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         ISL_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         ISL_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         ISL_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(struct isl_map *map,
 170         enum isl_dim_type type, unsigned first, unsigned n)
 171 {
 172         int i;
 173
 174         if (!map)
 175                 goto error;
 176
 177         isl_assert(map->ctx, first + n <= isl_map_dim(map, type), 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(map->dim, type, 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(map->p[i], type, first, n);
 190                 if (!map->p[i])
 191                         goto error;
 192         }
 193         ISL_F_CLR(map, ISL_MAP_NORMALIZED);
 194
 195         return map;
 196 error:
 197         isl_map_free(map);
 198         return NULL;
 199 }
 200
 201 struct isl_map *isl_map_drop_inputs(
 202                 struct isl_map *map, unsigned first, unsigned n)
 203 {
 204         return isl_map_drop(map, isl_dim_in, first, n);
 205 }
 206
 207 /*
 208  * We don't cow, as the div is assumed to be redundant.
 209  */
 210 static struct isl_basic_map *isl_basic_map_drop_div(
 211                 struct isl_basic_map *bmap, unsigned div)
 212 {
 213         int i;
 214         unsigned pos;
 215
 216         if (!bmap)
 217                 goto error;
 218
 219         pos = 1 + isl_dim_total(bmap->dim) + div;
 220
 221         isl_assert(bmap->ctx, div < bmap->n_div, goto error);
 222
 223         for (i = 0; i < bmap->n_eq; ++i)
 224                 constraint_drop_vars(bmap->eq[i]+pos, 1, bmap->extra-div-1);
 225
 226         for (i = 0; i < bmap->n_ineq; ++i) {
 227                 if (!isl_int_is_zero(bmap->ineq[i][pos])) {
 228                         isl_basic_map_drop_inequality(bmap, i);
 229                         --i;
 230                         continue;
 231                 }
 232                 constraint_drop_vars(bmap->ineq[i]+pos, 1, bmap->extra-div-1);
 233         }
 234
 235         for (i = 0; i < bmap->n_div; ++i)
 236                 constraint_drop_vars(bmap->div[i]+1+pos, 1, bmap->extra-div-1);
 237
 238         if (div != bmap->n_div - 1) {
 239                 int j;
 240                 isl_int *t = bmap->div[div];
 241
 242                 for (j = div; j < bmap->n_div - 1; ++j)
 243                         bmap->div[j] = bmap->div[j+1];
 244
 245                 bmap->div[bmap->n_div - 1] = t;
 246         }
 247         ISL_F_CLR(bmap, ISL_BASIC_MAP_NORMALIZED);
 248         isl_basic_map_free_div(bmap, 1);
 249
 250         return bmap;
 251 error:
 252         isl_basic_map_free(bmap);
 253         return NULL;
 254 }
 255
 256 struct isl_basic_map *isl_basic_map_normalize_constraints(
 257         struct isl_basic_map *bmap)
 258 {
 259         int i;
 260         isl_int gcd;
 261         unsigned total = isl_basic_map_total_dim(bmap);
 262
 263         isl_int_init(gcd);
 264         for (i = bmap->n_eq - 1; i >= 0; --i) {
 265                 isl_seq_gcd(bmap->eq[i]+1, total, &gcd);
 266                 if (isl_int_is_zero(gcd)) {
 267                         if (!isl_int_is_zero(bmap->eq[i][0])) {
 268                                 bmap = isl_basic_map_set_to_empty(bmap);
 269                                 break;
 270                         }
 271                         isl_basic_map_drop_equality(bmap, i);
 272                         continue;
 273                 }
 274                 if (ISL_F_ISSET(bmap, ISL_BASIC_MAP_RATIONAL))
 275                         isl_int_gcd(gcd, gcd, bmap->eq[i][0]);
 276                 if (isl_int_is_one(gcd))
 277                         continue;
 278                 if (!isl_int_is_divisible_by(bmap->eq[i][0], gcd)) {
 279                         bmap = isl_basic_map_set_to_empty(bmap);
 280                         break;
 281                 }
 282                 isl_seq_scale_down(bmap->eq[i], bmap->eq[i], gcd, 1+total);
 283         }
 284
 285         for (i = bmap->n_ineq - 1; i >= 0; --i) {
 286                 isl_seq_gcd(bmap->ineq[i]+1, total, &gcd);
 287                 if (isl_int_is_zero(gcd)) {
 288                         if (isl_int_is_neg(bmap->ineq[i][0])) {
 289                                 bmap = isl_basic_map_set_to_empty(bmap);
 290                                 break;
 291                         }
 292                         isl_basic_map_drop_inequality(bmap, i);
 293                         continue;
 294                 }
 295                 if (ISL_F_ISSET(bmap, ISL_BASIC_MAP_RATIONAL))
 296                         isl_int_gcd(gcd, gcd, bmap->ineq[i][0]);
 297                 if (isl_int_is_one(gcd))
 298                         continue;
 299                 isl_int_fdiv_q(bmap->ineq[i][0], bmap->ineq[i][0], gcd);
 300                 isl_seq_scale_down(bmap->ineq[i]+1, bmap->ineq[i]+1, gcd, total);
 301         }
 302         isl_int_clear(gcd);
 303
 304         return bmap;
 305 }
 306
 307 struct isl_basic_set *isl_basic_set_normalize_constraints(
 308         struct isl_basic_set *bset)
 309 {
 310         (struct isl_basic_set *)isl_basic_map_normalize_constraints(
 311                 (struct isl_basic_map *)bset);
 312 }
 313
 314 static void eliminate_div(struct isl_basic_map *bmap, isl_int *eq, unsigned div)
 315 {
 316         int i;
 317         unsigned pos = 1 + isl_dim_total(bmap->dim) + div;
 318         unsigned len;
 319         len = 1 + isl_basic_map_total_dim(bmap);
 320
 321         for (i = 0; i < bmap->n_eq; ++i)
 322                 if (bmap->eq[i] != eq)
 323                         isl_seq_elim(bmap->eq[i], eq, pos, len, NULL);
 324
 325         for (i = 0; i < bmap->n_ineq; ++i)
 326                 isl_seq_elim(bmap->ineq[i], eq, pos, len, NULL);
 327
 328         /* We need to be careful about circular definitions,
 329          * so for now we just remove the definitions of other divs that
 330          * depend on this div and (possibly) recompute them later.
