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         if (dims_ok)
 876                 ext->sample = isl_vec_copy(base->sample);
 877         flags = base->flags;
 878         ext = add_constraints(ext, base, 0, 0);
 879         if (ext) {
 880                 ext->flags = flags;
 881                 ISL_F_CLR(ext, ISL_BASIC_SET_FINAL);
 882         }
 883
 884         return ext;
 885
 886 error:
 887         isl_dim_free(dim);
 888         isl_basic_map_free(base);
 889         return NULL;
 890 }
 891
 892 struct isl_basic_set *isl_basic_set_extend_dim(struct isl_basic_set *base,
 893                 struct isl_dim *dim, unsigned extra,
 894                 unsigned n_eq, unsigned n_ineq)
 895 {
 896         return (struct isl_basic_set *)
 897                 isl_basic_map_extend_dim((struct isl_basic_map *)base, dim,
 898                                                         extra, n_eq, n_ineq);
 899 }
 900
 901 struct isl_basic_map *isl_basic_map_extend_constraints(
 902                 struct isl_basic_map *base, unsigned n_eq, unsigned n_ineq)
 903 {
 904         if (!base)
 905                 return NULL;
 906         return isl_basic_map_extend_dim(base, isl_dim_copy(base->dim),
 907                                         0, n_eq, n_ineq);
 908 }
 909
 910 struct isl_basic_map *isl_basic_map_extend(struct isl_basic_map *base,
 911                 unsigned nparam, unsigned n_in, unsigned n_out, unsigned extra,
 912                 unsigned n_eq, unsigned n_ineq)
 913 {
 914         struct isl_basic_map *bmap;
 915         struct isl_dim *dim;
 916
 917         if (!base)
 918                 return NULL;
 919         dim = isl_dim_alloc(base->ctx, nparam, n_in, n_out);
 920         if (!dim)
 921                 return NULL;
 922
 923         bmap = isl_basic_map_extend_dim(base, dim, extra, n_eq, n_ineq);
 924         return bmap;
 925 }
 926
 927 struct isl_basic_set *isl_basic_set_extend(struct isl_basic_set *base,
 928                 unsigned nparam, unsigned dim, unsigned extra,
 929                 unsigned n_eq, unsigned n_ineq)
 930 {
 931         return (struct isl_basic_set *)
 932                 isl_basic_map_extend((struct isl_basic_map *)base,
 933                                         nparam, 0, dim, extra, n_eq, n_ineq);
 934 }
 935
 936 struct isl_basic_set *isl_basic_set_extend_constraints(
 937                 struct isl_basic_set *base, unsigned n_eq, unsigned n_ineq)
 938 {
 939         return (struct isl_basic_set *)
 940                 isl_basic_map_extend_constraints((struct isl_basic_map *)base,
 941                                                     n_eq, n_ineq);
 942 }
 943
 944 struct isl_basic_set *isl_basic_set_cow(struct isl_basic_set *bset)
 945 {
 946         return (struct isl_basic_set *)
 947                 isl_basic_map_cow((struct isl_basic_map *)bset);
 948 }
 949
 950 struct isl_basic_map *isl_basic_map_cow(struct isl_basic_map *bmap)
 951 {
 952         if (!bmap)
 953                 return NULL;
 954
 955         if (bmap->ref > 1) {
 956                 bmap->ref--;
 957                 bmap = isl_basic_map_dup(bmap);
 958         }
 959         ISL_F_CLR(bmap, ISL_BASIC_SET_FINAL);
 960         return bmap;
 961 }
 962
 963 struct isl_set *isl_set_cow(struct isl_set *set)
 964 {
 965         if (!set)
 966                 return NULL;
 967
 968         if (set->ref == 1)
 969                 return set;
 970         set->ref--;
 971         return isl_set_dup(set);
 972 }
 973
 974 struct isl_map *isl_map_cow(struct isl_map *map)
 975 {
 976         if (!map)
 977                 return NULL;
 978
 979         if (map->ref == 1)
 980                 return map;
 981         map->ref--;
 982         return isl_map_dup(map);
 983 }
 984
 985 static void swap_vars(struct isl_blk blk, isl_int *a,
 986                         unsigned a_len, unsigned b_len)
 987 {
 988         isl_seq_cpy(blk.data, a+a_len, b_len);
 989         isl_seq_cpy(blk.data+b_len, a, a_len);
 990         isl_seq_cpy(a, blk.data, b_len+a_len);
 991 }
 992
 993 struct isl_basic_set *isl_basic_set_swap_vars(
 994                 struct isl_basic_set *bset, unsigned n)
 995 {
 996         int i;
 997         struct isl_blk blk;
 998         unsigned dim;
 999         unsigned nparam;
1000
1001         if (!bset)
1002                 goto error;
1003
1004         nparam = isl_basic_set_n_param(bset);
1005         dim = isl_basic_set_n_dim(bset);
1006         isl_assert(bset->ctx, n <= dim, goto error);
1007
1008         if (n == dim)
1009                 return bset;
1010
1011         bset = isl_basic_set_cow(bset);
1012         if (!bset)
1013                 return NULL;
1014
1015         blk = isl_blk_alloc(bset->ctx, dim);
1016         if (isl_blk_is_error(blk))
1017                 goto error;
1018
1019         for (i = 0; i < bset->n_eq; ++i)
1020                 swap_vars(blk,
1021                           bset->eq[i]+1+nparam, n, dim - n);
1022
1023         for (i = 0; i < bset->n_ineq; ++i)
1024                 swap_vars(blk,
1025                           bset->ineq[i]+1+nparam, n, dim - n);
1026
1027         for (i = 0; i < bset->n_div; ++i)
1028                 swap_vars(blk,
1029                           bset->div[i]+1+1+nparam, n, dim - n);
1030
1031         isl_blk_free(bset->ctx, blk);
1032
1033         ISL_F_CLR(bset, ISL_BASIC_SET_NORMALIZED);
1034         return bset;
1035
1036 error:
1037         isl_basic_set_free(bset);
1038         return NULL;
1039 }
1040
1041 struct isl_set *isl_set_swap_vars(struct isl_set *set, unsigned n)
1042 {
1043         int i;
1044         set = isl_set_cow(set);
1045         if (!set)
1046                 return NULL;
1047
1048         for (i = 0; i < set->n; ++i) {
1049                 set->p[i] = isl_basic_set_swap_vars(set->p[i], n);
1050                 if (!set->p[i]) {
1051                         isl_set_free(set);
1052                         return NULL;
1053                 }
1054         }
1055         ISL_F_CLR(set, ISL_SET_NORMALIZED);
1056         return set;
1057 }
1058
1059 struct isl_basic_map *isl_basic_map_set_to_empty(struct isl_basic_map *bmap)
1060 {
1061         int i = 0;
1062         unsigned total;
1063         if (!bmap)
1064                 goto error;
1065         total = isl_basic_map_total_dim(bmap);
1066         isl_basic_map_free_div(bmap, bmap->n_div);
1067         isl_basic_map_free_inequality(bmap, bmap->n_ineq);
1068         if (bmap->n_eq > 0)
1069                 isl_basic_map_free_equality(bmap, bmap->n_eq-1);
1070         else {
1071                 isl_basic_map_alloc_equality(bmap);
1072                 if (i < 0)
1073                         goto error;
1074         }
1075         isl_int_set_si(bmap->eq[i][0], 1);
1076         isl_seq_clr(bmap->eq[i]+1, total);
1077         ISL_F_SET(bmap, ISL_BASIC_MAP_EMPTY);
1078         return isl_basic_map_finalize(bmap);
1079 error:
1080         isl_basic_map_free(bmap);
1081         return NULL;
1082 }
1083
1084 struct isl_basic_set *isl_basic_set_set_to_empty(struct isl_basic_set *bset)
1085 {
1086         return (struct isl_basic_set *)
1087                 isl_basic_map_set_to_empty((struct isl_basic_map *)bset);
1088 }
1089
1090 void isl_basic_map_swap_div(struct isl_basic_map *bmap, int a, int b)
1091 {
1092         int i;
1093         unsigned off = isl_dim_total(bmap->dim);
1094         isl_int *t = bmap->div[a];
1095         bmap->div[a] = bmap->div[b];
1096         bmap->div[b] = t;
1097
1098         for (i = 0; i < bmap->n_eq; ++i)
1099                 isl_int_swap(bmap->eq[i][1+off+a], bmap->eq[i][1+off+b]);
1100
1101         for (i = 0; i < bmap->n_ineq; ++i)
1102                 isl_int_swap(bmap->ineq[i][1+off+a], bmap->ineq[i][1+off+b]);
1103
1104         for (i = 0; i < bmap->n_div; ++i)
1105                 isl_int_swap(bmap->div[i][1+1+off+a], bmap->div[i][1+1+off+b]);
1106         ISL_F_CLR(bmap, ISL_BASIC_MAP_NORMALIZED);
1107 }
1108
1109 /* Eliminate the specified n dimensions starting at first from the
1110  * constraints using Fourier-Motzkin, The dimensions themselves
1111  * are not removed.
1112  */
1113 struct isl_set *isl_set_eliminate_dims(struct isl_set *set,
1114         unsigned first, unsigned n)
1115 {
1116         int i;
1117         unsigned nparam;
1118
1119         if (!set)
1120                 return NULL;
1121         if (n == 0)
1122                 return set;
1123
1124         set = isl_set_cow(set);
1125         if (!set)
1126                 return NULL;
1127         isl_assert(set->ctx, first+n <= isl_set_n_dim(set), goto error);
1128         nparam = isl_set_n_param(set);
1129
1130         for (i = 0; i < set->n; ++i) {
1131                 set->p[i] = isl_basic_set_eliminate_vars(set->p[i],
1132                                                             nparam + first, n);
1133                 if (!set->p[i])
1134                         goto error;
1135         }
1136         return set;
1137 error:
1138         isl_set_free(set);
1139         return NULL;
1140 }
1141
1142 /* Project out n dimensions starting at first using Fourier-Motzkin */
1143 struct isl_set *isl_set_remove_dims(struct isl_set *set,
1144         unsigned first, unsigned n)
1145 {
1146         set = isl_set_eliminate_dims(set, first, n);
1147         set = isl_set_drop_dims(set, first, n);
1148         return set;
1149 }
1150
1151 struct isl_basic_set *isl_basic_set_remove_divs(struct isl_basic_set *bset)
1152 {
1153         bset = isl_basic_set_eliminate_vars(bset, isl_dim_total(bset->dim),
1154                                                 bset->n_div);
1155         if (!bset)
1156                 return NULL;
1157         bset->n_div = 0;
1158         return bset;
1159 }
1160
1161 struct isl_set *isl_set_remove_divs(struct isl_set *set)
1162 {
1163         int i;
1164
1165         if (!set)
1166                 return NULL;
1167         if (set->n == 0)
1168                 return set;
1169
1170         set = isl_set_cow(set);
1171         if (!set)
1172                 return NULL;
1173
1174         for (i = 0; i < set->n; ++i) {
1175                 set->p[i] = isl_basic_set_remove_divs(set->p[i]);
1176                 if (!set->p[i])
1177                         goto error;
1178         }
1179         return set;
1180 error:
1181         isl_set_free(set);
1182         return NULL;
1183 }
1184
1185 struct isl_basic_map *isl_basic_map_remove(struct isl_basic_map *bmap,
1186         enum isl_dim_type type, unsigned first, unsigned n)
1187 {
1188         if (!bmap)
1189                 return NULL;
1190         isl_assert(bmap->ctx, first + n <= isl_basic_map_dim(bmap, type),
1191                         goto error);
1192         if (n == 0)
1193                 return bmap;
1194         bmap = isl_basic_map_eliminate_vars(bmap,
1195                         isl_basic_map_offset(bmap, type) - 1 + first, n);
1196         if (!bmap)
1197                 return bmap;
1198         if (ISL_F_ISSET(bmap, ISL_BASIC_MAP_EMPTY) && type == isl_dim_div)
1199                 return bmap;
1200         bmap = isl_basic_map_drop(bmap, type, first, n);
1201         return bmap;
1202 error:
1203         isl_basic_map_free(bmap);
1204         return NULL;
1205 }
1206
1207 struct isl_map *isl_map_remove(struct isl_map *map,
1208         enum isl_dim_type type, unsigned first, unsigned n)
1209 {
1210         int i;
1211         unsigned nparam;
1212
1213         if (n == 0)
1214                 return map;
1215
1216         map = isl_map_cow(map);
1217         if (!map)
1218                 return NULL;
1219         isl_assert(map->ctx, first + n <= isl_map_dim(map, type), goto error);
1220
1221         for (i = 0; i < map->n; ++i) {
1222                 map->p[i] = isl_basic_map_eliminate_vars(map->p[i],
1223                         isl_basic_map_offset(map->p[i], type) - 1 + first, n);
1224                 if (!map->p[i])
1225                         goto error;
1226         }
1227         map = isl_map_drop(map, type, first, n);
1228         return map;
1229 error:
1230         isl_map_free(map);
1231         return NULL;
1232 }
1233
1234 /* Project out n inputs starting at first using Fourier-Motzkin */
1235 struct isl_map *isl_map_remove_inputs(struct isl_map *map,
1236         unsigned first, unsigned n)
1237 {
1238         return isl_map_remove(map, isl_dim_in, first, n);
1239 }
1240
1241 /* Project out n dimensions starting at first using Fourier-Motzkin */
1242 struct isl_basic_set *isl_basic_set_remove_dims(struct isl_basic_set *bset,
1243         unsigned first, unsigned n)
1244 {
1245         unsigned nparam = isl_basic_set_n_param(bset);
1246         bset = isl_basic_set_eliminate_vars(bset, nparam + first, n);
1247         bset = isl_basic_set_drop_dims(bset, first, n);
1248         return bset;
1249 }
1250
1251 static void dump_term(struct isl_basic_map *bmap,
1252                         isl_int c, int pos, FILE *out)
1253 {
1254         const char *name;
1255         unsigned in = isl_basic_map_n_in(bmap);
1256         unsigned dim = in + isl_basic_map_n_out(bmap);
1257         unsigned nparam = isl_basic_map_n_param(bmap);
1258         if (!pos)
1259                 isl_int_print(out, c, 0);
1260         else {
1261                 if (!isl_int_is_one(c))
1262                         isl_int_print(out, c, 0);
1263                 if (pos < 1 + nparam) {
1264                         name = isl_dim_get_name(bmap->dim,
1265                                                 isl_dim_param, pos - 1);
1266                         if (name)
1267                                 fprintf(out, "%s", name);
1268                         else
1269                                 fprintf(out, "p%d", pos - 1);
1270                 } else if (pos < 1 + nparam + in)
1271                         fprintf(out, "i%d", pos - 1 - nparam);
1272                 else if (pos < 1 + nparam + dim)
1273                         fprintf(out, "o%d", pos - 1 - nparam - in);
1274                 else
1275                         fprintf(out, "e%d", pos - 1 - nparam - dim);
1276         }
1277 }
1278
1279 static void dump_constraint_sign(struct isl_basic_map *bmap, isl_int *c,
1280                                 int sign, FILE *out)
1281 {
1282         int i;
1283         int first;
1284         unsigned len = 1 + isl_basic_map_total_dim(bmap);
1285         isl_int v;
1286
1287         isl_int_init(v);
1288         for (i = 0, first = 1; i < len; ++i) {
1289                 if (isl_int_sgn(c[i]) * sign <= 0)
1290                         continue;
1291                 if (!first)
1292                         fprintf(out, " + ");
1293                 first = 0;
1294                 isl_int_abs(v, c[i]);
1295                 dump_term(bmap, v, i, out);
1296         }
1297         isl_int_clear(v);
1298         if (first)
1299                 fprintf(out, "0");
1300 }
1301
1302 static void dump_constraint(struct isl_basic_map *bmap, isl_int *c,
1303                                 const char *op, FILE *out, int indent)
1304 {
1305         int i;
1306
1307         fprintf(out, "%*s", indent, "");
1308
1309         dump_constraint_sign(bmap, c, 1, out);
1310         fprintf(out, " %s ", op);
1311         dump_constraint_sign(bmap, c, -1, out);
1312
1313         fprintf(out, "\n");
1314
1315         for (i = bmap->n_div; i < bmap->extra; ++i) {
1316                 if (isl_int_is_zero(c[1+isl_dim_total(bmap->dim)+i]))
1317                         continue;
1318                 fprintf(out, "%*s", indent, "");
1319                 fprintf(out, "ERROR: unused div coefficient not zero\n");
1320                 abort();
1321         }
1322 }
1323
1324 static void dump_constraints(struct isl_basic_map *bmap,
1325                                 isl_int **c, unsigned n,
1326                                 const char *op, FILE *out, int indent)
1327 {
1328         int i;
1329
1330         for (i = 0; i < n; ++i)
1331                 dump_constraint(bmap, c[i], op, out, indent);
1332 }
1333
1334 static void dump_affine(struct isl_basic_map *bmap, isl_int *exp, FILE *out)
1335 {
1336         int j;
1337         int first = 1;
1338         unsigned total = isl_basic_map_total_dim(bmap);
1339
1340         for (j = 0; j < 1 + total; ++j) {
1341                 if (isl_int_is_zero(exp[j]))
1342                         continue;
1343                 if (!first && isl_int_is_pos(exp[j]))
1344                         fprintf(out, "+");
1345                 dump_term(bmap, exp[j], j, out);
1346                 first = 0;
1347         }
1348 }
1349
1350 static void dump(struct isl_basic_map *bmap, FILE *out, int indent)
1351 {
1352         int i;
1353
1354         dump_constraints(bmap, bmap->eq, bmap->n_eq, "=", out, indent);
1355         dump_constraints(bmap, bmap->ineq, bmap->n_ineq, ">=", out, indent);
1356
1357         for (i = 0; i < bmap->n_div; ++i) {
1358                 fprintf(out, "%*s", indent, "");
1359                 fprintf(out, "e%d = [(", i);
1360                 dump_affine(bmap, bmap->div[i]+1, out);
1361                 fprintf(out, ")/");
1362                 isl_int_print(out, bmap->div[i][0], 0);
1363                 fprintf(out, "]\n");
1364         }
1365 }
1366
1367 void isl_basic_set_dump(struct isl_basic_set *bset, FILE *out, int indent)
1368 {
1369         if (!bset) {
1370                 fprintf(out, "null basic set\n");
1371                 return;
1372         }
1373
1374         fprintf(out, "%*s", indent, "");
1375         fprintf(out, "ref: %d, nparam: %d, dim: %d, extra: %d, flags: %x\n",
1376                         bset->ref, bset->dim->nparam, bset->dim->n_out,
1377                         bset->extra, bset->flags);
1378         dump((struct isl_basic_map *)bset, out, indent);
1379 }
1380
1381 void isl_basic_map_dump(struct isl_basic_map *bmap, FILE *out, int indent)
1382 {
1383         if (!bmap) {
1384                 fprintf(out, "null basic map\n");
1385                 return;
1386         }
1387
1388         fprintf(out, "%*s", indent, "");
1389         fprintf(out, "ref: %d, nparam: %d, in: %d, out: %d, extra: %d, "
1390                         "flags: %x, n_name: %d\n",
1391                 bmap->ref,
1392                 bmap->dim->nparam, bmap->dim->n_in, bmap->dim->n_out,
1393                 bmap->extra, bmap->flags, bmap->dim->n_name);
1394         dump(bmap, out, indent);
1395 }
1396
1397 int isl_inequality_negate(struct isl_basic_map *bmap, unsigned pos)
1398 {
1399         unsigned total;
1400         if (!bmap)
1401                 return -1;
1402         total = isl_basic_map_total_dim(bmap);
1403         isl_assert(bmap->ctx, pos < bmap->n_ineq, return -1);
1404         isl_seq_neg(bmap->ineq[pos], bmap->ineq[pos], 1 + total);
1405         isl_int_sub_ui(bmap->ineq[pos][0], bmap->ineq[pos][0], 1);
1406         ISL_F_CLR(bmap, ISL_BASIC_MAP_NORMALIZED);
1407         return 0;
1408 }
1409
1410 struct isl_set *isl_set_alloc_dim(struct isl_dim *dim, int n, unsigned flags)
1411 {
1412         struct isl_set *set;
1413
1414         if (!dim)
1415                 return NULL;
1416         isl_assert(dim->ctx, dim->n_in == 0, return NULL);
1417         isl_assert(dim->ctx, n >= 0, return NULL);
1418         set = isl_alloc(dim->ctx, struct isl_set,
1419                         sizeof(struct isl_set) +
1420                         n * sizeof(struct isl_basic_set *));
1421         if (!set)
1422                 goto error;
1423
1424         set->ctx = dim->ctx;
1425         isl_ctx_ref(set->ctx);
1426         set->ref = 1;
1427         set->size = n;
1428         set->n = 0;
1429         set->dim = dim;
1430         set->flags = flags;
1431         return set;
1432 error:
1433         isl_dim_free(dim);
1434         return NULL;
1435 }
1436
1437 struct isl_set *isl_set_alloc(struct isl_ctx *ctx,
1438                 unsigned nparam, unsigned dim, int n, unsigned flags)
1439 {
1440         struct isl_set *set;
1441         struct isl_dim *dims;
1442
1443         dims = isl_dim_alloc(ctx, nparam, 0, dim);
1444         if (!dims)
1445                 return NULL;
1446
1447         set = isl_set_alloc_dim(dims, n, flags);
1448         return set;
1449 }
1450
1451 /* Make sure "map" has room for at least "n" more basic maps.
