isl_morph.c

   1 /*
   2  * Copyright 2010-2011 INRIA Saclay
   3  * Copyright 2014      Ecole Normale Superieure
   4  *
   5  * Use of this software is governed by the MIT license
   6  *
   7  * Written by Sven Verdoolaege, INRIA Saclay - Ile-de-France,
   8  * Parc Club Orsay Universite, ZAC des vignes, 4 rue Jacques Monod,
   9  * 91893 Orsay, France
  10  * and Ecole Normale Superieure, 45 rue d'Ulm, 75230 Paris, France
  11  */
  12
  13 #include <isl_map_private.h>
  14 #include <isl_aff_private.h>
  15 #include <isl_morph.h>
  16 #include <isl_seq.h>
  17 #include <isl_mat_private.h>
  18 #include <isl_space_private.h>
  19 #include <isl_equalities.h>
  20 #include <isl_id_private.h>
  21
  22 isl_ctx *isl_morph_get_ctx(__isl_keep isl_morph *morph)
  23 {
  24         if (!morph)
  25                 return NULL;
  26         return isl_basic_set_get_ctx(morph->dom);
  27 }
  28
  29 __isl_give isl_morph *isl_morph_alloc(
  30         __isl_take isl_basic_set *dom, __isl_take isl_basic_set *ran,
  31         __isl_take isl_mat *map, __isl_take isl_mat *inv)
  32 {
  33         isl_morph *morph;
  34
  35         if (!dom || !ran || !map || !inv)
  36                 goto error;
  37
  38         morph = isl_alloc_type(dom->ctx, struct isl_morph);
  39         if (!morph)
  40                 goto error;
  41
  42         morph->ref = 1;
  43         morph->dom = dom;
  44         morph->ran = ran;
  45         morph->map = map;
  46         morph->inv = inv;
  47
  48         return morph;
  49 error:
  50         isl_basic_set_free(dom);
  51         isl_basic_set_free(ran);
  52         isl_mat_free(map);
  53         isl_mat_free(inv);
  54         return NULL;
  55 }
  56
  57 __isl_give isl_morph *isl_morph_copy(__isl_keep isl_morph *morph)
  58 {
  59         if (!morph)
  60                 return NULL;
  61
  62         morph->ref++;
  63         return morph;
  64 }
  65
  66 __isl_give isl_morph *isl_morph_dup(__isl_keep isl_morph *morph)
  67 {
  68         if (!morph)
  69                 return NULL;
  70
  71         return isl_morph_alloc(isl_basic_set_copy(morph->dom),
  72                 isl_basic_set_copy(morph->ran),
  73                 isl_mat_copy(morph->map), isl_mat_copy(morph->inv));
  74 }
  75
  76 __isl_give isl_morph *isl_morph_cow(__isl_take isl_morph *morph)
  77 {
  78         if (!morph)
  79                 return NULL;
  80
  81         if (morph->ref == 1)
  82                 return morph;
  83         morph->ref--;
  84         return isl_morph_dup(morph);
  85 }
  86
  87 __isl_null isl_morph *isl_morph_free(__isl_take isl_morph *morph)
  88 {
  89         if (!morph)
  90                 return NULL;
  91
  92         if (--morph->ref > 0)
  93                 return NULL;
  94
  95         isl_basic_set_free(morph->dom);
  96         isl_basic_set_free(morph->ran);
  97         isl_mat_free(morph->map);
  98         isl_mat_free(morph->inv);
  99         free(morph);
 100
 101         return NULL;
 102 }
 103
 104 /* Is "morph" an identity on the parameters?
 105  */
 106 static int identity_on_parameters(__isl_keep isl_morph *morph)
 107 {
 108         int is_identity;
 109         unsigned nparam;
 110         isl_mat *sub;
 111
 112         nparam = isl_morph_dom_dim(morph, isl_dim_param);
 113         if (nparam != isl_morph_ran_dim(morph, isl_dim_param))
 114                 return 0;
 115         if (nparam == 0)
 116                 return 1;
 117         sub = isl_mat_sub_alloc(morph->map, 0, 1 + nparam, 0, 1 + nparam);
 118         is_identity = isl_mat_is_scaled_identity(sub);
 119         isl_mat_free(sub);
 120
 121         return is_identity;
 122 }
 123
 124 /* Return an affine expression of the variables of the range of "morph"
 125  * in terms of the parameters and the variables of the domain on "morph".
