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         bset = isl_basic_set_drop_redundant_divs(bset);
1881         return isl_basic_set_finalize(bset);
1882 error:
1883         isl_basic_set_free(bset);
1884         return NULL;
1885 }
1886
1887 static struct isl_basic_map *add_divs(struct isl_basic_map *bmap, unsigned n)
1888 {
1889         int i, j;
1890
1891         for (i = 0; i < n; ++i) {
1892                 j = isl_basic_map_alloc_div(bmap);
1893                 if (j < 0)
1894                         goto error;
1895                 isl_seq_clr(bmap->div[j], 1+1+isl_basic_map_total_dim(bmap));
1896         }
1897         return bmap;
1898 error:
1899         isl_basic_map_free(bmap);
1900         return NULL;
1901 }
1902
1903 struct isl_basic_map *isl_basic_map_apply_range(
1904                 struct isl_basic_map *bmap1, struct isl_basic_map *bmap2)
1905 {
1906         struct isl_dim *dim_result = NULL;
1907         struct isl_basic_map *bmap;
1908         unsigned n_in, n_out, n, nparam, total, pos;
1909         struct isl_dim_map *dim_map1, *dim_map2;
1910
1911         if (!bmap1 || !bmap2)
1912                 goto error;
1913
1914         dim_result = isl_dim_join(isl_dim_copy(bmap1->dim),
1915                                   isl_dim_copy(bmap2->dim));
1916
1917         n_in = isl_basic_map_n_in(bmap1);
1918         n_out = isl_basic_map_n_out(bmap2);
1919         n = isl_basic_map_n_out(bmap1);
1920         nparam = isl_basic_map_n_param(bmap1);
1921
1922         total = nparam + n_in + n_out + bmap1->n_div + bmap2->n_div + n;
1923         dim_map1 = isl_dim_map_alloc(bmap1->ctx, total);
1924         dim_map2 = isl_dim_map_alloc(bmap1->ctx, total);
1925         isl_dim_map_dim(dim_map1, bmap1->dim, isl_dim_param, pos = 0);
1926         isl_dim_map_dim(dim_map2, bmap2->dim, isl_dim_param, pos = 0);
1927         isl_dim_map_dim(dim_map1, bmap1->dim, isl_dim_in, pos += nparam);
1928         isl_dim_map_dim(dim_map2, bmap2->dim, isl_dim_out, pos += n_in);
1929         isl_dim_map_div(dim_map1, bmap1, pos += n_out);
1930         isl_dim_map_div(dim_map2, bmap2, pos += bmap1->n_div);
1931         isl_dim_map_dim(dim_map1, bmap1->dim, isl_dim_out, pos += bmap2->n_div);
1932         isl_dim_map_dim(dim_map2, bmap2->dim, isl_dim_in, pos);
1933
1934         bmap = isl_basic_map_alloc_dim(dim_result,
1935                         bmap1->n_div + bmap2->n_div + n,
1936                         bmap1->n_eq + bmap2->n_eq,
1937                         bmap1->n_ineq + bmap2->n_ineq);
1938         bmap = add_constraints_dim_map(bmap, bmap1, dim_map1);
1939         bmap = add_constraints_dim_map(bmap, bmap2, dim_map2);
1940         bmap = add_divs(bmap, n);
1941         bmap = isl_basic_map_simplify(bmap);
1942         bmap = isl_basic_map_drop_redundant_divs(bmap);
1943         return isl_basic_map_finalize(bmap);
1944 error:
1945         isl_basic_map_free(bmap1);
1946         isl_basic_map_free(bmap2);
1947         return NULL;
1948 }
1949
1950 struct isl_basic_set *isl_basic_set_apply(
1951                 struct isl_basic_set *bset, struct isl_basic_map *bmap)
1952 {
1953         if (!bset || !bmap)
1954                 goto error;
1955
1956         isl_assert(set->ctx, isl_basic_map_compatible_domain(bmap, bset),
1957                     goto error);
1958
1959         return (struct isl_basic_set *)
1960                 isl_basic_map_apply_range((struct isl_basic_map *)bset, bmap);
1961 error:
1962         isl_basic_set_free(bset);
1963         isl_basic_map_free(bmap);
1964         return NULL;
1965 }
1966
1967 struct isl_basic_map *isl_basic_map_apply_domain(
1968                 struct isl_basic_map *bmap1, struct isl_basic_map *bmap2)
1969 {
1970         if (!bmap1 || !bmap2)
1971                 goto error;
1972
1973         isl_assert(ctx,
1974             isl_basic_map_n_in(bmap1) == isl_basic_map_n_in(bmap2), goto error);
1975         isl_assert(ctx,
1976             isl_basic_map_n_param(bmap1) == isl_basic_map_n_param(bmap2),
1977             goto error);
1978
1979         bmap1 = isl_basic_map_reverse(bmap1);
1980         bmap1 = isl_basic_map_apply_range(bmap1, bmap2);
1981         return isl_basic_map_reverse(bmap1);
1982 error:
1983         isl_basic_map_free(bmap1);
1984         isl_basic_map_free(bmap2);
1985         return NULL;
1986 }
1987
1988 /* Given two basic maps A -> f(A) and B -> g(B), construct a basic map
1989  * A \cap B -> f(A) + f(B)
1990  */
1991 struct isl_basic_map *isl_basic_map_sum(
1992                 struct isl_basic_map *bmap1, struct isl_basic_map *bmap2)
1993 {
1994         unsigned n_in, n_out, nparam, total, pos;
1995         struct isl_basic_map *bmap = NULL;
1996         struct isl_dim_map *dim_map1, *dim_map2;
1997         int i;
1998
1999         if (!bmap1 || !bmap2)
2000                 goto error;
2001
2002         isl_assert(bmap1->ctx, isl_dim_equal(bmap1->dim, bmap2->dim),
2003                 goto error);
2004
2005         nparam = isl_basic_map_n_param(bmap1);
2006         n_in = isl_basic_map_n_in(bmap1);
2007         n_out = isl_basic_map_n_out(bmap1);
2008
2009         total = nparam + n_in + n_out + bmap1->n_div + bmap2->n_div + 2 * n_out;
2010         dim_map1 = isl_dim_map_alloc(bmap1->ctx, total);
2011         dim_map2 = isl_dim_map_alloc(bmap2->ctx, total);
2012         isl_dim_map_dim(dim_map1, bmap1->dim, isl_dim_param, pos = 0);
2013         isl_dim_map_dim(dim_map2, bmap2->dim, isl_dim_param, pos);
2014         isl_dim_map_dim(dim_map1, bmap1->dim, isl_dim_in, pos += nparam);
2015         isl_dim_map_dim(dim_map2, bmap2->dim, isl_dim_in, pos);
2016         isl_dim_map_div(dim_map1, bmap1, pos += n_in + n_out);
2017         isl_dim_map_div(dim_map2, bmap2, pos += bmap1->n_div);
2018         isl_dim_map_dim(dim_map1, bmap1->dim, isl_dim_out, pos += bmap2->n_div);
2019         isl_dim_map_dim(dim_map2, bmap2->dim, isl_dim_out, pos += n_out);
2020
2021         bmap = isl_basic_map_alloc_dim(isl_dim_copy(bmap1->dim),
2022                         bmap1->n_div + bmap2->n_div + 2 * n_out,
2023                         bmap1->n_eq + bmap2->n_eq + n_out,
2024                         bmap1->n_ineq + bmap2->n_ineq);
2025         for (i = 0; i < n_out; ++i) {
2026                 int j = isl_basic_map_alloc_equality(bmap);
2027                 if (j < 0)
2028                         goto error;
2029                 isl_seq_clr(bmap->eq[j], 1+total);
2030                 isl_int_set_si(bmap->eq[j][1+nparam+n_in+i], -1);
2031                 isl_int_set_si(bmap->eq[j][1+pos+i], 1);
2032                 isl_int_set_si(bmap->eq[j][1+pos-n_out+i], 1);
2033         }
2034         bmap = add_constraints_dim_map(bmap, bmap1, dim_map1);
2035         bmap = add_constraints_dim_map(bmap, bmap2, dim_map2);
2036         bmap = add_divs(bmap, 2 * n_out);
2037
2038         bmap = isl_basic_map_simplify(bmap);
2039         return isl_basic_map_finalize(bmap);
2040 error:
2041         isl_basic_map_free(bmap);
2042         isl_basic_map_free(bmap1);
2043         isl_basic_map_free(bmap2);
2044         return NULL;
2045 }
2046
2047 /* Given a basic map A -> f(A), construct A -> -f(A).
2048  */
2049 struct isl_basic_map *isl_basic_map_neg(struct isl_basic_map *bmap)
2050 {
2051         int i, j;
2052         unsigned off, n;
2053
2054         bmap = isl_basic_map_cow(bmap);
2055         if (!bmap)
2056                 return NULL;
2057
2058         n = isl_basic_map_dim(bmap, isl_dim_out);
2059         off = isl_basic_map_offset(bmap, isl_dim_out);
2060         for (i = 0; i < bmap->n_eq; ++i)
2061                 for (j = 0; j < n; ++j)
2062                         isl_int_neg(bmap->eq[i][off+j], bmap->eq[i][off+j]);
2063         for (i = 0; i < bmap->n_ineq; ++i)
2064                 for (j = 0; j < n; ++j)
2065                         isl_int_neg(bmap->ineq[i][off+j], bmap->ineq[i][off+j]);
2066         for (i = 0; i < bmap->n_div; ++i)
2067                 for (j = 0; j < n; ++j)
2068                         isl_int_neg(bmap->div[i][1+off+j], bmap->div[i][1+off+j]);
2069         return isl_basic_map_finalize(bmap);
2070 }
2071
2072 /* Given a map A -> f(A), construct A -> -f(A).
2073  */
2074 struct isl_map *isl_map_neg(struct isl_map *map)
2075 {
2076         int i;
2077
2078         map = isl_map_cow(map);
2079         if (!map)
2080                 return NULL;
2081
2082         for (i = 0; i < map->n; ++i) {
2083                 map->p[i] = isl_basic_map_neg(map->p[i]);
2084                 if (!map->p[i])
2085                         goto error;
2086         }
2087
2088         return map;
2089 error:
2090         isl_map_free(map);
2091         return NULL;
2092 }
2093
2094 /* Given a basic map A -> f(A) and an integer d, construct a basic map
2095  * A -> floor(f(A)/d).
2096  */
2097 struct isl_basic_map *isl_basic_map_floordiv(struct isl_basic_map *bmap,
2098                 isl_int d)
2099 {
2100         unsigned n_in, n_out, nparam, total, pos;
2101         struct isl_basic_map *result = NULL;
2102         struct isl_dim_map *dim_map;
2103         int i;
2104
2105         if (!bmap)
2106                 return NULL;
2107
2108         nparam = isl_basic_map_n_param(bmap);
2109         n_in = isl_basic_map_n_in(bmap);
2110         n_out = isl_basic_map_n_out(bmap);
2111
2112         total = nparam + n_in + n_out + bmap->n_div + n_out;
2113         dim_map = isl_dim_map_alloc(bmap->ctx, total);
2114         isl_dim_map_dim(dim_map, bmap->dim, isl_dim_param, pos = 0);
2115         isl_dim_map_dim(dim_map, bmap->dim, isl_dim_in, pos += nparam);
2116         isl_dim_map_div(dim_map, bmap, pos += n_in + n_out);
2117         isl_dim_map_dim(dim_map, bmap->dim, isl_dim_out, pos += bmap->n_div);
2118
2119         result = isl_basic_map_alloc_dim(isl_dim_copy(bmap->dim),
2120                         bmap->n_div + n_out,
2121                         bmap->n_eq, bmap->n_ineq + 2 * n_out);
2122         result = add_constraints_dim_map(result, bmap, dim_map);
2123         result = add_divs(result, n_out);
2124         for (i = 0; i < n_out; ++i) {
2125                 int j;
2126                 j = isl_basic_map_alloc_inequality(result);
2127                 if (j < 0)
2128                         goto error;
2129                 isl_seq_clr(result->ineq[j], 1+total);
2130                 isl_int_neg(result->ineq[j][1+nparam+n_in+i], d);
2131                 isl_int_set_si(result->ineq[j][1+pos+i], 1);
2132                 j = isl_basic_map_alloc_inequality(result);
2133                 if (j < 0)
2134                         goto error;
2135                 isl_seq_clr(result->ineq[j], 1+total);
2136                 isl_int_set(result->ineq[j][1+nparam+n_in+i], d);
2137                 isl_int_set_si(result->ineq[j][1+pos+i], -1);
2138                 isl_int_sub_ui(result->ineq[j][0], d, 1);
2139         }
2140
2141         result = isl_basic_map_simplify(result);
2142         return isl_basic_map_finalize(result);
2143 error:
2144         isl_basic_map_free(result);
2145         return NULL;
2146 }
2147
2148 static struct isl_basic_map *var_equal(struct isl_basic_map *bmap, unsigned pos)
2149 {
2150         int i;
2151         unsigned nparam;
2152         unsigned n_in;
2153
2154         i = isl_basic_map_alloc_equality(bmap);
2155         if (i < 0)
2156                 goto error;
2157         nparam = isl_basic_map_n_param(bmap);
2158         n_in = isl_basic_map_n_in(bmap);
2159         isl_seq_clr(bmap->eq[i], 1 + isl_basic_map_total_dim(bmap));
2160         isl_int_set_si(bmap->eq[i][1+nparam+pos], -1);
2161         isl_int_set_si(bmap->eq[i][1+nparam+n_in+pos], 1);
2162         return isl_basic_map_finalize(bmap);
2163 error:
2164         isl_basic_map_free(bmap);
2165         return NULL;
2166 }
2167
2168 static struct isl_basic_map *var_more(struct isl_basic_map *bmap, unsigned pos)
2169 {
2170         int i;
2171         unsigned nparam;
2172         unsigned n_in;
2173
2174         i = isl_basic_map_alloc_inequality(bmap);
2175         if (i < 0)
2176                 goto error;
2177         nparam = isl_basic_map_n_param(bmap);
2178         n_in = isl_basic_map_n_in(bmap);
2179         isl_seq_clr(bmap->ineq[i], 1 + isl_basic_map_total_dim(bmap));
2180         isl_int_set_si(bmap->ineq[i][0], -1);
2181         isl_int_set_si(bmap->ineq[i][1+nparam+pos], -1);
2182         isl_int_set_si(bmap->ineq[i][1+nparam+n_in+pos], 1);
2183         return isl_basic_map_finalize(bmap);
2184 error:
2185         isl_basic_map_free(bmap);
2186         return NULL;
2187 }
2188
2189 static struct isl_basic_map *var_less(struct isl_basic_map *bmap, unsigned pos)
2190 {
2191         int i;
2192         unsigned nparam;
2193         unsigned n_in;
2194
2195         i = isl_basic_map_alloc_inequality(bmap);
2196         if (i < 0)
2197                 goto error;
2198         nparam = isl_basic_map_n_param(bmap);
2199         n_in = isl_basic_map_n_in(bmap);
2200         isl_seq_clr(bmap->ineq[i], 1 + isl_basic_map_total_dim(bmap));
2201         isl_int_set_si(bmap->ineq[i][0], -1);
2202         isl_int_set_si(bmap->ineq[i][1+nparam+pos], 1);
2203         isl_int_set_si(bmap->ineq[i][1+nparam+n_in+pos], -1);
2204         return isl_basic_map_finalize(bmap);
2205 error:
2206         isl_basic_map_free(bmap);
2207         return NULL;
2208 }
2209
2210 struct isl_basic_map *isl_basic_map_equal(struct isl_dim *dim, unsigned n_equal)
2211 {
2212         int i;
2213         struct isl_basic_map *bmap;
2214         bmap = isl_basic_map_alloc_dim(dim, 0, n_equal, 0);
2215         if (!bmap)
2216                 return NULL;
2217         for (i = 0; i < n_equal && bmap; ++i)
2218                 bmap = var_equal(bmap, i);
2219         return isl_basic_map_finalize(bmap);
2220 }
2221
2222 struct isl_basic_map *isl_basic_map_less_at(struct isl_dim *dim, unsigned pos)
2223 {
2224         int i;
2225         struct isl_basic_map *bmap;
2226         bmap = isl_basic_map_alloc_dim(dim, 0, pos, 1);
2227         if (!bmap)
2228                 return NULL;
2229         for (i = 0; i < pos && bmap; ++i)
2230                 bmap = var_equal(bmap, i);
2231         if (bmap)
2232                 bmap = var_less(bmap, pos);
2233         return isl_basic_map_finalize(bmap);
2234 }
2235
2236 struct isl_basic_map *isl_basic_map_more_at(struct isl_dim *dim, unsigned pos)
2237 {
2238         int i;
2239         struct isl_basic_map *bmap;
2240         bmap = isl_basic_map_alloc_dim(dim, 0, pos, 1);
2241         if (!bmap)
2242                 return NULL;
2243         for (i = 0; i < pos && bmap; ++i)
2244                 bmap = var_equal(bmap, i);
2245         if (bmap)
2246                 bmap = var_more(bmap, pos);
2247         return isl_basic_map_finalize(bmap);
