isl_fold.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 #define ISL_DIM_H
  12 #include <isl_map_private.h>
  13 #include <isl_union_map_private.h>
  14 #include <isl_polynomial_private.h>
  15 #include <isl_point_private.h>
  16 #include <isl_space_private.h>
  17 #include <isl/lp.h>
  18 #include <isl/seq.h>
  19 #include <isl_mat_private.h>
  20 #include <isl_config.h>
  21
  22 enum isl_fold isl_fold_type_negate(enum isl_fold type)
  23 {
  24         switch (type) {
  25         case isl_fold_min:
  26                 return isl_fold_max;
  27         case isl_fold_max:
  28                 return isl_fold_min;
  29         case isl_fold_list:
  30                 return isl_fold_list;
  31         }
  32
  33         isl_die(NULL, isl_error_internal, "unhandled isl_fold type", abort());
  34 }
  35
  36 static __isl_give isl_qpolynomial_fold *qpolynomial_fold_alloc(
  37         enum isl_fold type, __isl_take isl_space *dim, int n)
  38 {
  39         isl_qpolynomial_fold *fold;
  40
  41         if (!dim)
  42                 goto error;
  43
  44         isl_assert(dim->ctx, n >= 0, goto error);
  45         fold = isl_calloc(dim->ctx, struct isl_qpolynomial_fold,
  46                         sizeof(struct isl_qpolynomial_fold) +
  47                         (n - 1) * sizeof(struct isl_qpolynomial *));
  48         if (!fold)
  49                 goto error;
  50
  51         fold->ref = 1;
  52         fold->size = n;
  53         fold->n = 0;
  54         fold->type = type;
  55         fold->dim = dim;
  56
  57         return fold;
  58 error:
  59         isl_space_free(dim);
  60         return NULL;
  61 }
  62
  63 isl_ctx *isl_qpolynomial_fold_get_ctx(__isl_keep isl_qpolynomial_fold *fold)
  64 {
  65         return fold ? fold->dim->ctx : NULL;
  66 }
  67
  68 __isl_give isl_space *isl_qpolynomial_fold_get_domain_space(
  69         __isl_keep isl_qpolynomial_fold *fold)
  70 {
  71         return fold ? isl_space_copy(fold->dim) : NULL;
  72 }
  73
  74 __isl_give isl_space *isl_qpolynomial_fold_get_space(
  75         __isl_keep isl_qpolynomial_fold *fold)
  76 {
  77         isl_space *space;
  78         if (!fold)
  79                 return NULL;
  80         space = isl_space_copy(fold->dim);
  81         space = isl_space_from_domain(space);
  82         space = isl_space_add_dims(space, isl_dim_out, 1);
  83         return space;
  84 }
  85
  86 __isl_give isl_qpolynomial_fold *isl_qpolynomial_fold_reset_domain_space(
  87         __isl_take isl_qpolynomial_fold *fold, __isl_take isl_space *dim)
  88 {
  89         int i;
  90
  91         fold = isl_qpolynomial_fold_cow(fold);
  92         if (!fold || !dim)
  93                 goto error;
  94
  95         for (i = 0; i < fold->n; ++i) {
  96                 fold->qp[i] = isl_qpolynomial_reset_domain_space(fold->qp[i],
  97                                                         isl_space_copy(dim));
  98                 if (!fold->qp[i])
  99                         goto error;
 100         }
 101
 102         isl_space_free(fold->dim);
 103         fold->dim = dim;
 104
 105         return fold;
 106 error:
 107         isl_qpolynomial_fold_free(fold);
 108         isl_space_free(dim);
 109         return NULL;
 110 }
 111
 112 /* Reset the space of "fold".  This function is called from isl_pw_templ.c
 113  * and doesn't know if the space of an element object is represented
 114  * directly or through its domain.  It therefore passes along both.
 115  */
 116 __isl_give isl_qpolynomial_fold *isl_qpolynomial_fold_reset_space_and_domain(
 117         __isl_take isl_qpolynomial_fold *fold, __isl_take isl_space *space,
 118         __isl_take isl_space *domain)
 119 {
 120         isl_space_free(space);
 121         return isl_qpolynomial_fold_reset_domain_space(fold, domain);
 122 }
 123
 124 int isl_qpolynomial_fold_involves_dims(__isl_keep isl_qpolynomial_fold *fold,
 125         enum isl_dim_type type, unsigned first, unsigned n)
 126 {
 127         int i;
 128
 129         if (!fold)
 130                 return -1;
 131         if (fold->n == 0 || n == 0)
 132                 return 0;
 133
 134         for (i = 0; i < fold->n; ++i) {
 135                 int involves = isl_qpolynomial_involves_dims(fold->qp[i],
 136                                                             type, first, n);
 137                 if (involves < 0 || involves)
 138                         return involves;
 139         }
 140         return 0;
 141 }
 142
 143 __isl_give isl_qpolynomial_fold *isl_qpolynomial_fold_set_dim_name(
 144         __isl_take isl_qpolynomial_fold *fold,
 145         enum isl_dim_type type, unsigned pos, const char *s)
 146 {
 147         int i;
 148
 149         fold = isl_qpolynomial_fold_cow(fold);
 150         if (!fold)
 151                 return NULL;
 152         fold->dim = isl_space_set_dim_name(fold->dim, type, pos, s);
 153         if (!fold->dim)
 154                 goto error;
 155
 156         for (i = 0; i < fold->n; ++i) {
 157                 fold->qp[i] = isl_qpolynomial_set_dim_name(fold->qp[i],
 158                                                             type, pos, s);
 159                 if (!fold->qp[i])
 160                         goto error;
 161         }
 162
 163         return fold;
 164 error:
 165         isl_qpolynomial_fold_free(fold);
 166         return NULL;
 167 }
 168
 169 __isl_give isl_qpolynomial_fold *isl_qpolynomial_fold_drop_dims(
 170         __isl_take isl_qpolynomial_fold *fold,
 171         enum isl_dim_type type, unsigned first, unsigned n)
 172 {
 173         int i;
 174         enum isl_dim_type set_type;
 175
 176         if (!fold)
 177                 return NULL;
 178         if (n == 0)
 179                 return fold;
 180
 181         set_type = type == isl_dim_in ? isl_dim_set : type;
 182
 183         fold = isl_qpolynomial_fold_cow(fold);
 184         if (!fold)
 185                 return NULL;
 186         fold->dim = isl_space_drop_dims(fold->dim, set_type, first, n);
 187         if (!fold->dim)
 188                 goto error;
 189
 190         for (i = 0; i < fold->n; ++i) {
 191                 fold->qp[i] = isl_qpolynomial_drop_dims(fold->qp[i],
 192                                                             type, first, n);
 193                 if (!fold->qp[i])
 194                         goto error;
 195         }
 196
 197         return fold;
 198 error:
 199         isl_qpolynomial_fold_free(fold);
 200         return NULL;
 201 }
 202
 203 __isl_give isl_qpolynomial_fold *isl_qpolynomial_fold_insert_dims(
 204         __isl_take isl_qpolynomial_fold *fold,
 205         enum isl_dim_type type, unsigned first, unsigned n)
 206 {
 207         int i;
 208
 209         if (!fold)
 210                 return NULL;
 211         if (n == 0 && !isl_space_is_named_or_nested(fold->dim, type))
 212                 return fold;
 213
 214         fold = isl_qpolynomial_fold_cow(fold);
 215         if (!fold)
 216                 return NULL;
 217         fold->dim = isl_space_insert_dims(fold->dim, type, first, n);
 218         if (!fold->dim)
 219                 goto error;
 220
 221         for (i = 0; i < fold->n; ++i) {
 222                 fold->qp[i] = isl_qpolynomial_insert_dims(fold->qp[i],
 223                                                             type, first, n);
 224                 if (!fold->qp[i])
 225                         goto error;
 226         }
 227
 228         return fold;
 229 error:
 230         isl_qpolynomial_fold_free(fold);
 231         return NULL;
 232 }
 233
 234 static int isl_qpolynomial_cst_sign(__isl_keep isl_qpolynomial *qp)
 235 {
 236         struct isl_upoly_cst *cst;
 237
 238         cst = isl_upoly_as_cst(qp->upoly);
 239         if (!cst)
 240                 return 0;
 241
 242         return isl_int_sgn(cst->n) < 0 ? -1 : 1;
 243 }
 244
 245 static int isl_qpolynomial_aff_sign(__isl_keep isl_set *set,
 246         __isl_keep isl_qpolynomial *qp)
 247 {
 248         enum isl_lp_result res;
 249         isl_vec *aff;
 250         isl_int opt;
 251         int sgn = 0;
 252
 253         aff = isl_qpolynomial_extract_affine(qp);
 254         if (!aff)
 255                 return 0;
 256
 257         isl_int_init(opt);
 258
 259         res = isl_set_solve_lp(set, 0, aff->el + 1, aff->el[0],
 260                                 &opt, NULL, NULL);
 261         if (res == isl_lp_error)
 262                 goto done;
 263         if (res == isl_lp_empty ||
 264             (res == isl_lp_ok && !isl_int_is_neg(opt))) {
 265                 sgn = 1;
 266                 goto done;
 267         }
 268
 269         res = isl_set_solve_lp(set, 1, aff->el + 1, aff->el[0],
 270                                 &opt, NULL, NULL);
 271         if (res == isl_lp_ok && !isl_int_is_pos(opt))
 272                 sgn = -1;
 273
 274 done:
 275         isl_int_clear(opt);
 276         isl_vec_free(aff);
 277         return sgn;
 278 }
 279
 280 /* Determine, if possible, the sign of the quasipolynomial "qp" on
 281  * the domain "set".
