isl_morph.c

   1 /*
   2  * Copyright 2010      INRIA Saclay
   3  *
   4  * Use of this software is governed by the MIT 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         morph = isl_morph_cow(morph);
 176         if (!morph)
 177                 return NULL;
 178         n = isl_basic_set_dim(morph->dom, isl_dim_set);
 179         morph = isl_morph_remove_dom_dims(morph, isl_dim_set, 0, n);
 180         if (!morph)
 181                 return NULL;
 182         morph->dom = isl_basic_set_params(morph->dom);
 183         if (morph->dom)
 184                 return morph;
 185
 186         isl_morph_free(morph);
 187         return NULL;
 188 }
 189
 190 /* Project range of morph onto its parameter domain.
 191  */
 192 __isl_give isl_morph *isl_morph_ran_params(__isl_take isl_morph *morph)
 193 {
 194         unsigned n;
 195
 196         morph = isl_morph_cow(morph);
 197         if (!morph)
 198                 return NULL;
 199         n = isl_basic_set_dim(morph->ran, isl_dim_set);
 200         morph = isl_morph_remove_ran_dims(morph, isl_dim_set, 0, n);
 201         if (!morph)
 202                 return NULL;
 203         morph->ran = isl_basic_set_params(morph->ran);
 204         if (morph->ran)
 205                 return morph;
 206
 207         isl_morph_free(morph);
 208         return NULL;
 209 }
 210
 211 void isl_morph_print_internal(__isl_take isl_morph *morph, FILE *out)
 212 {
 213         if (!morph)
 214                 return;
 215
 216         isl_basic_set_print(morph->dom, out, 0, "", "", ISL_FORMAT_ISL);
 217         isl_basic_set_print(morph->ran, out, 0, "", "", ISL_FORMAT_ISL);
 218         isl_mat_print_internal(morph->map, out, 4);
 219         isl_mat_print_internal(morph->inv, out, 4);
 220 }
 221
 222 void isl_morph_dump(__isl_take isl_morph *morph)
 223 {
 224         isl_morph_print_internal(morph, stderr);
 225 }
 226
 227 __isl_give isl_morph *isl_morph_identity(__isl_keep isl_basic_set *bset)
 228 {
 229         isl_mat *id;
 230         isl_basic_set *universe;
 231         unsigned total;
 232
 233         if (!bset)
 234                 return NULL;
 235
 236         total = isl_basic_set_total_dim(bset);
 237         id = isl_mat_identity(bset->ctx, 1 + total);
 238         universe = isl_basic_set_universe(isl_space_copy(bset->dim));
 239
 240         return isl_morph_alloc(universe, isl_basic_set_copy(universe),
 241                 id, isl_mat_copy(id));
 242 }
 243
 244 /* Create a(n identity) morphism between empty sets of the same dimension
 245  * a "bset".
 246  */
 247 __isl_give isl_morph *isl_morph_empty(__isl_keep isl_basic_set *bset)
 248 {
 249         isl_mat *id;
 250         isl_basic_set *empty;
 251         unsigned total;
 252
 253         if (!bset)
 254                 return NULL;
 255
 256         total = isl_basic_set_total_dim(bset);
 257         id = isl_mat_identity(bset->ctx, 1 + total);
 258         empty = isl_basic_set_empty(isl_space_copy(bset->dim));
 259
 260         return isl_morph_alloc(empty, isl_basic_set_copy(empty),
 261                 id, isl_mat_copy(id));
 262 }
 263
 264 /* Given a matrix that maps a (possibly) parametric domain to
 265  * a parametric domain, add in rows that map the "nparam" parameters onto
 266  * themselves.
 267  */
 268 static __isl_give isl_mat *insert_parameter_rows(__isl_take isl_mat *mat,
 269         unsigned nparam)
 270 {
 271         int i;
 272
 273         if (nparam == 0)
 274                 return mat;
 275         if (!mat)
 276                 return NULL;
 277
 278         mat = isl_mat_insert_rows(mat, 1, nparam);
 279         if (!mat)
 280                 return NULL;
 281
 282         for (i = 0; i < nparam; ++i) {
 283                 isl_seq_clr(mat->row[1 + i], mat->n_col);
 284                 isl_int_set(mat->row[1 + i][1 + i], mat->row[0][0]);
 285         }
 286
 287         return mat;
 288 }
 289
 290 /* Construct a basic set described by the "n" equalities of "bset" starting
 291  * at "first".
