isl_map.c

   1 #include <string.h>
   2 #include <strings.h>
   3 #include "isl_ctx.h"
   4 #include "isl_blk.h"
   5 #include "isl_dim.h"
   6 #include "isl_equalities.h"
   7 #include "isl_list.h"
   8 #include "isl_lp.h"
   9 #include "isl_seq.h"
  10 #include "isl_set.h"
  11 #include "isl_map.h"
  12 #include "isl_map_private.h"
  13 #include "isl_map_piplib.h"
  14 #include "isl_sample.h"
  15 #include "isl_vec.h"
  16
  17 /* Maps dst positions to src positions */
  18 struct isl_dim_map {
  19         unsigned len;
  20         int pos[1];
  21 };
  22
  23 static struct isl_dim_map *isl_dim_map_alloc(struct isl_ctx *ctx, unsigned len)
  24 {
  25         int i;
  26         struct isl_dim_map *dim_map;
  27         dim_map = isl_alloc(ctx, struct isl_dim_map,
  28                                 sizeof(struct isl_dim_map) + len * sizeof(int));
  29         if (!dim_map)
  30                 return NULL;
  31         dim_map->len = 1 + len;
  32         dim_map->pos[0] = 0;
  33         for (i = 0; i < len; ++i)
  34                 dim_map->pos[1 + i] = -1;
  35         return dim_map;
  36 }
  37
  38 static unsigned n(struct isl_dim *dim, enum isl_dim_type type)
  39 {
  40         switch (type) {
  41         case isl_dim_param:     return dim->nparam;
  42         case isl_dim_in:        return dim->n_in;
  43         case isl_dim_out:       return dim->n_out;
  44         }
  45 }
  46
  47 static unsigned pos(struct isl_dim *dim, enum isl_dim_type type)
  48 {
  49         switch (type) {
  50         case isl_dim_param:     return 1;
  51         case isl_dim_in:        return 1 + dim->nparam;
  52         case isl_dim_out:       return 1 + dim->nparam + dim->n_in;
  53         }
  54 }
  55
  56 static void isl_dim_map_dim(struct isl_dim_map *dim_map, struct isl_dim *dim,
  57                 enum isl_dim_type type, unsigned dst_pos)
  58 {
  59         int i;
  60         unsigned src_pos;
  61
  62         if (!dim_map || !dim)
  63                 return;
  64
  65         src_pos = pos(dim, type);
  66         for (i = 0; i < n(dim, type); ++i)
  67                 dim_map->pos[1 + dst_pos + i] = src_pos + i;
  68 }
  69
  70 static void isl_dim_map_div(struct isl_dim_map *dim_map,
  71                 struct isl_basic_map *bmap, unsigned dst_pos)
  72 {
  73         int i;
  74         unsigned src_pos;
  75
  76         if (!dim_map || !bmap)
  77                 return;
  78
  79         src_pos = 1 + isl_dim_total(bmap->dim);
  80         for (i = 0; i < bmap->n_div; ++i)
  81                 dim_map->pos[1 + dst_pos + i] = src_pos + i;
  82 }
  83
  84 static void isl_dim_map_dump(struct isl_dim_map *dim_map)
  85 {
  86         int i;
  87
  88         for (i = 0; i < dim_map->len; ++i)
  89                 fprintf(stderr, "%d -> %d; ", i, dim_map->pos[i]);
  90         fprintf(stderr, "\n");
  91 }
  92
  93 unsigned isl_basic_set_n_dim(const struct isl_basic_set *bset)
  94 {
  95         return bset->dim->n_out;
  96 }
  97
  98 unsigned isl_basic_set_n_param(const struct isl_basic_set *bset)
  99 {
 100         return bset->dim->nparam;
 101 }
 102
 103 unsigned isl_basic_set_total_dim(const struct isl_basic_set *bset)
 104 {
 105         return isl_dim_total(bset->dim) + bset->n_div;
 106 }
 107
 108 unsigned isl_set_n_dim(const struct isl_set *set)
 109 {
 110         return set->dim->n_out;
 111 }
 112
 113 unsigned isl_set_n_param(const struct isl_set *set)
 114 {
 115         return set->dim->nparam;
 116 }
 117
 118 unsigned isl_basic_map_n_in(const struct isl_basic_map *bmap)
 119 {
 120         return bmap->dim->n_in;
 121 }
 122
 123 unsigned isl_basic_map_n_out(const struct isl_basic_map *bmap)
 124 {
 125         return bmap->dim->n_out;
 126 }
 127
 128 unsigned isl_basic_map_n_param(const struct isl_basic_map *bmap)
 129 {
 130         return bmap->dim->nparam;
 131 }
 132
 133 unsigned isl_basic_map_n_div(const struct isl_basic_map *bmap)
 134 {
 135         return bmap->n_div;
 136 }
 137
 138 unsigned isl_basic_map_total_dim(const struct isl_basic_map *bmap)
 139 {
 140         return isl_dim_total(bmap->dim) + bmap->n_div;
 141 }
 142
 143 unsigned isl_map_n_in(const struct isl_map *map)
 144 {
 145         return map->dim->n_in;
 146 }
 147
 148 unsigned isl_map_n_out(const struct isl_map *map)
 149 {
 150         return map->dim->n_out;
 151 }
 152
 153 unsigned isl_map_n_param(const struct isl_map *map)
 154 {
 155         return map->dim->nparam;
 156 }
 157
 158 int isl_map_compatible_domain(struct isl_map *map, struct isl_set *set)
 159 {
 160         return map->dim->n_in == set->dim->n_out &&
 161                map->dim->nparam == set->dim->nparam;
 162 }
 163
 164 int isl_basic_map_compatible_domain(struct isl_basic_map *bmap,
 165                 struct isl_basic_set *bset)
 166 {
 167         return bmap->dim->n_in == bset->dim->n_out &&
 168                bmap->dim->nparam == bset->dim->nparam;
 169 }
 170
 171 int isl_basic_map_compatible_range(struct isl_basic_map *bmap,
 172                 struct isl_basic_set *bset)
 173 {
 174         return bmap->dim->n_out == bset->dim->n_out &&
 175                bmap->dim->nparam == bset->dim->nparam;
 176 }
 177
 178 static struct isl_basic_map *basic_map_init(struct isl_ctx *ctx,
 179                 struct isl_basic_map *bmap, unsigned extra,
 180                 unsigned n_eq, unsigned n_ineq)
 181 {
 182         int i;
 183         size_t row_size = 1 + isl_dim_total(bmap->dim) + extra;
 184
 185         bmap->block = isl_blk_alloc(ctx, (n_eq + n_ineq) * row_size);
 186         if (isl_blk_is_error(bmap->block)) {
 187                 free(bmap);
 188                 return NULL;
 189         }
 190
 191         bmap->eq = isl_alloc_array(ctx, isl_int *, n_eq + n_ineq);
 192         if (!bmap->eq) {
 193                 isl_blk_free(ctx, bmap->block);
 194                 free(bmap);
 195                 return NULL;
 196         }
 197
 198         if (extra == 0) {
 199                 bmap->block2 = isl_blk_empty();
 200                 bmap->div = NULL;
 201         } else {
 202                 bmap->block2 = isl_blk_alloc(ctx, extra * (1 + row_size));
 203                 if (isl_blk_is_error(bmap->block2)) {
 204                         free(bmap->eq);
 205                         isl_blk_free(ctx, bmap->block);
 206                         free(bmap);
 207                         return NULL;
 208                 }
 209
 210                 bmap->div = isl_alloc_array(ctx, isl_int *, extra);
 211                 if (!bmap->div) {
 212                         isl_blk_free(ctx, bmap->block2);
 213                         free(bmap->eq);
 214                         isl_blk_free(ctx, bmap->block);
 215                         free(bmap);
 216                         return NULL;
 217                 }
 218         }
 219
 220         for (i = 0; i < n_eq + n_ineq; ++i)
 221                 bmap->eq[i] = bmap->block.data + i * row_size;
 222
 223         for (i = 0; i < extra; ++i)
 224                 bmap->div[i] = bmap->block2.data + i * (1 + row_size);
 225
 226         bmap->ctx = ctx;
 227         isl_ctx_ref(ctx);
 228         bmap->ref = 1;
 229         bmap->flags = 0;
 230         bmap->c_size = n_eq + n_ineq;
 231         bmap->ineq = bmap->eq + n_eq;
 232         bmap->extra = extra;
 233         bmap->n_eq = 0;
 234         bmap->n_ineq = 0;
 235         bmap->n_div = 0;
 236         bmap->sample = NULL;
 237
 238         return bmap;
 239 error:
 240         isl_basic_map_free(bmap);
 241         return NULL;
 242 }
 243
 244 struct isl_basic_set *isl_basic_set_alloc(struct isl_ctx *ctx,
 245                 unsigned nparam, unsigned dim, unsigned extra,
 246                 unsigned n_eq, unsigned n_ineq)
 247 {
 248         struct isl_basic_map *bmap;
 249         bmap = isl_basic_map_alloc(ctx, nparam, 0, dim, extra, n_eq, n_ineq);
 250         return (struct isl_basic_set *)bmap;
 251 }
 252
 253 struct isl_basic_set *isl_basic_set_alloc_dim(struct isl_dim *dim,
 254                 unsigned extra, unsigned n_eq, unsigned n_ineq)
 255 {
 256         struct isl_basic_map *bmap;
 257         if (!dim)
 258                 return NULL;
 259         isl_assert(dim->ctx, dim->n_in == 0, return NULL);
 260         bmap = isl_basic_map_alloc_dim(dim, extra, n_eq, n_ineq);
 261         return (struct isl_basic_set *)bmap;
 262 }
 263
 264 struct isl_basic_map *isl_basic_map_alloc_dim(struct isl_dim *dim,
 265                 unsigned extra, unsigned n_eq, unsigned n_ineq)
 266 {
 267         struct isl_basic_map *bmap;
 268
 269         if (!dim)
 270                 return NULL;
 271         bmap = isl_alloc_type(dim->ctx, struct isl_basic_map);
 272         if (!bmap)
 273                 goto error;
 274         bmap->dim = dim;
 275
 276         return basic_map_init(dim->ctx, bmap, extra, n_eq, n_ineq);
 277 error:
 278         isl_dim_free(dim);
 279         return NULL;
 280 }
 281
 282 struct isl_basic_map *isl_basic_map_alloc(struct isl_ctx *ctx,
 283                 unsigned nparam, unsigned in, unsigned out, unsigned extra,
 284                 unsigned n_eq, unsigned n_ineq)
 285 {
 286         struct isl_basic_map *bmap;
 287         struct isl_dim *dim;
 288
 289         dim = isl_dim_alloc(ctx, nparam, in, out);
 290         if (!dim)
 291                 return NULL;
 292
 293         bmap = isl_basic_map_alloc_dim(dim, extra, n_eq, n_ineq);
 294         return bmap;
 295 }
 296
 297 static void dup_constraints(
 298                 struct isl_basic_map *dst, struct isl_basic_map *src)
 299 {
 300         int i;
 301         unsigned total = isl_basic_map_total_dim(src);
 302
 303         for (i = 0; i < src->n_eq; ++i) {
 304                 int j = isl_basic_map_alloc_equality(dst);
 305                 isl_seq_cpy(dst->eq[j], src->eq[i], 1+total);
 306         }
 307
 308         for (i = 0; i < src->n_ineq; ++i) {
 309                 int j = isl_basic_map_alloc_inequality(dst);
 310                 isl_seq_cpy(dst->ineq[j], src->ineq[i], 1+total);
 311         }
 312
 313         for (i = 0; i < src->n_div; ++i) {
 314                 int j = isl_basic_map_alloc_div(dst);
 315                 isl_seq_cpy(dst->div[j], src->div[i], 1+1+total);
 316         }
 317         F_SET(dst, ISL_BASIC_SET_FINAL);
 318 }
 319
 320 struct isl_basic_map *isl_basic_map_dup(struct isl_basic_map *bmap)
 321 {
 322         struct isl_basic_map *dup;
 323
 324         if (!bmap)
 325                 return NULL;
 326         dup = isl_basic_map_alloc_dim(isl_dim_copy(bmap->dim),
 327                         bmap->n_div, bmap->n_eq, bmap->n_ineq);
 328         if (!dup)
 329                 return NULL;
 330         dup->flags = bmap->flags;
 331         dup_constraints(dup, bmap);
 332         dup->sample = isl_vec_copy(bmap->ctx, bmap->sample);
 333         return dup;
 334 }
 335
 336 struct isl_basic_set *isl_basic_set_dup(struct isl_basic_set *bset)
 337 {
 338         struct isl_basic_map *dup;
 339
 340         dup = isl_basic_map_dup((struct isl_basic_map *)bset);
 341         return (struct isl_basic_set *)dup;
 342 }
 343
 344 struct isl_basic_set *isl_basic_set_copy(struct isl_basic_set *bset)
 345 {
 346         if (!bset)
 347                 return NULL;
 348
 349         if (F_ISSET(bset, ISL_BASIC_SET_FINAL)) {
 350                 bset->ref++;
 351                 return bset;
 352         }
 353         return isl_basic_set_dup(bset);
 354 }
 355
 356 struct isl_set *isl_set_copy(struct isl_set *set)
 357 {
 358         if (!set)
 359                 return NULL;
 360
 361         set->ref++;
 362         return set;
 363 }
 364
 365 struct isl_basic_map *isl_basic_map_copy(struct isl_basic_map *bmap)
 366 {
 367         if (!bmap)
 368                 return NULL;
 369
 370         if (F_ISSET(bmap, ISL_BASIC_SET_FINAL)) {
 371                 bmap->ref++;
 372                 return bmap;
 373         }
 374         return isl_basic_map_dup(bmap);
 375 }
 376
 377 struct isl_map *isl_map_copy(struct isl_map *map)
 378 {
 379         if (!map)
 380                 return NULL;
 381
 382         map->ref++;
 383         return map;
 384 }
 385
 386 void isl_basic_map_free(struct isl_basic_map *bmap)
 387 {
 388         if (!bmap)
 389                 return;
 390
 391         if (--bmap->ref > 0)
 392                 return;
 393
 394         isl_ctx_deref(bmap->ctx);
 395         free(bmap->div);
 396         isl_blk_free(bmap->ctx, bmap->block2);
 397         free(bmap->eq);
 398         isl_blk_free(bmap->ctx, bmap->block);
 399         isl_vec_free(bmap->ctx, bmap->sample);
 400         isl_dim_free(bmap->dim);
 401         free(bmap);
 402 }
 403
 404 void isl_basic_set_free(struct isl_basic_set *bset)
 405 {
 406         isl_basic_map_free((struct isl_basic_map *)bset);
 407 }
 408
 409 int isl_basic_map_alloc_equality(struct isl_basic_map *bmap)
 410 {
 411         struct isl_ctx *ctx;
 412         if (!bmap)
 413                 return -1;
 414         ctx = bmap->ctx;
 415         isl_assert(ctx, bmap->n_eq + bmap->n_ineq < bmap->c_size, return -1);
 416         isl_assert(ctx, bmap->eq + bmap->n_eq <= bmap->ineq, return -1);
 417         if (bmap->eq + bmap->n_eq == bmap->ineq) {
 418                 isl_int *t;
 419                 int j = isl_basic_map_alloc_inequality(bmap);
 420                 if (j < 0)
 421                         return -1;
 422                 t = bmap->ineq[0];
 423                 bmap->ineq[0] = bmap->ineq[j];
 424                 bmap->ineq[j] = t;
 425                 bmap->n_ineq--;
 426                 bmap->ineq++;
 427         } else
 428                 isl_seq_clr(bmap->eq[bmap->n_eq] +
 429                       1 + isl_basic_map_total_dim(bmap),
 430                       bmap->extra - bmap->n_div);
 431         return bmap->n_eq++;
 432 }
 433
 434 int isl_basic_set_alloc_equality(struct isl_basic_set *bset)
 435 {
 436         return isl_basic_map_alloc_equality((struct isl_basic_map *)bset);
 437 }
 438
 439 int isl_basic_map_free_equality(struct isl_basic_map *bmap, unsigned n)
 440 {
 441         if (!bmap)
 442                 return -1;
 443         isl_assert(bmap->ctx, n <= bmap->n_eq, return -1);
 444         bmap->n_eq -= n;
 445         return 0;
 446 }
 447
 448 int isl_basic_map_drop_equality(struct isl_basic_map *bmap, unsigned pos)
 449 {
 450         isl_int *t;
 451         if (!bmap)
 452                 return -1;
 453         isl_assert(bmap->ctx, pos < bmap->n_eq, return -1);
 454
 455         if (pos != bmap->n_eq - 1) {
 456                 t = bmap->eq[pos];
 457                 bmap->eq[pos] = bmap->eq[bmap->n_eq - 1];
 458                 bmap->eq[bmap->n_eq - 1] = t;
 459         }
 460         bmap->n_eq--;
 461         return 0;
 462 }
 463
 464 int isl_basic_set_drop_equality(struct isl_basic_set *bset, unsigned pos)
 465 {
 466         return isl_basic_map_drop_equality((struct isl_basic_map *)bset, pos);
 467 }
 468
 469 void isl_basic_map_inequality_to_equality(
 470                 struct isl_basic_map *bmap, unsigned pos)
 471 {
 472         isl_int *t;
 473
 474         t = bmap->ineq[pos];
 475         bmap->ineq[pos] = bmap->ineq[0];
 476         bmap->ineq[0] = bmap->eq[bmap->n_eq];
 477         bmap->eq[bmap->n_eq] = t;
 478         bmap->n_eq++;
 479         bmap->n_ineq--;
 480         bmap->ineq++;
 481         F_CLR(bmap, ISL_BASIC_MAP_NORMALIZED);
 482 }
 483
 484 int isl_basic_map_alloc_inequality(struct isl_basic_map *bmap)
 485 {
 486         struct isl_ctx *ctx;
 487         if (!bmap)
 488                 return -1;
 489         ctx = bmap->ctx;
 490         isl_assert(ctx, (bmap->ineq - bmap->eq) + bmap->n_ineq < bmap->c_size,
 491                         return -1);
 492         F_CLR(bmap, ISL_BASIC_MAP_NO_IMPLICIT);
 493         F_CLR(bmap, ISL_BASIC_MAP_NO_REDUNDANT);
 494         F_CLR(bmap, ISL_BASIC_MAP_NORMALIZED);
 495         isl_seq_clr(bmap->ineq[bmap->n_ineq] +
 496                       1 + isl_basic_map_total_dim(bmap),
 497                       bmap->extra - bmap->n_div);
 498         return bmap->n_ineq++;
 499 }
 500
 501 int isl_basic_set_alloc_inequality(struct isl_basic_set *bset)
 502 {
 503         return isl_basic_map_alloc_inequality((struct isl_basic_map *)bset);
 504 }
 505
 506 int isl_basic_map_free_inequality(struct isl_basic_map *bmap, unsigned n)
 507 {
 508         if (!bmap)
 509                 return -1;
 510         isl_assert(bmap->ctx, n <= bmap->n_ineq, return -1);
 511         bmap->n_ineq -= n;
 512         return 0;
 513 }
 514
 515 int isl_basic_set_free_inequality(struct isl_basic_set *bset, unsigned n)
 516 {
 517         return isl_basic_map_free_inequality((struct isl_basic_map *)bset, n);
 518 }
 519
 520 int isl_basic_map_drop_inequality(struct isl_basic_map *bmap, unsigned pos)
 521 {
 522         isl_int *t;
 523         if (!bmap)
 524                 return -1;
 525         isl_assert(bmap->ctx, pos < bmap->n_ineq, return -1);
 526
 527         if (pos != bmap->n_ineq - 1) {
 528                 t = bmap->ineq[pos];
 529                 bmap->ineq[pos] = bmap->ineq[bmap->n_ineq - 1];
 530                 bmap->ineq[bmap->n_ineq - 1] = t;
 531                 F_CLR(bmap, ISL_BASIC_MAP_NORMALIZED);
 532         }
 533         bmap->n_ineq--;
 534         return 0;
 535 }
 536
 537 int isl_basic_set_drop_inequality(struct isl_basic_set *bset, unsigned pos)
 538 {
 539         return isl_basic_map_drop_inequality((struct isl_basic_map *)bset, pos);
 540 }
 541
 542 int isl_basic_map_alloc_div(struct isl_basic_map *bmap)
 543 {
 544         if (!bmap)
 545                 return -1;
 546         isl_assert(bmap->ctx, bmap->n_div < bmap->extra, return -1);
 547         isl_seq_clr(bmap->div[bmap->n_div] +
 548                       1 + 1 + isl_basic_map_total_dim(bmap),
 549                       bmap->extra - bmap->n_div);
 550         return bmap->n_div++;
 551 }
 552
 553 int isl_basic_map_free_div(struct isl_basic_map *bmap, unsigned n)
 554 {
 555         if (!bmap)
 556                 return -1;
 557         isl_assert(bmap->ctx, n <= bmap->n_div, return -1);
 558         bmap->n_div -= n;
 559         return 0;
 560 }
 561
 562 /* Copy constraint from src to dst, putting the vars of src at offset
 563  * dim_off in dst and the divs of src at offset div_off in dst.
 564  * If both sets are actually map, then dim_off applies to the input
 565  * variables.