 282  *
 283  * If qp is a constant, then the problem is trivial.
 284  * If qp is linear, then we check if the minimum of the corresponding
 285  * affine constraint is non-negative or if the maximum is non-positive.
 286  *
 287  * Otherwise, we check if the outermost variable "v" has a lower bound "l"
 288  * in "set".  If so, we write qp(v,v') as
 289  *
 290  *      q(v,v') * (v - l) + r(v')
 291  *
 292  * if q(v,v') and r(v') have the same known sign, then the original
 293  * quasipolynomial has the same sign as well.
 294  *
 295  * Return
 296  *      -1 if qp <= 0
 297  *       1 if qp >= 0
 298  *       0 if unknown
 299  */
 300 static int isl_qpolynomial_sign(__isl_keep isl_set *set,
 301         __isl_keep isl_qpolynomial *qp)
 302 {
 303         int d;
 304         int i;
 305         int is;
 306         struct isl_upoly_rec *rec;
 307         isl_vec *v;
 308         isl_int l;
 309         enum isl_lp_result res;
 310         int sgn = 0;
 311
 312         is = isl_qpolynomial_is_cst(qp, NULL, NULL);
 313         if (is < 0)
 314                 return 0;
 315         if (is)
 316                 return isl_qpolynomial_cst_sign(qp);
 317
 318         is = isl_qpolynomial_is_affine(qp);
 319         if (is < 0)
 320                 return 0;
 321         if (is)
 322                 return isl_qpolynomial_aff_sign(set, qp);
 323
 324         if (qp->div->n_row > 0)
 325                 return 0;
 326
 327         rec = isl_upoly_as_rec(qp->upoly);
 328         if (!rec)
 329                 return 0;
 330
 331         d = isl_space_dim(qp->dim, isl_dim_all);
 332         v = isl_vec_alloc(set->ctx, 2 + d);
 333         if (!v)
 334                 return 0;
 335
 336         isl_seq_clr(v->el + 1, 1 + d);
 337         isl_int_set_si(v->el[0], 1);
 338         isl_int_set_si(v->el[2 + qp->upoly->var], 1);
 339
 340         isl_int_init(l);
 341
 342         res = isl_set_solve_lp(set, 0, v->el + 1, v->el[0], &l, NULL, NULL);
 343         if (res == isl_lp_ok) {
 344                 isl_qpolynomial *min;
 345                 isl_qpolynomial *base;
 346                 isl_qpolynomial *r, *q;
 347                 isl_qpolynomial *t;
 348
 349                 min = isl_qpolynomial_cst_on_domain(isl_space_copy(qp->dim), l);
 350                 base = isl_qpolynomial_var_pow_on_domain(isl_space_copy(qp->dim),
 351                                                 qp->upoly->var, 1);
 352
 353                 r = isl_qpolynomial_alloc(isl_space_copy(qp->dim), 0,
 354                                           isl_upoly_copy(rec->p[rec->n - 1]));
 355                 q = isl_qpolynomial_copy(r);
 356
 357                 for (i = rec->n - 2; i >= 0; --i) {
 358                         r = isl_qpolynomial_mul(r, isl_qpolynomial_copy(min));
 359                         t = isl_qpolynomial_alloc(isl_space_copy(qp->dim), 0,
 360                                                   isl_upoly_copy(rec->p[i]));
 361                         r = isl_qpolynomial_add(r, t);
 362                         if (i == 0)
 363                                 break;
 364                         q = isl_qpolynomial_mul(q, isl_qpolynomial_copy(base));
 365                         q = isl_qpolynomial_add(q, isl_qpolynomial_copy(r));
 366                 }
 367
 368                 if (isl_qpolynomial_is_zero(q))
 369                         sgn = isl_qpolynomial_sign(set, r);
 370                 else if (isl_qpolynomial_is_zero(r))
 371                         sgn = isl_qpolynomial_sign(set, q);
 372                 else {
 373                         int sgn_q, sgn_r;
 374                         sgn_r = isl_qpolynomial_sign(set, r);
 375                         sgn_q = isl_qpolynomial_sign(set, q);
 376                         if (sgn_r == sgn_q)
 377                                 sgn = sgn_r;
 378                 }
 379
 380                 isl_qpolynomial_free(min);
 381                 isl_qpolynomial_free(base);
 382                 isl_qpolynomial_free(q);
 383                 isl_qpolynomial_free(r);
 384         }
 385
 386         isl_int_clear(l);
 387
 388         isl_vec_free(v);
 389
 390         return sgn;
 391 }
 392
 393 __isl_give isl_qpolynomial_fold *isl_qpolynomial_fold_fold_on_domain(
 394         __isl_keep isl_set *set,
 395         __isl_take isl_qpolynomial_fold *fold1,
 396         __isl_take isl_qpolynomial_fold *fold2)
 397 {
 398         int i, j;
 399         int n1;
 400         struct isl_qpolynomial_fold *res = NULL;
 401         int better;
 402
 403         if (!fold1 || !fold2)
 404                 goto error;
 405
 406         isl_assert(fold1->dim->ctx, fold1->type == fold2->type, goto error);
 407         isl_assert(fold1->dim->ctx, isl_space_is_equal(fold1->dim, fold2->dim),
 408                         goto error);
 409
 410         better = fold1->type == isl_fold_max ? -1 : 1;
 411
 412         if (isl_qpolynomial_fold_is_empty(fold1)) {
 413                 isl_qpolynomial_fold_free(fold1);
 414                 return fold2;
 415         }
 416
 417         if (isl_qpolynomial_fold_is_empty(fold2)) {
 418                 isl_qpolynomial_fold_free(fold2);
 419                 return fold1;
 420         }
 421
 422         res = qpolynomial_fold_alloc(fold1->type, isl_space_copy(fold1->dim),
 423                                         fold1->n + fold2->n);
 424         if (!res)
 425                 goto error;
 426
 427         for (i = 0; i < fold1->n; ++i) {
 428                 res->qp[res->n] = isl_qpolynomial_copy(fold1->qp[i]);
 429                 if (!res->qp[res->n])
 430                         goto error;
 431                 res->n++;
 432         }
 433         n1 = res->n;
 434
 435         for (i = 0; i < fold2->n; ++i) {
 436                 for (j = n1 - 1; j >= 0; --j) {
 437                         isl_qpolynomial *d;
 438                         int sgn;
 439                         d = isl_qpolynomial_sub(
 440                                 isl_qpolynomial_copy(res->qp[j]),
 441                                 isl_qpolynomial_copy(fold2->qp[i]));
 442                         sgn = isl_qpolynomial_sign(set, d);
 443                         isl_qpolynomial_free(d);
 444                         if (sgn == 0)
 445                                 continue;
 446                         if (sgn != better)
 447                                 break;
 448                         isl_qpolynomial_free(res->qp[j]);
 449                         if (j != n1 - 1)
 450                                 res->qp[j] = res->qp[n1 - 1];
 451                         n1--;
 452                         if (n1 != res->n - 1)
 453                                 res->qp[n1] = res->qp[res->n - 1];
 454                         res->n--;
 455                 }
 456                 if (j >= 0)
 457                         continue;
 458                 res->qp[res->n] = isl_qpolynomial_copy(fold2->qp[i]);
 459                 if (!res->qp[res->n])
 460                         goto error;
 461                 res->n++;
 462         }
 463
 464         isl_qpolynomial_fold_free(fold1);
 465         isl_qpolynomial_fold_free(fold2);
 466
 467         return res;
 468 error:
 469         isl_qpolynomial_fold_free(res);
