isl_map_simplify.c

   1 #include "isl_equalities.h"
   2 #include "isl_map.h"
   3 #include "isl_map_private.h"
   4
   5 static void swap_equality(struct isl_basic_map *bmap, int a, int b)
   6 {
   7         isl_int *t = bmap->eq[a];
   8         bmap->eq[a] = bmap->eq[b];
   9         bmap->eq[b] = t;
  10 }
  11
  12 static void swap_inequality(struct isl_basic_map *bmap, int a, int b)
  13 {
  14         if (a != b) {
  15                 isl_int *t = bmap->ineq[a];
  16                 bmap->ineq[a] = bmap->ineq[b];
  17                 bmap->ineq[b] = t;
  18         }
  19 }
  20
  21 static void set_swap_inequality(struct isl_basic_set *bset, int a, int b)
  22 {
  23         swap_inequality((struct isl_basic_map *)bset, a, b);
  24 }
  25
  26 static void constraint_drop_vars(isl_int *c, unsigned n, unsigned rem)
  27 {
  28         isl_seq_cpy(c, c + n, rem);
  29         isl_seq_clr(c + rem, n);
  30 }
  31
  32 /* Drop n dimensions starting at first.
  33  *
  34  * In principle, this frees up some extra variables as the number
  35  * of columns remains constant, but we would have to extend
  36  * the div array too as the number of rows in this array is assumed
  37  * to be equal to extra.
  38  */
  39 struct isl_basic_set *isl_basic_set_drop_dims(
  40                 struct isl_basic_set *bset, unsigned first, unsigned n)
  41 {
  42         int i;
  43
  44         if (!bset)
  45                 goto error;
  46
  47         isl_assert(bset->ctx, first + n <= bset->dim->n_out, goto error);
  48
  49         if (n == 0)
  50                 return bset;
  51
  52         bset = isl_basic_set_cow(bset);
  53         if (!bset)
  54                 return NULL;
  55
  56         for (i = 0; i < bset->n_eq; ++i)
  57                 constraint_drop_vars(bset->eq[i]+1+bset->dim->nparam+first, n,
  58                                      (bset->dim->n_out-first-n)+bset->extra);
  59
  60         for (i = 0; i < bset->n_ineq; ++i)
  61                 constraint_drop_vars(bset->ineq[i]+1+bset->dim->nparam+first, n,
  62                                      (bset->dim->n_out-first-n)+bset->extra);
  63
  64         for (i = 0; i < bset->n_div; ++i)
  65                 constraint_drop_vars(bset->div[i]+1+1+bset->dim->nparam+first, n,
  66                                      (bset->dim->n_out-first-n)+bset->extra);
  67
  68         bset->dim = isl_dim_drop_outputs(bset->dim, first, n);
  69         if (!bset->dim)
  70                 goto error;
  71
  72         F_CLR(bset, ISL_BASIC_SET_NORMALIZED);
  73         bset = isl_basic_set_simplify(bset);
  74         return isl_basic_set_finalize(bset);
  75 error:
  76         isl_basic_set_free(bset);
  77         return NULL;
  78 }
  79
  80 struct isl_set *isl_set_drop_dims(
  81                 struct isl_set *set, unsigned first, unsigned n)
  82 {
  83         int i;
  84
  85         if (!set)
  86                 goto error;
  87
  88         isl_assert(set->ctx, first + n <= set->dim->n_out, goto error);
  89
  90         if (n == 0)
  91                 return set;
  92         set = isl_set_cow(set);
  93         if (!set)
  94                 goto error;
  95         set->dim = isl_dim_drop_outputs(set->dim, first, n);
  96         if (!set->dim)
  97                 goto error;
  98
  99         for (i = 0; i < set->n; ++i) {
 100                 set->p[i] = isl_basic_set_drop_dims(set->p[i], first, n);
 101                 if (!set->p[i])
 102                         goto error;
 103         }
 104
 105         F_CLR(set, ISL_SET_NORMALIZED);
 106         return set;
 107 error:
 108         isl_set_free(set);
 109         return NULL;
 110 }
 111
 112 /* Drop n input dimensions starting at first.
 113  *
 114  * In principle, this frees up some extra variables as the number
 115  * of columns remains constant, but we would have to extend
 116  * the div array too as the number of rows in this array is assumed
 117  * to be equal to extra.
 118  */
 119 struct isl_basic_map *isl_basic_map_drop_inputs(
 120                 struct isl_basic_map *bmap, unsigned first, unsigned n)
 121 {
 122         int i;
 123         unsigned nparam;
 124         unsigned n_in;
 125         unsigned n_out;
 126
 127         if (!bmap)
 128                 goto error;
 129
 130         nparam = isl_basic_map_n_param(bmap);
 131         n_in = isl_basic_map_n_in(bmap);
 132         n_out = isl_basic_map_n_out(bmap);
 133         isl_assert(bmap->ctx, first + n <= n_in, goto error);
 134
 135         if (n == 0)
 136                 return bmap;
 137
 138         bmap = isl_basic_map_cow(bmap);
 139         if (!bmap)
 140                 return NULL;
 141
 142         for (i = 0; i < bmap->n_eq; ++i)
 143                 constraint_drop_vars(bmap->eq[i]+1+nparam+first, n,
 144                                  (n_in-first-n)+n_out+bmap->extra);
 145
 146         for (i = 0; i < bmap->n_ineq; ++i)
 147                 constraint_drop_vars(bmap->ineq[i]+1+nparam+first, n,
 148                                  (n_in-first-n)+n_out+bmap->extra);
 149
 150         for (i = 0; i < bmap->n_div; ++i)
 151                 constraint_drop_vars(bmap->div[i]+1+1+nparam+first, n,
 152                                  (n_in-first-n)+n_out+bmap->extra);
 153
 154         bmap->dim = isl_dim_drop_inputs(bmap->dim, first, n);
 155         if (!bmap->dim)
 156                 goto error;
 157
 158         F_CLR(bmap, ISL_BASIC_MAP_NORMALIZED);
 159         bmap = isl_basic_map_simplify(bmap);
 160         return isl_basic_map_finalize(bmap);
 161 error:
 162         isl_basic_map_free(bmap);
 163         return NULL;
 164 }
 165
 166 struct isl_map *isl_map_drop_inputs(
 167                 struct isl_map *map, unsigned first, unsigned n)
 168 {
 169         int i;
 170
 171         if (!map)
 172                 goto error;
 173
 174         isl_assert(map->ctx, first + n <= map->dim->n_in, goto error);
 175
 176         if (n == 0)
 177                 return map;
 178         map = isl_map_cow(map);
 179         if (!map)
 180                 goto error;
 181         map->dim = isl_dim_drop_inputs(map->dim, first, n);
 182         if (!map->dim)
 183                 goto error;
 184
 185         for (i = 0; i < map->n; ++i) {
 186                 map->p[i] = isl_basic_map_drop_inputs(map->p[i], first, n);
 187                 if (!map->p[i])
 188                         goto error;
 189         }
 190         F_CLR(map, ISL_MAP_NORMALIZED);
 191
 192         return map;
 193 error:
 194         isl_map_free(map);
 195         return NULL;
 196 }
 197
 198 /*
 199  * We don't cow, as the div is assumed to be redundant.