 566  */
 567 static void copy_constraint(struct isl_basic_map *dst_map, isl_int *dst,
 568                             struct isl_basic_map *src_map, isl_int *src,
 569                             unsigned in_off, unsigned out_off, unsigned div_off)
 570 {
 571         unsigned src_nparam = isl_basic_map_n_param(src_map);
 572         unsigned dst_nparam = isl_basic_map_n_param(dst_map);
 573         unsigned src_in = isl_basic_map_n_in(src_map);
 574         unsigned dst_in = isl_basic_map_n_in(dst_map);
 575         unsigned src_out = isl_basic_map_n_out(src_map);
 576         unsigned dst_out = isl_basic_map_n_out(dst_map);
 577         isl_int_set(dst[0], src[0]);
 578         isl_seq_cpy(dst+1, src+1, isl_min(dst_nparam, src_nparam));
 579         if (dst_nparam > src_nparam)
 580                 isl_seq_clr(dst+1+src_nparam,
 581                                 dst_nparam - src_nparam);
 582         isl_seq_clr(dst+1+dst_nparam, in_off);
 583         isl_seq_cpy(dst+1+dst_nparam+in_off,
 584                     src+1+src_nparam,
 585                     isl_min(dst_in-in_off, src_in));
 586         if (dst_in-in_off > src_in)
 587                 isl_seq_clr(dst+1+dst_nparam+in_off+src_in,
 588                                 dst_in - in_off - src_in);
 589         isl_seq_clr(dst+1+dst_nparam+dst_in, out_off);
 590         isl_seq_cpy(dst+1+dst_nparam+dst_in+out_off,
 591                     src+1+src_nparam+src_in,
 592                     isl_min(dst_out-out_off, src_out));
 593         if (dst_out-out_off > src_out)
 594                 isl_seq_clr(dst+1+dst_nparam+dst_in+out_off+src_out,
 595                                 dst_out - out_off - src_out);
 596         isl_seq_clr(dst+1+dst_nparam+dst_in+dst_out, div_off);
 597         isl_seq_cpy(dst+1+dst_nparam+dst_in+dst_out+div_off,
 598                     src+1+src_nparam+src_in+src_out,
 599                     isl_min(dst_map->extra-div_off, src_map->n_div));
 600         if (dst_map->n_div-div_off > src_map->n_div)
 601                 isl_seq_clr(dst+1+dst_nparam+dst_in+dst_out+
 602                                 div_off+src_map->n_div,
 603                                 dst_map->n_div - div_off - src_map->n_div);
 604 }
 605
 606 static void copy_div(struct isl_basic_map *dst_map, isl_int *dst,
 607                      struct isl_basic_map *src_map, isl_int *src,
 608                      unsigned in_off, unsigned out_off, unsigned div_off)
 609 {
 610         isl_int_set(dst[0], src[0]);
 611         copy_constraint(dst_map, dst+1, src_map, src+1, in_off, out_off, div_off);
 612 }
 613
 614 static struct isl_basic_map *add_constraints(struct isl_basic_map *bmap1,
 615                 struct isl_basic_map *bmap2, unsigned i_pos, unsigned o_pos)
 616 {
 617         int i;
 618         unsigned div_off;
 619
 620         if (!bmap1 || !bmap2)
 621                 goto error;
 622
 623         div_off = bmap1->n_div;
 624
 625         for (i = 0; i < bmap2->n_eq; ++i) {
 626                 int i1 = isl_basic_map_alloc_equality(bmap1);
 627                 if (i1 < 0)
 628                         goto error;
 629                 copy_constraint(bmap1, bmap1->eq[i1], bmap2, bmap2->eq[i],
 630                                 i_pos, o_pos, div_off);
 631         }
 632
 633         for (i = 0; i < bmap2->n_ineq; ++i) {
 634                 int i1 = isl_basic_map_alloc_inequality(bmap1);
 635                 if (i1 < 0)
 636                         goto error;
 637                 copy_constraint(bmap1, bmap1->ineq[i1], bmap2, bmap2->ineq[i],
 638                                 i_pos, o_pos, div_off);
 639         }
 640
 641         for (i = 0; i < bmap2->n_div; ++i) {
 642                 int i1 = isl_basic_map_alloc_div(bmap1);
 643                 if (i1 < 0)
 644                         goto error;
 645                 copy_div(bmap1, bmap1->div[i1], bmap2, bmap2->div[i],
 646                          i_pos, o_pos, div_off);
 647         }
 648
 649         isl_basic_map_free(bmap2);
 650
 651         return bmap1;
 652
 653 error:
 654         isl_basic_map_free(bmap1);
 655         isl_basic_map_free(bmap2);
 656         return NULL;
 657 }
 658
 659 static void copy_constraint_dim_map(isl_int *dst, isl_int *src,
 660                                         struct isl_dim_map *dim_map)
 661 {
 662         int i;
 663
 664         for (i = 0; i < dim_map->len; ++i) {
 665                 if (dim_map->pos[i] < 0)
 666                         isl_int_set_si(dst[i], 0);
 667                 else
 668                         isl_int_set(dst[i], src[dim_map->pos[i]]);
 669         }
 670 }
 671
 672 static void copy_div_dim_map(isl_int *dst, isl_int *src,
 673                                         struct isl_dim_map *dim_map)
 674 {
 675         isl_int_set(dst[0], src[0]);
 676         copy_constraint_dim_map(dst+1, src+1, dim_map);
 677 }
 678
 679 static struct isl_basic_map *add_constraints_dim_map(struct isl_basic_map *dst,
 680                 struct isl_basic_map *src, struct isl_dim_map *dim_map)
 681 {
 682         int i;
 683
 684         if (!src || !dst || !dim_map)
 685                 goto error;
 686
 687         for (i = 0; i < src->n_eq; ++i) {
 688                 int i1 = isl_basic_map_alloc_equality(dst);
 689                 if (i1 < 0)
 690                         goto error;
 691                 copy_constraint_dim_map(dst->eq[i1], src->eq[i], dim_map);
 692         }
 693
 694         for (i = 0; i < src->n_ineq; ++i) {
 695                 int i1 = isl_basic_map_alloc_inequality(dst);
 696                 if (i1 < 0)
 697                         goto error;
 698                 copy_constraint_dim_map(dst->ineq[i1], src->ineq[i], dim_map);
 699         }
 700
 701         for (i = 0; i < src->n_div; ++i) {
 702                 int i1 = isl_basic_map_alloc_div(dst);
 703                 if (i1 < 0)
 704                         goto error;
 705                 copy_div_dim_map(dst->div[i1], src->div[i], dim_map);
 706         }
 707
 708         free(dim_map);
 709         isl_basic_map_free(src);
 710
 711         return dst;
 712 error:
 713         free(dim_map);
 714         isl_basic_map_free(src);
 715         isl_basic_map_free(dst);
 716         return NULL;
 717 }
 718
 719 static struct isl_basic_set *set_add_constraints(struct isl_basic_set *bset1,
 720                 struct isl_basic_set *bset2, unsigned pos)
 721 {
 722         return (struct isl_basic_set *)
 723                 add_constraints((struct isl_basic_map *)bset1,
 724                                 (struct isl_basic_map *)bset2, 0, pos);
 725 }
 726
 727 struct isl_basic_map *isl_basic_map_extend_dim(struct isl_basic_map *base,
 728                 struct isl_dim *dim, unsigned extra,
 729                 unsigned n_eq, unsigned n_ineq)
 730 {
 731         struct isl_basic_map *ext;
 732         unsigned flags;
 733         int dims_ok;
 734
 735         if (!dim)
 736                 goto error;
 737
 738         base = isl_basic_map_cow(base);
 739         if (!base)
 740                 goto error;
 741
 742         dims_ok = isl_dim_equal(base->dim, dim) &&
 743                   base->extra >= base->n_div + extra;
 744
 745         if (dims_ok && n_eq == 0 && n_ineq == 0) {
 746                 isl_dim_free(dim);
 747                 return base;
 748         }
 749
 750         isl_assert(base->ctx, base->dim->nparam <= dim->nparam, goto error);
 751         isl_assert(base->ctx, base->dim->n_in <= dim->n_in, goto error);
 752         isl_assert(base->ctx, base->dim->n_out <= dim->n_out, goto error);
 753         extra += base->extra;
 754         n_eq += base->n_eq;
 755         n_ineq += base->n_ineq;
 756
 757         ext = isl_basic_map_alloc_dim(dim, extra, n_eq, n_ineq);
 758         dim = NULL;
 759         if (!ext)
 760                 goto error;
 761
 762         flags = base->flags;
 763         ext = add_constraints(ext, base, 0, 0);
 764         if (ext) {
 765                 ext->flags = flags;
 766                 F_CLR(ext, ISL_BASIC_SET_FINAL);
 767         }
 768
 769         return ext;
 770
 771 error:
 772         isl_dim_free(dim);
 773         isl_basic_map_free(base);
 774         return NULL;
 775 }
 776
 777 struct isl_basic_map *isl_basic_map_extend_constraints(
 778                 struct isl_basic_map *base, unsigned n_eq, unsigned n_ineq)
 779 {
 780         if (!base)
 781                 return NULL;
 782         return isl_basic_map_extend_dim(base, isl_dim_copy(base->dim),
 783                                         0, n_eq, n_ineq);
 784 }
 785
 786 struct isl_basic_map *isl_basic_map_extend(struct isl_basic_map *base,
 787                 unsigned nparam, unsigned n_in, unsigned n_out, unsigned extra,
 788                 unsigned n_eq, unsigned n_ineq)
 789 {
 790         struct isl_basic_map *bmap;
 791         struct isl_dim *dim;
 792
 793         if (!base)
 794                 return NULL;
 795         dim = isl_dim_alloc(base->ctx, nparam, n_in, n_out);
 796         if (!dim)
 797                 return NULL;
 798
 799         bmap = isl_basic_map_extend_dim(base, dim, extra, n_eq, n_ineq);
 800         return bmap;
 801 }
 802
 803 struct isl_basic_set *isl_basic_set_extend(struct isl_basic_set *base,
 804                 unsigned nparam, unsigned dim, unsigned extra,
 805                 unsigned n_eq, unsigned n_ineq)
 806 {
 807         return (struct isl_basic_set *)
 808                 isl_basic_map_extend((struct isl_basic_map *)base,
 809                                         nparam, 0, dim, extra, n_eq, n_ineq);
 810 }
 811
 812 struct isl_basic_set *isl_basic_set_extend_constraints(
 813                 struct isl_basic_set *base, unsigned n_eq, unsigned n_ineq)
 814 {
 815         return (struct isl_basic_set *)
 816                 isl_basic_map_extend_constraints((struct isl_basic_map *)base,
 817                                                     n_eq, n_ineq);
 818 }
 819
 820 struct isl_basic_set *isl_basic_set_cow(struct isl_basic_set *bset)
 821 {
 822         return (struct isl_basic_set *)
 823                 isl_basic_map_cow((struct isl_basic_map *)bset);
 824 }
 825
 826 struct isl_basic_map *isl_basic_map_cow(struct isl_basic_map *bmap)
 827 {
 828         if (!bmap)
 829                 return NULL;
 830
 831         if (bmap->ref > 1) {
 832                 bmap->ref--;
 833                 bmap = isl_basic_map_dup(bmap);
 834         }
 835         F_CLR(bmap, ISL_BASIC_SET_FINAL);
 836         return bmap;
 837 }
 838
 839 struct isl_set *isl_set_cow(struct isl_set *set)
 840 {
 841         if (!set)
 842                 return NULL;
 843
 844         if (set->ref == 1)
 845                 return set;
 846         set->ref--;
 847         return isl_set_dup(set);
 848 }
 849
 850 struct isl_map *isl_map_cow(struct isl_map *map)
 851 {
 852         if (!map)
 853                 return NULL;
 854
 855         if (map->ref == 1)
 856                 return map;
 857         map->ref--;
 858         return isl_map_dup(map);
 859 }
 860
 861 static void swap_vars(struct isl_blk blk, isl_int *a,
 862                         unsigned a_len, unsigned b_len)
 863 {
 864         isl_seq_cpy(blk.data, a+a_len, b_len);
 865         isl_seq_cpy(blk.data+b_len, a, a_len);
 866         isl_seq_cpy(a, blk.data, b_len+a_len);
 867 }
 868
 869 struct isl_basic_set *isl_basic_set_swap_vars(
 870                 struct isl_basic_set *bset, unsigned n)
 871 {
 872         int i;
 873         struct isl_blk blk;
 874         unsigned dim;
 875         unsigned nparam;
 876
 877         if (!bset)
 878                 goto error;
 879
 880         nparam = isl_basic_set_n_param(bset);
 881         dim = isl_basic_set_n_dim(bset);
 882         isl_assert(bset->ctx, n <= dim, goto error);
 883
 884         if (n == dim)
 885                 return bset;
 886
 887         bset = isl_basic_set_cow(bset);
 888         if (!bset)
 889                 return NULL;
 890
 891         blk = isl_blk_alloc(bset->ctx, dim);
 892         if (isl_blk_is_error(blk))
 893                 goto error;
 894
 895         for (i = 0; i < bset->n_eq; ++i)
 896                 swap_vars(blk,
 897                           bset->eq[i]+1+nparam, n, dim - n);
 898
 899         for (i = 0; i < bset->n_ineq; ++i)
 900                 swap_vars(blk,
 901                           bset->ineq[i]+1+nparam, n, dim - n);
 902
 903         for (i = 0; i < bset->n_div; ++i)
 904                 swap_vars(blk,
 905                           bset->div[i]+1+1+nparam, n, dim - n);
 906
 907         isl_blk_free(bset->ctx, blk);
 908
 909         F_CLR(bset, ISL_BASIC_SET_NORMALIZED);
 910         return bset;
 911
 912 error:
 913         isl_basic_set_free(bset);
 914         return NULL;
 915 }
 916
 917 struct isl_set *isl_set_swap_vars(struct isl_set *set, unsigned n)
 918 {
 919         int i;
 920         set = isl_set_cow(set);
 921         if (!set)
 922                 return NULL;
 923
 924         for (i = 0; i < set->n; ++i) {
 925                 set->p[i] = isl_basic_set_swap_vars(set->p[i], n);
 926                 if (!set->p[i]) {
 927                         isl_set_free(set);
 928                         return NULL;
 929                 }
 930         }
 931         F_CLR(set, ISL_SET_NORMALIZED);
 932         return set;
 933 }
 934
 935 static void constraint_drop_vars(isl_int *c, unsigned n, unsigned rem)
 936 {
 937         isl_seq_cpy(c, c + n, rem);
 938         isl_seq_clr(c + rem, n);
 939 }
 940
 941 /* Drop n dimensions starting at first.
 942  *
 943  * In principle, this frees up some extra variables as the number
 944  * of columns remains constant, but we would have to extend
 945  * the div array too as the number of rows in this array is assumed
 946  * to be equal to extra.
 947  */
 948 struct isl_basic_set *isl_basic_set_drop_dims(
 949                 struct isl_basic_set *bset, unsigned first, unsigned n)
 950 {
 951         int i;
 952
 953         if (!bset)
 954                 goto error;
 955
 956         isl_assert(bset->ctx, first + n <= bset->dim->n_out, goto error);
 957
 958         if (n == 0)
 959                 return bset;
 960
 961         bset = isl_basic_set_cow(bset);
 962         if (!bset)
 963                 return NULL;
 964
 965         for (i = 0; i < bset->n_eq; ++i)
 966                 constraint_drop_vars(bset->eq[i]+1+bset->dim->nparam+first, n,
 967                                      (bset->dim->n_out-first-n)+bset->extra);
 968
 969         for (i = 0; i < bset->n_ineq; ++i)
 970                 constraint_drop_vars(bset->ineq[i]+1+bset->dim->nparam+first, n,
 971                                      (bset->dim->n_out-first-n)+bset->extra);
 972
 973         for (i = 0; i < bset->n_div; ++i)
 974                 constraint_drop_vars(bset->div[i]+1+1+bset->dim->nparam+first, n,
 975                                      (bset->dim->n_out-first-n)+bset->extra);
 976
 977         bset->dim = isl_dim_drop_outputs(bset->dim, first, n);
 978         if (!bset->dim)
 979                 goto error;
 980
 981         F_CLR(bset, ISL_BASIC_SET_NORMALIZED);
 982         bset = isl_basic_set_simplify(bset);
 983         return isl_basic_set_finalize(bset);
 984 error:
 985         isl_basic_set_free(bset);
 986         return NULL;
 987 }
 988
 989 static struct isl_set *isl_set_drop_dims(
 990                 struct isl_set *set, unsigned first, unsigned n)
 991 {
 992         int i;
 993
 994         if (!set)
 995                 goto error;
 996
 997         isl_assert(set->ctx, first + n <= set->dim->n_out, goto error);
 998
 999         if (n == 0)
1000                 return set;
1001         set = isl_set_cow(set);
1002         if (!set)
1003                 goto error;
1004         set->dim = isl_dim_drop_outputs(set->dim, first, n);
1005         if (!set->dim)
1006                 goto error;
1007
1008         for (i = 0; i < set->n; ++i) {
1009                 set->p[i] = isl_basic_set_drop_dims(set->p[i], first, n);
1010                 if (!set->p[i])
1011                         goto error;
1012         }
1013
1014         F_CLR(set, ISL_SET_NORMALIZED);
1015         return set;
1016 error:
1017         isl_set_free(set);
1018         return NULL;
1019 }
1020
1021 /* Drop n input dimensions starting at first.
1022  *
1023  * In principle, this frees up some extra variables as the number
1024  * of columns remains constant, but we would have to extend
1025  * the div array too as the number of rows in this array is assumed
1026  * to be equal to extra.
1027  */
1028 struct isl_basic_map *isl_basic_map_drop_inputs(
1029                 struct isl_basic_map *bmap, unsigned first, unsigned n)
1030 {
1031         int i;
1032         unsigned nparam;
1033         unsigned n_in;
1034         unsigned n_out;
1035
1036         if (!bmap)
1037                 goto error;
1038
1039         nparam = isl_basic_map_n_param(bmap);
1040         n_in = isl_basic_map_n_in(bmap);
1041         n_out = isl_basic_map_n_out(bmap);
1042         isl_assert(bmap->ctx, first + n <= n_in, goto error);
1043
1044         if (n == 0)
1045                 return bmap;
1046
1047         bmap = isl_basic_map_cow(bmap);
1048         if (!bmap)
1049                 return NULL;
1050
1051         for (i = 0; i < bmap->n_eq; ++i)
1052                 constraint_drop_vars(bmap->eq[i]+1+nparam+first, n,
1053                                  (n_in-first-n)+n_out+bmap->extra);
1054
1055         for (i = 0; i < bmap->n_ineq; ++i)
1056                 constraint_drop_vars(bmap->ineq[i]+1+nparam+first, n,
1057                                  (n_in-first-n)+n_out+bmap->extra);
1058
1059         for (i = 0; i < bmap->n_div; ++i)
1060                 constraint_drop_vars(bmap->div[i]+1+1+nparam+first, n,
1061                                  (n_in-first-n)+n_out+bmap->extra);
1062
1063         bmap->dim = isl_dim_drop_inputs(bmap->dim, first, n);
1064         if (!bmap->dim)
1065                 goto error;
1066
1067         F_CLR(bmap, ISL_BASIC_MAP_NORMALIZED);
1068         bmap = isl_basic_map_simplify(bmap);
1069         return isl_basic_map_finalize(bmap);
1070 error:
1071         isl_basic_map_free(bmap);
1072         return NULL;
1073 }
1074
1075 static struct isl_map *isl_map_drop_inputs(
1076                 struct isl_map *map, unsigned first, unsigned n)
1077 {
1078         int i;
1079
1080         if (!map)
1081                 goto error;
1082
1083         isl_assert(map->ctx, first + n <= map->dim->n_in, goto error);
1084
1085         if (n == 0)
1086                 return map;
1087         map = isl_map_cow(map);
1088         if (!map)
1089                 goto error;
1090         map->dim = isl_dim_drop_inputs(map->dim, first, n);
1091         if (!map->dim)
1092                 goto error;
1093
1094         for (i = 0; i < map->n; ++i) {
1095                 map->p[i] = isl_basic_map_drop_inputs(map->p[i], first, n);
1096                 if (!map->p[i])
1097                         goto error;
1098         }
1099         F_CLR(map, ISL_MAP_NORMALIZED);
1100
1101         return map;
1102 error:
1103         isl_map_free(map);
1104         return NULL;
1105 }
1106
1107 /*
1108  * We don't cow, as the div is assumed to be redundant.
1109  */
1110 static struct isl_basic_map *isl_basic_map_drop_div(
1111                 struct isl_basic_map *bmap, unsigned div)
1112 {
1113         int i;
1114         unsigned pos;
1115
1116         if (!bmap)
1117                 goto error;
1118
1119         pos = 1 + isl_dim_total(bmap->dim) + div;
1120
1121         isl_assert(bmap->ctx, div < bmap->n_div, goto error);
1122
1123         for (i = 0; i < bmap->n_eq; ++i)
1124                 constraint_drop_vars(bmap->eq[i]+pos, 1, bmap->extra-div-1);
1125
1126         for (i = 0; i < bmap->n_ineq; ++i) {
1127                 if (!isl_int_is_zero(bmap->ineq[i][pos])) {
1128                         isl_basic_map_drop_inequality(bmap, i);
1129                         --i;
1130                         continue;
1131                 }
1132                 constraint_drop_vars(bmap->ineq[i]+pos, 1, bmap->extra-div-1);
1133         }
1134
1135         for (i = 0; i < bmap->n_div; ++i)
1136                 constraint_drop_vars(bmap->div[i]+1+pos, 1, bmap->extra-div-1);
1137
1138         if (div != bmap->n_div - 1) {
1139                 int j;
1140                 isl_int *t = bmap->div[div];
1141
1142                 for (j = div; j < bmap->n_div - 1; ++j)
1143                         bmap->div[j] = bmap->div[j+1];
1144
1145                 bmap->div[bmap->n_div - 1] = t;
1146         }
1147         F_CLR(bmap, ISL_BASIC_MAP_NORMALIZED);
1148         isl_basic_map_free_div(bmap, 1);
1149
1150         return bmap;
1151 error:
1152         isl_basic_map_free(bmap);
1153         return NULL;
1154 }
1155
1156 static void eliminate_div(struct isl_basic_map *bmap, isl_int *eq, unsigned div)
1157 {
1158         int i;
1159         unsigned pos = 1 + isl_dim_total(bmap->dim) + div;
1160         unsigned len;
1161         len = 1 + isl_basic_map_total_dim(bmap);
1162
1163         for (i = 0; i < bmap->n_eq; ++i)
1164                 if (bmap->eq[i] != eq)
1165                         isl_seq_elim(bmap->eq[i], eq, pos, len, NULL);
1166
1167         for (i = 0; i < bmap->n_ineq; ++i)
1168                 isl_seq_elim(bmap->ineq[i], eq, pos, len, NULL);
1169
1170         /* We need to be careful about circular definitions,
1171          * so for now we just remove the definitions of other divs that
1172          * depend on this div and (possibly) recompute them later.
1173          */
1174         for (i = 0; i < bmap->n_div; ++i)
1175                 if (!isl_int_is_zero(bmap->div[i][0]) &&
1176                     !isl_int_is_zero(bmap->div[i][1 + pos]))
1177                         isl_seq_clr(bmap->div[i], 1 + len);
1178
1179         isl_basic_map_drop_div(bmap, div);
1180 }
1181
1182 struct isl_basic_map *isl_basic_map_set_to_empty(struct isl_basic_map *bmap)
1183 {
1184         int i = 0;
1185         unsigned total;
1186         if (!bmap)
1187                 goto error;
1188         total = isl_basic_map_total_dim(bmap);
1189         isl_basic_map_free_div(bmap, bmap->n_div);
1190         isl_basic_map_free_inequality(bmap, bmap->n_ineq);
1191         if (bmap->n_eq > 0)
1192                 isl_basic_map_free_equality(bmap, bmap->n_eq-1);
1193         else {
1194                 isl_basic_map_alloc_equality(bmap);
1195                 if (i < 0)
1196                         goto error;
1197         }
1198         isl_int_set_si(bmap->eq[i][0], 1);
1199         isl_seq_clr(bmap->eq[i]+1, total);
1200         F_SET(bmap, ISL_BASIC_MAP_EMPTY);
1201         return isl_basic_map_finalize(bmap);
1202 error:
1203         isl_basic_map_free(bmap);
1204         return NULL;
1205 }
1206
1207 struct isl_basic_set *isl_basic_set_set_to_empty(struct isl_basic_set *bset)
1208 {
1209         return (struct isl_basic_set *)
1210                 isl_basic_map_set_to_empty((struct isl_basic_map *)bset);
1211 }
1212
1213 static void swap_equality(struct isl_basic_map *bmap, int a, int b)
1214 {
1215         isl_int *t = bmap->eq[a];
1216         bmap->eq[a] = bmap->eq[b];
1217         bmap->eq[b] = t;
1218 }
1219
1220 static void swap_inequality(struct isl_basic_map *bmap, int a, int b)
1221 {
1222         if (a != b) {
1223                 isl_int *t = bmap->ineq[a];
1224                 bmap->ineq[a] = bmap->ineq[b];
1225                 bmap->ineq[b] = t;
1226         }
1227 }
1228
1229 static void set_swap_inequality(struct isl_basic_set *bset, int a, int b)
1230 {
1231         swap_inequality((struct isl_basic_map *)bset, a, b);
1232 }
1233
1234 static void swap_div(struct isl_basic_map *bmap, int a, int b)
1235 {
1236         int i;
1237         unsigned off = isl_dim_total(bmap->dim);
1238         isl_int *t = bmap->div[a];
1239         bmap->div[a] = bmap->div[b];
1240         bmap->div[b] = t;
1241
1242         for (i = 0; i < bmap->n_eq; ++i)
1243                 isl_int_swap(bmap->eq[i][1+off+a], bmap->eq[i][1+off+b]);
1244
1245         for (i = 0; i < bmap->n_ineq; ++i)
1246                 isl_int_swap(bmap->ineq[i][1+off+a], bmap->ineq[i][1+off+b]);
1247
1248         for (i = 0; i < bmap->n_div; ++i)
1249                 isl_int_swap(bmap->div[i][1+1+off+a], bmap->div[i][1+1+off+b]);
1250         F_CLR(bmap, ISL_BASIC_MAP_NORMALIZED);
1251 }
1252
1253 static void eliminate_var_using_equality(struct isl_basic_map *bmap,
1254         unsigned pos, isl_int *eq, int *progress)
1255 {
1256         unsigned total;
1257         int k;
1258
1259         total = isl_basic_map_total_dim(bmap);
1260         for (k = 0; k < bmap->n_eq; ++k) {
1261                 if (bmap->eq[k] == eq)
1262                         continue;
1263                 if (isl_int_is_zero(bmap->eq[k][1+pos]))
1264                         continue;
1265                 if (progress)
1266                         *progress = 1;
1267                 isl_seq_elim(bmap->eq[k], eq, 1+pos, 1+total, NULL);
1268         }
1269
1270         for (k = 0; k < bmap->n_ineq; ++k) {
1271                 if (isl_int_is_zero(bmap->ineq[k][1+pos]))
1272                         continue;
1273                 if (progress)
1274                         *progress = 1;
1275                 isl_seq_elim(bmap->ineq[k], eq, 1+pos, 1+total, NULL);
1276                 F_CLR(bmap, ISL_BASIC_MAP_NORMALIZED);
1277         }
1278
1279         for (k = 0; k < bmap->n_div; ++k) {
1280                 if (isl_int_is_zero(bmap->div[k][0]))
1281                         continue;
1282                 if (isl_int_is_zero(bmap->div[k][1+1+pos]))
1283                         continue;
1284                 if (progress)
1285                         *progress = 1;
1286                 isl_seq_elim(bmap->div[k]+1, eq,
1287                                 1+pos, 1+total, &bmap->div[k][0]);
1288                 F_CLR(bmap, ISL_BASIC_MAP_NORMALIZED);
1289         }
1290 }
1291
1292
1293 struct isl_basic_map *isl_basic_map_gauss(
1294         struct isl_basic_map *bmap, int *progress)
1295 {
1296         int k;
1297         int done;
1298         int last_var;
1299         unsigned total_var;
1300         unsigned total;
1301
1302         if (!bmap)
1303                 return NULL;
1304
1305         total = isl_basic_map_total_dim(bmap);
1306         total_var = total - bmap->n_div;
1307
1308         last_var = total - 1;
1309         for (done = 0; done < bmap->n_eq; ++done) {
1310                 for (; last_var >= 0; --last_var) {
1311                         for (k = done; k < bmap->n_eq; ++k)
1312                                 if (!isl_int_is_zero(bmap->eq[k][1+last_var]))
1313                                         break;
1314                         if (k < bmap->n_eq)
1315                                 break;
1316                 }
1317                 if (last_var < 0)
1318                         break;
1319                 if (k != done)
1320                         swap_equality(bmap, k, done);
1321                 if (isl_int_is_neg(bmap->eq[done][1+last_var]))
1322                         isl_seq_neg(bmap->eq[done], bmap->eq[done], 1+total);
1323
1324                 eliminate_var_using_equality(bmap, last_var, bmap->eq[done],
1325                                                 progress);
1326
1327                 if (last_var >= total_var &&
1328                     isl_int_is_zero(bmap->div[last_var - total_var][0])) {
1329                         unsigned div = last_var - total_var;
1330                         isl_seq_neg(bmap->div[div]+1, bmap->eq[done], 1+total);
1331                         isl_int_set_si(bmap->div[div][1+1+last_var], 0);
1332                         isl_int_set(bmap->div[div][0],
1333                                     bmap->eq[done][1+last_var]);
1334                         F_CLR(bmap, ISL_BASIC_MAP_NORMALIZED);
1335                 }
1336         }
1337         if (done == bmap->n_eq)
1338                 return bmap;
1339         for (k = done; k < bmap->n_eq; ++k) {
1340                 if (isl_int_is_zero(bmap->eq[k][0]))
1341                         continue;
1342                 return isl_basic_map_set_to_empty(bmap);
1343         }
1344         isl_basic_map_free_equality(bmap, bmap->n_eq-done);
1345         return bmap;
1346 }
1347
1348 struct isl_basic_set *isl_basic_set_gauss(
1349         struct isl_basic_set *bset, int *progress)
1350 {
1351         return (struct isl_basic_set*)isl_basic_map_gauss(
1352                         (struct isl_basic_map *)bset, progress);
1353 }
1354
1355 static unsigned int round_up(unsigned int v)
1356 {
1357         int old_v = v;
1358
1359         while (v) {
1360                 old_v = v;
1361                 v ^= v & -v;
1362         }
1363         return old_v << 1;
1364 }
1365
1366 static int hash_index(isl_int ***index, unsigned int size, int bits,
1367                         struct isl_basic_map *bmap, int k)
1368 {
1369         int h;
1370         unsigned total = isl_basic_map_total_dim(bmap);
1371         uint32_t hash = isl_seq_get_hash_bits(bmap->ineq[k]+1, total, bits);
1372         for (h = hash; index[h]; h = (h+1) % size)
1373                 if (&bmap->ineq[k] != index[h] &&
1374                     isl_seq_eq(bmap->ineq[k]+1, index[h][0]+1, total))
1375                         break;
1376         return h;
1377 }
1378
1379 static int set_hash_index(isl_int ***index, unsigned int size, int bits,
1380                           struct isl_basic_set *bset, int k)
1381 {
1382         return hash_index(index, size, bits, (struct isl_basic_map *)bset, k);
1383 }
1384
1385 static struct isl_basic_map *remove_duplicate_constraints(
1386         struct isl_basic_map *bmap, int *progress)
1387 {
1388         unsigned int size;
1389         isl_int ***index;
1390         int k, l, h;
1391         int bits;
1392         unsigned total = isl_basic_map_total_dim(bmap);
1393         isl_int sum;
1394
1395         if (bmap->n_ineq <= 1)
1396                 return bmap;
1397
1398         size = round_up(4 * (bmap->n_ineq+1) / 3 - 1);
1399         bits = ffs(size) - 1;
1400         index = isl_calloc_array(ctx, isl_int **, size);
1401         if (!index)
1402                 return bmap;
1403
1404         index[isl_seq_get_hash_bits(bmap->ineq[0]+1, total, bits)] = &bmap->ineq[0];
1405         for (k = 1; k < bmap->n_ineq; ++k) {
1406                 h = hash_index(index, size, bits, bmap, k);
1407                 if (!index[h]) {
1408                         index[h] = &bmap->ineq[k];
1409                         continue;
1410                 }
1411                 if (progress)
1412                         *progress = 1;
1413                 l = index[h] - &bmap->ineq[0];
1414                 if (isl_int_lt(bmap->ineq[k][0], bmap->ineq[l][0]))
1415                         swap_inequality(bmap, k, l);
1416                 isl_basic_map_drop_inequality(bmap, k);
1417                 --k;
1418         }
1419         isl_int_init(sum);
1420         for (k = 0; k < bmap->n_ineq-1; ++k) {
1421                 isl_seq_neg(bmap->ineq[k]+1, bmap->ineq[k]+1, total);
1422                 h = hash_index(index, size, bits, bmap, k);
1423                 isl_seq_neg(bmap->ineq[k]+1, bmap->ineq[k]+1, total);
1424                 if (!index[h])
1425                         continue;
1426                 l = index[h] - &bmap->ineq[0];
1427                 isl_int_add(sum, bmap->ineq[k][0], bmap->ineq[l][0]);
1428                 if (isl_int_is_pos(sum))
1429                         continue;
1430                 if (isl_int_is_zero(sum)) {
1431                         /* We need to break out of the loop after these
1432                          * changes since the contents of the hash
1433                          * will no longer be valid.
