isl_map_simplify.c

   1 #include "isl_equalities.h"
   2 #include "isl_map.h"
   3 #include "isl_map_private.h"
   4 #include "isl_tab.h"
   5
   6 static void swap_equality(struct isl_basic_map *bmap, int a, int b)
   7 {
   8         isl_int *t = bmap->eq[a];
   9         bmap->eq[a] = bmap->eq[b];
  10         bmap->eq[b] = t;
  11 }
  12
  13 static void swap_inequality(struct isl_basic_map *bmap, int a, int b)
  14 {
  15         if (a != b) {
  16                 isl_int *t = bmap->ineq[a];
  17                 bmap->ineq[a] = bmap->ineq[b];
  18                 bmap->ineq[b] = t;
  19         }
  20 }
  21
  22 static void set_swap_inequality(struct isl_basic_set *bset, int a, int b)
  23 {
  24         swap_inequality((struct isl_basic_map *)bset, a, b);
  25 }
  26
  27 static void constraint_drop_vars(isl_int *c, unsigned n, unsigned rem)
  28 {
  29         isl_seq_cpy(c, c + n, rem);
  30         isl_seq_clr(c + rem, n);
  31 }
  32
  33 /* Drop n dimensions starting at first.
  34  *
  35  * In principle, this frees up some extra variables as the number
  36  * of columns remains constant, but we would have to extend
  37  * the div array too as the number of rows in this array is assumed
  38  * to be equal to extra.
  39  */
  40 struct isl_basic_set *isl_basic_set_drop_dims(
  41                 struct isl_basic_set *bset, unsigned first, unsigned n)
  42 {
  43         int i;
  44
  45         if (!bset)
  46                 goto error;
  47
  48         isl_assert(bset->ctx, first + n <= bset->dim->n_out, goto error);
  49
  50         if (n == 0)
  51                 return bset;
  52
  53         bset = isl_basic_set_cow(bset);
  54         if (!bset)
  55                 return NULL;
  56
  57         for (i = 0; i < bset->n_eq; ++i)
  58                 constraint_drop_vars(bset->eq[i]+1+bset->dim->nparam+first, n,
  59                                      (bset->dim->n_out-first-n)+bset->extra);
  60
  61         for (i = 0; i < bset->n_ineq; ++i)
  62                 constraint_drop_vars(bset->ineq[i]+1+bset->dim->nparam+first, n,
  63                                      (bset->dim->n_out-first-n)+bset->extra);
  64
  65         for (i = 0; i < bset->n_div; ++i)
  66                 constraint_drop_vars(bset->div[i]+1+1+bset->dim->nparam+first, n,
  67                                      (bset->dim->n_out-first-n)+bset->extra);
  68
  69         bset->dim = isl_dim_drop_outputs(bset->dim, first, n);
  70         if (!bset->dim)
  71                 goto error;
  72
  73         ISL_F_CLR(bset, ISL_BASIC_SET_NORMALIZED);
  74         bset = isl_basic_set_simplify(bset);
  75         return isl_basic_set_finalize(bset);
  76 error:
  77         isl_basic_set_free(bset);
  78         return NULL;
  79 }
  80
  81 struct isl_set *isl_set_drop_dims(
  82                 struct isl_set *set, unsigned first, unsigned n)
  83 {
  84         int i;
  85
  86         if (!set)
  87                 goto error;
  88
  89         isl_assert(set->ctx, first + n <= set->dim->n_out, goto error);
  90
  91         if (n == 0)
  92                 return set;
  93         set = isl_set_cow(set);
  94         if (!set)
  95                 goto error;
  96         set->dim = isl_dim_drop_outputs(set->dim, first, n);
  97         if (!set->dim)
  98                 goto error;
  99
 100         for (i = 0; i < set->n; ++i) {
 101                 set->p[i] = isl_basic_set_drop_dims(set->p[i], first, n);
 102                 if (!set->p[i])
 103                         goto error;
 104         }
 105
 106         ISL_F_CLR(set, ISL_SET_NORMALIZED);
 107         return set;
 108 error:
 109         isl_set_free(set);
 110         return NULL;
 111 }
 112
 113 /* Move "n" divs starting at "first" to the end of the list of divs.
 114  */
 115 static struct isl_basic_map *move_divs_last(struct isl_basic_map *bmap,
 116         unsigned first, unsigned n)
 117 {
 118         isl_int **div;
 119         int i;
 120
 121         if (first + n == bmap->n_div)
 122                 return bmap;
 123
 124         div = isl_alloc_array(bmap->ctx, isl_int *, n);
 125         if (!div)
 126                 goto error;
 127         for (i = 0; i < n; ++i)
 128                 div[i] = bmap->div[first + i];
 129         for (i = 0; i < bmap->n_div - first - n; ++i)
 130                 bmap->div[first + i] = bmap->div[first + n + i];
 131         for (i = 0; i < n; ++i)
 132                 bmap->div[bmap->n_div - n + i] = div[i];
 133         free(div);
 134         return bmap;
 135 error:
 136         isl_basic_map_free(bmap);
 137         return NULL;
 138 }
 139
 140 /* Drop "n" dimensions of type "type" starting at "first".
 141  *
 142  * In principle, this frees up some extra variables as the number
 143  * of columns remains constant, but we would have to extend
 144  * the div array too as the number of rows in this array is assumed
 145  * to be equal to extra.
 146  */
 147 struct isl_basic_map *isl_basic_map_drop(struct isl_basic_map *bmap,
 148         enum isl_dim_type type, unsigned first, unsigned n)
 149 {
 150         int i;
 151         unsigned dim;
 152         unsigned offset;
 153         unsigned left;
 154
 155         if (!bmap)
 156                 goto error;
 157
 158         dim = isl_basic_map_dim(bmap, type);
 159         isl_assert(bmap->ctx, first + n <= dim, goto error);
 160
 161         if (n == 0)
 162                 return bmap;
 163
 164         bmap = isl_basic_map_cow(bmap);
 165         if (!bmap)
 166                 return NULL;
 167
 168         offset = isl_basic_map_offset(bmap, type) + first;
 169         left = isl_basic_map_total_dim(bmap) - (offset - 1) - n;
 170         for (i = 0; i < bmap->n_eq; ++i)
 171                 constraint_drop_vars(bmap->eq[i]+offset, n, left);
 172
 173         for (i = 0; i < bmap->n_ineq; ++i)
 174                 constraint_drop_vars(bmap->ineq[i]+offset, n, left);
 175
 176         for (i = 0; i < bmap->n_div; ++i)
 177                 constraint_drop_vars(bmap->div[i]+1+offset, n, left);
 178
 179         if (type == isl_dim_div) {
 180                 bmap = move_divs_last(bmap, first, n);
 181                 if (!bmap)
 182                         goto error;
 183                 isl_basic_map_free_div(bmap, n);
 184         } else
 185                 bmap->dim = isl_dim_drop(bmap->dim, type, first, n);
 186         if (!bmap->dim)
 187                 goto error;
 188
 189         ISL_F_CLR(bmap, ISL_BASIC_MAP_NORMALIZED);
 190         bmap = isl_basic_map_simplify(bmap);
 191         return isl_basic_map_finalize(bmap);
 192 error:
 193         isl_basic_map_free(bmap);
 194         return NULL;
 195 }
 196
 197 struct isl_basic_map *isl_basic_map_drop_inputs(
 198                 struct isl_basic_map *bmap, unsigned first, unsigned n)
 199 {
 200         return isl_basic_map_drop(bmap, isl_dim_in, first, n);
 201 }
 202
 203 struct isl_map *isl_map_drop(struct isl_map *map,
 204         enum isl_dim_type type, unsigned first, unsigned n)
 205 {
 206         int i;
 207
 208         if (!map)
 209                 goto error;
 210
 211         isl_assert(map->ctx, first + n <= isl_map_dim(map, type), goto error);
 212
 213         if (n == 0)
 214                 return map;
 215         map = isl_map_cow(map);
 216         if (!map)
 217                 goto error;
 218         map->dim = isl_dim_drop(map->dim, type, first, n);
 219         if (!map->dim)
 220                 goto error;
 221
 222         for (i = 0; i < map->n; ++i) {
 223                 map->p[i] = isl_basic_map_drop(map->p[i], type, first, n);
 224                 if (!map->p[i])
 225                         goto error;
 226         }
 227         ISL_F_CLR(map, ISL_MAP_NORMALIZED);
 228
 229         return map;
 230 error:
 231         isl_map_free(map);
 232         return NULL;
 233 }
 234
 235 struct isl_map *isl_map_drop_inputs(
 236                 struct isl_map *map, unsigned first, unsigned n)
 237 {
 238         return isl_map_drop(map, isl_dim_in, first, n);
 239 }
 240
 241 /*
 242  * We don't cow, as the div is assumed to be redundant.
