isl_map.c

   1 #include <string.h>
   2 #include <strings.h>
   3 #include "isl_ctx.h"
   4 #include "isl_blk.h"
   5 #include "isl_dim.h"
   6 #include "isl_equalities.h"
   7 #include "isl_list.h"
   8 #include "isl_lp.h"
   9 #include "isl_seq.h"
  10 #include "isl_set.h"
  11 #include "isl_map.h"
  12 #include "isl_map_private.h"
  13 #include "isl_map_piplib.h"
  14 #include "isl_sample.h"
  15 #include "isl_tab.h"
  16 #include "isl_vec.h"
  17
  18 /* Maps dst positions to src positions */
  19 struct isl_dim_map {
  20         unsigned len;
  21         int pos[1];
  22 };
  23
  24 static struct isl_dim_map *isl_dim_map_alloc(struct isl_ctx *ctx, unsigned len)
  25 {
  26         int i;
  27         struct isl_dim_map *dim_map;
  28         dim_map = isl_alloc(ctx, struct isl_dim_map,
  29                                 sizeof(struct isl_dim_map) + len * sizeof(int));
  30         if (!dim_map)
  31                 return NULL;
  32         dim_map->len = 1 + len;
  33         dim_map->pos[0] = 0;
  34         for (i = 0; i < len; ++i)
  35                 dim_map->pos[1 + i] = -1;
  36         return dim_map;
  37 }
  38
  39 static unsigned n(struct isl_dim *dim, enum isl_dim_type type)
  40 {
  41         switch (type) {
  42         case isl_dim_param:     return dim->nparam;
  43         case isl_dim_in:        return dim->n_in;
  44         case isl_dim_out:       return dim->n_out;
  45         case isl_dim_all:       return dim->nparam + dim->n_in + dim->n_out;
  46         }
  47 }
  48
  49 static unsigned pos(struct isl_dim *dim, enum isl_dim_type type)
  50 {
  51         switch (type) {
  52         case isl_dim_param:     return 1;
  53         case isl_dim_in:        return 1 + dim->nparam;
  54         case isl_dim_out:       return 1 + dim->nparam + dim->n_in;
  55         }
  56 }
  57
  58 static void isl_dim_map_dim(struct isl_dim_map *dim_map, struct isl_dim *dim,
  59                 enum isl_dim_type type, unsigned dst_pos)
  60 {
  61         int i;
  62         unsigned src_pos;
  63
  64         if (!dim_map || !dim)
  65                 return;
  66
  67         src_pos = pos(dim, type);
  68         for (i = 0; i < n(dim, type); ++i)
  69                 dim_map->pos[1 + dst_pos + i] = src_pos + i;
  70 }
  71
  72 static void isl_dim_map_div(struct isl_dim_map *dim_map,
  73                 struct isl_basic_map *bmap, unsigned dst_pos)
  74 {
  75         int i;
  76         unsigned src_pos;
  77
  78         if (!dim_map || !bmap)
  79                 return;
  80
  81         src_pos = 1 + isl_dim_total(bmap->dim);
  82         for (i = 0; i < bmap->n_div; ++i)
  83                 dim_map->pos[1 + dst_pos + i] = src_pos + i;
  84 }
  85
  86 static void isl_dim_map_dump(struct isl_dim_map *dim_map)
  87 {
  88         int i;
  89
  90         for (i = 0; i < dim_map->len; ++i)
  91                 fprintf(stderr, "%d -> %d; ", i, dim_map->pos[i]);
  92         fprintf(stderr, "\n");
  93 }
  94
  95 unsigned isl_basic_map_dim(const struct isl_basic_map *bmap,
  96                                 enum isl_dim_type type)
  97 {
  98         struct isl_dim *dim = bmap->dim;
  99         switch (type) {
 100         case isl_dim_param:
 101         case isl_dim_in:
 102         case isl_dim_out:       return isl_dim_size(bmap->dim, type);
 103         case isl_dim_div:       return bmap->n_div;
 104         case isl_dim_all:       return isl_basic_map_total_dim(bmap);
 105         }
 106 }
 107
 108 unsigned isl_map_dim(const struct isl_map *map, enum isl_dim_type type)
 109 {
 110         return n(map->dim, type);
 111 }
 112
 113 unsigned isl_set_dim(const struct isl_set *set, enum isl_dim_type type)
 114 {
 115         return n(set->dim, type);
 116 }
 117
 118 unsigned isl_basic_map_offset(struct isl_basic_map *bmap,
 119                                         enum isl_dim_type type)
 120 {
 121         struct isl_dim *dim = bmap->dim;
 122         switch (type) {
 123         case isl_dim_param:     return 1;
 124         case isl_dim_in:        return 1 + dim->nparam;
 125         case isl_dim_out:       return 1 + dim->nparam + dim->n_in;
 126         case isl_dim_div:       return 1 + dim->nparam + dim->n_in + dim->n_out;
 127         }
 128 }
 129
 130 static unsigned map_offset(struct isl_map *map, enum isl_dim_type type)
 131 {
 132         return pos(map->dim, type);
 133 }
 134
 135 unsigned isl_basic_set_dim(const struct isl_basic_set *bset,
 136                                 enum isl_dim_type type)
 137 {
 138         return isl_basic_map_dim((const struct isl_basic_map*)bset, type);
 139 }
 140
 141 unsigned isl_basic_set_n_dim(const struct isl_basic_set *bset)
 142 {
 143         return bset->dim->n_out;
 144 }
 145
 146 unsigned isl_basic_set_n_param(const struct isl_basic_set *bset)
 147 {
 148         return bset->dim->nparam;
 149 }
 150
 151 unsigned isl_basic_set_total_dim(const struct isl_basic_set *bset)
 152 {
 153         return isl_dim_total(bset->dim) + bset->n_div;
 154 }
 155
 156 unsigned isl_set_n_dim(const struct isl_set *set)
 157 {
 158         return set->dim->n_out;
 159 }
 160
 161 unsigned isl_set_n_param(const struct isl_set *set)
 162 {
 163         return set->dim->nparam;
 164 }
 165
 166 unsigned isl_basic_map_n_in(const struct isl_basic_map *bmap)
 167 {
 168         return bmap->dim->n_in;
 169 }
 170
 171 unsigned isl_basic_map_n_out(const struct isl_basic_map *bmap)
 172 {
 173         return bmap->dim->n_out;
 174 }
 175
 176 unsigned isl_basic_map_n_param(const struct isl_basic_map *bmap)
 177 {
 178         return bmap->dim->nparam;
 179 }
 180
 181 unsigned isl_basic_map_n_div(const struct isl_basic_map *bmap)
 182 {
 183         return bmap->n_div;
 184 }
 185
 186 unsigned isl_basic_map_total_dim(const struct isl_basic_map *bmap)
 187 {
 188         return isl_dim_total(bmap->dim) + bmap->n_div;
 189 }
 190
 191 unsigned isl_map_n_in(const struct isl_map *map)
 192 {
 193         return map->dim->n_in;
 194 }
 195
 196 unsigned isl_map_n_out(const struct isl_map *map)
 197 {
 198         return map->dim->n_out;
 199 }
 200
 201 unsigned isl_map_n_param(const struct isl_map *map)
 202 {
 203         return map->dim->nparam;
 204 }
 205
 206 int isl_map_compatible_domain(struct isl_map *map, struct isl_set *set)
 207 {
 208         return map->dim->n_in == set->dim->n_out &&
 209                map->dim->nparam == set->dim->nparam;
 210 }
 211
 212 int isl_basic_map_compatible_domain(struct isl_basic_map *bmap,
 213                 struct isl_basic_set *bset)
 214 {
 215         return bmap->dim->n_in == bset->dim->n_out &&
 216                bmap->dim->nparam == bset->dim->nparam;
 217 }
 218
 219 int isl_basic_map_compatible_range(struct isl_basic_map *bmap,
 220                 struct isl_basic_set *bset)
 221 {
 222         return bmap->dim->n_out == bset->dim->n_out &&
 223                bmap->dim->nparam == bset->dim->nparam;
 224 }
 225
 226 struct isl_dim *isl_basic_map_get_dim(struct isl_basic_map *bmap)
 227 {
 228         if (!bmap)
 229                 return NULL;
 230         return isl_dim_copy(bmap->dim);
 231 }
 232
 233 struct isl_dim *isl_basic_set_get_dim(struct isl_basic_set *bset)
 234 {
 235         if (!bset)
 236                 return NULL;
 237         return isl_dim_copy(bset->dim);
 238 }
 239
 240 struct isl_dim *isl_map_get_dim(struct isl_map *map)
 241 {
 242         if (!map)
 243                 return NULL;
 244         return isl_dim_copy(map->dim);
 245 }
 246
 247 struct isl_dim *isl_set_get_dim(struct isl_set *set)
 248 {
 249         if (!set)
 250                 return NULL;
 251         return isl_dim_copy(set->dim);
 252 }
 253
 254 static struct isl_basic_map *basic_map_init(struct isl_ctx *ctx,
 255                 struct isl_basic_map *bmap, unsigned extra,
 256                 unsigned n_eq, unsigned n_ineq)
 257 {
 258         int i;
 259         size_t row_size = 1 + isl_dim_total(bmap->dim) + extra;
 260
 261         bmap->block = isl_blk_alloc(ctx, (n_ineq + n_eq) * row_size);
 262         if (isl_blk_is_error(bmap->block)) {
 263                 free(bmap);
 264                 return NULL;
 265         }
 266
 267         bmap->ineq = isl_alloc_array(ctx, isl_int *, n_ineq + n_eq);
 268         if (!bmap->ineq) {
 269                 isl_blk_free(ctx, bmap->block);
 270                 free(bmap);
 271                 return NULL;
 272         }
 273
 274         if (extra == 0) {
 275                 bmap->block2 = isl_blk_empty();
 276                 bmap->div = NULL;
 277         } else {
 278                 bmap->block2 = isl_blk_alloc(ctx, extra * (1 + row_size));
 279                 if (isl_blk_is_error(bmap->block2)) {
 280                         free(bmap->ineq);
 281                         isl_blk_free(ctx, bmap->block);
 282                         free(bmap);
 283                         return NULL;
 284                 }
 285
 286                 bmap->div = isl_alloc_array(ctx, isl_int *, extra);
 287                 if (!bmap->div) {
 288                         isl_blk_free(ctx, bmap->block2);
 289                         free(bmap->ineq);
 290                         isl_blk_free(ctx, bmap->block);
 291                         free(bmap);
 292                         return NULL;
 293                 }
 294         }
 295
 296         for (i = 0; i < n_ineq + n_eq; ++i)
 297                 bmap->ineq[i] = bmap->block.data + i * row_size;
 298
 299         for (i = 0; i < extra; ++i)
 300                 bmap->div[i] = bmap->block2.data + i * (1 + row_size);
 301
 302         bmap->ctx = ctx;
 303         isl_ctx_ref(ctx);
 304         bmap->ref = 1;
 305         bmap->flags = 0;
 306         bmap->c_size = n_eq + n_ineq;
 307         bmap->eq = bmap->ineq + n_ineq;
 308         bmap->extra = extra;
 309         bmap->n_eq = 0;
 310         bmap->n_ineq = 0;
 311         bmap->n_div = 0;
 312         bmap->sample = NULL;
 313
 314         return bmap;
 315 error:
 316         isl_basic_map_free(bmap);
 317         return NULL;
 318 }
 319
 320 struct isl_basic_set *isl_basic_set_alloc(struct isl_ctx *ctx,
 321                 unsigned nparam, unsigned dim, unsigned extra,
 322                 unsigned n_eq, unsigned n_ineq)
 323 {
 324         struct isl_basic_map *bmap;
 325         bmap = isl_basic_map_alloc(ctx, nparam, 0, dim, extra, n_eq, n_ineq);
 326         return (struct isl_basic_set *)bmap;
 327 }
 328
 329 struct isl_basic_set *isl_basic_set_alloc_dim(struct isl_dim *dim,
 330                 unsigned extra, unsigned n_eq, unsigned n_ineq)
 331 {
 332         struct isl_basic_map *bmap;
 333         if (!dim)
 334                 return NULL;
 335         isl_assert(dim->ctx, dim->n_in == 0, return NULL);
 336         bmap = isl_basic_map_alloc_dim(dim, extra, n_eq, n_ineq);
 337         return (struct isl_basic_set *)bmap;
 338 }
 339
 340 struct isl_basic_map *isl_basic_map_alloc_dim(struct isl_dim *dim,
 341                 unsigned extra, unsigned n_eq, unsigned n_ineq)
 342 {
 343         struct isl_basic_map *bmap;
 344
 345         if (!dim)
 346                 return NULL;
 347         bmap = isl_alloc_type(dim->ctx, struct isl_basic_map);
 348         if (!bmap)
 349                 goto error;
 350         bmap->dim = dim;
 351
 352         return basic_map_init(dim->ctx, bmap, extra, n_eq, n_ineq);
 353 error:
 354         isl_dim_free(dim);
 355         return NULL;
 356 }
 357
 358 struct isl_basic_map *isl_basic_map_alloc(struct isl_ctx *ctx,
 359                 unsigned nparam, unsigned in, unsigned out, unsigned extra,
 360                 unsigned n_eq, unsigned n_ineq)
 361 {
 362         struct isl_basic_map *bmap;
 363         struct isl_dim *dim;
 364
 365         dim = isl_dim_alloc(ctx, nparam, in, out);
 366         if (!dim)
 367                 return NULL;
 368
 369         bmap = isl_basic_map_alloc_dim(dim, extra, n_eq, n_ineq);
 370         return bmap;
 371 }
 372
 373 static void dup_constraints(
 374                 struct isl_basic_map *dst, struct isl_basic_map *src)
 375 {
 376         int i;
 377         unsigned total = isl_basic_map_total_dim(src);
 378
 379         for (i = 0; i < src->n_eq; ++i) {
 380                 int j = isl_basic_map_alloc_equality(dst);
 381                 isl_seq_cpy(dst->eq[j], src->eq[i], 1+total);
 382         }
 383
 384         for (i = 0; i < src->n_ineq; ++i) {
 385                 int j = isl_basic_map_alloc_inequality(dst);
 386                 isl_seq_cpy(dst->ineq[j], src->ineq[i], 1+total);
 387         }
 388
 389         for (i = 0; i < src->n_div; ++i) {
 390                 int j = isl_basic_map_alloc_div(dst);
 391                 isl_seq_cpy(dst->div[j], src->div[i], 1+1+total);
 392         }
 393         ISL_F_SET(dst, ISL_BASIC_SET_FINAL);
 394 }
 395
 396 struct isl_basic_map *isl_basic_map_dup(struct isl_basic_map *bmap)
 397 {
 398         struct isl_basic_map *dup;
 399
 400         if (!bmap)
 401                 return NULL;
 402         dup = isl_basic_map_alloc_dim(isl_dim_copy(bmap->dim),
 403                         bmap->n_div, bmap->n_eq, bmap->n_ineq);
 404         if (!dup)
 405                 return NULL;
 406         dup_constraints(dup, bmap);
 407         dup->flags = bmap->flags;
 408         dup->sample = isl_vec_copy(bmap->sample);
 409         return dup;
 410 }
 411
 412 struct isl_basic_set *isl_basic_set_dup(struct isl_basic_set *bset)
 413 {
 414         struct isl_basic_map *dup;
 415
 416         dup = isl_basic_map_dup((struct isl_basic_map *)bset);
 417         return (struct isl_basic_set *)dup;
 418 }
 419
 420 struct isl_basic_set *isl_basic_set_copy(struct isl_basic_set *bset)
 421 {
 422         if (!bset)
 423                 return NULL;
 424
 425         if (ISL_F_ISSET(bset, ISL_BASIC_SET_FINAL)) {
 426                 bset->ref++;
 427                 return bset;
 428         }
 429         return isl_basic_set_dup(bset);
 430 }
 431
 432 struct isl_set *isl_set_copy(struct isl_set *set)
 433 {
 434         if (!set)
 435                 return NULL;
 436
 437         set->ref++;
 438         return set;
 439 }
 440
 441 struct isl_basic_map *isl_basic_map_copy(struct isl_basic_map *bmap)
 442 {
 443         if (!bmap)
 444                 return NULL;
 445
 446         if (ISL_F_ISSET(bmap, ISL_BASIC_SET_FINAL)) {
 447                 bmap->ref++;
 448                 return bmap;
 449         }
 450         return isl_basic_map_dup(bmap);
 451 }
 452
 453 struct isl_map *isl_map_copy(struct isl_map *map)
 454 {
 455         if (!map)
 456                 return NULL;
 457
 458         map->ref++;
 459         return map;
 460 }
 461
 462 void isl_basic_map_free(struct isl_basic_map *bmap)
 463 {
 464         if (!bmap)
 465                 return;
 466
 467         if (--bmap->ref > 0)
 468                 return;
 469
 470         isl_ctx_deref(bmap->ctx);
 471         free(bmap->div);
 472         isl_blk_free(bmap->ctx, bmap->block2);
 473         free(bmap->ineq);
 474         isl_blk_free(bmap->ctx, bmap->block);
 475         isl_vec_free(bmap->sample);
 476         isl_dim_free(bmap->dim);
 477         free(bmap);
 478 }
 479
 480 void isl_basic_set_free(struct isl_basic_set *bset)
 481 {
 482         isl_basic_map_free((struct isl_basic_map *)bset);
 483 }
 484
 485 static int room_for_con(struct isl_basic_map *bmap, unsigned n)
 486 {
 487         return bmap->n_eq + bmap->n_ineq + n <= bmap->c_size;
 488 }
 489
 490 int isl_basic_map_alloc_equality(struct isl_basic_map *bmap)
 491 {
 492         struct isl_ctx *ctx;
 493         if (!bmap)
 494                 return -1;
 495         ctx = bmap->ctx;
 496         isl_assert(ctx, room_for_con(bmap, 1), return -1);
 497         isl_assert(ctx, (bmap->eq - bmap->ineq) + bmap->n_eq <= bmap->c_size,
 498                         return -1);
 499         ISL_F_CLR(bmap, ISL_BASIC_MAP_NORMALIZED);
 500         ISL_F_CLR(bmap, ISL_BASIC_MAP_NO_REDUNDANT);
 501         ISL_F_CLR(bmap, ISL_BASIC_MAP_NO_IMPLICIT);
 502         ISL_F_CLR(bmap, ISL_BASIC_MAP_ALL_EQUALITIES);
 503         ISL_F_CLR(bmap, ISL_BASIC_MAP_NORMALIZED_DIVS);
 504         if ((bmap->eq - bmap->ineq) + bmap->n_eq == bmap->c_size) {
 505                 isl_int *t;
 506                 int j = isl_basic_map_alloc_inequality(bmap);
 507                 if (j < 0)
 508                         return -1;
 509                 t = bmap->ineq[j];
 510                 bmap->ineq[j] = bmap->ineq[bmap->n_ineq - 1];
 511                 bmap->ineq[bmap->n_ineq - 1] = bmap->eq[-1];
 512                 bmap->eq[-1] = t;
 513                 bmap->n_eq++;
 514                 bmap->n_ineq--;
 515                 bmap->eq--;
 516                 return 0;
 517         }
 518         isl_seq_clr(bmap->eq[bmap->n_eq] + 1 + isl_basic_map_total_dim(bmap),
 519                       bmap->extra - bmap->n_div);
 520         return bmap->n_eq++;
 521 }
 522
 523 int isl_basic_set_alloc_equality(struct isl_basic_set *bset)
 524 {
 525         return isl_basic_map_alloc_equality((struct isl_basic_map *)bset);
 526 }
 527
 528 int isl_basic_map_free_equality(struct isl_basic_map *bmap, unsigned n)
 529 {
 530         if (!bmap)
 531                 return -1;
 532         isl_assert(bmap->ctx, n <= bmap->n_eq, return -1);
 533         bmap->n_eq -= n;
 534         return 0;
 535 }
 536
 537 int isl_basic_set_free_equality(struct isl_basic_set *bset, unsigned n)
 538 {
 539         return isl_basic_map_free_equality((struct isl_basic_map *)bset, n);
 540 }
 541
 542 int isl_basic_map_drop_equality(struct isl_basic_map *bmap, unsigned pos)
 543 {
 544         isl_int *t;
 545         if (!bmap)
 546                 return -1;
 547         isl_assert(bmap->ctx, pos < bmap->n_eq, return -1);
 548
 549         if (pos != bmap->n_eq - 1) {
 550                 t = bmap->eq[pos];
 551                 bmap->eq[pos] = bmap->eq[bmap->n_eq - 1];
 552                 bmap->eq[bmap->n_eq - 1] = t;
 553         }
 554         bmap->n_eq--;
 555         return 0;
 556 }
 557
 558 int isl_basic_set_drop_equality(struct isl_basic_set *bset, unsigned pos)
 559 {
 560         return isl_basic_map_drop_equality((struct isl_basic_map *)bset, pos);
 561 }
 562
 563 void isl_basic_map_inequality_to_equality(
 564                 struct isl_basic_map *bmap, unsigned pos)
 565 {
 566         isl_int *t;
 567
 568         t = bmap->ineq[pos];
 569         bmap->ineq[pos] = bmap->ineq[bmap->n_ineq - 1];
 570         bmap->ineq[bmap->n_ineq - 1] = bmap->eq[-1];
 571         bmap->eq[-1] = t;
 572         bmap->n_eq++;
 573         bmap->n_ineq--;
 574         bmap->eq--;
 575         ISL_F_CLR(bmap, ISL_BASIC_MAP_NO_REDUNDANT);
 576         ISL_F_CLR(bmap, ISL_BASIC_MAP_NORMALIZED);
 577         ISL_F_CLR(bmap, ISL_BASIC_MAP_NORMALIZED_DIVS);
 578         ISL_F_CLR(bmap, ISL_BASIC_MAP_ALL_EQUALITIES);
 579 }
 580
 581 static int room_for_ineq(struct isl_basic_map *bmap, unsigned n)
 582 {
 583         return bmap->n_ineq + n <= bmap->eq - bmap->ineq;
 584 }
 585
 586 int isl_basic_map_alloc_inequality(struct isl_basic_map *bmap)
 587 {
 588         struct isl_ctx *ctx;
 589         if (!bmap)
 590                 return -1;
 591         ctx = bmap->ctx;
 592         isl_assert(ctx, room_for_ineq(bmap, 1), return -1);
 593         ISL_F_CLR(bmap, ISL_BASIC_MAP_NO_IMPLICIT);
 594         ISL_F_CLR(bmap, ISL_BASIC_MAP_NO_REDUNDANT);
 595         ISL_F_CLR(bmap, ISL_BASIC_MAP_NORMALIZED);
 596         ISL_F_CLR(bmap, ISL_BASIC_MAP_ALL_EQUALITIES);
 597         isl_seq_clr(bmap->ineq[bmap->n_ineq] +
 598                       1 + isl_basic_map_total_dim(bmap),
 599                       bmap->extra - bmap->n_div);
 600         return bmap->n_ineq++;
 601 }
 602
 603 int isl_basic_set_alloc_inequality(struct isl_basic_set *bset)
 604 {
 605         return isl_basic_map_alloc_inequality((struct isl_basic_map *)bset);
 606 }
 607
 608 int isl_basic_map_free_inequality(struct isl_basic_map *bmap, unsigned n)
 609 {
 610         if (!bmap)
 611                 return -1;
 612         isl_assert(bmap->ctx, n <= bmap->n_ineq, return -1);
 613         bmap->n_ineq -= n;
 614         return 0;
 615 }
 616
 617 int isl_basic_set_free_inequality(struct isl_basic_set *bset, unsigned n)
 618 {
 619         return isl_basic_map_free_inequality((struct isl_basic_map *)bset, n);
 620 }
 621
 622 int isl_basic_map_drop_inequality(struct isl_basic_map *bmap, unsigned pos)
 623 {
 624         isl_int *t;
 625         if (!bmap)
 626                 return -1;
 627         isl_assert(bmap->ctx, pos < bmap->n_ineq, return -1);
 628
 629         if (pos != bmap->n_ineq - 1) {
 630                 t = bmap->ineq[pos];
 631                 bmap->ineq[pos] = bmap->ineq[bmap->n_ineq - 1];
 632                 bmap->ineq[bmap->n_ineq - 1] = t;
 633                 ISL_F_CLR(bmap, ISL_BASIC_MAP_NORMALIZED);
 634         }
 635         bmap->n_ineq--;
 636         return 0;
 637 }
 638
 639 int isl_basic_set_drop_inequality(struct isl_basic_set *bset, unsigned pos)
 640 {
 641         return isl_basic_map_drop_inequality((struct isl_basic_map *)bset, pos);
 642 }
 643
 644 int isl_basic_map_alloc_div(struct isl_basic_map *bmap)
 645 {
 646         if (!bmap)
 647                 return -1;
 648         isl_assert(bmap->ctx, bmap->n_div < bmap->extra, return -1);
 649         isl_seq_clr(bmap->div[bmap->n_div] +
 650                       1 + 1 + isl_basic_map_total_dim(bmap),
 651                       bmap->extra - bmap->n_div);
 652         ISL_F_CLR(bmap, ISL_BASIC_MAP_NORMALIZED_DIVS);
 653         return bmap->n_div++;
 654 }
 655
 656 int isl_basic_set_alloc_div(struct isl_basic_set *bset)
 657 {
 658         return isl_basic_map_alloc_div((struct isl_basic_map *)bset);
 659 }
 660
 661 int isl_basic_map_free_div(struct isl_basic_map *bmap, unsigned n)
 662 {
 663         if (!bmap)
 664                 return -1;
 665         isl_assert(bmap->ctx, n <= bmap->n_div, return -1);
 666         bmap->n_div -= n;
 667         return 0;
 668 }
 669
 670 int isl_basic_set_free_div(struct isl_basic_set *bset, unsigned n)
 671 {
 672         return isl_basic_map_free_div((struct isl_basic_map *)bset, n);
 673 }
 674
 675 /* Copy constraint from src to dst, putting the vars of src at offset
 676  * dim_off in dst and the divs of src at offset div_off in dst.