 200  */
 201 static struct isl_basic_map *isl_basic_map_drop_div(
 202                 struct isl_basic_map *bmap, unsigned div)
 203 {
 204         int i;
 205         unsigned pos;
 206
 207         if (!bmap)
 208                 goto error;
 209
 210         pos = 1 + isl_dim_total(bmap->dim) + div;
 211
 212         isl_assert(bmap->ctx, div < bmap->n_div, goto error);
 213
 214         for (i = 0; i < bmap->n_eq; ++i)
 215                 constraint_drop_vars(bmap->eq[i]+pos, 1, bmap->extra-div-1);
 216
 217         for (i = 0; i < bmap->n_ineq; ++i) {
 218                 if (!isl_int_is_zero(bmap->ineq[i][pos])) {
 219                         isl_basic_map_drop_inequality(bmap, i);
 220                         --i;
 221                         continue;
 222                 }
 223                 constraint_drop_vars(bmap->ineq[i]+pos, 1, bmap->extra-div-1);
 224         }
 225
 226         for (i = 0; i < bmap->n_div; ++i)
 227                 constraint_drop_vars(bmap->div[i]+1+pos, 1, bmap->extra-div-1);
 228
 229         if (div != bmap->n_div - 1) {
 230                 int j;
 231                 isl_int *t = bmap->div[div];
 232
 233                 for (j = div; j < bmap->n_div - 1; ++j)
 234                         bmap->div[j] = bmap->div[j+1];
 235
 236                 bmap->div[bmap->n_div - 1] = t;
 237         }
 238         F_CLR(bmap, ISL_BASIC_MAP_NORMALIZED);
 239         isl_basic_map_free_div(bmap, 1);
 240
 241         return bmap;
 242 error:
 243         isl_basic_map_free(bmap);
 244         return NULL;
 245 }
 246
 247 static struct isl_basic_map *normalize_constraints(struct isl_basic_map *bmap)
 248 {
 249         int i;
 250         isl_int gcd;
 251         unsigned total = isl_basic_map_total_dim(bmap);
 252
 253         isl_int_init(gcd);
 254         for (i = bmap->n_eq - 1; i >= 0; --i) {
 255                 isl_seq_gcd(bmap->eq[i]+1, total, &gcd);
 256                 if (isl_int_is_zero(gcd)) {
 257                         if (!isl_int_is_zero(bmap->eq[i][0])) {
 258                                 bmap = isl_basic_map_set_to_empty(bmap);
 259                                 break;
 260                         }
 261                         isl_basic_map_drop_equality(bmap, i);
 262                         continue;
 263                 }
 264                 if (F_ISSET(bmap, ISL_BASIC_MAP_RATIONAL))
 265                         isl_int_gcd(gcd, gcd, bmap->eq[i][0]);
 266                 if (isl_int_is_one(gcd))
 267                         continue;
 268                 if (!isl_int_is_divisible_by(bmap->eq[i][0], gcd)) {
 269                         bmap = isl_basic_map_set_to_empty(bmap);
 270                         break;
 271                 }
 272                 isl_seq_scale_down(bmap->eq[i], bmap->eq[i], gcd, 1+total);
 273         }
 274
 275         for (i = bmap->n_ineq - 1; i >= 0; --i) {
 276                 isl_seq_gcd(bmap->ineq[i]+1, total, &gcd);
 277                 if (isl_int_is_zero(gcd)) {
 278                         if (isl_int_is_neg(bmap->ineq[i][0])) {
 279                                 bmap = isl_basic_map_set_to_empty(bmap);
 280                                 break;
 281                         }
 282                         isl_basic_map_drop_inequality(bmap, i);
 283                         continue;
 284                 }
 285                 if (F_ISSET(bmap, ISL_BASIC_MAP_RATIONAL))
 286                         isl_int_gcd(gcd, gcd, bmap->ineq[i][0]);
 287                 if (isl_int_is_one(gcd))
 288                         continue;
 289                 isl_int_fdiv_q(bmap->ineq[i][0], bmap->ineq[i][0], gcd);
 290                 isl_seq_scale_down(bmap->ineq[i]+1, bmap->ineq[i]+1, gcd, total);
 291         }
 292         isl_int_clear(gcd);
 293
 294         return bmap;
 295 }
 296
 297 static void eliminate_div(struct isl_basic_map *bmap, isl_int *eq, unsigned div)
 298 {
 299         int i;
 300         unsigned pos = 1 + isl_dim_total(bmap->dim) + div;
 301         unsigned len;
 302         len = 1 + isl_basic_map_total_dim(bmap);
 303
 304         for (i = 0; i < bmap->n_eq; ++i)
 305                 if (bmap->eq[i] != eq)
 306                         isl_seq_elim(bmap->eq[i], eq, pos, len, NULL);
 307
 308         for (i = 0; i < bmap->n_ineq; ++i)
 309                 isl_seq_elim(bmap->ineq[i], eq, pos, len, NULL);
 310
 311         /* We need to be careful about circular definitions,
 312          * so for now we just remove the definitions of other divs that
 313          * depend on this div and (possibly) recompute them later.
 314          */
 315         for (i = 0; i < bmap->n_div; ++i)
 316                 if (!isl_int_is_zero(bmap->div[i][0]) &&
 317                     !isl_int_is_zero(bmap->div[i][1 + pos]))
 318                         isl_seq_clr(bmap->div[i], 1 + len);
 319
 320         isl_basic_map_drop_div(bmap, div);
 321 }
 322
 323 /* Elimininate divs based on equalities
 324  */
 325 static struct isl_basic_map *eliminate_divs_eq(
 326                 struct isl_basic_map *bmap, int *progress)
 327 {
 328         int d;
 329         int i;
 330         int modified = 0;
 331         unsigned off;
 332
 333         if (!bmap)
 334                 return NULL;
 335
 336         off = 1 + isl_dim_total(bmap->dim);
 337
 338         for (d = bmap->n_div - 1; d >= 0 ; --d) {
 339                 for (i = 0; i < bmap->n_eq; ++i) {
 340                         if (!isl_int_is_one(bmap->eq[i][off + d]) &&
 341                             !isl_int_is_negone(bmap->eq[i][off + d]))
 342                                 continue;
 343                         modified = 1;
 344                         *progress = 1;
 345                         eliminate_div(bmap, bmap->eq[i], d);
 346                         isl_basic_map_drop_equality(bmap, i);
 347                         break;
 348                 }
 349         }
 350         if (modified)
 351                 return eliminate_divs_eq(bmap, progress);
 352         return bmap;
 353 }
 354
 355 /* Elimininate divs based on inequalities
 356  */
 357 static struct isl_basic_map *eliminate_divs_ineq(
 358                 struct isl_basic_map *bmap, int *progress)
 359 {
 360         int d;
 361         int i;
 362         unsigned off;
 363         struct isl_ctx *ctx;
 364
 365         if (!bmap)
 366                 return NULL;
 367
 368         ctx = bmap->ctx;
 369         off = 1 + isl_dim_total(bmap->dim);
 370
 371         for (d = bmap->n_div - 1; d >= 0 ; --d) {
 372                 for (i = 0; i < bmap->n_eq; ++i)
 373                         if (!isl_int_is_zero(bmap->eq[i][off + d]))
 374                                 break;
 375                 if (i < bmap->n_eq)
 376                         continue;
 377                 for (i = 0; i < bmap->n_ineq; ++i)
 378                         if (isl_int_abs_gt(bmap->ineq[i][off + d], ctx->one))
 379                                 break;
 380                 if (i < bmap->n_ineq)
 381                         continue;
 382                 *progress = 1;
 383                 bmap = isl_basic_map_eliminate_vars(bmap, (off-1)+d, 1);
 384                 if (F_ISSET(bmap, ISL_BASIC_MAP_EMPTY))
 385                         break;
 386                 bmap = isl_basic_map_drop_div(bmap, d);
 387                 if (!bmap)
 388                         break;
 389         }
 390         return bmap;
 391 }
 392
 393 static void eliminate_var_using_equality(struct isl_basic_map *bmap,
