isl_map.c

   1 #include <string.h>
   2 #include <strings.h>
   3 #include "isl_ctx.h"
   4 #include "isl_blk.h"
   5 #include "isl_seq.h"
   6 #include "isl_set.h"
   7 #include "isl_map.h"
   8 #include "isl_map_private.h"
   9 #include "isl_map_piplib.h"
  10 #include "isl_sample.h"
  11 #include "isl_vec.h"
  12
  13 static struct isl_basic_map *basic_map_init(struct isl_ctx *ctx,
  14                 struct isl_basic_map *bmap,
  15                 unsigned nparam, unsigned n_in, unsigned n_out, unsigned extra,
  16                 unsigned n_eq, unsigned n_ineq)
  17 {
  18         int i;
  19         size_t row_size = 1 + nparam + n_in + n_out + extra;
  20
  21         bmap->block = isl_blk_alloc(ctx, (n_eq + n_ineq) * row_size);
  22         if (isl_blk_is_error(bmap->block)) {
  23                 free(bmap);
  24                 return NULL;
  25         }
  26
  27         bmap->eq = isl_alloc_array(ctx, isl_int *, n_eq + n_ineq);
  28         if (!bmap->eq) {
  29                 isl_blk_free(ctx, bmap->block);
  30                 free(bmap);
  31                 return NULL;
  32         }
  33
  34         if (extra == 0) {
  35                 bmap->block2 = isl_blk_empty();
  36                 bmap->div = NULL;
  37         } else {
  38                 bmap->block2 = isl_blk_alloc(ctx, extra * (1 + row_size));
  39                 if (isl_blk_is_error(bmap->block2)) {
  40                         free(bmap->eq);
  41                         isl_blk_free(ctx, bmap->block);
  42                         free(bmap);
  43                         return NULL;
  44                 }
  45
  46                 bmap->div = isl_alloc_array(ctx, isl_int *, extra);
  47                 if (!bmap->div) {
  48                         isl_blk_free(ctx, bmap->block2);
  49                         free(bmap->eq);
  50                         isl_blk_free(ctx, bmap->block);
  51                         free(bmap);
  52                         return NULL;
  53                 }
  54         }
  55
  56         for (i = 0; i < n_eq + n_ineq; ++i)
  57                 bmap->eq[i] = bmap->block.data + i * row_size;
  58
  59         for (i = 0; i < extra; ++i)
  60                 bmap->div[i] = bmap->block2.data + i * (1 + row_size);
  61
  62         bmap->ctx = ctx;
  63         isl_ctx_ref(ctx);
  64         bmap->ref = 1;
  65         bmap->flags = 0;
  66         bmap->c_size = n_eq + n_ineq;
  67         bmap->ineq = bmap->eq + n_eq;
  68         bmap->nparam = nparam;
  69         bmap->n_in = n_in;
  70         bmap->n_out = n_out;
  71         bmap->extra = extra;
  72         bmap->n_eq = 0;
  73         bmap->n_ineq = 0;
  74         bmap->n_div = 0;
  75         bmap->sample = NULL;
  76
  77         return bmap;
  78 }
  79
  80 struct isl_basic_set *isl_basic_set_alloc(struct isl_ctx *ctx,
  81                 unsigned nparam, unsigned dim, unsigned extra,
  82                 unsigned n_eq, unsigned n_ineq)
  83 {
  84         struct isl_basic_map *bmap;
  85         bmap = isl_basic_map_alloc(ctx, nparam, 0, dim, extra, n_eq, n_ineq);
  86         return (struct isl_basic_set *)bmap;
  87 }
  88
  89 struct isl_basic_map *isl_basic_map_alloc(struct isl_ctx *ctx,
  90                 unsigned nparam, unsigned in, unsigned out, unsigned extra,
  91                 unsigned n_eq, unsigned n_ineq)
  92 {
  93         struct isl_basic_map *bmap;
  94
  95         bmap = isl_alloc_type(ctx, struct isl_basic_map);
  96         if (!bmap)
  97                 return NULL;
  98
  99         return basic_map_init(ctx, bmap,
 100                                nparam, in, out, extra, n_eq, n_ineq);
 101 }
 102
 103 static void dup_constraints(
 104                 struct isl_basic_map *dst, struct isl_basic_map *src)
 105 {
 106         int i;
 107         unsigned total = src->nparam + src->n_in + src->n_out + src->n_div;
 108
 109         for (i = 0; i < src->n_eq; ++i) {
 110                 int j = isl_basic_map_alloc_equality(dst);
 111                 isl_seq_cpy(dst->eq[j], src->eq[i], 1+total);
 112         }
 113
 114         for (i = 0; i < src->n_ineq; ++i) {
 115                 int j = isl_basic_map_alloc_inequality(dst);
 116                 isl_seq_cpy(dst->ineq[j], src->ineq[i], 1+total);
 117         }
 118
 119         for (i = 0; i < src->n_div; ++i) {
 120                 int j = isl_basic_map_alloc_div(dst);
 121                 isl_seq_cpy(dst->div[j], src->div[i], 1+1+total);
 122         }
 123         F_SET(dst, ISL_BASIC_SET_FINAL);
 124 }
 125
 126 struct isl_basic_map *isl_basic_map_dup(struct isl_basic_map *bmap)
 127 {
 128         struct isl_basic_map *dup;
 129
 130         if (!bmap)
 131                 return NULL;
 132         dup = isl_basic_map_alloc(bmap->ctx, bmap->nparam,
 133                         bmap->n_in, bmap->n_out,
 134                         bmap->n_div, bmap->n_eq, bmap->n_ineq);
 135         if (!dup)
 136                 return NULL;
 137         dup->flags = bmap->flags;
 138         dup_constraints(dup, bmap);
 139         dup->sample = isl_vec_copy(bmap->ctx, bmap->sample);
 140         return dup;
 141 }
 142
 143 struct isl_basic_set *isl_basic_set_dup(struct isl_basic_set *bset)
 144 {
 145         struct isl_basic_map *dup;
 146
 147         dup = isl_basic_map_dup((struct isl_basic_map *)bset);
 148         return (struct isl_basic_set *)dup;
 149 }
 150
 151 struct isl_basic_set *isl_basic_set_copy(struct isl_basic_set *bset)
 152 {
 153         if (!bset)
 154                 return NULL;
 155
 156         if (F_ISSET(bset, ISL_BASIC_SET_FINAL)) {
 157                 bset->ref++;
 158                 return bset;
 159         }
 160         return isl_basic_set_dup(bset);
 161 }
 162
 163 struct isl_set *isl_set_copy(struct isl_set *set)
 164 {
 165         if (!set)
 166                 return NULL;
 167
 168         set->ref++;
 169         return set;
 170 }
 171
 172 struct isl_basic_map *isl_basic_map_copy(struct isl_basic_map *bmap)
 173 {
 174         if (!bmap)
 175                 return NULL;
 176
 177         if (F_ISSET(bmap, ISL_BASIC_SET_FINAL)) {
 178                 bmap->ref++;
 179                 return bmap;
 180         }
 181         return isl_basic_map_dup(bmap);
 182 }
 183
 184 struct isl_map *isl_map_copy(struct isl_map *map)
 185 {
 186         if (!map)
 187                 return NULL;
 188
 189         map->ref++;
 190         return map;
 191 }
 192
 193 void isl_basic_map_free(struct isl_basic_map *bmap)
 194 {
 195         if (!bmap)
 196                 return;
 197
 198         if (--bmap->ref > 0)
 199                 return;
 200
 201         isl_ctx_deref(bmap->ctx);
 202         free(bmap->div);
 203         isl_blk_free(bmap->ctx, bmap->block2);
 204         free(bmap->eq);
 205         isl_blk_free(bmap->ctx, bmap->block);
 206         isl_vec_free(bmap->ctx, bmap->sample);
 207         free(bmap);
 208 }
 209
 210 void isl_basic_set_free(struct isl_basic_set *bset)
 211 {
 212         isl_basic_map_free((struct isl_basic_map *)bset);
 213 }
 214
 215 int isl_basic_map_alloc_equality(struct isl_basic_map *bmap)
 216 {
 217         struct isl_ctx *ctx;
 218         if (!bmap)
 219                 return -1;
 220         ctx = bmap->ctx;
 221         isl_assert(ctx, bmap->n_eq + bmap->n_ineq < bmap->c_size, return -1);
 222         isl_assert(ctx, bmap->eq + bmap->n_eq <= bmap->ineq, return -1);
 223         if (bmap->eq + bmap->n_eq == bmap->ineq) {
 224                 isl_int *t;
 225                 int j = isl_basic_map_alloc_inequality(bmap);
 226                 if (j < 0)
 227                         return -1;
 228                 t = bmap->ineq[0];
 229                 bmap->ineq[0] = bmap->ineq[j];
 230                 bmap->ineq[j] = t;
 231                 bmap->n_ineq--;
 232                 bmap->ineq++;
 233         }
 234         return bmap->n_eq++;
 235 }
 236
 237 int isl_basic_set_alloc_equality(struct isl_basic_set *bset)
 238 {
 239         return isl_basic_map_alloc_equality((struct isl_basic_map *)bset);
 240 }
 241
 242 int isl_basic_map_free_equality(struct isl_basic_map *bmap, unsigned n)
 243 {
 244         if (!bmap)
 245                 return -1;
 246         isl_assert(bmap->ctx, n <= bmap->n_eq, return -1);
 247         bmap->n_eq -= n;
 248         return 0;
 249 }
 250
 251 int isl_basic_map_drop_equality(struct isl_basic_map *bmap, unsigned pos)
 252 {
 253         isl_int *t;
 254         if (!bmap)
 255                 return -1;
 256         isl_assert(bmap->ctx, pos < bmap->n_eq, return -1);
 257
 258         if (pos != bmap->n_eq - 1) {
 259                 t = bmap->eq[pos];
 260                 bmap->eq[pos] = bmap->eq[bmap->n_eq - 1];
 261                 bmap->eq[bmap->n_eq - 1] = t;
 262         }
 263         bmap->n_eq--;
 264         return 0;
 265 }
 266
 267 int isl_basic_set_drop_equality(struct isl_basic_set *bset, unsigned pos)
 268 {
 269         return isl_basic_map_drop_equality((struct isl_basic_map *)bset, pos);
 270 }
 271
 272 void isl_basic_map_inequality_to_equality(
 273                 struct isl_basic_map *bmap, unsigned pos)
 274 {
 275         isl_int *t;
 276
 277         t = bmap->ineq[pos];
 278         bmap->ineq[pos] = bmap->ineq[0];
 279         bmap->ineq[0] = bmap->eq[bmap->n_eq];
 280         bmap->eq[bmap->n_eq] = t;
 281         bmap->n_eq++;
 282         bmap->n_ineq--;
 283         bmap->ineq++;
 284 }
 285
 286 int isl_basic_map_alloc_inequality(struct isl_basic_map *bmap)
 287 {
 288         struct isl_ctx *ctx;
 289         if (!bmap)
 290                 return -1;
 291         ctx = bmap->ctx;
 292         isl_assert(ctx, (bmap->ineq - bmap->eq) + bmap->n_ineq < bmap->c_size,
 293                         return -1);
 294         F_CLR(bmap, ISL_BASIC_MAP_NO_IMPLICIT);
 295         F_CLR(bmap, ISL_BASIC_MAP_NO_REDUNDANT);
 296         return bmap->n_ineq++;
 297 }
 298
 299 int isl_basic_set_alloc_inequality(struct isl_basic_set *bset)
 300 {
 301         return isl_basic_map_alloc_inequality((struct isl_basic_map *)bset);
 302 }
 303
 304 int isl_basic_map_free_inequality(struct isl_basic_map *bmap, unsigned n)
 305 {
 306         if (!bmap)
 307                 return -1;
 308         isl_assert(bmap->ctx, n <= bmap->n_ineq, return -1);
 309         bmap->n_ineq -= n;
 310         return 0;
 311 }
 312
 313 int isl_basic_set_free_inequality(struct isl_basic_set *bset, unsigned n)
 314 {
 315         return isl_basic_map_free_inequality((struct isl_basic_map *)bset, n);
 316 }
 317
 318 int isl_basic_map_drop_inequality(struct isl_basic_map *bmap, unsigned pos)
 319 {
 320         isl_int *t;
 321         if (!bmap)
 322                 return -1;
 323         isl_assert(bmap->ctx, pos < bmap->n_ineq, return -1);
 324
 325         if (pos != bmap->n_ineq - 1) {
 326                 t = bmap->ineq[pos];
 327                 bmap->ineq[pos] = bmap->ineq[bmap->n_ineq - 1];
 328                 bmap->ineq[bmap->n_ineq - 1] = t;
 329         }
 330         bmap->n_ineq--;
 331         return 0;
 332 }
 333
 334 int isl_basic_set_drop_inequality(struct isl_basic_set *bset, unsigned pos)
 335 {
 336         return isl_basic_map_drop_inequality((struct isl_basic_map *)bset, pos);
 337 }
 338
 339 int isl_basic_map_alloc_div(struct isl_basic_map *bmap)
 340 {
 341         if (!bmap)
 342                 return -1;
 343         isl_assert(bmap->ctx, bmap->n_div < bmap->extra, return -1);
 344         return bmap->n_div++;
 345 }
 346
 347 int isl_basic_map_free_div(struct isl_basic_map *bmap, unsigned n)
 348 {
 349         if (!bmap)
 350                 return -1;
 351         isl_assert(bmap->ctx, n <= bmap->n_div, return -1);
 352         bmap->n_div -= n;
 353         return 0;
 354 }
 355
 356 /* Copy constraint from src to dst, putting the vars of src at offset
 357  * dim_off in dst and the divs of src at offset div_off in dst.
 358  * If both sets are actually map, then dim_off applies to the input
 359  * variables.