 243  */
 244 static struct isl_basic_map *isl_basic_map_drop_div(
 245                 struct isl_basic_map *bmap, unsigned div)
 246 {
 247         int i;
 248         unsigned pos;
 249
 250         if (!bmap)
 251                 goto error;
 252
 253         pos = 1 + isl_dim_total(bmap->dim) + div;
 254
 255         isl_assert(bmap->ctx, div < bmap->n_div, goto error);
 256
 257         for (i = 0; i < bmap->n_eq; ++i)
 258                 constraint_drop_vars(bmap->eq[i]+pos, 1, bmap->extra-div-1);
 259
 260         for (i = 0; i < bmap->n_ineq; ++i) {
 261                 if (!isl_int_is_zero(bmap->ineq[i][pos])) {
 262                         isl_basic_map_drop_inequality(bmap, i);
 263                         --i;
 264                         continue;
 265                 }
 266                 constraint_drop_vars(bmap->ineq[i]+pos, 1, bmap->extra-div-1);
 267         }
 268
 269         for (i = 0; i < bmap->n_div; ++i)
 270                 constraint_drop_vars(bmap->div[i]+1+pos, 1, bmap->extra-div-1);
 271
 272         if (div != bmap->n_div - 1) {
 273                 int j;
 274                 isl_int *t = bmap->div[div];
 275
 276                 for (j = div; j < bmap->n_div - 1; ++j)
 277                         bmap->div[j] = bmap->div[j+1];
 278
 279                 bmap->div[bmap->n_div - 1] = t;
 280         }
 281         ISL_F_CLR(bmap, ISL_BASIC_MAP_NORMALIZED);
 282         isl_basic_map_free_div(bmap, 1);
 283
 284         return bmap;
 285 error:
 286         isl_basic_map_free(bmap);
 287         return NULL;
 288 }
 289
 290 struct isl_basic_map *isl_basic_map_normalize_constraints(
 291         struct isl_basic_map *bmap)
 292 {
 293         int i;
 294         isl_int gcd;
 295         unsigned total = isl_basic_map_total_dim(bmap);
 296
 297         isl_int_init(gcd);
 298         for (i = bmap->n_eq - 1; i >= 0; --i) {
 299                 isl_seq_gcd(bmap->eq[i]+1, total, &gcd);
 300                 if (isl_int_is_zero(gcd)) {
 301                         if (!isl_int_is_zero(bmap->eq[i][0])) {
 302                                 bmap = isl_basic_map_set_to_empty(bmap);
 303                                 break;
 304                         }
 305                         isl_basic_map_drop_equality(bmap, i);
 306                         continue;
 307                 }
 308                 if (ISL_F_ISSET(bmap, ISL_BASIC_MAP_RATIONAL))
 309                         isl_int_gcd(gcd, gcd, bmap->eq[i][0]);
 310                 if (isl_int_is_one(gcd))
 311                         continue;
 312                 if (!isl_int_is_divisible_by(bmap->eq[i][0], gcd)) {
 313                         bmap = isl_basic_map_set_to_empty(bmap);
 314                         break;
 315                 }
 316                 isl_seq_scale_down(bmap->eq[i], bmap->eq[i], gcd, 1+total);
 317         }
 318
 319         for (i = bmap->n_ineq - 1; i >= 0; --i) {
 320                 isl_seq_gcd(bmap->ineq[i]+1, total, &gcd);
 321                 if (isl_int_is_zero(gcd)) {
 322                         if (isl_int_is_neg(bmap->ineq[i][0])) {
 323                                 bmap = isl_basic_map_set_to_empty(bmap);
 324                                 break;
 325                         }
 326                         isl_basic_map_drop_inequality(bmap, i);
 327                         continue;
 328                 }
 329                 if (ISL_F_ISSET(bmap, ISL_BASIC_MAP_RATIONAL))
 330                         isl_int_gcd(gcd, gcd, bmap->ineq[i][0]);
 331                 if (isl_int_is_one(gcd))
 332                         continue;
 333                 isl_int_fdiv_q(bmap->ineq[i][0], bmap->ineq[i][0], gcd);
 334                 isl_seq_scale_down(bmap->ineq[i]+1, bmap->ineq[i]+1, gcd, total);
 335         }
 336         isl_int_clear(gcd);
 337
 338         return bmap;
 339 }
 340
 341 struct isl_basic_set *isl_basic_set_normalize_constraints(
 342         struct isl_basic_set *bset)
 343 {
 344         (struct isl_basic_set *)isl_basic_map_normalize_constraints(
 345                 (struct isl_basic_map *)bset);
 346 }
 347
 348 static void eliminate_div(struct isl_basic_map *bmap, isl_int *eq, unsigned div)
 349 {
 350         int i;
 351         unsigned pos = 1 + isl_dim_total(bmap->dim) + div;
 352         unsigned len;
 353         len = 1 + isl_basic_map_total_dim(bmap);
 354
 355         for (i = 0; i < bmap->n_eq; ++i)
 356                 if (bmap->eq[i] != eq)
 357                         isl_seq_elim(bmap->eq[i], eq, pos, len, NULL);
 358
 359         for (i = 0; i < bmap->n_ineq; ++i)
 360                 isl_seq_elim(bmap->ineq[i], eq, pos, len, NULL);
 361
 362         /* We need to be careful about circular definitions,
 363          * so for now we just remove the definitions of other divs that
 364          * depend on this div and (possibly) recompute them later.
 365          */
 366         for (i = 0; i < bmap->n_div; ++i)
 367                 if (!isl_int_is_zero(bmap->div[i][0]) &&
 368                     !isl_int_is_zero(bmap->div[i][1 + pos]))
 369                         isl_seq_clr(bmap->div[i], 1 + len);
 370
 371         isl_basic_map_drop_div(bmap, div);
 372 }
 373
 374 /* Elimininate divs based on equalities
 375  */
 376 static struct isl_basic_map *eliminate_divs_eq(
 377                 struct isl_basic_map *bmap, int *progress)
 378 {
 379         int d;
 380         int i;
 381         int modified = 0;
 382         unsigned off;
 383
 384         if (!bmap)
 385                 return NULL;
 386
 387         off = 1 + isl_dim_total(bmap->dim);
 388
 389         for (d = bmap->n_div - 1; d >= 0 ; --d) {
 390                 for (i = 0; i < bmap->n_eq; ++i) {
 391                         if (!isl_int_is_one(bmap->eq[i][off + d]) &&
 392                             !isl_int_is_negone(bmap->eq[i][off + d]))
 393                                 continue;
 394                         modified = 1;
 395                         *progress = 1;
 396                         eliminate_div(bmap, bmap->eq[i], d);
 397                         isl_basic_map_drop_equality(bmap, i);
 398                         break;
 399                 }
 400         }
 401         if (modified)
 402                 return eliminate_divs_eq(bmap, progress);
 403         return bmap;
 404 }
 405
 406 /* Elimininate divs based on inequalities
 407  */
 408 static struct isl_basic_map *eliminate_divs_ineq(
 409                 struct isl_basic_map *bmap, int *progress)
 410 {
 411         int d;
 412         int i;
 413         unsigned off;
 414         struct isl_ctx *ctx;
 415
 416         if (!bmap)
 417                 return NULL;
 418
 419         ctx = bmap->ctx;
 420         off = 1 + isl_dim_total(bmap->dim);
 421
 422         for (d = bmap->n_div - 1; d >= 0 ; --d) {
 423                 for (i = 0; i < bmap->n_eq; ++i)
 424                         if (!isl_int_is_zero(bmap->eq[i][off + d]))
 425                                 break;
 426                 if (i < bmap->n_eq)
 427                         continue;
 428                 for (i = 0; i < bmap->n_ineq; ++i)
 429                         if (isl_int_abs_gt(bmap->ineq[i][off + d], ctx->one))
 430                                 break;
 431                 if (i < bmap->n_ineq)
 432                         continue;
 433                 *progress = 1;
 434                 bmap = isl_basic_map_eliminate_vars(bmap, (off-1)+d, 1);
 435                 if (ISL_F_ISSET(bmap, ISL_BASIC_MAP_EMPTY))
 436                         break;
 437                 bmap = isl_basic_map_drop_div(bmap, d);
 438                 if (!bmap)
 439                         break;
 440         }
 441         return bmap;
 442 }
 443
 444 static void eliminate_var_using_equality(struct isl_basic_map *bmap,
 445         unsigned pos, isl_int *eq, int *progress)
 446 {
 447         unsigned total;
 448         int k;
 449         int contains_divs;
 450
 451         total = isl_basic_map_total_dim(bmap);
 452         contains_divs =
 453                 isl_seq_first_non_zero(eq + 1 + isl_dim_total(bmap->dim),
 454                                                 bmap->n_div) != -1;
 455         for (k = 0; k < bmap->n_eq; ++k) {
 456                 if (bmap->eq[k] == eq)
 457                         continue;
 458                 if (isl_int_is_zero(bmap->eq[k][1+pos]))
 459                         continue;
 460                 if (progress)
 461                         *progress = 1;
 462                 isl_seq_elim(bmap->eq[k], eq, 1+pos, 1+total, NULL);
 463         }
 464
 465         for (k = 0; k < bmap->n_ineq; ++k) {
 466                 if (isl_int_is_zero(bmap->ineq[k][1+pos]))
 467                         continue;
 468                 if (progress)
 469                         *progress = 1;
 470                 isl_seq_elim(bmap->ineq[k], eq, 1+pos, 1+total, NULL);
 471                 ISL_F_CLR(bmap, ISL_BASIC_MAP_NORMALIZED);
 472         }
 473
 474         for (k = 0; k < bmap->n_div; ++k) {
 475                 if (isl_int_is_zero(bmap->div[k][0]))
 476                         continue;
 477                 if (isl_int_is_zero(bmap->div[k][1+1+pos]))
 478                         continue;
 479                 if (progress)
 480                         *progress = 1;
 481                 /* We need to be careful about circular definitions,
 482                  * so for now we just remove the definition of div k
 483                  * if the equality contains any divs.
