isl_map_simplify.c

   1 #include "isl_equalities.h"
   2 #include "isl_map.h"
   3 #include "isl_map_private.h"
   4 #include "isl_tab.h"
   5
   6 static void swap_equality(struct isl_basic_map *bmap, int a, int b)
   7 {
   8         isl_int *t = bmap->eq[a];
   9         bmap->eq[a] = bmap->eq[b];
  10         bmap->eq[b] = t;
  11 }
  12
  13 static void swap_inequality(struct isl_basic_map *bmap, int a, int b)
  14 {
  15         if (a != b) {
  16                 isl_int *t = bmap->ineq[a];
  17                 bmap->ineq[a] = bmap->ineq[b];
  18                 bmap->ineq[b] = t;
  19         }
  20 }
  21
  22 static void set_swap_inequality(struct isl_basic_set *bset, int a, int b)
  23 {
  24         swap_inequality((struct isl_basic_map *)bset, a, b);
  25 }
  26
  27 static void constraint_drop_vars(isl_int *c, unsigned n, unsigned rem)
  28 {
  29         isl_seq_cpy(c, c + n, rem);
  30         isl_seq_clr(c + rem, n);
  31 }
  32
  33 /* Drop n dimensions starting at first.
  34  *
  35  * In principle, this frees up some extra variables as the number
  36  * of columns remains constant, but we would have to extend
  37  * the div array too as the number of rows in this array is assumed
  38  * to be equal to extra.
  39  */
  40 struct isl_basic_set *isl_basic_set_drop_dims(
  41                 struct isl_basic_set *bset, unsigned first, unsigned n)
  42 {
  43         int i;
  44
  45         if (!bset)
  46                 goto error;
  47
  48         isl_assert(bset->ctx, first + n <= bset->dim->n_out, goto error);
  49
  50         if (n == 0)
  51                 return bset;
  52
  53         bset = isl_basic_set_cow(bset);
  54         if (!bset)
  55                 return NULL;
  56
  57         for (i = 0; i < bset->n_eq; ++i)
  58                 constraint_drop_vars(bset->eq[i]+1+bset->dim->nparam+first, n,
  59                                      (bset->dim->n_out-first-n)+bset->extra);
  60
  61         for (i = 0; i < bset->n_ineq; ++i)
  62                 constraint_drop_vars(bset->ineq[i]+1+bset->dim->nparam+first, n,
  63                                      (bset->dim->n_out-first-n)+bset->extra);
  64
  65         for (i = 0; i < bset->n_div; ++i)
  66                 constraint_drop_vars(bset->div[i]+1+1+bset->dim->nparam+first, n,
  67                                      (bset->dim->n_out-first-n)+bset->extra);
  68
  69         bset->dim = isl_dim_drop_outputs(bset->dim, first, n);
  70         if (!bset->dim)
  71                 goto error;
  72
  73         ISL_F_CLR(bset, ISL_BASIC_SET_NORMALIZED);
  74         bset = isl_basic_set_simplify(bset);
  75         return isl_basic_set_finalize(bset);
  76 error:
  77         isl_basic_set_free(bset);
  78         return NULL;
  79 }
  80
  81 struct isl_set *isl_set_drop_dims(
  82                 struct isl_set *set, unsigned first, unsigned n)
  83 {
  84         int i;
  85
  86         if (!set)
  87                 goto error;
  88
  89         isl_assert(set->ctx, first + n <= set->dim->n_out, goto error);
  90
  91         if (n == 0)
  92                 return set;
  93         set = isl_set_cow(set);
  94         if (!set)
  95                 goto error;
  96         set->dim = isl_dim_drop_outputs(set->dim, first, n);
  97         if (!set->dim)
  98                 goto error;
  99
 100         for (i = 0; i < set->n; ++i) {
 101                 set->p[i] = isl_basic_set_drop_dims(set->p[i], first, n);
 102                 if (!set->p[i])
 103                         goto error;
 104         }
 105
 106         ISL_F_CLR(set, ISL_SET_NORMALIZED);
 107         return set;
 108 error:
 109         isl_set_free(set);
 110         return NULL;
 111 }
 112
 113 /* Drop n input dimensions starting at first.
 114  *
 115  * In principle, this frees up some extra variables as the number
 116  * of columns remains constant, but we would have to extend
 117  * the div array too as the number of rows in this array is assumed
 118  * to be equal to extra.
 119  */
 120 struct isl_basic_map *isl_basic_map_drop(struct isl_basic_map *bmap,
 121         enum isl_dim_type type, unsigned first, unsigned n)
 122 {
 123         int i;
 124         unsigned dim;
 125         unsigned offset;
 126         unsigned left;
 127
 128         if (!bmap)
 129                 goto error;
 130
 131         dim = isl_basic_map_dim(bmap, type);
 132         isl_assert(bmap->ctx, first + n <= dim, goto error);
 133
 134         if (n == 0)
 135                 return bmap;
 136
 137         bmap = isl_basic_map_cow(bmap);
 138         if (!bmap)
 139                 return NULL;
 140
 141         offset = isl_basic_map_offset(bmap, type) + first;
 142         left = isl_basic_map_total_dim(bmap) - (offset - 1) - n;
 143         for (i = 0; i < bmap->n_eq; ++i)
 144                 constraint_drop_vars(bmap->eq[i]+offset, n, left);
 145
 146         for (i = 0; i < bmap->n_ineq; ++i)
 147                 constraint_drop_vars(bmap->ineq[i]+offset, n, left);
 148
 149         for (i = 0; i < bmap->n_div; ++i)
 150                 constraint_drop_vars(bmap->div[i]+1+offset, n, left);
 151
 152         bmap->dim = isl_dim_drop(bmap->dim, type, first, n);
 153         if (!bmap->dim)
 154                 goto error;
 155
 156         ISL_F_CLR(bmap, ISL_BASIC_MAP_NORMALIZED);
 157         bmap = isl_basic_map_simplify(bmap);
 158         return isl_basic_map_finalize(bmap);
 159 error:
 160         isl_basic_map_free(bmap);
 161         return NULL;
 162 }
 163
 164 struct isl_basic_map *isl_basic_map_drop_inputs(
 165                 struct isl_basic_map *bmap, unsigned first, unsigned n)
 166 {
 167         return isl_basic_map_drop(bmap, isl_dim_in, first, n);
 168 }
 169
 170 struct isl_map *isl_map_drop(struct isl_map *map,
 171         enum isl_dim_type type, unsigned first, unsigned n)
 172 {
 173         int i;
 174
 175         if (!map)
 176                 goto error;
 177
 178         isl_assert(map->ctx, first + n <= isl_map_dim(map, type), goto error);
 179
 180         if (n == 0)
 181                 return map;
 182         map = isl_map_cow(map);
 183         if (!map)
 184                 goto error;
 185         map->dim = isl_dim_drop(map->dim, type, first, n);
 186         if (!map->dim)
 187                 goto error;
 188
 189         for (i = 0; i < map->n; ++i) {
 190                 map->p[i] = isl_basic_map_drop(map->p[i], type, first, n);
 191                 if (!map->p[i])
 192                         goto error;
 193         }
 194         ISL_F_CLR(map, ISL_MAP_NORMALIZED);
 195
 196         return map;
 197 error:
 198         isl_map_free(map);
 199         return NULL;
 200 }
 201
 202 struct isl_map *isl_map_drop_inputs(
 203                 struct isl_map *map, unsigned first, unsigned n)
 204 {
 205         return isl_map_drop(map, isl_dim_in, first, n);
 206 }
 207
 208 /*
 209  * We don't cow, as the div is assumed to be redundant.