1434                          * Plus, we probably we want to regauss first.
1435                          */
1436                         isl_basic_map_drop_inequality(bmap, l);
1437                         isl_basic_map_inequality_to_equality(bmap, k);
1438                 } else
1439                         bmap = isl_basic_map_set_to_empty(bmap);
1440                 break;
1441         }
1442         isl_int_clear(sum);
1443
1444         free(index);
1445         return bmap;
1446 }
1447
1448 static void compute_elimination_index(struct isl_basic_map *bmap, int *elim)
1449 {
1450         int d, i;
1451         unsigned total;
1452
1453         total = isl_dim_total(bmap->dim);
1454         for (d = 0; d < total; ++d)
1455                 elim[d] = -1;
1456         for (d = total - 1, i = 0; d >= 0 && i < bmap->n_eq; ++i) {
1457                 for (; d >= 0; --d) {
1458                         if (isl_int_is_zero(bmap->eq[i][1+d]))
1459                                 continue;
1460                         elim[d] = i;
1461                         break;
1462                 }
1463         }
1464 }
1465
1466 static void set_compute_elimination_index(struct isl_basic_set *bset, int *elim)
1467 {
1468         return compute_elimination_index((struct isl_basic_map *)bset, elim);
1469 }
1470
1471 static int reduced_using_equalities(isl_int *dst, isl_int *src,
1472         struct isl_basic_map *bmap, int *elim)
1473 {
1474         int d, i;
1475         int copied = 0;
1476         unsigned total;
1477
1478         total = isl_dim_total(bmap->dim);
1479         for (d = total - 1; d >= 0; --d) {
1480                 if (isl_int_is_zero(src[1+d]))
1481                         continue;
1482                 if (elim[d] == -1)
1483                         continue;
1484                 if (!copied) {
1485                         isl_seq_cpy(dst, src, 1 + total);
1486                         copied = 1;
1487                 }
1488                 isl_seq_elim(dst, bmap->eq[elim[d]], 1 + d, 1 + total, NULL);
1489         }
1490         return copied;
1491 }
1492
1493 static int set_reduced_using_equalities(isl_int *dst, isl_int *src,
1494         struct isl_basic_set *bset, int *elim)
1495 {
1496         return reduced_using_equalities(dst, src,
1497                                         (struct isl_basic_map *)bset, elim);
1498 }
1499
1500 /* Quick check to see if two basic maps are disjoint.
1501  * In particular, we reduce the equalities and inequalities of
1502  * one basic map in the context of the equalities of the other
1503  * basic map and check if we get a contradiction.
1504  */
1505 int isl_basic_map_fast_is_disjoint(struct isl_basic_map *bmap1,
1506         struct isl_basic_map *bmap2)
1507 {
1508         struct isl_vec *v = NULL;
1509         int *elim = NULL;
1510         unsigned total;
1511         int d, i;
1512
1513         if (!bmap1 || !bmap2)
1514                 return -1;
1515         isl_assert(bmap1->ctx, isl_dim_equal(bmap1->dim, bmap2->dim),
1516                         return -1);
1517         if (bmap1->n_div || bmap2->n_div)
1518                 return 0;
1519         if (!bmap1->n_eq && !bmap2->n_eq)
1520                 return 0;
1521
1522         total = isl_dim_total(bmap1->dim);
1523         if (total == 0)
1524                 return 0;
1525         v = isl_vec_alloc(bmap1->ctx, 1 + total);
1526         if (!v)
1527                 goto error;
1528         elim = isl_alloc_array(bmap1->ctx, int, total);
1529         if (!elim)
1530                 goto error;
1531         compute_elimination_index(bmap1, elim);
1532         for (i = 0; i < bmap2->n_eq; ++i) {
1533                 int reduced;
1534                 reduced = reduced_using_equalities(v->block.data, bmap2->eq[i],
1535                                                         bmap1, elim);
1536                 if (reduced && !isl_int_is_zero(v->block.data[0]) &&
1537                     isl_seq_first_non_zero(v->block.data + 1, total) == -1)
1538                         goto disjoint;
1539         }
1540         for (i = 0; i < bmap2->n_ineq; ++i) {
1541                 int reduced;
1542                 reduced = reduced_using_equalities(v->block.data,
1543                                                 bmap2->ineq[i], bmap1, elim);
1544                 if (reduced && isl_int_is_neg(v->block.data[0]) &&
1545                     isl_seq_first_non_zero(v->block.data + 1, total) == -1)
1546                         goto disjoint;
1547         }
1548         compute_elimination_index(bmap2, elim);
1549         for (i = 0; i < bmap1->n_ineq; ++i) {
1550                 int reduced;
1551                 reduced = reduced_using_equalities(v->block.data,
1552                                                 bmap1->ineq[i], bmap2, elim);
1553                 if (reduced && isl_int_is_neg(v->block.data[0]) &&
1554                     isl_seq_first_non_zero(v->block.data + 1, total) == -1)
1555                         goto disjoint;
1556         }
1557         isl_vec_free(bmap1->ctx, v);
1558         free(elim);
1559         return 0;
1560 disjoint:
1561         isl_vec_free(bmap1->ctx, v);
1562         free(elim);
1563         return 1;
1564 error:
1565         isl_vec_free(bmap1->ctx, v);
1566         free(elim);
1567         return -1;
1568 }
1569
1570 int isl_basic_set_fast_is_disjoint(struct isl_basic_set *bset1,
1571         struct isl_basic_set *bset2)
1572 {
1573         return isl_basic_map_fast_is_disjoint((struct isl_basic_map *)bset1,
1574                                               (struct isl_basic_map *)bset2);
1575 }
1576
1577 int isl_map_fast_is_disjoint(struct isl_map *map1, struct isl_map *map2)
1578 {
1579         int i, j;
1580
1581         if (!map1 || !map2)
1582                 return -1;
1583
1584         if (isl_map_fast_is_equal(map1, map2))
1585                 return 0;
1586
1587         for (i = 0; i < map1->n; ++i) {
1588                 for (j = 0; j < map2->n; ++j) {
1589                         int d = isl_basic_map_fast_is_disjoint(map1->p[i],
1590                                                                map2->p[j]);
1591                         if (d != 1)
1592                                 return d;
1593                 }
1594         }
1595         return 1;
1596 }
1597
1598 int isl_set_fast_is_disjoint(struct isl_set *set1, struct isl_set *set2)
1599 {
1600         return isl_map_fast_is_disjoint((struct isl_map *)set1,
1601                                         (struct isl_map *)set2);
1602 }
1603
1604 static struct isl_basic_map *remove_duplicate_divs(
1605         struct isl_basic_map *bmap, int *progress)
1606 {
1607         unsigned int size;
1608         int *index;
1609         int k, l, h;
1610         int bits;
1611         struct isl_blk eq;
1612         unsigned total_var = isl_dim_total(bmap->dim);
1613         unsigned total = total_var + bmap->n_div;
1614         struct isl_ctx *ctx;
1615
1616         if (bmap->n_div <= 1)
1617                 return bmap;
1618
1619         ctx = bmap->ctx;
1620         for (k = bmap->n_div - 1; k >= 0; --k)
1621                 if (!isl_int_is_zero(bmap->div[k][0]))
1622                         break;
1623         if (k <= 0)
1624                 return bmap;
1625
1626         size = round_up(4 * bmap->n_div / 3 - 1);
1627         bits = ffs(size) - 1;
1628         index = isl_calloc_array(ctx, int, size);
1629         if (!index)
1630                 return bmap;
1631         eq = isl_blk_alloc(ctx, 1+total);
1632         if (isl_blk_is_error(eq))
1633                 goto out;
1634
1635         isl_seq_clr(eq.data, 1+total);
1636         index[isl_seq_get_hash_bits(bmap->div[k], 2+total, bits)] = k + 1;
1637         for (--k; k >= 0; --k) {
1638                 uint32_t hash;
1639
1640                 if (isl_int_is_zero(bmap->div[k][0]))
1641                         continue;
1642
1643                 hash = isl_seq_get_hash_bits(bmap->div[k], 2+total, bits);
1644                 for (h = hash; index[h]; h = (h+1) % size)
1645                         if (isl_seq_eq(bmap->div[k],
1646                                        bmap->div[index[h]-1], 2+total))
1647                                 break;
1648                 if (index[h]) {
1649                         *progress = 1;
1650                         l = index[h] - 1;
1651                         isl_int_set_si(eq.data[1+total_var+k], -1);
1652                         isl_int_set_si(eq.data[1+total_var+l], 1);
1653                         eliminate_div(bmap, eq.data, l);
1654                         isl_int_set_si(eq.data[1+total_var+k], 0);
1655                         isl_int_set_si(eq.data[1+total_var+l], 0);
1656                 }
1657                 index[h] = k+1;
1658         }
1659
1660         isl_blk_free(ctx, eq);
1661 out:
1662         free(index);
1663         return bmap;
1664 }
1665
1666 /* Elimininate divs based on equalities
1667  */
1668 static struct isl_basic_map *eliminate_divs_eq(
1669                 struct isl_basic_map *bmap, int *progress)
1670 {
1671         int d;
1672         int i;
1673         int modified = 0;
1674         unsigned off;
1675
1676         if (!bmap)
1677                 return NULL;
1678
1679         off = 1 + isl_dim_total(bmap->dim);
1680
1681         for (d = bmap->n_div - 1; d >= 0 ; --d) {
1682                 for (i = 0; i < bmap->n_eq; ++i) {
1683                         if (!isl_int_is_one(bmap->eq[i][off + d]) &&
1684                             !isl_int_is_negone(bmap->eq[i][off + d]))
1685                                 continue;
1686                         modified = 1;
1687                         *progress = 1;
1688                         eliminate_div(bmap, bmap->eq[i], d);
1689                         isl_basic_map_drop_equality(bmap, i);
1690                         break;
1691                 }
1692         }
1693         if (modified)
1694                 return eliminate_divs_eq(bmap, progress);
1695         return bmap;
1696 }
1697
1698 static struct isl_basic_map *normalize_constraints(struct isl_basic_map *bmap)
1699 {
1700         int i;
1701         isl_int gcd;
1702         unsigned total = isl_basic_map_total_dim(bmap);
1703
1704         isl_int_init(gcd);
1705         for (i = bmap->n_eq - 1; i >= 0; --i) {
1706                 isl_seq_gcd(bmap->eq[i]+1, total, &gcd);
1707                 if (isl_int_is_zero(gcd)) {
1708                         if (!isl_int_is_zero(bmap->eq[i][0])) {
1709                                 bmap = isl_basic_map_set_to_empty(bmap);
1710                                 break;
1711                         }
1712                         isl_basic_map_drop_equality(bmap, i);
1713                         continue;
1714                 }
1715                 if (F_ISSET(bmap, ISL_BASIC_MAP_RATIONAL))
1716                         isl_int_gcd(gcd, gcd, bmap->eq[i][0]);
1717                 if (isl_int_is_one(gcd))
1718                         continue;
1719                 if (!isl_int_is_divisible_by(bmap->eq[i][0], gcd)) {
1720                         bmap = isl_basic_map_set_to_empty(bmap);
1721                         break;
1722                 }
1723                 isl_seq_scale_down(bmap->eq[i], bmap->eq[i], gcd, 1+total);
1724         }
1725
1726         for (i = bmap->n_ineq - 1; i >= 0; --i) {
1727                 isl_seq_gcd(bmap->ineq[i]+1, total, &gcd);
1728                 if (isl_int_is_zero(gcd)) {
1729                         if (isl_int_is_neg(bmap->ineq[i][0])) {
1730                                 bmap = isl_basic_map_set_to_empty(bmap);
1731                                 break;
1732                         }
1733                         isl_basic_map_drop_inequality(bmap, i);
1734                         continue;
1735                 }
1736                 if (F_ISSET(bmap, ISL_BASIC_MAP_RATIONAL))
1737                         isl_int_gcd(gcd, gcd, bmap->ineq[i][0]);
1738                 if (isl_int_is_one(gcd))
1739                         continue;
1740                 isl_int_fdiv_q(bmap->ineq[i][0], bmap->ineq[i][0], gcd);
1741                 isl_seq_scale_down(bmap->ineq[i]+1, bmap->ineq[i]+1, gcd, total);
1742         }
1743         isl_int_clear(gcd);
1744
1745         return bmap;
1746 }
1747
1748
1749 /* Eliminate the specified variables from the constraints using
1750  * Fourier-Motzkin.  The variables themselves are not removed.
1751  */
1752 struct isl_basic_map *isl_basic_map_eliminate_vars(
1753         struct isl_basic_map *bmap, int pos, unsigned n)
1754 {
1755         int d;
1756         int i, j, k;
1757         unsigned total;
1758
1759         if (n == 0)
1760                 return bmap;
1761         if (!bmap)
1762                 return NULL;
1763         total = isl_basic_map_total_dim(bmap);
1764
1765         bmap = isl_basic_map_cow(bmap);
1766         for (d = pos + n - 1; d >= pos; --d) {
1767                 int n_lower, n_upper;
1768                 if (!bmap)
1769                         return NULL;
1770                 for (i = 0; i < bmap->n_eq; ++i) {
1771                         if (isl_int_is_zero(bmap->eq[i][1+d]))
1772                                 continue;
1773                         eliminate_var_using_equality(bmap, d, bmap->eq[i], NULL);
1774                         isl_basic_map_drop_equality(bmap, i);
1775                         break;
1776                 }
1777                 if (i < bmap->n_eq)
1778                         continue;
1779                 n_lower = 0;
1780                 n_upper = 0;
1781                 for (i = 0; i < bmap->n_ineq; ++i) {
1782                         if (isl_int_is_pos(bmap->ineq[i][1+d]))
1783                                 n_lower++;
1784                         else if (isl_int_is_neg(bmap->ineq[i][1+d]))
1785                                 n_upper++;
1786                 }
1787                 bmap = isl_basic_map_extend_constraints(bmap,
1788                                 0, n_lower * n_upper);
1789                 for (i = bmap->n_ineq - 1; i >= 0; --i) {
1790                         int last;
1791                         if (isl_int_is_zero(bmap->ineq[i][1+d]))
1792                                 continue;
1793                         last = -1;
1794                         for (j = 0; j < i; ++j) {
1795                                 if (isl_int_is_zero(bmap->ineq[j][1+d]))
1796                                         continue;
1797                                 last = j;
1798                                 if (isl_int_sgn(bmap->ineq[i][1+d]) ==
1799                                     isl_int_sgn(bmap->ineq[j][1+d]))
1800                                         continue;
1801                                 k = isl_basic_map_alloc_inequality(bmap);
1802                                 if (k < 0)
1803                                         goto error;
1804                                 isl_seq_cpy(bmap->ineq[k], bmap->ineq[i],
1805                                                 1+total);
1806                                 isl_seq_elim(bmap->ineq[k], bmap->ineq[j],
1807                                                 1+d, 1+total, NULL);
1808                         }
1809                         isl_basic_map_drop_inequality(bmap, i);
1810                         i = last + 1;
1811                 }
1812                 if (n_lower > 0 && n_upper > 0) {
1813                         bmap = normalize_constraints(bmap);
1814                         bmap = remove_duplicate_constraints(bmap, NULL);
1815                         bmap = isl_basic_map_gauss(bmap, NULL);
1816                         bmap = isl_basic_map_convex_hull(bmap);
1817                         if (!bmap)
1818                                 goto error;
1819                         if (F_ISSET(bmap, ISL_BASIC_MAP_EMPTY))
1820                                 break;
1821                 }
1822         }
1823         F_CLR(bmap, ISL_BASIC_MAP_NORMALIZED);
1824         return bmap;
1825 error:
1826         isl_basic_map_free(bmap);
1827         return NULL;
1828 }
1829
1830 struct isl_basic_set *isl_basic_set_eliminate_vars(
1831         struct isl_basic_set *bset, unsigned pos, unsigned n)
1832 {
1833         return (struct isl_basic_set *)isl_basic_map_eliminate_vars(
1834                         (struct isl_basic_map *)bset, pos, n);
1835 }
1836
1837 /* Eliminate the specified n dimensions starting at first from the
1838  * constraints using Fourier-Motzkin, The dimensions themselves
1839  * are not removed.