 484                  */
 485                 if (contains_divs)
 486                         isl_seq_clr(bmap->div[k], 1 + total);
 487                 else
 488                         isl_seq_elim(bmap->div[k]+1, eq,
 489                                         1+pos, 1+total, &bmap->div[k][0]);
 490                 ISL_F_CLR(bmap, ISL_BASIC_MAP_NORMALIZED);
 491         }
 492 }
 493
 494 struct isl_basic_map *isl_basic_map_gauss(
 495         struct isl_basic_map *bmap, int *progress)
 496 {
 497         int k;
 498         int done;
 499         int last_var;
 500         unsigned total_var;
 501         unsigned total;
 502
 503         if (!bmap)
 504                 return NULL;
 505
 506         total = isl_basic_map_total_dim(bmap);
 507         total_var = total - bmap->n_div;
 508
 509         last_var = total - 1;
 510         for (done = 0; done < bmap->n_eq; ++done) {
 511                 for (; last_var >= 0; --last_var) {
 512                         for (k = done; k < bmap->n_eq; ++k)
 513                                 if (!isl_int_is_zero(bmap->eq[k][1+last_var]))
 514                                         break;
 515                         if (k < bmap->n_eq)
 516                                 break;
 517                 }
 518                 if (last_var < 0)
 519                         break;
 520                 if (k != done)
 521                         swap_equality(bmap, k, done);
 522                 if (isl_int_is_neg(bmap->eq[done][1+last_var]))
 523                         isl_seq_neg(bmap->eq[done], bmap->eq[done], 1+total);
 524
 525                 eliminate_var_using_equality(bmap, last_var, bmap->eq[done],
 526                                                 progress);
 527
 528                 if (last_var >= total_var &&
 529                     isl_int_is_zero(bmap->div[last_var - total_var][0])) {
 530                         unsigned div = last_var - total_var;
 531                         isl_seq_neg(bmap->div[div]+1, bmap->eq[done], 1+total);
 532                         isl_int_set_si(bmap->div[div][1+1+last_var], 0);
 533                         isl_int_set(bmap->div[div][0],
 534                                     bmap->eq[done][1+last_var]);
 535                         ISL_F_CLR(bmap, ISL_BASIC_MAP_NORMALIZED);
 536                 }
 537         }
 538         if (done == bmap->n_eq)
 539                 return bmap;
 540         for (k = done; k < bmap->n_eq; ++k) {
 541                 if (isl_int_is_zero(bmap->eq[k][0]))
 542                         continue;
 543                 return isl_basic_map_set_to_empty(bmap);
 544         }
 545         isl_basic_map_free_equality(bmap, bmap->n_eq-done);
 546         return bmap;
 547 }
 548
 549 struct isl_basic_set *isl_basic_set_gauss(
 550         struct isl_basic_set *bset, int *progress)
 551 {
 552         return (struct isl_basic_set*)isl_basic_map_gauss(
 553                         (struct isl_basic_map *)bset, progress);
 554 }
 555
 556
 557 static unsigned int round_up(unsigned int v)
 558 {
 559         int old_v = v;
 560
 561         while (v) {
 562                 old_v = v;
 563                 v ^= v & -v;
 564         }
 565         return old_v << 1;
 566 }
 567
 568 static int hash_index(isl_int ***index, unsigned int size, int bits,
 569                         struct isl_basic_map *bmap, int k)
 570 {
 571         int h;
 572         unsigned total = isl_basic_map_total_dim(bmap);
 573         uint32_t hash = isl_seq_get_hash_bits(bmap->ineq[k]+1, total, bits);
 574         for (h = hash; index[h]; h = (h+1) % size)
 575                 if (&bmap->ineq[k] != index[h] &&
 576                     isl_seq_eq(bmap->ineq[k]+1, index[h][0]+1, total))
 577                         break;
 578         return h;
 579 }
 580
 581 static int set_hash_index(isl_int ***index, unsigned int size, int bits,
 582                           struct isl_basic_set *bset, int k)
 583 {
 584         return hash_index(index, size, bits, (struct isl_basic_map *)bset, k);
 585 }
 586
 587 /* If we can eliminate more than one div, then we need to make
 588  * sure we do it from last div to first div, in order not to
 589  * change the position of the other divs that still need to
 590  * be removed.
 591  */
 592 static struct isl_basic_map *remove_duplicate_divs(
 593         struct isl_basic_map *bmap, int *progress)
 594 {
 595         unsigned int size;
 596         int *index;
 597         int *elim_for;
 598         int k, l, h;
 599         int bits;
 600         struct isl_blk eq;
 601         unsigned total_var = isl_dim_total(bmap->dim);
 602         unsigned total = total_var + bmap->n_div;
 603         struct isl_ctx *ctx;
 604
 605         if (bmap->n_div <= 1)
 606                 return bmap;
 607
 608         ctx = bmap->ctx;
 609         for (k = bmap->n_div - 1; k >= 0; --k)
 610                 if (!isl_int_is_zero(bmap->div[k][0]))
 611                         break;
 612         if (k <= 0)
 613                 return bmap;
 614
 615         elim_for = isl_calloc_array(ctx, int, bmap->n_div);
 616         size = round_up(4 * bmap->n_div / 3 - 1);
 617         bits = ffs(size) - 1;
 618         index = isl_calloc_array(ctx, int, size);
 619         if (!index)
 620                 return bmap;
 621         eq = isl_blk_alloc(ctx, 1+total);
 622         if (isl_blk_is_error(eq))
 623                 goto out;
 624
 625         isl_seq_clr(eq.data, 1+total);
 626         index[isl_seq_get_hash_bits(bmap->div[k], 2+total, bits)] = k + 1;
 627         for (--k; k >= 0; --k) {
 628                 uint32_t hash;
 629
 630                 if (isl_int_is_zero(bmap->div[k][0]))
 631                         continue;
 632
 633                 hash = isl_seq_get_hash_bits(bmap->div[k], 2+total, bits);
 634                 for (h = hash; index[h]; h = (h+1) % size)
 635                         if (isl_seq_eq(bmap->div[k],
 636                                        bmap->div[index[h]-1], 2+total))
 637                                 break;
 638                 if (index[h]) {
 639                         *progress = 1;
 640                         l = index[h] - 1;
 641                         elim_for[l] = k + 1;
 642                 }
 643                 index[h] = k+1;
 644         }
 645         for (l = bmap->n_div - 1; l >= 0; --l) {
 646                 if (!elim_for[l])
 647                         continue;
 648                 k = elim_for[l] - 1;
 649                 isl_int_set_si(eq.data[1+total_var+k], -1);
 650                 isl_int_set_si(eq.data[1+total_var+l], 1);
 651                 eliminate_div(bmap, eq.data, l);
 652                 isl_int_set_si(eq.data[1+total_var+k], 0);
 653                 isl_int_set_si(eq.data[1+total_var+l], 0);
 654         }
 655
 656         isl_blk_free(ctx, eq);
 657 out:
 658         free(index);
 659         free(elim_for);
 660         return bmap;
 661 }
 662
 663 static int n_pure_div_eq(struct isl_basic_map *bmap)
 664 {
 665         int i, j;
 666         unsigned total;
 667
 668         total = isl_dim_total(bmap->dim);
 669         for (i = 0, j = bmap->n_div-1; i < bmap->n_eq; ++i) {
 670                 while (j >= 0 && isl_int_is_zero(bmap->eq[i][1 + total + j]))
 671                         --j;
 672                 if (j < 0)
 673                         break;
 674                 if (isl_seq_first_non_zero(bmap->eq[i] + 1 + total, j) != -1)
 675                         return 0;
 676         }
 677         return i;
 678 }
 679
 680 /* Normalize divs that appear in equalities.
