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 static int n_pure_div_eq(struct isl_basic_map *bmap)
 631 {
 632         int i, j;
 633         unsigned total;
 634
 635         total = isl_dim_total(bmap->dim);
 636         for (i = 0, j = bmap->n_div-1; i < bmap->n_eq; ++i) {
 637                 while (j >= 0 && isl_int_is_zero(bmap->eq[i][1 + total + j]))
 638                         --j;
 639                 if (j < 0)
 640                         break;
 641                 if (isl_seq_first_non_zero(bmap->eq[i] + 1 + total, j) != -1)
 642                         return 0;
 643         }
 644         return i;
 645 }
 646
 647 /* Normalize divs that appear in equalities.
 648  *
 649  * In particular, we assume that bmap contains some equalities
 650  * of the form
 651  *
 652  *      a x = m * e_i
 653  *
 654  * and we want to replace the set of e_i by a minimal set and
 655  * such that the new e_i have a canonical representation in terms
 656  * of the vector x.
 657  * If any of the equalities involves more than one divs, then
 658  * we currently simply bail out.
 659  *
 660  * Let us first additionally assume that all equalities involve
 661  * a div.  The equalities then express modulo constraints on the
 662  * remaining variables and we can use "parameter compression"
 663  * to find a minimal set of constraints.  The result is a transformation
 664  *
 665  *      x = T(x') = x_0 + G x'
 666  *
 667  * with G a lower-triangular matrix with all elements below the diagonal
 668  * non-negative and smaller than the diagonal element on the same row.
 669  * We first normalize x_0 by making the same property hold in the affine
 670  * T matrix.
 671  * The rows i of G with a 1 on the diagonal do not impose any modulo
 672  * constraint and simply express x_i = x'_i.
 673  * For each of the remaining rows i, we introduce a div and a corresponding
 674  * equality.  In particular
 675  *
 676  *      g_ii e_j = x_i - g_i(x')
 677  *
 678  * where each x'_k is replaced either by x_k (if g_kk = 1) or the
 679  * corresponding div (if g_kk != 1).
 680  *
 681  * If there are any equalities not involving any div, then we
 682  * first apply a variable compression on the variables x:
 683  *
 684  *      x = C x''       x'' = C_2 x
 685  *
 686  * and perform the above parameter compression on A C instead of on A.
 687  * The resulting compression is then of the form
 688  *
 689  *      x'' = T(x') = x_0 + G x'
 690  *
 691  * and in constructing the new divs and the corresponding equalities,
 692  * we have to replace each x'', i.e., the x'_k with (g_kk = 1),
 693  * by the corresponding row from C_2.
 694  */
 695 static struct isl_basic_map *normalize_divs(
 696         struct isl_basic_map *bmap, int *progress)
 697 {
 698         int i, j, k;
 699         int total;
 700         int div_eq;
 701         struct isl_mat *B;
 702         struct isl_vec *d;
 703         struct isl_mat *T = NULL;
 704         struct isl_mat *C = NULL;
 705         struct isl_mat *C2 = NULL;
 706         isl_int v;
 707         int *pos;
 708         int dropped, needed;
 709
 710         if (!bmap)
 711                 return NULL;
 712
 713         if (bmap->n_div == 0)
 714                 return bmap;
 715
 716         if (bmap->n_eq == 0)
 717                 return bmap;
 718
 719         if (ISL_F_ISSET(bmap, ISL_BASIC_MAP_NORMALIZED_DIVS))
 720                 return bmap;
 721
 722         total = isl_dim_total(bmap->dim);
 723         div_eq = n_pure_div_eq(bmap);
 724         if (div_eq == 0)
 725                 return bmap;
 726
 727         if (div_eq < bmap->n_eq) {
 728                 B = isl_mat_sub_alloc(bmap->ctx, bmap->eq, div_eq,
 729                                         bmap->n_eq - div_eq, 0, 1 + total);
 730                 C = isl_mat_variable_compression(bmap->ctx, B, &C2);
 731                 if (!C || !C2)
 732                         goto error;
 733                 if (C->n_col == 0) {
 734                         bmap = isl_basic_map_set_to_empty(bmap);
 735                         isl_mat_free(bmap->ctx, C);
 736                         isl_mat_free(bmap->ctx, C2);
 737                         goto done;
 738                 }
 739         }
 740
 741         d = isl_vec_alloc(bmap->ctx, div_eq);
 742         if (!d)
 743                 goto error;
 744         for (i = 0, j = bmap->n_div-1; i < div_eq; ++i) {
 745                 while (j >= 0 && isl_int_is_zero(bmap->eq[i][1 + total + j]))
 746                         --j;
 747                 isl_int_set(d->block.data[i], bmap->eq[i][1 + total + j]);
 748         }
 749         B = isl_mat_sub_alloc(bmap->ctx, bmap->eq, 0, div_eq, 0, 1 + total);
 750
 751         if (C) {
 752                 B = isl_mat_product(bmap->ctx, B, C);
 753                 C = NULL;
 754         }
 755
 756         T = isl_mat_parameter_compression(bmap->ctx, B, d);
 757         if (!T)
 758                 goto error;
 759         if (T->n_col == 0) {
 760                 bmap = isl_basic_map_set_to_empty(bmap);
 761                 isl_mat_free(bmap->ctx, C2);
 762                 isl_mat_free(bmap->ctx, T);
 763                 goto done;
 764         }
 765         isl_int_init(v);
 766         for (i = 0; i < T->n_row - 1; ++i) {
 767                 isl_int_fdiv_q(v, T->row[1 + i][0], T->row[1 + i][1 + i]);
 768                 if (isl_int_is_zero(v))