 210  */
 211 static struct isl_basic_map *isl_basic_map_drop_div(
 212                 struct isl_basic_map *bmap, unsigned div)
 213 {
 214         int i;
 215         unsigned pos;
 216
 217         if (!bmap)
 218                 goto error;
 219
 220         pos = 1 + isl_dim_total(bmap->dim) + div;
 221
 222         isl_assert(bmap->ctx, div < bmap->n_div, goto error);
 223
 224         for (i = 0; i < bmap->n_eq; ++i)
 225                 constraint_drop_vars(bmap->eq[i]+pos, 1, bmap->extra-div-1);
 226
 227         for (i = 0; i < bmap->n_ineq; ++i) {
 228                 if (!isl_int_is_zero(bmap->ineq[i][pos])) {
 229                         isl_basic_map_drop_inequality(bmap, i);
 230                         --i;
 231                         continue;
 232                 }
 233                 constraint_drop_vars(bmap->ineq[i]+pos, 1, bmap->extra-div-1);
 234         }
 235
 236         for (i = 0; i < bmap->n_div; ++i)
 237                 constraint_drop_vars(bmap->div[i]+1+pos, 1, bmap->extra-div-1);
 238
 239         if (div != bmap->n_div - 1) {
 240                 int j;
 241                 isl_int *t = bmap->div[div];
 242
 243                 for (j = div; j < bmap->n_div - 1; ++j)
 244                         bmap->div[j] = bmap->div[j+1];
 245
 246                 bmap->div[bmap->n_div - 1] = t;
 247         }
 248         ISL_F_CLR(bmap, ISL_BASIC_MAP_NORMALIZED);
 249         isl_basic_map_free_div(bmap, 1);
 250
 251         return bmap;
 252 error:
 253         isl_basic_map_free(bmap);
 254         return NULL;
 255 }
 256
 257 struct isl_basic_map *isl_basic_map_normalize_constraints(
 258         struct isl_basic_map *bmap)
 259 {
 260         int i;
 261         isl_int gcd;
 262         unsigned total = isl_basic_map_total_dim(bmap);
 263
 264         isl_int_init(gcd);
 265         for (i = bmap->n_eq - 1; i >= 0; --i) {
 266                 isl_seq_gcd(bmap->eq[i]+1, total, &gcd);
 267                 if (isl_int_is_zero(gcd)) {
 268                         if (!isl_int_is_zero(bmap->eq[i][0])) {
 269                                 bmap = isl_basic_map_set_to_empty(bmap);
 270                                 break;
 271                         }
 272                         isl_basic_map_drop_equality(bmap, i);
 273                         continue;
 274                 }
 275                 if (ISL_F_ISSET(bmap, ISL_BASIC_MAP_RATIONAL))
 276                         isl_int_gcd(gcd, gcd, bmap->eq[i][0]);
 277                 if (isl_int_is_one(gcd))
 278                         continue;
 279                 if (!isl_int_is_divisible_by(bmap->eq[i][0], gcd)) {
 280                         bmap = isl_basic_map_set_to_empty(bmap);
 281                         break;
 282                 }
 283                 isl_seq_scale_down(bmap->eq[i], bmap->eq[i], gcd, 1+total);
 284         }
 285
 286         for (i = bmap->n_ineq - 1; i >= 0; --i) {
 287                 isl_seq_gcd(bmap->ineq[i]+1, total, &gcd);
 288                 if (isl_int_is_zero(gcd)) {
 289                         if (isl_int_is_neg(bmap->ineq[i][0])) {
 290                                 bmap = isl_basic_map_set_to_empty(bmap);
 291                                 break;
 292                         }
 293                         isl_basic_map_drop_inequality(bmap, i);
 294                         continue;
 295                 }
 296                 if (ISL_F_ISSET(bmap, ISL_BASIC_MAP_RATIONAL))
 297                         isl_int_gcd(gcd, gcd, bmap->ineq[i][0]);
 298                 if (isl_int_is_one(gcd))
 299                         continue;
 300                 isl_int_fdiv_q(bmap->ineq[i][0], bmap->ineq[i][0], gcd);
 301                 isl_seq_scale_down(bmap->ineq[i]+1, bmap->ineq[i]+1, gcd, total);
 302         }
 303         isl_int_clear(gcd);
 304
 305         return bmap;
 306 }
 307
 308 struct isl_basic_set *isl_basic_set_normalize_constraints(
 309         struct isl_basic_set *bset)
 310 {
 311         (struct isl_basic_set *)isl_basic_map_normalize_constraints(
 312                 (struct isl_basic_map *)bset);
 313 }
 314
 315 static void eliminate_div(struct isl_basic_map *bmap, isl_int *eq, unsigned div)
 316 {
 317         int i;
 318         unsigned pos = 1 + isl_dim_total(bmap->dim) + div;
 319         unsigned len;
 320         len = 1 + isl_basic_map_total_dim(bmap);
 321
 322         for (i = 0; i < bmap->n_eq; ++i)
 323                 if (bmap->eq[i] != eq)
 324                         isl_seq_elim(bmap->eq[i], eq, pos, len, NULL);
 325
 326         for (i = 0; i < bmap->n_ineq; ++i)
 327                 isl_seq_elim(bmap->ineq[i], eq, pos, len, NULL);
 328
 329         /* We need to be careful about circular definitions,
 330          * so for now we just remove the definitions of other divs that
 331          * depend on this div and (possibly) recompute them later.
 332          */
 333         for (i = 0; i < bmap->n_div; ++i)
 334                 if (!isl_int_is_zero(bmap->div[i][0]) &&
 335                     !isl_int_is_zero(bmap->div[i][1 + pos]))
 336                         isl_seq_clr(bmap->div[i], 1 + len);
 337
 338         isl_basic_map_drop_div(bmap, div);
 339 }
 340
 341 /* Elimininate divs based on equalities
 342  */
 343 static struct isl_basic_map *eliminate_divs_eq(
 344                 struct isl_basic_map *bmap, int *progress)
 345 {
 346         int d;
 347         int i;
 348         int modified = 0;
 349         unsigned off;
 350
 351         if (!bmap)
 352                 return NULL;
 353
 354         off = 1 + isl_dim_total(bmap->dim);
 355
 356         for (d = bmap->n_div - 1; d >= 0 ; --d) {
 357                 for (i = 0; i < bmap->n_eq; ++i) {
 358                         if (!isl_int_is_one(bmap->eq[i][off + d]) &&
 359                             !isl_int_is_negone(bmap->eq[i][off + d]))
 360                                 continue;
 361                         modified = 1;
 362                         *progress = 1;
 363                         eliminate_div(bmap, bmap->eq[i], d);
 364                         isl_basic_map_drop_equality(bmap, i);
 365                         break;
 366                 }
 367         }
 368         if (modified)
 369                 return eliminate_divs_eq(bmap, progress);
 370         return bmap;
 371 }
 372
 373 /* Elimininate divs based on inequalities
 374  */
 375 static struct isl_basic_map *eliminate_divs_ineq(
 376                 struct isl_basic_map *bmap, int *progress)
 377 {
 378         int d;
 379         int i;
 380         unsigned off;
 381         struct isl_ctx *ctx;
 382
 383         if (!bmap)
 384                 return NULL;
 385
 386         ctx = bmap->ctx;
 387         off = 1 + isl_dim_total(bmap->dim);
 388
 389         for (d = bmap->n_div - 1; d >= 0 ; --d) {
 390                 for (i = 0; i < bmap->n_eq; ++i)
 391                         if (!isl_int_is_zero(bmap->eq[i][off + d]))
 392                                 break;
 393                 if (i < bmap->n_eq)
 394                         continue;
 395                 for (i = 0; i < bmap->n_ineq; ++i)
 396                         if (isl_int_abs_gt(bmap->ineq[i][off + d], ctx->one))
 397                                 break;
 398                 if (i < bmap->n_ineq)
 399                         continue;
 400                 *progress = 1;
 401                 bmap = isl_basic_map_eliminate_vars(bmap, (off-1)+d, 1);
 402                 if (ISL_F_ISSET(bmap, ISL_BASIC_MAP_EMPTY))
 403                         break;
 404                 bmap = isl_basic_map_drop_div(bmap, d);
 405                 if (!bmap)
 406                         break;
 407         }
 408         return bmap;
 409 }
 410
 411 static void eliminate_var_using_equality(struct isl_basic_map *bmap,
 412         unsigned pos, isl_int *eq, int *progress)
 413 {
 414         unsigned total;
 415         int k;
 416         int contains_divs;
 417
 418         total = isl_basic_map_total_dim(bmap);
 419         contains_divs =
 420                 isl_seq_first_non_zero(eq + 1 + isl_dim_total(bmap->dim),
 421                                                 bmap->n_div) != -1;
 422         for (k = 0; k < bmap->n_eq; ++k) {
 423                 if (bmap->eq[k] == eq)
 424                         continue;
 425                 if (isl_int_is_zero(bmap->eq[k][1+pos]))
 426                         continue;
 427                 if (progress)
 428                         *progress = 1;
 429                 isl_seq_elim(bmap->eq[k], eq, 1+pos, 1+total, NULL);
 430         }
 431
 432         for (k = 0; k < bmap->n_ineq; ++k) {
 433                 if (isl_int_is_zero(bmap->ineq[k][1+pos]))
 434                         continue;
 435                 if (progress)
 436                         *progress = 1;
 437                 isl_seq_elim(bmap->ineq[k], eq, 1+pos, 1+total, NULL);
 438                 ISL_F_CLR(bmap, ISL_BASIC_MAP_NORMALIZED);
 439         }
 440
 441         for (k = 0; k < bmap->n_div; ++k) {
 442                 if (isl_int_is_zero(bmap->div[k][0]))
 443                         continue;
 444                 if (isl_int_is_zero(bmap->div[k][1+1+pos]))
 445                         continue;
 446                 if (progress)
 447                         *progress = 1;
 448                 /* We need to be careful about circular definitions,
 449                  * so for now we just remove the definition of div k
 450                  * if the equality contains any divs.