 681  *
 682  * In particular, we assume that bmap contains some equalities
 683  * of the form
 684  *
 685  *      a x = m * e_i
 686  *
 687  * and we want to replace the set of e_i by a minimal set and
 688  * such that the new e_i have a canonical representation in terms
 689  * of the vector x.
 690  * If any of the equalities involves more than one divs, then
 691  * we currently simply bail out.
 692  *
 693  * Let us first additionally assume that all equalities involve
 694  * a div.  The equalities then express modulo constraints on the
 695  * remaining variables and we can use "parameter compression"
 696  * to find a minimal set of constraints.  The result is a transformation
 697  *
 698  *      x = T(x') = x_0 + G x'
 699  *
 700  * with G a lower-triangular matrix with all elements below the diagonal
 701  * non-negative and smaller than the diagonal element on the same row.
 702  * We first normalize x_0 by making the same property hold in the affine
 703  * T matrix.
 704  * The rows i of G with a 1 on the diagonal do not impose any modulo
 705  * constraint and simply express x_i = x'_i.
 706  * For each of the remaining rows i, we introduce a div and a corresponding
 707  * equality.  In particular
 708  *
 709  *      g_ii e_j = x_i - g_i(x')
 710  *
 711  * where each x'_k is replaced either by x_k (if g_kk = 1) or the
 712  * corresponding div (if g_kk != 1).
 713  *
 714  * If there are any equalities not involving any div, then we
 715  * first apply a variable compression on the variables x:
 716  *
 717  *      x = C x''       x'' = C_2 x
 718  *
 719  * and perform the above parameter compression on A C instead of on A.
 720  * The resulting compression is then of the form
 721  *
 722  *      x'' = T(x') = x_0 + G x'
 723  *
 724  * and in constructing the new divs and the corresponding equalities,
 725  * we have to replace each x'', i.e., the x'_k with (g_kk = 1),
 726  * by the corresponding row from C_2.
 727  */
 728 static struct isl_basic_map *normalize_divs(
 729         struct isl_basic_map *bmap, int *progress)
 730 {
 731         int i, j, k;
 732         int total;
 733         int div_eq;
 734         struct isl_mat *B;
 735         struct isl_vec *d;
 736         struct isl_mat *T = NULL;
 737         struct isl_mat *C = NULL;
 738         struct isl_mat *C2 = NULL;
 739         isl_int v;
 740         int *pos;
 741         int dropped, needed;
 742
 743         if (!bmap)
 744                 return NULL;
 745
 746         if (bmap->n_div == 0)
 747                 return bmap;
 748
 749         if (bmap->n_eq == 0)
 750                 return bmap;
 751
 752         if (ISL_F_ISSET(bmap, ISL_BASIC_MAP_NORMALIZED_DIVS))
 753                 return bmap;
 754
 755         total = isl_dim_total(bmap->dim);
 756         div_eq = n_pure_div_eq(bmap);
 757         if (div_eq == 0)
 758                 return bmap;
 759
 760         if (div_eq < bmap->n_eq) {
 761                 B = isl_mat_sub_alloc(bmap->ctx, bmap->eq, div_eq,
 762                                         bmap->n_eq - div_eq, 0, 1 + total);
 763                 C = isl_mat_variable_compression(bmap->ctx, B, &C2);
 764                 if (!C || !C2)
 765                         goto error;
 766                 if (C->n_col == 0) {
 767                         bmap = isl_basic_map_set_to_empty(bmap);
 768                         isl_mat_free(bmap->ctx, C);
 769                         isl_mat_free(bmap->ctx, C2);
 770                         goto done;
 771                 }
 772         }
 773
 774         d = isl_vec_alloc(bmap->ctx, div_eq);
 775         if (!d)
 776                 goto error;
 777         for (i = 0, j = bmap->n_div-1; i < div_eq; ++i) {
 778                 while (j >= 0 && isl_int_is_zero(bmap->eq[i][1 + total + j]))
 779                         --j;
 780                 isl_int_set(d->block.data[i], bmap->eq[i][1 + total + j]);
 781         }
 782         B = isl_mat_sub_alloc(bmap->ctx, bmap->eq, 0, div_eq, 0, 1 + total);
 783
 784         if (C) {
 785                 B = isl_mat_product(bmap->ctx, B, C);
 786                 C = NULL;
 787         }
 788
 789         T = isl_mat_parameter_compression(bmap->ctx, B, d);
 790         if (!T)
 791                 goto error;
 792         if (T->n_col == 0) {
 793                 bmap = isl_basic_map_set_to_empty(bmap);
 794                 isl_mat_free(bmap->ctx, C2);
 795                 isl_mat_free(bmap->ctx, T);
 796                 goto done;
 797         }
 798         isl_int_init(v);
 799         for (i = 0; i < T->n_row - 1; ++i) {
 800                 isl_int_fdiv_q(v, T->row[1 + i][0], T->row[1 + i][1 + i]);
 801                 if (isl_int_is_zero(v))
 802                         continue;
 803                 isl_mat_col_submul(T, 0, v, 1 + i);
 804         }
 805         isl_int_clear(v);
 806         pos = isl_alloc_array(bmap->ctx, int, T->n_row);
 807         /* We have to be careful because dropping equalities may reorder them */
 808         dropped = 0;
 809         for (j = bmap->n_div - 1; j >= 0; --j) {
 810                 for (i = 0; i < bmap->n_eq; ++i)
 811                         if (!isl_int_is_zero(bmap->eq[i][1 + total + j]))
 812                                 break;
 813                 if (i < bmap->n_eq) {
 814                         bmap = isl_basic_map_drop_div(bmap, j);
 815                         isl_basic_map_drop_equality(bmap, i);
 816                         ++dropped;
 817                 }
 818         }
 819         pos[0] = 0;
 820         needed = 0;
 821         for (i = 1; i < T->n_row; ++i) {
 822                 if (isl_int_is_one(T->row[i][i]))
 823                         pos[i] = i;
 824                 else
 825                         needed++;
 826         }
 827         if (needed > dropped) {
 828                 bmap = isl_basic_map_extend_dim(bmap, isl_dim_copy(bmap->dim),
 829                                 needed, needed, 0);
 830                 if (!bmap)
 831                         goto error;
 832         }
 833         for (i = 1; i < T->n_row; ++i) {
 834                 if (isl_int_is_one(T->row[i][i]))
 835                         continue;
 836                 k = isl_basic_map_alloc_div(bmap);
 837                 pos[i] = 1 + total + k;
 838                 isl_seq_clr(bmap->div[k] + 1, 1 + total + bmap->n_div);
 839                 isl_int_set(bmap->div[k][0], T->row[i][i]);
 840                 if (C2)
 841                         isl_seq_cpy(bmap->div[k] + 1, C2->row[i], 1 + total);
 842                 else
 843                         isl_int_set_si(bmap->div[k][1 + i], 1);
 844                 for (j = 0; j < i; ++j) {
 845                         if (isl_int_is_zero(T->row[i][j]))
 846                                 continue;
 847                         if (pos[j] < T->n_row && C2)
 848                                 isl_seq_submul(bmap->div[k] + 1, T->row[i][j],
 849                                                 C2->row[pos[j]], 1 + total);
 850                         else
 851                                 isl_int_neg(bmap->div[k][1 + pos[j]],
 852                                                                 T->row[i][j]);
 853                 }
 854                 j = isl_basic_map_alloc_equality(bmap);
 855                 isl_seq_neg(bmap->eq[j], bmap->div[k]+1, 1+total+bmap->n_div);
 856                 isl_int_set(bmap->eq[j][pos[i]], bmap->div[k][0]);
 857         }
 858         free(pos);
 859         isl_mat_free(bmap->ctx, C2);
 860         isl_mat_free(bmap->ctx, T);
 861
 862         if (progress)
 863                 *progress = 1;
 864 done:
 865         ISL_F_SET(bmap, ISL_BASIC_MAP_NORMALIZED_DIVS);
 866
 867         return bmap;
 868 error:
 869         isl_mat_free(bmap->ctx, C);
 870         isl_mat_free(bmap->ctx, C2);
 871         isl_mat_free(bmap->ctx, T);
 872         return bmap;
 873 }
 874
 875 static struct isl_basic_map *remove_duplicate_constraints(
 876         struct isl_basic_map *bmap, int *progress)
 877 {
 878         unsigned int size;
 879         isl_int ***index;
 880         int k, l, h;
 881         int bits;
 882         unsigned total = isl_basic_map_total_dim(bmap);
 883         isl_int sum;
 884
 885         if (bmap->n_ineq <= 1)
 886                 return bmap;
 887
 888         size = round_up(4 * (bmap->n_ineq+1) / 3 - 1);
 889         bits = ffs(size) - 1;
 890         index = isl_calloc_array(ctx, isl_int **, size);
 891         if (!index)
 892                 return bmap;
 893
 894         index[isl_seq_get_hash_bits(bmap->ineq[0]+1, total, bits)] = &bmap->ineq[0];
 895         for (k = 1; k < bmap->n_ineq; ++k) {
 896                 h = hash_index(index, size, bits, bmap, k);
 897                 if (!index[h]) {
 898                         index[h] = &bmap->ineq[k];
 899                         continue;
 900                 }
 901                 if (progress)
 902                         *progress = 1;
 903                 l = index[h] - &bmap->ineq[0];
 904                 if (isl_int_lt(bmap->ineq[k][0], bmap->ineq[l][0]))
 905                         swap_inequality(bmap, k, l);
 906                 isl_basic_map_drop_inequality(bmap, k);
 907                 --k;
 908         }
 909         isl_int_init(sum);
 910         for (k = 0; k < bmap->n_ineq-1; ++k) {
 911                 isl_seq_neg(bmap->ineq[k]+1, bmap->ineq[k]+1, total);
 912                 h = hash_index(index, size, bits, bmap, k);
 913                 isl_seq_neg(bmap->ineq[k]+1, bmap->ineq[k]+1, total);
 914                 if (!index[h])
 915                         continue;
 916                 l = index[h] - &bmap->ineq[0];
 917                 isl_int_add(sum, bmap->ineq[k][0], bmap->ineq[l][0]);
 918                 if (isl_int_is_pos(sum))
 919                         continue;
 920                 if (isl_int_is_zero(sum)) {
 921                         /* We need to break out of the loop after these
 922                          * changes since the contents of the hash
 923                          * will no longer be valid.