 126  *
 127  * In order for the space manipulations to make sense, we require
 128  * that the parameters are not modified by "morph".
 129  */
 130 __isl_give isl_multi_aff *isl_morph_get_var_multi_aff(
 131         __isl_keep isl_morph *morph)
 132 {
 133         isl_space *dom, *ran, *space;
 134         isl_local_space *ls;
 135         isl_multi_aff *ma;
 136         unsigned nparam, nvar;
 137         int i;
 138         int is_identity;
 139
 140         if (!morph)
 141                 return NULL;
 142
 143         is_identity = identity_on_parameters(morph);
 144         if (is_identity < 0)
 145                 return NULL;
 146         if (!is_identity)
 147                 isl_die(isl_morph_get_ctx(morph), isl_error_invalid,
 148                         "cannot handle parameter compression", return NULL);
 149
 150         dom = isl_morph_get_dom_space(morph);
 151         ls = isl_local_space_from_space(isl_space_copy(dom));
 152         ran = isl_morph_get_ran_space(morph);
 153         space = isl_space_map_from_domain_and_range(dom, ran);
 154         ma = isl_multi_aff_zero(space);
 155
 156         nparam = isl_multi_aff_dim(ma, isl_dim_param);
 157         nvar = isl_multi_aff_dim(ma, isl_dim_out);
 158         for (i = 0; i < nvar; ++i) {
 159                 isl_val *val;
 160                 isl_vec *v;
 161                 isl_aff *aff;
 162
 163                 v = isl_mat_get_row(morph->map, 1 + nparam + i);
 164                 v = isl_vec_insert_els(v, 0, 1);
 165                 val = isl_mat_get_element_val(morph->map, 0, 0);
 166                 v = isl_vec_set_element_val(v, 0, val);
 167                 aff = isl_aff_alloc_vec(isl_local_space_copy(ls), v);
 168                 ma = isl_multi_aff_set_aff(ma, i, aff);
 169         }
 170
 171         isl_local_space_free(ls);
 172         return ma;
 173 }
 174
 175 /* Return the domain space of "morph".
 176  */
 177 __isl_give isl_space *isl_morph_get_dom_space(__isl_keep isl_morph *morph)
 178 {
 179         if (!morph)
 180                 return NULL;
 181
 182         return isl_basic_set_get_space(morph->dom);
 183 }
 184
 185 __isl_give isl_space *isl_morph_get_ran_space(__isl_keep isl_morph *morph)
 186 {
 187         if (!morph)
 188                 return NULL;
 189
 190         return isl_space_copy(morph->ran->dim);
 191 }
 192
 193 unsigned isl_morph_dom_dim(__isl_keep isl_morph *morph, enum isl_dim_type type)
 194 {
 195         if (!morph)
 196                 return 0;
 197
 198         return isl_basic_set_dim(morph->dom, type);
 199 }
 200
 201 unsigned isl_morph_ran_dim(__isl_keep isl_morph *morph, enum isl_dim_type type)
 202 {
 203         if (!morph)
 204                 return 0;
 205
 206         return isl_basic_set_dim(morph->ran, type);
 207 }
 208
 209 __isl_give isl_morph *isl_morph_remove_dom_dims(__isl_take isl_morph *morph,
 210         enum isl_dim_type type, unsigned first, unsigned n)
 211 {
 212         unsigned dom_offset;
 213
 214         if (n == 0)
 215                 return morph;
 216
 217         morph = isl_morph_cow(morph);
 218         if (!morph)
 219                 return NULL;
 220
 221         dom_offset = 1 + isl_space_offset(morph->dom->dim, type);
 222
 223         morph->dom = isl_basic_set_remove_dims(morph->dom, type, first, n);
 224
 225         morph->map = isl_mat_drop_cols(morph->map, dom_offset + first, n);
 226
 227         morph->inv = isl_mat_drop_rows(morph->inv, dom_offset + first, n);
 228
 229         if (morph->dom && morph->ran && morph->map && morph->inv)
