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         int contains_divs;
 399
 400         total = isl_basic_map_total_dim(bmap);
 401         contains_divs =
 402                 isl_seq_first_non_zero(eq + 1 + isl_dim_total(bmap->dim),
 403                                                 bmap->n_div) != -1;
 404         for (k = 0; k < bmap->n_eq; ++k) {
 405                 if (bmap->eq[k] == eq)
 406                         continue;
 407                 if (isl_int_is_zero(bmap->eq[k][1+pos]))
 408                         continue;
 409                 if (progress)
 410                         *progress = 1;
 411                 isl_seq_elim(bmap->eq[k], eq, 1+pos, 1+total, NULL);
 412         }
 413
 414         for (k = 0; k < bmap->n_ineq; ++k) {
 415                 if (isl_int_is_zero(bmap->ineq[k][1+pos]))
 416                         continue;
 417                 if (progress)
 418                         *progress = 1;
 419                 isl_seq_elim(bmap->ineq[k], eq, 1+pos, 1+total, NULL);
 420                 F_CLR(bmap, ISL_BASIC_MAP_NORMALIZED);
 421         }
 422
 423         for (k = 0; k < bmap->n_div; ++k) {
 424                 if (isl_int_is_zero(bmap->div[k][0]))
 425                         continue;
 426                 if (isl_int_is_zero(bmap->div[k][1+1+pos]))
 427                         continue;
 428                 if (progress)
 429                         *progress = 1;
 430                 /* We need to be careful about circular definitions,
 431                  * so for now we just remove the definition of div k
 432                  * if the equality contains any divs.
 433                  */
 434                 if (contains_divs)
 435                         isl_seq_clr(bmap->div[k], 1 + total);
 436                 else
 437                         isl_seq_elim(bmap->div[k]+1, eq,
 438                                         1+pos, 1+total, &bmap->div[k][0]);
 439                 F_CLR(bmap, ISL_BASIC_MAP_NORMALIZED);
 440         }
 441 }
 442
 443 struct isl_basic_map *isl_basic_map_gauss(
 444         struct isl_basic_map *bmap, int *progress)
 445 {
 446         int k;
 447         int done;
 448         int last_var;
 449         unsigned total_var;
 450         unsigned total;
 451
 452         if (!bmap)
 453                 return NULL;
 454
 455         total = isl_basic_map_total_dim(bmap);
 456         total_var = total - bmap->n_div;
 457
 458         last_var = total - 1;
 459         for (done = 0; done < bmap->n_eq; ++done) {
 460                 for (; last_var >= 0; --last_var) {
 461                         for (k = done; k < bmap->n_eq; ++k)
 462                                 if (!isl_int_is_zero(bmap->eq[k][1+last_var]))
 463                                         break;
 464                         if (k < bmap->n_eq)
 465                                 break;
 466                 }
 467                 if (last_var < 0)
 468                         break;
 469                 if (k != done)
 470                         swap_equality(bmap, k, done);
 471                 if (isl_int_is_neg(bmap->eq[done][1+last_var]))
 472                         isl_seq_neg(bmap->eq[done], bmap->eq[done], 1+total);
 473
 474                 eliminate_var_using_equality(bmap, last_var, bmap->eq[done],
 475                                                 progress);
 476
 477                 if (last_var >= total_var &&
 478                     isl_int_is_zero(bmap->div[last_var - total_var][0])) {
 479                         unsigned div = last_var - total_var;
 480                         isl_seq_neg(bmap->div[div]+1, bmap->eq[done], 1+total);
 481                         isl_int_set_si(bmap->div[div][1+1+last_var], 0);
 482                         isl_int_set(bmap->div[div][0],
 483                                     bmap->eq[done][1+last_var]);
 484                         F_CLR(bmap, ISL_BASIC_MAP_NORMALIZED);
 485                 }
 486         }
 487         if (done == bmap->n_eq)
 488                 return bmap;
 489         for (k = done; k < bmap->n_eq; ++k) {
 490                 if (isl_int_is_zero(bmap->eq[k][0]))
 491                         continue;
 492                 return isl_basic_map_set_to_empty(bmap);
 493         }
 494         isl_basic_map_free_equality(bmap, bmap->n_eq-done);
 495         return bmap;
 496 }
 497
 498 struct isl_basic_set *isl_basic_set_gauss(
 499         struct isl_basic_set *bset, int *progress)
 500 {
 501         return (struct isl_basic_set*)isl_basic_map_gauss(
 502                         (struct isl_basic_map *)bset, progress);
 503 }
 504
 505
 506 static unsigned int round_up(unsigned int v)
 507 {
 508         int old_v = v;
 509
 510         while (v) {
 511                 old_v = v;
 512                 v ^= v & -v;
 513         }
 514         return old_v << 1;
 515 }
 516
 517 static int hash_index(isl_int ***index, unsigned int size, int bits,
 518                         struct isl_basic_map *bmap, int k)
 519 {
