isl_polynomial.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 <stdlib.h>
  12 #define ISL_DIM_H
  13 #include <isl_ctx_private.h>
  14 #include <isl_map_private.h>
  15 #include <isl_factorization.h>
  16 #include <isl_lp_private.h>
  17 #include <isl_seq.h>
  18 #include <isl_union_map_private.h>
  19 #include <isl_constraint_private.h>
  20 #include <isl_polynomial_private.h>
  21 #include <isl_point_private.h>
  22 #include <isl_space_private.h>
  23 #include <isl_mat_private.h>
  24 #include <isl_vec_private.h>
  25 #include <isl_range.h>
  26 #include <isl_local_space_private.h>
  27 #include <isl_aff_private.h>
  28 #include <isl_val_private.h>
  29 #include <isl_config.h>
  30 #include <isl/deprecated/polynomial_int.h>
  31
  32 static unsigned pos(__isl_keep isl_space *dim, enum isl_dim_type type)
  33 {
  34         switch (type) {
  35         case isl_dim_param:     return 0;
  36         case isl_dim_in:        return dim->nparam;
  37         case isl_dim_out:       return dim->nparam + dim->n_in;
  38         default:                return 0;
  39         }
  40 }
  41
  42 int isl_upoly_is_cst(__isl_keep struct isl_upoly *up)
  43 {
  44         if (!up)
  45                 return -1;
  46
  47         return up->var < 0;
  48 }
  49
  50 __isl_keep struct isl_upoly_cst *isl_upoly_as_cst(__isl_keep struct isl_upoly *up)
  51 {
  52         if (!up)
  53                 return NULL;
  54
  55         isl_assert(up->ctx, up->var < 0, return NULL);
  56
  57         return (struct isl_upoly_cst *)up;
  58 }
  59
  60 __isl_keep struct isl_upoly_rec *isl_upoly_as_rec(__isl_keep struct isl_upoly *up)
  61 {
  62         if (!up)
  63                 return NULL;
  64
  65         isl_assert(up->ctx, up->var >= 0, return NULL);
  66
  67         return (struct isl_upoly_rec *)up;
  68 }
  69
  70 int isl_upoly_is_equal(__isl_keep struct isl_upoly *up1,
  71         __isl_keep struct isl_upoly *up2)
  72 {
  73         int i;
  74         struct isl_upoly_rec *rec1, *rec2;
  75
  76         if (!up1 || !up2)
  77                 return -1;
  78         if (up1 == up2)
  79                 return 1;
  80         if (up1->var != up2->var)
  81                 return 0;
  82         if (isl_upoly_is_cst(up1)) {
  83                 struct isl_upoly_cst *cst1, *cst2;
  84                 cst1 = isl_upoly_as_cst(up1);
  85                 cst2 = isl_upoly_as_cst(up2);
  86                 if (!cst1 || !cst2)
  87                         return -1;
  88                 return isl_int_eq(cst1->n, cst2->n) &&
  89                        isl_int_eq(cst1->d, cst2->d);
  90         }
  91
  92         rec1 = isl_upoly_as_rec(up1);
  93         rec2 = isl_upoly_as_rec(up2);
  94         if (!rec1 || !rec2)
  95                 return -1;
  96
  97         if (rec1->n != rec2->n)
  98                 return 0;
  99
 100         for (i = 0; i < rec1->n; ++i) {
 101                 int eq = isl_upoly_is_equal(rec1->p[i], rec2->p[i]);
 102                 if (eq < 0 || !eq)
 103                         return eq;
 104         }
 105
 106         return 1;
 107 }
 108
 109 int isl_upoly_is_zero(__isl_keep struct isl_upoly *up)
 110 {
 111         struct isl_upoly_cst *cst;
 112
 113         if (!up)
 114                 return -1;
 115         if (!isl_upoly_is_cst(up))
 116                 return 0;
 117
 118         cst = isl_upoly_as_cst(up);
 119         if (!cst)
 120                 return -1;
 121
 122         return isl_int_is_zero(cst->n) && isl_int_is_pos(cst->d);
 123 }
 124
 125 int isl_upoly_sgn(__isl_keep struct isl_upoly *up)
 126 {
 127         struct isl_upoly_cst *cst;
 128
 129         if (!up)
 130                 return 0;
 131         if (!isl_upoly_is_cst(up))
 132                 return 0;
 133
 134         cst = isl_upoly_as_cst(up);
 135         if (!cst)
 136                 return 0;
 137
 138         return isl_int_sgn(cst->n);
 139 }
 140
 141 int isl_upoly_is_nan(__isl_keep struct isl_upoly *up)
 142 {
 143         struct isl_upoly_cst *cst;
 144
 145         if (!up)
 146                 return -1;
 147         if (!isl_upoly_is_cst(up))
 148                 return 0;
 149
 150         cst = isl_upoly_as_cst(up);
 151         if (!cst)
 152                 return -1;
 153
 154         return isl_int_is_zero(cst->n) && isl_int_is_zero(cst->d);
 155 }
 156
 157 int isl_upoly_is_infty(__isl_keep struct isl_upoly *up)
 158 {
 159         struct isl_upoly_cst *cst;
 160
 161         if (!up)
 162                 return -1;
 163         if (!isl_upoly_is_cst(up))
 164                 return 0;
 165
 166         cst = isl_upoly_as_cst(up);
 167         if (!cst)
 168                 return -1;
 169
 170         return isl_int_is_pos(cst->n) && isl_int_is_zero(cst->d);
 171 }
 172
 173 int isl_upoly_is_neginfty(__isl_keep struct isl_upoly *up)
 174 {
 175         struct isl_upoly_cst *cst;
 176
 177         if (!up)
 178                 return -1;
 179         if (!isl_upoly_is_cst(up))
 180                 return 0;
 181
 182         cst = isl_upoly_as_cst(up);
 183         if (!cst)
 184                 return -1;
 185
 186         return isl_int_is_neg(cst->n) && isl_int_is_zero(cst->d);
 187 }
 188
 189 int isl_upoly_is_one(__isl_keep struct isl_upoly *up)
 190 {
 191         struct isl_upoly_cst *cst;
 192
 193         if (!up)
 194                 return -1;
 195         if (!isl_upoly_is_cst(up))
 196                 return 0;
 197
 198         cst = isl_upoly_as_cst(up);
 199         if (!cst)
 200                 return -1;
 201
 202         return isl_int_eq(cst->n, cst->d) && isl_int_is_pos(cst->d);
 203 }
 204
 205 int isl_upoly_is_negone(__isl_keep struct isl_upoly *up)
 206 {
 207         struct isl_upoly_cst *cst;
 208
 209         if (!up)
 210                 return -1;
 211         if (!isl_upoly_is_cst(up))
 212                 return 0;
 213
 214         cst = isl_upoly_as_cst(up);
 215         if (!cst)
 216                 return -1;
 217
 218         return isl_int_is_negone(cst->n) && isl_int_is_one(cst->d);
 219 }
 220
 221 __isl_give struct isl_upoly_cst *isl_upoly_cst_alloc(struct isl_ctx *ctx)
 222 {
 223         struct isl_upoly_cst *cst;
 224
 225         cst = isl_alloc_type(ctx, struct isl_upoly_cst);
 226         if (!cst)
 227                 return NULL;
 228
 229         cst->up.ref = 1;
 230         cst->up.ctx = ctx;
 231         isl_ctx_ref(ctx);
 232         cst->up.var = -1;
 233
 234         isl_int_init(cst->n);
 235         isl_int_init(cst->d);
 236
 237         return cst;
 238 }
 239
 240 __isl_give struct isl_upoly *isl_upoly_zero(struct isl_ctx *ctx)
 241 {
 242         struct isl_upoly_cst *cst;
 243
 244         cst = isl_upoly_cst_alloc(ctx);
 245         if (!cst)
 246                 return NULL;
 247
 248         isl_int_set_si(cst->n, 0);
 249         isl_int_set_si(cst->d, 1);
 250
 251         return &cst->up;
 252 }
 253
 254 __isl_give struct isl_upoly *isl_upoly_one(struct isl_ctx *ctx)
 255 {
 256         struct isl_upoly_cst *cst;
 257
 258         cst = isl_upoly_cst_alloc(ctx);
 259         if (!cst)
 260                 return NULL;
 261
 262         isl_int_set_si(cst->n, 1);
 263         isl_int_set_si(cst->d, 1);
 264
 265         return &cst->up;
 266 }
 267
 268 __isl_give struct isl_upoly *isl_upoly_infty(struct isl_ctx *ctx)
 269 {
 270         struct isl_upoly_cst *cst;
 271
 272         cst = isl_upoly_cst_alloc(ctx);
 273         if (!cst)
 274                 return NULL;
 275
 276         isl_int_set_si(cst->n, 1);
 277         isl_int_set_si(cst->d, 0);
 278
 279         return &cst->up;
 280 }
 281
 282 __isl_give struct isl_upoly *isl_upoly_neginfty(struct isl_ctx *ctx)
 283 {
 284         struct isl_upoly_cst *cst;
 285
 286         cst = isl_upoly_cst_alloc(ctx);
 287         if (!cst)
 288                 return NULL;
 289
 290         isl_int_set_si(cst->n, -1);
 291         isl_int_set_si(cst->d, 0);
 292
 293         return &cst->up;
 294 }
 295
 296 __isl_give struct isl_upoly *isl_upoly_nan(struct isl_ctx *ctx)
 297 {
 298         struct isl_upoly_cst *cst;
 299
 300         cst = isl_upoly_cst_alloc(ctx);
 301         if (!cst)
 302                 return NULL;
 303
 304         isl_int_set_si(cst->n, 0);
 305         isl_int_set_si(cst->d, 0);
 306
 307         return &cst->up;
 308 }
 309
 310 __isl_give struct isl_upoly *isl_upoly_rat_cst(struct isl_ctx *ctx,
 311         isl_int n, isl_int d)
 312 {
 313         struct isl_upoly_cst *cst;
 314
 315         cst = isl_upoly_cst_alloc(ctx);
 316         if (!cst)
 317                 return NULL;
 318
 319         isl_int_set(cst->n, n);
 320         isl_int_set(cst->d, d);
 321
 322         return &cst->up;
 323 }
 324
 325 __isl_give struct isl_upoly_rec *isl_upoly_alloc_rec(struct isl_ctx *ctx,
 326         int var, int size)
 327 {
 328         struct isl_upoly_rec *rec;
 329
 330         isl_assert(ctx, var >= 0, return NULL);
 331         isl_assert(ctx, size >= 0, return NULL);
 332         rec = isl_calloc(ctx, struct isl_upoly_rec,
 333                         sizeof(struct isl_upoly_rec) +
 334                         size * sizeof(struct isl_upoly *));
 335         if (!rec)
 336                 return NULL;
 337
 338         rec->up.ref = 1;
 339         rec->up.ctx = ctx;
 340         isl_ctx_ref(ctx);
 341         rec->up.var = var;
 342
 343         rec->n = 0;
 344         rec->size = size;
 345
 346         return rec;
 347 }
 348
 349 __isl_give isl_qpolynomial *isl_qpolynomial_reset_domain_space(
 350         __isl_take isl_qpolynomial *qp, __isl_take isl_space *dim)
 351 {
 352         qp = isl_qpolynomial_cow(qp);
 353         if (!qp || !dim)
 354                 goto error;
 355
 356         isl_space_free(qp->dim);
 357         qp->dim = dim;
 358
 359         return qp;
 360 error:
 361         isl_qpolynomial_free(qp);
 362         isl_space_free(dim);
 363         return NULL;
 364 }
 365
 366 /* Reset the space of "qp".  This function is called from isl_pw_templ.c
 367  * and doesn't know if the space of an element object is represented
 368  * directly or through its domain.  It therefore passes along both.