2248 }
2249
2250 struct isl_basic_map *isl_basic_map_from_basic_set(
2251                 struct isl_basic_set *bset, struct isl_dim *dim)
2252 {
2253         struct isl_basic_map *bmap;
2254
2255         bset = isl_basic_set_cow(bset);
2256         if (!bset || !dim)
2257                 goto error;
2258
2259         isl_assert(bset->ctx, isl_dim_compatible(bset->dim, dim), goto error);
2260         isl_dim_free(bset->dim);
2261         bmap = (struct isl_basic_map *) bset;
2262         bmap->dim = dim;
2263         return isl_basic_map_finalize(bmap);
2264 error:
2265         isl_basic_set_free(bset);
2266         isl_dim_free(dim);
2267         return NULL;
2268 }
2269
2270 struct isl_basic_set *isl_basic_set_from_basic_map(struct isl_basic_map *bmap)
2271 {
2272         if (!bmap)
2273                 goto error;
2274         if (bmap->dim->n_in == 0)
2275                 return (struct isl_basic_set *)bmap;
2276         bmap = isl_basic_map_cow(bmap);
2277         if (!bmap)
2278                 goto error;
2279         bmap->dim = isl_dim_cow(bmap->dim);
2280         if (!bmap->dim)
2281                 goto error;
2282         bmap->dim->n_out += bmap->dim->n_in;
2283         bmap->dim->n_in = 0;
2284         bmap = isl_basic_map_finalize(bmap);
2285         return (struct isl_basic_set *)bmap;
2286 error:
2287         isl_basic_map_free(bmap);
2288         return NULL;
2289 }
2290
2291 /* For a div d = floor(f/m), add the constraints
2292  *
2293  *              f - m d >= 0
2294  *              -(f-(n-1)) + m d >= 0
2295  *
2296  * Note that the second constraint is the negation of
2297  *
2298  *              f - m d >= n
2299  */
2300 static int add_div_constraints(struct isl_basic_map *bmap, unsigned div)
2301 {
2302         int i, j;
2303         unsigned total = isl_basic_map_total_dim(bmap);
2304         unsigned div_pos = 1 + total - bmap->n_div + div;
2305
2306         i = isl_basic_map_alloc_inequality(bmap);
2307         if (i < 0)
2308                 return -1;
2309         isl_seq_cpy(bmap->ineq[i], bmap->div[div]+1, 1+total);
2310         isl_int_neg(bmap->ineq[i][div_pos], bmap->div[div][0]);
2311
2312         j = isl_basic_map_alloc_inequality(bmap);
2313         if (j < 0)
2314                 return -1;
2315         isl_seq_neg(bmap->ineq[j], bmap->ineq[i], 1 + total);
2316         isl_int_add(bmap->ineq[j][0], bmap->ineq[j][0], bmap->ineq[j][div_pos]);
2317         isl_int_sub_ui(bmap->ineq[j][0], bmap->ineq[j][0], 1);
2318         return j;
2319 }
2320
2321 struct isl_basic_set *isl_basic_map_underlying_set(
2322                 struct isl_basic_map *bmap)
2323 {
2324         if (!bmap)
2325                 goto error;
2326         if (bmap->dim->nparam == 0 && bmap->dim->n_in == 0 && bmap->n_div == 0)
2327                 return (struct isl_basic_set *)bmap;
2328         bmap = isl_basic_map_cow(bmap);
2329         if (!bmap)
2330                 goto error;
2331         bmap->dim = isl_dim_underlying(bmap->dim, bmap->n_div);
2332         if (!bmap->dim)
2333                 goto error;
2334         bmap->extra -= bmap->n_div;
2335         bmap->n_div = 0;
2336         bmap = isl_basic_map_finalize(bmap);
2337         return (struct isl_basic_set *)bmap;
2338 error:
2339         return NULL;
2340 }
2341
2342 struct isl_basic_map *isl_basic_map_overlying_set(
2343         struct isl_basic_set *bset, struct isl_basic_map *like)
2344 {
2345         struct isl_basic_map *bmap;
2346         struct isl_ctx *ctx;
2347         unsigned total;
2348         int i;
2349
2350         if (!bset || !like)
2351                 goto error;
2352         ctx = bset->ctx;
2353         isl_assert(ctx, bset->n_div == 0, goto error);
2354         isl_assert(ctx, isl_basic_set_n_param(bset) == 0, goto error);
2355         isl_assert(ctx, bset->dim->n_out == isl_basic_map_total_dim(like),
2356                         goto error);
2357         if (isl_dim_equal(bset->dim, like->dim) && like->n_div == 0) {
2358                 isl_basic_map_free(like);
2359                 return (struct isl_basic_map *)bset;
2360         }
2361         bset = isl_basic_set_cow(bset);
2362         if (!bset)
2363                 goto error;
2364         total = bset->dim->n_out + bset->extra;
2365         bmap = (struct isl_basic_map *)bset;
2366         isl_dim_free(bmap->dim);
2367         bmap->dim = isl_dim_copy(like->dim);
2368         if (!bmap->dim)
2369                 goto error;
2370         bmap->n_div = like->n_div;
2371         bmap->extra += like->n_div;
2372         if (bmap->extra) {
2373                 unsigned ltotal;
2374                 ltotal = total - bmap->extra + like->extra;
2375                 if (ltotal > total)
2376                         ltotal = total;
2377                 bmap->block2 = isl_blk_extend(ctx, bmap->block2,
2378                                         bmap->extra * (1 + 1 + total));
2379                 if (isl_blk_is_error(bmap->block2))
2380                         goto error;
2381                 bmap->div = isl_realloc_array(ctx, bmap->div, isl_int *,
2382                                                 bmap->extra);
2383                 if (!bmap->div)
2384                         goto error;
2385                 for (i = 0; i < bmap->extra; ++i)
2386                         bmap->div[i] = bmap->block2.data + i * (1 + 1 + total);
2387                 for (i = 0; i < like->n_div; ++i) {
2388                         isl_seq_cpy(bmap->div[i], like->div[i], 1 + 1 + ltotal);
2389                         isl_seq_clr(bmap->div[i]+1+1+ltotal, total - ltotal);
2390                 }
2391                 bmap = isl_basic_map_extend_constraints(bmap,
2392                                                         0, 2 * like->n_div);
2393                 for (i = 0; i < like->n_div; ++i) {
2394                         if (isl_int_is_zero(bmap->div[i][0]))
2395                                 continue;
2396                         if (add_div_constraints(bmap, i) < 0)
2397                                 goto error;
2398                 }
2399         }
2400         isl_basic_map_free(like);
2401         bmap = isl_basic_map_simplify(bmap);
2402         bmap = isl_basic_map_finalize(bmap);
2403         return bmap;
2404 error:
2405         isl_basic_map_free(like);
2406         isl_basic_set_free(bset);
2407         return NULL;
2408 }
2409
2410 struct isl_basic_set *isl_basic_set_from_underlying_set(
2411         struct isl_basic_set *bset, struct isl_basic_set *like)
2412 {
2413         return (struct isl_basic_set *)
2414                 isl_basic_map_overlying_set(bset, (struct isl_basic_map *)like);
2415 }
2416
2417 struct isl_set *isl_set_from_underlying_set(
2418         struct isl_set *set, struct isl_basic_set *like)
2419 {
2420         int i;
2421
2422         if (!set || !like)
2423                 goto error;
2424         isl_assert(set->ctx, set->dim->n_out == isl_basic_set_total_dim(like),
2425                     goto error);
2426         if (isl_dim_equal(set->dim, like->dim) && like->n_div == 0) {
2427                 isl_basic_set_free(like);
2428                 return set;
2429         }
2430         set = isl_set_cow(set);
2431         if (!set)
2432                 goto error;
2433         for (i = 0; i < set->n; ++i) {
2434                 set->p[i] = isl_basic_set_from_underlying_set(set->p[i],
2435                                                       isl_basic_set_copy(like));
2436                 if (!set->p[i])
2437                         goto error;
2438         }
2439         isl_dim_free(set->dim);
2440         set->dim = isl_dim_copy(like->dim);
2441         if (!set->dim)
2442                 goto error;
2443         isl_basic_set_free(like);
2444         return set;
2445 error:
2446         isl_basic_set_free(like);
2447         isl_set_free(set);
2448         return NULL;
2449 }
2450
2451 struct isl_set *isl_map_underlying_set(struct isl_map *map)
2452 {
2453         int i;
2454
2455         map = isl_map_cow(map);
2456         if (!map)
2457                 return NULL;
2458         map->dim = isl_dim_cow(map->dim);
2459         if (!map->dim)
2460                 goto error;
2461
2462         for (i = 1; i < map->n; ++i)
2463                 isl_assert(map->ctx, map->p[0]->n_div == map->p[i]->n_div,
2464                                 goto error);
2465         for (i = 0; i < map->n; ++i) {
2466                 map->p[i] = (struct isl_basic_map *)
2467                                 isl_basic_map_underlying_set(map->p[i]);
2468                 if (!map->p[i])
2469                         goto error;
2470         }
2471         if (map->n == 0)
2472                 map->dim = isl_dim_underlying(map->dim, 0);
2473         else {
2474                 isl_dim_free(map->dim);
2475                 map->dim = isl_dim_copy(map->p[0]->dim);
2476         }
2477         if (!map->dim)
2478                 goto error;
2479         return (struct isl_set *)map;
2480 error:
2481         isl_map_free(map);
2482         return NULL;
2483 }
2484
2485 struct isl_set *isl_set_to_underlying_set(struct isl_set *set)
2486 {
2487         return (struct isl_set *)isl_map_underlying_set((struct isl_map *)set);
2488 }
2489
2490 struct isl_basic_set *isl_basic_map_domain(struct isl_basic_map *bmap)
2491 {
2492         struct isl_basic_set *domain;
2493         unsigned n_out;
2494         if (!bmap)
2495                 return NULL;
2496         n_out = isl_basic_map_n_out(bmap);
2497         domain = isl_basic_set_from_basic_map(bmap);
2498         return isl_basic_set_project_out(domain, n_out, 0);
2499 }
2500
2501 struct isl_basic_set *isl_basic_map_range(struct isl_basic_map *bmap)
2502 {
2503         return isl_basic_map_domain(isl_basic_map_reverse(bmap));
2504 }
2505
2506 struct isl_set *isl_map_range(struct isl_map *map)
2507 {
2508         int i;
2509         struct isl_set *set;
2510
2511         if (!map)
2512                 goto error;
2513         map = isl_map_cow(map);
2514         if (!map)
2515                 goto error;
2516
2517         set = (struct isl_set *) map;
2518         if (set->dim->n_in != 0) {
2519                 set->dim = isl_dim_drop_inputs(set->dim, 0, set->dim->n_in);
2520                 if (!set->dim)
2521                         goto error;
2522         }
2523         for (i = 0; i < map->n; ++i) {
2524                 set->p[i] = isl_basic_map_range(map->p[i]);
2525                 if (!set->p[i])
2526                         goto error;
2527         }
2528         ISL_F_CLR(set, ISL_MAP_DISJOINT);
2529         ISL_F_CLR(set, ISL_SET_NORMALIZED);
2530         return set;
2531 error:
2532         isl_map_free(map);
2533         return NULL;
2534 }
2535
2536 struct isl_map *isl_map_from_set(struct isl_set *set, struct isl_dim *dim)
2537 {
2538         int i;
2539         struct isl_map *map = NULL;
2540
2541         set = isl_set_cow(set);
2542         if (!set || !dim)
2543                 goto error;
2544         isl_assert(set->ctx, isl_dim_compatible(set->dim, dim), goto error);
2545         map = (struct isl_map *)set;
2546         for (i = 0; i < set->n; ++i) {
2547                 map->p[i] = isl_basic_map_from_basic_set(
2548                                 set->p[i], isl_dim_copy(dim));
2549                 if (!map->p[i])
2550                         goto error;
2551         }
2552         isl_dim_free(map->dim);
2553         map->dim = dim;
2554         return map;
2555 error:
2556         isl_dim_free(dim);
2557         isl_set_free(set);
2558         return NULL;
2559 }
2560
2561 struct isl_map *isl_map_from_range(struct isl_set *set)
2562 {
2563         return (struct isl_map *)set;
2564 }
2565
2566 struct isl_set *isl_set_from_map(struct isl_map *map)
2567 {
2568         int i;
2569         struct isl_set *set = NULL;
2570
2571         if (!map)
2572                 return NULL;
2573         map = isl_map_cow(map);
2574         if (!map)
2575                 return NULL;
2576         map->dim = isl_dim_cow(map->dim);
2577         if (!map->dim)
2578                 goto error;
2579         map->dim->n_out += map->dim->n_in;
2580         map->dim->n_in = 0;
2581         set = (struct isl_set *)map;
2582         for (i = 0; i < map->n; ++i) {
2583                 set->p[i] = isl_basic_set_from_basic_map(map->p[i]);
2584                 if (!set->p[i])
2585                         goto error;
2586         }
2587         return set;
2588 error:
2589         isl_map_free(map);
2590         return NULL;
2591 }
2592
2593 struct isl_map *isl_map_alloc_dim(struct isl_dim *dim, int n, unsigned flags)
2594 {
2595         struct isl_map *map;
2596
2597         if (!dim)
2598                 return NULL;
2599         isl_assert(dim->ctx, n >= 0, return NULL);
2600         map = isl_alloc(dim->ctx, struct isl_map,
2601                         sizeof(struct isl_map) +
2602                         n * sizeof(struct isl_basic_map *));
2603         if (!map)
2604                 goto error;
2605
2606         map->ctx = dim->ctx;
2607         isl_ctx_ref(map->ctx);
2608         map->ref = 1;
2609         map->size = n;
2610         map->n = 0;
2611         map->dim = dim;
2612         map->flags = flags;
2613         return map;
2614 error:
2615         isl_dim_free(dim);
2616         return NULL;
2617 }
2618
2619 struct isl_map *isl_map_alloc(struct isl_ctx *ctx,
2620                 unsigned nparam, unsigned in, unsigned out, int n,
2621                 unsigned flags)
2622 {
2623         struct isl_map *map;
2624         struct isl_dim *dims;
2625
2626         dims = isl_dim_alloc(ctx, nparam, in, out);
2627         if (!dims)
2628                 return NULL;
2629
2630         map = isl_map_alloc_dim(dims, n, flags);
2631         return map;
2632 }
2633
2634 struct isl_basic_map *isl_basic_map_empty(struct isl_ctx *ctx,
2635                 unsigned nparam, unsigned in, unsigned out)
2636 {
2637         struct isl_basic_map *bmap;
2638         bmap = isl_basic_map_alloc(ctx, nparam, in, out, 0, 1, 0);
2639         bmap = isl_basic_map_set_to_empty(bmap);
2640         return bmap;
2641 }
2642
2643 struct isl_basic_set *isl_basic_set_empty(struct isl_dim *dim)
2644 {
2645         struct isl_basic_set *bset;
2646         bset = isl_basic_set_alloc_dim(dim, 0, 1, 0);
2647         bset = isl_basic_set_set_to_empty(bset);
2648         return bset;
2649 }
2650
2651 struct isl_basic_map *isl_basic_map_empty_like(struct isl_basic_map *model)
2652 {
2653         struct isl_basic_map *bmap;
2654         if (!model)
2655                 return NULL;
2656         bmap = isl_basic_map_alloc_dim(isl_dim_copy(model->dim), 0, 1, 0);
2657         bmap = isl_basic_map_set_to_empty(bmap);
2658         return bmap;