 520         int h;
 521         unsigned total = isl_basic_map_total_dim(bmap);
 522         uint32_t hash = isl_seq_get_hash_bits(bmap->ineq[k]+1, total, bits);
 523         for (h = hash; index[h]; h = (h+1) % size)
 524                 if (&bmap->ineq[k] != index[h] &&
 525                     isl_seq_eq(bmap->ineq[k]+1, index[h][0]+1, total))
 526                         break;
 527         return h;
 528 }
 529
 530 static int set_hash_index(isl_int ***index, unsigned int size, int bits,
 531                           struct isl_basic_set *bset, int k)
 532 {
 533         return hash_index(index, size, bits, (struct isl_basic_map *)bset, k);
 534 }
 535
 536 static struct isl_basic_map *remove_duplicate_divs(
 537         struct isl_basic_map *bmap, int *progress)
 538 {
 539         unsigned int size;
 540         int *index;
 541         int k, l, h;
 542         int bits;
 543         struct isl_blk eq;
 544         unsigned total_var = isl_dim_total(bmap->dim);
 545         unsigned total = total_var + bmap->n_div;
 546         struct isl_ctx *ctx;
 547
 548         if (bmap->n_div <= 1)
 549                 return bmap;
 550
 551         ctx = bmap->ctx;
 552         for (k = bmap->n_div - 1; k >= 0; --k)
 553                 if (!isl_int_is_zero(bmap->div[k][0]))
 554                         break;
 555         if (k <= 0)
 556                 return bmap;
 557
 558         size = round_up(4 * bmap->n_div / 3 - 1);
 559         bits = ffs(size) - 1;
 560         index = isl_calloc_array(ctx, int, size);
 561         if (!index)
 562                 return bmap;
 563         eq = isl_blk_alloc(ctx, 1+total);
 564         if (isl_blk_is_error(eq))
 565                 goto out;
 566
 567         isl_seq_clr(eq.data, 1+total);
 568         index[isl_seq_get_hash_bits(bmap->div[k], 2+total, bits)] = k + 1;
 569         for (--k; k >= 0; --k) {
 570                 uint32_t hash;
 571
 572                 if (isl_int_is_zero(bmap->div[k][0]))
 573                         continue;
 574
 575                 hash = isl_seq_get_hash_bits(bmap->div[k], 2+total, bits);
 576                 for (h = hash; index[h]; h = (h+1) % size)
 577                         if (isl_seq_eq(bmap->div[k],
 578                                        bmap->div[index[h]-1], 2+total))
 579                                 break;
 580                 if (index[h]) {
 581                         *progress = 1;
 582                         l = index[h] - 1;
 583                         isl_int_set_si(eq.data[1+total_var+k], -1);
 584                         isl_int_set_si(eq.data[1+total_var+l], 1);
 585                         eliminate_div(bmap, eq.data, l);
 586                         isl_int_set_si(eq.data[1+total_var+k], 0);
 587                         isl_int_set_si(eq.data[1+total_var+l], 0);
 588                 }
 589                 index[h] = k+1;
 590         }
 591
 592         isl_blk_free(ctx, eq);
 593 out:
 594         free(index);
 595         return bmap;
 596 }
 597
 598 /* Normalize divs that appear in equalities.
 599  *
 600  * In particular, we assume that bmap contains some equalities
 601  * of the form
 602  *
 603  *      a x = m * e_i
 604  *
 605  * and we want to replace the set of e_i by a minimal set and
 606  * such that the new e_i have a canonical representation in terms
 607  * of the vector x.
 608  * If any of the equalities involves more than one divs, then
 609  * we currently simply bail out.
 610  *
 611  * Let us first additionally assume that all equalities involve
 612  * a div.  The equalities then express modulo constraints on the
 613  * remaining variables and we can use "parameter compression"
 614  * to find a minimal set of constraints.  The result is a transformation
 615  *
 616  *      x = T(x') = x_0 + G x'
 617  *
 618  * with G a lower-triangular matrix with all elements below the diagonal
 619  * non-negative and smaller than the diagonal element on the same row.
 620  * We first normalize x_0 by making the same property hold in the affine
 621  * T matrix.
 622  * The rows i of G with a 1 on the diagonal do not impose any modulo
 623  * constraint and simply express x_i = x'_i.
 624  * For each of the remaining rows i, we introduce a div and a corresponding
 625  * equality.  In particular
 626  *
 627  *      g_ii e_j = x_i - g_i(x')
 628  *
 629  * where each x'_k is replaced either by x_k (if g_kk = 1) or the
 630  * corresponding div (if g_kk != 1).
 631  *
 632  * If there are any equalities not involving any div, then we
 633  * first apply a variable compression on the variables x:
 634  *
 635  *      x = C x''       x'' = C_2 x
 636  *
 637  * and perform the above parameter compression on A C instead of on A.
 638  * The resulting compression is then of the form
 639  *
 640  *      x'' = T(x') = x_0 + G x'
 641  *
 642  * and in constructing the new divs and the corresponding equalities,
 643  * we have to replace each x'', i.e., the x'_k with (g_kk = 1),
 644  * by the corresponding row from C_2.