1840  */
1841 struct isl_set *isl_set_eliminate_dims(struct isl_set *set,
1842         unsigned first, unsigned n)
1843 {
1844         int i;
1845         unsigned nparam;
1846
1847         if (!set)
1848                 return NULL;
1849         if (n == 0)
1850                 return set;
1851
1852         set = isl_set_cow(set);
1853         if (!set)
1854                 return NULL;
1855         isl_assert(set->ctx, first+n <= isl_set_n_dim(set), goto error);
1856         nparam = isl_set_n_param(set);
1857
1858         for (i = 0; i < set->n; ++i) {
1859                 set->p[i] = isl_basic_set_eliminate_vars(set->p[i],
1860                                                             nparam + first, n);
1861                 if (!set->p[i])
1862                         goto error;
1863         }
1864         return set;
1865 error:
1866         isl_set_free(set);
1867         return NULL;
1868 }
1869
1870 /* Project out n dimensions starting at first using Fourier-Motzkin */
1871 struct isl_set *isl_set_remove_dims(struct isl_set *set,
1872         unsigned first, unsigned n)
1873 {
1874         set = isl_set_eliminate_dims(set, first, n);
1875         set = isl_set_drop_dims(set, first, n);
1876         return set;
1877 }
1878
1879 struct isl_basic_set *isl_basic_set_remove_divs(struct isl_basic_set *bset)
1880 {
1881         bset = isl_basic_set_eliminate_vars(bset, isl_dim_total(bset->dim),
1882                                                 bset->n_div);
1883         if (!bset)
1884                 return NULL;
1885         bset->n_div = 0;
1886         return bset;
1887 }
1888
1889 struct isl_set *isl_set_remove_divs(struct isl_set *set)
1890 {
1891         int i;
1892
1893         if (!set)
1894                 return NULL;
1895         if (set->n == 0)
1896                 return set;
1897
1898         set = isl_set_cow(set);
1899         if (!set)
1900                 return NULL;
1901
1902         for (i = 0; i < set->n; ++i) {
1903                 set->p[i] = isl_basic_set_remove_divs(set->p[i]);
1904                 if (!set->p[i])
1905                         goto error;
1906         }
1907         return set;
1908 error:
1909         isl_set_free(set);
1910         return NULL;
1911 }
1912
1913 /* Project out n inputs starting at first using Fourier-Motzkin */
1914 struct isl_map *isl_map_remove_inputs(struct isl_map *map,
1915         unsigned first, unsigned n)
1916 {
1917         int i;
1918         unsigned nparam;
1919
1920         if (n == 0)
1921                 return map;
1922
1923         map = isl_map_cow(map);
1924         if (!map)
1925                 return NULL;
1926         nparam = isl_map_n_param(map);
1927         isl_assert(map->ctx, first+n <= isl_map_n_in(map), goto error);
1928
1929         for (i = 0; i < map->n; ++i) {
1930                 map->p[i] = isl_basic_map_eliminate_vars(map->p[i],
1931                                                             nparam + first, n);
1932                 if (!map->p[i])
1933                         goto error;
1934         }
1935         map = isl_map_drop_inputs(map, first, n);
1936         return map;
1937 error:
1938         isl_map_free(map);
1939         return NULL;
1940 }
1941
1942 /* Project out n dimensions starting at first using Fourier-Motzkin */
1943 struct isl_basic_set *isl_basic_set_remove_dims(struct isl_basic_set *bset,
1944         unsigned first, unsigned n)
1945 {
1946         unsigned nparam = isl_basic_set_n_param(bset);
1947         bset = isl_basic_set_eliminate_vars(bset, nparam + first, n);
1948         bset = isl_basic_set_drop_dims(bset, first, n);
1949         return bset;
1950 }
1951
1952 /* Elimininate divs based on inequalities
1953  */
1954 static struct isl_basic_map *eliminate_divs_ineq(
1955                 struct isl_basic_map *bmap, int *progress)
1956 {
1957         int d;
1958         int i;
1959         unsigned off;
1960         struct isl_ctx *ctx;
1961
1962         if (!bmap)
1963                 return NULL;
1964
1965         ctx = bmap->ctx;
1966         off = 1 + isl_dim_total(bmap->dim);
1967
1968         for (d = bmap->n_div - 1; d >= 0 ; --d) {
1969                 for (i = 0; i < bmap->n_eq; ++i)
1970                         if (!isl_int_is_zero(bmap->eq[i][off + d]))
1971                                 break;
1972                 if (i < bmap->n_eq)
1973                         continue;
1974                 for (i = 0; i < bmap->n_ineq; ++i)
1975                         if (isl_int_abs_gt(bmap->ineq[i][off + d], ctx->one))
1976                                 break;
1977                 if (i < bmap->n_ineq)
1978                         continue;
1979                 *progress = 1;
1980                 bmap = isl_basic_map_eliminate_vars(bmap, (off-1)+d, 1);
1981                 if (F_ISSET(bmap, ISL_BASIC_MAP_EMPTY))
1982                         break;
1983                 bmap = isl_basic_map_drop_div(bmap, d);
1984                 if (!bmap)
1985                         break;
1986         }
1987         return bmap;
1988 }
1989
1990 struct isl_basic_map *isl_basic_map_simplify(struct isl_basic_map *bmap)
1991 {
1992         int progress = 1;
1993         if (!bmap)
1994                 return NULL;
1995         while (progress) {
1996                 progress = 0;
1997                 bmap = normalize_constraints(bmap);
1998                 bmap = eliminate_divs_eq(bmap, &progress);
1999                 bmap = eliminate_divs_ineq(bmap, &progress);
2000                 bmap = isl_basic_map_gauss(bmap, &progress);
2001                 bmap = remove_duplicate_divs(bmap, &progress);
2002                 bmap = remove_duplicate_constraints(bmap, &progress);
2003         }
2004         return bmap;
2005 }
2006
2007 struct isl_basic_set *isl_basic_set_simplify(struct isl_basic_set *bset)
2008 {
2009         return (struct isl_basic_set *)
2010                 isl_basic_map_simplify((struct isl_basic_map *)bset);
2011 }
2012
2013 static void dump_term(struct isl_basic_map *bmap,
2014                         isl_int c, int pos, FILE *out)
2015 {
2016         const char *name;
2017         unsigned in = isl_basic_map_n_in(bmap);
2018         unsigned dim = in + isl_basic_map_n_out(bmap);
2019         unsigned nparam = isl_basic_map_n_param(bmap);
2020         if (!pos)
2021                 isl_int_print(out, c, 0);
2022         else {
2023                 if (!isl_int_is_one(c))
2024                         isl_int_print(out, c, 0);
2025                 if (pos < 1 + nparam) {
2026                         name = isl_dim_get_name(bmap->dim,
2027                                                 isl_dim_param, pos - 1);
2028                         if (name)
2029                                 fprintf(out, "%s", name);
2030                         else
2031                                 fprintf(out, "p%d", pos - 1);
2032                 } else if (pos < 1 + nparam + in)
2033                         fprintf(out, "i%d", pos - 1 - nparam);
2034                 else if (pos < 1 + nparam + dim)
2035                         fprintf(out, "o%d", pos - 1 - nparam - in);
2036                 else
2037                         fprintf(out, "e%d", pos - 1 - nparam - dim);
2038         }
2039 }
2040
2041 static void dump_constraint_sign(struct isl_basic_map *bmap, isl_int *c,
2042                                 int sign, FILE *out)
2043 {
2044         int i;
2045         int first;
2046         unsigned len = 1 + isl_basic_map_total_dim(bmap);
2047         isl_int v;
2048
2049         isl_int_init(v);
2050         for (i = 0, first = 1; i < len; ++i) {
2051                 if (isl_int_sgn(c[i]) * sign <= 0)
2052                         continue;
2053                 if (!first)
2054                         fprintf(out, " + ");
2055                 first = 0;
2056                 isl_int_abs(v, c[i]);
2057                 dump_term(bmap, v, i, out);
2058         }
2059         isl_int_clear(v);
2060         if (first)
2061                 fprintf(out, "0");
2062 }
2063
2064 static void dump_constraint(struct isl_basic_map *bmap, isl_int *c,
2065                                 const char *op, FILE *out, int indent)
2066 {
2067         int i;
2068
2069         fprintf(out, "%*s", indent, "");
2070
2071         dump_constraint_sign(bmap, c, 1, out);
2072         fprintf(out, " %s ", op);
2073         dump_constraint_sign(bmap, c, -1, out);
2074
2075         fprintf(out, "\n");
2076
2077         for (i = bmap->n_div; i < bmap->extra; ++i) {
2078                 if (isl_int_is_zero(c[1+isl_dim_total(bmap->dim)+i]))
2079                         continue;
2080                 fprintf(out, "%*s", indent, "");
2081                 fprintf(out, "ERROR: unused div coefficient not zero\n");
2082                 abort();
2083         }
2084 }
2085
2086 static void dump_constraints(struct isl_basic_map *bmap,
2087                                 isl_int **c, unsigned n,
2088                                 const char *op, FILE *out, int indent)
2089 {
2090         int i;
2091
2092         for (i = 0; i < n; ++i)
2093                 dump_constraint(bmap, c[i], op, out, indent);
2094 }
2095
2096 static void dump_affine(struct isl_basic_map *bmap, isl_int *exp, FILE *out)
2097 {
2098         int j;
2099         int first = 1;
2100         unsigned total = isl_basic_map_total_dim(bmap);
2101
2102         for (j = 0; j < 1 + total; ++j) {
2103                 if (isl_int_is_zero(exp[j]))
2104                         continue;
2105                 if (!first && isl_int_is_pos(exp[j]))
2106                         fprintf(out, "+");
2107                 dump_term(bmap, exp[j], j, out);
2108                 first = 0;
2109         }
2110 }
2111
2112 static void dump(struct isl_basic_map *bmap, FILE *out, int indent)
2113 {
2114         int i;
2115
2116         dump_constraints(bmap, bmap->eq, bmap->n_eq, "=", out, indent);
2117         dump_constraints(bmap, bmap->ineq, bmap->n_ineq, ">=", out, indent);
2118
2119         for (i = 0; i < bmap->n_div; ++i) {
2120                 fprintf(out, "%*s", indent, "");
2121                 fprintf(out, "e%d = [(", i);
2122                 dump_affine(bmap, bmap->div[i]+1, out);
2123                 fprintf(out, ")/");
2124                 isl_int_print(out, bmap->div[i][0], 0);
2125                 fprintf(out, "]\n");
2126         }
2127 }
2128
2129 void isl_basic_set_dump(struct isl_basic_set *bset, FILE *out, int indent)
2130 {
2131         if (!bset) {
2132                 fprintf(out, "null basic set\n");
2133                 return;
2134         }
2135
2136         fprintf(out, "%*s", indent, "");
2137         fprintf(out, "ref: %d, nparam: %d, dim: %d, extra: %d, flags: %x\n",
2138                         bset->ref, bset->dim->nparam, bset->dim->n_out,
2139                         bset->extra, bset->flags);
2140         dump((struct isl_basic_map *)bset, out, indent);
2141 }
2142
2143 void isl_basic_map_dump(struct isl_basic_map *bmap, FILE *out, int indent)
2144 {
2145         if (!bmap) {
2146                 fprintf(out, "null basic map\n");
2147                 return;
2148         }
2149
2150         fprintf(out, "%*s", indent, "");
2151         fprintf(out, "ref: %d, nparam: %d, in: %d, out: %d, extra: %d, "
2152                         "flags: %x, n_name: %d\n",
2153                 bmap->ref,
2154                 bmap->dim->nparam, bmap->dim->n_in, bmap->dim->n_out,
2155                 bmap->extra, bmap->flags, bmap->dim->n_name);
2156         dump(bmap, out, indent);
2157 }
2158
2159 int isl_inequality_negate(struct isl_basic_map *bmap, unsigned pos)
2160 {
2161         unsigned total;
2162         if (!bmap)
2163                 return -1;
2164         total = isl_basic_map_total_dim(bmap);
2165         isl_assert(bmap->ctx, pos < bmap->n_ineq, return -1);
2166         isl_seq_neg(bmap->ineq[pos], bmap->ineq[pos], 1 + total);
2167         isl_int_sub_ui(bmap->ineq[pos][0], bmap->ineq[pos][0], 1);
2168         F_CLR(bmap, ISL_BASIC_MAP_NORMALIZED);
2169         return 0;
2170 }
2171
2172 struct isl_set *isl_set_alloc_dim(struct isl_dim *dim, int n, unsigned flags)
2173 {
2174         struct isl_set *set;
2175
2176         if (!dim)
2177                 return NULL;
2178         isl_assert(dim->ctx, dim->n_in == 0, return NULL);
2179         isl_assert(dim->ctx, n >= 0, return NULL);
2180         set = isl_alloc(dim->ctx, struct isl_set,
2181                         sizeof(struct isl_set) +
2182                         n * sizeof(struct isl_basic_set *));
2183         if (!set)
2184                 goto error;
2185
2186         set->ctx = dim->ctx;
2187         isl_ctx_ref(set->ctx);
2188         set->ref = 1;
2189         set->size = n;
2190         set->n = 0;
2191         set->dim = dim;
2192         set->flags = flags;
2193         return set;
2194 error:
2195         isl_dim_free(dim);
2196         return NULL;
2197 }
2198
2199 struct isl_set *isl_set_alloc(struct isl_ctx *ctx,
2200                 unsigned nparam, unsigned dim, int n, unsigned flags)
2201 {
2202         struct isl_set *set;
2203         struct isl_dim *dims;
2204
2205         dims = isl_dim_alloc(ctx, nparam, 0, dim);
2206         if (!dims)
2207                 return NULL;
2208
2209         set = isl_set_alloc_dim(dims, n, flags);
2210         return set;
2211 }
2212
2213 struct isl_set *isl_set_dup(struct isl_set *set)
2214 {
2215         int i;
2216         struct isl_set *dup;
2217
2218         if (!set)
2219                 return NULL;
2220
2221         dup = isl_set_alloc_dim(isl_dim_copy(set->dim), set->n, set->flags);
2222         if (!dup)
2223                 return NULL;
2224         for (i = 0; i < set->n; ++i)
2225                 dup = isl_set_add(dup, isl_basic_set_copy(set->p[i]));
2226         return dup;
2227 }
2228
2229 struct isl_set *isl_set_from_basic_set(struct isl_basic_set *bset)
2230 {
2231         struct isl_set *set;
2232
2233         if (!bset)
2234                 return NULL;
2235
2236         set = isl_set_alloc_dim(isl_dim_copy(bset->dim), 1, ISL_MAP_DISJOINT);
2237         if (!set) {
2238                 isl_basic_set_free(bset);
2239                 return NULL;
2240         }
2241         return isl_set_add(set, bset);
2242 }
2243
2244 struct isl_map *isl_map_from_basic_map(struct isl_basic_map *bmap)
2245 {
2246         struct isl_map *map;
2247
2248         if (!bmap)
2249                 return NULL;
2250
2251         map = isl_map_alloc_dim(isl_dim_copy(bmap->dim), 1, ISL_MAP_DISJOINT);
2252         if (!map) {
2253                 isl_basic_map_free(bmap);
2254                 return NULL;
2255         }
2256         return isl_map_add(map, bmap);
2257 }
2258
2259 struct isl_set *isl_set_add(struct isl_set *set, struct isl_basic_set *bset)
2260 {
2261         if (!bset || !set)
2262                 goto error;
2263         isl_assert(set->ctx, isl_dim_equal(set->dim, bset->dim), goto error);
2264         isl_assert(set->ctx, set->n < set->size, goto error);
2265         set->p[set->n] = bset;
2266         set->n++;
2267         return set;
2268 error:
2269         if (set)
2270                 isl_set_free(set);
2271         if (bset)
2272                 isl_basic_set_free(bset);
2273         return NULL;
2274 }
2275
2276 void isl_set_free(struct isl_set *set)
2277 {
2278         int i;
2279
2280         if (!set)
2281                 return;
2282
2283         if (--set->ref > 0)
2284                 return;
2285
2286         isl_ctx_deref(set->ctx);
2287         for (i = 0; i < set->n; ++i)
2288                 isl_basic_set_free(set->p[i]);
2289         isl_dim_free(set->dim);
2290         free(set);
2291 }
2292
2293 void isl_set_dump(struct isl_set *set, FILE *out, int indent)
2294 {
2295         int i;
2296
2297         if (!set) {
2298                 fprintf(out, "null set\n");
2299                 return;
2300         }
2301
2302         fprintf(out, "%*s", indent, "");
2303         fprintf(out, "ref: %d, n: %d, nparam: %d, dim: %d, flags: %x\n",
2304                         set->ref, set->n, set->dim->nparam, set->dim->n_out,
2305                         set->flags);
2306         for (i = 0; i < set->n; ++i) {
2307                 fprintf(out, "%*s", indent, "");
2308                 fprintf(out, "basic set %d:\n", i);
2309                 isl_basic_set_dump(set->p[i], out, indent+4);
2310         }
2311 }
2312
2313 void isl_map_dump(struct isl_map *map, FILE *out, int indent)
2314 {
2315         int i;
2316
2317         if (!map) {
2318                 fprintf(out, "null map\n");
2319                 return;
2320         }
2321
2322         fprintf(out, "%*s", indent, "");
2323         fprintf(out, "ref: %d, n: %d, nparam: %d, in: %d, out: %d, "
2324                      "flags: %x, n_name: %d\n",
2325                         map->ref, map->n, map->dim->nparam, map->dim->n_in,
2326                         map->dim->n_out, map->flags, map->dim->n_name);
2327         for (i = 0; i < map->n; ++i) {
2328                 fprintf(out, "%*s", indent, "");
2329                 fprintf(out, "basic map %d:\n", i);
2330                 isl_basic_map_dump(map->p[i], out, indent+4);
2331         }
2332 }
2333
2334 struct isl_basic_map *isl_basic_map_intersect_domain(
2335                 struct isl_basic_map *bmap, struct isl_basic_set *bset)
2336 {
2337         struct isl_basic_map *bmap_domain;
2338         struct isl_dim *dim;
2339
2340         if (!bmap || !bset)
2341                 goto error;
2342
2343         isl_assert(set->ctx, isl_basic_map_compatible_domain(bmap, bset),
2344                     goto error);
2345
2346         bmap = isl_basic_map_extend_dim(bmap, isl_dim_copy(bmap->dim),
2347                         bset->n_div, bset->n_eq, bset->n_ineq);
2348         if (!bmap)
2349                 goto error;
2350         dim = isl_dim_reverse(isl_dim_copy(bset->dim));
2351         bmap_domain = isl_basic_map_from_basic_set(bset, dim);
2352         bmap = add_constraints(bmap, bmap_domain, 0, 0);
2353
2354         bmap = isl_basic_map_simplify(bmap);
2355         return isl_basic_map_finalize(bmap);
2356 error:
2357         isl_basic_map_free(bmap);
2358         isl_basic_set_free(bset);
2359         return NULL;
2360 }
2361
2362 struct isl_basic_map *isl_basic_map_intersect_range(
2363                 struct isl_basic_map *bmap, struct isl_basic_set *bset)
2364 {
2365         struct isl_basic_map *bmap_range;
2366
2367         if (!bmap || !bset)
2368                 goto error;
2369
2370         isl_assert(bset->ctx, isl_basic_map_compatible_range(bmap, bset),
2371                    goto error);
2372
2373         bmap = isl_basic_map_extend_dim(bmap, isl_dim_copy(bmap->dim),
2374                         bset->n_div, bset->n_eq, bset->n_ineq);
2375         if (!bmap)
2376                 goto error;
2377         bmap_range = isl_basic_map_from_basic_set(bset, isl_dim_copy(bset->dim));
2378         bmap = add_constraints(bmap, bmap_range, 0, 0);
2379
2380         bmap = isl_basic_map_simplify(bmap);
2381         return isl_basic_map_finalize(bmap);
2382 error:
2383         isl_basic_map_free(bmap);
2384         isl_basic_set_free(bset);
2385         return NULL;
2386 }
2387
2388 struct isl_basic_map *isl_basic_map_intersect(
2389                 struct isl_basic_map *bmap1, struct isl_basic_map *bmap2)
2390 {
2391         if (!bmap1 || !bmap2)
2392                 goto error;
2393
2394         isl_assert(map1->ctx, isl_dim_equal(bmap1->dim, bmap2->dim), goto error);
2395
2396         bmap1 = isl_basic_map_extend_dim(bmap1, isl_dim_copy(bmap1->dim),
2397                         bmap2->n_div, bmap2->n_eq, bmap2->n_ineq);
2398         if (!bmap1)
2399                 goto error;
2400         bmap1 = add_constraints(bmap1, bmap2, 0, 0);
2401
2402         bmap1 = isl_basic_map_simplify(bmap1);
2403         return isl_basic_map_finalize(bmap1);
2404 error:
2405         isl_basic_map_free(bmap1);
2406         isl_basic_map_free(bmap2);
2407         return NULL;
2408 }
2409
2410 struct isl_basic_set *isl_basic_set_intersect(
2411                 struct isl_basic_set *bset1, struct isl_basic_set *bset2)
2412 {
2413         return (struct isl_basic_set *)
2414                 isl_basic_map_intersect(
2415                         (struct isl_basic_map *)bset1,
2416                         (struct isl_basic_map *)bset2);
2417 }
2418
2419 struct isl_map *isl_map_intersect(struct isl_map *map1, struct isl_map *map2)
2420 {
2421         unsigned flags = 0;
2422         struct isl_map *result;
2423         int i, j;
2424
2425         if (!map1 || !map2)
2426                 goto error;
2427
2428         if (F_ISSET(map1, ISL_MAP_DISJOINT) &&
2429             F_ISSET(map2, ISL_MAP_DISJOINT))
2430                 FL_SET(flags, ISL_MAP_DISJOINT);
2431
2432         result = isl_map_alloc_dim(isl_dim_copy(map1->dim),
2433                                 map1->n * map2->n, flags);
2434         if (!result)
2435                 goto error;
2436         for (i = 0; i < map1->n; ++i)
2437                 for (j = 0; j < map2->n; ++j) {
2438                         struct isl_basic_map *part;
2439                         part = isl_basic_map_intersect(
2440                                     isl_basic_map_copy(map1->p[i]),
2441                                     isl_basic_map_copy(map2->p[j]));
2442                         if (isl_basic_map_is_empty(part))
2443                                 isl_basic_map_free(part);
2444                         else
2445                                 result = isl_map_add(result, part);
2446                         if (!result)
2447                                 goto error;
2448                 }
2449         isl_map_free(map1);
2450         isl_map_free(map2);
2451         return result;
2452 error:
2453         isl_map_free(map1);
2454         isl_map_free(map2);
2455         return NULL;
2456 }
2457
2458 struct isl_set *isl_set_intersect(struct isl_set *set1, struct isl_set *set2)
2459 {
2460         return (struct isl_set *)
2461                 isl_map_intersect((struct isl_map *)set1,
2462                                   (struct isl_map *)set2);
2463 }
2464
2465 struct isl_basic_map *isl_basic_map_reverse(struct isl_basic_map *bmap)
2466 {
2467         struct isl_dim *dim;
2468         struct isl_basic_set *bset;
2469         unsigned in;
2470
2471         if (!bmap)
2472                 return NULL;
2473         bmap = isl_basic_map_cow(bmap);
2474         if (!bmap)
2475                 return NULL;
2476         dim = isl_dim_reverse(isl_dim_copy(bmap->dim));
2477         in = isl_basic_map_n_in(bmap);
2478         bset = isl_basic_set_from_basic_map(bmap);
2479         bset = isl_basic_set_swap_vars(bset, in);
2480         return isl_basic_map_from_basic_set(bset, dim);
2481 }
2482
2483 /* Turn final n dimensions into existentially quantified variables.