 394         unsigned pos, isl_int *eq, int *progress)
 395 {
 396         unsigned total;
 397         int k;
 398
 399         total = isl_basic_map_total_dim(bmap);
 400         for (k = 0; k < bmap->n_eq; ++k) {
 401                 if (bmap->eq[k] == eq)
 402                         continue;
 403                 if (isl_int_is_zero(bmap->eq[k][1+pos]))
 404                         continue;
 405                 if (progress)
 406                         *progress = 1;
 407                 isl_seq_elim(bmap->eq[k], eq, 1+pos, 1+total, NULL);
 408         }
 409
 410         for (k = 0; k < bmap->n_ineq; ++k) {
 411                 if (isl_int_is_zero(bmap->ineq[k][1+pos]))
 412                         continue;
 413                 if (progress)
 414                         *progress = 1;
 415                 isl_seq_elim(bmap->ineq[k], eq, 1+pos, 1+total, NULL);
 416                 F_CLR(bmap, ISL_BASIC_MAP_NORMALIZED);
 417         }
 418
 419         for (k = 0; k < bmap->n_div; ++k) {
 420                 if (isl_int_is_zero(bmap->div[k][0]))
 421                         continue;
 422                 if (isl_int_is_zero(bmap->div[k][1+1+pos]))
 423                         continue;
 424                 if (progress)
 425                         *progress = 1;
 426                 isl_seq_elim(bmap->div[k]+1, eq,
 427                                 1+pos, 1+total, &bmap->div[k][0]);
 428                 F_CLR(bmap, ISL_BASIC_MAP_NORMALIZED);
 429         }
 430 }
 431
 432 struct isl_basic_map *isl_basic_map_gauss(
 433         struct isl_basic_map *bmap, int *progress)
 434 {
 435         int k;
 436         int done;
 437         int last_var;
 438         unsigned total_var;
 439         unsigned total;
 440
 441         if (!bmap)
 442                 return NULL;
 443
 444         total = isl_basic_map_total_dim(bmap);
 445         total_var = total - bmap->n_div;
 446
 447         last_var = total - 1;
 448         for (done = 0; done < bmap->n_eq; ++done) {
 449                 for (; last_var >= 0; --last_var) {
 450                         for (k = done; k < bmap->n_eq; ++k)
 451                                 if (!isl_int_is_zero(bmap->eq[k][1+last_var]))
 452                                         break;
 453                         if (k < bmap->n_eq)
 454                                 break;
 455                 }
 456                 if (last_var < 0)
 457                         break;
 458                 if (k != done)
 459                         swap_equality(bmap, k, done);
 460                 if (isl_int_is_neg(bmap->eq[done][1+last_var]))
 461                         isl_seq_neg(bmap->eq[done], bmap->eq[done], 1+total);
 462
 463                 eliminate_var_using_equality(bmap, last_var, bmap->eq[done],
 464                                                 progress);
 465
 466                 if (last_var >= total_var &&
 467                     isl_int_is_zero(bmap->div[last_var - total_var][0])) {
 468                         unsigned div = last_var - total_var;
 469                         isl_seq_neg(bmap->div[div]+1, bmap->eq[done], 1+total);
 470                         isl_int_set_si(bmap->div[div][1+1+last_var], 0);
 471                         isl_int_set(bmap->div[div][0],
 472                                     bmap->eq[done][1+last_var]);
 473                         F_CLR(bmap, ISL_BASIC_MAP_NORMALIZED);
 474                 }
 475         }
 476         if (done == bmap->n_eq)
 477                 return bmap;
 478         for (k = done; k < bmap->n_eq; ++k) {
 479                 if (isl_int_is_zero(bmap->eq[k][0]))
 480                         continue;
 481                 return isl_basic_map_set_to_empty(bmap);
 482         }
 483         isl_basic_map_free_equality(bmap, bmap->n_eq-done);
 484         return bmap;
 485 }
 486
 487 struct isl_basic_set *isl_basic_set_gauss(
 488         struct isl_basic_set *bset, int *progress)
 489 {
 490         return (struct isl_basic_set*)isl_basic_map_gauss(
 491                         (struct isl_basic_map *)bset, progress);
 492 }
 493
 494
 495 static unsigned int round_up(unsigned int v)
 496 {
 497         int old_v = v;
 498
 499         while (v) {
 500                 old_v = v;
 501                 v ^= v & -v;
 502         }
 503         return old_v << 1;
 504 }
 505
 506 static int hash_index(isl_int ***index, unsigned int size, int bits,
 507                         struct isl_basic_map *bmap, int k)
 508 {
 509         int h;
 510         unsigned total = isl_basic_map_total_dim(bmap);
 511         uint32_t hash = isl_seq_get_hash_bits(bmap->ineq[k]+1, total, bits);
 512         for (h = hash; index[h]; h = (h+1) % size)
 513                 if (&bmap->ineq[k] != index[h] &&
 514                     isl_seq_eq(bmap->ineq[k]+1, index[h][0]+1, total))
 515                         break;
 516         return h;
 517 }
 518
 519 static int set_hash_index(isl_int ***index, unsigned int size, int bits,
 520                           struct isl_basic_set *bset, int k)
 521 {
 522         return hash_index(index, size, bits, (struct isl_basic_map *)bset, k);
 523 }
 524
 525 static struct isl_basic_map *remove_duplicate_divs(
 526         struct isl_basic_map *bmap, int *progress)
 527 {
 528         unsigned int size;
 529         int *index;
 530         int k, l, h;
 531         int bits;
 532         struct isl_blk eq;
 533         unsigned total_var = isl_dim_total(bmap->dim);
 534         unsigned total = total_var + bmap->n_div;
 535         struct isl_ctx *ctx;
 536
 537         if (bmap->n_div <= 1)
 538                 return bmap;
 539
 540         ctx = bmap->ctx;
 541         for (k = bmap->n_div - 1; k >= 0; --k)
 542                 if (!isl_int_is_zero(bmap->div[k][0]))
 543                         break;
 544         if (k <= 0)
 545                 return bmap;
 546
 547         size = round_up(4 * bmap->n_div / 3 - 1);
 548         bits = ffs(size) - 1;
 549         index = isl_calloc_array(ctx, int, size);
 550         if (!index)
 551                 return bmap;
 552         eq = isl_blk_alloc(ctx, 1+total);
 553         if (isl_blk_is_error(eq))
 554                 goto out;
 555
 556         isl_seq_clr(eq.data, 1+total);
 557         index[isl_seq_get_hash_bits(bmap->div[k], 2+total, bits)] = k + 1;
 558         for (--k; k >= 0; --k) {
 559                 uint32_t hash;
 560
 561                 if (isl_int_is_zero(bmap->div[k][0]))
 562                         continue;
 563
 564                 hash = isl_seq_get_hash_bits(bmap->div[k], 2+total, bits);
 565                 for (h = hash; index[h]; h = (h+1) % size)
 566                         if (isl_seq_eq(bmap->div[k],
 567                                        bmap->div[index[h]-1], 2+total))
 568                                 break;
 569                 if (index[h]) {
 570                         *progress = 1;
 571                         l = index[h] - 1;
 572                         isl_int_set_si(eq.data[1+total_var+k], -1);
 573                         isl_int_set_si(eq.data[1+total_var+l], 1);
 574                         eliminate_div(bmap, eq.data, l);
 575                         isl_int_set_si(eq.data[1+total_var+k], 0);
 576                         isl_int_set_si(eq.data[1+total_var+l], 0);
 577                 }
 578                 index[h] = k+1;
 579         }
 580
 581         isl_blk_free(ctx, eq);
 582 out:
 583         free(index);
 584         return bmap;
 585 }
 586
 587 /* Normalize divs that appear in equalities.
