isl_morph.c

   1 /*
   2  * Copyright 2010      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_morph.h>
  12 #include <isl_seq.h>
  13 #include <isl_map_private.h>
  14 #include <isl_dim_private.h>
  15 #include <isl_equalities.h>
  16
  17 __isl_give isl_morph *isl_morph_alloc(
  18         __isl_take isl_basic_set *dom, __isl_take isl_basic_set *ran,
  19         __isl_take isl_mat *map, __isl_take isl_mat *inv)
  20 {
  21         isl_morph *morph;
  22
  23         if (!dom || !ran || !map || !inv)
  24                 goto error;
  25
  26         morph = isl_alloc_type(dom->ctx, struct isl_morph);
  27         if (!morph)
  28                 goto error;
  29
  30         morph->ref = 1;
  31         morph->dom = dom;
  32         morph->ran = ran;
  33         morph->map = map;
  34         morph->inv = inv;
  35
  36         return morph;
  37 error:
  38         isl_basic_set_free(dom);
  39         isl_basic_set_free(ran);
  40         isl_mat_free(map);
  41         isl_mat_free(inv);
  42         return NULL;
  43 }
  44
  45 __isl_give isl_morph *isl_morph_copy(__isl_keep isl_morph *morph)
  46 {
  47         if (!morph)
  48                 return NULL;
  49
  50         morph->ref++;
  51         return morph;
  52 }
  53
  54 __isl_give isl_morph *isl_morph_dup(__isl_keep isl_morph *morph)
  55 {
  56         if (!morph)
  57                 return NULL;
  58
  59         return isl_morph_alloc(isl_basic_set_copy(morph->dom),
  60                 isl_basic_set_copy(morph->ran),
  61                 isl_mat_copy(morph->map), isl_mat_copy(morph->inv));
  62 }
  63
  64 __isl_give isl_morph *isl_morph_cow(__isl_take isl_morph *morph)
  65 {
  66         if (!morph)
  67                 return NULL;
  68
  69         if (morph->ref == 1)
  70                 return morph;
  71         morph->ref--;
  72         return isl_morph_dup(morph);
  73 }
  74
  75 void isl_morph_free(__isl_take isl_morph *morph)
  76 {
  77         if (!morph)
  78                 return;
  79
  80         if (--morph->ref > 0)
  81                 return;
  82
  83         isl_basic_set_free(morph->dom);
  84         isl_basic_set_free(morph->ran);
  85         isl_mat_free(morph->map);
  86         isl_mat_free(morph->inv);
  87         free(morph);
  88 }
  89
  90 __isl_give isl_dim *isl_morph_get_ran_dim(__isl_keep isl_morph *morph)
  91 {
  92         if (!morph)
  93                 return NULL;
  94
  95         return isl_dim_copy(morph->ran->dim);
  96 }
  97
  98 unsigned isl_morph_dom_dim(__isl_keep isl_morph *morph, enum isl_dim_type type)
  99 {
 100         if (!morph)
 101                 return 0;
 102
 103         return isl_basic_set_dim(morph->dom, type);
 104 }
 105
 106 unsigned isl_morph_ran_dim(__isl_keep isl_morph *morph, enum isl_dim_type type)
 107 {
 108         if (!morph)
 109                 return 0;
 110
 111         return isl_basic_set_dim(morph->ran, type);
 112 }
 113
 114 __isl_give isl_morph *isl_morph_remove_dom_dims(__isl_take isl_morph *morph,
 115         enum isl_dim_type type, unsigned first, unsigned n)
 116 {
 117         unsigned dom_offset;
 118
 119         if (n == 0)
 120                 return morph;
 121
 122         morph = isl_morph_cow(morph);
 123         if (!morph)
 124                 return NULL;
 125
 126         dom_offset = 1 + isl_dim_offset(morph->dom->dim, type);
 127
 128         morph->dom = isl_basic_set_remove(morph->dom, type, first, n);
 129
 130         morph->map = isl_mat_drop_cols(morph->map, dom_offset + first, n);
 131
 132         morph->inv = isl_mat_drop_rows(morph->inv, dom_offset + first, n);