 451                  */
 452                 if (contains_divs)
 453                         isl_seq_clr(bmap->div[k], 1 + total);
 454                 else
 455                         isl_seq_elim(bmap->div[k]+1, eq,
 456                                         1+pos, 1+total, &bmap->div[k][0]);
 457                 ISL_F_CLR(bmap, ISL_BASIC_MAP_NORMALIZED);
 458         }
 459 }
 460
 461 struct isl_basic_map *isl_basic_map_gauss(
 462         struct isl_basic_map *bmap, int *progress)
 463 {
 464         int k;
 465         int done;
 466         int last_var;
 467         unsigned total_var;
 468         unsigned total;
 469
 470         if (!bmap)
 471                 return NULL;
 472
 473         total = isl_basic_map_total_dim(bmap);
 474         total_var = total - bmap->n_div;
 475
 476         last_var = total - 1;
 477         for (done = 0; done < bmap->n_eq; ++done) {
 478                 for (; last_var >= 0; --last_var) {
 479                         for (k = done; k < bmap->n_eq; ++k)
 480                                 if (!isl_int_is_zero(bmap->eq[k][1+last_var]))
 481                                         break;
 482                         if (k < bmap->n_eq)
 483                                 break;
 484                 }
 485                 if (last_var < 0)
 486                         break;
 487                 if (k != done)
 488                         swap_equality(bmap, k, done);
 489                 if (isl_int_is_neg(bmap->eq[done][1+last_var]))
 490                         isl_seq_neg(bmap->eq[done], bmap->eq[done], 1+total);
 491
 492                 eliminate_var_using_equality(bmap, last_var, bmap->eq[done],
 493                                                 progress);
 494
 495                 if (last_var >= total_var &&
 496                     isl_int_is_zero(bmap->div[last_var - total_var][0])) {
 497                         unsigned div = last_var - total_var;
 498                         isl_seq_neg(bmap->div[div]+1, bmap->eq[done], 1+total);
 499                         isl_int_set_si(bmap->div[div][1+1+last_var], 0);
 500                         isl_int_set(bmap->div[div][0],
 501                                     bmap->eq[done][1+last_var]);
 502                         ISL_F_CLR(bmap, ISL_BASIC_MAP_NORMALIZED);
 503                 }
 504         }
 505         if (done == bmap->n_eq)
 506                 return bmap;
 507         for (k = done; k < bmap->n_eq; ++k) {
 508                 if (isl_int_is_zero(bmap->eq[k][0]))
 509                         continue;
 510                 return isl_basic_map_set_to_empty(bmap);
 511         }
 512         isl_basic_map_free_equality(bmap, bmap->n_eq-done);
 513         return bmap;
 514 }
 515
 516 struct isl_basic_set *isl_basic_set_gauss(
 517         struct isl_basic_set *bset, int *progress)
 518 {
 519         return (struct isl_basic_set*)isl_basic_map_gauss(
 520                         (struct isl_basic_map *)bset, progress);
 521 }
 522
 523
 524 static unsigned int round_up(unsigned int v)
 525 {
 526         int old_v = v;
 527
 528         while (v) {
 529                 old_v = v;
 530                 v ^= v & -v;
 531         }
 532         return old_v << 1;
 533 }
 534
 535 static int hash_index(isl_int ***index, unsigned int size, int bits,
 536                         struct isl_basic_map *bmap, int k)
 537 {
 538         int h;
 539         unsigned total = isl_basic_map_total_dim(bmap);
 540         uint32_t hash = isl_seq_get_hash_bits(bmap->ineq[k]+1, total, bits);
 541         for (h = hash; index[h]; h = (h+1) % size)
 542                 if (&bmap->ineq[k] != index[h] &&
 543                     isl_seq_eq(bmap->ineq[k]+1, index[h][0]+1, total))
 544                         break;
 545         return h;
 546 }
 547
 548 static int set_hash_index(isl_int ***index, unsigned int size, int bits,
 549                           struct isl_basic_set *bset, int k)
 550 {
 551         return hash_index(index, size, bits, (struct isl_basic_map *)bset, k);
 552 }
 553
 554 /* If we can eliminate more than one div, then we need to make
 555  * sure we do it from last div to first div, in order not to
 556  * change the position of the other divs that still need to
 557  * be removed.
 558  */
 559 static struct isl_basic_map *remove_duplicate_divs(
 560         struct isl_basic_map *bmap, int *progress)
 561 {
 562         unsigned int size;
 563         int *index;
 564         int *elim_for;
 565         int k, l, h;
 566         int bits;
 567         struct isl_blk eq;
 568         unsigned total_var = isl_dim_total(bmap->dim);
 569         unsigned total = total_var + bmap->n_div;
 570         struct isl_ctx *ctx;
 571
 572         if (bmap->n_div <= 1)
 573                 return bmap;
 574
 575         ctx = bmap->ctx;
 576         for (k = bmap->n_div - 1; k >= 0; --k)
 577                 if (!isl_int_is_zero(bmap->div[k][0]))
 578                         break;
 579         if (k <= 0)
 580                 return bmap;
 581
 582         elim_for = isl_calloc_array(ctx, int, bmap->n_div);
 583         size = round_up(4 * bmap->n_div / 3 - 1);
 584         bits = ffs(size) - 1;
 585         index = isl_calloc_array(ctx, int, size);
 586         if (!index)
 587                 return bmap;
 588         eq = isl_blk_alloc(ctx, 1+total);
 589         if (isl_blk_is_error(eq))
 590                 goto out;
 591
 592         isl_seq_clr(eq.data, 1+total);
 593         index[isl_seq_get_hash_bits(bmap->div[k], 2+total, bits)] = k + 1;
 594         for (--k; k >= 0; --k) {
 595                 uint32_t hash;
 596
 597                 if (isl_int_is_zero(bmap->div[k][0]))
 598                         continue;
 599
 600                 hash = isl_seq_get_hash_bits(bmap->div[k], 2+total, bits);
 601                 for (h = hash; index[h]; h = (h+1) % size)
 602                         if (isl_seq_eq(bmap->div[k],
 603                                        bmap->div[index[h]-1], 2+total))
 604                                 break;
 605                 if (index[h]) {
 606                         *progress = 1;
 607                         l = index[h] - 1;
 608                         elim_for[l] = k + 1;
 609                 }
 610                 index[h] = k+1;
 611         }
 612         for (l = bmap->n_div - 1; l >= 0; --l) {
 613                 if (!elim_for[l])
 614                         continue;
 615                 k = elim_for[l] - 1;
 616                 isl_int_set_si(eq.data[1+total_var+k], -1);
 617                 isl_int_set_si(eq.data[1+total_var+l], 1);
 618                 eliminate_div(bmap, eq.data, l);
 619                 isl_int_set_si(eq.data[1+total_var+k], 0);
 620                 isl_int_set_si(eq.data[1+total_var+l], 0);
 621         }
 622
 623         isl_blk_free(ctx, eq);
 624 out:
 625         free(index);
 626         free(elim_for);
 627         return bmap;
 628 }
 629
 630 /* Normalize divs that appear in equalities.
 631  *
 632  * In particular, we assume that bmap contains some equalities
 633  * of the form
 634  *
 635  *      a x = m * e_i
 636  *
 637  * and we want to replace the set of e_i by a minimal set and
 638  * such that the new e_i have a canonical representation in terms
 639  * of the vector x.
 640  * If any of the equalities involves more than one divs, then
 641  * we currently simply bail out.
