isl_local_space.c

   1 /*
   2  * Copyright 2011      INRIA Saclay
   3  *
   4  * Use of this software is governed by the GNU LGPLv2.1 license
   5  *
   6  * Written by Sven Verdoolaege, INRIA Saclay - Ile-de-France,
   7  * Parc Club Orsay Universite, ZAC des vignes, 4 rue Jacques Monod,
   8  * 91893 Orsay, France
   9  */
  10
  11 #include <isl_ctx_private.h>
  12 #include <isl_map_private.h>
  13 #include <isl_local_space_private.h>
  14 #include <isl_space_private.h>
  15 #include <isl_mat_private.h>
  16 #include <isl_aff_private.h>
  17 #include <isl/seq.h>
  18
  19 isl_ctx *isl_local_space_get_ctx(__isl_keep isl_local_space *ls)
  20 {
  21         return ls ? ls->dim->ctx : NULL;
  22 }
  23
  24 __isl_give isl_local_space *isl_local_space_alloc_div(__isl_take isl_space *dim,
  25         __isl_take isl_mat *div)
  26 {
  27         isl_ctx *ctx;
  28         isl_local_space *ls = NULL;
  29
  30         if (!dim || !div)
  31                 goto error;
  32
  33         ctx = isl_space_get_ctx(dim);
  34         ls = isl_calloc_type(ctx, struct isl_local_space);
  35         if (!ls)
  36                 goto error;
  37
  38         ls->ref = 1;
  39         ls->dim = dim;
  40         ls->div = div;
  41
  42         return ls;
  43 error:
  44         isl_mat_free(div);
  45         isl_space_free(dim);
  46         isl_local_space_free(ls);
  47         return NULL;
  48 }
  49
  50 __isl_give isl_local_space *isl_local_space_alloc(__isl_take isl_space *dim,
  51         unsigned n_div)
  52 {
  53         isl_ctx *ctx;
  54         isl_mat *div;
  55         unsigned total;
  56
  57         if (!dim)
  58                 return NULL;
  59
  60         total = isl_space_dim(dim, isl_dim_all);
  61
  62         ctx = isl_space_get_ctx(dim);
  63         div = isl_mat_alloc(ctx, n_div, 1 + 1 + total + n_div);
  64         return isl_local_space_alloc_div(dim, div);
  65 }
  66
  67 __isl_give isl_local_space *isl_local_space_from_space(__isl_take isl_space *dim)
  68 {
  69         return isl_local_space_alloc(dim, 0);
  70 }
  71
  72 __isl_give isl_local_space *isl_local_space_copy(__isl_keep isl_local_space *ls)
  73 {
  74         if (!ls)
  75                 return NULL;
  76
  77         ls->ref++;
  78         return ls;
  79 }
  80
  81 __isl_give isl_local_space *isl_local_space_dup(__isl_keep isl_local_space *ls)
  82 {
  83         if (!ls)
  84                 return NULL;
  85
  86         return isl_local_space_alloc_div(isl_space_copy(ls->dim),
  87                                          isl_mat_copy(ls->div));
  88
  89 }
  90
  91 __isl_give isl_local_space *isl_local_space_cow(__isl_take isl_local_space *ls)
  92 {
  93         if (!ls)
  94                 return NULL;
  95
  96         if (ls->ref == 1)
  97                 return ls;
  98         ls->ref--;
  99         return isl_local_space_dup(ls);
 100 }
 101
 102 void *isl_local_space_free(__isl_take isl_local_space *ls)
 103 {
 104         if (!ls)
 105                 return NULL;
 106
 107         if (--ls->ref > 0)
 108                 return NULL;
 109
 110         isl_space_free(ls->dim);
 111         isl_mat_free(ls->div);
 112
 113         free(ls);
 114
 115         return NULL;
 116 }
 117
 118 /* Is the local space that of a set?
 119  */
 120 int isl_local_space_is_set(__isl_keep isl_local_space *ls)
 121 {
 122         return ls ? isl_space_is_set(ls->dim) : -1;
 123 }
 124
 125 /* Return true if the two local spaces are identical, with identical
 126  * expressions for the integer divisions.