 331          */
 332         for (i = 0; i < bmap->n_div; ++i)
 333                 if (!isl_int_is_zero(bmap->div[i][0]) &&
 334                     !isl_int_is_zero(bmap->div[i][1 + pos]))
 335                         isl_seq_clr(bmap->div[i], 1 + len);
 336
 337         isl_basic_map_drop_div(bmap, div);
 338 }
 339
 340 /* Elimininate divs based on equalities
 341  */
 342 static struct isl_basic_map *eliminate_divs_eq(
 343                 struct isl_basic_map *bmap, int *progress)
 344 {
 345         int d;
 346         int i;
 347         int modified = 0;
 348         unsigned off;
 349
 350         if (!bmap)
 351                 return NULL;
 352
 353         off = 1 + isl_dim_total(bmap->dim);
 354
 355         for (d = bmap->n_div - 1; d >= 0 ; --d) {
 356                 for (i = 0; i < bmap->n_eq; ++i) {
 357                         if (!isl_int_is_one(bmap->eq[i][off + d]) &&
 358                             !isl_int_is_negone(bmap->eq[i][off + d]))
 359                                 continue;
 360                         modified = 1;
 361                         *progress = 1;
 362                         eliminate_div(bmap, bmap->eq[i], d);
 363                         isl_basic_map_drop_equality(bmap, i);
 364                         break;
 365                 }
 366         }
 367         if (modified)
 368                 return eliminate_divs_eq(bmap, progress);
 369         return bmap;
 370 }
 371
 372 /* Elimininate divs based on inequalities
 373  */
 374 static struct isl_basic_map *eliminate_divs_ineq(
 375                 struct isl_basic_map *bmap, int *progress)
 376 {
 377         int d;
 378         int i;
 379         unsigned off;
 380         struct isl_ctx *ctx;
 381
 382         if (!bmap)
 383                 return NULL;
 384
 385         ctx = bmap->ctx;
 386         off = 1 + isl_dim_total(bmap->dim);
 387
 388         for (d = bmap->n_div - 1; d >= 0 ; --d) {
 389                 for (i = 0; i < bmap->n_eq; ++i)
 390                         if (!isl_int_is_zero(bmap->eq[i][off + d]))
 391                                 break;
 392                 if (i < bmap->n_eq)
 393                         continue;
 394                 for (i = 0; i < bmap->n_ineq; ++i)
 395                         if (isl_int_abs_gt(bmap->ineq[i][off + d], ctx->one))
 396                                 break;
 397                 if (i < bmap->n_ineq)
 398                         continue;
 399                 *progress = 1;
 400                 bmap = isl_basic_map_eliminate_vars(bmap, (off-1)+d, 1);
 401                 if (ISL_F_ISSET(bmap, ISL_BASIC_MAP_EMPTY))
 402                         break;
 403                 bmap = isl_basic_map_drop_div(bmap, d);
 404                 if (!bmap)
 405                         break;
 406         }
 407         return bmap;
 408 }
 409
 410 static void eliminate_var_using_equality(struct isl_basic_map *bmap,
 411         unsigned pos, isl_int *eq, int *progress)
 412 {
 413         unsigned total;
 414         int k;
 415         int contains_divs;
 416
 417         total = isl_basic_map_total_dim(bmap);
 418         contains_divs =
 419                 isl_seq_first_non_zero(eq + 1 + isl_dim_total(bmap->dim),
 420                                                 bmap->n_div) != -1;
 421         for (k = 0; k < bmap->n_eq; ++k) {
 422                 if (bmap->eq[k] == eq)
 423                         continue;
 424                 if (isl_int_is_zero(bmap->eq[k][1+pos]))
 425                         continue;
 426                 if (progress)
 427                         *progress = 1;
 428                 isl_seq_elim(bmap->eq[k], eq, 1+pos, 1+total, NULL);
 429         }
 430
 431         for (k = 0; k < bmap->n_ineq; ++k) {
 432                 if (isl_int_is_zero(bmap->ineq[k][1+pos]))
 433                         continue;
 434                 if (progress)
 435                         *progress = 1;
 436                 isl_seq_elim(bmap->ineq[k], eq, 1+pos, 1+total, NULL);
 437                 ISL_F_CLR(bmap, ISL_BASIC_MAP_NORMALIZED);
 438         }
 439
 440         for (k = 0; k < bmap->n_div; ++k) {
 441                 if (isl_int_is_zero(bmap->div[k][0]))
 442                         continue;
 443                 if (isl_int_is_zero(bmap->div[k][1+1+pos]))
 444                         continue;
 445                 if (progress)
 446                         *progress = 1;
 447                 /* We need to be careful about circular definitions,
 448                  * so for now we just remove the definition of div k
 449                  * if the equality contains any divs.
 450                  */
 451                 if (contains_divs)
 452                         isl_seq_clr(bmap->div[k], 1 + total);
 453                 else
 454                         isl_seq_elim(bmap->div[k]+1, eq,
 455                                         1+pos, 1+total, &bmap->div[k][0]);
 456                 ISL_F_CLR(bmap, ISL_BASIC_MAP_NORMALIZED);
 457         }
 458 }
 459
 460 struct isl_basic_map *isl_basic_map_gauss(
 461         struct isl_basic_map *bmap, int *progress)
 462 {
 463         int k;
 464         int done;
 465         int last_var;
 466         unsigned total_var;
 467         unsigned total;
 468
 469         if (!bmap)
 470                 return NULL;
 471
 472         total = isl_basic_map_total_dim(bmap);
 473         total_var = total - bmap->n_div;
 474
 475         last_var = total - 1;
 476         for (done = 0; done < bmap->n_eq; ++done) {
 477                 for (; last_var >= 0; --last_var) {
 478                         for (k = done; k < bmap->n_eq; ++k)
 479                                 if (!isl_int_is_zero(bmap->eq[k][1+last_var]))
 480                                         break;
 481                         if (k < bmap->n_eq)
 482                                 break;
 483                 }
 484                 if (last_var < 0)
 485                         break;
 486                 if (k != done)
 487                         swap_equality(bmap, k, done);
 488                 if (isl_int_is_neg(bmap->eq[done][1+last_var]))
 489                         isl_seq_neg(bmap->eq[done], bmap->eq[done], 1+total);
 490
 491                 eliminate_var_using_equality(bmap, last_var, bmap->eq[done],
 492                                                 progress);
 493
 494                 if (last_var >= total_var &&
 495                     isl_int_is_zero(bmap->div[last_var - total_var][0])) {
 496                         unsigned div = last_var - total_var;
 497                         isl_seq_neg(bmap->div[div]+1, bmap->eq[done], 1+total);
 498                         isl_int_set_si(bmap->div[div][1+1+last_var], 0);
 499                         isl_int_set(bmap->div[div][0],
 500                                     bmap->eq[done][1+last_var]);
 501                         ISL_F_CLR(bmap, ISL_BASIC_MAP_NORMALIZED);
 502                 }
 503         }
 504         if (done == bmap->n_eq)
 505                 return bmap;
 506         for (k = done; k < bmap->n_eq; ++k) {
 507                 if (isl_int_is_zero(bmap->eq[k][0]))
 508                         continue;
 509                 return isl_basic_map_set_to_empty(bmap);
 510         }
 511         isl_basic_map_free_equality(bmap, bmap->n_eq-done);
 512         return bmap;
 513 }
 514
 515 struct isl_basic_set *isl_basic_set_gauss(
 516         struct isl_basic_set *bset, int *progress)
 517 {
 518         return (struct isl_basic_set*)isl_basic_map_gauss(
 519                         (struct isl_basic_map *)bset, progress);
 520 }
 521
 522
 523 static unsigned int round_up(unsigned int v)
 524 {
 525         int old_v = v;
 526
 527         while (v) {
 528                 old_v = v;
 529                 v ^= v & -v;
 530         }
 531         return old_v << 1;
 532 }
 533
 534 static int hash_index(isl_int ***index, unsigned int size, int bits,
 535                         struct isl_basic_map *bmap, int k)
 536 {
 537         int h;
 538         unsigned total = isl_basic_map_total_dim(bmap);
 539         uint32_t hash = isl_seq_get_hash_bits(bmap->ineq[k]+1, total, bits);
 540         for (h = hash; index[h]; h = (h+1) % size)
 541                 if (&bmap->ineq[k] != index[h] &&
 542                     isl_seq_eq(bmap->ineq[k]+1, index[h][0]+1, total))
 543                         break;
 544         return h;
 545 }
 546
 547 static int set_hash_index(isl_int ***index, unsigned int size, int bits,
 548                           struct isl_basic_set *bset, int k)
 549 {
 550         return hash_index(index, size, bits, (struct isl_basic_map *)bset, k);
 551 }
 552
 553 /* If we can eliminate more than one div, then we need to make
 554  * sure we do it from last div to first div, in order not to
 555  * change the position of the other divs that still need to
 556  * be removed.