 769                         continue;
 770                 isl_mat_col_submul(T, 0, v, 1 + i);
 771         }
 772         isl_int_clear(v);
 773         pos = isl_alloc_array(bmap->ctx, int, T->n_row);
 774         /* We have to be careful because dropping equalities may reorder them */
 775         dropped = 0;
 776         for (j = bmap->n_div - 1; j >= 0; --j) {
 777                 for (i = 0; i < bmap->n_eq; ++i)
 778                         if (!isl_int_is_zero(bmap->eq[i][1 + total + j]))
 779                                 break;
 780                 if (i < bmap->n_eq) {
 781                         bmap = isl_basic_map_drop_div(bmap, j);
 782                         isl_basic_map_drop_equality(bmap, i);
 783                         ++dropped;
 784                 }
 785         }
 786         pos[0] = 0;
 787         needed = 0;
 788         for (i = 1; i < T->n_row; ++i) {
 789                 if (isl_int_is_one(T->row[i][i]))
 790                         pos[i] = i;
 791                 else
 792                         needed++;
 793         }
 794         if (needed > dropped) {
 795                 bmap = isl_basic_map_extend_dim(bmap, isl_dim_copy(bmap->dim),
 796                                 needed, needed, 0);
 797                 if (!bmap)
 798                         goto error;
 799         }
 800         for (i = 1; i < T->n_row; ++i) {
 801                 if (isl_int_is_one(T->row[i][i]))
 802                         continue;
 803                 k = isl_basic_map_alloc_div(bmap);
 804                 pos[i] = 1 + total + k;
 805                 isl_seq_clr(bmap->div[k] + 1, 1 + total + bmap->n_div);
 806                 isl_int_set(bmap->div[k][0], T->row[i][i]);
 807                 if (C2)
 808                         isl_seq_cpy(bmap->div[k] + 1, C2->row[i], 1 + total);
 809                 else
 810                         isl_int_set_si(bmap->div[k][1 + i], 1);
 811                 for (j = 0; j < i; ++j) {
 812                         if (isl_int_is_zero(T->row[i][j]))
 813                                 continue;
 814                         if (pos[j] < T->n_row && C2)
 815                                 isl_seq_submul(bmap->div[k] + 1, T->row[i][j],
 816                                                 C2->row[pos[j]], 1 + total);
 817                         else
 818                                 isl_int_neg(bmap->div[k][1 + pos[j]],
 819                                                                 T->row[i][j]);
 820                 }
 821                 j = isl_basic_map_alloc_equality(bmap);
 822                 isl_seq_neg(bmap->eq[j], bmap->div[k]+1, 1+total+bmap->n_div);
 823                 isl_int_set(bmap->eq[j][pos[i]], bmap->div[k][0]);
 824         }
 825         free(pos);
 826         isl_mat_free(bmap->ctx, C2);
 827         isl_mat_free(bmap->ctx, T);
 828
 829         if (progress)
 830                 *progress = 1;
 831 done:
 832         ISL_F_SET(bmap, ISL_BASIC_MAP_NORMALIZED_DIVS);
 833
 834         return bmap;
 835 error:
 836         isl_mat_free(bmap->ctx, C);
 837         isl_mat_free(bmap->ctx, C2);
 838         isl_mat_free(bmap->ctx, T);
 839         return bmap;
 840 }
 841
 842 static struct isl_basic_map *remove_duplicate_constraints(
 843         struct isl_basic_map *bmap, int *progress)
 844 {
 845         unsigned int size;
 846         isl_int ***index;
 847         int k, l, h;
 848         int bits;
 849         unsigned total = isl_basic_map_total_dim(bmap);
 850         isl_int sum;
 851
 852         if (bmap->n_ineq <= 1)
 853                 return bmap;
 854
 855         size = round_up(4 * (bmap->n_ineq+1) / 3 - 1);
 856         bits = ffs(size) - 1;
 857         index = isl_calloc_array(ctx, isl_int **, size);
 858         if (!index)
 859                 return bmap;
 860
 861         index[isl_seq_get_hash_bits(bmap->ineq[0]+1, total, bits)] = &bmap->ineq[0];
 862         for (k = 1; k < bmap->n_ineq; ++k) {
 863                 h = hash_index(index, size, bits, bmap, k);
 864                 if (!index[h]) {
 865                         index[h] = &bmap->ineq[k];
 866                         continue;
 867                 }
 868                 if (progress)
 869                         *progress = 1;
 870                 l = index[h] - &bmap->ineq[0];
 871                 if (isl_int_lt(bmap->ineq[k][0], bmap->ineq[l][0]))
 872                         swap_inequality(bmap, k, l);
 873                 isl_basic_map_drop_inequality(bmap, k);
 874                 --k;
 875         }
 876         isl_int_init(sum);
 877         for (k = 0; k < bmap->n_ineq-1; ++k) {
 878                 isl_seq_neg(bmap->ineq[k]+1, bmap->ineq[k]+1, total);
 879                 h = hash_index(index, size, bits, bmap, k);
 880                 isl_seq_neg(bmap->ineq[k]+1, bmap->ineq[k]+1, total);
 881                 if (!index[h])
 882                         continue;
 883                 l = index[h] - &bmap->ineq[0];
 884                 isl_int_add(sum, bmap->ineq[k][0], bmap->ineq[l][0]);
 885                 if (isl_int_is_pos(sum))
 886                         continue;
 887                 if (isl_int_is_zero(sum)) {
 888                         /* We need to break out of the loop after these
 889                          * changes since the contents of the hash
 890                          * will no longer be valid.
