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_dims(
 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 static struct isl_set *isl_set_drop_dims(
 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_dims(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 /* Project out n dimensions starting at first using Fourier-Motzkin */
1226 struct isl_set *isl_set_remove_dims(struct isl_set *set,
1227         unsigned first, unsigned n)
1228 {
1229         int i;
1230
1231         if (n == 0)
1232                 return set;
1233
1234         set = isl_set_cow(set);
1235         if (!set)
1236                 return NULL;
1237         isl_assert(set->ctx, first+n <= set->dim, goto error);
1238
1239         for (i = 0; i < set->n; ++i) {
1240                 set->p[i] = isl_basic_set_eliminate_vars(set->p[i],
1241                                                         set->nparam + first, n);
1242                 if (!set->p[i])
1243                         goto error;
1244         }
1245         set = isl_set_drop_dims(set, first, n);
1246         return set;
1247 error:
1248         isl_set_free(set);
1249         return NULL;
1250 }
1251
1252 /* Elimininate divs based on inequalities
1253  */
1254 static struct isl_basic_map *eliminate_divs_ineq(
1255                 struct isl_basic_map *bmap, int *progress)
1256 {
1257         int d;
1258         int i;
1259         unsigned off;
1260         struct isl_ctx *ctx;
1261
1262         if (!bmap)
1263                 return NULL;
1264
1265         ctx = bmap->ctx;
1266         off = 1 + bmap->nparam + bmap->n_in + bmap->n_out;
1267
1268         for (d = bmap->n_div - 1; d >= 0 ; --d) {
1269                 for (i = 0; i < bmap->n_eq; ++i)
1270                         if (!isl_int_is_zero(bmap->eq[i][off + d]))
1271                                 break;
1272                 if (i < bmap->n_eq)
1273                         continue;
1274                 for (i = 0; i < bmap->n_ineq; ++i)
1275                         if (isl_int_abs_gt(bmap->ineq[i][off + d], ctx->one))
1276                                 break;
1277                 if (i < bmap->n_ineq)
1278                         continue;
1279                 *progress = 1;
1280                 bmap = isl_basic_map_eliminate_vars(bmap, (off-1)+d, 1);
1281                 if (F_ISSET(bmap, ISL_BASIC_MAP_EMPTY))
1282                         break;
1283                 bmap = isl_basic_map_drop_div(bmap, d);
1284                 if (!bmap)
1285                         break;
1286         }
1287         return bmap;
1288 }
1289
1290 struct isl_basic_map *isl_basic_map_simplify(struct isl_basic_map *bmap)
1291 {
1292         int progress = 1;
1293         if (!bmap)
1294                 return NULL;
1295         while (progress) {
1296                 progress = 0;
1297                 bmap = normalize_constraints(bmap);
1298                 bmap = eliminate_divs_eq(bmap, &progress);
1299                 bmap = eliminate_divs_ineq(bmap, &progress);
1300                 bmap = isl_basic_map_gauss(bmap, &progress);
1301                 bmap = remove_duplicate_divs(bmap, &progress);
1302                 bmap = remove_duplicate_constraints(bmap, &progress);
1303         }
1304         return bmap;
1305 }
1306
1307 struct isl_basic_set *isl_basic_set_simplify(struct isl_basic_set *bset)
1308 {
1309         return (struct isl_basic_set *)
1310                 isl_basic_map_simplify((struct isl_basic_map *)bset);
1311 }
1312
1313 static void dump_term(struct isl_basic_map *bmap,
1314                         isl_int c, int pos, FILE *out)
1315 {
1316         unsigned in = bmap->n_in;
1317         unsigned dim = bmap->n_in + bmap->n_out;
1318         if (!pos)
1319                 isl_int_print(out, c);
1320         else {
1321                 if (!isl_int_is_one(c))
1322                         isl_int_print(out, c);
1323                 if (pos < 1 + bmap->nparam)
1324                         fprintf(out, "p%d", pos - 1);
1325                 else if (pos < 1 + bmap->nparam + in)
1326                         fprintf(out, "i%d", pos - 1 - bmap->nparam);
1327                 else if (pos < 1 + bmap->nparam + dim)
1328                         fprintf(out, "o%d", pos - 1 - bmap->nparam - in);
1329                 else
1330                         fprintf(out, "e%d", pos - 1 - bmap->nparam - dim);
1331         }
1332 }
1333
1334 static void dump_constraint_sign(struct isl_basic_map *bmap, isl_int *c,
1335                                 int sign, FILE *out)
1336 {
1337         int i;
1338         int first;
1339         unsigned len = 1 + bmap->nparam + bmap->n_in + bmap->n_out + bmap->n_div;
1340         isl_int v;
1341
1342         isl_int_init(v);
1343         for (i = 0, first = 1; i < len; ++i) {
1344                 if (isl_int_sgn(c[i]) * sign <= 0)
1345                         continue;
1346                 if (!first)
1347                         fprintf(out, " + ");
1348                 first = 0;
1349                 isl_int_abs(v, c[i]);
1350                 dump_term(bmap, v, i, out);
1351         }
1352         isl_int_clear(v);
1353         if (first)
1354                 fprintf(out, "0");
1355 }
1356
1357 static void dump_constraint(struct isl_basic_map *bmap, isl_int *c,
1358                                 const char *op, FILE *out, int indent)
1359 {
1360         int i;
1361
1362         fprintf(out, "%*s", indent, "");
1363
1364         dump_constraint_sign(bmap, c, 1, out);
1365         fprintf(out, " %s ", op);
1366         dump_constraint_sign(bmap, c, -1, out);
1367
1368         fprintf(out, "\n");
1369
1370         for (i = bmap->n_div; i < bmap->extra; ++i) {
1371                 if (isl_int_is_zero(c[1+bmap->nparam+bmap->n_in+bmap->n_out+i]))
1372                         continue;
1373                 fprintf(out, "%*s", indent, "");
1374                 fprintf(out, "ERROR: unused div coefficient not zero\n");
1375         }
1376 }
1377
1378 static void dump_constraints(struct isl_basic_map *bmap,
1379                                 isl_int **c, unsigned n,
1380                                 const char *op, FILE *out, int indent)
1381 {
1382         int i;
1383
1384         for (i = 0; i < n; ++i)
1385                 dump_constraint(bmap, c[i], op, out, indent);
1386 }
1387
1388 static void dump_affine(struct isl_basic_map *bmap, isl_int *exp, FILE *out)
1389 {
1390         int j;
1391         int first = 1;
1392         unsigned total = bmap->nparam + bmap->n_in + bmap->n_out + bmap->n_div;
1393
1394         for (j = 0; j < 1 + total; ++j) {
1395                 if (isl_int_is_zero(exp[j]))
1396                         continue;
1397                 if (!first && isl_int_is_pos(exp[j]))
1398                         fprintf(out, "+");
1399                 dump_term(bmap, exp[j], j, out);
1400                 first = 0;
1401         }
1402 }
1403
1404 static void dump(struct isl_basic_map *bmap, FILE *out, int indent)
1405 {
1406         int i;
1407
1408         dump_constraints(bmap, bmap->eq, bmap->n_eq, "=", out, indent);
1409         dump_constraints(bmap, bmap->ineq, bmap->n_ineq, ">=", out, indent);
1410
1411         for (i = 0; i < bmap->n_div; ++i) {
1412                 fprintf(out, "%*s", indent, "");
1413                 fprintf(out, "e%d = [(", i);
1414                 dump_affine(bmap, bmap->div[i]+1, out);
1415                 fprintf(out, ")/");
1416                 isl_int_print(out, bmap->div[i][0]);
1417                 fprintf(out, "]\n");
1418         }
1419 }
1420
1421 void isl_basic_set_dump(struct isl_basic_set *bset, FILE *out, int indent)
1422 {
1423         if (!bset) {
1424                 fprintf(out, "null basic set\n");
1425                 return;
1426         }
1427
1428         fprintf(out, "%*s", indent, "");
1429         fprintf(out, "nparam: %d, dim: %d, extra: %d\n",
1430                         bset->nparam, bset->dim, bset->extra);
1431         dump((struct isl_basic_map *)bset, out, indent);
1432 }
1433
1434 void isl_basic_map_dump(struct isl_basic_map *bmap, FILE *out, int indent)
1435 {
1436         if (!bmap) {
1437                 fprintf(out, "null basic map\n");
1438                 return;
1439         }
1440
1441         fprintf(out, "%*s", indent, "");
1442         fprintf(out, "ref: %d, nparam: %d, in: %d, out: %d, extra: %d, flags: %x\n",
1443                 bmap->ref,
1444                 bmap->nparam, bmap->n_in, bmap->n_out, bmap->extra, bmap->flags);
1445         dump(bmap, out, indent);
1446 }
1447
1448 int isl_inequality_negate(struct isl_basic_map *bmap, unsigned pos)
1449 {
1450         unsigned total = bmap->nparam + bmap->n_in + bmap->n_out + bmap->n_div;
1451         if (!bmap)
1452                 return -1;
1453         isl_assert(bmap->ctx, pos < bmap->n_ineq, return -1);
1454         isl_seq_neg(bmap->ineq[pos], bmap->ineq[pos], 1 + total);
1455         isl_int_sub_ui(bmap->ineq[pos][0], bmap->ineq[pos][0], 1);
1456         return 0;
1457 }
1458
1459 struct isl_set *isl_set_alloc(struct isl_ctx *ctx,
1460                 unsigned nparam, unsigned dim, int n, unsigned flags)
1461 {
1462         struct isl_set *set;
1463
1464         isl_assert(ctx, n >= 0, return NULL);
1465         set = isl_alloc(ctx, struct isl_set,
1466                         sizeof(struct isl_set) +
1467                         n * sizeof(struct isl_basic_set *));
1468         if (!set)
1469                 return NULL;
1470
1471         set->ctx = ctx;
1472         isl_ctx_ref(ctx);