 642  *
 643  * Let us first additionally assume that all equalities involve
 644  * a div.  The equalities then express modulo constraints on the
 645  * remaining variables and we can use "parameter compression"
 646  * to find a minimal set of constraints.  The result is a transformation
 647  *
 648  *      x = T(x') = x_0 + G x'
 649  *
 650  * with G a lower-triangular matrix with all elements below the diagonal
 651  * non-negative and smaller than the diagonal element on the same row.
 652  * We first normalize x_0 by making the same property hold in the affine
 653  * T matrix.
 654  * The rows i of G with a 1 on the diagonal do not impose any modulo
 655  * constraint and simply express x_i = x'_i.
 656  * For each of the remaining rows i, we introduce a div and a corresponding
 657  * equality.  In particular
 658  *
 659  *      g_ii e_j = x_i - g_i(x')
 660  *
 661  * where each x'_k is replaced either by x_k (if g_kk = 1) or the
 662  * corresponding div (if g_kk != 1).
 663  *
 664  * If there are any equalities not involving any div, then we
 665  * first apply a variable compression on the variables x:
 666  *
 667  *      x = C x''       x'' = C_2 x
 668  *
 669  * and perform the above parameter compression on A C instead of on A.
 670  * The resulting compression is then of the form
 671  *
 672  *      x'' = T(x') = x_0 + G x'
 673  *
 674  * and in constructing the new divs and the corresponding equalities,
 675  * we have to replace each x'', i.e., the x'_k with (g_kk = 1),
 676  * by the corresponding row from C_2.
 677  */
 678 static struct isl_basic_map *normalize_divs(
 679         struct isl_basic_map *bmap, int *progress)
 680 {
 681         int i, j, k;
 682         int total;
 683         int div_eq;
 684         struct isl_mat *B;
 685         struct isl_vec *d;
 686         struct isl_mat *T = NULL;
 687         struct isl_mat *C = NULL;
 688         struct isl_mat *C2 = NULL;
 689         isl_int v;
 690         int *pos;
 691         int dropped, needed;
 692
 693         if (!bmap)
 694                 return NULL;
 695
 696         if (bmap->n_div == 0)
 697                 return bmap;
 698
 699         if (bmap->n_eq == 0)
 700                 return bmap;
 701
 702         if (ISL_F_ISSET(bmap, ISL_BASIC_MAP_NORMALIZED_DIVS))
 703                 return bmap;
 704
 705         total = isl_dim_total(bmap->dim);
 706         for (i = 0, j = bmap->n_div-1; i < bmap->n_eq; ++i) {
 707                 while (j >= 0 && isl_int_is_zero(bmap->eq[i][1 + total + j]))
 708                         --j;
 709                 if (j < 0)
 710                         break;
 711                 if (isl_seq_first_non_zero(bmap->eq[i] + 1 + total, j) != -1)
 712                         goto done;
 713         }
 714         div_eq = i;
 715         if (div_eq == 0)
 716                 return bmap;
 717
 718         if (div_eq < bmap->n_eq) {
 719                 B = isl_mat_sub_alloc(bmap->ctx, bmap->eq, div_eq,
 720                                         bmap->n_eq - div_eq, 0, 1 + total);
 721                 C = isl_mat_variable_compression(bmap->ctx, B, &C2);
 722                 if (!C || !C2)
 723                         goto error;
 724                 if (C->n_col == 0) {
 725                         bmap = isl_basic_map_set_to_empty(bmap);
 726                         isl_mat_free(bmap->ctx, C);
 727                         isl_mat_free(bmap->ctx, C2);
 728                         goto done;
 729                 }
 730         }
 731
 732         d = isl_vec_alloc(bmap->ctx, div_eq);
 733         if (!d)
 734                 goto error;
 735         for (i = 0, j = bmap->n_div-1; i < div_eq; ++i) {
 736                 while (j >= 0 && isl_int_is_zero(bmap->eq[i][1 + total + j]))
 737                         --j;
 738                 isl_int_set(d->block.data[i], bmap->eq[i][1 + total + j]);
 739         }
 740         B = isl_mat_sub_alloc(bmap->ctx, bmap->eq, 0, div_eq, 0, 1 + total);
 741
 742         if (C) {
 743                 B = isl_mat_product(bmap->ctx, B, C);
 744                 C = NULL;
 745         }
 746
 747         T = isl_mat_parameter_compression(bmap->ctx, B, d);
 748         if (!T)
 749                 goto error;
 750         if (T->n_col == 0) {
 751                 bmap = isl_basic_map_set_to_empty(bmap);
 752                 isl_mat_free(bmap->ctx, C2);
 753                 isl_mat_free(bmap->ctx, T);
 754                 goto done;
 755         }
 756         isl_int_init(v);
 757         for (i = 0; i < T->n_row - 1; ++i) {
 758                 isl_int_fdiv_q(v, T->row[1 + i][0], T->row[1 + i][1 + i]);
 759                 if (isl_int_is_zero(v))
 760                         continue;
 761                 isl_mat_col_submul(T, 0, v, 1 + i);
 762         }
 763         isl_int_clear(v);
 764         pos = isl_alloc_array(bmap->ctx, int, T->n_row);
 765         /* We have to be careful because dropping equalities may reorder them */
 766         dropped = 0;
 767         for (j = bmap->n_div - 1; j >= 0; --j) {
 768                 for (i = 0; i < bmap->n_eq; ++i)
 769                         if (!isl_int_is_zero(bmap->eq[i][1 + total + j]))
 770                                 break;
 771                 if (i < bmap->n_eq) {
 772                         bmap = isl_basic_map_drop_div(bmap, j);
 773                         isl_basic_map_drop_equality(bmap, i);
 774                         ++dropped;
 775                 }
 776         }
 777         pos[0] = 0;
 778         needed = 0;
 779         for (i = 1; i < T->n_row; ++i) {
 780                 if (isl_int_is_one(T->row[i][i]))
 781                         pos[i] = i;
 782                 else
 783                         needed++;
 784         }
 785         if (needed > dropped) {
 786                 bmap = isl_basic_map_extend_dim(bmap, isl_dim_copy(bmap->dim),
 787                                 needed, needed, 0);
 788                 if (!bmap)
 789                         goto error;
 790         }
 791         for (i = 1; i < T->n_row; ++i) {
 792                 if (isl_int_is_one(T->row[i][i]))
 793                         continue;
 794                 k = isl_basic_map_alloc_div(bmap);
 795                 pos[i] = 1 + total + k;
 796                 isl_seq_clr(bmap->div[k] + 1, 1 + total + bmap->n_div);
 797                 isl_int_set(bmap->div[k][0], T->row[i][i]);
 798                 if (C2)
 799                         isl_seq_cpy(bmap->div[k] + 1, C2->row[i], 1 + total);
 800                 else
 801                         isl_int_set_si(bmap->div[k][1 + i], 1);
 802                 for (j = 0; j < i; ++j) {
 803                         if (isl_int_is_zero(T->row[i][j]))
 804                                 continue;
 805                         if (pos[j] < T->n_row && C2)
 806                                 isl_seq_submul(bmap->div[k] + 1, T->row[i][j],
 807                                                 C2->row[pos[j]], 1 + total);
 808                         else
 809                                 isl_int_neg(bmap->div[k][1 + pos[j]],
 810                                                                 T->row[i][j]);
 811                 }
 812                 j = isl_basic_map_alloc_equality(bmap);
 813                 isl_seq_neg(bmap->eq[j], bmap->div[k]+1, 1+total+bmap->n_div);
 814                 isl_int_set(bmap->eq[j][pos[i]], bmap->div[k][0]);
 815         }
 816         free(pos);
 817         isl_mat_free(bmap->ctx, C2);
 818         isl_mat_free(bmap->ctx, T);
 819
 820         *progress = 1;
 821 done:
 822         ISL_F_SET(bmap, ISL_BASIC_MAP_NORMALIZED_DIVS);
 823
 824         return bmap;
 825 error:
 826         isl_mat_free(bmap->ctx, C);
 827         isl_mat_free(bmap->ctx, C2);
 828         isl_mat_free(bmap->ctx, T);
 829         return bmap;
 830 }
 831
 832 static struct isl_basic_map *remove_duplicate_constraints(
 833         struct isl_basic_map *bmap, int *progress)
 834 {
 835         unsigned int size;
 836         isl_int ***index;
 837         int k, l, h;
 838         int bits;
 839         unsigned total = isl_basic_map_total_dim(bmap);
 840         isl_int sum;
 841
 842         if (bmap->n_ineq <= 1)
 843                 return bmap;
 844
 845         size = round_up(4 * (bmap->n_ineq+1) / 3 - 1);
 846         bits = ffs(size) - 1;
 847         index = isl_calloc_array(ctx, isl_int **, size);
 848         if (!index)
 849                 return bmap;
 850
 851         index[isl_seq_get_hash_bits(bmap->ineq[0]+1, total, bits)] = &bmap->ineq[0];
 852         for (k = 1; k < bmap->n_ineq; ++k) {
 853                 h = hash_index(index, size, bits, bmap, k);
 854                 if (!index[h]) {
 855                         index[h] = &bmap->ineq[k];
 856                         continue;
 857                 }
 858                 if (progress)
 859                         *progress = 1;
 860                 l = index[h] - &bmap->ineq[0];
 861                 if (isl_int_lt(bmap->ineq[k][0], bmap->ineq[l][0]))
 862                         swap_inequality(bmap, k, l);
 863                 isl_basic_map_drop_inequality(bmap, k);
 864                 --k;
 865         }
 866         isl_int_init(sum);
 867         for (k = 0; k < bmap->n_ineq-1; ++k) {
 868                 isl_seq_neg(bmap->ineq[k]+1, bmap->ineq[k]+1, total);
 869                 h = hash_index(index, size, bits, bmap, k);
 870                 isl_seq_neg(bmap->ineq[k]+1, bmap->ineq[k]+1, total);
 871                 if (!index[h])
 872                         continue;
 873                 l = index[h] - &bmap->ineq[0];
 874                 isl_int_add(sum, bmap->ineq[k][0], bmap->ineq[l][0]);
 875                 if (isl_int_is_pos(sum))
 876                         continue;
 877                 if (isl_int_is_zero(sum)) {
 878                         /* We need to break out of the loop after these
 879                          * changes since the contents of the hash
 880                          * will no longer be valid.