1452  */
1453 struct isl_map *isl_map_grow(struct isl_map *map, int n)
1454 {
1455         int i;
1456         struct isl_map *grown = NULL;
1457
1458         if (!map)
1459                 return NULL;
1460         isl_assert(map->ctx, n >= 0, goto error);
1461         if (map->n + n <= map->size)
1462                 return map;
1463         grown = isl_map_alloc_dim(isl_map_get_dim(map), map->n + n, map->flags);
1464         if (!grown)
1465                 goto error;
1466         for (i = 0; i < map->n; ++i) {
1467                 grown->p[i] = isl_basic_map_copy(map->p[i]);
1468                 if (!grown->p[i])
1469                         goto error;
1470                 grown->n++;
1471         }
1472         isl_map_free(map);
1473         return grown;
1474 error:
1475         isl_map_free(grown);
1476         isl_map_free(map);
1477         return NULL;
1478 }
1479
1480 /* Make sure "set" has room for at least "n" more basic sets.
1481  */
1482 struct isl_set *isl_set_grow(struct isl_set *set, int n)
1483 {
1484         return (struct isl_set *)isl_map_grow((struct isl_map *)set, n);
1485 }
1486
1487 struct isl_set *isl_set_dup(struct isl_set *set)
1488 {
1489         int i;
1490         struct isl_set *dup;
1491
1492         if (!set)
1493                 return NULL;
1494
1495         dup = isl_set_alloc_dim(isl_dim_copy(set->dim), set->n, set->flags);
1496         if (!dup)
1497                 return NULL;
1498         for (i = 0; i < set->n; ++i)
1499                 dup = isl_set_add(dup, isl_basic_set_copy(set->p[i]));
1500         return dup;
1501 }
1502
1503 struct isl_set *isl_set_from_basic_set(struct isl_basic_set *bset)
1504 {
1505         struct isl_set *set;
1506
1507         if (!bset)
1508                 return NULL;
1509
1510         set = isl_set_alloc_dim(isl_dim_copy(bset->dim), 1, ISL_MAP_DISJOINT);
1511         if (!set) {
1512                 isl_basic_set_free(bset);
1513                 return NULL;
1514         }
1515         return isl_set_add(set, bset);
1516 }
1517
1518 struct isl_map *isl_map_from_basic_map(struct isl_basic_map *bmap)
1519 {
1520         struct isl_map *map;
1521
1522         if (!bmap)
1523                 return NULL;
1524
1525         map = isl_map_alloc_dim(isl_dim_copy(bmap->dim), 1, ISL_MAP_DISJOINT);
1526         if (!map) {
1527                 isl_basic_map_free(bmap);
1528                 return NULL;
1529         }
1530         return isl_map_add(map, bmap);
1531 }
1532
1533 struct isl_set *isl_set_add(struct isl_set *set, struct isl_basic_set *bset)
1534 {
1535         return (struct isl_set *)isl_map_add((struct isl_map *)set,
1536                                                 (struct isl_basic_map *)bset);
1537 }
1538
1539 void isl_set_free(struct isl_set *set)
1540 {
1541         int i;
1542
1543         if (!set)
1544                 return;
1545
1546         if (--set->ref > 0)
1547                 return;
1548
1549         isl_ctx_deref(set->ctx);
1550         for (i = 0; i < set->n; ++i)
1551                 isl_basic_set_free(set->p[i]);
1552         isl_dim_free(set->dim);
1553         free(set);
1554 }
1555
1556 void isl_set_dump(struct isl_set *set, FILE *out, int indent)
1557 {
1558         int i;
1559
1560         if (!set) {
1561                 fprintf(out, "null set\n");
1562                 return;
1563         }
1564
1565         fprintf(out, "%*s", indent, "");
1566         fprintf(out, "ref: %d, n: %d, nparam: %d, dim: %d, flags: %x\n",
1567                         set->ref, set->n, set->dim->nparam, set->dim->n_out,
1568                         set->flags);
1569         for (i = 0; i < set->n; ++i) {
1570                 fprintf(out, "%*s", indent, "");
1571                 fprintf(out, "basic set %d:\n", i);
1572                 isl_basic_set_dump(set->p[i], out, indent+4);
1573         }
1574 }
1575
1576 void isl_map_dump(struct isl_map *map, FILE *out, int indent)
1577 {
1578         int i;
1579
1580         if (!map) {
1581                 fprintf(out, "null map\n");
1582                 return;
1583         }
1584
1585         fprintf(out, "%*s", indent, "");
1586         fprintf(out, "ref: %d, n: %d, nparam: %d, in: %d, out: %d, "
1587                      "flags: %x, n_name: %d\n",
1588                         map->ref, map->n, map->dim->nparam, map->dim->n_in,
1589                         map->dim->n_out, map->flags, map->dim->n_name);
1590         for (i = 0; i < map->n; ++i) {
1591                 fprintf(out, "%*s", indent, "");
1592                 fprintf(out, "basic map %d:\n", i);
1593                 isl_basic_map_dump(map->p[i], out, indent+4);
1594         }
1595 }
1596
1597 struct isl_basic_map *isl_basic_map_intersect_domain(
1598                 struct isl_basic_map *bmap, struct isl_basic_set *bset)
1599 {
1600         struct isl_basic_map *bmap_domain;
1601         struct isl_dim *dim;
1602
1603         if (!bmap || !bset)
1604                 goto error;
1605
1606         isl_assert(bset->ctx, isl_dim_match(bmap->dim, isl_dim_param,
1607                                         bset->dim, isl_dim_param), goto error);
1608
1609         if (isl_dim_size(bset->dim, isl_dim_set) != 0)
1610                 isl_assert(bset->ctx,
1611                     isl_basic_map_compatible_domain(bmap, bset), goto error);
1612
1613         bmap = isl_basic_map_cow(bmap);
1614         bmap = isl_basic_map_extend_dim(bmap, isl_dim_copy(bmap->dim),
1615                         bset->n_div, bset->n_eq, bset->n_ineq);
1616         if (!bmap)
1617                 goto error;
1618         dim = isl_dim_reverse(isl_dim_copy(bset->dim));
1619         bmap_domain = isl_basic_map_from_basic_set(bset, dim);
1620         bmap = add_constraints(bmap, bmap_domain, 0, 0);
1621
1622         bmap = isl_basic_map_simplify(bmap);
1623         return isl_basic_map_finalize(bmap);
1624 error:
1625         isl_basic_map_free(bmap);
1626         isl_basic_set_free(bset);
1627         return NULL;
1628 }
1629
1630 struct isl_basic_map *isl_basic_map_intersect_range(
1631                 struct isl_basic_map *bmap, struct isl_basic_set *bset)
1632 {
1633         struct isl_basic_map *bmap_range;
1634
1635         if (!bmap || !bset)
1636                 goto error;
1637
1638         isl_assert(bset->ctx, isl_dim_match(bmap->dim, isl_dim_param,
1639                                         bset->dim, isl_dim_param), goto error);
1640
1641         if (isl_dim_size(bset->dim, isl_dim_set) != 0)
1642                 isl_assert(bset->ctx,
1643                     isl_basic_map_compatible_range(bmap, bset), goto error);
1644
1645         bmap = isl_basic_map_cow(bmap);
1646         bmap = isl_basic_map_extend_dim(bmap, isl_dim_copy(bmap->dim),
1647                         bset->n_div, bset->n_eq, bset->n_ineq);
1648         if (!bmap)
1649                 goto error;
1650         bmap_range = isl_basic_map_from_basic_set(bset, isl_dim_copy(bset->dim));
1651         bmap = add_constraints(bmap, bmap_range, 0, 0);
1652
1653         bmap = isl_basic_map_simplify(bmap);
1654         return isl_basic_map_finalize(bmap);
1655 error:
1656         isl_basic_map_free(bmap);
1657         isl_basic_set_free(bset);
1658         return NULL;
1659 }
1660
1661 static int basic_map_contains(struct isl_basic_map *bmap, struct isl_vec *vec)
1662 {
1663         int i;
1664         unsigned total;
1665         isl_int s;
1666
1667         total = 1 + isl_basic_map_total_dim(bmap);
1668         if (total != vec->size)
1669                 return -1;
1670
1671         isl_int_init(s);
1672
1673         for (i = 0; i < bmap->n_eq; ++i) {
1674                 isl_seq_inner_product(vec->el, bmap->eq[i], total, &s);
1675                 if (!isl_int_is_zero(s)) {
1676                         isl_int_clear(s);
1677                         return 0;
1678                 }
1679         }
1680
1681         for (i = 0; i < bmap->n_ineq; ++i) {
1682                 isl_seq_inner_product(vec->el, bmap->ineq[i], total, &s);
1683                 if (isl_int_is_neg(s)) {
1684                         isl_int_clear(s);
1685                         return 0;
1686                 }
1687         }
1688
1689         isl_int_clear(s);
1690
1691         return 1;
1692 }
1693
1694 int isl_basic_set_contains(struct isl_basic_set *bset, struct isl_vec *vec)
1695 {
1696         return basic_map_contains((struct isl_basic_map *)bset, vec);
1697 }
1698
1699 struct isl_basic_map *isl_basic_map_intersect(
1700                 struct isl_basic_map *bmap1, struct isl_basic_map *bmap2)
1701 {
1702         struct isl_vec *sample = NULL;
1703
1704         if (!bmap1 || !bmap2)
1705                 goto error;
1706
1707         isl_assert(bmap1->ctx, isl_dim_match(bmap1->dim, isl_dim_param,
1708                                      bmap2->dim, isl_dim_param), goto error);
1709         if (isl_dim_total(bmap1->dim) ==
1710                                 isl_dim_size(bmap1->dim, isl_dim_param) &&
1711             isl_dim_total(bmap2->dim) !=
1712                                 isl_dim_size(bmap2->dim, isl_dim_param))
1713                 return isl_basic_map_intersect(bmap2, bmap1);
1714
1715         if (isl_dim_total(bmap2->dim) !=
1716                                         isl_dim_size(bmap2->dim, isl_dim_param))
1717                 isl_assert(bmap1->ctx,
1718                             isl_dim_equal(bmap1->dim, bmap2->dim), goto error);
1719
1720         if (bmap1->sample &&
1721             basic_map_contains(bmap1, bmap1->sample) > 0 &&
1722             basic_map_contains(bmap2, bmap1->sample) > 0)
1723                 sample = isl_vec_copy(bmap1->sample);
1724         else if (bmap2->sample &&
1725             basic_map_contains(bmap1, bmap2->sample) > 0 &&
1726             basic_map_contains(bmap2, bmap2->sample) > 0)
1727                 sample = isl_vec_copy(bmap2->sample);
1728
1729         bmap1 = isl_basic_map_cow(bmap1);
1730         bmap1 = isl_basic_map_extend_dim(bmap1, isl_dim_copy(bmap1->dim),
1731                         bmap2->n_div, bmap2->n_eq, bmap2->n_ineq);
1732         if (!bmap1)
1733                 goto error;
1734         bmap1 = add_constraints(bmap1, bmap2, 0, 0);
1735
1736         if (sample) {
1737                 isl_vec_free(bmap1->sample);
1738                 bmap1->sample = sample;
1739         }
1740
1741         bmap1 = isl_basic_map_simplify(bmap1);
1742         return isl_basic_map_finalize(bmap1);
1743 error:
1744         if (sample)
1745                 isl_vec_free(sample);
1746         isl_basic_map_free(bmap1);
1747         isl_basic_map_free(bmap2);
1748         return NULL;
1749 }
1750
1751 struct isl_basic_set *isl_basic_set_intersect(
1752                 struct isl_basic_set *bset1, struct isl_basic_set *bset2)
1753 {
1754         return (struct isl_basic_set *)
1755                 isl_basic_map_intersect(
1756                         (struct isl_basic_map *)bset1,
1757                         (struct isl_basic_map *)bset2);
1758 }
1759
1760 struct isl_map *isl_map_intersect(struct isl_map *map1, struct isl_map *map2)
1761 {
1762         unsigned flags = 0;
1763         struct isl_map *result;
1764         int i, j;
1765
1766         if (!map1 || !map2)
1767                 goto error;
1768
1769         isl_assert(map1->ctx, isl_dim_match(map1->dim, isl_dim_param,
1770                                          map2->dim, isl_dim_param), goto error);
1771         if (isl_dim_total(map1->dim) ==
1772                                 isl_dim_size(map1->dim, isl_dim_param) &&
1773             isl_dim_total(map2->dim) != isl_dim_size(map2->dim, isl_dim_param))
1774                 return isl_map_intersect(map2, map1);
1775
1776         if (isl_dim_total(map2->dim) != isl_dim_size(map2->dim, isl_dim_param))
1777                 isl_assert(map1->ctx,
1778                             isl_dim_equal(map1->dim, map2->dim), goto error);
1779
1780         if (ISL_F_ISSET(map1, ISL_MAP_DISJOINT) &&
1781             ISL_F_ISSET(map2, ISL_MAP_DISJOINT))
1782                 ISL_FL_SET(flags, ISL_MAP_DISJOINT);
1783
1784         result = isl_map_alloc_dim(isl_dim_copy(map1->dim),
1785                                 map1->n * map2->n, flags);
1786         if (!result)
1787                 goto error;
1788         for (i = 0; i < map1->n; ++i)
1789                 for (j = 0; j < map2->n; ++j) {
1790                         struct isl_basic_map *part;
1791                         part = isl_basic_map_intersect(
1792                                     isl_basic_map_copy(map1->p[i]),
1793                                     isl_basic_map_copy(map2->p[j]));
1794                         if (isl_basic_map_is_empty(part))
1795                                 isl_basic_map_free(part);
1796                         else
1797                                 result = isl_map_add(result, part);
1798                         if (!result)
1799                                 goto error;
1800                 }
1801         isl_map_free(map1);
1802         isl_map_free(map2);
1803         return result;
1804 error:
1805         isl_map_free(map1);
1806         isl_map_free(map2);
1807         return NULL;
1808 }
1809
1810 struct isl_set *isl_set_intersect(struct isl_set *set1, struct isl_set *set2)
1811 {
1812         return (struct isl_set *)
1813                 isl_map_intersect((struct isl_map *)set1,
1814                                   (struct isl_map *)set2);
1815 }
1816
1817 struct isl_basic_map *isl_basic_map_reverse(struct isl_basic_map *bmap)
1818 {
1819         struct isl_dim *dim;
1820         struct isl_basic_set *bset;
1821         unsigned in;
1822
1823         if (!bmap)
1824                 return NULL;
1825         bmap = isl_basic_map_cow(bmap);
1826         if (!bmap)
1827                 return NULL;
1828         dim = isl_dim_reverse(isl_dim_copy(bmap->dim));
1829         in = isl_basic_map_n_in(bmap);
1830         bset = isl_basic_set_from_basic_map(bmap);
1831         bset = isl_basic_set_swap_vars(bset, in);
1832         return isl_basic_map_from_basic_set(bset, dim);
1833 }
1834
1835 /* Turn final n dimensions into existentially quantified variables.