2484  */
2485 struct isl_basic_set *isl_basic_set_project_out(
2486                 struct isl_basic_set *bset, unsigned n, unsigned flags)
2487 {
2488         int i;
2489         size_t row_size;
2490         isl_int **new_div;
2491         isl_int *old;
2492
2493         if (!bset)
2494                 return NULL;
2495
2496         isl_assert(bset->ctx, n <= isl_basic_set_n_dim(bset), goto error);
2497
2498         if (n == 0)
2499                 return bset;
2500
2501         bset = isl_basic_set_cow(bset);
2502
2503         row_size = 1 + isl_dim_total(bset->dim) + bset->extra;
2504         old = bset->block2.data;
2505         bset->block2 = isl_blk_extend(bset->ctx, bset->block2,
2506                                         (bset->extra + n) * (1 + row_size));
2507         if (!bset->block2.data)
2508                 goto error;
2509         new_div = isl_alloc_array(ctx, isl_int *, bset->extra + n);
2510         if (!new_div)
2511                 goto error;
2512         for (i = 0; i < n; ++i) {
2513                 new_div[i] = bset->block2.data +
2514                                 (bset->extra + i) * (1 + row_size);
2515                 isl_seq_clr(new_div[i], 1 + row_size);
2516         }
2517         for (i = 0; i < bset->extra; ++i)
2518                 new_div[n + i] = bset->block2.data + (bset->div[i] - old);
2519         free(bset->div);
2520         bset->div = new_div;
2521         bset->n_div += n;
2522         bset->extra += n;
2523         bset->dim = isl_dim_drop_outputs(bset->dim,
2524                                             isl_basic_set_n_dim(bset) - n, n);
2525         if (!bset->dim)
2526                 goto error;
2527         bset = isl_basic_set_simplify(bset);
2528         return isl_basic_set_finalize(bset);
2529 error:
2530         isl_basic_set_free(bset);
2531         return NULL;
2532 }
2533
2534 struct isl_basic_map *add_divs(struct isl_basic_map *bmap, unsigned n)
2535 {
2536         int i, j;
2537
2538         for (i = 0; i < n; ++i) {
2539                 j = isl_basic_map_alloc_div(bmap);
2540                 if (j < 0)
2541                         goto error;
2542                 isl_seq_clr(bmap->div[j], 1+1+isl_basic_map_total_dim(bmap));
2543         }
2544         return bmap;
2545 error:
2546         isl_basic_map_free(bmap);
2547         return NULL;
2548 }
2549
2550 struct isl_basic_map *isl_basic_map_apply_range(
2551                 struct isl_basic_map *bmap1, struct isl_basic_map *bmap2)
2552 {
2553         struct isl_dim *dim_result = NULL;
2554         struct isl_basic_map *bmap;
2555         unsigned n_in, n_out, n, nparam, total, pos;
2556         struct isl_dim_map *dim_map1, *dim_map2;
2557
2558         if (!bmap1 || !bmap2)
2559                 goto error;
2560
2561         dim_result = isl_dim_join(isl_dim_copy(bmap1->dim),
2562                                   isl_dim_copy(bmap2->dim));
2563
2564         n_in = isl_basic_map_n_in(bmap1);
2565         n_out = isl_basic_map_n_out(bmap2);
2566         n = isl_basic_map_n_out(bmap1);
2567         nparam = isl_basic_map_n_param(bmap1);
2568
2569         total = nparam + n_in + n_out + bmap1->n_div + bmap2->n_div + n;
2570         dim_map1 = isl_dim_map_alloc(bmap1->ctx, total);
2571         dim_map2 = isl_dim_map_alloc(bmap1->ctx, total);
2572         isl_dim_map_dim(dim_map1, bmap1->dim, isl_dim_param, pos = 0);
2573         isl_dim_map_dim(dim_map2, bmap2->dim, isl_dim_param, pos = 0);
2574         isl_dim_map_dim(dim_map1, bmap1->dim, isl_dim_in, pos += nparam);
2575         isl_dim_map_dim(dim_map2, bmap2->dim, isl_dim_out, pos += n_in);
2576         isl_dim_map_div(dim_map1, bmap1, pos += n_out);
2577         isl_dim_map_div(dim_map2, bmap2, pos += bmap1->n_div);
2578         isl_dim_map_dim(dim_map1, bmap1->dim, isl_dim_out, pos += bmap2->n_div);
2579         isl_dim_map_dim(dim_map2, bmap2->dim, isl_dim_in, pos);
2580
2581         bmap = isl_basic_map_alloc_dim(dim_result,
2582                         bmap1->n_div + bmap2->n_div + n,
2583                         bmap1->n_eq + bmap2->n_eq,
2584                         bmap1->n_ineq + bmap2->n_ineq);
2585         bmap = add_constraints_dim_map(bmap, bmap1, dim_map1);
2586         bmap = add_constraints_dim_map(bmap, bmap2, dim_map2);
2587         bmap = add_divs(bmap, n);
2588         bmap = isl_basic_map_simplify(bmap);
2589         return isl_basic_map_finalize(bmap);
2590 error:
2591         isl_basic_map_free(bmap1);
2592         isl_basic_map_free(bmap2);
2593         return NULL;
2594 }
2595
2596 struct isl_basic_set *isl_basic_set_apply(
2597                 struct isl_basic_set *bset, struct isl_basic_map *bmap)
2598 {
2599         if (!bset || !bmap)
2600                 goto error;
2601
2602         isl_assert(set->ctx, isl_basic_map_compatible_domain(bmap, bset),
2603                     goto error);
2604
2605         return (struct isl_basic_set *)
2606                 isl_basic_map_apply_range((struct isl_basic_map *)bset, bmap);
2607 error:
2608         isl_basic_set_free(bset);
2609         isl_basic_map_free(bmap);
2610         return NULL;
2611 }
2612
2613 struct isl_basic_map *isl_basic_map_apply_domain(
2614                 struct isl_basic_map *bmap1, struct isl_basic_map *bmap2)
2615 {
2616         if (!bmap1 || !bmap2)
2617                 goto error;
2618
2619         isl_assert(ctx,
2620             isl_basic_map_n_in(bmap1) == isl_basic_map_n_in(bmap2), goto error);
2621         isl_assert(ctx,
2622             isl_basic_map_n_param(bmap1) == isl_basic_map_n_param(bmap2),
2623             goto error);
2624
2625         bmap1 = isl_basic_map_reverse(bmap1);
2626         bmap1 = isl_basic_map_apply_range(bmap1, bmap2);
2627         return isl_basic_map_reverse(bmap1);
2628 error:
2629         isl_basic_map_free(bmap1);
2630         isl_basic_map_free(bmap2);
2631         return NULL;
2632 }
2633
2634 static struct isl_basic_map *var_equal(struct isl_ctx *ctx,
2635                 struct isl_basic_map *bmap, unsigned pos)
2636 {
2637         int i;
2638         unsigned nparam;
2639         unsigned n_in;
2640
2641         i = isl_basic_map_alloc_equality(bmap);
2642         if (i < 0)
2643                 goto error;
2644         nparam = isl_basic_map_n_param(bmap);
2645         n_in = isl_basic_map_n_in(bmap);
2646         isl_seq_clr(bmap->eq[i], 1 + isl_basic_map_total_dim(bmap));
2647         isl_int_set_si(bmap->eq[i][1+nparam+pos], -1);
2648         isl_int_set_si(bmap->eq[i][1+nparam+n_in+pos], 1);
2649         return isl_basic_map_finalize(bmap);
2650 error:
2651         isl_basic_map_free(bmap);
2652         return NULL;
2653 }
2654
2655 static struct isl_basic_map *var_more(struct isl_ctx *ctx,
2656                 struct isl_basic_map *bmap, unsigned pos)
2657 {
2658         int i;
2659         unsigned nparam;
2660         unsigned n_in;
2661
2662         i = isl_basic_map_alloc_inequality(bmap);
2663         if (i < 0)
2664                 goto error;
2665         nparam = isl_basic_map_n_param(bmap);
2666         n_in = isl_basic_map_n_in(bmap);
2667         isl_seq_clr(bmap->ineq[i], 1 + isl_basic_map_total_dim(bmap));
2668         isl_int_set_si(bmap->ineq[i][0], -1);
2669         isl_int_set_si(bmap->ineq[i][1+nparam+pos], -1);
2670         isl_int_set_si(bmap->ineq[i][1+nparam+n_in+pos], 1);
2671         return isl_basic_map_finalize(bmap);
2672 error:
2673         isl_basic_map_free(bmap);
2674         return NULL;
2675 }
2676
2677 static struct isl_basic_map *var_less(struct isl_ctx *ctx,
2678                 struct isl_basic_map *bmap, unsigned pos)
2679 {
2680         int i;
2681         unsigned nparam;
2682         unsigned n_in;
2683
2684         i = isl_basic_map_alloc_inequality(bmap);
2685         if (i < 0)
2686                 goto error;
2687         nparam = isl_basic_map_n_param(bmap);
2688         n_in = isl_basic_map_n_in(bmap);
2689         isl_seq_clr(bmap->ineq[i], 1 + isl_basic_map_total_dim(bmap));
2690         isl_int_set_si(bmap->ineq[i][0], -1);
2691         isl_int_set_si(bmap->ineq[i][1+nparam+pos], 1);
2692         isl_int_set_si(bmap->ineq[i][1+nparam+n_in+pos], -1);
2693         return isl_basic_map_finalize(bmap);
2694 error:
2695         isl_basic_map_free(bmap);
2696         return NULL;
2697 }
2698
2699 struct isl_basic_map *isl_basic_map_equal(struct isl_ctx *ctx,
2700                 unsigned nparam, unsigned in, unsigned out, unsigned n_equal)
2701 {
2702         int i;
2703         struct isl_basic_map *bmap;
2704         bmap = isl_basic_map_alloc(ctx, nparam, in, out, 0, n_equal, 0);
2705         if (!bmap)
2706                 return NULL;
2707         for (i = 0; i < n_equal && bmap; ++i)
2708                 bmap = var_equal(ctx, bmap, i);
2709         return isl_basic_map_finalize(bmap);
2710 }
2711
2712 struct isl_basic_map *isl_basic_map_less_at(struct isl_ctx *ctx,
2713                 unsigned nparam, unsigned in, unsigned out, unsigned pos)
2714 {
2715         int i;
2716         struct isl_basic_map *bmap;
2717         bmap = isl_basic_map_alloc(ctx, nparam, in, out, 0, pos, 1);
2718         if (!bmap)
2719                 return NULL;
2720         for (i = 0; i < pos && bmap; ++i)
2721                 bmap = var_equal(ctx, bmap, i);
2722         if (bmap)
2723                 bmap = var_less(ctx, bmap, pos);
2724         return isl_basic_map_finalize(bmap);
2725 }
2726
2727 struct isl_basic_map *isl_basic_map_more_at(struct isl_ctx *ctx,
2728                 unsigned nparam, unsigned in, unsigned out, unsigned pos)
2729 {
2730         int i;
2731         struct isl_basic_map *bmap;
2732         bmap = isl_basic_map_alloc(ctx, nparam, in, out, 0, pos, 1);
2733         if (!bmap)
2734                 return NULL;
2735         for (i = 0; i < pos && bmap; ++i)
2736                 bmap = var_equal(ctx, bmap, i);
2737         if (bmap)
2738                 bmap = var_more(ctx, bmap, pos);
2739         return isl_basic_map_finalize(bmap);
2740 }
2741
2742 struct isl_basic_map *isl_basic_map_from_basic_set(
2743                 struct isl_basic_set *bset, struct isl_dim *dim)
2744 {
2745         struct isl_basic_map *bmap;
2746
2747         bset = isl_basic_set_cow(bset);
2748         if (!bset || !dim)
2749                 goto error;
2750
2751         isl_assert(bset->ctx, isl_dim_compatible(bset->dim, dim), goto error);
2752         isl_dim_free(bset->dim);
2753         bmap = (struct isl_basic_map *) bset;
2754         bmap->dim = dim;
2755         return isl_basic_map_finalize(bmap);
2756 error:
2757         isl_basic_set_free(bset);
2758         isl_dim_free(dim);
2759         return NULL;
2760 }
2761
2762 struct isl_basic_set *isl_basic_set_from_basic_map(struct isl_basic_map *bmap)
2763 {
2764         if (!bmap)
2765                 goto error;
2766         if (bmap->dim->n_in == 0)
2767                 return (struct isl_basic_set *)bmap;
2768         bmap = isl_basic_map_cow(bmap);
2769         if (!bmap)
2770                 goto error;
2771         bmap->dim = isl_dim_cow(bmap->dim);
2772         if (!bmap->dim)
2773                 goto error;
2774         bmap->dim->n_out += bmap->dim->n_in;
2775         bmap->dim->n_in = 0;
2776         bmap = isl_basic_map_finalize(bmap);
2777         return (struct isl_basic_set *)bmap;
2778 error:
2779         isl_basic_map_free(bmap);
2780         return NULL;
2781 }
2782
2783 /* For a div d = floor(f/m), add the constraints
2784  *
2785  *              f - m d >= 0
2786  *              -(f-(n-1)) + m d >= 0
2787  *
2788  * Note that the second constraint is the negation of
2789  *
2790  *              f - m d >= n
2791  */
2792 static int add_div_constraints(struct isl_basic_map *bmap, unsigned div)
2793 {
2794         int i, j;
2795         unsigned total = isl_basic_map_total_dim(bmap);
2796         unsigned div_pos = 1 + total - bmap->n_div + div;
2797
2798         i = isl_basic_map_alloc_inequality(bmap);
2799         if (i < 0)
2800                 return -1;
2801         isl_seq_cpy(bmap->ineq[i], bmap->div[div]+1, 1+total);
2802         isl_int_neg(bmap->ineq[i][div_pos], bmap->div[div][0]);
2803
2804         j = isl_basic_map_alloc_inequality(bmap);
2805         if (j < 0)
2806                 return -1;
2807         isl_seq_neg(bmap->ineq[j], bmap->ineq[i], 1 + total);
2808         isl_int_add(bmap->ineq[j][0], bmap->ineq[j][0], bmap->ineq[j][div_pos]);
2809         isl_int_sub_ui(bmap->ineq[j][0], bmap->ineq[j][0], 1);
2810         return j;
2811 }
2812
2813 struct isl_basic_set *isl_basic_map_underlying_set(
2814                 struct isl_basic_map *bmap)
2815 {
2816         if (!bmap)
2817                 goto error;
2818         if (bmap->dim->nparam == 0 && bmap->dim->n_in == 0 && bmap->n_div == 0)
2819                 return (struct isl_basic_set *)bmap;
2820         bmap = isl_basic_map_cow(bmap);
2821         if (!bmap)
2822                 goto error;
2823         bmap->dim = isl_dim_cow(bmap->dim);
2824         if (!bmap->dim)
2825                 goto error;
2826         bmap->dim->n_out += bmap->dim->nparam + bmap->dim->n_in + bmap->n_div;
2827         bmap->dim->nparam = 0;
2828         bmap->dim->n_in = 0;
2829         bmap->extra -= bmap->n_div;
2830         bmap->n_div = 0;
2831         bmap = isl_basic_map_finalize(bmap);
2832         return (struct isl_basic_set *)bmap;
2833 error:
2834         return NULL;
2835 }
2836
2837 struct isl_basic_map *isl_basic_map_overlying_set(
2838         struct isl_basic_set *bset, struct isl_basic_map *like)
2839 {
2840         struct isl_basic_map *bmap;
2841         struct isl_ctx *ctx;
2842         unsigned total;
2843         int i, k;
2844
2845         if (!bset || !like)
2846                 goto error;
2847         ctx = bset->ctx;
2848         isl_assert(ctx, bset->dim->n_out == isl_basic_map_total_dim(like),
2849                         goto error);
2850         if (isl_dim_equal(bset->dim, like->dim) && like->n_div == 0) {
2851                 isl_basic_map_free(like);
2852                 return (struct isl_basic_map *)bset;
2853         }
2854         bset = isl_basic_set_cow(bset);
2855         if (!bset)
2856                 goto error;
2857         total = bset->dim->n_out + bset->extra;
2858         bmap = (struct isl_basic_map *)bset;
2859         isl_dim_free(bmap->dim);
2860         bmap->dim = isl_dim_copy(like->dim);
2861         if (!bmap->dim)
2862                 goto error;
2863         bmap->extra += like->n_div;
2864         if (bmap->extra) {
2865                 unsigned ltotal;
2866                 ltotal = total - bmap->extra + like->extra;
2867                 if (ltotal > total)
2868                         ltotal = total;
2869                 bmap->block2 = isl_blk_extend(ctx, bmap->block2,
2870                                         bmap->extra * (1 + 1 + total));
2871                 if (isl_blk_is_error(bmap->block2))
2872                         goto error;
2873                 bmap->div = isl_realloc_array(ctx, bmap->div, isl_int *,
2874                                                 bmap->extra);
2875                 if (!bmap->div)
2876                         goto error;
2877                 bmap = isl_basic_map_extend_constraints(bmap,
2878                                                         0, 2 * like->n_div);
2879                 for (i = 0; i < like->n_div; ++i) {
2880                         k = isl_basic_map_alloc_div(bmap);
2881                         if (k < 0)
2882                                 goto error;
2883                         isl_seq_cpy(bmap->div[k], like->div[i], 1 + 1 + ltotal);
2884                         isl_seq_clr(bmap->div[k]+1+1+ltotal, total - ltotal);
2885                         if (add_div_constraints(bmap, k) < 0)
2886                                 goto error;
2887                 }
2888         }
2889         isl_basic_map_free(like);
2890         bmap = isl_basic_map_finalize(bmap);
2891         return bmap;
2892 error:
2893         isl_basic_map_free(like);
2894         isl_basic_set_free(bset);
2895         return NULL;
2896 }
2897
2898 struct isl_basic_set *isl_basic_set_from_underlying_set(
2899         struct isl_basic_set *bset, struct isl_basic_set *like)
2900 {
2901         return (struct isl_basic_set *)
2902                 isl_basic_map_overlying_set(bset, (struct isl_basic_map *)like);
2903 }
2904
2905 struct isl_set *isl_set_from_underlying_set(
2906         struct isl_set *set, struct isl_basic_set *like)
2907 {
2908         int i;
2909
2910         if (!set || !like)
2911                 goto error;
2912         isl_assert(set->ctx, set->dim->n_out == isl_basic_set_total_dim(like),
2913                     goto error);
2914         if (isl_dim_equal(set->dim, like->dim) && like->n_div == 0) {
2915                 isl_basic_set_free(like);
2916                 return set;
2917         }
2918         set = isl_set_cow(set);
2919         if (!set)
2920                 goto error;
2921         for (i = 0; i < set->n; ++i) {
2922                 set->p[i] = isl_basic_set_from_underlying_set(set->p[i],
2923                                                       isl_basic_set_copy(like));
2924                 if (!set->p[i])
2925                         goto error;
2926         }
2927         isl_dim_free(set->dim);
2928         set->dim = isl_dim_copy(like->dim);
2929         if (!set->dim)
2930                 goto error;
2931         isl_basic_set_free(like);
2932         return set;
2933 error:
2934         isl_basic_set_free(like);
2935         isl_set_free(set);
2936         return NULL;
2937 }
2938
2939 struct isl_set *isl_map_underlying_set(struct isl_map *map)
2940 {
2941         int i;
2942
2943         map = isl_map_align_divs(map);
2944         map = isl_map_cow(map);
2945         if (!map)
2946                 return NULL;
2947         map->dim = isl_dim_cow(map->dim);
2948         if (!map->dim)
2949                 goto error;
2950
2951         for (i = 0; i < map->n; ++i) {
2952                 map->p[i] = (struct isl_basic_map *)
2953                                 isl_basic_map_underlying_set(map->p[i]);
2954                 if (!map->p[i])
2955                         goto error;
2956         }
2957         if (map->n == 0)
2958                 map->dim->n_out += map->dim->nparam + map->dim->n_in;
2959         else
2960                 map->dim->n_out = map->p[0]->dim->n_out;
2961         map->dim->nparam = 0;
2962         map->dim->n_in = 0;
2963         return (struct isl_set *)map;
2964 error:
2965         isl_map_free(map);
2966         return NULL;
2967 }
2968
2969 struct isl_set *isl_set_to_underlying_set(struct isl_set *set)
2970 {
2971         return (struct isl_set *)isl_map_underlying_set((struct isl_map *)set);
2972 }
2973
2974 struct isl_basic_set *isl_basic_map_domain(struct isl_basic_map *bmap)
2975 {
2976         struct isl_basic_set *domain;
2977         unsigned n_out;
2978         if (!bmap)
2979                 return NULL;
2980         n_out = isl_basic_map_n_out(bmap);
2981         domain = isl_basic_set_from_basic_map(bmap);
2982         return isl_basic_set_project_out(domain, n_out, 0);
2983 }
2984
2985 struct isl_basic_set *isl_basic_map_range(struct isl_basic_map *bmap)
2986 {
2987         return isl_basic_map_domain(isl_basic_map_reverse(bmap));
2988 }
2989
2990 struct isl_set *isl_map_range(struct isl_map *map)
2991 {
2992         int i;
2993         struct isl_set *set;
2994
2995         if (!map)
2996                 goto error;
2997         map = isl_map_cow(map);
2998         if (!map)
2999                 goto error;
3000
3001         set = (struct isl_set *) map;
3002         if (set->dim->n_in != 0) {
3003                 set->dim = isl_dim_drop_inputs(set->dim, 0, set->dim->n_in);
3004                 if (!set->dim)
3005                         goto error;
3006         }
3007         for (i = 0; i < map->n; ++i) {
3008                 set->p[i] = isl_basic_map_range(map->p[i]);
3009                 if (!set->p[i])
3010                         goto error;
3011         }
3012         F_CLR(set, ISL_MAP_DISJOINT);
3013         F_CLR(set, ISL_SET_NORMALIZED);
3014         return set;
3015 error:
3016         isl_map_free(map);
3017         return NULL;
3018 }
3019
3020 struct isl_map *isl_map_from_set(struct isl_set *set, struct isl_dim *dim)
3021 {
3022         int i;
3023         struct isl_map *map = NULL;
3024
3025         set = isl_set_cow(set);
3026         if (!set || !dim)
3027                 goto error;
3028         isl_assert(set->ctx, isl_dim_compatible(set->dim, dim), goto error);
3029         map = (struct isl_map *)set;
3030         for (i = 0; i < set->n; ++i) {
3031                 map->p[i] = isl_basic_map_from_basic_set(
3032                                 set->p[i], isl_dim_copy(dim));
3033                 if (!map->p[i])
3034                         goto error;
3035         }
3036         isl_dim_free(map->dim);
3037         map->dim = dim;
3038         return map;
3039 error:
3040         isl_dim_free(dim);
3041         isl_set_free(set);
3042         return NULL;
3043 }
3044
3045 struct isl_set *isl_set_from_map(struct isl_map *map)
3046 {
3047         int i;
3048         struct isl_set *set = NULL;
3049
3050         if (!map)
3051                 return NULL;
3052         map = isl_map_cow(map);
3053         if (!map)
3054                 return NULL;
3055         map->dim = isl_dim_cow(map->dim);
3056         if (!map->dim)
3057                 goto error;
3058         map->dim->n_out += map->dim->n_in;
3059         map->dim->n_in = 0;
3060         set = (struct isl_set *)map;
3061         for (i = 0; i < map->n; ++i) {
3062                 set->p[i] = isl_basic_set_from_basic_map(map->p[i]);
3063                 if (!set->p[i])
3064                         goto error;
3065         }
3066         return set;
3067 error:
3068         isl_map_free(map);
3069         return NULL;
3070 }
3071
3072 struct isl_map *isl_map_alloc_dim(struct isl_dim *dim, int n, unsigned flags)
3073 {
3074         struct isl_map *map;
3075
3076         if (!dim)
3077                 return NULL;
3078         isl_assert(dim->ctx, n >= 0, return NULL);
3079         map = isl_alloc(dim->ctx, struct isl_map,
3080                         sizeof(struct isl_map) +
3081                         n * sizeof(struct isl_basic_map *));
3082         if (!map)
3083                 goto error;
3084
3085         map->ctx = dim->ctx;
3086         isl_ctx_ref(map->ctx);
3087         map->ref = 1;
3088         map->size = n;
3089         map->n = 0;
3090         map->dim = dim;
3091         map->flags = flags;
3092         return map;
3093 error:
3094         isl_dim_free(dim);
3095         return NULL;
3096 }
3097
3098 struct isl_map *isl_map_alloc(struct isl_ctx *ctx,
3099                 unsigned nparam, unsigned in, unsigned out, int n,
3100                 unsigned flags)
3101 {
3102         struct isl_map *map;
3103         struct isl_dim *dims;
3104
3105         dims = isl_dim_alloc(ctx, nparam, in, out);
3106         if (!dims)
3107                 return NULL;
3108
3109         map = isl_map_alloc_dim(dims, n, flags);
3110         return map;
3111 }
3112
3113 struct isl_basic_map *isl_basic_map_empty(struct isl_ctx *ctx,
3114                 unsigned nparam, unsigned in, unsigned out)
3115 {
3116         struct isl_basic_map *bmap;
3117         bmap = isl_basic_map_alloc(ctx, nparam, in, out, 0, 1, 0);
3118         bmap = isl_basic_map_set_to_empty(bmap);
3119         return bmap;
3120 }
3121
3122 struct isl_basic_set *isl_basic_set_empty(struct isl_dim *dim)
3123 {
3124         struct isl_basic_set *bset;
3125         bset = isl_basic_set_alloc_dim(dim, 0, 1, 0);
3126         bset = isl_basic_set_set_to_empty(bset);
3127         return bset;
3128 }
3129
3130 struct isl_basic_map *isl_basic_map_empty_like(struct isl_basic_map *model)
3131 {
3132         struct isl_basic_map *bmap;
3133         if (!model)
3134                 return NULL;
3135         bmap = isl_basic_map_alloc_dim(isl_dim_copy(model->dim), 0, 1, 0);
3136         bmap = isl_basic_map_set_to_empty(bmap);
3137         return bmap;
3138 }
3139
3140 struct isl_basic_map *isl_basic_map_empty_like_map(struct isl_map *model)
3141 {
3142         struct isl_basic_map *bmap;
3143         if (!model)
3144                 return NULL;
3145         bmap = isl_basic_map_alloc_dim(isl_dim_copy(model->dim), 0, 1, 0);