 881                          * Plus, we probably we want to regauss first.
 882                          */
 883                         isl_basic_map_drop_inequality(bmap, l);
 884                         isl_basic_map_inequality_to_equality(bmap, k);
 885                 } else
 886                         bmap = isl_basic_map_set_to_empty(bmap);
 887                 break;
 888         }
 889         isl_int_clear(sum);
 890
 891         free(index);
 892         return bmap;
 893 }
 894
 895
 896 struct isl_basic_map *isl_basic_map_simplify(struct isl_basic_map *bmap)
 897 {
 898         int progress = 1;
 899         if (!bmap)
 900                 return NULL;
 901         while (progress) {
 902                 progress = 0;
 903                 bmap = isl_basic_map_normalize_constraints(bmap);
 904                 bmap = eliminate_divs_eq(bmap, &progress);
 905                 bmap = eliminate_divs_ineq(bmap, &progress);
 906                 bmap = isl_basic_map_gauss(bmap, &progress);
 907                 /* requires equalities in normal form */
 908                 bmap = normalize_divs(bmap, &progress);
 909                 bmap = remove_duplicate_divs(bmap, &progress);
 910                 bmap = remove_duplicate_constraints(bmap, &progress);
 911         }
 912         return bmap;
 913 }
 914
 915 struct isl_basic_set *isl_basic_set_simplify(struct isl_basic_set *bset)
 916 {
 917         return (struct isl_basic_set *)
 918                 isl_basic_map_simplify((struct isl_basic_map *)bset);
 919 }
 920
 921
 922 /* If the only constraints a div d=floor(f/m)
 923  * appears in are its two defining constraints
 924  *
 925  *      f - m d >=0
 926  *      -(f - (m - 1)) + m d >= 0
 927  *
 928  * then it can safely be removed.
 929  */
 930 static int div_is_redundant(struct isl_basic_map *bmap, int div)
 931 {
 932         int i;
 933         unsigned pos = 1 + isl_dim_total(bmap->dim) + div;
 934
 935         for (i = 0; i < bmap->n_eq; ++i)
 936                 if (!isl_int_is_zero(bmap->eq[i][pos]))
 937                         return 0;
 938
 939         for (i = 0; i < bmap->n_ineq; ++i) {
 940                 if (isl_int_is_zero(bmap->ineq[i][pos]))
 941                         continue;
 942                 if (isl_int_eq(bmap->ineq[i][pos], bmap->div[div][0])) {
 943                         int neg;
 944                         isl_int_sub(bmap->div[div][1],
 945                                         bmap->div[div][1], bmap->div[div][0]);
 946                         isl_int_add_ui(bmap->div[div][1], bmap->div[div][1], 1);
 947                         neg = isl_seq_is_neg(bmap->ineq[i], bmap->div[div]+1, pos);
 948                         isl_int_sub_ui(bmap->div[div][1], bmap->div[div][1], 1);
 949                         isl_int_add(bmap->div[div][1],
 950                                         bmap->div[div][1], bmap->div[div][0]);
 951                         if (!neg)
 952                                 return 0;
 953                         if (isl_seq_first_non_zero(bmap->ineq[i]+pos+1,
 954                                                     bmap->n_div-div-1) != -1)
 955                                 return 0;
 956                 } else if (isl_int_abs_eq(bmap->ineq[i][pos], bmap->div[div][0])) {
 957                         if (!isl_seq_eq(bmap->ineq[i], bmap->div[div]+1, pos))
 958                                 return 0;
 959                         if (isl_seq_first_non_zero(bmap->ineq[i]+pos+1,
 960                                                     bmap->n_div-div-1) != -1)
 961                                 return 0;
 962                 } else
 963                         return 0;
 964         }
 965
 966         for (i = 0; i < bmap->n_div; ++i)
 967                 if (!isl_int_is_zero(bmap->div[i][1+pos]))
 968                         return 0;
 969
 970         return 1;
 971 }
 972
 973 /*
 974  * Remove divs that don't occur in any of the constraints or other divs.
 975  * These can arise when dropping some of the variables in a quast
 976  * returned by piplib.
 977  */
 978 static struct isl_basic_map *remove_redundant_divs(struct isl_basic_map *bmap)
 979 {
 980         int i;
 981
 982         if (!bmap)
 983                 return NULL;
 984
 985         for (i = bmap->n_div-1; i >= 0; --i) {
 986                 if (!div_is_redundant(bmap, i))
 987                         continue;
 988                 bmap = isl_basic_map_drop_div(bmap, i);
 989         }
 990         return bmap;
 991 }
 992
 993 struct isl_basic_map *isl_basic_map_finalize(struct isl_basic_map *bmap)
 994 {
 995         bmap = remove_redundant_divs(bmap);
 996         if (!bmap)
 997                 return NULL;
 998         ISL_F_SET(bmap, ISL_BASIC_SET_FINAL);
 999         return bmap;
1000 }
1001
1002 struct isl_basic_set *isl_basic_set_finalize(struct isl_basic_set *bset)
1003 {
1004         return (struct isl_basic_set *)
1005                 isl_basic_map_finalize((struct isl_basic_map *)bset);
1006 }
1007
1008 struct isl_set *isl_set_finalize(struct isl_set *set)
1009 {
1010         int i;
1011
1012         if (!set)
1013                 return NULL;
1014         for (i = 0; i < set->n; ++i) {
1015                 set->p[i] = isl_basic_set_finalize(set->p[i]);
1016                 if (!set->p[i])
1017                         goto error;
1018         }
1019         return set;
1020 error:
1021         isl_set_free(set);
1022         return NULL;
1023 }
1024
1025 struct isl_map *isl_map_finalize(struct isl_map *map)
1026 {
1027         int i;
1028
1029         if (!map)
1030                 return NULL;
1031         for (i = 0; i < map->n; ++i) {
1032                 map->p[i] = isl_basic_map_finalize(map->p[i]);
1033                 if (!map->p[i])
1034                         goto error;
1035         }
1036         ISL_F_CLR(map, ISL_MAP_NORMALIZED);
1037         return map;
1038 error:
1039         isl_map_free(map);
1040         return NULL;
1041 }
1042
1043
1044 /* Remove any div that is defined in terms of the given variable.