1836  */
1837 struct isl_basic_set *isl_basic_set_project_out(
1838                 struct isl_basic_set *bset, unsigned n, unsigned flags)
1839 {
1840         int i;
1841         size_t row_size;
1842         isl_int **new_div;
1843         isl_int *old;
1844
1845         if (!bset)
1846                 return NULL;
1847
1848         isl_assert(bset->ctx, n <= isl_basic_set_n_dim(bset), goto error);
1849
1850         if (n == 0)
1851                 return bset;
1852
1853         bset = isl_basic_set_cow(bset);
1854
1855         row_size = 1 + isl_dim_total(bset->dim) + bset->extra;
1856         old = bset->block2.data;
1857         bset->block2 = isl_blk_extend(bset->ctx, bset->block2,
1858                                         (bset->extra + n) * (1 + row_size));
1859         if (!bset->block2.data)
1860                 goto error;
1861         new_div = isl_alloc_array(ctx, isl_int *, bset->extra + n);
1862         if (!new_div)
1863                 goto error;
1864         for (i = 0; i < n; ++i) {
1865                 new_div[i] = bset->block2.data +
1866                                 (bset->extra + i) * (1 + row_size);
1867                 isl_seq_clr(new_div[i], 1 + row_size);
1868         }
1869         for (i = 0; i < bset->extra; ++i)
1870                 new_div[n + i] = bset->block2.data + (bset->div[i] - old);
1871         free(bset->div);
1872         bset->div = new_div;
1873         bset->n_div += n;
1874         bset->extra += n;
1875         bset->dim = isl_dim_drop_outputs(bset->dim,
1876                                             isl_basic_set_n_dim(bset) - n, n);
1877         if (!bset->dim)
1878                 goto error;
1879         bset = isl_basic_set_simplify(bset);
1880         return isl_basic_set_finalize(bset);
1881 error:
1882         isl_basic_set_free(bset);
1883         return NULL;
1884 }
1885
1886 static struct isl_basic_map *add_divs(struct isl_basic_map *bmap, unsigned n)
1887 {
1888         int i, j;
1889
1890         for (i = 0; i < n; ++i) {
1891                 j = isl_basic_map_alloc_div(bmap);
1892                 if (j < 0)
1893                         goto error;
1894                 isl_seq_clr(bmap->div[j], 1+1+isl_basic_map_total_dim(bmap));
1895         }
1896         return bmap;
1897 error:
1898         isl_basic_map_free(bmap);
1899         return NULL;
1900 }
1901
1902 struct isl_basic_map *isl_basic_map_apply_range(
1903                 struct isl_basic_map *bmap1, struct isl_basic_map *bmap2)
1904 {
1905         struct isl_dim *dim_result = NULL;
1906         struct isl_basic_map *bmap;
1907         unsigned n_in, n_out, n, nparam, total, pos;
1908         struct isl_dim_map *dim_map1, *dim_map2;
1909
1910         if (!bmap1 || !bmap2)
1911                 goto error;
1912
1913         dim_result = isl_dim_join(isl_dim_copy(bmap1->dim),
1914                                   isl_dim_copy(bmap2->dim));
1915
1916         n_in = isl_basic_map_n_in(bmap1);
1917         n_out = isl_basic_map_n_out(bmap2);
1918         n = isl_basic_map_n_out(bmap1);
1919         nparam = isl_basic_map_n_param(bmap1);
1920
1921         total = nparam + n_in + n_out + bmap1->n_div + bmap2->n_div + n;
1922         dim_map1 = isl_dim_map_alloc(bmap1->ctx, total);
1923         dim_map2 = isl_dim_map_alloc(bmap1->ctx, total);
1924         isl_dim_map_dim(dim_map1, bmap1->dim, isl_dim_param, pos = 0);
1925         isl_dim_map_dim(dim_map2, bmap2->dim, isl_dim_param, pos = 0);
1926         isl_dim_map_dim(dim_map1, bmap1->dim, isl_dim_in, pos += nparam);
1927         isl_dim_map_dim(dim_map2, bmap2->dim, isl_dim_out, pos += n_in);
1928         isl_dim_map_div(dim_map1, bmap1, pos += n_out);
1929         isl_dim_map_div(dim_map2, bmap2, pos += bmap1->n_div);
1930         isl_dim_map_dim(dim_map1, bmap1->dim, isl_dim_out, pos += bmap2->n_div);
1931         isl_dim_map_dim(dim_map2, bmap2->dim, isl_dim_in, pos);
1932
1933         bmap = isl_basic_map_alloc_dim(dim_result,
1934                         bmap1->n_div + bmap2->n_div + n,
1935                         bmap1->n_eq + bmap2->n_eq,
1936                         bmap1->n_ineq + bmap2->n_ineq);
1937         bmap = add_constraints_dim_map(bmap, bmap1, dim_map1);
1938         bmap = add_constraints_dim_map(bmap, bmap2, dim_map2);
1939         bmap = add_divs(bmap, n);
1940         bmap = isl_basic_map_simplify(bmap);
1941         return isl_basic_map_finalize(bmap);
1942 error:
1943         isl_basic_map_free(bmap1);
1944         isl_basic_map_free(bmap2);
1945         return NULL;
1946 }
1947
1948 struct isl_basic_set *isl_basic_set_apply(
1949                 struct isl_basic_set *bset, struct isl_basic_map *bmap)
1950 {
1951         if (!bset || !bmap)
1952                 goto error;
1953
1954         isl_assert(set->ctx, isl_basic_map_compatible_domain(bmap, bset),
1955                     goto error);
1956
1957         return (struct isl_basic_set *)
1958                 isl_basic_map_apply_range((struct isl_basic_map *)bset, bmap);
1959 error:
1960         isl_basic_set_free(bset);
1961         isl_basic_map_free(bmap);
1962         return NULL;
1963 }
1964
1965 struct isl_basic_map *isl_basic_map_apply_domain(
1966                 struct isl_basic_map *bmap1, struct isl_basic_map *bmap2)
1967 {
1968         if (!bmap1 || !bmap2)
1969                 goto error;
1970
1971         isl_assert(ctx,
1972             isl_basic_map_n_in(bmap1) == isl_basic_map_n_in(bmap2), goto error);
1973         isl_assert(ctx,
1974             isl_basic_map_n_param(bmap1) == isl_basic_map_n_param(bmap2),
1975             goto error);
1976
1977         bmap1 = isl_basic_map_reverse(bmap1);
1978         bmap1 = isl_basic_map_apply_range(bmap1, bmap2);
1979         return isl_basic_map_reverse(bmap1);
1980 error:
1981         isl_basic_map_free(bmap1);
1982         isl_basic_map_free(bmap2);
1983         return NULL;
1984 }
1985
1986 /* Given two basic maps A -> f(A) and B -> g(B), construct a basic map
1987  * A \cap B -> f(A) + f(B)
1988  */
1989 struct isl_basic_map *isl_basic_map_sum(
1990                 struct isl_basic_map *bmap1, struct isl_basic_map *bmap2)
1991 {
1992         unsigned n_in, n_out, nparam, total, pos;
1993         struct isl_basic_map *bmap = NULL;
1994         struct isl_dim_map *dim_map1, *dim_map2;
1995         int i;
1996
1997         if (!bmap1 || !bmap2)
1998                 goto error;
1999
2000         isl_assert(bmap1->ctx, isl_dim_equal(bmap1->dim, bmap2->dim),
2001                 goto error);
2002
2003         nparam = isl_basic_map_n_param(bmap1);
2004         n_in = isl_basic_map_n_in(bmap1);
2005         n_out = isl_basic_map_n_out(bmap1);
2006
2007         total = nparam + n_in + n_out + bmap1->n_div + bmap2->n_div + 2 * n_out;
2008         dim_map1 = isl_dim_map_alloc(bmap1->ctx, total);
2009         dim_map2 = isl_dim_map_alloc(bmap2->ctx, total);
2010         isl_dim_map_dim(dim_map1, bmap1->dim, isl_dim_param, pos = 0);
2011         isl_dim_map_dim(dim_map2, bmap2->dim, isl_dim_param, pos);
2012         isl_dim_map_dim(dim_map1, bmap1->dim, isl_dim_in, pos += nparam);
2013         isl_dim_map_dim(dim_map2, bmap2->dim, isl_dim_in, pos);
2014         isl_dim_map_div(dim_map1, bmap1, pos += n_in + n_out);
2015         isl_dim_map_div(dim_map2, bmap2, pos += bmap1->n_div);
2016         isl_dim_map_dim(dim_map1, bmap1->dim, isl_dim_out, pos += bmap2->n_div);
2017         isl_dim_map_dim(dim_map2, bmap2->dim, isl_dim_out, pos += n_out);
2018
2019         bmap = isl_basic_map_alloc_dim(isl_dim_copy(bmap1->dim),
2020                         bmap1->n_div + bmap2->n_div + 2 * n_out,
2021                         bmap1->n_eq + bmap2->n_eq + n_out,
2022                         bmap1->n_ineq + bmap2->n_ineq);
2023         for (i = 0; i < n_out; ++i) {
2024                 int j = isl_basic_map_alloc_equality(bmap);
2025                 if (j < 0)
2026                         goto error;
2027                 isl_seq_clr(bmap->eq[j], 1+total);
2028                 isl_int_set_si(bmap->eq[j][1+nparam+n_in+i], -1);
2029                 isl_int_set_si(bmap->eq[j][1+pos+i], 1);
2030                 isl_int_set_si(bmap->eq[j][1+pos-n_out+i], 1);
2031         }
2032         bmap = add_constraints_dim_map(bmap, bmap1, dim_map1);
2033         bmap = add_constraints_dim_map(bmap, bmap2, dim_map2);
2034         bmap = add_divs(bmap, 2 * n_out);
2035
2036         bmap = isl_basic_map_simplify(bmap);
2037         return isl_basic_map_finalize(bmap);
2038 error:
2039         isl_basic_map_free(bmap);
2040         isl_basic_map_free(bmap1);
2041         isl_basic_map_free(bmap2);
2042         return NULL;
2043 }
2044
2045 /* Given a basic map A -> f(A), construct A -> -f(A).
2046  */
2047 struct isl_basic_map *isl_basic_map_neg(struct isl_basic_map *bmap)
2048 {
2049         int i, j;
2050         unsigned off, n;
2051
2052         bmap = isl_basic_map_cow(bmap);
2053         if (!bmap)
2054                 return NULL;
2055
2056         n = isl_basic_map_dim(bmap, isl_dim_out);
2057         off = isl_basic_map_offset(bmap, isl_dim_out);
2058         for (i = 0; i < bmap->n_eq; ++i)
2059                 for (j = 0; j < n; ++j)
2060                         isl_int_neg(bmap->eq[i][off+j], bmap->eq[i][off+j]);
2061         for (i = 0; i < bmap->n_ineq; ++i)
2062                 for (j = 0; j < n; ++j)
2063                         isl_int_neg(bmap->ineq[i][off+j], bmap->ineq[i][off+j]);
2064         for (i = 0; i < bmap->n_div; ++i)
2065                 for (j = 0; j < n; ++j)
2066                         isl_int_neg(bmap->div[i][1+off+j], bmap->div[i][1+off+j]);
2067         return isl_basic_map_finalize(bmap);
2068 }
2069
2070 /* Given a basic map A -> f(A) and an integer d, construct a basic map
2071  * A -> floor(f(A)/d).
2072  */
2073 struct isl_basic_map *isl_basic_map_floordiv(struct isl_basic_map *bmap,
2074                 isl_int d)
2075 {
2076         unsigned n_in, n_out, nparam, total, pos;
2077         struct isl_basic_map *result = NULL;
2078         struct isl_dim_map *dim_map;
2079         int i;
2080
2081         if (!bmap)
2082                 return NULL;
2083
2084         nparam = isl_basic_map_n_param(bmap);
2085         n_in = isl_basic_map_n_in(bmap);
2086         n_out = isl_basic_map_n_out(bmap);
2087
2088         total = nparam + n_in + n_out + bmap->n_div + n_out;
2089         dim_map = isl_dim_map_alloc(bmap->ctx, total);
2090         isl_dim_map_dim(dim_map, bmap->dim, isl_dim_param, pos = 0);
2091         isl_dim_map_dim(dim_map, bmap->dim, isl_dim_in, pos += nparam);
2092         isl_dim_map_div(dim_map, bmap, pos += n_in + n_out);
2093         isl_dim_map_dim(dim_map, bmap->dim, isl_dim_out, pos += bmap->n_div);
2094
2095         result = isl_basic_map_alloc_dim(isl_dim_copy(bmap->dim),
2096                         bmap->n_div + n_out,
2097                         bmap->n_eq, bmap->n_ineq + 2 * n_out);
2098         result = add_constraints_dim_map(result, bmap, dim_map);
2099         result = add_divs(result, n_out);
2100         for (i = 0; i < n_out; ++i) {
2101                 int j;
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_neg(result->ineq[j][1+nparam+n_in+i], d);
2107                 isl_int_set_si(result->ineq[j][1+pos+i], 1);
2108                 j = isl_basic_map_alloc_inequality(result);
2109                 if (j < 0)
2110                         goto error;
2111                 isl_seq_clr(result->ineq[j], 1+total);
2112                 isl_int_set(result->ineq[j][1+nparam+n_in+i], d);
2113                 isl_int_set_si(result->ineq[j][1+pos+i], -1);
2114                 isl_int_sub_ui(result->ineq[j][0], d, 1);
2115         }
2116
2117         result = isl_basic_map_simplify(result);
2118         return isl_basic_map_finalize(result);
2119 error:
2120         isl_basic_map_free(result);
2121         return NULL;
2122 }
2123
2124 static struct isl_basic_map *var_equal(struct isl_basic_map *bmap, unsigned pos)
2125 {
2126         int i;
2127         unsigned nparam;
2128         unsigned n_in;
2129
2130         i = isl_basic_map_alloc_equality(bmap);
2131         if (i < 0)
2132                 goto error;
2133         nparam = isl_basic_map_n_param(bmap);
2134         n_in = isl_basic_map_n_in(bmap);
2135         isl_seq_clr(bmap->eq[i], 1 + isl_basic_map_total_dim(bmap));
2136         isl_int_set_si(bmap->eq[i][1+nparam+pos], -1);
2137         isl_int_set_si(bmap->eq[i][1+nparam+n_in+pos], 1);
2138         return isl_basic_map_finalize(bmap);
2139 error:
2140         isl_basic_map_free(bmap);
2141         return NULL;
2142 }
2143
2144 static struct isl_basic_map *var_more(struct isl_basic_map *bmap, unsigned pos)
2145 {
2146         int i;
2147         unsigned nparam;
2148         unsigned n_in;
2149
2150         i = isl_basic_map_alloc_inequality(bmap);
2151         if (i < 0)
2152                 goto error;
2153         nparam = isl_basic_map_n_param(bmap);
2154         n_in = isl_basic_map_n_in(bmap);
2155         isl_seq_clr(bmap->ineq[i], 1 + isl_basic_map_total_dim(bmap));
2156         isl_int_set_si(bmap->ineq[i][0], -1);
2157         isl_int_set_si(bmap->ineq[i][1+nparam+pos], -1);
2158         isl_int_set_si(bmap->ineq[i][1+nparam+n_in+pos], 1);
2159         return isl_basic_map_finalize(bmap);
2160 error:
2161         isl_basic_map_free(bmap);
2162         return NULL;
2163 }
2164
2165 static struct isl_basic_map *var_less(struct isl_basic_map *bmap, unsigned pos)
2166 {
2167         int i;
2168         unsigned nparam;
2169         unsigned n_in;
2170
2171         i = isl_basic_map_alloc_inequality(bmap);
2172         if (i < 0)
2173                 goto error;
2174         nparam = isl_basic_map_n_param(bmap);
2175         n_in = isl_basic_map_n_in(bmap);
2176         isl_seq_clr(bmap->ineq[i], 1 + isl_basic_map_total_dim(bmap));
2177         isl_int_set_si(bmap->ineq[i][0], -1);
2178         isl_int_set_si(bmap->ineq[i][1+nparam+pos], 1);
2179         isl_int_set_si(bmap->ineq[i][1+nparam+n_in+pos], -1);
2180         return isl_basic_map_finalize(bmap);
2181 error:
2182         isl_basic_map_free(bmap);
2183         return NULL;
2184 }
2185
2186 struct isl_basic_map *isl_basic_map_equal(struct isl_dim *dim, unsigned n_equal)
2187 {
2188         int i;
2189         struct isl_basic_map *bmap;
2190         bmap = isl_basic_map_alloc_dim(dim, 0, n_equal, 0);
2191         if (!bmap)
2192                 return NULL;
2193         for (i = 0; i < n_equal && bmap; ++i)
2194                 bmap = var_equal(bmap, i);
2195         return isl_basic_map_finalize(bmap);
2196 }
2197
2198 struct isl_basic_map *isl_basic_map_less_at(struct isl_dim *dim, unsigned pos)
2199 {
2200         int i;
2201         struct isl_basic_map *bmap;
2202         bmap = isl_basic_map_alloc_dim(dim, 0, pos, 1);
2203         if (!bmap)
2204                 return NULL;
2205         for (i = 0; i < pos && bmap; ++i)
2206                 bmap = var_equal(bmap, i);
2207         if (bmap)
2208                 bmap = var_less(bmap, pos);
2209         return isl_basic_map_finalize(bmap);
2210 }
2211
2212 struct isl_basic_map *isl_basic_map_more_at(struct isl_dim *dim, unsigned pos)
2213 {
2214         int i;
2215         struct isl_basic_map *bmap;
2216         bmap = isl_basic_map_alloc_dim(dim, 0, pos, 1);
2217         if (!bmap)
2218                 return NULL;
2219         for (i = 0; i < pos && bmap; ++i)
2220                 bmap = var_equal(bmap, i);
2221         if (bmap)
2222                 bmap = var_more(bmap, pos);
2223         return isl_basic_map_finalize(bmap);
2224 }
2225
2226 struct isl_basic_map *isl_basic_map_from_basic_set(
2227                 struct isl_basic_set *bset, struct isl_dim *dim)
2228 {
2229         struct isl_basic_map *bmap;
2230
2231         bset = isl_basic_set_cow(bset);
2232         if (!bset || !dim)
2233                 goto error;
2234
2235         isl_assert(bset->ctx, isl_dim_compatible(bset->dim, dim), goto error);
2236         isl_dim_free(bset->dim);
2237         bmap = (struct isl_basic_map *) bset;
2238         bmap->dim = dim;
2239         return isl_basic_map_finalize(bmap);
2240 error:
2241         isl_basic_set_free(bset);
2242         isl_dim_free(dim);
2243         return NULL;
2244 }
2245
2246 struct isl_basic_set *isl_basic_set_from_basic_map(struct isl_basic_map *bmap)
2247 {
2248         if (!bmap)
2249                 goto error;
2250         if (bmap->dim->n_in == 0)
2251                 return (struct isl_basic_set *)bmap;
2252         bmap = isl_basic_map_cow(bmap);
2253         if (!bmap)
2254                 goto error;
2255         bmap->dim = isl_dim_cow(bmap->dim);
2256         if (!bmap->dim)
2257                 goto error;
2258         bmap->dim->n_out += bmap->dim->n_in;
2259         bmap->dim->n_in = 0;
2260         bmap = isl_basic_map_finalize(bmap);
2261         return (struct isl_basic_set *)bmap;
2262 error:
2263         isl_basic_map_free(bmap);
2264         return NULL;
2265 }
2266
2267 /* For a div d = floor(f/m), add the constraints
2268  *
2269  *              f - m d >= 0
2270  *              -(f-(n-1)) + m d >= 0
2271  *
2272  * Note that the second constraint is the negation of
2273  *
2274  *              f - m d >= n
2275  */
2276 static int add_div_constraints(struct isl_basic_map *bmap, unsigned div)
2277 {
2278         int i, j;
2279         unsigned total = isl_basic_map_total_dim(bmap);
2280         unsigned div_pos = 1 + total - bmap->n_div + div;
2281
2282         i = isl_basic_map_alloc_inequality(bmap);
2283         if (i < 0)
2284                 return -1;
2285         isl_seq_cpy(bmap->ineq[i], bmap->div[div]+1, 1+total);
2286         isl_int_neg(bmap->ineq[i][div_pos], bmap->div[div][0]);
2287
2288         j = isl_basic_map_alloc_inequality(bmap);
2289         if (j < 0)
2290                 return -1;
2291         isl_seq_neg(bmap->ineq[j], bmap->ineq[i], 1 + total);
2292         isl_int_add(bmap->ineq[j][0], bmap->ineq[j][0], bmap->ineq[j][div_pos]);
2293         isl_int_sub_ui(bmap->ineq[j][0], bmap->ineq[j][0], 1);
2294         return j;
2295 }
2296
2297 struct isl_basic_set *isl_basic_map_underlying_set(
2298                 struct isl_basic_map *bmap)
2299 {
2300         if (!bmap)
2301                 goto error;
2302         if (bmap->dim->nparam == 0 && bmap->dim->n_in == 0 && bmap->n_div == 0)
2303                 return (struct isl_basic_set *)bmap;
2304         bmap = isl_basic_map_cow(bmap);
2305         if (!bmap)
2306                 goto error;
2307         bmap->dim = isl_dim_underlying(bmap->dim, bmap->n_div);
2308         if (!bmap->dim)
2309                 goto error;
2310         bmap->extra -= bmap->n_div;
2311         bmap->n_div = 0;
2312         bmap = isl_basic_map_finalize(bmap);
2313         return (struct isl_basic_set *)bmap;
2314 error:
2315         return NULL;
2316 }
2317
2318 struct isl_basic_map *isl_basic_map_overlying_set(
2319         struct isl_basic_set *bset, struct isl_basic_map *like)
2320 {
2321         struct isl_basic_map *bmap;
2322         struct isl_ctx *ctx;
2323         unsigned total;
2324         int i;
2325
2326         if (!bset || !like)
2327                 goto error;
2328         ctx = bset->ctx;
2329         isl_assert(ctx, bset->n_div == 0, goto error);
2330         isl_assert(ctx, isl_basic_set_n_param(bset) == 0, goto error);
2331         isl_assert(ctx, bset->dim->n_out == isl_basic_map_total_dim(like),
2332                         goto error);
2333         if (isl_dim_equal(bset->dim, like->dim) && like->n_div == 0) {
2334                 isl_basic_map_free(like);
2335                 return (struct isl_basic_map *)bset;
2336         }
2337         bset = isl_basic_set_cow(bset);
2338         if (!bset)
2339                 goto error;
2340         total = bset->dim->n_out + bset->extra;
2341         bmap = (struct isl_basic_map *)bset;
2342         isl_dim_free(bmap->dim);
2343         bmap->dim = isl_dim_copy(like->dim);
2344         if (!bmap->dim)
2345                 goto error;
2346         bmap->n_div = like->n_div;
2347         bmap->extra += like->n_div;
2348         if (bmap->extra) {
2349                 unsigned ltotal;
2350                 ltotal = total - bmap->extra + like->extra;
2351                 if (ltotal > total)
2352                         ltotal = total;
2353                 bmap->block2 = isl_blk_extend(ctx, bmap->block2,
2354                                         bmap->extra * (1 + 1 + total));
2355                 if (isl_blk_is_error(bmap->block2))
2356                         goto error;
2357                 bmap->div = isl_realloc_array(ctx, bmap->div, isl_int *,
2358                                                 bmap->extra);
2359                 if (!bmap->div)
2360                         goto error;
2361                 for (i = 0; i < bmap->extra; ++i)
2362                         bmap->div[i] = bmap->block2.data + i * (1 + 1 + total);
2363                 for (i = 0; i < like->n_div; ++i) {
2364                         isl_seq_cpy(bmap->div[i], like->div[i], 1 + 1 + ltotal);
2365                         isl_seq_clr(bmap->div[i]+1+1+ltotal, total - ltotal);
2366                 }
2367                 bmap = isl_basic_map_extend_constraints(bmap,
2368                                                         0, 2 * like->n_div);
2369                 for (i = 0; i < like->n_div; ++i) {
2370                         if (isl_int_is_zero(bmap->div[i][0]))
2371                                 continue;
2372                         if (add_div_constraints(bmap, i) < 0)
2373                                 goto error;
2374                 }
2375         }
2376         isl_basic_map_free(like);
2377         bmap = isl_basic_map_simplify(bmap);
2378         bmap = isl_basic_map_finalize(bmap);
2379         return bmap;
2380 error:
2381         isl_basic_map_free(like);
2382         isl_basic_set_free(bset);
2383         return NULL;
2384 }
2385
2386 struct isl_basic_set *isl_basic_set_from_underlying_set(
2387         struct isl_basic_set *bset, struct isl_basic_set *like)
2388 {
2389         return (struct isl_basic_set *)
2390                 isl_basic_map_overlying_set(bset, (struct isl_basic_map *)like);
2391 }
2392
2393 struct isl_set *isl_set_from_underlying_set(
2394         struct isl_set *set, struct isl_basic_set *like)
2395 {
2396         int i;
2397
2398         if (!set || !like)
2399                 goto error;
2400         isl_assert(set->ctx, set->dim->n_out == isl_basic_set_total_dim(like),