 230                 return morph;
 231
 232         isl_morph_free(morph);
 233         return NULL;
 234 }
 235
 236 __isl_give isl_morph *isl_morph_remove_ran_dims(__isl_take isl_morph *morph,
 237         enum isl_dim_type type, unsigned first, unsigned n)
 238 {
 239         unsigned ran_offset;
 240
 241         if (n == 0)
 242                 return morph;
 243
 244         morph = isl_morph_cow(morph);
 245         if (!morph)
 246                 return NULL;
 247
 248         ran_offset = 1 + isl_space_offset(morph->ran->dim, type);
 249
 250         morph->ran = isl_basic_set_remove_dims(morph->ran, type, first, n);
 251
 252         morph->map = isl_mat_drop_rows(morph->map, ran_offset + first, n);
 253
 254         morph->inv = isl_mat_drop_cols(morph->inv, ran_offset + first, n);
 255
 256         if (morph->dom && morph->ran && morph->map && morph->inv)
 257                 return morph;
 258
 259         isl_morph_free(morph);
 260         return NULL;
 261 }
 262
 263 /* Project domain of morph onto its parameter domain.
 264  */
 265 __isl_give isl_morph *isl_morph_dom_params(__isl_take isl_morph *morph)
 266 {
 267         unsigned n;
 268
 269         morph = isl_morph_cow(morph);
 270         if (!morph)
 271                 return NULL;
 272         n = isl_basic_set_dim(morph->dom, isl_dim_set);
 273         morph = isl_morph_remove_dom_dims(morph, isl_dim_set, 0, n);
 274         if (!morph)
 275                 return NULL;
 276         morph->dom = isl_basic_set_params(morph->dom);
 277         if (morph->dom)
 278                 return morph;
 279
 280         isl_morph_free(morph);
 281         return NULL;
 282 }
 283
 284 /* Project range of morph onto its parameter domain.
 285  */
 286 __isl_give isl_morph *isl_morph_ran_params(__isl_take isl_morph *morph)
 287 {
 288         unsigned n;
 289
 290         morph = isl_morph_cow(morph);
 291         if (!morph)
 292                 return NULL;
 293         n = isl_basic_set_dim(morph->ran, isl_dim_set);
 294         morph = isl_morph_remove_ran_dims(morph, isl_dim_set, 0, n);
 295         if (!morph)
 296                 return NULL;
 297         morph->ran = isl_basic_set_params(morph->ran);
 298         if (morph->ran)
 299                 return morph;
 300
 301         isl_morph_free(morph);
 302         return NULL;
 303 }
 304
 305 void isl_morph_print_internal(__isl_take isl_morph *morph, FILE *out)
 306 {
 307         if (!morph)
 308                 return;
 309
 310         isl_basic_set_dump(morph->dom);
 311         isl_basic_set_dump(morph->ran);
 312         isl_mat_print_internal(morph->map, out, 4);
 313         isl_mat_print_internal(morph->inv, out, 4);
 314 }
 315
 316 void isl_morph_dump(__isl_take isl_morph *morph)
 317 {
 318         isl_morph_print_internal(morph, stderr);
 319 }
 320
 321 __isl_give isl_morph *isl_morph_identity(__isl_keep isl_basic_set *bset)
 322 {
 323         isl_mat *id;
 324         isl_basic_set *universe;
 325         unsigned total;
 326
 327         if (!bset)
 328                 return NULL;
 329
 330         total = isl_basic_set_total_dim(bset);
 331         id = isl_mat_identity(bset->ctx, 1 + total);
 332         universe = isl_basic_set_universe(isl_space_copy(bset->dim));
 333
 334         return isl_morph_alloc(universe, isl_basic_set_copy(universe),
 335                 id, isl_mat_copy(id));
 336 }
 337
 338 /* Create a(n identity) morphism between empty sets of the same dimension
 339  * a "bset".
