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_map_private.h>
  12 #include <isl_morph.h>
  13 #include <isl/seq.h>
  14 #include <isl_mat_private.h>
  15 #include <isl_space_private.h>
  16 #include <isl_equalities.h>
  17
  18 __isl_give isl_morph *isl_morph_alloc(
  19         __isl_take isl_basic_set *dom, __isl_take isl_basic_set *ran,
  20         __isl_take isl_mat *map, __isl_take isl_mat *inv)
  21 {
  22         isl_morph *morph;
  23
  24         if (!dom || !ran || !map || !inv)
  25                 goto error;
  26
  27         morph = isl_alloc_type(dom->ctx, struct isl_morph);
  28         if (!morph)
  29                 goto error;
  30
  31         morph->ref = 1;
  32         morph->dom = dom;
  33         morph->ran = ran;
  34         morph->map = map;
  35         morph->inv = inv;
  36
  37         return morph;
  38 error:
  39         isl_basic_set_free(dom);
  40         isl_basic_set_free(ran);
  41         isl_mat_free(map);
  42         isl_mat_free(inv);
  43         return NULL;
  44 }
  45
  46 __isl_give isl_morph *isl_morph_copy(__isl_keep isl_morph *morph)
  47 {
  48         if (!morph)
  49                 return NULL;
  50
  51         morph->ref++;
  52         return morph;
  53 }
  54
  55 __isl_give isl_morph *isl_morph_dup(__isl_keep isl_morph *morph)
  56 {
  57         if (!morph)
  58                 return NULL;
  59
  60         return isl_morph_alloc(isl_basic_set_copy(morph->dom),
  61                 isl_basic_set_copy(morph->ran),
  62                 isl_mat_copy(morph->map), isl_mat_copy(morph->inv));
  63 }
  64
  65 __isl_give isl_morph *isl_morph_cow(__isl_take isl_morph *morph)
  66 {
  67         if (!morph)
  68                 return NULL;
  69
  70         if (morph->ref == 1)
  71                 return morph;
  72         morph->ref--;
  73         return isl_morph_dup(morph);
  74 }
  75
  76 void isl_morph_free(__isl_take isl_morph *morph)
  77 {
  78         if (!morph)
  79                 return;
  80
  81         if (--morph->ref > 0)
  82                 return;
  83
  84         isl_basic_set_free(morph->dom);
  85         isl_basic_set_free(morph->ran);
  86         isl_mat_free(morph->map);
  87         isl_mat_free(morph->inv);
  88         free(morph);
  89 }
  90
  91 __isl_give isl_space *isl_morph_get_ran_space(__isl_keep isl_morph *morph)
  92 {
  93         if (!morph)
  94                 return NULL;
  95
  96         return isl_space_copy(morph->ran->dim);
  97 }
  98
  99 unsigned isl_morph_dom_dim(__isl_keep isl_morph *morph, enum isl_dim_type type)
 100 {
 101         if (!morph)
 102                 return 0;
 103
 104         return isl_basic_set_dim(morph->dom, type);
 105 }
 106
 107 unsigned isl_morph_ran_dim(__isl_keep isl_morph *morph, enum isl_dim_type type)
 108 {
 109         if (!morph)
 110                 return 0;
 111
 112         return isl_basic_set_dim(morph->ran, type);
 113 }
 114
 115 __isl_give isl_morph *isl_morph_remove_dom_dims(__isl_take isl_morph *morph,
 116         enum isl_dim_type type, unsigned first, unsigned n)
 117 {
 118         unsigned dom_offset;
 119
 120         if (n == 0)
 121                 return morph;
 122
 123         morph = isl_morph_cow(morph);
 124         if (!morph)
 125                 return NULL;
 126
 127         dom_offset = 1 + isl_space_offset(morph->dom->dim, type);
 128
 129         morph->dom = isl_basic_set_remove_dims(morph->dom, type, first, n);
 130
 131         morph->map = isl_mat_drop_cols(morph->map, dom_offset + first, n);
 132
 133         morph->inv = isl_mat_drop_rows(morph->inv, dom_offset + first, n);