 645  */
 646 static struct isl_basic_map *normalize_divs(
 647         struct isl_basic_map *bmap, int *progress)
 648 {
 649         int i, j, k;
 650         int total;
 651         int div_eq;
 652         struct isl_mat *B;
 653         struct isl_vec *d;
 654         struct isl_mat *T = NULL;
 655         struct isl_mat *C = NULL;
 656         struct isl_mat *C2 = NULL;
 657         isl_int v;
 658         int *pos;
 659         int dropped, needed;
 660
 661         if (!bmap)
 662                 return NULL;
 663
 664         if (bmap->n_div == 0)
 665                 return bmap;
 666
 667         if (bmap->n_eq == 0)
 668                 return bmap;
 669
 670         if (F_ISSET(bmap, ISL_BASIC_MAP_NORMALIZED_DIVS))
 671                 return bmap;
 672
 673         total = isl_dim_total(bmap->dim);
 674         for (i = 0, j = bmap->n_div-1; i < bmap->n_eq; ++i) {
 675                 while (j >= 0 && isl_int_is_zero(bmap->eq[i][1 + total + j]))
 676                         --j;
 677                 if (j < 0)
 678                         break;
 679                 if (isl_seq_first_non_zero(bmap->eq[i] + 1 + total, j) != -1)
 680                         goto done;
 681         }
 682         div_eq = i;
 683         if (div_eq == 0)
 684                 return bmap;
 685
 686         if (div_eq < bmap->n_eq) {
 687                 B = isl_mat_sub_alloc(bmap->ctx, bmap->eq, div_eq,
 688                                         bmap->n_eq - div_eq, 0, 1 + total);
 689                 C = isl_mat_variable_compression(bmap->ctx, B, &C2);
 690                 if (!C || !C2)
 691                         goto error;
 692                 if (C->n_col == 0) {
 693                         bmap = isl_basic_map_set_to_empty(bmap);
 694                         isl_mat_free(bmap->ctx, C);
 695                         isl_mat_free(bmap->ctx, C2);
 696                         goto done;
 697                 }
 698         }
 699
 700         d = isl_vec_alloc(bmap->ctx, div_eq);
 701         if (!d)
 702                 goto error;
 703         for (i = 0, j = bmap->n_div-1; i < div_eq; ++i) {
 704                 while (j >= 0 && isl_int_is_zero(bmap->eq[i][1 + total + j]))
 705                         --j;
 706                 isl_int_set(d->block.data[i], bmap->eq[i][1 + total + j]);
 707         }
 708         B = isl_mat_sub_alloc(bmap->ctx, bmap->eq, 0, div_eq, 0, 1 + total);
 709
 710         if (C) {
 711                 B = isl_mat_product(bmap->ctx, B, C);
 712                 C = NULL;
 713         }
 714
 715         T = isl_mat_parameter_compression(bmap->ctx, B, d);
 716         if (!T)
 717                 goto error;
 718         if (T->n_col == 0) {
 719                 bmap = isl_basic_map_set_to_empty(bmap);
 720                 isl_mat_free(bmap->ctx, C2);
 721                 isl_mat_free(bmap->ctx, T);
 722                 goto done;
 723         }
 724         isl_int_init(v);
 725         for (i = 0; i < T->n_row - 1; ++i) {
 726                 isl_int_fdiv_q(v, T->row[1 + i][0], T->row[1 + i][1 + i]);
 727                 if (isl_int_is_zero(v))
 728                         continue;
 729                 isl_mat_col_submul(T, 0, v, 1 + i);
 730         }
 731         isl_int_clear(v);
 732         pos = isl_alloc_array(bmap->ctx, int, T->n_row);
 733         /* We have to be careful because dropping equalities may reorder them */
 734         dropped = 0;
 735         for (j = bmap->n_div - 1; j >= 0; --j) {
 736                 for (i = 0; i < bmap->n_eq; ++i)
 737                         if (!isl_int_is_zero(bmap->eq[i][1 + total + j]))
 738                                 break;
 739                 if (i < bmap->n_eq) {
 740                         bmap = isl_basic_map_drop_div(bmap, j);
 741                         isl_basic_map_drop_equality(bmap, i);
 742                         ++dropped;
 743                 }
 744         }
 745         pos[0] = 0;
 746         needed = 0;
 747         for (i = 1; i < T->n_row; ++i) {
 748                 if (isl_int_is_one(T->row[i][i]))
 749                         pos[i] = i;
 750                 else
 751                         needed++;
 752         }
 753         if (needed > dropped) {
 754                 bmap = isl_basic_map_extend_dim(bmap, isl_dim_copy(bmap->dim),
 755                                 needed, needed, 0);
 756                 if (!bmap)
 757                         goto error;
 758         }
 759         for (i = 1; i < T->n_row; ++i) {
 760                 if (isl_int_is_one(T->row[i][i]))
 761                         continue;
 762                 k = isl_basic_map_alloc_div(bmap);
 763                 pos[i] = 1 + total + k;
 764                 isl_seq_clr(bmap->div[k] + 1, 1 + total + bmap->n_div);
 765                 isl_int_set(bmap->div[k][0], T->row[i][i]);
 766                 if (C2)
 767                         isl_seq_cpy(bmap->div[k] + 1, C2->row[i], 1 + total);
 768                 else
 769                         isl_int_set_si(bmap->div[k][1 + i], 1);
 770                 for (j = 0; j < i; ++j) {
 771                         if (isl_int_is_zero(T->row[i][j]))
 772                                 continue;
 773                         if (pos[j] < T->n_row && C2)
 774                                 isl_seq_submul(bmap->div[k] + 1, T->row[i][j],
 775                                                 C2->row[pos[j]], 1 + total);
 776                         else
 777                                 isl_int_neg(bmap->div[k][1 + pos[j]],
 778                                                                 T->row[i][j]);
 779                 }
 780                 j = isl_basic_map_alloc_equality(bmap);
 781                 isl_seq_neg(bmap->eq[j], bmap->div[k]+1, 1+total+bmap->n_div);
 782                 isl_int_set(bmap->eq[j][pos[i]], bmap->div[k][0]);
 783         }
 784         free(pos);
 785         isl_mat_free(bmap->ctx, C2);
 786         isl_mat_free(bmap->ctx, T);
 787
 788         *progress = 1;
 789 done:
 790         F_SET(bmap, ISL_BASIC_MAP_NORMALIZED_DIVS);
 791
 792         return bmap;
 793 error:
 794         isl_mat_free(bmap->ctx, C);
 795         isl_mat_free(bmap->ctx, C2);