 677  * If both sets are actually map, then dim_off applies to the input
 678  * variables.
 679  */
 680 static void copy_constraint(struct isl_basic_map *dst_map, isl_int *dst,
 681                             struct isl_basic_map *src_map, isl_int *src,
 682                             unsigned in_off, unsigned out_off, unsigned div_off)
 683 {
 684         unsigned src_nparam = isl_basic_map_n_param(src_map);
 685         unsigned dst_nparam = isl_basic_map_n_param(dst_map);
 686         unsigned src_in = isl_basic_map_n_in(src_map);
 687         unsigned dst_in = isl_basic_map_n_in(dst_map);
 688         unsigned src_out = isl_basic_map_n_out(src_map);
 689         unsigned dst_out = isl_basic_map_n_out(dst_map);
 690         isl_int_set(dst[0], src[0]);
 691         isl_seq_cpy(dst+1, src+1, isl_min(dst_nparam, src_nparam));
 692         if (dst_nparam > src_nparam)
 693                 isl_seq_clr(dst+1+src_nparam,
 694                                 dst_nparam - src_nparam);
 695         isl_seq_clr(dst+1+dst_nparam, in_off);
 696         isl_seq_cpy(dst+1+dst_nparam+in_off,
 697                     src+1+src_nparam,
 698                     isl_min(dst_in-in_off, src_in));
 699         if (dst_in-in_off > src_in)
 700                 isl_seq_clr(dst+1+dst_nparam+in_off+src_in,
 701                                 dst_in - in_off - src_in);
 702         isl_seq_clr(dst+1+dst_nparam+dst_in, out_off);
 703         isl_seq_cpy(dst+1+dst_nparam+dst_in+out_off,
 704                     src+1+src_nparam+src_in,
 705                     isl_min(dst_out-out_off, src_out));
 706         if (dst_out-out_off > src_out)
 707                 isl_seq_clr(dst+1+dst_nparam+dst_in+out_off+src_out,
 708                                 dst_out - out_off - src_out);
 709         isl_seq_clr(dst+1+dst_nparam+dst_in+dst_out, div_off);
 710         isl_seq_cpy(dst+1+dst_nparam+dst_in+dst_out+div_off,
 711                     src+1+src_nparam+src_in+src_out,
 712                     isl_min(dst_map->extra-div_off, src_map->n_div));
 713         if (dst_map->n_div-div_off > src_map->n_div)
 714                 isl_seq_clr(dst+1+dst_nparam+dst_in+dst_out+
 715                                 div_off+src_map->n_div,
 716                                 dst_map->n_div - div_off - src_map->n_div);
 717 }
 718
 719 static void copy_div(struct isl_basic_map *dst_map, isl_int *dst,
 720                      struct isl_basic_map *src_map, isl_int *src,
 721                      unsigned in_off, unsigned out_off, unsigned div_off)
 722 {
 723         isl_int_set(dst[0], src[0]);
 724         copy_constraint(dst_map, dst+1, src_map, src+1, in_off, out_off, div_off);
 725 }
 726
 727 static struct isl_basic_map *add_constraints(struct isl_basic_map *bmap1,
 728                 struct isl_basic_map *bmap2, unsigned i_pos, unsigned o_pos)
 729 {
 730         int i;
 731         unsigned div_off;
 732
 733         if (!bmap1 || !bmap2)
 734                 goto error;
 735
 736         div_off = bmap1->n_div;
 737
 738         for (i = 0; i < bmap2->n_eq; ++i) {
 739                 int i1 = isl_basic_map_alloc_equality(bmap1);
 740                 if (i1 < 0)
 741                         goto error;
 742                 copy_constraint(bmap1, bmap1->eq[i1], bmap2, bmap2->eq[i],
 743                                 i_pos, o_pos, div_off);
 744         }
 745
 746         for (i = 0; i < bmap2->n_ineq; ++i) {
 747                 int i1 = isl_basic_map_alloc_inequality(bmap1);
 748                 if (i1 < 0)
 749                         goto error;
 750                 copy_constraint(bmap1, bmap1->ineq[i1], bmap2, bmap2->ineq[i],
 751                                 i_pos, o_pos, div_off);
 752         }
 753
 754         for (i = 0; i < bmap2->n_div; ++i) {
 755                 int i1 = isl_basic_map_alloc_div(bmap1);
 756                 if (i1 < 0)
 757                         goto error;
 758                 copy_div(bmap1, bmap1->div[i1], bmap2, bmap2->div[i],
 759                          i_pos, o_pos, div_off);
 760         }
 761
 762         isl_basic_map_free(bmap2);
 763
 764         return bmap1;
 765
 766 error:
 767         isl_basic_map_free(bmap1);
 768         isl_basic_map_free(bmap2);
 769         return NULL;
 770 }
 771
 772 static void copy_constraint_dim_map(isl_int *dst, isl_int *src,
 773                                         struct isl_dim_map *dim_map)
 774 {
 775         int i;
 776
 777         for (i = 0; i < dim_map->len; ++i) {
 778                 if (dim_map->pos[i] < 0)
 779                         isl_int_set_si(dst[i], 0);
 780                 else
 781                         isl_int_set(dst[i], src[dim_map->pos[i]]);
 782         }
 783 }
 784
 785 static void copy_div_dim_map(isl_int *dst, isl_int *src,
 786                                         struct isl_dim_map *dim_map)
 787 {
 788         isl_int_set(dst[0], src[0]);
 789         copy_constraint_dim_map(dst+1, src+1, dim_map);
 790 }
 791
 792 static struct isl_basic_map *add_constraints_dim_map(struct isl_basic_map *dst,
 793                 struct isl_basic_map *src, struct isl_dim_map *dim_map)
 794 {
 795         int i;
 796
 797         if (!src || !dst || !dim_map)
 798                 goto error;
 799
 800         for (i = 0; i < src->n_eq; ++i) {
 801                 int i1 = isl_basic_map_alloc_equality(dst);
 802                 if (i1 < 0)
 803                         goto error;
 804                 copy_constraint_dim_map(dst->eq[i1], src->eq[i], dim_map);
 805         }
 806
 807         for (i = 0; i < src->n_ineq; ++i) {
 808                 int i1 = isl_basic_map_alloc_inequality(dst);
 809                 if (i1 < 0)
 810                         goto error;
 811                 copy_constraint_dim_map(dst->ineq[i1], src->ineq[i], dim_map);
 812         }
 813
 814         for (i = 0; i < src->n_div; ++i) {
 815                 int i1 = isl_basic_map_alloc_div(dst);
 816                 if (i1 < 0)
 817                         goto error;
 818                 copy_div_dim_map(dst->div[i1], src->div[i], dim_map);
 819         }
 820
 821         free(dim_map);
 822         isl_basic_map_free(src);
 823
 824         return dst;
 825 error:
 826         free(dim_map);
 827         isl_basic_map_free(src);
 828         isl_basic_map_free(dst);
 829         return NULL;
 830 }
 831
 832 struct isl_basic_set *isl_basic_set_add_constraints(struct isl_basic_set *bset1,
 833                 struct isl_basic_set *bset2, unsigned pos)
 834 {
 835         return (struct isl_basic_set *)
 836                 add_constraints((struct isl_basic_map *)bset1,
 837                                 (struct isl_basic_map *)bset2, 0, pos);
 838 }
 839
 840 struct isl_basic_map *isl_basic_map_extend_dim(struct isl_basic_map *base,
 841                 struct isl_dim *dim, unsigned extra,
 842                 unsigned n_eq, unsigned n_ineq)
 843 {
 844         struct isl_basic_map *ext;
 845         unsigned flags;
 846         int dims_ok;
 847
 848         if (!dim)
 849                 goto error;
 850
 851         if (!base)
 852                 goto error;
 853
 854         dims_ok = isl_dim_equal(base->dim, dim) &&
 855                   base->extra >= base->n_div + extra;
 856
 857         if (dims_ok && room_for_con(base, n_eq + n_ineq) &&
 858                        room_for_ineq(base, n_ineq)) {
 859                 isl_dim_free(dim);
 860                 return base;
 861         }
 862
 863         isl_assert(base->ctx, base->dim->nparam <= dim->nparam, goto error);
 864         isl_assert(base->ctx, base->dim->n_in <= dim->n_in, goto error);
 865         isl_assert(base->ctx, base->dim->n_out <= dim->n_out, goto error);
 866         extra += base->extra;
 867         n_eq += base->n_eq;
 868         n_ineq += base->n_ineq;
 869
 870         ext = isl_basic_map_alloc_dim(dim, extra, n_eq, n_ineq);
 871         dim = NULL;
 872         if (!ext)
 873                 goto error;
 874
 875         flags = base->flags;
 876         ext = add_constraints(ext, base, 0, 0);
 877         if (ext) {
 878                 ext->flags = flags;
 879                 ISL_F_CLR(ext, ISL_BASIC_SET_FINAL);
 880         }
 881
 882         return ext;
 883
 884 error:
 885         isl_dim_free(dim);
 886         isl_basic_map_free(base);
 887         return NULL;
 888 }
 889
 890 struct isl_basic_set *isl_basic_set_extend_dim(struct isl_basic_set *base,
 891                 struct isl_dim *dim, unsigned extra,
 892                 unsigned n_eq, unsigned n_ineq)
 893 {
 894         return (struct isl_basic_set *)
 895                 isl_basic_map_extend_dim((struct isl_basic_map *)base, dim,
 896                                                         extra, n_eq, n_ineq);
 897 }
 898
 899 struct isl_basic_map *isl_basic_map_extend_constraints(
 900                 struct isl_basic_map *base, unsigned n_eq, unsigned n_ineq)
 901 {
 902         if (!base)
 903                 return NULL;
 904         return isl_basic_map_extend_dim(base, isl_dim_copy(base->dim),
 905                                         0, n_eq, n_ineq);
 906 }
 907
 908 struct isl_basic_map *isl_basic_map_extend(struct isl_basic_map *base,
 909                 unsigned nparam, unsigned n_in, unsigned n_out, unsigned extra,
 910                 unsigned n_eq, unsigned n_ineq)
 911 {
 912         struct isl_basic_map *bmap;
 913         struct isl_dim *dim;
 914
 915         if (!base)
 916                 return NULL;
 917         dim = isl_dim_alloc(base->ctx, nparam, n_in, n_out);
 918         if (!dim)
 919                 return NULL;
 920
 921         bmap = isl_basic_map_extend_dim(base, dim, extra, n_eq, n_ineq);
 922         return bmap;
 923 }
 924
 925 struct isl_basic_set *isl_basic_set_extend(struct isl_basic_set *base,
 926                 unsigned nparam, unsigned dim, unsigned extra,
 927                 unsigned n_eq, unsigned n_ineq)
 928 {
 929         return (struct isl_basic_set *)
 930                 isl_basic_map_extend((struct isl_basic_map *)base,
 931                                         nparam, 0, dim, extra, n_eq, n_ineq);
 932 }
 933
 934 struct isl_basic_set *isl_basic_set_extend_constraints(
 935                 struct isl_basic_set *base, unsigned n_eq, unsigned n_ineq)
 936 {
 937         return (struct isl_basic_set *)
 938                 isl_basic_map_extend_constraints((struct isl_basic_map *)base,
 939                                                     n_eq, n_ineq);
 940 }
 941
 942 struct isl_basic_set *isl_basic_set_cow(struct isl_basic_set *bset)
 943 {
 944         return (struct isl_basic_set *)
 945                 isl_basic_map_cow((struct isl_basic_map *)bset);
 946 }
 947
 948 struct isl_basic_map *isl_basic_map_cow(struct isl_basic_map *bmap)
 949 {
 950         if (!bmap)
 951                 return NULL;
 952
 953         if (bmap->ref > 1) {
 954                 bmap->ref--;
 955                 bmap = isl_basic_map_dup(bmap);
 956         }
 957         ISL_F_CLR(bmap, ISL_BASIC_SET_FINAL);
 958         return bmap;
 959 }
 960
 961 struct isl_set *isl_set_cow(struct isl_set *set)
 962 {
 963         if (!set)
 964                 return NULL;
 965
 966         if (set->ref == 1)
 967                 return set;
 968         set->ref--;
 969         return isl_set_dup(set);
 970 }
 971
 972 struct isl_map *isl_map_cow(struct isl_map *map)
 973 {
 974         if (!map)
 975                 return NULL;
 976
 977         if (map->ref == 1)
 978                 return map;
 979         map->ref--;
 980         return isl_map_dup(map);
 981 }
 982
 983 static void swap_vars(struct isl_blk blk, isl_int *a,
 984                         unsigned a_len, unsigned b_len)
 985 {
 986         isl_seq_cpy(blk.data, a+a_len, b_len);
 987         isl_seq_cpy(blk.data+b_len, a, a_len);
 988         isl_seq_cpy(a, blk.data, b_len+a_len);
 989 }
 990
 991 struct isl_basic_set *isl_basic_set_swap_vars(
 992                 struct isl_basic_set *bset, unsigned n)
 993 {
 994         int i;
 995         struct isl_blk blk;
 996         unsigned dim;
 997         unsigned nparam;
 998
 999         if (!bset)
1000                 goto error;
1001
1002         nparam = isl_basic_set_n_param(bset);
1003         dim = isl_basic_set_n_dim(bset);
1004         isl_assert(bset->ctx, n <= dim, goto error);
1005
1006         if (n == dim)
1007                 return bset;
1008
1009         bset = isl_basic_set_cow(bset);
1010         if (!bset)
1011                 return NULL;
1012
1013         blk = isl_blk_alloc(bset->ctx, dim);
1014         if (isl_blk_is_error(blk))
1015                 goto error;
1016
1017         for (i = 0; i < bset->n_eq; ++i)
1018                 swap_vars(blk,
1019                           bset->eq[i]+1+nparam, n, dim - n);
1020
1021         for (i = 0; i < bset->n_ineq; ++i)
1022                 swap_vars(blk,
1023                           bset->ineq[i]+1+nparam, n, dim - n);
1024
1025         for (i = 0; i < bset->n_div; ++i)
1026                 swap_vars(blk,
1027                           bset->div[i]+1+1+nparam, n, dim - n);
1028
1029         isl_blk_free(bset->ctx, blk);
1030
1031         ISL_F_CLR(bset, ISL_BASIC_SET_NORMALIZED);
1032         return bset;
1033
1034 error:
1035         isl_basic_set_free(bset);
1036         return NULL;
1037 }
1038
1039 struct isl_set *isl_set_swap_vars(struct isl_set *set, unsigned n)
1040 {
1041         int i;
1042         set = isl_set_cow(set);
1043         if (!set)
1044                 return NULL;
1045
1046         for (i = 0; i < set->n; ++i) {
1047                 set->p[i] = isl_basic_set_swap_vars(set->p[i], n);
1048                 if (!set->p[i]) {
1049                         isl_set_free(set);
1050                         return NULL;
1051                 }
1052         }
1053         ISL_F_CLR(set, ISL_SET_NORMALIZED);
1054         return set;
1055 }
1056
1057 struct isl_basic_map *isl_basic_map_set_to_empty(struct isl_basic_map *bmap)
1058 {
1059         int i = 0;
1060         unsigned total;
1061         if (!bmap)
1062                 goto error;
1063         total = isl_basic_map_total_dim(bmap);
1064         isl_basic_map_free_div(bmap, bmap->n_div);
1065         isl_basic_map_free_inequality(bmap, bmap->n_ineq);
1066         if (bmap->n_eq > 0)
1067                 isl_basic_map_free_equality(bmap, bmap->n_eq-1);
1068         else {
1069                 isl_basic_map_alloc_equality(bmap);
1070                 if (i < 0)
1071                         goto error;
1072         }
1073         isl_int_set_si(bmap->eq[i][0], 1);
1074         isl_seq_clr(bmap->eq[i]+1, total);
1075         ISL_F_SET(bmap, ISL_BASIC_MAP_EMPTY);
1076         return isl_basic_map_finalize(bmap);
1077 error:
1078         isl_basic_map_free(bmap);
1079         return NULL;
1080 }
1081
1082 struct isl_basic_set *isl_basic_set_set_to_empty(struct isl_basic_set *bset)
1083 {
1084         return (struct isl_basic_set *)
1085                 isl_basic_map_set_to_empty((struct isl_basic_map *)bset);
1086 }
1087
1088 void isl_basic_map_swap_div(struct isl_basic_map *bmap, int a, int b)
1089 {
1090         int i;
1091         unsigned off = isl_dim_total(bmap->dim);
1092         isl_int *t = bmap->div[a];
1093         bmap->div[a] = bmap->div[b];
1094         bmap->div[b] = t;
1095
1096         for (i = 0; i < bmap->n_eq; ++i)
1097                 isl_int_swap(bmap->eq[i][1+off+a], bmap->eq[i][1+off+b]);
1098
1099         for (i = 0; i < bmap->n_ineq; ++i)
1100                 isl_int_swap(bmap->ineq[i][1+off+a], bmap->ineq[i][1+off+b]);
1101
1102         for (i = 0; i < bmap->n_div; ++i)
1103                 isl_int_swap(bmap->div[i][1+1+off+a], bmap->div[i][1+1+off+b]);
1104         ISL_F_CLR(bmap, ISL_BASIC_MAP_NORMALIZED);
1105 }
1106
1107 /* Eliminate the specified n dimensions starting at first from the
1108  * constraints using Fourier-Motzkin, The dimensions themselves
1109  * are not removed.
