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(struct isl_basic_map *bmap,
 120         enum isl_dim_type type, unsigned first, unsigned n)
 121 {
 122         int i;
 123         unsigned dim;
 124         unsigned offset;
 125         unsigned left;
 126
 127         if (!bmap)
 128                 goto error;
 129
 130         dim = isl_basic_map_dim(bmap, type);
 131         isl_assert(bmap->ctx, first + n <= dim, goto error);
 132
 133         if (n == 0)
 134                 return bmap;
 135
 136         bmap = isl_basic_map_cow(bmap);
 137         if (!bmap)
 138                 return NULL;
 139
 140         offset = isl_basic_map_offset(bmap, type) + first;
 141         left = isl_basic_map_total_dim(bmap) - (offset - 1) - n;
 142         for (i = 0; i < bmap->n_eq; ++i)
 143                 constraint_drop_vars(bmap->eq[i]+offset, n, left);
 144
 145         for (i = 0; i < bmap->n_ineq; ++i)
 146                 constraint_drop_vars(bmap->ineq[i]+offset, n, left);
 147
 148         for (i = 0; i < bmap->n_div; ++i)
 149                 constraint_drop_vars(bmap->div[i]+1+offset, n, left);
 150
 151         bmap->dim = isl_dim_drop(bmap->dim, type, first, n);
 152         if (!bmap->dim)
 153                 goto error;
 154
 155         F_CLR(bmap, ISL_BASIC_MAP_NORMALIZED);
 156         bmap = isl_basic_map_simplify(bmap);
 157         return isl_basic_map_finalize(bmap);
 158 error:
 159         isl_basic_map_free(bmap);
 160         return NULL;
 161 }
 162
 163 struct isl_basic_map *isl_basic_map_drop_inputs(
 164                 struct isl_basic_map *bmap, unsigned first, unsigned n)
 165 {
 166         return isl_basic_map_drop(bmap, isl_dim_in, first, n);
 167 }
 168
 169 struct isl_map *isl_map_drop_inputs(
 170                 struct isl_map *map, unsigned first, unsigned n)
 171 {
 172         int i;
 173
 174         if (!map)
 175                 goto error;
 176
 177         isl_assert(map->ctx, first + n <= map->dim->n_in, goto error);
 178
 179         if (n == 0)
 180                 return map;
 181         map = isl_map_cow(map);
 182         if (!map)
 183                 goto error;
 184         map->dim = isl_dim_drop_inputs(map->dim, first, n);
 185         if (!map->dim)
 186                 goto error;
 187
 188         for (i = 0; i < map->n; ++i) {
 189                 map->p[i] = isl_basic_map_drop_inputs(map->p[i], first, n);
 190                 if (!map->p[i])
 191                         goto error;
 192         }
 193         F_CLR(map, ISL_MAP_NORMALIZED);
 194
 195         return map;
 196 error:
 197         isl_map_free(map);
 198         return NULL;
 199 }
 200
 201 /*
 202  * We don't cow, as the div is assumed to be redundant.
 203  */
 204 static struct isl_basic_map *isl_basic_map_drop_div(
 205                 struct isl_basic_map *bmap, unsigned div)
 206 {
 207         int i;
 208         unsigned pos;
 209
 210         if (!bmap)
 211                 goto error;
 212
 213         pos = 1 + isl_dim_total(bmap->dim) + div;
 214
 215         isl_assert(bmap->ctx, div < bmap->n_div, goto error);
 216
 217         for (i = 0; i < bmap->n_eq; ++i)
 218                 constraint_drop_vars(bmap->eq[i]+pos, 1, bmap->extra-div-1);
 219
 220         for (i = 0; i < bmap->n_ineq; ++i) {
 221                 if (!isl_int_is_zero(bmap->ineq[i][pos])) {
 222                         isl_basic_map_drop_inequality(bmap, i);
 223                         --i;
 224                         continue;
 225                 }
 226                 constraint_drop_vars(bmap->ineq[i]+pos, 1, bmap->extra-div-1);
 227         }
 228
 229         for (i = 0; i < bmap->n_div; ++i)
 230                 constraint_drop_vars(bmap->div[i]+1+pos, 1, bmap->extra-div-1);
 231
 232         if (div != bmap->n_div - 1) {
 233                 int j;
 234                 isl_int *t = bmap->div[div];
 235
 236                 for (j = div; j < bmap->n_div - 1; ++j)
 237                         bmap->div[j] = bmap->div[j+1];
 238
 239                 bmap->div[bmap->n_div - 1] = t;
 240         }
 241         F_CLR(bmap, ISL_BASIC_MAP_NORMALIZED);
 242         isl_basic_map_free_div(bmap, 1);
 243
 244         return bmap;
 245 error:
 246         isl_basic_map_free(bmap);
 247         return NULL;
 248 }
 249
 250 static struct isl_basic_map *normalize_constraints(struct isl_basic_map *bmap)
 251 {
 252         int i;
 253         isl_int gcd;
 254         unsigned total = isl_basic_map_total_dim(bmap);
 255
 256         isl_int_init(gcd);
 257         for (i = bmap->n_eq - 1; i >= 0; --i) {
 258                 isl_seq_gcd(bmap->eq[i]+1, total, &gcd);
 259                 if (isl_int_is_zero(gcd)) {
 260                         if (!isl_int_is_zero(bmap->eq[i][0])) {
 261                                 bmap = isl_basic_map_set_to_empty(bmap);
 262                                 break;
 263                         }
 264                         isl_basic_map_drop_equality(bmap, i);
 265                         continue;
 266                 }
 267                 if (F_ISSET(bmap, ISL_BASIC_MAP_RATIONAL))
 268                         isl_int_gcd(gcd, gcd, bmap->eq[i][0]);
 269                 if (isl_int_is_one(gcd))
 270                         continue;
 271                 if (!isl_int_is_divisible_by(bmap->eq[i][0], gcd)) {
 272                         bmap = isl_basic_map_set_to_empty(bmap);
 273                         break;
 274                 }
 275                 isl_seq_scale_down(bmap->eq[i], bmap->eq[i], gcd, 1+total);
 276         }
 277
 278         for (i = bmap->n_ineq - 1; i >= 0; --i) {
 279                 isl_seq_gcd(bmap->ineq[i]+1, total, &gcd);
 280                 if (isl_int_is_zero(gcd)) {
 281                         if (isl_int_is_neg(bmap->ineq[i][0])) {
 282                                 bmap = isl_basic_map_set_to_empty(bmap);
 283                                 break;
 284                         }
 285                         isl_basic_map_drop_inequality(bmap, i);
 286                         continue;
 287                 }
 288                 if (F_ISSET(bmap, ISL_BASIC_MAP_RATIONAL))
 289                         isl_int_gcd(gcd, gcd, bmap->ineq[i][0]);
 290                 if (isl_int_is_one(gcd))
 291                         continue;
 292                 isl_int_fdiv_q(bmap->ineq[i][0], bmap->ineq[i][0], gcd);
 293                 isl_seq_scale_down(bmap->ineq[i]+1, bmap->ineq[i]+1, gcd, total);
 294         }
 295         isl_int_clear(gcd);
 296
 297         return bmap;
 298 }
 299
 300 static void eliminate_div(struct isl_basic_map *bmap, isl_int *eq, unsigned div)
 301 {
 302         int i;
 303         unsigned pos = 1 + isl_dim_total(bmap->dim) + div;
 304         unsigned len;
 305         len = 1 + isl_basic_map_total_dim(bmap);
 306
 307         for (i = 0; i < bmap->n_eq; ++i)
 308                 if (bmap->eq[i] != eq)
 309                         isl_seq_elim(bmap->eq[i], eq, pos, len, NULL);
 310
 311         for (i = 0; i < bmap->n_ineq; ++i)
 312                 isl_seq_elim(bmap->ineq[i], eq, pos, len, NULL);
 313
 314         /* We need to be careful about circular definitions,
 315          * so for now we just remove the definitions of other divs that
 316          * depend on this div and (possibly) recompute them later.