 133
 134         if (morph->dom && morph->ran && morph->map && morph->inv)
 135                 return morph;
 136
 137         isl_morph_free(morph);
 138         return NULL;
 139 }
 140
 141 __isl_give isl_morph *isl_morph_remove_ran_dims(__isl_take isl_morph *morph,
 142         enum isl_dim_type type, unsigned first, unsigned n)
 143 {
 144         unsigned ran_offset;
 145
 146         if (n == 0)
 147                 return morph;
 148
 149         morph = isl_morph_cow(morph);
 150         if (!morph)
 151                 return NULL;
 152
 153         ran_offset = 1 + isl_dim_offset(morph->ran->dim, type);
 154
 155         morph->ran = isl_basic_set_remove(morph->ran, type, first, n);
 156
 157         morph->map = isl_mat_drop_rows(morph->map, ran_offset + first, n);
 158
 159         morph->inv = isl_mat_drop_cols(morph->inv, ran_offset + first, n);
 160
 161         if (morph->dom && morph->ran && morph->map && morph->inv)
 162                 return morph;
 163
 164         isl_morph_free(morph);
 165         return NULL;
 166 }
 167
 168 void isl_morph_dump(__isl_take isl_morph *morph, FILE *out)
 169 {
 170         if (!morph)
 171                 return;
 172
 173         isl_basic_set_print(morph->dom, out, 0, "", "", ISL_FORMAT_ISL);
 174         isl_basic_set_print(morph->ran, out, 0, "", "", ISL_FORMAT_ISL);
 175         isl_mat_dump(morph->map, out, 4);
 176         isl_mat_dump(morph->inv, out, 4);
 177 }
 178
 179 __isl_give isl_morph *isl_morph_identity(__isl_keep isl_basic_set *bset)
 180 {
 181         isl_mat *id;
 182         isl_basic_set *universe;
 183         unsigned total;
 184
 185         if (!bset)
 186                 return NULL;
 187
 188         total = isl_basic_set_total_dim(bset);
 189         id = isl_mat_identity(bset->ctx, 1 + total);
 190         universe = isl_basic_set_universe(isl_dim_copy(bset->dim));
 191
 192         return isl_morph_alloc(universe, isl_basic_set_copy(universe),
 193                 id, isl_mat_copy(id));
 194 }
 195
 196 /* Create a(n identity) morphism between empty sets of the same dimension
 197  * a "bset".
 198  */
 199 __isl_give isl_morph *isl_morph_empty(__isl_keep isl_basic_set *bset)
 200 {
 201         isl_mat *id;
 202         isl_basic_set *empty;
 203         unsigned total;
 204
 205         if (!bset)
 206                 return NULL;
 207
 208         total = isl_basic_set_total_dim(bset);
 209         id = isl_mat_identity(bset->ctx, 1 + total);
 210         empty = isl_basic_set_empty(isl_dim_copy(bset->dim));
 211
 212         return isl_morph_alloc(empty, isl_basic_set_copy(empty),
 213                 id, isl_mat_copy(id));
 214 }
 215
 216 /* Given a matrix that maps a (possibly) parametric domain to
 217  * a parametric domain, add in rows that map the "nparam" parameters onto
 218  * themselves.
 219  */
 220 static __isl_give isl_mat *insert_parameter_rows(__isl_take isl_mat *mat,
 221         unsigned nparam)
 222 {
 223         int i;
 224
 225         if (nparam == 0)
 226                 return mat;
 227         if (!mat)
 228                 return NULL;
 229
 230         mat = isl_mat_insert_rows(mat, 1, nparam);
 231         if (!mat)
 232                 return NULL;
 233
 234         for (i = 0; i < nparam; ++i) {
 235                 isl_seq_clr(mat->row[1 + i], mat->n_col);
 236                 isl_int_set(mat->row[1 + i][1 + i], mat->row[0][0]);
 237         }
 238
 239         return mat;
 240 }
 241
 242 /* Construct a basic set described by the "n" equalities of "bset" starting
 243  * at "first".