1110  */
1111 struct isl_set *isl_set_eliminate_dims(struct isl_set *set,
1112         unsigned first, unsigned n)
1113 {
1114         int i;
1115         unsigned nparam;
1116
1117         if (!set)
1118                 return NULL;
1119         if (n == 0)
1120                 return set;
1121
1122         set = isl_set_cow(set);
1123         if (!set)
1124                 return NULL;
1125         isl_assert(set->ctx, first+n <= isl_set_n_dim(set), goto error);
1126         nparam = isl_set_n_param(set);
1127
1128         for (i = 0; i < set->n; ++i) {
1129                 set->p[i] = isl_basic_set_eliminate_vars(set->p[i],
1130                                                             nparam + first, n);
1131                 if (!set->p[i])
1132                         goto error;
1133         }
1134         return set;
1135 error:
1136         isl_set_free(set);
1137         return NULL;
1138 }
1139
1140 /* Project out n dimensions starting at first using Fourier-Motzkin */
1141 struct isl_set *isl_set_remove_dims(struct isl_set *set,
1142         unsigned first, unsigned n)
1143 {
1144         set = isl_set_eliminate_dims(set, first, n);
1145         set = isl_set_drop_dims(set, first, n);
1146         return set;
1147 }
1148
1149 struct isl_basic_set *isl_basic_set_remove_divs(struct isl_basic_set *bset)
1150 {
1151         bset = isl_basic_set_eliminate_vars(bset, isl_dim_total(bset->dim),
1152                                                 bset->n_div);
1153         if (!bset)
1154                 return NULL;
1155         bset->n_div = 0;
1156         return bset;
1157 }
1158
1159 struct isl_set *isl_set_remove_divs(struct isl_set *set)
1160 {
1161         int i;
1162
1163         if (!set)
1164                 return NULL;
1165         if (set->n == 0)
1166                 return set;
1167
1168         set = isl_set_cow(set);
1169         if (!set)
1170                 return NULL;
1171
1172         for (i = 0; i < set->n; ++i) {
1173                 set->p[i] = isl_basic_set_remove_divs(set->p[i]);
1174                 if (!set->p[i])
1175                         goto error;
1176         }
1177         return set;
1178 error:
1179         isl_set_free(set);
1180         return NULL;
1181 }
1182
1183 struct isl_basic_map *isl_basic_map_remove(struct isl_basic_map *bmap,
1184         enum isl_dim_type type, unsigned first, unsigned n)
1185 {
1186         if (!bmap)
1187                 return NULL;
1188         isl_assert(bmap->ctx, first + n <= isl_basic_map_dim(bmap, type),
1189                         goto error);
1190         if (n == 0)
1191                 return bmap;
1192         bmap = isl_basic_map_eliminate_vars(bmap,
1193                         isl_basic_map_offset(bmap, type) - 1 + first, n);
1194         bmap = isl_basic_map_drop(bmap, type, first, n);
1195         return bmap;
1196 error:
1197         isl_basic_map_free(bmap);
1198         return NULL;
1199 }
1200
1201 struct isl_map *isl_map_remove(struct isl_map *map,
1202         enum isl_dim_type type, unsigned first, unsigned n)
1203 {
1204         int i;
1205         unsigned nparam;
1206
1207         if (n == 0)
1208                 return map;
1209
1210         map = isl_map_cow(map);
1211         if (!map)
1212                 return NULL;
1213         isl_assert(map->ctx, first + n <= isl_map_dim(map, type), goto error);
1214
1215         for (i = 0; i < map->n; ++i) {
1216                 map->p[i] = isl_basic_map_eliminate_vars(map->p[i],
1217                         isl_basic_map_offset(map->p[i], type) - 1 + first, n);
1218                 if (!map->p[i])
1219                         goto error;
1220         }
1221         map = isl_map_drop(map, type, first, n);
1222         return map;
1223 error:
1224         isl_map_free(map);
1225         return NULL;
1226 }
1227
1228 /* Project out n inputs starting at first using Fourier-Motzkin */
1229 struct isl_map *isl_map_remove_inputs(struct isl_map *map,
1230         unsigned first, unsigned n)
1231 {
1232         return isl_map_remove(map, isl_dim_in, first, n);
1233 }
1234
1235 /* Project out n dimensions starting at first using Fourier-Motzkin */
1236 struct isl_basic_set *isl_basic_set_remove_dims(struct isl_basic_set *bset,
1237         unsigned first, unsigned n)
1238 {
1239         unsigned nparam = isl_basic_set_n_param(bset);
1240         bset = isl_basic_set_eliminate_vars(bset, nparam + first, n);
1241         bset = isl_basic_set_drop_dims(bset, first, n);
1242         return bset;
1243 }
1244
1245 static void dump_term(struct isl_basic_map *bmap,
1246                         isl_int c, int pos, FILE *out)
1247 {
1248         const char *name;
1249         unsigned in = isl_basic_map_n_in(bmap);
1250         unsigned dim = in + isl_basic_map_n_out(bmap);
1251         unsigned nparam = isl_basic_map_n_param(bmap);
1252         if (!pos)
1253                 isl_int_print(out, c, 0);
1254         else {
1255                 if (!isl_int_is_one(c))
1256                         isl_int_print(out, c, 0);
1257                 if (pos < 1 + nparam) {
1258                         name = isl_dim_get_name(bmap->dim,
1259                                                 isl_dim_param, pos - 1);
1260                         if (name)
1261                                 fprintf(out, "%s", name);
1262                         else
1263                                 fprintf(out, "p%d", pos - 1);
1264                 } else if (pos < 1 + nparam + in)
1265                         fprintf(out, "i%d", pos - 1 - nparam);
1266                 else if (pos < 1 + nparam + dim)
1267                         fprintf(out, "o%d", pos - 1 - nparam - in);
1268                 else
1269                         fprintf(out, "e%d", pos - 1 - nparam - dim);
1270         }
1271 }
1272
1273 static void dump_constraint_sign(struct isl_basic_map *bmap, isl_int *c,
1274                                 int sign, FILE *out)
1275 {
1276         int i;
1277         int first;
1278         unsigned len = 1 + isl_basic_map_total_dim(bmap);
1279         isl_int v;
1280
1281         isl_int_init(v);
1282         for (i = 0, first = 1; i < len; ++i) {
1283                 if (isl_int_sgn(c[i]) * sign <= 0)
1284                         continue;
1285                 if (!first)
1286                         fprintf(out, " + ");
1287                 first = 0;
1288                 isl_int_abs(v, c[i]);
1289                 dump_term(bmap, v, i, out);
1290         }
1291         isl_int_clear(v);
1292         if (first)
1293                 fprintf(out, "0");
1294 }
1295
1296 static void dump_constraint(struct isl_basic_map *bmap, isl_int *c,
1297                                 const char *op, FILE *out, int indent)
1298 {
1299         int i;
1300
1301         fprintf(out, "%*s", indent, "");
1302
1303         dump_constraint_sign(bmap, c, 1, out);
1304         fprintf(out, " %s ", op);
1305         dump_constraint_sign(bmap, c, -1, out);
1306
1307         fprintf(out, "\n");
1308
1309         for (i = bmap->n_div; i < bmap->extra; ++i) {
1310                 if (isl_int_is_zero(c[1+isl_dim_total(bmap->dim)+i]))
1311                         continue;
1312                 fprintf(out, "%*s", indent, "");
1313                 fprintf(out, "ERROR: unused div coefficient not zero\n");
1314                 abort();
1315         }
1316 }
1317
1318 static void dump_constraints(struct isl_basic_map *bmap,
1319                                 isl_int **c, unsigned n,
1320                                 const char *op, FILE *out, int indent)
1321 {
1322         int i;
1323
1324         for (i = 0; i < n; ++i)
1325                 dump_constraint(bmap, c[i], op, out, indent);
1326 }
1327
1328 static void dump_affine(struct isl_basic_map *bmap, isl_int *exp, FILE *out)
1329 {
1330         int j;
1331         int first = 1;
1332         unsigned total = isl_basic_map_total_dim(bmap);
1333
1334         for (j = 0; j < 1 + total; ++j) {
1335                 if (isl_int_is_zero(exp[j]))
1336                         continue;
1337                 if (!first && isl_int_is_pos(exp[j]))
1338                         fprintf(out, "+");
1339                 dump_term(bmap, exp[j], j, out);
1340                 first = 0;
1341         }
1342 }
1343
1344 static void dump(struct isl_basic_map *bmap, FILE *out, int indent)
1345 {
1346         int i;
1347
1348         dump_constraints(bmap, bmap->eq, bmap->n_eq, "=", out, indent);
1349         dump_constraints(bmap, bmap->ineq, bmap->n_ineq, ">=", out, indent);
1350
1351         for (i = 0; i < bmap->n_div; ++i) {
1352                 fprintf(out, "%*s", indent, "");
1353                 fprintf(out, "e%d = [(", i);
1354                 dump_affine(bmap, bmap->div[i]+1, out);
1355                 fprintf(out, ")/");
1356                 isl_int_print(out, bmap->div[i][0], 0);
1357                 fprintf(out, "]\n");
1358         }
1359 }
1360
1361 void isl_basic_set_dump(struct isl_basic_set *bset, FILE *out, int indent)
1362 {
1363         if (!bset) {
1364                 fprintf(out, "null basic set\n");
1365                 return;
1366         }
1367
1368         fprintf(out, "%*s", indent, "");
1369         fprintf(out, "ref: %d, nparam: %d, dim: %d, extra: %d, flags: %x\n",
1370                         bset->ref, bset->dim->nparam, bset->dim->n_out,
1371                         bset->extra, bset->flags);
1372         dump((struct isl_basic_map *)bset, out, indent);
1373 }
1374
1375 void isl_basic_map_dump(struct isl_basic_map *bmap, FILE *out, int indent)
1376 {
1377         if (!bmap) {
1378                 fprintf(out, "null basic map\n");
1379                 return;
1380         }
1381
1382         fprintf(out, "%*s", indent, "");
1383         fprintf(out, "ref: %d, nparam: %d, in: %d, out: %d, extra: %d, "
1384                         "flags: %x, n_name: %d\n",
1385                 bmap->ref,
1386                 bmap->dim->nparam, bmap->dim->n_in, bmap->dim->n_out,
1387                 bmap->extra, bmap->flags, bmap->dim->n_name);
1388         dump(bmap, out, indent);
1389 }
1390
1391 int isl_inequality_negate(struct isl_basic_map *bmap, unsigned pos)
1392 {
1393         unsigned total;
1394         if (!bmap)
1395                 return -1;
1396         total = isl_basic_map_total_dim(bmap);
1397         isl_assert(bmap->ctx, pos < bmap->n_ineq, return -1);
1398         isl_seq_neg(bmap->ineq[pos], bmap->ineq[pos], 1 + total);
1399         isl_int_sub_ui(bmap->ineq[pos][0], bmap->ineq[pos][0], 1);
1400         ISL_F_CLR(bmap, ISL_BASIC_MAP_NORMALIZED);
1401         return 0;
1402 }
1403
1404 struct isl_set *isl_set_alloc_dim(struct isl_dim *dim, int n, unsigned flags)
1405 {
1406         struct isl_set *set;
1407
1408         if (!dim)
1409                 return NULL;
1410         isl_assert(dim->ctx, dim->n_in == 0, return NULL);
1411         isl_assert(dim->ctx, n >= 0, return NULL);
1412         set = isl_alloc(dim->ctx, struct isl_set,
1413                         sizeof(struct isl_set) +
1414                         n * sizeof(struct isl_basic_set *));
1415         if (!set)
1416                 goto error;
1417
1418         set->ctx = dim->ctx;
1419         isl_ctx_ref(set->ctx);
1420         set->ref = 1;
1421         set->size = n;
1422         set->n = 0;
1423         set->dim = dim;
1424         set->flags = flags;
1425         return set;
1426 error:
1427         isl_dim_free(dim);
1428         return NULL;
1429 }
1430
1431 struct isl_set *isl_set_alloc(struct isl_ctx *ctx,
1432                 unsigned nparam, unsigned dim, int n, unsigned flags)
1433 {
1434         struct isl_set *set;
1435         struct isl_dim *dims;
1436
1437         dims = isl_dim_alloc(ctx, nparam, 0, dim);
1438         if (!dims)
1439                 return NULL;
1440
1441         set = isl_set_alloc_dim(dims, n, flags);
1442         return set;
1443 }
1444
1445 /* Make sure "map" has room for at least "n" more basic maps.
1446  */
1447 struct isl_map *isl_map_grow(struct isl_map *map, int n)
1448 {
1449         int i;
1450         struct isl_map *grown = NULL;
1451
1452         if (!map)
1453                 return NULL;
1454         isl_assert(map->ctx, n >= 0, goto error);
1455         if (map->n + n <= map->size)
1456                 return map;
1457         grown = isl_map_alloc_dim(isl_map_get_dim(map), map->n + n, map->flags);
1458         if (!grown)
1459                 goto error;
1460         for (i = 0; i < map->n; ++i) {
1461                 grown->p[i] = isl_basic_map_copy(map->p[i]);
1462                 if (!grown->p[i])
1463                         goto error;
1464                 grown->n++;
1465         }
1466         isl_map_free(map);
1467         return grown;
1468 error:
1469         isl_map_free(grown);
1470         isl_map_free(map);
1471         return NULL;
1472 }
1473
1474 /* Make sure "set" has room for at least "n" more basic sets.
1475  */
1476 struct isl_set *isl_set_grow(struct isl_set *set, int n)
1477 {
1478         return (struct isl_set *)isl_map_grow((struct isl_map *)set, n);
1479 }
1480
1481 struct isl_set *isl_set_dup(struct isl_set *set)
1482 {
1483         int i;
1484         struct isl_set *dup;
1485
1486         if (!set)
1487                 return NULL;
1488
1489         dup = isl_set_alloc_dim(isl_dim_copy(set->dim), set->n, set->flags);
1490         if (!dup)
1491                 return NULL;
1492         for (i = 0; i < set->n; ++i)
1493                 dup = isl_set_add(dup, isl_basic_set_copy(set->p[i]));
1494         return dup;
1495 }
1496
1497 struct isl_set *isl_set_from_basic_set(struct isl_basic_set *bset)
1498 {
1499         struct isl_set *set;
1500
1501         if (!bset)
1502                 return NULL;
1503
1504         set = isl_set_alloc_dim(isl_dim_copy(bset->dim), 1, ISL_MAP_DISJOINT);
1505         if (!set) {
1506                 isl_basic_set_free(bset);
1507                 return NULL;
1508         }
1509         return isl_set_add(set, bset);
1510 }
1511
1512 struct isl_map *isl_map_from_basic_map(struct isl_basic_map *bmap)
1513 {
1514         struct isl_map *map;
1515
1516         if (!bmap)
1517                 return NULL;
1518
1519         map = isl_map_alloc_dim(isl_dim_copy(bmap->dim), 1, ISL_MAP_DISJOINT);
1520         if (!map) {
1521                 isl_basic_map_free(bmap);
1522                 return NULL;
1523         }
1524         return isl_map_add(map, bmap);
1525 }
1526
1527 struct isl_set *isl_set_add(struct isl_set *set, struct isl_basic_set *bset)
1528 {
1529         return (struct isl_set *)isl_map_add((struct isl_map *)set,
1530                                                 (struct isl_basic_map *)bset);
1531 }
1532
1533 void isl_set_free(struct isl_set *set)
1534 {
1535         int i;
1536
1537         if (!set)
1538                 return;
1539
1540         if (--set->ref > 0)
1541                 return;
1542
1543         isl_ctx_deref(set->ctx);
1544         for (i = 0; i < set->n; ++i)
1545                 isl_basic_set_free(set->p[i]);
1546         isl_dim_free(set->dim);
1547         free(set);
1548 }
1549
1550 void isl_set_dump(struct isl_set *set, FILE *out, int indent)
1551 {
1552         int i;
1553
1554         if (!set) {
1555                 fprintf(out, "null set\n");
1556                 return;
1557         }
1558
1559         fprintf(out, "%*s", indent, "");
1560         fprintf(out, "ref: %d, n: %d, nparam: %d, dim: %d, flags: %x\n",
1561                         set->ref, set->n, set->dim->nparam, set->dim->n_out,
1562                         set->flags);
1563         for (i = 0; i < set->n; ++i) {
1564                 fprintf(out, "%*s", indent, "");
1565                 fprintf(out, "basic set %d:\n", i);
1566                 isl_basic_set_dump(set->p[i], out, indent+4);
1567         }
1568 }
1569
1570 void isl_map_dump(struct isl_map *map, FILE *out, int indent)
1571 {
1572         int i;
1573
1574         if (!map) {
1575                 fprintf(out, "null map\n");
1576                 return;
1577         }
1578
1579         fprintf(out, "%*s", indent, "");
1580         fprintf(out, "ref: %d, n: %d, nparam: %d, in: %d, out: %d, "
1581                      "flags: %x, n_name: %d\n",
1582                         map->ref, map->n, map->dim->nparam, map->dim->n_in,
1583                         map->dim->n_out, map->flags, map->dim->n_name);
1584         for (i = 0; i < map->n; ++i) {
1585                 fprintf(out, "%*s", indent, "");
1586                 fprintf(out, "basic map %d:\n", i);
1587                 isl_basic_map_dump(map->p[i], out, indent+4);
1588         }
1589 }
1590
1591 struct isl_basic_map *isl_basic_map_intersect_domain(
1592                 struct isl_basic_map *bmap, struct isl_basic_set *bset)
1593 {
1594         struct isl_basic_map *bmap_domain;
1595         struct isl_dim *dim;
1596
1597         if (!bmap || !bset)
1598                 goto error;
1599
1600         isl_assert(bset->ctx, isl_dim_match(bmap->dim, isl_dim_param,
1601                                         bset->dim, isl_dim_param), goto error);
1602
1603         if (isl_dim_size(bset->dim, isl_dim_set) != 0)
1604                 isl_assert(bset->ctx,
1605                     isl_basic_map_compatible_domain(bmap, bset), goto error);
1606
1607         bmap = isl_basic_map_cow(bmap);
1608         bmap = isl_basic_map_extend_dim(bmap, isl_dim_copy(bmap->dim),
1609                         bset->n_div, bset->n_eq, bset->n_ineq);
1610         if (!bmap)
1611                 goto error;
1612         dim = isl_dim_reverse(isl_dim_copy(bset->dim));
1613         bmap_domain = isl_basic_map_from_basic_set(bset, dim);
1614         bmap = add_constraints(bmap, bmap_domain, 0, 0);
1615
1616         bmap = isl_basic_map_simplify(bmap);
1617         return isl_basic_map_finalize(bmap);
1618 error:
1619         isl_basic_map_free(bmap);
1620         isl_basic_set_free(bset);
1621         return NULL;
1622 }
1623
1624 struct isl_basic_map *isl_basic_map_intersect_range(
1625                 struct isl_basic_map *bmap, struct isl_basic_set *bset)
1626 {
1627         struct isl_basic_map *bmap_range;
1628
1629         if (!bmap || !bset)
1630                 goto error;
1631
1632         isl_assert(bset->ctx, isl_dim_match(bmap->dim, isl_dim_param,
1633                                         bset->dim, isl_dim_param), goto error);
1634
1635         if (isl_dim_size(bset->dim, isl_dim_set) != 0)
1636                 isl_assert(bset->ctx,
1637                     isl_basic_map_compatible_range(bmap, bset), goto error);
1638
1639         bmap = isl_basic_map_cow(bmap);
1640         bmap = isl_basic_map_extend_dim(bmap, isl_dim_copy(bmap->dim),
1641                         bset->n_div, bset->n_eq, bset->n_ineq);
1642         if (!bmap)
1643                 goto error;
1644         bmap_range = isl_basic_map_from_basic_set(bset, isl_dim_copy(bset->dim));
1645         bmap = add_constraints(bmap, bmap_range, 0, 0);
1646
1647         bmap = isl_basic_map_simplify(bmap);
1648         return isl_basic_map_finalize(bmap);
1649 error:
1650         isl_basic_map_free(bmap);
1651         isl_basic_set_free(bset);
1652         return NULL;
1653 }
1654
1655 static int basic_map_contains(struct isl_basic_map *bmap, struct isl_vec *vec)
1656 {
1657         int i;
1658         unsigned total;
1659         isl_int s;
1660
1661         total = 1 + isl_basic_map_total_dim(bmap);
1662         if (total != vec->size)
1663                 return -1;
1664
1665         isl_int_init(s);
1666
1667         for (i = 0; i < bmap->n_eq; ++i) {
1668                 isl_seq_inner_product(vec->el, bmap->eq[i], total, &s);
1669                 if (!isl_int_is_zero(s)) {
1670                         isl_int_clear(s);
1671                         return 0;
1672                 }
1673         }
1674
1675         for (i = 0; i < bmap->n_ineq; ++i) {
1676                 isl_seq_inner_product(vec->el, bmap->ineq[i], total, &s);
1677                 if (isl_int_is_neg(s)) {
1678                         isl_int_clear(s);
1679                         return 0;
1680                 }
1681         }
1682
1683         isl_int_clear(s);
1684
1685         return 1;
1686 }
1687
1688 int isl_basic_set_contains(struct isl_basic_set *bset, struct isl_vec *vec)
1689 {
1690         return basic_map_contains((struct isl_basic_map *)bset, vec);
1691 }
1692
1693 struct isl_basic_map *isl_basic_map_intersect(
1694                 struct isl_basic_map *bmap1, struct isl_basic_map *bmap2)
1695 {
1696         struct isl_vec *sample = NULL;
1697
1698         if (!bmap1 || !bmap2)
1699                 goto error;
1700
1701         isl_assert(bmap1->ctx, isl_dim_match(bmap1->dim, isl_dim_param,
1702                                      bmap2->dim, isl_dim_param), goto error);
1703         if (isl_dim_total(bmap1->dim) ==
1704                                 isl_dim_size(bmap1->dim, isl_dim_param) &&
1705             isl_dim_total(bmap2->dim) !=
1706                                 isl_dim_size(bmap2->dim, isl_dim_param))
1707                 return isl_basic_map_intersect(bmap2, bmap1);
1708
1709         if (isl_dim_total(bmap2->dim) !=
1710                                         isl_dim_size(bmap2->dim, isl_dim_param))
1711                 isl_assert(bmap1->ctx,
1712                             isl_dim_equal(bmap1->dim, bmap2->dim), goto error);
1713
1714         if (bmap1->sample &&
1715             basic_map_contains(bmap1, bmap1->sample) > 0 &&
1716             basic_map_contains(bmap2, bmap1->sample) > 0)
1717                 sample = isl_vec_copy(bmap1->sample);
1718         else if (bmap2->sample &&
1719             basic_map_contains(bmap1, bmap2->sample) > 0 &&
1720             basic_map_contains(bmap2, bmap2->sample) > 0)
1721                 sample = isl_vec_copy(bmap2->sample);
1722
1723         bmap1 = isl_basic_map_cow(bmap1);
1724         bmap1 = isl_basic_map_extend_dim(bmap1, isl_dim_copy(bmap1->dim),
1725                         bmap2->n_div, bmap2->n_eq, bmap2->n_ineq);
1726         if (!bmap1)
1727                 goto error;
1728         bmap1 = add_constraints(bmap1, bmap2, 0, 0);
1729
1730         if (sample) {
1731                 isl_vec_free(bmap1->sample);
1732                 bmap1->sample = sample;
1733         }
1734
1735         bmap1 = isl_basic_map_simplify(bmap1);
1736         return isl_basic_map_finalize(bmap1);
1737 error:
1738         if (sample)
1739                 isl_vec_free(sample);
1740         isl_basic_map_free(bmap1);
1741         isl_basic_map_free(bmap2);
1742         return NULL;
1743 }
1744
1745 struct isl_basic_set *isl_basic_set_intersect(
1746                 struct isl_basic_set *bset1, struct isl_basic_set *bset2)
1747 {
1748         return (struct isl_basic_set *)
1749                 isl_basic_map_intersect(
1750                         (struct isl_basic_map *)bset1,
1751                         (struct isl_basic_map *)bset2);
1752 }
1753
1754 struct isl_map *isl_map_intersect(struct isl_map *map1, struct isl_map *map2)
1755 {
1756         unsigned flags = 0;
1757         struct isl_map *result;
1758         int i, j;
1759
1760         if (!map1 || !map2)
1761                 goto error;
1762
1763         isl_assert(map1->ctx, isl_dim_match(map1->dim, isl_dim_param,
1764                                          map2->dim, isl_dim_param), goto error);
1765         if (isl_dim_total(map1->dim) ==
1766                                 isl_dim_size(map1->dim, isl_dim_param) &&
1767             isl_dim_total(map2->dim) != isl_dim_size(map2->dim, isl_dim_param))
1768                 return isl_map_intersect(map2, map1);
1769
1770         if (isl_dim_total(map2->dim) != isl_dim_size(map2->dim, isl_dim_param))
1771                 isl_assert(map1->ctx,
1772                             isl_dim_equal(map1->dim, map2->dim), goto error);
1773
1774         if (ISL_F_ISSET(map1, ISL_MAP_DISJOINT) &&
1775             ISL_F_ISSET(map2, ISL_MAP_DISJOINT))
1776                 ISL_FL_SET(flags, ISL_MAP_DISJOINT);
1777
1778         result = isl_map_alloc_dim(isl_dim_copy(map1->dim),
1779                                 map1->n * map2->n, flags);
1780         if (!result)
1781                 goto error;
1782         for (i = 0; i < map1->n; ++i)
1783                 for (j = 0; j < map2->n; ++j) {
1784                         struct isl_basic_map *part;
1785                         part = isl_basic_map_intersect(
1786                                     isl_basic_map_copy(map1->p[i]),
1787                                     isl_basic_map_copy(map2->p[j]));
1788                         if (isl_basic_map_is_empty(part))
1789                                 isl_basic_map_free(part);
1790                         else
1791                                 result = isl_map_add(result, part);
1792                         if (!result)
1793                                 goto error;
1794                 }
1795         isl_map_free(map1);
1796         isl_map_free(map2);
1797         return result;
1798 error:
1799         isl_map_free(map1);
1800         isl_map_free(map2);
1801         return NULL;
1802 }
1803
1804 struct isl_set *isl_set_intersect(struct isl_set *set1, struct isl_set *set2)
1805 {
1806         return (struct isl_set *)
1807                 isl_map_intersect((struct isl_map *)set1,
1808                                   (struct isl_map *)set2);
1809 }
1810
1811 struct isl_basic_map *isl_basic_map_reverse(struct isl_basic_map *bmap)
1812 {
1813         struct isl_dim *dim;
1814         struct isl_basic_set *bset;
1815         unsigned in;
1816
1817         if (!bmap)
1818                 return NULL;
1819         bmap = isl_basic_map_cow(bmap);
1820         if (!bmap)
1821                 return NULL;
1822         dim = isl_dim_reverse(isl_dim_copy(bmap->dim));
1823         in = isl_basic_map_n_in(bmap);
1824         bset = isl_basic_set_from_basic_map(bmap);
1825         bset = isl_basic_set_swap_vars(bset, in);
1826         return isl_basic_map_from_basic_set(bset, dim);
1827 }
1828
1829 /* Turn final n dimensions into existentially quantified variables.