1473         set->ref = 1;
1474         set->size = n;
1475         set->n = 0;
1476         set->nparam = nparam;
1477         set->zero = 0;
1478         set->dim = dim;
1479         set->flags = flags;
1480         return set;
1481 }
1482
1483 struct isl_set *isl_set_dup(struct isl_set *set)
1484 {
1485         int i;
1486         struct isl_set *dup;
1487
1488         if (!set)
1489                 return NULL;
1490
1491         dup = isl_set_alloc(set->ctx, set->nparam, set->dim, set->n, set->flags);
1492         if (!dup)
1493                 return NULL;
1494         for (i = 0; i < set->n; ++i)
1495                 dup = isl_set_add(dup,
1496                                   isl_basic_set_dup(set->p[i]));
1497         return dup;
1498 }
1499
1500 struct isl_set *isl_set_from_basic_set(struct isl_basic_set *bset)
1501 {
1502         struct isl_set *set;
1503
1504         if (!bset)
1505                 return NULL;
1506
1507         set = isl_set_alloc(bset->ctx, bset->nparam, bset->dim, 1, ISL_MAP_DISJOINT);
1508         if (!set) {
1509                 isl_basic_set_free(bset);
1510                 return NULL;
1511         }
1512         return isl_set_add(set, bset);
1513 }
1514
1515 struct isl_map *isl_map_from_basic_map(struct isl_basic_map *bmap)
1516 {
1517         struct isl_map *map;
1518
1519         if (!bmap)
1520                 return NULL;
1521
1522         map = isl_map_alloc(bmap->ctx, bmap->nparam, bmap->n_in, bmap->n_out, 1,
1523                                 ISL_MAP_DISJOINT);
1524         if (!map) {
1525                 isl_basic_map_free(bmap);
1526                 return NULL;
1527         }
1528         return isl_map_add(map, bmap);
1529 }
1530
1531 struct isl_set *isl_set_add(struct isl_set *set, struct isl_basic_set *bset)
1532 {
1533         if (!bset || !set)
1534                 goto error;
1535         isl_assert(set->ctx, set->nparam == bset->nparam, goto error);
1536         isl_assert(set->ctx, set->dim == bset->dim, goto error);
1537         isl_assert(set->ctx, set->n < set->size, goto error);
1538         set->p[set->n] = bset;
1539         set->n++;
1540         return set;
1541 error:
1542         if (set)
1543                 isl_set_free(set);
1544         if (bset)
1545                 isl_basic_set_free(bset);
1546         return NULL;
1547 }
1548
1549 void isl_set_free(struct isl_set *set)
1550 {
1551         int i;
1552
1553         if (!set)
1554                 return;
1555
1556         if (--set->ref > 0)
1557                 return;
1558
1559         isl_ctx_deref(set->ctx);
1560         for (i = 0; i < set->n; ++i)
1561                 isl_basic_set_free(set->p[i]);
1562         free(set);
1563 }
1564
1565 void isl_set_dump(struct isl_set *set, FILE *out, int indent)
1566 {
1567         int i;
1568
1569         if (!set) {
1570                 fprintf(out, "null set\n");
1571                 return;
1572         }
1573
1574         fprintf(out, "%*s", indent, "");
1575         fprintf(out, "ref: %d, n: %d, nparam: %d, dim: %d, flags: %x\n",
1576                         set->ref, set->n, set->nparam, set->dim, set->flags);
1577         for (i = 0; i < set->n; ++i) {
1578                 fprintf(out, "%*s", indent, "");
1579                 fprintf(out, "basic set %d:\n", i);
1580                 isl_basic_set_dump(set->p[i], out, indent+4);
1581         }
1582 }
1583
1584 void isl_map_dump(struct isl_map *map, FILE *out, int indent)
1585 {
1586         int i;
1587
1588         if (!map) {
1589                 fprintf(out, "null map\n");
1590                 return;
1591         }
1592
1593         fprintf(out, "%*s", indent, "");
1594         fprintf(out, "ref: %d, n: %d, nparam: %d, in: %d, out: %d, flags: %x\n",
1595                         map->ref, map->n, map->nparam, map->n_in, map->n_out,
1596                         map->flags);
1597         for (i = 0; i < map->n; ++i) {
1598                 fprintf(out, "%*s", indent, "");
1599                 fprintf(out, "basic map %d:\n", i);
1600                 isl_basic_map_dump(map->p[i], out, indent+4);
1601         }
1602 }
1603
1604 struct isl_basic_map *isl_basic_map_intersect_domain(
1605                 struct isl_basic_map *bmap, struct isl_basic_set *bset)
1606 {
1607         struct isl_basic_map *bmap_domain;
1608
1609         if (!bmap || !bset)
1610                 goto error;
1611
1612         isl_assert(bset->ctx, bset->dim == bmap->n_in, 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_domain = isl_basic_map_from_basic_set(bset,
1621                                                 bset->dim, 0);
1622         bmap = add_constraints(bmap, bmap_domain, 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_range(
1633                 struct isl_basic_map *bmap, struct isl_basic_set *bset)
1634 {
1635         struct isl_basic_map *bmap_range;
1636
1637         if (!bmap || !bset)
1638                 goto error;
1639
1640         isl_assert(bset->ctx, bset->dim == bmap->n_out, goto error);
1641         isl_assert(bset->ctx, bset->nparam == bmap->nparam, goto error);
1642
1643         bmap = isl_basic_map_extend(bmap,
1644                         bset->nparam, bmap->n_in, bmap->n_out,
1645                         bset->n_div, bset->n_eq, bset->n_ineq);
1646         if (!bmap)
1647                 goto error;
1648         bmap_range = isl_basic_map_from_basic_set(bset,
1649                                                 0, bset->dim);
1650         bmap = add_constraints(bmap, bmap_range, 0, 0);
1651
1652         bmap = isl_basic_map_simplify(bmap);
1653         return isl_basic_map_finalize(bmap);
1654 error:
1655         isl_basic_map_free(bmap);
1656         isl_basic_set_free(bset);
1657         return NULL;
1658 }
1659
1660 struct isl_basic_map *isl_basic_map_intersect(
1661                 struct isl_basic_map *bmap1, struct isl_basic_map *bmap2)
1662 {
1663         if (!bmap1 || !bmap2)
1664                 goto error;
1665
1666         isl_assert(bmap1->ctx, bmap1->nparam == bmap2->nparam, goto error);
1667         isl_assert(bmap1->ctx, bmap1->n_in == bmap2->n_in, goto error);
1668         isl_assert(bmap1->ctx, bmap1->n_out == bmap2->n_out, goto error);
1669
1670         bmap1 = isl_basic_map_extend(bmap1,
1671                         bmap1->nparam, bmap1->n_in, bmap1->n_out,
1672                         bmap2->n_div, bmap2->n_eq, bmap2->n_ineq);
1673         if (!bmap1)
1674                 goto error;
1675         bmap1 = add_constraints(bmap1, bmap2, 0, 0);
1676
1677         bmap1 = isl_basic_map_simplify(bmap1);
1678         return isl_basic_map_finalize(bmap1);
1679 error:
1680         isl_basic_map_free(bmap1);
1681         isl_basic_map_free(bmap2);
1682         return NULL;
1683 }
1684
1685 struct isl_basic_set *isl_basic_set_intersect(
1686                 struct isl_basic_set *bset1, struct isl_basic_set *bset2)
1687 {
1688         return (struct isl_basic_set *)
1689                 isl_basic_map_intersect(
1690                         (struct isl_basic_map *)bset1,
1691                         (struct isl_basic_map *)bset2);
1692 }
1693
1694 struct isl_map *isl_map_intersect(struct isl_map *map1, struct isl_map *map2)
1695 {
1696         unsigned flags = 0;
1697         struct isl_map *result;
1698         int i, j;
1699
1700         if (!map1 || !map2)
1701                 goto error;
1702
1703         if (F_ISSET(map1, ISL_MAP_DISJOINT) &&
1704             F_ISSET(map2, ISL_MAP_DISJOINT))
1705                 FL_SET(flags, ISL_MAP_DISJOINT);
1706
1707         result = isl_map_alloc(map1->ctx, map1->nparam, map1->n_in, map1->n_out,
1708                                 map1->n * map2->n, flags);
1709         if (!result)
1710                 goto error;
1711         for (i = 0; i < map1->n; ++i)
1712                 for (j = 0; j < map2->n; ++j) {
1713                         struct isl_basic_map *part;
1714                         part = isl_basic_map_intersect(
1715                                     isl_basic_map_copy(map1->p[i]),
1716                                     isl_basic_map_copy(map2->p[j]));
1717                         if (isl_basic_map_is_empty(part))
1718                                 isl_basic_map_free(part);
1719                         else
1720                                 result = isl_map_add(result, part);
1721                         if (!result)
1722                                 goto error;
1723                 }
1724         isl_map_free(map1);
1725         isl_map_free(map2);
1726         return result;
1727 error:
1728         isl_map_free(map1);
1729         isl_map_free(map2);
1730         return NULL;
1731 }
1732
1733 struct isl_set *isl_set_intersect(struct isl_set *set1, struct isl_set *set2)
1734 {
1735         return (struct isl_set *)
1736                 isl_map_intersect((struct isl_map *)set1,
1737                                   (struct isl_map *)set2);
1738 }
1739
1740 struct isl_basic_map *isl_basic_map_reverse(struct isl_basic_map *bmap)
1741 {
1742         struct isl_basic_set *bset;
1743         unsigned in;
1744
1745         if (!bmap)
1746                 return NULL;
1747         bmap = isl_basic_map_cow(bmap);
1748         if (!bmap)
1749                 return NULL;
1750         in = bmap->n_in;
1751         bset = isl_basic_set_from_basic_map(bmap);
1752         bset = isl_basic_set_swap_vars(bset, in);
1753         return isl_basic_map_from_basic_set(bset, bset->dim-in, in);
1754 }
1755
1756 /* Turn final n dimensions into existentially quantified variables.