 796         isl_mat_free(bmap->ctx, T);
 797         return bmap;
 798 }
 799
 800 static struct isl_basic_map *remove_duplicate_constraints(
 801         struct isl_basic_map *bmap, int *progress)
 802 {
 803         unsigned int size;
 804         isl_int ***index;
 805         int k, l, h;
 806         int bits;
 807         unsigned total = isl_basic_map_total_dim(bmap);
 808         isl_int sum;
 809
 810         if (bmap->n_ineq <= 1)
 811                 return bmap;
 812
 813         size = round_up(4 * (bmap->n_ineq+1) / 3 - 1);
 814         bits = ffs(size) - 1;
 815         index = isl_calloc_array(ctx, isl_int **, size);
 816         if (!index)
 817                 return bmap;
 818
 819         index[isl_seq_get_hash_bits(bmap->ineq[0]+1, total, bits)] = &bmap->ineq[0];
 820         for (k = 1; k < bmap->n_ineq; ++k) {
 821                 h = hash_index(index, size, bits, bmap, k);
 822                 if (!index[h]) {
 823                         index[h] = &bmap->ineq[k];
 824                         continue;
 825                 }
 826                 if (progress)
 827                         *progress = 1;
 828                 l = index[h] - &bmap->ineq[0];
 829                 if (isl_int_lt(bmap->ineq[k][0], bmap->ineq[l][0]))
 830                         swap_inequality(bmap, k, l);
 831                 isl_basic_map_drop_inequality(bmap, k);
 832                 --k;
 833         }
 834         isl_int_init(sum);
 835         for (k = 0; k < bmap->n_ineq-1; ++k) {
 836                 isl_seq_neg(bmap->ineq[k]+1, bmap->ineq[k]+1, total);
 837                 h = hash_index(index, size, bits, bmap, k);
 838                 isl_seq_neg(bmap->ineq[k]+1, bmap->ineq[k]+1, total);
 839                 if (!index[h])
 840                         continue;
 841                 l = index[h] - &bmap->ineq[0];
 842                 isl_int_add(sum, bmap->ineq[k][0], bmap->ineq[l][0]);
 843                 if (isl_int_is_pos(sum))
 844                         continue;
 845                 if (isl_int_is_zero(sum)) {
 846                         /* We need to break out of the loop after these
 847                          * changes since the contents of the hash
 848                          * will no longer be valid.
 849                          * Plus, we probably we want to regauss first.
 850                          */
 851                         isl_basic_map_drop_inequality(bmap, l);
 852                         isl_basic_map_inequality_to_equality(bmap, k);
 853                 } else
 854                         bmap = isl_basic_map_set_to_empty(bmap);
 855                 break;
 856         }
 857         isl_int_clear(sum);
 858
 859         free(index);
 860         return bmap;
 861 }
 862
 863
 864 struct isl_basic_map *isl_basic_map_simplify(struct isl_basic_map *bmap)
 865 {
 866         int progress = 1;
 867         if (!bmap)
 868                 return NULL;
 869         while (progress) {
 870                 progress = 0;
 871                 bmap = normalize_constraints(bmap);
 872                 bmap = eliminate_divs_eq(bmap, &progress);
 873                 bmap = eliminate_divs_ineq(bmap, &progress);
 874                 bmap = isl_basic_map_gauss(bmap, &progress);
 875                 /* requires equalities in normal form */
 876                 bmap = normalize_divs(bmap, &progress);
 877                 bmap = remove_duplicate_divs(bmap, &progress);
 878                 bmap = remove_duplicate_constraints(bmap, &progress);
 879         }
 880         return bmap;
 881 }
 882
 883 struct isl_basic_set *isl_basic_set_simplify(struct isl_basic_set *bset)
 884 {
 885         return (struct isl_basic_set *)
 886                 isl_basic_map_simplify((struct isl_basic_map *)bset);
 887 }
 888
 889
 890 /* If the only constraints a div d=floor(f/m)
 891  * appears in are its two defining constraints
 892  *
 893  *      f - m d >=0
 894  *      -(f - (m - 1)) + m d >= 0
 895  *
 896  * then it can safely be removed.
 897  */
 898 static int div_is_redundant(struct isl_basic_map *bmap, int div)
 899 {
 900         int i;
 901         unsigned pos = 1 + isl_dim_total(bmap->dim) + div;
 902
 903         for (i = 0; i < bmap->n_eq; ++i)
 904                 if (!isl_int_is_zero(bmap->eq[i][pos]))
 905                         return 0;
 906
 907         for (i = 0; i < bmap->n_ineq; ++i) {
 908                 if (isl_int_is_zero(bmap->ineq[i][pos]))
 909                         continue;
 910                 if (isl_int_eq(bmap->ineq[i][pos], bmap->div[div][0])) {
 911                         int neg;
 912                         isl_int_sub(bmap->div[div][1],
 913                                         bmap->div[div][1], bmap->div[div][0]);
 914                         isl_int_add_ui(bmap->div[div][1], bmap->div[div][1], 1);
 915                         neg = isl_seq_is_neg(bmap->ineq[i], bmap->div[div]+1, pos);
 916                         isl_int_sub_ui(bmap->div[div][1], bmap->div[div][1], 1);
 917                         isl_int_add(bmap->div[div][1],
 918                                         bmap->div[div][1], bmap->div[div][0]);
 919                         if (!neg)
 920                                 return 0;
 921                         if (isl_seq_first_non_zero(bmap->ineq[i]+pos+1,
 922                                                     bmap->n_div-div-1) != -1)
 923                                 return 0;
 924                 } else if (isl_int_abs_eq(bmap->ineq[i][pos], bmap->div[div][0])) {
 925                         if (!isl_seq_eq(bmap->ineq[i], bmap->div[div]+1, pos))
 926                                 return 0;
 927                         if (isl_seq_first_non_zero(bmap->ineq[i]+pos+1,
 928                                                     bmap->n_div-div-1) != -1)
 929                                 return 0;
 930                 } else
 931                         return 0;
 932         }
 933
 934         for (i = 0; i < bmap->n_div; ++i)
 935                 if (!isl_int_is_zero(bmap->div[i][1+pos]))
 936                         return 0;
 937
 938         return 1;
 939 }
 940
 941 /*
 942  * Remove divs that don't occur in any of the constraints or other divs.