 317          */
 318         for (i = 0; i < bmap->n_div; ++i)
 319                 if (!isl_int_is_zero(bmap->div[i][0]) &&
 320                     !isl_int_is_zero(bmap->div[i][1 + pos]))
 321                         isl_seq_clr(bmap->div[i], 1 + len);
 322
 323         isl_basic_map_drop_div(bmap, div);
 324 }
 325
 326 /* Elimininate divs based on equalities
 327  */
 328 static struct isl_basic_map *eliminate_divs_eq(
 329                 struct isl_basic_map *bmap, int *progress)
 330 {
 331         int d;
 332         int i;
 333         int modified = 0;
 334         unsigned off;
 335
 336         if (!bmap)
 337                 return NULL;
 338
 339         off = 1 + isl_dim_total(bmap->dim);
 340
 341         for (d = bmap->n_div - 1; d >= 0 ; --d) {
 342                 for (i = 0; i < bmap->n_eq; ++i) {
 343                         if (!isl_int_is_one(bmap->eq[i][off + d]) &&
 344                             !isl_int_is_negone(bmap->eq[i][off + d]))
 345                                 continue;
 346                         modified = 1;
 347                         *progress = 1;
 348                         eliminate_div(bmap, bmap->eq[i], d);
 349                         isl_basic_map_drop_equality(bmap, i);
 350                         break;
 351                 }
 352         }
 353         if (modified)
 354                 return eliminate_divs_eq(bmap, progress);
 355         return bmap;
 356 }
 357
 358 /* Elimininate divs based on inequalities
 359  */
 360 static struct isl_basic_map *eliminate_divs_ineq(
 361                 struct isl_basic_map *bmap, int *progress)
 362 {
 363         int d;
 364         int i;
 365         unsigned off;
 366         struct isl_ctx *ctx;
 367
 368         if (!bmap)
 369                 return NULL;
 370
 371         ctx = bmap->ctx;
 372         off = 1 + isl_dim_total(bmap->dim);
 373
 374         for (d = bmap->n_div - 1; d >= 0 ; --d) {
 375                 for (i = 0; i < bmap->n_eq; ++i)
 376                         if (!isl_int_is_zero(bmap->eq[i][off + d]))
 377                                 break;
 378                 if (i < bmap->n_eq)
 379                         continue;
 380                 for (i = 0; i < bmap->n_ineq; ++i)
 381                         if (isl_int_abs_gt(bmap->ineq[i][off + d], ctx->one))
 382                                 break;
 383                 if (i < bmap->n_ineq)
 384                         continue;
 385                 *progress = 1;
 386                 bmap = isl_basic_map_eliminate_vars(bmap, (off-1)+d, 1);
 387                 if (F_ISSET(bmap, ISL_BASIC_MAP_EMPTY))
 388                         break;
 389                 bmap = isl_basic_map_drop_div(bmap, d);
 390                 if (!bmap)
 391                         break;
 392         }
 393         return bmap;
 394 }
 395
 396 static void eliminate_var_using_equality(struct isl_basic_map *bmap,
 397         unsigned pos, isl_int *eq, int *progress)
 398 {
 399         unsigned total;
 400         int k;
 401         int contains_divs;
 402
 403         total = isl_basic_map_total_dim(bmap);
 404         contains_divs =
 405                 isl_seq_first_non_zero(eq + 1 + isl_dim_total(bmap->dim),
 406                                                 bmap->n_div) != -1;
 407         for (k = 0; k < bmap->n_eq; ++k) {
 408                 if (bmap->eq[k] == eq)
 409                         continue;
 410                 if (isl_int_is_zero(bmap->eq[k][1+pos]))
 411                         continue;
 412                 if (progress)
 413                         *progress = 1;
 414                 isl_seq_elim(bmap->eq[k], eq, 1+pos, 1+total, NULL);
 415         }
 416
 417         for (k = 0; k < bmap->n_ineq; ++k) {
 418                 if (isl_int_is_zero(bmap->ineq[k][1+pos]))
 419                         continue;
 420                 if (progress)
 421                         *progress = 1;
 422                 isl_seq_elim(bmap->ineq[k], eq, 1+pos, 1+total, NULL);
 423                 F_CLR(bmap, ISL_BASIC_MAP_NORMALIZED);
 424         }
 425
 426         for (k = 0; k < bmap->n_div; ++k) {
 427                 if (isl_int_is_zero(bmap->div[k][0]))
 428                         continue;
 429                 if (isl_int_is_zero(bmap->div[k][1+1+pos]))
 430                         continue;
 431                 if (progress)
 432                         *progress = 1;
 433                 /* We need to be careful about circular definitions,
 434                  * so for now we just remove the definition of div k
 435                  * if the equality contains any divs.