 127  */
 128 int isl_local_space_is_equal(__isl_keep isl_local_space *ls1,
 129         __isl_keep isl_local_space *ls2)
 130 {
 131         int equal;
 132
 133         if (!ls1 || !ls2)
 134                 return -1;
 135
 136         equal = isl_space_is_equal(ls1->dim, ls2->dim);
 137         if (equal < 0 || !equal)
 138                 return equal;
 139
 140         if (!isl_local_space_divs_known(ls1))
 141                 return 0;
 142         if (!isl_local_space_divs_known(ls2))
 143                 return 0;
 144
 145         return isl_mat_is_equal(ls1->div, ls2->div);
 146 }
 147
 148 int isl_local_space_dim(__isl_keep isl_local_space *ls,
 149         enum isl_dim_type type)
 150 {
 151         if (!ls)
 152                 return 0;
 153         if (type == isl_dim_div)
 154                 return ls->div->n_row;
 155         if (type == isl_dim_all)
 156                 return isl_space_dim(ls->dim, isl_dim_all) + ls->div->n_row;
 157         return isl_space_dim(ls->dim, type);
 158 }
 159
 160 unsigned isl_local_space_offset(__isl_keep isl_local_space *ls,
 161         enum isl_dim_type type)
 162 {
 163         isl_space *dim;
 164
 165         if (!ls)
 166                 return 0;
 167
 168         dim = ls->dim;
 169         switch (type) {
 170         case isl_dim_cst:       return 0;
 171         case isl_dim_param:     return 1;
 172         case isl_dim_in:        return 1 + dim->nparam;
 173         case isl_dim_out:       return 1 + dim->nparam + dim->n_in;
 174         case isl_dim_div:       return 1 + dim->nparam + dim->n_in + dim->n_out;
 175         default:                return 0;
 176         }
 177 }
 178
 179 const char *isl_local_space_get_dim_name(__isl_keep isl_local_space *ls,
 180         enum isl_dim_type type, unsigned pos)
 181 {
 182         return ls ? isl_space_get_dim_name(ls->dim, type, pos) : NULL;
 183 }
 184
 185 __isl_give isl_aff *isl_local_space_get_div(__isl_keep isl_local_space *ls,
 186         int pos)
 187 {
 188         isl_aff *aff;
 189
 190         if (!ls)
 191                 return NULL;
 192
 193         if (pos < 0 || pos >= ls->div->n_row)
 194                 isl_die(isl_local_space_get_ctx(ls), isl_error_invalid,
 195                         "index out of bounds", return NULL);
 196
 197         if (isl_int_is_zero(ls->div->row[pos][0]))
 198                 isl_die(isl_local_space_get_ctx(ls), isl_error_invalid,
 199                         "expression of div unknown", return NULL);
 200
 201         aff = isl_aff_alloc(isl_local_space_copy(ls));
 202         if (!aff)
 203                 return NULL;
 204         isl_seq_cpy(aff->v->el, ls->div->row[pos], aff->v->size);
 205         return aff;
 206 }
 207
 208 __isl_give isl_space *isl_local_space_get_space(__isl_keep isl_local_space *ls)
 209 {
 210         if (!ls)
 211                 return NULL;
 212
 213         return isl_space_copy(ls->dim);
 214 }
 215
 216 __isl_give isl_local_space *isl_local_space_set_dim_name(
 217         __isl_take isl_local_space *ls,
 218         enum isl_dim_type type, unsigned pos, const char *s)
 219 {
 220         ls = isl_local_space_cow(ls);
 221         if (!ls)
 222                 return NULL;
 223         ls->dim = isl_space_set_dim_name(ls->dim, type, pos, s);
 224         if (!ls->dim)
 225                 return isl_local_space_free(ls);
 226
 227         return ls;
 228 }
 229
 230 __isl_give isl_local_space *isl_local_space_set_dim_id(
 231         __isl_take isl_local_space *ls,
 232         enum isl_dim_type type, unsigned pos, __isl_take isl_id *id)
 233 {
 234         ls = isl_local_space_cow(ls);
 235         if (!ls)
 236                 return isl_id_free(id);
 237         ls->dim = isl_space_set_dim_id(ls->dim, type, pos, id);
 238         if (!ls->dim)
 239                 return isl_local_space_free(ls);
 240
 241         return ls;
 242 }
 243
 244 __isl_give isl_local_space *isl_local_space_reset_space(
 245         __isl_take isl_local_space *ls, __isl_take isl_space *dim)
 246 {
 247         ls = isl_local_space_cow(ls);
 248         if (!ls || !dim)
 249                 goto error;
 250
 251         isl_space_free(ls->dim);
 252         ls->dim = dim;
 253
 254         return ls;
 255 error:
 256         isl_local_space_free(ls);
 257         isl_space_free(dim);
 258         return NULL;
 259 }
 260
 261 /* Reorder the columns of the given div definitions according to the
 262  * given reordering.