2401                     goto error);
2402         if (isl_dim_equal(set->dim, like->dim) && like->n_div == 0) {
2403                 isl_basic_set_free(like);
2404                 return set;
2405         }
2406         set = isl_set_cow(set);
2407         if (!set)
2408                 goto error;
2409         for (i = 0; i < set->n; ++i) {
2410                 set->p[i] = isl_basic_set_from_underlying_set(set->p[i],
2411                                                       isl_basic_set_copy(like));
2412                 if (!set->p[i])
2413                         goto error;
2414         }
2415         isl_dim_free(set->dim);
2416         set->dim = isl_dim_copy(like->dim);
2417         if (!set->dim)
2418                 goto error;
2419         isl_basic_set_free(like);
2420         return set;
2421 error:
2422         isl_basic_set_free(like);
2423         isl_set_free(set);
2424         return NULL;
2425 }
2426
2427 struct isl_set *isl_map_underlying_set(struct isl_map *map)
2428 {
2429         int i;
2430
2431         map = isl_map_cow(map);
2432         if (!map)
2433                 return NULL;
2434         map->dim = isl_dim_cow(map->dim);
2435         if (!map->dim)
2436                 goto error;
2437
2438         for (i = 1; i < map->n; ++i)
2439                 isl_assert(map->ctx, map->p[0]->n_div == map->p[i]->n_div,
2440                                 goto error);
2441         for (i = 0; i < map->n; ++i) {
2442                 map->p[i] = (struct isl_basic_map *)
2443                                 isl_basic_map_underlying_set(map->p[i]);
2444                 if (!map->p[i])
2445                         goto error;
2446         }
2447         if (map->n == 0)
2448                 map->dim = isl_dim_underlying(map->dim, 0);
2449         else {
2450                 isl_dim_free(map->dim);
2451                 map->dim = isl_dim_copy(map->p[0]->dim);
2452         }
2453         if (!map->dim)
2454                 goto error;
2455         return (struct isl_set *)map;
2456 error:
2457         isl_map_free(map);
2458         return NULL;
2459 }
2460
2461 struct isl_set *isl_set_to_underlying_set(struct isl_set *set)
2462 {
2463         return (struct isl_set *)isl_map_underlying_set((struct isl_map *)set);
2464 }
2465
2466 struct isl_basic_set *isl_basic_map_domain(struct isl_basic_map *bmap)
2467 {
2468         struct isl_basic_set *domain;
2469         unsigned n_out;
2470         if (!bmap)
2471                 return NULL;
2472         n_out = isl_basic_map_n_out(bmap);
2473         domain = isl_basic_set_from_basic_map(bmap);
2474         return isl_basic_set_project_out(domain, n_out, 0);
2475 }
2476
2477 struct isl_basic_set *isl_basic_map_range(struct isl_basic_map *bmap)
2478 {
2479         return isl_basic_map_domain(isl_basic_map_reverse(bmap));
2480 }
2481
2482 struct isl_set *isl_map_range(struct isl_map *map)
2483 {
2484         int i;
2485         struct isl_set *set;
2486
2487         if (!map)
2488                 goto error;
2489         map = isl_map_cow(map);
2490         if (!map)
2491                 goto error;
2492
2493         set = (struct isl_set *) map;
2494         if (set->dim->n_in != 0) {
2495                 set->dim = isl_dim_drop_inputs(set->dim, 0, set->dim->n_in);
2496                 if (!set->dim)
2497                         goto error;
2498         }
2499         for (i = 0; i < map->n; ++i) {
2500                 set->p[i] = isl_basic_map_range(map->p[i]);
2501                 if (!set->p[i])
2502                         goto error;
2503         }
2504         ISL_F_CLR(set, ISL_MAP_DISJOINT);
2505         ISL_F_CLR(set, ISL_SET_NORMALIZED);
2506         return set;
2507 error:
2508         isl_map_free(map);
2509         return NULL;
2510 }
2511
2512 struct isl_map *isl_map_from_set(struct isl_set *set, struct isl_dim *dim)
2513 {
2514         int i;
2515         struct isl_map *map = NULL;
2516
2517         set = isl_set_cow(set);
2518         if (!set || !dim)
2519                 goto error;
2520         isl_assert(set->ctx, isl_dim_compatible(set->dim, dim), goto error);
2521         map = (struct isl_map *)set;
2522         for (i = 0; i < set->n; ++i) {
2523                 map->p[i] = isl_basic_map_from_basic_set(
2524                                 set->p[i], isl_dim_copy(dim));
2525                 if (!map->p[i])
2526                         goto error;
2527         }
2528         isl_dim_free(map->dim);
2529         map->dim = dim;
2530         return map;
2531 error:
2532         isl_dim_free(dim);
2533         isl_set_free(set);
2534         return NULL;
2535 }
2536
2537 struct isl_map *isl_map_from_range(struct isl_set *set)
2538 {
2539         return (struct isl_map *)set;
2540 }
2541
2542 struct isl_set *isl_set_from_map(struct isl_map *map)
2543 {
2544         int i;
2545         struct isl_set *set = NULL;
2546
2547         if (!map)
2548                 return NULL;
2549         map = isl_map_cow(map);
2550         if (!map)
2551                 return NULL;
2552         map->dim = isl_dim_cow(map->dim);
2553         if (!map->dim)
2554                 goto error;
2555         map->dim->n_out += map->dim->n_in;
2556         map->dim->n_in = 0;
2557         set = (struct isl_set *)map;
2558         for (i = 0; i < map->n; ++i) {
2559                 set->p[i] = isl_basic_set_from_basic_map(map->p[i]);
2560                 if (!set->p[i])
2561                         goto error;
2562         }
2563         return set;
2564 error:
2565         isl_map_free(map);
2566         return NULL;
2567 }
2568
2569 struct isl_map *isl_map_alloc_dim(struct isl_dim *dim, int n, unsigned flags)
2570 {
2571         struct isl_map *map;
2572
2573         if (!dim)
2574                 return NULL;
2575         isl_assert(dim->ctx, n >= 0, return NULL);
2576         map = isl_alloc(dim->ctx, struct isl_map,
2577                         sizeof(struct isl_map) +
2578                         n * sizeof(struct isl_basic_map *));
2579         if (!map)
2580                 goto error;
2581
2582         map->ctx = dim->ctx;
2583         isl_ctx_ref(map->ctx);
2584         map->ref = 1;
2585         map->size = n;
2586         map->n = 0;
2587         map->dim = dim;
2588         map->flags = flags;
2589         return map;
2590 error:
2591         isl_dim_free(dim);
2592         return NULL;
2593 }
2594
2595 struct isl_map *isl_map_alloc(struct isl_ctx *ctx,
2596                 unsigned nparam, unsigned in, unsigned out, int n,
2597                 unsigned flags)
2598 {
2599         struct isl_map *map;
2600         struct isl_dim *dims;
2601
2602         dims = isl_dim_alloc(ctx, nparam, in, out);
2603         if (!dims)
2604                 return NULL;
2605
2606         map = isl_map_alloc_dim(dims, n, flags);
2607         return map;
2608 }
2609
2610 struct isl_basic_map *isl_basic_map_empty(struct isl_ctx *ctx,
2611                 unsigned nparam, unsigned in, unsigned out)
2612 {
2613         struct isl_basic_map *bmap;
2614         bmap = isl_basic_map_alloc(ctx, nparam, in, out, 0, 1, 0);
2615         bmap = isl_basic_map_set_to_empty(bmap);
2616         return bmap;
2617 }
2618
2619 struct isl_basic_set *isl_basic_set_empty(struct isl_dim *dim)
2620 {
2621         struct isl_basic_set *bset;
2622         bset = isl_basic_set_alloc_dim(dim, 0, 1, 0);
2623         bset = isl_basic_set_set_to_empty(bset);
2624         return bset;
2625 }
2626
2627 struct isl_basic_map *isl_basic_map_empty_like(struct isl_basic_map *model)
2628 {
2629         struct isl_basic_map *bmap;
2630         if (!model)
2631                 return NULL;
2632         bmap = isl_basic_map_alloc_dim(isl_dim_copy(model->dim), 0, 1, 0);
2633         bmap = isl_basic_map_set_to_empty(bmap);
2634         return bmap;
2635 }
2636
2637 struct isl_basic_map *isl_basic_map_empty_like_map(struct isl_map *model)
2638 {
2639         struct isl_basic_map *bmap;
2640         if (!model)
2641                 return NULL;
2642         bmap = isl_basic_map_alloc_dim(isl_dim_copy(model->dim), 0, 1, 0);
2643         bmap = isl_basic_map_set_to_empty(bmap);
2644         return bmap;
2645 }
2646
2647 struct isl_basic_set *isl_basic_set_empty_like(struct isl_basic_set *model)
2648 {
2649         struct isl_basic_set *bset;
2650         if (!model)
2651                 return NULL;
2652         bset = isl_basic_set_alloc_dim(isl_dim_copy(model->dim), 0, 1, 0);
2653         bset = isl_basic_set_set_to_empty(bset);
2654         return bset;
2655 }
2656
2657 struct isl_basic_map *isl_basic_map_universe(struct isl_dim *dim)
2658 {
2659         struct isl_basic_map *bmap;
2660         bmap = isl_basic_map_alloc_dim(dim, 0, 0, 0);
2661         return bmap;
2662 }
2663
2664 struct isl_basic_set *isl_basic_set_universe(struct isl_dim *dim)
2665 {
2666         struct isl_basic_set *bset;
2667         bset = isl_basic_set_alloc_dim(dim, 0, 0, 0);
2668         return bset;
2669 }
2670
2671 struct isl_basic_set *isl_basic_set_universe_like(struct isl_basic_set *model)
2672 {
2673         if (!model)
2674                 return NULL;
2675         return isl_basic_set_alloc_dim(isl_dim_copy(model->dim), 0, 0, 0);
2676 }
2677
2678 struct isl_map *isl_map_empty(struct isl_dim *dim)
2679 {
2680         return isl_map_alloc_dim(dim, 0, ISL_MAP_DISJOINT);
2681 }
2682
2683 struct isl_map *isl_map_empty_like(struct isl_map *model)
2684 {
2685         if (!model)
2686                 return NULL;
2687         return isl_map_alloc_dim(isl_dim_copy(model->dim), 0, ISL_MAP_DISJOINT);
2688 }
2689
2690 struct isl_map *isl_map_empty_like_basic_map(struct isl_basic_map *model)
2691 {
2692         if (!model)
2693                 return NULL;
2694         return isl_map_alloc_dim(isl_dim_copy(model->dim), 0, ISL_MAP_DISJOINT);
2695 }
2696
2697 struct isl_set *isl_set_empty(struct isl_dim *dim)
2698 {
2699         return isl_set_alloc_dim(dim, 0, ISL_MAP_DISJOINT);
2700 }
2701
2702 struct isl_set *isl_set_empty_like(struct isl_set *model)
2703 {
2704         if (!model)
2705                 return NULL;
2706         return isl_set_empty(isl_dim_copy(model->dim));
2707 }
2708
2709 struct isl_map *isl_map_universe(struct isl_dim *dim)
2710 {
2711         struct isl_map *map;
2712         if (!dim)
2713                 return NULL;
2714         map = isl_map_alloc_dim(isl_dim_copy(dim), 1, ISL_MAP_DISJOINT);
2715         map = isl_map_add(map, isl_basic_map_universe(dim));
2716         return map;
2717 }
2718
2719 struct isl_set *isl_set_universe(struct isl_dim *dim)
2720 {
2721         struct isl_set *set;
2722         if (!dim)
2723                 return NULL;
2724         set = isl_set_alloc_dim(isl_dim_copy(dim), 1, ISL_MAP_DISJOINT);
2725         set = isl_set_add(set, isl_basic_set_universe(dim));
2726         return set;
2727 }
2728
2729 struct isl_map *isl_map_dup(struct isl_map *map)
2730 {
2731         int i;
2732         struct isl_map *dup;
2733
2734         if (!map)
2735                 return NULL;
2736         dup = isl_map_alloc_dim(isl_dim_copy(map->dim), map->n, map->flags);
2737         for (i = 0; i < map->n; ++i)
2738                 dup = isl_map_add(dup, isl_basic_map_copy(map->p[i]));
2739         return dup;
2740 }
2741
2742 struct isl_map *isl_map_add(struct isl_map *map, struct isl_basic_map *bmap)
2743 {
2744         if (!bmap || !map)
2745                 goto error;
2746         if (isl_basic_map_fast_is_empty(bmap)) {
2747                 isl_basic_map_free(bmap);
2748                 return map;
2749         }
2750         isl_assert(map->ctx, isl_dim_equal(map->dim, bmap->dim), goto error);
2751         isl_assert(map->ctx, map->n < map->size, goto error);
2752         map->p[map->n] = bmap;
2753         map->n++;
2754         ISL_F_CLR(map, ISL_MAP_NORMALIZED);
2755         return map;
2756 error:
2757         if (map)
2758                 isl_map_free(map);
2759         if (bmap)
2760                 isl_basic_map_free(bmap);
2761         return NULL;
2762 }
2763
2764 void isl_map_free(struct isl_map *map)
2765 {
2766         int i;
2767
2768         if (!map)
2769                 return;
2770
2771         if (--map->ref > 0)
2772                 return;
2773
2774         isl_ctx_deref(map->ctx);
2775         for (i = 0; i < map->n; ++i)
2776                 isl_basic_map_free(map->p[i]);
2777         isl_dim_free(map->dim);
2778         free(map);
2779 }
2780
2781 struct isl_map *isl_map_extend(struct isl_map *base,
2782                 unsigned nparam, unsigned n_in, unsigned n_out)
2783 {
2784         int i;
2785
2786         base = isl_map_cow(base);
2787         if (!base)
2788                 return NULL;
2789
2790         base->dim = isl_dim_extend(base->dim, nparam, n_in, n_out);
2791         if (!base->dim)
2792                 goto error;
2793         for (i = 0; i < base->n; ++i) {
2794                 base->p[i] = isl_basic_map_extend_dim(base->p[i],
2795                                 isl_dim_copy(base->dim), 0, 0, 0);
2796                 if (!base->p[i])
2797                         goto error;
2798         }
2799         return base;
2800 error:
2801         isl_map_free(base);
2802         return NULL;
2803 }
2804
2805 struct isl_set *isl_set_extend(struct isl_set *base,
2806                 unsigned nparam, unsigned dim)
2807 {
2808         return (struct isl_set *)isl_map_extend((struct isl_map *)base,
2809                                                         nparam, 0, dim);
2810 }
2811
2812 static struct isl_basic_map *isl_basic_map_fix_pos(struct isl_basic_map *bmap,
2813                 unsigned pos, int value)
2814 {
2815         int j;
2816
2817         bmap = isl_basic_map_cow(bmap);
2818         bmap = isl_basic_map_extend_constraints(bmap, 1, 0);
2819         j = isl_basic_map_alloc_equality(bmap);
2820         if (j < 0)
2821                 goto error;
2822         isl_seq_clr(bmap->eq[j] + 1, isl_basic_map_total_dim(bmap));
2823         isl_int_set_si(bmap->eq[j][pos], -1);
2824         isl_int_set_si(bmap->eq[j][0], value);
2825         bmap = isl_basic_map_simplify(bmap);
2826         return isl_basic_map_finalize(bmap);
2827 error:
2828         isl_basic_map_free(bmap);
2829         return NULL;
2830 }
2831
2832 struct isl_basic_map *isl_basic_map_fix_si(struct isl_basic_map *bmap,
2833                 enum isl_dim_type type, unsigned pos, int value)
2834 {
2835         if (!bmap)
2836                 return NULL;
2837         isl_assert(bmap->ctx, pos < isl_basic_map_dim(bmap, type), goto error);
2838         return isl_basic_map_fix_pos(bmap, isl_basic_map_offset(bmap, type) + pos,
2839                                         value);
2840 error:
2841         isl_basic_map_free(bmap);
2842         return NULL;
2843 }
2844
2845 struct isl_basic_set *isl_basic_set_fix_si(struct isl_basic_set *bset,
2846                 enum isl_dim_type type, unsigned pos, int value)
2847 {
2848         return (struct isl_basic_set *)
2849                 isl_basic_map_fix_si((struct isl_basic_map *)bset,
2850                                         type, pos, value);
2851 }
2852
2853 struct isl_basic_map *isl_basic_map_fix_input_si(struct isl_basic_map *bmap,
2854                 unsigned input, int value)
2855 {
2856         return isl_basic_map_fix_si(bmap, isl_dim_in, input, value);
2857 }
2858
2859 struct isl_basic_set *isl_basic_set_fix_dim_si(struct isl_basic_set *bset,
2860                 unsigned dim, int value)
2861 {
2862         return (struct isl_basic_set *)
2863                 isl_basic_map_fix_si((struct isl_basic_map *)bset,
2864                                         isl_dim_set, dim, value);
2865 }
2866
2867 struct isl_map *isl_map_fix_si(struct isl_map *map,
2868                 enum isl_dim_type type, unsigned pos, int value)
2869 {
2870         int i;
2871
2872         map = isl_map_cow(map);
2873         if (!map)
2874                 return NULL;
2875
2876         isl_assert(ctx, pos < isl_map_dim(map, type), goto error);
2877         for (i = 0; i < map->n; ++i) {
2878                 map->p[i] = isl_basic_map_fix_si(map->p[i], type, pos, value);
2879                 if (!map->p[i])
2880                         goto error;
2881         }
2882         ISL_F_CLR(map, ISL_MAP_NORMALIZED);
2883         return map;
2884 error:
2885         isl_map_free(map);
2886         return NULL;
2887 }
2888
2889 struct isl_map *isl_map_fix_input_si(struct isl_map *map,
2890                 unsigned input, int value)
2891 {
2892         return isl_map_fix_si(map, isl_dim_in, input, value);
2893 }
2894
2895 struct isl_set *isl_set_fix_dim_si(struct isl_set *set, unsigned dim, int value)
2896 {
2897         return (struct isl_set *)
2898                 isl_map_fix_si((struct isl_map *)set, isl_dim_set, dim, value);
2899 }
2900
2901 struct isl_basic_set *isl_basic_set_lower_bound_dim(struct isl_basic_set *bset,
2902         unsigned dim, isl_int value)
2903 {
2904         int j;
2905         unsigned nparam;
2906
2907         bset = isl_basic_set_cow(bset);
2908         bset = isl_basic_set_extend_constraints(bset, 0, 1);
2909         j = isl_basic_set_alloc_inequality(bset);
2910         if (j < 0)
2911                 goto error;
2912         isl_seq_clr(bset->ineq[j], 1 + isl_basic_set_total_dim(bset));
2913         isl_int_set_si(bset->ineq[j][1 + isl_basic_set_n_param(bset) + dim], 1);
2914         isl_int_neg(bset->ineq[j][0], value);
2915         bset = isl_basic_set_simplify(bset);
2916         return isl_basic_set_finalize(bset);
2917 error:
2918         isl_basic_set_free(bset);
2919         return NULL;
2920 }
2921
2922 struct isl_set *isl_set_lower_bound_dim(struct isl_set *set, unsigned dim,
2923                                         isl_int value)
2924 {
2925         int i;
2926
2927         set = isl_set_cow(set);
2928         if (!set)
2929                 return NULL;
2930
2931         isl_assert(set->ctx, dim < isl_set_n_dim(set), goto error);
2932         for (i = 0; i < set->n; ++i) {
2933                 set->p[i] = isl_basic_set_lower_bound_dim(set->p[i], dim, value);
2934                 if (!set->p[i])
2935                         goto error;
2936         }
2937         return set;
2938 error:
2939         isl_set_free(set);
2940         return NULL;
2941 }
2942
2943 struct isl_map *isl_map_reverse(struct isl_map *map)
2944 {
2945         int i;
2946         unsigned t;
2947
2948         map = isl_map_cow(map);
2949         if (!map)
2950                 return NULL;
2951
2952         map->dim = isl_dim_reverse(map->dim);
2953         if (!map->dim)
2954                 goto error;
2955         for (i = 0; i < map->n; ++i) {
2956                 map->p[i] = isl_basic_map_reverse(map->p[i]);
2957                 if (!map->p[i])
2958                         goto error;
2959         }
2960         ISL_F_CLR(map, ISL_MAP_NORMALIZED);
2961         return map;
2962 error:
2963         isl_map_free(map);
2964         return NULL;
2965 }
2966
2967 static struct isl_map *isl_basic_map_partial_lexopt(
2968                 struct isl_basic_map *bmap, struct isl_basic_set *dom,
2969                 struct isl_set **empty, int max)
2970 {
2971         if (!bmap)
2972                 goto error;
2973         if (bmap->ctx->pip == ISL_PIP_PIP)
2974                 return isl_pip_basic_map_lexopt(bmap, dom, empty, max);
2975         else
2976                 return isl_tab_basic_map_partial_lexopt(bmap, dom, empty, max);
2977 error:
2978         isl_basic_map_free(bmap);
2979         isl_basic_set_free(dom);
2980         if (empty)
2981                 *empty = NULL;
2982         return NULL;
2983 }
2984
2985 struct isl_map *isl_basic_map_partial_lexmax(
2986                 struct isl_basic_map *bmap, struct isl_basic_set *dom,
2987                 struct isl_set **empty)
2988 {
2989         return isl_basic_map_partial_lexopt(bmap, dom, empty, 1);
2990 }
2991
2992 struct isl_map *isl_basic_map_partial_lexmin(
2993                 struct isl_basic_map *bmap, struct isl_basic_set *dom,
2994                 struct isl_set **empty)
2995 {
2996         return isl_basic_map_partial_lexopt(bmap, dom, empty, 0);
2997 }
2998
2999 struct isl_set *isl_basic_set_partial_lexmin(
3000                 struct isl_basic_set *bset, struct isl_basic_set *dom,
3001                 struct isl_set **empty)
3002 {
3003         return (struct isl_set *)
3004                 isl_basic_map_partial_lexmin((struct isl_basic_map *)bset,
3005                         dom, empty);
3006 }
3007
3008 struct isl_set *isl_basic_set_partial_lexmax(
3009                 struct isl_basic_set *bset, struct isl_basic_set *dom,
3010                 struct isl_set **empty)
3011 {
3012         return (struct isl_set *)
3013                 isl_basic_map_partial_lexmax((struct isl_basic_map *)bset,
3014                         dom, empty);
3015 }
3016
3017 struct isl_set *isl_basic_set_lexmin(struct isl_basic_set *bset)
3018 {
3019         struct isl_basic_map *bmap = NULL;
3020         struct isl_basic_set *dom = NULL;
3021         struct isl_map *min;
3022         struct isl_dim *param_dim;
3023
3024         if (!bset)
3025                 goto error;
3026         bmap = isl_basic_map_from_basic_set(bset, isl_dim_copy(bset->dim));
3027         if (!bmap)
3028                 goto error;
3029         param_dim = isl_dim_domain(isl_dim_copy(bmap->dim));
3030         dom = isl_basic_set_universe(param_dim);
3031         if (!dom)
3032                 goto error;
3033         min = isl_basic_map_partial_lexmin(bmap, dom, NULL);
3034         return isl_map_range(min);
3035 error:
3036         isl_basic_map_free(bmap);
3037         return NULL;
3038 }
3039
3040 static struct isl_map *isl_map_reset_dim(struct isl_map *map,
3041         struct isl_dim *dim)
3042 {
3043         int i;
3044
3045         if (!map || !dim)
3046                 goto error;
3047
3048         for (i = 0; i < map->n; ++i) {
3049                 isl_dim_free(map->p[i]->dim);
3050                 map->p[i]->dim = isl_dim_copy(dim);
3051         }
3052         isl_dim_free(map->dim);
3053         map->dim = dim;
3054
3055         return map;
3056 error:
3057         isl_map_free(map);
3058         isl_dim_free(dim);
3059         return NULL;
3060 }
3061
3062 static struct isl_set *isl_set_reset_dim(struct isl_set *set,
3063         struct isl_dim *dim)
3064 {
3065         return (struct isl_set *) isl_map_reset_dim((struct isl_map *)set, dim);
3066 }
3067
3068 /* Apply a preimage specified by "mat" on the parameters of "bset".