 436                  */
 437                 if (contains_divs)
 438                         isl_seq_clr(bmap->div[k], 1 + total);
 439                 else
 440                         isl_seq_elim(bmap->div[k]+1, eq,
 441                                         1+pos, 1+total, &bmap->div[k][0]);
 442                 F_CLR(bmap, ISL_BASIC_MAP_NORMALIZED);
 443         }
 444 }
 445
 446 struct isl_basic_map *isl_basic_map_gauss(
 447         struct isl_basic_map *bmap, int *progress)
 448 {
 449         int k;
 450         int done;
 451         int last_var;
 452         unsigned total_var;
 453         unsigned total;
 454
 455         if (!bmap)
 456                 return NULL;
 457
 458         total = isl_basic_map_total_dim(bmap);
 459         total_var = total - bmap->n_div;
 460
 461         last_var = total - 1;
 462         for (done = 0; done < bmap->n_eq; ++done) {
 463                 for (; last_var >= 0; --last_var) {
 464                         for (k = done; k < bmap->n_eq; ++k)
 465                                 if (!isl_int_is_zero(bmap->eq[k][1+last_var]))
 466                                         break;
 467                         if (k < bmap->n_eq)
 468                                 break;
 469                 }
 470                 if (last_var < 0)
 471                         break;
 472                 if (k != done)
 473                         swap_equality(bmap, k, done);
 474                 if (isl_int_is_neg(bmap->eq[done][1+last_var]))
 475                         isl_seq_neg(bmap->eq[done], bmap->eq[done], 1+total);
 476
 477                 eliminate_var_using_equality(bmap, last_var, bmap->eq[done],
 478                                                 progress);
 479
 480                 if (last_var >= total_var &&
 481                     isl_int_is_zero(bmap->div[last_var - total_var][0])) {
 482                         unsigned div = last_var - total_var;
 483                         isl_seq_neg(bmap->div[div]+1, bmap->eq[done], 1+total);
 484                         isl_int_set_si(bmap->div[div][1+1+last_var], 0);
 485                         isl_int_set(bmap->div[div][0],
 486                                     bmap->eq[done][1+last_var]);
 487                         F_CLR(bmap, ISL_BASIC_MAP_NORMALIZED);
 488                 }
 489         }
 490         if (done == bmap->n_eq)
 491                 return bmap;
 492         for (k = done; k < bmap->n_eq; ++k) {
 493                 if (isl_int_is_zero(bmap->eq[k][0]))
 494                         continue;
 495                 return isl_basic_map_set_to_empty(bmap);
 496         }
 497         isl_basic_map_free_equality(bmap, bmap->n_eq-done);
 498         return bmap;
 499 }
 500
 501 struct isl_basic_set *isl_basic_set_gauss(
 502         struct isl_basic_set *bset, int *progress)
 503 {
 504         return (struct isl_basic_set*)isl_basic_map_gauss(
 505                         (struct isl_basic_map *)bset, progress);
 506 }
 507
 508
 509 static unsigned int round_up(unsigned int v)
 510 {
 511         int old_v = v;
 512
 513         while (v) {
 514                 old_v = v;
 515                 v ^= v & -v;
 516         }
 517         return old_v << 1;
 518 }
 519
 520 static int hash_index(isl_int ***index, unsigned int size, int bits,
 521                         struct isl_basic_map *bmap, int k)
 522 {
 523         int h;
 524         unsigned total = isl_basic_map_total_dim(bmap);
 525         uint32_t hash = isl_seq_get_hash_bits(bmap->ineq[k]+1, total, bits);
 526         for (h = hash; index[h]; h = (h+1) % size)
 527                 if (&bmap->ineq[k] != index[h] &&
 528                     isl_seq_eq(bmap->ineq[k]+1, index[h][0]+1, total))
 529                         break;
 530         return h;
 531 }
 532
 533 static int set_hash_index(isl_int ***index, unsigned int size, int bits,
 534                           struct isl_basic_set *bset, int k)
 535 {
 536         return hash_index(index, size, bits, (struct isl_basic_map *)bset, k);
 537 }
 538
 539 /* If we can eliminate more than one div, then we need to make
 540  * sure we do it from last div to first div, in order not to
 541  * change the position of the other divs that still need to
 542  * be removed.
 543  */
 544 static struct isl_basic_map *remove_duplicate_divs(
 545         struct isl_basic_map *bmap, int *progress)
 546 {
 547         unsigned int size;
 548         int *index;
 549         int *elim_for;
 550         int k, l, h;
 551         int bits;
 552         struct isl_blk eq;
 553         unsigned total_var = isl_dim_total(bmap->dim);
 554         unsigned total = total_var + bmap->n_div;
 555         struct isl_ctx *ctx;
 556
 557         if (bmap->n_div <= 1)
 558                 return bmap;
 559
 560         ctx = bmap->ctx;
 561         for (k = bmap->n_div - 1; k >= 0; --k)
 562                 if (!isl_int_is_zero(bmap->div[k][0]))
 563                         break;
 564         if (k <= 0)
 565                 return bmap;
 566
 567         elim_for = isl_calloc_array(ctx, int, bmap->n_div);
 568         size = round_up(4 * bmap->n_div / 3 - 1);
 569         bits = ffs(size) - 1;
 570         index = isl_calloc_array(ctx, int, size);
 571         if (!index)
 572                 return bmap;
 573         eq = isl_blk_alloc(ctx, 1+total);
 574         if (isl_blk_is_error(eq))
 575                 goto out;
 576
 577         isl_seq_clr(eq.data, 1+total);
 578         index[isl_seq_get_hash_bits(bmap->div[k], 2+total, bits)] = k + 1;
 579         for (--k; k >= 0; --k) {
 580                 uint32_t hash;
 581
 582                 if (isl_int_is_zero(bmap->div[k][0]))
 583                         continue;
 584
 585                 hash = isl_seq_get_hash_bits(bmap->div[k], 2+total, bits);
 586                 for (h = hash; index[h]; h = (h+1) % size)
 587                         if (isl_seq_eq(bmap->div[k],
 588                                        bmap->div[index[h]-1], 2+total))
 589                                 break;
 590                 if (index[h]) {
 591                         *progress = 1;
 592                         l = index[h] - 1;
 593                         elim_for[l] = k + 1;
 594                 }
 595                 index[h] = k+1;
 596         }
 597         for (l = bmap->n_div - 1; l >= 0; --l) {
 598                 if (!elim_for[l])
 599                         continue;
 600                 k = elim_for[l] - 1;
 601                 isl_int_set_si(eq.data[1+total_var+k], -1);
 602                 isl_int_set_si(eq.data[1+total_var+l], 1);
 603                 eliminate_div(bmap, eq.data, l);
 604                 isl_int_set_si(eq.data[1+total_var+k], 0);
 605                 isl_int_set_si(eq.data[1+total_var+l], 0);
 606         }
 607
 608         isl_blk_free(ctx, eq);
 609 out:
 610         free(index);
 611         free(elim_for);
 612         return bmap;
 613 }
 614
 615 /* Normalize divs that appear in equalities.
 616  *
 617  * In particular, we assume that bmap contains some equalities
 618  * of the form
 619  *
 620  *      a x = m * e_i
 621  *
 622  * and we want to replace the set of e_i by a minimal set and
 623  * such that the new e_i have a canonical representation in terms
 624  * of the vector x.
 625  * If any of the equalities involves more than one divs, then
 626  * we currently simply bail out.
 627  *
 628  * Let us first additionally assume that all equalities involve
 629  * a div.  The equalities then express modulo constraints on the
 630  * remaining variables and we can use "parameter compression"
 631  * to find a minimal set of constraints.  The result is a transformation
 632  *
 633  *      x = T(x') = x_0 + G x'
 634  *
 635  * with G a lower-triangular matrix with all elements below the diagonal
 636  * non-negative and smaller than the diagonal element on the same row.
 637  * We first normalize x_0 by making the same property hold in the affine
 638  * T matrix.
 639  * The rows i of G with a 1 on the diagonal do not impose any modulo
 640  * constraint and simply express x_i = x'_i.
 641  * For each of the remaining rows i, we introduce a div and a corresponding
 642  * equality.  In particular
 643  *
 644  *      g_ii e_j = x_i - g_i(x')
 645  *
 646  * where each x'_k is replaced either by x_k (if g_kk = 1) or the
 647  * corresponding div (if g_kk != 1).
 648  *
 649  * If there are any equalities not involving any div, then we
 650  * first apply a variable compression on the variables x:
 651  *
 652  *      x = C x''       x'' = C_2 x
 653  *
 654  * and perform the above parameter compression on A C instead of on A.