 943  * These can arise when dropping some of the variables in a quast
 944  * returned by piplib.
 945  */
 946 static struct isl_basic_map *remove_redundant_divs(struct isl_basic_map *bmap)
 947 {
 948         int i;
 949
 950         if (!bmap)
 951                 return NULL;
 952
 953         for (i = bmap->n_div-1; i >= 0; --i) {
 954                 if (!div_is_redundant(bmap, i))
 955                         continue;
 956                 bmap = isl_basic_map_drop_div(bmap, i);
 957         }
 958         return bmap;
 959 }
 960
 961 struct isl_basic_map *isl_basic_map_finalize(struct isl_basic_map *bmap)
 962 {
 963         bmap = remove_redundant_divs(bmap);
 964         if (!bmap)
 965                 return NULL;
 966         F_SET(bmap, ISL_BASIC_SET_FINAL);
 967         return bmap;
 968 }
 969
 970 struct isl_basic_set *isl_basic_set_finalize(struct isl_basic_set *bset)
 971 {
 972         return (struct isl_basic_set *)
 973                 isl_basic_map_finalize((struct isl_basic_map *)bset);
 974 }
 975
 976 struct isl_set *isl_set_finalize(struct isl_set *set)
 977 {
 978         int i;
 979
 980         if (!set)
 981                 return NULL;
 982         for (i = 0; i < set->n; ++i) {
 983                 set->p[i] = isl_basic_set_finalize(set->p[i]);
 984                 if (!set->p[i])
 985                         goto error;
 986         }
 987         return set;
 988 error:
 989         isl_set_free(set);
 990         return NULL;
 991 }
 992
 993 struct isl_map *isl_map_finalize(struct isl_map *map)
 994 {
 995         int i;
 996
 997         if (!map)
 998                 return NULL;
 999         for (i = 0; i < map->n; ++i) {
1000                 map->p[i] = isl_basic_map_finalize(map->p[i]);
1001                 if (!map->p[i])
1002                         goto error;
1003         }
1004         F_CLR(map, ISL_MAP_NORMALIZED);
1005         return map;
1006 error:
1007         isl_map_free(map);
1008         return NULL;
1009 }
1010
1011
1012 /* Remove any div that is defined in terms of the given variable.
1013  */
1014 static struct isl_basic_map *remove_dependent_vars(struct isl_basic_map *bmap,
1015                                                                         int pos)
1016 {
1017         int i;
1018         unsigned dim = isl_dim_total(bmap->dim);
1019
1020         for (i = 0; i < bmap->n_div; ++i) {
1021                 if (isl_int_is_zero(bmap->div[i][0]))
1022                         continue;
1023                 if (isl_int_is_zero(bmap->div[i][1+1+pos]))
1024                         continue;
1025                 bmap = isl_basic_map_eliminate_vars(bmap, dim + i, 1);
1026                 if (!bmap)
1027                         return NULL;
1028         }
1029         return bmap;
1030 }
1031
1032 /* Eliminate the specified variables from the constraints using
1033  * Fourier-Motzkin.  The variables themselves are not removed.
1034  */
1035 struct isl_basic_map *isl_basic_map_eliminate_vars(
1036         struct isl_basic_map *bmap, unsigned pos, unsigned n)
1037 {
1038         int d;
1039         int i, j, k;
1040         unsigned total;
1041
1042         if (n == 0)
1043                 return bmap;
1044         if (!bmap)
1045                 return NULL;
1046         total = isl_basic_map_total_dim(bmap);
1047
1048         bmap = isl_basic_map_cow(bmap);
1049         for (d = pos + n - 1; d >= 0 && d >= pos; --d) {
1050                 int n_lower, n_upper;
1051                 bmap = remove_dependent_vars(bmap, d);
1052                 if (!bmap)
1053                         return NULL;
1054                 if (d >= total - bmap->n_div)
1055                         isl_seq_clr(bmap->div[d-(total-bmap->n_div)], 2+total);
1056                 for (i = 0; i < bmap->n_eq; ++i) {
1057                         if (isl_int_is_zero(bmap->eq[i][1+d]))
1058                                 continue;
1059                         eliminate_var_using_equality(bmap, d, bmap->eq[i], NULL);
1060                         isl_basic_map_drop_equality(bmap, i);
1061                         break;
1062                 }
1063                 if (i < bmap->n_eq)
1064                         continue;
1065                 n_lower = 0;
1066                 n_upper = 0;
1067                 for (i = 0; i < bmap->n_ineq; ++i) {
1068                         if (isl_int_is_pos(bmap->ineq[i][1+d]))
1069                                 n_lower++;
1070                         else if (isl_int_is_neg(bmap->ineq[i][1+d]))
1071                                 n_upper++;
1072                 }
1073                 bmap = isl_basic_map_extend_constraints(bmap,
1074                                 0, n_lower * n_upper);
1075                 for (i = bmap->n_ineq - 1; i >= 0; --i) {
1076                         int last;
1077                         if (isl_int_is_zero(bmap->ineq[i][1+d]))
1078                                 continue;
1079                         last = -1;
1080                         for (j = 0; j < i; ++j) {
1081                                 if (isl_int_is_zero(bmap->ineq[j][1+d]))
1082                                         continue;
1083                                 last = j;
1084                                 if (isl_int_sgn(bmap->ineq[i][1+d]) ==
1085                                     isl_int_sgn(bmap->ineq[j][1+d]))
1086                                         continue;
1087                                 k = isl_basic_map_alloc_inequality(bmap);
1088                                 if (k < 0)
1089                                         goto error;
1090                                 isl_seq_cpy(bmap->ineq[k], bmap->ineq[i],
1091                                                 1+total);