 340  */
 341 __isl_give isl_morph *isl_morph_empty(__isl_keep isl_basic_set *bset)
 342 {
 343         isl_mat *id;
 344         isl_basic_set *empty;
 345         unsigned total;
 346
 347         if (!bset)
 348                 return NULL;
 349
 350         total = isl_basic_set_total_dim(bset);
 351         id = isl_mat_identity(bset->ctx, 1 + total);
 352         empty = isl_basic_set_empty(isl_space_copy(bset->dim));
 353
 354         return isl_morph_alloc(empty, isl_basic_set_copy(empty),
 355                 id, isl_mat_copy(id));
 356 }
 357
 358 /* Construct a basic set described by the "n" equalities of "bset" starting
 359  * at "first".
 360  */
 361 static __isl_give isl_basic_set *copy_equalities(__isl_keep isl_basic_set *bset,
 362         unsigned first, unsigned n)
 363 {
 364         int i, k;
 365         isl_basic_set *eq;
 366         unsigned total;
 367
 368         isl_assert(bset->ctx, bset->n_div == 0, return NULL);
 369
 370         total = isl_basic_set_total_dim(bset);
 371         eq = isl_basic_set_alloc_space(isl_space_copy(bset->dim), 0, n, 0);
 372         if (!eq)
 373                 return NULL;
 374         for (i = 0; i < n; ++i) {
 375                 k = isl_basic_set_alloc_equality(eq);
 376                 if (k < 0)
 377                         goto error;
 378                 isl_seq_cpy(eq->eq[k], bset->eq[first + i], 1 + total);
 379         }
 380
 381         return eq;
 382 error:
 383         isl_basic_set_free(eq);
 384         return NULL;
 385 }
 386
 387 /* Given a basic set, exploit the equalities in the basic set to construct
 388  * a morphism that maps the basic set to a lower-dimensional space
 389  * with identifier "id".
 390  * Specifically, the morphism reduces the number of dimensions of type "type".
 391  *
 392  * We first select the equalities of interest, that is those that involve
 393  * variables of type "type" and no later variables.
 394  * Denote those equalities as
 395  *
 396  *              -C(p) + M x = 0
 397  *
 398  * where C(p) depends on the parameters if type == isl_dim_set and
 399  * is a constant if type == isl_dim_param.
 400  *
 401  * Use isl_mat_final_variable_compression to construct a compression
 402  *
 403  *      x = T x'
 404  *
 405  *      x' = Q x
 406  *
 407  * If T is a zero-column matrix, then the set of equality constraints
 408  * do not admit a solution.  In this case, an empty morphism is returned.
 409  *
 410  * Both matrices are extended to map the full original space to the full
 411  * compressed space.
 412  */
 413 __isl_give isl_morph *isl_basic_set_variable_compression_with_id(
 414         __isl_keep isl_basic_set *bset, enum isl_dim_type type,
 415         __isl_keep isl_id *id)
 416 {
 417         unsigned otype;
 418         unsigned ntype;
 419         unsigned orest;
 420         unsigned nrest;
 421         int f_eq, n_eq;
 422         isl_space *space;
 423         isl_mat *E, *Q, *C;
 424         isl_basic_set *dom, *ran;
 425
 426         if (!bset)
 427                 return NULL;
 428
 429         if (isl_basic_set_plain_is_empty(bset))
 430                 return isl_morph_empty(bset);
 431
 432         isl_assert(bset->ctx, bset->n_div == 0, return NULL);
 433
 434         otype = 1 + isl_space_offset(bset->dim, type);
 435         ntype = isl_basic_set_dim(bset, type);
 436         orest = otype + ntype;
 437         nrest = isl_basic_set_total_dim(bset) - (orest - 1);
 438