 292  */
 293 static __isl_give isl_basic_set *copy_equalities(__isl_keep isl_basic_set *bset,
 294         unsigned first, unsigned n)
 295 {
 296         int i, k;
 297         isl_basic_set *eq;
 298         unsigned total;
 299
 300         isl_assert(bset->ctx, bset->n_div == 0, return NULL);
 301
 302         total = isl_basic_set_total_dim(bset);
 303         eq = isl_basic_set_alloc_space(isl_space_copy(bset->dim), 0, n, 0);
 304         if (!eq)
 305                 return NULL;
 306         for (i = 0; i < n; ++i) {
 307                 k = isl_basic_set_alloc_equality(eq);
 308                 if (k < 0)
 309                         goto error;
 310                 isl_seq_cpy(eq->eq[k], bset->eq[first + k], 1 + total);
 311         }
 312
 313         return eq;
 314 error:
 315         isl_basic_set_free(eq);
 316         return NULL;
 317 }
 318
 319 /* Given a basic set, exploit the equalties in the basic set to construct
 320  * a morphishm that maps the basic set to a lower-dimensional space.
 321  * Specifically, the morphism reduces the number of dimensions of type "type".
 322  *
 323  * This function is a slight generalization of isl_mat_variable_compression
 324  * in that it allows the input to be parametric and that it allows for the
 325  * compression of either parameters or set variables.
 326  *
 327  * We first select the equalities of interest, that is those that involve
 328  * variables of type "type" and no later variables.
 329  * Denote those equalities as
 330  *
 331  *              -C(p) + M x = 0
 332  *
 333  * where C(p) depends on the parameters if type == isl_dim_set and
 334  * is a constant if type == isl_dim_param.
 335  *
 336  * First compute the (left) Hermite normal form of M,
 337  *
 338  *              M [U1 U2] = M U = H = [H1 0]
 339  * or
 340  *                            M = H Q = [H1 0] [Q1]
 341  *                                             [Q2]
 342  *
 343  * with U, Q unimodular, Q = U^{-1} (and H lower triangular).
 344  * Define the transformed variables as
 345  *
 346  *              x = [U1 U2] [ x1' ] = [U1 U2] [Q1] x
 347  *                          [ x2' ]           [Q2]
 348  *
 349  * The equalities then become
 350  *
 351  *              -C(p) + H1 x1' = 0   or   x1' = H1^{-1} C(p) = C'(p)
 352  *
 353  * If the denominator of the constant term does not divide the
 354  * the common denominator of the parametric terms, then every
 355  * integer point is mapped to a non-integer point and then the original set has no
 356  * integer solutions (since the x' are a unimodular transformation
 357  * of the x).  In this case, an empty morphism is returned.
 358  * Otherwise, the transformation is given by
 359  *
 360  *              x = U1 H1^{-1} C(p) + U2 x2'
 361  *
 362  * The inverse transformation is simply
 363  *
 364  *              x2' = Q2 x
 365  *
 366  * Both matrices are extended to map the full original space to the full
 367  * compressed space.
 368  */
 369 __isl_give isl_morph *isl_basic_set_variable_compression(
 370         __isl_keep isl_basic_set *bset, enum isl_dim_type type)
 371 {
 372         unsigned otype;
 373         unsigned ntype;
 374         unsigned orest;
 375         unsigned nrest;
 376         int f_eq, n_eq;
 377         isl_space *dim;
 378         isl_mat *H, *U, *Q, *C = NULL, *H1, *U1, *U2;
 379         isl_basic_set *dom, *ran;
 380
 381         if (!bset)
 382                 return NULL;
 383
 384         if (isl_basic_set_plain_is_empty(bset))
 385                 return isl_morph_empty(bset);
 386
 387         isl_assert(bset->ctx, bset->n_div == 0, return NULL);
 388
 389         otype = 1 + isl_space_offset(bset->dim, type);
 390         ntype = isl_basic_set_dim(bset, type);
 391         orest = otype + ntype;
 392         nrest = isl_basic_set_total_dim(bset) - (orest - 1);