1830  */
1831 struct isl_basic_set *isl_basic_set_project_out(
1832                 struct isl_basic_set *bset, unsigned n, unsigned flags)
1833 {
1834         int i;
1835         size_t row_size;
1836         isl_int **new_div;
1837         isl_int *old;
1838
1839         if (!bset)
1840                 return NULL;
1841
1842         isl_assert(bset->ctx, n <= isl_basic_set_n_dim(bset), goto error);
1843
1844         if (n == 0)
1845                 return bset;
1846
1847         bset = isl_basic_set_cow(bset);
1848
1849         row_size = 1 + isl_dim_total(bset->dim) + bset->extra;
1850         old = bset->block2.data;
1851         bset->block2 = isl_blk_extend(bset->ctx, bset->block2,
1852                                         (bset->extra + n) * (1 + row_size));
1853         if (!bset->block2.data)
1854                 goto error;
1855         new_div = isl_alloc_array(ctx, isl_int *, bset->extra + n);
1856         if (!new_div)
1857                 goto error;
1858         for (i = 0; i < n; ++i) {
1859                 new_div[i] = bset->block2.data +
1860                                 (bset->extra + i) * (1 + row_size);
1861                 isl_seq_clr(new_div[i], 1 + row_size);
1862         }
1863         for (i = 0; i < bset->extra; ++i)
1864                 new_div[n + i] = bset->block2.data + (bset->div[i] - old);
1865         free(bset->div);
1866         bset->div = new_div;
1867         bset->n_div += n;
1868         bset->extra += n;
1869         bset->dim = isl_dim_drop_outputs(bset->dim,
1870                                             isl_basic_set_n_dim(bset) - n, n);
1871         if (!bset->dim)
1872                 goto error;
1873         bset = isl_basic_set_simplify(bset);
1874         return isl_basic_set_finalize(bset);
1875 error:
1876         isl_basic_set_free(bset);
1877         return NULL;
1878 }
1879
1880 static struct isl_basic_map *add_divs(struct isl_basic_map *bmap, unsigned n)
1881 {
1882         int i, j;
1883
1884         for (i = 0; i < n; ++i) {
1885                 j = isl_basic_map_alloc_div(bmap);
1886                 if (j < 0)
1887                         goto error;
1888                 isl_seq_clr(bmap->div[j], 1+1+isl_basic_map_total_dim(bmap));
1889         }
1890         return bmap;
1891 error:
1892         isl_basic_map_free(bmap);
1893         return NULL;
1894 }
1895
1896 struct isl_basic_map *isl_basic_map_apply_range(
1897                 struct isl_basic_map *bmap1, struct isl_basic_map *bmap2)
1898 {
1899         struct isl_dim *dim_result = NULL;
1900         struct isl_basic_map *bmap;
1901         unsigned n_in, n_out, n, nparam, total, pos;
1902         struct isl_dim_map *dim_map1, *dim_map2;
1903
1904         if (!bmap1 || !bmap2)
1905                 goto error;
1906
1907         dim_result = isl_dim_join(isl_dim_copy(bmap1->dim),
1908                                   isl_dim_copy(bmap2->dim));
1909
1910         n_in = isl_basic_map_n_in(bmap1);
1911         n_out = isl_basic_map_n_out(bmap2);
1912         n = isl_basic_map_n_out(bmap1);
1913         nparam = isl_basic_map_n_param(bmap1);
1914
1915         total = nparam + n_in + n_out + bmap1->n_div + bmap2->n_div + n;
1916         dim_map1 = isl_dim_map_alloc(bmap1->ctx, total);
1917         dim_map2 = isl_dim_map_alloc(bmap1->ctx, total);
1918         isl_dim_map_dim(dim_map1, bmap1->dim, isl_dim_param, pos = 0);
1919         isl_dim_map_dim(dim_map2, bmap2->dim, isl_dim_param, pos = 0);
1920         isl_dim_map_dim(dim_map1, bmap1->dim, isl_dim_in, pos += nparam);
1921         isl_dim_map_dim(dim_map2, bmap2->dim, isl_dim_out, pos += n_in);
1922         isl_dim_map_div(dim_map1, bmap1, pos += n_out);
1923         isl_dim_map_div(dim_map2, bmap2, pos += bmap1->n_div);
1924         isl_dim_map_dim(dim_map1, bmap1->dim, isl_dim_out, pos += bmap2->n_div);
1925         isl_dim_map_dim(dim_map2, bmap2->dim, isl_dim_in, pos);
1926
1927         bmap = isl_basic_map_alloc_dim(dim_result,
1928                         bmap1->n_div + bmap2->n_div + n,
1929                         bmap1->n_eq + bmap2->n_eq,
1930                         bmap1->n_ineq + bmap2->n_ineq);
1931         bmap = add_constraints_dim_map(bmap, bmap1, dim_map1);
1932         bmap = add_constraints_dim_map(bmap, bmap2, dim_map2);
1933         bmap = add_divs(bmap, n);
1934         bmap = isl_basic_map_simplify(bmap);
1935         return isl_basic_map_finalize(bmap);
1936 error:
1937         isl_basic_map_free(bmap1);
1938         isl_basic_map_free(bmap2);
1939         return NULL;
1940 }
1941
1942 struct isl_basic_set *isl_basic_set_apply(
1943                 struct isl_basic_set *bset, struct isl_basic_map *bmap)
1944 {
1945         if (!bset || !bmap)
1946                 goto error;
1947
1948         isl_assert(set->ctx, isl_basic_map_compatible_domain(bmap, bset),
1949                     goto error);
1950
1951         return (struct isl_basic_set *)
1952                 isl_basic_map_apply_range((struct isl_basic_map *)bset, bmap);
1953 error:
1954         isl_basic_set_free(bset);
1955         isl_basic_map_free(bmap);
1956         return NULL;
1957 }
1958
1959 struct isl_basic_map *isl_basic_map_apply_domain(
1960                 struct isl_basic_map *bmap1, struct isl_basic_map *bmap2)
1961 {
1962         if (!bmap1 || !bmap2)
1963                 goto error;
1964
1965         isl_assert(ctx,
1966             isl_basic_map_n_in(bmap1) == isl_basic_map_n_in(bmap2), goto error);
1967         isl_assert(ctx,
1968             isl_basic_map_n_param(bmap1) == isl_basic_map_n_param(bmap2),
1969             goto error);
1970
1971         bmap1 = isl_basic_map_reverse(bmap1);
1972         bmap1 = isl_basic_map_apply_range(bmap1, bmap2);
1973         return isl_basic_map_reverse(bmap1);
1974 error:
1975         isl_basic_map_free(bmap1);
1976         isl_basic_map_free(bmap2);
1977         return NULL;
1978 }
1979
1980 /* Given two basic maps A -> f(A) and B -> g(B), construct a basic map
1981  * A \cap B -> f(A) + f(B)
1982  */
1983 struct isl_basic_map *isl_basic_map_sum(
1984                 struct isl_basic_map *bmap1, struct isl_basic_map *bmap2)
1985 {
1986         unsigned n_in, n_out, nparam, total, pos;
1987         struct isl_basic_map *bmap = NULL;
1988         struct isl_dim_map *dim_map1, *dim_map2;
1989         int i;
1990
1991         if (!bmap1 || !bmap2)
1992                 goto error;
1993
1994         isl_assert(bmap1->ctx, isl_dim_equal(bmap1->dim, bmap2->dim),
1995                 goto error);
1996
1997         nparam = isl_basic_map_n_param(bmap1);
1998         n_in = isl_basic_map_n_in(bmap1);
1999         n_out = isl_basic_map_n_out(bmap1);
2000
2001         total = nparam + n_in + n_out + bmap1->n_div + bmap2->n_div + 2 * n_out;
2002         dim_map1 = isl_dim_map_alloc(bmap1->ctx, total);
2003         dim_map2 = isl_dim_map_alloc(bmap2->ctx, total);
2004         isl_dim_map_dim(dim_map1, bmap1->dim, isl_dim_param, pos = 0);
2005         isl_dim_map_dim(dim_map2, bmap2->dim, isl_dim_param, pos);
2006         isl_dim_map_dim(dim_map1, bmap1->dim, isl_dim_in, pos += nparam);
2007         isl_dim_map_dim(dim_map2, bmap2->dim, isl_dim_in, pos);
2008         isl_dim_map_div(dim_map1, bmap1, pos += n_in + n_out);
2009         isl_dim_map_div(dim_map2, bmap2, pos += bmap1->n_div);
2010         isl_dim_map_dim(dim_map1, bmap1->dim, isl_dim_out, pos += bmap2->n_div);
2011         isl_dim_map_dim(dim_map2, bmap2->dim, isl_dim_out, pos += n_out);
2012
2013         bmap = isl_basic_map_alloc_dim(isl_dim_copy(bmap1->dim),
2014                         bmap1->n_div + bmap2->n_div + 2 * n_out,
2015                         bmap1->n_eq + bmap2->n_eq + n_out,
2016                         bmap1->n_ineq + bmap2->n_ineq);
2017         for (i = 0; i < n_out; ++i) {
2018                 int j = isl_basic_map_alloc_equality(bmap);
2019                 if (j < 0)
2020                         goto error;
2021                 isl_seq_clr(bmap->eq[j], 1+total);
2022                 isl_int_set_si(bmap->eq[j][1+nparam+n_in+i], -1);
2023                 isl_int_set_si(bmap->eq[j][1+pos+i], 1);
2024                 isl_int_set_si(bmap->eq[j][1+pos-n_out+i], 1);
2025         }
2026         bmap = add_constraints_dim_map(bmap, bmap1, dim_map1);
2027         bmap = add_constraints_dim_map(bmap, bmap2, dim_map2);
2028         bmap = add_divs(bmap, 2 * n_out);
2029
2030         bmap = isl_basic_map_simplify(bmap);
2031         return isl_basic_map_finalize(bmap);
2032 error:
2033         isl_basic_map_free(bmap);
2034         isl_basic_map_free(bmap1);
2035         isl_basic_map_free(bmap2);
2036         return NULL;
2037 }
2038
2039 /* Given a basic map A -> f(A), construct A -> -f(A).
2040  */
2041 struct isl_basic_map *isl_basic_map_neg(struct isl_basic_map *bmap)
2042 {
2043         int i, j;
2044         unsigned off, n;
2045
2046         bmap = isl_basic_map_cow(bmap);
2047         if (!bmap)
2048                 return NULL;
2049
2050         n = isl_basic_map_dim(bmap, isl_dim_out);
2051         off = isl_basic_map_offset(bmap, isl_dim_out);
2052         for (i = 0; i < bmap->n_eq; ++i)
2053                 for (j = 0; j < n; ++j)
2054                         isl_int_neg(bmap->eq[i][off+j], bmap->eq[i][off+j]);
2055         for (i = 0; i < bmap->n_ineq; ++i)
2056                 for (j = 0; j < n; ++j)
2057                         isl_int_neg(bmap->ineq[i][off+j], bmap->ineq[i][off+j]);
2058         for (i = 0; i < bmap->n_div; ++i)
2059                 for (j = 0; j < n; ++j)
2060                         isl_int_neg(bmap->div[i][1+off+j], bmap->div[i][1+off+j]);
2061         return isl_basic_map_finalize(bmap);
2062 }
2063
2064 /* Given a basic map A -> f(A) and an integer d, construct a basic map
2065  * A -> floor(f(A)/d).
2066  */
2067 struct isl_basic_map *isl_basic_map_floordiv(struct isl_basic_map *bmap,
2068                 isl_int d)
2069 {
2070         unsigned n_in, n_out, nparam, total, pos;
2071         struct isl_basic_map *result = NULL;
2072         struct isl_dim_map *dim_map;
2073         int i;
2074
2075         if (!bmap)
2076                 return NULL;
2077
2078         nparam = isl_basic_map_n_param(bmap);
2079         n_in = isl_basic_map_n_in(bmap);
2080         n_out = isl_basic_map_n_out(bmap);
2081
2082         total = nparam + n_in + n_out + bmap->n_div + n_out;
2083         dim_map = isl_dim_map_alloc(bmap->ctx, total);
2084         isl_dim_map_dim(dim_map, bmap->dim, isl_dim_param, pos = 0);
2085         isl_dim_map_dim(dim_map, bmap->dim, isl_dim_in, pos += nparam);
2086         isl_dim_map_div(dim_map, bmap, pos += n_in + n_out);
2087         isl_dim_map_dim(dim_map, bmap->dim, isl_dim_out, pos += bmap->n_div);
2088
2089         result = isl_basic_map_alloc_dim(isl_dim_copy(bmap->dim),
2090                         bmap->n_div + n_out,
2091                         bmap->n_eq, bmap->n_ineq + 2 * n_out);
2092         result = add_constraints_dim_map(result, bmap, dim_map);
2093         result = add_divs(result, n_out);
2094         for (i = 0; i < n_out; ++i) {
2095                 int j;
2096                 j = isl_basic_map_alloc_inequality(result);
2097                 if (j < 0)
2098                         goto error;
2099                 isl_seq_clr(result->ineq[j], 1+total);
2100                 isl_int_neg(result->ineq[j][1+nparam+n_in+i], d);
2101                 isl_int_set_si(result->ineq[j][1+pos+i], 1);
2102                 j = isl_basic_map_alloc_inequality(result);
2103                 if (j < 0)
2104                         goto error;
2105                 isl_seq_clr(result->ineq[j], 1+total);
2106                 isl_int_set(result->ineq[j][1+nparam+n_in+i], d);
2107                 isl_int_set_si(result->ineq[j][1+pos+i], -1);
2108                 isl_int_sub_ui(result->ineq[j][0], d, 1);
2109         }
2110
2111         result = isl_basic_map_simplify(result);
2112         return isl_basic_map_finalize(result);
2113 error:
2114         isl_basic_map_free(result);
2115         return NULL;
2116 }
2117
2118 static struct isl_basic_map *var_equal(struct isl_basic_map *bmap, unsigned pos)
2119 {
2120         int i;
2121         unsigned nparam;
2122         unsigned n_in;
2123
2124         i = isl_basic_map_alloc_equality(bmap);
2125         if (i < 0)
2126                 goto error;
2127         nparam = isl_basic_map_n_param(bmap);
2128         n_in = isl_basic_map_n_in(bmap);
2129         isl_seq_clr(bmap->eq[i], 1 + isl_basic_map_total_dim(bmap));
2130         isl_int_set_si(bmap->eq[i][1+nparam+pos], -1);
2131         isl_int_set_si(bmap->eq[i][1+nparam+n_in+pos], 1);
2132         return isl_basic_map_finalize(bmap);
2133 error:
2134         isl_basic_map_free(bmap);
2135         return NULL;
2136 }
2137
2138 static struct isl_basic_map *var_more(struct isl_basic_map *bmap, unsigned pos)
2139 {
2140         int i;
2141         unsigned nparam;
2142         unsigned n_in;
2143
2144         i = isl_basic_map_alloc_inequality(bmap);
2145         if (i < 0)
2146                 goto error;
2147         nparam = isl_basic_map_n_param(bmap);
2148         n_in = isl_basic_map_n_in(bmap);
2149         isl_seq_clr(bmap->ineq[i], 1 + isl_basic_map_total_dim(bmap));
2150         isl_int_set_si(bmap->ineq[i][0], -1);
2151         isl_int_set_si(bmap->ineq[i][1+nparam+pos], -1);
2152         isl_int_set_si(bmap->ineq[i][1+nparam+n_in+pos], 1);
2153         return isl_basic_map_finalize(bmap);
2154 error:
2155         isl_basic_map_free(bmap);
2156         return NULL;
2157 }
2158
2159 static struct isl_basic_map *var_less(struct isl_basic_map *bmap, unsigned pos)
2160 {
2161         int i;
2162         unsigned nparam;
2163         unsigned n_in;
2164
2165         i = isl_basic_map_alloc_inequality(bmap);
2166         if (i < 0)
2167                 goto error;
2168         nparam = isl_basic_map_n_param(bmap);
2169         n_in = isl_basic_map_n_in(bmap);
2170         isl_seq_clr(bmap->ineq[i], 1 + isl_basic_map_total_dim(bmap));
2171         isl_int_set_si(bmap->ineq[i][0], -1);
2172         isl_int_set_si(bmap->ineq[i][1+nparam+pos], 1);
2173         isl_int_set_si(bmap->ineq[i][1+nparam+n_in+pos], -1);
2174         return isl_basic_map_finalize(bmap);
2175 error:
2176         isl_basic_map_free(bmap);
2177         return NULL;
2178 }
2179
2180 struct isl_basic_map *isl_basic_map_equal(struct isl_dim *dim, unsigned n_equal)
2181 {
2182         int i;
2183         struct isl_basic_map *bmap;
2184         bmap = isl_basic_map_alloc_dim(dim, 0, n_equal, 0);
2185         if (!bmap)
2186                 return NULL;
2187         for (i = 0; i < n_equal && bmap; ++i)
2188                 bmap = var_equal(bmap, i);
2189         return isl_basic_map_finalize(bmap);
2190 }
2191
2192 struct isl_basic_map *isl_basic_map_less_at(struct isl_dim *dim, unsigned pos)
2193 {
2194         int i;
2195         struct isl_basic_map *bmap;
2196         bmap = isl_basic_map_alloc_dim(dim, 0, pos, 1);
2197         if (!bmap)
2198                 return NULL;
2199         for (i = 0; i < pos && bmap; ++i)
2200                 bmap = var_equal(bmap, i);
2201         if (bmap)
2202                 bmap = var_less(bmap, pos);
2203         return isl_basic_map_finalize(bmap);
2204 }
2205
2206 struct isl_basic_map *isl_basic_map_more_at(struct isl_dim *dim, unsigned pos)
2207 {
2208         int i;
2209         struct isl_basic_map *bmap;
2210         bmap = isl_basic_map_alloc_dim(dim, 0, pos, 1);
2211         if (!bmap)
2212                 return NULL;
2213         for (i = 0; i < pos && bmap; ++i)
2214                 bmap = var_equal(bmap, i);
2215         if (bmap)
2216                 bmap = var_more(bmap, pos);
2217         return isl_basic_map_finalize(bmap);
2218 }
2219
2220 struct isl_basic_map *isl_basic_map_from_basic_set(
2221                 struct isl_basic_set *bset, struct isl_dim *dim)
2222 {
2223         struct isl_basic_map *bmap;
2224
2225         bset = isl_basic_set_cow(bset);
2226         if (!bset || !dim)
2227                 goto error;
2228
2229         isl_assert(bset->ctx, isl_dim_compatible(bset->dim, dim), goto error);
2230         isl_dim_free(bset->dim);
2231         bmap = (struct isl_basic_map *) bset;
2232         bmap->dim = dim;
2233         return isl_basic_map_finalize(bmap);
2234 error:
2235         isl_basic_set_free(bset);
2236         isl_dim_free(dim);
2237         return NULL;
2238 }
2239
2240 struct isl_basic_set *isl_basic_set_from_basic_map(struct isl_basic_map *bmap)
2241 {
2242         if (!bmap)
2243                 goto error;
2244         if (bmap->dim->n_in == 0)
2245                 return (struct isl_basic_set *)bmap;
2246         bmap = isl_basic_map_cow(bmap);
2247         if (!bmap)
2248                 goto error;
2249         bmap->dim = isl_dim_cow(bmap->dim);
2250         if (!bmap->dim)
2251                 goto error;
2252         bmap->dim->n_out += bmap->dim->n_in;
2253         bmap->dim->n_in = 0;
2254         bmap = isl_basic_map_finalize(bmap);
2255         return (struct isl_basic_set *)bmap;
2256 error:
2257         isl_basic_map_free(bmap);
2258         return NULL;
2259 }
2260
2261 /* For a div d = floor(f/m), add the constraints
2262  *
2263  *              f - m d >= 0
2264  *              -(f-(n-1)) + m d >= 0
2265  *
2266  * Note that the second constraint is the negation of
2267  *
2268  *              f - m d >= n
2269  */
2270 static int add_div_constraints(struct isl_basic_map *bmap, unsigned div)
2271 {
2272         int i, j;
2273         unsigned total = isl_basic_map_total_dim(bmap);
2274         unsigned div_pos = 1 + total - bmap->n_div + div;
2275
2276         i = isl_basic_map_alloc_inequality(bmap);
2277         if (i < 0)
2278                 return -1;
2279         isl_seq_cpy(bmap->ineq[i], bmap->div[div]+1, 1+total);
2280         isl_int_neg(bmap->ineq[i][div_pos], bmap->div[div][0]);
2281
2282         j = isl_basic_map_alloc_inequality(bmap);
2283         if (j < 0)
2284                 return -1;
2285         isl_seq_neg(bmap->ineq[j], bmap->ineq[i], 1 + total);
2286         isl_int_add(bmap->ineq[j][0], bmap->ineq[j][0], bmap->ineq[j][div_pos]);
2287         isl_int_sub_ui(bmap->ineq[j][0], bmap->ineq[j][0], 1);
2288         return j;
2289 }
2290
2291 struct isl_basic_set *isl_basic_map_underlying_set(
2292                 struct isl_basic_map *bmap)
2293 {
2294         if (!bmap)
2295                 goto error;
2296         if (bmap->dim->nparam == 0 && bmap->dim->n_in == 0 && bmap->n_div == 0)
2297                 return (struct isl_basic_set *)bmap;
2298         bmap = isl_basic_map_cow(bmap);
2299         if (!bmap)
2300                 goto error;
2301         bmap->dim = isl_dim_underlying(bmap->dim, bmap->n_div);
2302         if (!bmap->dim)
2303                 goto error;
2304         bmap->extra -= bmap->n_div;
2305         bmap->n_div = 0;
2306         bmap = isl_basic_map_finalize(bmap);
2307         return (struct isl_basic_set *)bmap;
2308 error:
2309         return NULL;
2310 }
2311
2312 struct isl_basic_map *isl_basic_map_overlying_set(
2313         struct isl_basic_set *bset, struct isl_basic_map *like)
2314 {
2315         struct isl_basic_map *bmap;
2316         struct isl_ctx *ctx;
2317         unsigned total;
2318         int i;
2319
2320         if (!bset || !like)
2321                 goto error;
2322         ctx = bset->ctx;
2323         isl_assert(ctx, bset->n_div == 0, goto error);
2324         isl_assert(ctx, isl_basic_set_n_param(bset) == 0, goto error);
2325         isl_assert(ctx, bset->dim->n_out == isl_basic_map_total_dim(like),
2326                         goto error);
2327         if (isl_dim_equal(bset->dim, like->dim) && like->n_div == 0) {
2328                 isl_basic_map_free(like);
2329                 return (struct isl_basic_map *)bset;
2330         }
2331         bset = isl_basic_set_cow(bset);
2332         if (!bset)
2333                 goto error;
2334         total = bset->dim->n_out + bset->extra;
2335         bmap = (struct isl_basic_map *)bset;
2336         isl_dim_free(bmap->dim);
2337         bmap->dim = isl_dim_copy(like->dim);
2338         if (!bmap->dim)
2339                 goto error;
2340         bmap->n_div = like->n_div;
2341         bmap->extra += like->n_div;
2342         if (bmap->extra) {
2343                 unsigned ltotal;
2344                 ltotal = total - bmap->extra + like->extra;
2345                 if (ltotal > total)
2346                         ltotal = total;
2347                 bmap->block2 = isl_blk_extend(ctx, bmap->block2,
2348                                         bmap->extra * (1 + 1 + total));
2349                 if (isl_blk_is_error(bmap->block2))
2350                         goto error;
2351                 bmap->div = isl_realloc_array(ctx, bmap->div, isl_int *,
2352                                                 bmap->extra);
2353                 if (!bmap->div)
2354                         goto error;
2355                 for (i = 0; i < bmap->extra; ++i)
2356                         bmap->div[i] = bmap->block2.data + i * (1 + 1 + total);
2357                 for (i = 0; i < like->n_div; ++i) {
2358                         isl_seq_cpy(bmap->div[i], like->div[i], 1 + 1 + ltotal);
2359                         isl_seq_clr(bmap->div[i]+1+1+ltotal, total - ltotal);
2360                 }
2361                 bmap = isl_basic_map_extend_constraints(bmap,
2362                                                         0, 2 * like->n_div);
2363                 for (i = 0; i < like->n_div; ++i) {
2364                         if (isl_int_is_zero(bmap->div[i][0]))
2365                                 continue;
2366                         if (add_div_constraints(bmap, i) < 0)
2367                                 goto error;
2368                 }
2369         }
2370         isl_basic_map_free(like);
2371         bmap = isl_basic_map_simplify(bmap);
2372         bmap = isl_basic_map_finalize(bmap);
2373         return bmap;
2374 error:
2375         isl_basic_map_free(like);
2376         isl_basic_set_free(bset);
2377         return NULL;
2378 }
2379
2380 struct isl_basic_set *isl_basic_set_from_underlying_set(
2381         struct isl_basic_set *bset, struct isl_basic_set *like)
2382 {
2383         return (struct isl_basic_set *)
2384                 isl_basic_map_overlying_set(bset, (struct isl_basic_map *)like);
2385 }
2386
2387 struct isl_set *isl_set_from_underlying_set(
2388         struct isl_set *set, struct isl_basic_set *like)
2389 {
2390         int i;
2391
2392         if (!set || !like)
2393                 goto error;
2394         isl_assert(set->ctx, set->dim->n_out == isl_basic_set_total_dim(like),
2395                     goto error);
2396         if (isl_dim_equal(set->dim, like->dim) && like->n_div == 0) {
2397                 isl_basic_set_free(like);
2398                 return set;
2399         }
2400         set = isl_set_cow(set);
2401         if (!set)
2402                 goto error;
2403         for (i = 0; i < set->n; ++i) {
2404                 set->p[i] = isl_basic_set_from_underlying_set(set->p[i],
2405                                                       isl_basic_set_copy(like));
2406                 if (!set->p[i])
2407                         goto error;
2408         }
2409         isl_dim_free(set->dim);
2410         set->dim = isl_dim_copy(like->dim);
2411         if (!set->dim)
2412                 goto error;
2413         isl_basic_set_free(like);
2414         return set;
2415 error:
2416         isl_basic_set_free(like);
2417         isl_set_free(set);
2418         return NULL;
2419 }
2420
2421 struct isl_set *isl_map_underlying_set(struct isl_map *map)
2422 {
2423         int i;
2424
2425         map = isl_map_cow(map);
2426         if (!map)
2427                 return NULL;