1092                                 isl_seq_elim(bmap->ineq[k], bmap->ineq[j],
1093                                                 1+d, 1+total, NULL);
1094                         }
1095                         isl_basic_map_drop_inequality(bmap, i);
1096                         i = last + 1;
1097                 }
1098                 if (n_lower > 0 && n_upper > 0) {
1099                         bmap = normalize_constraints(bmap);
1100                         bmap = remove_duplicate_constraints(bmap, NULL);
1101                         bmap = isl_basic_map_gauss(bmap, NULL);
1102                         bmap = isl_basic_map_convex_hull(bmap);
1103                         if (!bmap)
1104                                 goto error;
1105                         if (F_ISSET(bmap, ISL_BASIC_MAP_EMPTY))
1106                                 break;
1107                 }
1108         }
1109         F_CLR(bmap, ISL_BASIC_MAP_NORMALIZED);
1110         return bmap;
1111 error:
1112         isl_basic_map_free(bmap);
1113         return NULL;
1114 }
1115
1116 struct isl_basic_set *isl_basic_set_eliminate_vars(
1117         struct isl_basic_set *bset, unsigned pos, unsigned n)
1118 {
1119         return (struct isl_basic_set *)isl_basic_map_eliminate_vars(
1120                         (struct isl_basic_map *)bset, pos, n);
1121 }
1122
1123 static void compute_elimination_index(struct isl_basic_map *bmap, int *elim)
1124 {
1125         int d, i;
1126         unsigned total;
1127
1128         total = isl_dim_total(bmap->dim);
1129         for (d = 0; d < total; ++d)
1130                 elim[d] = -1;
1131         for (d = total - 1, i = 0; d >= 0 && i < bmap->n_eq; ++i) {
1132                 for (; d >= 0; --d) {
1133                         if (isl_int_is_zero(bmap->eq[i][1+d]))
1134                                 continue;
1135                         elim[d] = i;
1136                         break;
1137                 }
1138         }
1139 }
1140
1141 static void set_compute_elimination_index(struct isl_basic_set *bset, int *elim)
1142 {
1143         return compute_elimination_index((struct isl_basic_map *)bset, elim);
1144 }
1145
1146 static int reduced_using_equalities(isl_int *dst, isl_int *src,
1147         struct isl_basic_map *bmap, int *elim)
1148 {
1149         int d, i;
1150         int copied = 0;
1151         unsigned total;
1152
1153         total = isl_dim_total(bmap->dim);
1154         for (d = total - 1; d >= 0; --d) {
1155                 if (isl_int_is_zero(src[1+d]))
1156                         continue;
1157                 if (elim[d] == -1)
1158                         continue;
1159                 if (!copied) {
1160                         isl_seq_cpy(dst, src, 1 + total);
1161                         copied = 1;
1162                 }
1163                 isl_seq_elim(dst, bmap->eq[elim[d]], 1 + d, 1 + total, NULL);
1164         }
1165         return copied;
1166 }
1167
1168 static int set_reduced_using_equalities(isl_int *dst, isl_int *src,
1169         struct isl_basic_set *bset, int *elim)
1170 {
1171         return reduced_using_equalities(dst, src,
1172                                         (struct isl_basic_map *)bset, elim);
1173 }
1174
1175 static struct isl_basic_set *isl_basic_set_reduce_using_equalities(
1176         struct isl_basic_set *bset, struct isl_basic_set *context)
1177 {
1178         int i;
1179         int *elim;
1180
1181         if (!bset || !context)
1182                 goto error;
1183
1184         bset = isl_basic_set_cow(bset);
1185         if (!bset)
1186                 goto error;
1187
1188         elim = isl_alloc_array(ctx, int, isl_basic_set_n_dim(bset));
1189         if (!elim)
1190                 goto error;
1191         set_compute_elimination_index(context, elim);
1192         for (i = 0; i < bset->n_eq; ++i)
1193                 set_reduced_using_equalities(bset->eq[i], bset->eq[i],
1194                                                         context, elim);
1195         for (i = 0; i < bset->n_ineq; ++i)
1196                 set_reduced_using_equalities(bset->ineq[i], bset->ineq[i],
1197                                                         context, elim);
1198         isl_basic_set_free(context);
1199         free(elim);
1200         bset = isl_basic_set_simplify(bset);
1201         bset = isl_basic_set_finalize(bset);
1202         return bset;
1203 error:
1204         isl_basic_set_free(bset);
1205         isl_basic_set_free(context);
1206         return NULL;
1207 }
1208
1209 static struct isl_basic_set *remove_shifted_constraints(
1210         struct isl_basic_set *bset, struct isl_basic_set *context)
1211 {
1212         unsigned int size;
1213         isl_int ***index;
1214         int bits;
1215         int k, h, l;
1216
1217         if (!bset)
1218                 return NULL;
1219
1220         size = round_up(4 * (context->n_ineq+1) / 3 - 1);
1221         bits = ffs(size) - 1;
1222         index = isl_calloc_array(ctx, isl_int **, size);
1223         if (!index)
1224                 return bset;
1225
1226         for (k = 0; k < context->n_ineq; ++k) {
1227                 h = set_hash_index(index, size, bits, context, k);
1228                 index[h] = &context->ineq[k];
1229         }
1230         for (k = 0; k < bset->n_ineq; ++k) {
1231                 h = set_hash_index(index, size, bits, bset, k);
1232                 if (!index[h])
1233                         continue;
1234                 l = index[h] - &context->ineq[0];
1235                 if (isl_int_lt(bset->ineq[k][0], context->ineq[l][0]))
1236                         continue;
1237                 bset = isl_basic_set_cow(bset);
1238                 if (!bset)
1239                         goto error;