 588  *
 589  * In particular, we assume that bmap contains some equalities
 590  * of the form
 591  *
 592  *      a x = m * e_i
 593  *
 594  * and we want to replace the set of e_i by a minimal set and
 595  * such that the new e_i have a canonical representation in terms
 596  * of the vector x.
 597  * If any of the equalities involves more than one divs, then
 598  * we currently simply bail out.
 599  *
 600  * Let us first additionally assume that all equalities involve
 601  * a div.  The equalities then express modulo constraints on the
 602  * remaining variables and we can use "parameter compression"
 603  * to find a minimal set of constraints.  The result is a transformation
 604  *
 605  *      x = T(x') = x_0 + G x'
 606  *
 607  * with G a lower-triangular matrix with all elements below the diagonal
 608  * non-negative and smaller than the diagonal element on the same row.
 609  * We first normalize x_0 by making the same property hold in the affine
 610  * T matrix.
 611  * The rows i of G with a 1 on the diagonal do not impose any modulo
 612  * constraint and simply express x_i = x'_i.
 613  * For each of the remaining rows i, we introduce a div and a corresponding
 614  * equality.  In particular
 615  *
 616  *      g_ii e_j = x_i - g_i(x')
 617  *
 618  * where each x'_k is replaced either by x_k (if g_kk = 1) or the
 619  * corresponding div (if g_kk != 1).
 620  *
 621  * If there are any equalities not involving any div, then we
 622  * first apply a variable compression on the variables x:
 623  *
 624  *      x = C x''       x'' = C_2 x
 625  *
 626  * and perform the above parameter compression on A C instead of on A.
 627  * The resulting compression is then of the form
 628  *
 629  *      x'' = T(x') = x_0 + G x'
 630  *
 631  * and in constructing the new divs and the corresponding equalities,
 632  * we have to replace each x'' by the corresponding row from C_2.
 633  */
 634 static struct isl_basic_map *normalize_divs(
 635         struct isl_basic_map *bmap, int *progress)
 636 {
 637         int i, j, k;
 638         int total;
 639         int div_eq;
 640         struct isl_mat *B;
 641         struct isl_vec *d;
 642         struct isl_mat *T = NULL;
 643         struct isl_mat *C = NULL;
 644         struct isl_mat *C2 = NULL;
 645         isl_int v;
 646         int *pos;
 647         int dropped, needed;
 648
 649         if (!bmap)
 650                 return NULL;
 651
 652         if (bmap->n_div == 0)
 653                 return bmap;
 654
 655         if (bmap->n_eq == 0)
 656                 return bmap;
 657
 658         if (F_ISSET(bmap, ISL_BASIC_MAP_NORMALIZED_DIVS))
 659                 return bmap;
 660
 661         total = isl_dim_total(bmap->dim);
 662         for (i = 0, j = bmap->n_div-1; i < bmap->n_eq; ++i) {
 663                 while (j >= 0 && isl_int_is_zero(bmap->eq[i][1 + total + j]))
 664                         --j;
 665                 if (j < 0)
 666                         break;
 667                 if (isl_seq_first_non_zero(bmap->eq[i] + 1 + total, j) != -1)
 668                         goto done;
 669         }
 670         div_eq = i;
 671         if (div_eq == 0)
 672                 return bmap;
 673
 674         if (div_eq < bmap->n_eq) {
 675                 B = isl_mat_sub_alloc(bmap->ctx, bmap->eq, div_eq,
 676                                         bmap->n_eq - div_eq, 0, 1 + total);
 677                 C = isl_mat_variable_compression(bmap->ctx, B, &C2);
 678                 if (!C || !C2)
 679                         goto error;
 680                 if (C->n_col == 0) {
 681                         bmap = isl_basic_map_set_to_empty(bmap);
 682                         isl_mat_free(bmap->ctx, C);
 683                         isl_mat_free(bmap->ctx, C2);
 684                         goto done;
 685                 }
 686         }
 687
 688         d = isl_vec_alloc(bmap->ctx, div_eq);
 689         if (!d)
 690                 goto error;
 691         for (i = 0, j = bmap->n_div-1; i < div_eq; ++i) {
 692                 while (j >= 0 && isl_int_is_zero(bmap->eq[i][1 + total + j]))
 693                         --j;
 694                 isl_int_set(d->block.data[i], bmap->eq[i][1 + total + j]);
 695         }
 696         B = isl_mat_sub_alloc(bmap->ctx, bmap->eq, 0, div_eq, 0, 1 + total);
 697
 698         if (C) {
 699                 B = isl_mat_product(bmap->ctx, B, C);
 700                 C = NULL;
 701         }
 702
 703         T = isl_mat_parameter_compression(bmap->ctx, B, d);
 704         if (!T)
 705                 goto error;
 706         if (T->n_col == 0) {
 707                 bmap = isl_basic_map_set_to_empty(bmap);
 708                 isl_mat_free(bmap->ctx, C2);
 709                 isl_mat_free(bmap->ctx, T);
 710                 goto done;
 711         }
 712         isl_int_init(v);
 713         for (i = 0; i < T->n_row - 1; ++i) {
 714                 isl_int_fdiv_q(v, T->row[1 + i][0], T->row[1 + i][1 + i]);
 715                 if (isl_int_is_zero(v))
 716                         continue;
 717                 isl_mat_col_submul(T, 0, v, 1 + i);
 718         }
 719         isl_int_clear(v);
 720         pos = isl_alloc_array(bmap->ctx, int, T->n_row);
 721         /* We have to be careful because dropping equalities may reorder them */
 722         dropped = 0;
 723         for (j = bmap->n_div - 1; j >= 0; --j) {
 724                 for (i = 0; i < bmap->n_eq; ++i)
 725                         if (!isl_int_is_zero(bmap->eq[i][1 + total + j]))
 726                                 break;
 727                 if (i < bmap->n_eq) {
 728                         bmap = isl_basic_map_drop_div(bmap, j);
 729                         isl_basic_map_drop_equality(bmap, i);
 730                         ++dropped;
 731                 }
 732         }
 733         pos[0] = 0;
 734         needed = 0;
 735         for (i = 1; i < T->n_row; ++i) {
 736                 if (isl_int_is_one(T->row[i][i]))
 737                         pos[i] = i;
 738                 else
 739                         needed++;
 740         }
 741         if (needed > dropped) {
 742                 bmap = isl_basic_map_extend_dim(bmap, isl_dim_copy(bmap->dim),
 743                                 needed, needed, 0);
 744                 if (!bmap)
 745                         goto error;
 746         }
 747         for (i = 1; i < T->n_row; ++i) {
 748                 if (isl_int_is_one(T->row[i][i]))
 749                         continue;
 750                 k = isl_basic_map_alloc_div(bmap);
 751                 pos[i] = 1 + total + k;
 752                 isl_seq_clr(bmap->div[k] + 1, 1 + total + bmap->n_div);
 753                 isl_int_set(bmap->div[k][0], T->row[i][i]);
 754                 if (C2)
 755                         isl_seq_cpy(bmap->div[k] + 1, C2->row[i], 1 + total);
 756                 else
 757                         isl_int_set_si(bmap->div[k][1 + i], 1);
 758                 for (j = 0; j < i; ++j) {
 759                         if (isl_int_is_zero(T->row[i][j]))
 760                                 continue;
 761                         if (C2)
 762                                 isl_seq_submul(bmap->div[k] + 1, T->row[i][j],