2659 }
2660
2661 struct isl_basic_map *isl_basic_map_empty_like_map(struct isl_map *model)
2662 {
2663         struct isl_basic_map *bmap;
2664         if (!model)
2665                 return NULL;
2666         bmap = isl_basic_map_alloc_dim(isl_dim_copy(model->dim), 0, 1, 0);
2667         bmap = isl_basic_map_set_to_empty(bmap);
2668         return bmap;
2669 }
2670
2671 struct isl_basic_set *isl_basic_set_empty_like(struct isl_basic_set *model)
2672 {
2673         struct isl_basic_set *bset;
2674         if (!model)
2675                 return NULL;
2676         bset = isl_basic_set_alloc_dim(isl_dim_copy(model->dim), 0, 1, 0);
2677         bset = isl_basic_set_set_to_empty(bset);
2678         return bset;
2679 }
2680
2681 struct isl_basic_map *isl_basic_map_universe(struct isl_dim *dim)
2682 {
2683         struct isl_basic_map *bmap;
2684         bmap = isl_basic_map_alloc_dim(dim, 0, 0, 0);
2685         return bmap;
2686 }
2687
2688 struct isl_basic_set *isl_basic_set_universe(struct isl_dim *dim)
2689 {
2690         struct isl_basic_set *bset;
2691         bset = isl_basic_set_alloc_dim(dim, 0, 0, 0);
2692         return bset;
2693 }
2694
2695 struct isl_basic_set *isl_basic_set_universe_like(struct isl_basic_set *model)
2696 {
2697         if (!model)
2698                 return NULL;
2699         return isl_basic_set_alloc_dim(isl_dim_copy(model->dim), 0, 0, 0);
2700 }
2701
2702 struct isl_map *isl_map_empty(struct isl_dim *dim)
2703 {
2704         return isl_map_alloc_dim(dim, 0, ISL_MAP_DISJOINT);
2705 }
2706
2707 struct isl_map *isl_map_empty_like(struct isl_map *model)
2708 {
2709         if (!model)
2710                 return NULL;
2711         return isl_map_alloc_dim(isl_dim_copy(model->dim), 0, ISL_MAP_DISJOINT);
2712 }
2713
2714 struct isl_map *isl_map_empty_like_basic_map(struct isl_basic_map *model)
2715 {
2716         if (!model)
2717                 return NULL;
2718         return isl_map_alloc_dim(isl_dim_copy(model->dim), 0, ISL_MAP_DISJOINT);
2719 }
2720
2721 struct isl_set *isl_set_empty(struct isl_dim *dim)
2722 {
2723         return isl_set_alloc_dim(dim, 0, ISL_MAP_DISJOINT);
2724 }
2725
2726 struct isl_set *isl_set_empty_like(struct isl_set *model)
2727 {
2728         if (!model)
2729                 return NULL;
2730         return isl_set_empty(isl_dim_copy(model->dim));
2731 }
2732
2733 struct isl_map *isl_map_universe(struct isl_dim *dim)
2734 {
2735         struct isl_map *map;
2736         if (!dim)
2737                 return NULL;
2738         map = isl_map_alloc_dim(isl_dim_copy(dim), 1, ISL_MAP_DISJOINT);
2739         map = isl_map_add(map, isl_basic_map_universe(dim));
2740         return map;
2741 }
2742
2743 struct isl_set *isl_set_universe(struct isl_dim *dim)
2744 {
2745         struct isl_set *set;
2746         if (!dim)
2747                 return NULL;
2748         set = isl_set_alloc_dim(isl_dim_copy(dim), 1, ISL_MAP_DISJOINT);
2749         set = isl_set_add(set, isl_basic_set_universe(dim));
2750         return set;
2751 }
2752
2753 struct isl_map *isl_map_dup(struct isl_map *map)
2754 {
2755         int i;
2756         struct isl_map *dup;
2757
2758         if (!map)
2759                 return NULL;
2760         dup = isl_map_alloc_dim(isl_dim_copy(map->dim), map->n, map->flags);
2761         for (i = 0; i < map->n; ++i)
2762                 dup = isl_map_add(dup, isl_basic_map_copy(map->p[i]));
2763         return dup;
2764 }
2765
2766 struct isl_map *isl_map_add(struct isl_map *map, struct isl_basic_map *bmap)
2767 {
2768         if (!bmap || !map)
2769                 goto error;
2770         if (isl_basic_map_fast_is_empty(bmap)) {
2771                 isl_basic_map_free(bmap);
2772                 return map;
2773         }
2774         isl_assert(map->ctx, isl_dim_equal(map->dim, bmap->dim), goto error);
2775         isl_assert(map->ctx, map->n < map->size, goto error);
2776         map->p[map->n] = bmap;
2777         map->n++;
2778         ISL_F_CLR(map, ISL_MAP_NORMALIZED);
2779         return map;
2780 error:
2781         if (map)
2782                 isl_map_free(map);
2783         if (bmap)
2784                 isl_basic_map_free(bmap);
2785         return NULL;
2786 }
2787
2788 void isl_map_free(struct isl_map *map)
2789 {
2790         int i;
2791
2792         if (!map)
2793                 return;
2794
2795         if (--map->ref > 0)
2796                 return;
2797
2798         isl_ctx_deref(map->ctx);
2799         for (i = 0; i < map->n; ++i)
2800                 isl_basic_map_free(map->p[i]);
2801         isl_dim_free(map->dim);
2802         free(map);
2803 }
2804
2805 struct isl_map *isl_map_extend(struct isl_map *base,
2806                 unsigned nparam, unsigned n_in, unsigned n_out)
2807 {
2808         int i;
2809
2810         base = isl_map_cow(base);
2811         if (!base)
2812                 return NULL;
2813
2814         base->dim = isl_dim_extend(base->dim, nparam, n_in, n_out);
2815         if (!base->dim)
2816                 goto error;
2817         for (i = 0; i < base->n; ++i) {
2818                 base->p[i] = isl_basic_map_extend_dim(base->p[i],
2819                                 isl_dim_copy(base->dim), 0, 0, 0);
2820                 if (!base->p[i])
2821                         goto error;
2822         }
2823         return base;
2824 error:
2825         isl_map_free(base);
2826         return NULL;
2827 }
2828
2829 struct isl_set *isl_set_extend(struct isl_set *base,
2830                 unsigned nparam, unsigned dim)
2831 {
2832         return (struct isl_set *)isl_map_extend((struct isl_map *)base,
2833                                                         nparam, 0, dim);
2834 }
2835
2836 static struct isl_basic_map *isl_basic_map_fix_pos(struct isl_basic_map *bmap,
2837                 unsigned pos, int value)
2838 {
2839         int j;
2840
2841         bmap = isl_basic_map_cow(bmap);
2842         bmap = isl_basic_map_extend_constraints(bmap, 1, 0);
2843         j = isl_basic_map_alloc_equality(bmap);
2844         if (j < 0)
2845                 goto error;
2846         isl_seq_clr(bmap->eq[j] + 1, isl_basic_map_total_dim(bmap));
2847         isl_int_set_si(bmap->eq[j][pos], -1);
2848         isl_int_set_si(bmap->eq[j][0], value);
2849         bmap = isl_basic_map_simplify(bmap);
2850         return isl_basic_map_finalize(bmap);
2851 error:
2852         isl_basic_map_free(bmap);
2853         return NULL;
2854 }
2855
2856 struct isl_basic_map *isl_basic_map_fix_si(struct isl_basic_map *bmap,
2857                 enum isl_dim_type type, unsigned pos, int value)
2858 {
2859         if (!bmap)
2860                 return NULL;
2861         isl_assert(bmap->ctx, pos < isl_basic_map_dim(bmap, type), goto error);
2862         return isl_basic_map_fix_pos(bmap, isl_basic_map_offset(bmap, type) + pos,
2863                                         value);
2864 error:
2865         isl_basic_map_free(bmap);
2866         return NULL;
2867 }
2868
2869 struct isl_basic_set *isl_basic_set_fix_si(struct isl_basic_set *bset,
2870                 enum isl_dim_type type, unsigned pos, int value)
2871 {
2872         return (struct isl_basic_set *)
2873                 isl_basic_map_fix_si((struct isl_basic_map *)bset,
2874                                         type, pos, value);
2875 }
2876
2877 struct isl_basic_map *isl_basic_map_fix_input_si(struct isl_basic_map *bmap,
2878                 unsigned input, int value)
2879 {
2880         return isl_basic_map_fix_si(bmap, isl_dim_in, input, value);
2881 }
2882
2883 struct isl_basic_set *isl_basic_set_fix_dim_si(struct isl_basic_set *bset,
2884                 unsigned dim, int value)
2885 {
2886         return (struct isl_basic_set *)
2887                 isl_basic_map_fix_si((struct isl_basic_map *)bset,
2888                                         isl_dim_set, dim, value);
2889 }
2890
2891 struct isl_map *isl_map_fix_si(struct isl_map *map,
2892                 enum isl_dim_type type, unsigned pos, int value)
2893 {
2894         int i;
2895
2896         map = isl_map_cow(map);
2897         if (!map)
2898                 return NULL;
2899
2900         isl_assert(ctx, pos < isl_map_dim(map, type), goto error);
2901         for (i = 0; i < map->n; ++i) {
2902                 map->p[i] = isl_basic_map_fix_si(map->p[i], type, pos, value);
2903                 if (!map->p[i])
2904                         goto error;
2905         }
2906         ISL_F_CLR(map, ISL_MAP_NORMALIZED);
2907         return map;
2908 error:
2909         isl_map_free(map);
2910         return NULL;
2911 }
2912
2913 struct isl_map *isl_map_fix_input_si(struct isl_map *map,
2914                 unsigned input, int value)
2915 {
2916         return isl_map_fix_si(map, isl_dim_in, input, value);
2917 }
2918
2919 struct isl_set *isl_set_fix_dim_si(struct isl_set *set, unsigned dim, int value)
2920 {
2921         return (struct isl_set *)
2922                 isl_map_fix_si((struct isl_map *)set, isl_dim_set, dim, value);
2923 }
2924
2925 struct isl_basic_set *isl_basic_set_lower_bound_dim(struct isl_basic_set *bset,
2926         unsigned dim, isl_int value)
2927 {
2928         int j;
2929         unsigned nparam;
2930
2931         bset = isl_basic_set_cow(bset);
2932         bset = isl_basic_set_extend_constraints(bset, 0, 1);
2933         j = isl_basic_set_alloc_inequality(bset);
2934         if (j < 0)
2935                 goto error;
2936         isl_seq_clr(bset->ineq[j], 1 + isl_basic_set_total_dim(bset));
2937         isl_int_set_si(bset->ineq[j][1 + isl_basic_set_n_param(bset) + dim], 1);
2938         isl_int_neg(bset->ineq[j][0], value);
2939         bset = isl_basic_set_simplify(bset);
2940         return isl_basic_set_finalize(bset);
2941 error:
2942         isl_basic_set_free(bset);
2943         return NULL;
2944 }
2945
2946 struct isl_set *isl_set_lower_bound_dim(struct isl_set *set, unsigned dim,
2947                                         isl_int value)
2948 {
2949         int i;
2950
2951         set = isl_set_cow(set);
2952         if (!set)
2953                 return NULL;
2954
2955         isl_assert(set->ctx, dim < isl_set_n_dim(set), goto error);
2956         for (i = 0; i < set->n; ++i) {
2957                 set->p[i] = isl_basic_set_lower_bound_dim(set->p[i], dim, value);
2958                 if (!set->p[i])
2959                         goto error;
2960         }
2961         return set;
2962 error:
2963         isl_set_free(set);
2964         return NULL;
2965 }
2966
2967 struct isl_map *isl_map_reverse(struct isl_map *map)
2968 {
2969         int i;
2970         unsigned t;
2971
2972         map = isl_map_cow(map);
2973         if (!map)
2974                 return NULL;
2975
2976         map->dim = isl_dim_reverse(map->dim);
2977         if (!map->dim)
2978                 goto error;
2979         for (i = 0; i < map->n; ++i) {
2980                 map->p[i] = isl_basic_map_reverse(map->p[i]);
2981                 if (!map->p[i])
2982                         goto error;
2983         }
2984         ISL_F_CLR(map, ISL_MAP_NORMALIZED);
2985         return map;
2986 error:
2987         isl_map_free(map);
2988         return NULL;
2989 }
2990
2991 static struct isl_map *isl_basic_map_partial_lexopt(
2992                 struct isl_basic_map *bmap, struct isl_basic_set *dom,
2993                 struct isl_set **empty, int max)
2994 {
2995         if (!bmap)
2996                 goto error;
2997         if (bmap->ctx->pip == ISL_PIP_PIP)
2998                 return isl_pip_basic_map_lexopt(bmap, dom, empty, max);
2999         else
3000                 return isl_tab_basic_map_partial_lexopt(bmap, dom, empty, max);
3001 error:
3002         isl_basic_map_free(bmap);
3003         isl_basic_set_free(dom);
3004         if (empty)
3005                 *empty = NULL;
3006         return NULL;
3007 }
3008
3009 struct isl_map *isl_basic_map_partial_lexmax(
3010                 struct isl_basic_map *bmap, struct isl_basic_set *dom,
3011                 struct isl_set **empty)
3012 {
3013         return isl_basic_map_partial_lexopt(bmap, dom, empty, 1);
3014 }
3015
3016 struct isl_map *isl_basic_map_partial_lexmin(
3017                 struct isl_basic_map *bmap, struct isl_basic_set *dom,
3018                 struct isl_set **empty)
3019 {
3020         return isl_basic_map_partial_lexopt(bmap, dom, empty, 0);
3021 }
3022
3023 struct isl_set *isl_basic_set_partial_lexmin(
3024                 struct isl_basic_set *bset, struct isl_basic_set *dom,
3025                 struct isl_set **empty)
3026 {
3027         return (struct isl_set *)
3028                 isl_basic_map_partial_lexmin((struct isl_basic_map *)bset,
3029                         dom, empty);
3030 }
3031
3032 struct isl_set *isl_basic_set_partial_lexmax(
3033                 struct isl_basic_set *bset, struct isl_basic_set *dom,
3034                 struct isl_set **empty)
3035 {
3036         return (struct isl_set *)
3037                 isl_basic_map_partial_lexmax((struct isl_basic_map *)bset,
3038                         dom, empty);
3039 }
3040
3041 struct isl_set *isl_basic_set_lexmin(struct isl_basic_set *bset)
3042 {
3043         struct isl_basic_map *bmap = NULL;
3044         struct isl_basic_set *dom = NULL;
3045         struct isl_map *min;
3046         struct isl_dim *param_dim;
3047
3048         if (!bset)
3049                 goto error;
3050         bmap = isl_basic_map_from_basic_set(bset, isl_dim_copy(bset->dim));
3051         if (!bmap)
3052                 goto error;
3053         param_dim = isl_dim_domain(isl_dim_copy(bmap->dim));
3054         dom = isl_basic_set_universe(param_dim);
3055         if (!dom)
3056                 goto error;
3057         min = isl_basic_map_partial_lexmin(bmap, dom, NULL);
3058         return isl_map_range(min);
3059 error:
3060         isl_basic_map_free(bmap);
3061         return NULL;
3062 }
3063
3064 static struct isl_map *isl_map_reset_dim(struct isl_map *map,
3065         struct isl_dim *dim)
3066 {
3067         int i;
3068
3069         if (!map || !dim)
3070                 goto error;
3071
3072         for (i = 0; i < map->n; ++i) {
3073                 isl_dim_free(map->p[i]->dim);
3074                 map->p[i]->dim = isl_dim_copy(dim);
3075         }
3076         isl_dim_free(map->dim);
3077         map->dim = dim;
3078
3079         return map;
3080 error:
3081         isl_map_free(map);
3082         isl_dim_free(dim);
3083         return NULL;
3084 }
3085
3086 static struct isl_set *isl_set_reset_dim(struct isl_set *set,
3087         struct isl_dim *dim)
3088 {
3089         return (struct isl_set *) isl_map_reset_dim((struct isl_map *)set, dim);
3090 }
3091
3092 /* Apply a preimage specified by "mat" on the parameters of "bset".