 263  * The order of the divs themselves is assumed not to change.
 264  */
 265 static __isl_give isl_mat *reorder_divs(__isl_take isl_mat *div,
 266         __isl_take isl_reordering *r)
 267 {
 268         int i, j;
 269         isl_mat *mat;
 270         int extra;
 271
 272         if (!div || !r)
 273                 goto error;
 274
 275         extra = isl_space_dim(r->dim, isl_dim_all) + div->n_row - r->len;
 276         mat = isl_mat_alloc(div->ctx, div->n_row, div->n_col + extra);
 277         if (!mat)
 278                 goto error;
 279
 280         for (i = 0; i < div->n_row; ++i) {
 281                 isl_seq_cpy(mat->row[i], div->row[i], 2);
 282                 isl_seq_clr(mat->row[i] + 2, mat->n_col - 2);
 283                 for (j = 0; j < r->len; ++j)
 284                         isl_int_set(mat->row[i][2 + r->pos[j]],
 285                                     div->row[i][2 + j]);
 286         }
 287
 288         isl_reordering_free(r);
 289         isl_mat_free(div);
 290         return mat;
 291 error:
 292         isl_reordering_free(r);
 293         isl_mat_free(div);
 294         return NULL;
 295 }
 296
 297 /* Reorder the dimensions of "ls" according to the given reordering.
 298  * The reordering r is assumed to have been extended with the local
 299  * variables, leaving them in the same order.
 300  */
 301 __isl_give isl_local_space *isl_local_space_realign(
 302         __isl_take isl_local_space *ls, __isl_take isl_reordering *r)
 303 {
 304         ls = isl_local_space_cow(ls);
 305         if (!ls || !r)
 306                 goto error;
 307
 308         ls->div = reorder_divs(ls->div, isl_reordering_copy(r));
 309         if (!ls->div)
 310                 goto error;
 311
 312         ls = isl_local_space_reset_space(ls, isl_space_copy(r->dim));
 313
 314         isl_reordering_free(r);
 315         return ls;
 316 error:
 317         isl_local_space_free(ls);
 318         isl_reordering_free(r);
 319         return NULL;
 320 }
 321
 322 __isl_give isl_local_space *isl_local_space_add_div(
 323         __isl_take isl_local_space *ls, __isl_take isl_vec *div)
 324 {
 325         ls = isl_local_space_cow(ls);
 326         if (!ls || !div)
 327                 goto error;
 328
 329         if (ls->div->n_col != div->size)
 330                 isl_die(isl_local_space_get_ctx(ls), isl_error_invalid,
 331                         "incompatible dimensions", goto error);
 332
 333         ls->div = isl_mat_add_zero_cols(ls->div, 1);
 334         ls->div = isl_mat_add_rows(ls->div, 1);
 335         if (!ls->div)
 336                 goto error;
 337
 338         isl_seq_cpy(ls->div->row[ls->div->n_row - 1], div->el, div->size);
 339         isl_int_set_si(ls->div->row[ls->div->n_row - 1][div->size], 0);
 340
 341         isl_vec_free(div);
 342         return ls;
 343 error:
 344         isl_local_space_free(ls);
 345         isl_vec_free(div);
 346         return NULL;
 347 }
 348
 349 __isl_give isl_local_space *isl_local_space_replace_divs(
 350         __isl_take isl_local_space *ls, __isl_take isl_mat *div)
 351 {
 352         ls = isl_local_space_cow(ls);
 353
 354         if (!ls || !div)
 355                 goto error;
 356
 357         isl_mat_free(ls->div);
 358         ls->div = div;
 359         return ls;
 360 error:
 361         isl_mat_free(div);
 362         isl_local_space_free(ls);
 363         return NULL;
 364 }
 365
 366 /* Copy row "s" of "src" to row "d" of "dst", applying the expansion
 367  * defined by "exp".