 470         isl_qpolynomial_fold_free(fold1);
 471         isl_qpolynomial_fold_free(fold2);
 472         return NULL;
 473 }
 474
 475 __isl_give isl_qpolynomial_fold *isl_qpolynomial_fold_add_qpolynomial(
 476         __isl_take isl_qpolynomial_fold *fold, __isl_take isl_qpolynomial *qp)
 477 {
 478         int i;
 479
 480         if (!fold || !qp)
 481                 goto error;
 482
 483         if (isl_qpolynomial_is_zero(qp)) {
 484                 isl_qpolynomial_free(qp);
 485                 return fold;
 486         }
 487
 488         fold = isl_qpolynomial_fold_cow(fold);
 489         if (!fold)
 490                 goto error;
 491
 492         for (i = 0; i < fold->n; ++i) {
 493                 fold->qp[i] = isl_qpolynomial_add(fold->qp[i],
 494                                                 isl_qpolynomial_copy(qp));
 495                 if (!fold->qp[i])
 496                         goto error;
 497         }
 498
 499         isl_qpolynomial_free(qp);
 500         return fold;
 501 error:
 502         isl_qpolynomial_fold_free(fold);
 503         isl_qpolynomial_free(qp);
 504         return NULL;
 505 }
 506
 507 __isl_give isl_qpolynomial_fold *isl_qpolynomial_fold_add_on_domain(
 508         __isl_keep isl_set *dom,
 509         __isl_take isl_qpolynomial_fold *fold1,
 510         __isl_take isl_qpolynomial_fold *fold2)
 511 {
 512         int i;
 513         isl_qpolynomial_fold *res = NULL;
 514
 515         if (!fold1 || !fold2)
 516                 goto error;
 517
 518         if (isl_qpolynomial_fold_is_empty(fold1)) {
 519                 isl_qpolynomial_fold_free(fold1);
 520                 return fold2;
 521         }
 522
 523         if (isl_qpolynomial_fold_is_empty(fold2)) {
 524                 isl_qpolynomial_fold_free(fold2);
 525                 return fold1;
 526         }
 527
 528         if (fold1->n == 1 && fold2->n != 1)
 529                 return isl_qpolynomial_fold_add_on_domain(dom, fold2, fold1);
 530
 531         if (fold2->n == 1) {
 532                 res = isl_qpolynomial_fold_add_qpolynomial(fold1,
 533                                         isl_qpolynomial_copy(fold2->qp[0]));
 534                 isl_qpolynomial_fold_free(fold2);
 535                 return res;
 536         }
 537
 538         res = isl_qpolynomial_fold_add_qpolynomial(
 539                                 isl_qpolynomial_fold_copy(fold1),
 540                                 isl_qpolynomial_copy(fold2->qp[0]));
 541
 542         for (i = 1; i < fold2->n; ++i) {
 543                 isl_qpolynomial_fold *res_i;
 544                 res_i = isl_qpolynomial_fold_add_qpolynomial(
 545                                         isl_qpolynomial_fold_copy(fold1),
 546                                         isl_qpolynomial_copy(fold2->qp[i]));
 547                 res = isl_qpolynomial_fold_fold_on_domain(dom, res, res_i);
 548         }
 549
 550         isl_qpolynomial_fold_free(fold1);
 551         isl_qpolynomial_fold_free(fold2);
 552         return res;
 553 error:
 554         isl_qpolynomial_fold_free(res);
 555         isl_qpolynomial_fold_free(fold1);
 556         isl_qpolynomial_fold_free(fold2);
 557         return NULL;
 558 }
 559
 560 __isl_give isl_qpolynomial_fold *isl_qpolynomial_fold_substitute_equalities(
 561         __isl_take isl_qpolynomial_fold *fold, __isl_take isl_basic_set *eq)
 562 {
 563         int i;
 564
 565         if (!fold || !eq)
 566                 goto error;
 567
 568         fold = isl_qpolynomial_fold_cow(fold);
 569         if (!fold)
 570                 return NULL;
 571
 572         for (i = 0; i < fold->n; ++i) {
 573                 fold->qp[i] = isl_qpolynomial_substitute_equalities(fold->qp[i],
 574                                                         isl_basic_set_copy(eq));
 575                 if (!fold->qp[i])
 576                         goto error;
 577         }
 578
 579         isl_basic_set_free(eq);
 580         return fold;
 581 error:
 582         isl_basic_set_free(eq);
 583         isl_qpolynomial_fold_free(fold);
 584         return NULL;
 585 }
 586
 587 __isl_give isl_qpolynomial_fold *isl_qpolynomial_fold_gist(
 588         __isl_take isl_qpolynomial_fold *fold, __isl_take isl_set *context)
 589 {
 590         int i;
 591
 592         if (!fold || !context)
 593                 goto error;
 594
 595         fold = isl_qpolynomial_fold_cow(fold);
 596         if (!fold)
 597                 return NULL;
 598
 599         for (i = 0; i < fold->n; ++i) {
 600                 fold->qp[i] = isl_qpolynomial_gist(fold->qp[i],
 601                                                         isl_set_copy(context));
 602                 if (!fold->qp[i])
 603                         goto error;
 604         }
 605
 606         isl_set_free(context);
 607         return fold;
 608 error:
 609         isl_set_free(context);
 610         isl_qpolynomial_fold_free(fold);
 611         return NULL;
 612 }
 613
 614 __isl_give isl_qpolynomial_fold *isl_qpolynomial_fold_gist_params(
 615         __isl_take isl_qpolynomial_fold *fold, __isl_take isl_set *context)
 616 {
 617         isl_space *space = isl_qpolynomial_fold_get_domain_space(fold);
 618         isl_set *dom_context = isl_set_universe(space);
 619         dom_context = isl_set_intersect_params(dom_context, context);
 620         return isl_qpolynomial_fold_gist(fold, dom_context);
 621 }
 622
 623 #define HAS_TYPE
 624
 625 #undef PW
 626 #define PW isl_pw_qpolynomial_fold
 627 #undef EL
 628 #define EL isl_qpolynomial_fold
 629 #undef EL_IS_ZERO
 630 #define EL_IS_ZERO is_empty
 631 #undef ZERO
 632 #define ZERO zero
 633 #undef IS_ZERO
 634 #define IS_ZERO is_zero
 635 #undef FIELD
 636 #define FIELD fold
 637 #undef DEFAULT_IS_ZERO
 638 #define DEFAULT_IS_ZERO 1
 639
 640 #define NO_NEG
 641 #define NO_PULLBACK
 642
 643 #include <isl_pw_templ.c>
 644
 645 #undef UNION
 646 #define UNION isl_union_pw_qpolynomial_fold
 647 #undef PART
 648 #define PART isl_pw_qpolynomial_fold
 649 #undef PARTS
 650 #define PARTS pw_qpolynomial_fold
 651 #define ALIGN_DOMAIN
 652
 653 #define NO_SUB
 654
 655 #include <isl_union_templ.c>
 656
 657 __isl_give isl_qpolynomial_fold *isl_qpolynomial_fold_empty(enum isl_fold type,
 658         __isl_take isl_space *dim)
 659 {
 660         return qpolynomial_fold_alloc(type, dim, 0);
 661 }
 662
 663 __isl_give isl_qpolynomial_fold *isl_qpolynomial_fold_alloc(
 664         enum isl_fold type, __isl_take isl_qpolynomial *qp)
 665 {
 666         isl_qpolynomial_fold *fold;
 667
 668         if (!qp)
 669                 return NULL;
 670
 671         fold = qpolynomial_fold_alloc(type, isl_space_copy(qp->dim), 1);
 672         if (!fold)
 673                 goto error;
 674
 675         fold->qp[0] = qp;
 676         fold->n++;
 677
 678         return fold;
 679 error:
 680         isl_qpolynomial_fold_free(fold);
 681         isl_qpolynomial_free(qp);
 682         return NULL;
 683 }
 684
 685 __isl_give isl_qpolynomial_fold *isl_qpolynomial_fold_copy(
 686         __isl_keep isl_qpolynomial_fold *fold)
 687 {
 688         if (!fold)
 689                 return NULL;
 690
 691         fold->ref++;
 692         return fold;
 693 }
 694
 695 __isl_give isl_qpolynomial_fold *isl_qpolynomial_fold_dup(