 891                          * Plus, we probably we want to regauss first.
 892                          */
 893                         isl_basic_map_drop_inequality(bmap, l);
 894                         isl_basic_map_inequality_to_equality(bmap, k);
 895                 } else
 896                         bmap = isl_basic_map_set_to_empty(bmap);
 897                 break;
 898         }
 899         isl_int_clear(sum);
 900
 901         free(index);
 902         return bmap;
 903 }
 904
 905
 906 struct isl_basic_map *isl_basic_map_simplify(struct isl_basic_map *bmap)
 907 {
 908         int progress = 1;
 909         if (!bmap)
 910                 return NULL;
 911         while (progress) {
 912                 progress = 0;
 913                 bmap = isl_basic_map_normalize_constraints(bmap);
 914                 bmap = remove_duplicate_divs(bmap, &progress);
 915                 bmap = eliminate_divs_eq(bmap, &progress);
 916                 bmap = eliminate_divs_ineq(bmap, &progress);
 917                 bmap = isl_basic_map_gauss(bmap, &progress);
 918                 /* requires equalities in normal form */
 919                 bmap = normalize_divs(bmap, &progress);
 920                 bmap = remove_duplicate_constraints(bmap, &progress);
 921         }
 922         return bmap;
 923 }
 924
 925 struct isl_basic_set *isl_basic_set_simplify(struct isl_basic_set *bset)
 926 {
 927         return (struct isl_basic_set *)
 928                 isl_basic_map_simplify((struct isl_basic_map *)bset);
 929 }
 930
 931
 932 /* If the only constraints a div d=floor(f/m)
 933  * appears in are its two defining constraints
 934  *
 935  *      f - m d >=0
 936  *      -(f - (m - 1)) + m d >= 0
 937  *
 938  * then it can safely be removed.
 939  */
 940 static int div_is_redundant(struct isl_basic_map *bmap, int div)
 941 {
 942         int i;
 943         unsigned pos = 1 + isl_dim_total(bmap->dim) + div;
 944
 945         for (i = 0; i < bmap->n_eq; ++i)
 946                 if (!isl_int_is_zero(bmap->eq[i][pos]))
 947                         return 0;
 948
 949         for (i = 0; i < bmap->n_ineq; ++i) {
 950                 if (isl_int_is_zero(bmap->ineq[i][pos]))
 951                         continue;
 952                 if (isl_int_eq(bmap->ineq[i][pos], bmap->div[div][0])) {
 953                         int neg;
 954                         isl_int_sub(bmap->div[div][1],
 955                                         bmap->div[div][1], bmap->div[div][0]);
 956                         isl_int_add_ui(bmap->div[div][1], bmap->div[div][1], 1);
 957                         neg = isl_seq_is_neg(bmap->ineq[i], bmap->div[div]+1, pos);
 958                         isl_int_sub_ui(bmap->div[div][1], bmap->div[div][1], 1);
 959                         isl_int_add(bmap->div[div][1],
 960                                         bmap->div[div][1], bmap->div[div][0]);
 961                         if (!neg)
 962                                 return 0;
 963                         if (isl_seq_first_non_zero(bmap->ineq[i]+pos+1,
 964                                                     bmap->n_div-div-1) != -1)
 965                                 return 0;
 966                 } else if (isl_int_abs_eq(bmap->ineq[i][pos], bmap->div[div][0])) {
 967                         if (!isl_seq_eq(bmap->ineq[i], bmap->div[div]+1, pos))
 968                                 return 0;
 969                         if (isl_seq_first_non_zero(bmap->ineq[i]+pos+1,
 970                                                     bmap->n_div-div-1) != -1)
 971                                 return 0;
 972                 } else
 973                         return 0;
 974         }
 975
 976         for (i = 0; i < bmap->n_div; ++i)
 977                 if (!isl_int_is_zero(bmap->div[i][1+pos]))
 978                         return 0;
 979
 980         return 1;
 981 }
 982
 983 /*
 984  * Remove divs that don't occur in any of the constraints or other divs.
 985  * These can arise when dropping some of the variables in a quast
 986  * returned by piplib.
 987  */
 988 static struct isl_basic_map *remove_redundant_divs(struct isl_basic_map *bmap)
 989 {
 990         int i;
 991
 992         if (!bmap)
 993                 return NULL;
 994
 995         for (i = bmap->n_div-1; i >= 0; --i) {
 996                 if (!div_is_redundant(bmap, i))
 997                         continue;
 998                 bmap = isl_basic_map_drop_div(bmap, i);
 999         }
1000         return bmap;
1001 }
1002
1003 struct isl_basic_map *isl_basic_map_finalize(struct isl_basic_map *bmap)
1004 {
1005         bmap = remove_redundant_divs(bmap);
1006         if (!bmap)
1007                 return NULL;
1008         ISL_F_SET(bmap, ISL_BASIC_SET_FINAL);
1009         return bmap;
1010 }
1011
1012 struct isl_basic_set *isl_basic_set_finalize(struct isl_basic_set *bset)
1013 {
1014         return (struct isl_basic_set *)
1015                 isl_basic_map_finalize((struct isl_basic_map *)bset);
1016 }
1017
1018 struct isl_set *isl_set_finalize(struct isl_set *set)
1019 {
1020         int i;
1021
1022         if (!set)
1023                 return NULL;
1024         for (i = 0; i < set->n; ++i) {
1025                 set->p[i] = isl_basic_set_finalize(set->p[i]);
1026                 if (!set->p[i])
1027                         goto error;
1028         }
1029         return set;
1030 error:
1031         isl_set_free(set);
1032         return NULL;
1033 }
1034
1035 struct isl_map *isl_map_finalize(struct isl_map *map)
1036 {
1037         int i;
1038
1039         if (!map)
1040                 return NULL;
1041         for (i = 0; i < map->n; ++i) {
1042                 map->p[i] = isl_basic_map_finalize(map->p[i]);
1043                 if (!map->p[i])
1044                         goto error;
1045         }
1046         ISL_F_CLR(map, ISL_MAP_NORMALIZED);
1047         return map;
1048 error:
1049         isl_map_free(map);
1050         return NULL;
1051 }
1052
1053
1054 /* Remove any div that is defined in terms of the given variable.