 369  */
 370 __isl_give isl_qpolynomial *isl_qpolynomial_reset_space_and_domain(
 371         __isl_take isl_qpolynomial *qp, __isl_take isl_space *space,
 372         __isl_take isl_space *domain)
 373 {
 374         isl_space_free(space);
 375         return isl_qpolynomial_reset_domain_space(qp, domain);
 376 }
 377
 378 isl_ctx *isl_qpolynomial_get_ctx(__isl_keep isl_qpolynomial *qp)
 379 {
 380         return qp ? qp->dim->ctx : NULL;
 381 }
 382
 383 __isl_give isl_space *isl_qpolynomial_get_domain_space(
 384         __isl_keep isl_qpolynomial *qp)
 385 {
 386         return qp ? isl_space_copy(qp->dim) : NULL;
 387 }
 388
 389 __isl_give isl_space *isl_qpolynomial_get_space(__isl_keep isl_qpolynomial *qp)
 390 {
 391         isl_space *space;
 392         if (!qp)
 393                 return NULL;
 394         space = isl_space_copy(qp->dim);
 395         space = isl_space_from_domain(space);
 396         space = isl_space_add_dims(space, isl_dim_out, 1);
 397         return space;
 398 }
 399
 400 /* Externally, an isl_qpolynomial has a map space, but internally, the
 401  * ls field corresponds to the domain of that space.
 402  */
 403 unsigned isl_qpolynomial_dim(__isl_keep isl_qpolynomial *qp,
 404         enum isl_dim_type type)
 405 {
 406         if (!qp)
 407                 return 0;
 408         if (type == isl_dim_out)
 409                 return 1;
 410         if (type == isl_dim_in)
 411                 type = isl_dim_set;
 412         return isl_space_dim(qp->dim, type);
 413 }
 414
 415 int isl_qpolynomial_is_zero(__isl_keep isl_qpolynomial *qp)
 416 {
 417         return qp ? isl_upoly_is_zero(qp->upoly) : -1;
 418 }
 419
 420 int isl_qpolynomial_is_one(__isl_keep isl_qpolynomial *qp)
 421 {
 422         return qp ? isl_upoly_is_one(qp->upoly) : -1;
 423 }
 424
 425 int isl_qpolynomial_is_nan(__isl_keep isl_qpolynomial *qp)
 426 {
 427         return qp ? isl_upoly_is_nan(qp->upoly) : -1;
 428 }
 429
 430 int isl_qpolynomial_is_infty(__isl_keep isl_qpolynomial *qp)
 431 {
 432         return qp ? isl_upoly_is_infty(qp->upoly) : -1;
 433 }
 434
 435 int isl_qpolynomial_is_neginfty(__isl_keep isl_qpolynomial *qp)
 436 {
 437         return qp ? isl_upoly_is_neginfty(qp->upoly) : -1;
 438 }
 439
 440 int isl_qpolynomial_sgn(__isl_keep isl_qpolynomial *qp)
 441 {
 442         return qp ? isl_upoly_sgn(qp->upoly) : 0;
 443 }
 444
 445 static void upoly_free_cst(__isl_take struct isl_upoly_cst *cst)
 446 {
 447         isl_int_clear(cst->n);
 448         isl_int_clear(cst->d);
 449 }
 450
 451 static void upoly_free_rec(__isl_take struct isl_upoly_rec *rec)
 452 {
 453         int i;
 454
 455         for (i = 0; i < rec->n; ++i)
 456                 isl_upoly_free(rec->p[i]);
 457 }
 458
 459 __isl_give struct isl_upoly *isl_upoly_copy(__isl_keep struct isl_upoly *up)
 460 {
 461         if (!up)
 462                 return NULL;
 463
 464         up->ref++;
 465         return up;
 466 }
 467
 468 __isl_give struct isl_upoly *isl_upoly_dup_cst(__isl_keep struct isl_upoly *up)
 469 {
 470         struct isl_upoly_cst *cst;
 471         struct isl_upoly_cst *dup;
 472
 473         cst = isl_upoly_as_cst(up);
 474         if (!cst)
 475                 return NULL;
 476
 477         dup = isl_upoly_as_cst(isl_upoly_zero(up->ctx));
 478         if (!dup)
 479                 return NULL;
 480         isl_int_set(dup->n, cst->n);
 481         isl_int_set(dup->d, cst->d);
 482
 483         return &dup->up;
 484 }
 485
 486 __isl_give struct isl_upoly *isl_upoly_dup_rec(__isl_keep struct isl_upoly *up)
 487 {
 488         int i;
 489         struct isl_upoly_rec *rec;
 490         struct isl_upoly_rec *dup;
 491
 492         rec = isl_upoly_as_rec(up);
 493         if (!rec)
 494                 return NULL;
 495
 496         dup = isl_upoly_alloc_rec(up->ctx, up->var, rec->n);
 497         if (!dup)
 498                 return NULL;
 499
 500         for (i = 0; i < rec->n; ++i) {
 501                 dup->p[i] = isl_upoly_copy(rec->p[i]);
 502                 if (!dup->p[i])
 503                         goto error;
 504                 dup->n++;
 505         }
 506
 507         return &dup->up;
 508 error:
 509         isl_upoly_free(&dup->up);
 510         return NULL;
 511 }
 512
 513 __isl_give struct isl_upoly *isl_upoly_dup(__isl_keep struct isl_upoly *up)
 514 {
 515         if (!up)
 516                 return NULL;
 517
 518         if (isl_upoly_is_cst(up))
 519                 return isl_upoly_dup_cst(up);
 520         else
 521                 return isl_upoly_dup_rec(up);
 522 }
 523
 524 __isl_give struct isl_upoly *isl_upoly_cow(__isl_take struct isl_upoly *up)
 525 {
 526         if (!up)
 527                 return NULL;
 528
 529         if (up->ref == 1)
 530                 return up;
 531         up->ref--;
 532         return isl_upoly_dup(up);
 533 }
 534
 535 void isl_upoly_free(__isl_take struct isl_upoly *up)
 536 {
 537         if (!up)
 538                 return;
 539
 540         if (--up->ref > 0)
 541                 return;
 542
 543         if (up->var < 0)
 544                 upoly_free_cst((struct isl_upoly_cst *)up);
 545         else
 546                 upoly_free_rec((struct isl_upoly_rec *)up);
 547
 548         isl_ctx_deref(up->ctx);
 549         free(up);
 550 }
 551
 552 static void isl_upoly_cst_reduce(__isl_keep struct isl_upoly_cst *cst)
 553 {
 554         isl_int gcd;
 555
 556         isl_int_init(gcd);
 557         isl_int_gcd(gcd, cst->n, cst->d);
 558         if (!isl_int_is_zero(gcd) && !isl_int_is_one(gcd)) {
 559                 isl_int_divexact(cst->n, cst->n, gcd);
 560                 isl_int_divexact(cst->d, cst->d, gcd);
 561         }
 562         isl_int_clear(gcd);
 563 }
 564
 565 __isl_give struct isl_upoly *isl_upoly_sum_cst(__isl_take struct isl_upoly *up1,
 566         __isl_take struct isl_upoly *up2)
 567 {
 568         struct isl_upoly_cst *cst1;
 569         struct isl_upoly_cst *cst2;
 570
 571         up1 = isl_upoly_cow(up1);
 572         if (!up1 || !up2)
 573                 goto error;
 574
 575         cst1 = isl_upoly_as_cst(up1);
 576         cst2 = isl_upoly_as_cst(up2);
 577
 578         if (isl_int_eq(cst1->d, cst2->d))
 579                 isl_int_add(cst1->n, cst1->n, cst2->n);
 580         else {
 581                 isl_int_mul(cst1->n, cst1->n, cst2->d);
 582                 isl_int_addmul(cst1->n, cst2->n, cst1->d);
 583                 isl_int_mul(cst1->d, cst1->d, cst2->d);
 584         }
 585
 586         isl_upoly_cst_reduce(cst1);
 587
 588         isl_upoly_free(up2);
 589         return up1;
 590 error:
 591         isl_upoly_free(up1);
 592         isl_upoly_free(up2);
 593         return NULL;
 594 }
 595
 596 static __isl_give struct isl_upoly *replace_by_zero(