 924                          * Plus, we probably we want to regauss first.
 925                          */
 926                         isl_basic_map_drop_inequality(bmap, l);
 927                         isl_basic_map_inequality_to_equality(bmap, k);
 928                 } else
 929                         bmap = isl_basic_map_set_to_empty(bmap);
 930                 break;
 931         }
 932         isl_int_clear(sum);
 933
 934         free(index);
 935         return bmap;
 936 }
 937
 938
 939 struct isl_basic_map *isl_basic_map_simplify(struct isl_basic_map *bmap)
 940 {
 941         int progress = 1;
 942         if (!bmap)
 943                 return NULL;
 944         while (progress) {
 945                 progress = 0;
 946                 bmap = isl_basic_map_normalize_constraints(bmap);
 947                 bmap = remove_duplicate_divs(bmap, &progress);
 948                 bmap = eliminate_divs_eq(bmap, &progress);
 949                 bmap = eliminate_divs_ineq(bmap, &progress);
 950                 bmap = isl_basic_map_gauss(bmap, &progress);
 951                 /* requires equalities in normal form */
 952                 bmap = normalize_divs(bmap, &progress);
 953                 bmap = remove_duplicate_constraints(bmap, &progress);
 954         }
 955         return bmap;
 956 }
 957
 958 struct isl_basic_set *isl_basic_set_simplify(struct isl_basic_set *bset)
 959 {
 960         return (struct isl_basic_set *)
 961                 isl_basic_map_simplify((struct isl_basic_map *)bset);
 962 }
 963
 964
 965 /* If the only constraints a div d=floor(f/m)
 966  * appears in are its two defining constraints
 967  *
 968  *      f - m d >=0
 969  *      -(f - (m - 1)) + m d >= 0
 970  *
 971  * then it can safely be removed.
 972  */
 973 static int div_is_redundant(struct isl_basic_map *bmap, int div)
 974 {
 975         int i;
 976         unsigned pos = 1 + isl_dim_total(bmap->dim) + div;
 977
 978         for (i = 0; i < bmap->n_eq; ++i)
 979                 if (!isl_int_is_zero(bmap->eq[i][pos]))
 980                         return 0;
 981
 982         for (i = 0; i < bmap->n_ineq; ++i) {
 983                 if (isl_int_is_zero(bmap->ineq[i][pos]))
 984                         continue;
 985                 if (isl_int_eq(bmap->ineq[i][pos], bmap->div[div][0])) {
 986                         int neg;
 987                         isl_int_sub(bmap->div[div][1],
 988                                         bmap->div[div][1], bmap->div[div][0]);
 989                         isl_int_add_ui(bmap->div[div][1], bmap->div[div][1], 1);
 990                         neg = isl_seq_is_neg(bmap->ineq[i], bmap->div[div]+1, pos);
 991                         isl_int_sub_ui(bmap->div[div][1], bmap->div[div][1], 1);
 992                         isl_int_add(bmap->div[div][1],
 993                                         bmap->div[div][1], bmap->div[div][0]);
 994                         if (!neg)
 995                                 return 0;
 996                         if (isl_seq_first_non_zero(bmap->ineq[i]+pos+1,
 997                                                     bmap->n_div-div-1) != -1)
 998                                 return 0;
 999                 } else if (isl_int_abs_eq(bmap->ineq[i][pos], bmap->div[div][0])) {
1000                         if (!isl_seq_eq(bmap->ineq[i], bmap->div[div]+1, pos))
1001                                 return 0;
1002                         if (isl_seq_first_non_zero(bmap->ineq[i]+pos+1,
1003                                                     bmap->n_div-div-1) != -1)
1004                                 return 0;
1005                 } else
1006                         return 0;
1007         }
1008
1009         for (i = 0; i < bmap->n_div; ++i)
1010                 if (!isl_int_is_zero(bmap->div[i][1+pos]))
1011                         return 0;
1012
1013         return 1;
1014 }
1015
1016 /*
1017  * Remove divs that don't occur in any of the constraints or other divs.
1018  * These can arise when dropping some of the variables in a quast
1019  * returned by piplib.
1020  */
1021 static struct isl_basic_map *remove_redundant_divs(struct isl_basic_map *bmap)
1022 {
1023         int i;
1024
1025         if (!bmap)
1026                 return NULL;
1027
1028         for (i = bmap->n_div-1; i >= 0; --i) {
1029                 if (!div_is_redundant(bmap, i))
1030                         continue;
1031                 bmap = isl_basic_map_drop_div(bmap, i);
1032         }
1033         return bmap;
1034 }
1035
1036 struct isl_basic_map *isl_basic_map_finalize(struct isl_basic_map *bmap)
1037 {
1038         bmap = remove_redundant_divs(bmap);
1039         if (!bmap)
1040                 return NULL;
1041         ISL_F_SET(bmap, ISL_BASIC_SET_FINAL);
1042         return bmap;
1043 }
1044
1045 struct isl_basic_set *isl_basic_set_finalize(struct isl_basic_set *bset)
1046 {
1047         return (struct isl_basic_set *)
1048                 isl_basic_map_finalize((struct isl_basic_map *)bset);
1049 }
1050
1051 struct isl_set *isl_set_finalize(struct isl_set *set)
1052 {
1053         int i;
1054
1055         if (!set)
1056                 return NULL;
1057         for (i = 0; i < set->n; ++i) {
1058                 set->p[i] = isl_basic_set_finalize(set->p[i]);
1059                 if (!set->p[i])
1060                         goto error;
1061         }
1062         return set;
1063 error:
1064         isl_set_free(set);
1065         return NULL;
1066 }
1067
1068 struct isl_map *isl_map_finalize(struct isl_map *map)
1069 {
1070         int i;
1071
1072         if (!map)
1073                 return NULL;
1074         for (i = 0; i < map->n; ++i) {
1075                 map->p[i] = isl_basic_map_finalize(map->p[i]);
1076                 if (!map->p[i])
1077                         goto error;
1078         }
1079         ISL_F_CLR(map, ISL_MAP_NORMALIZED);
1080         return map;
1081 error:
1082         isl_map_free(map);
1083         return NULL;
1084 }
1085
1086
1087 /* Remove any div that is defined in terms of the given variable.
1088  */
1089 static struct isl_basic_map *remove_dependent_vars(struct isl_basic_map *bmap,
1090                                                                         int pos)
1091 {
1092         int i;
1093         unsigned dim = isl_dim_total(bmap->dim);
1094
1095         for (i = 0; i < bmap->n_div; ++i) {
1096                 if (isl_int_is_zero(bmap->div[i][0]))
1097                         continue;
1098                 if (isl_int_is_zero(bmap->div[i][1+1+pos]))
1099                         continue;
1100                 bmap = isl_basic_map_eliminate_vars(bmap, dim + i, 1);
1101                 if (!bmap)
1102                         return NULL;
1103         }
1104         return bmap;
1105 }
1106
1107 /* Eliminate the specified variables from the constraints using
1108  * Fourier-Motzkin.  The variables themselves are not removed.
