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