isl_map_simplify.c

   1 #include "isl_equalities.h"
   2 #include "isl_map.h"
   3 #include "isl_map_private.h"
   4
   5 static void swap_equality(struct isl_basic_map *bmap, int a, int b)
   6 {
   7         isl_int *t = bmap->eq[a];
   8         bmap->eq[a] = bmap->eq[b];
   9         bmap->eq[b] = t;
  10 }
  11
  12 static void swap_inequality(struct isl_basic_map *bmap, int a, int b)
  13 {
  14         if (a != b) {
  15                 isl_int *t = bmap->ineq[a];
  16                 bmap->ineq[a] = bmap->ineq[b];
  17                 bmap->ineq[b] = t;
  18         }
  19 }
  20
  21 static void set_swap_inequality(struct isl_basic_set *bset, int a, int b)
  22 {
  23         swap_inequality((struct isl_basic_map *)bset, a, b);
  24 }
  25
  26 static void constraint_drop_vars(isl_int *c, unsigned n, unsigned rem)
  27 {
  28         isl_seq_cpy(c, c + n, rem);
  29         isl_seq_clr(c + rem, n);
  30 }
  31
  32 /* Drop n dimensions starting at first.
  33  *
  34  * In principle, this frees up some extra variables as the number
  35  * of columns remains constant, but we would have to extend
  36  * the div array too as the number of rows in this array is assumed
  37  * to be equal to extra.
  38  */
  39 struct isl_basic_set *isl_basic_set_drop_dims(
  40                 struct isl_basic_set *bset, unsigned first, unsigned n)
  41 {
  42         int i;
  43
  44         if (!bset)
  45                 goto error;
  46
  47         isl_assert(bset->ctx, first + n <= bset->dim->n_out, goto error);
  48
  49         if (n == 0)
  50                 return bset;
  51
  52         bset = isl_basic_set_cow(bset);
  53         if (!bset)
  54                 return NULL;
  55
  56         for (i = 0; i < bset->n_eq; ++i)
  57                 constraint_drop_vars(bset->eq[i]+1+bset->dim->nparam+first, n,
  58                                      (bset->dim->n_out-first-n)+bset->extra);
  59
  60         for (i = 0; i < bset->n_ineq; ++i)
  61                 constraint_drop_vars(bset->ineq[i]+1+bset->dim->nparam+first, n,
  62                                      (bset->dim->n_out-first-n)+bset->extra);
  63
  64         for (i = 0; i < bset->n_div; ++i)
  65                 constraint_drop_vars(bset->div[i]+1+1+bset->dim->nparam+first, n,
  66                                      (bset->dim->n_out-first-n)+bset->extra);
  67
  68         bset->dim = isl_dim_drop_outputs(bset->dim, first, n);
  69         if (!bset->dim)
  70                 goto error;
  71
  72         F_CLR(bset, ISL_BASIC_SET_NORMALIZED);
  73         bset = isl_basic_set_simplify(bset);
  74         return isl_basic_set_finalize(bset);
  75 error:
  76         isl_basic_set_free(bset);
  77         return NULL;
  78 }
  79
  80 struct isl_set *isl_set_drop_dims(
  81                 struct isl_set *set, unsigned first, unsigned n)
  82 {
  83         int i;
  84
  85         if (!set)
  86                 goto error;
  87
  88         isl_assert(set->ctx, first + n <= set->dim->n_out, goto error);
  89
  90         if (n == 0)
  91                 return set;
  92         set = isl_set_cow(set);
  93         if (!set)
  94                 goto error;
  95         set->dim = isl_dim_drop_outputs(set->dim, first, n);
  96         if (!set->dim)
  97                 goto error;
  98
  99         for (i = 0; i < set->n; ++i) {
 100                 set->p[i] = isl_basic_set_drop_dims(set->p[i], first, n);
 101                 if (!set->p[i])
 102                         goto error;
 103         }
 104
 105         F_CLR(set, ISL_SET_NORMALIZED);
 106         return set;
 107 error:
 108         isl_set_free(set);
 109         return NULL;
 110 }
 111
 112 /* Drop n input dimensions starting at first.
 113  *
 114  * In principle, this frees up some extra variables as the number
 115  * of columns remains constant, but we would have to extend
 116  * the div array too as the number of rows in this array is assumed
 117  * to be equal to extra.
 118  */
 119 struct isl_basic_map *isl_basic_map_drop_inputs(
 120                 struct isl_basic_map *bmap, unsigned first, unsigned n)
 121 {
 122         int i;
 123         unsigned nparam;
 124         unsigned n_in;
 125         unsigned n_out;
 126
 127         if (!bmap)
 128                 goto error;
 129
 130         nparam = isl_basic_map_n_param(bmap);
 131         n_in = isl_basic_map_n_in(bmap);
 132         n_out = isl_basic_map_n_out(bmap);
 133         isl_assert(bmap->ctx, first + n <= n_in, goto error);
 134
 135         if (n == 0)
 136                 return bmap;
 137
 138         bmap = isl_basic_map_cow(bmap);
 139         if (!bmap)
 140                 return NULL;
 141
 142         for (i = 0; i < bmap->n_eq; ++i)
 143                 constraint_drop_vars(bmap->eq[i]+1+nparam+first, n,
 144                                  (n_in-first-n)+n_out+bmap->extra);
 145
 146         for (i = 0; i < bmap->n_ineq; ++i)
 147                 constraint_drop_vars(bmap->ineq[i]+1+nparam+first, n,
 148                                  (n_in-first-n)+n_out+bmap->extra);
 149
 150         for (i = 0; i < bmap->n_div; ++i)
 151                 constraint_drop_vars(bmap->div[i]+1+1+nparam+first, n,
 152                                  (n_in-first-n)+n_out+bmap->extra);
 153
 154         bmap->dim = isl_dim_drop_inputs(bmap->dim, first, n);
 155         if (!bmap->dim)
 156                 goto error;
 157
 158         F_CLR(bmap, ISL_BASIC_MAP_NORMALIZED);
 159         bmap = isl_basic_map_simplify(bmap);
 160         return isl_basic_map_finalize(bmap);
 161 error:
 162         isl_basic_map_free(bmap);
 163         return NULL;
 164 }
 165
 166 struct isl_map *isl_map_drop_inputs(
 167                 struct isl_map *map, unsigned first, unsigned n)
 168 {
 169         int i;
 170
 171         if (!map)
 172                 goto error;
 173
 174         isl_assert(map->ctx, first + n <= map->dim->n_in, goto error);
 175
 176         if (n == 0)
 177                 return map;
 178         map = isl_map_cow(map);
 179         if (!map)
 180                 goto error;
 181         map->dim = isl_dim_drop_inputs(map->dim, first, n);
 182         if (!map->dim)
 183                 goto error;
 184
 185         for (i = 0; i < map->n; ++i) {
 186                 map->p[i] = isl_basic_map_drop_inputs(map->p[i], first, n);
 187                 if (!map->p[i])
 188                         goto error;
 189         }
 190         F_CLR(map, ISL_MAP_NORMALIZED);
 191
 192         return map;
 193 error:
 194         isl_map_free(map);
 195         return NULL;
 196 }
 197
 198 /*
 199  * We don't cow, as the div is assumed to be redundant.