1109  */
1110 struct isl_basic_map *isl_basic_map_eliminate_vars(
1111         struct isl_basic_map *bmap, unsigned pos, unsigned n)
1112 {
1113         int d;
1114         int i, j, k;
1115         unsigned total;
1116
1117         if (n == 0)
1118                 return bmap;
1119         if (!bmap)
1120                 return NULL;
1121         total = isl_basic_map_total_dim(bmap);
1122
1123         bmap = isl_basic_map_cow(bmap);
1124         for (d = pos + n - 1; d >= 0 && d >= pos; --d)
1125                 bmap = remove_dependent_vars(bmap, d);
1126
1127         for (d = pos + n - 1;
1128              d >= 0 && d >= total - bmap->n_div && d >= pos; --d)
1129                 isl_seq_clr(bmap->div[d-(total-bmap->n_div)], 2+total);
1130         for (d = pos + n - 1; d >= 0 && d >= pos; --d) {
1131                 int n_lower, n_upper;
1132                 if (!bmap)
1133                         return NULL;
1134                 for (i = 0; i < bmap->n_eq; ++i) {
1135                         if (isl_int_is_zero(bmap->eq[i][1+d]))
1136                                 continue;
1137                         eliminate_var_using_equality(bmap, d, bmap->eq[i], NULL);
1138                         isl_basic_map_drop_equality(bmap, i);
1139                         break;
1140                 }
1141                 if (i < bmap->n_eq)
1142                         continue;
1143                 n_lower = 0;
1144                 n_upper = 0;
1145                 for (i = 0; i < bmap->n_ineq; ++i) {
1146                         if (isl_int_is_pos(bmap->ineq[i][1+d]))
1147                                 n_lower++;
1148                         else if (isl_int_is_neg(bmap->ineq[i][1+d]))
1149                                 n_upper++;
1150                 }
1151                 bmap = isl_basic_map_extend_constraints(bmap,
1152                                 0, n_lower * n_upper);
1153                 for (i = bmap->n_ineq - 1; i >= 0; --i) {
1154                         int last;
1155                         if (isl_int_is_zero(bmap->ineq[i][1+d]))
1156                                 continue;
1157                         last = -1;
1158                         for (j = 0; j < i; ++j) {
1159                                 if (isl_int_is_zero(bmap->ineq[j][1+d]))
1160                                         continue;
1161                                 last = j;
1162                                 if (isl_int_sgn(bmap->ineq[i][1+d]) ==
1163                                     isl_int_sgn(bmap->ineq[j][1+d]))
1164                                         continue;
1165                                 k = isl_basic_map_alloc_inequality(bmap);
1166                                 if (k < 0)
1167                                         goto error;
1168                                 isl_seq_cpy(bmap->ineq[k], bmap->ineq[i],
1169                                                 1+total);
1170                                 isl_seq_elim(bmap->ineq[k], bmap->ineq[j],
1171                                                 1+d, 1+total, NULL);
1172                         }
1173                         isl_basic_map_drop_inequality(bmap, i);
1174                         i = last + 1;
1175                 }
1176                 if (n_lower > 0 && n_upper > 0) {
1177                         bmap = isl_basic_map_normalize_constraints(bmap);
1178                         bmap = remove_duplicate_constraints(bmap, NULL);
1179                         bmap = isl_basic_map_gauss(bmap, NULL);
1180                         bmap = isl_basic_map_convex_hull(bmap);
1181                         if (!bmap)
1182                                 goto error;
1183                         if (ISL_F_ISSET(bmap, ISL_BASIC_MAP_EMPTY))
1184                                 break;
1185                 }
1186         }
1187         ISL_F_CLR(bmap, ISL_BASIC_MAP_NORMALIZED);
1188         return bmap;
1189 error:
1190         isl_basic_map_free(bmap);
1191         return NULL;
1192 }
1193
1194 struct isl_basic_set *isl_basic_set_eliminate_vars(
1195         struct isl_basic_set *bset, unsigned pos, unsigned n)
1196 {
1197         return (struct isl_basic_set *)isl_basic_map_eliminate_vars(
1198                         (struct isl_basic_map *)bset, pos, n);
1199 }
1200
1201 /* Don't assume equalities are in order, because align_divs
1202  * may have changed the order of the divs.
1203  */
1204 static void compute_elimination_index(struct isl_basic_map *bmap, int *elim)
1205 {
1206         int d, i;
1207         unsigned total;
1208
1209         total = isl_dim_total(bmap->dim);
1210         for (d = 0; d < total; ++d)
1211                 elim[d] = -1;
1212         for (i = 0; i < bmap->n_eq; ++i) {
1213                 for (d = total - 1; d >= 0; --d) {
1214                         if (isl_int_is_zero(bmap->eq[i][1+d]))
1215                                 continue;
1216                         elim[d] = i;
1217                         break;
1218                 }
1219         }
1220 }
1221
1222 static void set_compute_elimination_index(struct isl_basic_set *bset, int *elim)
1223 {
1224         return compute_elimination_index((struct isl_basic_map *)bset, elim);
1225 }
1226
1227 static int reduced_using_equalities(isl_int *dst, isl_int *src,
1228         struct isl_basic_map *bmap, int *elim)
1229 {
1230         int d, i;
1231         int copied = 0;
1232         unsigned total;
1233
1234         total = isl_dim_total(bmap->dim);
1235         for (d = total - 1; d >= 0; --d) {
1236                 if (isl_int_is_zero(src[1+d]))
1237                         continue;
1238                 if (elim[d] == -1)
1239                         continue;
1240                 if (!copied) {
1241                         isl_seq_cpy(dst, src, 1 + total);
1242                         copied = 1;
1243                 }
1244                 isl_seq_elim(dst, bmap->eq[elim[d]], 1 + d, 1 + total, NULL);
1245         }
1246         return copied;
1247 }
1248
1249 static int set_reduced_using_equalities(isl_int *dst, isl_int *src,
1250         struct isl_basic_set *bset, int *elim)
1251 {
1252         return reduced_using_equalities(dst, src,
1253                                         (struct isl_basic_map *)bset, elim);
1254 }
1255
1256 static struct isl_basic_set *isl_basic_set_reduce_using_equalities(
1257         struct isl_basic_set *bset, struct isl_basic_set *context)
1258 {
1259         int i;
1260         int *elim;
1261
1262         if (!bset || !context)
1263                 goto error;
1264
1265         bset = isl_basic_set_cow(bset);
1266         if (!bset)
1267                 goto error;
1268
1269         elim = isl_alloc_array(ctx, int, isl_basic_set_n_dim(bset));
1270         if (!elim)
1271                 goto error;
1272         set_compute_elimination_index(context, elim);
1273         for (i = 0; i < bset->n_eq; ++i)
1274                 set_reduced_using_equalities(bset->eq[i], bset->eq[i],
1275                                                         context, elim);
1276         for (i = 0; i < bset->n_ineq; ++i)
1277                 set_reduced_using_equalities(bset->ineq[i], bset->ineq[i],
1278                                                         context, elim);
1279         isl_basic_set_free(context);
1280         free(elim);
1281         bset = isl_basic_set_simplify(bset);
1282         bset = isl_basic_set_finalize(bset);
1283         return bset;
1284 error:
1285         isl_basic_set_free(bset);
1286         isl_basic_set_free(context);
1287         return NULL;
1288 }
1289
1290 static struct isl_basic_set *remove_shifted_constraints(
1291         struct isl_basic_set *bset, struct isl_basic_set *context)
1292 {
1293         unsigned int size;
1294         isl_int ***index;
1295         int bits;
1296         int k, h, l;
1297
1298         if (!bset)
1299                 return NULL;
1300
1301         size = round_up(4 * (context->n_ineq+1) / 3 - 1);
1302         bits = ffs(size) - 1;
1303         index = isl_calloc_array(ctx, isl_int **, size);
1304         if (!index)
1305                 return bset;
1306
1307         for (k = 0; k < context->n_ineq; ++k) {
1308                 h = set_hash_index(index, size, bits, context, k);
1309                 index[h] = &context->ineq[k];
1310         }
1311         for (k = 0; k < bset->n_ineq; ++k) {
1312                 h = set_hash_index(index, size, bits, bset, k);
1313                 if (!index[h])
1314                         continue;
1315                 l = index[h] - &context->ineq[0];
1316                 if (isl_int_lt(bset->ineq[k][0], context->ineq[l][0]))
1317                         continue;
1318                 bset = isl_basic_set_cow(bset);
1319                 if (!bset)
1320                         goto error;
1321                 isl_basic_set_drop_inequality(bset, k);
1322                 --k;
1323         }
1324         free(index);
1325         return bset;
1326 error:
1327         free(index);
1328         return bset;
1329 }
1330
1331 /* Tighten (decrease) the constant terms of the inequalities based
1332  * on the equalities, without removing any integer points.