 763                                                 C2->row[pos[j]], 1 + total);
 764                         else
 765                                 isl_int_neg(bmap->div[k][1 + pos[j]],
 766                                                                 T->row[i][j]);
 767                 }
 768                 j = isl_basic_map_alloc_equality(bmap);
 769                 isl_seq_neg(bmap->eq[j], bmap->div[k]+1, 1+total+bmap->n_div);
 770                 isl_int_set(bmap->eq[j][pos[i]], bmap->div[k][0]);
 771         }
 772         free(pos);
 773         isl_mat_free(bmap->ctx, C2);
 774         isl_mat_free(bmap->ctx, T);
 775
 776         *progress = 1;
 777 done:
 778         F_SET(bmap, ISL_BASIC_MAP_NORMALIZED_DIVS);
 779
 780         return bmap;
 781 error:
 782         isl_mat_free(bmap->ctx, C);
 783         isl_mat_free(bmap->ctx, C2);
 784         isl_mat_free(bmap->ctx, T);
 785         return bmap;
 786 }
 787
 788 static struct isl_basic_map *remove_duplicate_constraints(
 789         struct isl_basic_map *bmap, int *progress)
 790 {
 791         unsigned int size;
 792         isl_int ***index;
 793         int k, l, h;
 794         int bits;
 795         unsigned total = isl_basic_map_total_dim(bmap);
 796         isl_int sum;
 797
 798         if (bmap->n_ineq <= 1)
 799                 return bmap;
 800
 801         size = round_up(4 * (bmap->n_ineq+1) / 3 - 1);
 802         bits = ffs(size) - 1;
 803         index = isl_calloc_array(ctx, isl_int **, size);
 804         if (!index)
 805                 return bmap;
 806
 807         index[isl_seq_get_hash_bits(bmap->ineq[0]+1, total, bits)] = &bmap->ineq[0];
 808         for (k = 1; k < bmap->n_ineq; ++k) {
 809                 h = hash_index(index, size, bits, bmap, k);
 810                 if (!index[h]) {
 811                         index[h] = &bmap->ineq[k];
 812                         continue;
 813                 }
 814                 if (progress)
 815                         *progress = 1;
 816                 l = index[h] - &bmap->ineq[0];
 817                 if (isl_int_lt(bmap->ineq[k][0], bmap->ineq[l][0]))
 818                         swap_inequality(bmap, k, l);
 819                 isl_basic_map_drop_inequality(bmap, k);
 820                 --k;
 821         }
 822         isl_int_init(sum);
 823         for (k = 0; k < bmap->n_ineq-1; ++k) {
 824                 isl_seq_neg(bmap->ineq[k]+1, bmap->ineq[k]+1, total);
 825                 h = hash_index(index, size, bits, bmap, k);
 826                 isl_seq_neg(bmap->ineq[k]+1, bmap->ineq[k]+1, total);
 827                 if (!index[h])
 828                         continue;
 829                 l = index[h] - &bmap->ineq[0];
 830                 isl_int_add(sum, bmap->ineq[k][0], bmap->ineq[l][0]);
 831                 if (isl_int_is_pos(sum))
 832                         continue;
 833                 if (isl_int_is_zero(sum)) {
 834                         /* We need to break out of the loop after these
 835                          * changes since the contents of the hash
 836                          * will no longer be valid.
 837                          * Plus, we probably we want to regauss first.
 838                          */
 839                         isl_basic_map_drop_inequality(bmap, l);
 840                         isl_basic_map_inequality_to_equality(bmap, k);
 841                 } else
 842                         bmap = isl_basic_map_set_to_empty(bmap);
 843                 break;
 844         }
 845         isl_int_clear(sum);
 846
 847         free(index);
 848         return bmap;
 849 }
 850
 851
 852 struct isl_basic_map *isl_basic_map_simplify(struct isl_basic_map *bmap)
 853 {
 854         int progress = 1;
 855         if (!bmap)
 856                 return NULL;
 857         while (progress) {
 858                 progress = 0;
 859                 bmap = normalize_constraints(bmap);
 860                 bmap = eliminate_divs_eq(bmap, &progress);
 861                 bmap = eliminate_divs_ineq(bmap, &progress);
 862                 bmap = isl_basic_map_gauss(bmap, &progress);
 863                 /* requires equalities in normal form */
 864                 bmap = normalize_divs(bmap, &progress);
 865                 bmap = remove_duplicate_divs(bmap, &progress);
 866                 bmap = remove_duplicate_constraints(bmap, &progress);
 867         }
 868         return bmap;
 869 }
 870
 871 struct isl_basic_set *isl_basic_set_simplify(struct isl_basic_set *bset)
 872 {
 873         return (struct isl_basic_set *)
 874                 isl_basic_map_simplify((struct isl_basic_map *)bset);
 875 }
 876
 877
 878 /* If the only constraints a div d=floor(f/m)
 879  * appears in are its two defining constraints
 880  *
 881  *      f - m d >=0
 882  *      -(f - (m - 1)) + m d >= 0
 883  *
 884  * then it can safely be removed.
 885  */
 886 static int div_is_redundant(struct isl_basic_map *bmap, int div)
 887 {
 888         int i;
 889         unsigned pos = 1 + isl_dim_total(bmap->dim) + div;
 890
 891         for (i = 0; i < bmap->n_eq; ++i)
 892                 if (!isl_int_is_zero(bmap->eq[i][pos]))
 893                         return 0;
 894
 895         for (i = 0; i < bmap->n_ineq; ++i) {
 896                 if (isl_int_is_zero(bmap->ineq[i][pos]))
 897                         continue;
 898                 if (isl_int_eq(bmap->ineq[i][pos], bmap->div[div][0])) {
 899                         int neg;
 900                         isl_int_sub(bmap->div[div][1],
 901                                         bmap->div[div][1], bmap->div[div][0]);
 902                         isl_int_add_ui(bmap->div[div][1], bmap->div[div][1], 1);
 903                         neg = isl_seq_is_neg(bmap->ineq[i], bmap->div[div]+1, pos);
 904                         isl_int_sub_ui(bmap->div[div][1], bmap->div[div][1], 1);
 905                         isl_int_add(bmap->div[div][1],
 906                                         bmap->div[div][1], bmap->div[div][0]);
 907                         if (!neg)
 908                                 return 0;
 909                         if (isl_seq_first_non_zero(bmap->ineq[i]+pos+1,
 910                                                     bmap->n_div-div-1) != -1)
 911                                 return 0;
 912                 } else if (isl_int_abs_eq(bmap->ineq[i][pos], bmap->div[div][0])) {
 913                         if (!isl_seq_eq(bmap->ineq[i], bmap->div[div]+1, pos))
 914                                 return 0;
 915                         if (isl_seq_first_non_zero(bmap->ineq[i]+pos+1,
 916                                                     bmap->n_div-div-1) != -1)
 917                                 return 0;
 918                 } else
 919                         return 0;
 920         }
 921
 922         for (i = 0; i < bmap->n_div; ++i)
 923                 if (!isl_int_is_zero(bmap->div[i][1+pos]))
 924                         return 0;
 925
 926         return 1;
 927 }
 928
 929 /*
 930  * Remove divs that don't occur in any of the constraints or other divs.
 931  * These can arise when dropping some of the variables in a quast
 932  * returned by piplib.