1240                 isl_basic_set_drop_inequality(bset, k);
1241                 --k;
1242         }
1243         free(index);
1244         return bset;
1245 error:
1246         free(index);
1247         return bset;
1248 }
1249
1250 static struct isl_basic_set *uset_gist(struct isl_basic_set *bset,
1251         struct isl_basic_set *context);
1252
1253 static struct isl_basic_set *uset_gist_context_eq(struct isl_basic_set *bset,
1254         struct isl_basic_set *context)
1255 {
1256         struct isl_mat *T;
1257         struct isl_mat *T2;
1258         struct isl_ctx *ctx = context->ctx;
1259         struct isl_basic_set *reduced_context;
1260         reduced_context = isl_basic_set_remove_equalities(
1261                                 isl_basic_set_copy(context), &T, &T2);
1262         if (!reduced_context)
1263                 goto error;
1264         bset = isl_basic_set_preimage(ctx, bset, T);
1265         bset = uset_gist(bset, reduced_context);
1266         bset = isl_basic_set_preimage(ctx, bset, T2);
1267         bset = isl_basic_set_reduce_using_equalities(bset, context);
1268         return bset;
1269 error:
1270         isl_basic_set_free(context);
1271         isl_basic_set_free(bset);
1272         return NULL;
1273 }
1274
1275 static struct isl_basic_set *uset_gist_set_eq(struct isl_basic_set *bset,
1276         struct isl_basic_set *context)
1277 {
1278         struct isl_mat *T;
1279         struct isl_mat *T2;
1280         struct isl_ctx *ctx = context->ctx;
1281         struct isl_basic_set *affine_hull = NULL;
1282
1283         affine_hull = isl_basic_set_copy(bset);
1284         affine_hull = isl_basic_set_cow(affine_hull);
1285         if (!affine_hull)
1286                 goto error;
1287         isl_basic_set_free_inequality(affine_hull, affine_hull->n_ineq);
1288
1289         bset = isl_basic_set_remove_equalities(bset, &T, &T2);
1290         if (!bset)
1291                 goto error;
1292         context = isl_basic_set_preimage(ctx, context, T);
1293         bset = uset_gist(bset, context);
1294         bset = isl_basic_set_preimage(ctx, bset, T2);
1295         bset = isl_basic_set_intersect(bset, affine_hull);
1296         return bset;
1297 error:
1298         isl_basic_set_free(affine_hull);
1299         isl_basic_set_free(context);
1300         isl_basic_set_free(bset);
1301         return NULL;
1302 }
1303
1304 /* Remove all information from bset that is redundant in the context
1305  * of context.  In particular, equalities that are linear combinations
1306  * of those in context are removed.  Then the inequalities that are
1307  * redundant in the context of the equalities and inequalities of
1308  * context are removed.
1309  */
1310 static struct isl_basic_set *uset_gist(struct isl_basic_set *bset,
1311         struct isl_basic_set *context)
1312 {
1313         int i;
1314         isl_int opt;
1315         struct isl_basic_set *combined;
1316         struct isl_ctx *ctx;
1317
1318         if (!bset || !context)
1319                 goto error;
1320
1321         if (context->n_eq > 0)
1322                 return uset_gist_context_eq(bset, context);
1323         if (!context->n_ineq)
1324                 goto done;
1325         if (bset->n_eq > 0)
1326                 return uset_gist_set_eq(bset, context);
1327         bset = remove_shifted_constraints(bset, context);
1328         combined = isl_basic_set_extend_constraints(isl_basic_set_copy(bset),
1329                         context->n_eq, context->n_ineq);
1330         context = isl_basic_set_add_constraints(combined, context, 0);
1331         if (!context)
1332                 goto error;
1333         ctx = context->ctx;
1334         isl_int_init(opt);
1335         for (i = bset->n_ineq-1; i >= 0; --i) {
1336                 int redundant;
1337                 set_swap_inequality(context, i, context->n_ineq-1);
1338                 context->n_ineq--;
1339                 redundant = isl_basic_set_constraint_is_redundant(&context,
1340                                 context->ineq[context->n_ineq], &opt, NULL);
1341                 if (redundant == -1) {
1342                         isl_int_clear(opt);
1343                         goto error;
1344                 }
1345                 if (F_ISSET(context, ISL_BASIC_MAP_EMPTY)) {
1346                         bset = isl_basic_set_set_to_empty(bset);
1347                         break;
1348                 }
1349                 context->n_ineq++;
1350                 set_swap_inequality(context, i, context->n_ineq-1);
1351                 if (redundant) {
1352                         isl_basic_set_drop_inequality(context, i);
1353                         isl_basic_set_drop_inequality(bset, i);
1354                 }
1355         }
1356         isl_int_clear(opt);
1357 done:
1358         isl_basic_set_free(context);
1359         return bset;
1360 error:
1361         isl_basic_set_free(context);
1362         isl_basic_set_free(bset);
1363         return NULL;
1364 }
1365
1366 struct isl_basic_map *isl_basic_map_gist(struct isl_basic_map *bmap,
1367         struct isl_basic_map *context)
1368 {
1369         struct isl_basic_set *bset;
1370
1371         if (!bmap || !context)
1372                 goto error;
1373
1374         context = isl_basic_map_align_divs(context, bmap);
1375         bmap = isl_basic_map_align_divs(bmap, context);
1376
1377         bset = uset_gist(isl_basic_map_underlying_set(isl_basic_map_copy(bmap)),
1378                          isl_basic_map_underlying_set(context));
1379
1380         return isl_basic_map_overlying_set(bset, bmap);
1381 error:
1382         isl_basic_map_free(bmap);
1383         isl_basic_map_free(context);
1384         return NULL;
1385 }
1386
1387 /*
1388  * Assumes context has no implicit divs.