 655  * The resulting compression is then of the form
 656  *
 657  *      x'' = T(x') = x_0 + G x'
 658  *
 659  * and in constructing the new divs and the corresponding equalities,
 660  * we have to replace each x'', i.e., the x'_k with (g_kk = 1),
 661  * by the corresponding row from C_2.
 662  */
 663 static struct isl_basic_map *normalize_divs(
 664         struct isl_basic_map *bmap, int *progress)
 665 {
 666         int i, j, k;
 667         int total;
 668         int div_eq;
 669         struct isl_mat *B;
 670         struct isl_vec *d;
 671         struct isl_mat *T = NULL;
 672         struct isl_mat *C = NULL;
 673         struct isl_mat *C2 = NULL;
 674         isl_int v;
 675         int *pos;
 676         int dropped, needed;
 677
 678         if (!bmap)
 679                 return NULL;
 680
 681         if (bmap->n_div == 0)
 682                 return bmap;
 683
 684         if (bmap->n_eq == 0)
 685                 return bmap;
 686
 687         if (F_ISSET(bmap, ISL_BASIC_MAP_NORMALIZED_DIVS))
 688                 return bmap;
 689
 690         total = isl_dim_total(bmap->dim);
 691         for (i = 0, j = bmap->n_div-1; i < bmap->n_eq; ++i) {
 692                 while (j >= 0 && isl_int_is_zero(bmap->eq[i][1 + total + j]))
 693                         --j;
 694                 if (j < 0)
 695                         break;
 696                 if (isl_seq_first_non_zero(bmap->eq[i] + 1 + total, j) != -1)
 697                         goto done;
 698         }
 699         div_eq = i;
 700         if (div_eq == 0)
 701                 return bmap;
 702
 703         if (div_eq < bmap->n_eq) {
 704                 B = isl_mat_sub_alloc(bmap->ctx, bmap->eq, div_eq,
 705                                         bmap->n_eq - div_eq, 0, 1 + total);
 706                 C = isl_mat_variable_compression(bmap->ctx, B, &C2);
 707                 if (!C || !C2)
 708                         goto error;
 709                 if (C->n_col == 0) {
 710                         bmap = isl_basic_map_set_to_empty(bmap);
 711                         isl_mat_free(bmap->ctx, C);
 712                         isl_mat_free(bmap->ctx, C2);
 713                         goto done;
 714                 }
 715         }
 716
 717         d = isl_vec_alloc(bmap->ctx, div_eq);
 718         if (!d)
 719                 goto error;
 720         for (i = 0, j = bmap->n_div-1; i < div_eq; ++i) {
 721                 while (j >= 0 && isl_int_is_zero(bmap->eq[i][1 + total + j]))
 722                         --j;
 723                 isl_int_set(d->block.data[i], bmap->eq[i][1 + total + j]);
 724         }
 725         B = isl_mat_sub_alloc(bmap->ctx, bmap->eq, 0, div_eq, 0, 1 + total);
 726
 727         if (C) {
 728                 B = isl_mat_product(bmap->ctx, B, C);
 729                 C = NULL;
 730         }
 731
 732         T = isl_mat_parameter_compression(bmap->ctx, B, d);
 733         if (!T)
 734                 goto error;
 735         if (T->n_col == 0) {
 736                 bmap = isl_basic_map_set_to_empty(bmap);
 737                 isl_mat_free(bmap->ctx, C2);
 738                 isl_mat_free(bmap->ctx, T);
 739                 goto done;
 740         }
 741         isl_int_init(v);
 742         for (i = 0; i < T->n_row - 1; ++i) {
 743                 isl_int_fdiv_q(v, T->row[1 + i][0], T->row[1 + i][1 + i]);
 744                 if (isl_int_is_zero(v))
 745                         continue;
 746                 isl_mat_col_submul(T, 0, v, 1 + i);
 747         }
 748         isl_int_clear(v);
 749         pos = isl_alloc_array(bmap->ctx, int, T->n_row);
 750         /* We have to be careful because dropping equalities may reorder them */
 751         dropped = 0;
 752         for (j = bmap->n_div - 1; j >= 0; --j) {
 753                 for (i = 0; i < bmap->n_eq; ++i)
 754                         if (!isl_int_is_zero(bmap->eq[i][1 + total + j]))
 755                                 break;
 756                 if (i < bmap->n_eq) {
 757                         bmap = isl_basic_map_drop_div(bmap, j);
 758                         isl_basic_map_drop_equality(bmap, i);
 759                         ++dropped;
 760                 }
 761         }
 762         pos[0] = 0;
 763         needed = 0;
 764         for (i = 1; i < T->n_row; ++i) {
 765                 if (isl_int_is_one(T->row[i][i]))
 766                         pos[i] = i;
 767                 else
 768                         needed++;
 769         }
 770         if (needed > dropped) {
 771                 bmap = isl_basic_map_extend_dim(bmap, isl_dim_copy(bmap->dim),
 772                                 needed, needed, 0);
 773                 if (!bmap)
 774                         goto error;
 775         }
 776         for (i = 1; i < T->n_row; ++i) {
 777                 if (isl_int_is_one(T->row[i][i]))
 778                         continue;
 779                 k = isl_basic_map_alloc_div(bmap);
 780                 pos[i] = 1 + total + k;
 781                 isl_seq_clr(bmap->div[k] + 1, 1 + total + bmap->n_div);
 782                 isl_int_set(bmap->div[k][0], T->row[i][i]);
 783                 if (C2)
 784                         isl_seq_cpy(bmap->div[k] + 1, C2->row[i], 1 + total);
 785                 else
 786                         isl_int_set_si(bmap->div[k][1 + i], 1);
 787                 for (j = 0; j < i; ++j) {
 788                         if (isl_int_is_zero(T->row[i][j]))
 789                                 continue;
 790                         if (pos[j] < T->n_row && C2)
 791                                 isl_seq_submul(bmap->div[k] + 1, T->row[i][j],
 792                                                 C2->row[pos[j]], 1 + total);
 793                         else
 794                                 isl_int_neg(bmap->div[k][1 + pos[j]],
 795                                                                 T->row[i][j]);
 796                 }
 797                 j = isl_basic_map_alloc_equality(bmap);
 798                 isl_seq_neg(bmap->eq[j], bmap->div[k]+1, 1+total+bmap->n_div);
 799                 isl_int_set(bmap->eq[j][pos[i]], bmap->div[k][0]);
 800         }
 801         free(pos);
 802         isl_mat_free(bmap->ctx, C2);
 803         isl_mat_free(bmap->ctx, T);
 804
 805         *progress = 1;
 806 done:
 807         F_SET(bmap, ISL_BASIC_MAP_NORMALIZED_DIVS);
 808
 809         return bmap;
 810 error:
 811         isl_mat_free(bmap->ctx, C);
 812         isl_mat_free(bmap->ctx, C2);
 813         isl_mat_free(bmap->ctx, T);
 814         return bmap;
 815 }
 816
 817 static struct isl_basic_map *remove_duplicate_constraints(
 818         struct isl_basic_map *bmap, int *progress)
 819 {
 820         unsigned int size;
 821         isl_int ***index;
 822         int k, l, h;
 823         int bits;
 824         unsigned total = isl_basic_map_total_dim(bmap);
 825         isl_int sum;
 826
 827         if (bmap->n_ineq <= 1)
 828                 return bmap;
 829
 830         size = round_up(4 * (bmap->n_ineq+1) / 3 - 1);
 831         bits = ffs(size) - 1;
 832         index = isl_calloc_array(ctx, isl_int **, size);
 833         if (!index)
 834                 return bmap;
 835
 836         index[isl_seq_get_hash_bits(bmap->ineq[0]+1, total, bits)] = &bmap->ineq[0];
 837         for (k = 1; k < bmap->n_ineq; ++k) {
 838                 h = hash_index(index, size, bits, bmap, k);
 839                 if (!index[h]) {
 840                         index[h] = &bmap->ineq[k];
 841                         continue;
 842                 }
 843                 if (progress)
 844                         *progress = 1;
 845                 l = index[h] - &bmap->ineq[0];
 846                 if (isl_int_lt(bmap->ineq[k][0], bmap->ineq[l][0]))
 847                         swap_inequality(bmap, k, l);
 848                 isl_basic_map_drop_inequality(bmap, k);
 849                 --k;
 850         }
 851         isl_int_init(sum);
 852         for (k = 0; k < bmap->n_ineq-1; ++k) {
 853                 isl_seq_neg(bmap->ineq[k]+1, bmap->ineq[k]+1, total);
 854                 h = hash_index(index, size, bits, bmap, k);
 855                 isl_seq_neg(bmap->ineq[k]+1, bmap->ineq[k]+1, total);
 856                 if (!index[h])
 857                         continue;
 858                 l = index[h] - &bmap->ineq[0];
 859                 isl_int_add(sum, bmap->ineq[k][0], bmap->ineq[l][0]);
 860                 if (isl_int_is_pos(sum))
 861                         continue;
 862                 if (isl_int_is_zero(sum)) {
 863                         /* We need to break out of the loop after these
 864                          * changes since the contents of the hash
 865                          * will no longer be valid.