1055  */
1056 static struct isl_basic_map *remove_dependent_vars(struct isl_basic_map *bmap,
1057                                                                         int pos)
1058 {
1059         int i;
1060         unsigned dim = isl_dim_total(bmap->dim);
1061
1062         for (i = 0; i < bmap->n_div; ++i) {
1063                 if (isl_int_is_zero(bmap->div[i][0]))
1064                         continue;
1065                 if (isl_int_is_zero(bmap->div[i][1+1+pos]))
1066                         continue;
1067                 bmap = isl_basic_map_eliminate_vars(bmap, dim + i, 1);
1068                 if (!bmap)
1069                         return NULL;
1070         }
1071         return bmap;
1072 }
1073
1074 /* Eliminate the specified variables from the constraints using
1075  * Fourier-Motzkin.  The variables themselves are not removed.
1076  */
1077 struct isl_basic_map *isl_basic_map_eliminate_vars(
1078         struct isl_basic_map *bmap, unsigned pos, unsigned n)
1079 {
1080         int d;
1081         int i, j, k;
1082         unsigned total;
1083
1084         if (n == 0)
1085                 return bmap;
1086         if (!bmap)
1087                 return NULL;
1088         total = isl_basic_map_total_dim(bmap);
1089
1090         bmap = isl_basic_map_cow(bmap);
1091         for (d = pos + n - 1; d >= 0 && d >= pos; --d)
1092                 bmap = remove_dependent_vars(bmap, d);
1093
1094         for (d = pos + n - 1;
1095              d >= 0 && d >= total - bmap->n_div && d >= pos; --d)
1096                 isl_seq_clr(bmap->div[d-(total-bmap->n_div)], 2+total);
1097         for (d = pos + n - 1; d >= 0 && d >= pos; --d) {
1098                 int n_lower, n_upper;
1099                 if (!bmap)
1100                         return NULL;
1101                 for (i = 0; i < bmap->n_eq; ++i) {
1102                         if (isl_int_is_zero(bmap->eq[i][1+d]))
1103                                 continue;
1104                         eliminate_var_using_equality(bmap, d, bmap->eq[i], NULL);
1105                         isl_basic_map_drop_equality(bmap, i);
1106                         break;
1107                 }
1108                 if (i < bmap->n_eq)
1109                         continue;
1110                 n_lower = 0;
1111                 n_upper = 0;
1112                 for (i = 0; i < bmap->n_ineq; ++i) {
1113                         if (isl_int_is_pos(bmap->ineq[i][1+d]))
1114                                 n_lower++;
1115                         else if (isl_int_is_neg(bmap->ineq[i][1+d]))
1116                                 n_upper++;
1117                 }
1118                 bmap = isl_basic_map_extend_constraints(bmap,
1119                                 0, n_lower * n_upper);
1120                 for (i = bmap->n_ineq - 1; i >= 0; --i) {
1121                         int last;
1122                         if (isl_int_is_zero(bmap->ineq[i][1+d]))
1123                                 continue;
1124                         last = -1;
1125                         for (j = 0; j < i; ++j) {
1126                                 if (isl_int_is_zero(bmap->ineq[j][1+d]))
1127                                         continue;
1128                                 last = j;
1129                                 if (isl_int_sgn(bmap->ineq[i][1+d]) ==
1130                                     isl_int_sgn(bmap->ineq[j][1+d]))
1131                                         continue;
1132                                 k = isl_basic_map_alloc_inequality(bmap);
1133                                 if (k < 0)
1134                                         goto error;
1135                                 isl_seq_cpy(bmap->ineq[k], bmap->ineq[i],
1136                                                 1+total);
1137                                 isl_seq_elim(bmap->ineq[k], bmap->ineq[j],
1138                                                 1+d, 1+total, NULL);
1139                         }
1140                         isl_basic_map_drop_inequality(bmap, i);
1141                         i = last + 1;
1142                 }
1143                 if (n_lower > 0 && n_upper > 0) {
1144                         bmap = isl_basic_map_normalize_constraints(bmap);
1145                         bmap = remove_duplicate_constraints(bmap, NULL);
1146                         bmap = isl_basic_map_gauss(bmap, NULL);
1147                         bmap = isl_basic_map_convex_hull(bmap);
1148                         if (!bmap)
1149                                 goto error;
1150                         if (ISL_F_ISSET(bmap, ISL_BASIC_MAP_EMPTY))
1151                                 break;
1152                 }
1153         }
1154         ISL_F_CLR(bmap, ISL_BASIC_MAP_NORMALIZED);
1155         return bmap;
1156 error:
1157         isl_basic_map_free(bmap);
1158         return NULL;
1159 }
1160
1161 struct isl_basic_set *isl_basic_set_eliminate_vars(
1162         struct isl_basic_set *bset, unsigned pos, unsigned n)
1163 {
1164         return (struct isl_basic_set *)isl_basic_map_eliminate_vars(
1165                         (struct isl_basic_map *)bset, pos, n);
1166 }
1167
1168 /* Don't assume equalities are in order, because align_divs
1169  * may have changed the order of the divs.