 134
 135         if (morph->dom && morph->ran && morph->map && morph->inv)
 136                 return morph;
 137
 138         isl_morph_free(morph);
 139         return NULL;
 140 }
 141
 142 __isl_give isl_morph *isl_morph_remove_ran_dims(__isl_take isl_morph *morph,
 143         enum isl_dim_type type, unsigned first, unsigned n)
 144 {
 145         unsigned ran_offset;
 146
 147         if (n == 0)
 148                 return morph;
 149
 150         morph = isl_morph_cow(morph);
 151         if (!morph)
 152                 return NULL;
 153
 154         ran_offset = 1 + isl_space_offset(morph->ran->dim, type);
 155
 156         morph->ran = isl_basic_set_remove_dims(morph->ran, type, first, n);
 157
 158         morph->map = isl_mat_drop_rows(morph->map, ran_offset + first, n);
 159
 160         morph->inv = isl_mat_drop_cols(morph->inv, ran_offset + first, n);
 161
 162         if (morph->dom && morph->ran && morph->map && morph->inv)
 163                 return morph;
 164
 165         isl_morph_free(morph);
 166         return NULL;
 167 }
 168
 169 /* Project domain of morph onto its parameter domain.
 170  */
 171 __isl_give isl_morph *isl_morph_dom_params(__isl_take isl_morph *morph)
 172 {
 173         unsigned n;
 174
 175         if (!morph)
 176                 return NULL;
 177         n = isl_basic_set_dim(morph->dom, isl_dim_set);
 178         morph = isl_morph_remove_dom_dims(morph, isl_dim_set, 0, n);
 179         if (!morph)
 180                 return NULL;
 181         morph->dom = isl_basic_set_params(morph->dom);
 182         if (morph->dom)
 183                 return morph;
 184
 185         isl_morph_free(morph);
 186         return NULL;
 187 }
 188
 189 /* Project range of morph onto its parameter domain.
 190  */
 191 __isl_give isl_morph *isl_morph_ran_params(__isl_take isl_morph *morph)
 192 {
 193         unsigned n;
 194
 195         if (!morph)
 196                 return NULL;
 197         n = isl_basic_set_dim(morph->ran, isl_dim_set);
 198         morph = isl_morph_remove_ran_dims(morph, isl_dim_set, 0, n);
 199         if (!morph)
 200                 return NULL;
 201         morph->ran = isl_basic_set_params(morph->ran);
 202         if (morph->ran)
 203                 return morph;
 204
 205         isl_morph_free(morph);
 206         return NULL;
 207 }
 208
 209 void isl_morph_print_internal(__isl_take isl_morph *morph, FILE *out)
 210 {
 211         if (!morph)
 212                 return;
 213
 214         isl_basic_set_print(morph->dom, out, 0, "", "", ISL_FORMAT_ISL);
 215         isl_basic_set_print(morph->ran, out, 0, "", "", ISL_FORMAT_ISL);
 216         isl_mat_print_internal(morph->map, out, 4);
 217         isl_mat_print_internal(morph->inv, out, 4);
 218 }
 219
 220 void isl_morph_dump(__isl_take isl_morph *morph)
 221 {
 222         isl_morph_print_internal(morph, stderr);
 223 }
 224
 225 __isl_give isl_morph *isl_morph_identity(__isl_keep isl_basic_set *bset)
 226 {
 227         isl_mat *id;
 228         isl_basic_set *universe;
 229         unsigned total;
 230
 231         if (!bset)
 232                 return NULL;
 233
 234         total = isl_basic_set_total_dim(bset);
 235         id = isl_mat_identity(bset->ctx, 1 + total);
 236         universe = isl_basic_set_universe(isl_space_copy(bset->dim));
 237
 238         return isl_morph_alloc(universe, isl_basic_set_copy(universe),
 239                 id, isl_mat_copy(id));
 240 }
 241
 242 /* Create a(n identity) morphism between empty sets of the same dimension
 243  * a "bset".