 696         __isl_keep isl_qpolynomial_fold *fold)
 697 {
 698         int i;
 699         isl_qpolynomial_fold *dup;
 700
 701         if (!fold)
 702                 return NULL;
 703         dup = qpolynomial_fold_alloc(fold->type,
 704                                         isl_space_copy(fold->dim), fold->n);
 705         if (!dup)
 706                 return NULL;
 707
 708         dup->n = fold->n;
 709         for (i = 0; i < fold->n; ++i) {
 710                 dup->qp[i] = isl_qpolynomial_copy(fold->qp[i]);
 711                 if (!dup->qp[i])
 712                         goto error;
 713         }
 714
 715         return dup;
 716 error:
 717         isl_qpolynomial_fold_free(dup);
 718         return NULL;
 719 }
 720
 721 __isl_give isl_qpolynomial_fold *isl_qpolynomial_fold_cow(
 722         __isl_take isl_qpolynomial_fold *fold)
 723 {
 724         if (!fold)
 725                 return NULL;
 726
 727         if (fold->ref == 1)
 728                 return fold;
 729         fold->ref--;
 730         return isl_qpolynomial_fold_dup(fold);
 731 }
 732
 733 void isl_qpolynomial_fold_free(__isl_take isl_qpolynomial_fold *fold)
 734 {
 735         int i;
 736
 737         if (!fold)
 738                 return;
 739         if (--fold->ref > 0)
 740                 return;
 741
 742         for (i = 0; i < fold->n; ++i)
 743                 isl_qpolynomial_free(fold->qp[i]);
 744         isl_space_free(fold->dim);
 745         free(fold);
 746 }
 747
 748 int isl_qpolynomial_fold_is_empty(__isl_keep isl_qpolynomial_fold *fold)
 749 {
 750         if (!fold)
 751                 return -1;
 752
 753         return fold->n == 0;
 754 }
 755
 756 __isl_give isl_qpolynomial_fold *isl_qpolynomial_fold_fold(
 757         __isl_take isl_qpolynomial_fold *fold1,
 758         __isl_take isl_qpolynomial_fold *fold2)
 759 {
 760         int i;
 761         struct isl_qpolynomial_fold *res = NULL;
 762
 763         if (!fold1 || !fold2)
 764                 goto error;
 765
 766         isl_assert(fold1->dim->ctx, fold1->type == fold2->type, goto error);
 767         isl_assert(fold1->dim->ctx, isl_space_is_equal(fold1->dim, fold2->dim),
 768                         goto error);
 769
 770         if (isl_qpolynomial_fold_is_empty(fold1)) {
 771                 isl_qpolynomial_fold_free(fold1);
 772                 return fold2;
 773         }
 774
 775         if (isl_qpolynomial_fold_is_empty(fold2)) {
 776                 isl_qpolynomial_fold_free(fold2);
 777                 return fold1;
 778         }
 779
 780         res = qpolynomial_fold_alloc(fold1->type, isl_space_copy(fold1->dim),
 781                                         fold1->n + fold2->n);
 782         if (!res)
 783                 goto error;
 784
 785         for (i = 0; i < fold1->n; ++i) {
 786                 res->qp[res->n] = isl_qpolynomial_copy(fold1->qp[i]);
 787                 if (!res->qp[res->n])
 788                         goto error;
 789                 res->n++;
 790         }
 791
 792         for (i = 0; i < fold2->n; ++i) {
 793                 res->qp[res->n] = isl_qpolynomial_copy(fold2->qp[i]);
 794                 if (!res->qp[res->n])
 795                         goto error;
 796                 res->n++;
 797         }
 798
 799         isl_qpolynomial_fold_free(fold1);
 800         isl_qpolynomial_fold_free(fold2);
 801
 802         return res;
 803 error:
 804         isl_qpolynomial_fold_free(res);
 805         isl_qpolynomial_fold_free(fold1);
 806         isl_qpolynomial_fold_free(fold2);
 807         return NULL;
 808 }
 809
 810 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_fold(
 811         __isl_take isl_pw_qpolynomial_fold *pw1,
 812         __isl_take isl_pw_qpolynomial_fold *pw2)
 813 {
 814         int i, j, n;
 815         struct isl_pw_qpolynomial_fold *res;
 816         isl_set *set;
 817
 818         if (!pw1 || !pw2)
 819                 goto error;
 820
 821         isl_assert(pw1->dim->ctx, isl_space_is_equal(pw1->dim, pw2->dim), goto error);
 822
 823         if (isl_pw_qpolynomial_fold_is_zero(pw1)) {
 824                 isl_pw_qpolynomial_fold_free(pw1);
 825                 return pw2;
 826         }
 827
 828         if (isl_pw_qpolynomial_fold_is_zero(pw2)) {
 829                 isl_pw_qpolynomial_fold_free(pw2);
 830                 return pw1;
 831         }
 832
 833         if (pw1->type != pw2->type)
 834                 isl_die(pw1->dim->ctx, isl_error_invalid,
 835                         "fold types don't match", goto error);
 836
 837         n = (pw1->n + 1) * (pw2->n + 1);
 838         res = isl_pw_qpolynomial_fold_alloc_size(isl_space_copy(pw1->dim),
 839                                                 pw1->type, n);
 840
 841         for (i = 0; i < pw1->n; ++i) {
 842                 set = isl_set_copy(pw1->p[i].set);
 843                 for (j = 0; j < pw2->n; ++j) {
 844                         struct isl_set *common;
 845                         isl_qpolynomial_fold *sum;
 846                         set = isl_set_subtract(set,
 847                                         isl_set_copy(pw2->p[j].set));
 848                         common = isl_set_intersect(isl_set_copy(pw1->p[i].set),
 849                                                 isl_set_copy(pw2->p[j].set));
 850                         if (isl_set_plain_is_empty(common)) {
 851                                 isl_set_free(common);
 852                                 continue;
 853                         }
 854
 855                         sum = isl_qpolynomial_fold_fold_on_domain(common,
 856                                isl_qpolynomial_fold_copy(pw1->p[i].fold),
 857                                isl_qpolynomial_fold_copy(pw2->p[j].fold));
 858
 859                         res = isl_pw_qpolynomial_fold_add_piece(res, common, sum);
 860                 }
 861                 res = isl_pw_qpolynomial_fold_add_piece(res, set,
 862                         isl_qpolynomial_fold_copy(pw1->p[i].fold));
 863         }
 864
 865         for (j = 0; j < pw2->n; ++j) {
 866                 set = isl_set_copy(pw2->p[j].set);
 867                 for (i = 0; i < pw1->n; ++i)
 868                         set = isl_set_subtract(set, isl_set_copy(pw1->p[i].set));
 869                 res = isl_pw_qpolynomial_fold_add_piece(res, set,
 870                                     isl_qpolynomial_fold_copy(pw2->p[j].fold));
 871         }
 872
 873         isl_pw_qpolynomial_fold_free(pw1);
 874         isl_pw_qpolynomial_fold_free(pw2);
 875
 876         return res;
 877 error:
 878         isl_pw_qpolynomial_fold_free(pw1);
 879         isl_pw_qpolynomial_fold_free(pw2);
 880         return NULL;
 881 }
 882
 883 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_fold_fold_pw_qpolynomial_fold(
 884         __isl_take isl_union_pw_qpolynomial_fold *u,
 885         __isl_take isl_pw_qpolynomial_fold *part)
 886 {
 887         uint32_t hash;
 888         struct isl_hash_table_entry *entry;
 889
 890         u = isl_union_pw_qpolynomial_fold_cow(u);
 891
 892         if (!part || !u)
 893                 goto error;
 894
 895         isl_assert(u->dim->ctx, isl_space_match(part->dim, isl_dim_param, u->dim,