 557  */
 558 static struct isl_basic_map *remove_duplicate_divs(
 559         struct isl_basic_map *bmap, int *progress)
 560 {
 561         unsigned int size;
 562         int *index;
 563         int *elim_for;
 564         int k, l, h;
 565         int bits;
 566         struct isl_blk eq;
 567         unsigned total_var = isl_dim_total(bmap->dim);
 568         unsigned total = total_var + bmap->n_div;
 569         struct isl_ctx *ctx;
 570
 571         if (bmap->n_div <= 1)
 572                 return bmap;
 573
 574         ctx = bmap->ctx;
 575         for (k = bmap->n_div - 1; k >= 0; --k)
 576                 if (!isl_int_is_zero(bmap->div[k][0]))
 577                         break;
 578         if (k <= 0)
 579                 return bmap;
 580
 581         elim_for = isl_calloc_array(ctx, int, bmap->n_div);
 582         size = round_up(4 * bmap->n_div / 3 - 1);
 583         bits = ffs(size) - 1;
 584         index = isl_calloc_array(ctx, int, size);
 585         if (!index)
 586                 return bmap;
 587         eq = isl_blk_alloc(ctx, 1+total);
 588         if (isl_blk_is_error(eq))
 589                 goto out;
 590
 591         isl_seq_clr(eq.data, 1+total);
 592         index[isl_seq_get_hash_bits(bmap->div[k], 2+total, bits)] = k + 1;
 593         for (--k; k >= 0; --k) {
 594                 uint32_t hash;
 595
 596                 if (isl_int_is_zero(bmap->div[k][0]))
 597                         continue;
 598
 599                 hash = isl_seq_get_hash_bits(bmap->div[k], 2+total, bits);
 600                 for (h = hash; index[h]; h = (h+1) % size)
 601                         if (isl_seq_eq(bmap->div[k],
 602                                        bmap->div[index[h]-1], 2+total))
 603                                 break;
 604                 if (index[h]) {
 605                         *progress = 1;
 606                         l = index[h] - 1;
 607                         elim_for[l] = k + 1;
 608                 }
 609                 index[h] = k+1;
 610         }
 611         for (l = bmap->n_div - 1; l >= 0; --l) {
 612                 if (!elim_for[l])
 613                         continue;
 614                 k = elim_for[l] - 1;
 615                 isl_int_set_si(eq.data[1+total_var+k], -1);
 616                 isl_int_set_si(eq.data[1+total_var+l], 1);
 617                 eliminate_div(bmap, eq.data, l);
 618                 isl_int_set_si(eq.data[1+total_var+k], 0);
 619                 isl_int_set_si(eq.data[1+total_var+l], 0);
 620         }
 621
 622         isl_blk_free(ctx, eq);
 623 out:
 624         free(index);
 625         free(elim_for);
 626         return bmap;
 627 }
 628
 629 /* Normalize divs that appear in equalities.
 630  *
 631  * In particular, we assume that bmap contains some equalities
 632  * of the form
 633  *
 634  *      a x = m * e_i
 635  *
 636  * and we want to replace the set of e_i by a minimal set and
 637  * such that the new e_i have a canonical representation in terms
 638  * of the vector x.
 639  * If any of the equalities involves more than one divs, then
 640  * we currently simply bail out.
 641  *
 642  * Let us first additionally assume that all equalities involve
 643  * a div.  The equalities then express modulo constraints on the
 644  * remaining variables and we can use "parameter compression"
 645  * to find a minimal set of constraints.  The result is a transformation
 646  *
 647  *      x = T(x') = x_0 + G x'
 648  *
 649  * with G a lower-triangular matrix with all elements below the diagonal
 650  * non-negative and smaller than the diagonal element on the same row.
 651  * We first normalize x_0 by making the same property hold in the affine
 652  * T matrix.
 653  * The rows i of G with a 1 on the diagonal do not impose any modulo
 654  * constraint and simply express x_i = x'_i.
 655  * For each of the remaining rows i, we introduce a div and a corresponding
 656  * equality.  In particular
 657  *
 658  *      g_ii e_j = x_i - g_i(x')
 659  *
 660  * where each x'_k is replaced either by x_k (if g_kk = 1) or the
 661  * corresponding div (if g_kk != 1).
 662  *
 663  * If there are any equalities not involving any div, then we
 664  * first apply a variable compression on the variables x:
 665  *
 666  *      x = C x''       x'' = C_2 x
 667  *
 668  * and perform the above parameter compression on A C instead of on A.
 669  * The resulting compression is then of the form
 670  *
 671  *      x'' = T(x') = x_0 + G x'
 672  *
 673  * and in constructing the new divs and the corresponding equalities,
 674  * we have to replace each x'', i.e., the x'_k with (g_kk = 1),
 675  * by the corresponding row from C_2.