 866                          * Plus, we probably we want to regauss first.
 867                          */
 868                         isl_basic_map_drop_inequality(bmap, l);
 869                         isl_basic_map_inequality_to_equality(bmap, k);
 870                 } else
 871                         bmap = isl_basic_map_set_to_empty(bmap);
 872                 break;
 873         }
 874         isl_int_clear(sum);
 875
 876         free(index);
 877         return bmap;
 878 }
 879
 880
 881 struct isl_basic_map *isl_basic_map_simplify(struct isl_basic_map *bmap)
 882 {
 883         int progress = 1;
 884         if (!bmap)
 885                 return NULL;
 886         while (progress) {
 887                 progress = 0;
 888                 bmap = normalize_constraints(bmap);
 889                 bmap = eliminate_divs_eq(bmap, &progress);
 890                 bmap = eliminate_divs_ineq(bmap, &progress);
 891                 bmap = isl_basic_map_gauss(bmap, &progress);
 892                 /* requires equalities in normal form */
 893                 bmap = normalize_divs(bmap, &progress);
 894                 bmap = remove_duplicate_divs(bmap, &progress);
 895                 bmap = remove_duplicate_constraints(bmap, &progress);
 896         }
 897         return bmap;
 898 }
 899
 900 struct isl_basic_set *isl_basic_set_simplify(struct isl_basic_set *bset)
 901 {
 902         return (struct isl_basic_set *)
 903                 isl_basic_map_simplify((struct isl_basic_map *)bset);
 904 }
 905
 906
 907 /* If the only constraints a div d=floor(f/m)
 908  * appears in are its two defining constraints
 909  *
 910  *      f - m d >=0
 911  *      -(f - (m - 1)) + m d >= 0
 912  *
 913  * then it can safely be removed.
 914  */
 915 static int div_is_redundant(struct isl_basic_map *bmap, int div)
 916 {
 917         int i;
 918         unsigned pos = 1 + isl_dim_total(bmap->dim) + div;
 919
 920         for (i = 0; i < bmap->n_eq; ++i)
 921                 if (!isl_int_is_zero(bmap->eq[i][pos]))
 922                         return 0;
 923
 924         for (i = 0; i < bmap->n_ineq; ++i) {
 925                 if (isl_int_is_zero(bmap->ineq[i][pos]))
 926                         continue;
 927                 if (isl_int_eq(bmap->ineq[i][pos], bmap->div[div][0])) {
 928                         int neg;
 929                         isl_int_sub(bmap->div[div][1],
 930                                         bmap->div[div][1], bmap->div[div][0]);
 931                         isl_int_add_ui(bmap->div[div][1], bmap->div[div][1], 1);
 932                         neg = isl_seq_is_neg(bmap->ineq[i], bmap->div[div]+1, pos);
 933                         isl_int_sub_ui(bmap->div[div][1], bmap->div[div][1], 1);
 934                         isl_int_add(bmap->div[div][1],
 935                                         bmap->div[div][1], bmap->div[div][0]);
 936                         if (!neg)
 937                                 return 0;
 938                         if (isl_seq_first_non_zero(bmap->ineq[i]+pos+1,
 939                                                     bmap->n_div-div-1) != -1)
 940                                 return 0;
 941                 } else if (isl_int_abs_eq(bmap->ineq[i][pos], bmap->div[div][0])) {
 942                         if (!isl_seq_eq(bmap->ineq[i], bmap->div[div]+1, pos))
 943                                 return 0;
 944                         if (isl_seq_first_non_zero(bmap->ineq[i]+pos+1,
 945                                                     bmap->n_div-div-1) != -1)
 946                                 return 0;
 947                 } else
 948                         return 0;
 949         }
 950
 951         for (i = 0; i < bmap->n_div; ++i)
 952                 if (!isl_int_is_zero(bmap->div[i][1+pos]))
 953                         return 0;
 954
 955         return 1;
 956 }
 957
 958 /*
 959  * Remove divs that don't occur in any of the constraints or other divs.
 960  * These can arise when dropping some of the variables in a quast
 961  * returned by piplib.
 962  */
 963 static struct isl_basic_map *remove_redundant_divs(struct isl_basic_map *bmap)
 964 {
 965         int i;
 966
 967         if (!bmap)
 968                 return NULL;
 969
 970         for (i = bmap->n_div-1; i >= 0; --i) {
 971                 if (!div_is_redundant(bmap, i))
 972                         continue;
 973                 bmap = isl_basic_map_drop_div(bmap, i);
 974         }
 975         return bmap;
 976 }
 977
 978 struct isl_basic_map *isl_basic_map_finalize(struct isl_basic_map *bmap)
 979 {
 980         bmap = remove_redundant_divs(bmap);
 981         if (!bmap)
 982                 return NULL;
 983         F_SET(bmap, ISL_BASIC_SET_FINAL);
 984         return bmap;
 985 }
 986
 987 struct isl_basic_set *isl_basic_set_finalize(struct isl_basic_set *bset)
 988 {
 989         return (struct isl_basic_set *)
 990                 isl_basic_map_finalize((struct isl_basic_map *)bset);
 991 }
 992
 993 struct isl_set *isl_set_finalize(struct isl_set *set)
 994 {
 995         int i;
 996
 997         if (!set)
 998                 return NULL;
 999         for (i = 0; i < set->n; ++i) {
1000                 set->p[i] = isl_basic_set_finalize(set->p[i]);
1001                 if (!set->p[i])
1002                         goto error;
1003         }
1004         return set;
1005 error:
1006         isl_set_free(set);
1007         return NULL;
1008 }
1009
1010 struct isl_map *isl_map_finalize(struct isl_map *map)
1011 {
1012         int i;
1013
1014         if (!map)
1015                 return NULL;
1016         for (i = 0; i < map->n; ++i) {
1017                 map->p[i] = isl_basic_map_finalize(map->p[i]);
1018                 if (!map->p[i])
1019                         goto error;
1020         }
1021         F_CLR(map, ISL_MAP_NORMALIZED);
1022         return map;
1023 error:
1024         isl_map_free(map);
1025         return NULL;
1026 }
1027
1028
1029 /* Remove any div that is defined in terms of the given variable.