1333  * For example, if there is an equality
1334  *
1335  *              i = 3 * j
1336  *
1337  * and an inequality
1338  *
1339  *              i >= 1
1340  *
1341  * then we want to replace the inequality by
1342  *
1343  *              i >= 3
1344  *
1345  * We do this by computing a variable compression and translating
1346  * the constraints to the compressed space.
1347  * If any constraint has coefficients (except the contant term)
1348  * with a common factor "f", then we can replace the constant term "c"
1349  * by
1350  *
1351  *              f * floor(c/f)
1352  *
1353  * That is, we add
1354  *
1355  *              f * floor(c/f) - c = -fract(c/f)
1356  *
1357  * and we can add the same value to the original constraint.
1358  *
1359  * In the example, the compressed space only contains "j",
1360  * and the inequality translates to
1361  *
1362  *              3 * j - 1 >= 0
1363  *
1364  * We add -fract(-1/3) = -2 to the original constraint to obtain
1365  *
1366  *              i - 3 >= 0
1367  */
1368 static struct isl_basic_set *normalize_constraints_in_compressed_space(
1369         struct isl_basic_set *bset)
1370 {
1371         int i;
1372         unsigned total;
1373         struct isl_mat *B, *C;
1374         isl_int gcd;
1375
1376         if (!bset)
1377                 return NULL;
1378
1379         if (ISL_F_ISSET(bset, ISL_BASIC_SET_RATIONAL))
1380                 return bset;
1381
1382         if (!bset->n_ineq)
1383                 return bset;
1384
1385         bset = isl_basic_set_cow(bset);
1386         if (!bset)
1387                 return NULL;
1388
1389         total = isl_basic_set_total_dim(bset);
1390         B = isl_mat_sub_alloc(bset->ctx, bset->eq, 0, bset->n_eq, 0, 1 + total);
1391         C = isl_mat_variable_compression(bset->ctx, B, NULL);
1392         if (!C)
1393                 return bset;
1394         if (C->n_col == 0) {
1395                 isl_mat_free(bset->ctx, C);
1396                 return isl_basic_set_set_to_empty(bset);
1397         }
1398         B = isl_mat_sub_alloc(bset->ctx, bset->ineq,
1399                                                 0, bset->n_ineq, 0, 1 + total);
1400         C = isl_mat_product(bset->ctx, B, C);
1401         if (!C)
1402                 return bset;
1403
1404         isl_int_init(gcd);
1405         for (i = 0; i < bset->n_ineq; ++i) {
1406                 isl_seq_gcd(C->row[i] + 1, C->n_col - 1, &gcd);
1407                 if (isl_int_is_one(gcd))
1408                         continue;
1409                 isl_int_fdiv_r(C->row[i][0], C->row[i][0], gcd);
1410                 isl_int_sub(bset->ineq[i][0], bset->ineq[i][0], C->row[i][0]);
1411         }
1412         isl_int_clear(gcd);
1413
1414         isl_mat_free(bset->ctx, C);
1415
1416         return bset;
1417 }
1418
1419 /* Remove all information from bset that is redundant in the context
1420  * of context.  In particular, equalities that are linear combinations
1421  * of those in context are removed.  Then the inequalities that are
1422  * redundant in the context of the equalities and inequalities of
1423  * context are removed.
1424  *
1425  * We first simplify the constraints of "bset" in the context of the
1426  * equalities of "context".
1427  * Then we simplify the inequalities of the context in the context
1428  * of the equalities of bset and remove the inequalities from "bset"
1429  * that are obviously redundant with respect to some inequality in "context".
1430  *
1431  * If there are any inequalities left, we construct a tableau for
1432  * the context and then add the inequalities of "bset".
1433  * Before adding these equalities, we freeze all constraints such that
1434  * they won't be considered redundant in terms of the constraints of "bset".
1435  * Then we detect all equalities and redundant constraints (among the
1436  * constraints that weren't frozen) and update bset according to the results.
1437  * We have to be careful here because we don't want any of the context
1438  * constraints to remain and because we haven't added the equalities of "bset"
1439  * to the tableau so we temporarily have to pretend that there were no
1440  * equalities.
1441  */
1442 static struct isl_basic_set *uset_gist(struct isl_basic_set *bset,
1443         struct isl_basic_set *context)
1444 {
1445         int i;
1446         struct isl_tab *tab;
1447         unsigned context_ineq;
1448         struct isl_basic_set *combined = NULL;
1449
1450         if (!context || !bset)
1451                 goto error;
1452
1453         if (context->n_eq > 0)
1454                 bset = isl_basic_set_reduce_using_equalities(bset,
1455                                         isl_basic_set_copy(context));
1456         if (!bset)
1457                 goto error;
1458         if (isl_basic_set_fast_is_empty(bset))
1459                 goto done;
1460         if (!bset->n_ineq)
1461                 goto done;
1462
1463         if (bset->n_eq > 0) {
1464                 struct isl_basic_set *affine_hull;
1465                 affine_hull = isl_basic_set_copy(bset);
1466                 affine_hull = isl_basic_set_cow(affine_hull);
1467                 if (!affine_hull)
1468                         goto error;
1469                 isl_basic_set_free_inequality(affine_hull, affine_hull->n_ineq);
1470                 context = isl_basic_set_intersect(context, affine_hull);
1471                 context = isl_basic_set_gauss(context, NULL);
1472                 context = normalize_constraints_in_compressed_space(context);
1473         }
1474         if (!context)
1475                 goto error;
1476         if (ISL_F_ISSET(context, ISL_BASIC_SET_EMPTY)) {
1477                 isl_basic_set_free(bset);
1478                 return context;
1479         }
1480         if (!context->n_ineq)
1481                 goto done;
1482         bset = remove_shifted_constraints(bset, context);
1483         if (!bset->n_ineq)
1484                 goto done;
1485         isl_basic_set_free_equality(context, context->n_eq);
1486         context_ineq = context->n_ineq;
1487         combined = isl_basic_set_cow(isl_basic_set_copy(context));
1488         combined = isl_basic_set_extend_constraints(combined,
1489                                                     bset->n_eq, bset->n_ineq);
1490         tab = isl_tab_from_basic_set(combined);
1491         if (!tab)
1492                 goto error;
1493         for (i = 0; i < context_ineq; ++i)
1494                 tab->con[i].frozen = 1;
1495         tab = isl_tab_extend(bset->ctx, tab, bset->n_ineq);
1496         if (!tab)
1497                 goto error;
1498         for (i = 0; i < bset->n_ineq; ++i)
1499                 tab = isl_tab_add_ineq(bset->ctx, tab, bset->ineq[i]);
1500         bset = isl_basic_set_add_constraints(combined, bset, 0);
1501         tab = isl_tab_detect_equalities(bset->ctx, tab);
1502         tab = isl_tab_detect_redundant(bset->ctx, tab);
1503         if (!tab)
1504                 goto error2;
1505         for (i = 0; i < context_ineq; ++i) {
1506                 tab->con[i].is_zero = 0;
1507                 tab->con[i].is_redundant = 1;
1508         }
1509         bset = isl_basic_set_update_from_tab(bset, tab);
1510         isl_tab_free(bset->ctx, tab);
1511         ISL_F_SET(bset, ISL_BASIC_SET_NO_IMPLICIT);
1512         ISL_F_SET(bset, ISL_BASIC_SET_NO_REDUNDANT);
1513 done:
1514         bset = isl_basic_set_simplify(bset);
1515         bset = isl_basic_set_finalize(bset);
1516         isl_basic_set_free(context);
1517         return bset;
1518 error:
1519         isl_basic_set_free(combined);
1520 error2:
1521         isl_basic_set_free(bset);
1522         isl_basic_set_free(context);
1523         return NULL;
1524 }
1525
1526 /* Normalize the divs in "bmap" in the context of the equalities in "context".
1527  * We simply add the equalities in context to bmap and then do a regular
1528  * div normalizations.  Better results can be obtained by normalizing
1529  * only the divs in bmap than do not also appear in context.
1530  * We need to be careful to reduce the divs using the equalities
1531  * so that later calls to isl_basic_map_overlying_set wouldn't introduce
1532  * spurious constraints.