 360  */
 361 static void copy_constraint(struct isl_basic_map *dst_map, isl_int *dst,
 362                             struct isl_basic_map *src_map, isl_int *src,
 363                             unsigned in_off, unsigned out_off, unsigned div_off)
 364 {
 365         isl_int_set(dst[0], src[0]);
 366         isl_seq_cpy(dst+1, src+1, isl_min(dst_map->nparam, src_map->nparam));
 367         if (dst_map->nparam > src_map->nparam)
 368                 isl_seq_clr(dst+1+src_map->nparam,
 369                                 dst_map->nparam - src_map->nparam);
 370         isl_seq_clr(dst+1+dst_map->nparam, in_off);
 371         isl_seq_cpy(dst+1+dst_map->nparam+in_off,
 372                     src+1+src_map->nparam,
 373                     isl_min(dst_map->n_in-in_off, src_map->n_in));
 374         if (dst_map->n_in-in_off > src_map->n_in)
 375                 isl_seq_clr(dst+1+dst_map->nparam+in_off+src_map->n_in,
 376                                 dst_map->n_in - in_off - src_map->n_in);
 377         isl_seq_clr(dst+1+dst_map->nparam+dst_map->n_in, out_off);
 378         isl_seq_cpy(dst+1+dst_map->nparam+dst_map->n_in+out_off,
 379                     src+1+src_map->nparam+src_map->n_in,
 380                     isl_min(dst_map->n_out-out_off, src_map->n_out));
 381         if (dst_map->n_out-out_off > src_map->n_out)
 382                 isl_seq_clr(dst+1+dst_map->nparam+dst_map->n_in+out_off+src_map->n_out,
 383                                 dst_map->n_out - out_off - src_map->n_out);
 384         isl_seq_clr(dst+1+dst_map->nparam+dst_map->n_in+dst_map->n_out, div_off);
 385         isl_seq_cpy(dst+1+dst_map->nparam+dst_map->n_in+dst_map->n_out+div_off,
 386                     src+1+src_map->nparam+src_map->n_in+src_map->n_out,
 387                     isl_min(dst_map->extra-div_off, src_map->extra));
 388         if (dst_map->extra-div_off > src_map->extra)
 389                 isl_seq_clr(dst+1+dst_map->nparam+dst_map->n_in+dst_map->n_out+
 390                                 div_off+src_map->extra,
 391                                 dst_map->extra - div_off - src_map->extra);
 392 }
 393
 394 static void copy_div(struct isl_basic_map *dst_map, isl_int *dst,
 395                      struct isl_basic_map *src_map, isl_int *src,
 396                      unsigned in_off, unsigned out_off, unsigned div_off)
 397 {
 398         isl_int_set(dst[0], src[0]);
 399         copy_constraint(dst_map, dst+1, src_map, src+1, in_off, out_off, div_off);
 400 }
 401
 402 static struct isl_basic_map *add_constraints(struct isl_basic_map *bmap1,
 403                 struct isl_basic_map *bmap2, unsigned i_pos, unsigned o_pos)
 404 {
 405         int i;
 406         unsigned div_off = bmap1->n_div;
 407
 408         for (i = 0; i < bmap2->n_eq; ++i) {
 409                 int i1 = isl_basic_map_alloc_equality(bmap1);
 410                 if (i1 < 0)
 411                         goto error;
 412                 copy_constraint(bmap1, bmap1->eq[i1], bmap2, bmap2->eq[i],
 413                                 i_pos, o_pos, div_off);
 414         }
 415
 416         for (i = 0; i < bmap2->n_ineq; ++i) {
 417                 int i1 = isl_basic_map_alloc_inequality(bmap1);
 418                 if (i1 < 0)
 419                         goto error;
 420                 copy_constraint(bmap1, bmap1->ineq[i1], bmap2, bmap2->ineq[i],
 421                                 i_pos, o_pos, div_off);
 422         }
 423
 424         for (i = 0; i < bmap2->n_div; ++i) {
 425                 int i1 = isl_basic_map_alloc_div(bmap1);
 426                 if (i1 < 0)
 427                         goto error;
 428                 copy_div(bmap1, bmap1->div[i1], bmap2, bmap2->div[i],
 429                          i_pos, o_pos, div_off);
 430         }
 431
 432         isl_basic_map_free(bmap2);
 433
 434         return bmap1;
 435
 436 error:
 437         isl_basic_map_free(bmap1);
 438         isl_basic_map_free(bmap2);
 439         return NULL;
 440 }
 441
 442 struct isl_basic_map *isl_basic_map_extend(struct isl_basic_map *base,
 443                 unsigned nparam, unsigned n_in, unsigned n_out, unsigned extra,
 444                 unsigned n_eq, unsigned n_ineq)
 445 {
 446         struct isl_basic_map *ext;
 447         unsigned flags;
 448         int dims_ok;
 449
 450         base = isl_basic_map_cow(base);
 451         if (!base)
 452                 goto error;
 453
 454         dims_ok = base && base->nparam == nparam &&
 455                   base->n_in == n_in && base->n_out == n_out &&
 456                   base->extra >= base->n_div + extra;
 457
 458         if (dims_ok && n_eq == 0 && n_ineq == 0)
 459                 return base;
 460
 461         isl_assert(base->ctx, base->nparam <= nparam, goto error);
 462         isl_assert(base->ctx, base->n_in <= n_in, goto error);
 463         isl_assert(base->ctx, base->n_out <= n_out, goto error);
 464         extra += base->extra;
 465         n_eq += base->n_eq;
 466         n_ineq += base->n_ineq;
 467
 468         ext = isl_basic_map_alloc(base->ctx, nparam, n_in, n_out,
 469                                         extra, n_eq, n_ineq);
 470         if (!base)
 471                 return ext;
 472         if (!ext)
 473                 goto error;
 474
 475         flags = base->flags;
 476         ext = add_constraints(ext, base, 0, 0);
 477         if (ext) {
 478                 ext->flags = flags;
 479                 F_CLR(ext, ISL_BASIC_SET_FINAL);
 480         }
 481
 482         return ext;
 483
 484 error:
 485         isl_basic_map_free(base);
 486         return NULL;
 487 }
 488
 489 struct isl_basic_set *isl_basic_set_extend(struct isl_basic_set *base,
 490                 unsigned nparam, unsigned dim, unsigned extra,
 491                 unsigned n_eq, unsigned n_ineq)
 492 {
 493         return (struct isl_basic_set *)
 494                 isl_basic_map_extend((struct isl_basic_map *)base,
 495                                         nparam, 0, dim, extra, n_eq, n_ineq);
 496 }
 497
 498 struct isl_basic_set *isl_basic_set_cow(struct isl_basic_set *bset)
 499 {
 500         return (struct isl_basic_set *)
 501                 isl_basic_map_cow((struct isl_basic_map *)bset);
 502 }
 503
 504 struct isl_basic_map *isl_basic_map_cow(struct isl_basic_map *bmap)
 505 {
 506         if (!bmap)
 507                 return NULL;
 508
 509         if (bmap->ref > 1) {
 510                 bmap->ref--;
 511                 bmap = isl_basic_map_dup(bmap);
 512         }
 513         F_CLR(bmap, ISL_BASIC_SET_FINAL);
 514         return bmap;
 515 }
 516
 517 struct isl_set *isl_set_cow(struct isl_set *set)
 518 {
 519         if (!set)
 520                 return NULL;
 521
 522         if (set->ref == 1)
 523                 return set;
 524         set->ref--;
 525         return isl_set_dup(set);
 526 }
 527
 528 struct isl_map *isl_map_cow(struct isl_map *map)
 529 {
 530         if (!map)
 531                 return NULL;
 532
 533         if (map->ref == 1)
 534                 return map;
 535         map->ref--;
 536         return isl_map_dup(map);
 537 }
 538
 539 static void swap_vars(struct isl_blk blk, isl_int *a,
 540                         unsigned a_len, unsigned b_len)
 541 {
 542         isl_seq_cpy(blk.data, a+a_len, b_len);
 543         isl_seq_cpy(blk.data+b_len, a, a_len);
 544         isl_seq_cpy(a, blk.data, b_len+a_len);
 545 }
 546
 547 struct isl_basic_set *isl_basic_set_swap_vars(
 548                 struct isl_basic_set *bset, unsigned n)
 549 {
 550         int i;
 551         struct isl_blk blk;
 552
 553         if (!bset)
 554                 goto error;
 555
 556         isl_assert(bset->ctx, n <= bset->dim, goto error);
 557
 558         if (n == bset->dim)
 559                 return bset;
 560
 561         bset = isl_basic_set_cow(bset);
 562         if (!bset)
 563                 return NULL;
 564
 565         blk = isl_blk_alloc(bset->ctx, bset->dim);
 566         if (isl_blk_is_error(blk))
 567                 goto error;
 568
 569         for (i = 0; i < bset->n_eq; ++i)
 570                 swap_vars(blk,
 571                           bset->eq[i]+1+bset->nparam, n, bset->dim - n);
 572
 573         for (i = 0; i < bset->n_ineq; ++i)
 574                 swap_vars(blk,
 575                           bset->ineq[i]+1+bset->nparam, n, bset->dim - n);
 576
 577         for (i = 0; i < bset->n_div; ++i)
 578                 swap_vars(blk,
 579                           bset->div[i]+1+1+bset->nparam, n, bset->dim - n);
 580
 581         isl_blk_free(bset->ctx, blk);
 582
 583         return bset;
 584
 585 error:
 586         isl_basic_set_free(bset);
 587         return NULL;
 588 }
 589
 590 struct isl_set *isl_set_swap_vars(struct isl_set *set, unsigned n)
 591 {
 592         int i;
 593         set = isl_set_cow(set);
 594         if (!set)
 595                 return NULL;
 596
 597         for (i = 0; i < set->n; ++i) {
 598                 set->p[i] = isl_basic_set_swap_vars(set->p[i], n);
 599                 if (!set->p[i]) {
 600                         isl_set_free(set);
 601                         return NULL;
 602                 }
 603         }
 604         return set;
 605 }
 606
 607 static void constraint_drop_vars(isl_int *c, unsigned n, unsigned rem)
 608 {
 609         isl_seq_cpy(c, c + n, rem);
 610         isl_seq_clr(c + rem, n);
 611 }
 612
 613 struct isl_basic_set *isl_basic_set_drop_vars(
 614                 struct isl_basic_set *bset, unsigned first, unsigned n)
 615 {
 616         int i;
 617
 618         if (!bset)
 619                 goto error;
 620
 621         isl_assert(bset->ctx, first + n <= bset->dim, goto error);
 622
 623         if (n == 0)
 624                 return bset;
 625
 626         bset = isl_basic_set_cow(bset);
 627         if (!bset)
 628                 return NULL;
 629
 630         for (i = 0; i < bset->n_eq; ++i)
 631                 constraint_drop_vars(bset->eq[i]+1+bset->nparam+first, n,
 632                                      (bset->dim-first-n)+bset->extra);
 633
 634         for (i = 0; i < bset->n_ineq; ++i)
 635                 constraint_drop_vars(bset->ineq[i]+1+bset->nparam+first, n,
 636                                      (bset->dim-first-n)+bset->extra);
 637
 638         for (i = 0; i < bset->n_div; ++i)
 639                 constraint_drop_vars(bset->div[i]+1+1+bset->nparam+first, n,
 640                                      (bset->dim-first-n)+bset->extra);
 641
 642         bset->dim -= n;
 643         bset->extra += n;
 644
 645         return isl_basic_set_finalize(bset);
 646 error:
 647         isl_basic_set_free(bset);
 648         return NULL;
 649 }
 650
 651 struct isl_set *isl_set_drop_vars(
 652                 struct isl_set *set, unsigned first, unsigned n)
 653 {
 654         int i;
 655
 656         if (!set)
 657                 goto error;
 658
 659         isl_assert(set->ctx, first + n <= set->dim, goto error);
 660
 661         if (n == 0)
 662                 return set;
 663         set = isl_set_cow(set);
 664         if (!set)
 665                 goto error;
 666
 667         for (i = 0; i < set->n; ++i) {
 668                 set->p[i] = isl_basic_set_drop_vars(set->p[i], first, n);
 669                 if (!set->p[i])
 670                         goto error;
 671         }
 672         set->dim -= n;
 673
 674         return set;
 675 error:
 676         isl_set_free(set);
 677         return NULL;
 678 }
 679
 680 /*
 681  * We don't cow, as the div is assumed to be redundant.
 682  */
 683 static struct isl_basic_map *isl_basic_map_drop_div(
 684                 struct isl_basic_map *bmap, unsigned div)
 685 {
 686         int i;
 687         unsigned pos;
 688
 689         if (!bmap)
 690                 goto error;
 691
 692         pos = 1 + bmap->nparam + bmap->n_in + bmap->n_out + div;
 693
 694         isl_assert(bmap->ctx, div < bmap->n_div, goto error);
 695
 696         for (i = 0; i < bmap->n_eq; ++i)
 697                 constraint_drop_vars(bmap->eq[i]+pos, 1, bmap->extra-div-1);
 698
 699         for (i = 0; i < bmap->n_ineq; ++i) {
 700                 if (!isl_int_is_zero(bmap->ineq[i][pos])) {
 701                         isl_basic_map_drop_inequality(bmap, i);
 702                         --i;
 703                         continue;
 704                 }
 705                 constraint_drop_vars(bmap->ineq[i]+pos, 1, bmap->extra-div-1);
 706         }
 707
 708         for (i = 0; i < bmap->n_div; ++i)
 709                 constraint_drop_vars(bmap->div[i]+1+pos, 1, bmap->extra-div-1);
 710
 711         if (div != bmap->n_div - 1) {
 712                 int j;
 713                 isl_int *t = bmap->div[div];
 714
 715                 for (j = div; j < bmap->n_div - 1; ++j)
 716                         bmap->div[j] = bmap->div[j+1];
 717
 718                 bmap->div[bmap->n_div - 1] = t;
 719         }
 720         isl_basic_map_free_div(bmap, 1);
 721
 722         return bmap;
 723 error:
 724         isl_basic_map_free(bmap);
 725         return NULL;
 726 }
 727
 728 static void eliminate_div(struct isl_basic_map *bmap, isl_int *eq, unsigned div)
 729 {
 730         int i;
 731         unsigned pos = 1 + bmap->nparam + bmap->n_in + bmap->n_out + div;
 732         unsigned len;
 733         len = 1 + bmap->nparam + bmap->n_in + bmap->n_out + bmap->n_div;
 734
 735         for (i = 0; i < bmap->n_eq; ++i)
 736                 if (bmap->eq[i] != eq)
 737                         isl_seq_elim(bmap->eq[i], eq, pos, len, NULL);
 738
 739         for (i = 0; i < bmap->n_ineq; ++i)
 740                 isl_seq_elim(bmap->ineq[i], eq, pos, len, NULL);
 741
 742         /* We need to be careful about circular definitions,
 743          * so for now we just remove the definitions of other divs that
 744          * depend on this div and (possibly) recompute them later.
