq_cpy(bmap->eq[j], hull->eq[i],
 643                                 1 + isl_basic_set_total_dim(hull));
 644         }
 645         isl_basic_set_free(hull);
 646         ISL_F_SET(bmap, ISL_BASIC_MAP_NO_IMPLICIT | ISL_BASIC_MAP_ALL_EQUALITIES);
 647         bmap = isl_basic_map_simplify(bmap);
 648         return isl_basic_map_finalize(bmap);
 649 error:
 650         isl_basic_set_free(hull);
 651         isl_basic_map_free(bmap);
 652         return NULL;
 653 }
 654
 655 struct isl_map *isl_map_detect_equalities(struct isl_map *map)
 656 {
 657         struct isl_basic_map *bmap;
 658         int i;
 659
 660         if (!map)
 661                 return NULL;
 662
 663         for (i = 0; i < map->n; ++i) {
 664                 bmap = isl_basic_map_copy(map->p[i]);
 665                 bmap = isl_basic_map_detect_equalities(bmap);
 666                 if (!bmap)
 667                         goto error;
 668                 isl_basic_map_free(map->p[i]);
 669                 map->p[i] = bmap;
 670         }
 671
 672         return map;
 673 error:
 674         isl_map_free(map);
 675         return NULL;
 676 }
 677
 678 /* After computing the rational affine hull (by detecting the implicit
 679  * equalities), we compute the additional equalities satisfied by
 680  * the integer points (if any) and add the original equalities back in.
 681  */
 682 struct isl_basic_map *isl_basic_map_affine_hull(struct isl_basic_map *bmap)
 683 {
 684         struct isl_basic_set *hull = NULL;
 685
 686         bmap = isl_basic_map_detect_equalities(bmap);
 687         bmap = isl_basic_map_cow(bmap);
 688         isl_basic_map_free_inequality(bmap, bmap->n_ineq);
 689         return bmap;
 690 }
 691
 692 struct isl_basic_set *isl_basic_set_affine_hull(struct isl_basic_set *bset)
 693 {
 694         return (struct isl_basic_set *)
 695                 isl_basic_map_affine_hull((struct isl_basic_map *)bset);
 696 }
 697
 698 struct isl_basic_map *isl_map_affine_hull(struct isl_map *map)
 699 {
 700         int i;
 701         struct isl_basic_map *model = NULL;
 702         struct isl_basic_map *hull = NULL;
 703         struct isl_set *set;
 704
 705         if (!map)
 706                 return NULL;
 707
 708         if (map->n == 0) {
 709                 hull = isl_basic_map_empty_like_map(map);
 710                 isl_map_free(map);
 711                 return hull;
 712         }
 713
 714         map = isl_map_detect_equalities(map);
 715         map = isl_map_align_divs(map);
 716         if (!map)
 717                 return NULL;
 718         model = isl_basic_map_copy(map->p[0]);
 719         set = isl_map_underlying_set(map);
 720         set = isl_set_cow(set);
 721         if (!set)
 722                 goto error;
 723
 724         for (i = 0; i < set->n; ++i) {
 725                 set->p[i] = isl_basic_set_cow(set->p[i]);
 726                 set->p[i] = isl_basic_set_affine_hull(set->p[i]);
 727                 set->p[i] = isl_basic_set_gauss(set->p[i], NULL);
 728                 if (!set->p[i])
 729                         goto error;
 730         }
 731         set = isl_set_remove_empty_parts(set);
 732         if (set->n == 0) {
 733                 hull = isl_basic_map_empty_like(model);
 734                 isl_basic_map_free(model);
 735         } else {
 736                 struct isl_basic_set *bset;
 737                 while (set->n > 1) {
 738                         set->p[0] = affine_hull(set->p[0], set->p[--set->n]);
 739                         if (!set->p[0])
 740                                 goto error;
 741                 }
 742                 bset = isl_basic_set_copy(set->p[0]);
 743                 hull = isl_basic_map_overlying_set(bset, model);
 744         }
 745         isl_set_free(set);
 746         hull = isl_basic_map_simplify(hull);
 747         return isl_basic_map_finalize(hull);
 748 error:
 749         isl_basic_map_free(model);
 750         isl_set_free(set);
 751         return NULL;
 752 }
 753
 754 struct isl_basic_set *isl_set_affine_hull(struct isl_set *set)
 755 {
 756         return (struct isl_basic_set *)
 757                 isl_map_affine_hull((struct isl_map *)set);
 758 }