 597         __isl_take struct isl_upoly *up)
 598 {
 599         struct isl_ctx *ctx;
 600
 601         if (!up)
 602                 return NULL;
 603         ctx = up->ctx;
 604         isl_upoly_free(up);
 605         return isl_upoly_zero(ctx);
 606 }
 607
 608 static __isl_give struct isl_upoly *replace_by_constant_term(
 609         __isl_take struct isl_upoly *up)
 610 {
 611         struct isl_upoly_rec *rec;
 612         struct isl_upoly *cst;
 613
 614         if (!up)
 615                 return NULL;
 616
 617         rec = isl_upoly_as_rec(up);
 618         if (!rec)
 619                 goto error;
 620         cst = isl_upoly_copy(rec->p[0]);
 621         isl_upoly_free(up);
 622         return cst;
 623 error:
 624         isl_upoly_free(up);
 625         return NULL;
 626 }
 627
 628 __isl_give struct isl_upoly *isl_upoly_sum(__isl_take struct isl_upoly *up1,
 629         __isl_take struct isl_upoly *up2)
 630 {
 631         int i;
 632         struct isl_upoly_rec *rec1, *rec2;
 633
 634         if (!up1 || !up2)
 635                 goto error;
 636
 637         if (isl_upoly_is_nan(up1)) {
 638                 isl_upoly_free(up2);
 639                 return up1;
 640         }
 641
 642         if (isl_upoly_is_nan(up2)) {
 643                 isl_upoly_free(up1);
 644                 return up2;
 645         }
 646
 647         if (isl_upoly_is_zero(up1)) {
 648                 isl_upoly_free(up1);
 649                 return up2;
 650         }
 651
 652         if (isl_upoly_is_zero(up2)) {
 653                 isl_upoly_free(up2);
 654                 return up1;
 655         }
 656
 657         if (up1->var < up2->var)
 658                 return isl_upoly_sum(up2, up1);
 659
 660         if (up2->var < up1->var) {
 661                 struct isl_upoly_rec *rec;
 662                 if (isl_upoly_is_infty(up2) || isl_upoly_is_neginfty(up2)) {
 663                         isl_upoly_free(up1);
 664                         return up2;
 665                 }
 666                 up1 = isl_upoly_cow(up1);
 667                 rec = isl_upoly_as_rec(up1);
 668                 if (!rec)
 669                         goto error;
 670                 rec->p[0] = isl_upoly_sum(rec->p[0], up2);
 671                 if (rec->n == 1)
 672                         up1 = replace_by_constant_term(up1);
 673                 return up1;
 674         }
 675
 676         if (isl_upoly_is_cst(up1))
 677                 return isl_upoly_sum_cst(up1, up2);
 678
 679         rec1 = isl_upoly_as_rec(up1);
 680         rec2 = isl_upoly_as_rec(up2);
 681         if (!rec1 || !rec2)
 682                 goto error;
 683
 684         if (rec1->n < rec2->n)
 685                 return isl_upoly_sum(up2, up1);
 686
 687         up1 = isl_upoly_cow(up1);
 688         rec1 = isl_upoly_as_rec(up1);
 689         if (!rec1)
 690                 goto error;
 691
 692         for (i = rec2->n - 1; i >= 0; --i) {
 693                 rec1->p[i] = isl_upoly_sum(rec1->p[i],
 694                                             isl_upoly_copy(rec2->p[i]));
 695                 if (!rec1->p[i])
 696                         goto error;
 697                 if (i == rec1->n - 1 && isl_upoly_is_zero(rec1->p[i])) {
 698                         isl_upoly_free(rec1->p[i]);
 699                         rec1->n--;
 700                 }
 701         }
 702
 703         if (rec1->n == 0)
 704                 up1 = replace_by_zero(up1);
 705         else if (rec1->n == 1)
 706                 up1 = replace_by_constant_term(up1);
 707
 708         isl_upoly_free(up2);
 709
 710         return up1;
 711 error:
 712         isl_upoly_free(up1);
 713         isl_upoly_free(up2);
 714         return NULL;
 715 }
 716
 717 __isl_give struct isl_upoly *isl_upoly_cst_add_isl_int(
 718         __isl_take struct isl_upoly *up, isl_int v)
 719 {
 720         struct isl_upoly_cst *cst;
 721
 722         up = isl_upoly_cow(up);
 723         if (!up)
 724                 return NULL;
 725
 726         cst = isl_upoly_as_cst(up);
 727
 728         isl_int_addmul(cst->n, cst->d, v);
 729
 730         return up;
 731 }
 732
 733 __isl_give struct isl_upoly *isl_upoly_add_isl_int(
 734         __isl_take struct isl_upoly *up, isl_int v)
 735 {
 736         struct isl_upoly_rec *rec;
 737
 738         if (!up)
 739                 return NULL;
 740
 741         if (isl_upoly_is_cst(up))
 742                 return isl_upoly_cst_add_isl_int(up, v);
 743
 744         up = isl_upoly_cow(up);
 745         rec = isl_upoly_as_rec(up);
 746         if (!rec)
 747                 goto error;
 748
 749         rec->p[0] = isl_upoly_add_isl_int(rec->p[0], v);
 750         if (!rec->p[0])
 751                 goto error;
 752
 753         return up;
 754 error:
 755         isl_upoly_free(up);
 756         return NULL;
 757 }
 758
 759 __isl_give struct isl_upoly *isl_upoly_cst_mul_isl_int(
 760         __isl_take struct isl_upoly *up, isl_int v)
 761 {
 762         struct isl_upoly_cst *cst;
 763
 764         if (isl_upoly_is_zero(up))
 765                 return up;
 766
 767         up = isl_upoly_cow(up);
 768         if (!up)
 769                 return NULL;
 770
 771         cst = isl_upoly_as_cst(up);
 772
 773         isl_int_mul(cst->n, cst->n, v);
 774
 775         return up;
 776 }
 777
 778 __isl_give struct isl_upoly *isl_upoly_mul_isl_int(
 779         __isl_take struct isl_upoly *up, isl_int v)
 780 {
 781         int i;
 782         struct isl_upoly_rec *rec;
 783
 784         if (!up)
 785                 return NULL;
 786
 787         if (isl_upoly_is_cst(up))
 788                 return isl_upoly_cst_mul_isl_int(up, v);
 789
 790         up = isl_upoly_cow(up);
 791         rec = isl_upoly_as_rec(up);
 792         if (!rec)
 793                 goto error;
 794
 795         for (i = 0; i < rec->n; ++i) {
 796                 rec->p[i] = isl_upoly_mul_isl_int(rec->p[i], v);
 797                 if (!rec->p[i])
 798                         goto error;
 799         }
 800
 801         return up;
 802 error:
 803         isl_upoly_free(up);
 804         return NULL;
 805 }
 806
 807 /* Multiply the constant polynomial "up" by "v".
 808  */
 809 static __isl_give struct isl_upoly *isl_upoly_cst_scale_val(
 810         __isl_take struct isl_upoly *up, __isl_keep isl_val *v)
 811 {
 812         struct isl_upoly_cst *cst;
 813
 814         if (isl_upoly_is_zero(up))
 815                 return up;
 816
 817         up = isl_upoly_cow(up);
 818         if (!up)
 819                 return NULL;
 820
 821         cst = isl_upoly_as_cst(up);
 822
 823         isl_int_mul(cst->n, cst->n, v->n);
 824         isl_int_mul(cst->d, cst->d, v->d);
 825         isl_upoly_cst_reduce(cst);
 826
 827         return up;
 828 }
 829
 830 /* Multiply the polynomial "up" by "v".