 368  */
 369 static void expand_row(__isl_keep isl_mat *dst, int d,
 370         __isl_keep isl_mat *src, int s, int *exp)
 371 {
 372         int i;
 373         unsigned c = src->n_col - src->n_row;
 374
 375         isl_seq_cpy(dst->row[d], src->row[s], c);
 376         isl_seq_clr(dst->row[d] + c, dst->n_col - c);
 377
 378         for (i = 0; i < s; ++i)
 379                 isl_int_set(dst->row[d][c + exp[i]], src->row[s][c + i]);
 380 }
 381
 382 /* Compare (known) divs.
 383  * Return non-zero if at least one of the two divs is unknown.
 384  */
 385 static int cmp_row(__isl_keep isl_mat *div, int i, int j)
 386 {
 387         int li, lj;
 388
 389         if (isl_int_is_zero(div->row[j][0]))
 390                 return -1;
 391         if (isl_int_is_zero(div->row[i][0]))
 392                 return 1;
 393
 394         li = isl_seq_last_non_zero(div->row[i], div->n_col);
 395         lj = isl_seq_last_non_zero(div->row[j], div->n_col);
 396
 397         if (li != lj)
 398                 return li - lj;
 399
 400         return isl_seq_cmp(div->row[i], div->row[j], div->n_col);
 401 }
 402
 403 /* Combine the two lists of divs into a single list.
 404  * For each row i in div1, exp1[i] is set to the position of the corresponding
 405  * row in the result.  Similarly for div2 and exp2.
 406  * This function guarantees
 407  *      exp1[i] >= i
 408  *      exp1[i+1] > exp1[i]
 409  * For optimal merging, the two input list should have been sorted.
 410  */
 411 __isl_give isl_mat *isl_merge_divs(__isl_keep isl_mat *div1,
 412         __isl_keep isl_mat *div2, int *exp1, int *exp2)
 413 {
 414         int i, j, k;
 415         isl_mat *div = NULL;
 416         unsigned d;
 417
 418         if (!div1 || !div2)
 419                 return NULL;
 420
 421         d = div1->n_col - div1->n_row;
 422         div = isl_mat_alloc(div1->ctx, 1 + div1->n_row + div2->n_row,
 423                                 d + div1->n_row + div2->n_row);
 424         if (!div)
 425                 return NULL;
 426
 427         for (i = 0, j = 0, k = 0; i < div1->n_row && j < div2->n_row; ++k) {
 428                 int cmp;
 429
 430                 expand_row(div, k, div1, i, exp1);
 431                 expand_row(div, k + 1, div2, j, exp2);
 432
 433                 cmp = cmp_row(div, k, k + 1);
 434                 if (cmp == 0) {
 435                         exp1[i++] = k;
 436                         exp2[j++] = k;
 437                 } else if (cmp < 0) {
 438                         exp1[i++] = k;
 439                 } else {
 440                         exp2[j++] = k;
 441                         isl_seq_cpy(div->row[k], div->row[k + 1], div->n_col);
 442                 }
 443         }
 444         for (; i < div1->n_row; ++i, ++k) {
 445                 expand_row(div, k, div1, i, exp1);
 446                 exp1[i] = k;
 447         }
 448         for (; j < div2->n_row; ++j, ++k) {
 449                 expand_row(div, k, div2, j, exp2);
 450                 exp2[j] = k;
 451         }
 452
 453         div->n_row = k;
 454         div->n_col = d + k;
 455
 456         return div;
 457 }
 458
 459 /* Construct a local space that contains all the divs in either
 460  * "ls1" or "ls2".