1170  */
1171 static void compute_elimination_index(struct isl_basic_map *bmap, int *elim)
1172 {
1173         int d, i;
1174         unsigned total;
1175
1176         total = isl_dim_total(bmap->dim);
1177         for (d = 0; d < total; ++d)
1178                 elim[d] = -1;
1179         for (i = 0; i < bmap->n_eq; ++i) {
1180                 for (d = total - 1; d >= 0; --d) {
1181                         if (isl_int_is_zero(bmap->eq[i][1+d]))
1182                                 continue;
1183                         elim[d] = i;
1184                         break;
1185                 }
1186         }
1187 }
1188
1189 static void set_compute_elimination_index(struct isl_basic_set *bset, int *elim)
1190 {
1191         return compute_elimination_index((struct isl_basic_map *)bset, elim);
1192 }
1193
1194 static int reduced_using_equalities(isl_int *dst, isl_int *src,
1195         struct isl_basic_map *bmap, int *elim)
1196 {
1197         int d, i;
1198         int copied = 0;
1199         unsigned total;
1200
1201         total = isl_dim_total(bmap->dim);
1202         for (d = total - 1; d >= 0; --d) {
1203                 if (isl_int_is_zero(src[1+d]))
1204                         continue;
1205                 if (elim[d] == -1)
1206                         continue;
1207                 if (!copied) {
1208                         isl_seq_cpy(dst, src, 1 + total);
1209                         copied = 1;
1210                 }
1211                 isl_seq_elim(dst, bmap->eq[elim[d]], 1 + d, 1 + total, NULL);
1212         }
1213         return copied;
1214 }
1215
1216 static int set_reduced_using_equalities(isl_int *dst, isl_int *src,
1217         struct isl_basic_set *bset, int *elim)
1218 {
1219         return reduced_using_equalities(dst, src,
1220                                         (struct isl_basic_map *)bset, elim);
1221 }
1222
1223 static struct isl_basic_set *isl_basic_set_reduce_using_equalities(
1224         struct isl_basic_set *bset, struct isl_basic_set *context)
1225 {
1226         int i;
1227         int *elim;
1228
1229         if (!bset || !context)
1230                 goto error;
1231
1232         bset = isl_basic_set_cow(bset);
1233         if (!bset)
1234                 goto error;
1235
1236         elim = isl_alloc_array(ctx, int, isl_basic_set_n_dim(bset));
1237         if (!elim)
1238                 goto error;
1239         set_compute_elimination_index(context, elim);
1240         for (i = 0; i < bset->n_eq; ++i)
1241                 set_reduced_using_equalities(bset->eq[i], bset->eq[i],
1242                                                         context, elim);
1243         for (i = 0; i < bset->n_ineq; ++i)
1244                 set_reduced_using_equalities(bset->ineq[i], bset->ineq[i],
1245                                                         context, elim);
1246         isl_basic_set_free(context);
1247         free(elim);
1248         bset = isl_basic_set_simplify(bset);
1249         bset = isl_basic_set_finalize(bset);
1250         return bset;
1251 error:
1252         isl_basic_set_free(bset);
1253         isl_basic_set_free(context);
1254         return NULL;
1255 }
1256
1257 static struct isl_basic_set *remove_shifted_constraints(
1258         struct isl_basic_set *bset, struct isl_basic_set *context)
1259 {
1260         unsigned int size;
1261         isl_int ***index;
1262         int bits;
1263         int k, h, l;
1264
1265         if (!bset)
1266                 return NULL;
1267
1268         size = round_up(4 * (context->n_ineq+1) / 3 - 1);
1269         bits = ffs(size) - 1;
1270         index = isl_calloc_array(ctx, isl_int **, size);
1271         if (!index)
1272                 return bset;
1273
1274         for (k = 0; k < context->n_ineq; ++k) {
1275                 h = set_hash_index(index, size, bits, context, k);
1276                 index[h] = &context->ineq[k];
1277         }
1278         for (k = 0; k < bset->n_ineq; ++k) {
1279                 h = set_hash_index(index, size, bits, bset, k);
1280                 if (!index[h])
1281                         continue;
1282                 l = index[h] - &context->ineq[0];
1283                 if (isl_int_lt(bset->ineq[k][0], context->ineq[l][0]))
1284                         continue;
1285                 bset = isl_basic_set_cow(bset);
1286                 if (!bset)
1287                         goto error;
1288                 isl_basic_set_drop_inequality(bset, k);
1289                 --k;
1290         }
1291         free(index);
1292         return bset;
1293 error:
1294         free(index);
1295         return bset;
1296 }
1297
1298 /* Tighten (decrease) the constant terms of the inequalities based
1299  * on the equalities, without removing any integer points.
1300  * For example, if there is an equality
1301  *
1302  *              i = 3 * j
1303  *
1304  * and an inequality
1305  *
1306  *              i >= 1
1307  *
1308  * then we want to replace the inequality by
1309  *
1310  *              i >= 3
1311  *
1312  * We do this by computing a variable compression and translating
1313  * the constraints to the compressed space.
1314  * If any constraint has coefficients (except the contant term)
1315  * with a common factor "f", then we can replace the constant term "c"
1316  * by
1317  *
1318  *              f * floor(c/f)
1319  *
1320  * That is, we add
1321  *
1322  *              f * floor(c/f) - c = -fract(c/f)
1323  *
1324  * and we can add the same value to the original constraint.