 244  */
 245 static __isl_give isl_basic_set *copy_equalities(__isl_keep isl_basic_set *bset,
 246         unsigned first, unsigned n)
 247 {
 248         int i, k;
 249         isl_basic_set *eq;
 250         unsigned total;
 251
 252         isl_assert(bset->ctx, bset->n_div == 0, return NULL);
 253
 254         total = isl_basic_set_total_dim(bset);
 255         eq = isl_basic_set_alloc_dim(isl_dim_copy(bset->dim), 0, n, 0);
 256         if (!eq)
 257                 return NULL;
 258         for (i = 0; i < n; ++i) {
 259                 k = isl_basic_set_alloc_equality(eq);
 260                 if (k < 0)
 261                         goto error;
 262                 isl_seq_cpy(eq->eq[k], bset->eq[first + k], 1 + total);
 263         }
 264
 265         return eq;
 266 error:
 267         isl_basic_set_free(eq);
 268         return NULL;
 269 }
 270
 271 /* Given a basic set, exploit the equalties in the a basic set to construct
 272  * a morphishm that maps the basic set to a lower-dimensional space.
 273  * Specifically, the morphism reduces the number of dimensions of type "type".
 274  *
 275  * This function is a slight generalization of isl_mat_variable_compression
 276  * in that it allows the input to be parametric and that it allows for the
 277  * compression of either parameters or set variables.
 278  *
 279  * We first select the equalities of interest, that is those that involve
 280  * variables of type "type" and no later variables.
 281  * Denote those equalities as
 282  *
 283  *              -C(p) + M x = 0
 284  *
 285  * where C(p) depends on the parameters if type == isl_dim_set and
 286  * is a constant if type == isl_dim_param.
 287  *
 288  * First compute the (left) Hermite normal form of M,
 289  *
 290  *              M [U1 U2] = M U = H = [H1 0]
 291  * or
 292  *                            M = H Q = [H1 0] [Q1]
 293  *                                             [Q2]
 294  *
 295  * with U, Q unimodular, Q = U^{-1} (and H lower triangular).
 296  * Define the transformed variables as
 297  *
 298  *              x = [U1 U2] [ x1' ] = [U1 U2] [Q1] x
 299  *                          [ x2' ]           [Q2]
 300  *
 301  * The equalities then become
 302  *
 303  *              -C(p) + H1 x1' = 0   or   x1' = H1^{-1} C(p) = C'(p)
 304  *
 305  * If the denominator of the constant term does not divide the
 306  * the common denominator of the parametric terms, then every
 307  * integer point is mapped to a non-integer point and then the original set has no
 308  * integer solutions (since the x' are a unimodular transformation
 309  * of the x).  In this case, an empty morphism is returned.
 310  * Otherwise, the transformation is given by
 311  *
 312  *              x = U1 H1^{-1} C(p) + U2 x2'
 313  *
 314  * The inverse transformation is simply
 315  *
 316  *              x2' = Q2 x
 317  *
 318  * Both matrices are extended to map the full original space to the full
 319  * compressed space.
 320  */
 321 __isl_give isl_morph *isl_basic_set_variable_compression(
 322         __isl_keep isl_basic_set *bset, enum isl_dim_type type)
 323 {
 324         unsigned otype;
 325         unsigned ntype;
 326         unsigned orest;
 327         unsigned nrest;
 328         unsigned total;
 329         int f_eq, n_eq;
 330         isl_dim *dim;
 331         isl_mat *H, *U, *Q, *C = NULL, *H1, *U1, *U2;
 332         isl_basic_set *dom, *ran;
 333
 334         if (!bset)
 335                 return NULL;
 336
 337         if (isl_basic_set_fast_is_empty(bset))
 338                 return isl_morph_empty(bset);
 339
 340         isl_assert(bset->ctx, bset->n_div == 0, return NULL);
 341
 342         otype = 1 + isl_dim_offset(bset->dim, type);
 343         ntype = isl_basic_set_dim(bset, type);
 344         orest = otype + ntype;