3093  * bset is assumed to have only parameters and divs.
3094  */
3095 static struct isl_basic_set *basic_set_parameter_preimage(
3096         struct isl_basic_set *bset, struct isl_mat *mat)
3097 {
3098         unsigned nparam;
3099
3100         if (!bset || !mat)
3101                 goto error;
3102
3103         bset->dim = isl_dim_cow(bset->dim);
3104         if (!bset->dim)
3105                 goto error;
3106
3107         nparam = isl_basic_set_dim(bset, isl_dim_param);
3108
3109         isl_assert(bset->ctx, mat->n_row == 1 + nparam, goto error);
3110
3111         bset->dim->nparam = 0;
3112         bset->dim->n_out = nparam;
3113         bset = isl_basic_set_preimage(bset, mat);
3114         if (bset) {
3115                 bset->dim->nparam = bset->dim->n_out;
3116                 bset->dim->n_out = 0;
3117         }
3118         return bset;
3119 error:
3120         isl_mat_free(mat);
3121         isl_basic_set_free(bset);
3122         return NULL;
3123 }
3124
3125 /* Apply a preimage specified by "mat" on the parameters of "set".
3126  * set is assumed to have only parameters and divs.
3127  */
3128 static struct isl_set *set_parameter_preimage(
3129         struct isl_set *set, struct isl_mat *mat)
3130 {
3131         struct isl_dim *dim = NULL;
3132         unsigned nparam;
3133
3134         if (!set || !mat)
3135                 goto error;
3136
3137         dim = isl_dim_copy(set->dim);
3138         dim = isl_dim_cow(dim);
3139         if (!dim)
3140                 goto error;
3141
3142         nparam = isl_set_dim(set, isl_dim_param);
3143
3144         isl_assert(set->ctx, mat->n_row == 1 + nparam, goto error);
3145
3146         dim->nparam = 0;
3147         dim->n_out = nparam;
3148         isl_set_reset_dim(set, dim);
3149         set = isl_set_preimage(set, mat);
3150         if (!set)
3151                 goto error2;
3152         dim = isl_dim_copy(set->dim);
3153         dim = isl_dim_cow(dim);
3154         if (!dim)
3155                 goto error2;
3156         dim->nparam = dim->n_out;
3157         dim->n_out = 0;
3158         isl_set_reset_dim(set, dim);
3159         return set;
3160 error:
3161         isl_dim_free(dim);
3162         isl_mat_free(mat);
3163 error2:
3164         isl_set_free(set);
3165         return NULL;
3166 }
3167
3168 /* Intersect the basic set "bset" with the affine space specified by the
3169  * equalities in "eq".
3170  */
3171 static struct isl_basic_set *basic_set_append_equalities(
3172         struct isl_basic_set *bset, struct isl_mat *eq)
3173 {
3174         int i, k;
3175         unsigned len;
3176
3177         if (!bset || !eq)
3178                 goto error;
3179
3180         bset = isl_basic_set_extend_dim(bset, isl_dim_copy(bset->dim), 0,
3181                                         eq->n_row, 0);
3182         if (!bset)
3183                 goto error;
3184
3185         len = 1 + isl_dim_total(bset->dim) + bset->extra;
3186         for (i = 0; i < eq->n_row; ++i) {
3187                 k = isl_basic_set_alloc_equality(bset);
3188                 if (k < 0)
3189                         goto error;
3190                 isl_seq_cpy(bset->eq[k], eq->row[i], eq->n_col);
3191                 isl_seq_clr(bset->eq[k] + eq->n_col, len - eq->n_col);
3192         }
3193         isl_mat_free(eq);
3194
3195         return bset;
3196 error:
3197         isl_mat_free(eq);
3198         isl_basic_set_free(bset);
3199         return NULL;
3200 }
3201
3202 /* Intersect the set "set" with the affine space specified by the
3203  * equalities in "eq".
3204  */
3205 static struct isl_set *set_append_equalities(struct isl_set *set,
3206         struct isl_mat *eq)
3207 {
3208         int i;
3209
3210         if (!set || !eq)
3211                 goto error;
3212
3213         for (i = 0; i < set->n; ++i) {
3214                 set->p[i] = basic_set_append_equalities(set->p[i],
3215                                         isl_mat_copy(eq));
3216                 if (!set->p[i])
3217                         goto error;
3218         }
3219         isl_mat_free(eq);
3220         return set;
3221 error:
3222         isl_mat_free(eq);
3223         isl_set_free(set);
3224         return NULL;
3225 }
3226
3227 /* Project the given basic set onto its parameter domain, possibly introducing
3228  * new, explicit, existential variables in the constraints.
3229  * The input has parameters and (possibly implicit) existential variables.
3230  * The output has the same parameters, but only
3231  * explicit existentially quantified variables.
3232  *
3233  * The actual projection is performed by pip, but pip doesn't seem
3234  * to like equalities very much, so we first remove the equalities
3235  * among the parameters by performing a variable compression on
3236  * the parameters.  Afterward, an inverse transformation is performed
3237  * and the equalities among the parameters are inserted back in.
3238  */
3239 static struct isl_set *parameter_compute_divs(struct isl_basic_set *bset)
3240 {
3241         int i, j;
3242         struct isl_mat *eq;
3243         struct isl_mat *T, *T2;
3244         struct isl_set *set;
3245         unsigned nparam, n_div;
3246
3247         bset = isl_basic_set_cow(bset);
3248         if (!bset)
3249                 return NULL;
3250
3251         if (bset->n_eq == 0)
3252                 return isl_basic_set_lexmin(bset);
3253
3254         isl_basic_set_gauss(bset, NULL);
3255
3256         nparam = isl_basic_set_dim(bset, isl_dim_param);
3257         n_div = isl_basic_set_dim(bset, isl_dim_div);
3258
3259         for (i = 0, j = n_div - 1; i < bset->n_eq && j >= 0; --j) {
3260                 if (!isl_int_is_zero(bset->eq[i][1 + nparam + j]))
3261                         ++i;
3262         }
3263         if (i == bset->n_eq)
3264                 return isl_basic_set_lexmin(bset);
3265
3266         eq = isl_mat_sub_alloc(bset->ctx, bset->eq, i, bset->n_eq - i,
3267                 0, 1 + nparam);
3268         eq = isl_mat_cow(eq);
3269         T = isl_mat_variable_compression(isl_mat_copy(eq), &T2);
3270         bset = basic_set_parameter_preimage(bset, T);
3271
3272         set = isl_basic_set_lexmin(bset);
3273         set = set_parameter_preimage(set, T2);
3274         set = set_append_equalities(set, eq);
3275         return set;
3276 }
3277
3278 /* Compute an explicit representation for all the existentially
3279  * quantified variables.
3280  * The input and output dimensions are first turned into parameters.
3281  * compute_divs then returns a map with the same parameters and
3282  * no input or output dimensions and the dimension specification
3283  * is reset to that of the input.
3284  */
3285 static struct isl_map *compute_divs(struct isl_basic_map *bmap)
3286 {
3287         struct isl_basic_set *bset;
3288         struct isl_set *set;
3289         struct isl_map *map;
3290         struct isl_dim *dim, *orig_dim = NULL;
3291         unsigned         nparam;
3292         unsigned         n_in;
3293         unsigned         n_out;
3294
3295         bmap = isl_basic_map_cow(bmap);
3296         if (!bmap)
3297                 return NULL;
3298
3299         nparam = isl_basic_map_dim(bmap, isl_dim_param);
3300         n_in = isl_basic_map_dim(bmap, isl_dim_in);
3301         n_out = isl_basic_map_dim(bmap, isl_dim_out);
3302         dim = isl_dim_set_alloc(bmap->ctx, nparam + n_in + n_out, 0);
3303         if (!dim)
3304                 goto error;
3305
3306         orig_dim = bmap->dim;
3307         bmap->dim = dim;
3308         bset = (struct isl_basic_set *)bmap;
3309
3310         set = parameter_compute_divs(bset);
3311         map = (struct isl_map *)set;
3312         map = isl_map_reset_dim(map, orig_dim);
3313
3314         return map;
3315 error:
3316         isl_basic_map_free(bmap);
3317         return NULL;
3318 }
3319
3320 /* If bmap contains any unknown divs, then compute explicit
3321  * expressions for them.  However, this computation may be
3322  * quite expensive, so first try to remove divs that aren't
3323  * strictly needed.
3324  */
3325 struct isl_map *isl_basic_map_compute_divs(struct isl_basic_map *bmap)
3326 {
3327         int i;
3328         unsigned off;
3329
3330         if (!bmap)
3331                 return NULL;
3332         off = isl_dim_total(bmap->dim);
3333         for (i = 0; i < bmap->n_div; ++i) {
3334                 if (isl_int_is_zero(bmap->div[i][0]))
3335                         break;
3336                 isl_assert(bmap->ctx, isl_int_is_zero(bmap->div[i][1+1+off+i]),
3337                                 goto error);
3338         }
3339         if (i == bmap->n_div)
3340                 return isl_map_from_basic_map(bmap);
3341         bmap = isl_basic_map_drop_redundant_divs(bmap);
3342         if (!bmap)
3343                 goto error;
3344         for (i = 0; i < bmap->n_div; ++i)
3345                 if (isl_int_is_zero(bmap->div[i][0]))
3346                         break;
3347         if (i == bmap->n_div)
3348                 return isl_map_from_basic_map(bmap);
3349         struct isl_map *map = compute_divs(bmap);
3350         return map;
3351 error:
3352         isl_basic_map_free(bmap);
3353         return NULL;
3354 }
3355
3356 struct isl_map *isl_map_compute_divs(struct isl_map *map)
3357 {
3358         int i;
3359         struct isl_map *res;
3360
3361         if (!map)
3362                 return NULL;
3363         if (map->n == 0)
3364                 return map;
3365         res = isl_basic_map_compute_divs(isl_basic_map_copy(map->p[0]));
3366         for (i = 1 ; i < map->n; ++i) {
3367                 struct isl_map *r2;
3368                 r2 = isl_basic_map_compute_divs(isl_basic_map_copy(map->p[i]));
3369                 if (ISL_F_ISSET(map, ISL_MAP_DISJOINT))
3370                         res = isl_map_union_disjoint(res, r2);
3371                 else
3372                         res = isl_map_union(res, r2);
3373         }
3374         isl_map_free(map);
3375
3376         return res;
3377 }
3378
3379 struct isl_set *isl_basic_set_compute_divs(struct isl_basic_set *bset)
3380 {
3381         return (struct isl_set *)
3382                 isl_basic_map_compute_divs((struct isl_basic_map *)bset);
3383 }
3384
3385 struct isl_set *isl_set_compute_divs(struct isl_set *set)
3386 {
3387         return (struct isl_set *)
3388                 isl_map_compute_divs((struct isl_map *)set);
3389 }
3390
3391 struct isl_set *isl_map_domain(struct isl_map *map)
3392 {
3393         int i;
3394         struct isl_set *set;
3395
3396         if (!map)
3397                 goto error;
3398
3399         map = isl_map_cow(map);
3400         if (!map)
3401                 return NULL;
3402
3403         set = (struct isl_set *)map;
3404         set->dim = isl_dim_domain(set->dim);
3405         if (!set->dim)
3406                 goto error;
3407         for (i = 0; i < map->n; ++i) {
3408                 set->p[i] = isl_basic_map_domain(map->p[i]);
3409                 if (!set->p[i])
3410                         goto error;
3411         }
3412         ISL_F_CLR(set, ISL_MAP_DISJOINT);
3413         ISL_F_CLR(set, ISL_SET_NORMALIZED);
3414         return set;
3415 error:
3416         isl_map_free(map);
3417         return NULL;
3418 }
3419
3420 struct isl_map *isl_map_union_disjoint(
3421                         struct isl_map *map1, struct isl_map *map2)
3422 {
3423         int i;
3424         unsigned flags = 0;
3425         struct isl_map *map = NULL;
3426
3427         if (!map1 || !map2)
3428                 goto error;
3429
3430         if (map1->n == 0) {
3431                 isl_map_free(map1);
3432                 return map2;
3433         }
3434         if (map2->n == 0) {
3435                 isl_map_free(map2);
3436                 return map1;
3437         }
3438
3439         isl_assert(map1->ctx, isl_dim_equal(map1->dim, map2->dim), goto error);
3440
3441         if (ISL_F_ISSET(map1, ISL_MAP_DISJOINT) &&
3442             ISL_F_ISSET(map2, ISL_MAP_DISJOINT))
3443                 ISL_FL_SET(flags, ISL_MAP_DISJOINT);
3444
3445         map = isl_map_alloc_dim(isl_dim_copy(map1->dim),
3446                                 map1->n + map2->n, flags);
3447         if (!map)
3448                 goto error;
3449         for (i = 0; i < map1->n; ++i) {
3450                 map = isl_map_add(map,
3451                                   isl_basic_map_copy(map1->p[i]));
3452                 if (!map)
3453                         goto error;
3454         }
3455         for (i = 0; i < map2->n; ++i) {
3456                 map = isl_map_add(map,
3457                                   isl_basic_map_copy(map2->p[i]));
3458                 if (!map)
3459                         goto error;
3460         }
3461         isl_map_free(map1);
3462         isl_map_free(map2);
3463         return map;
3464 error:
3465         isl_map_free(map);
3466         isl_map_free(map1);
3467         isl_map_free(map2);
3468         return NULL;
3469 }
3470
3471 struct isl_map *isl_map_union(struct isl_map *map1, struct isl_map *map2)
3472 {
3473         map1 = isl_map_union_disjoint(map1, map2);
3474         if (!map1)
3475                 return NULL;
3476         if (map1->n > 1)
3477                 ISL_F_CLR(map1, ISL_MAP_DISJOINT);
3478         return map1;
3479 }
3480
3481 struct isl_set *isl_set_union_disjoint(
3482                         struct isl_set *set1, struct isl_set *set2)
3483 {
3484         return (struct isl_set *)
3485                 isl_map_union_disjoint(
3486                         (struct isl_map *)set1, (struct isl_map *)set2);
3487 }
3488
3489 struct isl_set *isl_set_union(struct isl_set *set1, struct isl_set *set2)
3490 {
3491         return (struct isl_set *)
3492                 isl_map_union((struct isl_map *)set1, (struct isl_map *)set2);
3493 }
3494
3495 struct isl_map *isl_map_intersect_range(
3496                 struct isl_map *map, struct isl_set *set)
3497 {
3498         unsigned flags = 0;
3499         struct isl_map *result;
3500         int i, j;
3501
3502         if (!map || !set)
3503                 goto error;
3504
3505         if (ISL_F_ISSET(map, ISL_MAP_DISJOINT) &&
3506             ISL_F_ISSET(set, ISL_MAP_DISJOINT))
3507                 ISL_FL_SET(flags, ISL_MAP_DISJOINT);
3508
3509         result = isl_map_alloc_dim(isl_dim_copy(map->dim),
3510                                         map->n * set->n, flags);
3511         if (!result)
3512                 goto error;
3513         for (i = 0; i < map->n; ++i)
3514                 for (j = 0; j < set->n; ++j) {
3515                         result = isl_map_add(result,
3516                             isl_basic_map_intersect_range(
3517                                 isl_basic_map_copy(map->p[i]),
3518                                 isl_basic_set_copy(set->p[j])));
3519                         if (!result)
3520                                 goto error;
3521                 }
3522         isl_map_free(map);
3523         isl_set_free(set);
3524         return result;
3525 error:
3526         isl_map_free(map);
3527         isl_set_free(set);
3528         return NULL;
3529 }
3530
3531 struct isl_map *isl_map_intersect_domain(
3532                 struct isl_map *map, struct isl_set *set)
3533 {
3534         return isl_map_reverse(
3535                 isl_map_intersect_range(isl_map_reverse(map), set));
3536 }
3537
3538 struct isl_map *isl_map_apply_domain(
3539                 struct isl_map *map1, struct isl_map *map2)
3540 {
3541         if (!map1 || !map2)
3542                 goto error;
3543         map1 = isl_map_reverse(map1);
3544         map1 = isl_map_apply_range(map1, map2);
3545         return isl_map_reverse(map1);
3546 error:
3547         isl_map_free(map1);
3548         isl_map_free(map2);
3549         return NULL;
3550 }
3551
3552 struct isl_map *isl_map_apply_range(
3553                 struct isl_map *map1, struct isl_map *map2)
3554 {
3555         struct isl_dim *dim_result;
3556         struct isl_map *result;
3557         int i, j;
3558         unsigned nparam;
3559         unsigned n_in;
3560         unsigned n_out;
3561
3562         if (!map1 || !map2)
3563                 goto error;
3564
3565         dim_result = isl_dim_join(isl_dim_copy(map1->dim),