 244  */
 245 __isl_give isl_morph *isl_morph_empty(__isl_keep isl_basic_set *bset)
 246 {
 247         isl_mat *id;
 248         isl_basic_set *empty;
 249         unsigned total;
 250
 251         if (!bset)
 252                 return NULL;
 253
 254         total = isl_basic_set_total_dim(bset);
 255         id = isl_mat_identity(bset->ctx, 1 + total);
 256         empty = isl_basic_set_empty(isl_space_copy(bset->dim));
 257
 258         return isl_morph_alloc(empty, isl_basic_set_copy(empty),
 259                 id, isl_mat_copy(id));
 260 }
 261
 262 /* Given a matrix that maps a (possibly) parametric domain to
 263  * a parametric domain, add in rows that map the "nparam" parameters onto
 264  * themselves.
 265  */
 266 static __isl_give isl_mat *insert_parameter_rows(__isl_take isl_mat *mat,
 267         unsigned nparam)
 268 {
 269         int i;
 270
 271         if (nparam == 0)
 272                 return mat;
 273         if (!mat)
 274                 return NULL;
 275
 276         mat = isl_mat_insert_rows(mat, 1, nparam);
 277         if (!mat)
 278                 return NULL;
 279
 280         for (i = 0; i < nparam; ++i) {
 281                 isl_seq_clr(mat->row[1 + i], mat->n_col);
 282                 isl_int_set(mat->row[1 + i][1 + i], mat->row[0][0]);
 283         }
 284
 285         return mat;
 286 }
 287
 288 /* Construct a basic set described by the "n" equalities of "bset" starting
 289  * at "first".
 290  */
 291 static __isl_give isl_basic_set *copy_equalities(__isl_keep isl_basic_set *bset,
 292         unsigned first, unsigned n)
 293 {
 294         int i, k;
 295         isl_basic_set *eq;
 296         unsigned total;
 297
 298         isl_assert(bset->ctx, bset->n_div == 0, return NULL);
 299
 300         total = isl_basic_set_total_dim(bset);
 301         eq = isl_basic_set_alloc_space(isl_space_copy(bset->dim), 0, n, 0);
 302         if (!eq)
 303                 return NULL;
 304         for (i = 0; i < n; ++i) {
 305                 k = isl_basic_set_alloc_equality(eq);
 306                 if (k < 0)
 307                         goto error;
 308                 isl_seq_cpy(eq->eq[k], bset->eq[first + k], 1 + total);
 309         }
 310
 311         return eq;
 312 error:
 313         isl_basic_set_free(eq);
 314         return NULL;
 315 }
 316
 317 /* Given a basic set, exploit the equalties in the a basic set to construct
 318  * a morphishm that maps the basic set to a lower-dimensional space.
 319  * Specifically, the morphism reduces the number of dimensions of type "type".
 320  *
 321  * This function is a slight generalization of isl_mat_variable_compression
 322  * in that it allows the input to be parametric and that it allows for the
 323  * compression of either parameters or set variables.
 324  *
 325  * We first select the equalities of interest, that is those that involve
 326  * variables of type "type" and no later variables.
 327  * Denote those equalities as
 328  *
 329  *              -C(p) + M x = 0
 330  *
 331  * where C(p) depends on the parameters if type == isl_dim_set and
 332  * is a constant if type == isl_dim_param.
 333  *
 334  * First compute the (left) Hermite normal form of M,
 335  *
 336  *              M [U1 U2] = M U = H = [H1 0]
 337  * or
 338  *                            M = H Q = [H1 0] [Q1]
 339  *                                             [Q2]
 340  *
 341  * with U, Q unimodular, Q = U^{-1} (and H lower triangular).