 345         nrest = isl_basic_set_total_dim(bset) - (orest - 1);
 346
 347         for (f_eq = 0; f_eq < bset->n_eq; ++f_eq)
 348                 if (isl_seq_first_non_zero(bset->eq[f_eq] + orest, nrest) == -1)
 349                         break;
 350         for (n_eq = 0; f_eq + n_eq < bset->n_eq; ++n_eq)
 351                 if (isl_seq_first_non_zero(bset->eq[f_eq + n_eq] + otype, ntype) == -1)
 352                         break;
 353         if (n_eq == 0)
 354                 return isl_morph_identity(bset);
 355
 356         H = isl_mat_sub_alloc(bset->ctx, bset->eq, f_eq, n_eq, otype, ntype);
 357         H = isl_mat_left_hermite(H, 0, &U, &Q);
 358         if (!H || !U || !Q)
 359                 goto error;
 360         Q = isl_mat_drop_rows(Q, 0, n_eq);
 361         Q = isl_mat_diagonal(isl_mat_identity(bset->ctx, otype), Q);
 362         Q = isl_mat_diagonal(Q, isl_mat_identity(bset->ctx, nrest));
 363         C = isl_mat_alloc(bset->ctx, 1 + n_eq, otype);
 364         if (!C)
 365                 goto error;
 366         isl_int_set_si(C->row[0][0], 1);
 367         isl_seq_clr(C->row[0] + 1, otype - 1);
 368         isl_mat_sub_neg(C->ctx, C->row + 1, bset->eq + f_eq, n_eq, 0, 0, otype);
 369         H1 = isl_mat_sub_alloc(H->ctx, H->row, 0, H->n_row, 0, H->n_row);
 370         H1 = isl_mat_lin_to_aff(H1);
 371         C = isl_mat_inverse_product(H1, C);
 372         if (!C)
 373                 goto error;
 374         isl_mat_free(H);
 375
 376         if (!isl_int_is_one(C->row[0][0])) {
 377                 int i;
 378                 isl_int g;
 379
 380                 isl_int_init(g);
 381                 for (i = 0; i < n_eq; ++i) {
 382                         isl_seq_gcd(C->row[1 + i] + 1, otype - 1, &g);
 383                         isl_int_gcd(g, g, C->row[0][0]);
 384                         if (!isl_int_is_divisible_by(C->row[1 + i][0], g))
 385                                 break;
 386                 }
 387                 isl_int_clear(g);
 388
 389                 if (i < n_eq) {
 390                         isl_mat_free(C);
 391                         isl_mat_free(U);
 392                         isl_mat_free(Q);
 393                         return isl_morph_empty(bset);
 394                 }
 395
 396                 C = isl_mat_normalize(C);
 397         }
 398
 399         U1 = isl_mat_sub_alloc(U->ctx, U->row, 0, U->n_row, 0, n_eq);
 400         U1 = isl_mat_lin_to_aff(U1);
 401         U2 = isl_mat_sub_alloc(U->ctx, U->row, 0, U->n_row, n_eq, U->n_row - n_eq);
 402         U2 = isl_mat_lin_to_aff(U2);
 403         isl_mat_free(U);
 404
 405         C = isl_mat_product(U1, C);
 406         C = isl_mat_aff_direct_sum(C, U2);
 407         C = insert_parameter_rows(C, otype - 1);
 408         C = isl_mat_diagonal(C, isl_mat_identity(bset->ctx, nrest));
 409
 410         dim = isl_dim_copy(bset->dim);
 411         dim = isl_dim_drop(dim, type, 0, ntype);
 412         dim = isl_dim_add(dim, type, ntype - n_eq);
 413         ran = isl_basic_set_universe(dim);
 414         dom = copy_equalities(bset, f_eq, n_eq);
 415
 416         return isl_morph_alloc(dom, ran, Q, C);
 417 error:
 418         isl_mat_free(C);
 419         isl_mat_free(H);
 420         isl_mat_free(U);
 421         isl_mat_free(Q);
 422         return NULL;
 423 }
 424
 425 /* Construct a parameter compression for "bset".
 426  * We basically just call isl_mat_parameter_compression with the right input
 427  * and then extend the resulting matrix to include the variables.
 428  *
 429  * Let the equalities be given as
 430  *
 431  *      B(p) + A x = 0
 432  *
 433  * and let [H 0] be the Hermite Normal Form of A, then
 434  *
 435  *      H^-1 B(p)
 436  *
 437  * needs to be integer, so we impose that each row is divisible by
 438  * the denominator.