2428         map->dim = isl_dim_cow(map->dim);
2429         if (!map->dim)
2430                 goto error;
2431
2432         for (i = 1; i < map->n; ++i)
2433                 isl_assert(map->ctx, map->p[0]->n_div == map->p[i]->n_div,
2434                                 goto error);
2435         for (i = 0; i < map->n; ++i) {
2436                 map->p[i] = (struct isl_basic_map *)
2437                                 isl_basic_map_underlying_set(map->p[i]);
2438                 if (!map->p[i])
2439                         goto error;
2440         }
2441         if (map->n == 0)
2442                 map->dim = isl_dim_underlying(map->dim, 0);
2443         else {
2444                 isl_dim_free(map->dim);
2445                 map->dim = isl_dim_copy(map->p[0]->dim);
2446         }
2447         if (!map->dim)
2448                 goto error;
2449         return (struct isl_set *)map;
2450 error:
2451         isl_map_free(map);
2452         return NULL;
2453 }
2454
2455 struct isl_set *isl_set_to_underlying_set(struct isl_set *set)
2456 {
2457         return (struct isl_set *)isl_map_underlying_set((struct isl_map *)set);
2458 }
2459
2460 struct isl_basic_set *isl_basic_map_domain(struct isl_basic_map *bmap)
2461 {
2462         struct isl_basic_set *domain;
2463         unsigned n_out;
2464         if (!bmap)
2465                 return NULL;
2466         n_out = isl_basic_map_n_out(bmap);
2467         domain = isl_basic_set_from_basic_map(bmap);
2468         return isl_basic_set_project_out(domain, n_out, 0);
2469 }
2470
2471 struct isl_basic_set *isl_basic_map_range(struct isl_basic_map *bmap)
2472 {
2473         return isl_basic_map_domain(isl_basic_map_reverse(bmap));
2474 }
2475
2476 struct isl_set *isl_map_range(struct isl_map *map)
2477 {
2478         int i;
2479         struct isl_set *set;
2480
2481         if (!map)
2482                 goto error;
2483         map = isl_map_cow(map);
2484         if (!map)
2485                 goto error;
2486
2487         set = (struct isl_set *) map;
2488         if (set->dim->n_in != 0) {
2489                 set->dim = isl_dim_drop_inputs(set->dim, 0, set->dim->n_in);
2490                 if (!set->dim)
2491                         goto error;
2492         }
2493         for (i = 0; i < map->n; ++i) {
2494                 set->p[i] = isl_basic_map_range(map->p[i]);
2495                 if (!set->p[i])
2496                         goto error;
2497         }
2498         ISL_F_CLR(set, ISL_MAP_DISJOINT);
2499         ISL_F_CLR(set, ISL_SET_NORMALIZED);
2500         return set;
2501 error:
2502         isl_map_free(map);
2503         return NULL;
2504 }
2505
2506 struct isl_map *isl_map_from_set(struct isl_set *set, struct isl_dim *dim)
2507 {
2508         int i;
2509         struct isl_map *map = NULL;
2510
2511         set = isl_set_cow(set);
2512         if (!set || !dim)
2513                 goto error;
2514         isl_assert(set->ctx, isl_dim_compatible(set->dim, dim), goto error);
2515         map = (struct isl_map *)set;
2516         for (i = 0; i < set->n; ++i) {
2517                 map->p[i] = isl_basic_map_from_basic_set(
2518                                 set->p[i], isl_dim_copy(dim));
2519                 if (!map->p[i])
2520                         goto error;
2521         }
2522         isl_dim_free(map->dim);
2523         map->dim = dim;
2524         return map;
2525 error:
2526         isl_dim_free(dim);
2527         isl_set_free(set);
2528         return NULL;
2529 }
2530
2531 struct isl_map *isl_map_from_range(struct isl_set *set)
2532 {
2533         return (struct isl_map *)set;
2534 }
2535
2536 struct isl_set *isl_set_from_map(struct isl_map *map)
2537 {
2538         int i;
2539         struct isl_set *set = NULL;
2540
2541         if (!map)
2542                 return NULL;
2543         map = isl_map_cow(map);
2544         if (!map)
2545                 return NULL;
2546         map->dim = isl_dim_cow(map->dim);
2547         if (!map->dim)
2548                 goto error;
2549         map->dim->n_out += map->dim->n_in;
2550         map->dim->n_in = 0;
2551         set = (struct isl_set *)map;
2552         for (i = 0; i < map->n; ++i) {
2553                 set->p[i] = isl_basic_set_from_basic_map(map->p[i]);
2554                 if (!set->p[i])
2555                         goto error;
2556         }
2557         return set;
2558 error:
2559         isl_map_free(map);
2560         return NULL;
2561 }
2562
2563 struct isl_map *isl_map_alloc_dim(struct isl_dim *dim, int n, unsigned flags)
2564 {
2565         struct isl_map *map;
2566
2567         if (!dim)
2568                 return NULL;
2569         isl_assert(dim->ctx, n >= 0, return NULL);
2570         map = isl_alloc(dim->ctx, struct isl_map,
2571                         sizeof(struct isl_map) +
2572                         n * sizeof(struct isl_basic_map *));
2573         if (!map)
2574                 goto error;
2575
2576         map->ctx = dim->ctx;
2577         isl_ctx_ref(map->ctx);
2578         map->ref = 1;
2579         map->size = n;
2580         map->n = 0;
2581         map->dim = dim;
2582         map->flags = flags;
2583         return map;
2584 error:
2585         isl_dim_free(dim);
2586         return NULL;
2587 }
2588
2589 struct isl_map *isl_map_alloc(struct isl_ctx *ctx,
2590                 unsigned nparam, unsigned in, unsigned out, int n,
2591                 unsigned flags)
2592 {
2593         struct isl_map *map;
2594         struct isl_dim *dims;
2595
2596         dims = isl_dim_alloc(ctx, nparam, in, out);
2597         if (!dims)
2598                 return NULL;
2599
2600         map = isl_map_alloc_dim(dims, n, flags);
2601         return map;
2602 }
2603
2604 struct isl_basic_map *isl_basic_map_empty(struct isl_ctx *ctx,
2605                 unsigned nparam, unsigned in, unsigned out)
2606 {
2607         struct isl_basic_map *bmap;
2608         bmap = isl_basic_map_alloc(ctx, nparam, in, out, 0, 1, 0);
2609         bmap = isl_basic_map_set_to_empty(bmap);
2610         return bmap;
2611 }
2612
2613 struct isl_basic_set *isl_basic_set_empty(struct isl_dim *dim)
2614 {
2615         struct isl_basic_set *bset;
2616         bset = isl_basic_set_alloc_dim(dim, 0, 1, 0);
2617         bset = isl_basic_set_set_to_empty(bset);
2618         return bset;
2619 }
2620
2621 struct isl_basic_map *isl_basic_map_empty_like(struct isl_basic_map *model)
2622 {
2623         struct isl_basic_map *bmap;
2624         if (!model)
2625                 return NULL;
2626         bmap = isl_basic_map_alloc_dim(isl_dim_copy(model->dim), 0, 1, 0);
2627         bmap = isl_basic_map_set_to_empty(bmap);
2628         return bmap;
2629 }
2630
2631 struct isl_basic_map *isl_basic_map_empty_like_map(struct isl_map *model)
2632 {
2633         struct isl_basic_map *bmap;
2634         if (!model)
2635                 return NULL;
2636         bmap = isl_basic_map_alloc_dim(isl_dim_copy(model->dim), 0, 1, 0);
2637         bmap = isl_basic_map_set_to_empty(bmap);
2638         return bmap;
2639 }
2640
2641 struct isl_basic_set *isl_basic_set_empty_like(struct isl_basic_set *model)
2642 {
2643         struct isl_basic_set *bset;
2644         if (!model)
2645                 return NULL;
2646         bset = isl_basic_set_alloc_dim(isl_dim_copy(model->dim), 0, 1, 0);
2647         bset = isl_basic_set_set_to_empty(bset);
2648         return bset;
2649 }
2650
2651 struct isl_basic_map *isl_basic_map_universe(struct isl_dim *dim)
2652 {
2653         struct isl_basic_map *bmap;
2654         bmap = isl_basic_map_alloc_dim(dim, 0, 0, 0);
2655         return bmap;
2656 }
2657
2658 struct isl_basic_set *isl_basic_set_universe(struct isl_dim *dim)
2659 {
2660         struct isl_basic_set *bset;
2661         bset = isl_basic_set_alloc_dim(dim, 0, 0, 0);
2662         return bset;
2663 }
2664
2665 struct isl_basic_set *isl_basic_set_universe_like(struct isl_basic_set *model)
2666 {
2667         if (!model)
2668                 return NULL;
2669         return isl_basic_set_alloc_dim(isl_dim_copy(model->dim), 0, 0, 0);
2670 }
2671
2672 struct isl_map *isl_map_empty(struct isl_dim *dim)
2673 {
2674         return isl_map_alloc_dim(dim, 0, ISL_MAP_DISJOINT);
2675 }
2676
2677 struct isl_map *isl_map_empty_like(struct isl_map *model)
2678 {
2679         if (!model)
2680                 return NULL;
2681         return isl_map_alloc_dim(isl_dim_copy(model->dim), 0, ISL_MAP_DISJOINT);
2682 }
2683
2684 struct isl_map *isl_map_empty_like_basic_map(struct isl_basic_map *model)
2685 {
2686         if (!model)
2687                 return NULL;
2688         return isl_map_alloc_dim(isl_dim_copy(model->dim), 0, ISL_MAP_DISJOINT);
2689 }
2690
2691 struct isl_set *isl_set_empty(struct isl_dim *dim)
2692 {
2693         return isl_set_alloc_dim(dim, 0, ISL_MAP_DISJOINT);
2694 }
2695
2696 struct isl_set *isl_set_empty_like(struct isl_set *model)
2697 {
2698         if (!model)
2699                 return NULL;
2700         return isl_set_empty(isl_dim_copy(model->dim));
2701 }
2702
2703 struct isl_map *isl_map_universe(struct isl_dim *dim)
2704 {
2705         struct isl_map *map;
2706         if (!dim)
2707                 return NULL;
2708         map = isl_map_alloc_dim(isl_dim_copy(dim), 1, ISL_MAP_DISJOINT);
2709         map = isl_map_add(map, isl_basic_map_universe(dim));
2710         return map;
2711 }
2712
2713 struct isl_set *isl_set_universe(struct isl_dim *dim)
2714 {
2715         struct isl_set *set;
2716         if (!dim)
2717                 return NULL;
2718         set = isl_set_alloc_dim(isl_dim_copy(dim), 1, ISL_MAP_DISJOINT);
2719         set = isl_set_add(set, isl_basic_set_universe(dim));
2720         return set;
2721 }
2722
2723 struct isl_map *isl_map_dup(struct isl_map *map)
2724 {
2725         int i;
2726         struct isl_map *dup;
2727
2728         if (!map)
2729                 return NULL;
2730         dup = isl_map_alloc_dim(isl_dim_copy(map->dim), map->n, map->flags);
2731         for (i = 0; i < map->n; ++i)
2732                 dup = isl_map_add(dup, isl_basic_map_copy(map->p[i]));
2733         return dup;
2734 }
2735
2736 struct isl_map *isl_map_add(struct isl_map *map, struct isl_basic_map *bmap)
2737 {
2738         if (!bmap || !map)
2739                 goto error;
2740         if (isl_basic_map_fast_is_empty(bmap)) {
2741                 isl_basic_map_free(bmap);
2742                 return map;
2743         }
2744         isl_assert(map->ctx, isl_dim_equal(map->dim, bmap->dim), goto error);
2745         isl_assert(map->ctx, map->n < map->size, goto error);
2746         map->p[map->n] = bmap;
2747         map->n++;
2748         ISL_F_CLR(map, ISL_MAP_NORMALIZED);
2749         return map;
2750 error:
2751         if (map)
2752                 isl_map_free(map);
2753         if (bmap)
2754                 isl_basic_map_free(bmap);
2755         return NULL;
2756 }
2757
2758 void isl_map_free(struct isl_map *map)
2759 {
2760         int i;
2761
2762         if (!map)
2763                 return;
2764
2765         if (--map->ref > 0)
2766                 return;
2767
2768         isl_ctx_deref(map->ctx);
2769         for (i = 0; i < map->n; ++i)
2770                 isl_basic_map_free(map->p[i]);
2771         isl_dim_free(map->dim);
2772         free(map);
2773 }
2774
2775 struct isl_map *isl_map_extend(struct isl_map *base,
2776                 unsigned nparam, unsigned n_in, unsigned n_out)
2777 {
2778         int i;
2779
2780         base = isl_map_cow(base);
2781         if (!base)
2782                 return NULL;
2783
2784         base->dim = isl_dim_extend(base->dim, nparam, n_in, n_out);
2785         if (!base->dim)
2786                 goto error;
2787         for (i = 0; i < base->n; ++i) {
2788                 base->p[i] = isl_basic_map_extend_dim(base->p[i],
2789                                 isl_dim_copy(base->dim), 0, 0, 0);
2790                 if (!base->p[i])
2791                         goto error;
2792         }
2793         return base;
2794 error:
2795         isl_map_free(base);
2796         return NULL;
2797 }
2798
2799 struct isl_set *isl_set_extend(struct isl_set *base,
2800                 unsigned nparam, unsigned dim)
2801 {
2802         return (struct isl_set *)isl_map_extend((struct isl_map *)base,
2803                                                         nparam, 0, dim);
2804 }
2805
2806 static struct isl_basic_map *isl_basic_map_fix_pos(struct isl_basic_map *bmap,
2807                 unsigned pos, int value)
2808 {
2809         int j;
2810
2811         bmap = isl_basic_map_cow(bmap);
2812         bmap = isl_basic_map_extend_constraints(bmap, 1, 0);
2813         j = isl_basic_map_alloc_equality(bmap);
2814         if (j < 0)
2815                 goto error;
2816         isl_seq_clr(bmap->eq[j] + 1, isl_basic_map_total_dim(bmap));
2817         isl_int_set_si(bmap->eq[j][pos], -1);
2818         isl_int_set_si(bmap->eq[j][0], value);
2819         bmap = isl_basic_map_simplify(bmap);
2820         return isl_basic_map_finalize(bmap);
2821 error:
2822         isl_basic_map_free(bmap);
2823         return NULL;
2824 }
2825
2826 struct isl_basic_map *isl_basic_map_fix_si(struct isl_basic_map *bmap,
2827                 enum isl_dim_type type, unsigned pos, int value)
2828 {
2829         if (!bmap)
2830                 return NULL;
2831         isl_assert(bmap->ctx, pos < isl_basic_map_dim(bmap, type), goto error);
2832         return isl_basic_map_fix_pos(bmap, isl_basic_map_offset(bmap, type) + pos,
2833                                         value);
2834 error:
2835         isl_basic_map_free(bmap);
2836         return NULL;
2837 }
2838
2839 struct isl_basic_set *isl_basic_set_fix_si(struct isl_basic_set *bset,
2840                 enum isl_dim_type type, unsigned pos, int value)
2841 {
2842         return (struct isl_basic_set *)
2843                 isl_basic_map_fix_si((struct isl_basic_map *)bset,
2844                                         type, pos, value);
2845 }
2846
2847 struct isl_basic_map *isl_basic_map_fix_input_si(struct isl_basic_map *bmap,
2848                 unsigned input, int value)
2849 {
2850         return isl_basic_map_fix_si(bmap, isl_dim_in, input, value);
2851 }
2852
2853 struct isl_basic_set *isl_basic_set_fix_dim_si(struct isl_basic_set *bset,
2854                 unsigned dim, int value)
2855 {
2856         return (struct isl_basic_set *)
2857                 isl_basic_map_fix_si((struct isl_basic_map *)bset,
2858                                         isl_dim_set, dim, value);
2859 }
2860
2861 struct isl_map *isl_map_fix_si(struct isl_map *map,
2862                 enum isl_dim_type type, unsigned pos, int value)
2863 {
2864         int i;
2865
2866         map = isl_map_cow(map);
2867         if (!map)
2868                 return NULL;
2869
2870         isl_assert(ctx, pos < isl_map_dim(map, type), goto error);
2871         for (i = 0; i < map->n; ++i) {
2872                 map->p[i] = isl_basic_map_fix_si(map->p[i], type, pos, value);
2873                 if (!map->p[i])
2874                         goto error;
2875         }
2876         ISL_F_CLR(map, ISL_MAP_NORMALIZED);
2877         return map;
2878 error:
2879         isl_map_free(map);
2880         return NULL;
2881 }
2882
2883 struct isl_map *isl_map_fix_input_si(struct isl_map *map,
2884                 unsigned input, int value)
2885 {
2886         return isl_map_fix_si(map, isl_dim_in, input, value);
2887 }
2888
2889 struct isl_set *isl_set_fix_dim_si(struct isl_set *set, unsigned dim, int value)
2890 {
2891         return (struct isl_set *)
2892                 isl_map_fix_si((struct isl_map *)set, isl_dim_set, dim, value);
2893 }
2894
2895 struct isl_basic_set *isl_basic_set_lower_bound_dim(struct isl_basic_set *bset,
2896         unsigned dim, isl_int value)
2897 {
2898         int j;
2899         unsigned nparam;
2900
2901         bset = isl_basic_set_cow(bset);
2902         bset = isl_basic_set_extend_constraints(bset, 0, 1);
2903         j = isl_basic_set_alloc_inequality(bset);
2904         if (j < 0)
2905                 goto error;
2906         isl_seq_clr(bset->ineq[j], 1 + isl_basic_set_total_dim(bset));
2907         isl_int_set_si(bset->ineq[j][1 + isl_basic_set_n_param(bset) + dim], 1);
2908         isl_int_neg(bset->ineq[j][0], value);
2909         bset = isl_basic_set_simplify(bset);
2910         return isl_basic_set_finalize(bset);
2911 error:
2912         isl_basic_set_free(bset);
2913         return NULL;
2914 }
2915
2916 struct isl_set *isl_set_lower_bound_dim(struct isl_set *set, unsigned dim,
2917                                         isl_int value)
2918 {
2919         int i;
2920
2921         set = isl_set_cow(set);
2922         if (!set)
2923                 return NULL;
2924
2925         isl_assert(set->ctx, dim < isl_set_n_dim(set), goto error);
2926         for (i = 0; i < set->n; ++i) {
2927                 set->p[i] = isl_basic_set_lower_bound_dim(set->p[i], dim, value);
2928                 if (!set->p[i])
2929                         goto error;
2930         }
2931         return set;
2932 error:
2933         isl_set_free(set);
2934         return NULL;
2935 }
2936
2937 struct isl_map *isl_map_reverse(struct isl_map *map)
2938 {
2939         int i;
2940         unsigned t;
2941
2942         map = isl_map_cow(map);
2943         if (!map)
2944                 return NULL;
2945
2946         map->dim = isl_dim_reverse(map->dim);
2947         if (!map->dim)
2948                 goto error;
2949         for (i = 0; i < map->n; ++i) {
2950                 map->p[i] = isl_basic_map_reverse(map->p[i]);
2951                 if (!map->p[i])
2952                         goto error;
2953         }
2954         ISL_F_CLR(map, ISL_MAP_NORMALIZED);
2955         return map;
2956 error:
2957         isl_map_free(map);
2958         return NULL;
2959 }
2960
2961 static struct isl_map *isl_basic_map_partial_lexopt(
2962                 struct isl_basic_map *bmap, struct isl_basic_set *dom,
2963                 struct isl_set **empty, int max)
2964 {
2965         if (!bmap)
2966                 goto error;
2967         if (bmap->ctx->pip == ISL_PIP_PIP)
2968                 return isl_pip_basic_map_lexopt(bmap, dom, empty, max);
2969         else
2970                 return isl_tab_basic_map_partial_lexopt(bmap, dom, empty, max);
2971 error:
2972         isl_basic_map_free(bmap);
2973         isl_basic_set_free(dom);
2974         if (empty)
2975                 *empty = NULL;
2976         return NULL;
2977 }
2978
2979 struct isl_map *isl_basic_map_partial_lexmax(
2980                 struct isl_basic_map *bmap, struct isl_basic_set *dom,
2981                 struct isl_set **empty)
2982 {
2983         return isl_basic_map_partial_lexopt(bmap, dom, empty, 1);
2984 }
2985
2986 struct isl_map *isl_basic_map_partial_lexmin(
2987                 struct isl_basic_map *bmap, struct isl_basic_set *dom,
2988                 struct isl_set **empty)
2989 {
2990         return isl_basic_map_partial_lexopt(bmap, dom, empty, 0);
2991 }
2992
2993 struct isl_set *isl_basic_set_partial_lexmin(
2994                 struct isl_basic_set *bset, struct isl_basic_set *dom,
2995                 struct isl_set **empty)
2996 {
2997         return (struct isl_set *)
2998                 isl_basic_map_partial_lexmin((struct isl_basic_map *)bset,
2999                         dom, empty);
3000 }
3001
3002 struct isl_set *isl_basic_set_partial_lexmax(
3003                 struct isl_basic_set *bset, struct isl_basic_set *dom,
3004                 struct isl_set **empty)
3005 {
3006         return (struct isl_set *)
3007                 isl_basic_map_partial_lexmax((struct isl_basic_map *)bset,
3008                         dom, empty);
3009 }
3010
3011 struct isl_set *isl_basic_set_lexmin(struct isl_basic_set *bset)
3012 {
3013         struct isl_basic_map *bmap = NULL;
3014         struct isl_basic_set *dom = NULL;
3015         struct isl_map *min;
3016         struct isl_dim *param_dim;
3017
3018         if (!bset)
3019                 goto error;
3020         bmap = isl_basic_map_from_basic_set(bset, isl_dim_copy(bset->dim));
3021         if (!bmap)
3022                 goto error;
3023         param_dim = isl_dim_domain(isl_dim_copy(bmap->dim));
3024         dom = isl_basic_set_universe(param_dim);
3025         if (!dom)
3026                 goto error;
3027         min = isl_basic_map_partial_lexmin(bmap, dom, NULL);
3028         return isl_map_range(min);
3029 error:
3030         isl_basic_map_free(bmap);
3031         return NULL;
3032 }
3033
3034 static struct isl_map *isl_map_reset_dim(struct isl_map *map,
3035         struct isl_dim *dim)
3036 {
3037         int i;
3038
3039         if (!map || !dim)
3040                 goto error;
3041
3042         for (i = 0; i < map->n; ++i) {
3043                 isl_dim_free(map->p[i]->dim);
3044                 map->p[i]->dim = isl_dim_copy(dim);
3045         }
3046         isl_dim_free(map->dim);
3047         map->dim = dim;
3048
3049         return map;
3050 error:
3051         isl_map_free(map);
3052         isl_dim_free(dim);
3053         return NULL;
3054 }
3055
3056 static struct isl_set *isl_set_reset_dim(struct isl_set *set,
3057         struct isl_dim *dim)
3058 {
3059         return (struct isl_set *) isl_map_reset_dim((struct isl_map *)set, dim);
3060 }
3061
3062 /* Apply a preimage specified by "mat" on the parameters of "bset".
3063  * bset is assumed to have only parameters and divs.
3064  */
3065 static struct isl_basic_set *basic_set_parameter_preimage(
3066         struct isl_basic_set *bset, struct isl_mat *mat)
3067 {
3068         unsigned nparam;
3069
3070         if (!bset || !mat)
3071                 goto error;
3072
3073         bset->dim = isl_dim_cow(bset->dim);
3074         if (!bset->dim)
3075                 goto error;
3076
3077         nparam = isl_basic_set_dim(bset, isl_dim_param);
3078
3079         isl_assert(bset->ctx, mat->n_row == 1 + nparam, goto error);
3080
3081         bset->dim->nparam = 0;
3082         bset->dim->n_out = nparam;
3083         bset = isl_basic_set_preimage(bset, mat);
3084         if (bset) {
3085                 bset->dim->nparam = bset->dim->n_out;
3086                 bset->dim->n_out = 0;
3087         }
3088         return bset;
3089 error:
3090         isl_mat_free(mat);
3091         isl_basic_set_free(bset);
3092         return NULL;
3093 }
3094
3095 /* Apply a preimage specified by "mat" on the parameters of "set".
3096  * set is assumed to have only parameters and divs.
3097  */
3098 static struct isl_set *set_parameter_preimage(
3099         struct isl_set *set, struct isl_mat *mat)
3100 {
3101         struct isl_dim *dim = NULL;
3102         unsigned nparam;
3103
3104         if (!set || !mat)
3105                 goto error;
3106
3107         dim = isl_dim_copy(set->dim);
3108         dim = isl_dim_cow(dim);
3109         if (!dim)
3110                 goto error;
3111
3112         nparam = isl_set_dim(set, isl_dim_param);
3113
3114         isl_assert(set->ctx, mat->n_row == 1 + nparam, goto error);
3115
3116         dim->nparam = 0;
3117         dim->n_out = nparam;
3118         isl_set_reset_dim(set, dim);
3119         set = isl_set_preimage(set, mat);
3120         if (!set)
3121                 goto error2;
3122         dim = isl_dim_copy(set->dim);
3123         dim = isl_dim_cow(dim);
3124         if (!dim)
3125                 goto error2;
3126         dim->nparam = dim->n_out;
3127         dim->n_out = 0;
3128         isl_set_reset_dim(set, dim);
3129         return set;
3130 error:
3131         isl_dim_free(dim);
3132         isl_mat_free(mat);
3133 error2:
3134         isl_set_free(set);
3135         return NULL;
3136 }
3137
3138 /* Intersect the basic set "bset" with the affine space specified by the
3139  * equalities in "eq".