 393
 394         for (f_eq = 0; f_eq < bset->n_eq; ++f_eq)
 395                 if (isl_seq_first_non_zero(bset->eq[f_eq] + orest, nrest) == -1)
 396                         break;
 397         for (n_eq = 0; f_eq + n_eq < bset->n_eq; ++n_eq)
 398                 if (isl_seq_first_non_zero(bset->eq[f_eq + n_eq] + otype, ntype) == -1)
 399                         break;
 400         if (n_eq == 0)
 401                 return isl_morph_identity(bset);
 402
 403         H = isl_mat_sub_alloc6(bset->ctx, bset->eq, f_eq, n_eq, otype, ntype);
 404         H = isl_mat_left_hermite(H, 0, &U, &Q);
 405         if (!H || !U || !Q)
 406                 goto error;
 407         Q = isl_mat_drop_rows(Q, 0, n_eq);
 408         Q = isl_mat_diagonal(isl_mat_identity(bset->ctx, otype), Q);
 409         Q = isl_mat_diagonal(Q, isl_mat_identity(bset->ctx, nrest));
 410         C = isl_mat_alloc(bset->ctx, 1 + n_eq, otype);
 411         if (!C)
 412                 goto error;
 413         isl_int_set_si(C->row[0][0], 1);
 414         isl_seq_clr(C->row[0] + 1, otype - 1);
 415         isl_mat_sub_neg(C->ctx, C->row + 1, bset->eq + f_eq, n_eq, 0, 0, otype);
 416         H1 = isl_mat_sub_alloc(H, 0, H->n_row, 0, H->n_row);
 417         H1 = isl_mat_lin_to_aff(H1);
 418         C = isl_mat_inverse_product(H1, C);
 419         if (!C)
 420                 goto error;
 421         isl_mat_free(H);
 422
 423         if (!isl_int_is_one(C->row[0][0])) {
 424                 int i;
 425                 isl_int g;
 426
 427                 isl_int_init(g);
 428                 for (i = 0; i < n_eq; ++i) {
 429                         isl_seq_gcd(C->row[1 + i] + 1, otype - 1, &g);
 430                         isl_int_gcd(g, g, C->row[0][0]);
 431                         if (!isl_int_is_divisible_by(C->row[1 + i][0], g))
 432                                 break;
 433                 }
 434                 isl_int_clear(g);
 435
 436                 if (i < n_eq) {
 437                         isl_mat_free(C);
 438                         isl_mat_free(U);
 439                         isl_mat_free(Q);
 440                         return isl_morph_empty(bset);
 441                 }
 442
 443                 C = isl_mat_normalize(C);
 444         }
 445
 446         U1 = isl_mat_sub_alloc(U, 0, U->n_row, 0, n_eq);
 447         U1 = isl_mat_lin_to_aff(U1);
 448         U2 = isl_mat_sub_alloc(U, 0, U->n_row, n_eq, U->n_row - n_eq);
 449         U2 = isl_mat_lin_to_aff(U2);
 450         isl_mat_free(U);
 451
 452         C = isl_mat_product(U1, C);
 453         C = isl_mat_aff_direct_sum(C, U2);
 454         C = insert_parameter_rows(C, otype - 1);
 455         C = isl_mat_diagonal(C, isl_mat_identity(bset->ctx, nrest));
 456
 457         dim = isl_space_copy(bset->dim);
 458         dim = isl_space_drop_dims(dim, type, 0, ntype);
 459         dim = isl_space_add_dims(dim, type, ntype - n_eq);
 460         ran = isl_basic_set_universe(dim);
 461         dom = copy_equalities(bset, f_eq, n_eq);
 462
 463         return isl_morph_alloc(dom, ran, Q, C);
 464 error:
 465         isl_mat_free(C);
 466         isl_mat_free(H);
 467         isl_mat_free(U);
 468         isl_mat_free(Q);
 469         return NULL;
 470 }
 471
 472 /* Construct a parameter compression for "bset".
 473  * We basically just call isl_mat_parameter_compression with the right input
 474  * and then extend the resulting matrix to include the variables.
 475  *
 476  * The implementation assumes that "bset" does not have any equalities
 477  * that only involve the parameters and that isl_basic_set_gauss has
 478  * been applied to "bset".
 479  *
 480  * Let the equalities be given as
 481  *
 482  *      B(p) + A x = 0.
 483  *
 484  * We use isl_mat_parameter_compression_ext to compute the compression
 485  *
 486  *      p = T p'.