 439  */
 440 __isl_give isl_morph *isl_basic_set_parameter_compression(
 441         __isl_keep isl_basic_set *bset)
 442 {
 443         unsigned nparam;
 444         unsigned nvar;
 445         int n_eq;
 446         isl_mat *H, *B;
 447         isl_vec *d;
 448         isl_mat *map, *inv;
 449         isl_basic_set *dom, *ran;
 450
 451         if (!bset)
 452                 return NULL;
 453
 454         if (isl_basic_set_fast_is_empty(bset))
 455                 return isl_morph_empty(bset);
 456         if (bset->n_eq == 0)
 457                 return isl_morph_identity(bset);
 458
 459         isl_assert(bset->ctx, bset->n_div == 0, return NULL);
 460
 461         n_eq = bset->n_eq;
 462         nparam = isl_basic_set_dim(bset, isl_dim_param);
 463         nvar = isl_basic_set_dim(bset, isl_dim_set);
 464
 465         isl_assert(bset->ctx, n_eq <= nvar, return NULL);
 466
 467         d = isl_vec_alloc(bset->ctx, n_eq);
 468         B = isl_mat_sub_alloc(bset->ctx, bset->eq, 0, n_eq, 0, 1 + nparam);
 469         H = isl_mat_sub_alloc(bset->ctx, bset->eq, 0, n_eq, 1 + nparam, nvar);
 470         H = isl_mat_left_hermite(H, 0, NULL, NULL);
 471         H = isl_mat_drop_cols(H, n_eq, nvar - n_eq);
 472         H = isl_mat_lin_to_aff(H);
 473         H = isl_mat_right_inverse(H);
 474         if (!H || !d)
 475                 goto error;
 476         isl_seq_set(d->el, H->row[0][0], d->size);
 477         H = isl_mat_drop_rows(H, 0, 1);
 478         H = isl_mat_drop_cols(H, 0, 1);
 479         B = isl_mat_product(H, B);
 480         inv = isl_mat_parameter_compression(B, d);
 481         inv = isl_mat_diagonal(inv, isl_mat_identity(bset->ctx, nvar));
 482         map = isl_mat_right_inverse(isl_mat_copy(inv));
 483
 484         dom = isl_basic_set_universe(isl_dim_copy(bset->dim));
 485         ran = isl_basic_set_universe(isl_dim_copy(bset->dim));
 486
 487         return isl_morph_alloc(dom, ran, map, inv);
 488 error:
 489         isl_mat_free(H);
 490         isl_mat_free(B);
 491         isl_vec_free(d);
 492         return NULL;
 493 }
 494
 495 /* Add stride constraints to "bset" based on the inverse mapping
 496  * that was plugged in.  In particular, if morph maps x' to x,
 497  * the the constraints of the original input
 498  *
 499  *      A x' + b >= 0
 500  *
 501  * have been rewritten to
 502  *
 503  *      A inv x + b >= 0
 504  *
 505  * However, this substitution may loose information on the integrality of x',
 506  * so we need to impose that
 507  *
 508  *      inv x
 509  *
 510  * is integral.  If inv = B/d, this means that we need to impose that
 511  *
 512  *      B x = 0         mod d
 513  *
 514  * or
 515  *
 516  *      exists alpha in Z^m: B x = d alpha
 517  *
 518  */
 519 static __isl_give isl_basic_set *add_strides(__isl_take isl_basic_set *bset,
 520         __isl_keep isl_morph *morph)
 521 {
 522         int i, div, k;
 523         isl_int gcd;
 524
 525         if (isl_int_is_one(morph->inv->row[0][0]))
 526                 return bset;
 527
 528         isl_int_init(gcd);
 529
 530         for (i = 0; 1 + i < morph->inv->n_row; ++i) {
 531                 isl_seq_gcd(morph->inv->row[1 + i], morph->inv->n_col, &gcd);
 532                 if (isl_int_is_divisible_by(gcd, morph->inv->row[0][0]))
 533                         continue;
 534                 div = isl_basic_set_alloc_div(bset);
 535                 if (div < 0)
 536                         goto error;
 537                 k = isl_basic_set_alloc_equality(bset);
 538                 if (k < 0)
 539                         goto error;
 540                 isl_seq_cpy(bset->eq[k], morph->inv->row[1 + i],
 541                             morph->inv->n_col);
 542                 isl_seq_clr(bset->eq[k] + morph->inv->n_col, bset->n_div);
 543                 isl_int_set(bset->eq[k][morph->inv->n_col + div],
 544                             morph->inv->row[0][0]);
 545         }
 546
 547         isl_int_clear(gcd);
 548
 549         return bset;
 550 error:
 551         isl_int_clear(gcd);
 552         isl_basic_set_free(bset);
 553         return NULL;
 554 }
 555
 556 /* Apply the morphism to the basic set.