 896                                               isl_dim_param), goto error);
 897
 898         hash = isl_space_get_hash(part->dim);
 899         entry = isl_hash_table_find(u->dim->ctx, &u->table, hash,
 900                                     &has_dim, part->dim, 1);
 901         if (!entry)
 902                 goto error;
 903
 904         if (!entry->data)
 905                 entry->data = part;
 906         else {
 907                 entry->data = isl_pw_qpolynomial_fold_fold(entry->data,
 908                                             isl_pw_qpolynomial_fold_copy(part));
 909                 if (!entry->data)
 910                         goto error;
 911                 isl_pw_qpolynomial_fold_free(part);
 912         }
 913
 914         return u;
 915 error:
 916         isl_pw_qpolynomial_fold_free(part);
 917         isl_union_pw_qpolynomial_fold_free(u);
 918         return NULL;
 919 }
 920
 921 static int fold_part(__isl_take isl_pw_qpolynomial_fold *part, void *user)
 922 {
 923         isl_union_pw_qpolynomial_fold **u;
 924         u = (isl_union_pw_qpolynomial_fold **)user;
 925
 926         *u = isl_union_pw_qpolynomial_fold_fold_pw_qpolynomial_fold(*u, part);
 927
 928         return 0;
 929 }
 930
 931 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_fold_fold(
 932         __isl_take isl_union_pw_qpolynomial_fold *u1,
 933         __isl_take isl_union_pw_qpolynomial_fold *u2)
 934 {
 935         u1 = isl_union_pw_qpolynomial_fold_cow(u1);
 936
 937         if (!u1 || !u2)
 938                 goto error;
 939
 940         if (isl_union_pw_qpolynomial_fold_foreach_pw_qpolynomial_fold(u2,
 941                                                         &fold_part, &u1) < 0)
 942                 goto error;
 943
 944         isl_union_pw_qpolynomial_fold_free(u2);
 945
 946         return u1;
 947 error:
 948         isl_union_pw_qpolynomial_fold_free(u1);
 949         isl_union_pw_qpolynomial_fold_free(u2);
 950         return NULL;
 951 }
 952
 953 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_from_pw_qpolynomial(
 954         enum isl_fold type, __isl_take isl_pw_qpolynomial *pwqp)
 955 {
 956         int i;
 957         isl_pw_qpolynomial_fold *pwf;
 958
 959         if (!pwqp)
 960                 return NULL;
 961
 962         pwf = isl_pw_qpolynomial_fold_alloc_size(isl_space_copy(pwqp->dim),
 963                                                 type, pwqp->n);
 964
 965         for (i = 0; i < pwqp->n; ++i)
 966                 pwf = isl_pw_qpolynomial_fold_add_piece(pwf,
 967                         isl_set_copy(pwqp->p[i].set),
 968                         isl_qpolynomial_fold_alloc(type,
 969                                 isl_qpolynomial_copy(pwqp->p[i].qp)));
 970
 971         isl_pw_qpolynomial_free(pwqp);
 972
 973         return pwf;
 974 }
 975
 976 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_add(
 977         __isl_take isl_pw_qpolynomial_fold *pwf1,
 978         __isl_take isl_pw_qpolynomial_fold *pwf2)
 979 {
 980         return isl_pw_qpolynomial_fold_union_add_(pwf1, pwf2);
 981 }
 982
 983 int isl_qpolynomial_fold_plain_is_equal(__isl_keep isl_qpolynomial_fold *fold1,
 984         __isl_keep isl_qpolynomial_fold *fold2)
 985 {
 986         int i;
 987
 988         if (!fold1 || !fold2)
 989                 return -1;
 990
 991         if (fold1->n != fold2->n)
 992                 return 0;
 993
 994         /* We probably want to sort the qps first... */
 995         for (i = 0; i < fold1->n; ++i) {
 996                 int eq = isl_qpolynomial_plain_is_equal(fold1->qp[i], fold2->qp[i]);
 997                 if (eq < 0 || !eq)
 998                         return eq;
 999         }
1000
1001         return 1;
1002 }
1003
1004 __isl_give isl_qpolynomial *isl_qpolynomial_fold_eval(
1005         __isl_take isl_qpolynomial_fold *fold, __isl_take isl_point *pnt)
1006 {
1007         isl_qpolynomial *qp;
1008
1009         if (!fold || !pnt)
1010                 goto error;
1011         isl_assert(pnt->dim->ctx, isl_space_is_equal(pnt->dim, fold->dim), goto error);
1012         isl_assert(pnt->dim->ctx,
1013                 fold->type == isl_fold_max || fold->type == isl_fold_min,
1014                 goto error);
1015
1016         if (fold->n == 0)
1017                 qp = isl_qpolynomial_zero_on_domain(isl_space_copy(fold->dim));
1018         else {
1019                 int i;
1020                 qp = isl_qpolynomial_eval(isl_qpolynomial_copy(fold->qp[0]),
1021                                                 isl_point_copy(pnt));
1022                 for (i = 1; i < fold->n; ++i) {
1023                         isl_qpolynomial *qp_i;
1024                         qp_i = isl_qpolynomial_eval(
1025                                             isl_qpolynomial_copy(fold->qp[i]),
1026                                             isl_point_copy(pnt));
1027                         if (fold->type == isl_fold_max)
1028                                 qp = isl_qpolynomial_max_cst(qp, qp_i);
1029                         else
1030                                 qp = isl_qpolynomial_min_cst(qp, qp_i);
1031                 }
1032         }
1033         isl_qpolynomial_fold_free(fold);
1034         isl_point_free(pnt);
1035
1036         return qp;
1037 error:
1038         isl_qpolynomial_fold_free(fold);
1039         isl_point_free(pnt);
1040         return NULL;
1041 }
1042
1043 size_t isl_pw_qpolynomial_fold_size(__isl_keep isl_pw_qpolynomial_fold *pwf)
1044 {
1045         int i;
1046         size_t n = 0;
1047
1048         for (i = 0; i < pwf->n; ++i)
1049                 n += pwf->p[i].fold->n;
1050
1051         return n;
1052 }
1053
1054 __isl_give isl_qpolynomial *isl_qpolynomial_fold_opt_on_domain(
1055         __isl_take isl_qpolynomial_fold *fold, __isl_take isl_set *set, int max)
1056 {
1057         int i;
1058         isl_qpolynomial *opt;
1059
1060         if (!set || !fold)
1061                 goto error;
1062
1063         if (fold->n == 0) {
1064                 isl_space *dim = isl_space_copy(fold->dim);
1065                 isl_set_free(set);
1066                 isl_qpolynomial_fold_free(fold);
1067                 return isl_qpolynomial_zero_on_domain(dim);
1068         }
1069
1070         opt = isl_qpolynomial_opt_on_domain(isl_qpolynomial_copy(fold->qp[0]),
1071                                                 isl_set_copy(set), max);
1072         for (i = 1; i < fold->n; ++i) {
1073                 isl_qpolynomial *opt_i;
1074                 opt_i = isl_qpolynomial_opt_on_domain(
1075                                 isl_qpolynomial_copy(fold->qp[i]),
1076                                 isl_set_copy(set), max);
1077                 if (max)
1078                         opt = isl_qpolynomial_max_cst(opt, opt_i);
1079                 else
1080                         opt = isl_qpolynomial_min_cst(opt, opt_i);
1081         }
1082
1083         isl_set_free(set);
1084         isl_qpolynomial_fold_free(fold);
1085
1086         return opt;
1087 error:
1088         isl_set_free(set);
1089         isl_qpolynomial_fold_free(fold);
1090         return NULL;
1091 }
1092
1093 /* Check whether for each quasi-polynomial in "fold2" there is
1094  * a quasi-polynomial in "fold1" that dominates it on "set".