3069  * bset is assumed to have only parameters and divs.
3070  */
3071 static struct isl_basic_set *basic_set_parameter_preimage(
3072         struct isl_basic_set *bset, struct isl_mat *mat)
3073 {
3074         unsigned nparam;
3075
3076         if (!bset || !mat)
3077                 goto error;
3078
3079         bset->dim = isl_dim_cow(bset->dim);
3080         if (!bset->dim)
3081                 goto error;
3082
3083         nparam = isl_basic_set_dim(bset, isl_dim_param);
3084
3085         isl_assert(bset->ctx, mat->n_row == 1 + nparam, goto error);
3086
3087         bset->dim->nparam = 0;
3088         bset->dim->n_out = nparam;
3089         bset = isl_basic_set_preimage(bset, mat);
3090         if (bset) {
3091                 bset->dim->nparam = bset->dim->n_out;
3092                 bset->dim->n_out = 0;
3093         }
3094         return bset;
3095 error:
3096         isl_mat_free(mat);
3097         isl_basic_set_free(bset);
3098         return NULL;
3099 }
3100
3101 /* Apply a preimage specified by "mat" on the parameters of "set".
3102  * set is assumed to have only parameters and divs.
3103  */
3104 static struct isl_set *set_parameter_preimage(
3105         struct isl_set *set, struct isl_mat *mat)
3106 {
3107         struct isl_dim *dim = NULL;
3108         unsigned nparam;
3109
3110         if (!set || !mat)
3111                 goto error;
3112
3113         dim = isl_dim_copy(set->dim);
3114         dim = isl_dim_cow(dim);
3115         if (!dim)
3116                 goto error;
3117
3118         nparam = isl_set_dim(set, isl_dim_param);
3119
3120         isl_assert(set->ctx, mat->n_row == 1 + nparam, goto error);
3121
3122         dim->nparam = 0;
3123         dim->n_out = nparam;
3124         isl_set_reset_dim(set, dim);
3125         set = isl_set_preimage(set, mat);
3126         if (!set)
3127                 goto error2;
3128         dim = isl_dim_copy(set->dim);
3129         dim = isl_dim_cow(dim);
3130         if (!dim)
3131                 goto error2;
3132         dim->nparam = dim->n_out;
3133         dim->n_out = 0;
3134         isl_set_reset_dim(set, dim);
3135         return set;
3136 error:
3137         isl_dim_free(dim);
3138         isl_mat_free(mat);
3139 error2:
3140         isl_set_free(set);
3141         return NULL;
3142 }
3143
3144 /* Intersect the basic set "bset" with the affine space specified by the
3145  * equalities in "eq".
3146  */
3147 static struct isl_basic_set *basic_set_append_equalities(
3148         struct isl_basic_set *bset, struct isl_mat *eq)
3149 {
3150         int i, k;
3151         unsigned len;
3152
3153         if (!bset || !eq)
3154                 goto error;
3155
3156         bset = isl_basic_set_extend_dim(bset, isl_dim_copy(bset->dim), 0,
3157                                         eq->n_row, 0);
3158         if (!bset)
3159                 goto error;
3160
3161         len = 1 + isl_dim_total(bset->dim) + bset->extra;
3162         for (i = 0; i < eq->n_row; ++i) {
3163                 k = isl_basic_set_alloc_equality(bset);
3164                 if (k < 0)
3165                         goto error;
3166                 isl_seq_cpy(bset->eq[k], eq->row[i], eq->n_col);
3167                 isl_seq_clr(bset->eq[k] + eq->n_col, len - eq->n_col);
3168         }
3169         isl_mat_free(eq);
3170
3171         return bset;
3172 error:
3173         isl_mat_free(eq);
3174         isl_basic_set_free(bset);
3175         return NULL;
3176 }
3177
3178 /* Intersect the set "set" with the affine space specified by the
3179  * equalities in "eq".
3180  */
3181 static struct isl_set *set_append_equalities(struct isl_set *set,
3182         struct isl_mat *eq)
3183 {
3184         int i;
3185
3186         if (!set || !eq)
3187                 goto error;
3188
3189         for (i = 0; i < set->n; ++i) {
3190                 set->p[i] = basic_set_append_equalities(set->p[i],
3191                                         isl_mat_copy(eq));
3192                 if (!set->p[i])
3193                         goto error;
3194         }
3195         isl_mat_free(eq);
3196         return set;
3197 error:
3198         isl_mat_free(eq);
3199         isl_set_free(set);
3200         return NULL;
3201 }
3202
3203 /* Project the given basic set onto its parameter domain, possibly introducing
3204  * new, explicit, existential variables in the constraints.
3205  * The input has parameters and (possibly implicit) existential variables.
3206  * The output has the same parameters, but only
3207  * explicit existentially quantified variables.
3208  *
3209  * The actual projection is performed by pip, but pip doesn't seem
3210  * to like equalities very much, so we first remove the equalities
3211  * among the parameters by performing a variable compression on
3212  * the parameters.  Afterward, an inverse transformation is performed
3213  * and the equalities among the parameters are inserted back in.
3214  */
3215 static struct isl_set *parameter_compute_divs(struct isl_basic_set *bset)
3216 {
3217         int i, j;
3218         struct isl_mat *eq;
3219         struct isl_mat *T, *T2;
3220         struct isl_set *set;
3221         unsigned nparam, n_div;
3222
3223         bset = isl_basic_set_cow(bset);
3224         if (!bset)
3225                 return NULL;
3226
3227         if (bset->n_eq == 0)
3228                 return isl_basic_set_lexmin(bset);
3229
3230         isl_basic_set_gauss(bset, NULL);
3231
3232         nparam = isl_basic_set_dim(bset, isl_dim_param);
3233         n_div = isl_basic_set_dim(bset, isl_dim_div);
3234
3235         for (i = 0, j = n_div - 1; i < bset->n_eq && j >= 0; --j) {
3236                 if (!isl_int_is_zero(bset->eq[i][1 + nparam + j]))
3237                         ++i;
3238         }
3239         if (i == bset->n_eq)
3240                 return isl_basic_set_lexmin(bset);
3241
3242         eq = isl_mat_sub_alloc(bset->ctx, bset->eq, i, bset->n_eq - i,
3243                 0, 1 + nparam);
3244         eq = isl_mat_cow(eq);
3245         T = isl_mat_variable_compression(isl_mat_copy(eq), &T2);
3246         bset = basic_set_parameter_preimage(bset, T);
3247
3248         set = isl_basic_set_lexmin(bset);
3249         set = set_parameter_preimage(set, T2);
3250         set = set_append_equalities(set, eq);
3251         return set;
3252 }
3253
3254 /* Compute an explicit representation for all the existentially
3255  * quantified variables.
3256  * The input and output dimensions are first turned into parameters.
3257  * compute_divs then returns a map with the same parameters and
3258  * no input or output dimensions and the dimension specification
3259  * is reset to that of the input.
3260  */
3261 static struct isl_map *compute_divs(struct isl_basic_map *bmap)
3262 {
3263         struct isl_basic_set *bset;
3264         struct isl_set *set;
3265         struct isl_map *map;
3266         struct isl_dim *dim, *orig_dim = NULL;
3267         unsigned         nparam;
3268         unsigned         n_in;
3269         unsigned         n_out;
3270
3271         bmap = isl_basic_map_cow(bmap);
3272         if (!bmap)
3273                 return NULL;
3274
3275         nparam = isl_basic_map_dim(bmap, isl_dim_param);
3276         n_in = isl_basic_map_dim(bmap, isl_dim_in);
3277         n_out = isl_basic_map_dim(bmap, isl_dim_out);
3278         dim = isl_dim_set_alloc(bmap->ctx, nparam + n_in + n_out, 0);
3279         if (!dim)
3280                 goto error;
3281
3282         orig_dim = bmap->dim;
3283         bmap->dim = dim;
3284         bset = (struct isl_basic_set *)bmap;
3285
3286         set = parameter_compute_divs(bset);
3287         map = (struct isl_map *)set;
3288         map = isl_map_reset_dim(map, orig_dim);
3289
3290         return map;
3291 error:
3292         isl_basic_map_free(bmap);
3293         return NULL;
3294 }
3295
3296 /* If bmap contains any unknown divs, then compute explicit
3297  * expressions for them.  However, this computation may be
3298  * quite expensive, so first try to remove divs that aren't
3299  * strictly needed.
3300  */
3301 struct isl_map *isl_basic_map_compute_divs(struct isl_basic_map *bmap)
3302 {
3303         int i;
3304         unsigned off;
3305
3306         if (!bmap)
3307                 return NULL;
3308         off = isl_dim_total(bmap->dim);
3309         for (i = 0; i < bmap->n_div; ++i) {
3310                 if (isl_int_is_zero(bmap->div[i][0]))
3311                         break;
3312                 isl_assert(bmap->ctx, isl_int_is_zero(bmap->div[i][1+1+off+i]),
3313                                 goto error);
3314         }
3315         if (i == bmap->n_div)
3316                 return isl_map_from_basic_map(bmap);
3317         bmap = isl_basic_map_drop_redundant_divs(bmap);
3318         if (!bmap)
3319                 goto error;
3320         for (i = 0; i < bmap->n_div; ++i)
3321                 if (isl_int_is_zero(bmap->div[i][0]))
3322                         break;
3323         if (i == bmap->n_div)
3324                 return isl_map_from_basic_map(bmap);
3325         struct isl_map *map = compute_divs(bmap);
3326         return map;
3327 error:
3328         isl_basic_map_free(bmap);
3329         return NULL;
3330 }
3331
3332 struct isl_map *isl_map_compute_divs(struct isl_map *map)
3333 {
3334         int i;
3335         struct isl_map *res;
3336
3337         if (!map)
3338                 return NULL;
3339         if (map->n == 0)
3340                 return map;
3341         res = isl_basic_map_compute_divs(isl_basic_map_copy(map->p[0]));
3342         for (i = 1 ; i < map->n; ++i) {
3343                 struct isl_map *r2;
3344                 r2 = isl_basic_map_compute_divs(isl_basic_map_copy(map->p[i]));
3345                 if (ISL_F_ISSET(map, ISL_MAP_DISJOINT))
3346                         res = isl_map_union_disjoint(res, r2);
3347                 else
3348                         res = isl_map_union(res, r2);
3349         }
3350         isl_map_free(map);
3351
3352         return res;
3353 }
3354
3355 struct isl_set *isl_basic_set_compute_divs(struct isl_basic_set *bset)
3356 {
3357         return (struct isl_set *)
3358                 isl_basic_map_compute_divs((struct isl_basic_map *)bset);
3359 }
3360
3361 struct isl_set *isl_set_compute_divs(struct isl_set *set)
3362 {
3363         return (struct isl_set *)
3364                 isl_map_compute_divs((struct isl_map *)set);
3365 }
3366
3367 struct isl_set *isl_map_domain(struct isl_map *map)
3368 {
3369         int i;
3370         struct isl_set *set;
3371
3372         if (!map)
3373                 goto error;
3374
3375         map = isl_map_cow(map);
3376         if (!map)
3377                 return NULL;
3378
3379         set = (struct isl_set *)map;
3380         set->dim = isl_dim_domain(set->dim);
3381         if (!set->dim)
3382                 goto error;
3383         for (i = 0; i < map->n; ++i) {
3384                 set->p[i] = isl_basic_map_domain(map->p[i]);
3385                 if (!set->p[i])
3386                         goto error;
3387         }
3388         ISL_F_CLR(set, ISL_MAP_DISJOINT);
3389         ISL_F_CLR(set, ISL_SET_NORMALIZED);
3390         return set;
3391 error:
3392         isl_map_free(map);
3393         return NULL;
3394 }
3395
3396 struct isl_map *isl_map_union_disjoint(
3397                         struct isl_map *map1, struct isl_map *map2)
3398 {
3399         int i;
3400         unsigned flags = 0;
3401         struct isl_map *map = NULL;
3402
3403         if (!map1 || !map2)
3404                 goto error;
3405
3406         if (map1->n == 0) {
3407                 isl_map_free(map1);
3408                 return map2;
3409         }
3410         if (map2->n == 0) {
3411                 isl_map_free(map2);
3412                 return map1;
3413         }
3414
3415         isl_assert(map1->ctx, isl_dim_equal(map1->dim, map2->dim), goto error);
3416
3417         if (ISL_F_ISSET(map1, ISL_MAP_DISJOINT) &&
3418             ISL_F_ISSET(map2, ISL_MAP_DISJOINT))
3419                 ISL_FL_SET(flags, ISL_MAP_DISJOINT);
3420
3421         map = isl_map_alloc_dim(isl_dim_copy(map1->dim),
3422                                 map1->n + map2->n, flags);
3423         if (!map)
3424                 goto error;
3425         for (i = 0; i < map1->n; ++i) {
3426                 map = isl_map_add(map,
3427                                   isl_basic_map_copy(map1->p[i]));
3428                 if (!map)
3429                         goto error;
3430         }
3431         for (i = 0; i < map2->n; ++i) {
3432                 map = isl_map_add(map,
3433                                   isl_basic_map_copy(map2->p[i]));
3434                 if (!map)
3435                         goto error;
3436         }
3437         isl_map_free(map1);
3438         isl_map_free(map2);
3439         return map;
3440 error:
3441         isl_map_free(map);
3442         isl_map_free(map1);
3443         isl_map_free(map2);
3444         return NULL;
3445 }
3446
3447 struct isl_map *isl_map_union(struct isl_map *map1, struct isl_map *map2)
3448 {
3449         map1 = isl_map_union_disjoint(map1, map2);
3450         if (!map1)
3451                 return NULL;
3452         if (map1->n > 1)
3453                 ISL_F_CLR(map1, ISL_MAP_DISJOINT);
3454         return map1;
3455 }
3456
3457 struct isl_set *isl_set_union_disjoint(
3458                         struct isl_set *set1, struct isl_set *set2)
3459 {
3460         return (struct isl_set *)
3461                 isl_map_union_disjoint(
3462                         (struct isl_map *)set1, (struct isl_map *)set2);
3463 }
3464
3465 struct isl_set *isl_set_union(struct isl_set *set1, struct isl_set *set2)
3466 {
3467         return (struct isl_set *)
3468                 isl_map_union((struct isl_map *)set1, (struct isl_map *)set2);
3469 }
3470
3471 struct isl_map *isl_map_intersect_range(
3472                 struct isl_map *map, struct isl_set *set)
3473 {
3474         unsigned flags = 0;
3475         struct isl_map *result;
3476         int i, j;
3477
3478         if (!map || !set)
3479                 goto error;
3480
3481         if (ISL_F_ISSET(map, ISL_MAP_DISJOINT) &&
3482             ISL_F_ISSET(set, ISL_MAP_DISJOINT))
3483                 ISL_FL_SET(flags, ISL_MAP_DISJOINT);
3484
3485         result = isl_map_alloc_dim(isl_dim_copy(map->dim),
3486                                         map->n * set->n, flags);
3487         if (!result)
3488                 goto error;
3489         for (i = 0; i < map->n; ++i)
3490                 for (j = 0; j < set->n; ++j) {
3491                         result = isl_map_add(result,
3492                             isl_basic_map_intersect_range(
3493                                 isl_basic_map_copy(map->p[i]),
3494                                 isl_basic_set_copy(set->p[j])));
3495                         if (!result)
3496                                 goto error;
3497                 }
3498         isl_map_free(map);
3499         isl_set_free(set);
3500         return result;
3501 error:
3502         isl_map_free(map);
3503         isl_set_free(set);
3504         return NULL;
3505 }
3506
3507 struct isl_map *isl_map_intersect_domain(
3508                 struct isl_map *map, struct isl_set *set)
3509 {
3510         return isl_map_reverse(
3511                 isl_map_intersect_range(isl_map_reverse(map), set));
3512 }
3513
3514 struct isl_map *isl_map_apply_domain(
3515                 struct isl_map *map1, struct isl_map *map2)
3516 {
3517         if (!map1 || !map2)
3518                 goto error;
3519         map1 = isl_map_reverse(map1);
3520         map1 = isl_map_apply_range(map1, map2);
3521         return isl_map_reverse(map1);
3522 error:
3523         isl_map_free(map1);
3524         isl_map_free(map2);
3525         return NULL;
3526 }
3527
3528 struct isl_map *isl_map_apply_range(
3529                 struct isl_map *map1, struct isl_map *map2)
3530 {
3531         struct isl_dim *dim_result;