 200  */
 201 static struct isl_basic_map *isl_basic_map_drop_div(
 202                 struct isl_basic_map *bmap, unsigned div)
 203 {
 204         int i;
 205         unsigned pos;
 206
 207         if (!bmap)
 208                 goto error;
 209
 210         pos = 1 + isl_dim_total(bmap->dim) + div;
 211
 212         isl_assert(bmap->ctx, div < bmap->n_div, goto error);
 213
 214         for (i = 0; i < bmap->n_eq; ++i)
 215                 constraint_drop_vars(bmap->eq[i]+pos, 1, bmap->extra-div-1);
 216
 217         for (i = 0; i < bmap->n_ineq; ++i) {
 218                 if (!isl_int_is_zero(bmap->ineq[i][pos])) {
 219                         isl_basic_map_drop_inequality(bmap, i);
 220                         --i;
 221                         continue;
 222                 }
 223                 constraint_drop_vars(bmap->ineq[i]+pos, 1, bmap->extra-div-1);
 224         }
 225
 226         for (i = 0; i < bmap->n_div; ++i)
 227                 constraint_drop_vars(bmap->div[i]+1+pos, 1, bmap->extra-div-1);
 228
 229         if (div != bmap->n_div - 1) {
 230                 int j;
 231                 isl_int *t = bmap->div[div];
 232
 233                 for (j = div; j < bmap->n_div - 1; ++j)
 234                         bmap->div[j] = bmap->div[j+1];
 235
 236                 bmap->div[bmap->n_div - 1] = t;
 237         }
 238         F_CLR(bmap, ISL_BASIC_MAP_NORMALIZED);
 239         isl_basic_map_free_div(bmap, 1);
 240
 241         return bmap;
 242 error:
 243         isl_basic_map_free(bmap);
 244         return NULL;
 245 }
 246
 247 static struct isl_basic_map *normalize_constraints(struct isl_basic_map *bmap)
 248 {
 249         int i;
 250         isl_int gcd;
 251         unsigned total = isl_basic_map_total_dim(bmap);
 252
 253         isl_int_init(gcd);
 254         for (i = bmap->n_eq - 1; i >= 0; --i) {
 255                 isl_seq_gcd(bmap->eq[i]+1, total, &gcd);
 256                 if (isl_int_is_zero(gcd)) {
 257                         if (!isl_int_is_zero(bmap->eq[i][0])) {
 258                                 bmap = isl_basic_map_set_to_empty(bmap);
 259                                 break;
 260                         }
 261                         isl_basic_map_drop_equality(bmap, i);
 262                         continue;
 263                 }
 264                 if (F_ISSET(bmap, ISL_BASIC_MAP_RATIONAL))
 265                         isl_int_gcd(gcd, gcd, bmap->eq[i][0]);
 266                 if (isl_int_is_one(gcd))
 267                         continue;
 268                 if (!isl_int_is_divisible_by(bmap->eq[i][0], gcd)) {
 269                         bmap = isl_basic_map_set_to_empty(bmap);
 270                         break;
 271                 }
 272                 isl_seq_scale_down(bmap->eq[i], bmap->eq[i], gcd, 1+total);
 273         }
 274
 275         for (i = bmap->n_ineq - 1; i >= 0; --i) {
 276                 isl_seq_gcd(bmap->ineq[i]+1, total, &gcd);
 277                 if (isl_int_is_zero(gcd)) {
 278                         if (isl_int_is_neg(bmap->ineq[i][0])) {
 279                                 bmap = isl_basic_map_set_to_empty(bmap);
 280                                 break;
 281                         }
 282                         isl_basic_map_drop_inequality(bmap, i);
 283                         continue;
 284                 }
 285                 if (F_ISSET(bmap, ISL_BASIC_MAP_RATIONAL))
 286                         isl_int_gcd(gcd, gcd, bmap->ineq[i][0]);
 287                 if (isl_int_is_one(gcd))
 288                         continue;
 289                 isl_int_fdiv_q(bmap->ineq[i][0], bmap->ineq[i][0], gcd);
 290                 isl_seq_scale_down(bmap->ineq[i]+1, bmap->ineq[i]+1, gcd, total);
 291         }
 292         isl_int_clear(gcd);
 293
 294         return bmap;
 295 }
 296
 297 static void eliminate_div(struct isl_basic_map *bmap, isl_int *eq, unsigned div)
 298 {
 299         int i;
 300         unsigned pos = 1 + isl_dim_total(bmap->dim) + div;
 301         unsigned len;
 302         len = 1 + isl_basic_map_total_dim(bmap);
 303
 304         for (i = 0; i < bmap->n_eq; ++i)
 305                 if (bmap->eq[i] != eq)
 306                         isl_seq_elim(bmap->eq[i], eq, pos, len, NULL);
 307
 308         for (i = 0; i < bmap->n_ineq; ++i)
 309                 isl_seq_elim(bmap->ineq[i], eq, pos, len, NULL);
 310
 311         /* We need to be careful about circular definitions,
 312          * so for now we just remove the definitions of other divs that
 313          * depend on this div and (possibly) recompute them later.
 314          */
 315         for (i = 0; i < bmap->n_div; ++i)
 316                 if (!isl_int_is_zero(bmap->div[i][0]) &&
 317                     !isl_int_is_zero(bmap->div[i][1 + pos]))
 318                         isl_seq_clr(bmap->div[i], 1 + len);
 319
 320         isl_basic_map_drop_div(bmap, div);
 321 }
 322
 323 /* Elimininate divs based on equalities
 324  */
 325 static struct isl_basic_map *eliminate_divs_eq(
 326                 struct isl_basic_map *bmap, int *progress)
 327 {
 328         int d;
 329         int i;
 330         int modified = 0;
 331         unsigned off;
 332
 333         if (!bmap)
 334                 return NULL;
 335
 336         off = 1 + isl_dim_total(bmap->dim);
 337
 338         for (d = bmap->n_div - 1; d >= 0 ; --d) {
 339                 for (i = 0; i < bmap->n_eq; ++i) {
 340                         if (!isl_int_is_one(bmap->eq[i][off + d]) &&
 341                             !isl_int_is_negone(bmap->eq[i][off + d]))
 342                                 continue;
 343                         modified = 1;
 344                         *progress = 1;
 345                         eliminate_div(bmap, bmap->eq[i], d);
 346                         isl_basic_map_drop_equality(bmap, i);
 347                         break;
 348                 }
 349         }
 350         if (modified)
 351                 return eliminate_divs_eq(bmap, progress);
 352         return bmap;
 353 }
 354
 355 /* Elimininate divs based on inequalities
 356  */
 357 static struct isl_basic_map *eliminate_divs_ineq(
 358                 struct isl_basic_map *bmap, int *progress)
 359 {
 360         int d;
 361         int i;
 362         unsigned off;
 363         struct isl_ctx *ctx;
 364
 365         if (!bmap)
 366                 return NULL;
 367
 368         ctx = bmap->ctx;
 369         off = 1 + isl_dim_total(bmap->dim);
 370
 371         for (d = bmap->n_div - 1; d >= 0 ; --d) {
 372                 for (i = 0; i < bmap->n_eq; ++i)
 373                         if (!isl_int_is_zero(bmap->eq[i][off + d]))
 374                                 break;
 375                 if (i < bmap->n_eq)
 376                         continue;
 377                 for (i = 0; i < bmap->n_ineq; ++i)
 378                         if (isl_int_abs_gt(bmap->ineq[i][off + d], ctx->one))
 379                                 break;
 380                 if (i < bmap->n_ineq)
 381                         continue;
 382                 *progress = 1;
 383                 bmap = isl_basic_map_eliminate_vars(bmap, (off-1)+d, 1);
 384                 if (F_ISSET(bmap, ISL_BASIC_MAP_EMPTY))
 385                         break;
 386                 bmap = isl_basic_map_drop_div(bmap, d);
 387                 if (!bmap)
 388                         break;
 389         }
 390         return bmap;
 391 }
 392
 393 static void eliminate_var_using_equality(struct isl_basic_map *bmap,
 394         unsigned pos, isl_int *eq, int *progress)
 395 {
 396         unsigned total;
 397         int k;
 398         int contains_divs;
 399
 400         total = isl_basic_map_total_dim(bmap);
 401         contains_divs =
 402                 isl_seq_first_non_zero(eq + 1 + isl_dim_total(bmap->dim),
 403                                                 bmap->n_div) != -1;
 404         for (k = 0; k < bmap->n_eq; ++k) {
 405                 if (bmap->eq[k] == eq)
 406                         continue;
 407                 if (isl_int_is_zero(bmap->eq[k][1+pos]))
 408                         continue;
 409                 if (progress)
 410                         *progress = 1;
 411                 isl_seq_elim(bmap->eq[k], eq, 1+pos, 1+total, NULL);
 412         }
 413
 414         for (k = 0; k < bmap->n_ineq; ++k) {
 415                 if (isl_int_is_zero(bmap->ineq[k][1+pos]))
 416                         continue;
 417                 if (progress)
 418                         *progress = 1;
 419                 isl_seq_elim(bmap->ineq[k], eq, 1+pos, 1+total, NULL);
 420                 F_CLR(bmap, ISL_BASIC_MAP_NORMALIZED);
 421         }
 422
 423         for (k = 0; k < bmap->n_div; ++k) {
 424                 if (isl_int_is_zero(bmap->div[k][0]))
 425                         continue;
 426                 if (isl_int_is_zero(bmap->div[k][1+1+pos]))
 427                         continue;
 428                 if (progress)
 429                         *progress = 1;
 430                 /* We need to be careful about circular definitions,
 431                  * so for now we just remove the definition of div k
 432                  * if the equality contains any divs.