 676  */
 677 static struct isl_basic_map *normalize_divs(
 678         struct isl_basic_map *bmap, int *progress)
 679 {
 680         int i, j, k;
 681         int total;
 682         int div_eq;
 683         struct isl_mat *B;
 684         struct isl_vec *d;
 685         struct isl_mat *T = NULL;
 686         struct isl_mat *C = NULL;
 687         struct isl_mat *C2 = NULL;
 688         isl_int v;
 689         int *pos;
 690         int dropped, needed;
 691
 692         if (!bmap)
 693                 return NULL;
 694
 695         if (bmap->n_div == 0)
 696                 return bmap;
 697
 698         if (bmap->n_eq == 0)
 699                 return bmap;
 700
 701         if (ISL_F_ISSET(bmap, ISL_BASIC_MAP_NORMALIZED_DIVS))
 702                 return bmap;
 703
 704         total = isl_dim_total(bmap->dim);
 705         for (i = 0, j = bmap->n_div-1; i < bmap->n_eq; ++i) {
 706                 while (j >= 0 && isl_int_is_zero(bmap->eq[i][1 + total + j]))
 707                         --j;
 708                 if (j < 0)
 709                         break;
 710                 if (isl_seq_first_non_zero(bmap->eq[i] + 1 + total, j) != -1)
 711                         goto done;
 712         }
 713         div_eq = i;
 714         if (div_eq == 0)
 715                 return bmap;
 716
 717         if (div_eq < bmap->n_eq) {
 718                 B = isl_mat_sub_alloc(bmap->ctx, bmap->eq, div_eq,
 719                                         bmap->n_eq - div_eq, 0, 1 + total);
 720                 C = isl_mat_variable_compression(bmap->ctx, B, &C2);
 721                 if (!C || !C2)
 722                         goto error;
 723                 if (C->n_col == 0) {
 724                         bmap = isl_basic_map_set_to_empty(bmap);
 725                         isl_mat_free(bmap->ctx, C);
 726                         isl_mat_free(bmap->ctx, C2);
 727                         goto done;
 728                 }
 729         }
 730
 731         d = isl_vec_alloc(bmap->ctx, div_eq);
 732         if (!d)
 733                 goto error;
 734         for (i = 0, j = bmap->n_div-1; i < div_eq; ++i) {
 735                 while (j >= 0 && isl_int_is_zero(bmap->eq[i][1 + total + j]))
 736                         --j;
 737                 isl_int_set(d->block.data[i], bmap->eq[i][1 + total + j]);
 738         }
 739         B = isl_mat_sub_alloc(bmap->ctx, bmap->eq, 0, div_eq, 0, 1 + total);
 740
 741         if (C) {
 742                 B = isl_mat_product(bmap->ctx, B, C);
 743                 C = NULL;
 744         }
 745
 746         T = isl_mat_parameter_compression(bmap->ctx, B, d);
 747         if (!T)
 748                 goto error;
 749         if (T->n_col == 0) {
 750                 bmap = isl_basic_map_set_to_empty(bmap);
 751                 isl_mat_free(bmap->ctx, C2);
 752                 isl_mat_free(bmap->ctx, T);
 753                 goto done;
 754         }
 755         isl_int_init(v);
 756         for (i = 0; i < T->n_row - 1; ++i) {
 757                 isl_int_fdiv_q(v, T->row[1 + i][0], T->row[1 + i][1 + i]);
 758                 if (isl_int_is_zero(v))
 759                         continue;
 760                 isl_mat_col_submul(T, 0, v, 1 + i);
 761         }
 762         isl_int_clear(v);
 763         pos = isl_alloc_array(bmap->ctx, int, T->n_row);
 764         /* We have to be careful because dropping equalities may reorder them */
 765         dropped = 0;
 766         for (j = bmap->n_div - 1; j >= 0; --j) {
 767                 for (i = 0; i < bmap->n_eq; ++i)
 768                         if (!isl_int_is_zero(bmap->eq[i][1 + total + j]))
 769                                 break;
 770                 if (i < bmap->n_eq) {
 771                         bmap = isl_basic_map_drop_div(bmap, j);
 772                         isl_basic_map_drop_equality(bmap, i);
 773                         ++dropped;
 774                 }
 775         }
 776         pos[0] = 0;
 777         needed = 0;
 778         for (i = 1; i < T->n_row; ++i) {
 779                 if (isl_int_is_one(T->row[i][i]))
 780                         pos[i] = i;
 781                 else
 782                         needed++;
 783         }
 784         if (needed > dropped) {
 785                 bmap = isl_basic_map_extend_dim(bmap, isl_dim_copy(bmap->dim),
 786                                 needed, needed, 0);
 787                 if (!bmap)
 788                         goto error;
 789         }
 790         for (i = 1; i < T->n_row; ++i) {
 791                 if (isl_int_is_one(T->row[i][i]))
 792                         continue;
 793                 k = isl_basic_map_alloc_div(bmap);
 794                 pos[i] = 1 + total + k;
 795                 isl_seq_clr(bmap->div[k] + 1, 1 + total + bmap->n_div);
 796                 isl_int_set(bmap->div[k][0], T->row[i][i]);
 797                 if (C2)
 798                         isl_seq_cpy(bmap->div[k] + 1, C2->row[i], 1 + total);
 799                 else
 800                         isl_int_set_si(bmap->div[k][1 + i], 1);
 801                 for (j = 0; j < i; ++j) {
 802                         if (isl_int_is_zero(T->row[i][j]))
 803                                 continue;
 804                         if (pos[j] < T->n_row && C2)
 805                                 isl_seq_submul(bmap->div[k] + 1, T->row[i][j],
 806                                                 C2->row[pos[j]], 1 + total);
 807                         else
 808                                 isl_int_neg(bmap->div[k][1 + pos[j]],
 809                                                                 T->row[i][j]);
 810                 }
 811                 j = isl_basic_map_alloc_equality(bmap);
 812                 isl_seq_neg(bmap->eq[j], bmap->div[k]+1, 1+total+bmap->n_div);
 813                 isl_int_set(bmap->eq[j][pos[i]], bmap->div[k][0]);
 814         }
 815         free(pos);
 816         isl_mat_free(bmap->ctx, C2);
 817         isl_mat_free(bmap->ctx, T);
 818
 819         *progress = 1;
 820 done:
 821         ISL_F_SET(bmap, ISL_BASIC_MAP_NORMALIZED_DIVS);
 822
 823         return bmap;
 824 error:
 825         isl_mat_free(bmap->ctx, C);
 826         isl_mat_free(bmap->ctx, C2);
 827         isl_mat_free(bmap->ctx, T);
 828         return bmap;
 829 }
 830
 831 static struct isl_basic_map *remove_duplicate_constraints(
 832         struct isl_basic_map *bmap, int *progress)
 833 {
 834         unsigned int size;
 835         isl_int ***index;
 836         int k, l, h;
 837         int bits;
 838         unsigned total = isl_basic_map_total_dim(bmap);
 839         isl_int sum;
 840
 841         if (bmap->n_ineq <= 1)
 842                 return bmap;
 843
 844         size = round_up(4 * (bmap->n_ineq+1) / 3 - 1);
 845         bits = ffs(size) - 1;
 846         index = isl_calloc_array(ctx, isl_int **, size);
 847         if (!index)
 848                 return bmap;
 849
 850         index[isl_seq_get_hash_bits(bmap->ineq[0]+1, total, bits)] = &bmap->ineq[0];
 851         for (k = 1; k < bmap->n_ineq; ++k) {
 852                 h = hash_index(index, size, bits, bmap, k);
 853                 if (!index[h]) {
 854                         index[h] = &bmap->ineq[k];
 855                         continue;
 856                 }
 857                 if (progress)
 858                         *progress = 1;
 859                 l = index[h] - &bmap->ineq[0];
 860                 if (isl_int_lt(bmap->ineq[k][0], bmap->ineq[l][0]))
 861                         swap_inequality(bmap, k, l);
 862                 isl_basic_map_drop_inequality(bmap, k);
 863                 --k;
 864         }
 865         isl_int_init(sum);
 866         for (k = 0; k < bmap->n_ineq-1; ++k) {
 867                 isl_seq_neg(bmap->ineq[k]+1, bmap->ineq[k]+1, total);
 868                 h = hash_index(index, size, bits, bmap, k);
 869                 isl_seq_neg(bmap->ineq[k]+1, bmap->ineq[k]+1, total);
 870                 if (!index[h])
 871                         continue;
 872                 l = index[h] - &bmap->ineq[0];
 873                 isl_int_add(sum, bmap->ineq[k][0], bmap->ineq[l][0]);
 874                 if (isl_int_is_pos(sum))
 875                         continue;
 876                 if (isl_int_is_zero(sum)) {
 877                         /* We need to break out of the loop after these
 878                          * changes since the contents of the hash
 879                          * will no longer be valid.