3532         struct isl_map *result;
3533         int i, j;
3534         unsigned nparam;
3535         unsigned n_in;
3536         unsigned n_out;
3537
3538         if (!map1 || !map2)
3539                 goto error;
3540
3541         dim_result = isl_dim_join(isl_dim_copy(map1->dim),
3542                                   isl_dim_copy(map2->dim));
3543
3544         result = isl_map_alloc_dim(dim_result, map1->n * map2->n, 0);
3545         if (!result)
3546                 goto error;
3547         for (i = 0; i < map1->n; ++i)
3548                 for (j = 0; j < map2->n; ++j) {
3549                         result = isl_map_add(result,
3550                             isl_basic_map_apply_range(
3551                                 isl_basic_map_copy(map1->p[i]),
3552                                 isl_basic_map_copy(map2->p[j])));
3553                         if (!result)
3554                                 goto error;
3555                 }
3556         isl_map_free(map1);
3557         isl_map_free(map2);
3558         if (result && result->n <= 1)
3559                 ISL_F_SET(result, ISL_MAP_DISJOINT);
3560         return result;
3561 error:
3562         isl_map_free(map1);
3563         isl_map_free(map2);
3564         return NULL;
3565 }
3566
3567 /*
3568  * returns range - domain
3569  */
3570 struct isl_basic_set *isl_basic_map_deltas(struct isl_basic_map *bmap)
3571 {
3572         struct isl_basic_set *bset;
3573         unsigned dim;
3574         unsigned nparam;
3575         int i;
3576
3577         if (!bmap)
3578                 goto error;
3579         dim = isl_basic_map_n_in(bmap);
3580         nparam = isl_basic_map_n_param(bmap);
3581         isl_assert(bmap->ctx, dim == isl_basic_map_n_out(bmap), goto error);
3582         bset = isl_basic_set_from_basic_map(bmap);
3583         bset = isl_basic_set_cow(bset);
3584         bset = isl_basic_set_extend(bset, nparam, 3*dim, 0, dim, 0);
3585         bset = isl_basic_set_swap_vars(bset, 2*dim);
3586         for (i = 0; i < dim; ++i) {
3587                 int j = isl_basic_map_alloc_equality(
3588                                             (struct isl_basic_map *)bset);
3589                 if (j < 0)
3590                         goto error;
3591                 isl_seq_clr(bset->eq[j], 1 + isl_basic_set_total_dim(bset));
3592                 isl_int_set_si(bset->eq[j][1+nparam+i], 1);
3593                 isl_int_set_si(bset->eq[j][1+nparam+dim+i], 1);
3594                 isl_int_set_si(bset->eq[j][1+nparam+2*dim+i], -1);
3595         }
3596         return isl_basic_set_project_out(bset, 2*dim, 0);
3597 error:
3598         isl_basic_map_free(bmap);
3599         return NULL;
3600 }
3601
3602 /*
3603  * returns range - domain
3604  */
3605 struct isl_set *isl_map_deltas(struct isl_map *map)
3606 {
3607         int i;
3608         struct isl_set *result;
3609
3610         if (!map)
3611                 return NULL;
3612
3613         isl_assert(map->ctx, isl_map_n_in(map) == isl_map_n_out(map), goto error);
3614         result = isl_set_alloc(map->ctx, isl_map_n_param(map),
3615                                         isl_map_n_in(map), map->n, map->flags);
3616         if (!result)
3617                 goto error;
3618         for (i = 0; i < map->n; ++i)
3619                 result = isl_set_add(result,
3620                           isl_basic_map_deltas(isl_basic_map_copy(map->p[i])));
3621         isl_map_free(map);
3622         return result;
3623 error:
3624         isl_map_free(map);
3625         return NULL;
3626 }
3627
3628 static struct isl_basic_map *basic_map_identity(struct isl_dim *dims)
3629 {
3630         struct isl_basic_map *bmap;
3631         unsigned nparam;
3632         unsigned dim;
3633         int i;
3634
3635         if (!dims)
3636                 return NULL;
3637
3638         nparam = dims->nparam;
3639         dim = dims->n_out;
3640         bmap = isl_basic_map_alloc_dim(dims, 0, dim, 0);
3641         if (!bmap)
3642                 goto error;
3643
3644         for (i = 0; i < dim; ++i) {
3645                 int j = isl_basic_map_alloc_equality(bmap);
3646                 if (j < 0)
3647                         goto error;
3648                 isl_seq_clr(bmap->eq[j], 1 + isl_basic_map_total_dim(bmap));
3649                 isl_int_set_si(bmap->eq[j][1+nparam+i], 1);
3650                 isl_int_set_si(bmap->eq[j][1+nparam+dim+i], -1);
3651         }
3652         return isl_basic_map_finalize(bmap);
3653 error:
3654         isl_basic_map_free(bmap);
3655         return NULL;
3656 }
3657
3658 struct isl_basic_map *isl_basic_map_identity(struct isl_dim *set_dim)
3659 {
3660         struct isl_dim *dim = isl_dim_map(set_dim);
3661         if (!dim)
3662                 return NULL;
3663         return basic_map_identity(dim);
3664 }
3665
3666 struct isl_basic_map *isl_basic_map_identity_like(struct isl_basic_map *model)
3667 {
3668         if (!model || !model->dim)
3669                 return NULL;
3670         isl_assert(model->ctx,
3671                         model->dim->n_in == model->dim->n_out, return NULL);
3672         return basic_map_identity(isl_dim_copy(model->dim));
3673 }
3674
3675 static struct isl_map *map_identity(struct isl_dim *dim)
3676 {
3677         struct isl_map *map = isl_map_alloc_dim(dim, 1, ISL_MAP_DISJOINT);
3678         return isl_map_add(map, basic_map_identity(isl_dim_copy(dim)));
3679 }
3680
3681 struct isl_map *isl_map_identity(struct isl_dim *set_dim)
3682 {
3683         struct isl_dim *dim = isl_dim_map(set_dim);
3684         if (!dim)
3685                 return NULL;
3686         return map_identity(dim);
3687 }
3688
3689 struct isl_map *isl_map_identity_like(struct isl_basic_map *model)
3690 {
3691         if (!model || !model->dim)
3692                 return NULL;
3693         isl_assert(model->ctx,
3694                         model->dim->n_in == model->dim->n_out, return NULL);
3695         return map_identity(isl_dim_copy(model->dim));
3696 }
3697
3698 /* Construct a basic set with all set dimensions having only non-negative
3699  * values.
3700  */
3701 struct isl_basic_set *isl_basic_set_positive_orthant(struct isl_dim *dims)
3702 {
3703         int i;
3704         unsigned nparam;
3705         unsigned dim;
3706         struct isl_basic_set *bset;
3707
3708         if (!dims)
3709                 return NULL;
3710         nparam = dims->nparam;
3711         dim = dims->n_out;
3712         bset = isl_basic_set_alloc_dim(dims, 0, 0, dim);
3713         if (!bset)
3714                 return NULL;
3715         for (i = 0; i < dim; ++i) {
3716                 int k = isl_basic_set_alloc_inequality(bset);
3717                 if (k < 0)
3718                         goto error;
3719                 isl_seq_clr(bset->ineq[k], 1 + isl_basic_set_total_dim(bset));
3720                 isl_int_set_si(bset->ineq[k][1 + nparam + i], 1);
3721         }
3722         return bset;
3723 error:
3724         isl_basic_set_free(bset);
3725         return NULL;
3726 }
3727
3728 int isl_set_is_equal(struct isl_set *set1, struct isl_set *set2)
3729 {
3730         return isl_map_is_equal((struct isl_map *)set1, (struct isl_map *)set2);
3731 }
3732
3733 int isl_set_is_subset(struct isl_set *set1, struct isl_set *set2)
3734 {
3735         return isl_map_is_subset(
3736                         (struct isl_map *)set1, (struct isl_map *)set2);
3737 }
3738
3739 int isl_basic_map_is_subset(
3740                 struct isl_basic_map *bmap1, struct isl_basic_map *bmap2)
3741 {
3742         int is_subset;
3743         struct isl_map *map1;
3744         struct isl_map *map2;
3745
3746         if (!bmap1 || !bmap2)
3747                 return -1;
3748
3749         map1 = isl_map_from_basic_map(isl_basic_map_copy(bmap1));
3750         map2 = isl_map_from_basic_map(isl_basic_map_copy(bmap2));
3751
3752         is_subset = isl_map_is_subset(map1, map2);
3753
3754         isl_map_free(map1);
3755         isl_map_free(map2);
3756
3757         return is_subset;
3758 }
3759
3760 int isl_basic_map_is_equal(
3761                 struct isl_basic_map *bmap1, struct isl_basic_map *bmap2)
3762 {
3763         int is_subset;
3764
3765         if (!bmap1 || !bmap2)
3766                 return -1;
3767         is_subset = isl_basic_map_is_subset(bmap1, bmap2);
3768         if (is_subset != 1)
3769                 return is_subset;
3770         is_subset = isl_basic_map_is_subset(bmap2, bmap1);
3771         return is_subset;
3772 }
3773
3774 int isl_basic_set_is_equal(
3775                 struct isl_basic_set *bset1, struct isl_basic_set *bset2)
3776 {
3777         return isl_basic_map_is_equal(
3778                 (struct isl_basic_map *)bset1, (struct isl_basic_map *)bset2);
3779 }
3780
3781 int isl_map_is_empty(struct isl_map *map)
3782 {
3783         int i;
3784         int is_empty;
3785
3786         if (!map)
3787                 return -1;
3788         for (i = 0; i < map->n; ++i) {
3789                 is_empty = isl_basic_map_is_empty(map->p[i]);
3790                 if (is_empty < 0)
3791                         return -1;
3792                 if (!is_empty)
3793                         return 0;
3794         }
3795         return 1;
3796 }
3797
3798 int isl_map_fast_is_empty(struct isl_map *map)
3799 {
3800         return map->n == 0;
3801 }
3802
3803 int isl_set_is_empty(struct isl_set *set)
3804 {
3805         return isl_map_is_empty((struct isl_map *)set);
3806 }
3807
3808 int isl_map_is_subset(struct isl_map *map1, struct isl_map *map2)
3809 {
3810         int i;
3811         int is_subset = 0;
3812         struct isl_map *diff;
3813
3814         if (!map1 || !map2)
3815                 return -1;
3816
3817         if (isl_map_is_empty(map1))
3818                 return 1;
3819
3820         if (isl_map_is_empty(map2))
3821                 return 0;
3822
3823         diff = isl_map_subtract(isl_map_copy(map1), isl_map_copy(map2));
3824         if (!diff)
3825                 return -1;
3826
3827         is_subset = isl_map_is_empty(diff);
3828         isl_map_free(diff);
3829
3830         return is_subset;
3831 }
3832
3833 int isl_map_is_equal(struct isl_map *map1, struct isl_map *map2)
3834 {
3835         int is_subset;
3836
3837         if (!map1 || !map2)
3838                 return -1;
3839         is_subset = isl_map_is_subset(map1, map2);
3840         if (is_subset != 1)
3841                 return is_subset;
3842         is_subset = isl_map_is_subset(map2, map1);
3843         return is_subset;
3844 }
3845
3846 int isl_basic_map_is_strict_subset(
3847                 struct isl_basic_map *bmap1, struct isl_basic_map *bmap2)
3848 {
3849         int is_subset;
3850
3851         if (!bmap1 || !bmap2)
3852                 return -1;
3853         is_subset = isl_basic_map_is_subset(bmap1, bmap2);
3854         if (is_subset != 1)
3855                 return is_subset;
3856         is_subset = isl_basic_map_is_subset(bmap2, bmap1);
3857         if (is_subset == -1)
3858                 return is_subset;
3859         return !is_subset;
3860 }
3861
3862 int isl_basic_map_is_universe(struct isl_basic_map *bmap)
3863 {
3864         if (!bmap)
3865                 return -1;
3866         return bmap->n_eq == 0 && bmap->n_ineq == 0;
3867 }
3868
3869 int isl_basic_set_is_universe(struct isl_basic_set *bset)
3870 {
3871         if (!bset)
3872                 return -1;
3873         return bset->n_eq == 0 && bset->n_ineq == 0;
3874 }
3875
3876 int isl_basic_map_is_empty(struct isl_basic_map *bmap)
3877 {
3878         struct isl_basic_set *bset = NULL;
3879         struct isl_vec *sample = NULL;
3880         int empty;
3881         unsigned total;
3882
3883         if (!bmap)
3884                 return -1;
3885
3886         if (ISL_F_ISSET(bmap, ISL_BASIC_MAP_EMPTY))
3887                 return 1;
3888
3889         if (ISL_F_ISSET(bmap, ISL_BASIC_MAP_RATIONAL)) {
3890                 struct isl_basic_map *copy = isl_basic_map_copy(bmap);
3891                 copy = isl_basic_map_convex_hull(copy);
3892                 empty = ISL_F_ISSET(copy, ISL_BASIC_MAP_EMPTY);
3893                 isl_basic_map_free(copy);
3894                 return empty;
3895         }
3896
3897         total = 1 + isl_basic_map_total_dim(bmap);
3898         if (bmap->sample && bmap->sample->size == total) {
3899                 int contains = basic_map_contains(bmap, bmap->sample);
3900                 if (contains < 0)
3901                         return -1;
3902                 if (contains)
3903                         return 0;
3904         }
3905         isl_vec_free(bmap->sample);
3906         bmap->sample = NULL;
3907         bset = isl_basic_map_underlying_set(isl_basic_map_copy(bmap));
3908         if (!bset)
3909                 return -1;
3910         sample = isl_basic_set_sample(bset);
3911         if (!sample)
3912                 return -1;
3913         empty = sample->size == 0;
3914         isl_vec_free(bmap->sample);
3915         bmap->sample = sample;
3916         if (empty)
3917                 ISL_F_SET(bmap, ISL_BASIC_MAP_EMPTY);
3918
3919         return empty;
3920 }
3921
3922 int isl_basic_map_fast_is_empty(struct isl_basic_map *bmap)
3923 {
3924         if (!bmap)
3925                 return -1;
3926         return ISL_F_ISSET(bmap, ISL_BASIC_MAP_EMPTY);
3927 }
3928
3929 int isl_basic_set_fast_is_empty(struct isl_basic_set *bset)
3930 {
3931         if (!bset)
3932                 return -1;
3933         return ISL_F_ISSET(bset, ISL_BASIC_SET_EMPTY);
3934 }
3935
3936 int isl_basic_set_is_empty(struct isl_basic_set *bset)
3937 {
3938         return isl_basic_map_is_empty((struct isl_basic_map *)bset);
3939 }
3940
3941 struct isl_map *isl_basic_map_union(
3942         struct isl_basic_map *bmap1, struct isl_basic_map *bmap2)
3943 {
3944         struct isl_map *map;
3945         if (!bmap1 || !bmap2)
3946                 return NULL;
3947
3948         isl_assert(map1->ctx, isl_dim_equal(bmap1->dim, bmap2->dim), goto error);
3949
3950         map = isl_map_alloc_dim(isl_dim_copy(bmap1->dim), 2, 0);
3951         if (!map)
3952                 goto error;
3953         map = isl_map_add(map, bmap1);
3954         map = isl_map_add(map, bmap2);
3955         return map;
3956 error:
3957         isl_basic_map_free(bmap1);
3958         isl_basic_map_free(bmap2);
3959         return NULL;
3960 }
3961
3962 struct isl_set *isl_basic_set_union(
3963                 struct isl_basic_set *bset1, struct isl_basic_set *bset2)
3964 {
3965         return (struct isl_set *)isl_basic_map_union(
3966                                             (struct isl_basic_map *)bset1,
3967                                             (struct isl_basic_map *)bset2);
3968 }
3969
3970 /* Order divs such that any div only depends on previous divs */
3971 static struct isl_basic_map *order_divs(struct isl_basic_map *bmap)
3972 {
3973         int i;
3974         unsigned off = isl_dim_total(bmap->dim);
3975
3976         for (i = 0; i < bmap->n_div; ++i) {
3977                 int pos;
3978                 if (isl_int_is_zero(bmap->div[i][0]))
3979                         continue;
3980                 pos = isl_seq_first_non_zero(bmap->div[i]+1+1+off+i,
3981                                                             bmap->n_div-i);
3982                 if (pos == -1)
3983                         continue;
3984                 isl_basic_map_swap_div(bmap, i, i + pos);
3985                 --i;
3986         }
3987         return bmap;
3988 }
3989
3990 struct isl_basic_set *isl_basic_set_order_divs(struct isl_basic_set *bset)
3991 {
3992         return (struct isl_basic_set *)order_divs((struct isl_basic_map *)bset);
3993 }
3994
3995 /* Look for a div in dst that corresponds to the div "div" in src.
3996  * The divs before "div" in src and dst are assumed to be the same.
3997  *
3998  * Returns -1 if no corresponding div was found and the position
3999  * of the corresponding div in dst otherwise.