 342  * Define the transformed variables as
 343  *
 344  *              x = [U1 U2] [ x1' ] = [U1 U2] [Q1] x
 345  *                          [ x2' ]           [Q2]
 346  *
 347  * The equalities then become
 348  *
 349  *              -C(p) + H1 x1' = 0   or   x1' = H1^{-1} C(p) = C'(p)
 350  *
 351  * If the denominator of the constant term does not divide the
 352  * the common denominator of the parametric terms, then every
 353  * integer point is mapped to a non-integer point and then the original set has no
 354  * integer solutions (since the x' are a unimodular transformation
 355  * of the x).  In this case, an empty morphism is returned.
 356  * Otherwise, the transformation is given by
 357  *
 358  *              x = U1 H1^{-1} C(p) + U2 x2'
 359  *
 360  * The inverse transformation is simply
 361  *
 362  *              x2' = Q2 x
 363  *
 364  * Both matrices are extended to map the full original space to the full
 365  * compressed space.
 366  */
 367 __isl_give isl_morph *isl_basic_set_variable_compression(
 368         __isl_keep isl_basic_set *bset, enum isl_dim_type type)
 369 {
 370         unsigned otype;
 371         unsigned ntype;
 372         unsigned orest;
 373         unsigned nrest;
 374         int f_eq, n_eq;
 375         isl_space *dim;
 376         isl_mat *H, *U, *Q, *C = NULL, *H1, *U1, *U2;
 377         isl_basic_set *dom, *ran;
 378
 379         if (!bset)
 380                 return NULL;
 381
 382         if (isl_basic_set_plain_is_empty(bset))
 383                 return isl_morph_empty(bset);
 384
 385         isl_assert(bset->ctx, bset->n_div == 0, return NULL);
 386
 387         otype = 1 + isl_space_offset(bset->dim, type);
 388         ntype = isl_basic_set_dim(bset, type);
 389         orest = otype + ntype;
 390         nrest = isl_basic_set_total_dim(bset) - (orest - 1);
 391
 392         for (f_eq = 0; f_eq < bset->n_eq; ++f_eq)
 393                 if (isl_seq_first_non_zero(bset->eq[f_eq] + orest, nrest) == -1)
 394                         break;
 395         for (n_eq = 0; f_eq + n_eq < bset->n_eq; ++n_eq)
 396                 if (isl_seq_first_non_zero(bset->eq[f_eq + n_eq] + otype, ntype) == -1)
 397                         break;
 398         if (n_eq == 0)
 399                 return isl_morph_identity(bset);
 400
 401         H = isl_mat_sub_alloc6(bset->ctx, bset->eq, f_eq, n_eq, otype, ntype);
 402         H = isl_mat_left_hermite(H, 0, &U, &Q);
 403         if (!H || !U || !Q)
 404                 goto error;
 405         Q = isl_mat_drop_rows(Q, 0, n_eq);
 406         Q = isl_mat_diagonal(isl_mat_identity(bset->ctx, otype), Q);
 407         Q = isl_mat_diagonal(Q, isl_mat_identity(bset->ctx, nrest));
 408         C = isl_mat_alloc(bset->ctx, 1 + n_eq, otype);
 409         if (!C)
 410                 goto error;
 411         isl_int_set_si(C->row[0][0], 1);
 412         isl_seq_clr(C->row[0] + 1, otype - 1);
 413         isl_mat_sub_neg(C->ctx, C->row + 1, bset->eq + f_eq, n_eq, 0, 0, otype);
 414         H1 = isl_mat_sub_alloc(H, 0, H->n_row, 0, H->n_row);
 415         H1 = isl_mat_lin_to_aff(H1);
 416         C = isl_mat_inverse_product(H1, C);
 417         if (!C)
 418                 goto error;
 419         isl_mat_free(H);
 420
 421         if (!isl_int_is_one(C->row[0][0])) {
 422                 int i;