1325  *
1326  * In the example, the compressed space only contains "j",
1327  * and the inequality translates to
1328  *
1329  *              3 * j - 1 >= 0
1330  *
1331  * We add -fract(-1/3) = -2 to the original constraint to obtain
1332  *
1333  *              i - 3 >= 0
1334  */
1335 static struct isl_basic_set *normalize_constraints_in_compressed_space(
1336         struct isl_basic_set *bset)
1337 {
1338         int i;
1339         unsigned total;
1340         struct isl_mat *B, *C;
1341         isl_int gcd;
1342
1343         if (!bset)
1344                 return NULL;
1345
1346         if (ISL_F_ISSET(bset, ISL_BASIC_SET_RATIONAL))
1347                 return bset;
1348
1349         if (!bset->n_ineq)
1350                 return bset;
1351
1352         bset = isl_basic_set_cow(bset);
1353         if (!bset)
1354                 return NULL;
1355
1356         total = isl_basic_set_total_dim(bset);
1357         B = isl_mat_sub_alloc(bset->ctx, bset->eq, 0, bset->n_eq, 0, 1 + total);
1358         C = isl_mat_variable_compression(bset->ctx, B, NULL);
1359         if (!C)
1360                 return bset;
1361         if (C->n_col == 0) {
1362                 isl_mat_free(bset->ctx, C);
1363                 return isl_basic_set_set_to_empty(bset);
1364         }
1365         B = isl_mat_sub_alloc(bset->ctx, bset->ineq,
1366                                                 0, bset->n_ineq, 0, 1 + total);
1367         C = isl_mat_product(bset->ctx, B, C);
1368         if (!C)
1369                 return bset;
1370
1371         isl_int_init(gcd);
1372         for (i = 0; i < bset->n_ineq; ++i) {
1373                 isl_seq_gcd(C->row[i] + 1, C->n_col - 1, &gcd);
1374                 if (isl_int_is_one(gcd))
1375                         continue;
1376                 isl_int_fdiv_r(C->row[i][0], C->row[i][0], gcd);
1377                 isl_int_sub(bset->ineq[i][0], bset->ineq[i][0], C->row[i][0]);
1378         }
1379         isl_int_clear(gcd);
1380
1381         isl_mat_free(bset->ctx, C);
1382
1383         return bset;
1384 }
1385
1386 /* Remove all information from bset that is redundant in the context
1387  * of context.  In particular, equalities that are linear combinations
1388  * of those in context are removed.  Then the inequalities that are
1389  * redundant in the context of the equalities and inequalities of
1390  * context are removed.
1391  *
1392  * We first simplify the constraints of "bset" in the context of the
1393  * equalities of "context".
1394  * Then we simplify the inequalities of the context in the context
1395  * of the equalities of bset and remove the inequalities from "bset"
1396  * that are obviously redundant with respect to some inequality in "context".
1397  *
1398  * If there are any inequalities left, we construct a tableau for
1399  * the context and then add the inequalities of "bset".
1400  * Before adding these equalities, we freeze all constraints such that
1401  * they won't be considered redundant in terms of the constraints of "bset".
1402  * Then we detect all equalities and redundant constraints (among the
1403  * constraints that weren't frozen) and update bset according to the results.
1404  * We have to be careful here because we don't want any of the context
1405  * constraints to remain and because we haven't added the equalities of "bset"
1406  * to the tableau so we temporarily have to pretend that there were no
1407  * equalities.
1408  */
1409 static struct isl_basic_set *uset_gist(struct isl_basic_set *bset,
1410         struct isl_basic_set *context)
1411 {
1412         int i;
1413         struct isl_tab *tab;
1414         unsigned context_ineq;
1415         struct isl_basic_set *combined = NULL;
1416
1417         if (!context || !bset)
1418                 goto error;
1419
1420         if (context->n_eq > 0)
1421                 bset = isl_basic_set_reduce_using_equalities(bset,
1422                                         isl_basic_set_copy(context));
1423         if (!bset)
1424                 goto error;
1425         if (isl_basic_set_fast_is_empty(bset))
1426                 goto done;
1427         if (!bset->n_ineq)
1428                 goto done;
1429
1430         if (bset->n_eq > 0) {
1431                 struct isl_basic_set *affine_hull;
1432                 affine_hull = isl_basic_set_copy(bset);
1433                 affine_hull = isl_basic_set_cow(affine_hull);
1434                 if (!affine_hull)
1435                         goto error;
1436                 isl_basic_set_free_inequality(affine_hull, affine_hull->n_ineq);
1437                 context = isl_basic_set_intersect(context, affine_hull);
1438                 context = isl_basic_set_gauss(context, NULL);
1439                 context = normalize_constraints_in_compressed_space(context);
1440         }
1441         if (!context)
1442                 goto error;
1443         if (ISL_F_ISSET(context, ISL_BASIC_SET_EMPTY)) {
1444                 isl_basic_set_free(bset);
1445                 return context;
1446         }
1447         if (!context->n_ineq)
1448                 goto done;
1449         bset = remove_shifted_constraints(bset, context);
1450         if (!bset->n_ineq)
1451                 goto done;
1452         isl_basic_set_free_equality(context, context->n_eq);
1453         context_ineq = context->n_ineq;
1454         combined = isl_basic_set_cow(isl_basic_set_copy(context));
1455         combined = isl_basic_set_extend_constraints(combined,
1456                                                     bset->n_eq, bset->n_ineq);
1457         tab = isl_tab_from_basic_set(combined);
1458         if (!tab)
1459                 goto error;
1460         for (i = 0; i < context_ineq; ++i)
1461                 tab->con[i].frozen = 1;
1462         tab = isl_tab_extend(bset->ctx, tab, bset->n_ineq);
1463         if (!tab)
1464                 goto error;
1465         for (i = 0; i < bset->n_ineq; ++i)
1466                 tab = isl_tab_add_ineq(bset->ctx, tab, bset->ineq[i]);
1467         bset = isl_basic_set_add_constraints(combined, bset, 0);
1468         tab = isl_tab_detect_equalities(bset->ctx, tab);
1469         tab = isl_tab_detect_redundant(bset->ctx, tab);
1470         if (!tab)
1471                 goto error2;
1472         for (i = 0; i < context_ineq; ++i) {
1473                 tab->con[i].is_zero = 0;
1474                 tab->con[i].is_redundant = 1;
1475         }
1476         bset = isl_basic_set_update_from_tab(bset, tab);
1477         isl_tab_free(bset->ctx, tab);
1478         ISL_F_SET(bset, ISL_BASIC_SET_NO_IMPLICIT);
1479         ISL_F_SET(bset, ISL_BASIC_SET_NO_REDUNDANT);
1480 done:
1481         bset = isl_basic_set_simplify(bset);
1482         bset = isl_basic_set_finalize(bset);
1483         isl_basic_set_free(context);
1484         return bset;
1485 error:
1486         isl_basic_set_free(combined);
1487 error2:
1488         isl_basic_set_free(bset);
1489         isl_basic_set_free(context);
1490         return NULL;
1491 }
1492
1493 /* Normalize the divs in "bmap" in the context of the equalities in "context".