 461  */
 462 __isl_give isl_local_space *isl_local_space_intersect(
 463         __isl_take isl_local_space *ls1, __isl_take isl_local_space *ls2)
 464 {
 465         isl_ctx *ctx;
 466         int *exp1 = NULL;
 467         int *exp2 = NULL;
 468         isl_mat *div;
 469
 470         if (!ls1 || !ls2)
 471                 goto error;
 472
 473         ctx = isl_local_space_get_ctx(ls1);
 474         if (!isl_space_is_equal(ls1->dim, ls2->dim))
 475                 isl_die(ctx, isl_error_invalid,
 476                         "spaces should be identical", goto error);
 477
 478         if (ls2->div->n_row == 0) {
 479                 isl_local_space_free(ls2);
 480                 return ls1;
 481         }
 482
 483         if (ls1->div->n_row == 0) {
 484                 isl_local_space_free(ls1);
 485                 return ls2;
 486         }
 487
 488         exp1 = isl_alloc_array(ctx, int, ls1->div->n_row);
 489         exp2 = isl_alloc_array(ctx, int, ls2->div->n_row);
 490         if (!exp1 || !exp2)
 491                 goto error;
 492
 493         div = isl_merge_divs(ls1->div, ls2->div, exp1, exp2);
 494         if (!div)
 495                 goto error;
 496
 497         free(exp1);
 498         free(exp2);
 499         isl_local_space_free(ls2);
 500         isl_mat_free(ls1->div);
 501         ls1->div = div;
 502
 503         return ls1;
 504 error:
 505         free(exp1);
 506         free(exp2);
 507         isl_local_space_free(ls1);
 508         isl_local_space_free(ls2);
 509         return NULL;
 510 }
 511
 512 int isl_local_space_divs_known(__isl_keep isl_local_space *ls)
 513 {
 514         int i;
 515
 516         if (!ls)
 517                 return -1;
 518
 519         for (i = 0; i < ls->div->n_row; ++i)
 520                 if (isl_int_is_zero(ls->div->row[i][0]))
 521                         return 0;
 522
 523         return 1;
 524 }
 525
 526 __isl_give isl_local_space *isl_local_space_domain(
 527         __isl_take isl_local_space *ls)
 528 {
 529         ls = isl_local_space_drop_dims(ls, isl_dim_out,
 530                                         0, isl_local_space_dim(ls, isl_dim_out));
 531         ls = isl_local_space_cow(ls);
 532         if (!ls)
 533                 return NULL;
 534         ls->dim = isl_space_domain(ls->dim);
 535         if (!ls->dim)
 536                 return isl_local_space_free(ls);
 537         return ls;
 538 }
 539
 540 __isl_give isl_local_space *isl_local_space_range(
 541         __isl_take isl_local_space *ls)
 542 {
 543         ls = isl_local_space_drop_dims(ls, isl_dim_in,
 544                                         0, isl_local_space_dim(ls, isl_dim_in));
 545         ls = isl_local_space_cow(ls);
 546         if (!ls)
 547                 return NULL;
 548
 549         ls->dim = isl_space_range(ls->dim);
 550         if (!ls->dim)
 551                 return isl_local_space_free(ls);
 552         return ls;
 553 }
 554
 555 /* Construct a local space for a map that has the given local
 556  * space as domain and that has a zero-dimensional range.
 557  */
 558 __isl_give isl_local_space *isl_local_space_from_domain(
 559         __isl_take isl_local_space *ls)
 560 {
 561         ls = isl_local_space_cow(ls);
 562         if (!ls)
 563                 return NULL;
 564         ls->dim = isl_space_from_domain(ls->dim);
 565         if (!ls->dim)
 566                 return isl_local_space_free(ls);
 567         return ls;
 568 }
 569
 570 __isl_give isl_local_space *isl_local_space_add_dims(
 571         __isl_take isl_local_space *ls, enum isl_dim_type type, unsigned n)
 572 {
 573         int pos;
 574
 575         if (!ls)
 576                 return NULL;
 577         pos = isl_local_space_dim(ls, type);
 578         return isl_local_space_insert_dims(ls, type, pos, n);
 579 }
 580
 581 /* Remove common factor of non-constant terms and denominator.