 745          */
 746         for (i = 0; i < bmap->n_div; ++i)
 747                 if (!isl_int_is_zero(bmap->div[i][0]) &&
 748                     !isl_int_is_zero(bmap->div[i][1 + pos]))
 749                         isl_seq_clr(bmap->div[i], 1 + len);
 750
 751         isl_basic_map_drop_div(bmap, div);
 752 }
 753
 754 struct isl_basic_map *isl_basic_map_set_to_empty(struct isl_basic_map *bmap)
 755 {
 756         int i = 0;
 757         unsigned total;
 758         if (!bmap)
 759                 goto error;
 760         total = bmap->nparam + bmap->n_in + bmap->n_out + bmap->extra;
 761         isl_basic_map_free_div(bmap, bmap->n_div);
 762         isl_basic_map_free_inequality(bmap, bmap->n_ineq);
 763         if (bmap->n_eq > 0)
 764                 isl_basic_map_free_equality(bmap, bmap->n_eq-1);
 765         else {
 766                 isl_basic_map_alloc_equality(bmap);
 767                 if (i < 0)
 768                         goto error;
 769         }
 770         isl_int_set_si(bmap->eq[i][0], 1);
 771         isl_seq_clr(bmap->eq[i]+1, total);
 772         F_SET(bmap, ISL_BASIC_MAP_EMPTY);
 773         return isl_basic_map_finalize(bmap);
 774 error:
 775         isl_basic_map_free(bmap);
 776         return NULL;
 777 }
 778
 779 struct isl_basic_set *isl_basic_set_set_to_empty(struct isl_basic_set *bset)
 780 {
 781         return (struct isl_basic_set *)
 782                 isl_basic_map_set_to_empty((struct isl_basic_map *)bset);
 783 }
 784
 785 static void swap_equality(struct isl_basic_map *bmap, int a, int b)
 786 {
 787         isl_int *t = bmap->eq[a];
 788         bmap->eq[a] = bmap->eq[b];
 789         bmap->eq[b] = t;
 790 }
 791
 792 static void swap_inequality(struct isl_basic_map *bmap, int a, int b)
 793 {
 794         isl_int *t = bmap->ineq[a];
 795         bmap->ineq[a] = bmap->ineq[b];
 796         bmap->ineq[b] = t;
 797 }
 798
 799 static void swap_div(struct isl_basic_map *bmap, int a, int b)
 800 {
 801         int i;
 802         unsigned off = bmap->nparam + bmap->n_in + bmap->n_out;
 803         isl_int *t = bmap->div[a];
 804         bmap->div[a] = bmap->div[b];
 805         bmap->div[b] = t;
 806
 807         for (i = 0; i < bmap->n_eq; ++i)
 808                 isl_int_swap(bmap->eq[i][1+off+a], bmap->eq[i][1+off+b]);
 809
 810         for (i = 0; i < bmap->n_ineq; ++i)
 811                 isl_int_swap(bmap->ineq[i][1+off+a], bmap->ineq[i][1+off+b]);
 812
 813         for (i = 0; i < bmap->n_div; ++i)
 814                 isl_int_swap(bmap->div[i][1+1+off+a], bmap->div[i][1+1+off+b]);
 815 }
 816
 817 struct isl_basic_map *isl_basic_map_gauss(
 818         struct isl_basic_map *bmap, int *progress)
 819 {
 820         int k;
 821         int done;
 822         int last_var;
 823         unsigned total_var;
 824         unsigned total;
 825
 826         if (!bmap)
 827                 return NULL;
 828
 829         total_var = bmap->nparam + bmap->n_in + bmap->n_out;
 830         total = total_var + bmap->n_div;
 831
 832         last_var = total - 1;
 833         for (done = 0; done < bmap->n_eq; ++done) {
 834                 for (; last_var >= 0; --last_var) {
 835                         for (k = done; k < bmap->n_eq; ++k)
 836                                 if (!isl_int_is_zero(bmap->eq[k][1+last_var]))
 837                                         break;
 838                         if (k < bmap->n_eq)
 839                                 break;
 840                 }
 841                 if (last_var < 0)
 842                         break;
 843                 if (k != done)
 844                         swap_equality(bmap, k, done);
 845                 if (isl_int_is_neg(bmap->eq[done][1+last_var]))
 846                         isl_seq_neg(bmap->eq[done], bmap->eq[done], 1+total);
 847
 848                 for (k = 0; k < bmap->n_eq; ++k) {
 849                         if (k == done)
 850                                 continue;
 851                         if (isl_int_is_zero(bmap->eq[k][1+last_var]))
 852                                 continue;
 853                         if (progress)
 854                                 *progress = 1;
 855                         isl_seq_elim(bmap->eq[k], bmap->eq[done],
 856                                         1+last_var, 1+total, NULL);
 857                 }
 858
 859                 for (k = 0; k < bmap->n_ineq; ++k) {
 860                         if (isl_int_is_zero(bmap->ineq[k][1+last_var]))
 861                                 continue;
 862                         if (progress)
 863                                 *progress = 1;
 864                         isl_seq_elim(bmap->ineq[k], bmap->eq[done],
 865                                         1+last_var, 1+total, NULL);
 866                 }
 867
 868                 for (k = 0; k < bmap->n_div; ++k) {
 869                         if (isl_int_is_zero(bmap->div[k][0]))
 870                                 continue;
 871                         if (isl_int_is_zero(bmap->div[k][1+1+last_var]))
 872                                 continue;
 873                         if (progress)
 874                                 *progress = 1;
 875                         isl_seq_elim(bmap->div[k]+1, bmap->eq[done],
 876                                         1+last_var, 1+total, &bmap->div[k][0]);
 877                 }
 878
 879                 if (last_var >= total_var &&
 880                     isl_int_is_zero(bmap->div[last_var - total_var][0])) {
 881                         unsigned div = last_var - total_var;
 882                         isl_seq_neg(bmap->div[div]+1, bmap->eq[done], 1+total);
 883                         isl_int_set_si(bmap->div[div][1+1+last_var], 0);
 884                         isl_int_set(bmap->div[div][0],
 885                                     bmap->eq[done][1+last_var]);
 886                 }
 887         }
 888         if (done == bmap->n_eq)
 889                 return bmap;
 890         for (k = done; k < bmap->n_eq; ++k) {
 891                 if (isl_int_is_zero(bmap->eq[k][0]))
 892                         continue;
 893                 return isl_basic_map_set_to_empty(bmap);
 894         }
 895         isl_basic_map_free_equality(bmap, bmap->n_eq-done);
 896         return bmap;
 897 }
 898
 899 struct isl_basic_set *isl_basic_set_gauss(
 900         struct isl_basic_set *bset, int *progress)
 901 {
 902         return (struct isl_basic_set*)isl_basic_map_gauss(
 903                         (struct isl_basic_map *)bset, progress);
 904 }
 905
 906 static unsigned int round_up(unsigned int v)
 907 {
 908         int old_v = v;
 909
 910         while (v) {
 911                 old_v = v;
 912                 v ^= v & -v;
 913         }
 914         return old_v << 1;
 915 }
 916
 917 static int hash_index(int *index, unsigned int size, int bits,
 918                         struct isl_basic_map *bmap, int k)
 919 {
 920         int h;
 921         unsigned total = bmap->nparam + bmap->n_in + bmap->n_out + bmap->n_div;
 922         u_int32_t hash = isl_seq_hash(bmap->ineq[k]+1, total, bits);
 923         for (h = hash; index[h]; h = (h+1) % size)
 924                 if (k != index[h]-1 &&
 925                     isl_seq_eq(bmap->ineq[k]+1,
 926                                bmap->ineq[index[h]-1]+1, total))
 927                         break;
 928         return h;
 929 }
 930
 931 static struct isl_basic_map *remove_duplicate_constraints(
 932         struct isl_basic_map *bmap, int *progress)
 933 {
 934         unsigned int size;
 935         int *index;
 936         int k, l, h;
 937         int bits;
 938         unsigned total = bmap->nparam + bmap->n_in + bmap->n_out + bmap->n_div;
 939         isl_int sum;
 940
 941         if (bmap->n_ineq <= 1)
 942                 return bmap;
 943
 944         size = round_up(4 * (bmap->n_ineq+1) / 3 - 1);
 945         bits = ffs(size) - 1;
 946         index = isl_alloc_array(ctx, int, size);
 947         memset(index, 0, size * sizeof(int));
 948         if (!index)
 949                 return bmap;
 950
 951         index[isl_seq_hash(bmap->ineq[0]+1, total, bits)] = 1;
 952         for (k = 1; k < bmap->n_ineq; ++k) {
 953                 h = hash_index(index, size, bits, bmap, k);
 954                 if (!index[h]) {
 955                         index[h] = k+1;
 956                         continue;
 957                 }
 958                 *progress = 1;
 959                 l = index[h] - 1;
 960                 if (isl_int_lt(bmap->ineq[k][0], bmap->ineq[l][0]))
 961                         swap_inequality(bmap, k, l);
 962                 isl_basic_map_drop_inequality(bmap, k);
 963                 --k;
 964         }
 965         isl_int_init(sum);
 966         for (k = 0; k < bmap->n_ineq-1; ++k) {
 967                 isl_seq_neg(bmap->ineq[k]+1, bmap->ineq[k]+1, total);
 968                 h = hash_index(index, size, bits, bmap, k);
 969                 isl_seq_neg(bmap->ineq[k]+1, bmap->ineq[k]+1, total);
 970                 if (!index[h])
 971                         continue;
 972                 l = index[h] - 1;
 973                 isl_int_add(sum, bmap->ineq[k][0], bmap->ineq[l][0]);
 974                 if (isl_int_is_pos(sum))
 975                         continue;
 976                 if (isl_int_is_zero(sum)) {
 977                         /* We need to break out of the loop after these
 978                          * changes since the contents of the hash
 979                          * will no longer be valid.
 980                          * Plus, we probably we want to regauss first.
 981                          */
 982                         isl_basic_map_drop_inequality(bmap, l);
 983                         isl_basic_map_inequality_to_equality(bmap, k);
 984                 } else
 985                         bmap = isl_basic_map_set_to_empty(bmap);
 986                 break;
 987         }
 988         isl_int_clear(sum);
 989
 990         free(index);
 991         return bmap;
 992 }
 993
 994 static struct isl_basic_map *remove_duplicate_divs(
 995         struct isl_basic_map *bmap, int *progress)
 996 {
 997         unsigned int size;
 998         int *index;
 999         int k, l, h;
1000         int bits;
1001         struct isl_blk eq;
1002         unsigned total_var = bmap->nparam + bmap->n_in + bmap->n_out;
1003         unsigned total = total_var + bmap->n_div;
1004         struct isl_ctx *ctx;
1005
1006         if (bmap->n_div <= 1)
1007                 return bmap;
1008
1009         ctx = bmap->ctx;
1010         for (k = bmap->n_div - 1; k >= 0; --k)
1011                 if (!isl_int_is_zero(bmap->div[k][0]))
1012                         break;
1013         if (k <= 0)
1014                 return bmap;
1015
1016         size = round_up(4 * bmap->n_div / 3 - 1);
1017         bits = ffs(size) - 1;
1018         index = isl_alloc_array(ctx, int, size);
1019         memset(index, 0, size * sizeof(int));
1020         if (!index)
1021                 return bmap;
1022         eq = isl_blk_alloc(ctx, 1+total);
1023         if (isl_blk_is_error(eq))
1024                 goto out;
1025
1026         isl_seq_clr(eq.data, 1+total);
1027         index[isl_seq_hash(bmap->div[k], 2+total, bits)] = k + 1;
1028         for (--k; k >= 0; --k) {
1029                 u_int32_t hash;
1030
1031                 if (isl_int_is_zero(bmap->div[k][0]))
1032                         continue;
1033
1034                 hash = isl_seq_hash(bmap->div[k], 2+total, bits);
1035                 for (h = hash; index[h]; h = (h+1) % size)
1036                         if (isl_seq_eq(bmap->div[k],
1037                                        bmap->div[index[h]-1], 2+total))
1038                                 break;
1039                 if (index[h]) {
1040                         *progress = 1;
1041                         l = index[h] - 1;
1042                         isl_int_set_si(eq.data[1+total_var+k], -1);
1043                         isl_int_set_si(eq.data[1+total_var+l], 1);
1044                         eliminate_div(bmap, eq.data, l);
1045                         isl_int_set_si(eq.data[1+total_var+k], 0);
1046                         isl_int_set_si(eq.data[1+total_var+l], 0);
1047                 }
1048                 index[h] = k+1;
1049         }
1050
1051         isl_blk_free(ctx, eq);
1052 out:
1053         free(index);
1054         return bmap;
1055 }
1056
1057 /* Elimininate divs based on equalities
1058  */
1059 static struct isl_basic_map *eliminate_divs_eq(
1060                 struct isl_basic_map *bmap, int *progress)
1061 {
1062         int d;
1063         int i;
1064         int modified = 0;
1065         unsigned off;
1066
1067         if (!bmap)
1068                 return NULL;
1069
1070         off = 1 + bmap->nparam + bmap->n_in + bmap->n_out;
1071
1072         for (d = bmap->n_div - 1; d >= 0 ; --d) {
1073                 for (i = 0; i < bmap->n_eq; ++i) {
1074                         if (!isl_int_is_one(bmap->eq[i][off + d]) &&
1075                             !isl_int_is_negone(bmap->eq[i][off + d]))
1076                                 continue;
1077                         modified = 1;
1078                         *progress = 1;
1079                         eliminate_div(bmap, bmap->eq[i], d);
1080                         isl_basic_map_drop_equality(bmap, i);
1081                         break;
1082                 }
1083         }
1084         if (modified)
1085                 return eliminate_divs_eq(bmap, progress);
1086         return bmap;
1087 }
1088
1089 static struct isl_basic_map *normalize_constraints(struct isl_basic_map *bmap)
1090 {
1091         int i;
1092         isl_int gcd;
1093         unsigned total = bmap->nparam + bmap->n_in + bmap->n_out + bmap->n_div;
1094
1095         isl_int_init(gcd);
1096         for (i = bmap->n_eq - 1; i >= 0; --i) {
1097                 isl_seq_gcd(bmap->eq[i]+1, total, &gcd);
1098                 if (isl_int_is_zero(gcd)) {
1099                         if (!isl_int_is_zero(bmap->eq[i][0])) {
1100                                 bmap = isl_basic_map_set_to_empty(bmap);
1101                                 break;
1102                         }
1103                         isl_basic_map_drop_equality(bmap, i);
1104                         continue;
1105                 }
1106                 if (F_ISSET(bmap, ISL_BASIC_MAP_RATIONAL))
1107                         isl_int_gcd(gcd, gcd, bmap->eq[i][0]);
1108                 if (isl_int_is_one(gcd))
1109                         continue;
1110                 if (!isl_int_is_divisible_by(bmap->eq[i][0], gcd)) {
1111                         bmap = isl_basic_map_set_to_empty(bmap);
1112                         break;
1113                 }
1114                 isl_seq_scale_down(bmap->eq[i], bmap->eq[i], gcd, 1+total);
1115         }
1116
1117         for (i = bmap->n_ineq - 1; i >= 0; --i) {
1118                 isl_seq_gcd(bmap->ineq[i]+1, total, &gcd);
1119                 if (isl_int_is_zero(gcd)) {
1120                         if (isl_int_is_neg(bmap->ineq[i][0])) {
1121                                 bmap = isl_basic_map_set_to_empty(bmap);
1122                                 break;
1123                         }
1124                         isl_basic_map_drop_inequality(bmap, i);
1125                         continue;
1126                 }
1127                 if (F_ISSET(bmap, ISL_BASIC_MAP_RATIONAL))
1128                         isl_int_gcd(gcd, gcd, bmap->ineq[i][0]);
1129                 if (isl_int_is_one(gcd))
1130                         continue;
1131                 isl_int_fdiv_q(bmap->ineq[i][0], bmap->ineq[i][0], gcd);
1132                 isl_seq_scale_down(bmap->ineq[i]+1, bmap->ineq[i]+1, gcd, total);
1133         }
1134         isl_int_clear(gcd);
1135
1136         return bmap;
1137 }
1138
1139
1140 /* Eliminate the specified variables from the constraints using
1141  * Fourier-Motzkin.  The variables themselves are not removed.