1030  */
1031 static struct isl_basic_map *remove_dependent_vars(struct isl_basic_map *bmap,
1032                                                                         int pos)
1033 {
1034         int i;
1035         unsigned dim = isl_dim_total(bmap->dim);
1036
1037         for (i = 0; i < bmap->n_div; ++i) {
1038                 if (isl_int_is_zero(bmap->div[i][0]))
1039                         continue;
1040                 if (isl_int_is_zero(bmap->div[i][1+1+pos]))
1041                         continue;
1042                 bmap = isl_basic_map_eliminate_vars(bmap, dim + i, 1);
1043                 if (!bmap)
1044                         return NULL;
1045         }
1046         return bmap;
1047 }
1048
1049 /* Eliminate the specified variables from the constraints using
1050  * Fourier-Motzkin.  The variables themselves are not removed.
1051  */
1052 struct isl_basic_map *isl_basic_map_eliminate_vars(
1053         struct isl_basic_map *bmap, unsigned pos, unsigned n)
1054 {
1055         int d;
1056         int i, j, k;
1057         unsigned total;
1058
1059         if (n == 0)
1060                 return bmap;
1061         if (!bmap)
1062                 return NULL;
1063         total = isl_basic_map_total_dim(bmap);
1064
1065         bmap = isl_basic_map_cow(bmap);
1066         for (d = pos + n - 1; d >= 0 && d >= pos; --d) {
1067                 int n_lower, n_upper;
1068                 bmap = remove_dependent_vars(bmap, d);
1069                 if (!bmap)
1070                         return NULL;
1071                 if (d >= total - bmap->n_div)
1072                         isl_seq_clr(bmap->div[d-(total-bmap->n_div)], 2+total);
1073                 for (i = 0; i < bmap->n_eq; ++i) {
1074                         if (isl_int_is_zero(bmap->eq[i][1+d]))
1075                                 continue;
1076                         eliminate_var_using_equality(bmap, d, bmap->eq[i], NULL);
1077                         isl_basic_map_drop_equality(bmap, i);
1078                         break;
1079                 }
1080                 if (i < bmap->n_eq)
1081                         continue;
1082                 n_lower = 0;
1083                 n_upper = 0;
1084                 for (i = 0; i < bmap->n_ineq; ++i) {
1085                         if (isl_int_is_pos(bmap->ineq[i][1+d]))
1086                                 n_lower++;
1087                         else if (isl_int_is_neg(bmap->ineq[i][1+d]))
1088                                 n_upper++;
1089                 }
1090                 bmap = isl_basic_map_extend_constraints(bmap,
1091                                 0, n_lower * n_upper);
1092                 for (i = bmap->n_ineq - 1; i >= 0; --i) {
1093                         int last;
1094                         if (isl_int_is_zero(bmap->ineq[i][1+d]))
1095                                 continue;
1096                         last = -1;
1097                         for (j = 0; j < i; ++j) {
1098                                 if (isl_int_is_zero(bmap->ineq[j][1+d]))
1099                                         continue;
1100                                 last = j;
1101                                 if (isl_int_sgn(bmap->ineq[i][1+d]) ==
1102                                     isl_int_sgn(bmap->ineq[j][1+d]))
1103                                         continue;
1104                                 k = isl_basic_map_alloc_inequality(bmap);
1105                                 if (k < 0)
1106                                         goto error;
1107                                 isl_seq_cpy(bmap->ineq[k], bmap->ineq[i],
1108                                                 1+total);
1109                                 isl_seq_elim(bmap->ineq[k], bmap->ineq[j],
1110                                                 1+d, 1+total, NULL);
1111                         }
1112                         isl_basic_map_drop_inequality(bmap, i);
1113                         i = last + 1;
1114                 }
1115                 if (n_lower > 0 && n_upper > 0) {
1116                         bmap = normalize_constraints(bmap);
1117                         bmap = remove_duplicate_constraints(bmap, NULL);
1118                         bmap = isl_basic_map_gauss(bmap, NULL);
1119                         bmap = isl_basic_map_convex_hull(bmap);
1120                         if (!bmap)
1121                                 goto error;
1122                         if (F_ISSET(bmap, ISL_BASIC_MAP_EMPTY))
1123                                 break;
1124                 }
1125         }
1126         F_CLR(bmap, ISL_BASIC_MAP_NORMALIZED);
1127         return bmap;
1128 error:
1129         isl_basic_map_free(bmap);
1130         return NULL;
1131 }
1132
1133 struct isl_basic_set *isl_basic_set_eliminate_vars(
1134         struct isl_basic_set *bset, unsigned pos, unsigned n)
1135 {
1136         return (struct isl_basic_set *)isl_basic_map_eliminate_vars(
1137                         (struct isl_basic_map *)bset, pos, n);
1138 }
1139
1140 static void compute_elimination_index(struct isl_basic_map *bmap, int *elim)
1141 {
1142         int d, i;
1143         unsigned total;
1144
1145         total = isl_dim_total(bmap->dim);
1146         for (d = 0; d < total; ++d)
1147                 elim[d] = -1;
1148         for (d = total - 1, i = 0; d >= 0 && i < bmap->n_eq; ++i) {
1149                 for (; d >= 0; --d) {
1150                         if (isl_int_is_zero(bmap->eq[i][1+d]))
1151                                 continue;
1152                         elim[d] = i;
1153                         break;
1154                 }
1155         }
1156 }
1157
1158 static void set_compute_elimination_index(struct isl_basic_set *bset, int *elim)
1159 {
1160         return compute_elimination_index((struct isl_basic_map *)bset, elim);
1161 }
1162
1163 static int reduced_using_equalities(isl_int *dst, isl_int *src,
1164         struct isl_basic_map *bmap, int *elim)
1165 {
1166         int d, i;
1167         int copied = 0;
1168         unsigned total;
1169
1170         total = isl_dim_total(bmap->dim);
1171         for (d = total - 1; d >= 0; --d) {
1172                 if (isl_int_is_zero(src[1+d]))
1173                         continue;
1174                 if (elim[d] == -1)
1175                         continue;
1176                 if (!copied) {
1177                         isl_seq_cpy(dst, src, 1 + total);
1178                         copied = 1;
1179                 }
1180                 isl_seq_elim(dst, bmap->eq[elim[d]], 1 + d, 1 + total, NULL);
1181         }
1182         return copied;
1183 }
1184
1185 static int set_reduced_using_equalities(isl_int *dst, isl_int *src,
1186         struct isl_basic_set *bset, int *elim)
1187 {
1188         return reduced_using_equalities(dst, src,
1189                                         (struct isl_basic_map *)bset, elim);
1190 }
1191
1192 static struct isl_basic_set *isl_basic_set_reduce_using_equalities(
1193         struct isl_basic_set *bset, struct isl_basic_set *context)
1194 {
1195         int i;
1196         int *elim;
1197
1198         if (!bset || !context)
1199                 goto error;
1200
1201         bset = isl_basic_set_cow(bset);
1202         if (!bset)
1203                 goto error;
1204
1205         elim = isl_alloc_array(ctx, int, isl_basic_set_n_dim(bset));
1206         if (!elim)
1207                 goto error;
1208         set_compute_elimination_index(context, elim);
1209         for (i = 0; i < bset->n_eq; ++i)
1210                 set_reduced_using_equalities(bset->eq[i], bset->eq[i],