 439         for (f_eq = 0; f_eq < bset->n_eq; ++f_eq)
 440                 if (isl_seq_first_non_zero(bset->eq[f_eq] + orest, nrest) == -1)
 441                         break;
 442         for (n_eq = 0; f_eq + n_eq < bset->n_eq; ++n_eq)
 443                 if (isl_seq_first_non_zero(bset->eq[f_eq + n_eq] + otype, ntype) == -1)
 444                         break;
 445         if (n_eq == 0)
 446                 return isl_morph_identity(bset);
 447
 448         E = isl_mat_sub_alloc6(bset->ctx, bset->eq, f_eq, n_eq, 0, orest);
 449         C = isl_mat_final_variable_compression(E, otype - 1, &Q);
 450         if (!Q)
 451                 C = isl_mat_free(C);
 452         if (C && C->n_col == 0) {
 453                 isl_mat_free(C);
 454                 isl_mat_free(Q);
 455                 return isl_morph_empty(bset);
 456         }
 457
 458         Q = isl_mat_diagonal(Q, isl_mat_identity(bset->ctx, nrest));
 459         C = isl_mat_diagonal(C, isl_mat_identity(bset->ctx, nrest));
 460
 461         space = isl_space_copy(bset->dim);
 462         space = isl_space_drop_dims(space, type, 0, ntype);
 463         space = isl_space_add_dims(space, type, ntype - n_eq);
 464         space = isl_space_set_tuple_id(space, isl_dim_set, isl_id_copy(id));
 465         ran = isl_basic_set_universe(space);
 466         dom = copy_equalities(bset, f_eq, n_eq);
 467
 468         return isl_morph_alloc(dom, ran, Q, C);
 469 }
 470
 471 /* Given a basic set, exploit the equalities in the basic set to construct
 472  * a morphism that maps the basic set to a lower-dimensional space.
 473  * Specifically, the morphism reduces the number of dimensions of type "type".
 474  */
 475 __isl_give isl_morph *isl_basic_set_variable_compression(
 476         __isl_keep isl_basic_set *bset, enum isl_dim_type type)
 477 {
 478         return isl_basic_set_variable_compression_with_id(bset, type,
 479                                                         &isl_id_none);
 480 }
 481
 482 /* Construct a parameter compression for "bset".
 483  * We basically just call isl_mat_parameter_compression with the right input
 484  * and then extend the resulting matrix to include the variables.
 485  *
 486  * The implementation assumes that "bset" does not have any equalities
 487  * that only involve the parameters and that isl_basic_set_gauss has
 488  * been applied to "bset".
 489  *
 490  * Let the equalities be given as
 491  *
 492  *      B(p) + A x = 0.
 493  *
 494  * We use isl_mat_parameter_compression_ext to compute the compression
 495  *
 496  *      p = T p'.
 497  */
 498 __isl_give isl_morph *isl_basic_set_parameter_compression(
 499         __isl_keep isl_basic_set *bset)
 500 {
 501         unsigned nparam;
 502         unsigned nvar;
 503         unsigned n_div;
 504         int n_eq;
 505         isl_mat *H, *B;
 506         isl_mat *map, *inv;
 507         isl_basic_set *dom, *ran;
 508
 509         if (!bset)
 510                 return NULL;
 511
 512         if (isl_basic_set_plain_is_empty(bset))
 513                 return isl_morph_empty(bset);
 514         if (bset->n_eq == 0)
 515                 return isl_morph_identity(bset);
 516
 517         n_eq = bset->n_eq;
 518         nparam = isl_basic_set_dim(bset, isl_dim_param);
 519         nvar = isl_basic_set_dim(bset, isl_dim_set);
 520         n_div = isl_basic_set_dim(bset, isl_dim_div);
 521
 522         if (isl_seq_first_non_zero(bset->eq[bset->n_eq - 1] + 1 + nparam,