1045  */
1046 static struct isl_basic_map *remove_dependent_vars(struct isl_basic_map *bmap,
1047                                                                         int pos)
1048 {
1049         int i;
1050         unsigned dim = isl_dim_total(bmap->dim);
1051
1052         for (i = 0; i < bmap->n_div; ++i) {
1053                 if (isl_int_is_zero(bmap->div[i][0]))
1054                         continue;
1055                 if (isl_int_is_zero(bmap->div[i][1+1+pos]))
1056                         continue;
1057                 bmap = isl_basic_map_eliminate_vars(bmap, dim + i, 1);
1058                 if (!bmap)
1059                         return NULL;
1060         }
1061         return bmap;
1062 }
1063
1064 /* Eliminate the specified variables from the constraints using
1065  * Fourier-Motzkin.  The variables themselves are not removed.
1066  */
1067 struct isl_basic_map *isl_basic_map_eliminate_vars(
1068         struct isl_basic_map *bmap, unsigned pos, unsigned n)
1069 {
1070         int d;
1071         int i, j, k;
1072         unsigned total;
1073
1074         if (n == 0)
1075                 return bmap;
1076         if (!bmap)
1077                 return NULL;
1078         total = isl_basic_map_total_dim(bmap);
1079
1080         bmap = isl_basic_map_cow(bmap);
1081         for (d = pos + n - 1; d >= 0 && d >= pos; --d)
1082                 bmap = remove_dependent_vars(bmap, d);
1083
1084         for (d = pos + n - 1;
1085              d >= 0 && d >= total - bmap->n_div && d >= pos; --d)
1086                 isl_seq_clr(bmap->div[d-(total-bmap->n_div)], 2+total);
1087         for (d = pos + n - 1; d >= 0 && d >= pos; --d) {
1088                 int n_lower, n_upper;
1089                 if (!bmap)
1090                         return NULL;
1091                 for (i = 0; i < bmap->n_eq; ++i) {
1092                         if (isl_int_is_zero(bmap->eq[i][1+d]))
1093                                 continue;
1094                         eliminate_var_using_equality(bmap, d, bmap->eq[i], NULL);
1095                         isl_basic_map_drop_equality(bmap, i);
1096                         break;
1097                 }
1098                 if (i < bmap->n_eq)
1099                         continue;
1100                 n_lower = 0;
1101                 n_upper = 0;
1102                 for (i = 0; i < bmap->n_ineq; ++i) {
1103                         if (isl_int_is_pos(bmap->ineq[i][1+d]))
1104                                 n_lower++;
1105                         else if (isl_int_is_neg(bmap->ineq[i][1+d]))
1106                                 n_upper++;
1107                 }
1108                 bmap = isl_basic_map_extend_constraints(bmap,
1109                                 0, n_lower * n_upper);
1110                 for (i = bmap->n_ineq - 1; i >= 0; --i) {
1111                         int last;
1112                         if (isl_int_is_zero(bmap->ineq[i][1+d]))
1113                                 continue;
1114                         last = -1;
1115                         for (j = 0; j < i; ++j) {
1116                                 if (isl_int_is_zero(bmap->ineq[j][1+d]))
1117                                         continue;
1118                                 last = j;
1119                                 if (isl_int_sgn(bmap->ineq[i][1+d]) ==
1120                                     isl_int_sgn(bmap->ineq[j][1+d]))
1121                                         continue;
1122                                 k = isl_basic_map_alloc_inequality(bmap);
1123                                 if (k < 0)
1124                                         goto error;
1125                                 isl_seq_cpy(bmap->ineq[k], bmap->ineq[i],
1126                                                 1+total);
1127                                 isl_seq_elim(bmap->ineq[k], bmap->ineq[j],
1128                                                 1+d, 1+total, NULL);
1129                         }
1130                         isl_basic_map_drop_inequality(bmap, i);
1131                         i = last + 1;
1132                 }
1133                 if (n_lower > 0 && n_upper > 0) {
1134                         bmap = isl_basic_map_normalize_constraints(bmap);
1135                         bmap = remove_duplicate_constraints(bmap, NULL);
1136                         bmap = isl_basic_map_gauss(bmap, NULL);
1137                         bmap = isl_basic_map_convex_hull(bmap);
1138                         if (!bmap)
1139                                 goto error;
1140                         if (ISL_F_ISSET(bmap, ISL_BASIC_MAP_EMPTY))
1141                                 break;
1142                 }
1143         }
1144         ISL_F_CLR(bmap, ISL_BASIC_MAP_NORMALIZED);
1145         return bmap;
1146 error:
1147         isl_basic_map_free(bmap);
1148         return NULL;
1149 }
1150
1151 struct isl_basic_set *isl_basic_set_eliminate_vars(
1152         struct isl_basic_set *bset, unsigned pos, unsigned n)
1153 {
1154         return (struct isl_basic_set *)isl_basic_map_eliminate_vars(
1155                         (struct isl_basic_map *)bset, pos, n);
1156 }
1157
1158 /* Don't assume equalities are in order, because align_divs
1159  * may have changed the order of the divs.
1160  */
1161 static void compute_elimination_index(struct isl_basic_map *bmap, int *elim)
1162 {
1163         int d, i;
1164         unsigned total;
1165
1166         total = isl_dim_total(bmap->dim);
1167         for (d = 0; d < total; ++d)
1168                 elim[d] = -1;
1169         for (i = 0; i < bmap->n_eq; ++i) {
1170                 for (d = total - 1; d >= 0; --d) {
1171                         if (isl_int_is_zero(bmap->eq[i][1+d]))
1172                                 continue;
1173                         elim[d] = i;
1174                         break;
1175                 }
1176         }
1177 }
1178
1179 static void set_compute_elimination_index(struct isl_basic_set *bset, int *elim)
1180 {
1181         return compute_elimination_index((struct isl_basic_map *)bset, elim);
1182 }
1183
1184 static int reduced_using_equalities(isl_int *dst, isl_int *src,
1185         struct isl_basic_map *bmap, int *elim)
1186 {
1187         int d, i;
1188         int copied = 0;
1189         unsigned total;
1190
1191         total = isl_dim_total(bmap->dim);
1192         for (d = total - 1; d >= 0; --d) {
1193                 if (isl_int_is_zero(src[1+d]))
1194                         continue;
1195                 if (elim[d] == -1)
1196                         continue;
1197                 if (!copied) {
1198                         isl_seq_cpy(dst, src, 1 + total);
1199                         copied = 1;
1200                 }
1201                 isl_seq_elim(dst, bmap->eq[elim[d]], 1 + d, 1 + total, NULL);
1202         }
1203         return copied;
1204 }
1205
1206 static int set_reduced_using_equalities(isl_int *dst, isl_int *src,
1207         struct isl_basic_set *bset, int *elim)
1208 {
1209         return reduced_using_equalities(dst, src,
1210                                         (struct isl_basic_map *)bset, elim);
1211 }
1212
1213 static struct isl_basic_set *isl_basic_set_reduce_using_equalities(
1214         struct isl_basic_set *bset, struct isl_basic_set *context)
1215 {
1216         int i;
1217         int *elim;
1218
1219         if (!bset || !context)
1220                 goto error;
1221
1222         bset = isl_basic_set_cow(bset);
1223         if (!bset)
1224                 goto error;
1225
1226         elim = isl_alloc_array(ctx, int, isl_basic_set_n_dim(bset));
1227         if (!elim)
1228                 goto error;
1229         set_compute_elimination_index(context, elim);
1230         for (i = 0; i < bset->n_eq; ++i)
1231                 set_reduced_using_equalities(bset->eq[i], bset->eq[i],
1232                                                         context, elim);
1233         for (i = 0; i < bset->n_ineq; ++i)
1234                 set_reduced_using_equalities(bset->ineq[i], bset->ineq[i],
1235                                                         context, elim);
1236         isl_basic_set_free(context);
1237         free(elim);
1238         bset = isl_basic_set_simplify(bset);
1239         bset = isl_basic_set_finalize(bset);
1240         return bset;
1241 error:
1242         isl_basic_set_free(bset);
1243         isl_basic_set_free(context);
1244         return NULL;
1245 }
1246
1247 static struct isl_basic_set *remove_shifted_constraints(
1248         struct isl_basic_set *bset, struct isl_basic_set *context)
1249 {
1250         unsigned int size;
1251         isl_int ***index;
1252         int bits;
1253         int k, h, l;
1254
1255         if (!bset)
1256                 return NULL;
1257
1258         size = round_up(4 * (context->n_ineq+1) / 3 - 1);
1259         bits = ffs(size) - 1;
1260         index = isl_calloc_array(ctx, isl_int **, size);
1261         if (!index)
1262                 return bset;
1263
1264         for (k = 0; k < context->n_ineq; ++k) {
1265                 h = set_hash_index(index, size, bits, context, k);
1266                 index[h] = &context->ineq[k];
1267         }
1268         for (k = 0; k < bset->n_ineq; ++k) {
1269                 h = set_hash_index(index, size, bits, bset, k);
1270                 if (!index[h])
1271                         continue;
1272                 l = index[h] - &context->ineq[0];
1273                 if (isl_int_lt(bset->ineq[k][0], context->ineq[l][0]))
1274                         continue;
1275                 bset = isl_basic_set_cow(bset);
1276                 if (!bset)
1277                         goto error;
1278                 isl_basic_set_drop_inequality(bset, k);
1279                 --k;
1280         }
1281         free(index);
1282         return bset;
1283 error:
1284         free(index);
1285         return bset;
1286 }
1287
1288 /* Tighten (decrease) the constant terms of the inequalities based
1289  * on the equalities, without removing any integer points.