4000  */
4001 static int find_div(struct isl_basic_map *dst,
4002                         struct isl_basic_map *src, unsigned div)
4003 {
4004         int i;
4005
4006         unsigned total = isl_dim_total(src->dim);
4007
4008         isl_assert(dst->ctx, div <= dst->n_div, return -1);
4009         for (i = div; i < dst->n_div; ++i)
4010                 if (isl_seq_eq(dst->div[i], src->div[div], 1+1+total+div) &&
4011                     isl_seq_first_non_zero(dst->div[i]+1+1+total+div,
4012                                                 dst->n_div - div) == -1)
4013                         return i;
4014         return -1;
4015 }
4016
4017 struct isl_basic_map *isl_basic_map_align_divs(
4018                 struct isl_basic_map *dst, struct isl_basic_map *src)
4019 {
4020         int i;
4021         unsigned total = isl_dim_total(src->dim);
4022
4023         if (!dst || !src)
4024                 goto error;
4025
4026         if (src->n_div == 0)
4027                 return dst;
4028
4029         for (i = 0; i < src->n_div; ++i)
4030                 isl_assert(src->ctx, !isl_int_is_zero(src->div[i][0]), goto error);
4031
4032         src = order_divs(src);
4033         dst = isl_basic_map_cow(dst);
4034         dst = isl_basic_map_extend_dim(dst, isl_dim_copy(dst->dim),
4035                         src->n_div, 0, 2 * src->n_div);
4036         if (!dst)
4037                 return NULL;
4038         for (i = 0; i < src->n_div; ++i) {
4039                 int j = find_div(dst, src, i);
4040                 if (j < 0) {
4041                         j = isl_basic_map_alloc_div(dst);
4042                         if (j < 0)
4043                                 goto error;
4044                         isl_seq_cpy(dst->div[j], src->div[i], 1+1+total+i);
4045                         isl_seq_clr(dst->div[j]+1+1+total+i, dst->n_div - i);
4046                         if (add_div_constraints(dst, j) < 0)
4047                                 goto error;
4048                 }
4049                 if (j != i)
4050                         isl_basic_map_swap_div(dst, i, j);
4051         }
4052         return dst;
4053 error:
4054         isl_basic_map_free(dst);
4055         return NULL;
4056 }
4057
4058 struct isl_basic_set *isl_basic_set_align_divs(
4059                 struct isl_basic_set *dst, struct isl_basic_set *src)
4060 {
4061         return (struct isl_basic_set *)isl_basic_map_align_divs(
4062                 (struct isl_basic_map *)dst, (struct isl_basic_map *)src);
4063 }
4064
4065 struct isl_map *isl_map_align_divs(struct isl_map *map)
4066 {
4067         int i;
4068
4069         map = isl_map_compute_divs(map);
4070         map = isl_map_cow(map);
4071         if (!map)
4072                 return NULL;
4073
4074         for (i = 1; i < map->n; ++i)
4075                 map->p[0] = isl_basic_map_align_divs(map->p[0], map->p[i]);
4076         for (i = 1; i < map->n; ++i)
4077                 map->p[i] = isl_basic_map_align_divs(map->p[i], map->p[0]);
4078
4079         ISL_F_CLR(map, ISL_MAP_NORMALIZED);
4080         return map;
4081 }
4082
4083 struct isl_set *isl_set_align_divs(struct isl_set *set)
4084 {
4085         return (struct isl_set *)isl_map_align_divs((struct isl_map *)set);
4086 }
4087
4088 static struct isl_map *add_cut_constraint(struct isl_map *dst,
4089                 struct isl_basic_map *src, isl_int *c,
4090                 unsigned len, int oppose)
4091 {
4092         struct isl_basic_map *copy = NULL;
4093         int is_empty;
4094         int k;
4095         unsigned total;
4096
4097         copy = isl_basic_map_copy(src);
4098         copy = isl_basic_map_cow(copy);
4099         if (!copy)
4100                 goto error;
4101         copy = isl_basic_map_extend_constraints(copy, 0, 1);
4102         k = isl_basic_map_alloc_inequality(copy);
4103         if (k < 0)
4104                 goto error;
4105         if (oppose)
4106                 isl_seq_neg(copy->ineq[k], c, len);
4107         else
4108                 isl_seq_cpy(copy->ineq[k], c, len);
4109         total = 1 + isl_basic_map_total_dim(copy);
4110         isl_seq_clr(copy->ineq[k]+len, total - len);
4111         isl_inequality_negate(copy, k);
4112         copy = isl_basic_map_simplify(copy);
4113         copy = isl_basic_map_finalize(copy);
4114         is_empty = isl_basic_map_is_empty(copy);
4115         if (is_empty < 0)
4116                 goto error;
4117         if (!is_empty)
4118                 dst = isl_map_add(dst, copy);
4119         else
4120                 isl_basic_map_free(copy);
4121         return dst;
4122 error:
4123         isl_basic_map_free(copy);
4124         isl_map_free(dst);
4125         return NULL;
4126 }
4127
4128 static struct isl_map *subtract(struct isl_map *map, struct isl_basic_map *bmap)
4129 {
4130         int i, j, k;
4131         unsigned flags = 0;
4132         struct isl_map *rest = NULL;
4133         unsigned max;
4134         unsigned total = isl_basic_map_total_dim(bmap);
4135
4136         assert(bmap);
4137
4138         if (!map)
4139                 goto error;
4140
4141         if (ISL_F_ISSET(map, ISL_MAP_DISJOINT))
4142                 ISL_FL_SET(flags, ISL_MAP_DISJOINT);
4143
4144         max = map->n * (2 * bmap->n_eq + bmap->n_ineq);
4145         rest = isl_map_alloc_dim(isl_dim_copy(map->dim), max, flags);
4146         if (!rest)
4147                 goto error;
4148
4149         for (i = 0; i < map->n; ++i) {
4150                 map->p[i] = isl_basic_map_align_divs(map->p[i], bmap);
4151                 if (!map->p[i])
4152                         goto error;
4153         }
4154
4155         for (j = 0; j < map->n; ++j)
4156                 map->p[j] = isl_basic_map_cow(map->p[j]);
4157
4158         for (i = 0; i < bmap->n_eq; ++i) {
4159                 for (j = 0; j < map->n; ++j) {
4160                         rest = add_cut_constraint(rest,
4161                                 map->p[j], bmap->eq[i], 1+total, 0);
4162                         if (!rest)
4163                                 goto error;
4164
4165                         rest = add_cut_constraint(rest,
4166                                 map->p[j], bmap->eq[i], 1+total, 1);
4167                         if (!rest)
4168                                 goto error;
4169
4170                         map->p[j] = isl_basic_map_extend_constraints(map->p[j],
4171                                 1, 0);
4172                         if (!map->p[j])
4173                                 goto error;
4174                         k = isl_basic_map_alloc_equality(map->p[j]);
4175                         if (k < 0)
4176                                 goto error;
4177                         isl_seq_cpy(map->p[j]->eq[k], bmap->eq[i], 1+total);
4178                         isl_seq_clr(map->p[j]->eq[k]+1+total,
4179                                         map->p[j]->n_div - bmap->n_div);
4180                 }
4181         }
4182
4183         for (i = 0; i < bmap->n_ineq; ++i) {
4184                 for (j = 0; j < map->n; ++j) {
4185                         rest = add_cut_constraint(rest,
4186                                 map->p[j], bmap->ineq[i], 1+total, 0);
4187                         if (!rest)
4188                                 goto error;
4189
4190                         map->p[j] = isl_basic_map_extend_constraints(map->p[j],
4191                                 0, 1);
4192                         if (!map->p[j])
4193                                 goto error;
4194                         k = isl_basic_map_alloc_inequality(map->p[j]);
4195                         if (k < 0)
4196                                 goto error;
4197                         isl_seq_cpy(map->p[j]->ineq[k], bmap->ineq[i], 1+total);
4198                         isl_seq_clr(map->p[j]->ineq[k]+1+total,
4199                                         map->p[j]->n_div - bmap->n_div);
4200                 }
4201         }
4202
4203         isl_map_free(map);
4204         return rest;
4205 error:
4206         isl_map_free(map);
4207         isl_map_free(rest);
4208         return NULL;
4209 }
4210
4211 struct isl_map *isl_map_subtract(struct isl_map *map1, struct isl_map *map2)
4212 {
4213         int i;
4214         if (!map1 || !map2)
4215                 goto error;
4216
4217         isl_assert(map1->ctx, isl_dim_equal(map1->dim, map2->dim), goto error);
4218
4219         if (isl_map_is_empty(map2)) {
4220                 isl_map_free(map2);
4221                 return map1;
4222         }
4223
4224         map1 = isl_map_compute_divs(map1);
4225         map2 = isl_map_compute_divs(map2);
4226         if (!map1 || !map2)
4227                 goto error;
4228
4229         for (i = 0; map1 && i < map2->n; ++i)
4230                 map1 = subtract(map1, map2->p[i]);
4231
4232         isl_map_free(map2);
4233         return map1;
4234 error:
4235         isl_map_free(map1);
4236         isl_map_free(map2);
4237         return NULL;
4238 }
4239
4240 struct isl_set *isl_set_subtract(struct isl_set *set1, struct isl_set *set2)
4241 {
4242         return (struct isl_set *)
4243                 isl_map_subtract(
4244                         (struct isl_map *)set1, (struct isl_map *)set2);
4245 }
4246
4247 struct isl_set *isl_set_apply(struct isl_set *set, struct isl_map *map)
4248 {
4249         if (!set || !map)
4250                 goto error;
4251         isl_assert(set->ctx, isl_map_compatible_domain(map, set), goto error);
4252         map = isl_map_intersect_domain(map, set);
4253         set = isl_map_range(map);
4254         return set;
4255 error:
4256         isl_set_free(set);
4257         isl_map_free(map);
4258         return NULL;
4259 }
4260
4261 /* There is no need to cow as removing empty parts doesn't change
4262  * the meaning of the set.
4263  */
4264 struct isl_map *isl_map_remove_empty_parts(struct isl_map *map)
4265 {
4266         int i;
4267
4268         if (!map)
4269                 return NULL;
4270
4271         for (i = map->n-1; i >= 0; --i) {
4272                 if (!ISL_F_ISSET(map->p[i], ISL_BASIC_MAP_EMPTY))
4273                         continue;
4274                 isl_basic_map_free(map->p[i]);
4275                 if (i != map->n-1) {
4276                         ISL_F_CLR(map, ISL_MAP_NORMALIZED);
4277                         map->p[i] = map->p[map->n-1];
4278                 }
4279                 map->n--;
4280         }
4281
4282         return map;
4283 }
4284
4285 struct isl_set *isl_set_remove_empty_parts(struct isl_set *set)
4286 {
4287         return (struct isl_set *)
4288                 isl_map_remove_empty_parts((struct isl_map *)set);
4289 }
4290
4291 struct isl_basic_map *isl_map_copy_basic_map(struct isl_map *map)
4292 {
4293         struct isl_basic_map *bmap;
4294         if (!map || map->n == 0)
4295                 return NULL;
4296         bmap = map->p[map->n-1];
4297         isl_assert(map->ctx, ISL_F_ISSET(bmap, ISL_BASIC_SET_FINAL), return NULL);
4298         return isl_basic_map_copy(bmap);
4299 }
4300
4301 struct isl_basic_set *isl_set_copy_basic_set(struct isl_set *set)
4302 {
4303         (struct isl_basic_set *)isl_map_copy_basic_map((struct isl_map *)set);
4304 }
4305
4306 struct isl_map *isl_map_drop_basic_map(struct isl_map *map,
4307                                                 struct isl_basic_map *bmap)
4308 {
4309         int i;
4310
4311         if (!map || !bmap)
4312                 goto error;
4313         for (i = map->n-1; i >= 0; --i) {
4314                 if (map->p[i] != bmap)
4315                         continue;
4316                 map = isl_map_cow(map);
4317                 if (!map)
4318                         goto error;
4319                 isl_basic_map_free(map->p[i]);
4320                 if (i != map->n-1) {
4321                         ISL_F_CLR(map, ISL_SET_NORMALIZED);
4322                         map->p[i] = map->p[map->n-1];
4323                 }
4324                 map->n--;
4325                 return map;
4326         }
4327         isl_basic_map_free(bmap);
4328         return map;
4329 error:
4330         isl_map_free(map);
4331         isl_basic_map_free(bmap);
4332         return NULL;
4333 }
4334
4335 struct isl_set *isl_set_drop_basic_set(struct isl_set *set,
4336                                                 struct isl_basic_set *bset)
4337 {
4338         (struct isl_set *)isl_map_drop_basic_map((struct isl_map *)set,
4339                                                 (struct isl_basic_map *)bset);
4340 }
4341
4342 /* Given two _disjoint_ basic sets bset1 and bset2, check whether
4343  * for any common value of the parameters and dimensions preceding dim
4344  * in both basic sets, the values of dimension pos in bset1 are
4345  * smaller or larger than those in bset2.
4346  *
4347  * Returns
4348  *       1 if bset1 follows bset2
4349  *      -1 if bset1 precedes bset2
4350  *       0 if bset1 and bset2 are incomparable
4351  *      -2 if some error occurred.
4352  */
4353 int isl_basic_set_compare_at(struct isl_basic_set *bset1,
4354         struct isl_basic_set *bset2, int pos)
4355 {
4356         struct isl_dim *dims;
4357         struct isl_basic_map *bmap1 = NULL;
4358         struct isl_basic_map *bmap2 = NULL;
4359         struct isl_ctx *ctx;
4360         struct isl_vec *obj;
4361         unsigned total;
4362         unsigned nparam;
4363         unsigned dim1, dim2;
4364         isl_int num, den;
4365         enum isl_lp_result res;
4366         int cmp;
4367
4368         if (!bset1 || !bset2)
4369                 return -2;
4370
4371         nparam = isl_basic_set_n_param(bset1);
4372         dim1 = isl_basic_set_n_dim(bset1);
4373         dim2 = isl_basic_set_n_dim(bset2);
4374         dims = isl_dim_alloc(bset1->ctx, nparam, pos, dim1 - pos);
4375         bmap1 = isl_basic_map_from_basic_set(isl_basic_set_copy(bset1), dims);
4376         dims = isl_dim_alloc(bset2->ctx, nparam, pos, dim2 - pos);
4377         bmap2 = isl_basic_map_from_basic_set(isl_basic_set_copy(bset2), dims);
4378         if (!bmap1 || !bmap2)
4379                 goto error;
4380         bmap1 = isl_basic_map_cow(bmap1);
4381         bmap1 = isl_basic_map_extend(bmap1, nparam,
4382                         pos, (dim1 - pos) + (dim2 - pos),
4383                         bmap2->n_div, bmap2->n_eq, bmap2->n_ineq);
4384         bmap1 = add_constraints(bmap1, bmap2, 0, dim1 - pos);
4385         if (!bmap1)
4386                 goto error;
4387         total = isl_basic_map_total_dim(bmap1);
4388         ctx = bmap1->ctx;
4389         obj = isl_vec_alloc(ctx, 1 + total);
4390         isl_seq_clr(obj->block.data, 1 + total);
4391         isl_int_set_si(obj->block.data[1+nparam+pos], 1);
4392         isl_int_set_si(obj->block.data[1+nparam+pos+(dim1-pos)], -1);
4393         if (!obj)
4394                 goto error;
4395         isl_int_init(num);
4396         isl_int_init(den);
4397         res = isl_solve_lp(bmap1, 0, obj->block.data, ctx->one, &num, &den);
4398         if (res == isl_lp_empty)
4399                 cmp = 0;
4400         else if (res == isl_lp_ok && isl_int_is_pos(num))
4401                 cmp = 1;
4402         else if ((res == isl_lp_ok && isl_int_is_neg(num)) ||
4403                   res == isl_lp_unbounded)
4404                 cmp = -1;
4405         else
4406                 cmp = -2;
4407         isl_int_clear(num);
4408         isl_int_clear(den);
4409         isl_basic_map_free(bmap1);
4410         isl_vec_free(obj);
4411         return cmp;
4412 error:
4413         isl_basic_map_free(bmap1);
4414         isl_basic_map_free(bmap2);
4415         return -2;
4416 }
4417
4418 static int isl_basic_map_fast_has_fixed_var(struct isl_basic_map *bmap,
4419         unsigned pos, isl_int *val)
4420 {
4421         int i;
4422         int d;
4423         unsigned total;
4424
4425         if (!bmap)
4426                 return -1;
4427         total = isl_basic_map_total_dim(bmap);
4428         for (i = 0, d = total-1; i < bmap->n_eq && d+1 > pos; ++i) {
4429                 for (; d+1 > pos; --d)
4430                         if (!isl_int_is_zero(bmap->eq[i][1+d]))
4431                                 break;
4432                 if (d != pos)
4433                         continue;
4434                 if (isl_seq_first_non_zero(bmap->eq[i]+1, d) != -1)
4435                         return 0;
4436                 if (isl_seq_first_non_zero(bmap->eq[i]+1+d+1, total-d-1) != -1)
4437                         return 0;
4438                 if (!isl_int_is_one(bmap->eq[i][1+d]))
4439                         return 0;
4440                 if (val)
4441                         isl_int_neg(*val, bmap->eq[i][0]);
4442                 return 1;
4443         }
4444         return 0;
4445 }
4446
4447 static int isl_map_fast_has_fixed_var(struct isl_map *map,
4448         unsigned pos, isl_int *val)
4449 {
4450         int i;
4451         isl_int v;
4452         isl_int tmp;
4453         int fixed;
4454
4455         if (!map)
4456                 return -1;
4457         if (map->n == 0)
4458                 return 0;
4459         if (map->n == 1)
4460                 return isl_basic_map_fast_has_fixed_var(map->p[0], pos, val);
4461         isl_int_init(v);
4462         isl_int_init(tmp);
4463         fixed = isl_basic_map_fast_has_fixed_var(map->p[0], pos, &v);
4464         for (i = 1; fixed == 1 && i < map->n; ++i) {
4465                 fixed = isl_basic_map_fast_has_fixed_var(map->p[i], pos, &tmp);
4466                 if (fixed == 1 && isl_int_ne(tmp, v))
4467                         fixed = 0;
4468         }
4469         if (val)
4470                 isl_int_set(*val, v);
4471         isl_int_clear(tmp);
4472         isl_int_clear(v);
4473         return fixed;
4474 }
4475
4476 static int isl_basic_set_fast_has_fixed_var(struct isl_basic_set *bset,
4477         unsigned pos, isl_int *val)
4478 {
4479         return isl_basic_map_fast_has_fixed_var((struct isl_basic_map *)bset,
4480                                                 pos, val);
4481 }
4482
4483 static int isl_set_fast_has_fixed_var(struct isl_set *set, unsigned pos,
4484         isl_int *val)
4485 {
4486         return isl_map_fast_has_fixed_var((struct isl_map *)set, pos, val);
4487 }
4488
4489 int isl_basic_map_fast_is_fixed(struct isl_basic_map *bmap,
4490         enum isl_dim_type type, unsigned pos, isl_int *val)
4491 {
4492         if (pos >= isl_basic_map_dim(bmap, type))
4493                 return -1;
4494         return isl_basic_map_fast_has_fixed_var(bmap,
4495                 isl_basic_map_offset(bmap, type) - 1 + pos, val);
4496 }
4497
4498 /* Check if dimension dim has fixed value and if so and if val is not NULL,
4499  * then return this fixed value in *val.
4500  */
4501 int isl_basic_set_fast_dim_is_fixed(struct isl_basic_set *bset, unsigned dim,
4502         isl_int *val)
4503 {
4504         return isl_basic_set_fast_has_fixed_var(bset,
4505                                         isl_basic_set_n_param(bset) + dim, val);
4506 }
4507
4508 /* Check if dimension dim has fixed value and if so and if val is not NULL,
4509  * then return this fixed value in *val.
4510  */
4511 int isl_set_fast_dim_is_fixed(struct isl_set *set, unsigned dim, isl_int *val)
4512 {
4513         return isl_set_fast_has_fixed_var(set, isl_set_n_param(set) + dim, val);
4514 }
4515
4516 /* Check if input variable in has fixed value and if so and if val is not NULL,
4517  * then return this fixed value in *val.
4518  */
4519 int isl_map_fast_input_is_fixed(struct isl_map *map, unsigned in, isl_int *val)
4520 {
4521         return isl_map_fast_has_fixed_var(map, isl_map_n_param(map) + in, val);
4522 }
4523
4524 /* Check if dimension dim has an (obvious) fixed lower bound and if so
4525  * and if val is not NULL, then return this lower bound in *val.