1142  */
1143 struct isl_basic_map *isl_basic_map_eliminate_vars(
1144         struct isl_basic_map *bmap, int pos, unsigned n)
1145 {
1146         int d;
1147         int i, j, k;
1148         unsigned total;
1149         unsigned extra;
1150
1151         if (!bmap)
1152                 return NULL;
1153         total = bmap->nparam + bmap->n_in + bmap->n_out + bmap->n_div;
1154         extra = bmap->extra - bmap->n_div;
1155
1156         bmap = isl_basic_map_cow(bmap);
1157         bmap = isl_basic_map_gauss(bmap, NULL);
1158         for (d = pos + n - 1; d >= pos; --d) {
1159                 int n_lower, n_upper;
1160                 if (!bmap)
1161                         return NULL;
1162                 for (i = 0; i < bmap->n_eq; ++i) {
1163                         if (isl_int_is_zero(bmap->eq[i][1+d]))
1164                                 continue;
1165                         isl_basic_map_drop_equality(bmap, i);
1166                         break;
1167                 }
1168                 if (i < bmap->n_eq)
1169                         continue;
1170                 n_lower = 0;
1171                 n_upper = 0;
1172                 for (i = 0; i < bmap->n_ineq; ++i) {
1173                         if (isl_int_is_pos(bmap->ineq[i][1+d]))
1174                                 n_lower++;
1175                         else if (isl_int_is_neg(bmap->ineq[i][1+d]))
1176                                 n_upper++;
1177                 }
1178                 bmap = isl_basic_map_extend(bmap,
1179                                 bmap->nparam, bmap->n_in, bmap->n_out, 0,
1180                                 0, n_lower * n_upper);
1181                 for (i = bmap->n_ineq - 1; i >= 0; --i) {
1182                         int last;
1183                         if (isl_int_is_zero(bmap->ineq[i][1+d]))
1184                                 continue;
1185                         last = -1;
1186                         for (j = 0; j < i; ++j) {
1187                                 if (isl_int_is_zero(bmap->ineq[j][1+d]))
1188                                         continue;
1189                                 last = j;
1190                                 if (isl_int_sgn(bmap->ineq[i][1+d]) ==
1191                                     isl_int_sgn(bmap->ineq[j][1+d]))
1192                                         continue;
1193                                 k = isl_basic_map_alloc_inequality(bmap);
1194                                 if (k < 0)
1195                                         goto error;
1196                                 isl_seq_cpy(bmap->ineq[k], bmap->ineq[i],
1197                                                 1+total);
1198                                 isl_seq_clr(bmap->ineq[k]+1+total, extra);
1199                                 isl_seq_elim(bmap->ineq[k], bmap->ineq[j],
1200                                                 1+d, 1+total, NULL);
1201                         }
1202                         isl_basic_map_drop_inequality(bmap, i);
1203                         i = last + 1;
1204                 }
1205                 if (n_lower > 0 && n_upper > 0) {
1206                         bmap = normalize_constraints(bmap);
1207                         bmap = isl_basic_map_gauss(bmap, NULL);
1208                         if (F_ISSET(bmap, ISL_BASIC_MAP_EMPTY))
1209                                 break;
1210                 }
1211         }
1212         return bmap;
1213 error:
1214         isl_basic_map_free(bmap);
1215         return NULL;
1216 }
1217
1218 struct isl_basic_set *isl_basic_set_eliminate_vars(
1219         struct isl_basic_set *bset, unsigned pos, unsigned n)
1220 {
1221         return (struct isl_basic_set *)isl_basic_map_eliminate_vars(
1222                         (struct isl_basic_map *)bset, pos, n);
1223 }
1224
1225 /* Elimininate divs based on inequalities
1226  */
1227 static struct isl_basic_map *eliminate_divs_ineq(
1228                 struct isl_basic_map *bmap, int *progress)
1229 {
1230         int d;
1231         int i;
1232         unsigned off;
1233         struct isl_ctx *ctx;
1234
1235         if (!bmap)
1236                 return NULL;
1237
1238         ctx = bmap->ctx;
1239         off = 1 + bmap->nparam + bmap->n_in + bmap->n_out;
1240
1241         for (d = bmap->n_div - 1; d >= 0 ; --d) {
1242                 for (i = 0; i < bmap->n_eq; ++i)
1243                         if (!isl_int_is_zero(bmap->eq[i][off + d]))
1244                                 break;
1245                 if (i < bmap->n_eq)
1246                         continue;
1247                 for (i = 0; i < bmap->n_ineq; ++i)
1248                         if (isl_int_abs_gt(bmap->ineq[i][off + d], ctx->one))
1249                                 break;
1250                 if (i < bmap->n_ineq)
1251                         continue;
1252                 *progress = 1;
1253                 bmap = isl_basic_map_eliminate_vars(bmap, (off-1)+d, 1);
1254                 if (F_ISSET(bmap, ISL_BASIC_MAP_EMPTY))
1255                         break;
1256                 bmap = isl_basic_map_drop_div(bmap, d);
1257                 if (!bmap)
1258                         break;
1259         }
1260         return bmap;
1261 }
1262
1263 struct isl_basic_map *isl_basic_map_simplify(struct isl_basic_map *bmap)
1264 {
1265         int progress = 1;
1266         if (!bmap)
1267                 return NULL;
1268         while (progress) {
1269                 progress = 0;
1270                 bmap = normalize_constraints(bmap);
1271                 bmap = eliminate_divs_eq(bmap, &progress);
1272                 bmap = eliminate_divs_ineq(bmap, &progress);
1273                 bmap = isl_basic_map_gauss(bmap, &progress);
1274                 bmap = remove_duplicate_divs(bmap, &progress);
1275                 bmap = remove_duplicate_constraints(bmap, &progress);
1276         }
1277         return bmap;
1278 }
1279
1280 struct isl_basic_set *isl_basic_set_simplify(struct isl_basic_set *bset)
1281 {
1282         return (struct isl_basic_set *)
1283                 isl_basic_map_simplify((struct isl_basic_map *)bset);
1284 }
1285
1286 static void dump_term(struct isl_basic_map *bmap,
1287                         isl_int c, int pos, FILE *out)
1288 {
1289         unsigned in = bmap->n_in;
1290         unsigned dim = bmap->n_in + bmap->n_out;
1291         if (!pos)
1292                 isl_int_print(out, c);
1293         else {
1294                 if (!isl_int_is_one(c))
1295                         isl_int_print(out, c);
1296                 if (pos < 1 + bmap->nparam)
1297                         fprintf(out, "p%d", pos - 1);
1298                 else if (pos < 1 + bmap->nparam + in)
1299                         fprintf(out, "i%d", pos - 1 - bmap->nparam);
1300                 else if (pos < 1 + bmap->nparam + dim)
1301                         fprintf(out, "o%d", pos - 1 - bmap->nparam - in);
1302                 else
1303                         fprintf(out, "e%d", pos - 1 - bmap->nparam - dim);
1304         }
1305 }
1306
1307 static void dump_constraint_sign(struct isl_basic_map *bmap, isl_int *c,
1308                                 int sign, FILE *out)
1309 {
1310         int i;
1311         int first;
1312         unsigned len = 1 + bmap->nparam + bmap->n_in + bmap->n_out + bmap->n_div;
1313         isl_int v;
1314
1315         isl_int_init(v);
1316         for (i = 0, first = 1; i < len; ++i) {
1317                 if (isl_int_sgn(c[i]) * sign <= 0)
1318                         continue;
1319                 if (!first)
1320                         fprintf(out, " + ");
1321                 first = 0;
1322                 isl_int_abs(v, c[i]);
1323                 dump_term(bmap, v, i, out);
1324         }
1325         isl_int_clear(v);
1326         if (first)
1327                 fprintf(out, "0");
1328 }
1329
1330 static void dump_constraint(struct isl_basic_map *bmap, isl_int *c,
1331                                 const char *op, FILE *out, int indent)
1332 {
1333         int i;
1334
1335         fprintf(out, "%*s", indent, "");
1336
1337         dump_constraint_sign(bmap, c, 1, out);
1338         fprintf(out, " %s ", op);
1339         dump_constraint_sign(bmap, c, -1, out);
1340
1341         fprintf(out, "\n");
1342
1343         for (i = bmap->n_div; i < bmap->extra; ++i) {
1344                 if (isl_int_is_zero(c[1+bmap->nparam+bmap->n_in+bmap->n_out+i]))
1345                         continue;
1346                 fprintf(out, "%*s", indent, "");
1347                 fprintf(out, "ERROR: unused div coefficient not zero\n");
1348         }
1349 }
1350
1351 static void dump_constraints(struct isl_basic_map *bmap,
1352                                 isl_int **c, unsigned n,
1353                                 const char *op, FILE *out, int indent)
1354 {
1355         int i;
1356
1357         for (i = 0; i < n; ++i)
1358                 dump_constraint(bmap, c[i], op, out, indent);
1359 }
1360
1361 static void dump_affine(struct isl_basic_map *bmap, isl_int *exp, FILE *out)
1362 {
1363         int j;
1364         int first = 1;
1365         unsigned total = bmap->nparam + bmap->n_in + bmap->n_out + bmap->n_div;
1366
1367         for (j = 0; j < 1 + total; ++j) {
1368                 if (isl_int_is_zero(exp[j]))
1369                         continue;
1370                 if (!first && isl_int_is_pos(exp[j]))
1371                         fprintf(out, "+");
1372                 dump_term(bmap, exp[j], j, out);
1373                 first = 0;
1374         }
1375 }
1376
1377 static void dump(struct isl_basic_map *bmap, FILE *out, int indent)
1378 {
1379         int i;
1380
1381         dump_constraints(bmap, bmap->eq, bmap->n_eq, "=", out, indent);
1382         dump_constraints(bmap, bmap->ineq, bmap->n_ineq, ">=", out, indent);
1383
1384         for (i = 0; i < bmap->n_div; ++i) {
1385                 fprintf(out, "%*s", indent, "");
1386                 fprintf(out, "e%d = [(", i);
1387                 dump_affine(bmap, bmap->div[i]+1, out);
1388                 fprintf(out, ")/");
1389                 isl_int_print(out, bmap->div[i][0]);
1390                 fprintf(out, "]\n");
1391         }
1392 }
1393
1394 void isl_basic_set_dump(struct isl_basic_set *bset, FILE *out, int indent)
1395 {
1396         if (!bset) {
1397                 fprintf(out, "null basic set\n");
1398                 return;
1399         }
1400
1401         fprintf(out, "%*s", indent, "");
1402         fprintf(out, "nparam: %d, dim: %d, extra: %d\n",
1403                         bset->nparam, bset->dim, bset->extra);
1404         dump((struct isl_basic_map *)bset, out, indent);
1405 }
1406
1407 void isl_basic_map_dump(struct isl_basic_map *bmap, FILE *out, int indent)
1408 {
1409         if (!bmap) {
1410                 fprintf(out, "null basic map\n");
1411                 return;
1412         }
1413
1414         fprintf(out, "%*s", indent, "");
1415         fprintf(out, "ref: %d, nparam: %d, in: %d, out: %d, extra: %d, flags: %x\n",
1416                 bmap->ref,
1417                 bmap->nparam, bmap->n_in, bmap->n_out, bmap->extra, bmap->flags);
1418         dump(bmap, out, indent);
1419 }
1420
1421 int isl_inequality_negate(struct isl_basic_map *bmap, unsigned pos)
1422 {
1423         unsigned total = bmap->nparam + bmap->n_in + bmap->n_out + bmap->n_div;
1424         if (!bmap)
1425                 return -1;
1426         isl_assert(bmap->ctx, pos < bmap->n_ineq, return -1);
1427         isl_seq_neg(bmap->ineq[pos], bmap->ineq[pos], 1 + total);
1428         isl_int_sub_ui(bmap->ineq[pos][0], bmap->ineq[pos][0], 1);
1429         return 0;
1430 }
1431
1432 struct isl_set *isl_set_alloc(struct isl_ctx *ctx,
1433                 unsigned nparam, unsigned dim, int n, unsigned flags)
1434 {
1435         struct isl_set *set;
1436
1437         isl_assert(ctx, n >= 0, return NULL);
1438         set = isl_alloc(ctx, struct isl_set,
1439                         sizeof(struct isl_set) +
1440                         n * sizeof(struct isl_basic_set *));
1441         if (!set)
1442                 return NULL;
1443
1444         set->ctx = ctx;
1445         isl_ctx_ref(ctx);
1446         set->ref = 1;
1447         set->size = n;
1448         set->n = 0;
1449         set->nparam = nparam;
1450         set->zero = 0;
1451         set->dim = dim;
1452         set->flags = flags;
1453         return set;
1454 }
1455
1456 struct isl_set *isl_set_dup(struct isl_set *set)
1457 {
1458         int i;
1459         struct isl_set *dup;
1460
1461         if (!set)
1462                 return NULL;
1463
1464         dup = isl_set_alloc(set->ctx, set->nparam, set->dim, set->n, set->flags);
1465         if (!dup)
1466                 return NULL;
1467         for (i = 0; i < set->n; ++i)
1468                 dup = isl_set_add(dup,
1469                                   isl_basic_set_dup(set->p[i]));
1470         return dup;
1471 }
1472
1473 struct isl_set *isl_set_from_basic_set(struct isl_basic_set *bset)
1474 {
1475         struct isl_set *set;
1476
1477         if (!bset)
1478                 return NULL;
1479
1480         set = isl_set_alloc(bset->ctx, bset->nparam, bset->dim, 1, ISL_MAP_DISJOINT);
1481         if (!set) {
1482                 isl_basic_set_free(bset);
1483                 return NULL;
1484         }
1485         return isl_set_add(set, bset);
1486 }
1487
1488 struct isl_map *isl_map_from_basic_map(struct isl_basic_map *bmap)
1489 {
1490         struct isl_map *map;
1491
1492         if (!bmap)
1493                 return NULL;
1494
1495         map = isl_map_alloc(bmap->ctx, bmap->nparam, bmap->n_in, bmap->n_out, 1,
1496                                 ISL_MAP_DISJOINT);
1497         if (!map) {
1498                 isl_basic_map_free(bmap);
1499                 return NULL;
1500         }
1501         return isl_map_add(map, bmap);
1502 }
1503
1504 struct isl_set *isl_set_add(struct isl_set *set, struct isl_basic_set *bset)
1505 {
1506         if (!bset || !set)
1507                 goto error;
1508         isl_assert(set->ctx, set->nparam == bset->nparam, goto error);
1509         isl_assert(set->ctx, set->dim == bset->dim, goto error);
1510         isl_assert(set->ctx, set->n < set->size, goto error);
1511         set->p[set->n] = bset;
1512         set->n++;
1513         return set;
1514 error:
1515         if (set)
1516                 isl_set_free(set);
1517         if (bset)
1518                 isl_basic_set_free(bset);
1519         return NULL;
1520 }
1521
1522 void isl_set_free(struct isl_set *set)
1523 {
1524         int i;
1525
1526         if (!set)
1527                 return;
1528
1529         if (--set->ref > 0)
1530                 return;
1531
1532         isl_ctx_deref(set->ctx);
1533         for (i = 0; i < set->n; ++i)
1534                 isl_basic_set_free(set->p[i]);
1535         free(set);
1536 }
1537
1538 void isl_set_dump(struct isl_set *set, FILE *out, int indent)
1539 {
1540         int i;
1541
1542         if (!set) {
1543                 fprintf(out, "null set\n");
1544                 return;
1545         }
1546
1547         fprintf(out, "%*s", indent, "");
1548         fprintf(out, "ref: %d, n: %d\n", set->ref, set->n);
1549         for (i = 0; i < set->n; ++i) {
1550                 fprintf(out, "%*s", indent, "");
1551                 fprintf(out, "basic set %d:\n", i);
1552                 isl_basic_set_dump(set->p[i], out, indent+4);
1553         }
1554 }
1555
1556 void isl_map_dump(struct isl_map *map, FILE *out, int indent)
1557 {
1558         int i;
1559
1560         if (!map) {
1561                 fprintf(out, "null map\n");
1562                 return;
1563         }
1564
1565         fprintf(out, "%*s", indent, "");
1566         fprintf(out, "ref: %d, n: %d, nparam: %d, in: %d, out: %d, flags: %x\n",
1567                         map->ref, map->n, map->nparam, map->n_in, map->n_out,
1568                         map->flags);
1569         for (i = 0; i < map->n; ++i) {
1570                 fprintf(out, "%*s", indent, "");
1571                 fprintf(out, "basic map %d:\n", i);
1572                 isl_basic_map_dump(map->p[i], out, indent+4);
1573         }
1574 }
1575
1576 struct isl_basic_map *isl_basic_map_intersect_domain(
1577                 struct isl_basic_map *bmap, struct isl_basic_set *bset)
1578 {
1579         struct isl_basic_map *bmap_domain;
1580
1581         if (!bmap || !bset)
1582                 goto error;
1583
1584         isl_assert(bset->ctx, bset->dim == bmap->n_in, goto error);
1585         isl_assert(bset->ctx, bset->nparam == bmap->nparam, goto error);
1586
1587         bmap = isl_basic_map_extend(bmap,
1588                         bset->nparam, bmap->n_in, bmap->n_out,
1589                         bset->n_div, bset->n_eq, bset->n_ineq);
1590         if (!bmap)
1591                 goto error;
1592         bmap_domain = isl_basic_map_from_basic_set(bset,
1593                                                 bset->dim, 0);
1594         bmap = add_constraints(bmap, bmap_domain, 0, 0);
1595
1596         bmap = isl_basic_map_simplify(bmap);
1597         return isl_basic_map_finalize(bmap);
1598 error:
1599         isl_basic_map_free(bmap);
1600         isl_basic_set_free(bset);
1601         return NULL;
1602 }
1603
1604 struct isl_basic_map *isl_basic_map_intersect_range(
1605                 struct isl_basic_map *bmap, struct isl_basic_set *bset)
1606 {
1607         struct isl_basic_map *bmap_range;
1608
1609         if (!bmap || !bset)
1610                 goto error;
1611
1612         isl_assert(bset->ctx, bset->dim == bmap->n_out, goto error);
1613         isl_assert(bset->ctx, bset->nparam == bmap->nparam, goto error);
1614
1615         bmap = isl_basic_map_extend(bmap,
1616                         bset->nparam, bmap->n_in, bmap->n_out,
1617                         bset->n_div, bset->n_eq, bset->n_ineq);
1618         if (!bmap)
1619                 goto error;
1620         bmap_range = isl_basic_map_from_basic_set(bset,
1621                                                 0, bset->dim);
1622         bmap = add_constraints(bmap, bmap_range, 0, 0);
1623
1624         bmap = isl_basic_map_simplify(bmap);
1625         return isl_basic_map_finalize(bmap);
1626 error:
1627         isl_basic_map_free(bmap);
1628         isl_basic_set_free(bset);
1629         return NULL;
1630 }
1631
1632 struct isl_basic_map *isl_basic_map_intersect(
1633                 struct isl_basic_map *bmap1, struct isl_basic_map *bmap2)
1634 {
1635         if (!bmap1 || !bmap2)
1636                 goto error;
1637
1638         isl_assert(bmap1->ctx, bmap1->nparam == bmap2->nparam, goto error);
1639         isl_assert(bmap1->ctx, bmap1->n_in == bmap2->n_in, goto error);
1640         isl_assert(bmap1->ctx, bmap1->n_out == bmap2->n_out, goto error);
1641
1642         bmap1 = isl_basic_map_extend(bmap1,
1643                         bmap1->nparam, bmap1->n_in, bmap1->n_out,
1644                         bmap2->n_div, bmap2->n_eq, bmap2->n_ineq);
1645         if (!bmap1)
1646                 goto error;
1647         bmap1 = add_constraints(bmap1, bmap2, 0, 0);
1648
1649         bmap1 = isl_basic_map_simplify(bmap1);
1650         return isl_basic_map_finalize(bmap1);
1651 error:
1652         isl_basic_map_free(bmap1);
1653         isl_basic_map_free(bmap2);
1654         return NULL;
1655 }
1656
1657 struct isl_basic_set *isl_basic_set_intersect(
1658                 struct isl_basic_set *bset1, struct isl_basic_set *bset2)
1659 {
1660         return (struct isl_basic_set *)
1661                 isl_basic_map_intersect(
1662                         (struct isl_basic_map *)bset1,
1663                         (struct isl_basic_map *)bset2);
1664 }
1665
1666 struct isl_map *isl_map_intersect(struct isl_map *map1, struct isl_map *map2)
1667 {
1668         unsigned flags = 0;
1669         struct isl_map *result;
1670         int i, j;
1671
1672         if (!map1 || !map2)
1673                 goto error;
1674
1675         if (F_ISSET(map1, ISL_MAP_DISJOINT) &&
1676             F_ISSET(map2, ISL_MAP_DISJOINT))
1677                 FL_SET(flags, ISL_MAP_DISJOINT);
1678
1679         result = isl_map_alloc(map1->ctx, map1->nparam, map1->n_in, map1->n_out,
1680                                 map1->n * map2->n, flags);
1681         if (!result)
1682                 goto error;
1683         for (i = 0; i < map1->n; ++i)
1684                 for (j = 0; j < map2->n; ++j) {
1685                         struct isl_basic_map *part;
1686                         part = isl_basic_map_intersect(
1687                                     isl_basic_map_copy(map1->p[i]),
1688                                     isl_basic_map_copy(map2->p[j]));
1689                         if (isl_basic_map_is_empty(part))
1690                                 isl_basic_map_free(part);
1691                         else
1692                                 result = isl_map_add(result, part);
1693                         if (!result)
1694                                 goto error;
1695                 }
1696         isl_map_free(map1);
1697         isl_map_free(map2);
1698         return result;
1699 error:
1700         isl_map_free(map1);
1701         isl_map_free(map2);
1702         return NULL;
1703 }
1704
1705 struct isl_set *isl_set_intersect(struct isl_set *set1, struct isl_set *set2)
1706 {
1707         return (struct isl_set *)
1708                 isl_map_intersect((struct isl_map *)set1,
1709                                   (struct isl_map *)set2);
1710 }
1711
1712 struct isl_basic_map *isl_basic_map_reverse(struct isl_basic_map *bmap)
1713 {
1714         struct isl_basic_set *bset;
1715         unsigned in;
1716
1717         if (!bmap)
1718                 return NULL;
1719         bmap = isl_basic_map_cow(bmap);
1720         if (!bmap)
1721                 return NULL;
1722         in = bmap->n_in;
1723         bset = isl_basic_set_from_basic_map(bmap);
1724         bset = isl_basic_set_swap_vars(bset, in);
1725         return isl_basic_map_from_basic_set(bset, bset->dim-in, in);
1726 }
1727
1728 /* Turn final n dimensions into existentially quantified variables.