1290  * For example, if there is an equality
1291  *
1292  *              i = 3 * j
1293  *
1294  * and an inequality
1295  *
1296  *              i >= 1
1297  *
1298  * then we want to replace the inequality by
1299  *
1300  *              i >= 3
1301  *
1302  * We do this by computing a variable compression and translating
1303  * the constraints to the compressed space.
1304  * If any constraint has coefficients (except the contant term)
1305  * with a common factor "f", then we can replace the constant term "c"
1306  * by
1307  *
1308  *              f * floor(c/f)
1309  *
1310  * That is, we add
1311  *
1312  *              f * floor(c/f) - c = -fract(c/f)
1313  *
1314  * and we can add the same value to the original constraint.
1315  *
1316  * In the example, the compressed space only contains "j",
1317  * and the inequality translates to
1318  *
1319  *              3 * j - 1 >= 0
1320  *
1321  * We add -fract(-1/3) = -2 to the original constraint to obtain
1322  *
1323  *              i - 3 >= 0
1324  */
1325 static struct isl_basic_set *normalize_constraints_in_compressed_space(
1326         struct isl_basic_set *bset)
1327 {
1328         int i;
1329         unsigned total;
1330         struct isl_mat *B, *C;
1331         isl_int gcd;
1332
1333         if (!bset)
1334                 return NULL;
1335
1336         if (ISL_F_ISSET(bset, ISL_BASIC_SET_RATIONAL))
1337                 return bset;
1338
1339         bset = isl_basic_set_cow(bset);
1340         if (!bset)
1341                 return NULL;
1342
1343         total = isl_basic_set_total_dim(bset);
1344         B = isl_mat_sub_alloc(bset->ctx, bset->eq, 0, bset->n_eq, 0, 1 + total);
1345         C = isl_mat_variable_compression(bset->ctx, B, NULL);
1346         if (!C)
1347                 return bset;
1348         if (C->n_col == 0) {
1349                 isl_mat_free(bset->ctx, C);
1350                 return isl_basic_set_set_to_empty(bset);
1351         }
1352         B = isl_mat_sub_alloc(bset->ctx, bset->ineq,
1353                                                 0, bset->n_ineq, 0, 1 + total);
1354         C = isl_mat_product(bset->ctx, B, C);
1355         if (!C)
1356                 return bset;
1357
1358         isl_int_init(gcd);
1359         for (i = 0; i < bset->n_ineq; ++i) {
1360                 isl_seq_gcd(C->row[i] + 1, C->n_col - 1, &gcd);
1361                 if (isl_int_is_one(gcd))
1362                         continue;
1363                 isl_int_fdiv_r(C->row[i][0], C->row[i][0], gcd);
1364                 isl_int_sub(bset->ineq[i][0], bset->ineq[i][0], C->row[i][0]);
1365         }
1366         isl_int_clear(gcd);
1367
1368         isl_mat_free(bset->ctx, C);
1369
1370         return bset;
1371 }
1372
1373 /* Remove all information from bset that is redundant in the context
1374  * of context.  In particular, equalities that are linear combinations
1375  * of those in context are removed.  Then the inequalities that are
1376  * redundant in the context of the equalities and inequalities of
1377  * context are removed.
1378  *
1379  * We first simplify the constraints of "bset" in the context of the
1380  * equalities of "context".
1381  * Then we simplify the inequalities of the context in the context
1382  * of the equalities of bset and remove the inequalities from "bset"
1383  * that are obviously redundant with respect to some inequality in "context".
1384  *
1385  * If there are any inequalities left, we construct a tableau for
1386  * the context and then add the inequalities of "bset".
1387  * Before adding these equalities, we freeze all constraints such that
1388  * they won't be considered redundant in terms of the constraints of "bset".
1389  * Then we detect all equalities and redundant constraints (among the
1390  * constraints that weren't frozen) and update bset according to the results.
1391  * We have to be careful here because we don't want any of the context
1392  * constraints to remain and because we haven't added the equalities of "bset"
1393  * to the tableau so we temporarily have to pretend that there were no
1394  * equalities.
1395  */
1396 static struct isl_basic_set *uset_gist(struct isl_basic_set *bset,
1397         struct isl_basic_set *context)
1398 {
1399         int i;
1400         struct isl_tab *tab;
1401         unsigned context_ineq, bset_eq;
1402         struct isl_basic_set *combined = NULL;
1403
1404         if (!context || !bset)
1405                 goto error;
1406
1407         if (context->n_eq > 0)
1408                 bset = isl_basic_set_reduce_using_equalities(bset,
1409                                         isl_basic_set_copy(context));
1410         if (!bset)
1411                 goto error;
1412
1413         if (bset->n_eq > 0) {
1414                 struct isl_basic_set *affine_hull;
1415                 affine_hull = isl_basic_set_copy(bset);
1416                 affine_hull = isl_basic_set_cow(affine_hull);
1417                 if (!affine_hull)
1418                         goto error;
1419                 isl_basic_set_free_inequality(affine_hull, affine_hull->n_ineq);
1420                 context = isl_basic_set_intersect(context, affine_hull);
1421                 context = isl_basic_set_gauss(context, NULL);
1422                 context = normalize_constraints_in_compressed_space(context);
1423         }
1424         if (!context)
1425                 goto error;
1426         if (ISL_F_ISSET(context, ISL_BASIC_SET_EMPTY)) {
1427                 isl_basic_set_free(bset);
1428                 return context;
1429         }
1430         if (!context->n_ineq)
1431                 goto done;
1432         bset = remove_shifted_constraints(bset, context);
1433         if (!bset->n_ineq)
1434                 goto done;
1435         isl_basic_set_free_equality(context, context->n_eq);
1436         context_ineq = context->n_ineq;
1437         combined = isl_basic_set_cow(isl_basic_set_copy(context));
1438         combined = isl_basic_set_extend_constraints(combined,
1439                                                     bset->n_eq, bset->n_ineq);
1440         tab = isl_tab_from_basic_set(combined);
1441         if (!tab)
1442                 goto error;
1443         for (i = 0; i < context_ineq; ++i)
1444                 tab->con[i].frozen = 1;
1445         tab = isl_tab_extend(bset->ctx, tab, bset->n_ineq);
1446         if (!tab)
1447                 goto error;
1448         for (i = 0; i < bset->n_ineq; ++i)
1449                 tab = isl_tab_add_ineq(bset->ctx, tab, bset->ineq[i]);
1450         bset = isl_basic_set_add_constraints(combined, bset, 0);
1451         tab = isl_tab_detect_equalities(bset->ctx, tab);
1452         tab = isl_tab_detect_redundant(bset->ctx, tab);
1453         if (!tab)
1454                 goto error2;
1455         for (i = 0; i < context_ineq; ++i) {
1456                 tab->con[i].is_zero = 0;
1457                 tab->con[i].is_redundant = 1;
1458         }
1459         bset_eq = bset->n_eq;
1460         bset->n_eq = 0;
1461         bset = isl_basic_set_update_from_tab(bset, tab);
1462         bset->n_eq = bset_eq;
1463         isl_tab_free(bset->ctx, tab);
1464         ISL_F_SET(bset, ISL_BASIC_SET_NO_IMPLICIT);
1465         ISL_F_SET(bset, ISL_BASIC_SET_NO_REDUNDANT);
1466 done:
1467         bset = isl_basic_set_simplify(bset);
1468         bset = isl_basic_set_finalize(bset);
1469         isl_basic_set_free(context);
1470         return bset;
1471 error:
1472         isl_basic_set_free(combined);
1473 error2:
1474         isl_basic_set_free(bset);
1475         isl_basic_set_free(context);
1476         return NULL;
1477 }
1478
1479 struct isl_basic_map *isl_basic_map_gist(struct isl_basic_map *bmap,
1480         struct isl_basic_map *context)
1481 {
1482         struct isl_basic_set *bset;
1483
1484         if (!bmap || !context)
1485                 goto error;
1486
1487         if (isl_basic_map_is_universe(context)) {
1488                 isl_basic_map_free(context);
1489                 return bmap;
1490         }
1491         if (isl_basic_map_is_universe(bmap)) {
1492                 isl_basic_map_free(context);
1493                 return bmap;
1494         }
1495         if (isl_basic_map_fast_is_empty(context)) {
1496                 struct isl_dim *dim = isl_dim_copy(bmap->dim);
1497                 isl_basic_map_free(context);
1498                 isl_basic_map_free(bmap);
1499                 return isl_basic_map_universe(dim);
1500         }
1501         if (isl_basic_map_fast_is_empty(bmap)) {
1502                 isl_basic_map_free(context);
1503                 return bmap;
1504         }
1505
1506         bmap = isl_basic_map_convex_hull(bmap);
1507         context = isl_basic_map_convex_hull(context);
1508
1509         context = isl_basic_map_align_divs(context, bmap);
1510         bmap = isl_basic_map_align_divs(bmap, context);
1511
1512         bset = uset_gist(isl_basic_map_underlying_set(isl_basic_map_copy(bmap)),
1513                          isl_basic_map_underlying_set(context));
1514
1515         return isl_basic_map_overlying_set(bset, bmap);
1516 error:
1517         isl_basic_map_free(bmap);
1518         isl_basic_map_free(context);
1519         return NULL;
1520 }
1521
1522 /*
1523  * Assumes context has no implicit divs.