3140  */
3141 static struct isl_basic_set *basic_set_append_equalities(
3142         struct isl_basic_set *bset, struct isl_mat *eq)
3143 {
3144         int i, k;
3145         unsigned len;
3146
3147         if (!bset || !eq)
3148                 goto error;
3149
3150         bset = isl_basic_set_extend_dim(bset, isl_dim_copy(bset->dim), 0,
3151                                         eq->n_row, 0);
3152         if (!bset)
3153                 goto error;
3154
3155         len = 1 + isl_dim_total(bset->dim) + bset->extra;
3156         for (i = 0; i < eq->n_row; ++i) {
3157                 k = isl_basic_set_alloc_equality(bset);
3158                 if (k < 0)
3159                         goto error;
3160                 isl_seq_cpy(bset->eq[k], eq->row[i], eq->n_col);
3161                 isl_seq_clr(bset->eq[k] + eq->n_col, len - eq->n_col);
3162         }
3163         isl_mat_free(eq);
3164
3165         return bset;
3166 error:
3167         isl_mat_free(eq);
3168         isl_basic_set_free(bset);
3169         return NULL;
3170 }
3171
3172 /* Intersect the set "set" with the affine space specified by the
3173  * equalities in "eq".
3174  */
3175 static struct isl_set *set_append_equalities(struct isl_set *set,
3176         struct isl_mat *eq)
3177 {
3178         int i;
3179
3180         if (!set || !eq)
3181                 goto error;
3182
3183         for (i = 0; i < set->n; ++i) {
3184                 set->p[i] = basic_set_append_equalities(set->p[i],
3185                                         isl_mat_copy(eq));
3186                 if (!set->p[i])
3187                         goto error;
3188         }
3189         isl_mat_free(eq);
3190         return set;
3191 error:
3192         isl_mat_free(eq);
3193         isl_set_free(set);
3194         return NULL;
3195 }
3196
3197 /* Project the given basic set onto its parameter domain, possibly introducing
3198  * new, explicit, existential variables in the constraints.
3199  * The input has parameters and (possibly implicit) existential variables.
3200  * The output has the same parameters, but only
3201  * explicit existentially quantified variables.
3202  *
3203  * The actual projection is performed by pip, but pip doesn't seem
3204  * to like equalities very much, so we first remove the equalities
3205  * among the parameters by performing a variable compression on
3206  * the parameters.  Afterward, an inverse transformation is performed
3207  * and the equalities among the parameters are inserted back in.
3208  */
3209 static struct isl_set *parameter_compute_divs(struct isl_basic_set *bset)
3210 {
3211         int i, j;
3212         struct isl_mat *eq;
3213         struct isl_mat *T, *T2;
3214         struct isl_set *set;
3215         unsigned nparam, n_div;
3216
3217         bset = isl_basic_set_cow(bset);
3218         if (!bset)
3219                 return NULL;
3220
3221         if (bset->n_eq == 0)
3222                 return isl_basic_set_lexmin(bset);
3223
3224         isl_basic_set_gauss(bset, NULL);
3225
3226         nparam = isl_basic_set_dim(bset, isl_dim_param);
3227         n_div = isl_basic_set_dim(bset, isl_dim_div);
3228
3229         for (i = 0, j = n_div - 1; i < bset->n_eq && j >= 0; --j) {
3230                 if (!isl_int_is_zero(bset->eq[i][1 + nparam + j]))
3231                         ++i;
3232         }
3233         if (i == bset->n_eq)
3234                 return isl_basic_set_lexmin(bset);
3235
3236         eq = isl_mat_sub_alloc(bset->ctx, bset->eq, i, bset->n_eq - i,
3237                 0, 1 + nparam);
3238         eq = isl_mat_cow(eq);
3239         T = isl_mat_variable_compression(isl_mat_copy(eq), &T2);
3240         bset = basic_set_parameter_preimage(bset, T);
3241
3242         set = isl_basic_set_lexmin(bset);
3243         set = set_parameter_preimage(set, T2);
3244         set = set_append_equalities(set, eq);
3245         return set;
3246 }
3247
3248 /* Compute an explicit representation for all the existentially
3249  * quantified variables.
3250  * The input and output dimensions are first turned into parameters.
3251  * compute_divs then returns a map with the same parameters and
3252  * no input or output dimensions and the dimension specification
3253  * is reset to that of the input.
3254  */
3255 static struct isl_map *compute_divs(struct isl_basic_map *bmap)
3256 {
3257         struct isl_basic_set *bset;
3258         struct isl_set *set;
3259         struct isl_map *map;
3260         struct isl_dim *dim, *orig_dim = NULL;
3261         unsigned         nparam;
3262         unsigned         n_in;
3263         unsigned         n_out;
3264
3265         bmap = isl_basic_map_cow(bmap);
3266         if (!bmap)
3267                 return NULL;
3268
3269         nparam = isl_basic_map_dim(bmap, isl_dim_param);
3270         n_in = isl_basic_map_dim(bmap, isl_dim_in);
3271         n_out = isl_basic_map_dim(bmap, isl_dim_out);
3272         dim = isl_dim_set_alloc(bmap->ctx, nparam + n_in + n_out, 0);
3273         if (!dim)
3274                 goto error;
3275
3276         orig_dim = bmap->dim;
3277         bmap->dim = dim;
3278         bset = (struct isl_basic_set *)bmap;
3279
3280         set = parameter_compute_divs(bset);
3281         map = (struct isl_map *)set;
3282         map = isl_map_reset_dim(map, orig_dim);
3283
3284         return map;
3285 error:
3286         isl_basic_map_free(bmap);
3287         return NULL;
3288 }
3289
3290 /* If bmap contains any unknown divs, then compute explicit
3291  * expressions for them.  However, this computation may be
3292  * quite expensive, so first try to remove divs that aren't
3293  * strictly needed.
3294  */
3295 struct isl_map *isl_basic_map_compute_divs(struct isl_basic_map *bmap)
3296 {
3297         int i;
3298         unsigned off;
3299
3300         if (!bmap)
3301                 return NULL;
3302         off = isl_dim_total(bmap->dim);
3303         for (i = 0; i < bmap->n_div; ++i) {
3304                 if (isl_int_is_zero(bmap->div[i][0]))
3305                         break;
3306                 isl_assert(bmap->ctx, isl_int_is_zero(bmap->div[i][1+1+off+i]),
3307                                 goto error);
3308         }
3309         if (i == bmap->n_div)
3310                 return isl_map_from_basic_map(bmap);
3311         bmap = isl_basic_map_drop_redundant_divs(bmap);
3312         if (!bmap)
3313                 goto error;
3314         for (i = 0; i < bmap->n_div; ++i)
3315                 if (isl_int_is_zero(bmap->div[i][0]))
3316                         break;
3317         if (i == bmap->n_div)
3318                 return isl_map_from_basic_map(bmap);
3319         struct isl_map *map = compute_divs(bmap);
3320         return map;
3321 error:
3322         isl_basic_map_free(bmap);
3323         return NULL;
3324 }
3325
3326 struct isl_map *isl_map_compute_divs(struct isl_map *map)
3327 {
3328         int i;
3329         struct isl_map *res;
3330
3331         if (!map)
3332                 return NULL;
3333         if (map->n == 0)
3334                 return map;
3335         res = isl_basic_map_compute_divs(isl_basic_map_copy(map->p[0]));
3336         for (i = 1 ; i < map->n; ++i) {
3337                 struct isl_map *r2;
3338                 r2 = isl_basic_map_compute_divs(isl_basic_map_copy(map->p[i]));
3339                 if (ISL_F_ISSET(map, ISL_MAP_DISJOINT))
3340                         res = isl_map_union_disjoint(res, r2);
3341                 else
3342                         res = isl_map_union(res, r2);
3343         }
3344         isl_map_free(map);
3345
3346         return res;
3347 }
3348
3349 struct isl_set *isl_basic_set_compute_divs(struct isl_basic_set *bset)
3350 {
3351         return (struct isl_set *)
3352                 isl_basic_map_compute_divs((struct isl_basic_map *)bset);
3353 }
3354
3355 struct isl_set *isl_set_compute_divs(struct isl_set *set)
3356 {
3357         return (struct isl_set *)
3358                 isl_map_compute_divs((struct isl_map *)set);
3359 }
3360
3361 struct isl_set *isl_map_domain(struct isl_map *map)
3362 {
3363         int i;
3364         struct isl_set *set;
3365
3366         if (!map)
3367                 goto error;
3368
3369         map = isl_map_cow(map);
3370         if (!map)
3371                 return NULL;
3372
3373         set = (struct isl_set *)map;
3374         set->dim = isl_dim_domain(set->dim);
3375         if (!set->dim)
3376                 goto error;
3377         for (i = 0; i < map->n; ++i) {
3378                 set->p[i] = isl_basic_map_domain(map->p[i]);
3379                 if (!set->p[i])
3380                         goto error;
3381         }
3382         ISL_F_CLR(set, ISL_MAP_DISJOINT);
3383         ISL_F_CLR(set, ISL_SET_NORMALIZED);
3384         return set;
3385 error:
3386         isl_map_free(map);
3387         return NULL;
3388 }
3389
3390 struct isl_map *isl_map_union_disjoint(
3391                         struct isl_map *map1, struct isl_map *map2)
3392 {
3393         int i;
3394         unsigned flags = 0;
3395         struct isl_map *map = NULL;
3396
3397         if (!map1 || !map2)
3398                 goto error;
3399
3400         if (map1->n == 0) {
3401                 isl_map_free(map1);
3402                 return map2;
3403         }
3404         if (map2->n == 0) {
3405                 isl_map_free(map2);
3406                 return map1;
3407         }
3408
3409         isl_assert(map1->ctx, isl_dim_equal(map1->dim, map2->dim), goto error);
3410
3411         if (ISL_F_ISSET(map1, ISL_MAP_DISJOINT) &&
3412             ISL_F_ISSET(map2, ISL_MAP_DISJOINT))
3413                 ISL_FL_SET(flags, ISL_MAP_DISJOINT);
3414
3415         map = isl_map_alloc_dim(isl_dim_copy(map1->dim),
3416                                 map1->n + map2->n, flags);
3417         if (!map)
3418                 goto error;
3419         for (i = 0; i < map1->n; ++i) {
3420                 map = isl_map_add(map,
3421                                   isl_basic_map_copy(map1->p[i]));
3422                 if (!map)
3423                         goto error;
3424         }
3425         for (i = 0; i < map2->n; ++i) {
3426                 map = isl_map_add(map,
3427                                   isl_basic_map_copy(map2->p[i]));
3428                 if (!map)
3429                         goto error;
3430         }
3431         isl_map_free(map1);
3432         isl_map_free(map2);
3433         return map;
3434 error:
3435         isl_map_free(map);
3436         isl_map_free(map1);
3437         isl_map_free(map2);
3438         return NULL;
3439 }
3440
3441 struct isl_map *isl_map_union(struct isl_map *map1, struct isl_map *map2)
3442 {
3443         map1 = isl_map_union_disjoint(map1, map2);
3444         if (!map1)
3445                 return NULL;
3446         if (map1->n > 1)
3447                 ISL_F_CLR(map1, ISL_MAP_DISJOINT);
3448         return map1;
3449 }
3450
3451 struct isl_set *isl_set_union_disjoint(
3452                         struct isl_set *set1, struct isl_set *set2)
3453 {
3454         return (struct isl_set *)
3455                 isl_map_union_disjoint(
3456                         (struct isl_map *)set1, (struct isl_map *)set2);
3457 }
3458
3459 struct isl_set *isl_set_union(struct isl_set *set1, struct isl_set *set2)
3460 {
3461         return (struct isl_set *)
3462                 isl_map_union((struct isl_map *)set1, (struct isl_map *)set2);
3463 }
3464
3465 struct isl_map *isl_map_intersect_range(
3466                 struct isl_map *map, struct isl_set *set)
3467 {
3468         unsigned flags = 0;
3469         struct isl_map *result;
3470         int i, j;
3471
3472         if (!map || !set)
3473                 goto error;
3474
3475         if (ISL_F_ISSET(map, ISL_MAP_DISJOINT) &&
3476             ISL_F_ISSET(set, ISL_MAP_DISJOINT))
3477                 ISL_FL_SET(flags, ISL_MAP_DISJOINT);
3478
3479         result = isl_map_alloc_dim(isl_dim_copy(map->dim),
3480                                         map->n * set->n, flags);
3481         if (!result)
3482                 goto error;
3483         for (i = 0; i < map->n; ++i)
3484                 for (j = 0; j < set->n; ++j) {
3485                         result = isl_map_add(result,
3486                             isl_basic_map_intersect_range(
3487                                 isl_basic_map_copy(map->p[i]),
3488                                 isl_basic_set_copy(set->p[j])));
3489                         if (!result)
3490                                 goto error;
3491                 }
3492         isl_map_free(map);
3493         isl_set_free(set);
3494         return result;
3495 error:
3496         isl_map_free(map);
3497         isl_set_free(set);
3498         return NULL;
3499 }
3500
3501 struct isl_map *isl_map_intersect_domain(
3502                 struct isl_map *map, struct isl_set *set)
3503 {
3504         return isl_map_reverse(
3505                 isl_map_intersect_range(isl_map_reverse(map), set));
3506 }
3507
3508 struct isl_map *isl_map_apply_domain(
3509                 struct isl_map *map1, struct isl_map *map2)
3510 {
3511         if (!map1 || !map2)
3512                 goto error;
3513         map1 = isl_map_reverse(map1);
3514         map1 = isl_map_apply_range(map1, map2);
3515         return isl_map_reverse(map1);
3516 error:
3517         isl_map_free(map1);
3518         isl_map_free(map2);
3519         return NULL;
3520 }
3521
3522 struct isl_map *isl_map_apply_range(
3523                 struct isl_map *map1, struct isl_map *map2)
3524 {
3525         struct isl_dim *dim_result;
3526         struct isl_map *result;
3527         int i, j;
3528         unsigned nparam;
3529         unsigned n_in;
3530         unsigned n_out;
3531
3532         if (!map1 || !map2)
3533                 goto error;
3534
3535         dim_result = isl_dim_join(isl_dim_copy(map1->dim),
3536                                   isl_dim_copy(map2->dim));
3537
3538         result = isl_map_alloc_dim(dim_result, map1->n * map2->n, 0);
3539         if (!result)
3540                 goto error;
3541         for (i = 0; i < map1->n; ++i)
3542                 for (j = 0; j < map2->n; ++j) {
3543                         result = isl_map_add(result,
3544                             isl_basic_map_apply_range(
3545                                 isl_basic_map_copy(map1->p[i]),
3546                                 isl_basic_map_copy(map2->p[j])));
3547                         if (!result)
3548                                 goto error;
3549                 }
3550         isl_map_free(map1);
3551         isl_map_free(map2);
3552         if (result && result->n <= 1)
3553                 ISL_F_SET(result, ISL_MAP_DISJOINT);
3554         return result;
3555 error:
3556         isl_map_free(map1);
3557         isl_map_free(map2);
3558         return NULL;
3559 }
3560
3561 /*
3562  * returns range - domain
3563  */
3564 struct isl_basic_set *isl_basic_map_deltas(struct isl_basic_map *bmap)
3565 {
3566         struct isl_basic_set *bset;
3567         unsigned dim;
3568         unsigned nparam;
3569         int i;
3570
3571         if (!bmap)
3572                 goto error;
3573         dim = isl_basic_map_n_in(bmap);
3574         nparam = isl_basic_map_n_param(bmap);
3575         isl_assert(bmap->ctx, dim == isl_basic_map_n_out(bmap), goto error);
3576         bset = isl_basic_set_from_basic_map(bmap);
3577         bset = isl_basic_set_cow(bset);
3578         bset = isl_basic_set_extend(bset, nparam, 3*dim, 0, dim, 0);
3579         bset = isl_basic_set_swap_vars(bset, 2*dim);
3580         for (i = 0; i < dim; ++i) {
3581                 int j = isl_basic_map_alloc_equality(
3582                                             (struct isl_basic_map *)bset);
3583                 if (j < 0)
3584                         goto error;
3585                 isl_seq_clr(bset->eq[j], 1 + isl_basic_set_total_dim(bset));
3586                 isl_int_set_si(bset->eq[j][1+nparam+i], 1);
3587                 isl_int_set_si(bset->eq[j][1+nparam+dim+i], 1);
3588                 isl_int_set_si(bset->eq[j][1+nparam+2*dim+i], -1);
3589         }
3590         return isl_basic_set_project_out(bset, 2*dim, 0);
3591 error:
3592         isl_basic_map_free(bmap);
3593         return NULL;
3594 }
3595
3596 /*
3597  * returns range - domain
3598  */
3599 struct isl_set *isl_map_deltas(struct isl_map *map)
3600 {
3601         int i;
3602         struct isl_set *result;
3603
3604         if (!map)
3605                 return NULL;
3606
3607         isl_assert(map->ctx, isl_map_n_in(map) == isl_map_n_out(map), goto error);
3608         result = isl_set_alloc(map->ctx, isl_map_n_param(map),
3609                                         isl_map_n_in(map), map->n, map->flags);
3610         if (!result)
3611                 goto error;
3612         for (i = 0; i < map->n; ++i)
3613                 result = isl_set_add(result,
3614                           isl_basic_map_deltas(isl_basic_map_copy(map->p[i])));
3615         isl_map_free(map);
3616         return result;
3617 error:
3618         isl_map_free(map);
3619         return NULL;
3620 }
3621
3622 static struct isl_basic_map *basic_map_identity(struct isl_dim *dims)
3623 {
3624         struct isl_basic_map *bmap;
3625         unsigned nparam;
3626         unsigned dim;
3627         int i;
3628
3629         if (!dims)
3630                 return NULL;
3631
3632         nparam = dims->nparam;
3633         dim = dims->n_out;
3634         bmap = isl_basic_map_alloc_dim(dims, 0, dim, 0);
3635         if (!bmap)
3636                 goto error;
3637
3638         for (i = 0; i < dim; ++i) {
3639                 int j = isl_basic_map_alloc_equality(bmap);
3640                 if (j < 0)
3641                         goto error;
3642                 isl_seq_clr(bmap->eq[j], 1 + isl_basic_map_total_dim(bmap));
3643                 isl_int_set_si(bmap->eq[j][1+nparam+i], 1);
3644                 isl_int_set_si(bmap->eq[j][1+nparam+dim+i], -1);
3645         }
3646         return isl_basic_map_finalize(bmap);
3647 error:
3648         isl_basic_map_free(bmap);
3649         return NULL;
3650 }
3651
3652 struct isl_basic_map *isl_basic_map_identity(struct isl_dim *set_dim)
3653 {
3654         struct isl_dim *dim = isl_dim_map(set_dim);
3655         if (!dim)
3656                 return NULL;
3657         return basic_map_identity(dim);
3658 }
3659
3660 struct isl_basic_map *isl_basic_map_identity_like(struct isl_basic_map *model)
3661 {
3662         if (!model || !model->dim)
3663                 return NULL;
3664         isl_assert(model->ctx,
3665                         model->dim->n_in == model->dim->n_out, return NULL);
3666         return basic_map_identity(isl_dim_copy(model->dim));
3667 }
3668
3669 static struct isl_map *map_identity(struct isl_dim *dim)
3670 {
3671         struct isl_map *map = isl_map_alloc_dim(dim, 1, ISL_MAP_DISJOINT);
3672         return isl_map_add(map, basic_map_identity(isl_dim_copy(dim)));
3673 }
3674
3675 struct isl_map *isl_map_identity(struct isl_dim *set_dim)
3676 {
3677         struct isl_dim *dim = isl_dim_map(set_dim);
3678         if (!dim)
3679                 return NULL;
3680         return map_identity(dim);
3681 }
3682
3683 struct isl_map *isl_map_identity_like(struct isl_basic_map *model)
3684 {
3685         if (!model || !model->dim)
3686                 return NULL;
3687         isl_assert(model->ctx,
3688                         model->dim->n_in == model->dim->n_out, return NULL);
3689         return map_identity(isl_dim_copy(model->dim));
3690 }
3691
3692 /* Construct a basic set with all set dimensions having only non-negative
3693  * values.