1729  */
1730 struct isl_basic_set *isl_basic_set_project_out(
1731                 struct isl_basic_set *bset, unsigned n, unsigned flags)
1732 {
1733         int i;
1734         size_t row_size;
1735         isl_int **new_div;
1736         isl_int *old;
1737
1738         if (!bset)
1739                 return NULL;
1740
1741         isl_assert(bset->ctx, n <= bset->dim, goto error);
1742
1743         if (n == 0)
1744                 return bset;
1745
1746         bset = isl_basic_set_cow(bset);
1747
1748         row_size = 1 + bset->nparam + bset->dim + bset->extra;
1749         old = bset->block2.data;
1750         bset->block2 = isl_blk_extend(bset->ctx, bset->block2,
1751                                         (bset->extra + n) * (1 + row_size));
1752         if (!bset->block2.data)
1753                 goto error;
1754         new_div = isl_alloc_array(ctx, isl_int *, bset->extra + n);
1755         if (!new_div)
1756                 goto error;
1757         for (i = 0; i < n; ++i) {
1758                 new_div[i] = bset->block2.data +
1759                                 (bset->extra + i) * (1 + row_size);
1760                 isl_seq_clr(new_div[i], 1 + row_size);
1761         }
1762         for (i = 0; i < bset->extra; ++i)
1763                 new_div[n + i] = bset->block2.data + (bset->div[i] - old);
1764         free(bset->div);
1765         bset->div = new_div;
1766         bset->n_div += n;
1767         bset->extra += n;
1768         bset->dim -= n;
1769         bset = isl_basic_set_simplify(bset);
1770         return isl_basic_set_finalize(bset);
1771 error:
1772         isl_basic_set_free(bset);
1773         return NULL;
1774 }
1775
1776 struct isl_basic_map *isl_basic_map_apply_range(
1777                 struct isl_basic_map *bmap1, struct isl_basic_map *bmap2)
1778 {
1779         struct isl_basic_set *bset;
1780         unsigned n_in, n_out;
1781
1782         if (!bmap1 || !bmap2)
1783                 goto error;
1784
1785         isl_assert(bmap->ctx, bmap1->n_out == bmap2->n_in, goto error);
1786         isl_assert(bmap->ctx, bmap1->nparam == bmap2->nparam, goto error);
1787
1788         n_in = bmap1->n_in;
1789         n_out = bmap2->n_out;
1790
1791         bmap2 = isl_basic_map_reverse(bmap2);
1792         if (!bmap2)
1793                 goto error;
1794         bmap1 = isl_basic_map_extend(bmap1, bmap1->nparam,
1795                         bmap1->n_in + bmap2->n_in, bmap1->n_out,
1796                         bmap2->extra, bmap2->n_eq, bmap2->n_ineq);
1797         if (!bmap1)
1798                 goto error;
1799         bmap1 = add_constraints(bmap1, bmap2, bmap1->n_in - bmap2->n_in, 0);
1800         bmap1 = isl_basic_map_simplify(bmap1);
1801         bset = isl_basic_set_from_basic_map(bmap1);
1802         bset = isl_basic_set_project_out(bset,
1803                                                 bset->dim - (n_in + n_out), 0);
1804         return isl_basic_map_from_basic_set(bset, n_in, n_out);
1805 error:
1806         isl_basic_map_free(bmap1);
1807         isl_basic_map_free(bmap2);
1808         return NULL;
1809 }
1810
1811 struct isl_basic_set *isl_basic_set_apply(
1812                 struct isl_basic_set *bset, struct isl_basic_map *bmap)
1813 {
1814         if (!bset || !bmap)
1815                 goto error;
1816
1817         isl_assert(bset->ctx, bset->dim == bmap->n_in, goto error);
1818
1819         return (struct isl_basic_set *)
1820                 isl_basic_map_apply_range((struct isl_basic_map *)bset, bmap);
1821 error:
1822         isl_basic_set_free(bset);
1823         isl_basic_map_free(bmap);
1824         return NULL;
1825 }
1826
1827 struct isl_basic_map *isl_basic_map_apply_domain(
1828                 struct isl_basic_map *bmap1, struct isl_basic_map *bmap2)
1829 {
1830         if (!bmap1 || !bmap2)
1831                 goto error;
1832
1833         isl_assert(ctx, bmap1->n_in == bmap2->n_in, goto error);
1834         isl_assert(ctx, bmap1->nparam == bmap2->nparam, goto error);
1835
1836         bmap1 = isl_basic_map_reverse(bmap1);
1837         bmap1 = isl_basic_map_apply_range(bmap1, bmap2);
1838         return isl_basic_map_reverse(bmap1);
1839 error:
1840         isl_basic_map_free(bmap1);
1841         isl_basic_map_free(bmap2);
1842         return NULL;
1843 }
1844
1845 static struct isl_basic_map *var_equal(struct isl_ctx *ctx,
1846                 struct isl_basic_map *bmap, unsigned pos)
1847 {
1848         int i;
1849         i = isl_basic_map_alloc_equality(bmap);
1850         if (i < 0)
1851                 goto error;
1852         isl_seq_clr(bmap->eq[i],
1853                     1 + bmap->nparam + bmap->n_in + bmap->n_out + bmap->extra);
1854         isl_int_set_si(bmap->eq[i][1+bmap->nparam+pos], -1);
1855         isl_int_set_si(bmap->eq[i][1+bmap->nparam+bmap->n_in+pos], 1);
1856         return isl_basic_map_finalize(bmap);
1857 error:
1858         isl_basic_map_free(bmap);
1859         return NULL;
1860 }
1861
1862 static struct isl_basic_map *var_more(struct isl_ctx *ctx,
1863                 struct isl_basic_map *bmap, unsigned pos)
1864 {
1865         int i;
1866         i = isl_basic_map_alloc_inequality(bmap);
1867         if (i < 0)
1868                 goto error;
1869         isl_seq_clr(bmap->ineq[i],
1870                     1 + bmap->nparam + bmap->n_in + bmap->n_out + bmap->extra);
1871         isl_int_set_si(bmap->ineq[i][0], -1);
1872         isl_int_set_si(bmap->ineq[i][1+bmap->nparam+pos], -1);
1873         isl_int_set_si(bmap->ineq[i][1+bmap->nparam+bmap->n_in+pos], 1);
1874         return isl_basic_map_finalize(bmap);
1875 error:
1876         isl_basic_map_free(bmap);
1877         return NULL;
1878 }
1879
1880 static struct isl_basic_map *var_less(struct isl_ctx *ctx,
1881                 struct isl_basic_map *bmap, unsigned pos)
1882 {
1883         int i;
1884         i = isl_basic_map_alloc_inequality(bmap);
1885         if (i < 0)
1886                 goto error;
1887         isl_seq_clr(bmap->ineq[i],
1888                     1 + bmap->nparam + bmap->n_in + bmap->n_out + bmap->extra);
1889         isl_int_set_si(bmap->ineq[i][0], -1);
1890         isl_int_set_si(bmap->ineq[i][1+bmap->nparam+pos], 1);
1891         isl_int_set_si(bmap->ineq[i][1+bmap->nparam+bmap->n_in+pos], -1);
1892         return isl_basic_map_finalize(bmap);
1893 error:
1894         isl_basic_map_free(bmap);
1895         return NULL;
1896 }
1897
1898 struct isl_basic_map *isl_basic_map_equal(struct isl_ctx *ctx,
1899                 unsigned nparam, unsigned in, unsigned out, unsigned n_equal)
1900 {
1901         int i;
1902         struct isl_basic_map *bmap;
1903         bmap = isl_basic_map_alloc(ctx, nparam, in, out, 0, n_equal, 0);
1904         if (!bmap)
1905                 return NULL;
1906         for (i = 0; i < n_equal && bmap; ++i)
1907                 bmap = var_equal(ctx, bmap, i);
1908         return isl_basic_map_finalize(bmap);
1909 }
1910
1911 struct isl_basic_map *isl_basic_map_less_at(struct isl_ctx *ctx,
1912                 unsigned nparam, unsigned in, unsigned out, unsigned pos)
1913 {
1914         int i;
1915         struct isl_basic_map *bmap;
1916         bmap = isl_basic_map_alloc(ctx, nparam, in, out, 0, pos, 1);
1917         if (!bmap)
1918                 return NULL;
1919         for (i = 0; i < pos && bmap; ++i)
1920                 bmap = var_equal(ctx, bmap, i);
1921         if (bmap)
1922                 bmap = var_less(ctx, bmap, pos);
1923         return isl_basic_map_finalize(bmap);
1924 }
1925
1926 struct isl_basic_map *isl_basic_map_more_at(struct isl_ctx *ctx,
1927                 unsigned nparam, unsigned in, unsigned out, unsigned pos)
1928 {
1929         int i;
1930         struct isl_basic_map *bmap;
1931         bmap = isl_basic_map_alloc(ctx, nparam, in, out, 0, pos, 1);
1932         if (!bmap)
1933                 return NULL;
1934         for (i = 0; i < pos && bmap; ++i)
1935                 bmap = var_equal(ctx, bmap, i);
1936         if (bmap)
1937                 bmap = var_more(ctx, bmap, pos);
1938         return isl_basic_map_finalize(bmap);
1939 }
1940
1941 struct isl_basic_map *isl_basic_map_from_basic_set(
1942                 struct isl_basic_set *bset, unsigned n_in, unsigned n_out)
1943 {
1944         struct isl_basic_map *bmap;
1945
1946         bset = isl_basic_set_cow(bset);
1947         if (!bset)
1948                 return NULL;
1949
1950         isl_assert(ctx, bset->dim == n_in + n_out, goto error);
1951         bmap = (struct isl_basic_map *) bset;
1952         bmap->n_in = n_in;
1953         bmap->n_out = n_out;
1954         return isl_basic_map_finalize(bmap);
1955 error:
1956         isl_basic_set_free(bset);
1957         return NULL;
1958 }
1959
1960 struct isl_basic_set *isl_basic_set_from_basic_map(struct isl_basic_map *bmap)
1961 {
1962         if (!bmap)
1963                 goto error;
1964         if (bmap->n_in == 0)
1965                 return (struct isl_basic_set *)bmap;
1966         bmap = isl_basic_map_cow(bmap);
1967         if (!bmap)
1968                 goto error;
1969         bmap->n_out += bmap->n_in;
1970         bmap->n_in = 0;
1971         bmap = isl_basic_map_finalize(bmap);
1972         return (struct isl_basic_set *)bmap;
1973 error:
1974         return NULL;
1975 }
1976
1977 /* For a div d = floor(f/m), add the constraints
1978  *
1979  *              f - m d >= 0
1980  *              -(f-(n-1)) + m d >= 0
1981  *
1982  * Note that the second constraint is the negation of
1983  *
1984  *              f - m d >= n
1985  */
1986 static int add_div_constraints(struct isl_basic_map *bmap, unsigned div)
1987 {
1988         int i, j;
1989         unsigned div_pos = 1 + bmap->nparam + bmap->n_in + bmap->n_out + div;
1990         unsigned total = bmap->nparam + bmap->n_in + bmap->n_out + bmap->extra;
1991
1992         i = isl_basic_map_alloc_inequality(bmap);
1993         if (i < 0)
1994                 return -1;
1995         isl_seq_cpy(bmap->ineq[i], bmap->div[div]+1, 1+total);
1996         isl_int_neg(bmap->ineq[i][div_pos], bmap->div[div][0]);
1997
1998         j = isl_basic_map_alloc_inequality(bmap);
1999         if (j < 0)
2000                 return -1;
2001         isl_seq_neg(bmap->ineq[j], bmap->ineq[i], 1 + total);
2002         isl_int_add(bmap->ineq[j][0], bmap->ineq[j][0], bmap->ineq[j][div_pos]);
2003         isl_int_sub_ui(bmap->ineq[j][0], bmap->ineq[j][0], 1);
2004         return j;
2005 }
2006
2007 struct isl_basic_set *isl_basic_map_underlying_set(
2008                 struct isl_basic_map *bmap)
2009 {
2010         if (!bmap)
2011                 goto error;
2012         if (bmap->nparam == 0 && bmap->n_in == 0 && bmap->n_div == 0)
2013                 return (struct isl_basic_set *)bmap;
2014         bmap = isl_basic_map_cow(bmap);
2015         if (!bmap)
2016                 goto error;
2017         bmap->n_out += bmap->nparam + bmap->n_in + bmap->n_div;
2018         bmap->nparam = 0;
2019         bmap->n_in = 0;
2020         bmap->extra -= bmap->n_div;
2021         bmap->n_div = 0;
2022         bmap = isl_basic_map_finalize(bmap);
2023         return (struct isl_basic_set *)bmap;
2024 error:
2025         return NULL;
2026 }
2027
2028 struct isl_basic_map *isl_basic_map_overlying_set(
2029         struct isl_basic_set *bset, struct isl_basic_map *like)
2030 {
2031         struct isl_basic_map *bmap;
2032         struct isl_ctx *ctx;
2033         unsigned total;
2034         int i, k;
2035
2036         if (!bset || !like)
2037                 goto error;
2038         ctx = bset->ctx;
2039         isl_assert(ctx, bset->dim ==
2040                         like->nparam + like->n_in + like->n_out + like->n_div,
2041                         goto error);
2042         if (like->nparam == 0 && like->n_in == 0 && like->n_div == 0) {
2043                 isl_basic_map_free(like);
2044                 return (struct isl_basic_map *)bset;
2045         }
2046         bset = isl_basic_set_cow(bset);
2047         total = bset->dim + bset->extra;
2048         if (!bset)
2049                 goto error;
2050         bmap = (struct isl_basic_map *)bset;
2051         bmap->nparam = like->nparam;
2052         bmap->n_in = like->n_in;
2053         bmap->n_out = like->n_out;
2054         bmap->extra += like->n_div;
2055         if (bmap->extra) {
2056                 unsigned ltotal;
2057                 ltotal = total - bmap->extra + like->extra;
2058                 if (ltotal > total)
2059                         ltotal = total;
2060                 bmap->block2 = isl_blk_extend(ctx, bmap->block2,
2061                                         bmap->extra * (1 + 1 + total));
2062                 if (isl_blk_is_error(bmap->block2))
2063                         goto error;
2064                 bmap->div = isl_realloc_array(ctx, bmap->div, isl_int *,
2065                                                 bmap->extra);
2066                 if (!bmap->div)
2067                         goto error;
2068                 bmap = isl_basic_map_extend(bmap, bmap->nparam,
2069                         bmap->n_in, bmap->n_out, 0, 0, 2 * like->n_div);
2070                 for (i = 0; i < like->n_div; ++i) {
2071                         k = isl_basic_map_alloc_div(bmap);
2072                         if (k < 0)
2073                                 goto error;
2074                         isl_seq_cpy(bmap->div[k], like->div[i], 1 + 1 + ltotal);
2075                         isl_seq_clr(bmap->div[k]+1+1+ltotal, total - ltotal);
2076                         if (add_div_constraints(bmap, k) < 0)
2077                                 goto error;
2078                 }
2079         }
2080         isl_basic_map_free(like);
2081         bmap = isl_basic_map_finalize(bmap);
2082         return bmap;
2083 error:
2084         isl_basic_map_free(like);
2085         isl_basic_set_free(bset);
2086         return NULL;
2087 }
2088
2089 struct isl_set *isl_map_underlying_set(struct isl_map *map)
2090 {
2091         int i;
2092
2093         map = isl_map_align_divs(map);
2094         map = isl_map_cow(map);
2095         if (!map)
2096                 return NULL;
2097
2098         for (i = 0; i < map->n; ++i) {
2099                 map->p[i] = (struct isl_basic_map *)
2100                                 isl_basic_map_underlying_set(map->p[i]);
2101                 if (!map->p[i])
2102                         goto error;
2103         }
2104         if (map->n == 0)
2105                 map->n_out += map->nparam + map->n_in;
2106         else
2107                 map->n_out = map->p[0]->n_out;
2108         map->nparam = 0;
2109         map->n_in = 0;
2110         return (struct isl_set *)map;
2111 error:
2112         isl_map_free(map);
2113         return NULL;
2114 }
2115
2116 struct isl_basic_set *isl_basic_map_domain(struct isl_basic_map *bmap)
2117 {
2118         struct isl_basic_set *domain;
2119         unsigned n_out;
2120         if (!bmap)
2121                 return NULL;
2122         n_out = bmap->n_out;
2123         domain = isl_basic_set_from_basic_map(bmap);
2124         return isl_basic_set_project_out(domain, n_out, 0);
2125 }
2126
2127 struct isl_basic_set *isl_basic_map_range(struct isl_basic_map *bmap)
2128 {
2129         return isl_basic_map_domain(isl_basic_map_reverse(bmap));
2130 }
2131
2132 struct isl_set *isl_map_range(struct isl_map *map)
2133 {
2134         int i;
2135         struct isl_set *set;
2136
2137         if (!map)
2138                 goto error;