 433                  */
 434                 if (contains_divs)
 435                         isl_seq_clr(bmap->div[k], 1 + total);
 436                 else
 437                         isl_seq_elim(bmap->div[k]+1, eq,
 438                                         1+pos, 1+total, &bmap->div[k][0]);
 439                 F_CLR(bmap, ISL_BASIC_MAP_NORMALIZED);
 440         }
 441 }
 442
 443 struct isl_basic_map *isl_basic_map_gauss(
 444         struct isl_basic_map *bmap, int *progress)
 445 {
 446         int k;
 447         int done;
 448         int last_var;
 449         unsigned total_var;
 450         unsigned total;
 451
 452         if (!bmap)
 453                 return NULL;
 454
 455         total = isl_basic_map_total_dim(bmap);
 456         total_var = total - bmap->n_div;
 457
 458         last_var = total - 1;
 459         for (done = 0; done < bmap->n_eq; ++done) {
 460                 for (; last_var >= 0; --last_var) {
 461                         for (k = done; k < bmap->n_eq; ++k)
 462                                 if (!isl_int_is_zero(bmap->eq[k][1+last_var]))
 463                                         break;
 464                         if (k < bmap->n_eq)
 465                                 break;
 466                 }
 467                 if (last_var < 0)
 468                         break;
 469                 if (k != done)
 470                         swap_equality(bmap, k, done);
 471                 if (isl_int_is_neg(bmap->eq[done][1+last_var]))
 472                         isl_seq_neg(bmap->eq[done], bmap->eq[done], 1+total);
 473
 474                 eliminate_var_using_equality(bmap, last_var, bmap->eq[done],
 475                                                 progress);
 476
 477                 if (last_var >= total_var &&
 478                     isl_int_is_zero(bmap->div[last_var - total_var][0])) {
 479                         unsigned div = last_var - total_var;
 480                         isl_seq_neg(bmap->div[div]+1, bmap->eq[done], 1+total);
 481                         isl_int_set_si(bmap->div[div][1+1+last_var], 0);
 482                         isl_int_set(bmap->div[div][0],
 483                                     bmap->eq[done][1+last_var]);
 484                         F_CLR(bmap, ISL_BASIC_MAP_NORMALIZED);
 485                 }
 486         }
 487         if (done == bmap->n_eq)
 488                 return bmap;
 489         for (k = done; k < bmap->n_eq; ++k) {
 490                 if (isl_int_is_zero(bmap->eq[k][0]))
 491                         continue;
 492                 return isl_basic_map_set_to_empty(bmap);
 493         }
 494         isl_basic_map_free_equality(bmap, bmap->n_eq-done);
 495         return bmap;
 496 }
 497
 498 struct isl_basic_set *isl_basic_set_gauss(
 499         struct isl_basic_set *bset, int *progress)
 500 {
 501         return (struct isl_basic_set*)isl_basic_map_gauss(
 502                         (struct isl_basic_map *)bset, progress);
 503 }
 504
 505
 506 static unsigned int round_up(unsigned int v)
 507 {
 508         int old_v = v;
 509
 510         while (v) {
 511                 old_v = v;
 512                 v ^= v & -v;
 513         }
 514         return old_v << 1;
 515 }
 516
 517 static int hash_index(isl_int ***index, unsigned int size, int bits,
 518                         struct isl_basic_map *bmap, int k)
 519 {
 520         int h;
 521         unsigned total = isl_basic_map_total_dim(bmap);
 522         uint32_t hash = isl_seq_get_hash_bits(bmap->ineq[k]+1, total, bits);
 523         for (h = hash; index[h]; h = (h+1) % size)
 524                 if (&bmap->ineq[k] != index[h] &&
 525                     isl_seq_eq(bmap->ineq[k]+1, index[h][0]+1, total))
 526                         break;
 527         return h;
 528 }
 529
 530 static int set_hash_index(isl_int ***index, unsigned int size, int bits,
 531                           struct isl_basic_set *bset, int k)
 532 {
 533         return hash_index(index, size, bits, (struct isl_basic_map *)bset, k);
 534 }
 535
 536 /* If we can eliminate more than one div, then we need to make
 537  * sure we do it from last div to first div, in order not to
 538  * change the position of the other divs that still need to
 539  * be removed.
 540  */
 541 static struct isl_basic_map *remove_duplicate_divs(
 542         struct isl_basic_map *bmap, int *progress)
 543 {
 544         unsigned int size;
 545         int *index;
 546         int *elim_for;
 547         int k, l, h;
 548         int bits;
 549         struct isl_blk eq;
 550         unsigned total_var = isl_dim_total(bmap->dim);
 551         unsigned total = total_var + bmap->n_div;
 552         struct isl_ctx *ctx;
 553
 554         if (bmap->n_div <= 1)
 555                 return bmap;
 556
 557         ctx = bmap->ctx;
 558         for (k = bmap->n_div - 1; k >= 0; --k)
 559                 if (!isl_int_is_zero(bmap->div[k][0]))
 560                         break;
 561         if (k <= 0)
 562                 return bmap;
 563
 564         elim_for = isl_calloc_array(ctx, int, bmap->n_div);
 565         size = round_up(4 * bmap->n_div / 3 - 1);
 566         bits = ffs(size) - 1;
 567         index = isl_calloc_array(ctx, int, size);
 568         if (!index)
 569                 return bmap;
 570         eq = isl_blk_alloc(ctx, 1+total);
 571         if (isl_blk_is_error(eq))
 572                 goto out;
 573
 574         isl_seq_clr(eq.data, 1+total);
 575         index[isl_seq_get_hash_bits(bmap->div[k], 2+total, bits)] = k + 1;
 576         for (--k; k >= 0; --k) {
 577                 uint32_t hash;
 578
 579                 if (isl_int_is_zero(bmap->div[k][0]))
 580                         continue;
 581
 582                 hash = isl_seq_get_hash_bits(bmap->div[k], 2+total, bits);
 583                 for (h = hash; index[h]; h = (h+1) % size)
 584                         if (isl_seq_eq(bmap->div[k],
 585                                        bmap->div[index[h]-1], 2+total))
 586                                 break;
 587                 if (index[h]) {
 588                         *progress = 1;
 589                         l = index[h] - 1;
 590                         elim_for[l] = k + 1;
 591                 }
 592                 index[h] = k+1;
 593         }
 594         for (l = bmap->n_div - 1; l >= 0; --l) {
 595                 if (!elim_for[l])
 596                         continue;
 597                 k = elim_for[l] - 1;
 598                 isl_int_set_si(eq.data[1+total_var+k], -1);
 599                 isl_int_set_si(eq.data[1+total_var+l], 1);
 600                 eliminate_div(bmap, eq.data, l);
 601                 isl_int_set_si(eq.data[1+total_var+k], 0);
 602                 isl_int_set_si(eq.data[1+total_var+l], 0);
 603         }
 604
 605         isl_blk_free(ctx, eq);
 606 out:
 607         free(index);
 608         free(elim_for);
 609         return bmap;
 610 }
 611
 612 /* Normalize divs that appear in equalities.
