isl_map.c

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