1524  */
1525 struct isl_map *isl_map_gist(struct isl_map *map, struct isl_basic_map *context)
1526 {
1527         int i;
1528
1529         if (!map || !context)
1530                 goto error;;
1531
1532         if (isl_basic_map_is_universe(context)) {
1533                 isl_basic_map_free(context);
1534                 return map;
1535         }
1536         if (isl_basic_map_fast_is_empty(context)) {
1537                 struct isl_dim *dim = isl_dim_copy(map->dim);
1538                 isl_basic_map_free(context);
1539                 isl_map_free(map);
1540                 return isl_map_universe(dim);
1541         }
1542
1543         context = isl_basic_map_convex_hull(context);
1544         map = isl_map_cow(map);
1545         if (!map || !context)
1546                 goto error;;
1547         isl_assert(map->ctx, isl_dim_equal(map->dim, context->dim), goto error);
1548         map = isl_map_compute_divs(map);
1549         for (i = 0; i < map->n; ++i)
1550                 context = isl_basic_map_align_divs(context, map->p[i]);
1551         for (i = 0; i < map->n; ++i) {
1552                 map->p[i] = isl_basic_map_gist(map->p[i],
1553                                                 isl_basic_map_copy(context));
1554                 if (!map->p[i])
1555                         goto error;
1556         }
1557         isl_basic_map_free(context);
1558         ISL_F_CLR(map, ISL_MAP_NORMALIZED);
1559         return map;
1560 error:
1561         isl_map_free(map);
1562         isl_basic_map_free(context);
1563         return NULL;
1564 }
1565
1566 struct isl_basic_set *isl_basic_set_gist(struct isl_basic_set *bset,
1567                                                 struct isl_basic_set *context)
1568 {
1569         return (struct isl_basic_set *)isl_basic_map_gist(
1570                 (struct isl_basic_map *)bset, (struct isl_basic_map *)context);
1571 }
1572
1573 struct isl_set *isl_set_gist(struct isl_set *set, struct isl_basic_set *context)
1574 {
1575         return (struct isl_set *)isl_map_gist((struct isl_map *)set,
1576                                         (struct isl_basic_map *)context);
1577 }
1578
1579 /* Quick check to see if two basic maps are disjoint.
1580  * In particular, we reduce the equalities and inequalities of
1581  * one basic map in the context of the equalities of the other
1582  * basic map and check if we get a contradiction.
1583  */
1584 int isl_basic_map_fast_is_disjoint(struct isl_basic_map *bmap1,
1585         struct isl_basic_map *bmap2)
1586 {
1587         struct isl_vec *v = NULL;
1588         int *elim = NULL;
1589         unsigned total;
1590         int d, i;
1591
1592         if (!bmap1 || !bmap2)
1593                 return -1;
1594         isl_assert(bmap1->ctx, isl_dim_equal(bmap1->dim, bmap2->dim),
1595                         return -1);
1596         if (bmap1->n_div || bmap2->n_div)
1597                 return 0;
1598         if (!bmap1->n_eq && !bmap2->n_eq)
1599                 return 0;
1600
1601         total = isl_dim_total(bmap1->dim);
1602         if (total == 0)
1603                 return 0;
1604         v = isl_vec_alloc(bmap1->ctx, 1 + total);
1605         if (!v)
1606                 goto error;
1607         elim = isl_alloc_array(bmap1->ctx, int, total);
1608         if (!elim)
1609                 goto error;
1610         compute_elimination_index(bmap1, elim);
1611         for (i = 0; i < bmap2->n_eq; ++i) {
1612                 int reduced;
1613                 reduced = reduced_using_equalities(v->block.data, bmap2->eq[i],
1614                                                         bmap1, elim);
1615                 if (reduced && !isl_int_is_zero(v->block.data[0]) &&
1616                     isl_seq_first_non_zero(v->block.data + 1, total) == -1)
1617                         goto disjoint;
1618         }
1619         for (i = 0; i < bmap2->n_ineq; ++i) {
1620                 int reduced;
1621                 reduced = reduced_using_equalities(v->block.data,
1622                                                 bmap2->ineq[i], bmap1, elim);
1623                 if (reduced && isl_int_is_neg(v->block.data[0]) &&
1624                     isl_seq_first_non_zero(v->block.data + 1, total) == -1)
1625                         goto disjoint;
1626         }
1627         compute_elimination_index(bmap2, elim);
1628         for (i = 0; i < bmap1->n_ineq; ++i) {
1629                 int reduced;
1630                 reduced = reduced_using_equalities(v->block.data,
1631                                                 bmap1->ineq[i], bmap2, elim);
1632                 if (reduced && isl_int_is_neg(v->block.data[0]) &&
1633                     isl_seq_first_non_zero(v->block.data + 1, total) == -1)
1634                         goto disjoint;
1635         }
1636         isl_vec_free(bmap1->ctx, v);
1637         free(elim);
1638         return 0;
1639 disjoint:
1640         isl_vec_free(bmap1->ctx, v);
1641         free(elim);
1642         return 1;
1643 error:
1644         isl_vec_free(bmap1->ctx, v);
1645         free(elim);
1646         return -1;
1647 }
1648
1649 int isl_basic_set_fast_is_disjoint(struct isl_basic_set *bset1,
1650         struct isl_basic_set *bset2)
1651 {
1652         return isl_basic_map_fast_is_disjoint((struct isl_basic_map *)bset1,
1653                                               (struct isl_basic_map *)bset2);
1654 }
1655
1656 int isl_map_fast_is_disjoint(struct isl_map *map1, struct isl_map *map2)
1657 {
1658         int i, j;
1659
1660         if (!map1 || !map2)
1661                 return -1;
1662
1663         if (isl_map_fast_is_equal(map1, map2))
1664                 return 0;
1665
1666         for (i = 0; i < map1->n; ++i) {
1667                 for (j = 0; j < map2->n; ++j) {
1668                         int d = isl_basic_map_fast_is_disjoint(map1->p[i],
1669                                                                map2->p[j]);
1670                         if (d != 1)
1671                                 return d;
1672                 }
1673         }
1674         return 1;
1675 }
1676
1677 int isl_set_fast_is_disjoint(struct isl_set *set1, struct isl_set *set2)
1678 {
1679         return isl_map_fast_is_disjoint((struct isl_map *)set1,
1680                                         (struct isl_map *)set2);
1681 }