 523                                     nvar + n_div) == -1)
 524                 isl_die(isl_basic_set_get_ctx(bset), isl_error_invalid,
 525                         "input not allowed to have parameter equalities",
 526                         return NULL);
 527         if (n_eq > nvar + n_div)
 528                 isl_die(isl_basic_set_get_ctx(bset), isl_error_invalid,
 529                         "input not gaussed", return NULL);
 530
 531         B = isl_mat_sub_alloc6(bset->ctx, bset->eq, 0, n_eq, 0, 1 + nparam);
 532         H = isl_mat_sub_alloc6(bset->ctx, bset->eq,
 533                                 0, n_eq, 1 + nparam, nvar + n_div);
 534         inv = isl_mat_parameter_compression_ext(B, H);
 535         inv = isl_mat_diagonal(inv, isl_mat_identity(bset->ctx, nvar));
 536         map = isl_mat_right_inverse(isl_mat_copy(inv));
 537
 538         dom = isl_basic_set_universe(isl_space_copy(bset->dim));
 539         ran = isl_basic_set_universe(isl_space_copy(bset->dim));
 540
 541         return isl_morph_alloc(dom, ran, map, inv);
 542 }
 543
 544 /* Add stride constraints to "bset" based on the inverse mapping
 545  * that was plugged in.  In particular, if morph maps x' to x,
 546  * the the constraints of the original input
 547  *
 548  *      A x' + b >= 0
 549  *
 550  * have been rewritten to
 551  *
 552  *      A inv x + b >= 0
 553  *
 554  * However, this substitution may loose information on the integrality of x',
 555  * so we need to impose that
 556  *
 557  *      inv x
 558  *
 559  * is integral.  If inv = B/d, this means that we need to impose that
 560  *
 561  *      B x = 0         mod d
 562  *
 563  * or
 564  *
 565  *      exists alpha in Z^m: B x = d alpha
 566  *
 567  * This function is similar to add_strides in isl_affine_hull.c
 568  */
 569 static __isl_give isl_basic_set *add_strides(__isl_take isl_basic_set *bset,
 570         __isl_keep isl_morph *morph)
 571 {
 572         int i, div, k;
 573         isl_int gcd;
 574
 575         if (isl_int_is_one(morph->inv->row[0][0]))
 576                 return bset;
 577
 578         isl_int_init(gcd);
 579
 580         for (i = 0; 1 + i < morph->inv->n_row; ++i) {
 581                 isl_seq_gcd(morph->inv->row[1 + i], morph->inv->n_col, &gcd);
 582                 if (isl_int_is_divisible_by(gcd, morph->inv->row[0][0]))
 583                         continue;
 584                 div = isl_basic_set_alloc_div(bset);
 585                 if (div < 0)
 586                         goto error;
 587                 isl_int_set_si(bset->div[div][0], 0);
 588                 k = isl_basic_set_alloc_equality(bset);
 589                 if (k < 0)
 590                         goto error;
 591                 isl_seq_cpy(bset->eq[k], morph->inv->row[1 + i],
 592                             morph->inv->n_col);
 593                 isl_seq_clr(bset->eq[k] + morph->inv->n_col, bset->n_div);
 594                 isl_int_set(bset->eq[k][morph->inv->n_col + div],
 595                             morph->inv->row[0][0]);
 596         }
 597
 598         isl_int_clear(gcd);
 599
 600         return bset;
 601 error:
 602         isl_int_clear(gcd);
 603         isl_basic_set_free(bset);
 604         return NULL;
 605 }
 606
 607 /* Apply the morphism to the basic set.
 608  * We basically just compute the preimage of "bset" under the inverse mapping
 609  * in morph, add in stride constraints and intersect with the range
 610  * of the morphism.