 557  * We basically just compute the preimage of "bset" under the inverse mapping
 558  * in morph, add in stride constraints and intersect with the range
 559  * of the morphism.
 560  */
 561 __isl_give isl_basic_set *isl_morph_basic_set(__isl_take isl_morph *morph,
 562         __isl_take isl_basic_set *bset)
 563 {
 564         isl_basic_set *res = NULL;
 565         isl_mat *mat = NULL;
 566         int i, k;
 567         int max_stride;
 568
 569         if (!morph || !bset)
 570                 goto error;
 571
 572         isl_assert(bset->ctx, isl_dim_equal(bset->dim, morph->dom->dim),
 573                     goto error);
 574
 575         max_stride = morph->inv->n_row - 1;
 576         if (isl_int_is_one(morph->inv->row[0][0]))
 577                 max_stride = 0;
 578         res = isl_basic_set_alloc_dim(isl_dim_copy(morph->ran->dim),
 579                 bset->n_div + max_stride, bset->n_eq + max_stride, bset->n_ineq);
 580
 581         for (i = 0; i < bset->n_div; ++i)
 582                 if (isl_basic_set_alloc_div(res) < 0)
 583                         goto error;
 584
 585         mat = isl_mat_sub_alloc(bset->ctx, bset->eq, 0, bset->n_eq,
 586                                         0, morph->inv->n_row);
 587         mat = isl_mat_product(mat, isl_mat_copy(morph->inv));
 588         if (!mat)
 589                 goto error;
 590         for (i = 0; i < bset->n_eq; ++i) {
 591                 k = isl_basic_set_alloc_equality(res);
 592                 if (k < 0)
 593                         goto error;
 594                 isl_seq_cpy(res->eq[k], mat->row[i], mat->n_col);
 595                 isl_seq_scale(res->eq[k] + mat->n_col, bset->eq[i] + mat->n_col,
 596                                 morph->inv->row[0][0], bset->n_div);
 597         }
 598         isl_mat_free(mat);
 599
 600         mat = isl_mat_sub_alloc(bset->ctx, bset->ineq, 0, bset->n_ineq,
 601                                         0, morph->inv->n_row);
 602         mat = isl_mat_product(mat, isl_mat_copy(morph->inv));
 603         if (!mat)
 604                 goto error;
 605         for (i = 0; i < bset->n_ineq; ++i) {
 606                 k = isl_basic_set_alloc_inequality(res);
 607                 if (k < 0)
 608                         goto error;
 609                 isl_seq_cpy(res->ineq[k], mat->row[i], mat->n_col);
 610                 isl_seq_scale(res->ineq[k] + mat->n_col,
 611                                 bset->ineq[i] + mat->n_col,
 612                                 morph->inv->row[0][0], bset->n_div);
 613         }
 614         isl_mat_free(mat);
 615
 616         mat = isl_mat_sub_alloc(bset->ctx, bset->div, 0, bset->n_div,
 617                                         1, morph->inv->n_row);
 618         mat = isl_mat_product(mat, isl_mat_copy(morph->inv));
 619         if (!mat)
 620                 goto error;
 621         for (i = 0; i < bset->n_div; ++i) {
 622                 isl_int_mul(res->div[i][0],
 623                                 morph->inv->row[0][0], bset->div[i][0]);
 624                 isl_seq_cpy(res->div[i] + 1, mat->row[i], mat->n_col);
 625                 isl_seq_scale(res->div[i] + 1 + mat->n_col,
 626                                 bset->div[i] + 1 + mat->n_col,
 627                                 morph->inv->row[0][0], bset->n_div);
 628         }
 629         isl_mat_free(mat);
 630
 631         res = add_strides(res, morph);
 632
 633         res = isl_basic_set_simplify(res);
 634         res = isl_basic_set_finalize(res);
 635
 636         res = isl_basic_set_intersect(res, isl_basic_set_copy(morph->ran));
 637
 638         isl_morph_free(morph);
 639         isl_basic_set_free(bset);
 640         return res;
 641 error:
 642         isl_mat_free(mat);
 643         isl_morph_free(morph);
 644         isl_basic_set_free(bset);
 645         isl_basic_set_free(res);
 646         return NULL;
 647 }
 648
 649 /* Apply the morphism to the set.