 582  */
 583 static void normalize_div(__isl_keep isl_local_space *ls, int div)
 584 {
 585         isl_ctx *ctx = ls->div->ctx;
 586         unsigned total = ls->div->n_col - 2;
 587
 588         isl_seq_gcd(ls->div->row[div] + 2, total, &ctx->normalize_gcd);
 589         isl_int_gcd(ctx->normalize_gcd,
 590                     ctx->normalize_gcd, ls->div->row[div][0]);
 591         if (isl_int_is_one(ctx->normalize_gcd))
 592                 return;
 593
 594         isl_seq_scale_down(ls->div->row[div] + 2, ls->div->row[div] + 2,
 595                             ctx->normalize_gcd, total);
 596         isl_int_divexact(ls->div->row[div][0], ls->div->row[div][0],
 597                             ctx->normalize_gcd);
 598         isl_int_fdiv_q(ls->div->row[div][1], ls->div->row[div][1],
 599                             ctx->normalize_gcd);
 600 }
 601
 602 /* Exploit the equalities in "eq" to simplify the expressions of
 603  * the integer divisions in "ls".
 604  * The integer divisions in "ls" are assumed to appear as regular
 605  * dimensions in "eq".
 606  */
 607 __isl_give isl_local_space *isl_local_space_substitute_equalities(
 608         __isl_take isl_local_space *ls, __isl_take isl_basic_set *eq)
 609 {
 610         int i, j, k;
 611         unsigned total;
 612         unsigned n_div;
 613
 614         ls = isl_local_space_cow(ls);
 615         if (!ls || !eq)
 616                 goto error;
 617
 618         total = isl_space_dim(eq->dim, isl_dim_all);
 619         if (isl_local_space_dim(ls, isl_dim_all) != total)
 620                 isl_die(isl_local_space_get_ctx(ls), isl_error_invalid,
 621                         "dimensions don't match", goto error);
 622         total++;
 623         n_div = eq->n_div;
 624         for (i = 0; i < eq->n_eq; ++i) {
 625                 j = isl_seq_last_non_zero(eq->eq[i], total + n_div);
 626                 if (j < 0 || j == 0 || j >= total)
 627                         continue;
 628
 629                 for (k = 0; k < ls->div->n_row; ++k) {
 630                         if (isl_int_is_zero(ls->div->row[k][1 + j]))
 631                                 continue;
 632                         isl_seq_elim(ls->div->row[k] + 1, eq->eq[i], j, total,
 633                                         &ls->div->row[k][0]);
 634                         normalize_div(ls, k);
 635                 }
 636         }
 637
 638         isl_basic_set_free(eq);
 639         return ls;
 640 error:
 641         isl_basic_set_free(eq);
 642         isl_local_space_free(ls);
 643         return NULL;
 644 }
 645
 646 /* Plug in "subs" for dimension "type", "pos" in the integer divisions
 647  * of "ls".
 648  *
 649  * Let i be the dimension to replace and let "subs" be of the form
 650  *
 651  *      f/d
 652  *
 653  * Any integer division with a non-zero coefficient for i,
 654  *
 655  *      floor((a i + g)/m)
 656  *
 657  * is replaced by
 658  *
 659  *      floor((a f + d g)/(m d))
 660  */
 661 __isl_give isl_local_space *isl_local_space_substitute(
 662         __isl_take isl_local_space *ls,
 663         enum isl_dim_type type, unsigned pos, __isl_keep isl_aff *subs)
 664 {
 665         int i;
 666         isl_int v;
 667
 668         ls = isl_local_space_cow(ls);
 669         if (!ls || !subs)
 670                 return isl_local_space_free(ls);
 671
 672         if (!isl_space_is_equal(ls->dim, subs->ls->dim))
 673                 isl_die(isl_local_space_get_ctx(ls), isl_error_invalid,
 674                         "spaces don't match", return isl_local_space_free(ls));
 675         if (isl_local_space_dim(subs->ls, isl_dim_div) != 0)
 676                 isl_die(isl_local_space_get_ctx(ls), isl_error_unsupported,
 677                         "cannot handle divs yet",
 678                         return isl_local_space_free(ls));