 611  */
 612 __isl_give isl_basic_set *isl_morph_basic_set(__isl_take isl_morph *morph,
 613         __isl_take isl_basic_set *bset)
 614 {
 615         isl_basic_set *res = NULL;
 616         isl_mat *mat = NULL;
 617         int i, k;
 618         int max_stride;
 619
 620         if (!morph || !bset)
 621                 goto error;
 622
 623         isl_assert(bset->ctx, isl_space_is_equal(bset->dim, morph->dom->dim),
 624                     goto error);
 625
 626         max_stride = morph->inv->n_row - 1;
 627         if (isl_int_is_one(morph->inv->row[0][0]))
 628                 max_stride = 0;
 629         res = isl_basic_set_alloc_space(isl_space_copy(morph->ran->dim),
 630                 bset->n_div + max_stride, bset->n_eq + max_stride, bset->n_ineq);
 631
 632         for (i = 0; i < bset->n_div; ++i)
 633                 if (isl_basic_set_alloc_div(res) < 0)
 634                         goto error;
 635
 636         mat = isl_mat_sub_alloc6(bset->ctx, bset->eq, 0, bset->n_eq,
 637                                         0, morph->inv->n_row);
 638         mat = isl_mat_product(mat, isl_mat_copy(morph->inv));
 639         if (!mat)
 640                 goto error;
 641         for (i = 0; i < bset->n_eq; ++i) {
 642                 k = isl_basic_set_alloc_equality(res);
 643                 if (k < 0)
 644                         goto error;
 645                 isl_seq_cpy(res->eq[k], mat->row[i], mat->n_col);
 646                 isl_seq_scale(res->eq[k] + mat->n_col, bset->eq[i] + mat->n_col,
 647                                 morph->inv->row[0][0], bset->n_div);
 648         }
 649         isl_mat_free(mat);
 650
 651         mat = isl_mat_sub_alloc6(bset->ctx, bset->ineq, 0, bset->n_ineq,
 652                                         0, morph->inv->n_row);
 653         mat = isl_mat_product(mat, isl_mat_copy(morph->inv));
 654         if (!mat)
 655                 goto error;
 656         for (i = 0; i < bset->n_ineq; ++i) {
 657                 k = isl_basic_set_alloc_inequality(res);
 658                 if (k < 0)
 659                         goto error;
 660                 isl_seq_cpy(res->ineq[k], mat->row[i], mat->n_col);
 661                 isl_seq_scale(res->ineq[k] + mat->n_col,
 662                                 bset->ineq[i] + mat->n_col,
 663                                 morph->inv->row[0][0], bset->n_div);
 664         }
 665         isl_mat_free(mat);
 666
 667         mat = isl_mat_sub_alloc6(bset->ctx, bset->div, 0, bset->n_div,
 668                                         1, morph->inv->n_row);
 669         mat = isl_mat_product(mat, isl_mat_copy(morph->inv));
 670         if (!mat)
 671                 goto error;
 672         for (i = 0; i < bset->n_div; ++i) {
 673                 isl_int_mul(res->div[i][0],
 674                                 morph->inv->row[0][0], bset->div[i][0]);
 675                 isl_seq_cpy(res->div[i] + 1, mat->row[i], mat->n_col);
 676                 isl_seq_scale(res->div[i] + 1 + mat->n_col,
 677                                 bset->div[i] + 1 + mat->n_col,
 678                                 morph->inv->row[0][0], bset->n_div);
 679         }
 680         isl_mat_free(mat);
 681
 682         res = add_strides(res, morph);
 683
 684         if (isl_basic_set_is_rational(bset))
 685                 res = isl_basic_set_set_rational(res);
 686
 687         res = isl_basic_set_simplify(res);
 688         res = isl_basic_set_finalize(res);
 689
 690         res = isl_basic_set_intersect(res, isl_basic_set_copy(morph->ran));
 691
 692         isl_morph_free(morph);
 693         isl_basic_set_free(bset);
 694         return res;
 695 error:
 696         isl_mat_free(mat);
 697         isl_morph_free(morph);
 698         isl_basic_set_free(bset);
 699         isl_basic_set_free(res);
 700         return NULL;
 701 }
 702
 703 /* Apply the morphism to the set.
 704  */
 705 __isl_give isl_set *isl_morph_set(__isl_take isl_morph *morph,
 706         __isl_take isl_set *set)
 707 {
 708         int i;
 709
 710         if (!morph || !set)
 711                 goto error;
 712
 713         isl_assert(set->ctx, isl_space_is_equal(set->dim, morph->dom->dim), goto error);
 714
 715         set = isl_set_cow(set);
 716         if (!set)
 717                 goto error;
 718
 719         isl_space_free(set->dim);
 720         set->dim = isl_space_copy(morph->ran->dim);
 721         if (!set->dim)
 722                 goto error;
 723
 724         for (i = 0; i < set->n; ++i) {
 725                 set->p[i] = isl_morph_basic_set(isl_morph_copy(morph), set->p[i]);
 726                 if (!set->p[i])
 727                         goto error;
 728         }
 729
 730         isl_morph_free(morph);
 731
 732         ISL_F_CLR(set, ISL_SET_NORMALIZED);
 733
 734         return set;
 735 error:
 736         isl_set_free(set);
 737         isl_morph_free(morph);
 738         return NULL;
 739 }
 740
 741 /* Construct a morphism that first does morph2 and then morph1.