1757  */
1758 struct isl_basic_set *isl_basic_set_project_out(
1759                 struct isl_basic_set *bset, unsigned n, unsigned flags)
1760 {
1761         int i;
1762         size_t row_size;
1763         isl_int **new_div;
1764         isl_int *old;
1765
1766         if (!bset)
1767                 return NULL;
1768
1769         isl_assert(bset->ctx, n <= bset->dim, goto error);
1770
1771         if (n == 0)
1772                 return bset;
1773
1774         bset = isl_basic_set_cow(bset);
1775
1776         row_size = 1 + bset->nparam + bset->dim + bset->extra;
1777         old = bset->block2.data;
1778         bset->block2 = isl_blk_extend(bset->ctx, bset->block2,
1779                                         (bset->extra + n) * (1 + row_size));
1780         if (!bset->block2.data)
1781                 goto error;
1782         new_div = isl_alloc_array(ctx, isl_int *, bset->extra + n);
1783         if (!new_div)
1784                 goto error;
1785         for (i = 0; i < n; ++i) {
1786                 new_div[i] = bset->block2.data +
1787                                 (bset->extra + i) * (1 + row_size);
1788                 isl_seq_clr(new_div[i], 1 + row_size);
1789         }
1790         for (i = 0; i < bset->extra; ++i)
1791                 new_div[n + i] = bset->block2.data + (bset->div[i] - old);
1792         free(bset->div);
1793         bset->div = new_div;
1794         bset->n_div += n;
1795         bset->extra += n;
1796         bset->dim -= n;
1797         bset = isl_basic_set_simplify(bset);
1798         return isl_basic_set_finalize(bset);
1799 error:
1800         isl_basic_set_free(bset);
1801         return NULL;
1802 }
1803
1804 struct isl_basic_map *isl_basic_map_apply_range(
1805                 struct isl_basic_map *bmap1, struct isl_basic_map *bmap2)
1806 {
1807         struct isl_basic_set *bset;
1808         unsigned n_in, n_out;
1809
1810         if (!bmap1 || !bmap2)
1811                 goto error;
1812
1813         isl_assert(bmap->ctx, bmap1->n_out == bmap2->n_in, goto error);
1814         isl_assert(bmap->ctx, bmap1->nparam == bmap2->nparam, goto error);
1815
1816         n_in = bmap1->n_in;
1817         n_out = bmap2->n_out;
1818
1819         bmap2 = isl_basic_map_reverse(bmap2);
1820         if (!bmap2)
1821                 goto error;
1822         bmap1 = isl_basic_map_extend(bmap1, bmap1->nparam,
1823                         bmap1->n_in + bmap2->n_in, bmap1->n_out,
1824                         bmap2->extra, bmap2->n_eq, bmap2->n_ineq);
1825         if (!bmap1)
1826                 goto error;
1827         bmap1 = add_constraints(bmap1, bmap2, bmap1->n_in - bmap2->n_in, 0);
1828         bmap1 = isl_basic_map_simplify(bmap1);
1829         bset = isl_basic_set_from_basic_map(bmap1);
1830         bset = isl_basic_set_project_out(bset,
1831                                                 bset->dim - (n_in + n_out), 0);
1832         return isl_basic_map_from_basic_set(bset, n_in, n_out);
1833 error:
1834         isl_basic_map_free(bmap1);
1835         isl_basic_map_free(bmap2);
1836         return NULL;
1837 }
1838
1839 struct isl_basic_set *isl_basic_set_apply(
1840                 struct isl_basic_set *bset, struct isl_basic_map *bmap)
1841 {
1842         if (!bset || !bmap)
1843                 goto error;
1844
1845         isl_assert(bset->ctx, bset->dim == bmap->n_in, goto error);
1846
1847         return (struct isl_basic_set *)
1848                 isl_basic_map_apply_range((struct isl_basic_map *)bset, bmap);
1849 error:
1850         isl_basic_set_free(bset);
1851         isl_basic_map_free(bmap);
1852         return NULL;
1853 }
1854
1855 struct isl_basic_map *isl_basic_map_apply_domain(
1856                 struct isl_basic_map *bmap1, struct isl_basic_map *bmap2)
1857 {
1858         if (!bmap1 || !bmap2)
1859                 goto error;
1860
1861         isl_assert(ctx, bmap1->n_in == bmap2->n_in, goto error);
1862         isl_assert(ctx, bmap1->nparam == bmap2->nparam, goto error);
1863
1864         bmap1 = isl_basic_map_reverse(bmap1);
1865         bmap1 = isl_basic_map_apply_range(bmap1, bmap2);
1866         return isl_basic_map_reverse(bmap1);
1867 error:
1868         isl_basic_map_free(bmap1);
1869         isl_basic_map_free(bmap2);
1870         return NULL;
1871 }
1872
1873 static struct isl_basic_map *var_equal(struct isl_ctx *ctx,
1874                 struct isl_basic_map *bmap, unsigned pos)
1875 {
1876         int i;
1877         i = isl_basic_map_alloc_equality(bmap);
1878         if (i < 0)
1879                 goto error;
1880         isl_seq_clr(bmap->eq[i],
1881                     1 + bmap->nparam + bmap->n_in + bmap->n_out + bmap->extra);
1882         isl_int_set_si(bmap->eq[i][1+bmap->nparam+pos], -1);
1883         isl_int_set_si(bmap->eq[i][1+bmap->nparam+bmap->n_in+pos], 1);
1884         return isl_basic_map_finalize(bmap);
1885 error:
1886         isl_basic_map_free(bmap);
1887         return NULL;
1888 }
1889
1890 static struct isl_basic_map *var_more(struct isl_ctx *ctx,
1891                 struct isl_basic_map *bmap, unsigned pos)
1892 {
1893         int i;
1894         i = isl_basic_map_alloc_inequality(bmap);
1895         if (i < 0)
1896                 goto error;
1897         isl_seq_clr(bmap->ineq[i],
1898                     1 + bmap->nparam + bmap->n_in + bmap->n_out + bmap->extra);
1899         isl_int_set_si(bmap->ineq[i][0], -1);
1900         isl_int_set_si(bmap->ineq[i][1+bmap->nparam+pos], -1);
1901         isl_int_set_si(bmap->ineq[i][1+bmap->nparam+bmap->n_in+pos], 1);
1902         return isl_basic_map_finalize(bmap);
1903 error:
1904         isl_basic_map_free(bmap);
1905         return NULL;
1906 }
1907
1908 static struct isl_basic_map *var_less(struct isl_ctx *ctx,
1909                 struct isl_basic_map *bmap, unsigned pos)
1910 {
1911         int i;
1912         i = isl_basic_map_alloc_inequality(bmap);
1913         if (i < 0)
1914                 goto error;
1915         isl_seq_clr(bmap->ineq[i],
1916                     1 + bmap->nparam + bmap->n_in + bmap->n_out + bmap->extra);
1917         isl_int_set_si(bmap->ineq[i][0], -1);
1918         isl_int_set_si(bmap->ineq[i][1+bmap->nparam+pos], 1);
1919         isl_int_set_si(bmap->ineq[i][1+bmap->nparam+bmap->n_in+pos], -1);
1920         return isl_basic_map_finalize(bmap);
1921 error:
1922         isl_basic_map_free(bmap);
1923         return NULL;
1924 }
1925
1926 struct isl_basic_map *isl_basic_map_equal(struct isl_ctx *ctx,
1927                 unsigned nparam, unsigned in, unsigned out, unsigned n_equal)
1928 {
1929         int i;
1930         struct isl_basic_map *bmap;
1931         bmap = isl_basic_map_alloc(ctx, nparam, in, out, 0, n_equal, 0);
1932         if (!bmap)
1933                 return NULL;
1934         for (i = 0; i < n_equal && bmap; ++i)
1935                 bmap = var_equal(ctx, bmap, i);
1936         return isl_basic_map_finalize(bmap);
1937 }
1938
1939 struct isl_basic_map *isl_basic_map_less_at(struct isl_ctx *ctx,
1940                 unsigned nparam, unsigned in, unsigned out, unsigned pos)
1941 {
1942         int i;
1943         struct isl_basic_map *bmap;
1944         bmap = isl_basic_map_alloc(ctx, nparam, in, out, 0, pos, 1);
1945         if (!bmap)
1946                 return NULL;
1947         for (i = 0; i < pos && bmap; ++i)
1948                 bmap = var_equal(ctx, bmap, i);
1949         if (bmap)
1950                 bmap = var_less(ctx, bmap, pos);
1951         return isl_basic_map_finalize(bmap);
1952 }
1953
1954 struct isl_basic_map *isl_basic_map_more_at(struct isl_ctx *ctx,
1955                 unsigned nparam, unsigned in, unsigned out, unsigned pos)
1956 {
1957         int i;
1958         struct isl_basic_map *bmap;
1959         bmap = isl_basic_map_alloc(ctx, nparam, in, out, 0, pos, 1);
1960         if (!bmap)
1961                 return NULL;
1962         for (i = 0; i < pos && bmap; ++i)
1963                 bmap = var_equal(ctx, bmap, i);
1964         if (bmap)
1965                 bmap = var_more(ctx, bmap, pos);
1966         return isl_basic_map_finalize(bmap);
1967 }
1968
1969 struct isl_basic_map *isl_basic_map_from_basic_set(
1970                 struct isl_basic_set *bset, unsigned n_in, unsigned n_out)
1971 {
1972         struct isl_basic_map *bmap;
1973
1974         bset = isl_basic_set_cow(bset);
1975         if (!bset)
1976                 return NULL;
1977
1978         isl_assert(ctx, bset->dim == n_in + n_out, goto error);
1979         bmap = (struct isl_basic_map *) bset;
1980         bmap->n_in = n_in;
1981         bmap->n_out = n_out;
1982         return isl_basic_map_finalize(bmap);
1983 error:
1984         isl_basic_set_free(bset);
1985         return NULL;
1986 }
1987
1988 struct isl_basic_set *isl_basic_set_from_basic_map(struct isl_basic_map *bmap)
1989 {
1990         if (!bmap)
1991                 goto error;
1992         if (bmap->n_in == 0)
1993                 return (struct isl_basic_set *)bmap;
1994         bmap = isl_basic_map_cow(bmap);
1995         if (!bmap)
1996                 goto error;
1997         bmap->n_out += bmap->n_in;
1998         bmap->n_in = 0;
1999         bmap = isl_basic_map_finalize(bmap);
2000         return (struct isl_basic_set *)bmap;
2001 error:
2002         return NULL;
2003 }
2004
2005 /* For a div d = floor(f/m), add the constraints
2006  *
2007  *              f - m d >= 0
2008  *              -(f-(n-1)) + m d >= 0
2009  *
2010  * Note that the second constraint is the negation of
2011  *
2012  *              f - m d >= n
2013  */
2014 static int add_div_constraints(struct isl_basic_map *bmap, unsigned div)
2015 {
2016         int i, j;
2017         unsigned div_pos = 1 + bmap->nparam + bmap->n_in + bmap->n_out + div;
2018         unsigned total = bmap->nparam + bmap->n_in + bmap->n_out + bmap->extra;
2019
2020         i = isl_basic_map_alloc_inequality(bmap);
2021         if (i < 0)
2022                 return -1;
2023         isl_seq_cpy(bmap->ineq[i], bmap->div[div]+1, 1+total);
2024         isl_int_neg(bmap->ineq[i][div_pos], bmap->div[div][0]);
2025
2026         j = isl_basic_map_alloc_inequality(bmap);
2027         if (j < 0)
2028                 return -1;
2029         isl_seq_neg(bmap->ineq[j], bmap->ineq[i], 1 + total);
2030         isl_int_add(bmap->ineq[j][0], bmap->ineq[j][0], bmap->ineq[j][div_pos]);
2031         isl_int_sub_ui(bmap->ineq[j][0], bmap->ineq[j][0], 1);