 831  */
 832 static __isl_give struct isl_upoly *isl_upoly_scale_val(
 833         __isl_take struct isl_upoly *up, __isl_keep isl_val *v)
 834 {
 835         int i;
 836         struct isl_upoly_rec *rec;
 837
 838         if (!up)
 839                 return NULL;
 840
 841         if (isl_upoly_is_cst(up))
 842                 return isl_upoly_cst_scale_val(up, v);
 843
 844         up = isl_upoly_cow(up);
 845         rec = isl_upoly_as_rec(up);
 846         if (!rec)
 847                 goto error;
 848
 849         for (i = 0; i < rec->n; ++i) {
 850                 rec->p[i] = isl_upoly_scale_val(rec->p[i], v);
 851                 if (!rec->p[i])
 852                         goto error;
 853         }
 854
 855         return up;
 856 error:
 857         isl_upoly_free(up);
 858         return NULL;
 859 }
 860
 861 __isl_give struct isl_upoly *isl_upoly_mul_cst(__isl_take struct isl_upoly *up1,
 862         __isl_take struct isl_upoly *up2)
 863 {
 864         struct isl_upoly_cst *cst1;
 865         struct isl_upoly_cst *cst2;
 866
 867         up1 = isl_upoly_cow(up1);
 868         if (!up1 || !up2)
 869                 goto error;
 870
 871         cst1 = isl_upoly_as_cst(up1);
 872         cst2 = isl_upoly_as_cst(up2);
 873
 874         isl_int_mul(cst1->n, cst1->n, cst2->n);
 875         isl_int_mul(cst1->d, cst1->d, cst2->d);
 876
 877         isl_upoly_cst_reduce(cst1);
 878
 879         isl_upoly_free(up2);
 880         return up1;
 881 error:
 882         isl_upoly_free(up1);
 883         isl_upoly_free(up2);
 884         return NULL;
 885 }
 886
 887 __isl_give struct isl_upoly *isl_upoly_mul_rec(__isl_take struct isl_upoly *up1,
 888         __isl_take struct isl_upoly *up2)
 889 {
 890         struct isl_upoly_rec *rec1;
 891         struct isl_upoly_rec *rec2;
 892         struct isl_upoly_rec *res = NULL;
 893         int i, j;
 894         int size;
 895
 896         rec1 = isl_upoly_as_rec(up1);
 897         rec2 = isl_upoly_as_rec(up2);
 898         if (!rec1 || !rec2)
 899                 goto error;
 900         size = rec1->n + rec2->n - 1;
 901         res = isl_upoly_alloc_rec(up1->ctx, up1->var, size);
 902         if (!res)
 903                 goto error;
 904
 905         for (i = 0; i < rec1->n; ++i) {
 906                 res->p[i] = isl_upoly_mul(isl_upoly_copy(rec2->p[0]),
 907                                             isl_upoly_copy(rec1->p[i]));
 908                 if (!res->p[i])
 909                         goto error;
 910                 res->n++;
 911         }
 912         for (; i < size; ++i) {
 913                 res->p[i] = isl_upoly_zero(up1->ctx);
 914                 if (!res->p[i])
 915                         goto error;
 916                 res->n++;
 917         }
 918         for (i = 0; i < rec1->n; ++i) {
 919                 for (j = 1; j < rec2->n; ++j) {
 920                         struct isl_upoly *up;
 921                         up = isl_upoly_mul(isl_upoly_copy(rec2->p[j]),
 922                                             isl_upoly_copy(rec1->p[i]));
 923                         res->p[i + j] = isl_upoly_sum(res->p[i + j], up);
 924                         if (!res->p[i + j])
 925                                 goto error;
 926                 }
 927         }
 928
 929         isl_upoly_free(up1);
 930         isl_upoly_free(up2);
 931
 932         return &res->up;
 933 error:
 934         isl_upoly_free(up1);
 935         isl_upoly_free(up2);
 936         isl_upoly_free(&res->up);
 937         return NULL;
 938 }
 939
 940 __isl_give struct isl_upoly *isl_upoly_mul(__isl_take struct isl_upoly *up1,
 941         __isl_take struct isl_upoly *up2)
 942 {
 943         if (!up1 || !up2)
 944                 goto error;
 945
 946         if (isl_upoly_is_nan(up1)) {
 947                 isl_upoly_free(up2);
 948                 return up1;
 949         }
 950
 951         if (isl_upoly_is_nan(up2)) {
 952                 isl_upoly_free(up1);
 953                 return up2;
 954         }
 955
 956         if (isl_upoly_is_zero(up1)) {
 957                 isl_upoly_free(up2);
 958                 return up1;
 959         }
 960
 961         if (isl_upoly_is_zero(up2)) {
 962                 isl_upoly_free(up1);
 963                 return up2;
 964         }
 965
 966         if (isl_upoly_is_one(up1)) {
 967                 isl_upoly_free(up1);
 968                 return up2;
 969         }
 970
 971         if (isl_upoly_is_one(up2)) {
 972                 isl_upoly_free(up2);
 973                 return up1;
 974         }
 975
 976         if (up1->var < up2->var)
 977                 return isl_upoly_mul(up2, up1);
 978
 979         if (up2->var < up1->var) {
 980                 int i;
 981                 struct isl_upoly_rec *rec;
 982                 if (isl_upoly_is_infty(up2) || isl_upoly_is_neginfty(up2)) {
 983                         isl_ctx *ctx = up1->ctx;
 984                         isl_upoly_free(up1);
 985                         isl_upoly_free(up2);
 986                         return isl_upoly_nan(ctx);
 987                 }
 988                 up1 = isl_upoly_cow(up1);
 989                 rec = isl_upoly_as_rec(up1);
 990                 if (!rec)
 991                         goto error;
 992
 993                 for (i = 0; i < rec->n; ++i) {
 994                         rec->p[i] = isl_upoly_mul(rec->p[i],
 995                                                     isl_upoly_copy(up2));
 996                         if (!rec->p[i])
 997                                 goto error;
 998                 }
 999                 isl_upoly_free(up2);
1000                 return up1;
1001         }
1002
1003         if (isl_upoly_is_cst(up1))
1004                 return isl_upoly_mul_cst(up1, up2);
1005
1006         return isl_upoly_mul_rec(up1, up2);
1007 error:
1008         isl_upoly_free(up1);
1009         isl_upoly_free(up2);
1010         return NULL;
1011 }
1012
1013 __isl_give struct isl_upoly *isl_upoly_pow(__isl_take struct isl_upoly *up,
1014         unsigned power)
1015 {
1016         struct isl_upoly *res;
1017
1018         if (!up)
1019                 return NULL;
1020         if (power == 1)
1021                 return up;
1022
1023         if (power % 2)
1024                 res = isl_upoly_copy(up);
1025         else
1026                 res = isl_upoly_one(up->ctx);
1027
1028         while (power >>= 1) {
1029                 up = isl_upoly_mul(up, isl_upoly_copy(up));
1030                 if (power % 2)
1031                         res = isl_upoly_mul(res, isl_upoly_copy(up));
1032         }
1033
1034         isl_upoly_free(up);
1035         return res;
1036 }
1037
1038 __isl_give isl_qpolynomial *isl_qpolynomial_alloc(__isl_take isl_space *dim,
1039         unsigned n_div, __isl_take struct isl_upoly *up)
1040 {
1041         struct isl_qpolynomial *qp = NULL;
1042         unsigned total;
1043
1044         if (!dim || !up)
1045                 goto error;
1046
1047         if (!isl_space_is_set(dim))
1048                 isl_die(isl_space_get_ctx(dim), isl_error_invalid,
1049                         "domain of polynomial should be a set", goto error);
1050
1051         total = isl_space_dim(dim, isl_dim_all);
1052
1053         qp = isl_calloc_type(dim->ctx, struct isl_qpolynomial);
1054         if (!qp)
1055                 goto error;
1056
1057         qp->ref = 1;
1058         qp->div = isl_mat_alloc(dim->ctx, n_div, 1 + 1 + total + n_div);
1059         if (!qp->div)
1060                 goto error;
1061
1062         qp->dim = dim;
1063         qp->upoly = up;
1064
1065         return qp;
1066 error:
1067         isl_space_free(dim);
1068         isl_upoly_free(up);
1069         isl_qpolynomial_free(qp);
1070         return NULL;
1071 }
1072
1073 __isl_give isl_qpolynomial *isl_qpolynomial_copy(__isl_keep isl_qpolynomial *qp)
1074 {
1075         if (!qp)
1076                 return NULL;
1077
1078         qp->ref++;
1079         return qp;
1080 }
1081
1082 __isl_give isl_qpolynomial *isl_qpolynomial_dup(__isl_keep isl_qpolynomial *qp)
1083 {
1084         struct isl_qpolynomial *dup;
1085
1086         if (!qp)
1087                 return NULL;
1088
1089         dup = isl_qpolynomial_alloc(isl_space_copy(qp->dim), qp->div->n_row,
1090                                     isl_upoly_copy(qp->upoly));
1091         if (!dup)
1092                 return NULL;
1093         isl_mat_free(dup->div);
1094         dup->div = isl_mat_copy(qp->div);
1095         if (!dup->div)
1096                 goto error;
1097
1098         return dup;
1099 error:
1100         isl_qpolynomial_free(dup);
1101         return NULL;
1102 }
1103
1104 __isl_give isl_qpolynomial *isl_qpolynomial_cow(__isl_take isl_qpolynomial *qp)
1105 {
1106         if (!qp)
1107                 return NULL;
1108
1109         if (qp->ref == 1)
1110                 return qp;
1111         qp->ref--;
1112         return isl_qpolynomial_dup(qp);
1113 }
1114
1115 __isl_null isl_qpolynomial *isl_qpolynomial_free(
1116         __isl_take isl_qpolynomial *qp)
1117 {
1118         if (!qp)
1119                 return NULL;
1120
1121         if (--qp->ref > 0)
1122                 return NULL;
1123
1124         isl_space_free(qp->dim);
1125         isl_mat_free(qp->div);
1126         isl_upoly_free(qp->upoly);
1127
1128         free(qp);
1129         return NULL;
1130 }
1131
1132 __isl_give struct isl_upoly *isl_upoly_var_pow(isl_ctx *ctx, int pos, int power)
1133 {
1134         int i;
1135         struct isl_upoly_rec *rec;
1136         struct isl_upoly_cst *cst;
1137
1138         rec = isl_upoly_alloc_rec(ctx, pos, 1 + power);
1139         if (!rec)
1140                 return NULL;
1141         for (i = 0; i < 1 + power; ++i) {
1142                 rec->p[i] = isl_upoly_zero(ctx);
1143                 if (!rec->p[i])
1144                         goto error;
1145                 rec->n++;
1146         }
1147         cst = isl_upoly_as_cst(rec->p[power]);
1148         isl_int_set_si(cst->n, 1);
1149
1150         return &rec->up;
1151 error:
1152         isl_upoly_free(&rec->up);
1153         return NULL;
1154 }
1155
1156 /* r array maps original positions to new positions.