 880                          * Plus, we probably we want to regauss first.
 881                          */
 882                         isl_basic_map_drop_inequality(bmap, l);
 883                         isl_basic_map_inequality_to_equality(bmap, k);
 884                 } else
 885                         bmap = isl_basic_map_set_to_empty(bmap);
 886                 break;
 887         }
 888         isl_int_clear(sum);
 889
 890         free(index);
 891         return bmap;
 892 }
 893
 894
 895 struct isl_basic_map *isl_basic_map_simplify(struct isl_basic_map *bmap)
 896 {
 897         int progress = 1;
 898         if (!bmap)
 899                 return NULL;
 900         while (progress) {
 901                 progress = 0;
 902                 bmap = isl_basic_map_normalize_constraints(bmap);
 903                 bmap = eliminate_divs_eq(bmap, &progress);
 904                 bmap = eliminate_divs_ineq(bmap, &progress);
 905                 bmap = isl_basic_map_gauss(bmap, &progress);
 906                 /* requires equalities in normal form */
 907                 bmap = normalize_divs(bmap, &progress);
 908                 bmap = remove_duplicate_divs(bmap, &progress);
 909                 bmap = remove_duplicate_constraints(bmap, &progress);
 910         }
 911         return bmap;
 912 }
 913
 914 struct isl_basic_set *isl_basic_set_simplify(struct isl_basic_set *bset)
 915 {
 916         return (struct isl_basic_set *)
 917                 isl_basic_map_simplify((struct isl_basic_map *)bset);
 918 }
 919
 920
 921 /* If the only constraints a div d=floor(f/m)
 922  * appears in are its two defining constraints
 923  *
 924  *      f - m d >=0
 925  *      -(f - (m - 1)) + m d >= 0
 926  *
 927  * then it can safely be removed.
 928  */
 929 static int div_is_redundant(struct isl_basic_map *bmap, int div)
 930 {
 931         int i;
 932         unsigned pos = 1 + isl_dim_total(bmap->dim) + div;
 933
 934         for (i = 0; i < bmap->n_eq; ++i)
 935                 if (!isl_int_is_zero(bmap->eq[i][pos]))
 936                         return 0;
 937
 938         for (i = 0; i < bmap->n_ineq; ++i) {
 939                 if (isl_int_is_zero(bmap->ineq[i][pos]))
 940                         continue;
 941                 if (isl_int_eq(bmap->ineq[i][pos], bmap->div[div][0])) {
 942                         int neg;
 943                         isl_int_sub(bmap->div[div][1],
 944                                         bmap->div[div][1], bmap->div[div][0]);
 945                         isl_int_add_ui(bmap->div[div][1], bmap->div[div][1], 1);
 946                         neg = isl_seq_is_neg(bmap->ineq[i], bmap->div[div]+1, pos);
 947                         isl_int_sub_ui(bmap->div[div][1], bmap->div[div][1], 1);
 948                         isl_int_add(bmap->div[div][1],
 949                                         bmap->div[div][1], bmap->div[div][0]);
 950                         if (!neg)
 951                                 return 0;
 952                         if (isl_seq_first_non_zero(bmap->ineq[i]+pos+1,
 953                                                     bmap->n_div-div-1) != -1)
 954                                 return 0;
 955                 } else if (isl_int_abs_eq(bmap->ineq[i][pos], bmap->div[div][0])) {
 956                         if (!isl_seq_eq(bmap->ineq[i], bmap->div[div]+1, pos))
 957                                 return 0;
 958                         if (isl_seq_first_non_zero(bmap->ineq[i]+pos+1,
 959                                                     bmap->n_div-div-1) != -1)
 960                                 return 0;
 961                 } else
 962                         return 0;
 963         }
 964
 965         for (i = 0; i < bmap->n_div; ++i)
 966                 if (!isl_int_is_zero(bmap->div[i][1+pos]))
 967                         return 0;
 968
 969         return 1;
 970 }
 971
 972 /*
 973  * Remove divs that don't occur in any of the constraints or other divs.
 974  * These can arise when dropping some of the variables in a quast
 975  * returned by piplib.
 976  */
 977 static struct isl_basic_map *remove_redundant_divs(struct isl_basic_map *bmap)
 978 {
 979         int i;
 980
 981         if (!bmap)
 982                 return NULL;
 983
 984         for (i = bmap->n_div-1; i >= 0; --i) {
 985                 if (!div_is_redundant(bmap, i))
 986                         continue;
 987                 bmap = isl_basic_map_drop_div(bmap, i);
 988         }
 989         return bmap;
 990 }
 991
 992 struct isl_basic_map *isl_basic_map_finalize(struct isl_basic_map *bmap)
 993 {
 994         bmap = remove_redundant_divs(bmap);
 995         if (!bmap)
 996                 return NULL;
 997         ISL_F_SET(bmap, ISL_BASIC_SET_FINAL);
 998         return bmap;
 999 }
1000
1001 struct isl_basic_set *isl_basic_set_finalize(struct isl_basic_set *bset)
1002 {
1003         return (struct isl_basic_set *)
1004                 isl_basic_map_finalize((struct isl_basic_map *)bset);
1005 }
1006
1007 struct isl_set *isl_set_finalize(struct isl_set *set)
1008 {
1009         int i;
1010
1011         if (!set)
1012                 return NULL;
1013         for (i = 0; i < set->n; ++i) {
1014                 set->p[i] = isl_basic_set_finalize(set->p[i]);
1015                 if (!set->p[i])
1016                         goto error;
1017         }
1018         return set;
1019 error:
1020         isl_set_free(set);
1021         return NULL;
1022 }
1023
1024 struct isl_map *isl_map_finalize(struct isl_map *map)
1025 {
1026         int i;
1027
1028         if (!map)
1029                 return NULL;
1030         for (i = 0; i < map->n; ++i) {
1031                 map->p[i] = isl_basic_map_finalize(map->p[i]);
1032                 if (!map->p[i])
1033                         goto error;
1034         }
1035         ISL_F_CLR(map, ISL_MAP_NORMALIZED);
1036         return map;
1037 error:
1038         isl_map_free(map);
1039         return NULL;
1040 }
1041
1042
1043 /* Remove any div that is defined in terms of the given variable.