2032         return j;
2033 }
2034
2035 struct isl_basic_set *isl_basic_map_underlying_set(
2036                 struct isl_basic_map *bmap)
2037 {
2038         if (!bmap)
2039                 goto error;
2040         if (bmap->nparam == 0 && bmap->n_in == 0 && bmap->n_div == 0)
2041                 return (struct isl_basic_set *)bmap;
2042         bmap = isl_basic_map_cow(bmap);
2043         if (!bmap)
2044                 goto error;
2045         bmap->n_out += bmap->nparam + bmap->n_in + bmap->n_div;
2046         bmap->nparam = 0;
2047         bmap->n_in = 0;
2048         bmap->extra -= bmap->n_div;
2049         bmap->n_div = 0;
2050         bmap = isl_basic_map_finalize(bmap);
2051         return (struct isl_basic_set *)bmap;
2052 error:
2053         return NULL;
2054 }
2055
2056 struct isl_basic_map *isl_basic_map_overlying_set(
2057         struct isl_basic_set *bset, struct isl_basic_map *like)
2058 {
2059         struct isl_basic_map *bmap;
2060         struct isl_ctx *ctx;
2061         unsigned total;
2062         int i, k;
2063
2064         if (!bset || !like)
2065                 goto error;
2066         ctx = bset->ctx;
2067         isl_assert(ctx, bset->dim ==
2068                         like->nparam + like->n_in + like->n_out + like->n_div,
2069                         goto error);
2070         if (like->nparam == 0 && like->n_in == 0 && like->n_div == 0) {
2071                 isl_basic_map_free(like);
2072                 return (struct isl_basic_map *)bset;
2073         }
2074         bset = isl_basic_set_cow(bset);
2075         if (!bset)
2076                 goto error;
2077         total = bset->dim + bset->extra;
2078         bmap = (struct isl_basic_map *)bset;
2079         bmap->nparam = like->nparam;
2080         bmap->n_in = like->n_in;
2081         bmap->n_out = like->n_out;
2082         bmap->extra += like->n_div;
2083         if (bmap->extra) {
2084                 unsigned ltotal;
2085                 ltotal = total - bmap->extra + like->extra;
2086                 if (ltotal > total)
2087                         ltotal = total;
2088                 bmap->block2 = isl_blk_extend(ctx, bmap->block2,
2089                                         bmap->extra * (1 + 1 + total));
2090                 if (isl_blk_is_error(bmap->block2))
2091                         goto error;
2092                 bmap->div = isl_realloc_array(ctx, bmap->div, isl_int *,
2093                                                 bmap->extra);
2094                 if (!bmap->div)
2095                         goto error;
2096                 bmap = isl_basic_map_extend(bmap, bmap->nparam,
2097                         bmap->n_in, bmap->n_out, 0, 0, 2 * like->n_div);
2098                 for (i = 0; i < like->n_div; ++i) {
2099                         k = isl_basic_map_alloc_div(bmap);
2100                         if (k < 0)
2101                                 goto error;
2102                         isl_seq_cpy(bmap->div[k], like->div[i], 1 + 1 + ltotal);
2103                         isl_seq_clr(bmap->div[k]+1+1+ltotal, total - ltotal);
2104                         if (add_div_constraints(bmap, k) < 0)
2105                                 goto error;
2106                 }
2107         }
2108         isl_basic_map_free(like);
2109         bmap = isl_basic_map_finalize(bmap);
2110         return bmap;
2111 error:
2112         isl_basic_map_free(like);
2113         isl_basic_set_free(bset);
2114         return NULL;
2115 }
2116
2117 struct isl_basic_set *isl_basic_set_from_underlying_set(
2118         struct isl_basic_set *bset, struct isl_basic_set *like)
2119 {
2120         return (struct isl_basic_set *)
2121                 isl_basic_map_overlying_set(bset, (struct isl_basic_map *)like);
2122 }
2123
2124 struct isl_set *isl_set_from_underlying_set(
2125         struct isl_set *set, struct isl_basic_set *like)
2126 {
2127         int i;
2128
2129         if (!set || !like)
2130                 goto error;
2131         isl_assert(set->ctx, set->dim == like->nparam + like->dim + like->n_div,
2132                     goto error);
2133         if (like->nparam == 0 && like->n_div == 0) {
2134                 isl_basic_set_free(like);
2135                 return set;
2136         }
2137         set = isl_set_cow(set);
2138         if (!set)
2139                 goto error;
2140         for (i = 0; i < set->n; ++i) {
2141                 set->p[i] = isl_basic_set_from_underlying_set(set->p[i],
2142                                                       isl_basic_set_copy(like));
2143                 if (!set->p[i])
2144                         goto error;
2145         }
2146         set->nparam = like->nparam;
2147         set->dim = like->dim;
2148         isl_basic_set_free(like);
2149         return set;
2150 error:
2151         isl_basic_set_free(like);
2152         isl_set_free(set);
2153         return NULL;
2154 }
2155
2156 struct isl_set *isl_map_underlying_set(struct isl_map *map)
2157 {
2158         int i;
2159
2160         map = isl_map_align_divs(map);
2161         map = isl_map_cow(map);
2162         if (!map)
2163                 return NULL;
2164
2165         for (i = 0; i < map->n; ++i) {
2166                 map->p[i] = (struct isl_basic_map *)
2167                                 isl_basic_map_underlying_set(map->p[i]);
2168                 if (!map->p[i])
2169                         goto error;
2170         }
2171         if (map->n == 0)
2172                 map->n_out += map->nparam + map->n_in;
2173         else
2174                 map->n_out = map->p[0]->n_out;
2175         map->nparam = 0;
2176         map->n_in = 0;
2177         return (struct isl_set *)map;
2178 error:
2179         isl_map_free(map);
2180         return NULL;
2181 }
2182
2183 struct isl_set *isl_set_to_underlying_set(struct isl_set *set)
2184 {
2185         return (struct isl_set *)isl_map_underlying_set((struct isl_map *)set);
2186 }
2187
2188 struct isl_basic_set *isl_basic_map_domain(struct isl_basic_map *bmap)
2189 {
2190         struct isl_basic_set *domain;
2191         unsigned n_out;
2192         if (!bmap)
2193                 return NULL;
2194         n_out = bmap->n_out;
2195         domain = isl_basic_set_from_basic_map(bmap);
2196         return isl_basic_set_project_out(domain, n_out, 0);
2197 }
2198
2199 struct isl_basic_set *isl_basic_map_range(struct isl_basic_map *bmap)
2200 {
2201         return isl_basic_map_domain(isl_basic_map_reverse(bmap));
2202 }
2203
2204 struct isl_set *isl_map_range(struct isl_map *map)
2205 {
2206         int i;
2207         struct isl_set *set;
2208
2209         if (!map)
2210                 goto error;
2211         map = isl_map_cow(map);
2212         if (!map)
2213                 goto error;
2214
2215         set = (struct isl_set *) map;
2216         set->zero = 0;
2217         for (i = 0; i < map->n; ++i) {
2218                 set->p[i] = isl_basic_map_range(map->p[i]);
2219                 if (!set->p[i])
2220                         goto error;
2221         }
2222         F_CLR(set, ISL_MAP_DISJOINT);
2223         return set;
2224 error:
2225         isl_map_free(map);
2226         return NULL;
2227 }
2228
2229 struct isl_map *isl_map_from_set(struct isl_set *set,
2230                 unsigned n_in, unsigned n_out)
2231 {
2232         int i;
2233         struct isl_map *map = NULL;
2234
2235         if (!set)
2236                 return NULL;
2237         isl_assert(set->ctx, set->dim == n_in + n_out, goto error);
2238         set = isl_set_cow(set);
2239         if (!set)
2240                 return NULL;
2241         map = (struct isl_map *)set;
2242         for (i = 0; i < set->n; ++i) {
2243                 map->p[i] = isl_basic_map_from_basic_set(
2244                                 set->p[i], n_in, n_out);
2245                 if (!map->p[i])
2246                         goto error;
2247         }
2248         map->n_in = n_in;
2249         map->n_out = n_out;
2250         return map;
2251 error:
2252         isl_set_free(set);
2253         return NULL;
2254 }
2255
2256 struct isl_set *isl_set_from_map(struct isl_map *map)
2257 {
2258         int i;
2259         struct isl_set *set = NULL;
2260
2261         if (!map)
2262                 return NULL;
2263         map = isl_map_cow(map);
2264         if (!map)
2265                 return NULL;
2266         map->n_out += map->n_in;
2267         map->n_in = 0;
2268         set = (struct isl_set *)map;
2269         for (i = 0; i < map->n; ++i) {
2270                 set->p[i] = isl_basic_set_from_basic_map(map->p[i]);
2271                 if (!set->p[i])
2272                         goto error;
2273         }
2274         return set;
2275 error:
2276         isl_map_free(map);
2277         return NULL;
2278 }
2279
2280 struct isl_map *isl_map_alloc(struct isl_ctx *ctx,
2281                 unsigned nparam, unsigned in, unsigned out, int n,
2282                 unsigned flags)
2283 {
2284         struct isl_map *map;
2285
2286         map = isl_alloc(ctx, struct isl_map,
2287                         sizeof(struct isl_map) +
2288                         n * sizeof(struct isl_basic_map *));
2289         if (!map)
2290                 return NULL;
2291
2292         map->ctx = ctx;
2293         isl_ctx_ref(ctx);
2294         map->ref = 1;
2295         map->size = n;
2296         map->n = 0;
2297         map->nparam = nparam;
2298         map->n_in = in;
2299         map->n_out = out;
2300         map->flags = flags;
2301         return map;
2302 }
2303
2304 struct isl_basic_map *isl_basic_map_empty(struct isl_ctx *ctx,
2305                 unsigned nparam, unsigned in, unsigned out)
2306 {
2307         struct isl_basic_map *bmap;
2308         bmap = isl_basic_map_alloc(ctx, nparam, in, out, 0, 1, 0);
2309         bmap = isl_basic_map_set_to_empty(bmap);
2310         return bmap;
2311 }
2312
2313 struct isl_basic_set *isl_basic_set_empty(struct isl_ctx *ctx,
2314                 unsigned nparam, unsigned dim)
2315 {
2316         struct isl_basic_set *bset;
2317         bset = isl_basic_set_alloc(ctx, nparam, dim, 0, 1, 0);
2318         bset = isl_basic_set_set_to_empty(bset);
2319         return bset;
2320 }
2321
2322 struct isl_basic_map *isl_basic_map_universe(struct isl_ctx *ctx,
2323                 unsigned nparam, unsigned in, unsigned out)
2324 {
2325         struct isl_basic_map *bmap;