 613  *
 614  * In particular, we assume that bmap contains some equalities
 615  * of the form
 616  *
 617  *      a x = m * e_i
 618  *
 619  * and we want to replace the set of e_i by a minimal set and
 620  * such that the new e_i have a canonical representation in terms
 621  * of the vector x.
 622  * If any of the equalities involves more than one divs, then
 623  * we currently simply bail out.
 624  *
 625  * Let us first additionally assume that all equalities involve
 626  * a div.  The equalities then express modulo constraints on the
 627  * remaining variables and we can use "parameter compression"
 628  * to find a minimal set of constraints.  The result is a transformation
 629  *
 630  *      x = T(x') = x_0 + G x'
 631  *
 632  * with G a lower-triangular matrix with all elements below the diagonal
 633  * non-negative and smaller than the diagonal element on the same row.
 634  * We first normalize x_0 by making the same property hold in the affine
 635  * T matrix.
 636  * The rows i of G with a 1 on the diagonal do not impose any modulo
 637  * constraint and simply express x_i = x'_i.
 638  * For each of the remaining rows i, we introduce a div and a corresponding
 639  * equality.  In particular
 640  *
 641  *      g_ii e_j = x_i - g_i(x')
 642  *
 643  * where each x'_k is replaced either by x_k (if g_kk = 1) or the
 644  * corresponding div (if g_kk != 1).
 645  *
 646  * If there are any equalities not involving any div, then we
 647  * first apply a variable compression on the variables x:
 648  *
 649  *      x = C x''       x'' = C_2 x
 650  *
 651  * and perform the above parameter compression on A C instead of on A.
 652  * The resulting compression is then of the form
 653  *
 654  *      x'' = T(x') = x_0 + G x'
 655  *
 656  * and in constructing the new divs and the corresponding equalities,
 657  * we have to replace each x'', i.e., the x'_k with (g_kk = 1),
 658  * by the corresponding row from C_2.
 659  */
 660 static struct isl_basic_map *normalize_divs(
 661         struct isl_basic_map *bmap, int *progress)
 662 {
 663         int i, j, k;
 664         int total;
 665         int div_eq;
 666         struct isl_mat *B;
 667         struct isl_vec *d;
 668         struct isl_mat *T = NULL;
 669         struct isl_mat *C = NULL;
 670         struct isl_mat *C2 = NULL;
 671         isl_int v;
 672         int *pos;
 673         int dropped, needed;
 674
 675         if (!bmap)
 676                 return NULL;
 677
 678         if (bmap->n_div == 0)
 679                 return bmap;
 680
 681         if (bmap->n_eq == 0)
 682                 return bmap;
 683
 684         if (F_ISSET(bmap, ISL_BASIC_MAP_NORMALIZED_DIVS))
 685                 return bmap;
 686
 687         total = isl_dim_total(bmap->dim);
 688         for (i = 0, j = bmap->n_div-1; i < bmap->n_eq; ++i) {
 689                 while (j >= 0 && isl_int_is_zero(bmap->eq[i][1 + total + j]))
 690                         --j;
 691                 if (j < 0)
 692                         break;
 693                 if (isl_seq_first_non_zero(bmap->eq[i] + 1 + total, j) != -1)
 694                         goto done;
 695         }
 696         div_eq = i;
 697         if (div_eq == 0)
 698                 return bmap;
 699
 700         if (div_eq < bmap->n_eq) {
 701                 B = isl_mat_sub_alloc(bmap->ctx, bmap->eq, div_eq,
 702                                         bmap->n_eq - div_eq, 0, 1 + total);
 703                 C = isl_mat_variable_compression(bmap->ctx, B, &C2);
 704                 if (!C || !C2)
 705                         goto error;
 706                 if (C->n_col == 0) {
 707                         bmap = isl_basic_map_set_to_empty(bmap);
 708                         isl_mat_free(bmap->ctx, C);
 709                         isl_mat_free(bmap->ctx, C2);
 710                         goto done;
 711                 }
 712         }
 713
 714         d = isl_vec_alloc(bmap->ctx, div_eq);
 715         if (!d)
 716                 goto error;
 717         for (i = 0, j = bmap->n_div-1; i < div_eq; ++i) {
 718                 while (j >= 0 && isl_int_is_zero(bmap->eq[i][1 + total + j]))
 719                         --j;
 720                 isl_int_set(d->block.data[i], bmap->eq[i][1 + total + j]);
 721         }
 722         B = isl_mat_sub_alloc(bmap->ctx, bmap->eq, 0, div_eq, 0, 1 + total);
 723
 724         if (C) {
 725                 B = isl_mat_product(bmap->ctx, B, C);
 726                 C = NULL;
 727         }
 728
 729         T = isl_mat_parameter_compression(bmap->ctx, B, d);
 730         if (!T)
 731                 goto error;
 732         if (T->n_col == 0) {
 733                 bmap = isl_basic_map_set_to_empty(bmap);
 734                 isl_mat_free(bmap->ctx, C2);
 735                 isl_mat_free(bmap->ctx, T);
 736                 goto done;
 737         }
 738         isl_int_init(v);
 739         for (i = 0; i < T->n_row - 1; ++i) {
 740                 isl_int_fdiv_q(v, T->row[1 + i][0], T->row[1 + i][1 + i]);
 741                 if (isl_int_is_zero(v))
 742                         continue;
 743                 isl_mat_col_submul(T, 0, v, 1 + i);
 744         }
 745         isl_int_clear(v);
 746         pos = isl_alloc_array(bmap->ctx, int, T->n_row);
 747         /* We have to be careful because dropping equalities may reorder them */
 748         dropped = 0;
 749         for (j = bmap->n_div - 1; j >= 0; --j) {
 750                 for (i = 0; i < bmap->n_eq; ++i)
 751                         if (!isl_int_is_zero(bmap->eq[i][1 + total + j]))
 752                                 break;
 753                 if (i < bmap->n_eq) {
 754                         bmap = isl_basic_map_drop_div(bmap, j);
 755                         isl_basic_map_drop_equality(bmap, i);
 756                         ++dropped;
 757                 }
 758         }
 759         pos[0] = 0;
 760         needed = 0;
 761         for (i = 1; i < T->n_row; ++i) {
 762                 if (isl_int_is_one(T->row[i][i]))
 763                         pos[i] = i;
 764                 else
 765                         needed++;
 766         }
 767         if (needed > dropped) {
 768                 bmap = isl_basic_map_extend_dim(bmap, isl_dim_copy(bmap->dim),
 769                                 needed, needed, 0);
 770                 if (!bmap)
 771                         goto error;
 772         }
 773         for (i = 1; i < T->n_row; ++i) {
 774                 if (isl_int_is_one(T->row[i][i]))
 775                         continue;
 776                 k = isl_basic_map_alloc_div(bmap);
 777                 pos[i] = 1 + total + k;
 778                 isl_seq_clr(bmap->div[k] + 1, 1 + total + bmap->n_div);
 779                 isl_int_set(bmap->div[k][0], T->row[i][i]);
 780                 if (C2)
 781                         isl_seq_cpy(bmap->div[k] + 1, C2->row[i], 1 + total);
 782                 else
 783                         isl_int_set_si(bmap->div[k][1 + i], 1);
 784                 for (j = 0; j < i; ++j) {
 785                         if (isl_int_is_zero(T->row[i][j]))
 786                                 continue;
 787                         if (pos[j] < T->n_row && C2)