 742  */
 743 __isl_give isl_morph *isl_morph_compose(__isl_take isl_morph *morph1,
 744         __isl_take isl_morph *morph2)
 745 {
 746         isl_mat *map, *inv;
 747         isl_basic_set *dom, *ran;
 748
 749         if (!morph1 || !morph2)
 750                 goto error;
 751
 752         map = isl_mat_product(isl_mat_copy(morph1->map), isl_mat_copy(morph2->map));
 753         inv = isl_mat_product(isl_mat_copy(morph2->inv), isl_mat_copy(morph1->inv));
 754         dom = isl_morph_basic_set(isl_morph_inverse(isl_morph_copy(morph2)),
 755                                   isl_basic_set_copy(morph1->dom));
 756         dom = isl_basic_set_intersect(dom, isl_basic_set_copy(morph2->dom));
 757         ran = isl_morph_basic_set(isl_morph_copy(morph1),
 758                                   isl_basic_set_copy(morph2->ran));
 759         ran = isl_basic_set_intersect(ran, isl_basic_set_copy(morph1->ran));
 760
 761         isl_morph_free(morph1);
 762         isl_morph_free(morph2);
 763
 764         return isl_morph_alloc(dom, ran, map, inv);
 765 error:
 766         isl_morph_free(morph1);
 767         isl_morph_free(morph2);
 768         return NULL;
 769 }
 770
 771 __isl_give isl_morph *isl_morph_inverse(__isl_take isl_morph *morph)
 772 {
 773         isl_basic_set *bset;
 774         isl_mat *mat;
 775
 776         morph = isl_morph_cow(morph);
 777         if (!morph)
 778                 return NULL;
 779
 780         bset = morph->dom;
 781         morph->dom = morph->ran;
 782         morph->ran = bset;
 783
 784         mat = morph->map;
 785         morph->map = morph->inv;
 786         morph->inv = mat;
 787
 788         return morph;
 789 }
 790
 791 /* We detect all the equalities first to avoid implicit equalities
 792  * being discovered during the computations.  In particular,
 793  * the compression on the variables could expose additional stride
 794  * constraints on the parameters.  This would result in existentially
 795  * quantified variables after applying the resulting morph, which
 796  * in turn could break invariants of the calling functions.
 797  */
 798 __isl_give isl_morph *isl_basic_set_full_compression(
 799         __isl_keep isl_basic_set *bset)
 800 {
 801         isl_morph *morph, *morph2;
 802
 803         bset = isl_basic_set_copy(bset);
 804         bset = isl_basic_set_detect_equalities(bset);
 805
 806         morph = isl_basic_set_variable_compression(bset, isl_dim_param);
 807         bset = isl_morph_basic_set(isl_morph_copy(morph), bset);
 808
 809         morph2 = isl_basic_set_parameter_compression(bset);
 810         bset = isl_morph_basic_set(isl_morph_copy(morph2), bset);
 811
 812         morph = isl_morph_compose(morph2, morph);
 813
 814         morph2 = isl_basic_set_variable_compression(bset, isl_dim_set);
 815         isl_basic_set_free(bset);
 816
 817         morph = isl_morph_compose(morph2, morph);
 818
 819         return morph;
 820 }
 821
 822 __isl_give isl_vec *isl_morph_vec(__isl_take isl_morph *morph,
 823         __isl_take isl_vec *vec)
 824 {
 825         if (!morph)
 826                 goto error;
 827
 828         vec = isl_mat_vec_product(isl_mat_copy(morph->map), vec);
 829
 830         isl_morph_free(morph);
 831         return vec;
 832 error:
 833         isl_morph_free(morph);
 834         isl_vec_free(vec);
 835         return NULL;
 836 }