1494  * We simply add the equalities in context to bmap and then do a regular
1495  * div normalizations.  Better results can be obtained by normalizing
1496  * only the divs in bmap than do not also appear in context.
1497  * We need to be careful to reduce the divs using the equalities
1498  * so that later calls to isl_basic_map_overlying_set wouldn't introduce
1499  * spurious constraints.
1500  */
1501 static struct isl_basic_map *normalize_divs_in_context(
1502         struct isl_basic_map *bmap, struct isl_basic_map *context)
1503 {
1504         int i;
1505         unsigned total_context;
1506         int div_eq;
1507
1508         div_eq = n_pure_div_eq(bmap);
1509         if (div_eq == 0)
1510                 return bmap;
1511
1512         if (context->n_div > 0)
1513                 bmap = isl_basic_map_align_divs(bmap, context);
1514
1515         total_context = isl_basic_map_total_dim(context);
1516         bmap = isl_basic_map_extend_constraints(bmap, context->n_eq, 0);
1517         for (i = 0; i < context->n_eq; ++i) {
1518                 int k;
1519                 k = isl_basic_map_alloc_equality(bmap);
1520                 isl_seq_cpy(bmap->eq[k], context->eq[i], 1 + total_context);
1521                 isl_seq_clr(bmap->eq[k] + 1 + total_context,
1522                                 isl_basic_map_total_dim(bmap) - total_context);
1523         }
1524         bmap = isl_basic_map_gauss(bmap, NULL);
1525         bmap = normalize_divs(bmap, NULL);
1526         bmap = isl_basic_map_gauss(bmap, NULL);
1527         return bmap;
1528 }
1529
1530 struct isl_basic_map *isl_basic_map_gist(struct isl_basic_map *bmap,
1531         struct isl_basic_map *context)
1532 {
1533         struct isl_basic_set *bset;
1534
1535         if (!bmap || !context)
1536                 goto error;
1537
1538         if (isl_basic_map_is_universe(context)) {
1539                 isl_basic_map_free(context);
1540                 return bmap;
1541         }
1542         if (isl_basic_map_is_universe(bmap)) {
1543                 isl_basic_map_free(context);
1544                 return bmap;
1545         }
1546         if (isl_basic_map_fast_is_empty(context)) {
1547                 struct isl_dim *dim = isl_dim_copy(bmap->dim);
1548                 isl_basic_map_free(context);
1549                 isl_basic_map_free(bmap);
1550                 return isl_basic_map_universe(dim);
1551         }
1552         if (isl_basic_map_fast_is_empty(bmap)) {
1553                 isl_basic_map_free(context);
1554                 return bmap;
1555         }
1556
1557         bmap = isl_basic_map_convex_hull(bmap);
1558         context = isl_basic_map_convex_hull(context);
1559
1560         if (context->n_eq)
1561                 bmap = normalize_divs_in_context(bmap, context);
1562
1563         context = isl_basic_map_align_divs(context, bmap);
1564         bmap = isl_basic_map_align_divs(bmap, context);
1565
1566         bset = uset_gist(isl_basic_map_underlying_set(isl_basic_map_copy(bmap)),
1567                          isl_basic_map_underlying_set(context));
1568
1569         return isl_basic_map_overlying_set(bset, bmap);
1570 error:
1571         isl_basic_map_free(bmap);
1572         isl_basic_map_free(context);
1573         return NULL;
1574 }
1575
1576 /*
1577  * Assumes context has no implicit divs.