1095  */
1096 static int qpolynomial_fold_covers_on_domain(__isl_keep isl_set *set,
1097         __isl_keep isl_qpolynomial_fold *fold1,
1098         __isl_keep isl_qpolynomial_fold *fold2)
1099 {
1100         int i, j;
1101         int covers;
1102
1103         if (!set || !fold1 || !fold2)
1104                 return -1;
1105
1106         covers = fold1->type == isl_fold_max ? 1 : -1;
1107
1108         for (i = 0; i < fold2->n; ++i) {
1109                 for (j = 0; j < fold1->n; ++j) {
1110                         isl_qpolynomial *d;
1111                         int sgn;
1112
1113                         d = isl_qpolynomial_sub(
1114                                 isl_qpolynomial_copy(fold1->qp[j]),
1115                                 isl_qpolynomial_copy(fold2->qp[i]));
1116                         sgn = isl_qpolynomial_sign(set, d);
1117                         isl_qpolynomial_free(d);
1118                         if (sgn == covers)
1119                                 break;
1120                 }
1121                 if (j >= fold1->n)
1122                         return 0;
1123         }
1124
1125         return 1;
1126 }
1127
1128 /* Check whether "pwf1" dominated "pwf2", i.e., the domain of "pwf1" contains
1129  * that of "pwf2" and on each cell, the corresponding fold from pwf1 dominates
1130  * that of pwf2.
1131  */
1132 int isl_pw_qpolynomial_fold_covers(__isl_keep isl_pw_qpolynomial_fold *pwf1,
1133         __isl_keep isl_pw_qpolynomial_fold *pwf2)
1134 {
1135         int i, j;
1136         isl_set *dom1, *dom2;
1137         int is_subset;
1138
1139         if (!pwf1 || !pwf2)
1140                 return -1;
1141
1142         if (pwf2->n == 0)
1143                 return 1;
1144         if (pwf1->n == 0)
1145                 return 0;
1146
1147         dom1 = isl_pw_qpolynomial_fold_domain(isl_pw_qpolynomial_fold_copy(pwf1));
1148         dom2 = isl_pw_qpolynomial_fold_domain(isl_pw_qpolynomial_fold_copy(pwf2));
1149         is_subset = isl_set_is_subset(dom2, dom1);
1150         isl_set_free(dom1);
1151         isl_set_free(dom2);
1152
1153         if (is_subset < 0 || !is_subset)
1154                 return is_subset;
1155
1156         for (i = 0; i < pwf2->n; ++i) {
1157                 for (j = 0; j < pwf1->n; ++j) {
1158                         int is_empty;
1159                         isl_set *common;
1160                         int covers;
1161
1162                         common = isl_set_intersect(isl_set_copy(pwf1->p[j].set),
1163                                                    isl_set_copy(pwf2->p[i].set));
1164                         is_empty = isl_set_is_empty(common);
1165                         if (is_empty < 0 || is_empty) {
1166                                 isl_set_free(common);
1167                                 if (is_empty < 0)
1168                                         return -1;
1169                                 continue;
1170                         }
1171                         covers = qpolynomial_fold_covers_on_domain(common,
1172                                         pwf1->p[j].fold, pwf2->p[i].fold);
1173                         isl_set_free(common);
1174                         if (covers < 0 || !covers)
1175                                 return covers;
1176                 }
1177         }
1178
1179         return 1;
1180 }
1181
1182 __isl_give isl_qpolynomial_fold *isl_qpolynomial_fold_morph_domain(
1183         __isl_take isl_qpolynomial_fold *fold, __isl_take isl_morph *morph)
1184 {
1185         int i;
1186         isl_ctx *ctx;
1187
1188         if (!fold || !morph)
1189                 goto error;
1190
1191         ctx = fold->dim->ctx;
1192         isl_assert(ctx, isl_space_is_equal(fold->dim, morph->dom->dim), goto error);
1193
1194         fold = isl_qpolynomial_fold_cow(fold);
1195         if (!fold)
1196                 goto error;
1197
1198         isl_space_free(fold->dim);
1199         fold->dim = isl_space_copy(morph->ran->dim);
1200         if (!fold->dim)
1201                 goto error;
1202
1203         for (i = 0; i < fold->n; ++i) {
1204                 fold->qp[i] = isl_qpolynomial_morph_domain(fold->qp[i],
1205                                                 isl_morph_copy(morph));
1206                 if (!fold->qp[i])
1207                         goto error;
1208         }
1209
1210         isl_morph_free(morph);
1211
1212         return fold;
1213 error:
1214         isl_qpolynomial_fold_free(fold);
1215         isl_morph_free(morph);
1216         return NULL;
1217 }
1218
1219 enum isl_fold isl_qpolynomial_fold_get_type(__isl_keep isl_qpolynomial_fold *fold)
1220 {
1221         if (!fold)
1222                 return isl_fold_list;
1223         return fold->type;
1224 }
1225
1226 enum isl_fold isl_union_pw_qpolynomial_fold_get_type(
1227         __isl_keep isl_union_pw_qpolynomial_fold *upwf)
1228 {
1229         if (!upwf)
1230                 return isl_fold_list;
1231         return upwf->type;
1232 }
1233
1234 __isl_give isl_qpolynomial_fold *isl_qpolynomial_fold_lift(
1235         __isl_take isl_qpolynomial_fold *fold, __isl_take isl_space *dim)
1236 {
1237         int i;
1238
1239         if (!fold || !dim)
1240                 goto error;
1241
1242         if (isl_space_is_equal(fold->dim, dim)) {
1243                 isl_space_free(dim);
1244                 return fold;
1245         }
1246
1247         fold = isl_qpolynomial_fold_cow(fold);
1248         if (!fold)
1249                 goto error;
1250
1251         isl_space_free(fold->dim);
1252         fold->dim = isl_space_copy(dim);
1253         if (!fold->dim)
1254                 goto error;
1255
1256         for (i = 0; i < fold->n; ++i) {
1257                 fold->qp[i] = isl_qpolynomial_lift(fold->qp[i],
1258                                                 isl_space_copy(dim));
1259                 if (!fold->qp[i])
1260                         goto error;
1261         }
1262
1263         isl_space_free(dim);
1264
1265         return fold;
1266 error:
1267         isl_qpolynomial_fold_free(fold);
1268         isl_space_free(dim);
1269         return NULL;
1270 }
1271
1272 int isl_qpolynomial_fold_foreach_qpolynomial(
1273         __isl_keep isl_qpolynomial_fold *fold,
1274         int (*fn)(__isl_take isl_qpolynomial *qp, void *user), void *user)
1275 {
1276         int i;
1277
1278         if (!fold)
1279                 return -1;
1280
1281         for (i = 0; i < fold->n; ++i)
1282                 if (fn(isl_qpolynomial_copy(fold->qp[i]), user) < 0)
1283                         return -1;
1284
1285         return 0;
1286 }
1287
1288 __isl_give isl_qpolynomial_fold *isl_qpolynomial_fold_move_dims(
1289         __isl_take isl_qpolynomial_fold *fold,
1290         enum isl_dim_type dst_type, unsigned dst_pos,
1291         enum isl_dim_type src_type, unsigned src_pos, unsigned n)
1292 {
1293         int i;
1294
1295         if (n == 0)
1296                 return fold;
1297
1298         fold = isl_qpolynomial_fold_cow(fold);
1299         if (!fold)
1300                 return NULL;
1301
1302         fold->dim = isl_space_move_dims(fold->dim, dst_type, dst_pos,
1303                                                 src_type, src_pos, n);
1304         if (!fold->dim)
1305                 goto error;
1306
1307         for (i = 0; i < fold->n; ++i) {
1308                 fold->qp[i] = isl_qpolynomial_move_dims(fold->qp[i],
1309                                 dst_type, dst_pos, src_type, src_pos, n);
1310                 if (!fold->qp[i])
1311                         goto error;
1312         }
1313
1314         return fold;
1315 error:
1316         isl_qpolynomial_fold_free(fold);
1317         return NULL;
1318 }
1319
1320 /* For each 0 <= i < "n", replace variable "first" + i of type "type"
1321  * in fold->qp[k] by subs[i].