2326         bmap = isl_basic_map_alloc(ctx, nparam, in, out, 0, 0, 0);
2327         return bmap;
2328 }
2329
2330 struct isl_basic_set *isl_basic_set_universe(struct isl_ctx *ctx,
2331                 unsigned nparam, unsigned dim)
2332 {
2333         struct isl_basic_set *bset;
2334         bset = isl_basic_set_alloc(ctx, nparam, dim, 0, 0, 0);
2335         return bset;
2336 }
2337
2338 struct isl_map *isl_map_empty(struct isl_ctx *ctx,
2339                 unsigned nparam, unsigned in, unsigned out)
2340 {
2341         return isl_map_alloc(ctx, nparam, in, out, 0, ISL_MAP_DISJOINT);
2342 }
2343
2344 struct isl_set *isl_set_empty(struct isl_ctx *ctx,
2345                 unsigned nparam, unsigned dim)
2346 {
2347         return isl_set_alloc(ctx, nparam, dim, 0, ISL_MAP_DISJOINT);
2348 }
2349
2350 struct isl_map *isl_map_dup(struct isl_map *map)
2351 {
2352         int i;
2353         struct isl_map *dup;
2354
2355         if (!map)
2356                 return NULL;
2357         dup = isl_map_alloc(map->ctx, map->nparam, map->n_in, map->n_out, map->n,
2358                                 map->flags);
2359         for (i = 0; i < map->n; ++i)
2360                 dup = isl_map_add(dup,
2361                                   isl_basic_map_dup(map->p[i]));
2362         return dup;
2363 }
2364
2365 struct isl_map *isl_map_add(struct isl_map *map, struct isl_basic_map *bmap)
2366 {
2367         if (!bmap || !map)
2368                 goto error;
2369         isl_assert(map->ctx, map->nparam == bmap->nparam, goto error);
2370         isl_assert(map->ctx, map->n_in == bmap->n_in, goto error);
2371         isl_assert(map->ctx, map->n_out == bmap->n_out, goto error);
2372         isl_assert(map->ctx, map->n < map->size, goto error);
2373         map->p[map->n] = bmap;
2374         map->n++;
2375         return map;
2376 error:
2377         if (map)
2378                 isl_map_free(map);
2379         if (bmap)
2380                 isl_basic_map_free(bmap);
2381         return NULL;
2382 }
2383
2384 void isl_map_free(struct isl_map *map)
2385 {
2386         int i;
2387
2388         if (!map)
2389                 return;
2390
2391         if (--map->ref > 0)
2392                 return;
2393
2394         isl_ctx_deref(map->ctx);
2395         for (i = 0; i < map->n; ++i)
2396                 isl_basic_map_free(map->p[i]);
2397         free(map);
2398 }
2399
2400 struct isl_map *isl_map_extend(struct isl_map *base,
2401                 unsigned nparam, unsigned n_in, unsigned n_out)
2402 {
2403         int i;
2404
2405         base = isl_map_cow(base);
2406         if (!base)
2407                 return NULL;
2408
2409         isl_assert(base->ctx, base->nparam <= nparam, goto error);
2410         isl_assert(base->ctx, base->n_in <= n_in, goto error);
2411         isl_assert(base->ctx, base->n_out <= n_out, goto error);
2412         base->nparam = nparam;
2413         base->n_in = n_in;
2414         base->n_out = n_out;
2415         for (i = 0; i < base->n; ++i) {
2416                 base->p[i] = isl_basic_map_extend(base->p[i],
2417                                 nparam, n_in, n_out, 0, 0, 0);
2418                 if (!base->p[i])
2419                         goto error;
2420         }
2421         return base;
2422 error:
2423         isl_map_free(base);
2424         return NULL;
2425 }
2426
2427 struct isl_set *isl_set_extend(struct isl_set *base,
2428                 unsigned nparam, unsigned dim)
2429 {
2430         return (struct isl_set *)isl_map_extend((struct isl_map *)base,
2431                                                         nparam, 0, dim);
2432 }
2433
2434 static struct isl_basic_map *isl_basic_map_fix_var(struct isl_basic_map *bmap,
2435                 unsigned var, int value)
2436 {
2437         int j;
2438
2439         bmap = isl_basic_map_cow(bmap);
2440         bmap = isl_basic_map_extend(bmap,
2441                         bmap->nparam, bmap->n_in, bmap->n_out, 0, 1, 0);
2442         j = isl_basic_map_alloc_equality(bmap);
2443         if (j < 0)
2444                 goto error;
2445         isl_seq_clr(bmap->eq[j],
2446                     1 + bmap->nparam + bmap->n_in + bmap->n_out + bmap->extra);
2447         isl_int_set_si(bmap->eq[j][1 + var], -1);
2448         isl_int_set_si(bmap->eq[j][0], value);
2449         bmap = isl_basic_map_simplify(bmap);
2450         return isl_basic_map_finalize(bmap);
2451 error:
2452         isl_basic_map_free(bmap);
2453         return NULL;
2454 }
2455
2456 struct isl_basic_map *isl_basic_map_fix_input_si(struct isl_basic_map *bmap,
2457                 unsigned input, int value)
2458 {
2459         if (!bmap)
2460                 return NULL;
2461         isl_assert(bmap->ctx, input < bmap->n_in, goto error);
2462         return isl_basic_map_fix_var(bmap, bmap->nparam + input, value);
2463 error:
2464         isl_basic_map_free(bmap);
2465         return NULL;
2466 }
2467
2468 struct isl_basic_set *isl_basic_set_fix_dim_si(struct isl_basic_set *bset,
2469                 unsigned dim, int value)
2470 {
2471         if (!bset)
2472                 return NULL;
2473         isl_assert(bset->ctx, dim < bset->dim, goto error);
2474         return (struct isl_basic_set *)
2475                 isl_basic_map_fix_var((struct isl_basic_map *)bset,
2476                                                 bset->nparam + dim, value);
2477 error:
2478         isl_basic_set_free(bset);
2479         return NULL;
2480 }
2481
2482 struct isl_map *isl_map_fix_input_si(struct isl_map *map,
2483                 unsigned input, int value)
2484 {
2485         int i;
2486
2487         map = isl_map_cow(map);
2488         if (!map)
2489                 return NULL;
2490
2491         isl_assert(ctx, input < map->n_in, goto error);
2492         for (i = 0; i < map->n; ++i) {
2493                 map->p[i] = isl_basic_map_fix_input_si(map->p[i], input, value);
2494                 if (!map->p[i])
2495                         goto error;
2496         }
2497         return map;
2498 error:
2499         isl_map_free(map);
2500         return NULL;
2501 }
2502
2503 struct isl_set *isl_set_fix_dim_si(struct isl_set *set, unsigned dim, int value)
2504 {
2505         int i;
2506
2507         set = isl_set_cow(set);
2508         if (!set)
2509                 return NULL;
2510
2511         isl_assert(set->ctx, dim < set->dim, goto error);
2512         for (i = 0; i < set->n; ++i) {
2513                 set->p[i] = isl_basic_set_fix_dim_si(set->p[i], dim, value);
2514                 if (!set->p[i])
2515                         goto error;
2516         }
2517         return set;
2518 error:
2519         isl_set_free(set);
2520         return NULL;
2521 }
2522
2523 struct isl_map *isl_map_reverse(struct isl_map *map)
2524 {
2525         int i;
2526         unsigned t;
2527
2528         map = isl_map_cow(map);
2529         if (!map)
2530                 return NULL;
2531
2532         t = map->n_in;
2533         map->n_in = map->n_out;
2534         map->n_out = t;
2535         for (i = 0; i < map->n; ++i) {
2536                 map->p[i] = isl_basic_map_reverse(map->p[i]);
2537                 if (!map->p[i])
2538                         goto error;
2539         }
2540         return map;
2541 error:
2542         isl_map_free(map);
2543         return NULL;
2544 }
2545
2546 struct isl_map *isl_basic_map_lexmax(
2547                 struct isl_basic_map *bmap, struct isl_basic_set *dom,
2548                 struct isl_set **empty)
2549 {
2550         return isl_pip_basic_map_lexmax(bmap, dom, empty);
2551 }
2552
2553 struct isl_map *isl_basic_map_lexmin(
2554                 struct isl_basic_map *bmap, struct isl_basic_set *dom,
2555                 struct isl_set **empty)
2556 {
2557         return isl_pip_basic_map_lexmin(bmap, dom, empty);
2558 }
2559
2560 struct isl_set *isl_basic_set_lexmin(struct isl_basic_set *bset)
2561 {
2562         struct isl_basic_map *bmap = NULL;
2563         struct isl_basic_set *dom = NULL;
2564         struct isl_map *min;
2565
2566         if (!bset)
2567                 goto error;
2568         bmap = isl_basic_map_from_basic_set(bset, 0, bset->dim);
2569         if (!bmap)
2570                 goto error;
2571         dom = isl_basic_set_alloc(bmap->ctx, bmap->nparam, 0, 0, 0, 0);
2572         if (!dom)
2573                 goto error;
2574         min = isl_basic_map_lexmin(bmap, dom, NULL);
2575         return isl_map_range(min);
2576 error:
2577         isl_basic_map_free(bmap);
2578         return NULL;
2579 }
2580
2581 struct isl_map *isl_basic_map_compute_divs(struct isl_basic_map *bmap)
2582 {
2583         if (!bmap)
2584                 return NULL;
2585         if (bmap->n_div == 0)
2586                 return isl_map_from_basic_map(bmap);
2587         return isl_pip_basic_map_compute_divs(bmap);
2588 }
2589
2590 struct isl_map *isl_map_compute_divs(struct isl_map *map)
2591 {
2592         int i;
2593         struct isl_map *res;
2594
2595         if (!map)
2596                 return NULL;
2597         if (map->n == 0)
2598                 return map;
2599         res = isl_basic_map_compute_divs(isl_basic_map_copy(map->p[0]));
2600         for (i = 1 ; i < map->n; ++i) {
2601                 struct isl_map *r2;
2602                 r2 = isl_basic_map_compute_divs(isl_basic_map_copy(map->p[i]));
2603                 if (F_ISSET(map, ISL_MAP_DISJOINT))
2604                         res = isl_map_union_disjoint(res, r2);
2605                 else
2606                         res = isl_map_union(res, r2);
2607         }
2608         isl_map_free(map);
2609
2610         return res;
2611 }
2612
2613 struct isl_set *isl_basic_set_compute_divs(struct isl_basic_set *bset)
2614 {
2615         return (struct isl_set *)
2616                 isl_basic_map_compute_divs((struct isl_basic_map *)bset);
2617 }
2618
2619 struct isl_set *isl_set_compute_divs(struct isl_set *set)
2620 {
2621         return (struct isl_set *)
2622                 isl_map_compute_divs((struct isl_map *)set);
2623 }
2624
2625 struct isl_set *isl_map_domain(struct isl_map *map)
2626 {
2627         int i;
2628         struct isl_set *set;
2629
2630         if (!map)
2631                 goto error;
2632
2633         map = isl_map_cow(map);
2634         if (!map)
2635                 return NULL;
2636
2637         set = (struct isl_set *)map;
2638         set->dim = map->n_in;
2639         set->zero = 0;