1157  */
1158 static __isl_give struct isl_upoly *reorder(__isl_take struct isl_upoly *up,
1159         int *r)
1160 {
1161         int i;
1162         struct isl_upoly_rec *rec;
1163         struct isl_upoly *base;
1164         struct isl_upoly *res;
1165
1166         if (isl_upoly_is_cst(up))
1167                 return up;
1168
1169         rec = isl_upoly_as_rec(up);
1170         if (!rec)
1171                 goto error;
1172
1173         isl_assert(up->ctx, rec->n >= 1, goto error);
1174
1175         base = isl_upoly_var_pow(up->ctx, r[up->var], 1);
1176         res = reorder(isl_upoly_copy(rec->p[rec->n - 1]), r);
1177
1178         for (i = rec->n - 2; i >= 0; --i) {
1179                 res = isl_upoly_mul(res, isl_upoly_copy(base));
1180                 res = isl_upoly_sum(res, reorder(isl_upoly_copy(rec->p[i]), r));
1181         }
1182
1183         isl_upoly_free(base);
1184         isl_upoly_free(up);
1185
1186         return res;
1187 error:
1188         isl_upoly_free(up);
1189         return NULL;
1190 }
1191
1192 static int compatible_divs(__isl_keep isl_mat *div1, __isl_keep isl_mat *div2)
1193 {
1194         int n_row, n_col;
1195         int equal;
1196
1197         isl_assert(div1->ctx, div1->n_row >= div2->n_row &&
1198                                 div1->n_col >= div2->n_col, return -1);
1199
1200         if (div1->n_row == div2->n_row)
1201                 return isl_mat_is_equal(div1, div2);
1202
1203         n_row = div1->n_row;
1204         n_col = div1->n_col;
1205         div1->n_row = div2->n_row;
1206         div1->n_col = div2->n_col;
1207
1208         equal = isl_mat_is_equal(div1, div2);
1209
1210         div1->n_row = n_row;
1211         div1->n_col = n_col;
1212
1213         return equal;
1214 }
1215
1216 static int cmp_row(__isl_keep isl_mat *div, int i, int j)
1217 {
1218         int li, lj;
1219
1220         li = isl_seq_last_non_zero(div->row[i], div->n_col);
1221         lj = isl_seq_last_non_zero(div->row[j], div->n_col);
1222
1223         if (li != lj)
1224                 return li - lj;
1225
1226         return isl_seq_cmp(div->row[i], div->row[j], div->n_col);
1227 }
1228
1229 struct isl_div_sort_info {
1230         isl_mat *div;
1231         int      row;
1232 };
1233
1234 static int div_sort_cmp(const void *p1, const void *p2)
1235 {
1236         const struct isl_div_sort_info *i1, *i2;
1237         i1 = (const struct isl_div_sort_info *) p1;
1238         i2 = (const struct isl_div_sort_info *) p2;
1239
1240         return cmp_row(i1->div, i1->row, i2->row);
1241 }
1242
1243 /* Sort divs and remove duplicates.
1244  */
1245 static __isl_give isl_qpolynomial *sort_divs(__isl_take isl_qpolynomial *qp)
1246 {
1247         int i;
1248         int skip;
1249         int len;
1250         struct isl_div_sort_info *array = NULL;
1251         int *pos = NULL, *at = NULL;
1252         int *reordering = NULL;
1253         unsigned div_pos;
1254
1255         if (!qp)
1256                 return NULL;
1257         if (qp->div->n_row <= 1)
1258                 return qp;
1259
1260         div_pos = isl_space_dim(qp->dim, isl_dim_all);
1261
1262         array = isl_alloc_array(qp->div->ctx, struct isl_div_sort_info,
1263                                 qp->div->n_row);
1264         pos = isl_alloc_array(qp->div->ctx, int, qp->div->n_row);
1265         at = isl_alloc_array(qp->div->ctx, int, qp->div->n_row);
1266         len = qp->div->n_col - 2;
1267         reordering = isl_alloc_array(qp->div->ctx, int, len);
1268         if (!array || !pos || !at || !reordering)
1269                 goto error;
1270
1271         for (i = 0; i < qp->div->n_row; ++i) {
1272                 array[i].div = qp->div;
1273                 array[i].row = i;
1274                 pos[i] = i;
1275                 at[i] = i;
1276         }
1277
1278         qsort(array, qp->div->n_row, sizeof(struct isl_div_sort_info),
1279                 div_sort_cmp);
1280
1281         for (i = 0; i < div_pos; ++i)
1282                 reordering[i] = i;
1283
1284         for (i = 0; i < qp->div->n_row; ++i) {
1285                 if (pos[array[i].row] == i)
1286                         continue;
1287                 qp->div = isl_mat_swap_rows(qp->div, i, pos[array[i].row]);
1288                 pos[at[i]] = pos[array[i].row];
1289                 at[pos[array[i].row]] = at[i];
1290                 at[i] = array[i].row;
1291                 pos[array[i].row] = i;
1292         }
1293
1294         skip = 0;
1295         for (i = 0; i < len - div_pos; ++i) {
1296                 if (i > 0 &&
1297                     isl_seq_eq(qp->div->row[i - skip - 1],
1298                                qp->div->row[i - skip], qp->div->n_col)) {
1299                         qp->div = isl_mat_drop_rows(qp->div, i - skip, 1);
1300                         isl_mat_col_add(qp->div, 2 + div_pos + i - skip - 1,
1301                                                  2 + div_pos + i - skip);
1302                         qp->div = isl_mat_drop_cols(qp->div,
1303                                                     2 + div_pos + i - skip, 1);
1304                         skip++;
1305                 }
1306                 reordering[div_pos + array[i].row] = div_pos + i - skip;
1307         }
1308
1309         qp->upoly = reorder(qp->upoly, reordering);
1310
1311         if (!qp->upoly || !qp->div)
1312                 goto error;
1313
1314         free(at);
1315         free(pos);
1316         free(array);
1317         free(reordering);
1318
1319         return qp;
1320 error:
1321         free(at);
1322         free(pos);
1323         free(array);
1324         free(reordering);
1325         isl_qpolynomial_free(qp);
1326         return NULL;
1327 }
1328
1329 static __isl_give struct isl_upoly *expand(__isl_take struct isl_upoly *up,
1330         int *exp, int first)
1331 {
1332         int i;
1333         struct isl_upoly_rec *rec;
1334
1335         if (isl_upoly_is_cst(up))
1336                 return up;
1337
1338         if (up->var < first)
1339                 return up;
1340
1341         if (exp[up->var - first] == up->var - first)
1342                 return up;
1343
1344         up = isl_upoly_cow(up);
1345         if (!up)
1346                 goto error;
1347
1348         up->var = exp[up->var - first] + first;
1349
1350         rec = isl_upoly_as_rec(up);
1351         if (!rec)
1352                 goto error;
1353
1354         for (i = 0; i < rec->n; ++i) {
1355                 rec->p[i] = expand(rec->p[i], exp, first);
1356                 if (!rec->p[i])
1357                         goto error;
1358         }
1359
1360         return up;
1361 error:
1362         isl_upoly_free(up);
1363         return NULL;
1364 }
1365
1366 static __isl_give isl_qpolynomial *with_merged_divs(
1367         __isl_give isl_qpolynomial *(*fn)(__isl_take isl_qpolynomial *qp1,
1368                                           __isl_take isl_qpolynomial *qp2),
1369         __isl_take isl_qpolynomial *qp1, __isl_take isl_qpolynomial *qp2)
1370 {
1371         int *exp1 = NULL;
1372         int *exp2 = NULL;
1373         isl_mat *div = NULL;
1374         int n_div1, n_div2;
1375
1376         qp1 = isl_qpolynomial_cow(qp1);
1377         qp2 = isl_qpolynomial_cow(qp2);
1378
1379         if (!qp1 || !qp2)
1380                 goto error;
1381
1382         isl_assert(qp1->div->ctx, qp1->div->n_row >= qp2->div->n_row &&
1383                                 qp1->div->n_col >= qp2->div->n_col, goto error);
1384
1385         n_div1 = qp1->div->n_row;
1386         n_div2 = qp2->div->n_row;
1387         exp1 = isl_alloc_array(qp1->div->ctx, int, n_div1);
1388         exp2 = isl_alloc_array(qp2->div->ctx, int, n_div2);
1389         if ((n_div1 && !exp1) || (n_div2 && !exp2))
1390                 goto error;
1391
1392         div = isl_merge_divs(qp1->div, qp2->div, exp1, exp2);
1393         if (!div)
1394                 goto error;
1395
1396         isl_mat_free(qp1->div);
1397         qp1->div = isl_mat_copy(div);
1398         isl_mat_free(qp2->div);
1399         qp2->div = isl_mat_copy(div);
1400
1401         qp1->upoly = expand(qp1->upoly, exp1, div->n_col - div->n_row - 2);