 933  */
 934 static struct isl_basic_map *remove_redundant_divs(struct isl_basic_map *bmap)
 935 {
 936         int i;
 937
 938         if (!bmap)
 939                 return NULL;
 940
 941         for (i = bmap->n_div-1; i >= 0; --i) {
 942                 if (!div_is_redundant(bmap, i))
 943                         continue;
 944                 bmap = isl_basic_map_drop_div(bmap, i);
 945         }
 946         return bmap;
 947 }
 948
 949 struct isl_basic_map *isl_basic_map_finalize(struct isl_basic_map *bmap)
 950 {
 951         bmap = remove_redundant_divs(bmap);
 952         if (!bmap)
 953                 return NULL;
 954         F_SET(bmap, ISL_BASIC_SET_FINAL);
 955         return bmap;
 956 }
 957
 958 struct isl_basic_set *isl_basic_set_finalize(struct isl_basic_set *bset)
 959 {
 960         return (struct isl_basic_set *)
 961                 isl_basic_map_finalize((struct isl_basic_map *)bset);
 962 }
 963
 964 struct isl_set *isl_set_finalize(struct isl_set *set)
 965 {
 966         int i;
 967
 968         if (!set)
 969                 return NULL;
 970         for (i = 0; i < set->n; ++i) {
 971                 set->p[i] = isl_basic_set_finalize(set->p[i]);
 972                 if (!set->p[i])
 973                         goto error;
 974         }
 975         return set;
 976 error:
 977         isl_set_free(set);
 978         return NULL;
 979 }
 980
 981 struct isl_map *isl_map_finalize(struct isl_map *map)
 982 {
 983         int i;
 984
 985         if (!map)
 986                 return NULL;
 987         for (i = 0; i < map->n; ++i) {
 988                 map->p[i] = isl_basic_map_finalize(map->p[i]);
 989                 if (!map->p[i])
 990                         goto error;
 991         }
 992         F_CLR(map, ISL_MAP_NORMALIZED);
 993         return map;
 994 error:
 995         isl_map_free(map);
 996         return NULL;
 997 }
 998
 999
1000 /* Remove any div that is defined in terms of the given variable.
1001  */
1002 static struct isl_basic_map *remove_dependent_vars(struct isl_basic_map *bmap,
1003                                                                         int pos)
1004 {
1005         int i;
1006         unsigned dim = isl_dim_total(bmap->dim);
1007
1008         for (i = 0; i < bmap->n_div; ++i) {
1009                 if (isl_int_is_zero(bmap->div[i][0]))
1010                         continue;
1011                 if (isl_int_is_zero(bmap->div[i][1+1+pos]))
1012                         continue;
1013                 bmap = isl_basic_map_eliminate_vars(bmap, dim + i, 1);
1014                 if (!bmap)
1015                         return NULL;
1016         }
1017         return bmap;
1018 }
1019
1020 /* Eliminate the specified variables from the constraints using
1021  * Fourier-Motzkin.  The variables themselves are not removed.
1022  */
1023 struct isl_basic_map *isl_basic_map_eliminate_vars(
1024         struct isl_basic_map *bmap, unsigned pos, unsigned n)
1025 {
1026         int d;
1027         int i, j, k;
1028         unsigned total;
1029
1030         if (n == 0)
1031                 return bmap;
1032         if (!bmap)
1033                 return NULL;
1034         total = isl_basic_map_total_dim(bmap);
1035
1036         bmap = isl_basic_map_cow(bmap);
1037         for (d = pos + n - 1; d >= 0 && d >= pos; --d) {
1038                 int n_lower, n_upper;
1039                 bmap = remove_dependent_vars(bmap, d);
1040                 if (!bmap)
1041                         return NULL;
1042                 if (d >= total - bmap->n_div)
1043                         isl_seq_clr(bmap->div[d-(total-bmap->n_div)], 2+total);
1044                 for (i = 0; i < bmap->n_eq; ++i) {
1045                         if (isl_int_is_zero(bmap->eq[i][1+d]))
1046                                 continue;
1047                         eliminate_var_using_equality(bmap, d, bmap->eq[i], NULL);
1048                         isl_basic_map_drop_equality(bmap, i);
1049                         break;
1050                 }
1051                 if (i < bmap->n_eq)
1052                         continue;
1053                 n_lower = 0;
1054                 n_upper = 0;
1055                 for (i = 0; i < bmap->n_ineq; ++i) {
1056                         if (isl_int_is_pos(bmap->ineq[i][1+d]))
1057                                 n_lower++;
1058                         else if (isl_int_is_neg(bmap->ineq[i][1+d]))
1059                                 n_upper++;
1060                 }
1061                 bmap = isl_basic_map_extend_constraints(bmap,
1062                                 0, n_lower * n_upper);
1063                 for (i = bmap->n_ineq - 1; i >= 0; --i) {
1064                         int last;
1065                         if (isl_int_is_zero(bmap->ineq[i][1+d]))
1066                                 continue;
1067                         last = -1;
1068                         for (j = 0; j < i; ++j) {
1069                                 if (isl_int_is_zero(bmap->ineq[j][1+d]))
1070                                         continue;
1071                                 last = j;
1072                                 if (isl_int_sgn(bmap->ineq[i][1+d]) ==
1073                                     isl_int_sgn(bmap->ineq[j][1+d]))
1074                                         continue;
1075                                 k = isl_basic_map_alloc_inequality(bmap);
1076                                 if (k < 0)
1077                                         goto error;
1078                                 isl_seq_cpy(bmap->ineq[k], bmap->ineq[i],
1079                                                 1+total);
1080                                 isl_seq_elim(bmap->ineq[k], bmap->ineq[j],
1081                                                 1+d, 1+total, NULL);
1082                         }
1083                         isl_basic_map_drop_inequality(bmap, i);
1084                         i = last + 1;
1085                 }
1086                 if (n_lower > 0 && n_upper > 0) {
1087                         bmap = normalize_constraints(bmap);
1088                         bmap = remove_duplicate_constraints(bmap, NULL);
1089                         bmap = isl_basic_map_gauss(bmap, NULL);
1090                         bmap = isl_basic_map_convex_hull(bmap);
1091                         if (!bmap)
1092                                 goto error;
1093                         if (F_ISSET(bmap, ISL_BASIC_MAP_EMPTY))
1094                                 break;
1095                 }
1096         }
1097         F_CLR(bmap, ISL_BASIC_MAP_NORMALIZED);
1098         return bmap;
1099 error:
1100         isl_basic_map_free(bmap);
1101         return NULL;
1102 }
1103
1104 struct isl_basic_set *isl_basic_set_eliminate_vars(
1105         struct isl_basic_set *bset, unsigned pos, unsigned n)
1106 {
1107         return (struct isl_basic_set *)isl_basic_map_eliminate_vars(
1108                         (struct isl_basic_map *)bset, pos, n);
1109 }
1110
1111 static void compute_elimination_index(struct isl_basic_map *bmap, int *elim)