1044  */
1045 static struct isl_basic_map *remove_dependent_vars(struct isl_basic_map *bmap,
1046                                                                         int pos)
1047 {
1048         int i;
1049         unsigned dim = isl_dim_total(bmap->dim);
1050
1051         for (i = 0; i < bmap->n_div; ++i) {
1052                 if (isl_int_is_zero(bmap->div[i][0]))
1053                         continue;
1054                 if (isl_int_is_zero(bmap->div[i][1+1+pos]))
1055                         continue;
1056                 bmap = isl_basic_map_eliminate_vars(bmap, dim + i, 1);
1057                 if (!bmap)
1058                         return NULL;
1059         }
1060         return bmap;
1061 }
1062
1063 /* Eliminate the specified variables from the constraints using
1064  * Fourier-Motzkin.  The variables themselves are not removed.
1065  */
1066 struct isl_basic_map *isl_basic_map_eliminate_vars(
1067         struct isl_basic_map *bmap, unsigned pos, unsigned n)
1068 {
1069         int d;
1070         int i, j, k;
1071         unsigned total;
1072
1073         if (n == 0)
1074                 return bmap;
1075         if (!bmap)
1076                 return NULL;
1077         total = isl_basic_map_total_dim(bmap);
1078
1079         bmap = isl_basic_map_cow(bmap);
1080         for (d = pos + n - 1; d >= 0 && d >= pos; --d)
1081                 bmap = remove_dependent_vars(bmap, d);
1082
1083         for (d = pos + n - 1;
1084              d >= 0 && d >= total - bmap->n_div && d >= pos; --d)
1085                 isl_seq_clr(bmap->div[d-(total-bmap->n_div)], 2+total);
1086         for (d = pos + n - 1; d >= 0 && d >= pos; --d) {
1087                 int n_lower, n_upper;
1088                 if (!bmap)
1089                         return NULL;
1090                 for (i = 0; i < bmap->n_eq; ++i) {
1091                         if (isl_int_is_zero(bmap->eq[i][1+d]))
1092                                 continue;
1093                         eliminate_var_using_equality(bmap, d, bmap->eq[i], NULL);
1094                         isl_basic_map_drop_equality(bmap, i);
1095                         break;
1096                 }
1097                 if (i < bmap->n_eq)
1098                         continue;
1099                 n_lower = 0;
1100                 n_upper = 0;
1101                 for (i = 0; i < bmap->n_ineq; ++i) {
1102                         if (isl_int_is_pos(bmap->ineq[i][1+d]))
1103                                 n_lower++;
1104                         else if (isl_int_is_neg(bmap->ineq[i][1+d]))
1105                                 n_upper++;
1106                 }
1107                 bmap = isl_basic_map_extend_constraints(bmap,
1108                                 0, n_lower * n_upper);
1109                 for (i = bmap->n_ineq - 1; i >= 0; --i) {
1110                         int last;
1111                         if (isl_int_is_zero(bmap->ineq[i][1+d]))
1112                                 continue;
1113                         last = -1;
1114                         for (j = 0; j < i; ++j) {
1115                                 if (isl_int_is_zero(bmap->ineq[j][1+d]))
1116                                         continue;
1117                                 last = j;
1118                                 if (isl_int_sgn(bmap->ineq[i][1+d]) ==
1119                                     isl_int_sgn(bmap->ineq[j][1+d]))
1120                                         continue;
1121                                 k = isl_basic_map_alloc_inequality(bmap);
1122                                 if (k < 0)
1123                                         goto error;
1124                                 isl_seq_cpy(bmap->ineq[k], bmap->ineq[i],
1125                                                 1+total);
1126                                 isl_seq_elim(bmap->ineq[k], bmap->ineq[j],
1127                                                 1+d, 1+total, NULL);
1128                         }
1129                         isl_basic_map_drop_inequality(bmap, i);
1130                         i = last + 1;
1131                 }
1132                 if (n_lower > 0 && n_upper > 0) {
1133                         bmap = isl_basic_map_normalize_constraints(bmap);
1134                         bmap = remove_duplicate_constraints(bmap, NULL);
1135                         bmap = isl_basic_map_gauss(bmap, NULL);
1136                         bmap = isl_basic_map_convex_hull(bmap);
1137                         if (!bmap)
1138                                 goto error;
1139                         if (ISL_F_ISSET(bmap, ISL_BASIC_MAP_EMPTY))
1140                                 break;
1141                 }
1142         }
1143         ISL_F_CLR(bmap, ISL_BASIC_MAP_NORMALIZED);
1144         return bmap;
1145 error:
1146         isl_basic_map_free(bmap);
1147         return NULL;
1148 }
1149
1150 struct isl_basic_set *isl_basic_set_eliminate_vars(
1151         struct isl_basic_set *bset, unsigned pos, unsigned n)
1152 {
1153         return (struct isl_basic_set *)isl_basic_map_eliminate_vars(
1154                         (struct isl_basic_map *)bset, pos, n);
1155 }
1156
1157 static void compute_elimination_index(struct isl_basic_map *bmap, int *elim)
1158 {
1159         int d, i;
1160         unsigned total;
1161
1162         total = isl_dim_total(bmap->dim);
1163         for (d = 0; d < total; ++d)
1164                 elim[d] = -1;
1165         for (d = total - 1, i = 0; d >= 0 && i < bmap->n_eq; ++i) {
1166                 for (; d >= 0; --d) {
1167                         if (isl_int_is_zero(bmap->eq[i][1+d]))
1168                                 continue;
1169                         elim[d] = i;
1170                         break;
1171                 }
1172         }
1173 }
1174
1175 static void set_compute_elimination_index(struct isl_basic_set *bset, int *elim)
1176 {
1177         return compute_elimination_index((struct isl_basic_map *)bset, elim);
1178 }
1179
1180 static int reduced_using_equalities(isl_int *dst, isl_int *src,
1181         struct isl_basic_map *bmap, int *elim)
1182 {
1183         int d, i;
1184         int copied = 0;
1185         unsigned total;
1186
1187         total = isl_dim_total(bmap->dim);
1188         for (d = total - 1; d >= 0; --d) {
1189                 if (isl_int_is_zero(src[1+d]))
1190                         continue;
1191                 if (elim[d] == -1)
1192                         continue;
1193                 if (!copied) {
1194                         isl_seq_cpy(dst, src, 1 + total);
1195                         copied = 1;
1196                 }
1197                 isl_seq_elim(dst, bmap->eq[elim[d]], 1 + d, 1 + total, NULL);
1198         }
1199         return copied;
1200 }
1201
1202 static int set_reduced_using_equalities(isl_int *dst, isl_int *src,
1203         struct isl_basic_set *bset, int *elim)
1204 {
1205         return reduced_using_equalities(dst, src,
1206                                         (struct isl_basic_map *)bset, elim);
1207 }
1208
1209 static struct isl_basic_set *isl_basic_set_reduce_using_equalities(
1210         struct isl_basic_set *bset, struct isl_basic_set *context)
1211 {
1212         int i;
1213         int *elim;
1214
1215         if (!bset || !context)
1216                 goto error;
1217
1218         bset = isl_basic_set_cow(bset);
1219         if (!bset)
1220                 goto error;
1221
1222         elim = isl_alloc_array(ctx, int, isl_basic_set_n_dim(bset));
1223         if (!elim)
1224                 goto error;
1225         set_compute_elimination_index(context, elim);
1226         for (i = 0; i < bset->n_eq; ++i)
1227                 set_reduced_using_equalities(bset->eq[i], bset->eq[i],