 423                 isl_int g;
 424
 425                 isl_int_init(g);
 426                 for (i = 0; i < n_eq; ++i) {
 427                         isl_seq_gcd(C->row[1 + i] + 1, otype - 1, &g);
 428                         isl_int_gcd(g, g, C->row[0][0]);
 429                         if (!isl_int_is_divisible_by(C->row[1 + i][0], g))
 430                                 break;
 431                 }
 432                 isl_int_clear(g);
 433
 434                 if (i < n_eq) {
 435                         isl_mat_free(C);
 436                         isl_mat_free(U);
 437                         isl_mat_free(Q);
 438                         return isl_morph_empty(bset);
 439                 }
 440
 441                 C = isl_mat_normalize(C);
 442         }
 443
 444         U1 = isl_mat_sub_alloc(U, 0, U->n_row, 0, n_eq);
 445         U1 = isl_mat_lin_to_aff(U1);
 446         U2 = isl_mat_sub_alloc(U, 0, U->n_row, n_eq, U->n_row - n_eq);
 447         U2 = isl_mat_lin_to_aff(U2);
 448         isl_mat_free(U);
 449
 450         C = isl_mat_product(U1, C);
 451         C = isl_mat_aff_direct_sum(C, U2);
 452         C = insert_parameter_rows(C, otype - 1);
 453         C = isl_mat_diagonal(C, isl_mat_identity(bset->ctx, nrest));
 454
 455         dim = isl_space_copy(bset->dim);
 456         dim = isl_space_drop_dims(dim, type, 0, ntype);
 457         dim = isl_space_add_dims(dim, type, ntype - n_eq);
 458         ran = isl_basic_set_universe(dim);
 459         dom = copy_equalities(bset, f_eq, n_eq);
 460
 461         return isl_morph_alloc(dom, ran, Q, C);
 462 error:
 463         isl_mat_free(C);
 464         isl_mat_free(H);
 465         isl_mat_free(U);
 466         isl_mat_free(Q);
 467         return NULL;
 468 }
 469
 470 /* Construct a parameter compression for "bset".
 471  * We basically just call isl_mat_parameter_compression with the right input
 472  * and then extend the resulting matrix to include the variables.
 473  *
 474  * Let the equalities be given as
 475  *
 476  *      B(p) + A x = 0
 477  *
 478  * and let [H 0] be the Hermite Normal Form of A, then
 479  *
 480  *      H^-1 B(p)
 481  *
 482  * needs to be integer, so we impose that each row is divisible by
 483  * the denominator.
 484  */
 485 __isl_give isl_morph *isl_basic_set_parameter_compression(
 486         __isl_keep isl_basic_set *bset)
 487 {
 488         unsigned nparam;
 489         unsigned nvar;
 490         int n_eq;
 491         isl_mat *H, *B;
 492         isl_vec *d;
 493         isl_mat *map, *inv;
 494         isl_basic_set *dom, *ran;
 495
 496         if (!bset)
 497                 return NULL;
 498
 499         if (isl_basic_set_plain_is_empty(bset))
 500                 return isl_morph_empty(bset);
 501         if (bset->n_eq == 0)
 502                 return isl_morph_identity(bset);
 503
 504         isl_assert(bset->ctx, bset->n_div == 0, return NULL);
 505
 506         n_eq = bset->n_eq;
 507         nparam = isl_basic_set_dim(bset, isl_dim_param);
 508         nvar = isl_basic_set_dim(bset, isl_dim_set);
 509
 510         isl_assert(bset->ctx, n_eq <= nvar, return NULL);
 511
 512         d = isl_vec_alloc(bset->ctx, n_eq);
 513         B = isl_mat_sub_alloc6(bset->ctx, bset->eq, 0, n_eq, 0, 1 + nparam);