1112 {
1113         int d, i;
1114         unsigned total;
1115
1116         total = isl_dim_total(bmap->dim);
1117         for (d = 0; d < total; ++d)
1118                 elim[d] = -1;
1119         for (d = total - 1, i = 0; d >= 0 && i < bmap->n_eq; ++i) {
1120                 for (; d >= 0; --d) {
1121                         if (isl_int_is_zero(bmap->eq[i][1+d]))
1122                                 continue;
1123                         elim[d] = i;
1124                         break;
1125                 }
1126         }
1127 }
1128
1129 static void set_compute_elimination_index(struct isl_basic_set *bset, int *elim)
1130 {
1131         return compute_elimination_index((struct isl_basic_map *)bset, elim);
1132 }
1133
1134 static int reduced_using_equalities(isl_int *dst, isl_int *src,
1135         struct isl_basic_map *bmap, int *elim)
1136 {
1137         int d, i;
1138         int copied = 0;
1139         unsigned total;
1140
1141         total = isl_dim_total(bmap->dim);
1142         for (d = total - 1; d >= 0; --d) {
1143                 if (isl_int_is_zero(src[1+d]))
1144                         continue;
1145                 if (elim[d] == -1)
1146                         continue;
1147                 if (!copied) {
1148                         isl_seq_cpy(dst, src, 1 + total);
1149                         copied = 1;
1150                 }
1151                 isl_seq_elim(dst, bmap->eq[elim[d]], 1 + d, 1 + total, NULL);
1152         }
1153         return copied;
1154 }
1155
1156 static int set_reduced_using_equalities(isl_int *dst, isl_int *src,
1157         struct isl_basic_set *bset, int *elim)
1158 {
1159         return reduced_using_equalities(dst, src,
1160                                         (struct isl_basic_map *)bset, elim);
1161 }
1162
1163 static struct isl_basic_set *isl_basic_set_reduce_using_equalities(
1164         struct isl_basic_set *bset, struct isl_basic_set *context)
1165 {
1166         int i;
1167         int *elim;
1168
1169         if (!bset || !context)
1170                 goto error;
1171
1172         bset = isl_basic_set_cow(bset);
1173         if (!bset)
1174                 goto error;
1175
1176         elim = isl_alloc_array(ctx, int, isl_basic_set_n_dim(bset));
1177         if (!elim)
1178                 goto error;
1179         set_compute_elimination_index(context, elim);
1180         for (i = 0; i < bset->n_eq; ++i)
1181                 set_reduced_using_equalities(bset->eq[i], bset->eq[i],
1182                                                         context, elim);
1183         for (i = 0; i < bset->n_ineq; ++i)
1184                 set_reduced_using_equalities(bset->ineq[i], bset->ineq[i],
1185                                                         context, elim);
1186         isl_basic_set_free(context);
1187         free(elim);
1188         bset = isl_basic_set_simplify(bset);
1189         bset = isl_basic_set_finalize(bset);
1190         return bset;
1191 error:
1192         isl_basic_set_free(bset);
1193         isl_basic_set_free(context);
1194         return NULL;
1195 }
1196
1197 static struct isl_basic_set *remove_shifted_constraints(
1198         struct isl_basic_set *bset, struct isl_basic_set *context)
1199 {
1200         unsigned int size;
1201         isl_int ***index;
1202         int bits;
1203         int k, h, l;
1204
1205         if (!bset)
1206                 return NULL;
1207
1208         size = round_up(4 * (context->n_ineq+1) / 3 - 1);
1209         bits = ffs(size) - 1;
1210         index = isl_calloc_array(ctx, isl_int **, size);
1211         if (!index)
1212                 return bset;
1213
1214         for (k = 0; k < context->n_ineq; ++k) {
1215                 h = set_hash_index(index, size, bits, context, k);
1216                 index[h] = &context->ineq[k];
1217         }
1218         for (k = 0; k < bset->n_ineq; ++k) {
1219                 h = set_hash_index(index, size, bits, bset, k);
1220                 if (!index[h])
1221                         continue;
1222                 l = index[h] - &context->ineq[0];
1223                 if (isl_int_lt(bset->ineq[k][0], context->ineq[l][0]))
1224                         continue;
1225                 bset = isl_basic_set_cow(bset);
1226                 if (!bset)
1227                         goto error;
1228                 isl_basic_set_drop_inequality(bset, k);
1229                 --k;
1230         }
1231         free(index);
1232         return bset;
1233 error:
1234         free(index);
1235         return bset;
1236 }
1237
1238 static struct isl_basic_set *uset_gist(struct isl_basic_set *bset,
1239         struct isl_basic_set *context);
1240
1241 static struct isl_basic_set *uset_gist_context_eq(struct isl_basic_set *bset,
1242         struct isl_basic_set *context)
1243 {
1244         struct isl_mat *T;
1245         struct isl_mat *T2;
1246         struct isl_ctx *ctx = context->ctx;
1247         struct isl_basic_set *reduced_context;
1248         reduced_context = isl_basic_set_remove_equalities(
1249                                 isl_basic_set_copy(context), &T, &T2);
1250         if (!reduced_context)
1251                 goto error;
1252         bset = isl_basic_set_preimage(ctx, bset, T);
1253         bset = uset_gist(bset, reduced_context);
1254         bset = isl_basic_set_preimage(ctx, bset, T2);
1255         bset = isl_basic_set_reduce_using_equalities(bset, context);
1256         return bset;
1257 error:
1258         isl_basic_set_free(context);
1259         isl_basic_set_free(bset);
1260         return NULL;
1261 }
1262
1263 static struct isl_basic_set *uset_gist_set_eq(struct isl_basic_set *bset,
1264         struct isl_basic_set *context)
1265 {
1266         struct isl_mat *T;
1267         struct isl_mat *T2;
1268         struct isl_ctx *ctx = context->ctx;
1269         struct isl_basic_set *affine_hull = NULL;
1270
1271         affine_hull = isl_basic_set_copy(bset);
1272         affine_hull = isl_basic_set_cow(affine_hull);
1273         if (!affine_hull)
1274                 goto error;
1275         isl_basic_set_free_inequality(affine_hull, affine_hull->n_ineq);
1276
1277         bset = isl_basic_set_remove_equalities(bset, &T, &T2);
1278         if (!bset)
1279                 goto error;
1280         context = isl_basic_set_preimage(ctx, context, T);
1281         bset = uset_gist(bset, context);
1282         bset = isl_basic_set_preimage(ctx, bset, T2);
1283         bset = isl_basic_set_intersect(bset, affine_hull);
1284         return bset;
1285 error:
1286         isl_basic_set_free(affine_hull);
1287         isl_basic_set_free(context);
1288         isl_basic_set_free(bset);
1289         return NULL;
1290 }
1291
1292 /* Remove all information from bset that is redundant in the context
1293  * of context.  In particular, equalities that are linear combinations
1294  * of those in context are removed.  Then the inequalities that are
1295  * redundant in the context of the equalities and inequalities of
1296  * context are removed.