1228                                                         context, elim);
1229         for (i = 0; i < bset->n_ineq; ++i)
1230                 set_reduced_using_equalities(bset->ineq[i], bset->ineq[i],
1231                                                         context, elim);
1232         isl_basic_set_free(context);
1233         free(elim);
1234         bset = isl_basic_set_simplify(bset);
1235         bset = isl_basic_set_finalize(bset);
1236         return bset;
1237 error:
1238         isl_basic_set_free(bset);
1239         isl_basic_set_free(context);
1240         return NULL;
1241 }
1242
1243 static struct isl_basic_set *remove_shifted_constraints(
1244         struct isl_basic_set *bset, struct isl_basic_set *context)
1245 {
1246         unsigned int size;
1247         isl_int ***index;
1248         int bits;
1249         int k, h, l;
1250
1251         if (!bset)
1252                 return NULL;
1253
1254         size = round_up(4 * (context->n_ineq+1) / 3 - 1);
1255         bits = ffs(size) - 1;
1256         index = isl_calloc_array(ctx, isl_int **, size);
1257         if (!index)
1258                 return bset;
1259
1260         for (k = 0; k < context->n_ineq; ++k) {
1261                 h = set_hash_index(index, size, bits, context, k);
1262                 index[h] = &context->ineq[k];
1263         }
1264         for (k = 0; k < bset->n_ineq; ++k) {
1265                 h = set_hash_index(index, size, bits, bset, k);
1266                 if (!index[h])
1267                         continue;
1268                 l = index[h] - &context->ineq[0];
1269                 if (isl_int_lt(bset->ineq[k][0], context->ineq[l][0]))
1270                         continue;
1271                 bset = isl_basic_set_cow(bset);
1272                 if (!bset)
1273                         goto error;
1274                 isl_basic_set_drop_inequality(bset, k);
1275                 --k;
1276         }
1277         free(index);
1278         return bset;
1279 error:
1280         free(index);
1281         return bset;
1282 }
1283
1284 static struct isl_basic_set *uset_gist(struct isl_basic_set *bset,
1285         struct isl_basic_set *context);
1286
1287 static struct isl_basic_set *uset_gist_context_eq(struct isl_basic_set *bset,
1288         struct isl_basic_set *context)
1289 {
1290         struct isl_mat *T;
1291         struct isl_mat *T2;
1292         struct isl_ctx *ctx = context->ctx;
1293         struct isl_basic_set *reduced_context;
1294         reduced_context = isl_basic_set_remove_equalities(
1295                                 isl_basic_set_copy(context), &T, &T2);
1296         if (!reduced_context)
1297                 goto error;
1298         bset = isl_basic_set_preimage(bset, T);
1299         bset = uset_gist(bset, reduced_context);
1300         bset = isl_basic_set_preimage(bset, T2);
1301         bset = isl_basic_set_reduce_using_equalities(bset, context);
1302         return bset;
1303 error:
1304         isl_basic_set_free(context);
1305         isl_basic_set_free(bset);
1306         return NULL;
1307 }
1308
1309 static struct isl_basic_set *uset_gist_set_eq(struct isl_basic_set *bset,
1310         struct isl_basic_set *context)
1311 {
1312         struct isl_mat *T;
1313         struct isl_mat *T2;
1314         struct isl_ctx *ctx = context->ctx;
1315         struct isl_basic_set *affine_hull = NULL;
1316
1317         affine_hull = isl_basic_set_copy(bset);
1318         affine_hull = isl_basic_set_cow(affine_hull);
1319         if (!affine_hull)
1320                 goto error;
1321         isl_basic_set_free_inequality(affine_hull, affine_hull->n_ineq);
1322
1323         bset = isl_basic_set_remove_equalities(bset, &T, &T2);
1324         if (!bset)
1325                 goto error;
1326         context = isl_basic_set_preimage(context, T);
1327         bset = uset_gist(bset, context);
1328         bset = isl_basic_set_preimage(bset, T2);
1329         bset = isl_basic_set_intersect(bset, affine_hull);
1330         return bset;
1331 error:
1332         isl_basic_set_free(affine_hull);
1333         isl_basic_set_free(context);
1334         isl_basic_set_free(bset);
1335         return NULL;
1336 }
1337
1338 /* Remove all information from bset that is redundant in the context
1339  * of context.  In particular, equalities that are linear combinations
1340  * of those in context are removed.  Then the inequalities that are
1341  * redundant in the context of the equalities and inequalities of
1342  * context are removed.
1343  */
1344 static struct isl_basic_set *uset_gist(struct isl_basic_set *bset,
1345         struct isl_basic_set *context)
1346 {
1347         int i;
1348         isl_int opt;
1349         struct isl_basic_set *combined;
1350         struct isl_ctx *ctx;
1351
1352         if (!bset || !context)
1353                 goto error;
1354
1355         if (context->n_eq > 0)
1356                 return uset_gist_context_eq(bset, context);
1357         if (!context->n_ineq)
1358                 goto done;
1359         if (bset->n_eq > 0)
1360                 return uset_gist_set_eq(bset, context);
1361         bset = remove_shifted_constraints(bset, context);
1362         combined = isl_basic_set_cow(isl_basic_set_copy(bset));
1363         combined = isl_basic_set_extend_constraints(combined,
1364                         context->n_eq, context->n_ineq);
1365         context = isl_basic_set_add_constraints(combined, context, 0);
1366         if (!context)
1367                 goto error;
1368         ctx = context->ctx;
1369         isl_int_init(opt);
1370         for (i = bset->n_ineq-1; i >= 0; --i) {
1371                 int redundant;
1372                 set_swap_inequality(context, i, context->n_ineq-1);
1373                 context->n_ineq--;
1374                 redundant = isl_basic_set_constraint_is_redundant(&context,
1375                                 context->ineq[context->n_ineq], &opt, NULL);
1376                 if (redundant == -1) {
1377                         isl_int_clear(opt);
1378                         goto error;
1379                 }
1380                 if (ISL_F_ISSET(context, ISL_BASIC_MAP_EMPTY)) {
1381                         bset = isl_basic_set_set_to_empty(bset);
1382                         break;
1383                 }
1384                 context->n_ineq++;
1385                 set_swap_inequality(context, i, context->n_ineq-1);
1386                 if (redundant) {
1387                         isl_basic_set_drop_inequality(context, i);
1388                         isl_basic_set_drop_inequality(bset, i);
1389                 }
1390         }
1391         isl_int_clear(opt);
1392 done:
1393         isl_basic_set_free(context);
1394         return bset;
1395 error:
1396         isl_basic_set_free(context);
1397         isl_basic_set_free(bset);
1398         return NULL;
1399 }
1400
1401 struct isl_basic_map *isl_basic_map_gist(struct isl_basic_map *bmap,
1402         struct isl_basic_map *context)
1403 {
1404         struct isl_basic_set *bset;
1405
1406         if (!bmap || !context)
1407                 goto error;
1408
1409         context = isl_basic_map_align_divs(context, bmap);
1410         bmap = isl_basic_map_align_divs(bmap, context);
1411
1412         bset = uset_gist(isl_basic_map_underlying_set(isl_basic_map_copy(bmap)),
1413                          isl_basic_map_underlying_set(context));
1414
1415         return isl_basic_map_overlying_set(bset, bmap);
1416 error:
1417         isl_basic_map_free(bmap);
1418         isl_basic_map_free(context);
1419         return NULL;
1420 }
1421
1422 /*
1423  * Assumes context has no implicit divs.