 487  */
 488 __isl_give isl_morph *isl_basic_set_parameter_compression(
 489         __isl_keep isl_basic_set *bset)
 490 {
 491         unsigned nparam;
 492         unsigned nvar;
 493         unsigned n_div;
 494         int n_eq;
 495         isl_mat *H, *B;
 496         isl_mat *map, *inv;
 497         isl_basic_set *dom, *ran;
 498
 499         if (!bset)
 500                 return NULL;
 501
 502         if (isl_basic_set_plain_is_empty(bset))
 503                 return isl_morph_empty(bset);
 504         if (bset->n_eq == 0)
 505                 return isl_morph_identity(bset);
 506
 507         n_eq = bset->n_eq;
 508         nparam = isl_basic_set_dim(bset, isl_dim_param);
 509         nvar = isl_basic_set_dim(bset, isl_dim_set);
 510         n_div = isl_basic_set_dim(bset, isl_dim_div);
 511
 512         if (isl_seq_first_non_zero(bset->eq[bset->n_eq - 1] + 1 + nparam,
 513                                     nvar + n_div) == -1)
 514                 isl_die(isl_basic_set_get_ctx(bset), isl_error_invalid,
 515                         "input not allowed to have parameter equalities",
 516                         return NULL);
 517         if (n_eq > nvar + n_div)
 518                 isl_die(isl_basic_set_get_ctx(bset), isl_error_invalid,
 519                         "input not gaussed", return NULL);
 520
 521         B = isl_mat_sub_alloc6(bset->ctx, bset->eq, 0, n_eq, 0, 1 + nparam);
 522         H = isl_mat_sub_alloc6(bset->ctx, bset->eq,
 523                                 0, n_eq, 1 + nparam, nvar + n_div);
 524         inv = isl_mat_parameter_compression_ext(B, H);
 525         inv = isl_mat_diagonal(inv, isl_mat_identity(bset->ctx, nvar));
 526         map = isl_mat_right_inverse(isl_mat_copy(inv));
 527
 528         dom = isl_basic_set_universe(isl_space_copy(bset->dim));
 529         ran = isl_basic_set_universe(isl_space_copy(bset->dim));
 530
 531         return isl_morph_alloc(dom, ran, map, inv);
 532 }
 533
 534 /* Add stride constraints to "bset" based on the inverse mapping
 535  * that was plugged in.  In particular, if morph maps x' to x,
 536  * the the constraints of the original input
 537  *
 538  *      A x' + b >= 0
 539  *
 540  * have been rewritten to
 541  *
 542  *      A inv x + b >= 0
 543  *
 544  * However, this substitution may loose information on the integrality of x',
 545  * so we need to impose that
 546  *
 547  *      inv x
 548  *
 549  * is integral.  If inv = B/d, this means that we need to impose that
 550  *
 551  *      B x = 0         mod d
 552  *
 553  * or
 554  *
 555  *      exists alpha in Z^m: B x = d alpha
 556  *
 557  * This function is similar to add_strides in isl_affine_hull.c
 558  */
 559 static __isl_give isl_basic_set *add_strides(__isl_take isl_basic_set *bset,
 560         __isl_keep isl_morph *morph)
 561 {
 562         int i, div, k;
 563         isl_int gcd;
 564
 565         if (isl_int_is_one(morph->inv->row[0][0]))
 566                 return bset;
 567
 568         isl_int_init(gcd);
 569
 570         for (i = 0; 1 + i < morph->inv->n_row; ++i) {
 571                 isl_seq_gcd(morph->inv->row[1 + i], morph->inv->n_col, &gcd);
 572                 if (isl_int_is_divisible_by(gcd, morph->inv->row[0][0]))
 573                         continue;
 574                 div = isl_basic_set_alloc_div(bset);
 575                 if (div < 0)
 576                         goto error;
 577                 isl_int_set_si(bset->div[div][0], 0);
 578                 k = isl_basic_set_alloc_equality(bset);
 579                 if (k < 0)
 580                         goto error;
 581                 isl_seq_cpy(bset->eq[k], morph->inv->row[1 + i],
 582                             morph->inv->n_col);
 583                 isl_seq_clr(bset->eq[k] + morph->inv->n_col, bset->n_div);
 584                 isl_int_set(bset->eq[k][morph->inv->n_col + div],
 585                             morph->inv->row[0][0]);
 586         }
 587
 588         isl_int_clear(gcd);
 589
 590         return bset;
 591 error:
 592         isl_int_clear(gcd);
 593         isl_basic_set_free(bset);
 594         return NULL;
 595 }
 596
 597 /* Apply the morphism to the basic set.
 598  * We basically just compute the preimage of "bset" under the inverse mapping
 599  * in morph, add in stride constraints and intersect with the range
 600  * of the morphism.