 788                                 isl_seq_submul(bmap->div[k] + 1, T->row[i][j],
 789                                                 C2->row[pos[j]], 1 + total);
 790                         else
 791                                 isl_int_neg(bmap->div[k][1 + pos[j]],
 792                                                                 T->row[i][j]);
 793                 }
 794                 j = isl_basic_map_alloc_equality(bmap);
 795                 isl_seq_neg(bmap->eq[j], bmap->div[k]+1, 1+total+bmap->n_div);
 796                 isl_int_set(bmap->eq[j][pos[i]], bmap->div[k][0]);
 797         }
 798         free(pos);
 799         isl_mat_free(bmap->ctx, C2);
 800         isl_mat_free(bmap->ctx, T);
 801
 802         *progress = 1;
 803 done:
 804         F_SET(bmap, ISL_BASIC_MAP_NORMALIZED_DIVS);
 805
 806         return bmap;
 807 error:
 808         isl_mat_free(bmap->ctx, C);
 809         isl_mat_free(bmap->ctx, C2);
 810         isl_mat_free(bmap->ctx, T);
 811         return bmap;
 812 }
 813
 814 static struct isl_basic_map *remove_duplicate_constraints(
 815         struct isl_basic_map *bmap, int *progress)
 816 {
 817         unsigned int size;
 818         isl_int ***index;
 819         int k, l, h;
 820         int bits;
 821         unsigned total = isl_basic_map_total_dim(bmap);
 822         isl_int sum;
 823
 824         if (bmap->n_ineq <= 1)
 825                 return bmap;
 826
 827         size = round_up(4 * (bmap->n_ineq+1) / 3 - 1);
 828         bits = ffs(size) - 1;
 829         index = isl_calloc_array(ctx, isl_int **, size);
 830         if (!index)
 831                 return bmap;
 832
 833         index[isl_seq_get_hash_bits(bmap->ineq[0]+1, total, bits)] = &bmap->ineq[0];
 834         for (k = 1; k < bmap->n_ineq; ++k) {
 835                 h = hash_index(index, size, bits, bmap, k);
 836                 if (!index[h]) {
 837                         index[h] = &bmap->ineq[k];
 838                         continue;
 839                 }
 840                 if (progress)
 841                         *progress = 1;
 842                 l = index[h] - &bmap->ineq[0];
 843                 if (isl_int_lt(bmap->ineq[k][0], bmap->ineq[l][0]))
 844                         swap_inequality(bmap, k, l);
 845                 isl_basic_map_drop_inequality(bmap, k);
 846                 --k;
 847         }
 848         isl_int_init(sum);
 849         for (k = 0; k < bmap->n_ineq-1; ++k) {
 850                 isl_seq_neg(bmap->ineq[k]+1, bmap->ineq[k]+1, total);
 851                 h = hash_index(index, size, bits, bmap, k);
 852                 isl_seq_neg(bmap->ineq[k]+1, bmap->ineq[k]+1, total);
 853                 if (!index[h])
 854                         continue;
 855                 l = index[h] - &bmap->ineq[0];
 856                 isl_int_add(sum, bmap->ineq[k][0], bmap->ineq[l][0]);
 857                 if (isl_int_is_pos(sum))
 858                         continue;
 859                 if (isl_int_is_zero(sum)) {
 860                         /* We need to break out of the loop after these
 861                          * changes since the contents of the hash
 862                          * will no longer be valid.
 863                          * Plus, we probably we want to regauss first.
 864                          */
 865                         isl_basic_map_drop_inequality(bmap, l);
 866                         isl_basic_map_inequality_to_equality(bmap, k);
 867                 } else
 868                         bmap = isl_basic_map_set_to_empty(bmap);
 869                 break;
 870         }
 871         isl_int_clear(sum);
 872
 873         free(index);
 874         return bmap;
 875 }
 876
 877
 878 struct isl_basic_map *isl_basic_map_simplify(struct isl_basic_map *bmap)
 879 {
 880         int progress = 1;
 881         if (!bmap)
 882                 return NULL;
 883         while (progress) {
 884                 progress = 0;
 885                 bmap = normalize_constraints(bmap);
 886                 bmap = eliminate_divs_eq(bmap, &progress);
 887                 bmap = eliminate_divs_ineq(bmap, &progress);
 888                 bmap = isl_basic_map_gauss(bmap, &progress);
 889                 /* requires equalities in normal form */
 890                 bmap = normalize_divs(bmap, &progress);
 891                 bmap = remove_duplicate_divs(bmap, &progress);
 892                 bmap = remove_duplicate_constraints(bmap, &progress);
 893         }
 894         return bmap;
 895 }
 896
 897 struct isl_basic_set *isl_basic_set_simplify(struct isl_basic_set *bset)
 898 {
 899         return (struct isl_basic_set *)
 900                 isl_basic_map_simplify((struct isl_basic_map *)bset);
 901 }
 902
 903
 904 /* If the only constraints a div d=floor(f/m)
 905  * appears in are its two defining constraints
 906  *
 907  *      f - m d >=0
 908  *      -(f - (m - 1)) + m d >= 0
 909  *
 910  * then it can safely be removed.
 911  */
 912 static int div_is_redundant(struct isl_basic_map *bmap, int div)
 913 {
 914         int i;
 915         unsigned pos = 1 + isl_dim_total(bmap->dim) + div;
 916
 917         for (i = 0; i < bmap->n_eq; ++i)
 918                 if (!isl_int_is_zero(bmap->eq[i][pos]))
 919                         return 0;
 920
 921         for (i = 0; i < bmap->n_ineq; ++i) {
 922                 if (isl_int_is_zero(bmap->ineq[i][pos]))
 923                         continue;
 924                 if (isl_int_eq(bmap->ineq[i][pos], bmap->div[div][0])) {
 925                         int neg;
 926                         isl_int_sub(bmap->div[div][1],
 927                                         bmap->div[div][1], bmap->div[div][0]);
 928                         isl_int_add_ui(bmap->div[div][1], bmap->div[div][1], 1);
 929                         neg = isl_seq_is_neg(bmap->ineq[i], bmap->div[div]+1, pos);
 930                         isl_int_sub_ui(bmap->div[div][1], bmap->div[div][1], 1);
 931                         isl_int_add(bmap->div[div][1],
 932                                         bmap->div[div][1], bmap->div[div][0]);
 933                         if (!neg)
 934                                 return 0;
 935                         if (isl_seq_first_non_zero(bmap->ineq[i]+pos+1,
 936                                                     bmap->n_div-div-1) != -1)
 937                                 return 0;
 938                 } else if (isl_int_abs_eq(bmap->ineq[i][pos], bmap->div[div][0])) {
 939                         if (!isl_seq_eq(bmap->ineq[i], bmap->div[div]+1, pos))
 940                                 return 0;
 941                         if (isl_seq_first_non_zero(bmap->ineq[i]+pos+1,
 942                                                     bmap->n_div-div-1) != -1)
 943                                 return 0;
 944                 } else
 945                         return 0;
 946         }
 947
 948         for (i = 0; i < bmap->n_div; ++i)
 949                 if (!isl_int_is_zero(bmap->div[i][1+pos]))
 950                         return 0;
 951
 952         return 1;
 953 }
 954
 955 /*
 956  * Remove divs that don't occur in any of the constraints or other divs.