1402         qp2->upoly = expand(qp2->upoly, exp2, div->n_col - div->n_row - 2);
1403
1404         if (!qp1->upoly || !qp2->upoly)
1405                 goto error;
1406
1407         isl_mat_free(div);
1408         free(exp1);
1409         free(exp2);
1410
1411         return fn(qp1, qp2);
1412 error:
1413         isl_mat_free(div);
1414         free(exp1);
1415         free(exp2);
1416         isl_qpolynomial_free(qp1);
1417         isl_qpolynomial_free(qp2);
1418         return NULL;
1419 }
1420
1421 __isl_give isl_qpolynomial *isl_qpolynomial_add(__isl_take isl_qpolynomial *qp1,
1422         __isl_take isl_qpolynomial *qp2)
1423 {
1424         qp1 = isl_qpolynomial_cow(qp1);
1425
1426         if (!qp1 || !qp2)
1427                 goto error;
1428
1429         if (qp1->div->n_row < qp2->div->n_row)
1430                 return isl_qpolynomial_add(qp2, qp1);
1431
1432         isl_assert(qp1->dim->ctx, isl_space_is_equal(qp1->dim, qp2->dim), goto error);
1433         if (!compatible_divs(qp1->div, qp2->div))
1434                 return with_merged_divs(isl_qpolynomial_add, qp1, qp2);
1435
1436         qp1->upoly = isl_upoly_sum(qp1->upoly, isl_upoly_copy(qp2->upoly));
1437         if (!qp1->upoly)
1438                 goto error;
1439
1440         isl_qpolynomial_free(qp2);
1441
1442         return qp1;
1443 error:
1444         isl_qpolynomial_free(qp1);
1445         isl_qpolynomial_free(qp2);
1446         return NULL;
1447 }
1448
1449 __isl_give isl_qpolynomial *isl_qpolynomial_add_on_domain(
1450         __isl_keep isl_set *dom,
1451         __isl_take isl_qpolynomial *qp1,
1452         __isl_take isl_qpolynomial *qp2)
1453 {
1454         qp1 = isl_qpolynomial_add(qp1, qp2);
1455         qp1 = isl_qpolynomial_gist(qp1, isl_set_copy(dom));
1456         return qp1;
1457 }
1458
1459 __isl_give isl_qpolynomial *isl_qpolynomial_sub(__isl_take isl_qpolynomial *qp1,
1460         __isl_take isl_qpolynomial *qp2)
1461 {
1462         return isl_qpolynomial_add(qp1, isl_qpolynomial_neg(qp2));
1463 }
1464
1465 __isl_give isl_qpolynomial *isl_qpolynomial_add_isl_int(
1466         __isl_take isl_qpolynomial *qp, isl_int v)
1467 {
1468         if (isl_int_is_zero(v))
1469                 return qp;
1470
1471         qp = isl_qpolynomial_cow(qp);
1472         if (!qp)
1473                 return NULL;
1474
1475         qp->upoly = isl_upoly_add_isl_int(qp->upoly, v);
1476         if (!qp->upoly)
1477                 goto error;
1478
1479         return qp;
1480 error:
1481         isl_qpolynomial_free(qp);
1482         return NULL;
1483
1484 }
1485
1486 __isl_give isl_qpolynomial *isl_qpolynomial_neg(__isl_take isl_qpolynomial *qp)
1487 {
1488         if (!qp)
1489                 return NULL;
1490
1491         return isl_qpolynomial_mul_isl_int(qp, qp->dim->ctx->negone);
1492 }
1493
1494 __isl_give isl_qpolynomial *isl_qpolynomial_mul_isl_int(
1495         __isl_take isl_qpolynomial *qp, isl_int v)
1496 {
1497         if (isl_int_is_one(v))
1498                 return qp;
1499
1500         if (qp && isl_int_is_zero(v)) {
1501                 isl_qpolynomial *zero;
1502                 zero = isl_qpolynomial_zero_on_domain(isl_space_copy(qp->dim));
1503                 isl_qpolynomial_free(qp);
1504                 return zero;
1505         }
1506
1507         qp = isl_qpolynomial_cow(qp);
1508         if (!qp)
1509                 return NULL;
1510
1511         qp->upoly = isl_upoly_mul_isl_int(qp->upoly, v);
1512         if (!qp->upoly)
1513                 goto error;
1514
1515         return qp;
1516 error:
1517         isl_qpolynomial_free(qp);
1518         return NULL;
1519 }
1520
1521 __isl_give isl_qpolynomial *isl_qpolynomial_scale(
1522         __isl_take isl_qpolynomial *qp, isl_int v)
1523 {
1524         return isl_qpolynomial_mul_isl_int(qp, v);
1525 }
1526
1527 /* Multiply "qp" by "v".
1528  */
1529 __isl_give isl_qpolynomial *isl_qpolynomial_scale_val(
1530         __isl_take isl_qpolynomial *qp, __isl_take isl_val *v)
1531 {
1532         if (!qp || !v)
1533                 goto error;
1534
1535         if (!isl_val_is_rat(v))
1536                 isl_die(isl_qpolynomial_get_ctx(qp), isl_error_invalid,
1537                         "expecting rational factor", goto error);
1538
1539         if (isl_val_is_one(v)) {
1540                 isl_val_free(v);
1541                 return qp;
1542         }
1543
1544         if (isl_val_is_zero(v)) {
1545                 isl_space *space;
1546
1547                 space = isl_qpolynomial_get_domain_space(qp);
1548                 isl_qpolynomial_free(qp);
1549                 isl_val_free(v);
1550                 return isl_qpolynomial_zero_on_domain(space);
1551         }
1552
1553         qp = isl_qpolynomial_cow(qp);
1554         if (!qp)
1555                 goto error;
1556
1557         qp->upoly = isl_upoly_scale_val(qp->upoly, v);
1558         if (!qp->upoly)
1559                 qp = isl_qpolynomial_free(qp);
1560
1561         isl_val_free(v);
1562         return qp;
1563 error:
1564         isl_val_free(v);
1565         isl_qpolynomial_free(qp);
1566         return NULL;
1567 }
1568
1569 /* Divide "qp" by "v".
1570  */
1571 __isl_give isl_qpolynomial *isl_qpolynomial_scale_down_val(
1572         __isl_take isl_qpolynomial *qp, __isl_take isl_val *v)
1573 {
1574         if (!qp || !v)
1575                 goto error;
1576
1577         if (!isl_val_is_rat(v))
1578                 isl_die(isl_qpolynomial_get_ctx(qp), isl_error_invalid,
1579                         "expecting rational factor", goto error);
1580         if (isl_val_is_zero(v))
1581                 isl_die(isl_val_get_ctx(v), isl_error_invalid,
1582                         "cannot scale down by zero", goto error);
1583
1584         return isl_qpolynomial_scale_val(qp, isl_val_inv(v));
1585 error:
1586         isl_val_free(v);
1587         isl_qpolynomial_free(qp);
1588         return NULL;
1589 }
1590
1591 __isl_give isl_qpolynomial *isl_qpolynomial_mul(__isl_take isl_qpolynomial *qp1,
1592         __isl_take isl_qpolynomial *qp2)
1593 {
1594         qp1 = isl_qpolynomial_cow(qp1);
1595
1596         if (!qp1 || !qp2)
1597                 goto error;
1598
1599         if (qp1->div->n_row < qp2->div->n_row)
1600                 return isl_qpolynomial_mul(qp2, qp1);
1601
1602         isl_assert(qp1->dim->ctx, isl_space_is_equal(qp1->dim, qp2->dim), goto error);
1603         if (!compatible_divs(qp1->div, qp2->div))
1604                 return with_merged_divs(isl_qpolynomial_mul, qp1, qp2);
1605
1606         qp1->upoly = isl_upoly_mul(qp1->upoly, isl_upoly_copy(qp2->upoly));
1607         if (!qp1->upoly)
1608                 goto error;
1609
1610         isl_qpolynomial_free(qp2);
1611
1612         return qp1;
1613 error:
1614         isl_qpolynomial_free(qp1);
1615         isl_qpolynomial_free(qp2);
1616         return NULL;
1617 }
1618
1619 __isl_give isl_qpolynomial *isl_qpolynomial_pow(__isl_take isl_qpolynomial *qp,
1620         unsigned power)
1621 {
1622         qp = isl_qpolynomial_cow(qp);
1623
1624         if (!qp)
1625                 return NULL;
1626
1627         qp->upoly = isl_upoly_pow(qp->upoly, power);
1628         if (!qp->upoly)
1629                 goto error;
1630
1631         return qp;
1632 error:
1633         isl_qpolynomial_free(qp);
1634         return NULL;
1635 }
1636
1637 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_pow(
1638         __isl_take isl_pw_qpolynomial *pwqp, unsigned power)
1639 {
1640         int i;
1641
1642         if (power == 1)
1643                 return pwqp;
1644
1645         pwqp = isl_pw_qpolynomial_cow(pwqp);
1646         if (!pwqp)
1647                 return NULL;
1648
1649         for (i = 0; i < pwqp->n; ++i) {
1650                 pwqp->p[i].qp = isl_qpolynomial_pow(pwqp->p[i].qp, power);
1651                 if (!pwqp->p[i].qp)
1652                         return isl_pw_qpolynomial_free(pwqp);
1653         }
1654
1655         return pwqp;
1656 }
1657
1658 __isl_give isl_qpolynomial *isl_qpolynomial_zero_on_domain(
1659         __isl_take isl_space *dim)
1660 {
1661         if (!dim)
1662                 return NULL;