3694  */
3695 struct isl_basic_set *isl_basic_set_positive_orthant(struct isl_dim *dims)
3696 {
3697         int i;
3698         unsigned nparam;
3699         unsigned dim;
3700         struct isl_basic_set *bset;
3701
3702         if (!dims)
3703                 return NULL;
3704         nparam = dims->nparam;
3705         dim = dims->n_out;
3706         bset = isl_basic_set_alloc_dim(dims, 0, 0, dim);
3707         if (!bset)
3708                 return NULL;
3709         for (i = 0; i < dim; ++i) {
3710                 int k = isl_basic_set_alloc_inequality(bset);
3711                 if (k < 0)
3712                         goto error;
3713                 isl_seq_clr(bset->ineq[k], 1 + isl_basic_set_total_dim(bset));
3714                 isl_int_set_si(bset->ineq[k][1 + nparam + i], 1);
3715         }
3716         return bset;
3717 error:
3718         isl_basic_set_free(bset);
3719         return NULL;
3720 }
3721
3722 int isl_set_is_equal(struct isl_set *set1, struct isl_set *set2)
3723 {
3724         return isl_map_is_equal((struct isl_map *)set1, (struct isl_map *)set2);
3725 }
3726
3727 int isl_set_is_subset(struct isl_set *set1, struct isl_set *set2)
3728 {
3729         return isl_map_is_subset(
3730                         (struct isl_map *)set1, (struct isl_map *)set2);
3731 }
3732
3733 int isl_basic_map_is_subset(
3734                 struct isl_basic_map *bmap1, struct isl_basic_map *bmap2)
3735 {
3736         int is_subset;
3737         struct isl_map *map1;
3738         struct isl_map *map2;
3739
3740         if (!bmap1 || !bmap2)
3741                 return -1;
3742
3743         map1 = isl_map_from_basic_map(isl_basic_map_copy(bmap1));
3744         map2 = isl_map_from_basic_map(isl_basic_map_copy(bmap2));
3745
3746         is_subset = isl_map_is_subset(map1, map2);
3747
3748         isl_map_free(map1);
3749         isl_map_free(map2);
3750
3751         return is_subset;
3752 }
3753
3754 int isl_basic_map_is_equal(
3755                 struct isl_basic_map *bmap1, struct isl_basic_map *bmap2)
3756 {
3757         int is_subset;
3758
3759         if (!bmap1 || !bmap2)
3760                 return -1;
3761         is_subset = isl_basic_map_is_subset(bmap1, bmap2);
3762         if (is_subset != 1)
3763                 return is_subset;
3764         is_subset = isl_basic_map_is_subset(bmap2, bmap1);
3765         return is_subset;
3766 }
3767
3768 int isl_basic_set_is_equal(
3769                 struct isl_basic_set *bset1, struct isl_basic_set *bset2)
3770 {
3771         return isl_basic_map_is_equal(
3772                 (struct isl_basic_map *)bset1, (struct isl_basic_map *)bset2);
3773 }
3774
3775 int isl_map_is_empty(struct isl_map *map)
3776 {
3777         int i;
3778         int is_empty;
3779
3780         if (!map)
3781                 return -1;
3782         for (i = 0; i < map->n; ++i) {
3783                 is_empty = isl_basic_map_is_empty(map->p[i]);
3784                 if (is_empty < 0)
3785                         return -1;
3786                 if (!is_empty)
3787                         return 0;
3788         }
3789         return 1;
3790 }
3791
3792 int isl_map_fast_is_empty(struct isl_map *map)
3793 {
3794         return map->n == 0;
3795 }
3796
3797 int isl_set_is_empty(struct isl_set *set)
3798 {
3799         return isl_map_is_empty((struct isl_map *)set);
3800 }
3801
3802 int isl_map_is_subset(struct isl_map *map1, struct isl_map *map2)
3803 {
3804         int i;
3805         int is_subset = 0;
3806         struct isl_map *diff;
3807
3808         if (!map1 || !map2)
3809                 return -1;
3810
3811         if (isl_map_is_empty(map1))
3812                 return 1;
3813
3814         if (isl_map_is_empty(map2))
3815                 return 0;
3816
3817         diff = isl_map_subtract(isl_map_copy(map1), isl_map_copy(map2));
3818         if (!diff)
3819                 return -1;
3820
3821         is_subset = isl_map_is_empty(diff);
3822         isl_map_free(diff);
3823
3824         return is_subset;
3825 }
3826
3827 int isl_map_is_equal(struct isl_map *map1, struct isl_map *map2)
3828 {
3829         int is_subset;
3830
3831         if (!map1 || !map2)
3832                 return -1;
3833         is_subset = isl_map_is_subset(map1, map2);
3834         if (is_subset != 1)
3835                 return is_subset;
3836         is_subset = isl_map_is_subset(map2, map1);
3837         return is_subset;
3838 }
3839
3840 int isl_basic_map_is_strict_subset(
3841                 struct isl_basic_map *bmap1, struct isl_basic_map *bmap2)
3842 {
3843         int is_subset;
3844
3845         if (!bmap1 || !bmap2)
3846                 return -1;
3847         is_subset = isl_basic_map_is_subset(bmap1, bmap2);
3848         if (is_subset != 1)
3849                 return is_subset;
3850         is_subset = isl_basic_map_is_subset(bmap2, bmap1);
3851         if (is_subset == -1)
3852                 return is_subset;
3853         return !is_subset;
3854 }
3855
3856 int isl_basic_map_is_universe(struct isl_basic_map *bmap)
3857 {
3858         if (!bmap)
3859                 return -1;
3860         return bmap->n_eq == 0 && bmap->n_ineq == 0;
3861 }
3862
3863 int isl_basic_set_is_universe(struct isl_basic_set *bset)
3864 {
3865         if (!bset)
3866                 return -1;
3867         return bset->n_eq == 0 && bset->n_ineq == 0;
3868 }
3869
3870 int isl_basic_map_is_empty(struct isl_basic_map *bmap)
3871 {
3872         struct isl_basic_set *bset = NULL;
3873         struct isl_vec *sample = NULL;
3874         int empty;
3875         unsigned total;
3876
3877         if (!bmap)
3878                 return -1;
3879
3880         if (ISL_F_ISSET(bmap, ISL_BASIC_MAP_EMPTY))
3881                 return 1;
3882
3883         if (ISL_F_ISSET(bmap, ISL_BASIC_MAP_RATIONAL)) {
3884                 struct isl_basic_map *copy = isl_basic_map_copy(bmap);
3885                 copy = isl_basic_map_convex_hull(copy);
3886                 empty = ISL_F_ISSET(copy, ISL_BASIC_MAP_EMPTY);
3887                 isl_basic_map_free(copy);
3888                 return empty;
3889         }
3890
3891         total = 1 + isl_basic_map_total_dim(bmap);
3892         if (bmap->sample && bmap->sample->size == total) {
3893                 int contains = basic_map_contains(bmap, bmap->sample);
3894                 if (contains < 0)
3895                         return -1;
3896                 if (contains)
3897                         return 0;
3898         }
3899         isl_vec_free(bmap->sample);
3900         bmap->sample = NULL;
3901         bset = isl_basic_map_underlying_set(isl_basic_map_copy(bmap));
3902         if (!bset)
3903                 return -1;
3904         sample = isl_basic_set_sample(bset);
3905         if (!sample)
3906                 return -1;
3907         empty = sample->size == 0;
3908         isl_vec_free(bmap->sample);
3909         bmap->sample = sample;
3910         if (empty)
3911                 ISL_F_SET(bmap, ISL_BASIC_MAP_EMPTY);
3912
3913         return empty;
3914 }
3915
3916 int isl_basic_map_fast_is_empty(struct isl_basic_map *bmap)
3917 {
3918         if (!bmap)
3919                 return -1;
3920         return ISL_F_ISSET(bmap, ISL_BASIC_MAP_EMPTY);
3921 }
3922
3923 int isl_basic_set_fast_is_empty(struct isl_basic_set *bset)
3924 {
3925         if (!bset)
3926                 return -1;
3927         return ISL_F_ISSET(bset, ISL_BASIC_SET_EMPTY);
3928 }
3929
3930 int isl_basic_set_is_empty(struct isl_basic_set *bset)
3931 {
3932         return isl_basic_map_is_empty((struct isl_basic_map *)bset);
3933 }
3934
3935 struct isl_map *isl_basic_map_union(
3936         struct isl_basic_map *bmap1, struct isl_basic_map *bmap2)
3937 {
3938         struct isl_map *map;
3939         if (!bmap1 || !bmap2)
3940                 return NULL;
3941
3942         isl_assert(map1->ctx, isl_dim_equal(bmap1->dim, bmap2->dim), goto error);
3943
3944         map = isl_map_alloc_dim(isl_dim_copy(bmap1->dim), 2, 0);
3945         if (!map)
3946                 goto error;
3947         map = isl_map_add(map, bmap1);
3948         map = isl_map_add(map, bmap2);
3949         return map;
3950 error:
3951         isl_basic_map_free(bmap1);
3952         isl_basic_map_free(bmap2);
3953         return NULL;
3954 }
3955
3956 struct isl_set *isl_basic_set_union(
3957                 struct isl_basic_set *bset1, struct isl_basic_set *bset2)
3958 {
3959         return (struct isl_set *)isl_basic_map_union(
3960                                             (struct isl_basic_map *)bset1,
3961                                             (struct isl_basic_map *)bset2);
3962 }
3963
3964 /* Order divs such that any div only depends on previous divs */
3965 static struct isl_basic_map *order_divs(struct isl_basic_map *bmap)
3966 {
3967         int i;
3968         unsigned off = isl_dim_total(bmap->dim);
3969
3970         for (i = 0; i < bmap->n_div; ++i) {
3971                 int pos;
3972                 if (isl_int_is_zero(bmap->div[i][0]))
3973                         continue;
3974                 pos = isl_seq_first_non_zero(bmap->div[i]+1+1+off+i,
3975                                                             bmap->n_div-i);
3976                 if (pos == -1)
3977                         continue;
3978                 isl_basic_map_swap_div(bmap, i, i + pos);
3979                 --i;
3980         }
3981         return bmap;
3982 }
3983
3984 struct isl_basic_set *isl_basic_set_order_divs(struct isl_basic_set *bset)
3985 {
3986         return (struct isl_basic_set *)order_divs((struct isl_basic_map *)bset);
3987 }
3988
3989 /* Look for a div in dst that corresponds to the div "div" in src.
3990  * The divs before "div" in src and dst are assumed to be the same.
3991  *
3992  * Returns -1 if no corresponding div was found and the position
3993  * of the corresponding div in dst otherwise.
3994  */
3995 static int find_div(struct isl_basic_map *dst,
3996                         struct isl_basic_map *src, unsigned div)
3997 {
3998         int i;
3999
4000         unsigned total = isl_dim_total(src->dim);
4001
4002         isl_assert(dst->ctx, div <= dst->n_div, return -1);
4003         for (i = div; i < dst->n_div; ++i)
4004                 if (isl_seq_eq(dst->div[i], src->div[div], 1+1+total+div) &&
4005                     isl_seq_first_non_zero(dst->div[i]+1+1+total+div,
4006                                                 dst->n_div - div) == -1)
4007                         return i;
4008         return -1;
4009 }
4010
4011 struct isl_basic_map *isl_basic_map_align_divs(
4012                 struct isl_basic_map *dst, struct isl_basic_map *src)
4013 {
4014         int i;
4015         unsigned total = isl_dim_total(src->dim);
4016
4017         if (!dst || !src)
4018                 goto error;
4019
4020         if (src->n_div == 0)
4021                 return dst;
4022
4023         for (i = 0; i < src->n_div; ++i)
4024                 isl_assert(src->ctx, !isl_int_is_zero(src->div[i][0]), goto error);
4025
4026         src = order_divs(src);
4027         dst = isl_basic_map_cow(dst);
4028         dst = isl_basic_map_extend_dim(dst, isl_dim_copy(dst->dim),
4029                         src->n_div, 0, 2 * src->n_div);
4030         if (!dst)
4031                 return NULL;
4032         for (i = 0; i < src->n_div; ++i) {
4033                 int j = find_div(dst, src, i);
4034                 if (j < 0) {
4035                         j = isl_basic_map_alloc_div(dst);
4036                         if (j < 0)
4037                                 goto error;
4038                         isl_seq_cpy(dst->div[j], src->div[i], 1+1+total+i);
4039                         isl_seq_clr(dst->div[j]+1+1+total+i, dst->n_div - i);
4040                         if (add_div_constraints(dst, j) < 0)
4041                                 goto error;
4042                 }
4043                 if (j != i)
4044                         isl_basic_map_swap_div(dst, i, j);
4045         }
4046         return dst;
4047 error:
4048         isl_basic_map_free(dst);
4049         return NULL;
4050 }
4051
4052 struct isl_basic_set *isl_basic_set_align_divs(
4053                 struct isl_basic_set *dst, struct isl_basic_set *src)
4054 {
4055         return (struct isl_basic_set *)isl_basic_map_align_divs(
4056                 (struct isl_basic_map *)dst, (struct isl_basic_map *)src);
4057 }
4058
4059 struct isl_map *isl_map_align_divs(struct isl_map *map)
4060 {
4061         int i;
4062
4063         map = isl_map_compute_divs(map);
4064         map = isl_map_cow(map);
4065         if (!map)
4066                 return NULL;
4067
4068         for (i = 1; i < map->n; ++i)
4069                 map->p[0] = isl_basic_map_align_divs(map->p[0], map->p[i]);
4070         for (i = 1; i < map->n; ++i)
4071                 map->p[i] = isl_basic_map_align_divs(map->p[i], map->p[0]);
4072
4073         ISL_F_CLR(map, ISL_MAP_NORMALIZED);
4074         return map;
4075 }
4076
4077 struct isl_set *isl_set_align_divs(struct isl_set *set)
4078 {
4079         return (struct isl_set *)isl_map_align_divs((struct isl_map *)set);
4080 }
4081
4082 static struct isl_map *add_cut_constraint(struct isl_map *dst,
4083                 struct isl_basic_map *src, isl_int *c,
4084                 unsigned len, int oppose)
4085 {
4086         struct isl_basic_map *copy = NULL;
4087         int is_empty;
4088         int k;
4089         unsigned total;
4090
4091         copy = isl_basic_map_copy(src);
4092         copy = isl_basic_map_cow(copy);
4093         if (!copy)
4094                 goto error;
4095         copy = isl_basic_map_extend_constraints(copy, 0, 1);
4096         k = isl_basic_map_alloc_inequality(copy);
4097         if (k < 0)
4098                 goto error;
4099         if (oppose)
4100                 isl_seq_neg(copy->ineq[k], c, len);
4101         else
4102                 isl_seq_cpy(copy->ineq[k], c, len);
4103         total = 1 + isl_basic_map_total_dim(copy);
4104         isl_seq_clr(copy->ineq[k]+len, total - len);
4105         isl_inequality_negate(copy, k);
4106         copy = isl_basic_map_simplify(copy);
4107         copy = isl_basic_map_finalize(copy);
4108         is_empty = isl_basic_map_is_empty(copy);
4109         if (is_empty < 0)
4110                 goto error;
4111         if (!is_empty)
4112                 dst = isl_map_add(dst, copy);
4113         else
4114                 isl_basic_map_free(copy);
4115         return dst;
4116 error:
4117         isl_basic_map_free(copy);
4118         isl_map_free(dst);
4119         return NULL;
4120 }
4121
4122 static struct isl_map *subtract(struct isl_map *map, struct isl_basic_map *bmap)
4123 {
4124         int i, j, k;
4125         unsigned flags = 0;
4126         struct isl_map *rest = NULL;
4127         unsigned max;
4128         unsigned total = isl_basic_map_total_dim(bmap);
4129
4130         assert(bmap);
4131
4132         if (!map)
4133                 goto error;
4134
4135         if (ISL_F_ISSET(map, ISL_MAP_DISJOINT))
4136                 ISL_FL_SET(flags, ISL_MAP_DISJOINT);
4137
4138         max = map->n * (2 * bmap->n_eq + bmap->n_ineq);
4139         rest = isl_map_alloc_dim(isl_dim_copy(map->dim), max, flags);
4140         if (!rest)
4141                 goto error;
4142
4143         for (i = 0; i < map->n; ++i) {
4144                 map->p[i] = isl_basic_map_align_divs(map->p[i], bmap);
4145                 if (!map->p[i])
4146                         goto error;
4147         }
4148
4149         for (j = 0; j < map->n; ++j)
4150                 map->p[j] = isl_basic_map_cow(map->p[j]);
4151
4152         for (i = 0; i < bmap->n_eq; ++i) {
4153                 for (j = 0; j < map->n; ++j) {
4154                         rest = add_cut_constraint(rest,
4155                                 map->p[j], bmap->eq[i], 1+total, 0);
4156                         if (!rest)
4157                                 goto error;
4158
4159                         rest = add_cut_constraint(rest,
4160                                 map->p[j], bmap->eq[i], 1+total, 1);
4161                         if (!rest)
4162                                 goto error;
4163
4164                         map->p[j] = isl_basic_map_extend_constraints(map->p[j],
4165                                 1, 0);
4166                         if (!map->p[j])
4167                                 goto error;
4168                         k = isl_basic_map_alloc_equality(map->p[j]);
4169                         if (k < 0)
4170                                 goto error;
4171                         isl_seq_cpy(map->p[j]->eq[k], bmap->eq[i], 1+total);
4172                         isl_seq_clr(map->p[j]->eq[k]+1+total,
4173                                         map->p[j]->n_div - bmap->n_div);
4174                 }
4175         }
4176
4177         for (i = 0; i < bmap->n_ineq; ++i) {
4178                 for (j = 0; j < map->n; ++j) {
4179                         rest = add_cut_constraint(rest,
4180                                 map->p[j], bmap->ineq[i], 1+total, 0);
4181                         if (!rest)
4182                                 goto error;
4183
4184                         map->p[j] = isl_basic_map_extend_constraints(map->p[j],
4185                                 0, 1);
4186                         if (!map->p[j])
4187                                 goto error;
4188                         k = isl_basic_map_alloc_inequality(map->p[j]);
4189                         if (k < 0)
4190                                 goto error;
4191                         isl_seq_cpy(map->p[j]->ineq[k], bmap->ineq[i], 1+total);
4192                         isl_seq_clr(map->p[j]->ineq[k]+1+total,
4193                                         map->p[j]->n_div - bmap->n_div);
4194                 }
4195         }
4196
4197         isl_map_free(map);
4198         return rest;
4199 error:
4200         isl_map_free(map);
4201         isl_map_free(rest);
4202         return NULL;
4203 }
4204
4205 struct isl_map *isl_map_subtract(struct isl_map *map1, struct isl_map *map2)
4206 {
4207         int i;
4208         if (!map1 || !map2)
4209                 goto error;
4210
4211         isl_assert(map1->ctx, isl_dim_equal(map1->dim, map2->dim), goto error);
4212
4213         if (isl_map_is_empty(map2)) {
4214                 isl_map_free(map2);
4215                 return map1;
4216         }
4217
4218         map1 = isl_map_compute_divs(map1);
4219         map2 = isl_map_compute_divs(map2);
4220         if (!map1 || !map2)
4221                 goto error;
4222
4223         for (i = 0; map1 && i < map2->n; ++i)
4224                 map1 = subtract(map1, map2->p[i]);
4225
4226         isl_map_free(map2);
4227         return map1;
4228 error:
4229         isl_map_free(map1);
4230         isl_map_free(map2);
4231         return NULL;
4232 }
4233
4234 struct isl_set *isl_set_subtract(struct isl_set *set1, struct isl_set *set2)
4235 {
4236         return (struct isl_set *)
4237                 isl_map_subtract(
4238                         (struct isl_map *)set1, (struct isl_map *)set2);
4239 }
4240
4241 struct isl_set *isl_set_apply(struct isl_set *set, struct isl_map *map)
4242 {
4243         if (!set || !map)
4244                 goto error;
4245         isl_assert(set->ctx, isl_map_compatible_domain(map, set), goto error);
4246         map = isl_map_intersect_domain(map, set);
4247         set = isl_map_range(map);
4248         return set;
4249 error:
4250         isl_set_free(set);
4251         isl_map_free(map);
4252         return NULL;
4253 }
4254
4255 /* There is no need to cow as removing empty parts doesn't change
4256  * the meaning of the set.
4257  */
4258 struct isl_map *isl_map_remove_empty_parts(struct isl_map *map)
4259 {
4260         int i;
4261
4262         if (!map)
4263                 return NULL;
4264
4265         for (i = map->n-1; i >= 0; --i) {
4266                 if (!ISL_F_ISSET(map->p[i], ISL_BASIC_MAP_EMPTY))
4267                         continue;
4268                 isl_basic_map_free(map->p[i]);
4269                 if (i != map->n-1) {
4270                         ISL_F_CLR(map, ISL_MAP_NORMALIZED);
4271                         map->p[i] = map->p[map->n-1];
4272                 }
4273                 map->n--;
4274         }
4275
4276         return map;
4277 }
4278
4279 struct isl_set *isl_set_remove_empty_parts(struct isl_set *set)
4280 {
4281         return (struct isl_set *)
4282                 isl_map_remove_empty_parts((struct isl_map *)set);
4283 }
4284
4285 struct isl_basic_map *isl_map_copy_basic_map(struct isl_map *map)
4286 {
4287         struct isl_basic_map *bmap;
4288         if (!map || map->n == 0)
4289                 return NULL;
4290         bmap = map->p[map->n-1];
4291         isl_assert(map->ctx, ISL_F_ISSET(bmap, ISL_BASIC_SET_FINAL), return NULL);
4292         return isl_basic_map_copy(bmap);
4293 }
4294
4295 struct isl_basic_set *isl_set_copy_basic_set(struct isl_set *set)
4296 {
4297         (struct isl_basic_set *)isl_map_copy_basic_map((struct isl_map *)set);
4298 }
4299
4300 struct isl_map *isl_map_drop_basic_map(struct isl_map *map,
4301                                                 struct isl_basic_map *bmap)
4302 {
4303         int i;
4304
4305         if (!map || !bmap)
4306                 goto error;
4307         for (i = map->n-1; i >= 0; --i) {
4308                 if (map->p[i] != bmap)
4309                         continue;
4310                 map = isl_map_cow(map);
4311                 if (!map)
4312                         goto error;
4313                 isl_basic_map_free(map->p[i]);
4314                 if (i != map->n-1) {
4315                         ISL_F_CLR(map, ISL_SET_NORMALIZED);
4316                         map->p[i] = map->p[map->n-1];
4317                 }
4318                 map->n--;
4319                 return map;
4320         }
4321         isl_basic_map_free(bmap);
4322         return map;
4323 error:
4324         isl_map_free(map);
4325         isl_basic_map_free(bmap);
4326         return NULL;
4327 }
4328
4329 struct isl_set *isl_set_drop_basic_set(struct isl_set *set,
4330                                                 struct isl_basic_set *bset)
4331 {
4332         (struct isl_set *)isl_map_drop_basic_map((struct isl_map *)set,
4333                                                 (struct isl_basic_map *)bset);
4334 }
4335
4336 /* Given two _disjoint_ basic sets bset1 and bset2, check whether
4337  * for any common value of the parameters and dimensions preceding dim
4338  * in both basic sets, the values of dimension pos in bset1 are
4339  * smaller or larger than those in bset2.
4340  *
4341  * Returns
4342  *       1 if bset1 follows bset2
4343  *      -1 if bset1 precedes bset2
4344  *       0 if bset1 and bset2 are incomparable
4345  *      -2 if some error occurred.
4346  */
4347 int isl_basic_set_compare_at(struct isl_basic_set *bset1,
4348         struct isl_basic_set *bset2, int pos)
4349 {
4350         struct isl_dim *dims;
4351         struct isl_basic_map *bmap1 = NULL;
4352         struct isl_basic_map *bmap2 = NULL;
4353         struct isl_ctx *ctx;
4354         struct isl_vec *obj;
4355         unsigned total;
4356         unsigned nparam;
4357         unsigned dim1, dim2;
4358         isl_int num, den;
4359         enum isl_lp_result res;
4360         int cmp;
4361
4362         if (!bset1 || !bset2)
4363                 return -2;
4364
4365         nparam = isl_basic_set_n_param(bset1);
4366         dim1 = isl_basic_set_n_dim(bset1);
4367         dim2 = isl_basic_set_n_dim(bset2);
4368         dims = isl_dim_alloc(bset1->ctx, nparam, pos, dim1 - pos);
4369         bmap1 = isl_basic_map_from_basic_set(isl_basic_set_copy(bset1), dims);
4370         dims = isl_dim_alloc(bset2->ctx, nparam, pos, dim2 - pos);
4371         bmap2 = isl_basic_map_from_basic_set(isl_basic_set_copy(bset2), dims);
4372         if (!bmap1 || !bmap2)
4373                 goto error;
4374         bmap1 = isl_basic_map_cow(bmap1);
4375         bmap1 = isl_basic_map_extend(bmap1, nparam,
4376                         pos, (dim1 - pos) + (dim2 - pos),
4377                         bmap2->n_div, bmap2->n_eq, bmap2->n_ineq);
4378         bmap1 = add_constraints(bmap1, bmap2, 0, dim1 - pos);
4379         if (!bmap1)
4380                 goto error;
4381         total = isl_basic_map_total_dim(bmap1);
4382         ctx = bmap1->ctx;
4383         obj = isl_vec_alloc(ctx, 1 + total);
4384         isl_seq_clr(obj->block.data, 1 + total);
4385         isl_int_set_si(obj->block.data[1+nparam+pos], 1);
4386         isl_int_set_si(obj->block.data[1+nparam+pos+(dim1-pos)], -1);
4387         if (!obj)
4388                 goto error;
4389         isl_int_init(num);
4390         isl_int_init(den);
4391         res = isl_solve_lp(bmap1, 0, obj->block.data, ctx->one, &num, &den);
4392         if (res == isl_lp_empty)
4393                 cmp = 0;
4394         else if (res == isl_lp_ok && isl_int_is_pos(num))
4395                 cmp = 1;
4396         else if ((res == isl_lp_ok && isl_int_is_neg(num)) ||
4397                   res == isl_lp_unbounded)
4398                 cmp = -1;
4399         else
4400                 cmp = -2;
4401         isl_int_clear(num);
4402         isl_int_clear(den);
4403         isl_basic_map_free(bmap1);
4404         isl_vec_free(obj);
4405         return cmp;
4406 error:
4407         isl_basic_map_free(bmap1);
4408         isl_basic_map_free(bmap2);
4409         return -2;
4410 }
4411
4412 static int isl_basic_map_fast_has_fixed_var(struct isl_basic_map *bmap,
4413         unsigned pos, isl_int *val)
4414 {
4415         int i;
4416         int d;
4417         unsigned total;
4418
4419         if (!bmap)
4420                 return -1;
4421         total = isl_basic_map_total_dim(bmap);
4422         for (i = 0, d = total-1; i < bmap->n_eq && d+1 > pos; ++i) {
4423                 for (; d+1 > pos; --d)
4424                         if (!isl_int_is_zero(bmap->eq[i][1+d]))
4425                                 break;
4426                 if (d != pos)
4427                         continue;
4428                 if (isl_seq_first_non_zero(bmap->eq[i]+1, d) != -1)
4429                         return 0;
4430                 if (isl_seq_first_non_zero(bmap->eq[i]+1+d+1, total-d-1) != -1)
4431                         return 0;
4432                 if (!isl_int_is_one(bmap->eq[i][1+d]))
4433                         return 0;
4434                 if (val)
4435                         isl_int_neg(*val, bmap->eq[i][0]);
4436                 return 1;
4437         }
4438         return 0;
4439 }
4440
4441 static int isl_map_fast_has_fixed_var(struct isl_map *map,
4442         unsigned pos, isl_int *val)
4443 {
4444         int i;
4445         isl_int v;
4446         isl_int tmp;
4447         int fixed;
4448
4449         if (!map)
4450                 return -1;
4451         if (map->n == 0)
4452                 return 0;
4453         if (map->n == 1)
4454                 return isl_basic_map_fast_has_fixed_var(map->p[0], pos, val);
4455         isl_int_init(v);
4456         isl_int_init(tmp);
4457         fixed = isl_basic_map_fast_has_fixed_var(map->p[0], pos, &v);
4458         for (i = 1; fixed == 1 && i < map->n; ++i) {
4459                 fixed = isl_basic_map_fast_has_fixed_var(map->p[i], pos, &tmp);
4460                 if (fixed == 1 && isl_int_ne(tmp, v))
4461                         fixed = 0;
4462         }
4463         if (val)
4464                 isl_int_set(*val, v);
4465         isl_int_clear(tmp);
4466         isl_int_clear(v);
4467         return fixed;
4468 }
4469
4470 static int isl_basic_set_fast_has_fixed_var(struct isl_basic_set *bset,
4471         unsigned pos, isl_int *val)
4472 {
4473         return isl_basic_map_fast_has_fixed_var((struct isl_basic_map *)bset,
4474                                                 pos, val);
4475 }
4476
4477 static int isl_set_fast_has_fixed_var(struct isl_set *set, unsigned pos,
4478         isl_int *val)
4479 {
4480         return isl_map_fast_has_fixed_var((struct isl_map *)set, pos, val);
4481 }
4482
4483 int isl_basic_map_fast_is_fixed(struct isl_basic_map *bmap,
4484         enum isl_dim_type type, unsigned pos, isl_int *val)
4485 {
4486         if (pos >= isl_basic_map_dim(bmap, type))
4487                 return -1;
4488         return isl_basic_map_fast_has_fixed_var(bmap,
4489                 isl_basic_map_offset(bmap, type) - 1 + pos, val);
4490 }
4491
4492 /* Check if dimension dim has fixed value and if so and if val is not NULL,
4493  * then return this fixed value in *val.