1533  */
1534 static struct isl_basic_map *normalize_divs_in_context(
1535         struct isl_basic_map *bmap, struct isl_basic_map *context)
1536 {
1537         int i;
1538         unsigned total_context;
1539         int div_eq;
1540
1541         div_eq = n_pure_div_eq(bmap);
1542         if (div_eq == 0)
1543                 return bmap;
1544
1545         if (context->n_div > 0)
1546                 bmap = isl_basic_map_align_divs(bmap, context);
1547
1548         total_context = isl_basic_map_total_dim(context);
1549         bmap = isl_basic_map_extend_constraints(bmap, context->n_eq, 0);
1550         for (i = 0; i < context->n_eq; ++i) {
1551                 int k;
1552                 k = isl_basic_map_alloc_equality(bmap);
1553                 isl_seq_cpy(bmap->eq[k], context->eq[i], 1 + total_context);
1554                 isl_seq_clr(bmap->eq[k] + 1 + total_context,
1555                                 isl_basic_map_total_dim(bmap) - total_context);
1556         }
1557         bmap = isl_basic_map_gauss(bmap, NULL);
1558         bmap = normalize_divs(bmap, NULL);
1559         bmap = isl_basic_map_gauss(bmap, NULL);
1560         return bmap;
1561 }
1562
1563 struct isl_basic_map *isl_basic_map_gist(struct isl_basic_map *bmap,
1564         struct isl_basic_map *context)
1565 {
1566         struct isl_basic_set *bset;
1567
1568         if (!bmap || !context)
1569                 goto error;
1570
1571         if (isl_basic_map_is_universe(context)) {
1572                 isl_basic_map_free(context);
1573                 return bmap;
1574         }
1575         if (isl_basic_map_is_universe(bmap)) {
1576                 isl_basic_map_free(context);
1577                 return bmap;
1578         }
1579         if (isl_basic_map_fast_is_empty(context)) {
1580                 struct isl_dim *dim = isl_dim_copy(bmap->dim);
1581                 isl_basic_map_free(context);
1582                 isl_basic_map_free(bmap);
1583                 return isl_basic_map_universe(dim);
1584         }
1585         if (isl_basic_map_fast_is_empty(bmap)) {
1586                 isl_basic_map_free(context);
1587                 return bmap;
1588         }
1589
1590         bmap = isl_basic_map_convex_hull(bmap);
1591         context = isl_basic_map_convex_hull(context);
1592
1593         if (context->n_eq)
1594                 bmap = normalize_divs_in_context(bmap, context);
1595
1596         context = isl_basic_map_align_divs(context, bmap);
1597         bmap = isl_basic_map_align_divs(bmap, context);
1598
1599         bset = uset_gist(isl_basic_map_underlying_set(isl_basic_map_copy(bmap)),
1600                          isl_basic_map_underlying_set(context));
1601
1602         return isl_basic_map_overlying_set(bset, bmap);
1603 error:
1604         isl_basic_map_free(bmap);
1605         isl_basic_map_free(context);
1606         return NULL;
1607 }
1608
1609 /*
1610  * Assumes context has no implicit divs.
1611  */
1612 struct isl_map *isl_map_gist(struct isl_map *map, struct isl_basic_map *context)
1613 {
1614         int i;
1615
1616         if (!map || !context)
1617                 goto error;;
1618
1619         if (isl_basic_map_is_universe(context)) {
1620                 isl_basic_map_free(context);
1621                 return map;
1622         }
1623         if (isl_basic_map_fast_is_empty(context)) {
1624                 struct isl_dim *dim = isl_dim_copy(map->dim);
1625                 isl_basic_map_free(context);
1626                 isl_map_free(map);
1627                 return isl_map_universe(dim);
1628         }
1629
1630         context = isl_basic_map_convex_hull(context);
1631         map = isl_map_cow(map);
1632         if (!map || !context)
1633                 goto error;;
1634         isl_assert(map->ctx, isl_dim_equal(map->dim, context->dim), goto error);
1635         map = isl_map_compute_divs(map);
1636         for (i = 0; i < map->n; ++i)
1637                 context = isl_basic_map_align_divs(context, map->p[i]);
1638         for (i = 0; i < map->n; ++i) {
1639                 map->p[i] = isl_basic_map_gist(map->p[i],
1640                                                 isl_basic_map_copy(context));
1641                 if (!map->p[i])
1642                         goto error;
1643         }
1644         isl_basic_map_free(context);
1645         ISL_F_CLR(map, ISL_MAP_NORMALIZED);
1646         return map;
1647 error:
1648         isl_map_free(map);
1649         isl_basic_map_free(context);
1650         return NULL;
1651 }
1652
1653 struct isl_basic_set *isl_basic_set_gist(struct isl_basic_set *bset,
1654                                                 struct isl_basic_set *context)
1655 {
1656         return (struct isl_basic_set *)isl_basic_map_gist(
1657                 (struct isl_basic_map *)bset, (struct isl_basic_map *)context);
1658 }
1659
1660 struct isl_set *isl_set_gist(struct isl_set *set, struct isl_basic_set *context)
1661 {
1662         return (struct isl_set *)isl_map_gist((struct isl_map *)set,
1663                                         (struct isl_basic_map *)context);
1664 }
1665
1666 /* Quick check to see if two basic maps are disjoint.
1667  * In particular, we reduce the equalities and inequalities of
1668  * one basic map in the context of the equalities of the other
1669  * basic map and check if we get a contradiction.
1670  */
1671 int isl_basic_map_fast_is_disjoint(struct isl_basic_map *bmap1,
1672         struct isl_basic_map *bmap2)
1673 {
1674         struct isl_vec *v = NULL;
1675         int *elim = NULL;
1676         unsigned total;
1677         int d, i;
1678
1679         if (!bmap1 || !bmap2)
1680                 return -1;
1681         isl_assert(bmap1->ctx, isl_dim_equal(bmap1->dim, bmap2->dim),
1682                         return -1);
1683         if (bmap1->n_div || bmap2->n_div)
1684                 return 0;
1685         if (!bmap1->n_eq && !bmap2->n_eq)
1686                 return 0;
1687
1688         total = isl_dim_total(bmap1->dim);
1689         if (total == 0)
1690                 return 0;
1691         v = isl_vec_alloc(bmap1->ctx, 1 + total);
1692         if (!v)
1693                 goto error;
1694         elim = isl_alloc_array(bmap1->ctx, int, total);
1695         if (!elim)
1696                 goto error;
1697         compute_elimination_index(bmap1, elim);
1698         for (i = 0; i < bmap2->n_eq; ++i) {
1699                 int reduced;
1700                 reduced = reduced_using_equalities(v->block.data, bmap2->eq[i],
1701                                                         bmap1, elim);
1702                 if (reduced && !isl_int_is_zero(v->block.data[0]) &&
1703                     isl_seq_first_non_zero(v->block.data + 1, total) == -1)
1704                         goto disjoint;
1705         }
1706         for (i = 0; i < bmap2->n_ineq; ++i) {
1707                 int reduced;
1708                 reduced = reduced_using_equalities(v->block.data,
1709                                                 bmap2->ineq[i], bmap1, elim);
1710                 if (reduced && isl_int_is_neg(v->block.data[0]) &&
1711                     isl_seq_first_non_zero(v->block.data + 1, total) == -1)
1712                         goto disjoint;
1713         }
1714         compute_elimination_index(bmap2, elim);
1715         for (i = 0; i < bmap1->n_ineq; ++i) {
1716                 int reduced;
1717                 reduced = reduced_using_equalities(v->block.data,
1718                                                 bmap1->ineq[i], bmap2, elim);
1719                 if (reduced && isl_int_is_neg(v->block.data[0]) &&
1720                     isl_seq_first_non_zero(v->block.data + 1, total) == -1)
1721                         goto disjoint;
1722         }
1723         isl_vec_free(bmap1->ctx, v);
1724         free(elim);
1725         return 0;
1726 disjoint:
1727         isl_vec_free(bmap1->ctx, v);
1728         free(elim);
1729         return 1;
1730 error:
1731         isl_vec_free(bmap1->ctx, v);
1732         free(elim);
1733         return -1;
1734 }
1735
1736 int isl_basic_set_fast_is_disjoint(struct isl_basic_set *bset1,
1737         struct isl_basic_set *bset2)
1738 {
1739         return isl_basic_map_fast_is_disjoint((struct isl_basic_map *)bset1,
1740                                               (struct isl_basic_map *)bset2);
1741 }
1742
1743 int isl_map_fast_is_disjoint(struct isl_map *map1, struct isl_map *map2)
1744 {
1745         int i, j;
1746
1747         if (!map1 || !map2)
1748                 return -1;
1749
1750         if (isl_map_fast_is_equal(map1, map2))
1751                 return 0;
1752
1753         for (i = 0; i < map1->n; ++i) {
1754                 for (j = 0; j < map2->n; ++j) {
1755                         int d = isl_basic_map_fast_is_disjoint(map1->p[i],
1756                                                                map2->p[j]);
1757                         if (d != 1)
1758                                 return d;
1759                 }
1760         }
1761         return 1;
1762 }
1763
1764 int isl_set_fast_is_disjoint(struct isl_set *set1, struct isl_set *set2)
1765 {
1766         return isl_map_fast_is_disjoint((struct isl_map *)set1,
1767                                         (struct isl_map *)set2);
1768 }