 601  */
 602 __isl_give isl_basic_set *isl_morph_basic_set(__isl_take isl_morph *morph,
 603         __isl_take isl_basic_set *bset)
 604 {
 605         isl_basic_set *res = NULL;
 606         isl_mat *mat = NULL;
 607         int i, k;
 608         int max_stride;
 609
 610         if (!morph || !bset)
 611                 goto error;
 612
 613         isl_assert(bset->ctx, isl_space_is_equal(bset->dim, morph->dom->dim),
 614                     goto error);
 615
 616         max_stride = morph->inv->n_row - 1;
 617         if (isl_int_is_one(morph->inv->row[0][0]))
 618                 max_stride = 0;
 619         res = isl_basic_set_alloc_space(isl_space_copy(morph->ran->dim),
 620                 bset->n_div + max_stride, bset->n_eq + max_stride, bset->n_ineq);
 621
 622         for (i = 0; i < bset->n_div; ++i)
 623                 if (isl_basic_set_alloc_div(res) < 0)
 624                         goto error;
 625
 626         mat = isl_mat_sub_alloc6(bset->ctx, bset->eq, 0, bset->n_eq,
 627                                         0, morph->inv->n_row);
 628         mat = isl_mat_product(mat, isl_mat_copy(morph->inv));
 629         if (!mat)
 630                 goto error;
 631         for (i = 0; i < bset->n_eq; ++i) {
 632                 k = isl_basic_set_alloc_equality(res);
 633                 if (k < 0)
 634                         goto error;
 635                 isl_seq_cpy(res->eq[k], mat->row[i], mat->n_col);
 636                 isl_seq_scale(res->eq[k] + mat->n_col, bset->eq[i] + mat->n_col,
 637                                 morph->inv->row[0][0], bset->n_div);
 638         }
 639         isl_mat_free(mat);
 640
 641         mat = isl_mat_sub_alloc6(bset->ctx, bset->ineq, 0, bset->n_ineq,
 642                                         0, morph->inv->n_row);
 643         mat = isl_mat_product(mat, isl_mat_copy(morph->inv));
 644         if (!mat)
 645                 goto error;
 646         for (i = 0; i < bset->n_ineq; ++i) {
 647                 k = isl_basic_set_alloc_inequality(res);
 648                 if (k < 0)
 649                         goto error;
 650                 isl_seq_cpy(res->ineq[k], mat->row[i], mat->n_col);
 651                 isl_seq_scale(res->ineq[k] + mat->n_col,
 652                                 bset->ineq[i] + mat->n_col,
 653                                 morph->inv->row[0][0], bset->n_div);
 654         }
 655         isl_mat_free(mat);
 656
 657         mat = isl_mat_sub_alloc6(bset->ctx, bset->div, 0, bset->n_div,
 658                                         1, morph->inv->n_row);
 659         mat = isl_mat_product(mat, isl_mat_copy(morph->inv));
 660         if (!mat)
 661                 goto error;
 662         for (i = 0; i < bset->n_div; ++i) {
 663                 isl_int_mul(res->div[i][0],
 664                                 morph->inv->row[0][0], bset->div[i][0]);
 665                 isl_seq_cpy(res->div[i] + 1, mat->row[i], mat->n_col);
 666                 isl_seq_scale(res->div[i] + 1 + mat->n_col,
 667                                 bset->div[i] + 1 + mat->n_col,
 668                                 morph->inv->row[0][0], bset->n_div);
 669         }
 670         isl_mat_free(mat);
 671
 672         res = add_strides(res, morph);
 673
 674         if (isl_basic_set_is_rational(bset))
 675                 res = isl_basic_set_set_rational(res);
 676
 677         res = isl_basic_set_simplify(res);
 678         res = isl_basic_set_finalize(res);
 679
 680         res = isl_basic_set_intersect(res, isl_basic_set_copy(morph->ran));
 681
 682         isl_morph_free(morph);
 683         isl_basic_set_free(bset);
 684         return res;
 685 error:
 686         isl_mat_free(mat);
 687         isl_morph_free(morph);
 688         isl_basic_set_free(bset);
 689         isl_basic_set_free(res);
 690         return NULL;
 691 }
 692
 693 /* Apply the morphism to the set.