1389  */
1390 struct isl_map *isl_map_gist(struct isl_map *map, struct isl_basic_map *context)
1391 {
1392         int i;
1393
1394         map = isl_map_cow(map);
1395         if (!map || !context)
1396                 return NULL;
1397         isl_assert(map->ctx, isl_dim_equal(map->dim, context->dim), goto error);
1398         map = isl_map_compute_divs(map);
1399         for (i = 0; i < map->n; ++i)
1400                 context = isl_basic_map_align_divs(context, map->p[i]);
1401         for (i = 0; i < map->n; ++i) {
1402                 map->p[i] = isl_basic_map_gist(map->p[i],
1403                                                 isl_basic_map_copy(context));
1404                 if (!map->p[i])
1405                         goto error;
1406         }
1407         isl_basic_map_free(context);
1408         F_CLR(map, ISL_MAP_NORMALIZED);
1409         return map;
1410 error:
1411         isl_map_free(map);
1412         isl_basic_map_free(context);
1413         return NULL;
1414 }
1415
1416 struct isl_basic_set *isl_basic_set_gist(struct isl_basic_set *bset,
1417                                                 struct isl_basic_set *context)
1418 {
1419         return (struct isl_basic_set *)isl_basic_map_gist(
1420                 (struct isl_basic_map *)bset, (struct isl_basic_map *)context);
1421 }
1422
1423 struct isl_set *isl_set_gist(struct isl_set *set, struct isl_basic_set *context)
1424 {
1425         return (struct isl_set *)isl_map_gist((struct isl_map *)set,
1426                                         (struct isl_basic_map *)context);
1427 }
1428
1429 /* Quick check to see if two basic maps are disjoint.
1430  * In particular, we reduce the equalities and inequalities of
1431  * one basic map in the context of the equalities of the other
1432  * basic map and check if we get a contradiction.
1433  */
1434 int isl_basic_map_fast_is_disjoint(struct isl_basic_map *bmap1,
1435         struct isl_basic_map *bmap2)
1436 {
1437         struct isl_vec *v = NULL;
1438         int *elim = NULL;
1439         unsigned total;
1440         int d, i;
1441
1442         if (!bmap1 || !bmap2)
1443                 return -1;
1444         isl_assert(bmap1->ctx, isl_dim_equal(bmap1->dim, bmap2->dim),
1445                         return -1);
1446         if (bmap1->n_div || bmap2->n_div)
1447                 return 0;
1448         if (!bmap1->n_eq && !bmap2->n_eq)
1449                 return 0;
1450
1451         total = isl_dim_total(bmap1->dim);
1452         if (total == 0)
1453                 return 0;
1454         v = isl_vec_alloc(bmap1->ctx, 1 + total);
1455         if (!v)
1456                 goto error;
1457         elim = isl_alloc_array(bmap1->ctx, int, total);
1458         if (!elim)
1459                 goto error;
1460         compute_elimination_index(bmap1, elim);
1461         for (i = 0; i < bmap2->n_eq; ++i) {
1462                 int reduced;
1463                 reduced = reduced_using_equalities(v->block.data, bmap2->eq[i],
1464                                                         bmap1, elim);
1465                 if (reduced && !isl_int_is_zero(v->block.data[0]) &&
1466                     isl_seq_first_non_zero(v->block.data + 1, total) == -1)
1467                         goto disjoint;
1468         }
1469         for (i = 0; i < bmap2->n_ineq; ++i) {
1470                 int reduced;
1471                 reduced = reduced_using_equalities(v->block.data,
1472                                                 bmap2->ineq[i], bmap1, elim);
1473                 if (reduced && isl_int_is_neg(v->block.data[0]) &&
1474                     isl_seq_first_non_zero(v->block.data + 1, total) == -1)
1475                         goto disjoint;
1476         }
1477         compute_elimination_index(bmap2, elim);
1478         for (i = 0; i < bmap1->n_ineq; ++i) {
1479                 int reduced;
1480                 reduced = reduced_using_equalities(v->block.data,
1481                                                 bmap1->ineq[i], bmap2, elim);
1482                 if (reduced && isl_int_is_neg(v->block.data[0]) &&
1483                     isl_seq_first_non_zero(v->block.data + 1, total) == -1)
1484                         goto disjoint;
1485         }
1486         isl_vec_free(bmap1->ctx, v);
1487         free(elim);
1488         return 0;
1489 disjoint:
1490         isl_vec_free(bmap1->ctx, v);
1491         free(elim);
1492         return 1;
1493 error:
1494         isl_vec_free(bmap1->ctx, v);
1495         free(elim);
1496         return -1;
1497 }
1498
1499 int isl_basic_set_fast_is_disjoint(struct isl_basic_set *bset1,
1500         struct isl_basic_set *bset2)
1501 {
1502         return isl_basic_map_fast_is_disjoint((struct isl_basic_map *)bset1,
1503                                               (struct isl_basic_map *)bset2);
1504 }
1505
1506 int isl_map_fast_is_disjoint(struct isl_map *map1, struct isl_map *map2)
1507 {
1508         int i, j;
1509
1510         if (!map1 || !map2)
1511                 return -1;
1512
1513         if (isl_map_fast_is_equal(map1, map2))
1514                 return 0;
1515
1516         for (i = 0; i < map1->n; ++i) {
1517                 for (j = 0; j < map2->n; ++j) {
1518                         int d = isl_basic_map_fast_is_disjoint(map1->p[i],
1519                                                                map2->p[j]);
1520                         if (d != 1)
1521                                 return d;
1522                 }
1523         }
1524         return 1;
1525 }
1526
1527 int isl_set_fast_is_disjoint(struct isl_set *set1, struct isl_set *set2)
1528 {
1529         return isl_map_fast_is_disjoint((struct isl_map *)set1,
1530                                         (struct isl_map *)set2);
1531 }