1663         return isl_qpolynomial_alloc(dim, 0, isl_upoly_zero(dim->ctx));
1664 }
1665
1666 __isl_give isl_qpolynomial *isl_qpolynomial_one_on_domain(
1667         __isl_take isl_space *dim)
1668 {
1669         if (!dim)
1670                 return NULL;
1671         return isl_qpolynomial_alloc(dim, 0, isl_upoly_one(dim->ctx));
1672 }
1673
1674 __isl_give isl_qpolynomial *isl_qpolynomial_infty_on_domain(
1675         __isl_take isl_space *dim)
1676 {
1677         if (!dim)
1678                 return NULL;
1679         return isl_qpolynomial_alloc(dim, 0, isl_upoly_infty(dim->ctx));
1680 }
1681
1682 __isl_give isl_qpolynomial *isl_qpolynomial_neginfty_on_domain(
1683         __isl_take isl_space *dim)
1684 {
1685         if (!dim)
1686                 return NULL;
1687         return isl_qpolynomial_alloc(dim, 0, isl_upoly_neginfty(dim->ctx));
1688 }
1689
1690 __isl_give isl_qpolynomial *isl_qpolynomial_nan_on_domain(
1691         __isl_take isl_space *dim)
1692 {
1693         if (!dim)
1694                 return NULL;
1695         return isl_qpolynomial_alloc(dim, 0, isl_upoly_nan(dim->ctx));
1696 }
1697
1698 __isl_give isl_qpolynomial *isl_qpolynomial_cst_on_domain(
1699         __isl_take isl_space *dim,
1700         isl_int v)
1701 {
1702         struct isl_qpolynomial *qp;
1703         struct isl_upoly_cst *cst;
1704
1705         if (!dim)
1706                 return NULL;
1707
1708         qp = isl_qpolynomial_alloc(dim, 0, isl_upoly_zero(dim->ctx));
1709         if (!qp)
1710                 return NULL;
1711
1712         cst = isl_upoly_as_cst(qp->upoly);
1713         isl_int_set(cst->n, v);
1714
1715         return qp;
1716 }
1717
1718 int isl_qpolynomial_is_cst(__isl_keep isl_qpolynomial *qp,
1719         isl_int *n, isl_int *d)
1720 {
1721         struct isl_upoly_cst *cst;
1722
1723         if (!qp)
1724                 return -1;
1725
1726         if (!isl_upoly_is_cst(qp->upoly))
1727                 return 0;
1728
1729         cst = isl_upoly_as_cst(qp->upoly);
1730         if (!cst)
1731                 return -1;
1732
1733         if (n)
1734                 isl_int_set(*n, cst->n);
1735         if (d)
1736                 isl_int_set(*d, cst->d);
1737
1738         return 1;
1739 }
1740
1741 /* Return the constant term of "up".
1742  */
1743 static __isl_give isl_val *isl_upoly_get_constant_val(
1744         __isl_keep struct isl_upoly *up)
1745 {
1746         struct isl_upoly_cst *cst;
1747
1748         if (!up)
1749                 return NULL;
1750
1751         while (!isl_upoly_is_cst(up)) {
1752                 struct isl_upoly_rec *rec;
1753
1754                 rec = isl_upoly_as_rec(up);
1755                 if (!rec)
1756                         return NULL;
1757                 up = rec->p[0];
1758         }
1759
1760         cst = isl_upoly_as_cst(up);
1761         if (!cst)
1762                 return NULL;
1763         return isl_val_rat_from_isl_int(cst->up.ctx, cst->n, cst->d);
1764 }
1765
1766 /* Return the constant term of "qp".
1767  */
1768 __isl_give isl_val *isl_qpolynomial_get_constant_val(
1769         __isl_keep isl_qpolynomial *qp)
1770 {
1771         if (!qp)
1772                 return NULL;
1773
1774         return isl_upoly_get_constant_val(qp->upoly);
1775 }
1776
1777 int isl_upoly_is_affine(__isl_keep struct isl_upoly *up)
1778 {
1779         int is_cst;
1780         struct isl_upoly_rec *rec;
1781
1782         if (!up)
1783                 return -1;
1784
1785         if (up->var < 0)
1786                 return 1;
1787
1788         rec = isl_upoly_as_rec(up);
1789         if (!rec)
1790                 return -1;
1791
1792         if (rec->n > 2)
1793                 return 0;
1794
1795         isl_assert(up->ctx, rec->n > 1, return -1);
1796
1797         is_cst = isl_upoly_is_cst(rec->p[1]);
1798         if (is_cst < 0)
1799                 return -1;
1800         if (!is_cst)
1801                 return 0;
1802
1803         return isl_upoly_is_affine(rec->p[0]);
1804 }
1805
1806 int isl_qpolynomial_is_affine(__isl_keep isl_qpolynomial *qp)
1807 {
1808         if (!qp)
1809                 return -1;
1810
1811         if (qp->div->n_row > 0)
1812                 return 0;
1813
1814         return isl_upoly_is_affine(qp->upoly);
1815 }
1816
1817 static void update_coeff(__isl_keep isl_vec *aff,
1818         __isl_keep struct isl_upoly_cst *cst, int pos)
1819 {
1820         isl_int gcd;
1821         isl_int f;
1822
1823         if (isl_int_is_zero(cst->n))
1824                 return;
1825
1826         isl_int_init(gcd);
1827         isl_int_init(f);
1828         isl_int_gcd(gcd, cst->d, aff->el[0]);
1829         isl_int_divexact(f, cst->d, gcd);
1830         isl_int_divexact(gcd, aff->el[0], gcd);
1831         isl_seq_scale(aff->el, aff->el, f, aff->size);
1832         isl_int_mul(aff->el[1 + pos], gcd, cst->n);
1833         isl_int_clear(gcd);
1834         isl_int_clear(f);
1835 }
1836
1837 int isl_upoly_update_affine(__isl_keep struct isl_upoly *up,
1838         __isl_keep isl_vec *aff)
1839 {
1840         struct isl_upoly_cst *cst;
1841         struct isl_upoly_rec *rec;
1842
1843         if (!up || !aff)
1844                 return -1;
1845
1846         if (up->var < 0) {
1847                 struct isl_upoly_cst *cst;
1848
1849                 cst = isl_upoly_as_cst(up);
1850                 if (!cst)
1851                         return -1;
1852                 update_coeff(aff, cst, 0);
1853                 return 0;
1854         }
1855
1856         rec = isl_upoly_as_rec(up);
1857         if (!rec)
1858                 return -1;
1859         isl_assert(up->ctx, rec->n == 2, return -1);
1860
1861         cst = isl_upoly_as_cst(rec->p[1]);
1862         if (!cst)
1863                 return -1;
1864         update_coeff(aff, cst, 1 + up->var);
1865
1866         return isl_upoly_update_affine(rec->p[0], aff);
1867 }
1868
1869 __isl_give isl_vec *isl_qpolynomial_extract_affine(
1870         __isl_keep isl_qpolynomial *qp)
1871 {
1872         isl_vec *aff;
1873         unsigned d;
1874
1875         if (!qp)
1876                 return NULL;
1877
1878         d = isl_space_dim(qp->dim, isl_dim_all);
1879         aff = isl_vec_alloc(qp->div->ctx, 2 + d + qp->div->n_row);
1880         if (!aff)
1881                 return NULL;
1882
1883         isl_seq_clr(aff->el + 1, 1 + d + qp->div->n_row);
1884         isl_int_set_si(aff->el[0], 1);
1885
1886         if (isl_upoly_update_affine(qp->upoly, aff) < 0)
1887                 goto error;
1888
1889         return aff;
1890 error:
1891         isl_vec_free(aff);
1892         return NULL;
1893 }
1894
1895 int isl_qpolynomial_plain_is_equal(__isl_keep isl_qpolynomial *qp1,
1896         __isl_keep isl_qpolynomial *qp2)
1897 {
1898         int equal;
1899
1900         if (!qp1 || !qp2)
1901                 return -1;
1902
1903         equal = isl_space_is_equal(qp1->dim, qp2->dim);
1904         if (equal < 0 || !equal)
1905                 return equal;
1906
1907         equal = isl_mat_is_equal(qp1->div, qp2->div);
1908         if (equal < 0 || !equal)
1909                 return equal;
1910
1911         return isl_upoly_is_equal(qp1->upoly, qp2->upoly);
1912 }
1913
1914 static void upoly_update_den(__isl_keep struct isl_upoly *up, isl_int *d)
1915 {
1916         int i;
1917         struct isl_upoly_rec *rec;
1918
1919         if (isl_upoly_is_cst(up)) {
1920                 struct isl_upoly_cst *cst;
1921                 cst = isl_upoly_as_cst(up);
1922                 if (!cst)
1923                         return;
1924                 isl_int_lcm(*d, *d, cst->d);
1925                 return;
1926         }
1927
1928         rec = isl_upoly_as_rec(up);
1929         if (!rec)
1930                 return;
1931
1932         for (i = 0; i < rec->n; ++i)
1933                 upoly_update_den(rec->p[i], d);
1934 }
1935
1936 void isl_qpolynomial_get_den(__isl_keep isl_qpolynomial *qp, isl_int *d)
1937 {
1938         isl_int_set_si(*d, 1);
1939         if (!qp)
1940                 return;
1941         upoly_update_den(qp->upoly, d);
1942 }
1943
1944 __isl_give isl_qpolynomial *isl_qpolynomial_var_pow_on_domain(