 679
 680         pos += isl_local_space_offset(ls, type);
 681
 682         isl_int_init(v);
 683         for (i = 0; i < ls->div->n_row; ++i) {
 684                 if (isl_int_is_zero(ls->div->row[i][1 + pos]))
 685                         continue;
 686                 isl_int_set(v, ls->div->row[i][1 + pos]);
 687                 isl_int_set_si(ls->div->row[i][1 + pos], 0);
 688                 isl_seq_combine(ls->div->row[i] + 1,
 689                                 subs->v->el[0], ls->div->row[i] + 1,
 690                                 v, subs->v->el + 1, subs->v->size - 1);
 691                 isl_int_mul(ls->div->row[i][0],
 692                             ls->div->row[i][0], subs->v->el[0]);
 693                 normalize_div(ls, i);
 694         }
 695         isl_int_clear(v);
 696
 697         return ls;
 698 }
 699
 700 int isl_local_space_is_named_or_nested(__isl_keep isl_local_space *ls,
 701         enum isl_dim_type type)
 702 {
 703         if (!ls)
 704                 return -1;
 705         return isl_space_is_named_or_nested(ls->dim, type);
 706 }
 707
 708 __isl_give isl_local_space *isl_local_space_drop_dims(
 709         __isl_take isl_local_space *ls,
 710         enum isl_dim_type type, unsigned first, unsigned n)
 711 {
 712         isl_ctx *ctx;
 713
 714         if (!ls)
 715                 return NULL;
 716         if (n == 0 && !isl_local_space_is_named_or_nested(ls, type))
 717                 return ls;
 718
 719         ctx = isl_local_space_get_ctx(ls);
 720         if (first + n > isl_local_space_dim(ls, type))
 721                 isl_die(ctx, isl_error_invalid, "range out of bounds",
 722                         return isl_local_space_free(ls));
 723
 724         ls = isl_local_space_cow(ls);
 725         if (!ls)
 726                 return NULL;
 727
 728         if (type == isl_dim_div) {
 729                 ls->div = isl_mat_drop_rows(ls->div, first, n);
 730         } else {
 731                 ls->dim = isl_space_drop_dims(ls->dim, type, first, n);
 732                 if (!ls->dim)
 733                         return isl_local_space_free(ls);
 734         }
 735
 736         first += 1 + isl_local_space_offset(ls, type);
 737         ls->div = isl_mat_drop_cols(ls->div, first, n);
 738         if (!ls->div)
 739                 return isl_local_space_free(ls);
 740
 741         return ls;
 742 }
 743
 744 __isl_give isl_local_space *isl_local_space_insert_dims(
 745         __isl_take isl_local_space *ls,
 746         enum isl_dim_type type, unsigned first, unsigned n)
 747 {
 748         isl_ctx *ctx;
 749
 750         if (!ls)
 751                 return NULL;
 752         if (n == 0 && !isl_local_space_is_named_or_nested(ls, type))
 753                 return ls;
 754
 755         ctx = isl_local_space_get_ctx(ls);
 756         if (first > isl_local_space_dim(ls, type))
 757                 isl_die(ctx, isl_error_invalid, "position out of bounds",
 758                         return isl_local_space_free(ls));
 759
 760         ls = isl_local_space_cow(ls);
 761         if (!ls)
 762                 return NULL;
 763
 764         if (type == isl_dim_div) {
 765                 ls->div = isl_mat_insert_zero_rows(ls->div, first, n);
 766         } else {
 767                 ls->dim = isl_space_insert_dims(ls->dim, type, first, n);
 768                 if (!ls->dim)
 769                         return isl_local_space_free(ls);
 770         }
 771
 772         first += 1 + isl_local_space_offset(ls, type);
 773         ls->div = isl_mat_insert_zero_cols(ls->div, first, n);
 774         if (!ls->div)
 775                 return isl_local_space_free(ls);
 776
 777         return ls;
 778 }
 779
 780 /* Check if the constraints pointed to by "constraint" is a div
 781  * constraint corresponding to div "div" in "ls".