1211                                                         context, elim);
1212         for (i = 0; i < bset->n_ineq; ++i)
1213                 set_reduced_using_equalities(bset->ineq[i], bset->ineq[i],
1214                                                         context, elim);
1215         isl_basic_set_free(context);
1216         free(elim);
1217         bset = isl_basic_set_simplify(bset);
1218         bset = isl_basic_set_finalize(bset);
1219         return bset;
1220 error:
1221         isl_basic_set_free(bset);
1222         isl_basic_set_free(context);
1223         return NULL;
1224 }
1225
1226 static struct isl_basic_set *remove_shifted_constraints(
1227         struct isl_basic_set *bset, struct isl_basic_set *context)
1228 {
1229         unsigned int size;
1230         isl_int ***index;
1231         int bits;
1232         int k, h, l;
1233
1234         if (!bset)
1235                 return NULL;
1236
1237         size = round_up(4 * (context->n_ineq+1) / 3 - 1);
1238         bits = ffs(size) - 1;
1239         index = isl_calloc_array(ctx, isl_int **, size);
1240         if (!index)
1241                 return bset;
1242
1243         for (k = 0; k < context->n_ineq; ++k) {
1244                 h = set_hash_index(index, size, bits, context, k);
1245                 index[h] = &context->ineq[k];
1246         }
1247         for (k = 0; k < bset->n_ineq; ++k) {
1248                 h = set_hash_index(index, size, bits, bset, k);
1249                 if (!index[h])
1250                         continue;
1251                 l = index[h] - &context->ineq[0];
1252                 if (isl_int_lt(bset->ineq[k][0], context->ineq[l][0]))
1253                         continue;
1254                 bset = isl_basic_set_cow(bset);
1255                 if (!bset)
1256                         goto error;
1257                 isl_basic_set_drop_inequality(bset, k);
1258                 --k;
1259         }
1260         free(index);
1261         return bset;
1262 error:
1263         free(index);
1264         return bset;
1265 }
1266
1267 static struct isl_basic_set *uset_gist(struct isl_basic_set *bset,
1268         struct isl_basic_set *context);
1269
1270 static struct isl_basic_set *uset_gist_context_eq(struct isl_basic_set *bset,
1271         struct isl_basic_set *context)
1272 {
1273         struct isl_mat *T;
1274         struct isl_mat *T2;
1275         struct isl_ctx *ctx = context->ctx;
1276         struct isl_basic_set *reduced_context;
1277         reduced_context = isl_basic_set_remove_equalities(
1278                                 isl_basic_set_copy(context), &T, &T2);
1279         if (!reduced_context)
1280                 goto error;
1281         bset = isl_basic_set_preimage(ctx, bset, T);
1282         bset = uset_gist(bset, reduced_context);
1283         bset = isl_basic_set_preimage(ctx, bset, T2);
1284         bset = isl_basic_set_reduce_using_equalities(bset, context);
1285         return bset;
1286 error:
1287         isl_basic_set_free(context);
1288         isl_basic_set_free(bset);
1289         return NULL;
1290 }
1291
1292 static struct isl_basic_set *uset_gist_set_eq(struct isl_basic_set *bset,
1293         struct isl_basic_set *context)
1294 {
1295         struct isl_mat *T;
1296         struct isl_mat *T2;
1297         struct isl_ctx *ctx = context->ctx;
1298         struct isl_basic_set *affine_hull = NULL;
1299
1300         affine_hull = isl_basic_set_copy(bset);
1301         affine_hull = isl_basic_set_cow(affine_hull);
1302         if (!affine_hull)
1303                 goto error;
1304         isl_basic_set_free_inequality(affine_hull, affine_hull->n_ineq);
1305
1306         bset = isl_basic_set_remove_equalities(bset, &T, &T2);
1307         if (!bset)
1308                 goto error;
1309         context = isl_basic_set_preimage(ctx, context, T);
1310         bset = uset_gist(bset, context);
1311         bset = isl_basic_set_preimage(ctx, bset, T2);
1312         bset = isl_basic_set_intersect(bset, affine_hull);
1313         return bset;
1314 error:
1315         isl_basic_set_free(affine_hull);
1316         isl_basic_set_free(context);
1317         isl_basic_set_free(bset);
1318         return NULL;
1319 }
1320
1321 /* Remove all information from bset that is redundant in the context
1322  * of context.  In particular, equalities that are linear combinations
1323  * of those in context are removed.  Then the inequalities that are
1324  * redundant in the context of the equalities and inequalities of
1325  * context are removed.
1326  */
1327 static struct isl_basic_set *uset_gist(struct isl_basic_set *bset,
1328         struct isl_basic_set *context)
1329 {
1330         int i;
1331         isl_int opt;
1332         struct isl_basic_set *combined;
1333         struct isl_ctx *ctx;
1334
1335         if (!bset || !context)
1336                 goto error;
1337
1338         if (context->n_eq > 0)
1339                 return uset_gist_context_eq(bset, context);
1340         if (!context->n_ineq)
1341                 goto done;
1342         if (bset->n_eq > 0)
1343                 return uset_gist_set_eq(bset, context);
1344         bset = remove_shifted_constraints(bset, context);
1345         combined = isl_basic_set_extend_constraints(isl_basic_set_copy(bset),
1346                         context->n_eq, context->n_ineq);
1347         context = isl_basic_set_add_constraints(combined, context, 0);
1348         if (!context)
1349                 goto error;
1350         ctx = context->ctx;
1351         isl_int_init(opt);
1352         for (i = bset->n_ineq-1; i >= 0; --i) {
1353                 int redundant;
1354                 set_swap_inequality(context, i, context->n_ineq-1);
1355                 context->n_ineq--;
1356                 redundant = isl_basic_set_constraint_is_redundant(&context,
1357                                 context->ineq[context->n_ineq], &opt, NULL);
1358                 if (redundant == -1) {
1359                         isl_int_clear(opt);
1360                         goto error;
1361                 }
1362                 if (F_ISSET(context, ISL_BASIC_MAP_EMPTY)) {
1363                         bset = isl_basic_set_set_to_empty(bset);
1364                         break;
1365                 }
1366                 context->n_ineq++;
1367                 set_swap_inequality(context, i, context->n_ineq-1);
1368                 if (redundant) {
1369                         isl_basic_set_drop_inequality(context, i);
1370                         isl_basic_set_drop_inequality(bset, i);
1371                 }
1372         }
1373         isl_int_clear(opt);
1374 done:
1375         isl_basic_set_free(context);
1376         return bset;
1377 error:
1378         isl_basic_set_free(context);
1379         isl_basic_set_free(bset);
1380         return NULL;
1381 }
1382
1383 struct isl_basic_map *isl_basic_map_gist(struct isl_basic_map *bmap,
1384         struct isl_basic_map *context)
1385 {
1386         struct isl_basic_set *bset;
1387
1388         if (!bmap || !context)
1389                 goto error;
1390
1391         context = isl_basic_map_align_divs(context, bmap);
1392         bmap = isl_basic_map_align_divs(bmap, context);
1393
1394         bset = uset_gist(isl_basic_map_underlying_set(isl_basic_map_copy(bmap)),
1395                          isl_basic_map_underlying_set(context));
1396
1397         return isl_basic_map_overlying_set(bset, bmap);
1398 error:
1399         isl_basic_map_free(bmap);
1400         isl_basic_map_free(context);
1401         return NULL;
1402 }
1403
1404 /*
1405  * Assumes context has no implicit divs.