 514         H = isl_mat_sub_alloc6(bset->ctx, bset->eq, 0, n_eq, 1 + nparam, nvar);
 515         H = isl_mat_left_hermite(H, 0, NULL, NULL);
 516         H = isl_mat_drop_cols(H, n_eq, nvar - n_eq);
 517         H = isl_mat_lin_to_aff(H);
 518         H = isl_mat_right_inverse(H);
 519         if (!H || !d)
 520                 goto error;
 521         isl_seq_set(d->el, H->row[0][0], d->size);
 522         H = isl_mat_drop_rows(H, 0, 1);
 523         H = isl_mat_drop_cols(H, 0, 1);
 524         B = isl_mat_product(H, B);
 525         inv = isl_mat_parameter_compression(B, d);
 526         inv = isl_mat_diagonal(inv, isl_mat_identity(bset->ctx, nvar));
 527         map = isl_mat_right_inverse(isl_mat_copy(inv));
 528
 529         dom = isl_basic_set_universe(isl_space_copy(bset->dim));
 530         ran = isl_basic_set_universe(isl_space_copy(bset->dim));
 531
 532         return isl_morph_alloc(dom, ran, map, inv);
 533 error:
 534         isl_mat_free(H);
 535         isl_mat_free(B);
 536         isl_vec_free(d);
 537         return NULL;
 538 }
 539
 540 /* Add stride constraints to "bset" based on the inverse mapping
 541  * that was plugged in.  In particular, if morph maps x' to x,
 542  * the the constraints of the original input
 543  *
 544  *      A x' + b >= 0
 545  *
 546  * have been rewritten to
 547  *
 548  *      A inv x + b >= 0
 549  *
 550  * However, this substitution may loose information on the integrality of x',
 551  * so we need to impose that
 552  *
 553  *      inv x
 554  *
 555  * is integral.  If inv = B/d, this means that we need to impose that
 556  *
 557  *      B x = 0         mod d
 558  *
 559  * or
 560  *
 561  *      exists alpha in Z^m: B x = d alpha
 562  *
 563  */
 564 static __isl_give isl_basic_set *add_strides(__isl_take isl_basic_set *bset,
 565         __isl_keep isl_morph *morph)
 566 {
 567         int i, div, k;
 568         isl_int gcd;
 569
 570         if (isl_int_is_one(morph->inv->row[0][0]))
 571                 return bset;
 572
 573         isl_int_init(gcd);
 574
 575         for (i = 0; 1 + i < morph->inv->n_row; ++i) {
 576                 isl_seq_gcd(morph->inv->row[1 + i], morph->inv->n_col, &gcd);
 577                 if (isl_int_is_divisible_by(gcd, morph->inv->row[0][0]))
 578                         continue;
 579                 div = isl_basic_set_alloc_div(bset);
 580                 if (div < 0)
 581                         goto error;
 582                 k = isl_basic_set_alloc_equality(bset);
 583                 if (k < 0)
 584                         goto error;
 585                 isl_seq_cpy(bset->eq[k], morph->inv->row[1 + i],
 586                             morph->inv->n_col);
 587                 isl_seq_clr(bset->eq[k] + morph->inv->n_col, bset->n_div);
 588                 isl_int_set(bset->eq[k][morph->inv->n_col + div],
 589                             morph->inv->row[0][0]);
 590         }
 591
 592         isl_int_clear(gcd);
 593
 594         return bset;
 595 error:
 596         isl_int_clear(gcd);
 597         isl_basic_set_free(bset);
 598         return NULL;
 599 }
 600
 601 /* Apply the morphism to the basic set.
 602  * We basically just compute the preimage of "bset" under the inverse mapping
 603  * in morph, add in stride constraints and intersect with the range
 604  * of the morphism.