2139         map = isl_map_cow(map);
2140         if (!map)
2141                 goto error;
2142
2143         set = (struct isl_set *) map;
2144         set->zero = 0;
2145         for (i = 0; i < map->n; ++i) {
2146                 set->p[i] = isl_basic_map_range(map->p[i]);
2147                 if (!set->p[i])
2148                         goto error;
2149         }
2150         F_CLR(set, ISL_MAP_DISJOINT);
2151         return set;
2152 error:
2153         isl_map_free(map);
2154         return NULL;
2155 }
2156
2157 struct isl_map *isl_map_from_set(struct isl_set *set,
2158                 unsigned n_in, unsigned n_out)
2159 {
2160         int i;
2161         struct isl_map *map = NULL;
2162
2163         if (!set)
2164                 return NULL;
2165         isl_assert(set->ctx, set->dim == n_in + n_out, goto error);
2166         set = isl_set_cow(set);
2167         if (!set)
2168                 return NULL;
2169         map = (struct isl_map *)set;
2170         for (i = 0; i < set->n; ++i) {
2171                 map->p[i] = isl_basic_map_from_basic_set(
2172                                 set->p[i], n_in, n_out);
2173                 if (!map->p[i])
2174                         goto error;
2175         }
2176         map->n_in = n_in;
2177         map->n_out = n_out;
2178         return map;
2179 error:
2180         isl_set_free(set);
2181         return NULL;
2182 }
2183
2184 struct isl_set *isl_set_from_map(struct isl_map *map)
2185 {
2186         int i;
2187         struct isl_set *set = NULL;
2188
2189         if (!map)
2190                 return NULL;
2191         map = isl_map_cow(map);
2192         if (!map)
2193                 return NULL;
2194         map->n_out += map->n_in;
2195         map->n_in = 0;
2196         set = (struct isl_set *)map;
2197         for (i = 0; i < map->n; ++i) {
2198                 set->p[i] = isl_basic_set_from_basic_map(map->p[i]);
2199                 if (!set->p[i])
2200                         goto error;
2201         }
2202         return set;
2203 error:
2204         isl_map_free(map);
2205         return NULL;
2206 }
2207
2208 struct isl_map *isl_map_alloc(struct isl_ctx *ctx,
2209                 unsigned nparam, unsigned in, unsigned out, int n,
2210                 unsigned flags)
2211 {
2212         struct isl_map *map;
2213
2214         map = isl_alloc(ctx, struct isl_map,
2215                         sizeof(struct isl_map) +
2216                         n * sizeof(struct isl_basic_map *));
2217         if (!map)
2218                 return NULL;
2219
2220         map->ctx = ctx;
2221         isl_ctx_ref(ctx);
2222         map->ref = 1;
2223         map->size = n;
2224         map->n = 0;
2225         map->nparam = nparam;
2226         map->n_in = in;
2227         map->n_out = out;
2228         map->flags = flags;
2229         return map;
2230 }
2231
2232 struct isl_basic_map *isl_basic_map_empty(struct isl_ctx *ctx,
2233                 unsigned nparam, unsigned in, unsigned out)
2234 {
2235         struct isl_basic_map *bmap;
2236         bmap = isl_basic_map_alloc(ctx, nparam, in, out, 0, 1, 0);
2237         bmap = isl_basic_map_set_to_empty(bmap);
2238         return bmap;
2239 }
2240
2241 struct isl_basic_set *isl_basic_set_empty(struct isl_ctx *ctx,
2242                 unsigned nparam, unsigned dim)
2243 {
2244         struct isl_basic_set *bset;
2245         bset = isl_basic_set_alloc(ctx, nparam, dim, 0, 1, 0);
2246         bset = isl_basic_set_set_to_empty(bset);
2247         return bset;
2248 }
2249
2250 struct isl_basic_map *isl_basic_map_universe(struct isl_ctx *ctx,
2251                 unsigned nparam, unsigned in, unsigned out)
2252 {
2253         struct isl_basic_map *bmap;
2254         bmap = isl_basic_map_alloc(ctx, nparam, in, out, 0, 0, 0);
2255         return bmap;
2256 }
2257
2258 struct isl_basic_set *isl_basic_set_universe(struct isl_ctx *ctx,
2259                 unsigned nparam, unsigned dim)
2260 {
2261         struct isl_basic_set *bset;
2262         bset = isl_basic_set_alloc(ctx, nparam, dim, 0, 0, 0);
2263         return bset;
2264 }
2265
2266 struct isl_map *isl_map_empty(struct isl_ctx *ctx,
2267                 unsigned nparam, unsigned in, unsigned out)
2268 {
2269         return isl_map_alloc(ctx, nparam, in, out, 0, ISL_MAP_DISJOINT);
2270 }
2271
2272 struct isl_set *isl_set_empty(struct isl_ctx *ctx,
2273                 unsigned nparam, unsigned dim)
2274 {
2275         return isl_set_alloc(ctx, nparam, dim, 0, ISL_MAP_DISJOINT);
2276 }
2277
2278 struct isl_map *isl_map_dup(struct isl_map *map)
2279 {
2280         int i;
2281         struct isl_map *dup;
2282
2283         if (!map)
2284                 return NULL;
2285         dup = isl_map_alloc(map->ctx, map->nparam, map->n_in, map->n_out, map->n,
2286                                 map->flags);
2287         for (i = 0; i < map->n; ++i)
2288                 dup = isl_map_add(dup,
2289                                   isl_basic_map_dup(map->p[i]));
2290         return dup;
2291 }
2292
2293 struct isl_map *isl_map_add(struct isl_map *map, struct isl_basic_map *bmap)
2294 {
2295         if (!bmap || !map)
2296                 goto error;
2297         isl_assert(map->ctx, map->nparam == bmap->nparam, goto error);
2298         isl_assert(map->ctx, map->n_in == bmap->n_in, goto error);
2299         isl_assert(map->ctx, map->n_out == bmap->n_out, goto error);
2300         isl_assert(map->ctx, map->n < map->size, goto error);
2301         map->p[map->n] = bmap;
2302         map->n++;
2303         return map;
2304 error:
2305         if (map)
2306                 isl_map_free(map);
2307         if (bmap)
2308                 isl_basic_map_free(bmap);
2309         return NULL;
2310 }
2311
2312 void isl_map_free(struct isl_map *map)
2313 {
2314         int i;
2315
2316         if (!map)
2317                 return;
2318
2319         if (--map->ref > 0)
2320                 return;
2321
2322         isl_ctx_deref(map->ctx);
2323         for (i = 0; i < map->n; ++i)
2324                 isl_basic_map_free(map->p[i]);
2325         free(map);
2326 }
2327
2328 struct isl_map *isl_map_extend(struct isl_map *base,
2329                 unsigned nparam, unsigned n_in, unsigned n_out)
2330 {
2331         int i;
2332
2333         base = isl_map_cow(base);
2334         if (!base)
2335                 return NULL;
2336
2337         isl_assert(base->ctx, base->nparam <= nparam, goto error);
2338         isl_assert(base->ctx, base->n_in <= n_in, goto error);
2339         isl_assert(base->ctx, base->n_out <= n_out, goto error);
2340         base->nparam = nparam;
2341         base->n_in = n_in;
2342         base->n_out = n_out;
2343         for (i = 0; i < base->n; ++i) {
2344                 base->p[i] = isl_basic_map_extend(base->p[i],
2345                                 nparam, n_in, n_out, 0, 0, 0);
2346                 if (!base->p[i])
2347                         goto error;
2348         }
2349         return base;
2350 error:
2351         isl_map_free(base);
2352         return NULL;
2353 }
2354
2355 struct isl_set *isl_set_extend(struct isl_set *base,
2356                 unsigned nparam, unsigned dim)
2357 {
2358         return (struct isl_set *)isl_map_extend((struct isl_map *)base,
2359                                                         nparam, 0, dim);
2360 }
2361
2362 static struct isl_basic_map *isl_basic_map_fix_var(struct isl_basic_map *bmap,
2363                 unsigned var, int value)
2364 {
2365         int j;
2366
2367         bmap = isl_basic_map_cow(bmap);
2368         bmap = isl_basic_map_extend(bmap,
2369                         bmap->nparam, bmap->n_in, bmap->n_out, 0, 1, 0);
2370         j = isl_basic_map_alloc_equality(bmap);
2371         if (j < 0)
2372                 goto error;
2373         isl_seq_clr(bmap->eq[j],
2374                     1 + bmap->nparam + bmap->n_in + bmap->n_out + bmap->extra);
2375         isl_int_set_si(bmap->eq[j][1 + var], -1);
2376         isl_int_set_si(bmap->eq[j][0], value);
2377         bmap = isl_basic_map_simplify(bmap);
2378         return isl_basic_map_finalize(bmap);
2379 error:
2380         isl_basic_map_free(bmap);
2381         return NULL;
2382 }
2383
2384 struct isl_basic_map *isl_basic_map_fix_input_si(struct isl_basic_map *bmap,
2385                 unsigned input, int value)
2386 {
2387         if (!bmap)
2388                 return NULL;
2389         isl_assert(bmap->ctx, input < bmap->n_in, goto error);
2390         return isl_basic_map_fix_var(bmap, bmap->nparam + input, value);
2391 error:
2392         isl_basic_map_free(bmap);
2393         return NULL;
2394 }
2395
2396 struct isl_basic_set *isl_basic_set_fix_dim_si(struct isl_basic_set *bset,
2397                 unsigned dim, int value)
2398 {
2399         if (!bset)
2400                 return NULL;
2401         isl_assert(bset->ctx, dim < bset->dim, goto error);
2402         return (struct isl_basic_set *)
2403                 isl_basic_map_fix_var((struct isl_basic_map *)bset,
2404                                                 bset->nparam + dim, value);
2405 error:
2406         isl_basic_set_free(bset);
2407         return NULL;
2408 }
2409
2410 struct isl_map *isl_map_fix_input_si(struct isl_map *map,
2411                 unsigned input, int value)
2412 {
2413         int i;
2414
2415         map = isl_map_cow(map);
2416         if (!map)
2417                 return NULL;
2418
2419         isl_assert(ctx, input < map->n_in, goto error);
2420         for (i = 0; i < map->n; ++i) {
2421                 map->p[i] = isl_basic_map_fix_input_si(map->p[i], input, value);
2422                 if (!map->p[i])
2423                         goto error;
2424         }
2425         return map;
2426 error:
2427         isl_map_free(map);
2428         return NULL;
2429 }
2430
2431 struct isl_set *isl_set_fix_dim_si(struct isl_set *set, unsigned dim, int value)
2432 {
2433         int i;
2434
2435         set = isl_set_cow(set);
2436         if (!set)
2437                 return NULL;
2438
2439         isl_assert(set->ctx, dim < set->dim, goto error);
2440         for (i = 0; i < set->n; ++i) {
2441                 set->p[i] = isl_basic_set_fix_dim_si(set->p[i], dim, value);
2442                 if (!set->p[i])
2443                         goto error;
2444         }
2445         return set;
2446 error:
2447         isl_set_free(set);
2448         return NULL;
2449 }
2450
2451 struct isl_map *isl_map_reverse(struct isl_map *map)
2452 {
2453         int i;
2454         unsigned t;
2455
2456         map = isl_map_cow(map);
2457         if (!map)
2458                 return NULL;
2459
2460         t = map->n_in;
2461         map->n_in = map->n_out;
2462         map->n_out = t;
2463         for (i = 0; i < map->n; ++i) {
2464                 map->p[i] = isl_basic_map_reverse(map->p[i]);
2465                 if (!map->p[i])
2466                         goto error;
2467         }
2468         return map;
2469 error:
2470         isl_map_free(map);
2471         return NULL;
2472 }
2473
2474 struct isl_map *isl_basic_map_lexmax(
2475                 struct isl_basic_map *bmap, struct isl_basic_set *dom,
2476                 struct isl_set **empty)
2477 {
2478         return isl_pip_basic_map_lexmax(bmap, dom, empty);
2479 }
2480
2481 struct isl_map *isl_basic_map_lexmin(
2482                 struct isl_basic_map *bmap, struct isl_basic_set *dom,
2483                 struct isl_set **empty)
2484 {
2485         return isl_pip_basic_map_lexmin(bmap, dom, empty);
2486 }
2487
2488 struct isl_set *isl_basic_set_lexmin(struct isl_basic_set *bset)
2489 {
2490         struct isl_basic_map *bmap = NULL;
2491         struct isl_basic_set *dom = NULL;
2492         struct isl_map *min;
2493
2494         if (!bset)
2495                 goto error;
2496         bmap = isl_basic_map_from_basic_set(bset, 0, bset->dim);
2497         if (!bmap)
2498                 goto error;
2499         dom = isl_basic_set_alloc(bmap->ctx, bmap->nparam, 0, 0, 0, 0);
2500         if (!dom)
2501                 goto error;
2502         min = isl_basic_map_lexmin(bmap, dom, NULL);
2503         return isl_map_range(min);
2504 error:
2505         isl_basic_map_free(bmap);
2506         return NULL;
2507 }
2508
2509 struct isl_map *isl_basic_map_compute_divs(struct isl_basic_map *bmap)
2510 {
2511         if (!bmap)
2512                 return NULL;
2513         if (bmap->n_div == 0)
2514                 return isl_map_from_basic_map(bmap);
2515         return isl_pip_basic_map_compute_divs(bmap);
2516 }
2517
2518 struct isl_map *isl_map_compute_divs(struct isl_map *map)
2519 {
2520         int i;
2521         struct isl_map *res;
2522
2523         if (!map)
2524                 return NULL;
2525         if (map->n == 0)
2526                 return map;
2527         res = isl_basic_map_compute_divs(isl_basic_map_copy(map->p[0]));
2528         for (i = 1 ; i < map->n; ++i) {
2529                 struct isl_map *r2;
2530                 r2 = isl_basic_map_compute_divs(isl_basic_map_copy(map->p[i]));
2531                 if (F_ISSET(map, ISL_MAP_DISJOINT))
2532                         res = isl_map_union_disjoint(res, r2);
2533                 else
2534                         res = isl_map_union(res, r2);
2535         }
2536         isl_map_free(map);
2537
2538         return res;
2539 }
2540
2541 struct isl_set *isl_basic_set_compute_divs(struct isl_basic_set *bset)
2542 {
2543         return (struct isl_set *)
2544                 isl_basic_map_compute_divs((struct isl_basic_map *)bset);
2545 }
2546
2547 struct isl_set *isl_set_compute_divs(struct isl_set *set)
2548 {
2549         return (struct isl_set *)
2550                 isl_map_compute_divs((struct isl_map *)set);
2551 }
2552
2553 struct isl_set *isl_map_domain(struct isl_map *map)
2554 {
2555         int i;
2556         struct isl_set *set;
2557
2558         if (!map)
2559                 goto error;
2560
2561         map = isl_map_cow(map);
2562         if (!map)
2563                 return NULL;
2564
2565         set = (struct isl_set *)map;
2566         set->dim = map->n_in;
2567         set->zero = 0;
2568         for (i = 0; i < map->n; ++i) {
2569                 set->p[i] = isl_basic_map_domain(map->p[i]);
2570                 if (!set->p[i])
2571                         goto error;
2572         }
2573         F_CLR(set, ISL_MAP_DISJOINT);
2574         return set;
2575 error:
2576         isl_map_free(map);
2577         return NULL;
2578 }
2579
2580 struct isl_map *isl_map_union_disjoint(
2581                         struct isl_map *map1, struct isl_map *map2)
2582 {
2583         int i;
2584         unsigned flags = 0;
2585         struct isl_map *map = NULL;
2586
2587         if (!map1 || !map2)
2588                 goto error;
2589
2590         if (map1->n == 0) {
2591                 isl_map_free(map1);
2592                 return map2;
2593         }
2594         if (map2->n == 0) {
2595                 isl_map_free(map2);
2596                 return map1;
2597         }
2598
2599         isl_assert(map1->ctx, map1->nparam == map2->nparam, goto error);
2600         isl_assert(map1->ctx, map1->n_in == map2->n_in, goto error);
2601         isl_assert(map1->ctx, map1->n_out == map2->n_out, goto error);
2602
2603         if (F_ISSET(map1, ISL_MAP_DISJOINT) &&
2604             F_ISSET(map2, ISL_MAP_DISJOINT))
2605                 FL_SET(flags, ISL_MAP_DISJOINT);
2606
2607         map = isl_map_alloc(map1->ctx, map1->nparam, map1->n_in, map1->n_out,