4494  */
4495 int isl_basic_set_fast_dim_is_fixed(struct isl_basic_set *bset, unsigned dim,
4496         isl_int *val)
4497 {
4498         return isl_basic_set_fast_has_fixed_var(bset,
4499                                         isl_basic_set_n_param(bset) + dim, val);
4500 }
4501
4502 /* Check if dimension dim has fixed value and if so and if val is not NULL,
4503  * then return this fixed value in *val.
4504  */
4505 int isl_set_fast_dim_is_fixed(struct isl_set *set, unsigned dim, isl_int *val)
4506 {
4507         return isl_set_fast_has_fixed_var(set, isl_set_n_param(set) + dim, val);
4508 }
4509
4510 /* Check if input variable in has fixed value and if so and if val is not NULL,
4511  * then return this fixed value in *val.
4512  */
4513 int isl_map_fast_input_is_fixed(struct isl_map *map, unsigned in, isl_int *val)
4514 {
4515         return isl_map_fast_has_fixed_var(map, isl_map_n_param(map) + in, val);
4516 }
4517
4518 /* Check if dimension dim has an (obvious) fixed lower bound and if so
4519  * and if val is not NULL, then return this lower bound in *val.
4520  */
4521 int isl_basic_set_fast_dim_has_fixed_lower_bound(struct isl_basic_set *bset,
4522         unsigned dim, isl_int *val)
4523 {
4524         int i, i_eq = -1, i_ineq = -1;
4525         isl_int *c;
4526         unsigned total;
4527         unsigned nparam;
4528
4529         if (!bset)
4530                 return -1;
4531         total = isl_basic_set_total_dim(bset);
4532         nparam = isl_basic_set_n_param(bset);
4533         for (i = 0; i < bset->n_eq; ++i) {
4534                 if (isl_int_is_zero(bset->eq[i][1+nparam+dim]))
4535                         continue;
4536                 if (i_eq != -1)
4537                         return 0;
4538                 i_eq = i;
4539         }
4540         for (i = 0; i < bset->n_ineq; ++i) {
4541                 if (!isl_int_is_pos(bset->ineq[i][1+nparam+dim]))
4542                         continue;
4543                 if (i_eq != -1 || i_ineq != -1)
4544                         return 0;
4545                 i_ineq = i;
4546         }
4547         if (i_eq == -1 && i_ineq == -1)
4548                 return 0;
4549         c = i_eq != -1 ? bset->eq[i_eq] : bset->ineq[i_ineq];
4550         /* The coefficient should always be one due to normalization. */
4551         if (!isl_int_is_one(c[1+nparam+dim]))
4552                 return 0;
4553         if (isl_seq_first_non_zero(c+1, nparam+dim) != -1)
4554                 return 0;
4555         if (isl_seq_first_non_zero(c+1+nparam+dim+1,
4556                                         total - nparam - dim - 1) != -1)
4557                 return 0;
4558         if (val)
4559                 isl_int_neg(*val, c[0]);
4560         return 1;
4561 }
4562
4563 int isl_set_fast_dim_has_fixed_lower_bound(struct isl_set *set,
4564         unsigned dim, isl_int *val)
4565 {
4566         int i;
4567         isl_int v;
4568         isl_int tmp;
4569         int fixed;
4570
4571         if (!set)
4572                 return -1;
4573         if (set->n == 0)
4574                 return 0;
4575         if (set->n == 1)
4576                 return isl_basic_set_fast_dim_has_fixed_lower_bound(set->p[0],
4577                                                                 dim, val);
4578         isl_int_init(v);
4579         isl_int_init(tmp);
4580         fixed = isl_basic_set_fast_dim_has_fixed_lower_bound(set->p[0],
4581                                                                 dim, &v);
4582         for (i = 1; fixed == 1 && i < set->n; ++i) {
4583                 fixed = isl_basic_set_fast_dim_has_fixed_lower_bound(set->p[i],
4584                                                                 dim, &tmp);
4585                 if (fixed == 1 && isl_int_ne(tmp, v))
4586                         fixed = 0;
4587         }
4588         if (val)
4589                 isl_int_set(*val, v);
4590         isl_int_clear(tmp);
4591         isl_int_clear(v);
4592         return fixed;
4593 }
4594
4595 struct constraint {
4596         unsigned        size;
4597         isl_int         *c;
4598 };
4599
4600 static int qsort_constraint_cmp(const void *p1, const void *p2)
4601 {
4602         const struct constraint *c1 = (const struct constraint *)p1;
4603         const struct constraint *c2 = (const struct constraint *)p2;
4604         unsigned size = isl_min(c1->size, c2->size);
4605         return isl_seq_cmp(c1->c, c2->c, size);
4606 }
4607
4608 static struct isl_basic_map *isl_basic_map_sort_constraints(
4609         struct isl_basic_map *bmap)
4610 {
4611         int i;
4612         struct constraint *c;
4613         unsigned total;
4614
4615         if (!bmap)
4616                 return NULL;
4617         total = isl_basic_map_total_dim(bmap);
4618         c = isl_alloc_array(bmap->ctx, struct constraint, bmap->n_ineq);
4619         if (!c)
4620                 goto error;
4621         for (i = 0; i < bmap->n_ineq; ++i) {
4622                 c[i].size = total;
4623                 c[i].c = bmap->ineq[i];
4624         }
4625         qsort(c, bmap->n_ineq, sizeof(struct constraint), qsort_constraint_cmp);
4626         for (i = 0; i < bmap->n_ineq; ++i)
4627                 bmap->ineq[i] = c[i].c;
4628         free(c);
4629         return bmap;
4630 error:
4631         isl_basic_map_free(bmap);
4632         return NULL;
4633 }
4634
4635 struct isl_basic_map *isl_basic_map_normalize(struct isl_basic_map *bmap)
4636 {
4637         if (!bmap)
4638                 return NULL;
4639         if (ISL_F_ISSET(bmap, ISL_BASIC_MAP_NORMALIZED))
4640                 return bmap;
4641         bmap = isl_basic_map_convex_hull(bmap);
4642         bmap = isl_basic_map_sort_constraints(bmap);
4643         ISL_F_SET(bmap, ISL_BASIC_MAP_NORMALIZED);
4644         return bmap;
4645 }
4646
4647 struct isl_basic_set *isl_basic_set_normalize(struct isl_basic_set *bset)
4648 {
4649         return (struct isl_basic_set *)isl_basic_map_normalize(
4650                                                 (struct isl_basic_map *)bset);
4651 }
4652
4653 static int isl_basic_map_fast_cmp(const struct isl_basic_map *bmap1,
4654         const struct isl_basic_map *bmap2)
4655 {
4656         int i, cmp;
4657         unsigned total;
4658
4659         if (bmap1 == bmap2)
4660                 return 0;
4661         if (isl_basic_map_n_param(bmap1) != isl_basic_map_n_param(bmap2))
4662                 return isl_basic_map_n_param(bmap1) - isl_basic_map_n_param(bmap2);
4663         if (isl_basic_map_n_in(bmap1) != isl_basic_map_n_in(bmap2))
4664                 return isl_basic_map_n_out(bmap1) - isl_basic_map_n_out(bmap2);
4665         if (isl_basic_map_n_out(bmap1) != isl_basic_map_n_out(bmap2))
4666                 return isl_basic_map_n_out(bmap1) - isl_basic_map_n_out(bmap2);
4667         if (ISL_F_ISSET(bmap1, ISL_BASIC_MAP_EMPTY) &&
4668             ISL_F_ISSET(bmap2, ISL_BASIC_MAP_EMPTY))
4669                 return 0;
4670         if (ISL_F_ISSET(bmap1, ISL_BASIC_MAP_EMPTY))
4671                 return 1;
4672         if (ISL_F_ISSET(bmap2, ISL_BASIC_MAP_EMPTY))
4673                 return -1;
4674         if (bmap1->n_eq != bmap2->n_eq)
4675                 return bmap1->n_eq - bmap2->n_eq;
4676         if (bmap1->n_ineq != bmap2->n_ineq)
4677                 return bmap1->n_ineq - bmap2->n_ineq;
4678         if (bmap1->n_div != bmap2->n_div)
4679                 return bmap1->n_div - bmap2->n_div;
4680         total = isl_basic_map_total_dim(bmap1);
4681         for (i = 0; i < bmap1->n_eq; ++i) {
4682                 cmp = isl_seq_cmp(bmap1->eq[i], bmap2->eq[i], 1+total);
4683                 if (cmp)
4684                         return cmp;
4685         }
4686         for (i = 0; i < bmap1->n_ineq; ++i) {
4687                 cmp = isl_seq_cmp(bmap1->ineq[i], bmap2->ineq[i], 1+total);
4688                 if (cmp)
4689                         return cmp;
4690         }
4691         for (i = 0; i < bmap1->n_div; ++i) {
4692                 cmp = isl_seq_cmp(bmap1->div[i], bmap2->div[i], 1+1+total);
4693                 if (cmp)
4694                         return cmp;
4695         }
4696         return 0;
4697 }
4698
4699 static int isl_basic_map_fast_is_equal(struct isl_basic_map *bmap1,
4700         struct isl_basic_map *bmap2)
4701 {
4702         return isl_basic_map_fast_cmp(bmap1, bmap2) == 0;
4703 }
4704
4705 static int qsort_bmap_cmp(const void *p1, const void *p2)
4706 {
4707         const struct isl_basic_map *bmap1 = *(const struct isl_basic_map **)p1;
4708         const struct isl_basic_map *bmap2 = *(const struct isl_basic_map **)p2;
4709
4710         return isl_basic_map_fast_cmp(bmap1, bmap2);
4711 }
4712
4713 /* We normalize in place, but if anything goes wrong we need
4714  * to return NULL, so we need to make sure we don't change the
4715  * meaning of any possible other copies of map.
4716  */
4717 struct isl_map *isl_map_normalize(struct isl_map *map)
4718 {
4719         int i, j;
4720         struct isl_basic_map *bmap;
4721
4722         if (!map)
4723                 return NULL;
4724         if (ISL_F_ISSET(map, ISL_MAP_NORMALIZED))
4725                 return map;
4726         for (i = 0; i < map->n; ++i) {
4727                 bmap = isl_basic_map_normalize(isl_basic_map_copy(map->p[i]));
4728                 if (!bmap)
4729                         goto error;
4730                 isl_basic_map_free(map->p[i]);
4731                 map->p[i] = bmap;
4732         }
4733         qsort(map->p, map->n, sizeof(struct isl_basic_map *), qsort_bmap_cmp);
4734         ISL_F_SET(map, ISL_MAP_NORMALIZED);
4735         map = isl_map_remove_empty_parts(map);
4736         if (!map)
4737                 return NULL;
4738         for (i = map->n - 1; i >= 1; --i) {
4739                 if (!isl_basic_map_fast_is_equal(map->p[i-1], map->p[i]))
4740                         continue;
4741                 isl_basic_map_free(map->p[i-1]);
4742                 for (j = i; j < map->n; ++j)
4743                         map->p[j-1] = map->p[j];
4744                 map->n--;
4745         }
4746         return map;
4747 error:
4748         isl_map_free(map);
4749         return NULL;
4750
4751 }
4752
4753 struct isl_set *isl_set_normalize(struct isl_set *set)
4754 {
4755         return (struct isl_set *)isl_map_normalize((struct isl_map *)set);
4756 }
4757
4758 int isl_map_fast_is_equal(struct isl_map *map1, struct isl_map *map2)
4759 {
4760         int i;
4761         int equal;
4762
4763         if (!map1 || !map2)
4764                 return -1;
4765
4766         if (map1 == map2)
4767                 return 1;
4768         if (!isl_dim_equal(map1->dim, map2->dim))
4769                 return 0;
4770
4771         map1 = isl_map_copy(map1);
4772         map2 = isl_map_copy(map2);
4773         map1 = isl_map_normalize(map1);
4774         map2 = isl_map_normalize(map2);
4775         if (!map1 || !map2)
4776                 goto error;
4777         equal = map1->n == map2->n;
4778         for (i = 0; equal && i < map1->n; ++i) {
4779                 equal = isl_basic_map_fast_is_equal(map1->p[i], map2->p[i]);
4780                 if (equal < 0)
4781                         goto error;
4782         }
4783         isl_map_free(map1);
4784         isl_map_free(map2);
4785         return equal;
4786 error:
4787         isl_map_free(map1);
4788         isl_map_free(map2);
4789         return -1;
4790 }
4791
4792 int isl_set_fast_is_equal(struct isl_set *set1, struct isl_set *set2)
4793 {
4794         return isl_map_fast_is_equal((struct isl_map *)set1,
4795                                                 (struct isl_map *)set2);
4796 }
4797
4798 /* Return an interval that ranges from min to max (inclusive)
4799  */
4800 struct isl_basic_set *isl_basic_set_interval(struct isl_ctx *ctx,
4801         isl_int min, isl_int max)
4802 {
4803         int k;
4804         struct isl_basic_set *bset = NULL;
4805
4806         bset = isl_basic_set_alloc(ctx, 0, 1, 0, 0, 2);
4807         if (!bset)
4808                 goto error;
4809
4810         k = isl_basic_set_alloc_inequality(bset);
4811         if (k < 0)
4812                 goto error;
4813         isl_int_set_si(bset->ineq[k][1], 1);
4814         isl_int_neg(bset->ineq[k][0], min);
4815
4816         k = isl_basic_set_alloc_inequality(bset);
4817         if (k < 0)
4818                 goto error;
4819         isl_int_set_si(bset->ineq[k][1], -1);
4820         isl_int_set(bset->ineq[k][0], max);
4821
4822         return bset;
4823 error:
4824         isl_basic_set_free(bset);
4825         return NULL;
4826 }
4827
4828 /* Return the Cartesian product of the basic sets in list (in the given order).
4829  */
4830 struct isl_basic_set *isl_basic_set_product(struct isl_basic_set_list *list)
4831 {
4832         int i;
4833         unsigned dim;
4834         unsigned nparam;
4835         unsigned extra;
4836         unsigned n_eq;
4837         unsigned n_ineq;
4838         struct isl_basic_set *product = NULL;
4839
4840         if (!list)
4841                 goto error;
4842         isl_assert(list->ctx, list->n > 0, goto error);
4843         isl_assert(list->ctx, list->p[0], goto error);
4844         nparam = isl_basic_set_n_param(list->p[0]);
4845         dim = isl_basic_set_n_dim(list->p[0]);
4846         extra = list->p[0]->n_div;
4847         n_eq = list->p[0]->n_eq;
4848         n_ineq = list->p[0]->n_ineq;
4849         for (i = 1; i < list->n; ++i) {
4850                 isl_assert(list->ctx, list->p[i], goto error);
4851                 isl_assert(list->ctx,
4852                     nparam == isl_basic_set_n_param(list->p[i]), goto error);
4853                 dim += isl_basic_set_n_dim(list->p[i]);
4854                 extra += list->p[i]->n_div;
4855                 n_eq += list->p[i]->n_eq;
4856                 n_ineq += list->p[i]->n_ineq;
4857         }
4858         product = isl_basic_set_alloc(list->ctx, nparam, dim, extra,
4859                                         n_eq, n_ineq);
4860         if (!product)
4861                 goto error;
4862         dim = 0;
4863         for (i = 0; i < list->n; ++i) {
4864                 isl_basic_set_add_constraints(product,
4865                                         isl_basic_set_copy(list->p[i]), dim);
4866                 dim += isl_basic_set_n_dim(list->p[i]);
4867         }
4868         isl_basic_set_list_free(list);
4869         return product;
4870 error:
4871         isl_basic_set_free(product);
4872         isl_basic_set_list_free(list);
4873         return NULL;
4874 }
4875
4876 struct isl_basic_map *isl_basic_map_product(
4877                 struct isl_basic_map *bmap1, struct isl_basic_map *bmap2)
4878 {
4879         struct isl_dim *dim_result = NULL;
4880         struct isl_basic_map *bmap;
4881         unsigned in1, in2, out1, out2, nparam, total, pos;
4882         struct isl_dim_map *dim_map1, *dim_map2;
4883
4884         if (!bmap1 || !bmap2)
4885                 goto error;
4886
4887         isl_assert(map1->ctx, isl_dim_match(bmap1->dim, isl_dim_param,
4888                                      bmap2->dim, isl_dim_param), goto error);
4889         dim_result = isl_dim_product(isl_dim_copy(bmap1->dim),
4890                                                    isl_dim_copy(bmap2->dim));
4891
4892         in1 = isl_basic_map_n_in(bmap1);
4893         in2 = isl_basic_map_n_in(bmap2);
4894         out1 = isl_basic_map_n_out(bmap1);
4895         out2 = isl_basic_map_n_out(bmap2);
4896         nparam = isl_basic_map_n_param(bmap1);
4897
4898         total = nparam + in1 + in2 + out1 + out2 + bmap1->n_div + bmap2->n_div;
4899         dim_map1 = isl_dim_map_alloc(bmap1->ctx, total);
4900         dim_map2 = isl_dim_map_alloc(bmap1->ctx, total);
4901         isl_dim_map_dim(dim_map1, bmap1->dim, isl_dim_param, pos = 0);
4902         isl_dim_map_dim(dim_map2, bmap2->dim, isl_dim_param, pos = 0);
4903         isl_dim_map_dim(dim_map1, bmap1->dim, isl_dim_in, pos += nparam);
4904         isl_dim_map_dim(dim_map2, bmap2->dim, isl_dim_in, pos += in1);
4905         isl_dim_map_dim(dim_map1, bmap1->dim, isl_dim_out, pos += in2);
4906         isl_dim_map_dim(dim_map2, bmap2->dim, isl_dim_out, pos += out1);
4907         isl_dim_map_div(dim_map1, bmap1, pos += out2);
4908         isl_dim_map_div(dim_map2, bmap2, pos += bmap1->n_div);
4909
4910         bmap = isl_basic_map_alloc_dim(dim_result,
4911                         bmap1->n_div + bmap2->n_div,
4912                         bmap1->n_eq + bmap2->n_eq,
4913                         bmap1->n_ineq + bmap2->n_ineq);
4914         bmap = add_constraints_dim_map(bmap, bmap1, dim_map1);
4915         bmap = add_constraints_dim_map(bmap, bmap2, dim_map2);
4916         bmap = isl_basic_map_simplify(bmap);
4917         return isl_basic_map_finalize(bmap);
4918 error:
4919         isl_basic_map_free(bmap1);
4920         isl_basic_map_free(bmap2);
4921         return NULL;
4922 }
4923
4924 /* Given two maps A -> B and C -> D, construct a map (A, C) -> (B, D)
4925  */
4926 struct isl_map *isl_map_product(struct isl_map *map1, struct isl_map *map2)
4927 {
4928         unsigned flags = 0;
4929         struct isl_map *result;
4930         int i, j;
4931
4932         if (!map1 || !map2)
4933                 goto error;
4934
4935         isl_assert(map1->ctx, isl_dim_match(map1->dim, isl_dim_param,
4936                                          map2->dim, isl_dim_param), goto error);
4937
4938         if (ISL_F_ISSET(map1, ISL_MAP_DISJOINT) &&
4939             ISL_F_ISSET(map2, ISL_MAP_DISJOINT))
4940                 ISL_FL_SET(flags, ISL_MAP_DISJOINT);
4941
4942         result = isl_map_alloc_dim(isl_dim_product(isl_dim_copy(map1->dim),
4943                                                    isl_dim_copy(map2->dim)),
4944                                 map1->n * map2->n, flags);
4945         if (!result)
4946                 goto error;
4947         for (i = 0; i < map1->n; ++i)
4948                 for (j = 0; j < map2->n; ++j) {
4949                         struct isl_basic_map *part;
4950                         part = isl_basic_map_product(
4951                                     isl_basic_map_copy(map1->p[i]),
4952                                     isl_basic_map_copy(map2->p[j]));
4953                         if (isl_basic_map_is_empty(part))
4954                                 isl_basic_map_free(part);
4955                         else
4956                                 result = isl_map_add(result, part);
4957                         if (!result)
4958                                 goto error;
4959                 }
4960         isl_map_free(map1);
4961         isl_map_free(map2);
4962         return result;
4963 error:
4964         isl_map_free(map1);
4965         isl_map_free(map2);
4966         return NULL;
4967 }
4968
4969 /* Given two set A and B, construct its Cartesian product A x B.
4970  */
4971 struct isl_set *isl_set_product(struct isl_set *set1, struct isl_set *set2)
4972 {
4973         return (struct isl_set *)isl_map_product((struct isl_map *)set1,
4974                                                  (struct isl_map *)set2);
4975 }
4976
4977 uint32_t isl_basic_set_get_hash(struct isl_basic_set *bset)
4978 {
4979         int i;
4980         uint32_t hash;
4981         unsigned total;
4982
4983         if (!bset)
4984                 return 0;
4985         bset = isl_basic_set_copy(bset);
4986         bset = isl_basic_set_normalize(bset);
4987         if (!bset)
4988                 return 0;
4989         total = isl_basic_set_total_dim(bset);
4990         isl_hash_byte(hash, bset->n_eq & 0xFF);
4991         for (i = 0; i < bset->n_eq; ++i) {
4992                 uint32_t c_hash;
4993                 c_hash = isl_seq_get_hash(bset->eq[i], 1 + total);
4994                 isl_hash_hash(hash, c_hash);
4995         }
4996         isl_hash_byte(hash, bset->n_ineq & 0xFF);
4997         for (i = 0; i < bset->n_ineq; ++i) {
4998                 uint32_t c_hash;
4999                 c_hash = isl_seq_get_hash(bset->ineq[i], 1 + total);
5000                 isl_hash_hash(hash, c_hash);
5001         }
5002         isl_hash_byte(hash, bset->n_div & 0xFF);
5003         for (i = 0; i < bset->n_div; ++i) {
5004                 uint32_t c_hash;
5005                 if (isl_int_is_zero(bset->div[i][0]))
5006                         continue;
5007                 isl_hash_byte(hash, i & 0xFF);
5008                 c_hash = isl_seq_get_hash(bset->div[i], 1 + 1 + total);
5009                 isl_hash_hash(hash, c_hash);
5010         }
5011         isl_basic_set_free(bset);
5012         return hash;
5013 }
5014
5015 uint32_t isl_set_get_hash(struct isl_set *set)
5016 {
5017         int i;
5018         uint32_t hash;
5019
5020         if (!set)
5021                 return 0;
5022         set = isl_set_copy(set);
5023         set = isl_set_normalize(set);
5024         if (!set)
5025                 return 0;
5026
5027         hash = isl_hash_init();
5028         for (i = 0; i < set->n; ++i) {
5029                 uint32_t bset_hash;
5030                 bset_hash = isl_basic_set_get_hash(set->p[i]);
5031                 isl_hash_hash(hash, bset_hash);
5032         }
5033
5034         isl_set_free(set);
5035
5036         return hash;
5037 }
5038
5039 /* Check if the value for dimension dim is completely determined
5040  * by the values of the other parameters and variables.
5041  * That is, check if dimension dim is involved in an equality.
5042  */
5043 int isl_basic_set_dim_is_unique(struct isl_basic_set *bset, unsigned dim)
5044 {
5045         int i;
5046         unsigned nparam;
5047
5048         if (!bset)
5049                 return -1;
5050         nparam = isl_basic_set_n_param(bset);
5051         for (i = 0; i < bset->n_eq; ++i)
5052                 if (!isl_int_is_zero(bset->eq[i][1 + nparam + dim]))
5053                         return 1;
5054         return 0;
5055 }
5056
5057 /* Check if the value for dimension dim is completely determined
5058  * by the values of the other parameters and variables.
5059  * That is, check if dimension dim is involved in an equality
5060  * for each of the subsets.
5061  */
5062 int isl_set_dim_is_unique(struct isl_set *set, unsigned dim)
5063 {
5064         int i;
5065
5066         if (!set)
5067                 return -1;
5068         for (i = 0; i < set->n; ++i) {
5069                 int unique;
5070                 unique = isl_basic_set_dim_is_unique(set->p[i], dim);
5071                 if (unique != 1)
5072                         return unique;
5073         }
5074         return 1;
5075 }