3146         bmap = isl_basic_map_set_to_empty(bmap);
3147         return bmap;
3148 }
3149
3150 struct isl_basic_set *isl_basic_set_empty_like(struct isl_basic_set *model)
3151 {
3152         struct isl_basic_set *bset;
3153         if (!model)
3154                 return NULL;
3155         bset = isl_basic_set_alloc_dim(isl_dim_copy(model->dim), 0, 1, 0);
3156         bset = isl_basic_set_set_to_empty(bset);
3157         return bset;
3158 }
3159
3160 struct isl_basic_map *isl_basic_map_universe(struct isl_dim *dim)
3161 {
3162         struct isl_basic_map *bmap;
3163         bmap = isl_basic_map_alloc_dim(dim, 0, 0, 0);
3164         return bmap;
3165 }
3166
3167 struct isl_basic_set *isl_basic_set_universe(struct isl_dim *dim)
3168 {
3169         struct isl_basic_set *bset;
3170         bset = isl_basic_set_alloc_dim(dim, 0, 0, 0);
3171         return bset;
3172 }
3173
3174 struct isl_basic_set *isl_basic_set_universe_like(struct isl_basic_set *model)
3175 {
3176         if (!model)
3177                 return NULL;
3178         return isl_basic_set_alloc_dim(isl_dim_copy(model->dim), 0, 0, 0);
3179 }
3180
3181 struct isl_map *isl_map_empty(struct isl_ctx *ctx,
3182                 unsigned nparam, unsigned in, unsigned out)
3183 {
3184         return isl_map_alloc(ctx, nparam, in, out, 0, ISL_MAP_DISJOINT);
3185 }
3186
3187 struct isl_map *isl_map_empty_like_basic_map(struct isl_basic_map *model)
3188 {
3189         if (!model)
3190                 return NULL;
3191         return isl_map_alloc_dim(isl_dim_copy(model->dim), 0, ISL_MAP_DISJOINT);
3192 }
3193
3194 struct isl_set *isl_set_empty(struct isl_dim *dim)
3195 {
3196         return isl_set_alloc_dim(dim, 0, ISL_MAP_DISJOINT);
3197 }
3198
3199 struct isl_set *isl_set_empty_like(struct isl_set *model)
3200 {
3201         if (!model)
3202                 return NULL;
3203         return isl_set_empty(isl_dim_copy(model->dim));
3204 }
3205
3206 struct isl_set *isl_set_universe(struct isl_dim *dim)
3207 {
3208         struct isl_set *set;
3209         if (!dim)
3210                 return NULL;
3211         set = isl_set_alloc_dim(isl_dim_copy(dim), 1, ISL_MAP_DISJOINT);
3212         set = isl_set_add(set, isl_basic_set_universe(dim));
3213         return set;
3214 }
3215
3216 struct isl_map *isl_map_dup(struct isl_map *map)
3217 {
3218         int i;
3219         struct isl_map *dup;
3220
3221         if (!map)
3222                 return NULL;
3223         dup = isl_map_alloc_dim(isl_dim_copy(map->dim), map->n, map->flags);
3224         for (i = 0; i < map->n; ++i)
3225                 dup = isl_map_add(dup, isl_basic_map_copy(map->p[i]));
3226         return dup;
3227 }
3228
3229 struct isl_map *isl_map_add(struct isl_map *map, struct isl_basic_map *bmap)
3230 {
3231         if (!bmap || !map)
3232                 goto error;
3233         isl_assert(map->ctx, isl_dim_equal(map->dim, bmap->dim), goto error);
3234         isl_assert(map->ctx, map->n < map->size, goto error);
3235         map->p[map->n] = bmap;
3236         map->n++;
3237         F_CLR(map, ISL_MAP_NORMALIZED);
3238         return map;
3239 error:
3240         if (map)
3241                 isl_map_free(map);
3242         if (bmap)
3243                 isl_basic_map_free(bmap);
3244         return NULL;
3245 }
3246
3247 void isl_map_free(struct isl_map *map)
3248 {
3249         int i;
3250
3251         if (!map)
3252                 return;
3253
3254         if (--map->ref > 0)
3255                 return;
3256
3257         isl_ctx_deref(map->ctx);
3258         for (i = 0; i < map->n; ++i)
3259                 isl_basic_map_free(map->p[i]);
3260         isl_dim_free(map->dim);
3261         free(map);
3262 }
3263
3264 struct isl_map *isl_map_extend(struct isl_map *base,
3265                 unsigned nparam, unsigned n_in, unsigned n_out)
3266 {
3267         int i;
3268
3269         base = isl_map_cow(base);
3270         if (!base)
3271                 return NULL;
3272
3273         base->dim = isl_dim_extend(base->dim, nparam, n_in, n_out);
3274         if (!base->dim)
3275                 goto error;
3276         for (i = 0; i < base->n; ++i) {
3277                 base->p[i] = isl_basic_map_extend_dim(base->p[i],
3278                                 isl_dim_copy(base->dim), 0, 0, 0);
3279                 if (!base->p[i])
3280                         goto error;
3281         }
3282         return base;
3283 error:
3284         isl_map_free(base);
3285         return NULL;
3286 }
3287
3288 struct isl_set *isl_set_extend(struct isl_set *base,
3289                 unsigned nparam, unsigned dim)
3290 {
3291         return (struct isl_set *)isl_map_extend((struct isl_map *)base,
3292                                                         nparam, 0, dim);
3293 }
3294
3295 static struct isl_basic_map *isl_basic_map_fix_var(struct isl_basic_map *bmap,
3296                 unsigned var, int value)
3297 {
3298         int j;
3299
3300         bmap = isl_basic_map_cow(bmap);
3301         bmap = isl_basic_map_extend_constraints(bmap, 1, 0);
3302         j = isl_basic_map_alloc_equality(bmap);
3303         if (j < 0)
3304                 goto error;
3305         isl_seq_clr(bmap->eq[j], 1 + isl_basic_map_total_dim(bmap));
3306         isl_int_set_si(bmap->eq[j][1 + var], -1);
3307         isl_int_set_si(bmap->eq[j][0], value);
3308         bmap = isl_basic_map_simplify(bmap);
3309         return isl_basic_map_finalize(bmap);
3310 error:
3311         isl_basic_map_free(bmap);
3312         return NULL;
3313 }
3314
3315 struct isl_basic_map *isl_basic_map_fix_input_si(struct isl_basic_map *bmap,
3316                 unsigned input, int value)
3317 {
3318         if (!bmap)
3319                 return NULL;
3320         isl_assert(bmap->ctx, input < isl_basic_map_n_in(bmap), goto error);
3321         return isl_basic_map_fix_var(bmap, isl_basic_map_n_param(bmap) + input,
3322                                         value);
3323 error:
3324         isl_basic_map_free(bmap);
3325         return NULL;
3326 }
3327
3328 struct isl_basic_set *isl_basic_set_fix_dim_si(struct isl_basic_set *bset,
3329                 unsigned dim, int value)
3330 {
3331         if (!bset)
3332                 return NULL;
3333         isl_assert(bset->ctx, dim < isl_basic_set_n_dim(bset), goto error);
3334         return (struct isl_basic_set *)
3335                 isl_basic_map_fix_var((struct isl_basic_map *)bset,
3336                                     isl_basic_set_n_param(bset) + dim, value);
3337 error:
3338         isl_basic_set_free(bset);
3339         return NULL;
3340 }
3341
3342 struct isl_map *isl_map_fix_input_si(struct isl_map *map,
3343                 unsigned input, int value)
3344 {
3345         int i;
3346
3347         map = isl_map_cow(map);
3348         if (!map)
3349                 return NULL;
3350
3351         isl_assert(ctx, input < isl_map_n_in(map), goto error);
3352         for (i = 0; i < map->n; ++i) {
3353                 map->p[i] = isl_basic_map_fix_input_si(map->p[i], input, value);
3354                 if (!map->p[i])
3355                         goto error;
3356         }
3357         F_CLR(map, ISL_MAP_NORMALIZED);
3358         return map;
3359 error:
3360         isl_map_free(map);
3361         return NULL;
3362 }
3363
3364 struct isl_set *isl_set_fix_dim_si(struct isl_set *set, unsigned dim, int value)
3365 {
3366         int i;
3367
3368         set = isl_set_cow(set);
3369         if (!set)
3370                 return NULL;
3371
3372         isl_assert(set->ctx, dim < isl_set_n_dim(set), goto error);
3373         for (i = 0; i < set->n; ++i) {
3374                 set->p[i] = isl_basic_set_fix_dim_si(set->p[i], dim, value);
3375                 if (!set->p[i])
3376                         goto error;
3377         }
3378         return set;
3379 error:
3380         isl_set_free(set);
3381         return NULL;
3382 }
3383
3384 struct isl_basic_set *isl_basic_set_lower_bound_dim(struct isl_basic_set *bset,
3385         unsigned dim, isl_int value)
3386 {
3387         int j;
3388         unsigned nparam;
3389
3390         bset = isl_basic_set_cow(bset);
3391         bset = isl_basic_set_extend_constraints(bset, 0, 1);
3392         j = isl_basic_set_alloc_inequality(bset);
3393         if (j < 0)
3394                 goto error;
3395         isl_seq_clr(bset->ineq[j], 1 + isl_basic_set_total_dim(bset));
3396         isl_int_set_si(bset->ineq[j][1 + isl_basic_set_n_param(bset) + dim], 1);
3397         isl_int_neg(bset->ineq[j][0], value);
3398         bset = isl_basic_set_simplify(bset);
3399         return isl_basic_set_finalize(bset);
3400 error:
3401         isl_basic_set_free(bset);
3402         return NULL;
3403 }
3404
3405 struct isl_set *isl_set_lower_bound_dim(struct isl_set *set, unsigned dim,
3406                                         isl_int value)
3407 {
3408         int i;
3409
3410         set = isl_set_cow(set);
3411         if (!set)
3412                 return NULL;
3413
3414         isl_assert(set->ctx, dim < isl_set_n_dim(set), goto error);
3415         for (i = 0; i < set->n; ++i) {
3416                 set->p[i] = isl_basic_set_lower_bound_dim(set->p[i], dim, value);
3417                 if (!set->p[i])
3418                         goto error;
3419         }
3420         return set;
3421 error:
3422         isl_set_free(set);
3423         return NULL;
3424 }
3425
3426 struct isl_map *isl_map_reverse(struct isl_map *map)
3427 {
3428         int i;
3429         unsigned t;
3430
3431         map = isl_map_cow(map);
3432         if (!map)
3433                 return NULL;
3434
3435         map->dim = isl_dim_reverse(map->dim);
3436         if (!map->dim)
3437                 goto error;
3438         for (i = 0; i < map->n; ++i) {
3439                 map->p[i] = isl_basic_map_reverse(map->p[i]);
3440                 if (!map->p[i])
3441                         goto error;
3442         }
3443         F_CLR(map, ISL_MAP_NORMALIZED);
3444         return map;
3445 error:
3446         isl_map_free(map);
3447         return NULL;
3448 }
3449
3450 struct isl_map *isl_basic_map_lexmax(
3451                 struct isl_basic_map *bmap, struct isl_basic_set *dom,
3452                 struct isl_set **empty)
3453 {
3454         return isl_pip_basic_map_lexmax(bmap, dom, empty);
3455 }
3456
3457 struct isl_map *isl_basic_map_lexmin(
3458                 struct isl_basic_map *bmap, struct isl_basic_set *dom,
3459                 struct isl_set **empty)
3460 {
3461         return isl_pip_basic_map_lexmin(bmap, dom, empty);
3462 }
3463
3464 struct isl_set *isl_basic_set_lexmin(struct isl_basic_set *bset)
3465 {
3466         struct isl_basic_map *bmap = NULL;
3467         struct isl_basic_set *dom = NULL;
3468         struct isl_map *min;
3469         struct isl_dim *param_dim;
3470
3471         if (!bset)
3472                 goto error;
3473         bmap = isl_basic_map_from_basic_set(bset, isl_dim_copy(bset->dim));
3474         if (!bmap)
3475                 goto error;
3476         param_dim = isl_dim_domain(isl_dim_copy(bmap->dim));
3477         dom = isl_basic_set_universe(param_dim);
3478         if (!dom)
3479                 goto error;
3480         min = isl_basic_map_lexmin(bmap, dom, NULL);
3481         return isl_map_range(min);
3482 error:
3483         isl_basic_map_free(bmap);
3484         return NULL;
3485 }
3486
3487 struct isl_map *isl_basic_map_compute_divs(struct isl_basic_map *bmap)
3488 {
3489         if (!bmap)
3490                 return NULL;
3491         if (bmap->n_div == 0)
3492                 return isl_map_from_basic_map(bmap);
3493         return isl_pip_basic_map_compute_divs(bmap);
3494 }
3495
3496 struct isl_map *isl_map_compute_divs(struct isl_map *map)
3497 {
3498         int i;
3499         struct isl_map *res;
3500
3501         if (!map)
3502                 return NULL;
3503         if (map->n == 0)
3504                 return map;
3505         res = isl_basic_map_compute_divs(isl_basic_map_copy(map->p[0]));
3506         for (i = 1 ; i < map->n; ++i) {
3507                 struct isl_map *r2;
3508                 r2 = isl_basic_map_compute_divs(isl_basic_map_copy(map->p[i]));
3509                 if (F_ISSET(map, ISL_MAP_DISJOINT))
3510                         res = isl_map_union_disjoint(res, r2);
3511                 else
3512                         res = isl_map_union(res, r2);
3513         }
3514         isl_map_free(map);
3515
3516         return res;
3517 }
3518
3519 struct isl_set *isl_basic_set_compute_divs(struct isl_basic_set *bset)
3520 {
3521         return (struct isl_set *)
3522                 isl_basic_map_compute_divs((struct isl_basic_map *)bset);
3523 }
3524
3525 struct isl_set *isl_set_compute_divs(struct isl_set *set)
3526 {
3527         return (struct isl_set *)
3528                 isl_map_compute_divs((struct isl_map *)set);
3529 }
3530
3531 struct isl_set *isl_map_domain(struct isl_map *map)
3532 {
3533         int i;
3534         struct isl_set *set;
3535
3536         if (!map)
3537                 goto error;
3538
3539         map = isl_map_cow(map);
3540         if (!map)
3541                 return NULL;
3542
3543         set = (struct isl_set *)map;
3544         set->dim = isl_dim_domain(set->dim);
3545         if (!set->dim)
3546                 goto error;
3547         for (i = 0; i < map->n; ++i) {
3548                 set->p[i] = isl_basic_map_domain(map->p[i]);
3549                 if (!set->p[i])
3550                         goto error;
3551         }
3552         F_CLR(set, ISL_MAP_DISJOINT);
3553         F_CLR(set, ISL_SET_NORMALIZED);
3554         return set;
3555 error:
3556         isl_map_free(map);
3557         return NULL;
3558 }
3559
3560 struct isl_map *isl_map_union_disjoint(
3561                         struct isl_map *map1, struct isl_map *map2)
3562 {
3563         int i;
3564         unsigned flags = 0;
3565         struct isl_map *map = NULL;
3566
3567         if (!map1 || !map2)
3568                 goto error;
3569
3570         if (map1->n == 0) {
3571                 isl_map_free(map1);
3572                 return map2;
3573         }
3574         if (map2->n == 0) {
3575                 isl_map_free(map2);
3576                 return map1;
3577         }
3578
3579         isl_assert(map1->ctx, isl_dim_equal(map1->dim, map2->dim), goto error);
3580
3581         if (F_ISSET(map1, ISL_MAP_DISJOINT) &&
3582             F_ISSET(map2, ISL_MAP_DISJOINT))
3583                 FL_SET(flags, ISL_MAP_DISJOINT);
3584
3585         map = isl_map_alloc_dim(isl_dim_copy(map1->dim),
3586                                 map1->n + map2->n, flags);
3587         if (!map)
3588                 goto error;
3589         for (i = 0; i < map1->n; ++i) {
3590                 map = isl_map_add(map,
3591                                   isl_basic_map_copy(map1->p[i]));
3592                 if (!map)
3593                         goto error;
3594         }
3595         for (i = 0; i < map2->n; ++i) {
3596                 map = isl_map_add(map,
3597                                   isl_basic_map_copy(map2->p[i]));
3598                 if (!map)
3599                         goto error;
3600         }
3601         isl_map_free(map1);
3602         isl_map_free(map2);
3603         return map;
3604 error:
3605         isl_map_free(map);
3606         isl_map_free(map1);
3607         isl_map_free(map2);
3608         return NULL;
3609 }
3610
3611 struct isl_map *isl_map_union(struct isl_map *map1, struct isl_map *map2)
3612 {
3613         map1 = isl_map_union_disjoint(map1, map2);
3614         if (!map1)
3615                 return NULL;
3616         if (map1->n > 1)
3617                 F_CLR(map1, ISL_MAP_DISJOINT);
3618         return map1;
3619 }
3620
3621 struct isl_set *isl_set_union_disjoint(
3622                         struct isl_set *set1, struct isl_set *set2)
3623 {
3624         return (struct isl_set *)
3625                 isl_map_union_disjoint(
3626                         (struct isl_map *)set1, (struct isl_map *)set2);
3627 }
3628
3629 struct isl_set *isl_set_union(struct isl_set *set1, struct isl_set *set2)
3630 {
3631         return (struct isl_set *)
3632                 isl_map_union((struct isl_map *)set1, (struct isl_map *)set2);
3633 }
3634
3635 struct isl_map *isl_map_intersect_range(
3636                 struct isl_map *map, struct isl_set *set)
3637 {
3638         unsigned flags = 0;
3639         struct isl_map *result;
3640         int i, j;
3641
3642         if (!map || !set)
3643                 goto error;
3644
3645         if (F_ISSET(map, ISL_MAP_DISJOINT) &&
3646             F_ISSET(set, ISL_MAP_DISJOINT))
3647                 FL_SET(flags, ISL_MAP_DISJOINT);
3648
3649         result = isl_map_alloc_dim(isl_dim_copy(map->dim),
3650                                         map->n * set->n, flags);
3651         if (!result)
3652                 goto error;
3653         for (i = 0; i < map->n; ++i)
3654                 for (j = 0; j < set->n; ++j) {
3655                         result = isl_map_add(result,
3656                             isl_basic_map_intersect_range(
3657                                 isl_basic_map_copy(map->p[i]),
3658                                 isl_basic_set_copy(set->p[j])));
3659                         if (!result)
3660                                 goto error;
3661                 }
3662         isl_map_free(map);
3663         isl_set_free(set);
3664         return result;
3665 error:
3666         isl_map_free(map);
3667         isl_set_free(set);
3668         return NULL;
3669 }
3670
3671 struct isl_map *isl_map_intersect_domain(
3672                 struct isl_map *map, struct isl_set *set)
3673 {
3674         return isl_map_reverse(
3675                 isl_map_intersect_range(isl_map_reverse(map), set));
3676 }
3677
3678 struct isl_map *isl_map_apply_domain(
3679                 struct isl_map *map1, struct isl_map *map2)
3680 {
3681         if (!map1 || !map2)
3682                 goto error;
3683         map1 = isl_map_reverse(map1);
3684         map1 = isl_map_apply_range(map1, map2);
3685         return isl_map_reverse(map1);
3686 error:
3687         isl_map_free(map1);
3688         isl_map_free(map2);
3689         return NULL;
3690 }
3691
3692 struct isl_map *isl_map_apply_range(
3693                 struct isl_map *map1, struct isl_map *map2)
3694 {
3695         struct isl_dim *dim_result;
3696         struct isl_map *result;
3697         int i, j;
3698         unsigned nparam;
3699         unsigned n_in;
3700         unsigned n_out;
3701
3702         if (!map1 || !map2)
3703                 goto error;
3704
3705         dim_result = isl_dim_join(isl_dim_copy(map1->dim),
3706                                   isl_dim_copy(map2->dim));
3707
3708         result = isl_map_alloc_dim(dim_result, map1->n * map2->n, 0);
3709         if (!result)
3710                 goto error;
3711         for (i = 0; i < map1->n; ++i)
3712                 for (j = 0; j < map2->n; ++j) {
3713                         result = isl_map_add(result,
3714                             isl_basic_map_apply_range(
3715                                 isl_basic_map_copy(map1->p[i]),
3716                                 isl_basic_map_copy(map2->p[j])));
3717                         if (!result)
3718                                 goto error;
3719                 }
3720         isl_map_free(map1);
3721         isl_map_free(map2);
3722         if (result && result->n <= 1)
3723                 F_SET(result, ISL_MAP_DISJOINT);
3724         return result;
3725 error:
3726         isl_map_free(map1);
3727         isl_map_free(map2);
3728         return NULL;
3729 }
3730
3731 /*
3732  * returns range - domain
3733  */
3734 struct isl_basic_set *isl_basic_map_deltas(struct isl_basic_map *bmap)
3735 {
3736         struct isl_basic_set *bset;
3737         unsigned dim;
3738         unsigned nparam;
3739         int i;
3740
3741         if (!bmap)
3742                 goto error;
3743         dim = isl_basic_map_n_in(bmap);
3744         nparam = isl_basic_map_n_param(bmap);
3745         isl_assert(bmap->ctx, dim == isl_basic_map_n_out(bmap), goto error);
3746         bset = isl_basic_set_from_basic_map(bmap);
3747         bset = isl_basic_set_extend(bset, nparam, 3*dim, 0, dim, 0);
3748         bset = isl_basic_set_swap_vars(bset, 2*dim);
3749         for (i = 0; i < dim; ++i) {
3750                 int j = isl_basic_map_alloc_equality(
3751                                             (struct isl_basic_map *)bset);
3752                 if (j < 0)
3753                         goto error;
3754                 isl_seq_clr(bset->eq[j], 1 + isl_basic_set_total_dim(bset));
3755                 isl_int_set_si(bset->eq[j][1+nparam+i], 1);
3756                 isl_int_set_si(bset->eq[j][1+nparam+dim+i], 1);
3757                 isl_int_set_si(bset->eq[j][1+nparam+2*dim+i], -1);
3758         }
3759         return isl_basic_set_project_out(bset, 2*dim, 0);
3760 error:
3761         isl_basic_map_free(bmap);
3762         return NULL;
3763 }
3764
3765 /*
3766  * returns range - domain
3767  */
3768 struct isl_set *isl_map_deltas(struct isl_map *map)
3769 {
3770         int i;
3771         struct isl_set *result;
3772
3773         if (!map)
3774                 return NULL;
3775
3776         isl_assert(map->ctx, isl_map_n_in(map) == isl_map_n_out(map), goto error);
3777         result = isl_set_alloc(map->ctx, isl_map_n_param(map),
3778                                         isl_map_n_in(map), map->n, map->flags);
3779         if (!result)
3780                 goto error;
3781         for (i = 0; i < map->n; ++i)
3782                 result = isl_set_add(result,
3783                           isl_basic_map_deltas(isl_basic_map_copy(map->p[i])));
3784         isl_map_free(map);
3785         return result;
3786 error:
3787         isl_map_free(map);
3788         return NULL;
3789 }
3790
3791 /* If the only constraints a div d=floor(f/m)
3792  * appears in are its two defining constraints
3793  *
3794  *      f - m d >=0
3795  *      -(f - (m - 1)) + m d >= 0
3796  *
3797  * then it can safely be removed.
3798  */
3799 static int div_is_redundant(struct isl_basic_map *bmap, int div)
3800 {
3801         int i;
3802         unsigned pos = 1 + isl_dim_total(bmap->dim) + div;
3803
3804         for (i = 0; i < bmap->n_eq; ++i)
3805                 if (!isl_int_is_zero(bmap->eq[i][pos]))
3806                         return 0;
3807
3808         for (i = 0; i < bmap->n_ineq; ++i) {
3809                 if (isl_int_is_zero(bmap->ineq[i][pos]))
3810                         continue;
3811                 if (isl_int_eq(bmap->ineq[i][pos], bmap->div[div][0])) {
3812                         int neg;
3813                         isl_int_sub(bmap->div[div][1],
3814                                         bmap->div[div][1], bmap->div[div][0]);
3815                         isl_int_add_ui(bmap->div[div][1], bmap->div[div][1], 1);
3816                         neg = isl_seq_is_neg(bmap->ineq[i], bmap->div[div]+1, pos);
3817                         isl_int_sub_ui(bmap->div[div][1], bmap->div[div][1], 1);
3818                         isl_int_add(bmap->div[div][1],
3819                                         bmap->div[div][1], bmap->div[div][0]);
3820                         if (!neg)
3821                                 return 0;
3822                         if (isl_seq_first_non_zero(bmap->ineq[i]+pos+1,
3823                                                     bmap->n_div-div-1) != -1)
3824                                 return 0;
3825                 } else if (isl_int_abs_eq(bmap->ineq[i][pos], bmap->div[div][0])) {
3826                         if (!isl_seq_eq(bmap->ineq[i], bmap->div[div]+1, pos))
3827                                 return 0;
3828                         if (isl_seq_first_non_zero(bmap->ineq[i]+pos+1,
3829                                                     bmap->n_div-div-1) != -1)
3830                                 return 0;
3831                 } else
3832                         return 0;
3833         }
3834
3835         for (i = 0; i < bmap->n_div; ++i)
3836                 if (!isl_int_is_zero(bmap->div[i][1+pos]))
3837                         return 0;
3838
3839         return 1;
3840 }
3841
3842 /*
3843  * Remove divs that don't occur in any of the constraints or other divs.
3844  * These can arise when dropping some of the variables in a quast
3845  * returned by piplib.