2608                                 map1->n + map2->n, flags);
2609         if (!map)
2610                 goto error;
2611         for (i = 0; i < map1->n; ++i) {
2612                 map = isl_map_add(map,
2613                                   isl_basic_map_copy(map1->p[i]));
2614                 if (!map)
2615                         goto error;
2616         }
2617         for (i = 0; i < map2->n; ++i) {
2618                 map = isl_map_add(map,
2619                                   isl_basic_map_copy(map2->p[i]));
2620                 if (!map)
2621                         goto error;
2622         }
2623         isl_map_free(map1);
2624         isl_map_free(map2);
2625         return map;
2626 error:
2627         isl_map_free(map);
2628         isl_map_free(map1);
2629         isl_map_free(map2);
2630         return NULL;
2631 }
2632
2633 struct isl_map *isl_map_union(struct isl_map *map1, struct isl_map *map2)
2634 {
2635         map1 = isl_map_union_disjoint(map1, map2);
2636         if (!map1)
2637                 return NULL;
2638         if (map1->n > 1)
2639                 F_CLR(map1, ISL_MAP_DISJOINT);
2640         return map1;
2641 }
2642
2643 struct isl_set *isl_set_union_disjoint(
2644                         struct isl_set *set1, struct isl_set *set2)
2645 {
2646         return (struct isl_set *)
2647                 isl_map_union_disjoint(
2648                         (struct isl_map *)set1, (struct isl_map *)set2);
2649 }
2650
2651 struct isl_set *isl_set_union(struct isl_set *set1, struct isl_set *set2)
2652 {
2653         return (struct isl_set *)
2654                 isl_map_union((struct isl_map *)set1, (struct isl_map *)set2);
2655 }
2656
2657 struct isl_map *isl_map_intersect_range(
2658                 struct isl_map *map, struct isl_set *set)
2659 {
2660         unsigned flags = 0;
2661         struct isl_map *result;
2662         int i, j;
2663
2664         if (!map || !set)
2665                 goto error;
2666
2667         if (F_ISSET(map, ISL_MAP_DISJOINT) &&
2668             F_ISSET(set, ISL_MAP_DISJOINT))
2669                 FL_SET(flags, ISL_MAP_DISJOINT);
2670
2671         result = isl_map_alloc(map->ctx, map->nparam, map->n_in, map->n_out,
2672                                 map->n * set->n, flags);
2673         if (!result)
2674                 goto error;
2675         for (i = 0; i < map->n; ++i)
2676                 for (j = 0; j < set->n; ++j) {
2677                         result = isl_map_add(result,
2678                             isl_basic_map_intersect_range(
2679                                 isl_basic_map_copy(map->p[i]),
2680                                 isl_basic_set_copy(set->p[j])));
2681                         if (!result)
2682                                 goto error;
2683                 }
2684         isl_map_free(map);
2685         isl_set_free(set);
2686         return result;
2687 error:
2688         isl_map_free(map);
2689         isl_set_free(set);
2690         return NULL;
2691 }
2692
2693 struct isl_map *isl_map_intersect_domain(
2694                 struct isl_map *map, struct isl_set *set)
2695 {
2696         return isl_map_reverse(
2697                 isl_map_intersect_range(isl_map_reverse(map), set));
2698 }
2699
2700 struct isl_map *isl_map_apply_domain(
2701                 struct isl_map *map1, struct isl_map *map2)
2702 {
2703         if (!map1 || !map2)
2704                 goto error;
2705         map1 = isl_map_reverse(map1);
2706         map1 = isl_map_apply_range(map1, map2);
2707         return isl_map_reverse(map1);
2708 error:
2709         isl_map_free(map1);
2710         isl_map_free(map2);
2711         return NULL;
2712 }
2713
2714 struct isl_map *isl_map_apply_range(
2715                 struct isl_map *map1, struct isl_map *map2)
2716 {
2717         struct isl_map *result;
2718         int i, j;
2719
2720         if (!map1 || !map2)
2721                 goto error;
2722
2723         isl_assert(map1->ctx, map1->nparam == map2->nparam, goto error);
2724         isl_assert(map1->ctx, map1->n_out == map2->n_in, goto error);
2725
2726         result = isl_map_alloc(map1->ctx, map1->nparam, map1->n_in, map2->n_out,
2727                                 map1->n * map2->n, 0);
2728         if (!result)
2729                 goto error;
2730         for (i = 0; i < map1->n; ++i)
2731                 for (j = 0; j < map2->n; ++j) {
2732                         result = isl_map_add(result,
2733                             isl_basic_map_apply_range(
2734                                 isl_basic_map_copy(map1->p[i]),
2735                                 isl_basic_map_copy(map2->p[j])));
2736                         if (!result)
2737                                 goto error;
2738                 }
2739         isl_map_free(map1);
2740         isl_map_free(map2);
2741         if (result && result->n <= 1)
2742                 F_SET(result, ISL_MAP_DISJOINT);
2743         return result;
2744 error:
2745         isl_map_free(map1);
2746         isl_map_free(map2);
2747         return NULL;
2748 }
2749
2750 /*
2751  * returns range - domain
2752  */
2753 struct isl_basic_set *isl_basic_map_deltas(struct isl_basic_map *bmap)
2754 {
2755         struct isl_basic_set *bset;
2756         unsigned dim;
2757         int i;
2758
2759         if (!bmap)
2760                 goto error;
2761         isl_assert(bmap->ctx, bmap->n_in == bmap->n_out, goto error);
2762         dim = bmap->n_in;
2763         bset = isl_basic_set_from_basic_map(bmap);
2764         bset = isl_basic_set_extend(bset, bset->nparam, 3*dim, 0,
2765                                         dim, 0);
2766         bset = isl_basic_set_swap_vars(bset, 2*dim);
2767         for (i = 0; i < dim; ++i) {
2768                 int j = isl_basic_map_alloc_equality(
2769                                             (struct isl_basic_map *)bset);
2770                 if (j < 0)
2771                         goto error;
2772                 isl_seq_clr(bset->eq[j],
2773                             1 + bset->nparam + bset->dim + bset->extra);
2774                 isl_int_set_si(bset->eq[j][1+bset->nparam+i], 1);
2775                 isl_int_set_si(bset->eq[j][1+bset->nparam+dim+i], 1);
2776                 isl_int_set_si(bset->eq[j][1+bset->nparam+2*dim+i], -1);
2777         }
2778         return isl_basic_set_project_out(bset, 2*dim, 0);
2779 error:
2780         isl_basic_map_free(bmap);
2781         return NULL;
2782 }
2783
2784 /* If the only constraints a div d=floor(f/m)
2785  * appears in are its two defining constraints
2786  *
2787  *      f - m d >=0
2788  *      -(f - (m - 1)) + m d >= 0
2789  *
2790  * then it can safely be removed.
2791  */
2792 static int div_is_redundant(struct isl_basic_map *bmap, int div)
2793 {
2794         int i;
2795         unsigned pos = 1 + bmap->nparam + bmap->n_in + bmap->n_out + div;
2796
2797         for (i = 0; i < bmap->n_eq; ++i)
2798                 if (!isl_int_is_zero(bmap->eq[i][pos]))
2799                         return 0;
2800
2801         for (i = 0; i < bmap->n_ineq; ++i) {
2802                 if (isl_int_is_zero(bmap->ineq[i][pos]))
2803                         continue;
2804                 if (isl_int_eq(bmap->ineq[i][pos], bmap->div[div][0])) {
2805                         int neg;
2806                         isl_int_sub(bmap->div[div][1],
2807                                         bmap->div[div][1], bmap->div[div][0]);
2808                         isl_int_add_ui(bmap->div[div][1], bmap->div[div][1], 1);
2809                         neg = isl_seq_is_neg(bmap->ineq[i], bmap->div[div]+1, pos);
2810                         isl_int_sub_ui(bmap->div[div][1], bmap->div[div][1], 1);
2811                         isl_int_add(bmap->div[div][1],
2812                                         bmap->div[div][1], bmap->div[div][0]);
2813                         if (!neg)
2814                                 return 0;
2815                         if (isl_seq_first_non_zero(bmap->ineq[i]+pos+1,
2816                                                     bmap->n_div-div-1) != -1)
2817                                 return 0;
2818                 } else if (isl_int_abs_eq(bmap->ineq[i][pos], bmap->div[div][0])) {
2819                         if (!isl_seq_eq(bmap->ineq[i], bmap->div[div]+1, pos))
2820                                 return 0;
2821                         if (isl_seq_first_non_zero(bmap->ineq[i]+pos+1,
2822                                                     bmap->n_div-div-1) != -1)
2823                                 return 0;
2824                 } else
2825                         return 0;
2826         }
2827
2828         for (i = 0; i < bmap->n_div; ++i)
2829                 if (!isl_int_is_zero(bmap->div[i][1+pos]))
2830                         return 0;
2831
2832         return 1;
2833 }
2834
2835 /*
2836  * Remove divs that don't occur in any of the constraints or other divs.
2837  * These can arise when dropping some of the variables in a quast
2838  * returned by piplib.
2839  */
2840 static struct isl_basic_map *remove_redundant_divs(struct isl_basic_map *bmap)
2841 {
2842         int i;
2843
2844         if (!bmap)
2845                 return NULL;
2846
2847         for (i = bmap->n_div-1; i >= 0; --i) {
2848                 if (!div_is_redundant(bmap, i))
2849                         continue;
2850                 bmap = isl_basic_map_drop_div(bmap, i);
2851         }
2852         return bmap;
2853 }
2854
2855 struct isl_basic_map *isl_basic_map_finalize(struct isl_basic_map *bmap)
2856 {
2857         bmap = remove_redundant_divs(bmap);
2858         if (!bmap)
2859                 return NULL;
2860         F_SET(bmap, ISL_BASIC_SET_FINAL);
2861         return bmap;
2862 }
2863
2864 struct isl_basic_set *isl_basic_set_finalize(struct isl_basic_set *bset)
2865 {
2866         return (struct isl_basic_set *)
2867                 isl_basic_map_finalize((struct isl_basic_map *)bset);
2868 }
2869
2870 struct isl_set *isl_set_finalize(struct isl_set *set)
2871 {
2872         int i;
2873
2874         if (!set)
2875                 return NULL;
2876         for (i = 0; i < set->n; ++i) {
2877                 set->p[i] = isl_basic_set_finalize(set->p[i]);
2878                 if (!set->p[i])
2879                         goto error;
2880         }
2881         return set;
2882 error:
2883         isl_set_free(set);
2884         return NULL;
2885 }
2886
2887 struct isl_map *isl_map_finalize(struct isl_map *map)
2888 {
2889         int i;
2890
2891         if (!map)
2892                 return NULL;
2893         for (i = 0; i < map->n; ++i) {
2894                 map->p[i] = isl_basic_map_finalize(map->p[i]);
2895                 if (!map->p[i])
2896                         goto error;
2897         }
2898         return map;
2899 error:
2900         isl_map_free(map);
2901         return NULL;
2902 }
2903
2904 struct isl_basic_map *isl_basic_map_identity(struct isl_ctx *ctx,
2905                 unsigned nparam, unsigned dim)
2906 {
2907         struct isl_basic_map *bmap;
2908         int i;
2909
2910         bmap = isl_basic_map_alloc(ctx, nparam, dim, dim, 0, dim, 0);
2911         if (!bmap)
2912                 goto error;
2913
2914         for (i = 0; i < dim; ++i) {
2915                 int j = isl_basic_map_alloc_equality(bmap);
2916                 if (j < 0)
2917                         goto error;
2918                 isl_seq_clr(bmap->eq[j],
2919                     1 + bmap->nparam + bmap->n_in + bmap->n_out + bmap->extra);
2920                 isl_int_set_si(bmap->eq[j][1+nparam+i], 1);
2921                 isl_int_set_si(bmap->eq[j][1+nparam+dim+i], -1);
2922         }
2923         return isl_basic_map_finalize(bmap);
2924 error:
2925         isl_basic_map_free(bmap);
2926         return NULL;
2927 }
2928
2929 struct isl_map *isl_map_identity(struct isl_ctx *ctx,
2930                 unsigned nparam, unsigned dim)
2931 {
2932         struct isl_map *map = isl_map_alloc(ctx, nparam, dim, dim, 1,
2933                                                 ISL_MAP_DISJOINT);
2934         if (!map)
2935                 goto error;
2936         map = isl_map_add(map,
2937                 isl_basic_map_identity(ctx, nparam, dim));
2938         return map;
2939 error:
2940         isl_map_free(map);
2941         return NULL;
2942 }
2943
2944 int isl_set_is_equal(struct isl_set *set1, struct isl_set *set2)
2945 {
2946         return isl_map_is_equal((struct isl_map *)set1, (struct isl_map *)set2);
2947 }
2948
2949 int isl_set_is_subset(struct isl_set *set1, struct isl_set *set2)
2950 {
2951         return isl_map_is_subset(
2952                         (struct isl_map *)set1, (struct isl_map *)set2);
2953 }
2954
2955 int isl_basic_map_is_subset(
2956                 struct isl_basic_map *bmap1, struct isl_basic_map *bmap2)
2957 {
2958         int is_subset;
2959         struct isl_map *map1;
2960         struct isl_map *map2;
2961
2962         if (!bmap1 || !bmap2)
2963                 return -1;
2964
2965         map1 = isl_map_from_basic_map(isl_basic_map_copy(bmap1));
2966         map2 = isl_map_from_basic_map(isl_basic_map_copy(bmap2));
2967
2968         is_subset = isl_map_is_subset(map1, map2);
2969
2970         isl_map_free(map1);
2971         isl_map_free(map2);
2972
2973         return is_subset;
2974 }
2975
2976 int isl_basic_map_is_equal(
2977                 struct isl_basic_map *bmap1, struct isl_basic_map *bmap2)
2978 {
2979         int is_subset;
2980
2981         if (!bmap1 || !bmap2)
2982                 return -1;
2983         is_subset = isl_basic_map_is_subset(bmap1, bmap2);
2984         if (is_subset != 1)
2985                 return is_subset;
2986         is_subset = isl_basic_map_is_subset(bmap2, bmap1);
2987         return is_subset;
2988 }
2989
2990 int isl_basic_set_is_equal(
2991                 struct isl_basic_set *bset1, struct isl_basic_set *bset2)
2992 {
2993         return isl_basic_map_is_equal(
2994                 (struct isl_basic_map *)bset1, (struct isl_basic_map *)bset2);
2995 }
2996
2997 int isl_map_is_empty(struct isl_map *map)
2998 {
2999         int i;
3000         int is_empty;
3001
3002         if (!map)
3003                 return -1;
3004         for (i = 0; i < map->n; ++i) {
3005                 is_empty = isl_basic_map_is_empty(map->p[i]);
3006                 if (is_empty < 0)
3007                         return -1;
3008                 if (!is_empty)
3009                         return 0;
3010         }
3011         return 1;
3012 }
3013
3014 int isl_set_is_empty(struct isl_set *set)
3015 {
3016         return isl_map_is_empty((struct isl_map *)set);
3017 }
3018
3019 int isl_map_is_subset(struct isl_map *map1, struct isl_map *map2)
3020 {
3021         int i;
3022         int is_subset = 0;
3023         struct isl_map *diff;
3024
3025         if (!map1 || !map2)
3026                 return -1;
3027
3028         if (isl_map_is_empty(map1))
3029                 return 1;
3030
3031         if (isl_map_is_empty(map2))
3032                 return 0;
3033
3034         diff = isl_map_subtract(isl_map_copy(map1), isl_map_copy(map2));
3035         if (!diff)
3036                 return -1;
3037
3038         is_subset = isl_map_is_empty(diff);
3039         isl_map_free(diff);
3040
3041         return is_subset;
3042 }
3043
3044 int isl_map_is_equal(struct isl_map *map1, struct isl_map *map2)
3045 {
3046         int is_subset;
3047