3566                                   isl_dim_copy(map2->dim));
3567
3568         result = isl_map_alloc_dim(dim_result, map1->n * map2->n, 0);
3569         if (!result)
3570                 goto error;
3571         for (i = 0; i < map1->n; ++i)
3572                 for (j = 0; j < map2->n; ++j) {
3573                         result = isl_map_add(result,
3574                             isl_basic_map_apply_range(
3575                                 isl_basic_map_copy(map1->p[i]),
3576                                 isl_basic_map_copy(map2->p[j])));
3577                         if (!result)
3578                                 goto error;
3579                 }
3580         isl_map_free(map1);
3581         isl_map_free(map2);
3582         if (result && result->n <= 1)
3583                 ISL_F_SET(result, ISL_MAP_DISJOINT);
3584         return result;
3585 error:
3586         isl_map_free(map1);
3587         isl_map_free(map2);
3588         return NULL;
3589 }
3590
3591 /*
3592  * returns range - domain
3593  */
3594 struct isl_basic_set *isl_basic_map_deltas(struct isl_basic_map *bmap)
3595 {
3596         struct isl_basic_set *bset;
3597         unsigned dim;
3598         unsigned nparam;
3599         int i;
3600
3601         if (!bmap)
3602                 goto error;
3603         dim = isl_basic_map_n_in(bmap);
3604         nparam = isl_basic_map_n_param(bmap);
3605         isl_assert(bmap->ctx, dim == isl_basic_map_n_out(bmap), goto error);
3606         bset = isl_basic_set_from_basic_map(bmap);
3607         bset = isl_basic_set_cow(bset);
3608         bset = isl_basic_set_extend(bset, nparam, 3*dim, 0, dim, 0);
3609         bset = isl_basic_set_swap_vars(bset, 2*dim);
3610         for (i = 0; i < dim; ++i) {
3611                 int j = isl_basic_map_alloc_equality(
3612                                             (struct isl_basic_map *)bset);
3613                 if (j < 0)
3614                         goto error;
3615                 isl_seq_clr(bset->eq[j], 1 + isl_basic_set_total_dim(bset));
3616                 isl_int_set_si(bset->eq[j][1+nparam+i], 1);
3617                 isl_int_set_si(bset->eq[j][1+nparam+dim+i], 1);
3618                 isl_int_set_si(bset->eq[j][1+nparam+2*dim+i], -1);
3619         }
3620         return isl_basic_set_project_out(bset, 2*dim, 0);
3621 error:
3622         isl_basic_map_free(bmap);
3623         return NULL;
3624 }
3625
3626 /*
3627  * returns range - domain
3628  */
3629 struct isl_set *isl_map_deltas(struct isl_map *map)
3630 {
3631         int i;
3632         struct isl_set *result;
3633
3634         if (!map)
3635                 return NULL;
3636
3637         isl_assert(map->ctx, isl_map_n_in(map) == isl_map_n_out(map), goto error);
3638         result = isl_set_alloc(map->ctx, isl_map_n_param(map),
3639                                         isl_map_n_in(map), map->n, map->flags);
3640         if (!result)
3641                 goto error;
3642         for (i = 0; i < map->n; ++i)
3643                 result = isl_set_add(result,
3644                           isl_basic_map_deltas(isl_basic_map_copy(map->p[i])));
3645         isl_map_free(map);
3646         return result;
3647 error:
3648         isl_map_free(map);
3649         return NULL;
3650 }
3651
3652 static struct isl_basic_map *basic_map_identity(struct isl_dim *dims)
3653 {
3654         struct isl_basic_map *bmap;
3655         unsigned nparam;
3656         unsigned dim;
3657         int i;
3658
3659         if (!dims)
3660                 return NULL;
3661
3662         nparam = dims->nparam;
3663         dim = dims->n_out;
3664         bmap = isl_basic_map_alloc_dim(dims, 0, dim, 0);
3665         if (!bmap)
3666                 goto error;
3667
3668         for (i = 0; i < dim; ++i) {
3669                 int j = isl_basic_map_alloc_equality(bmap);
3670                 if (j < 0)
3671                         goto error;
3672                 isl_seq_clr(bmap->eq[j], 1 + isl_basic_map_total_dim(bmap));
3673                 isl_int_set_si(bmap->eq[j][1+nparam+i], 1);
3674                 isl_int_set_si(bmap->eq[j][1+nparam+dim+i], -1);
3675         }
3676         return isl_basic_map_finalize(bmap);
3677 error:
3678         isl_basic_map_free(bmap);
3679         return NULL;
3680 }
3681
3682 struct isl_basic_map *isl_basic_map_identity(struct isl_dim *set_dim)
3683 {
3684         struct isl_dim *dim = isl_dim_map(set_dim);
3685         if (!dim)
3686                 return NULL;
3687         return basic_map_identity(dim);
3688 }
3689
3690 struct isl_basic_map *isl_basic_map_identity_like(struct isl_basic_map *model)
3691 {
3692         if (!model || !model->dim)
3693                 return NULL;
3694         isl_assert(model->ctx,
3695                         model->dim->n_in == model->dim->n_out, return NULL);
3696         return basic_map_identity(isl_dim_copy(model->dim));
3697 }
3698
3699 static struct isl_map *map_identity(struct isl_dim *dim)
3700 {
3701         struct isl_map *map = isl_map_alloc_dim(dim, 1, ISL_MAP_DISJOINT);
3702         return isl_map_add(map, basic_map_identity(isl_dim_copy(dim)));
3703 }
3704
3705 struct isl_map *isl_map_identity(struct isl_dim *set_dim)
3706 {
3707         struct isl_dim *dim = isl_dim_map(set_dim);
3708         if (!dim)
3709                 return NULL;
3710         return map_identity(dim);
3711 }
3712
3713 struct isl_map *isl_map_identity_like(struct isl_map *model)
3714 {
3715         if (!model || !model->dim)
3716                 return NULL;
3717         isl_assert(model->ctx,
3718                         model->dim->n_in == model->dim->n_out, return NULL);
3719         return map_identity(isl_dim_copy(model->dim));
3720 }
3721
3722 struct isl_map *isl_map_identity_like_basic_map(struct isl_basic_map *model)
3723 {
3724         if (!model || !model->dim)
3725                 return NULL;
3726         isl_assert(model->ctx,
3727                         model->dim->n_in == model->dim->n_out, return NULL);
3728         return map_identity(isl_dim_copy(model->dim));
3729 }
3730
3731 /* Construct a basic set with all set dimensions having only non-negative
3732  * values.
3733  */
3734 struct isl_basic_set *isl_basic_set_positive_orthant(struct isl_dim *dims)
3735 {
3736         int i;
3737         unsigned nparam;
3738         unsigned dim;
3739         struct isl_basic_set *bset;
3740
3741         if (!dims)
3742                 return NULL;
3743         nparam = dims->nparam;
3744         dim = dims->n_out;
3745         bset = isl_basic_set_alloc_dim(dims, 0, 0, dim);
3746         if (!bset)
3747                 return NULL;
3748         for (i = 0; i < dim; ++i) {
3749                 int k = isl_basic_set_alloc_inequality(bset);
3750                 if (k < 0)
3751                         goto error;
3752                 isl_seq_clr(bset->ineq[k], 1 + isl_basic_set_total_dim(bset));
3753                 isl_int_set_si(bset->ineq[k][1 + nparam + i], 1);
3754         }
3755         return bset;
3756 error:
3757         isl_basic_set_free(bset);
3758         return NULL;
3759 }
3760
3761 int isl_set_is_equal(struct isl_set *set1, struct isl_set *set2)
3762 {
3763         return isl_map_is_equal((struct isl_map *)set1, (struct isl_map *)set2);
3764 }
3765
3766 int isl_set_is_subset(struct isl_set *set1, struct isl_set *set2)
3767 {
3768         return isl_map_is_subset(
3769                         (struct isl_map *)set1, (struct isl_map *)set2);
3770 }
3771
3772 int isl_basic_map_is_subset(
3773                 struct isl_basic_map *bmap1, struct isl_basic_map *bmap2)
3774 {
3775         int is_subset;
3776         struct isl_map *map1;
3777         struct isl_map *map2;
3778
3779         if (!bmap1 || !bmap2)
3780                 return -1;
3781
3782         map1 = isl_map_from_basic_map(isl_basic_map_copy(bmap1));
3783         map2 = isl_map_from_basic_map(isl_basic_map_copy(bmap2));
3784
3785         is_subset = isl_map_is_subset(map1, map2);
3786
3787         isl_map_free(map1);
3788         isl_map_free(map2);
3789
3790         return is_subset;
3791 }
3792
3793 int isl_basic_map_is_equal(
3794                 struct isl_basic_map *bmap1, struct isl_basic_map *bmap2)
3795 {
3796         int is_subset;
3797
3798         if (!bmap1 || !bmap2)
3799                 return -1;
3800         is_subset = isl_basic_map_is_subset(bmap1, bmap2);
3801         if (is_subset != 1)
3802                 return is_subset;
3803         is_subset = isl_basic_map_is_subset(bmap2, bmap1);
3804         return is_subset;
3805 }
3806
3807 int isl_basic_set_is_equal(
3808                 struct isl_basic_set *bset1, struct isl_basic_set *bset2)
3809 {
3810         return isl_basic_map_is_equal(
3811                 (struct isl_basic_map *)bset1, (struct isl_basic_map *)bset2);
3812 }
3813
3814 int isl_map_is_empty(struct isl_map *map)
3815 {
3816         int i;
3817         int is_empty;
3818
3819         if (!map)
3820                 return -1;
3821         for (i = 0; i < map->n; ++i) {
3822                 is_empty = isl_basic_map_is_empty(map->p[i]);
3823                 if (is_empty < 0)
3824                         return -1;
3825                 if (!is_empty)
3826                         return 0;
3827         }
3828         return 1;
3829 }
3830
3831 int isl_map_fast_is_empty(struct isl_map *map)
3832 {
3833         return map->n == 0;
3834 }
3835
3836 int isl_set_is_empty(struct isl_set *set)
3837 {
3838         return isl_map_is_empty((struct isl_map *)set);
3839 }
3840
3841 int isl_map_is_subset(struct isl_map *map1, struct isl_map *map2)
3842 {
3843         int i;
3844         int is_subset = 0;
3845         struct isl_map *diff;
3846
3847         if (!map1 || !map2)
3848                 return -1;
3849
3850         if (isl_map_is_empty(map1))
3851                 return 1;
3852
3853         if (isl_map_is_empty(map2))
3854                 return 0;
3855
3856         diff = isl_map_subtract(isl_map_copy(map1), isl_map_copy(map2));
3857         if (!diff)
3858                 return -1;
3859
3860         is_subset = isl_map_is_empty(diff);
3861         isl_map_free(diff);
3862
3863         return is_subset;
3864 }
3865
3866 int isl_map_is_equal(struct isl_map *map1, struct isl_map *map2)
3867 {
3868         int is_subset;
3869
3870         if (!map1 || !map2)
3871                 return -1;
3872         is_subset = isl_map_is_subset(map1, map2);
3873         if (is_subset != 1)
3874                 return is_subset;
3875         is_subset = isl_map_is_subset(map2, map1);
3876         return is_subset;
3877 }
3878
3879 int isl_basic_map_is_strict_subset(
3880                 struct isl_basic_map *bmap1, struct isl_basic_map *bmap2)
3881 {
3882         int is_subset;
3883
3884         if (!bmap1 || !bmap2)
3885                 return -1;
3886         is_subset = isl_basic_map_is_subset(bmap1, bmap2);
3887         if (is_subset != 1)
3888                 return is_subset;
3889         is_subset = isl_basic_map_is_subset(bmap2, bmap1);
3890         if (is_subset == -1)
3891                 return is_subset;
3892         return !is_subset;
3893 }
3894
3895 int isl_map_is_strict_subset(struct isl_map *map1, struct isl_map *map2)
3896 {
3897         int is_subset;
3898
3899         if (!map1 || !map2)
3900                 return -1;
3901         is_subset = isl_map_is_subset(map1, map2);
3902         if (is_subset != 1)
3903                 return is_subset;
3904         is_subset = isl_map_is_subset(map2, map1);
3905         if (is_subset == -1)
3906                 return is_subset;
3907         return !is_subset;
3908 }
3909
3910 int isl_basic_map_is_universe(struct isl_basic_map *bmap)
3911 {
3912         if (!bmap)
3913                 return -1;
3914         return bmap->n_eq == 0 && bmap->n_ineq == 0;
3915 }
3916
3917 int isl_basic_set_is_universe(struct isl_basic_set *bset)
3918 {
3919         if (!bset)
3920                 return -1;
3921         return bset->n_eq == 0 && bset->n_ineq == 0;
3922 }
3923
3924 int isl_basic_map_is_empty(struct isl_basic_map *bmap)
3925 {
3926         struct isl_basic_set *bset = NULL;
3927         struct isl_vec *sample = NULL;
3928         int empty;
3929         unsigned total;
3930
3931         if (!bmap)
3932                 return -1;
3933
3934         if (ISL_F_ISSET(bmap, ISL_BASIC_MAP_EMPTY))
3935                 return 1;
3936
3937         if (ISL_F_ISSET(bmap, ISL_BASIC_MAP_RATIONAL)) {
3938                 struct isl_basic_map *copy = isl_basic_map_copy(bmap);
3939                 copy = isl_basic_map_convex_hull(copy);
3940                 empty = ISL_F_ISSET(copy, ISL_BASIC_MAP_EMPTY);
3941                 isl_basic_map_free(copy);
3942                 return empty;
3943         }
3944
3945         total = 1 + isl_basic_map_total_dim(bmap);
3946         if (bmap->sample && bmap->sample->size == total) {
3947                 int contains = basic_map_contains(bmap, bmap->sample);
3948                 if (contains < 0)
3949                         return -1;
3950                 if (contains)
3951                         return 0;
3952         }
3953         isl_vec_free(bmap->sample);
3954         bmap->sample = NULL;
3955         bset = isl_basic_map_underlying_set(isl_basic_map_copy(bmap));
3956         if (!bset)
3957                 return -1;
3958         sample = isl_basic_set_sample(bset);
3959         if (!sample)
3960                 return -1;
3961         empty = sample->size == 0;
3962         isl_vec_free(bmap->sample);
3963         bmap->sample = sample;
3964         if (empty)
3965                 ISL_F_SET(bmap, ISL_BASIC_MAP_EMPTY);
3966
3967         return empty;
3968 }
3969
3970 int isl_basic_map_fast_is_empty(struct isl_basic_map *bmap)
3971 {
3972         if (!bmap)
3973                 return -1;
3974         return ISL_F_ISSET(bmap, ISL_BASIC_MAP_EMPTY);
3975 }
3976
3977 int isl_basic_set_fast_is_empty(struct isl_basic_set *bset)
3978 {
3979         if (!bset)
3980                 return -1;
3981         return ISL_F_ISSET(bset, ISL_BASIC_SET_EMPTY);
3982 }
3983
3984 int isl_basic_set_is_empty(struct isl_basic_set *bset)
3985 {
3986         return isl_basic_map_is_empty((struct isl_basic_map *)bset);
3987 }
3988
3989 struct isl_map *isl_basic_map_union(
3990         struct isl_basic_map *bmap1, struct isl_basic_map *bmap2)
3991 {
3992         struct isl_map *map;
3993         if (!bmap1 || !bmap2)
3994                 return NULL;
3995
3996         isl_assert(map1->ctx, isl_dim_equal(bmap1->dim, bmap2->dim), goto error);
3997
3998         map = isl_map_alloc_dim(isl_dim_copy(bmap1->dim), 2, 0);
3999         if (!map)
4000                 goto error;
4001         map = isl_map_add(map, bmap1);
4002         map = isl_map_add(map, bmap2);
4003         return map;
4004 error:
4005         isl_basic_map_free(bmap1);
4006         isl_basic_map_free(bmap2);
4007         return NULL;
4008 }
4009
4010 struct isl_set *isl_basic_set_union(
4011                 struct isl_basic_set *bset1, struct isl_basic_set *bset2)
4012 {
4013         return (struct isl_set *)isl_basic_map_union(
4014                                             (struct isl_basic_map *)bset1,
4015                                             (struct isl_basic_map *)bset2);
4016 }
4017
4018 /* Order divs such that any div only depends on previous divs */
4019 static struct isl_basic_map *order_divs(struct isl_basic_map *bmap)
4020 {
4021         int i;
4022         unsigned off = isl_dim_total(bmap->dim);
4023
4024         for (i = 0; i < bmap->n_div; ++i) {
4025                 int pos;
4026                 if (isl_int_is_zero(bmap->div[i][0]))
4027                         continue;
4028                 pos = isl_seq_first_non_zero(bmap->div[i]+1+1+off+i,
4029                                                             bmap->n_div-i);
4030                 if (pos == -1)
4031                         continue;
4032                 isl_basic_map_swap_div(bmap, i, i + pos);
4033                 --i;
4034         }
4035         return bmap;
4036 }
4037
4038 struct isl_basic_set *isl_basic_set_order_divs(struct isl_basic_set *bset)
4039 {
4040         return (struct isl_basic_set *)order_divs((struct isl_basic_map *)bset);
4041 }
4042
4043 /* Look for a div in dst that corresponds to the div "div" in src.