 650  */
 651 __isl_give isl_set *isl_morph_set(__isl_take isl_morph *morph,
 652         __isl_take isl_set *set)
 653 {
 654         int i;
 655
 656         if (!morph || !set)
 657                 goto error;
 658
 659         isl_assert(set->ctx, isl_dim_equal(set->dim, morph->dom->dim), goto error);
 660
 661         set = isl_set_cow(set);
 662         if (!set)
 663                 goto error;
 664
 665         isl_dim_free(set->dim);
 666         set->dim = isl_dim_copy(morph->ran->dim);
 667         if (!set->dim)
 668                 goto error;
 669
 670         for (i = 0; i < set->n; ++i) {
 671                 set->p[i] = isl_morph_basic_set(isl_morph_copy(morph), set->p[i]);
 672                 if (!set->p[i])
 673                         goto error;
 674         }
 675
 676         isl_morph_free(morph);
 677
 678         ISL_F_CLR(set, ISL_SET_NORMALIZED);
 679
 680         return set;
 681 error:
 682         isl_set_free(set);
 683         isl_morph_free(morph);
 684         return NULL;
 685 }
 686
 687 /* Construct a morphism that first does morph2 and then morph1.
 688  */
 689 __isl_give isl_morph *isl_morph_compose(__isl_take isl_morph *morph1,
 690         __isl_take isl_morph *morph2)
 691 {
 692         isl_mat *map, *inv;
 693         isl_basic_set *dom, *ran;
 694
 695         if (!morph1 || !morph2)
 696                 goto error;
 697
 698         map = isl_mat_product(isl_mat_copy(morph1->map), isl_mat_copy(morph2->map));
 699         inv = isl_mat_product(isl_mat_copy(morph2->inv), isl_mat_copy(morph1->inv));
 700         dom = isl_morph_basic_set(isl_morph_inverse(isl_morph_copy(morph2)),
 701                                   isl_basic_set_copy(morph1->dom));
 702         dom = isl_basic_set_intersect(dom, isl_basic_set_copy(morph2->dom));
 703         ran = isl_morph_basic_set(isl_morph_copy(morph1),
 704                                   isl_basic_set_copy(morph2->ran));
 705         ran = isl_basic_set_intersect(ran, isl_basic_set_copy(morph1->ran));
 706
 707         isl_morph_free(morph1);
 708         isl_morph_free(morph2);
 709
 710         return isl_morph_alloc(dom, ran, map, inv);
 711 error:
 712         isl_morph_free(morph1);
 713         isl_morph_free(morph2);
 714         return NULL;
 715 }
 716
 717 __isl_give isl_morph *isl_morph_inverse(__isl_take isl_morph *morph)
 718 {
 719         isl_basic_set *bset;
 720         isl_mat *mat;
 721
 722         morph = isl_morph_cow(morph);
 723         if (!morph)
 724                 return NULL;
 725
 726         bset = morph->dom;
 727         morph->dom = morph->ran;
 728         morph->ran = bset;
 729
 730         mat = morph->map;
 731         morph->map = morph->inv;
 732         morph->inv = mat;
 733
 734         return morph;
 735 }
 736
 737 __isl_give isl_morph *isl_basic_set_full_compression(
 738         __isl_keep isl_basic_set *bset)
 739 {
 740         isl_morph *morph, *morph2;
 741
 742         bset = isl_basic_set_copy(bset);
 743
 744         morph = isl_basic_set_variable_compression(bset, isl_dim_param);
 745         bset = isl_morph_basic_set(isl_morph_copy(morph), bset);
 746
 747         morph2 = isl_basic_set_parameter_compression(bset);
 748         bset = isl_morph_basic_set(isl_morph_copy(morph2), bset);
 749
 750         morph = isl_morph_compose(morph2, morph);
 751
 752         morph2 = isl_basic_set_variable_compression(bset, isl_dim_set);
 753         isl_basic_set_free(bset);
 754
 755         morph = isl_morph_compose(morph2, morph);
 756
 757         return morph;
 758 }