3846  */
3847 static struct isl_basic_map *remove_redundant_divs(struct isl_basic_map *bmap)
3848 {
3849         int i;
3850
3851         if (!bmap)
3852                 return NULL;
3853
3854         for (i = bmap->n_div-1; i >= 0; --i) {
3855                 if (!div_is_redundant(bmap, i))
3856                         continue;
3857                 bmap = isl_basic_map_drop_div(bmap, i);
3858         }
3859         return bmap;
3860 }
3861
3862 struct isl_basic_map *isl_basic_map_finalize(struct isl_basic_map *bmap)
3863 {
3864         bmap = remove_redundant_divs(bmap);
3865         if (!bmap)
3866                 return NULL;
3867         F_SET(bmap, ISL_BASIC_SET_FINAL);
3868         return bmap;
3869 }
3870
3871 struct isl_basic_set *isl_basic_set_finalize(struct isl_basic_set *bset)
3872 {
3873         return (struct isl_basic_set *)
3874                 isl_basic_map_finalize((struct isl_basic_map *)bset);
3875 }
3876
3877 struct isl_set *isl_set_finalize(struct isl_set *set)
3878 {
3879         int i;
3880
3881         if (!set)
3882                 return NULL;
3883         for (i = 0; i < set->n; ++i) {
3884                 set->p[i] = isl_basic_set_finalize(set->p[i]);
3885                 if (!set->p[i])
3886                         goto error;
3887         }
3888         return set;
3889 error:
3890         isl_set_free(set);
3891         return NULL;
3892 }
3893
3894 struct isl_map *isl_map_finalize(struct isl_map *map)
3895 {
3896         int i;
3897
3898         if (!map)
3899                 return NULL;
3900         for (i = 0; i < map->n; ++i) {
3901                 map->p[i] = isl_basic_map_finalize(map->p[i]);
3902                 if (!map->p[i])
3903                         goto error;
3904         }
3905         F_CLR(map, ISL_MAP_NORMALIZED);
3906         return map;
3907 error:
3908         isl_map_free(map);
3909         return NULL;
3910 }
3911
3912 static struct isl_basic_map *basic_map_identity(struct isl_dim *dims)
3913 {
3914         struct isl_basic_map *bmap;
3915         unsigned nparam;
3916         unsigned dim;
3917         int i;
3918
3919         if (!dims)
3920                 return NULL;
3921
3922         nparam = dims->nparam;
3923         dim = dims->n_out;
3924         bmap = isl_basic_map_alloc_dim(dims, 0, dim, 0);
3925         if (!bmap)
3926                 goto error;
3927
3928         for (i = 0; i < dim; ++i) {
3929                 int j = isl_basic_map_alloc_equality(bmap);
3930                 if (j < 0)
3931                         goto error;
3932                 isl_seq_clr(bmap->eq[j], 1 + isl_basic_map_total_dim(bmap));
3933                 isl_int_set_si(bmap->eq[j][1+nparam+i], 1);
3934                 isl_int_set_si(bmap->eq[j][1+nparam+dim+i], -1);
3935         }
3936         return isl_basic_map_finalize(bmap);
3937 error:
3938         isl_basic_map_free(bmap);
3939         return NULL;
3940 }
3941
3942 struct isl_basic_map *isl_basic_map_identity(struct isl_dim *set_dim)
3943 {
3944         struct isl_dim *dim = isl_dim_map(set_dim);
3945         if (!dim)
3946                 return NULL;
3947         return basic_map_identity(dim);
3948 }
3949
3950 struct isl_basic_map *isl_basic_map_identity_like(struct isl_basic_map *model)
3951 {
3952         if (!model || !model->dim)
3953                 return NULL;
3954         isl_assert(model->ctx,
3955                         model->dim->n_in == model->dim->n_out, return NULL);
3956         return basic_map_identity(isl_dim_copy(model->dim));
3957 }
3958
3959 static struct isl_map *map_identity(struct isl_dim *dim)
3960 {
3961         struct isl_map *map = isl_map_alloc_dim(dim, 1, ISL_MAP_DISJOINT);
3962         return isl_map_add(map, basic_map_identity(isl_dim_copy(dim)));
3963 }
3964
3965 struct isl_map *isl_map_identity(struct isl_dim *set_dim)
3966 {
3967         struct isl_dim *dim = isl_dim_map(set_dim);
3968         if (!dim)
3969                 return NULL;
3970         return map_identity(dim);
3971 }
3972
3973 struct isl_map *isl_map_identity_like(struct isl_basic_map *model)
3974 {
3975         if (!model || !model->dim)
3976                 return NULL;
3977         isl_assert(model->ctx,
3978                         model->dim->n_in == model->dim->n_out, return NULL);
3979         return map_identity(isl_dim_copy(model->dim));
3980 }
3981
3982 int isl_set_is_equal(struct isl_set *set1, struct isl_set *set2)
3983 {
3984         return isl_map_is_equal((struct isl_map *)set1, (struct isl_map *)set2);
3985 }
3986
3987 int isl_set_is_subset(struct isl_set *set1, struct isl_set *set2)
3988 {
3989         return isl_map_is_subset(
3990                         (struct isl_map *)set1, (struct isl_map *)set2);
3991 }
3992
3993 int isl_basic_map_is_subset(
3994                 struct isl_basic_map *bmap1, struct isl_basic_map *bmap2)
3995 {
3996         int is_subset;
3997         struct isl_map *map1;
3998         struct isl_map *map2;
3999
4000         if (!bmap1 || !bmap2)
4001                 return -1;
4002
4003         map1 = isl_map_from_basic_map(isl_basic_map_copy(bmap1));
4004         map2 = isl_map_from_basic_map(isl_basic_map_copy(bmap2));
4005
4006         is_subset = isl_map_is_subset(map1, map2);
4007
4008         isl_map_free(map1);
4009         isl_map_free(map2);
4010
4011         return is_subset;
4012 }
4013
4014 int isl_basic_map_is_equal(
4015                 struct isl_basic_map *bmap1, struct isl_basic_map *bmap2)
4016 {
4017         int is_subset;
4018
4019         if (!bmap1 || !bmap2)
4020                 return -1;
4021         is_subset = isl_basic_map_is_subset(bmap1, bmap2);
4022         if (is_subset != 1)
4023                 return is_subset;
4024         is_subset = isl_basic_map_is_subset(bmap2, bmap1);
4025         return is_subset;
4026 }
4027
4028 int isl_basic_set_is_equal(
4029                 struct isl_basic_set *bset1, struct isl_basic_set *bset2)
4030 {
4031         return isl_basic_map_is_equal(
4032                 (struct isl_basic_map *)bset1, (struct isl_basic_map *)bset2);
4033 }
4034
4035 int isl_map_is_empty(struct isl_map *map)
4036 {
4037         int i;
4038         int is_empty;
4039
4040         if (!map)
4041                 return -1;
4042         for (i = 0; i < map->n; ++i) {
4043                 is_empty = isl_basic_map_is_empty(map->p[i]);
4044                 if (is_empty < 0)
4045                         return -1;
4046                 if (!is_empty)
4047                         return 0;
4048         }
4049         return 1;
4050 }
4051
4052 int isl_set_is_empty(struct isl_set *set)
4053 {
4054         return isl_map_is_empty((struct isl_map *)set);
4055 }
4056
4057 int isl_map_is_subset(struct isl_map *map1, struct isl_map *map2)
4058 {
4059         int i;
4060         int is_subset = 0;
4061         struct isl_map *diff;
4062
4063         if (!map1 || !map2)
4064                 return -1;
4065
4066         if (isl_map_is_empty(map1))
4067                 return 1;
4068
4069         if (isl_map_is_empty(map2))
4070                 return 0;
4071
4072         diff = isl_map_subtract(isl_map_copy(map1), isl_map_copy(map2));
4073         if (!diff)
4074                 return -1;
4075
4076         is_subset = isl_map_is_empty(diff);
4077         isl_map_free(diff);
4078
4079         return is_subset;
4080 }
4081
4082 int isl_map_is_equal(struct isl_map *map1, struct isl_map *map2)
4083 {
4084         int is_subset;
4085
4086         if (!map1 || !map2)
4087                 return -1;
4088         is_subset = isl_map_is_subset(map1, map2);
4089         if (is_subset != 1)
4090                 return is_subset;
4091         is_subset = isl_map_is_subset(map2, map1);
4092         return is_subset;
4093 }
4094
4095 int isl_basic_map_is_strict_subset(
4096                 struct isl_basic_map *bmap1, struct isl_basic_map *bmap2)
4097 {
4098         int is_subset;
4099
4100         if (!bmap1 || !bmap2)
4101                 return -1;
4102         is_subset = isl_basic_map_is_subset(bmap1, bmap2);
4103         if (is_subset != 1)
4104                 return is_subset;
4105         is_subset = isl_basic_map_is_subset(bmap2, bmap1);
4106         if (is_subset == -1)
4107                 return is_subset;
4108         return !is_subset;
4109 }
4110
4111 static int basic_map_contains(struct isl_basic_map *bmap, struct isl_vec *vec)
4112 {
4113         int i;
4114         unsigned total;
4115         isl_int s;
4116
4117         total = 1 + isl_basic_map_total_dim(bmap);
4118         if (total != vec->size)
4119                 return -1;
4120
4121         isl_int_init(s);
4122
4123         for (i = 0; i < bmap->n_eq; ++i) {
4124                 isl_seq_inner_product(vec->block.data, bmap->eq[i], total, &s);
4125                 if (!isl_int_is_zero(s)) {
4126                         isl_int_clear(s);
4127                         return 0;
4128                 }
4129         }
4130
4131         for (i = 0; i < bmap->n_ineq; ++i) {
4132                 isl_seq_inner_product(vec->block.data, bmap->ineq[i], total, &s);
4133                 if (isl_int_is_neg(s)) {
4134                         isl_int_clear(s);
4135                         return 0;
4136                 }
4137         }
4138
4139         isl_int_clear(s);
4140
4141         return 1;
4142 }
4143
4144 int isl_basic_map_is_universe(struct isl_basic_map *bmap)
4145 {
4146         if (!bmap)
4147                 return -1;
4148         return bmap->n_eq == 0 && bmap->n_ineq == 0;
4149 }
4150
4151 int isl_basic_map_is_empty(struct isl_basic_map *bmap)
4152 {
4153         struct isl_basic_set *bset = NULL;
4154         struct isl_vec *sample = NULL;
4155         int empty;
4156         unsigned total;
4157
4158         if (!bmap)
4159                 return -1;
4160
4161         if (F_ISSET(bmap, ISL_BASIC_MAP_EMPTY))
4162                 return 1;
4163
4164         if (F_ISSET(bmap, ISL_BASIC_MAP_RATIONAL)) {
4165                 struct isl_basic_map *copy = isl_basic_map_copy(bmap);
4166                 copy = isl_basic_map_convex_hull(copy);
4167                 empty = F_ISSET(copy, ISL_BASIC_MAP_EMPTY);
4168                 isl_basic_map_free(copy);
4169                 return empty;
4170         }
4171
4172         total = 1 + isl_basic_map_total_dim(bmap);
4173         if (bmap->sample && bmap->sample->size == total) {
4174                 int contains = basic_map_contains(bmap, bmap->sample);
4175                 if (contains < 0)
4176                         return -1;
4177                 if (contains)
4178                         return 0;
4179         }
4180         bset = isl_basic_map_underlying_set(isl_basic_map_copy(bmap));
4181         if (!bset)
4182                 return -1;
4183         sample = isl_basic_set_sample(bset);
4184         if (!sample)
4185                 return -1;
4186         empty = sample->size == 0;
4187         if (bmap->sample)
4188                 isl_vec_free(bmap->ctx, bmap->sample);
4189         bmap->sample = sample;
4190
4191         return empty;
4192 }
4193
4194 struct isl_map *isl_basic_map_union(
4195         struct isl_basic_map *bmap1, struct isl_basic_map *bmap2)
4196 {
4197         struct isl_map *map;
4198         if (!bmap1 || !bmap2)
4199                 return NULL;
4200
4201         isl_assert(map1->ctx, isl_dim_equal(bmap1->dim, bmap2->dim), goto error);
4202
4203         map = isl_map_alloc_dim(isl_dim_copy(bmap1->dim), 2, 0);
4204         if (!map)
4205                 goto error;
4206         map = isl_map_add(map, bmap1);
4207         map = isl_map_add(map, bmap2);
4208         return map;
4209 error:
4210         isl_basic_map_free(bmap1);
4211         isl_basic_map_free(bmap2);
4212         return NULL;
4213 }
4214
4215 struct isl_set *isl_basic_set_union(
4216                 struct isl_basic_set *bset1, struct isl_basic_set *bset2)
4217 {
4218         return (struct isl_set *)isl_basic_map_union(
4219                                             (struct isl_basic_map *)bset1,
4220                                             (struct isl_basic_map *)bset2);
4221 }
4222
4223 /* Order divs such that any div only depends on previous divs */
4224 static struct isl_basic_map *order_divs(struct isl_basic_map *bmap)
4225 {
4226         int i;
4227         unsigned off = isl_dim_total(bmap->dim);
4228
4229         for (i = 0; i < bmap->n_div; ++i) {
4230                 int pos;
4231                 pos = isl_seq_first_non_zero(bmap->div[i]+1+1+off+i,
4232                                                             bmap->n_div-i);
4233                 if (pos == -1)
4234                         continue;
4235                 swap_div(bmap, i, pos);
4236                 --i;
4237         }
4238         return bmap;
4239 }
4240
4241 static int find_div(struct isl_basic_map *dst,
4242                         struct isl_basic_map *src, unsigned div)
4243 {
4244         int i;
4245
4246         unsigned total = isl_basic_map_total_dim(src);
4247
4248         for (i = 0; i < dst->n_div; ++i)
4249                 if (isl_seq_eq(dst->div[i], src->div[div], 1+1+total) &&
4250                     isl_seq_first_non_zero(dst->div[i]+1+1+total,
4251                                                 dst->n_div - src->n_div) == -1)
4252                         return i;
4253         return -1;
4254 }
4255
4256 struct isl_basic_map *isl_basic_map_align_divs(
4257                 struct isl_basic_map *dst, struct isl_basic_map *src)
4258 {
4259         int i;
4260         unsigned total = isl_basic_map_total_dim(src);
4261
4262         if (!dst || !src)
4263                 goto error;
4264
4265         if (src->n_div == 0)
4266                 return dst;
4267
4268         src = order_divs(src);
4269         dst = isl_basic_map_extend_dim(dst, isl_dim_copy(dst->dim),
4270                         src->n_div, 0, 2 * src->n_div);
4271         if (!dst)
4272                 return NULL;
4273         for (i = 0; i < src->n_div; ++i) {
4274                 int j = find_div(dst, src, i);
4275                 if (j < 0) {
4276                         j = isl_basic_map_alloc_div(dst);
4277                         if (j < 0)
4278                                 goto error;
4279                         isl_seq_cpy(dst->div[j], src->div[i], 1+1+total);
4280                         isl_seq_clr(dst->div[j]+1+1+total,
4281                                                     dst->n_div - src->n_div);
4282                         if (add_div_constraints(dst, j) < 0)
4283                                 goto error;
4284                 }
4285                 if (j != i)
4286                         swap_div(dst, i, j);
4287         }
4288         return dst;
4289 error:
4290         isl_basic_map_free(dst);
4291         return NULL;
4292 }
4293
4294 struct isl_basic_set *isl_basic_set_align_divs(
4295                 struct isl_basic_set *dst, struct isl_basic_set *src)
4296 {
4297         return (struct isl_basic_set *)isl_basic_map_align_divs(
4298                 (struct isl_basic_map *)dst, (struct isl_basic_map *)src);
4299 }
4300
4301 struct isl_map *isl_map_align_divs(struct isl_map *map)
4302 {
4303         int i;
4304
4305         map = isl_map_compute_divs(map);
4306         map = isl_map_cow(map);
4307         if (!map)
4308                 return NULL;
4309
4310         for (i = 1; i < map->n; ++i)
4311                 map->p[0] = isl_basic_map_align_divs(map->p[0], map->p[i]);
4312         for (i = 1; i < map->n; ++i)
4313                 map->p[i] = isl_basic_map_align_divs(map->p[i], map->p[0]);
4314
4315         F_CLR(map, ISL_MAP_NORMALIZED);
4316         return map;
4317 }
4318
4319 static struct isl_map *add_cut_constraint(struct isl_map *dst,
4320                 struct isl_basic_map *src, isl_int *c,
4321                 unsigned len, int oppose)
4322 {
4323         struct isl_basic_map *copy = NULL;
4324         int is_empty;
4325         int k;
4326         unsigned total;
4327
4328         copy = isl_basic_map_copy(src);
4329         copy = isl_basic_map_cow(copy);
4330         if (!copy)
4331                 goto error;
4332         copy = isl_basic_map_extend_constraints(copy, 0, 1);
4333         k = isl_basic_map_alloc_inequality(copy);
4334         if (k < 0)
4335                 goto error;
4336         if (oppose)
4337                 isl_seq_neg(copy->ineq[k], c, len);
4338         else
4339                 isl_seq_cpy(copy->ineq[k], c, len);
4340         total = 1 + isl_basic_map_total_dim(copy);
4341         isl_seq_clr(copy->ineq[k]+len, total - len);
4342         isl_inequality_negate(copy, k);
4343         copy = isl_basic_map_simplify(copy);
4344         copy = isl_basic_map_finalize(copy);
4345         is_empty = isl_basic_map_is_empty(copy);
4346         if (is_empty < 0)
4347                 goto error;
4348         if (!is_empty)
4349                 dst = isl_map_add(dst, copy);
4350         else
4351                 isl_basic_map_free(copy);
4352         return dst;
4353 error:
4354         isl_basic_map_free(copy);
4355         isl_map_free(dst);
4356         return NULL;
4357 }
4358
4359 static struct isl_map *subtract(struct isl_map *map, struct isl_basic_map *bmap)
4360 {
4361         int i, j, k;
4362         unsigned flags = 0;
4363         struct isl_map *rest = NULL;
4364         unsigned max;
4365         unsigned total = isl_basic_map_total_dim(bmap);
4366
4367         assert(bmap);
4368
4369         if (!map)
4370                 goto error;
4371
4372         if (F_ISSET(map, ISL_MAP_DISJOINT))
4373                 FL_SET(flags, ISL_MAP_DISJOINT);
4374
4375         max = map->n * (2 * bmap->n_eq + bmap->n_ineq);
4376         rest = isl_map_alloc_dim(isl_dim_copy(map->dim), max, flags);
4377         if (!rest)
4378                 goto error;
4379
4380         for (i = 0; i < map->n; ++i) {
4381                 map->p[i] = isl_basic_map_align_divs(map->p[i], bmap);
4382                 if (!map->p[i])
4383                         goto error;
4384         }
4385
4386         for (j = 0; j < map->n; ++j)
4387                 map->p[j] = isl_basic_map_cow(map->p[j]);
4388
4389         for (i = 0; i < bmap->n_eq; ++i) {
4390                 for (j = 0; j < map->n; ++j) {
4391                         rest = add_cut_constraint(rest,
4392                                 map->p[j], bmap->eq[i], 1+total, 0);
4393                         if (!rest)
4394                                 goto error;
4395
4396                         rest = add_cut_constraint(rest,
4397                                 map->p[j], bmap->eq[i], 1+total, 1);
4398                         if (!rest)
4399                                 goto error;
4400
4401                         map->p[j] = isl_basic_map_extend_constraints(map->p[j],
4402                                 1, 0);
4403                         if (!map->p[j])
4404                                 goto error;
4405                         k = isl_basic_map_alloc_equality(map->p[j]);
4406                         if (k < 0)
4407                                 goto error;
4408                         isl_seq_cpy(map->p[j]->eq[k], bmap->eq[i], 1+total);
4409                         isl_seq_clr(map->p[j]->eq[k]+1+total,
4410                                         map->p[j]->n_div - bmap->n_div);
4411                 }
4412         }
4413
4414         for (i = 0; i < bmap->n_ineq; ++i) {
4415                 for (j = 0; j < map->n; ++j) {
4416                         rest = add_cut_constraint(rest,
4417                                 map->p[j], bmap->ineq[i], 1+total, 0);
4418                         if (!rest)
4419                                 goto error;
4420
4421                         map->p[j] = isl_basic_map_extend_constraints(map->p[j],
4422                                 0, 1);
4423                         if (!map->p[j])
4424                                 goto error;
4425                         k = isl_basic_map_alloc_inequality(map->p[j]);
4426                         if (k < 0)
4427                                 goto error;
4428                         isl_seq_cpy(map->p[j]->ineq[k], bmap->ineq[i], 1+total);
4429                         isl_seq_clr(map->p[j]->ineq[k]+1+total,
4430                                         map->p[j]->n_div - bmap->n_div);
4431                 }
4432         }
4433
4434         isl_map_free(map);
4435         return rest;
4436 error:
4437         isl_map_free(map);
4438         isl_map_free(rest);
4439         return NULL;
4440 }
4441
4442 struct isl_map *isl_map_subtract(struct isl_map *map1, struct isl_map *map2)
4443 {
4444         int i;
4445         if (!map1 || !map2)
4446                 goto error;
4447
4448         isl_assert(map1->ctx, isl_dim_equal(map1->dim, map2->dim), goto error);
4449
4450         if (isl_map_is_empty(map2)) {
4451                 isl_map_free(map2);
4452                 return map1;
4453         }
4454
4455         map1 = isl_map_compute_divs(map1);
4456         map2 = isl_map_compute_divs(map2);
4457         if (!map1 || !map2)
4458                 goto error;
4459
4460         for (i = 0; map1 && i < map2->n; ++i)
4461                 map1 = subtract(map1, map2->p[i]);
4462
4463         isl_map_free(map2);
4464         return map1;
4465 error:
4466         isl_map_free(map1);
4467         isl_map_free(map2);
4468         return NULL;
4469 }
4470
4471 struct isl_set *isl_set_subtract(struct isl_set *set1, struct isl_set *set2)
4472 {
4473         return (struct isl_set *)
4474                 isl_map_subtract(
4475                         (struct isl_map *)set1, (struct isl_map *)set2);
4476 }
4477
4478 struct isl_set *isl_set_apply(struct isl_set *set, struct isl_map *map)
4479 {
4480         if (!set || !map)
4481                 goto error;
4482         isl_assert(set->ctx, isl_map_compatible_domain(map, set), goto error);
4483         map = isl_map_intersect_domain(map, set);
4484         set = isl_map_range(map);
4485         return set;
4486 error:
4487         isl_set_free(set);
4488         isl_map_free(map);
4489         return NULL;
4490 }
4491
4492 /* There is no need to cow as removing empty parts doesn't change
4493  * the meaning of the set.
4494  */
4495 struct isl_map *isl_map_remove_empty_parts(struct isl_map *map)
4496 {
4497         int i;
4498
4499         if (!map)
4500                 return NULL;
4501
4502         for (i = map->n-1; i >= 0; --i) {
4503                 if (!F_ISSET(map->p[i], ISL_BASIC_MAP_EMPTY))
4504                         continue;
4505                 isl_basic_map_free(map->p[i]);
4506                 if (i != map->n-1) {
4507                         F_CLR(map, ISL_MAP_NORMALIZED);
4508                         map->p[i] = map->p[map->n-1];
4509                 }
4510                 map->n--;
4511         }
4512
4513         return map;
4514 }
4515
4516 struct isl_set *isl_set_remove_empty_parts(struct isl_set *set)
4517 {
4518         return (struct isl_set *)
4519                 isl_map_remove_empty_parts((struct isl_map *)set);
4520 }
4521
4522 struct isl_basic_set *isl_set_copy_basic_set(struct isl_set *set)
4523 {
4524         struct isl_basic_set *bset;
4525         if (!set || set->n == 0)
4526                 return NULL;
4527         bset = set->p[set->n-1];
4528         isl_assert(set->ctx, F_ISSET(bset, ISL_BASIC_SET_FINAL), return NULL);
4529         return isl_basic_set_copy(bset);
4530 }
4531
4532 struct isl_set *isl_set_drop_basic_set(struct isl_set *set,
4533                                                 struct isl_basic_set *bset)
4534 {
4535         int i;
4536
4537         if (!set || !bset)
4538                 goto error;
4539         for (i = set->n-1; i >= 0; --i) {
4540                 if (set->p[i] != bset)
4541                         continue;
4542                 set = isl_set_cow(set);
4543                 if (!set)
4544                         goto error;
4545                 isl_basic_set_free(set->p[i]);
4546                 if (i != set->n-1) {
4547                         F_CLR(set, ISL_SET_NORMALIZED);
4548                         set->p[i] = set->p[set->n-1];
4549                 }
4550                 set->n--;
4551                 return set;
4552         }
4553         isl_basic_set_free(bset);
4554         return set;
4555 error:
4556         isl_set_free(set);
4557         isl_basic_set_free(bset);
4558         return NULL;
4559 }
4560
4561 /* Given two _disjoint_ basic sets bset1 and bset2, check whether
4562  * for any common value of the parameters and dimensions preceding dim
4563  * in both basic sets, the values of dimension pos in bset1 are
4564  * smaller or larger than those in bset2.
4565  *
4566  * Returns
4567  *       1 if bset1 follows bset2
4568  *      -1 if bset1 precedes bset2
4569  *       0 if bset1 and bset2 are incomparable
4570  *      -2 if some error occurred.
4571  */
4572 int isl_basic_set_compare_at(struct isl_basic_set *bset1,
4573         struct isl_basic_set *bset2, int pos)
4574 {
4575         struct isl_dim *dims;
4576         struct isl_basic_map *bmap1 = NULL;
4577         struct isl_basic_map *bmap2 = NULL;
4578         struct isl_ctx *ctx;
4579         struct isl_vec *obj;
4580         unsigned total;
4581         unsigned nparam;
4582         unsigned dim1, dim2;
4583         isl_int num, den;
4584         enum isl_lp_result res;
4585         int cmp;
4586
4587         if (!bset1 || !bset2)
4588                 return -2;
4589
4590         nparam = isl_basic_set_n_param(bset1);
4591         dim1 = isl_basic_set_n_dim(bset1);
4592         dim2 = isl_basic_set_n_dim(bset2);
4593         dims = isl_dim_alloc(bset1->ctx, nparam, pos, dim1 - pos);
4594         bmap1 = isl_basic_map_from_basic_set(isl_basic_set_copy(bset1), dims);
4595         dims = isl_dim_alloc(bset2->ctx, nparam, pos, dim2 - pos);
4596         bmap2 = isl_basic_map_from_basic_set(isl_basic_set_copy(bset2), dims);
4597         if (!bmap1 || !bmap2)
4598                 goto error;
4599         bmap1 = isl_basic_map_extend(bmap1, nparam,
4600                         pos, (dim1 - pos) + (dim2 - pos),
4601                         bmap2->n_div, bmap2->n_eq, bmap2->n_ineq);
4602         if (!bmap1)
4603                 goto error;
4604         total = isl_basic_map_total_dim(bmap1);
4605         ctx = bmap1->ctx;
4606         obj = isl_vec_alloc(ctx, total);
4607         isl_seq_clr(obj->block.data, total);
4608         isl_int_set_si(obj->block.data[nparam+pos], 1);
4609         isl_int_set_si(obj->block.data[nparam+pos+(dim1-pos)], -1);
4610         if (!obj)
4611                 goto error;
4612         bmap1 = add_constraints(bmap1, bmap2, 0, dim1 - pos);
4613         isl_int_init(num);
4614         isl_int_init(den);
4615         res = isl_solve_lp(bmap1, 0, obj->block.data, ctx->one, &num, &den);
4616         if (res == isl_lp_empty)
4617                 cmp = 0;
4618         else if (res == isl_lp_ok && isl_int_is_pos(num))
4619                 cmp = 1;
4620         else if ((res == isl_lp_ok && isl_int_is_neg(num)) ||
4621                   res == isl_lp_unbounded)
4622                 cmp = -1;
4623         else
4624                 cmp = -2;
4625         isl_int_clear(num);
4626         isl_int_clear(den);
4627         isl_basic_map_free(bmap1);
4628         isl_vec_free(ctx, obj);
4629         return cmp;
4630 error:
4631         isl_basic_map_free(bmap1);
4632         isl_basic_map_free(bmap2);
4633         return -2;
4634 }
4635
4636 static int isl_basic_map_fast_has_fixed_var(struct isl_basic_map *bmap,
4637         unsigned pos, isl_int *val)
4638 {
4639         int i;
4640         int d;
4641         unsigned total;
4642
4643         if (!bmap)
4644                 return -1;
4645         total = isl_basic_map_total_dim(bmap);
4646         for (i = 0, d = total-1; i < bmap->n_eq && d+1 > pos; ++i) {
4647                 for (; d+1 > pos; --d)
4648                         if (!isl_int_is_zero(bmap->eq[i][1+d]))
4649                                 break;
4650                 if (d != pos)
4651                         continue;
4652                 if (isl_seq_first_non_zero(bmap->eq[i]+1, d) != -1)
4653                         return 0;
4654                 if (isl_seq_first_non_zero(bmap->eq[i]+1+d+1, total-d-1) != -1)
4655                         return 0;
4656                 if (!isl_int_is_one(bmap->eq[i][1+d]))
4657                         return 0;
4658                 if (val)
4659                         isl_int_neg(*val, bmap->eq[i][0]);
4660                 return 1;
4661         }
4662         return 0;
4663 }
4664
4665 static int isl_map_fast_has_fixed_var(struct isl_map *map,
4666         unsigned pos, isl_int *val)
4667 {
4668         int i;
4669         isl_int v;
4670         isl_int tmp;
4671         int fixed;
4672
4673         if (!map)
4674                 return -1;
4675         if (map->n == 0)
4676                 return 0;
4677         if (map->n == 1)
4678                 return isl_basic_map_fast_has_fixed_var(map->p[0], pos, val);
4679         isl_int_init(v);
4680         isl_int_init(tmp);
4681         fixed = isl_basic_map_fast_has_fixed_var(map->p[0], pos, &v);
4682         for (i = 1; fixed == 1 && i < map->n; ++i) {
4683                 fixed = isl_basic_map_fast_has_fixed_var(map->p[i], pos, &tmp);
4684                 if (fixed == 1 && isl_int_ne(tmp, v))
4685                         fixed = 0;
4686         }
4687         if (val)
4688                 isl_int_set(*val, v);
4689         isl_int_clear(tmp);
4690         isl_int_clear(v);
4691         return fixed;
4692 }
4693
4694 static int isl_set_fast_has_fixed_var(struct isl_set *set, unsigned pos,
4695         isl_int *val)
4696 {
4697         return isl_map_fast_has_fixed_var((struct isl_map *)set, pos, val);
4698 }
4699
4700 /* Check if dimension dim has fixed value and if so and if val is not NULL,
4701  * then return this fixed value in *val.
4702  */
4703 int isl_set_fast_dim_is_fixed(struct isl_set *set, unsigned dim, isl_int *val)
4704 {
4705         return isl_set_fast_has_fixed_var(set, isl_set_n_param(set) + dim, val);
4706 }
4707
4708 /* Check if input variable in has fixed value and if so and if val is not NULL,
4709  * then return this fixed value in *val.
4710  */
4711 int isl_map_fast_input_is_fixed(struct isl_map *map, unsigned in, isl_int *val)
4712 {
4713         return isl_map_fast_has_fixed_var(map, isl_map_n_param(map) + in, val);
4714 }
4715
4716 /* Check if dimension dim has an (obvious) fixed lower bound and if so
4717  * and if val is not NULL, then return this lower bound in *val.