1297  */
1298 static struct isl_basic_set *uset_gist(struct isl_basic_set *bset,
1299         struct isl_basic_set *context)
1300 {
1301         int i;
1302         isl_int opt;
1303         struct isl_basic_set *combined;
1304         struct isl_ctx *ctx;
1305
1306         if (!bset || !context)
1307                 goto error;
1308
1309         if (context->n_eq > 0)
1310                 return uset_gist_context_eq(bset, context);
1311         if (!context->n_ineq)
1312                 goto done;
1313         if (bset->n_eq > 0)
1314                 return uset_gist_set_eq(bset, context);
1315         bset = remove_shifted_constraints(bset, context);
1316         combined = isl_basic_set_extend_constraints(isl_basic_set_copy(bset),
1317                         context->n_eq, context->n_ineq);
1318         context = isl_basic_set_add_constraints(combined, context, 0);
1319         if (!context)
1320                 goto error;
1321         ctx = context->ctx;
1322         isl_int_init(opt);
1323         for (i = bset->n_ineq-1; i >= 0; --i) {
1324                 int redundant;
1325                 set_swap_inequality(context, i, context->n_ineq-1);
1326                 context->n_ineq--;
1327                 redundant = isl_basic_set_constraint_is_redundant(&context,
1328                                 context->ineq[context->n_ineq], &opt, NULL);
1329                 if (redundant == -1) {
1330                         isl_int_clear(opt);
1331                         goto error;
1332                 }
1333                 if (F_ISSET(context, ISL_BASIC_MAP_EMPTY)) {
1334                         bset = isl_basic_set_set_to_empty(bset);
1335                         break;
1336                 }
1337                 context->n_ineq++;
1338                 set_swap_inequality(context, i, context->n_ineq-1);
1339                 if (redundant) {
1340                         isl_basic_set_drop_inequality(context, i);
1341                         isl_basic_set_drop_inequality(bset, i);
1342                 }
1343         }
1344         isl_int_clear(opt);
1345 done:
1346         isl_basic_set_free(context);
1347         return bset;
1348 error:
1349         isl_basic_set_free(context);
1350         isl_basic_set_free(bset);
1351         return NULL;
1352 }
1353
1354 struct isl_basic_map *isl_basic_map_gist(struct isl_basic_map *bmap,
1355         struct isl_basic_map *context)
1356 {
1357         struct isl_basic_set *bset;
1358
1359         if (!bmap || !context)
1360                 goto error;
1361
1362         context = isl_basic_map_align_divs(context, bmap);
1363         bmap = isl_basic_map_align_divs(bmap, context);
1364
1365         bset = uset_gist(isl_basic_map_underlying_set(isl_basic_map_copy(bmap)),
1366                          isl_basic_map_underlying_set(context));
1367
1368         return isl_basic_map_overlying_set(bset, bmap);
1369 error:
1370         isl_basic_map_free(bmap);
1371         isl_basic_map_free(context);
1372         return NULL;
1373 }
1374
1375 /*
1376  * Assumes context has no implicit divs.
1377  */
1378 struct isl_map *isl_map_gist(struct isl_map *map, struct isl_basic_map *context)
1379 {
1380         int i;
1381
1382         map = isl_map_cow(map);
1383         if (!map || !context)
1384                 return NULL;
1385         isl_assert(map->ctx, isl_dim_equal(map->dim, context->dim), goto error);
1386         map = isl_map_compute_divs(map);
1387         for (i = 0; i < map->n; ++i)
1388                 context = isl_basic_map_align_divs(context, map->p[i]);
1389         for (i = 0; i < map->n; ++i) {
1390                 map->p[i] = isl_basic_map_gist(map->p[i],
1391                                                 isl_basic_map_copy(context));
1392                 if (!map->p[i])
1393                         goto error;
1394         }
1395         isl_basic_map_free(context);
1396         F_CLR(map, ISL_MAP_NORMALIZED);
1397         return map;
1398 error:
1399         isl_map_free(map);
1400         isl_basic_map_free(context);
1401         return NULL;
1402 }
1403
1404 struct isl_basic_set *isl_basic_set_gist(struct isl_basic_set *bset,
1405                                                 struct isl_basic_set *context)
1406 {
1407         return (struct isl_basic_set *)isl_basic_map_gist(
1408                 (struct isl_basic_map *)bset, (struct isl_basic_map *)context);
1409 }
1410
1411 struct isl_set *isl_set_gist(struct isl_set *set, struct isl_basic_set *context)
1412 {
1413         return (struct isl_set *)isl_map_gist((struct isl_map *)set,
1414                                         (struct isl_basic_map *)context);
1415 }
1416
1417 /* Quick check to see if two basic maps are disjoint.
1418  * In particular, we reduce the equalities and inequalities of
1419  * one basic map in the context of the equalities of the other
1420  * basic map and check if we get a contradiction.
1421  */
1422 int isl_basic_map_fast_is_disjoint(struct isl_basic_map *bmap1,
1423         struct isl_basic_map *bmap2)
1424 {
1425         struct isl_vec *v = NULL;
1426         int *elim = NULL;
1427         unsigned total;
1428         int d, i;
1429
1430         if (!bmap1 || !bmap2)
1431                 return -1;
1432         isl_assert(bmap1->ctx, isl_dim_equal(bmap1->dim, bmap2->dim),
1433                         return -1);
1434         if (bmap1->n_div || bmap2->n_div)
1435                 return 0;
1436         if (!bmap1->n_eq && !bmap2->n_eq)
1437                 return 0;
1438
1439         total = isl_dim_total(bmap1->dim);
1440         if (total == 0)
1441                 return 0;
1442         v = isl_vec_alloc(bmap1->ctx, 1 + total);
1443         if (!v)
1444                 goto error;
1445         elim = isl_alloc_array(bmap1->ctx, int, total);
1446         if (!elim)
1447                 goto error;
1448         compute_elimination_index(bmap1, elim);
1449         for (i = 0; i < bmap2->n_eq; ++i) {
1450                 int reduced;
1451                 reduced = reduced_using_equalities(v->block.data, bmap2->eq[i],
1452                                                         bmap1, elim);
1453                 if (reduced && !isl_int_is_zero(v->block.data[0]) &&
1454                     isl_seq_first_non_zero(v->block.data + 1, total) == -1)
1455                         goto disjoint;
1456         }
1457         for (i = 0; i < bmap2->n_ineq; ++i) {
1458                 int reduced;
1459                 reduced = reduced_using_equalities(v->block.data,
1460                                                 bmap2->ineq[i], bmap1, elim);
1461                 if (reduced && isl_int_is_neg(v->block.data[0]) &&
1462                     isl_seq_first_non_zero(v->block.data + 1, total) == -1)
1463                         goto disjoint;
1464         }
1465         compute_elimination_index(bmap2, elim);
1466         for (i = 0; i < bmap1->n_ineq; ++i) {
1467                 int reduced;
1468                 reduced = reduced_using_equalities(v->block.data,
1469                                                 bmap1->ineq[i], bmap2, elim);
1470                 if (reduced && isl_int_is_neg(v->block.data[0]) &&
1471                     isl_seq_first_non_zero(v->block.data + 1, total) == -1)
1472                         goto disjoint;
1473         }
1474         isl_vec_free(bmap1->ctx, v);
1475         free(elim);
1476         return 0;
1477 disjoint:
1478         isl_vec_free(bmap1->ctx, v);
1479         free(elim);
1480         return 1;
1481 error:
1482         isl_vec_free(bmap1->ctx, v);
1483         free(elim);
1484         return -1;
1485 }
1486
1487 int isl_basic_set_fast_is_disjoint(struct isl_basic_set *bset1,
1488         struct isl_basic_set *bset2)
1489 {
1490         return isl_basic_map_fast_is_disjoint((struct isl_basic_map *)bset1,
1491                                               (struct isl_basic_map *)bset2);
1492 }
1493
1494 int isl_map_fast_is_disjoint(struct isl_map *map1, struct isl_map *map2)
1495 {
1496         int i, j;
1497
1498         if (!map1 || !map2)
1499                 return -1;
1500
1501         if (isl_map_fast_is_equal(map1, map2))
1502                 return 0;
1503
1504         for (i = 0; i < map1->n; ++i) {
1505                 for (j = 0; j < map2->n; ++j) {
1506                         int d = isl_basic_map_fast_is_disjoint(map1->p[i],
1507                                                                map2->p[j]);
1508                         if (d != 1)
1509                                 return d;
1510                 }
1511         }
1512         return 1;
1513 }
1514
1515 int isl_set_fast_is_disjoint(struct isl_set *set1, struct isl_set *set2)
1516 {
1517         return isl_map_fast_is_disjoint((struct isl_map *)set1,
1518                                         (struct isl_map *)set2);
1519 }