4526  */
4527 int isl_basic_set_fast_dim_has_fixed_lower_bound(struct isl_basic_set *bset,
4528         unsigned dim, isl_int *val)
4529 {
4530         int i, i_eq = -1, i_ineq = -1;
4531         isl_int *c;
4532         unsigned total;
4533         unsigned nparam;
4534
4535         if (!bset)
4536                 return -1;
4537         total = isl_basic_set_total_dim(bset);
4538         nparam = isl_basic_set_n_param(bset);
4539         for (i = 0; i < bset->n_eq; ++i) {
4540                 if (isl_int_is_zero(bset->eq[i][1+nparam+dim]))
4541                         continue;
4542                 if (i_eq != -1)
4543                         return 0;
4544                 i_eq = i;
4545         }
4546         for (i = 0; i < bset->n_ineq; ++i) {
4547                 if (!isl_int_is_pos(bset->ineq[i][1+nparam+dim]))
4548                         continue;
4549                 if (i_eq != -1 || i_ineq != -1)
4550                         return 0;
4551                 i_ineq = i;
4552         }
4553         if (i_eq == -1 && i_ineq == -1)
4554                 return 0;
4555         c = i_eq != -1 ? bset->eq[i_eq] : bset->ineq[i_ineq];
4556         /* The coefficient should always be one due to normalization. */
4557         if (!isl_int_is_one(c[1+nparam+dim]))
4558                 return 0;
4559         if (isl_seq_first_non_zero(c+1, nparam+dim) != -1)
4560                 return 0;
4561         if (isl_seq_first_non_zero(c+1+nparam+dim+1,
4562                                         total - nparam - dim - 1) != -1)
4563                 return 0;
4564         if (val)
4565                 isl_int_neg(*val, c[0]);
4566         return 1;
4567 }
4568
4569 int isl_set_fast_dim_has_fixed_lower_bound(struct isl_set *set,
4570         unsigned dim, isl_int *val)
4571 {
4572         int i;
4573         isl_int v;
4574         isl_int tmp;
4575         int fixed;
4576
4577         if (!set)
4578                 return -1;
4579         if (set->n == 0)
4580                 return 0;
4581         if (set->n == 1)
4582                 return isl_basic_set_fast_dim_has_fixed_lower_bound(set->p[0],
4583                                                                 dim, val);
4584         isl_int_init(v);
4585         isl_int_init(tmp);
4586         fixed = isl_basic_set_fast_dim_has_fixed_lower_bound(set->p[0],
4587                                                                 dim, &v);
4588         for (i = 1; fixed == 1 && i < set->n; ++i) {
4589                 fixed = isl_basic_set_fast_dim_has_fixed_lower_bound(set->p[i],
4590                                                                 dim, &tmp);
4591                 if (fixed == 1 && isl_int_ne(tmp, v))
4592                         fixed = 0;
4593         }
4594         if (val)
4595                 isl_int_set(*val, v);
4596         isl_int_clear(tmp);
4597         isl_int_clear(v);
4598         return fixed;
4599 }
4600
4601 struct constraint {
4602         unsigned        size;
4603         isl_int         *c;
4604 };
4605
4606 static int qsort_constraint_cmp(const void *p1, const void *p2)
4607 {
4608         const struct constraint *c1 = (const struct constraint *)p1;
4609         const struct constraint *c2 = (const struct constraint *)p2;
4610         unsigned size = isl_min(c1->size, c2->size);
4611         return isl_seq_cmp(c1->c, c2->c, size);
4612 }
4613
4614 static struct isl_basic_map *isl_basic_map_sort_constraints(
4615         struct isl_basic_map *bmap)
4616 {
4617         int i;
4618         struct constraint *c;
4619         unsigned total;
4620
4621         if (!bmap)
4622                 return NULL;
4623         total = isl_basic_map_total_dim(bmap);
4624         c = isl_alloc_array(bmap->ctx, struct constraint, bmap->n_ineq);
4625         if (!c)
4626                 goto error;
4627         for (i = 0; i < bmap->n_ineq; ++i) {
4628                 c[i].size = total;
4629                 c[i].c = bmap->ineq[i];
4630         }
4631         qsort(c, bmap->n_ineq, sizeof(struct constraint), qsort_constraint_cmp);
4632         for (i = 0; i < bmap->n_ineq; ++i)
4633                 bmap->ineq[i] = c[i].c;
4634         free(c);
4635         return bmap;
4636 error:
4637         isl_basic_map_free(bmap);
4638         return NULL;
4639 }
4640
4641 struct isl_basic_map *isl_basic_map_normalize(struct isl_basic_map *bmap)
4642 {
4643         if (!bmap)
4644                 return NULL;
4645         if (ISL_F_ISSET(bmap, ISL_BASIC_MAP_NORMALIZED))
4646                 return bmap;
4647         bmap = isl_basic_map_convex_hull(bmap);
4648         bmap = isl_basic_map_sort_constraints(bmap);
4649         ISL_F_SET(bmap, ISL_BASIC_MAP_NORMALIZED);
4650         return bmap;
4651 }
4652
4653 struct isl_basic_set *isl_basic_set_normalize(struct isl_basic_set *bset)
4654 {
4655         return (struct isl_basic_set *)isl_basic_map_normalize(
4656                                                 (struct isl_basic_map *)bset);
4657 }
4658
4659 static int isl_basic_map_fast_cmp(const struct isl_basic_map *bmap1,
4660         const struct isl_basic_map *bmap2)
4661 {
4662         int i, cmp;
4663         unsigned total;
4664
4665         if (bmap1 == bmap2)
4666                 return 0;
4667         if (isl_basic_map_n_param(bmap1) != isl_basic_map_n_param(bmap2))
4668                 return isl_basic_map_n_param(bmap1) - isl_basic_map_n_param(bmap2);
4669         if (isl_basic_map_n_in(bmap1) != isl_basic_map_n_in(bmap2))
4670                 return isl_basic_map_n_out(bmap1) - isl_basic_map_n_out(bmap2);
4671         if (isl_basic_map_n_out(bmap1) != isl_basic_map_n_out(bmap2))
4672                 return isl_basic_map_n_out(bmap1) - isl_basic_map_n_out(bmap2);
4673         if (ISL_F_ISSET(bmap1, ISL_BASIC_MAP_EMPTY) &&
4674             ISL_F_ISSET(bmap2, ISL_BASIC_MAP_EMPTY))
4675                 return 0;
4676         if (ISL_F_ISSET(bmap1, ISL_BASIC_MAP_EMPTY))
4677                 return 1;
4678         if (ISL_F_ISSET(bmap2, ISL_BASIC_MAP_EMPTY))
4679                 return -1;
4680         if (bmap1->n_eq != bmap2->n_eq)
4681                 return bmap1->n_eq - bmap2->n_eq;
4682         if (bmap1->n_ineq != bmap2->n_ineq)
4683                 return bmap1->n_ineq - bmap2->n_ineq;
4684         if (bmap1->n_div != bmap2->n_div)
4685                 return bmap1->n_div - bmap2->n_div;
4686         total = isl_basic_map_total_dim(bmap1);
4687         for (i = 0; i < bmap1->n_eq; ++i) {
4688                 cmp = isl_seq_cmp(bmap1->eq[i], bmap2->eq[i], 1+total);
4689                 if (cmp)
4690                         return cmp;
4691         }
4692         for (i = 0; i < bmap1->n_ineq; ++i) {
4693                 cmp = isl_seq_cmp(bmap1->ineq[i], bmap2->ineq[i], 1+total);
4694                 if (cmp)
4695                         return cmp;
4696         }
4697         for (i = 0; i < bmap1->n_div; ++i) {
4698                 cmp = isl_seq_cmp(bmap1->div[i], bmap2->div[i], 1+1+total);
4699                 if (cmp)
4700                         return cmp;
4701         }
4702         return 0;
4703 }
4704
4705 static int isl_basic_map_fast_is_equal(struct isl_basic_map *bmap1,
4706         struct isl_basic_map *bmap2)
4707 {
4708         return isl_basic_map_fast_cmp(bmap1, bmap2) == 0;
4709 }
4710
4711 static int qsort_bmap_cmp(const void *p1, const void *p2)
4712 {
4713         const struct isl_basic_map *bmap1 = *(const struct isl_basic_map **)p1;
4714         const struct isl_basic_map *bmap2 = *(const struct isl_basic_map **)p2;
4715
4716         return isl_basic_map_fast_cmp(bmap1, bmap2);
4717 }
4718
4719 /* We normalize in place, but if anything goes wrong we need
4720  * to return NULL, so we need to make sure we don't change the
4721  * meaning of any possible other copies of map.
4722  */
4723 struct isl_map *isl_map_normalize(struct isl_map *map)
4724 {
4725         int i, j;
4726         struct isl_basic_map *bmap;
4727
4728         if (!map)
4729                 return NULL;
4730         if (ISL_F_ISSET(map, ISL_MAP_NORMALIZED))
4731                 return map;
4732         for (i = 0; i < map->n; ++i) {
4733                 bmap = isl_basic_map_normalize(isl_basic_map_copy(map->p[i]));
4734                 if (!bmap)
4735                         goto error;
4736                 isl_basic_map_free(map->p[i]);
4737                 map->p[i] = bmap;
4738         }
4739         qsort(map->p, map->n, sizeof(struct isl_basic_map *), qsort_bmap_cmp);
4740         ISL_F_SET(map, ISL_MAP_NORMALIZED);
4741         map = isl_map_remove_empty_parts(map);
4742         if (!map)
4743                 return NULL;
4744         for (i = map->n - 1; i >= 1; --i) {
4745                 if (!isl_basic_map_fast_is_equal(map->p[i-1], map->p[i]))
4746                         continue;
4747                 isl_basic_map_free(map->p[i-1]);
4748                 for (j = i; j < map->n; ++j)
4749                         map->p[j-1] = map->p[j];
4750                 map->n--;
4751         }
4752         return map;
4753 error:
4754         isl_map_free(map);
4755         return NULL;
4756
4757 }
4758
4759 struct isl_set *isl_set_normalize(struct isl_set *set)
4760 {
4761         return (struct isl_set *)isl_map_normalize((struct isl_map *)set);
4762 }
4763
4764 int isl_map_fast_is_equal(struct isl_map *map1, struct isl_map *map2)
4765 {
4766         int i;
4767         int equal;
4768
4769         if (!map1 || !map2)
4770                 return -1;
4771
4772         if (map1 == map2)
4773                 return 1;
4774         if (!isl_dim_equal(map1->dim, map2->dim))
4775                 return 0;
4776
4777         map1 = isl_map_copy(map1);
4778         map2 = isl_map_copy(map2);
4779         map1 = isl_map_normalize(map1);
4780         map2 = isl_map_normalize(map2);
4781         if (!map1 || !map2)
4782                 goto error;
4783         equal = map1->n == map2->n;
4784         for (i = 0; equal && i < map1->n; ++i) {
4785                 equal = isl_basic_map_fast_is_equal(map1->p[i], map2->p[i]);
4786                 if (equal < 0)
4787                         goto error;
4788         }
4789         isl_map_free(map1);
4790         isl_map_free(map2);
4791         return equal;
4792 error:
4793         isl_map_free(map1);
4794         isl_map_free(map2);
4795         return -1;
4796 }
4797
4798 int isl_set_fast_is_equal(struct isl_set *set1, struct isl_set *set2)
4799 {
4800         return isl_map_fast_is_equal((struct isl_map *)set1,
4801                                                 (struct isl_map *)set2);
4802 }
4803
4804 /* Return an interval that ranges from min to max (inclusive)
4805  */
4806 struct isl_basic_set *isl_basic_set_interval(struct isl_ctx *ctx,
4807         isl_int min, isl_int max)
4808 {
4809         int k;
4810         struct isl_basic_set *bset = NULL;
4811
4812         bset = isl_basic_set_alloc(ctx, 0, 1, 0, 0, 2);
4813         if (!bset)
4814                 goto error;
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_neg(bset->ineq[k][0], min);
4821
4822         k = isl_basic_set_alloc_inequality(bset);
4823         if (k < 0)
4824                 goto error;
4825         isl_int_set_si(bset->ineq[k][1], -1);
4826         isl_int_set(bset->ineq[k][0], max);
4827
4828         return bset;
4829 error:
4830         isl_basic_set_free(bset);
4831         return NULL;
4832 }
4833
4834 /* Return the Cartesian product of the basic sets in list (in the given order).
4835  */
4836 struct isl_basic_set *isl_basic_set_product(struct isl_basic_set_list *list)
4837 {
4838         int i;
4839         unsigned dim;
4840         unsigned nparam;
4841         unsigned extra;
4842         unsigned n_eq;
4843         unsigned n_ineq;
4844         struct isl_basic_set *product = NULL;
4845
4846         if (!list)
4847                 goto error;
4848         isl_assert(list->ctx, list->n > 0, goto error);
4849         isl_assert(list->ctx, list->p[0], goto error);
4850         nparam = isl_basic_set_n_param(list->p[0]);
4851         dim = isl_basic_set_n_dim(list->p[0]);
4852         extra = list->p[0]->n_div;
4853         n_eq = list->p[0]->n_eq;
4854         n_ineq = list->p[0]->n_ineq;
4855         for (i = 1; i < list->n; ++i) {
4856                 isl_assert(list->ctx, list->p[i], goto error);
4857                 isl_assert(list->ctx,
4858                     nparam == isl_basic_set_n_param(list->p[i]), goto error);
4859                 dim += isl_basic_set_n_dim(list->p[i]);
4860                 extra += list->p[i]->n_div;
4861                 n_eq += list->p[i]->n_eq;
4862                 n_ineq += list->p[i]->n_ineq;
4863         }
4864         product = isl_basic_set_alloc(list->ctx, nparam, dim, extra,
4865                                         n_eq, n_ineq);
4866         if (!product)
4867                 goto error;
4868         dim = 0;
4869         for (i = 0; i < list->n; ++i) {
4870                 isl_basic_set_add_constraints(product,
4871                                         isl_basic_set_copy(list->p[i]), dim);
4872                 dim += isl_basic_set_n_dim(list->p[i]);
4873         }
4874         isl_basic_set_list_free(list);
4875         return product;
4876 error:
4877         isl_basic_set_free(product);
4878         isl_basic_set_list_free(list);
4879         return NULL;
4880 }
4881
4882 struct isl_basic_map *isl_basic_map_product(
4883                 struct isl_basic_map *bmap1, struct isl_basic_map *bmap2)
4884 {
4885         struct isl_dim *dim_result = NULL;
4886         struct isl_basic_map *bmap;
4887         unsigned in1, in2, out1, out2, nparam, total, pos;
4888         struct isl_dim_map *dim_map1, *dim_map2;
4889
4890         if (!bmap1 || !bmap2)
4891                 goto error;
4892
4893         isl_assert(map1->ctx, isl_dim_match(bmap1->dim, isl_dim_param,
4894                                      bmap2->dim, isl_dim_param), goto error);
4895         dim_result = isl_dim_product(isl_dim_copy(bmap1->dim),
4896                                                    isl_dim_copy(bmap2->dim));
4897
4898         in1 = isl_basic_map_n_in(bmap1);
4899         in2 = isl_basic_map_n_in(bmap2);
4900         out1 = isl_basic_map_n_out(bmap1);
4901         out2 = isl_basic_map_n_out(bmap2);
4902         nparam = isl_basic_map_n_param(bmap1);
4903
4904         total = nparam + in1 + in2 + out1 + out2 + bmap1->n_div + bmap2->n_div;
4905         dim_map1 = isl_dim_map_alloc(bmap1->ctx, total);
4906         dim_map2 = isl_dim_map_alloc(bmap1->ctx, total);
4907         isl_dim_map_dim(dim_map1, bmap1->dim, isl_dim_param, pos = 0);
4908         isl_dim_map_dim(dim_map2, bmap2->dim, isl_dim_param, pos = 0);
4909         isl_dim_map_dim(dim_map1, bmap1->dim, isl_dim_in, pos += nparam);
4910         isl_dim_map_dim(dim_map2, bmap2->dim, isl_dim_in, pos += in1);
4911         isl_dim_map_dim(dim_map1, bmap1->dim, isl_dim_out, pos += in2);
4912         isl_dim_map_dim(dim_map2, bmap2->dim, isl_dim_out, pos += out1);
4913         isl_dim_map_div(dim_map1, bmap1, pos += out2);
4914         isl_dim_map_div(dim_map2, bmap2, pos += bmap1->n_div);
4915
4916         bmap = isl_basic_map_alloc_dim(dim_result,
4917                         bmap1->n_div + bmap2->n_div,
4918                         bmap1->n_eq + bmap2->n_eq,
4919                         bmap1->n_ineq + bmap2->n_ineq);
4920         bmap = add_constraints_dim_map(bmap, bmap1, dim_map1);
4921         bmap = add_constraints_dim_map(bmap, bmap2, dim_map2);
4922         bmap = isl_basic_map_simplify(bmap);
4923         return isl_basic_map_finalize(bmap);
4924 error:
4925         isl_basic_map_free(bmap1);
4926         isl_basic_map_free(bmap2);
4927         return NULL;
4928 }
4929
4930 /* Given two maps A -> B and C -> D, construct a map (A, C) -> (B, D)
4931  */
4932 struct isl_map *isl_map_product(struct isl_map *map1, struct isl_map *map2)
4933 {
4934         unsigned flags = 0;
4935         struct isl_map *result;
4936         int i, j;
4937
4938         if (!map1 || !map2)
4939                 goto error;
4940
4941         isl_assert(map1->ctx, isl_dim_match(map1->dim, isl_dim_param,
4942                                          map2->dim, isl_dim_param), goto error);
4943
4944         if (ISL_F_ISSET(map1, ISL_MAP_DISJOINT) &&
4945             ISL_F_ISSET(map2, ISL_MAP_DISJOINT))
4946                 ISL_FL_SET(flags, ISL_MAP_DISJOINT);
4947
4948         result = isl_map_alloc_dim(isl_dim_product(isl_dim_copy(map1->dim),
4949                                                    isl_dim_copy(map2->dim)),
4950                                 map1->n * map2->n, flags);
4951         if (!result)
4952                 goto error;
4953         for (i = 0; i < map1->n; ++i)
4954                 for (j = 0; j < map2->n; ++j) {
4955                         struct isl_basic_map *part;
4956                         part = isl_basic_map_product(
4957                                     isl_basic_map_copy(map1->p[i]),
4958                                     isl_basic_map_copy(map2->p[j]));
4959                         if (isl_basic_map_is_empty(part))
4960                                 isl_basic_map_free(part);
4961                         else
4962                                 result = isl_map_add(result, part);
4963                         if (!result)
4964                                 goto error;
4965                 }
4966         isl_map_free(map1);
4967         isl_map_free(map2);
4968         return result;
4969 error:
4970         isl_map_free(map1);
4971         isl_map_free(map2);
4972         return NULL;
4973 }
4974
4975 /* Given two set A and B, construct its Cartesian product A x B.
4976  */
4977 struct isl_set *isl_set_product(struct isl_set *set1, struct isl_set *set2)
4978 {
4979         return (struct isl_set *)isl_map_product((struct isl_map *)set1,
4980                                                  (struct isl_map *)set2);
4981 }
4982
4983 uint32_t isl_basic_set_get_hash(struct isl_basic_set *bset)
4984 {
4985         int i;
4986         uint32_t hash;
4987         unsigned total;
4988
4989         if (!bset)
4990                 return 0;
4991         bset = isl_basic_set_copy(bset);
4992         bset = isl_basic_set_normalize(bset);
4993         if (!bset)
4994                 return 0;
4995         total = isl_basic_set_total_dim(bset);
4996         isl_hash_byte(hash, bset->n_eq & 0xFF);
4997         for (i = 0; i < bset->n_eq; ++i) {
4998                 uint32_t c_hash;
4999                 c_hash = isl_seq_get_hash(bset->eq[i], 1 + total);
5000                 isl_hash_hash(hash, c_hash);
5001         }
5002         isl_hash_byte(hash, bset->n_ineq & 0xFF);
5003         for (i = 0; i < bset->n_ineq; ++i) {
5004                 uint32_t c_hash;
5005                 c_hash = isl_seq_get_hash(bset->ineq[i], 1 + total);
5006                 isl_hash_hash(hash, c_hash);
5007         }
5008         isl_hash_byte(hash, bset->n_div & 0xFF);
5009         for (i = 0; i < bset->n_div; ++i) {
5010                 uint32_t c_hash;
5011                 if (isl_int_is_zero(bset->div[i][0]))
5012                         continue;
5013                 isl_hash_byte(hash, i & 0xFF);
5014                 c_hash = isl_seq_get_hash(bset->div[i], 1 + 1 + total);
5015                 isl_hash_hash(hash, c_hash);
5016         }
5017         isl_basic_set_free(bset);
5018         return hash;
5019 }
5020
5021 uint32_t isl_set_get_hash(struct isl_set *set)
5022 {
5023         int i;
5024         uint32_t hash;
5025
5026         if (!set)
5027                 return 0;
5028         set = isl_set_copy(set);
5029         set = isl_set_normalize(set);
5030         if (!set)
5031                 return 0;
5032
5033         hash = isl_hash_init();
5034         for (i = 0; i < set->n; ++i) {
5035                 uint32_t bset_hash;
5036                 bset_hash = isl_basic_set_get_hash(set->p[i]);
5037                 isl_hash_hash(hash, bset_hash);
5038         }
5039
5040         isl_set_free(set);
5041
5042         return hash;
5043 }
5044
5045 /* Check if the value for dimension dim is completely determined
5046  * by the values of the other parameters and variables.
5047  * That is, check if dimension dim is involved in an equality.
5048  */
5049 int isl_basic_set_dim_is_unique(struct isl_basic_set *bset, unsigned dim)
5050 {
5051         int i;
5052         unsigned nparam;
5053
5054         if (!bset)
5055                 return -1;
5056         nparam = isl_basic_set_n_param(bset);
5057         for (i = 0; i < bset->n_eq; ++i)
5058                 if (!isl_int_is_zero(bset->eq[i][1 + nparam + dim]))
5059                         return 1;
5060         return 0;
5061 }
5062
5063 /* Check if the value for dimension dim is completely determined
5064  * by the values of the other parameters and variables.
5065  * That is, check if dimension dim is involved in an equality
5066  * for each of the subsets.
5067  */
5068 int isl_set_dim_is_unique(struct isl_set *set, unsigned dim)
5069 {
5070         int i;
5071
5072         if (!set)
5073                 return -1;
5074         for (i = 0; i < set->n; ++i) {
5075                 int unique;
5076                 unique = isl_basic_set_dim_is_unique(set->p[i], dim);
5077                 if (unique != 1)
5078                         return unique;
5079         }
5080         return 1;
5081 }