4044  * The divs before "div" in src and dst are assumed to be the same.
4045  *
4046  * Returns -1 if no corresponding div was found and the position
4047  * of the corresponding div in dst otherwise.
4048  */
4049 static int find_div(struct isl_basic_map *dst,
4050                         struct isl_basic_map *src, unsigned div)
4051 {
4052         int i;
4053
4054         unsigned total = isl_dim_total(src->dim);
4055
4056         isl_assert(dst->ctx, div <= dst->n_div, return -1);
4057         for (i = div; i < dst->n_div; ++i)
4058                 if (isl_seq_eq(dst->div[i], src->div[div], 1+1+total+div) &&
4059                     isl_seq_first_non_zero(dst->div[i]+1+1+total+div,
4060                                                 dst->n_div - div) == -1)
4061                         return i;
4062         return -1;
4063 }
4064
4065 struct isl_basic_map *isl_basic_map_align_divs(
4066                 struct isl_basic_map *dst, struct isl_basic_map *src)
4067 {
4068         int i;
4069         unsigned total = isl_dim_total(src->dim);
4070
4071         if (!dst || !src)
4072                 goto error;
4073
4074         if (src->n_div == 0)
4075                 return dst;
4076
4077         for (i = 0; i < src->n_div; ++i)
4078                 isl_assert(src->ctx, !isl_int_is_zero(src->div[i][0]), goto error);
4079
4080         src = order_divs(src);
4081         dst = isl_basic_map_cow(dst);
4082         dst = isl_basic_map_extend_dim(dst, isl_dim_copy(dst->dim),
4083                         src->n_div, 0, 2 * src->n_div);
4084         if (!dst)
4085                 return NULL;
4086         for (i = 0; i < src->n_div; ++i) {
4087                 int j = find_div(dst, src, i);
4088                 if (j < 0) {
4089                         j = isl_basic_map_alloc_div(dst);
4090                         if (j < 0)
4091                                 goto error;
4092                         isl_seq_cpy(dst->div[j], src->div[i], 1+1+total+i);
4093                         isl_seq_clr(dst->div[j]+1+1+total+i, dst->n_div - i);
4094                         if (add_div_constraints(dst, j) < 0)
4095                                 goto error;
4096                 }
4097                 if (j != i)
4098                         isl_basic_map_swap_div(dst, i, j);
4099         }
4100         return dst;
4101 error:
4102         isl_basic_map_free(dst);
4103         return NULL;
4104 }
4105
4106 struct isl_basic_set *isl_basic_set_align_divs(
4107                 struct isl_basic_set *dst, struct isl_basic_set *src)
4108 {
4109         return (struct isl_basic_set *)isl_basic_map_align_divs(
4110                 (struct isl_basic_map *)dst, (struct isl_basic_map *)src);
4111 }
4112
4113 struct isl_map *isl_map_align_divs(struct isl_map *map)
4114 {
4115         int i;
4116
4117         map = isl_map_compute_divs(map);
4118         map = isl_map_cow(map);
4119         if (!map)
4120                 return NULL;
4121
4122         for (i = 1; i < map->n; ++i)
4123                 map->p[0] = isl_basic_map_align_divs(map->p[0], map->p[i]);
4124         for (i = 1; i < map->n; ++i)
4125                 map->p[i] = isl_basic_map_align_divs(map->p[i], map->p[0]);
4126
4127         ISL_F_CLR(map, ISL_MAP_NORMALIZED);
4128         return map;
4129 }
4130
4131 struct isl_set *isl_set_align_divs(struct isl_set *set)
4132 {
4133         return (struct isl_set *)isl_map_align_divs((struct isl_map *)set);
4134 }
4135
4136 static struct isl_map *add_cut_constraint(struct isl_map *dst,
4137                 struct isl_basic_map *src, isl_int *c,
4138                 unsigned len, int oppose)
4139 {
4140         struct isl_basic_map *copy = NULL;
4141         int is_empty;
4142         int k;
4143         unsigned total;
4144
4145         copy = isl_basic_map_copy(src);
4146         copy = isl_basic_map_cow(copy);
4147         if (!copy)
4148                 goto error;
4149         copy = isl_basic_map_extend_constraints(copy, 0, 1);
4150         k = isl_basic_map_alloc_inequality(copy);
4151         if (k < 0)
4152                 goto error;
4153         if (oppose)
4154                 isl_seq_neg(copy->ineq[k], c, len);
4155         else
4156                 isl_seq_cpy(copy->ineq[k], c, len);
4157         total = 1 + isl_basic_map_total_dim(copy);
4158         isl_seq_clr(copy->ineq[k]+len, total - len);
4159         isl_inequality_negate(copy, k);
4160         copy = isl_basic_map_simplify(copy);
4161         copy = isl_basic_map_finalize(copy);
4162         is_empty = isl_basic_map_is_empty(copy);
4163         if (is_empty < 0)
4164                 goto error;
4165         if (!is_empty)
4166                 dst = isl_map_add(dst, copy);
4167         else
4168                 isl_basic_map_free(copy);
4169         return dst;
4170 error:
4171         isl_basic_map_free(copy);
4172         isl_map_free(dst);
4173         return NULL;
4174 }
4175
4176 static struct isl_map *subtract(struct isl_map *map, struct isl_basic_map *bmap)
4177 {
4178         int i, j, k;
4179         unsigned flags = 0;
4180         struct isl_map *rest = NULL;
4181         unsigned max;
4182         unsigned total = isl_basic_map_total_dim(bmap);
4183
4184         assert(bmap);
4185
4186         if (!map)
4187                 goto error;
4188
4189         if (ISL_F_ISSET(map, ISL_MAP_DISJOINT))
4190                 ISL_FL_SET(flags, ISL_MAP_DISJOINT);
4191
4192         max = map->n * (2 * bmap->n_eq + bmap->n_ineq);
4193         rest = isl_map_alloc_dim(isl_dim_copy(map->dim), max, flags);
4194         if (!rest)
4195                 goto error;
4196
4197         for (i = 0; i < map->n; ++i) {
4198                 map->p[i] = isl_basic_map_align_divs(map->p[i], bmap);
4199                 if (!map->p[i])
4200                         goto error;
4201         }
4202
4203         for (j = 0; j < map->n; ++j)
4204                 map->p[j] = isl_basic_map_cow(map->p[j]);
4205
4206         for (i = 0; i < bmap->n_eq; ++i) {
4207                 for (j = 0; j < map->n; ++j) {
4208                         rest = add_cut_constraint(rest,
4209                                 map->p[j], bmap->eq[i], 1+total, 0);
4210                         if (!rest)
4211                                 goto error;
4212
4213                         rest = add_cut_constraint(rest,
4214                                 map->p[j], bmap->eq[i], 1+total, 1);
4215                         if (!rest)
4216                                 goto error;
4217
4218                         map->p[j] = isl_basic_map_extend_constraints(map->p[j],
4219                                 1, 0);
4220                         if (!map->p[j])
4221                                 goto error;
4222                         k = isl_basic_map_alloc_equality(map->p[j]);
4223                         if (k < 0)
4224                                 goto error;
4225                         isl_seq_cpy(map->p[j]->eq[k], bmap->eq[i], 1+total);
4226                         isl_seq_clr(map->p[j]->eq[k]+1+total,
4227                                         map->p[j]->n_div - bmap->n_div);
4228                 }
4229         }
4230
4231         for (i = 0; i < bmap->n_ineq; ++i) {
4232                 for (j = 0; j < map->n; ++j) {
4233                         rest = add_cut_constraint(rest,
4234                                 map->p[j], bmap->ineq[i], 1+total, 0);
4235                         if (!rest)
4236                                 goto error;
4237
4238                         map->p[j] = isl_basic_map_extend_constraints(map->p[j],
4239                                 0, 1);
4240                         if (!map->p[j])
4241                                 goto error;
4242                         k = isl_basic_map_alloc_inequality(map->p[j]);
4243                         if (k < 0)
4244                                 goto error;
4245                         isl_seq_cpy(map->p[j]->ineq[k], bmap->ineq[i], 1+total);
4246                         isl_seq_clr(map->p[j]->ineq[k]+1+total,
4247                                         map->p[j]->n_div - bmap->n_div);
4248                 }
4249         }
4250
4251         isl_map_free(map);
4252         return rest;
4253 error:
4254         isl_map_free(map);
4255         isl_map_free(rest);
4256         return NULL;
4257 }
4258
4259 struct isl_map *isl_map_subtract(struct isl_map *map1, struct isl_map *map2)
4260 {
4261         int i;
4262         if (!map1 || !map2)
4263                 goto error;
4264
4265         isl_assert(map1->ctx, isl_dim_equal(map1->dim, map2->dim), goto error);
4266
4267         if (isl_map_is_empty(map2)) {
4268                 isl_map_free(map2);
4269                 return map1;
4270         }
4271
4272         map1 = isl_map_compute_divs(map1);
4273         map2 = isl_map_compute_divs(map2);
4274         if (!map1 || !map2)
4275                 goto error;
4276
4277         for (i = 0; map1 && i < map2->n; ++i)
4278                 map1 = subtract(map1, map2->p[i]);
4279
4280         isl_map_free(map2);
4281         return map1;
4282 error:
4283         isl_map_free(map1);
4284         isl_map_free(map2);
4285         return NULL;
4286 }
4287
4288 struct isl_set *isl_set_subtract(struct isl_set *set1, struct isl_set *set2)
4289 {
4290         return (struct isl_set *)
4291                 isl_map_subtract(
4292                         (struct isl_map *)set1, (struct isl_map *)set2);
4293 }
4294
4295 struct isl_set *isl_set_apply(struct isl_set *set, struct isl_map *map)
4296 {
4297         if (!set || !map)
4298                 goto error;
4299         isl_assert(set->ctx, isl_map_compatible_domain(map, set), goto error);
4300         map = isl_map_intersect_domain(map, set);
4301         set = isl_map_range(map);
4302         return set;
4303 error:
4304         isl_set_free(set);
4305         isl_map_free(map);
4306         return NULL;
4307 }
4308
4309 /* There is no need to cow as removing empty parts doesn't change
4310  * the meaning of the set.
4311  */
4312 struct isl_map *isl_map_remove_empty_parts(struct isl_map *map)
4313 {
4314         int i;
4315
4316         if (!map)
4317                 return NULL;
4318
4319         for (i = map->n-1; i >= 0; --i) {
4320                 if (!ISL_F_ISSET(map->p[i], ISL_BASIC_MAP_EMPTY))
4321                         continue;
4322                 isl_basic_map_free(map->p[i]);
4323                 if (i != map->n-1) {
4324                         ISL_F_CLR(map, ISL_MAP_NORMALIZED);
4325                         map->p[i] = map->p[map->n-1];
4326                 }
4327                 map->n--;
4328         }
4329
4330         return map;
4331 }
4332
4333 struct isl_set *isl_set_remove_empty_parts(struct isl_set *set)
4334 {
4335         return (struct isl_set *)
4336                 isl_map_remove_empty_parts((struct isl_map *)set);
4337 }
4338
4339 struct isl_basic_map *isl_map_copy_basic_map(struct isl_map *map)
4340 {
4341         struct isl_basic_map *bmap;
4342         if (!map || map->n == 0)
4343                 return NULL;
4344         bmap = map->p[map->n-1];
4345         isl_assert(map->ctx, ISL_F_ISSET(bmap, ISL_BASIC_SET_FINAL), return NULL);
4346         return isl_basic_map_copy(bmap);
4347 }
4348
4349 struct isl_basic_set *isl_set_copy_basic_set(struct isl_set *set)
4350 {
4351         (struct isl_basic_set *)isl_map_copy_basic_map((struct isl_map *)set);
4352 }
4353
4354 struct isl_map *isl_map_drop_basic_map(struct isl_map *map,
4355                                                 struct isl_basic_map *bmap)
4356 {
4357         int i;
4358
4359         if (!map || !bmap)
4360                 goto error;
4361         for (i = map->n-1; i >= 0; --i) {
4362                 if (map->p[i] != bmap)
4363                         continue;
4364                 map = isl_map_cow(map);
4365                 if (!map)
4366                         goto error;
4367                 isl_basic_map_free(map->p[i]);
4368                 if (i != map->n-1) {
4369                         ISL_F_CLR(map, ISL_SET_NORMALIZED);
4370                         map->p[i] = map->p[map->n-1];
4371                 }
4372                 map->n--;
4373                 return map;
4374         }
4375         isl_basic_map_free(bmap);
4376         return map;
4377 error:
4378         isl_map_free(map);
4379         isl_basic_map_free(bmap);
4380         return NULL;
4381 }
4382
4383 struct isl_set *isl_set_drop_basic_set(struct isl_set *set,
4384                                                 struct isl_basic_set *bset)
4385 {
4386         (struct isl_set *)isl_map_drop_basic_map((struct isl_map *)set,
4387                                                 (struct isl_basic_map *)bset);
4388 }
4389
4390 /* Given two _disjoint_ basic sets bset1 and bset2, check whether
4391  * for any common value of the parameters and dimensions preceding dim
4392  * in both basic sets, the values of dimension pos in bset1 are
4393  * smaller or larger than those in bset2.