1424  */
1425 struct isl_map *isl_map_gist(struct isl_map *map, struct isl_basic_map *context)
1426 {
1427         int i;
1428
1429         map = isl_map_cow(map);
1430         if (!map || !context)
1431                 return NULL;
1432         isl_assert(map->ctx, isl_dim_equal(map->dim, context->dim), goto error);
1433         map = isl_map_compute_divs(map);
1434         for (i = 0; i < map->n; ++i)
1435                 context = isl_basic_map_align_divs(context, map->p[i]);
1436         for (i = 0; i < map->n; ++i) {
1437                 map->p[i] = isl_basic_map_gist(map->p[i],
1438                                                 isl_basic_map_copy(context));
1439                 if (!map->p[i])
1440                         goto error;
1441         }
1442         isl_basic_map_free(context);
1443         ISL_F_CLR(map, ISL_MAP_NORMALIZED);
1444         return map;
1445 error:
1446         isl_map_free(map);
1447         isl_basic_map_free(context);
1448         return NULL;
1449 }
1450
1451 struct isl_basic_set *isl_basic_set_gist(struct isl_basic_set *bset,
1452                                                 struct isl_basic_set *context)
1453 {
1454         return (struct isl_basic_set *)isl_basic_map_gist(
1455                 (struct isl_basic_map *)bset, (struct isl_basic_map *)context);
1456 }
1457
1458 struct isl_set *isl_set_gist(struct isl_set *set, struct isl_basic_set *context)
1459 {
1460         return (struct isl_set *)isl_map_gist((struct isl_map *)set,
1461                                         (struct isl_basic_map *)context);
1462 }
1463
1464 /* Quick check to see if two basic maps are disjoint.
1465  * In particular, we reduce the equalities and inequalities of
1466  * one basic map in the context of the equalities of the other
1467  * basic map and check if we get a contradiction.
1468  */
1469 int isl_basic_map_fast_is_disjoint(struct isl_basic_map *bmap1,
1470         struct isl_basic_map *bmap2)
1471 {
1472         struct isl_vec *v = NULL;
1473         int *elim = NULL;
1474         unsigned total;
1475         int d, i;
1476
1477         if (!bmap1 || !bmap2)
1478                 return -1;
1479         isl_assert(bmap1->ctx, isl_dim_equal(bmap1->dim, bmap2->dim),
1480                         return -1);
1481         if (bmap1->n_div || bmap2->n_div)
1482                 return 0;
1483         if (!bmap1->n_eq && !bmap2->n_eq)
1484                 return 0;
1485
1486         total = isl_dim_total(bmap1->dim);
1487         if (total == 0)
1488                 return 0;
1489         v = isl_vec_alloc(bmap1->ctx, 1 + total);
1490         if (!v)
1491                 goto error;
1492         elim = isl_alloc_array(bmap1->ctx, int, total);
1493         if (!elim)
1494                 goto error;
1495         compute_elimination_index(bmap1, elim);
1496         for (i = 0; i < bmap2->n_eq; ++i) {
1497                 int reduced;
1498                 reduced = reduced_using_equalities(v->block.data, bmap2->eq[i],
1499                                                         bmap1, elim);
1500                 if (reduced && !isl_int_is_zero(v->block.data[0]) &&
1501                     isl_seq_first_non_zero(v->block.data + 1, total) == -1)
1502                         goto disjoint;
1503         }
1504         for (i = 0; i < bmap2->n_ineq; ++i) {
1505                 int reduced;
1506                 reduced = reduced_using_equalities(v->block.data,
1507                                                 bmap2->ineq[i], bmap1, elim);
1508                 if (reduced && isl_int_is_neg(v->block.data[0]) &&
1509                     isl_seq_first_non_zero(v->block.data + 1, total) == -1)
1510                         goto disjoint;
1511         }
1512         compute_elimination_index(bmap2, elim);
1513         for (i = 0; i < bmap1->n_ineq; ++i) {
1514                 int reduced;
1515                 reduced = reduced_using_equalities(v->block.data,
1516                                                 bmap1->ineq[i], bmap2, elim);
1517                 if (reduced && isl_int_is_neg(v->block.data[0]) &&
1518                     isl_seq_first_non_zero(v->block.data + 1, total) == -1)
1519                         goto disjoint;
1520         }
1521         isl_vec_free(bmap1->ctx, v);
1522         free(elim);
1523         return 0;
1524 disjoint:
1525         isl_vec_free(bmap1->ctx, v);
1526         free(elim);
1527         return 1;
1528 error:
1529         isl_vec_free(bmap1->ctx, v);
1530         free(elim);
1531         return -1;
1532 }
1533
1534 int isl_basic_set_fast_is_disjoint(struct isl_basic_set *bset1,
1535         struct isl_basic_set *bset2)
1536 {
1537         return isl_basic_map_fast_is_disjoint((struct isl_basic_map *)bset1,
1538                                               (struct isl_basic_map *)bset2);
1539 }
1540
1541 int isl_map_fast_is_disjoint(struct isl_map *map1, struct isl_map *map2)
1542 {
1543         int i, j;
1544
1545         if (!map1 || !map2)
1546                 return -1;
1547
1548         if (isl_map_fast_is_equal(map1, map2))
1549                 return 0;
1550
1551         for (i = 0; i < map1->n; ++i) {
1552                 for (j = 0; j < map2->n; ++j) {
1553                         int d = isl_basic_map_fast_is_disjoint(map1->p[i],
1554                                                                map2->p[j]);
1555                         if (d != 1)
1556                                 return d;
1557                 }
1558         }
1559         return 1;
1560 }
1561
1562 int isl_set_fast_is_disjoint(struct isl_set *set1, struct isl_set *set2)
1563 {
1564         return isl_map_fast_is_disjoint((struct isl_map *)set1,
1565                                         (struct isl_map *)set2);
1566 }