 694  */
 695 __isl_give isl_set *isl_morph_set(__isl_take isl_morph *morph,
 696         __isl_take isl_set *set)
 697 {
 698         int i;
 699
 700         if (!morph || !set)
 701                 goto error;
 702
 703         isl_assert(set->ctx, isl_space_is_equal(set->dim, morph->dom->dim), goto error);
 704
 705         set = isl_set_cow(set);
 706         if (!set)
 707                 goto error;
 708
 709         isl_space_free(set->dim);
 710         set->dim = isl_space_copy(morph->ran->dim);
 711         if (!set->dim)
 712                 goto error;
 713
 714         for (i = 0; i < set->n; ++i) {
 715                 set->p[i] = isl_morph_basic_set(isl_morph_copy(morph), set->p[i]);
 716                 if (!set->p[i])
 717                         goto error;
 718         }
 719
 720         isl_morph_free(morph);
 721
 722         ISL_F_CLR(set, ISL_SET_NORMALIZED);
 723
 724         return set;
 725 error:
 726         isl_set_free(set);
 727         isl_morph_free(morph);
 728         return NULL;
 729 }
 730
 731 /* Construct a morphism that first does morph2 and then morph1.
 732  */
 733 __isl_give isl_morph *isl_morph_compose(__isl_take isl_morph *morph1,
 734         __isl_take isl_morph *morph2)
 735 {
 736         isl_mat *map, *inv;
 737         isl_basic_set *dom, *ran;
 738
 739         if (!morph1 || !morph2)
 740                 goto error;
 741
 742         map = isl_mat_product(isl_mat_copy(morph1->map), isl_mat_copy(morph2->map));
 743         inv = isl_mat_product(isl_mat_copy(morph2->inv), isl_mat_copy(morph1->inv));
 744         dom = isl_morph_basic_set(isl_morph_inverse(isl_morph_copy(morph2)),
 745                                   isl_basic_set_copy(morph1->dom));
 746         dom = isl_basic_set_intersect(dom, isl_basic_set_copy(morph2->dom));
 747         ran = isl_morph_basic_set(isl_morph_copy(morph1),
 748                                   isl_basic_set_copy(morph2->ran));
 749         ran = isl_basic_set_intersect(ran, isl_basic_set_copy(morph1->ran));
 750
 751         isl_morph_free(morph1);
 752         isl_morph_free(morph2);
 753
 754         return isl_morph_alloc(dom, ran, map, inv);
 755 error:
 756         isl_morph_free(morph1);
 757         isl_morph_free(morph2);
 758         return NULL;
 759 }
 760
 761 __isl_give isl_morph *isl_morph_inverse(__isl_take isl_morph *morph)
 762 {
 763         isl_basic_set *bset;
 764         isl_mat *mat;
 765
 766         morph = isl_morph_cow(morph);
 767         if (!morph)
 768                 return NULL;
 769
 770         bset = morph->dom;
 771         morph->dom = morph->ran;
 772         morph->ran = bset;
 773
 774         mat = morph->map;
 775         morph->map = morph->inv;
 776         morph->inv = mat;
 777
 778         return morph;
 779 }
 780
 781 /* We detect all the equalities first to avoid implicit equalties
 782  * being discovered during the computations.  In particular,
 783  * the compression on the variables could expose additional stride
 784  * constraints on the parameters.  This would result in existentially
 785  * quantified variables after applying the resulting morph, which
 786  * in turn could break invariants of the calling functions.
 787  */
 788 __isl_give isl_morph *isl_basic_set_full_compression(
 789         __isl_keep isl_basic_set *bset)
 790 {
 791         isl_morph *morph, *morph2;
 792
 793         bset = isl_basic_set_copy(bset);
 794         bset = isl_basic_set_detect_equalities(bset);
 795
 796         morph = isl_basic_set_variable_compression(bset, isl_dim_param);
 797         bset = isl_morph_basic_set(isl_morph_copy(morph), bset);
 798
 799         morph2 = isl_basic_set_parameter_compression(bset);
 800         bset = isl_morph_basic_set(isl_morph_copy(morph2), bset);
 801
 802         morph = isl_morph_compose(morph2, morph);
 803
 804         morph2 = isl_basic_set_variable_compression(bset, isl_dim_set);
 805         isl_basic_set_free(bset);
 806
 807         morph = isl_morph_compose(morph2, morph);
 808
 809         return morph;
 810 }
 811
 812 __isl_give isl_vec *isl_morph_vec(__isl_take isl_morph *morph,
 813         __isl_take isl_vec *vec)
 814 {
 815         if (!morph)
 816                 goto error;
 817
 818         vec = isl_mat_vec_product(isl_mat_copy(morph->map), vec);
 819
 820         isl_morph_free(morph);
 821         return vec;
 822 error:
 823         isl_morph_free(morph);
 824         isl_vec_free(vec);
 825         return NULL;
 826 }