 957  * These can arise when dropping some of the variables in a quast
 958  * returned by piplib.
 959  */
 960 static struct isl_basic_map *remove_redundant_divs(struct isl_basic_map *bmap)
 961 {
 962         int i;
 963
 964         if (!bmap)
 965                 return NULL;
 966
 967         for (i = bmap->n_div-1; i >= 0; --i) {
 968                 if (!div_is_redundant(bmap, i))
 969                         continue;
 970                 bmap = isl_basic_map_drop_div(bmap, i);
 971         }
 972         return bmap;
 973 }
 974
 975 struct isl_basic_map *isl_basic_map_finalize(struct isl_basic_map *bmap)
 976 {
 977         bmap = remove_redundant_divs(bmap);
 978         if (!bmap)
 979                 return NULL;
 980         F_SET(bmap, ISL_BASIC_SET_FINAL);
 981         return bmap;
 982 }
 983
 984 struct isl_basic_set *isl_basic_set_finalize(struct isl_basic_set *bset)
 985 {
 986         return (struct isl_basic_set *)
 987                 isl_basic_map_finalize((struct isl_basic_map *)bset);
 988 }
 989
 990 struct isl_set *isl_set_finalize(struct isl_set *set)
 991 {
 992         int i;
 993
 994         if (!set)
 995                 return NULL;
 996         for (i = 0; i < set->n; ++i) {
 997                 set->p[i] = isl_basic_set_finalize(set->p[i]);
 998                 if (!set->p[i])
 999                         goto error;
1000         }
1001         return set;
1002 error:
1003         isl_set_free(set);
1004         return NULL;
1005 }
1006
1007 struct isl_map *isl_map_finalize(struct isl_map *map)
1008 {
1009         int i;
1010
1011         if (!map)
1012                 return NULL;
1013         for (i = 0; i < map->n; ++i) {
1014                 map->p[i] = isl_basic_map_finalize(map->p[i]);
1015                 if (!map->p[i])
1016                         goto error;
1017         }
1018         F_CLR(map, ISL_MAP_NORMALIZED);
1019         return map;
1020 error:
1021         isl_map_free(map);
1022         return NULL;
1023 }
1024
1025
1026 /* Remove any div that is defined in terms of the given variable.
1027  */
1028 static struct isl_basic_map *remove_dependent_vars(struct isl_basic_map *bmap,
1029                                                                         int pos)
1030 {
1031         int i;
1032         unsigned dim = isl_dim_total(bmap->dim);
1033
1034         for (i = 0; i < bmap->n_div; ++i) {
1035                 if (isl_int_is_zero(bmap->div[i][0]))
1036                         continue;
1037                 if (isl_int_is_zero(bmap->div[i][1+1+pos]))
1038                         continue;
1039                 bmap = isl_basic_map_eliminate_vars(bmap, dim + i, 1);
1040                 if (!bmap)
1041                         return NULL;
1042         }
1043         return bmap;
1044 }
1045
1046 /* Eliminate the specified variables from the constraints using
1047  * Fourier-Motzkin.  The variables themselves are not removed.
1048  */
1049 struct isl_basic_map *isl_basic_map_eliminate_vars(
1050         struct isl_basic_map *bmap, unsigned pos, unsigned n)
1051 {
1052         int d;
1053         int i, j, k;
1054         unsigned total;
1055
1056         if (n == 0)
1057                 return bmap;
1058         if (!bmap)
1059                 return NULL;
1060         total = isl_basic_map_total_dim(bmap);
1061
1062         bmap = isl_basic_map_cow(bmap);
1063         for (d = pos + n - 1; d >= 0 && d >= pos; --d) {
1064                 int n_lower, n_upper;
1065                 bmap = remove_dependent_vars(bmap, d);
1066                 if (!bmap)
1067                         return NULL;
1068                 if (d >= total - bmap->n_div)
1069                         isl_seq_clr(bmap->div[d-(total-bmap->n_div)], 2+total);
1070                 for (i = 0; i < bmap->n_eq; ++i) {
1071                         if (isl_int_is_zero(bmap->eq[i][1+d]))
1072                                 continue;
1073                         eliminate_var_using_equality(bmap, d, bmap->eq[i], NULL);
1074                         isl_basic_map_drop_equality(bmap, i);
1075                         break;
1076                 }
1077                 if (i < bmap->n_eq)
1078                         continue;
1079                 n_lower = 0;
1080                 n_upper = 0;
1081                 for (i = 0; i < bmap->n_ineq; ++i) {
1082                         if (isl_int_is_pos(bmap->ineq[i][1+d]))
1083                                 n_lower++;
1084                         else if (isl_int_is_neg(bmap->ineq[i][1+d]))
1085                                 n_upper++;
1086                 }
1087                 bmap = isl_basic_map_extend_constraints(bmap,
1088                                 0, n_lower * n_upper);
1089                 for (i = bmap->n_ineq - 1; i >= 0; --i) {
1090                         int last;
1091                         if (isl_int_is_zero(bmap->ineq[i][1+d]))
1092                                 continue;
1093                         last = -1;
1094                         for (j = 0; j < i; ++j) {
1095                                 if (isl_int_is_zero(bmap->ineq[j][1+d]))
1096                                         continue;
1097                                 last = j;
1098                                 if (isl_int_sgn(bmap->ineq[i][1+d]) ==
1099                                     isl_int_sgn(bmap->ineq[j][1+d]))
1100                                         continue;
1101                                 k = isl_basic_map_alloc_inequality(bmap);
1102                                 if (k < 0)
1103                                         goto error;
1104                                 isl_seq_cpy(bmap->ineq[k], bmap->ineq[i],
1105                                                 1+total);
1106                                 isl_seq_elim(bmap->ineq[k], bmap->ineq[j],
1107                                                 1+d, 1+total, NULL);
1108                         }
1109                         isl_basic_map_drop_inequality(bmap, i);
1110                         i = last + 1;
1111                 }
1112                 if (n_lower > 0 && n_upper > 0) {
1113                         bmap = normalize_constraints(bmap);
1114                         bmap = remove_duplicate_constraints(bmap, NULL);
1115                         bmap = isl_basic_map_gauss(bmap, NULL);
1116                         bmap = isl_basic_map_convex_hull(bmap);
1117                         if (!bmap)
1118                                 goto error;
1119                         if (F_ISSET(bmap, ISL_BASIC_MAP_EMPTY))
1120                                 break;
1121                 }
1122         }
1123         F_CLR(bmap, ISL_BASIC_MAP_NORMALIZED);
1124         return bmap;
1125 error:
1126         isl_basic_map_free(bmap);
1127         return NULL;
1128 }
1129
1130 struct isl_basic_set *isl_basic_set_eliminate_vars(
1131         struct isl_basic_set *bset, unsigned pos, unsigned n)
1132 {
1133         return (struct isl_basic_set *)isl_basic_map_eliminate_vars(
1134                         (struct isl_basic_map *)bset, pos, n);
1135 }
1136