 605  */
 606 __isl_give isl_basic_set *isl_morph_basic_set(__isl_take isl_morph *morph,
 607         __isl_take isl_basic_set *bset)
 608 {
 609         isl_basic_set *res = NULL;
 610         isl_mat *mat = NULL;
 611         int i, k;
 612         int max_stride;
 613
 614         if (!morph || !bset)
 615                 goto error;
 616
 617         isl_assert(bset->ctx, isl_space_is_equal(bset->dim, morph->dom->dim),
 618                     goto error);
 619
 620         max_stride = morph->inv->n_row - 1;
 621         if (isl_int_is_one(morph->inv->row[0][0]))
 622                 max_stride = 0;
 623         res = isl_basic_set_alloc_space(isl_space_copy(morph->ran->dim),
 624                 bset->n_div + max_stride, bset->n_eq + max_stride, bset->n_ineq);
 625
 626         for (i = 0; i < bset->n_div; ++i)
 627                 if (isl_basic_set_alloc_div(res) < 0)
 628                         goto error;
 629
 630         mat = isl_mat_sub_alloc6(bset->ctx, bset->eq, 0, bset->n_eq,
 631                                         0, morph->inv->n_row);
 632         mat = isl_mat_product(mat, isl_mat_copy(morph->inv));
 633         if (!mat)
 634                 goto error;
 635         for (i = 0; i < bset->n_eq; ++i) {
 636                 k = isl_basic_set_alloc_equality(res);
 637                 if (k < 0)
 638                         goto error;
 639                 isl_seq_cpy(res->eq[k], mat->row[i], mat->n_col);
 640                 isl_seq_scale(res->eq[k] + mat->n_col, bset->eq[i] + mat->n_col,
 641                                 morph->inv->row[0][0], bset->n_div);
 642         }
 643         isl_mat_free(mat);
 644
 645         mat = isl_mat_sub_alloc6(bset->ctx, bset->ineq, 0, bset->n_ineq,
 646                                         0, morph->inv->n_row);
 647         mat = isl_mat_product(mat, isl_mat_copy(morph->inv));
 648         if (!mat)
 649                 goto error;
 650         for (i = 0; i < bset->n_ineq; ++i) {
 651                 k = isl_basic_set_alloc_inequality(res);
 652                 if (k < 0)
 653                         goto error;
 654                 isl_seq_cpy(res->ineq[k], mat->row[i], mat->n_col);
 655                 isl_seq_scale(res->ineq[k] + mat->n_col,
 656                                 bset->ineq[i] + mat->n_col,
 657                                 morph->inv->row[0][0], bset->n_div);
 658         }
 659         isl_mat_free(mat);
 660
 661         mat = isl_mat_sub_alloc6(bset->ctx, bset->div, 0, bset->n_div,
 662                                         1, morph->inv->n_row);
 663         mat = isl_mat_product(mat, isl_mat_copy(morph->inv));
 664         if (!mat)
 665                 goto error;
 666         for (i = 0; i < bset->n_div; ++i) {
 667                 isl_int_mul(res->div[i][0],
 668                                 morph->inv->row[0][0], bset->div[i][0]);
 669                 isl_seq_cpy(res->div[i] + 1, mat->row[i], mat->n_col);
 670                 isl_seq_scale(res->div[i] + 1 + mat->n_col,
 671                                 bset->div[i] + 1 + mat->n_col,
 672                                 morph->inv->row[0][0], bset->n_div);
 673         }
 674         isl_mat_free(mat);
 675
 676         res = add_strides(res, morph);
 677
 678         if (isl_basic_set_is_rational(bset))
 679                 res = isl_basic_set_set_rational(res);
 680
 681         res = isl_basic_set_simplify(res);
 682         res = isl_basic_set_finalize(res);
 683
 684         res = isl_basic_set_intersect(res, isl_basic_set_copy(morph->ran));
 685
 686         isl_morph_free(morph);
 687         isl_basic_set_free(bset);
 688         return res;
 689 error:
 690         isl_mat_free(mat);
 691         isl_morph_free(morph);
 692         isl_basic_set_free(bset);
 693         isl_basic_set_free(res);
 694         return NULL;
 695 }
 696
 697 /* Apply the morphism to the set.