3048         if (!map1 || !map2)
3049                 return -1;
3050         is_subset = isl_map_is_subset(map1, map2);
3051         if (is_subset != 1)
3052                 return is_subset;
3053         is_subset = isl_map_is_subset(map2, map1);
3054         return is_subset;
3055 }
3056
3057 int isl_basic_map_is_strict_subset(
3058                 struct isl_basic_map *bmap1, struct isl_basic_map *bmap2)
3059 {
3060         int is_subset;
3061
3062         if (!bmap1 || !bmap2)
3063                 return -1;
3064         is_subset = isl_basic_map_is_subset(bmap1, bmap2);
3065         if (is_subset != 1)
3066                 return is_subset;
3067         is_subset = isl_basic_map_is_subset(bmap2, bmap1);
3068         if (is_subset == -1)
3069                 return is_subset;
3070         return !is_subset;
3071 }
3072
3073 static int basic_map_contains(struct isl_basic_map *bmap, struct isl_vec *vec)
3074 {
3075         int i;
3076         unsigned total;
3077         isl_int s;
3078
3079         total = 1 + bmap->nparam + bmap->n_in + bmap->n_out + bmap->n_div;
3080         if (total != vec->size)
3081                 return -1;
3082
3083         isl_int_init(s);
3084
3085         for (i = 0; i < bmap->n_eq; ++i) {
3086                 isl_seq_inner_product(vec->block.data, bmap->eq[i], total, &s);
3087                 if (!isl_int_is_zero(s)) {
3088                         isl_int_clear(s);
3089                         return 0;
3090                 }
3091         }
3092
3093         for (i = 0; i < bmap->n_ineq; ++i) {
3094                 isl_seq_inner_product(vec->block.data, bmap->ineq[i], total, &s);
3095                 if (isl_int_is_neg(s)) {
3096                         isl_int_clear(s);
3097                         return 0;
3098                 }
3099         }
3100
3101         isl_int_clear(s);
3102
3103         return 1;
3104 }
3105
3106 int isl_basic_map_is_universe(struct isl_basic_map *bmap)
3107 {
3108         if (!bmap)
3109                 return -1;
3110         return bmap->n_eq == 0 && bmap->n_ineq == 0;
3111 }
3112
3113 int isl_basic_map_is_empty(struct isl_basic_map *bmap)
3114 {
3115         struct isl_basic_set *bset = NULL;
3116         struct isl_vec *sample = NULL;
3117         int empty;
3118         unsigned total;
3119
3120         if (!bmap)
3121                 return -1;
3122
3123         if (F_ISSET(bmap, ISL_BASIC_MAP_EMPTY))
3124                 return 1;
3125
3126         total = 1 + bmap->nparam + bmap->n_in + bmap->n_out + bmap->n_div;
3127         if (bmap->sample && bmap->sample->size == total) {
3128                 int contains = basic_map_contains(bmap, bmap->sample);
3129                 if (contains < 0)
3130                         return -1;
3131                 if (contains)
3132                         return 0;
3133         }
3134         bset = isl_basic_map_underlying_set(isl_basic_map_copy(bmap));
3135         if (!bset)
3136                 return -1;
3137         sample = isl_basic_set_sample(bset);
3138         if (!sample)
3139                 return -1;
3140         empty = sample->size == 0;
3141         if (bmap->sample)
3142                 isl_vec_free(bmap->ctx, bmap->sample);
3143         bmap->sample = sample;
3144
3145         return empty;
3146 }
3147
3148 struct isl_map *isl_basic_map_union(
3149         struct isl_basic_map *bmap1, struct isl_basic_map *bmap2)
3150 {
3151         struct isl_map *map;
3152         if (!bmap1 || !bmap2)
3153                 return NULL;
3154
3155         isl_assert(bmap1->ctx, bmap1->nparam == bmap2->nparam, goto error);
3156         isl_assert(bmap1->ctx, bmap1->n_in == bmap2->n_in, goto error);
3157         isl_assert(bmap1->ctx, bmap1->n_out == bmap2->n_out, goto error);
3158
3159         map = isl_map_alloc(bmap1->ctx, bmap1->nparam,
3160                                 bmap1->n_in, bmap1->n_out, 2, 0);
3161         if (!map)
3162                 goto error;
3163         map = isl_map_add(map, bmap1);
3164         map = isl_map_add(map, bmap2);
3165         return map;
3166 error:
3167         isl_basic_map_free(bmap1);
3168         isl_basic_map_free(bmap2);
3169         return NULL;
3170 }
3171
3172 struct isl_set *isl_basic_set_union(
3173                 struct isl_basic_set *bset1, struct isl_basic_set *bset2)
3174 {
3175         return (struct isl_set *)isl_basic_map_union(
3176                                             (struct isl_basic_map *)bset1,
3177                                             (struct isl_basic_map *)bset2);
3178 }
3179
3180 /* Order divs such that any div only depends on previous divs */
3181 static struct isl_basic_map *order_divs(struct isl_basic_map *bmap)
3182 {
3183         int i;
3184         unsigned off = bmap->nparam + bmap->n_in + bmap->n_out;
3185
3186         for (i = 0; i < bmap->n_div; ++i) {
3187                 int pos;
3188                 pos = isl_seq_first_non_zero(bmap->div[i]+1+1+off+i,
3189                                                             bmap->n_div-i);
3190                 if (pos == -1)
3191                         continue;
3192                 swap_div(bmap, i, pos);
3193                 --i;
3194         }
3195         return bmap;
3196 }
3197
3198 static int find_div(struct isl_basic_map *dst,
3199                         struct isl_basic_map *src, unsigned div)
3200 {
3201         int i;
3202
3203         unsigned total = src->nparam + src->n_in + src->n_out + src->n_div;
3204
3205         for (i = 0; i < dst->n_div; ++i)
3206                 if (isl_seq_eq(dst->div[i], src->div[div], 1+1+total) &&
3207                     isl_seq_first_non_zero(dst->div[i]+1+1+total,
3208                                                 dst->n_div - src->n_div) == -1)
3209                         return i;
3210         return -1;
3211 }
3212
3213 struct isl_basic_map *isl_basic_map_align_divs(
3214                 struct isl_basic_map *dst, struct isl_basic_map *src)
3215 {
3216         int i;
3217         unsigned total = src->nparam + src->n_in + src->n_out + src->n_div;
3218
3219         if (src->n_div == 0)
3220                 return dst;
3221
3222         src = order_divs(src);
3223         dst = isl_basic_map_extend(dst, dst->nparam, dst->n_in,
3224                         dst->n_out, src->n_div, 0, 2 * src->n_div);
3225         if (!dst)
3226                 return NULL;
3227         for (i = 0; i < src->n_div; ++i) {
3228                 int j = find_div(dst, src, i);
3229                 if (j < 0) {
3230                         j = isl_basic_map_alloc_div(dst);
3231                         if (j < 0)
3232                                 goto error;
3233                         isl_seq_cpy(dst->div[j], src->div[i], 1+1+total);
3234                         isl_seq_clr(dst->div[j]+1+1+total,
3235                                                     dst->extra - src->n_div);
3236                         if (add_div_constraints(dst, j) < 0)
3237                                 goto error;
3238                 }
3239                 if (j != i)
3240                         swap_div(dst, i, j);
3241         }
3242         return dst;
3243 error:
3244         isl_basic_map_free(dst);
3245         return NULL;
3246 }
3247
3248 struct isl_map *isl_map_align_divs(struct isl_map *map)
3249 {
3250         int i;
3251
3252         map = isl_map_compute_divs(map);
3253         map = isl_map_cow(map);
3254         if (!map)
3255                 return NULL;
3256
3257         for (i = 1; i < map->n; ++i)
3258                 map->p[0] = isl_basic_map_align_divs(map->p[0], map->p[i]);
3259         for (i = 1; i < map->n; ++i)
3260                 map->p[i] = isl_basic_map_align_divs(map->p[i], map->p[0]);
3261
3262         return map;
3263 }
3264
3265 static struct isl_map *add_cut_constraint(struct isl_map *dst,
3266                 struct isl_basic_map *src, isl_int *c,
3267                 unsigned len, int oppose)
3268 {
3269         struct isl_basic_map *copy = NULL;
3270         int is_empty;
3271         int k;
3272         unsigned total;
3273
3274         copy = isl_basic_map_copy(src);
3275         copy = isl_basic_map_cow(copy);
3276         if (!copy)
3277                 goto error;
3278         copy = isl_basic_map_extend(copy,
3279                 copy->nparam, copy->n_in, copy->n_out, 0, 0, 1);
3280         k = isl_basic_map_alloc_inequality(copy);
3281         if (k < 0)
3282                 goto error;
3283         if (oppose)
3284                 isl_seq_neg(copy->ineq[k], c, len);
3285         else
3286                 isl_seq_cpy(copy->ineq[k], c, len);
3287         total = 1 + copy->nparam + copy->n_in + copy->n_out + copy->extra;
3288         isl_seq_clr(copy->ineq[k]+len, total - len);
3289         isl_inequality_negate(copy, k);
3290         copy = isl_basic_map_simplify(copy);
3291         copy = isl_basic_map_finalize(copy);
3292         is_empty = isl_basic_map_is_empty(copy);
3293         if (is_empty < 0)
3294                 goto error;
3295         if (!is_empty)
3296                 dst = isl_map_add(dst, copy);
3297         else
3298                 isl_basic_map_free(copy);
3299         return dst;
3300 error:
3301         isl_basic_map_free(copy);
3302         isl_map_free(dst);
3303         return NULL;
3304 }
3305
3306 static struct isl_map *subtract(struct isl_map *map, struct isl_basic_map *bmap)
3307 {
3308         int i, j, k;
3309         unsigned flags = 0;
3310         struct isl_map *rest = NULL;
3311         unsigned max;
3312         unsigned total = bmap->nparam + bmap->n_in + bmap->n_out + bmap->n_div;
3313
3314         assert(bmap);
3315
3316         if (!map)
3317                 goto error;
3318
3319         if (F_ISSET(map, ISL_MAP_DISJOINT))
3320                 FL_SET(flags, ISL_MAP_DISJOINT);
3321
3322         max = map->n * (2 * bmap->n_eq + bmap->n_ineq);
3323         rest = isl_map_alloc(map->ctx, map->nparam, map->n_in, map->n_out,
3324                                 max, flags);
3325         if (!rest)
3326                 goto error;
3327
3328         for (i = 0; i < map->n; ++i) {
3329                 map->p[i] = isl_basic_map_align_divs(map->p[i], bmap);
3330                 if (!map->p[i])
3331                         goto error;
3332         }
3333
3334         for (j = 0; j < map->n; ++j)
3335                 map->p[j] = isl_basic_map_cow(map->p[j]);
3336
3337         for (i = 0; i < bmap->n_eq; ++i) {
3338                 for (j = 0; j < map->n; ++j) {
3339                         rest = add_cut_constraint(rest,
3340                                 map->p[j], bmap->eq[i], 1+total, 0);
3341                         if (!rest)
3342                                 goto error;
3343
3344                         rest = add_cut_constraint(rest,
3345                                 map->p[j], bmap->eq[i], 1+total, 1);
3346                         if (!rest)
3347                                 goto error;
3348
3349                         map->p[j] = isl_basic_map_extend(map->p[j],
3350                                 map->p[j]->nparam, map->p[j]->n_in,
3351                                 map->p[j]->n_out, 0, 1, 0);
3352                         if (!map->p[j])
3353                                 goto error;
3354                         k = isl_basic_map_alloc_equality(map->p[j]);
3355                         if (k < 0)
3356                                 goto error;
3357                         isl_seq_cpy(map->p[j]->eq[k], bmap->eq[i], 1+total);
3358                         isl_seq_clr(map->p[j]->eq[k]+1+total,
3359                                         map->p[j]->extra - bmap->n_div);
3360                 }
3361         }
3362
3363         for (i = 0; i < bmap->n_ineq; ++i) {
3364                 for (j = 0; j < map->n; ++j) {
3365                         rest = add_cut_constraint(rest,
3366                                 map->p[j], bmap->ineq[i], 1+total, 0);
3367                         if (!rest)
3368                                 goto error;
3369
3370                         map->p[j] = isl_basic_map_extend(map->p[j],
3371                                 map->p[j]->nparam, map->p[j]->n_in,
3372                                 map->p[j]->n_out, 0, 0, 1);
3373                         if (!map->p[j])
3374                                 goto error;
3375                         k = isl_basic_map_alloc_inequality(map->p[j]);
3376                         if (k < 0)
3377                                 goto error;
3378                         isl_seq_cpy(map->p[j]->ineq[k], bmap->ineq[i], 1+total);
3379                         isl_seq_clr(map->p[j]->ineq[k]+1+total,
3380                                         map->p[j]->extra - bmap->n_div);
3381                 }
3382         }
3383
3384         isl_map_free(map);
3385         return rest;
3386 error:
3387         isl_map_free(map);
3388         isl_map_free(rest);
3389         return NULL;
3390 }
3391
3392 struct isl_map *isl_map_subtract(struct isl_map *map1, struct isl_map *map2)
3393 {
3394         int i;
3395         if (!map1 || !map2)
3396                 goto error;
3397
3398         isl_assert(map1->ctx, map1->nparam == map2->nparam, goto error);
3399         isl_assert(map1->ctx, map1->n_in == map2->n_in, goto error);
3400         isl_assert(map1->ctx, map1->n_out == map2->n_out, goto error);
3401
3402         if (isl_map_is_empty(map2)) {
3403                 isl_map_free(map2);
3404                 return map1;
3405         }
3406
3407         map1 = isl_map_compute_divs(map1);
3408         map2 = isl_map_compute_divs(map2);
3409         if (!map1 || !map2)
3410                 goto error;
3411
3412         for (i = 0; map1 && i < map2->n; ++i)
3413                 map1 = subtract(map1, map2->p[i]);
3414
3415         isl_map_free(map2);
3416         return map1;
3417 error:
3418         isl_map_free(map1);
3419         isl_map_free(map2);
3420         return NULL;
3421 }
3422
3423 struct isl_set *isl_set_subtract(struct isl_set *set1, struct isl_set *set2)
3424 {
3425         return (struct isl_set *)
3426                 isl_map_subtract(
3427                         (struct isl_map *)set1, (struct isl_map *)set2);
3428 }
3429
3430 struct isl_set *isl_set_apply(struct isl_set *set, struct isl_map *map)
3431 {
3432         if (!set || !map)
3433                 goto error;
3434         isl_assert(set->ctx, set->dim == map->n_in, goto error);
3435         map = isl_map_intersect_domain(map, set);
3436         set = isl_map_range(map);
3437         return set;
3438 error:
3439         isl_set_free(set);
3440         isl_map_free(map);
3441         return NULL;
3442 }
3443
3444 /* There is no need to cow as removing empty parts doesn't change
3445  * the meaning of the set.
3446  */
3447 struct isl_map *isl_map_remove_empty_parts(struct isl_map *map)
3448 {
3449         int i;
3450
3451         if (!map)
3452                 return NULL;
3453
3454         for (i = map->n-1; i >= 0; --i) {
3455                 if (!F_ISSET(map->p[i], ISL_BASIC_MAP_EMPTY))
3456                         continue;
3457                 isl_basic_map_free(map->p[i]);
3458                 if (i != map->n-1)
3459                         map->p[i] = map->p[map->n-1];
3460                 map->n--;
3461         }
3462
3463         return map;
3464 }
3465
3466 struct isl_set *isl_set_remove_empty_parts(struct isl_set *set)
3467 {
3468         return (struct isl_set *)
3469                 isl_map_remove_empty_parts((struct isl_map *)set);
3470 }