1406  */
1407 struct isl_map *isl_map_gist(struct isl_map *map, struct isl_basic_map *context)
1408 {
1409         int i;
1410
1411         map = isl_map_cow(map);
1412         if (!map || !context)
1413                 return NULL;
1414         isl_assert(map->ctx, isl_dim_equal(map->dim, context->dim), goto error);
1415         map = isl_map_compute_divs(map);
1416         for (i = 0; i < map->n; ++i)
1417                 context = isl_basic_map_align_divs(context, map->p[i]);
1418         for (i = 0; i < map->n; ++i) {
1419                 map->p[i] = isl_basic_map_gist(map->p[i],
1420                                                 isl_basic_map_copy(context));
1421                 if (!map->p[i])
1422                         goto error;
1423         }
1424         isl_basic_map_free(context);
1425         F_CLR(map, ISL_MAP_NORMALIZED);
1426         return map;
1427 error:
1428         isl_map_free(map);
1429         isl_basic_map_free(context);
1430         return NULL;
1431 }
1432
1433 struct isl_basic_set *isl_basic_set_gist(struct isl_basic_set *bset,
1434                                                 struct isl_basic_set *context)
1435 {
1436         return (struct isl_basic_set *)isl_basic_map_gist(
1437                 (struct isl_basic_map *)bset, (struct isl_basic_map *)context);
1438 }
1439
1440 struct isl_set *isl_set_gist(struct isl_set *set, struct isl_basic_set *context)
1441 {
1442         return (struct isl_set *)isl_map_gist((struct isl_map *)set,
1443                                         (struct isl_basic_map *)context);
1444 }
1445
1446 /* Quick check to see if two basic maps are disjoint.
1447  * In particular, we reduce the equalities and inequalities of
1448  * one basic map in the context of the equalities of the other
1449  * basic map and check if we get a contradiction.
1450  */
1451 int isl_basic_map_fast_is_disjoint(struct isl_basic_map *bmap1,
1452         struct isl_basic_map *bmap2)
1453 {
1454         struct isl_vec *v = NULL;
1455         int *elim = NULL;
1456         unsigned total;
1457         int d, i;
1458
1459         if (!bmap1 || !bmap2)
1460                 return -1;
1461         isl_assert(bmap1->ctx, isl_dim_equal(bmap1->dim, bmap2->dim),
1462                         return -1);
1463         if (bmap1->n_div || bmap2->n_div)
1464                 return 0;
1465         if (!bmap1->n_eq && !bmap2->n_eq)
1466                 return 0;
1467
1468         total = isl_dim_total(bmap1->dim);
1469         if (total == 0)
1470                 return 0;
1471         v = isl_vec_alloc(bmap1->ctx, 1 + total);
1472         if (!v)
1473                 goto error;
1474         elim = isl_alloc_array(bmap1->ctx, int, total);
1475         if (!elim)
1476                 goto error;
1477         compute_elimination_index(bmap1, elim);
1478         for (i = 0; i < bmap2->n_eq; ++i) {
1479                 int reduced;
1480                 reduced = reduced_using_equalities(v->block.data, bmap2->eq[i],
1481                                                         bmap1, elim);
1482                 if (reduced && !isl_int_is_zero(v->block.data[0]) &&
1483                     isl_seq_first_non_zero(v->block.data + 1, total) == -1)
1484                         goto disjoint;
1485         }
1486         for (i = 0; i < bmap2->n_ineq; ++i) {
1487                 int reduced;
1488                 reduced = reduced_using_equalities(v->block.data,
1489                                                 bmap2->ineq[i], bmap1, elim);
1490                 if (reduced && isl_int_is_neg(v->block.data[0]) &&
1491                     isl_seq_first_non_zero(v->block.data + 1, total) == -1)
1492                         goto disjoint;
1493         }
1494         compute_elimination_index(bmap2, elim);
1495         for (i = 0; i < bmap1->n_ineq; ++i) {
1496                 int reduced;
1497                 reduced = reduced_using_equalities(v->block.data,
1498                                                 bmap1->ineq[i], bmap2, elim);
1499                 if (reduced && isl_int_is_neg(v->block.data[0]) &&
1500                     isl_seq_first_non_zero(v->block.data + 1, total) == -1)
1501                         goto disjoint;
1502         }
1503         isl_vec_free(bmap1->ctx, v);
1504         free(elim);
1505         return 0;
1506 disjoint:
1507         isl_vec_free(bmap1->ctx, v);
1508         free(elim);
1509         return 1;
1510 error:
1511         isl_vec_free(bmap1->ctx, v);
1512         free(elim);
1513         return -1;
1514 }
1515
1516 int isl_basic_set_fast_is_disjoint(struct isl_basic_set *bset1,
1517         struct isl_basic_set *bset2)
1518 {
1519         return isl_basic_map_fast_is_disjoint((struct isl_basic_map *)bset1,
1520                                               (struct isl_basic_map *)bset2);
1521 }
1522
1523 int isl_map_fast_is_disjoint(struct isl_map *map1, struct isl_map *map2)
1524 {
1525         int i, j;
1526
1527         if (!map1 || !map2)
1528                 return -1;
1529
1530         if (isl_map_fast_is_equal(map1, map2))
1531                 return 0;
1532
1533         for (i = 0; i < map1->n; ++i) {
1534                 for (j = 0; j < map2->n; ++j) {
1535                         int d = isl_basic_map_fast_is_disjoint(map1->p[i],
1536                                                                map2->p[j]);
1537                         if (d != 1)
1538                                 return d;
1539                 }
1540         }
1541         return 1;
1542 }
1543
1544 int isl_set_fast_is_disjoint(struct isl_set *set1, struct isl_set *set2)
1545 {
1546         return isl_map_fast_is_disjoint((struct isl_map *)set1,
1547                                         (struct isl_map *)set2);
1548 }