 782  *
 783  * That is, if div = floor(f/m), then check if the constraint is
 784  *
 785  *              f - m d >= 0
 786  * or
 787  *              -(f-(m-1)) + m d >= 0
 788  */
 789 int isl_local_space_is_div_constraint(__isl_keep isl_local_space *ls,
 790         isl_int *constraint, unsigned div)
 791 {
 792         unsigned pos;
 793
 794         if (!ls)
 795                 return -1;
 796
 797         if (isl_int_is_zero(ls->div->row[div][0]))
 798                 return 0;
 799
 800         pos = isl_local_space_offset(ls, isl_dim_div) + div;
 801
 802         if (isl_int_eq(constraint[pos], ls->div->row[div][0])) {
 803                 int neg;
 804                 isl_int_sub(ls->div->row[div][1],
 805                                 ls->div->row[div][1], ls->div->row[div][0]);
 806                 isl_int_add_ui(ls->div->row[div][1], ls->div->row[div][1], 1);
 807                 neg = isl_seq_is_neg(constraint, ls->div->row[div]+1, pos);
 808                 isl_int_sub_ui(ls->div->row[div][1], ls->div->row[div][1], 1);
 809                 isl_int_add(ls->div->row[div][1],
 810                                 ls->div->row[div][1], ls->div->row[div][0]);
 811                 if (!neg)
 812                         return 0;
 813                 if (isl_seq_first_non_zero(constraint+pos+1,
 814                                             ls->div->n_row-div-1) != -1)
 815                         return 0;
 816         } else if (isl_int_abs_eq(constraint[pos], ls->div->row[div][0])) {
 817                 if (!isl_seq_eq(constraint, ls->div->row[div]+1, pos))
 818                         return 0;
 819                 if (isl_seq_first_non_zero(constraint+pos+1,
 820                                             ls->div->n_row-div-1) != -1)
 821                         return 0;
 822         } else
 823                 return 0;
 824
 825         return 1;
 826 }
 827
 828 /*
 829  * Set active[i] to 1 if the dimension at position i is involved
 830  * in the linear expression l.
 831  */
 832 int *isl_local_space_get_active(__isl_keep isl_local_space *ls, isl_int *l)
 833 {
 834         int i, j;
 835         isl_ctx *ctx;
 836         int *active = NULL;
 837         unsigned total;
 838         unsigned offset;
 839
 840         ctx = isl_local_space_get_ctx(ls);
 841         total = isl_local_space_dim(ls, isl_dim_all);
 842         active = isl_calloc_array(ctx, int, total);
 843         if (!active)
 844                 return NULL;
 845
 846         for (i = 0; i < total; ++i)
 847                 active[i] = !isl_int_is_zero(l[i]);
 848
 849         offset = isl_local_space_offset(ls, isl_dim_div) - 1;
 850         for (i = ls->div->n_row - 1; i >= 0; --i) {
 851                 if (!active[offset + i])
 852                         continue;
 853                 for (j = 0; j < total; ++j)
 854                         active[j] |= !isl_int_is_zero(ls->div->row[i][2 + j]);
 855         }
 856
 857         return active;
 858 }
 859
 860 /* Given a local space "ls" of a set, create a local space
 861  * for the lift of the set.  In particular, the result
 862  * is of the form [dim -> local[..]], with ls->div->n_row variables in the
 863  * range of the wrapped map.
 864  */
 865 __isl_give isl_local_space *isl_local_space_lift(
 866         __isl_take isl_local_space *ls)
 867 {
 868         ls = isl_local_space_cow(ls);
 869         if (!ls)
 870                 return NULL;
 871
 872         ls->dim = isl_space_lift(ls->dim, ls->div->n_row);
 873         ls->div = isl_mat_drop_rows(ls->div, 0, ls->div->n_row);
 874         if (!ls->dim || !ls->div)
 875                 return isl_local_space_free(ls);
 876
 877         return ls;
 878 }
 879
 880 /* Construct a basic map that maps a set living in local space "ls"
 881  * to the corresponding lifted local space.
 882  */
 883 __isl_give isl_basic_map *isl_local_space_lifting(
 884         __isl_take isl_local_space *ls)
 885 {
 886         isl_basic_map *lifting;
 887         isl_basic_set *bset;
 888
 889         if (!ls)
 890                 return NULL;
 891         if (!isl_local_space_is_set(ls))
 892                 isl_die(isl_local_space_get_ctx(ls), isl_error_invalid,
 893                         "lifting only defined on set spaces",
 894                         return isl_local_space_free(ls));
 895
 896         bset = isl_basic_set_from_local_space(ls);
 897         lifting = isl_basic_set_unwrap(isl_basic_set_lift(bset));
 898         lifting = isl_basic_map_domain_map(lifting);
 899         lifting = isl_basic_map_reverse(lifting);
 900
 901         return lifting;
 902 }