 698  */
 699 __isl_give isl_set *isl_morph_set(__isl_take isl_morph *morph,
 700         __isl_take isl_set *set)
 701 {
 702         int i;
 703
 704         if (!morph || !set)
 705                 goto error;
 706
 707         isl_assert(set->ctx, isl_space_is_equal(set->dim, morph->dom->dim), goto error);
 708
 709         set = isl_set_cow(set);
 710         if (!set)
 711                 goto error;
 712
 713         isl_space_free(set->dim);
 714         set->dim = isl_space_copy(morph->ran->dim);
 715         if (!set->dim)
 716                 goto error;
 717
 718         for (i = 0; i < set->n; ++i) {
 719                 set->p[i] = isl_morph_basic_set(isl_morph_copy(morph), set->p[i]);
 720                 if (!set->p[i])
 721                         goto error;
 722         }
 723
 724         isl_morph_free(morph);
 725
 726         ISL_F_CLR(set, ISL_SET_NORMALIZED);
 727
 728         return set;
 729 error:
 730         isl_set_free(set);
 731         isl_morph_free(morph);
 732         return NULL;
 733 }
 734
 735 /* Construct a morphism that first does morph2 and then morph1.
 736  */
 737 __isl_give isl_morph *isl_morph_compose(__isl_take isl_morph *morph1,
 738         __isl_take isl_morph *morph2)
 739 {
 740         isl_mat *map, *inv;
 741         isl_basic_set *dom, *ran;
 742
 743         if (!morph1 || !morph2)
 744                 goto error;
 745
 746         map = isl_mat_product(isl_mat_copy(morph1->map), isl_mat_copy(morph2->map));
 747         inv = isl_mat_product(isl_mat_copy(morph2->inv), isl_mat_copy(morph1->inv));
 748         dom = isl_morph_basic_set(isl_morph_inverse(isl_morph_copy(morph2)),
 749                                   isl_basic_set_copy(morph1->dom));
 750         dom = isl_basic_set_intersect(dom, isl_basic_set_copy(morph2->dom));
 751         ran = isl_morph_basic_set(isl_morph_copy(morph1),
 752                                   isl_basic_set_copy(morph2->ran));
 753         ran = isl_basic_set_intersect(ran, isl_basic_set_copy(morph1->ran));
 754
 755         isl_morph_free(morph1);
 756         isl_morph_free(morph2);
 757
 758         return isl_morph_alloc(dom, ran, map, inv);
 759 error:
 760         isl_morph_free(morph1);
 761         isl_morph_free(morph2);
 762         return NULL;
 763 }
 764
 765 __isl_give isl_morph *isl_morph_inverse(__isl_take isl_morph *morph)
 766 {
 767         isl_basic_set *bset;
 768         isl_mat *mat;
 769
 770         morph = isl_morph_cow(morph);
 771         if (!morph)
 772                 return NULL;
 773
 774         bset = morph->dom;
 775         morph->dom = morph->ran;
 776         morph->ran = bset;
 777
 778         mat = morph->map;
 779         morph->map = morph->inv;
 780         morph->inv = mat;
 781
 782         return morph;
 783 }
 784
 785 __isl_give isl_morph *isl_basic_set_full_compression(
 786         __isl_keep isl_basic_set *bset)
 787 {
 788         isl_morph *morph, *morph2;
 789
 790         bset = isl_basic_set_copy(bset);
 791
 792         morph = isl_basic_set_variable_compression(bset, isl_dim_param);
 793         bset = isl_morph_basic_set(isl_morph_copy(morph), bset);
 794
 795         morph2 = isl_basic_set_parameter_compression(bset);
 796         bset = isl_morph_basic_set(isl_morph_copy(morph2), bset);
 797
 798         morph = isl_morph_compose(morph2, morph);
 799
 800         morph2 = isl_basic_set_variable_compression(bset, isl_dim_set);
 801         isl_basic_set_free(bset);
 802
 803         morph = isl_morph_compose(morph2, morph);
 804
 805         return morph;
 806 }
 807
 808 __isl_give isl_vec *isl_morph_vec(__isl_take isl_morph *morph,
 809         __isl_take isl_vec *vec)
 810 {
 811         if (!morph)
 812                 goto error;
 813
 814         vec = isl_mat_vec_product(isl_mat_copy(morph->map), vec);
 815
 816         isl_morph_free(morph);
 817         return vec;
 818 error:
 819         isl_morph_free(morph);
 820         isl_vec_free(vec);
 821         return NULL;
 822 }