1322  */
1323 __isl_give isl_qpolynomial_fold *isl_qpolynomial_fold_substitute(
1324         __isl_take isl_qpolynomial_fold *fold,
1325         enum isl_dim_type type, unsigned first, unsigned n,
1326         __isl_keep isl_qpolynomial **subs)
1327 {
1328         int i;
1329
1330         if (n == 0)
1331                 return fold;
1332
1333         fold = isl_qpolynomial_fold_cow(fold);
1334         if (!fold)
1335                 return NULL;
1336
1337         for (i = 0; i < fold->n; ++i) {
1338                 fold->qp[i] = isl_qpolynomial_substitute(fold->qp[i],
1339                                 type, first, n, subs);
1340                 if (!fold->qp[i])
1341                         goto error;
1342         }
1343
1344         return fold;
1345 error:
1346         isl_qpolynomial_fold_free(fold);
1347         return NULL;
1348 }
1349
1350 static int add_pwqp(__isl_take isl_pw_qpolynomial *pwqp, void *user)
1351 {
1352         isl_ctx *ctx;
1353         isl_pw_qpolynomial_fold *pwf;
1354         isl_union_pw_qpolynomial_fold **upwf;
1355         uint32_t hash;
1356         struct isl_hash_table_entry *entry;
1357
1358         upwf = (isl_union_pw_qpolynomial_fold **)user;
1359
1360         ctx = pwqp->dim->ctx;
1361         hash = isl_space_get_hash(pwqp->dim);
1362         entry = isl_hash_table_find(ctx, &(*upwf)->table,
1363                                      hash, &has_dim, pwqp->dim, 1);
1364         if (!entry)
1365                 goto error;
1366
1367         pwf = isl_pw_qpolynomial_fold_from_pw_qpolynomial((*upwf)->type, pwqp);
1368         if (!entry->data)
1369                 entry->data = pwf;
1370         else {
1371                 entry->data = isl_pw_qpolynomial_fold_add(entry->data, pwf);
1372                 if (!entry->data)
1373                         return -1;
1374                 if (isl_pw_qpolynomial_fold_is_zero(entry->data)) {
1375                         isl_pw_qpolynomial_fold_free(entry->data);
1376                         isl_hash_table_remove(ctx, &(*upwf)->table, entry);
1377                 }
1378         }
1379
1380         return 0;
1381 error:
1382         isl_pw_qpolynomial_free(pwqp);
1383         return -1;
1384 }
1385
1386 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_fold_add_union_pw_qpolynomial(
1387         __isl_take isl_union_pw_qpolynomial_fold *upwf,
1388         __isl_take isl_union_pw_qpolynomial *upwqp)
1389 {
1390         upwf = isl_union_pw_qpolynomial_fold_align_params(upwf,
1391                                 isl_union_pw_qpolynomial_get_space(upwqp));
1392         upwqp = isl_union_pw_qpolynomial_align_params(upwqp,
1393                                 isl_union_pw_qpolynomial_fold_get_space(upwf));
1394
1395         upwf = isl_union_pw_qpolynomial_fold_cow(upwf);
1396         if (!upwf || !upwqp)
1397                 goto error;
1398
1399         if (isl_union_pw_qpolynomial_foreach_pw_qpolynomial(upwqp, &add_pwqp,
1400                                                          &upwf) < 0)
1401                 goto error;
1402
1403         isl_union_pw_qpolynomial_free(upwqp);
1404
1405         return upwf;
1406 error:
1407         isl_union_pw_qpolynomial_fold_free(upwf);
1408         isl_union_pw_qpolynomial_free(upwqp);
1409         return NULL;
1410 }
1411
1412 static int join_compatible(__isl_keep isl_space *dim1, __isl_keep isl_space *dim2)
1413 {
1414         int m;
1415         m = isl_space_match(dim1, isl_dim_param, dim2, isl_dim_param);
1416         if (m < 0 || !m)
1417                 return m;
1418         return isl_space_tuple_match(dim1, isl_dim_out, dim2, isl_dim_in);
1419 }
1420
1421 /* Compute the intersection of the range of the map and the domain
1422  * of the piecewise quasipolynomial reduction and then compute a bound
1423  * on the associated quasipolynomial reduction over all elements
1424  * in this intersection.
1425  *
1426  * We first introduce some unconstrained dimensions in the
1427  * piecewise quasipolynomial, intersect the resulting domain
1428  * with the wrapped map and the compute the sum.