2640         for (i = 0; i < map->n; ++i) {
2641                 set->p[i] = isl_basic_map_domain(map->p[i]);
2642                 if (!set->p[i])
2643                         goto error;
2644         }
2645         F_CLR(set, ISL_MAP_DISJOINT);
2646         return set;
2647 error:
2648         isl_map_free(map);
2649         return NULL;
2650 }
2651
2652 struct isl_map *isl_map_union_disjoint(
2653                         struct isl_map *map1, struct isl_map *map2)
2654 {
2655         int i;
2656         unsigned flags = 0;
2657         struct isl_map *map = NULL;
2658
2659         if (!map1 || !map2)
2660                 goto error;
2661
2662         if (map1->n == 0) {
2663                 isl_map_free(map1);
2664                 return map2;
2665         }
2666         if (map2->n == 0) {
2667                 isl_map_free(map2);
2668                 return map1;
2669         }
2670
2671         isl_assert(map1->ctx, map1->nparam == map2->nparam, goto error);
2672         isl_assert(map1->ctx, map1->n_in == map2->n_in, goto error);
2673         isl_assert(map1->ctx, map1->n_out == map2->n_out, goto error);
2674
2675         if (F_ISSET(map1, ISL_MAP_DISJOINT) &&
2676             F_ISSET(map2, ISL_MAP_DISJOINT))
2677                 FL_SET(flags, ISL_MAP_DISJOINT);
2678
2679         map = isl_map_alloc(map1->ctx, map1->nparam, map1->n_in, map1->n_out,
2680                                 map1->n + map2->n, flags);
2681         if (!map)
2682                 goto error;
2683         for (i = 0; i < map1->n; ++i) {
2684                 map = isl_map_add(map,
2685                                   isl_basic_map_copy(map1->p[i]));
2686                 if (!map)
2687                         goto error;
2688         }
2689         for (i = 0; i < map2->n; ++i) {
2690                 map = isl_map_add(map,
2691                                   isl_basic_map_copy(map2->p[i]));
2692                 if (!map)
2693                         goto error;
2694         }
2695         isl_map_free(map1);
2696         isl_map_free(map2);
2697         return map;
2698 error:
2699         isl_map_free(map);
2700         isl_map_free(map1);
2701         isl_map_free(map2);
2702         return NULL;
2703 }
2704
2705 struct isl_map *isl_map_union(struct isl_map *map1, struct isl_map *map2)
2706 {
2707         map1 = isl_map_union_disjoint(map1, map2);
2708         if (!map1)
2709                 return NULL;
2710         if (map1->n > 1)
2711                 F_CLR(map1, ISL_MAP_DISJOINT);
2712         return map1;
2713 }
2714
2715 struct isl_set *isl_set_union_disjoint(
2716                         struct isl_set *set1, struct isl_set *set2)
2717 {
2718         return (struct isl_set *)
2719                 isl_map_union_disjoint(
2720                         (struct isl_map *)set1, (struct isl_map *)set2);
2721 }
2722
2723 struct isl_set *isl_set_union(struct isl_set *set1, struct isl_set *set2)
2724 {
2725         return (struct isl_set *)
2726                 isl_map_union((struct isl_map *)set1, (struct isl_map *)set2);
2727 }
2728
2729 struct isl_map *isl_map_intersect_range(
2730                 struct isl_map *map, struct isl_set *set)
2731 {
2732         unsigned flags = 0;
2733         struct isl_map *result;
2734         int i, j;
2735
2736         if (!map || !set)
2737                 goto error;
2738
2739         if (F_ISSET(map, ISL_MAP_DISJOINT) &&
2740             F_ISSET(set, ISL_MAP_DISJOINT))
2741                 FL_SET(flags, ISL_MAP_DISJOINT);
2742
2743         result = isl_map_alloc(map->ctx, map->nparam, map->n_in, map->n_out,
2744                                 map->n * set->n, flags);
2745         if (!result)
2746                 goto error;
2747         for (i = 0; i < map->n; ++i)
2748                 for (j = 0; j < set->n; ++j) {
2749                         result = isl_map_add(result,
2750                             isl_basic_map_intersect_range(
2751                                 isl_basic_map_copy(map->p[i]),
2752                                 isl_basic_set_copy(set->p[j])));
2753                         if (!result)
2754                                 goto error;
2755                 }
2756         isl_map_free(map);
2757         isl_set_free(set);
2758         return result;
2759 error:
2760         isl_map_free(map);
2761         isl_set_free(set);
2762         return NULL;
2763 }
2764
2765 struct isl_map *isl_map_intersect_domain(
2766                 struct isl_map *map, struct isl_set *set)
2767 {
2768         return isl_map_reverse(
2769                 isl_map_intersect_range(isl_map_reverse(map), set));
2770 }
2771
2772 struct isl_map *isl_map_apply_domain(
2773                 struct isl_map *map1, struct isl_map *map2)
2774 {
2775         if (!map1 || !map2)
2776                 goto error;
2777         map1 = isl_map_reverse(map1);
2778         map1 = isl_map_apply_range(map1, map2);
2779         return isl_map_reverse(map1);
2780 error:
2781         isl_map_free(map1);
2782         isl_map_free(map2);
2783         return NULL;
2784 }
2785
2786 struct isl_map *isl_map_apply_range(
2787                 struct isl_map *map1, struct isl_map *map2)
2788 {
2789         struct isl_map *result;
2790         int i, j;
2791
2792         if (!map1 || !map2)
2793                 goto error;
2794
2795         isl_assert(map1->ctx, map1->nparam == map2->nparam, goto error);
2796         isl_assert(map1->ctx, map1->n_out == map2->n_in, goto error);
2797
2798         result = isl_map_alloc(map1->ctx, map1->nparam, map1->n_in, map2->n_out,
2799                                 map1->n * map2->n, 0);
2800         if (!result)
2801                 goto error;
2802         for (i = 0; i < map1->n; ++i)
2803                 for (j = 0; j < map2->n; ++j) {
2804                         result = isl_map_add(result,
2805                             isl_basic_map_apply_range(
2806                                 isl_basic_map_copy(map1->p[i]),
2807                                 isl_basic_map_copy(map2->p[j])));
2808                         if (!result)
2809                                 goto error;
2810                 }
2811         isl_map_free(map1);
2812         isl_map_free(map2);
2813         if (result && result->n <= 1)
2814                 F_SET(result, ISL_MAP_DISJOINT);
2815         return result;
2816 error:
2817         isl_map_free(map1);
2818         isl_map_free(map2);
2819         return NULL;
2820 }
2821
2822 /*
2823  * returns range - domain
2824  */
2825 struct isl_basic_set *isl_basic_map_deltas(struct isl_basic_map *bmap)
2826 {
2827         struct isl_basic_set *bset;
2828         unsigned dim;
2829         int i;
2830
2831         if (!bmap)
2832                 goto error;
2833         isl_assert(bmap->ctx, bmap->n_in == bmap->n_out, goto error);
2834         dim = bmap->n_in;
2835         bset = isl_basic_set_from_basic_map(bmap);
2836         bset = isl_basic_set_extend(bset, bset->nparam, 3*dim, 0,
2837                                         dim, 0);
2838         bset = isl_basic_set_swap_vars(bset, 2*dim);
2839         for (i = 0; i < dim; ++i) {
2840                 int j = isl_basic_map_alloc_equality(
2841                                             (struct isl_basic_map *)bset);
2842                 if (j < 0)
2843                         goto error;
2844                 isl_seq_clr(bset->eq[j],
2845                             1 + bset->nparam + bset->dim + bset->extra);
2846                 isl_int_set_si(bset->eq[j][1+bset->nparam+i], 1);
2847                 isl_int_set_si(bset->eq[j][1+bset->nparam+dim+i], 1);
2848                 isl_int_set_si(bset->eq[j][1+bset->nparam+2*dim+i], -1);
2849         }
2850         return isl_basic_set_project_out(bset, 2*dim, 0);
2851 error:
2852         isl_basic_map_free(bmap);
2853         return NULL;
2854 }
2855
2856 /* If the only constraints a div d=floor(f/m)
2857  * appears in are its two defining constraints
2858  *
2859  *      f - m d >=0
2860  *      -(f - (m - 1)) + m d >= 0
2861  *
2862  * then it can safely be removed.
2863  */
2864 static int div_is_redundant(struct isl_basic_map *bmap, int div)
2865 {
2866         int i;
2867         unsigned pos = 1 + bmap->nparam + bmap->n_in + bmap->n_out + div;
2868
2869         for (i = 0; i < bmap->n_eq; ++i)
2870                 if (!isl_int_is_zero(bmap->eq[i][pos]))
2871                         return 0;
2872
2873         for (i = 0; i < bmap->n_ineq; ++i) {
2874                 if (isl_int_is_zero(bmap->ineq[i][pos]))
2875                         continue;
2876                 if (isl_int_eq(bmap->ineq[i][pos], bmap->div[div][0])) {
2877                         int neg;
2878                         isl_int_sub(bmap->div[div][1],
2879                                         bmap->div[div][1], bmap->div[div][0]);
2880                         isl_int_add_ui(bmap->div[div][1], bmap->div[div][1], 1);
2881                         neg = isl_seq_is_neg(bmap->ineq[i], bmap->div[div]+1, pos);
2882                         isl_int_sub_ui(bmap->div[div][1], bmap->div[div][1], 1);
2883                         isl_int_add(bmap->div[div][1],
2884                                         bmap->div[div][1], bmap->div[div][0]);
2885                         if (!neg)
2886                                 return 0;
2887                         if (isl_seq_first_non_zero(bmap->ineq[i]+pos+1,
2888                                                     bmap->n_div-div-1) != -1)
2889                                 return 0;
2890                 } else if (isl_int_abs_eq(bmap->ineq[i][pos], bmap->div[div][0])) {
2891                         if (!isl_seq_eq(bmap->ineq[i], bmap->div[div]+1, pos))
2892                                 return 0;
2893                         if (isl_seq_first_non_zero(bmap->ineq[i]+pos+1,
2894                                                     bmap->n_div-div-1) != -1)
2895                                 return 0;
2896                 } else
2897                         return 0;
2898         }
2899
2900         for (i = 0; i < bmap->n_div; ++i)
2901                 if (!isl_int_is_zero(bmap->div[i][1+pos]))
2902                         return 0;
2903
2904         return 1;
2905 }
2906
2907 /*
2908  * Remove divs that don't occur in any of the constraints or other divs.
2909  * These can arise when dropping some of the variables in a quast
2910  * returned by piplib.