4718  */
4719 int isl_basic_set_fast_dim_has_fixed_lower_bound(struct isl_basic_set *bset,
4720         unsigned dim, isl_int *val)
4721 {
4722         int i, i_eq = -1, i_ineq = -1;
4723         isl_int *c;
4724         unsigned total;
4725         unsigned nparam;
4726
4727         if (!bset)
4728                 return -1;
4729         total = isl_basic_set_total_dim(bset);
4730         nparam = isl_basic_set_n_param(bset);
4731         for (i = 0; i < bset->n_eq; ++i) {
4732                 if (isl_int_is_zero(bset->eq[i][1+nparam+dim]))
4733                         continue;
4734                 if (i_eq != -1)
4735                         return 0;
4736                 i_eq = i;
4737         }
4738         for (i = 0; i < bset->n_ineq; ++i) {
4739                 if (!isl_int_is_pos(bset->ineq[i][1+nparam+dim]))
4740                         continue;
4741                 if (i_eq != -1 || i_ineq != -1)
4742                         return 0;
4743                 i_ineq = i;
4744         }
4745         if (i_eq == -1 && i_ineq == -1)
4746                 return 0;
4747         c = i_eq != -1 ? bset->eq[i_eq] : bset->ineq[i_ineq];
4748         /* The coefficient should always be one due to normalization. */
4749         if (!isl_int_is_one(c[1+nparam+dim]))
4750                 return 0;
4751         if (isl_seq_first_non_zero(c+1, nparam+dim) != -1)
4752                 return 0;
4753         if (isl_seq_first_non_zero(c+1+nparam+dim+1,
4754                                         total - nparam - dim - 1) != -1)
4755                 return 0;
4756         if (val)
4757                 isl_int_neg(*val, c[0]);
4758         return 1;
4759 }
4760
4761 int isl_set_fast_dim_has_fixed_lower_bound(struct isl_set *set,
4762         unsigned dim, isl_int *val)
4763 {
4764         int i;
4765         isl_int v;
4766         isl_int tmp;
4767         int fixed;
4768
4769         if (!set)
4770                 return -1;
4771         if (set->n == 0)
4772                 return 0;
4773         if (set->n == 1)
4774                 return isl_basic_set_fast_dim_has_fixed_lower_bound(set->p[0],
4775                                                                 dim, val);
4776         isl_int_init(v);
4777         isl_int_init(tmp);
4778         fixed = isl_basic_set_fast_dim_has_fixed_lower_bound(set->p[0],
4779                                                                 dim, &v);
4780         for (i = 1; fixed == 1 && i < set->n; ++i) {
4781                 fixed = isl_basic_set_fast_dim_has_fixed_lower_bound(set->p[i],
4782                                                                 dim, &tmp);
4783                 if (fixed == 1 && isl_int_ne(tmp, v))
4784                         fixed = 0;
4785         }
4786         if (val)
4787                 isl_int_set(*val, v);
4788         isl_int_clear(tmp);
4789         isl_int_clear(v);
4790         return fixed;
4791 }
4792
4793 static struct isl_basic_set *isl_basic_set_reduce_using_equalities(
4794         struct isl_basic_set *bset, struct isl_basic_set *context)
4795 {
4796         int i;
4797         int *elim;
4798
4799         if (!bset || !context)
4800                 goto error;
4801
4802         bset = isl_basic_set_cow(bset);
4803         if (!bset)
4804                 goto error;
4805
4806         elim = isl_alloc_array(ctx, int, isl_basic_set_n_dim(bset));
4807         if (!elim)
4808                 goto error;
4809         set_compute_elimination_index(context, elim);
4810         for (i = 0; i < bset->n_eq; ++i)
4811                 set_reduced_using_equalities(bset->eq[i], bset->eq[i],
4812                                                         context, elim);
4813         for (i = 0; i < bset->n_ineq; ++i)
4814                 set_reduced_using_equalities(bset->ineq[i], bset->ineq[i],
4815                                                         context, elim);
4816         isl_basic_set_free(context);
4817         free(elim);
4818         bset = isl_basic_set_simplify(bset);
4819         bset = isl_basic_set_finalize(bset);
4820         return bset;
4821 error:
4822         isl_basic_set_free(bset);
4823         isl_basic_set_free(context);
4824         return NULL;
4825 }
4826
4827 static struct isl_basic_set *remove_shifted_constraints(
4828         struct isl_basic_set *bset, struct isl_basic_set *context)
4829 {
4830         unsigned int size;
4831         isl_int ***index;
4832         int bits;
4833         int k, h, l;
4834
4835         if (!bset)
4836                 return NULL;
4837
4838         size = round_up(4 * (context->n_ineq+1) / 3 - 1);
4839         bits = ffs(size) - 1;
4840         index = isl_calloc_array(ctx, isl_int **, size);
4841         if (!index)
4842                 return bset;
4843
4844         for (k = 0; k < context->n_ineq; ++k) {
4845                 h = set_hash_index(index, size, bits, context, k);
4846                 index[h] = &context->ineq[k];
4847         }
4848         for (k = 0; k < bset->n_ineq; ++k) {
4849                 h = set_hash_index(index, size, bits, bset, k);
4850                 if (!index[h])
4851                         continue;
4852                 l = index[h] - &context->ineq[0];
4853                 if (isl_int_lt(bset->ineq[k][0], context->ineq[l][0]))
4854                         continue;
4855                 bset = isl_basic_set_cow(bset);
4856                 if (!bset)
4857                         goto error;
4858                 isl_basic_set_drop_inequality(bset, k);
4859                 --k;
4860         }
4861         free(index);
4862         return bset;
4863 error:
4864         free(index);
4865         return bset;
4866 }
4867
4868 /* Remove all information from bset that is redundant in the context
4869  * of context.  In particular, equalities that are linear combinations
4870  * of those in context are removed.  Then the inequalities that are
4871  * redundant in the context of the equalities and inequalities of
4872  * context are removed.
4873  */
4874 static struct isl_basic_set *uset_gist(struct isl_basic_set *bset,
4875         struct isl_basic_set *context)
4876 {
4877         int i;
4878         isl_int opt;
4879         struct isl_basic_set *combined;
4880         struct isl_ctx *ctx;
4881
4882         if (!bset || !context)
4883                 goto error;
4884
4885         if (context->n_eq > 0) {
4886                 struct isl_mat *T;
4887                 struct isl_mat *T2;
4888                 struct isl_ctx *ctx = context->ctx;
4889                 struct isl_basic_set *reduced_context;
4890                 reduced_context = isl_basic_set_remove_equalities(
4891                                         isl_basic_set_copy(context), &T, &T2);
4892                 if (!reduced_context)
4893                         goto error;
4894                 bset = isl_basic_set_preimage(ctx, bset, T);
4895                 bset = uset_gist(bset, reduced_context);
4896                 bset = isl_basic_set_preimage(ctx, bset, T2);
4897                 bset = isl_basic_set_reduce_using_equalities(bset, context);
4898                 return bset;
4899         }
4900         if (!context->n_ineq)
4901                 goto done;
4902         bset = remove_shifted_constraints(bset, context);
4903         combined = isl_basic_set_extend_constraints(isl_basic_set_copy(bset),
4904                         context->n_eq, context->n_ineq);
4905         context = set_add_constraints(combined, context, 0);
4906         if (!context)
4907                 goto error;
4908         ctx = context->ctx;
4909         isl_int_init(opt);
4910         for (i = bset->n_ineq-1; i >= 0; --i) {
4911                 int redundant;
4912                 set_swap_inequality(context, i, context->n_ineq-1);
4913                 context->n_ineq--;
4914                 redundant = isl_basic_set_constraint_is_redundant(&context,
4915                                 context->ineq[context->n_ineq], &opt, NULL);
4916                 if (redundant == -1) {
4917                         isl_int_clear(opt);
4918                         goto error;
4919                 }
4920                 if (F_ISSET(context, ISL_BASIC_MAP_EMPTY)) {
4921                         bset = isl_basic_set_set_to_empty(bset);
4922                         break;
4923                 }
4924                 context->n_ineq++;
4925                 set_swap_inequality(context, i, context->n_ineq-1);
4926                 if (redundant) {
4927                         isl_basic_set_drop_inequality(context, i);
4928                         isl_basic_set_drop_inequality(bset, i);
4929                 }
4930         }
4931         isl_int_clear(opt);
4932 done:
4933         isl_basic_set_free(context);
4934         return bset;
4935 error:
4936         isl_basic_set_free(context);
4937         isl_basic_set_free(bset);
4938         return NULL;
4939 }
4940
4941 struct isl_basic_map *isl_basic_map_gist(struct isl_basic_map *bmap,
4942         struct isl_basic_map *context)
4943 {
4944         struct isl_basic_set *bset;
4945
4946         if (!bmap || !context)
4947                 goto error;
4948
4949         context = isl_basic_map_align_divs(context, bmap);
4950         bmap = isl_basic_map_align_divs(bmap, context);
4951
4952         bset = uset_gist(isl_basic_map_underlying_set(isl_basic_map_copy(bmap)),
4953                          isl_basic_map_underlying_set(context));
4954
4955         return isl_basic_map_overlying_set(bset, bmap);
4956 error:
4957         isl_basic_map_free(bmap);
4958         isl_basic_map_free(context);
4959         return NULL;
4960 }
4961
4962 struct isl_map *isl_map_gist(struct isl_map *map, struct isl_basic_map *context)
4963 {
4964         int i;
4965
4966         map = isl_map_cow(map);
4967         if (!map || !context)
4968                 return NULL;
4969         isl_assert(map->ctx, isl_dim_equal(map->dim, context->dim), goto error);
4970         for (i = 0; i < map->n; ++i)
4971                 context = isl_basic_map_align_divs(context, map->p[i]);
4972         for (i = 0; i < map->n; ++i) {
4973                 map->p[i] = isl_basic_map_gist(map->p[i],
4974                                                 isl_basic_map_copy(context));
4975                 if (!map->p[i])
4976                         goto error;
4977         }
4978         isl_basic_map_free(context);
4979         F_CLR(map, ISL_MAP_NORMALIZED);
4980         return map;
4981 error:
4982         isl_map_free(map);
4983         isl_basic_map_free(context);
4984         return NULL;
4985 }
4986
4987 struct isl_basic_set *isl_basic_set_gist(struct isl_basic_set *bset,
4988                                                 struct isl_basic_set *context)
4989 {
4990         return (struct isl_basic_set *)isl_basic_map_gist(
4991                 (struct isl_basic_map *)bset, (struct isl_basic_map *)context);
4992 }
4993
4994 struct isl_set *isl_set_gist(struct isl_set *set, struct isl_basic_set *context)
4995 {
4996         return (struct isl_set *)isl_map_gist((struct isl_map *)set,
4997                                         (struct isl_basic_map *)context);
4998 }
4999
5000 struct constraint {
5001         unsigned        size;
5002         isl_int         *c;
5003 };
5004
5005 static int qsort_constraint_cmp(const void *p1, const void *p2)
5006 {
5007         const struct constraint *c1 = (const struct constraint *)p1;
5008         const struct constraint *c2 = (const struct constraint *)p2;
5009         unsigned size = isl_min(c1->size, c2->size);
5010         return isl_seq_cmp(c1->c, c2->c, size);
5011 }
5012
5013 static struct isl_basic_map *isl_basic_map_sort_constraints(
5014         struct isl_basic_map *bmap)
5015 {
5016         int i;
5017         struct constraint *c;
5018         unsigned total;
5019
5020         if (!bmap)
5021                 return NULL;
5022         total = isl_basic_map_total_dim(bmap);
5023         c = isl_alloc_array(bmap->ctx, struct constraint, bmap->n_ineq);
5024         if (!c)
5025                 goto error;
5026         for (i = 0; i < bmap->n_ineq; ++i) {
5027                 c[i].size = total;
5028                 c[i].c = bmap->ineq[i];
5029         }
5030         qsort(c, bmap->n_ineq, sizeof(struct constraint), qsort_constraint_cmp);
5031         for (i = 0; i < bmap->n_ineq; ++i)
5032                 bmap->ineq[i] = c[i].c;
5033         free(c);
5034         return bmap;
5035 error:
5036         isl_basic_map_free(bmap);
5037         return NULL;
5038 }
5039
5040 struct isl_basic_map *isl_basic_map_normalize(struct isl_basic_map *bmap)
5041 {
5042         if (!bmap)
5043                 return NULL;
5044         if (F_ISSET(bmap, ISL_BASIC_MAP_NORMALIZED))
5045                 return bmap;
5046         bmap = isl_basic_map_convex_hull(bmap);
5047         bmap = isl_basic_map_sort_constraints(bmap);
5048         F_SET(bmap, ISL_BASIC_MAP_NORMALIZED);
5049         return bmap;
5050 }
5051
5052 struct isl_basic_set *isl_basic_set_normalize(struct isl_basic_set *bset)
5053 {
5054         return (struct isl_basic_set *)isl_basic_map_normalize(
5055                                                 (struct isl_basic_map *)bset);
5056 }
5057
5058 static int isl_basic_map_fast_cmp(const struct isl_basic_map *bmap1,
5059         const struct isl_basic_map *bmap2)
5060 {
5061         int i, cmp;
5062         unsigned total;
5063
5064         if (bmap1 == bmap2)
5065                 return 0;
5066         if (isl_basic_map_n_param(bmap1) != isl_basic_map_n_param(bmap2))
5067                 return isl_basic_map_n_param(bmap1) - isl_basic_map_n_param(bmap2);
5068         if (isl_basic_map_n_in(bmap1) != isl_basic_map_n_in(bmap2))
5069                 return isl_basic_map_n_out(bmap1) - isl_basic_map_n_out(bmap2);
5070         if (isl_basic_map_n_out(bmap1) != isl_basic_map_n_out(bmap2))
5071                 return isl_basic_map_n_out(bmap1) - isl_basic_map_n_out(bmap2);
5072         if (F_ISSET(bmap1, ISL_BASIC_MAP_EMPTY) &&
5073             F_ISSET(bmap2, ISL_BASIC_MAP_EMPTY))
5074                 return 0;
5075         if (F_ISSET(bmap1, ISL_BASIC_MAP_EMPTY))
5076                 return 1;
5077         if (F_ISSET(bmap2, ISL_BASIC_MAP_EMPTY))
5078                 return -1;
5079         if (bmap1->n_eq != bmap2->n_eq)
5080                 return bmap1->n_eq - bmap2->n_eq;
5081         if (bmap1->n_ineq != bmap2->n_ineq)
5082                 return bmap1->n_ineq - bmap2->n_ineq;
5083         if (bmap1->n_div != bmap2->n_div)
5084                 return bmap1->n_div - bmap2->n_div;
5085         total = isl_basic_map_total_dim(bmap1);
5086         for (i = 0; i < bmap1->n_eq; ++i) {
5087                 cmp = isl_seq_cmp(bmap1->eq[i], bmap2->eq[i], 1+total);
5088                 if (cmp)
5089                         return cmp;
5090         }
5091         for (i = 0; i < bmap1->n_ineq; ++i) {
5092                 cmp = isl_seq_cmp(bmap1->ineq[i], bmap2->ineq[i], 1+total);
5093                 if (cmp)
5094                         return cmp;
5095         }
5096         for (i = 0; i < bmap1->n_div; ++i) {
5097                 cmp = isl_seq_cmp(bmap1->div[i], bmap2->div[i], 1+1+total);
5098                 if (cmp)
5099                         return cmp;
5100         }
5101         return 0;
5102 }
5103
5104 static int isl_basic_map_fast_is_equal(struct isl_basic_map *bmap1,
5105         struct isl_basic_map *bmap2)
5106 {
5107         return isl_basic_map_fast_cmp(bmap1, bmap2) == 0;
5108 }
5109
5110 static int qsort_bmap_cmp(const void *p1, const void *p2)
5111 {
5112         const struct isl_basic_map *bmap1 = *(const struct isl_basic_map **)p1;
5113         const struct isl_basic_map *bmap2 = *(const struct isl_basic_map **)p2;
5114
5115         return isl_basic_map_fast_cmp(bmap1, bmap2);
5116 }
5117
5118 /* We normalize in place, but if anything goes wrong we need
5119  * to return NULL, so we need to make sure we don't change the
5120  * meaning of any possible other copies of map.
5121  */
5122 struct isl_map *isl_map_normalize(struct isl_map *map)
5123 {
5124         int i, j;
5125         struct isl_basic_map *bmap;
5126
5127         if (!map)
5128                 return NULL;
5129         if (F_ISSET(map, ISL_MAP_NORMALIZED))
5130                 return map;
5131         for (i = 0; i < map->n; ++i) {
5132                 bmap = isl_basic_map_normalize(isl_basic_map_copy(map->p[i]));
5133                 if (!bmap)
5134                         goto error;
5135                 isl_basic_map_free(map->p[i]);
5136                 map->p[i] = bmap;
5137         }
5138         qsort(map->p, map->n, sizeof(struct isl_basic_map *), qsort_bmap_cmp);
5139         F_SET(map, ISL_MAP_NORMALIZED);
5140         map = isl_map_remove_empty_parts(map);
5141         if (!map)
5142                 return NULL;
5143         for (i = map->n - 1; i >= 1; --i) {
5144                 if (!isl_basic_map_fast_is_equal(map->p[i-1], map->p[i]))
5145                         continue;
5146                 isl_basic_map_free(map->p[i-1]);
5147                 for (j = i; j < map->n; ++j)
5148                         map->p[j-1] = map->p[j];
5149                 map->n--;
5150         }
5151         return map;
5152 error:
5153         isl_map_free(map);
5154         return NULL;
5155
5156 }
5157
5158 struct isl_set *isl_set_normalize(struct isl_set *set)
5159 {
5160         return (struct isl_set *)isl_map_normalize((struct isl_map *)set);
5161 }
5162
5163 int isl_map_fast_is_equal(struct isl_map *map1, struct isl_map *map2)
5164 {
5165         int i;
5166         int equal;
5167
5168         if (!map1 || !map2)
5169                 return -1;
5170
5171         if (map1 == map2)
5172                 return 1;
5173         if (!isl_dim_equal(map1->dim, map2->dim))
5174                 return 0;
5175
5176         map1 = isl_map_copy(map1);
5177         map2 = isl_map_copy(map2);
5178         map1 = isl_map_normalize(map1);
5179         map2 = isl_map_normalize(map2);
5180         if (!map1 || !map2)
5181                 goto error;
5182         equal = map1->n == map2->n;
5183         for (i = 0; equal && i < map1->n; ++i) {
5184                 equal = isl_basic_map_fast_is_equal(map1->p[i], map2->p[i]);
5185                 if (equal < 0)
5186                         goto error;
5187         }
5188         isl_map_free(map1);
5189         isl_map_free(map2);
5190         return equal;
5191 error:
5192         isl_map_free(map1);
5193         isl_map_free(map2);
5194         return -1;
5195 }
5196
5197 int isl_set_fast_is_equal(struct isl_set *set1, struct isl_set *set2)
5198 {
5199         return isl_map_fast_is_equal((struct isl_map *)set1,
5200                                                 (struct isl_map *)set2);
5201 }
5202
5203 /* Return an interval that ranges from min to max (inclusive)
5204  */
5205 struct isl_basic_set *isl_basic_set_interval(struct isl_ctx *ctx,
5206         isl_int min, isl_int max)
5207 {
5208         int k;
5209         struct isl_basic_set *bset = NULL;
5210
5211         bset = isl_basic_set_alloc(ctx, 0, 1, 0, 0, 2);
5212         if (!bset)
5213                 goto error;
5214
5215         k = isl_basic_set_alloc_inequality(bset);
5216         if (k < 0)
5217                 goto error;
5218         isl_int_set_si(bset->ineq[k][1], 1);
5219         isl_int_neg(bset->ineq[k][0], min);
5220
5221         k = isl_basic_set_alloc_inequality(bset);
5222         if (k < 0)
5223                 goto error;
5224         isl_int_set_si(bset->ineq[k][1], -1);
5225         isl_int_set(bset->ineq[k][0], max);
5226
5227         return bset;
5228 error:
5229         isl_basic_set_free(bset);
5230         return NULL;
5231 }
5232
5233 /* Return the Cartesian product of the basic sets in list (in the given order).
5234  */
5235 struct isl_basic_set *isl_basic_set_product(struct isl_basic_set_list *list)
5236 {
5237         int i;
5238         unsigned dim;
5239         unsigned nparam;
5240         unsigned extra;
5241         unsigned n_eq;
5242         unsigned n_ineq;
5243         struct isl_basic_set *product = NULL;
5244
5245         if (!list)
5246                 goto error;
5247         isl_assert(list->ctx, list->n > 0, goto error);
5248         isl_assert(list->ctx, list->p[0], goto error);
5249         nparam = isl_basic_set_n_param(list->p[0]);
5250         dim = isl_basic_set_n_dim(list->p[0]);
5251         extra = list->p[0]->n_div;
5252         n_eq = list->p[0]->n_eq;
5253         n_ineq = list->p[0]->n_ineq;
5254         for (i = 1; i < list->n; ++i) {
5255                 isl_assert(list->ctx, list->p[i], goto error);
5256                 isl_assert(list->ctx,
5257                     nparam == isl_basic_set_n_param(list->p[i]), goto error);
5258                 dim += isl_basic_set_n_dim(list->p[i]);
5259                 extra += list->p[i]->n_div;
5260                 n_eq += list->p[i]->n_eq;
5261                 n_ineq += list->p[i]->n_ineq;
5262         }
5263         product = isl_basic_set_alloc(list->ctx, nparam, dim, extra,
5264                                         n_eq, n_ineq);
5265         if (!product)
5266                 goto error;
5267         dim = 0;
5268         for (i = 0; i < list->n; ++i) {
5269                 set_add_constraints(product,
5270                                         isl_basic_set_copy(list->p[i]), dim);
5271                 dim += isl_basic_set_n_dim(list->p[i]);
5272         }
5273         isl_basic_set_list_free(list);
5274         return product;
5275 error:
5276         isl_basic_set_free(product);
5277         isl_basic_set_list_free(list);
5278         return NULL;
5279 }
5280
5281 uint32_t isl_basic_set_get_hash(struct isl_basic_set *bset)
5282 {
5283         int i;
5284         uint32_t hash;
5285         unsigned total;
5286
5287         if (!bset)
5288                 return 0;
5289         bset = isl_basic_set_copy(bset);
5290         bset = isl_basic_set_normalize(bset);
5291         if (!bset)
5292                 return 0;
5293         total = isl_basic_set_total_dim(bset);
5294         isl_hash_byte(hash, bset->n_eq & 0xFF);
5295         for (i = 0; i < bset->n_eq; ++i) {
5296                 uint32_t c_hash;
5297                 c_hash = isl_seq_get_hash(bset->eq[i], 1 + total);
5298                 isl_hash_hash(hash, c_hash);
5299         }
5300         isl_hash_byte(hash, bset->n_ineq & 0xFF);
5301         for (i = 0; i < bset->n_ineq; ++i) {
5302                 uint32_t c_hash;
5303                 c_hash = isl_seq_get_hash(bset->ineq[i], 1 + total);
5304                 isl_hash_hash(hash, c_hash);
5305         }
5306         isl_hash_byte(hash, bset->n_div & 0xFF);
5307         for (i = 0; i < bset->n_div; ++i) {
5308                 uint32_t c_hash;
5309                 if (isl_int_is_zero(bset->div[i][0]))
5310                         continue;
5311                 isl_hash_byte(hash, i & 0xFF);
5312                 c_hash = isl_seq_get_hash(bset->div[i], 1 + 1 + total);
5313                 isl_hash_hash(hash, c_hash);
5314         }
5315         isl_basic_set_free(bset);
5316         return hash;
5317 }
5318
5319 uint32_t isl_set_get_hash(struct isl_set *set)
5320 {
5321         int i;
5322         uint32_t hash;
5323
5324         if (!set)
5325                 return 0;
5326         set = isl_set_copy(set);
5327         set = isl_set_normalize(set);
5328         if (!set)
5329                 return 0;
5330
5331         hash = isl_hash_init();
5332         for (i = 0; i < set->n; ++i) {
5333                 uint32_t bset_hash;
5334                 bset_hash = isl_basic_set_get_hash(set->p[i]);
5335                 isl_hash_hash(hash, bset_hash);
5336         }
5337
5338         isl_set_free(set);
5339
5340         return hash;
5341 }
5342
5343 /* Check if the value for dimension dim is completely determined
5344  * by the values of the other parameters and variables.
5345  * That is, check if dimension dim is involved in an equality.
5346  */
5347 int isl_basic_set_dim_is_unique(struct isl_basic_set *bset, unsigned dim)
5348 {
5349         int i;
5350         unsigned nparam;
5351
5352         if (!bset)
5353                 return -1;
5354         nparam = isl_basic_set_n_param(bset);
5355         for (i = 0; i < bset->n_eq; ++i)
5356                 if (!isl_int_is_zero(bset->eq[i][1 + nparam + dim]))
5357                         return 1;
5358         return 0;
5359 }
5360
5361 /* Check if the value for dimension dim is completely determined
5362  * by the values of the other parameters and variables.
5363  * That is, check if dimension dim is involved in an equality
5364  * for each of the subsets.
5365  */
5366 int isl_set_dim_is_unique(struct isl_set *set, unsigned dim)
5367 {
5368         int i;
5369
5370         if (!set)
5371                 return -1;
5372         for (i = 0; i < set->n; ++i) {
5373                 int unique;
5374                 unique = isl_basic_set_dim_is_unique(set->p[i], dim);
5375                 if (unique != 1)
5376                         return unique;
5377         }
5378         return 1;
5379 }