4394  *
4395  * Returns
4396  *       1 if bset1 follows bset2
4397  *      -1 if bset1 precedes bset2
4398  *       0 if bset1 and bset2 are incomparable
4399  *      -2 if some error occurred.
4400  */
4401 int isl_basic_set_compare_at(struct isl_basic_set *bset1,
4402         struct isl_basic_set *bset2, int pos)
4403 {
4404         struct isl_dim *dims;
4405         struct isl_basic_map *bmap1 = NULL;
4406         struct isl_basic_map *bmap2 = NULL;
4407         struct isl_ctx *ctx;
4408         struct isl_vec *obj;
4409         unsigned total;
4410         unsigned nparam;
4411         unsigned dim1, dim2;
4412         isl_int num, den;
4413         enum isl_lp_result res;
4414         int cmp;
4415
4416         if (!bset1 || !bset2)
4417                 return -2;
4418
4419         nparam = isl_basic_set_n_param(bset1);
4420         dim1 = isl_basic_set_n_dim(bset1);
4421         dim2 = isl_basic_set_n_dim(bset2);
4422         dims = isl_dim_alloc(bset1->ctx, nparam, pos, dim1 - pos);
4423         bmap1 = isl_basic_map_from_basic_set(isl_basic_set_copy(bset1), dims);
4424         dims = isl_dim_alloc(bset2->ctx, nparam, pos, dim2 - pos);
4425         bmap2 = isl_basic_map_from_basic_set(isl_basic_set_copy(bset2), dims);
4426         if (!bmap1 || !bmap2)
4427                 goto error;
4428         bmap1 = isl_basic_map_cow(bmap1);
4429         bmap1 = isl_basic_map_extend(bmap1, nparam,
4430                         pos, (dim1 - pos) + (dim2 - pos),
4431                         bmap2->n_div, bmap2->n_eq, bmap2->n_ineq);
4432         bmap1 = add_constraints(bmap1, bmap2, 0, dim1 - pos);
4433         if (!bmap1)
4434                 goto error;
4435         total = isl_basic_map_total_dim(bmap1);
4436         ctx = bmap1->ctx;
4437         obj = isl_vec_alloc(ctx, 1 + total);
4438         isl_seq_clr(obj->block.data, 1 + total);
4439         isl_int_set_si(obj->block.data[1+nparam+pos], 1);
4440         isl_int_set_si(obj->block.data[1+nparam+pos+(dim1-pos)], -1);
4441         if (!obj)
4442                 goto error;
4443         isl_int_init(num);
4444         isl_int_init(den);
4445         res = isl_basic_map_solve_lp(bmap1, 0, obj->block.data, ctx->one,
4446                                         &num, &den, NULL);
4447         if (res == isl_lp_empty)
4448                 cmp = 0;
4449         else if (res == isl_lp_ok && isl_int_is_pos(num))
4450                 cmp = 1;
4451         else if ((res == isl_lp_ok && isl_int_is_neg(num)) ||
4452                   res == isl_lp_unbounded)
4453                 cmp = -1;
4454         else
4455                 cmp = -2;
4456         isl_int_clear(num);
4457         isl_int_clear(den);
4458         isl_basic_map_free(bmap1);
4459         isl_vec_free(obj);
4460         return cmp;
4461 error:
4462         isl_basic_map_free(bmap1);
4463         isl_basic_map_free(bmap2);
4464         return -2;
4465 }
4466
4467 static int isl_basic_map_fast_has_fixed_var(struct isl_basic_map *bmap,
4468         unsigned pos, isl_int *val)
4469 {
4470         int i;
4471         int d;
4472         unsigned total;
4473
4474         if (!bmap)
4475                 return -1;
4476         total = isl_basic_map_total_dim(bmap);
4477         for (i = 0, d = total-1; i < bmap->n_eq && d+1 > pos; ++i) {
4478                 for (; d+1 > pos; --d)
4479                         if (!isl_int_is_zero(bmap->eq[i][1+d]))
4480                                 break;
4481                 if (d != pos)
4482                         continue;
4483                 if (isl_seq_first_non_zero(bmap->eq[i]+1, d) != -1)
4484                         return 0;
4485                 if (isl_seq_first_non_zero(bmap->eq[i]+1+d+1, total-d-1) != -1)
4486                         return 0;
4487                 if (!isl_int_is_one(bmap->eq[i][1+d]))
4488                         return 0;
4489                 if (val)
4490                         isl_int_neg(*val, bmap->eq[i][0]);
4491                 return 1;
4492         }
4493         return 0;
4494 }
4495
4496 static int isl_map_fast_has_fixed_var(struct isl_map *map,
4497         unsigned pos, isl_int *val)
4498 {
4499         int i;
4500         isl_int v;
4501         isl_int tmp;
4502         int fixed;
4503
4504         if (!map)
4505                 return -1;
4506         if (map->n == 0)
4507                 return 0;
4508         if (map->n == 1)
4509                 return isl_basic_map_fast_has_fixed_var(map->p[0], pos, val);
4510         isl_int_init(v);
4511         isl_int_init(tmp);
4512         fixed = isl_basic_map_fast_has_fixed_var(map->p[0], pos, &v);
4513         for (i = 1; fixed == 1 && i < map->n; ++i) {
4514                 fixed = isl_basic_map_fast_has_fixed_var(map->p[i], pos, &tmp);
4515                 if (fixed == 1 && isl_int_ne(tmp, v))
4516                         fixed = 0;
4517         }
4518         if (val)
4519                 isl_int_set(*val, v);
4520         isl_int_clear(tmp);
4521         isl_int_clear(v);
4522         return fixed;
4523 }
4524
4525 static int isl_basic_set_fast_has_fixed_var(struct isl_basic_set *bset,
4526         unsigned pos, isl_int *val)
4527 {
4528         return isl_basic_map_fast_has_fixed_var((struct isl_basic_map *)bset,
4529                                                 pos, val);
4530 }
4531
4532 static int isl_set_fast_has_fixed_var(struct isl_set *set, unsigned pos,
4533         isl_int *val)
4534 {
4535         return isl_map_fast_has_fixed_var((struct isl_map *)set, pos, val);
4536 }
4537
4538 int isl_basic_map_fast_is_fixed(struct isl_basic_map *bmap,
4539         enum isl_dim_type type, unsigned pos, isl_int *val)
4540 {
4541         if (pos >= isl_basic_map_dim(bmap, type))
4542                 return -1;
4543         return isl_basic_map_fast_has_fixed_var(bmap,
4544                 isl_basic_map_offset(bmap, type) - 1 + pos, val);
4545 }
4546
4547 int isl_map_fast_is_fixed(struct isl_map *map,
4548         enum isl_dim_type type, unsigned pos, isl_int *val)
4549 {
4550         if (pos >= isl_map_dim(map, type))
4551                 return -1;
4552         return isl_map_fast_has_fixed_var(map,
4553                 map_offset(map, type) - 1 + pos, val);
4554 }
4555
4556 /* Check if dimension dim has fixed value and if so and if val is not NULL,
4557  * then return this fixed value in *val.
4558  */
4559 int isl_basic_set_fast_dim_is_fixed(struct isl_basic_set *bset, unsigned dim,
4560         isl_int *val)
4561 {
4562         return isl_basic_set_fast_has_fixed_var(bset,
4563                                         isl_basic_set_n_param(bset) + dim, val);
4564 }
4565
4566 /* Check if dimension dim has fixed value and if so and if val is not NULL,
4567  * then return this fixed value in *val.
4568  */
4569 int isl_set_fast_dim_is_fixed(struct isl_set *set, unsigned dim, isl_int *val)
4570 {
4571         return isl_set_fast_has_fixed_var(set, isl_set_n_param(set) + dim, val);
4572 }
4573
4574 /* Check if input variable in has fixed value and if so and if val is not NULL,
4575  * then return this fixed value in *val.
4576  */
4577 int isl_map_fast_input_is_fixed(struct isl_map *map, unsigned in, isl_int *val)
4578 {
4579         return isl_map_fast_has_fixed_var(map, isl_map_n_param(map) + in, val);
4580 }
4581
4582 /* Check if dimension dim has an (obvious) fixed lower bound and if so
4583  * and if val is not NULL, then return this lower bound in *val.
4584  */
4585 int isl_basic_set_fast_dim_has_fixed_lower_bound(struct isl_basic_set *bset,
4586         unsigned dim, isl_int *val)
4587 {
4588         int i, i_eq = -1, i_ineq = -1;
4589         isl_int *c;
4590         unsigned total;
4591         unsigned nparam;
4592
4593         if (!bset)
4594                 return -1;
4595         total = isl_basic_set_total_dim(bset);
4596         nparam = isl_basic_set_n_param(bset);
4597         for (i = 0; i < bset->n_eq; ++i) {
4598                 if (isl_int_is_zero(bset->eq[i][1+nparam+dim]))
4599                         continue;
4600                 if (i_eq != -1)
4601                         return 0;
4602                 i_eq = i;
4603         }
4604         for (i = 0; i < bset->n_ineq; ++i) {
4605                 if (!isl_int_is_pos(bset->ineq[i][1+nparam+dim]))
4606                         continue;
4607                 if (i_eq != -1 || i_ineq != -1)
4608                         return 0;
4609                 i_ineq = i;
4610         }
4611         if (i_eq == -1 && i_ineq == -1)
4612                 return 0;
4613         c = i_eq != -1 ? bset->eq[i_eq] : bset->ineq[i_ineq];
4614         /* The coefficient should always be one due to normalization. */
4615         if (!isl_int_is_one(c[1+nparam+dim]))
4616                 return 0;
4617         if (isl_seq_first_non_zero(c+1, nparam+dim) != -1)
4618                 return 0;
4619         if (isl_seq_first_non_zero(c+1+nparam+dim+1,
4620                                         total - nparam - dim - 1) != -1)
4621                 return 0;
4622         if (val)
4623                 isl_int_neg(*val, c[0]);
4624         return 1;
4625 }
4626
4627 int isl_set_fast_dim_has_fixed_lower_bound(struct isl_set *set,
4628         unsigned dim, isl_int *val)
4629 {
4630         int i;
4631         isl_int v;
4632         isl_int tmp;
4633         int fixed;
4634
4635         if (!set)
4636                 return -1;
4637         if (set->n == 0)
4638                 return 0;
4639         if (set->n == 1)
4640                 return isl_basic_set_fast_dim_has_fixed_lower_bound(set->p[0],
4641                                                                 dim, val);
4642         isl_int_init(v);
4643         isl_int_init(tmp);
4644         fixed = isl_basic_set_fast_dim_has_fixed_lower_bound(set->p[0],
4645                                                                 dim, &v);
4646         for (i = 1; fixed == 1 && i < set->n; ++i) {
4647                 fixed = isl_basic_set_fast_dim_has_fixed_lower_bound(set->p[i],
4648                                                                 dim, &tmp);
4649                 if (fixed == 1 && isl_int_ne(tmp, v))
4650                         fixed = 0;
4651         }
4652         if (val)
4653                 isl_int_set(*val, v);
4654         isl_int_clear(tmp);
4655         isl_int_clear(v);
4656         return fixed;
4657 }
4658
4659 struct constraint {
4660         unsigned        size;
4661         isl_int         *c;
4662 };
4663
4664 static int qsort_constraint_cmp(const void *p1, const void *p2)
4665 {
4666         const struct constraint *c1 = (const struct constraint *)p1;
4667         const struct constraint *c2 = (const struct constraint *)p2;
4668         unsigned size = isl_min(c1->size, c2->size);
4669         return isl_seq_cmp(c1->c, c2->c, size);
4670 }
4671
4672 static struct isl_basic_map *isl_basic_map_sort_constraints(
4673         struct isl_basic_map *bmap)
4674 {
4675         int i;
4676         struct constraint *c;
4677         unsigned total;
4678
4679         if (!bmap)
4680                 return NULL;
4681         total = isl_basic_map_total_dim(bmap);
4682         c = isl_alloc_array(bmap->ctx, struct constraint, bmap->n_ineq);
4683         if (!c)
4684                 goto error;
4685         for (i = 0; i < bmap->n_ineq; ++i) {
4686                 c[i].size = total;
4687                 c[i].c = bmap->ineq[i];
4688         }
4689         qsort(c, bmap->n_ineq, sizeof(struct constraint), qsort_constraint_cmp);
4690         for (i = 0; i < bmap->n_ineq; ++i)
4691                 bmap->ineq[i] = c[i].c;
4692         free(c);
4693         return bmap;
4694 error:
4695         isl_basic_map_free(bmap);
4696         return NULL;
4697 }
4698
4699 struct isl_basic_map *isl_basic_map_normalize(struct isl_basic_map *bmap)
4700 {
4701         if (!bmap)
4702                 return NULL;
4703         if (ISL_F_ISSET(bmap, ISL_BASIC_MAP_NORMALIZED))
4704                 return bmap;
4705         bmap = isl_basic_map_convex_hull(bmap);
4706         bmap = isl_basic_map_sort_constraints(bmap);
4707         ISL_F_SET(bmap, ISL_BASIC_MAP_NORMALIZED);
4708         return bmap;
4709 }
4710
4711 struct isl_basic_set *isl_basic_set_normalize(struct isl_basic_set *bset)
4712 {
4713         return (struct isl_basic_set *)isl_basic_map_normalize(
4714                                                 (struct isl_basic_map *)bset);
4715 }
4716
4717 static int isl_basic_map_fast_cmp(const struct isl_basic_map *bmap1,
4718         const struct isl_basic_map *bmap2)
4719 {
4720         int i, cmp;
4721         unsigned total;
4722
4723         if (bmap1 == bmap2)
4724                 return 0;
4725         if (isl_basic_map_n_param(bmap1) != isl_basic_map_n_param(bmap2))
4726                 return isl_basic_map_n_param(bmap1) - isl_basic_map_n_param(bmap2);
4727         if (isl_basic_map_n_in(bmap1) != isl_basic_map_n_in(bmap2))
4728                 return isl_basic_map_n_out(bmap1) - isl_basic_map_n_out(bmap2);
4729         if (isl_basic_map_n_out(bmap1) != isl_basic_map_n_out(bmap2))
4730                 return isl_basic_map_n_out(bmap1) - isl_basic_map_n_out(bmap2);
4731         if (ISL_F_ISSET(bmap1, ISL_BASIC_MAP_EMPTY) &&
4732             ISL_F_ISSET(bmap2, ISL_BASIC_MAP_EMPTY))
4733                 return 0;
4734         if (ISL_F_ISSET(bmap1, ISL_BASIC_MAP_EMPTY))
4735                 return 1;
4736         if (ISL_F_ISSET(bmap2, ISL_BASIC_MAP_EMPTY))
4737                 return -1;
4738         if (bmap1->n_eq != bmap2->n_eq)
4739                 return bmap1->n_eq - bmap2->n_eq;
4740         if (bmap1->n_ineq != bmap2->n_ineq)
4741                 return bmap1->n_ineq - bmap2->n_ineq;
4742         if (bmap1->n_div != bmap2->n_div)
4743                 return bmap1->n_div - bmap2->n_div;
4744         total = isl_basic_map_total_dim(bmap1);
4745         for (i = 0; i < bmap1->n_eq; ++i) {
4746                 cmp = isl_seq_cmp(bmap1->eq[i], bmap2->eq[i], 1+total);
4747                 if (cmp)
4748                         return cmp;
4749         }
4750         for (i = 0; i < bmap1->n_ineq; ++i) {
4751                 cmp = isl_seq_cmp(bmap1->ineq[i], bmap2->ineq[i], 1+total);
4752                 if (cmp)
4753                         return cmp;
4754         }
4755         for (i = 0; i < bmap1->n_div; ++i) {
4756                 cmp = isl_seq_cmp(bmap1->div[i], bmap2->div[i], 1+1+total);
4757                 if (cmp)
4758                         return cmp;
4759         }
4760         return 0;
4761 }
4762
4763 static int isl_basic_map_fast_is_equal(struct isl_basic_map *bmap1,
4764         struct isl_basic_map *bmap2)
4765 {
4766         return isl_basic_map_fast_cmp(bmap1, bmap2) == 0;
4767 }
4768
4769 static int qsort_bmap_cmp(const void *p1, const void *p2)
4770 {
4771         const struct isl_basic_map *bmap1 = *(const struct isl_basic_map **)p1;
4772         const struct isl_basic_map *bmap2 = *(const struct isl_basic_map **)p2;
4773
4774         return isl_basic_map_fast_cmp(bmap1, bmap2);
4775 }
4776
4777 /* We normalize in place, but if anything goes wrong we need
4778  * to return NULL, so we need to make sure we don't change the
4779  * meaning of any possible other copies of map.