1578  */
1579 struct isl_map *isl_map_gist(struct isl_map *map, struct isl_basic_map *context)
1580 {
1581         int i;
1582
1583         if (!map || !context)
1584                 goto error;;
1585
1586         if (isl_basic_map_is_universe(context)) {
1587                 isl_basic_map_free(context);
1588                 return map;
1589         }
1590         if (isl_basic_map_fast_is_empty(context)) {
1591                 struct isl_dim *dim = isl_dim_copy(map->dim);
1592                 isl_basic_map_free(context);
1593                 isl_map_free(map);
1594                 return isl_map_universe(dim);
1595         }
1596
1597         context = isl_basic_map_convex_hull(context);
1598         map = isl_map_cow(map);
1599         if (!map || !context)
1600                 goto error;;
1601         isl_assert(map->ctx, isl_dim_equal(map->dim, context->dim), goto error);
1602         map = isl_map_compute_divs(map);
1603         for (i = 0; i < map->n; ++i)
1604                 context = isl_basic_map_align_divs(context, map->p[i]);
1605         for (i = 0; i < map->n; ++i) {
1606                 map->p[i] = isl_basic_map_gist(map->p[i],
1607                                                 isl_basic_map_copy(context));
1608                 if (!map->p[i])
1609                         goto error;
1610         }
1611         isl_basic_map_free(context);
1612         ISL_F_CLR(map, ISL_MAP_NORMALIZED);
1613         return map;
1614 error:
1615         isl_map_free(map);
1616         isl_basic_map_free(context);
1617         return NULL;
1618 }
1619
1620 struct isl_basic_set *isl_basic_set_gist(struct isl_basic_set *bset,
1621                                                 struct isl_basic_set *context)
1622 {
1623         return (struct isl_basic_set *)isl_basic_map_gist(
1624                 (struct isl_basic_map *)bset, (struct isl_basic_map *)context);
1625 }
1626
1627 struct isl_set *isl_set_gist(struct isl_set *set, struct isl_basic_set *context)
1628 {
1629         return (struct isl_set *)isl_map_gist((struct isl_map *)set,
1630                                         (struct isl_basic_map *)context);
1631 }
1632
1633 /* Quick check to see if two basic maps are disjoint.
1634  * In particular, we reduce the equalities and inequalities of
1635  * one basic map in the context of the equalities of the other
1636  * basic map and check if we get a contradiction.
1637  */
1638 int isl_basic_map_fast_is_disjoint(struct isl_basic_map *bmap1,
1639         struct isl_basic_map *bmap2)
1640 {
1641         struct isl_vec *v = NULL;
1642         int *elim = NULL;
1643         unsigned total;
1644         int d, i;
1645
1646         if (!bmap1 || !bmap2)
1647                 return -1;
1648         isl_assert(bmap1->ctx, isl_dim_equal(bmap1->dim, bmap2->dim),
1649                         return -1);
1650         if (bmap1->n_div || bmap2->n_div)
1651                 return 0;
1652         if (!bmap1->n_eq && !bmap2->n_eq)
1653                 return 0;
1654
1655         total = isl_dim_total(bmap1->dim);
1656         if (total == 0)
1657                 return 0;
1658         v = isl_vec_alloc(bmap1->ctx, 1 + total);
1659         if (!v)
1660                 goto error;
1661         elim = isl_alloc_array(bmap1->ctx, int, total);
1662         if (!elim)
1663                 goto error;
1664         compute_elimination_index(bmap1, elim);
1665         for (i = 0; i < bmap2->n_eq; ++i) {
1666                 int reduced;
1667                 reduced = reduced_using_equalities(v->block.data, bmap2->eq[i],
1668                                                         bmap1, elim);
1669                 if (reduced && !isl_int_is_zero(v->block.data[0]) &&
1670                     isl_seq_first_non_zero(v->block.data + 1, total) == -1)
1671                         goto disjoint;
1672         }
1673         for (i = 0; i < bmap2->n_ineq; ++i) {
1674                 int reduced;
1675                 reduced = reduced_using_equalities(v->block.data,
1676                                                 bmap2->ineq[i], bmap1, elim);
1677                 if (reduced && isl_int_is_neg(v->block.data[0]) &&
1678                     isl_seq_first_non_zero(v->block.data + 1, total) == -1)
1679                         goto disjoint;
1680         }
1681         compute_elimination_index(bmap2, elim);
1682         for (i = 0; i < bmap1->n_ineq; ++i) {
1683                 int reduced;
1684                 reduced = reduced_using_equalities(v->block.data,
1685                                                 bmap1->ineq[i], bmap2, elim);
1686                 if (reduced && isl_int_is_neg(v->block.data[0]) &&
1687                     isl_seq_first_non_zero(v->block.data + 1, total) == -1)
1688                         goto disjoint;
1689         }
1690         isl_vec_free(bmap1->ctx, v);
1691         free(elim);
1692         return 0;
1693 disjoint:
1694         isl_vec_free(bmap1->ctx, v);
1695         free(elim);
1696         return 1;
1697 error:
1698         isl_vec_free(bmap1->ctx, v);
1699         free(elim);
1700         return -1;
1701 }
1702
1703 int isl_basic_set_fast_is_disjoint(struct isl_basic_set *bset1,
1704         struct isl_basic_set *bset2)
1705 {
1706         return isl_basic_map_fast_is_disjoint((struct isl_basic_map *)bset1,
1707                                               (struct isl_basic_map *)bset2);
1708 }
1709
1710 int isl_map_fast_is_disjoint(struct isl_map *map1, struct isl_map *map2)
1711 {
1712         int i, j;
1713
1714         if (!map1 || !map2)
1715                 return -1;
1716
1717         if (isl_map_fast_is_equal(map1, map2))
1718                 return 0;
1719
1720         for (i = 0; i < map1->n; ++i) {
1721                 for (j = 0; j < map2->n; ++j) {
1722                         int d = isl_basic_map_fast_is_disjoint(map1->p[i],
1723                                                                map2->p[j]);
1724                         if (d != 1)
1725                                 return d;
1726                 }
1727         }
1728         return 1;
1729 }
1730
1731 int isl_set_fast_is_disjoint(struct isl_set *set1, struct isl_set *set2)
1732 {
1733         return isl_map_fast_is_disjoint((struct isl_map *)set1,
1734                                         (struct isl_map *)set2);
1735 }