1137 static void compute_elimination_index(struct isl_basic_map *bmap, int *elim)
1138 {
1139         int d, i;
1140         unsigned total;
1141
1142         total = isl_dim_total(bmap->dim);
1143         for (d = 0; d < total; ++d)
1144                 elim[d] = -1;
1145         for (d = total - 1, i = 0; d >= 0 && i < bmap->n_eq; ++i) {
1146                 for (; d >= 0; --d) {
1147                         if (isl_int_is_zero(bmap->eq[i][1+d]))
1148                                 continue;
1149                         elim[d] = i;
1150                         break;
1151                 }
1152         }
1153 }
1154
1155 static void set_compute_elimination_index(struct isl_basic_set *bset, int *elim)
1156 {
1157         return compute_elimination_index((struct isl_basic_map *)bset, elim);
1158 }
1159
1160 static int reduced_using_equalities(isl_int *dst, isl_int *src,
1161         struct isl_basic_map *bmap, int *elim)
1162 {
1163         int d, i;
1164         int copied = 0;
1165         unsigned total;
1166
1167         total = isl_dim_total(bmap->dim);
1168         for (d = total - 1; d >= 0; --d) {
1169                 if (isl_int_is_zero(src[1+d]))
1170                         continue;
1171                 if (elim[d] == -1)
1172                         continue;
1173                 if (!copied) {
1174                         isl_seq_cpy(dst, src, 1 + total);
1175                         copied = 1;
1176                 }
1177                 isl_seq_elim(dst, bmap->eq[elim[d]], 1 + d, 1 + total, NULL);
1178         }
1179         return copied;
1180 }
1181
1182 static int set_reduced_using_equalities(isl_int *dst, isl_int *src,
1183         struct isl_basic_set *bset, int *elim)
1184 {
1185         return reduced_using_equalities(dst, src,
1186                                         (struct isl_basic_map *)bset, elim);
1187 }
1188
1189 static struct isl_basic_set *isl_basic_set_reduce_using_equalities(
1190         struct isl_basic_set *bset, struct isl_basic_set *context)
1191 {
1192         int i;
1193         int *elim;
1194
1195         if (!bset || !context)
1196                 goto error;
1197
1198         bset = isl_basic_set_cow(bset);
1199         if (!bset)
1200                 goto error;
1201
1202         elim = isl_alloc_array(ctx, int, isl_basic_set_n_dim(bset));
1203         if (!elim)
1204                 goto error;
1205         set_compute_elimination_index(context, elim);
1206         for (i = 0; i < bset->n_eq; ++i)
1207                 set_reduced_using_equalities(bset->eq[i], bset->eq[i],
1208                                                         context, elim);
1209         for (i = 0; i < bset->n_ineq; ++i)
1210                 set_reduced_using_equalities(bset->ineq[i], bset->ineq[i],
1211                                                         context, elim);
1212         isl_basic_set_free(context);
1213         free(elim);
1214         bset = isl_basic_set_simplify(bset);
1215         bset = isl_basic_set_finalize(bset);
1216         return bset;
1217 error:
1218         isl_basic_set_free(bset);
1219         isl_basic_set_free(context);
1220         return NULL;
1221 }
1222
1223 static struct isl_basic_set *remove_shifted_constraints(
1224         struct isl_basic_set *bset, struct isl_basic_set *context)
1225 {
1226         unsigned int size;
1227         isl_int ***index;
1228         int bits;
1229         int k, h, l;
1230
1231         if (!bset)
1232                 return NULL;
1233
1234         size = round_up(4 * (context->n_ineq+1) / 3 - 1);
1235         bits = ffs(size) - 1;
1236         index = isl_calloc_array(ctx, isl_int **, size);
1237         if (!index)
1238                 return bset;
1239
1240         for (k = 0; k < context->n_ineq; ++k) {
1241                 h = set_hash_index(index, size, bits, context, k);
1242                 index[h] = &context->ineq[k];
1243         }
1244         for (k = 0; k < bset->n_ineq; ++k) {
1245                 h = set_hash_index(index, size, bits, bset, k);
1246                 if (!index[h])
1247                         continue;
1248                 l = index[h] - &context->ineq[0];
1249                 if (isl_int_lt(bset->ineq[k][0], context->ineq[l][0]))
1250                         continue;
1251                 bset = isl_basic_set_cow(bset);
1252                 if (!bset)
1253                         goto error;
1254                 isl_basic_set_drop_inequality(bset, k);
1255                 --k;
1256         }
1257         free(index);
1258         return bset;
1259 error:
1260         free(index);
1261         return bset;
1262 }
1263
1264 static struct isl_basic_set *uset_gist(struct isl_basic_set *bset,
1265         struct isl_basic_set *context);
1266
1267 static struct isl_basic_set *uset_gist_context_eq(struct isl_basic_set *bset,
1268         struct isl_basic_set *context)
1269 {
1270         struct isl_mat *T;
1271         struct isl_mat *T2;
1272         struct isl_ctx *ctx = context->ctx;
1273         struct isl_basic_set *reduced_context;
1274         reduced_context = isl_basic_set_remove_equalities(
1275                                 isl_basic_set_copy(context), &T, &T2);
1276         if (!reduced_context)
1277                 goto error;
1278         bset = isl_basic_set_preimage(ctx, bset, T);
1279         bset = uset_gist(bset, reduced_context);
1280         bset = isl_basic_set_preimage(ctx, bset, T2);
1281         bset = isl_basic_set_reduce_using_equalities(bset, context);
1282         return bset;
1283 error:
1284         isl_basic_set_free(context);
1285         isl_basic_set_free(bset);
1286         return NULL;
1287 }
1288
1289 static struct isl_basic_set *uset_gist_set_eq(struct isl_basic_set *bset,
1290         struct isl_basic_set *context)
1291 {
1292         struct isl_mat *T;
1293         struct isl_mat *T2;
1294         struct isl_ctx *ctx = context->ctx;
1295         struct isl_basic_set *affine_hull = NULL;
1296
1297         affine_hull = isl_basic_set_copy(bset);
1298         affine_hull = isl_basic_set_cow(affine_hull);
1299         if (!affine_hull)
1300                 goto error;
1301         isl_basic_set_free_inequality(affine_hull, affine_hull->n_ineq);
1302
1303         bset = isl_basic_set_remove_equalities(bset, &T, &T2);
1304         if (!bset)
1305                 goto error;
1306         context = isl_basic_set_preimage(ctx, context, T);
1307         bset = uset_gist(bset, context);
1308         bset = isl_basic_set_preimage(ctx, bset, T2);
1309         bset = isl_basic_set_intersect(bset, affine_hull);
1310         return bset;
1311 error:
1312         isl_basic_set_free(affine_hull);
1313         isl_basic_set_free(context);
1314         isl_basic_set_free(bset);
1315         return NULL;
1316 }
1317
1318 /* Remove all information from bset that is redundant in the context
1319  * of context.  In particular, equalities that are linear combinations
1320  * of those in context are removed.  Then the inequalities that are
1321  * redundant in the context of the equalities and inequalities of
1322  * context are removed.