1429  */
1430 __isl_give isl_pw_qpolynomial_fold *isl_map_apply_pw_qpolynomial_fold(
1431         __isl_take isl_map *map, __isl_take isl_pw_qpolynomial_fold *pwf,
1432         int *tight)
1433 {
1434         isl_ctx *ctx;
1435         isl_set *dom;
1436         isl_space *map_dim;
1437         isl_space *pwf_dim;
1438         unsigned n_in;
1439         int ok;
1440
1441         ctx = isl_map_get_ctx(map);
1442         if (!ctx)
1443                 goto error;
1444
1445         map_dim = isl_map_get_space(map);
1446         pwf_dim = isl_pw_qpolynomial_fold_get_space(pwf);
1447         ok = join_compatible(map_dim, pwf_dim);
1448         isl_space_free(map_dim);
1449         isl_space_free(pwf_dim);
1450         if (!ok)
1451                 isl_die(ctx, isl_error_invalid, "incompatible dimensions",
1452                         goto error);
1453
1454         n_in = isl_map_dim(map, isl_dim_in);
1455         pwf = isl_pw_qpolynomial_fold_insert_dims(pwf, isl_dim_in, 0, n_in);
1456
1457         dom = isl_map_wrap(map);
1458         pwf = isl_pw_qpolynomial_fold_reset_domain_space(pwf,
1459                                                 isl_set_get_space(dom));
1460
1461         pwf = isl_pw_qpolynomial_fold_intersect_domain(pwf, dom);
1462         pwf = isl_pw_qpolynomial_fold_bound(pwf, tight);
1463
1464         return pwf;
1465 error:
1466         isl_map_free(map);
1467         isl_pw_qpolynomial_fold_free(pwf);
1468         return NULL;
1469 }
1470
1471 __isl_give isl_pw_qpolynomial_fold *isl_set_apply_pw_qpolynomial_fold(
1472         __isl_take isl_set *set, __isl_take isl_pw_qpolynomial_fold *pwf,
1473         int *tight)
1474 {
1475         return isl_map_apply_pw_qpolynomial_fold(set, pwf, tight);
1476 }
1477
1478 struct isl_apply_fold_data {
1479         isl_union_pw_qpolynomial_fold *upwf;
1480         isl_union_pw_qpolynomial_fold *res;
1481         isl_map *map;
1482         int tight;
1483 };
1484
1485 static int pw_qpolynomial_fold_apply(__isl_take isl_pw_qpolynomial_fold *pwf,
1486         void *user)
1487 {
1488         isl_space *map_dim;
1489         isl_space *pwf_dim;
1490         struct isl_apply_fold_data *data = user;
1491         int ok;
1492
1493         map_dim = isl_map_get_space(data->map);
1494         pwf_dim = isl_pw_qpolynomial_fold_get_space(pwf);
1495         ok = join_compatible(map_dim, pwf_dim);
1496         isl_space_free(map_dim);
1497         isl_space_free(pwf_dim);
1498
1499         if (ok) {
1500                 pwf = isl_map_apply_pw_qpolynomial_fold(isl_map_copy(data->map),
1501                                     pwf, data->tight ? &data->tight : NULL);
1502                 data->res = isl_union_pw_qpolynomial_fold_fold_pw_qpolynomial_fold(
1503                                                         data->res, pwf);
1504         } else
1505                 isl_pw_qpolynomial_fold_free(pwf);
1506
1507         return 0;
1508 }
1509
1510 static int map_apply(__isl_take isl_map *map, void *user)
1511 {
1512         struct isl_apply_fold_data *data = user;
1513         int r;
1514
1515         data->map = map;
1516         r = isl_union_pw_qpolynomial_fold_foreach_pw_qpolynomial_fold(
1517                                 data->upwf, &pw_qpolynomial_fold_apply, data);
1518
1519         isl_map_free(map);
1520         return r;
1521 }
1522
1523 __isl_give isl_union_pw_qpolynomial_fold *isl_union_map_apply_union_pw_qpolynomial_fold(
1524         __isl_take isl_union_map *umap,
1525         __isl_take isl_union_pw_qpolynomial_fold *upwf, int *tight)
1526 {
1527         isl_space *dim;
1528         enum isl_fold type;
1529         struct isl_apply_fold_data data;
1530
1531         upwf = isl_union_pw_qpolynomial_fold_align_params(upwf,
1532                                 isl_union_map_get_space(umap));
1533         umap = isl_union_map_align_params(umap,
1534                                 isl_union_pw_qpolynomial_fold_get_space(upwf));
1535
1536         data.upwf = upwf;
1537         data.tight = tight ? 1 : 0;
1538         dim = isl_union_pw_qpolynomial_fold_get_space(upwf);
1539         type = isl_union_pw_qpolynomial_fold_get_type(upwf);
1540         data.res = isl_union_pw_qpolynomial_fold_zero(dim, type);
1541         if (isl_union_map_foreach_map(umap, &map_apply, &data) < 0)
1542                 goto error;
1543
1544         isl_union_map_free(umap);
1545         isl_union_pw_qpolynomial_fold_free(upwf);
1546
1547         if (tight)
1548                 *tight = data.tight;
1549
1550         return data.res;
1551 error:
1552         isl_union_map_free(umap);
1553         isl_union_pw_qpolynomial_fold_free(upwf);
1554         isl_union_pw_qpolynomial_fold_free(data.res);
1555         return NULL;
1556 }
1557
1558 __isl_give isl_union_pw_qpolynomial_fold *isl_union_set_apply_union_pw_qpolynomial_fold(
1559         __isl_take isl_union_set *uset,
1560         __isl_take isl_union_pw_qpolynomial_fold *upwf, int *tight)
1561 {
1562         return isl_union_map_apply_union_pw_qpolynomial_fold(uset, upwf, tight);
1563 }
1564
1565 /* Reorder the dimension of "fold" according to the given reordering.
1566  */
1567 __isl_give isl_qpolynomial_fold *isl_qpolynomial_fold_realign_domain(
1568         __isl_take isl_qpolynomial_fold *fold, __isl_take isl_reordering *r)
1569 {
1570         int i;
1571
1572         fold = isl_qpolynomial_fold_cow(fold);
1573         if (!fold || !r)
1574                 goto error;
1575
1576         for (i = 0; i < fold->n; ++i) {
1577                 fold->qp[i] = isl_qpolynomial_realign_domain(fold->qp[i],
1578                                                     isl_reordering_copy(r));
1579                 if (!fold->qp[i])
1580                         goto error;
1581         }
1582
1583         fold = isl_qpolynomial_fold_reset_domain_space(fold,
1584                                                     isl_space_copy(r->dim));
1585
1586         isl_reordering_free(r);
1587
1588         return fold;
1589 error:
1590         isl_qpolynomial_fold_free(fold);
1591         isl_reordering_free(r);
1592         return NULL;
1593 }
1594
1595 __isl_give isl_qpolynomial_fold *isl_qpolynomial_fold_mul_isl_int(
1596         __isl_take isl_qpolynomial_fold *fold, isl_int v)
1597 {
1598         int i;
1599
1600         if (isl_int_is_one(v))
1601                 return fold;
1602         if (fold && isl_int_is_zero(v)) {
1603                 isl_qpolynomial_fold *zero;
1604                 isl_space *dim = isl_space_copy(fold->dim);
1605                 zero = isl_qpolynomial_fold_empty(fold->type, dim);
1606                 isl_qpolynomial_fold_free(fold);
1607                 return zero;
1608         }
1609
1610         fold = isl_qpolynomial_fold_cow(fold);
1611         if (!fold)
1612                 return NULL;
1613
1614         if (isl_int_is_neg(v))
1615                 fold->type = isl_fold_type_negate(fold->type);
1616         for (i = 0; i < fold->n; ++i) {
1617                 fold->qp[i] = isl_qpolynomial_mul_isl_int(fold->qp[i], v);
1618                 if (!fold->qp[i])
1619                         goto error;
1620         }
1621
1622         return fold;
1623 error:
1624         isl_qpolynomial_fold_free(fold);
1625         return NULL;
1626 }
1627
1628 __isl_give isl_qpolynomial_fold *isl_qpolynomial_fold_scale(
1629         __isl_take isl_qpolynomial_fold *fold, isl_int v)
1630 {
1631         return isl_qpolynomial_fold_mul_isl_int(fold, v);
1632 }
1633
1634 /* Multiply "fold" by "v".
1635  */
1636 __isl_give isl_qpolynomial_fold *isl_qpolynomial_fold_scale_val(
1637         __isl_take isl_qpolynomial_fold *fold, __isl_take isl_val *v)
1638 {
1639         int i;
1640
1641         if (!fold || !v)
1642                 goto error;
1643
1644         if (isl_val_is_one(v)) {
1645                 isl_val_free(v);
1646                 return fold;
1647         }
1648         if (isl_val_is_zero(v)) {
1649                 isl_qpolynomial_fold *zero;
1650                 isl_space *space = isl_qpolynomial_fold_get_domain_space(fold);
1651                 zero = isl_qpolynomial_fold_empty(fold->type, space);
1652                 isl_qpolynomial_fold_free(fold);
1653                 isl_val_free(v);
1654                 return zero;
1655         }
1656         if (!isl_val_is_rat(v))
1657                 isl_die(isl_qpolynomial_fold_get_ctx(fold), isl_error_invalid,
1658                         "expecting rational factor", goto error);
1659
1660         fold = isl_qpolynomial_fold_cow(fold);
1661         if (!fold)
1662                 goto error;
1663
1664         if (isl_val_is_neg(v))
1665                 fold->type = isl_fold_type_negate(fold->type);
1666         for (i = 0; i < fold->n; ++i) {
1667                 fold->qp[i] = isl_qpolynomial_scale_val(fold->qp[i],
1668                                                         isl_val_copy(v));
1669                 if (!fold->qp[i])
1670                         goto error;
1671         }
1672
1673         isl_val_free(v);
1674         return fold;
1675 error:
1676         isl_val_free(v);
1677         isl_qpolynomial_fold_free(fold);
1678         return NULL;
1679 }