2911  */
2912 static struct isl_basic_map *remove_redundant_divs(struct isl_basic_map *bmap)
2913 {
2914         int i;
2915
2916         if (!bmap)
2917                 return NULL;
2918
2919         for (i = bmap->n_div-1; i >= 0; --i) {
2920                 if (!div_is_redundant(bmap, i))
2921                         continue;
2922                 bmap = isl_basic_map_drop_div(bmap, i);
2923         }
2924         return bmap;
2925 }
2926
2927 struct isl_basic_map *isl_basic_map_finalize(struct isl_basic_map *bmap)
2928 {
2929         bmap = remove_redundant_divs(bmap);
2930         if (!bmap)
2931                 return NULL;
2932         F_SET(bmap, ISL_BASIC_SET_FINAL);
2933         return bmap;
2934 }
2935
2936 struct isl_basic_set *isl_basic_set_finalize(struct isl_basic_set *bset)
2937 {
2938         return (struct isl_basic_set *)
2939                 isl_basic_map_finalize((struct isl_basic_map *)bset);
2940 }
2941
2942 struct isl_set *isl_set_finalize(struct isl_set *set)
2943 {
2944         int i;
2945
2946         if (!set)
2947                 return NULL;
2948         for (i = 0; i < set->n; ++i) {
2949                 set->p[i] = isl_basic_set_finalize(set->p[i]);
2950                 if (!set->p[i])
2951                         goto error;
2952         }
2953         return set;
2954 error:
2955         isl_set_free(set);
2956         return NULL;
2957 }
2958
2959 struct isl_map *isl_map_finalize(struct isl_map *map)
2960 {
2961         int i;
2962
2963         if (!map)
2964                 return NULL;
2965         for (i = 0; i < map->n; ++i) {
2966                 map->p[i] = isl_basic_map_finalize(map->p[i]);
2967                 if (!map->p[i])
2968                         goto error;
2969         }
2970         return map;
2971 error:
2972         isl_map_free(map);
2973         return NULL;
2974 }
2975
2976 struct isl_basic_map *isl_basic_map_identity(struct isl_ctx *ctx,
2977                 unsigned nparam, unsigned dim)
2978 {
2979         struct isl_basic_map *bmap;
2980         int i;
2981
2982         bmap = isl_basic_map_alloc(ctx, nparam, dim, dim, 0, dim, 0);
2983         if (!bmap)
2984                 goto error;
2985
2986         for (i = 0; i < dim; ++i) {
2987                 int j = isl_basic_map_alloc_equality(bmap);
2988                 if (j < 0)
2989                         goto error;
2990                 isl_seq_clr(bmap->eq[j],
2991                     1 + bmap->nparam + bmap->n_in + bmap->n_out + bmap->extra);
2992                 isl_int_set_si(bmap->eq[j][1+nparam+i], 1);
2993                 isl_int_set_si(bmap->eq[j][1+nparam+dim+i], -1);
2994         }
2995         return isl_basic_map_finalize(bmap);
2996 error:
2997         isl_basic_map_free(bmap);
2998         return NULL;
2999 }
3000
3001 struct isl_map *isl_map_identity(struct isl_ctx *ctx,
3002                 unsigned nparam, unsigned dim)
3003 {
3004         struct isl_map *map = isl_map_alloc(ctx, nparam, dim, dim, 1,
3005                                                 ISL_MAP_DISJOINT);
3006         if (!map)
3007                 goto error;
3008         map = isl_map_add(map,
3009                 isl_basic_map_identity(ctx, nparam, dim));
3010         return map;
3011 error:
3012         isl_map_free(map);
3013         return NULL;
3014 }
3015
3016 int isl_set_is_equal(struct isl_set *set1, struct isl_set *set2)
3017 {
3018         return isl_map_is_equal((struct isl_map *)set1, (struct isl_map *)set2);
3019 }
3020
3021 int isl_set_is_subset(struct isl_set *set1, struct isl_set *set2)
3022 {
3023         return isl_map_is_subset(
3024                         (struct isl_map *)set1, (struct isl_map *)set2);
3025 }
3026
3027 int isl_basic_map_is_subset(
3028                 struct isl_basic_map *bmap1, struct isl_basic_map *bmap2)
3029 {
3030         int is_subset;
3031         struct isl_map *map1;
3032         struct isl_map *map2;
3033
3034         if (!bmap1 || !bmap2)
3035                 return -1;
3036
3037         map1 = isl_map_from_basic_map(isl_basic_map_copy(bmap1));
3038         map2 = isl_map_from_basic_map(isl_basic_map_copy(bmap2));
3039
3040         is_subset = isl_map_is_subset(map1, map2);
3041
3042         isl_map_free(map1);
3043         isl_map_free(map2);
3044
3045         return is_subset;
3046 }
3047
3048 int isl_basic_map_is_equal(
3049                 struct isl_basic_map *bmap1, struct isl_basic_map *bmap2)
3050 {
3051         int is_subset;
3052
3053         if (!bmap1 || !bmap2)
3054                 return -1;
3055         is_subset = isl_basic_map_is_subset(bmap1, bmap2);
3056         if (is_subset != 1)
3057                 return is_subset;
3058         is_subset = isl_basic_map_is_subset(bmap2, bmap1);
3059         return is_subset;
3060 }
3061
3062 int isl_basic_set_is_equal(
3063                 struct isl_basic_set *bset1, struct isl_basic_set *bset2)
3064 {
3065         return isl_basic_map_is_equal(
3066                 (struct isl_basic_map *)bset1, (struct isl_basic_map *)bset2);
3067 }
3068
3069 int isl_map_is_empty(struct isl_map *map)
3070 {
3071         int i;
3072         int is_empty;
3073
3074         if (!map)
3075                 return -1;
3076         for (i = 0; i < map->n; ++i) {
3077                 is_empty = isl_basic_map_is_empty(map->p[i]);
3078                 if (is_empty < 0)
3079                         return -1;
3080                 if (!is_empty)
3081                         return 0;
3082         }
3083         return 1;
3084 }
3085
3086 int isl_set_is_empty(struct isl_set *set)
3087 {
3088         return isl_map_is_empty((struct isl_map *)set);
3089 }
3090
3091 int isl_map_is_subset(struct isl_map *map1, struct isl_map *map2)
3092 {
3093         int i;
3094         int is_subset = 0;
3095         struct isl_map *diff;
3096
3097         if (!map1 || !map2)
3098                 return -1;
3099
3100         if (isl_map_is_empty(map1))
3101                 return 1;
3102
3103         if (isl_map_is_empty(map2))
3104                 return 0;
3105
3106         diff = isl_map_subtract(isl_map_copy(map1), isl_map_copy(map2));
3107         if (!diff)
3108                 return -1;
3109
3110         is_subset = isl_map_is_empty(diff);
3111         isl_map_free(diff);
3112
3113         return is_subset;
3114 }
3115
3116 int isl_map_is_equal(struct isl_map *map1, struct isl_map *map2)
3117 {
3118         int is_subset;
3119
3120         if (!map1 || !map2)
3121                 return -1;
3122         is_subset = isl_map_is_subset(map1, map2);
3123         if (is_subset != 1)
3124                 return is_subset;
3125         is_subset = isl_map_is_subset(map2, map1);
3126         return is_subset;
3127 }
3128
3129 int isl_basic_map_is_strict_subset(
3130                 struct isl_basic_map *bmap1, struct isl_basic_map *bmap2)
3131 {
3132         int is_subset;
3133
3134         if (!bmap1 || !bmap2)
3135                 return -1;
3136         is_subset = isl_basic_map_is_subset(bmap1, bmap2);
3137         if (is_subset != 1)
3138                 return is_subset;
3139         is_subset = isl_basic_map_is_subset(bmap2, bmap1);
3140         if (is_subset == -1)
3141                 return is_subset;
3142         return !is_subset;
3143 }
3144
3145 static int basic_map_contains(struct isl_basic_map *bmap, struct isl_vec *vec)
3146 {
3147         int i;
3148         unsigned total;
3149         isl_int s;
3150
3151         total = 1 + bmap->nparam + bmap->n_in + bmap->n_out + bmap->n_div;
3152         if (total != vec->size)
3153                 return -1;
3154
3155         isl_int_init(s);
3156
3157         for (i = 0; i < bmap->n_eq; ++i) {
3158                 isl_seq_inner_product(vec->block.data, bmap->eq[i], total, &s);
3159                 if (!isl_int_is_zero(s)) {
3160                         isl_int_clear(s);
3161                         return 0;
3162                 }
3163         }
3164
3165         for (i = 0; i < bmap->n_ineq; ++i) {
3166                 isl_seq_inner_product(vec->block.data, bmap->ineq[i], total, &s);
3167                 if (isl_int_is_neg(s)) {
3168                         isl_int_clear(s);
3169                         return 0;
3170                 }
3171         }
3172
3173         isl_int_clear(s);
3174
3175         return 1;
3176 }
3177
3178 int isl_basic_map_is_universe(struct isl_basic_map *bmap)
3179 {
3180         if (!bmap)
3181                 return -1;
3182         return bmap->n_eq == 0 && bmap->n_ineq == 0;
3183 }
3184
3185 int isl_basic_map_is_empty(struct isl_basic_map *bmap)
3186 {
3187         struct isl_basic_set *bset = NULL;
3188         struct isl_vec *sample = NULL;
3189         int empty;
3190         unsigned total;
3191
3192         if (!bmap)
3193                 return -1;
3194
3195         if (F_ISSET(bmap, ISL_BASIC_MAP_EMPTY))
3196                 return 1;
3197
3198         total = 1 + bmap->nparam + bmap->n_in + bmap->n_out + bmap->n_div;
3199         if (bmap->sample && bmap->sample->size == total) {
3200                 int contains = basic_map_contains(bmap, bmap->sample);
3201                 if (contains < 0)
3202                         return -1;
3203                 if (contains)
3204                         return 0;
3205         }
3206         bset = isl_basic_map_underlying_set(isl_basic_map_copy(bmap));
3207         if (!bset)
3208                 return -1;
3209         sample = isl_basic_set_sample(bset);
3210         if (!sample)
3211                 return -1;
3212         empty = sample->size == 0;
3213         if (bmap->sample)
3214                 isl_vec_free(bmap->ctx, bmap->sample);
3215         bmap->sample = sample;
3216
3217         return empty;
3218 }
3219
3220 struct isl_map *isl_basic_map_union(
3221         struct isl_basic_map *bmap1, struct isl_basic_map *bmap2)
3222 {
3223         struct isl_map *map;
3224         if (!bmap1 || !bmap2)
3225                 return NULL;
3226
3227         isl_assert(bmap1->ctx, bmap1->nparam == bmap2->nparam, goto error);
3228         isl_assert(bmap1->ctx, bmap1->n_in == bmap2->n_in, goto error);
3229         isl_assert(bmap1->ctx, bmap1->n_out == bmap2->n_out, goto error);
3230
3231         map = isl_map_alloc(bmap1->ctx, bmap1->nparam,
3232                                 bmap1->n_in, bmap1->n_out, 2, 0);
3233         if (!map)
3234                 goto error;
3235         map = isl_map_add(map, bmap1);
3236         map = isl_map_add(map, bmap2);
3237         return map;
3238 error:
3239         isl_basic_map_free(bmap1);
3240         isl_basic_map_free(bmap2);
3241         return NULL;
3242 }
3243
3244 struct isl_set *isl_basic_set_union(
3245                 struct isl_basic_set *bset1, struct isl_basic_set *bset2)
3246 {
3247         return (struct isl_set *)isl_basic_map_union(
3248                                             (struct isl_basic_map *)bset1,
3249                                             (struct isl_basic_map *)bset2);
3250 }