1323  */
1324 static struct isl_basic_set *uset_gist(struct isl_basic_set *bset,
1325         struct isl_basic_set *context)
1326 {
1327         int i;
1328         isl_int opt;
1329         struct isl_basic_set *combined;
1330         struct isl_ctx *ctx;
1331
1332         if (!bset || !context)
1333                 goto error;
1334
1335         if (context->n_eq > 0)
1336                 return uset_gist_context_eq(bset, context);
1337         if (!context->n_ineq)
1338                 goto done;
1339         if (bset->n_eq > 0)
1340                 return uset_gist_set_eq(bset, context);
1341         bset = remove_shifted_constraints(bset, context);
1342         combined = isl_basic_set_extend_constraints(isl_basic_set_copy(bset),
1343                         context->n_eq, context->n_ineq);
1344         context = isl_basic_set_add_constraints(combined, context, 0);
1345         if (!context)
1346                 goto error;
1347         ctx = context->ctx;
1348         isl_int_init(opt);
1349         for (i = bset->n_ineq-1; i >= 0; --i) {
1350                 int redundant;
1351                 set_swap_inequality(context, i, context->n_ineq-1);
1352                 context->n_ineq--;
1353                 redundant = isl_basic_set_constraint_is_redundant(&context,
1354                                 context->ineq[context->n_ineq], &opt, NULL);
1355                 if (redundant == -1) {
1356                         isl_int_clear(opt);
1357                         goto error;
1358                 }
1359                 if (F_ISSET(context, ISL_BASIC_MAP_EMPTY)) {
1360                         bset = isl_basic_set_set_to_empty(bset);
1361                         break;
1362                 }
1363                 context->n_ineq++;
1364                 set_swap_inequality(context, i, context->n_ineq-1);
1365                 if (redundant) {
1366                         isl_basic_set_drop_inequality(context, i);
1367                         isl_basic_set_drop_inequality(bset, i);
1368                 }
1369         }
1370         isl_int_clear(opt);
1371 done:
1372         isl_basic_set_free(context);
1373         return bset;
1374 error:
1375         isl_basic_set_free(context);
1376         isl_basic_set_free(bset);
1377         return NULL;
1378 }
1379
1380 struct isl_basic_map *isl_basic_map_gist(struct isl_basic_map *bmap,
1381         struct isl_basic_map *context)
1382 {
1383         struct isl_basic_set *bset;
1384
1385         if (!bmap || !context)
1386                 goto error;
1387
1388         context = isl_basic_map_align_divs(context, bmap);
1389         bmap = isl_basic_map_align_divs(bmap, context);
1390
1391         bset = uset_gist(isl_basic_map_underlying_set(isl_basic_map_copy(bmap)),
1392                          isl_basic_map_underlying_set(context));
1393
1394         return isl_basic_map_overlying_set(bset, bmap);
1395 error:
1396         isl_basic_map_free(bmap);
1397         isl_basic_map_free(context);
1398         return NULL;
1399 }
1400
1401 /*
1402  * Assumes context has no implicit divs.
1403  */
1404 struct isl_map *isl_map_gist(struct isl_map *map, struct isl_basic_map *context)
1405 {
1406         int i;
1407
1408         map = isl_map_cow(map);
1409         if (!map || !context)
1410                 return NULL;
1411         isl_assert(map->ctx, isl_dim_equal(map->dim, context->dim), goto error);
1412         map = isl_map_compute_divs(map);
1413         for (i = 0; i < map->n; ++i)
1414                 context = isl_basic_map_align_divs(context, map->p[i]);
1415         for (i = 0; i < map->n; ++i) {
1416                 map->p[i] = isl_basic_map_gist(map->p[i],
1417                                                 isl_basic_map_copy(context));
1418                 if (!map->p[i])
1419                         goto error;
1420         }
1421         isl_basic_map_free(context);
1422         F_CLR(map, ISL_MAP_NORMALIZED);
1423         return map;
1424 error:
1425         isl_map_free(map);
1426         isl_basic_map_free(context);
1427         return NULL;
1428 }
1429
1430 struct isl_basic_set *isl_basic_set_gist(struct isl_basic_set *bset,
1431                                                 struct isl_basic_set *context)
1432 {
1433         return (struct isl_basic_set *)isl_basic_map_gist(
1434                 (struct isl_basic_map *)bset, (struct isl_basic_map *)context);
1435 }
1436
1437 struct isl_set *isl_set_gist(struct isl_set *set, struct isl_basic_set *context)
1438 {
1439         return (struct isl_set *)isl_map_gist((struct isl_map *)set,
1440                                         (struct isl_basic_map *)context);
1441 }
1442
1443 /* Quick check to see if two basic maps are disjoint.
1444  * In particular, we reduce the equalities and inequalities of
1445  * one basic map in the context of the equalities of the other
1446  * basic map and check if we get a contradiction.
1447  */
1448 int isl_basic_map_fast_is_disjoint(struct isl_basic_map *bmap1,
1449         struct isl_basic_map *bmap2)
1450 {
1451         struct isl_vec *v = NULL;
1452         int *elim = NULL;
1453         unsigned total;
1454         int d, i;
1455
1456         if (!bmap1 || !bmap2)
1457                 return -1;
1458         isl_assert(bmap1->ctx, isl_dim_equal(bmap1->dim, bmap2->dim),
1459                         return -1);
1460         if (bmap1->n_div || bmap2->n_div)
1461                 return 0;
1462         if (!bmap1->n_eq && !bmap2->n_eq)
1463                 return 0;
1464
1465         total = isl_dim_total(bmap1->dim);
1466         if (total == 0)
1467                 return 0;
1468         v = isl_vec_alloc(bmap1->ctx, 1 + total);
1469         if (!v)
1470                 goto error;
1471         elim = isl_alloc_array(bmap1->ctx, int, total);
1472         if (!elim)
1473                 goto error;
1474         compute_elimination_index(bmap1, elim);
1475         for (i = 0; i < bmap2->n_eq; ++i) {
1476                 int reduced;
1477                 reduced = reduced_using_equalities(v->block.data, bmap2->eq[i],
1478                                                         bmap1, elim);
1479                 if (reduced && !isl_int_is_zero(v->block.data[0]) &&
1480                     isl_seq_first_non_zero(v->block.data + 1, total) == -1)
1481                         goto disjoint;
1482         }
1483         for (i = 0; i < bmap2->n_ineq; ++i) {
1484                 int reduced;
1485                 reduced = reduced_using_equalities(v->block.data,
1486                                                 bmap2->ineq[i], bmap1, elim);
1487                 if (reduced && isl_int_is_neg(v->block.data[0]) &&
1488                     isl_seq_first_non_zero(v->block.data + 1, total) == -1)
1489                         goto disjoint;
1490         }
1491         compute_elimination_index(bmap2, elim);
1492         for (i = 0; i < bmap1->n_ineq; ++i) {
1493                 int reduced;
1494                 reduced = reduced_using_equalities(v->block.data,
1495                                                 bmap1->ineq[i], bmap2, elim);
1496                 if (reduced && isl_int_is_neg(v->block.data[0]) &&
1497                     isl_seq_first_non_zero(v->block.data + 1, total) == -1)
1498                         goto disjoint;
1499         }
1500         isl_vec_free(bmap1->ctx, v);
1501         free(elim);
1502         return 0;
1503 disjoint:
1504         isl_vec_free(bmap1->ctx, v);
1505         free(elim);
1506         return 1;
1507 error:
1508         isl_vec_free(bmap1->ctx, v);
1509         free(elim);
1510         return -1;
1511 }
1512
1513 int isl_basic_set_fast_is_disjoint(struct isl_basic_set *bset1,
1514         struct isl_basic_set *bset2)
1515 {
1516         return isl_basic_map_fast_is_disjoint((struct isl_basic_map *)bset1,
1517                                               (struct isl_basic_map *)bset2);
1518 }
1519
1520 int isl_map_fast_is_disjoint(struct isl_map *map1, struct isl_map *map2)
1521 {
1522         int i, j;
1523
1524         if (!map1 || !map2)
1525                 return -1;
1526
1527         if (isl_map_fast_is_equal(map1, map2))
1528                 return 0;
1529
1530         for (i = 0; i < map1->n; ++i) {
1531                 for (j = 0; j < map2->n; ++j) {
1532                         int d = isl_basic_map_fast_is_disjoint(map1->p[i],
1533                                                                map2->p[j]);
1534                         if (d != 1)
1535                                 return d;
1536                 }
1537         }
1538         return 1;
1539 }
1540
1541 int isl_set_fast_is_disjoint(struct isl_set *set1, struct isl_set *set2)
1542 {
1543         return isl_map_fast_is_disjoint((struct isl_map *)set1,
1544                                         (struct isl_map *)set2);
1545 }