4780  */
4781 struct isl_map *isl_map_normalize(struct isl_map *map)
4782 {
4783         int i, j;
4784         struct isl_basic_map *bmap;
4785
4786         if (!map)
4787                 return NULL;
4788         if (ISL_F_ISSET(map, ISL_MAP_NORMALIZED))
4789                 return map;
4790         for (i = 0; i < map->n; ++i) {
4791                 bmap = isl_basic_map_normalize(isl_basic_map_copy(map->p[i]));
4792                 if (!bmap)
4793                         goto error;
4794                 isl_basic_map_free(map->p[i]);
4795                 map->p[i] = bmap;
4796         }
4797         qsort(map->p, map->n, sizeof(struct isl_basic_map *), qsort_bmap_cmp);
4798         ISL_F_SET(map, ISL_MAP_NORMALIZED);
4799         map = isl_map_remove_empty_parts(map);
4800         if (!map)
4801                 return NULL;
4802         for (i = map->n - 1; i >= 1; --i) {
4803                 if (!isl_basic_map_fast_is_equal(map->p[i-1], map->p[i]))
4804                         continue;
4805                 isl_basic_map_free(map->p[i-1]);
4806                 for (j = i; j < map->n; ++j)
4807                         map->p[j-1] = map->p[j];
4808                 map->n--;
4809         }
4810         return map;
4811 error:
4812         isl_map_free(map);
4813         return NULL;
4814
4815 }
4816
4817 struct isl_set *isl_set_normalize(struct isl_set *set)
4818 {
4819         return (struct isl_set *)isl_map_normalize((struct isl_map *)set);
4820 }
4821
4822 int isl_map_fast_is_equal(struct isl_map *map1, struct isl_map *map2)
4823 {
4824         int i;
4825         int equal;
4826
4827         if (!map1 || !map2)
4828                 return -1;
4829
4830         if (map1 == map2)
4831                 return 1;
4832         if (!isl_dim_equal(map1->dim, map2->dim))
4833                 return 0;
4834
4835         map1 = isl_map_copy(map1);
4836         map2 = isl_map_copy(map2);
4837         map1 = isl_map_normalize(map1);
4838         map2 = isl_map_normalize(map2);
4839         if (!map1 || !map2)
4840                 goto error;
4841         equal = map1->n == map2->n;
4842         for (i = 0; equal && i < map1->n; ++i) {
4843                 equal = isl_basic_map_fast_is_equal(map1->p[i], map2->p[i]);
4844                 if (equal < 0)
4845                         goto error;
4846         }
4847         isl_map_free(map1);
4848         isl_map_free(map2);
4849         return equal;
4850 error:
4851         isl_map_free(map1);
4852         isl_map_free(map2);
4853         return -1;
4854 }
4855
4856 int isl_set_fast_is_equal(struct isl_set *set1, struct isl_set *set2)
4857 {
4858         return isl_map_fast_is_equal((struct isl_map *)set1,
4859                                                 (struct isl_map *)set2);
4860 }
4861
4862 /* Return an interval that ranges from min to max (inclusive)
4863  */
4864 struct isl_basic_set *isl_basic_set_interval(struct isl_ctx *ctx,
4865         isl_int min, isl_int max)
4866 {
4867         int k;
4868         struct isl_basic_set *bset = NULL;
4869
4870         bset = isl_basic_set_alloc(ctx, 0, 1, 0, 0, 2);
4871         if (!bset)
4872                 goto error;
4873
4874         k = isl_basic_set_alloc_inequality(bset);
4875         if (k < 0)
4876                 goto error;
4877         isl_int_set_si(bset->ineq[k][1], 1);
4878         isl_int_neg(bset->ineq[k][0], min);
4879
4880         k = isl_basic_set_alloc_inequality(bset);
4881         if (k < 0)
4882                 goto error;
4883         isl_int_set_si(bset->ineq[k][1], -1);
4884         isl_int_set(bset->ineq[k][0], max);
4885
4886         return bset;
4887 error:
4888         isl_basic_set_free(bset);
4889         return NULL;
4890 }
4891
4892 /* Return the Cartesian product of the basic sets in list (in the given order).
4893  */
4894 struct isl_basic_set *isl_basic_set_product(struct isl_basic_set_list *list)
4895 {
4896         int i;
4897         unsigned dim;
4898         unsigned nparam;
4899         unsigned extra;
4900         unsigned n_eq;
4901         unsigned n_ineq;
4902         struct isl_basic_set *product = NULL;
4903
4904         if (!list)
4905                 goto error;
4906         isl_assert(list->ctx, list->n > 0, goto error);
4907         isl_assert(list->ctx, list->p[0], goto error);
4908         nparam = isl_basic_set_n_param(list->p[0]);
4909         dim = isl_basic_set_n_dim(list->p[0]);
4910         extra = list->p[0]->n_div;
4911         n_eq = list->p[0]->n_eq;
4912         n_ineq = list->p[0]->n_ineq;
4913         for (i = 1; i < list->n; ++i) {
4914                 isl_assert(list->ctx, list->p[i], goto error);
4915                 isl_assert(list->ctx,
4916                     nparam == isl_basic_set_n_param(list->p[i]), goto error);
4917                 dim += isl_basic_set_n_dim(list->p[i]);
4918                 extra += list->p[i]->n_div;
4919                 n_eq += list->p[i]->n_eq;
4920                 n_ineq += list->p[i]->n_ineq;
4921         }
4922         product = isl_basic_set_alloc(list->ctx, nparam, dim, extra,
4923                                         n_eq, n_ineq);
4924         if (!product)
4925                 goto error;
4926         dim = 0;
4927         for (i = 0; i < list->n; ++i) {
4928                 isl_basic_set_add_constraints(product,
4929                                         isl_basic_set_copy(list->p[i]), dim);
4930                 dim += isl_basic_set_n_dim(list->p[i]);
4931         }
4932         isl_basic_set_list_free(list);
4933         return product;
4934 error:
4935         isl_basic_set_free(product);
4936         isl_basic_set_list_free(list);
4937         return NULL;
4938 }
4939
4940 struct isl_basic_map *isl_basic_map_product(
4941                 struct isl_basic_map *bmap1, struct isl_basic_map *bmap2)
4942 {
4943         struct isl_dim *dim_result = NULL;
4944         struct isl_basic_map *bmap;
4945         unsigned in1, in2, out1, out2, nparam, total, pos;
4946         struct isl_dim_map *dim_map1, *dim_map2;
4947
4948         if (!bmap1 || !bmap2)
4949                 goto error;
4950
4951         isl_assert(map1->ctx, isl_dim_match(bmap1->dim, isl_dim_param,
4952                                      bmap2->dim, isl_dim_param), goto error);
4953         dim_result = isl_dim_product(isl_dim_copy(bmap1->dim),
4954                                                    isl_dim_copy(bmap2->dim));
4955
4956         in1 = isl_basic_map_n_in(bmap1);
4957         in2 = isl_basic_map_n_in(bmap2);
4958         out1 = isl_basic_map_n_out(bmap1);
4959         out2 = isl_basic_map_n_out(bmap2);
4960         nparam = isl_basic_map_n_param(bmap1);
4961
4962         total = nparam + in1 + in2 + out1 + out2 + bmap1->n_div + bmap2->n_div;
4963         dim_map1 = isl_dim_map_alloc(bmap1->ctx, total);
4964         dim_map2 = isl_dim_map_alloc(bmap1->ctx, total);
4965         isl_dim_map_dim(dim_map1, bmap1->dim, isl_dim_param, pos = 0);
4966         isl_dim_map_dim(dim_map2, bmap2->dim, isl_dim_param, pos = 0);
4967         isl_dim_map_dim(dim_map1, bmap1->dim, isl_dim_in, pos += nparam);
4968         isl_dim_map_dim(dim_map2, bmap2->dim, isl_dim_in, pos += in1);
4969         isl_dim_map_dim(dim_map1, bmap1->dim, isl_dim_out, pos += in2);
4970         isl_dim_map_dim(dim_map2, bmap2->dim, isl_dim_out, pos += out1);
4971         isl_dim_map_div(dim_map1, bmap1, pos += out2);
4972         isl_dim_map_div(dim_map2, bmap2, pos += bmap1->n_div);
4973
4974         bmap = isl_basic_map_alloc_dim(dim_result,
4975                         bmap1->n_div + bmap2->n_div,
4976                         bmap1->n_eq + bmap2->n_eq,
4977                         bmap1->n_ineq + bmap2->n_ineq);
4978         bmap = add_constraints_dim_map(bmap, bmap1, dim_map1);
4979         bmap = add_constraints_dim_map(bmap, bmap2, dim_map2);
4980         bmap = isl_basic_map_simplify(bmap);
4981         return isl_basic_map_finalize(bmap);
4982 error:
4983         isl_basic_map_free(bmap1);
4984         isl_basic_map_free(bmap2);
4985         return NULL;
4986 }
4987
4988 /* Given two maps A -> B and C -> D, construct a map (A, C) -> (B, D)
4989  */
4990 struct isl_map *isl_map_product(struct isl_map *map1, struct isl_map *map2)
4991 {
4992         unsigned flags = 0;
4993         struct isl_map *result;
4994         int i, j;
4995
4996         if (!map1 || !map2)
4997                 goto error;
4998
4999         isl_assert(map1->ctx, isl_dim_match(map1->dim, isl_dim_param,
5000                                          map2->dim, isl_dim_param), goto error);
5001
5002         if (ISL_F_ISSET(map1, ISL_MAP_DISJOINT) &&
5003             ISL_F_ISSET(map2, ISL_MAP_DISJOINT))
5004                 ISL_FL_SET(flags, ISL_MAP_DISJOINT);
5005
5006         result = isl_map_alloc_dim(isl_dim_product(isl_dim_copy(map1->dim),
5007                                                    isl_dim_copy(map2->dim)),
5008                                 map1->n * map2->n, flags);
5009         if (!result)
5010                 goto error;
5011         for (i = 0; i < map1->n; ++i)
5012                 for (j = 0; j < map2->n; ++j) {
5013                         struct isl_basic_map *part;
5014                         part = isl_basic_map_product(
5015                                     isl_basic_map_copy(map1->p[i]),
5016                                     isl_basic_map_copy(map2->p[j]));
5017                         if (isl_basic_map_is_empty(part))
5018                                 isl_basic_map_free(part);
5019                         else
5020                                 result = isl_map_add(result, part);
5021                         if (!result)
5022                                 goto error;
5023                 }
5024         isl_map_free(map1);
5025         isl_map_free(map2);
5026         return result;
5027 error:
5028         isl_map_free(map1);
5029         isl_map_free(map2);
5030         return NULL;
5031 }
5032
5033 /* Given two set A and B, construct its Cartesian product A x B.
5034  */
5035 struct isl_set *isl_set_product(struct isl_set *set1, struct isl_set *set2)
5036 {
5037         return (struct isl_set *)isl_map_product((struct isl_map *)set1,
5038                                                  (struct isl_map *)set2);
5039 }
5040
5041 uint32_t isl_basic_set_get_hash(struct isl_basic_set *bset)
5042 {
5043         int i;
5044         uint32_t hash;
5045         unsigned total;
5046
5047         if (!bset)
5048                 return 0;
5049         bset = isl_basic_set_copy(bset);
5050         bset = isl_basic_set_normalize(bset);
5051         if (!bset)
5052                 return 0;
5053         total = isl_basic_set_total_dim(bset);
5054         isl_hash_byte(hash, bset->n_eq & 0xFF);
5055         for (i = 0; i < bset->n_eq; ++i) {
5056                 uint32_t c_hash;
5057                 c_hash = isl_seq_get_hash(bset->eq[i], 1 + total);
5058                 isl_hash_hash(hash, c_hash);
5059         }
5060         isl_hash_byte(hash, bset->n_ineq & 0xFF);
5061         for (i = 0; i < bset->n_ineq; ++i) {
5062                 uint32_t c_hash;
5063                 c_hash = isl_seq_get_hash(bset->ineq[i], 1 + total);
5064                 isl_hash_hash(hash, c_hash);
5065         }
5066         isl_hash_byte(hash, bset->n_div & 0xFF);
5067         for (i = 0; i < bset->n_div; ++i) {
5068                 uint32_t c_hash;
5069                 if (isl_int_is_zero(bset->div[i][0]))
5070                         continue;
5071                 isl_hash_byte(hash, i & 0xFF);
5072                 c_hash = isl_seq_get_hash(bset->div[i], 1 + 1 + total);
5073                 isl_hash_hash(hash, c_hash);
5074         }
5075         isl_basic_set_free(bset);
5076         return hash;
5077 }
5078
5079 uint32_t isl_set_get_hash(struct isl_set *set)
5080 {
5081         int i;
5082         uint32_t hash;
5083
5084         if (!set)
5085                 return 0;
5086         set = isl_set_copy(set);
5087         set = isl_set_normalize(set);
5088         if (!set)
5089                 return 0;
5090
5091         hash = isl_hash_init();
5092         for (i = 0; i < set->n; ++i) {
5093                 uint32_t bset_hash;
5094                 bset_hash = isl_basic_set_get_hash(set->p[i]);
5095                 isl_hash_hash(hash, bset_hash);
5096         }
5097
5098         isl_set_free(set);
5099
5100         return hash;
5101 }
5102
5103 /* Check if the value for dimension dim is completely determined
5104  * by the values of the other parameters and variables.
5105  * That is, check if dimension dim is involved in an equality.
5106  */
5107 int isl_basic_set_dim_is_unique(struct isl_basic_set *bset, unsigned dim)
5108 {
5109         int i;
5110         unsigned nparam;
5111
5112         if (!bset)
5113                 return -1;
5114         nparam = isl_basic_set_n_param(bset);
5115         for (i = 0; i < bset->n_eq; ++i)
5116                 if (!isl_int_is_zero(bset->eq[i][1 + nparam + dim]))
5117                         return 1;
5118         return 0;
5119 }
5120
5121 /* Check if the value for dimension dim is completely determined
5122  * by the values of the other parameters and variables.
5123  * That is, check if dimension dim is involved in an equality
5124  * for each of the subsets.
5125  */
5126 int isl_set_dim_is_unique(struct isl_set *set, unsigned dim)
5127 {
5128         int i;
5129
5130         if (!set)
5131                 return -1;
5132         for (i = 0; i < set->n; ++i) {
5133                 int unique;
5134                 unique = isl_basic_set_dim_is_unique(set->p[i], dim);
5135                 if (unique != 1)
5136                         return unique;
5137         }
5138         return 1;
5139 }