3251
3252 /* Order divs such that any div only depends on previous divs */
3253 static struct isl_basic_map *order_divs(struct isl_basic_map *bmap)
3254 {
3255         int i;
3256         unsigned off = bmap->nparam + bmap->n_in + bmap->n_out;
3257
3258         for (i = 0; i < bmap->n_div; ++i) {
3259                 int pos;
3260                 pos = isl_seq_first_non_zero(bmap->div[i]+1+1+off+i,
3261                                                             bmap->n_div-i);
3262                 if (pos == -1)
3263                         continue;
3264                 swap_div(bmap, i, pos);
3265                 --i;
3266         }
3267         return bmap;
3268 }
3269
3270 static int find_div(struct isl_basic_map *dst,
3271                         struct isl_basic_map *src, unsigned div)
3272 {
3273         int i;
3274
3275         unsigned total = src->nparam + src->n_in + src->n_out + src->n_div;
3276
3277         for (i = 0; i < dst->n_div; ++i)
3278                 if (isl_seq_eq(dst->div[i], src->div[div], 1+1+total) &&
3279                     isl_seq_first_non_zero(dst->div[i]+1+1+total,
3280                                                 dst->n_div - src->n_div) == -1)
3281                         return i;
3282         return -1;
3283 }
3284
3285 struct isl_basic_map *isl_basic_map_align_divs(
3286                 struct isl_basic_map *dst, struct isl_basic_map *src)
3287 {
3288         int i;
3289         unsigned total = src->nparam + src->n_in + src->n_out + src->n_div;
3290
3291         if (src->n_div == 0)
3292                 return dst;
3293
3294         src = order_divs(src);
3295         dst = isl_basic_map_extend(dst, dst->nparam, dst->n_in,
3296                         dst->n_out, src->n_div, 0, 2 * src->n_div);
3297         if (!dst)
3298                 return NULL;
3299         for (i = 0; i < src->n_div; ++i) {
3300                 int j = find_div(dst, src, i);
3301                 if (j < 0) {
3302                         j = isl_basic_map_alloc_div(dst);
3303                         if (j < 0)
3304                                 goto error;
3305                         isl_seq_cpy(dst->div[j], src->div[i], 1+1+total);
3306                         isl_seq_clr(dst->div[j]+1+1+total,
3307                                                     dst->extra - src->n_div);
3308                         if (add_div_constraints(dst, j) < 0)
3309                                 goto error;
3310                 }
3311                 if (j != i)
3312                         swap_div(dst, i, j);
3313         }
3314         return dst;
3315 error:
3316         isl_basic_map_free(dst);
3317         return NULL;
3318 }
3319
3320 struct isl_map *isl_map_align_divs(struct isl_map *map)
3321 {
3322         int i;
3323
3324         map = isl_map_compute_divs(map);
3325         map = isl_map_cow(map);
3326         if (!map)
3327                 return NULL;
3328
3329         for (i = 1; i < map->n; ++i)
3330                 map->p[0] = isl_basic_map_align_divs(map->p[0], map->p[i]);
3331         for (i = 1; i < map->n; ++i)
3332                 map->p[i] = isl_basic_map_align_divs(map->p[i], map->p[0]);
3333
3334         return map;
3335 }
3336
3337 static struct isl_map *add_cut_constraint(struct isl_map *dst,
3338                 struct isl_basic_map *src, isl_int *c,
3339                 unsigned len, int oppose)
3340 {
3341         struct isl_basic_map *copy = NULL;
3342         int is_empty;
3343         int k;
3344         unsigned total;
3345
3346         copy = isl_basic_map_copy(src);
3347         copy = isl_basic_map_cow(copy);
3348         if (!copy)
3349                 goto error;
3350         copy = isl_basic_map_extend(copy,
3351                 copy->nparam, copy->n_in, copy->n_out, 0, 0, 1);
3352         k = isl_basic_map_alloc_inequality(copy);
3353         if (k < 0)
3354                 goto error;
3355         if (oppose)
3356                 isl_seq_neg(copy->ineq[k], c, len);
3357         else
3358                 isl_seq_cpy(copy->ineq[k], c, len);
3359         total = 1 + copy->nparam + copy->n_in + copy->n_out + copy->extra;
3360         isl_seq_clr(copy->ineq[k]+len, total - len);
3361         isl_inequality_negate(copy, k);
3362         copy = isl_basic_map_simplify(copy);
3363         copy = isl_basic_map_finalize(copy);
3364         is_empty = isl_basic_map_is_empty(copy);
3365         if (is_empty < 0)
3366                 goto error;
3367         if (!is_empty)
3368                 dst = isl_map_add(dst, copy);
3369         else
3370                 isl_basic_map_free(copy);
3371         return dst;
3372 error:
3373         isl_basic_map_free(copy);
3374         isl_map_free(dst);
3375         return NULL;
3376 }
3377
3378 static struct isl_map *subtract(struct isl_map *map, struct isl_basic_map *bmap)
3379 {
3380         int i, j, k;
3381         unsigned flags = 0;
3382         struct isl_map *rest = NULL;
3383         unsigned max;
3384         unsigned total = bmap->nparam + bmap->n_in + bmap->n_out + bmap->n_div;
3385
3386         assert(bmap);
3387
3388         if (!map)
3389                 goto error;
3390
3391         if (F_ISSET(map, ISL_MAP_DISJOINT))
3392                 FL_SET(flags, ISL_MAP_DISJOINT);
3393
3394         max = map->n * (2 * bmap->n_eq + bmap->n_ineq);
3395         rest = isl_map_alloc(map->ctx, map->nparam, map->n_in, map->n_out,
3396                                 max, flags);
3397         if (!rest)
3398                 goto error;
3399
3400         for (i = 0; i < map->n; ++i) {
3401                 map->p[i] = isl_basic_map_align_divs(map->p[i], bmap);
3402                 if (!map->p[i])
3403                         goto error;
3404         }
3405
3406         for (j = 0; j < map->n; ++j)
3407                 map->p[j] = isl_basic_map_cow(map->p[j]);
3408
3409         for (i = 0; i < bmap->n_eq; ++i) {
3410                 for (j = 0; j < map->n; ++j) {
3411                         rest = add_cut_constraint(rest,
3412                                 map->p[j], bmap->eq[i], 1+total, 0);
3413                         if (!rest)
3414                                 goto error;
3415
3416                         rest = add_cut_constraint(rest,
3417                                 map->p[j], bmap->eq[i], 1+total, 1);
3418                         if (!rest)
3419                                 goto error;
3420
3421                         map->p[j] = isl_basic_map_extend(map->p[j],
3422                                 map->p[j]->nparam, map->p[j]->n_in,
3423                                 map->p[j]->n_out, 0, 1, 0);
3424                         if (!map->p[j])
3425                                 goto error;
3426                         k = isl_basic_map_alloc_equality(map->p[j]);
3427                         if (k < 0)
3428                                 goto error;
3429                         isl_seq_cpy(map->p[j]->eq[k], bmap->eq[i], 1+total);
3430                         isl_seq_clr(map->p[j]->eq[k]+1+total,
3431                                         map->p[j]->extra - bmap->n_div);
3432                 }
3433         }
3434
3435         for (i = 0; i < bmap->n_ineq; ++i) {
3436                 for (j = 0; j < map->n; ++j) {
3437                         rest = add_cut_constraint(rest,
3438                                 map->p[j], bmap->ineq[i], 1+total, 0);
3439                         if (!rest)
3440                                 goto error;
3441
3442                         map->p[j] = isl_basic_map_extend(map->p[j],
3443                                 map->p[j]->nparam, map->p[j]->n_in,
3444                                 map->p[j]->n_out, 0, 0, 1);
3445                         if (!map->p[j])
3446                                 goto error;
3447                         k = isl_basic_map_alloc_inequality(map->p[j]);
3448                         if (k < 0)
3449                                 goto error;
3450                         isl_seq_cpy(map->p[j]->ineq[k], bmap->ineq[i], 1+total);
3451                         isl_seq_clr(map->p[j]->ineq[k]+1+total,
3452                                         map->p[j]->extra - bmap->n_div);
3453                 }
3454         }
3455
3456         isl_map_free(map);
3457         return rest;
3458 error:
3459         isl_map_free(map);
3460         isl_map_free(rest);
3461         return NULL;
3462 }
3463
3464 struct isl_map *isl_map_subtract(struct isl_map *map1, struct isl_map *map2)
3465 {
3466         int i;
3467         if (!map1 || !map2)
3468                 goto error;
3469
3470         isl_assert(map1->ctx, map1->nparam == map2->nparam, goto error);
3471         isl_assert(map1->ctx, map1->n_in == map2->n_in, goto error);
3472         isl_assert(map1->ctx, map1->n_out == map2->n_out, goto error);
3473
3474         if (isl_map_is_empty(map2)) {
3475                 isl_map_free(map2);
3476                 return map1;
3477         }
3478
3479         map1 = isl_map_compute_divs(map1);
3480         map2 = isl_map_compute_divs(map2);
3481         if (!map1 || !map2)
3482                 goto error;
3483
3484         for (i = 0; map1 && i < map2->n; ++i)
3485                 map1 = subtract(map1, map2->p[i]);
3486
3487         isl_map_free(map2);
3488         return map1;
3489 error:
3490         isl_map_free(map1);
3491         isl_map_free(map2);
3492         return NULL;
3493 }
3494
3495 struct isl_set *isl_set_subtract(struct isl_set *set1, struct isl_set *set2)
3496 {
3497         return (struct isl_set *)
3498                 isl_map_subtract(
3499                         (struct isl_map *)set1, (struct isl_map *)set2);
3500 }
3501
3502 struct isl_set *isl_set_apply(struct isl_set *set, struct isl_map *map)
3503 {
3504         if (!set || !map)
3505                 goto error;
3506         isl_assert(set->ctx, set->dim == map->n_in, goto error);
3507         map = isl_map_intersect_domain(map, set);
3508         set = isl_map_range(map);
3509         return set;
3510 error:
3511         isl_set_free(set);
3512         isl_map_free(map);
3513         return NULL;
3514 }
3515
3516 /* There is no need to cow as removing empty parts doesn't change
3517  * the meaning of the set.
3518  */
3519 struct isl_map *isl_map_remove_empty_parts(struct isl_map *map)
3520 {
3521         int i;
3522
3523         if (!map)
3524                 return NULL;
3525
3526         for (i = map->n-1; i >= 0; --i) {
3527                 if (!F_ISSET(map->p[i], ISL_BASIC_MAP_EMPTY))
3528                         continue;
3529                 isl_basic_map_free(map->p[i]);
3530                 if (i != map->n-1)
3531                         map->p[i] = map->p[map->n-1];
3532                 map->n--;
3533         }
3534
3535         return map;
3536 }
3537
3538 struct isl_set *isl_set_remove_empty_parts(struct isl_set *set)
3539 {
3540         return (struct isl_set *)
3541                 isl_map_remove_empty_parts((struct isl_map *)set);
3542 }