1945         __isl_take isl_space *dim, int pos, int power)
1946 {
1947         struct isl_ctx *ctx;
1948
1949         if (!dim)
1950                 return NULL;
1951
1952         ctx = dim->ctx;
1953
1954         return isl_qpolynomial_alloc(dim, 0, isl_upoly_var_pow(ctx, pos, power));
1955 }
1956
1957 __isl_give isl_qpolynomial *isl_qpolynomial_var_on_domain(__isl_take isl_space *dim,
1958         enum isl_dim_type type, unsigned pos)
1959 {
1960         if (!dim)
1961                 return NULL;
1962
1963         isl_assert(dim->ctx, isl_space_dim(dim, isl_dim_in) == 0, goto error);
1964         isl_assert(dim->ctx, pos < isl_space_dim(dim, type), goto error);
1965
1966         if (type == isl_dim_set)
1967                 pos += isl_space_dim(dim, isl_dim_param);
1968
1969         return isl_qpolynomial_var_pow_on_domain(dim, pos, 1);
1970 error:
1971         isl_space_free(dim);
1972         return NULL;
1973 }
1974
1975 __isl_give struct isl_upoly *isl_upoly_subs(__isl_take struct isl_upoly *up,
1976         unsigned first, unsigned n, __isl_keep struct isl_upoly **subs)
1977 {
1978         int i;
1979         struct isl_upoly_rec *rec;
1980         struct isl_upoly *base, *res;
1981
1982         if (!up)
1983                 return NULL;
1984
1985         if (isl_upoly_is_cst(up))
1986                 return up;
1987
1988         if (up->var < first)
1989                 return up;
1990
1991         rec = isl_upoly_as_rec(up);
1992         if (!rec)
1993                 goto error;
1994
1995         isl_assert(up->ctx, rec->n >= 1, goto error);
1996
1997         if (up->var >= first + n)
1998                 base = isl_upoly_var_pow(up->ctx, up->var, 1);
1999         else
2000                 base = isl_upoly_copy(subs[up->var - first]);
2001
2002         res = isl_upoly_subs(isl_upoly_copy(rec->p[rec->n - 1]), first, n, subs);
2003         for (i = rec->n - 2; i >= 0; --i) {
2004                 struct isl_upoly *t;
2005                 t = isl_upoly_subs(isl_upoly_copy(rec->p[i]), first, n, subs);
2006                 res = isl_upoly_mul(res, isl_upoly_copy(base));
2007                 res = isl_upoly_sum(res, t);
2008         }
2009
2010         isl_upoly_free(base);
2011         isl_upoly_free(up);
2012
2013         return res;
2014 error:
2015         isl_upoly_free(up);
2016         return NULL;
2017 }
2018
2019 __isl_give struct isl_upoly *isl_upoly_from_affine(isl_ctx *ctx, isl_int *f,
2020         isl_int denom, unsigned len)
2021 {
2022         int i;
2023         struct isl_upoly *up;
2024
2025         isl_assert(ctx, len >= 1, return NULL);
2026
2027         up = isl_upoly_rat_cst(ctx, f[0], denom);
2028         for (i = 0; i < len - 1; ++i) {
2029                 struct isl_upoly *t;
2030                 struct isl_upoly *c;
2031
2032                 if (isl_int_is_zero(f[1 + i]))
2033                         continue;
2034
2035                 c = isl_upoly_rat_cst(ctx, f[1 + i], denom);
2036                 t = isl_upoly_var_pow(ctx, i, 1);
2037                 t = isl_upoly_mul(c, t);
2038                 up = isl_upoly_sum(up, t);
2039         }
2040
2041         return up;
2042 }
2043
2044 /* Remove common factor of non-constant terms and denominator.
2045  */
2046 static void normalize_div(__isl_keep isl_qpolynomial *qp, int div)
2047 {
2048         isl_ctx *ctx = qp->div->ctx;
2049         unsigned total = qp->div->n_col - 2;
2050
2051         isl_seq_gcd(qp->div->row[div] + 2, total, &ctx->normalize_gcd);
2052         isl_int_gcd(ctx->normalize_gcd,
2053                     ctx->normalize_gcd, qp->div->row[div][0]);
2054         if (isl_int_is_one(ctx->normalize_gcd))
2055                 return;
2056
2057         isl_seq_scale_down(qp->div->row[div] + 2, qp->div->row[div] + 2,
2058                             ctx->normalize_gcd, total);
2059         isl_int_divexact(qp->div->row[div][0], qp->div->row[div][0],
2060                             ctx->normalize_gcd);
2061         isl_int_fdiv_q(qp->div->row[div][1], qp->div->row[div][1],
2062                             ctx->normalize_gcd);
2063 }
2064
2065 /* Replace the integer division identified by "div" by the polynomial "s".
2066  * The integer division is assumed not to appear in the definition
2067  * of any other integer divisions.
2068  */
2069 static __isl_give isl_qpolynomial *substitute_div(
2070         __isl_take isl_qpolynomial *qp,
2071         int div, __isl_take struct isl_upoly *s)
2072 {
2073         int i;
2074         int total;
2075         int *reordering;
2076
2077         if (!qp || !s)
2078                 goto error;
2079
2080         qp = isl_qpolynomial_cow(qp);
2081         if (!qp)
2082                 goto error;
2083
2084         total = isl_space_dim(qp->dim, isl_dim_all);
2085         qp->upoly = isl_upoly_subs(qp->upoly, total + div, 1, &s);
2086         if (!qp->upoly)
2087                 goto error;
2088
2089         reordering = isl_alloc_array(qp->dim->ctx, int, total + qp->div->n_row);
2090         if (!reordering)
2091                 goto error;
2092         for (i = 0; i < total + div; ++i)
2093                 reordering[i] = i;
2094         for (i = total + div + 1; i < total + qp->div->n_row; ++i)
2095                 reordering[i] = i - 1;
2096         qp->div = isl_mat_drop_rows(qp->div, div, 1);
2097         qp->div = isl_mat_drop_cols(qp->div, 2 + total + div, 1);
2098         qp->upoly = reorder(qp->upoly, reordering);
2099         free(reordering);
2100
2101         if (!qp->upoly || !qp->div)
2102                 goto error;
2103
2104         isl_upoly_free(s);
2105         return qp;
2106 error:
2107         isl_qpolynomial_free(qp);
2108         isl_upoly_free(s);
2109         return NULL;
2110 }
2111
2112 /* Replace all integer divisions [e/d] that turn out to not actually be integer
2113  * divisions because d is equal to 1 by their definition, i.e., e.
2114  */
2115 static __isl_give isl_qpolynomial *substitute_non_divs(
2116         __isl_take isl_qpolynomial *qp)
2117 {
2118         int i, j;
2119         int total;
2120         struct isl_upoly *s;
2121
2122         if (!qp)
2123                 return NULL;
2124
2125         total = isl_space_dim(qp->dim, isl_dim_all);
2126         for (i = 0; qp && i < qp->div->n_row; ++i) {
2127                 if (!isl_int_is_one(qp->div->row[i][0]))
2128                         continue;
2129                 for (j = i + 1; j < qp->div->n_row; ++j) {
2130                         if (isl_int_is_zero(qp->div->row[j][2 + total + i]))
2131                                 continue;
2132                         isl_seq_combine(qp->div->row[j] + 1,
2133                                 qp->div->ctx->one, qp->div->row[j] + 1,
2134                                 qp->div->row[j][2 + total + i],
2135                                 qp->div->row[i] + 1, 1 + total + i);
2136                         isl_int_set_si(qp->div->row[j][2 + total + i], 0);
2137                         normalize_div(qp, j);
2138                 }
2139                 s = isl_upoly_from_affine(qp->dim->ctx, qp->div->row[i] + 1,
2140                                         qp->div->row[i][0], qp->div->n_col - 1);
2141                 qp = substitute_div(qp, i, s);
2142                 --i;
2143         }
2144
2145         return qp;
2146 }
2147
2148 /* Reduce the coefficients of div "div" to lie in the interval [0, d-1],
2149  * with d the denominator.  When replacing the coefficient e of x by
2150  * d * frac(e/d) = e - d * floor(e/d), we are subtracting d * floor(e/d) * x
2151  * inside the division, so we need to add floor(e/d) * x outside.
2152  * That is, we replace q by q' + floor(e/d) * x and we therefore need
2153  * to adjust the coefficient of x in each later div that depends on the
2154  * current div "div" and also in the affine expression "aff"
2155  * (if it too depends on "div").
2156  */
2157 static void reduce_div(__isl_keep isl_qpolynomial *qp, int div,
2158         __isl_keep isl_vec *aff)
2159 {
2160         int i, j;
2161         isl_int v;
2162         unsigned total = qp->div->n_col - qp->div->n_row - 2;
2163
2164         isl_int_init(v);
2165         for (i = 0; i < 1 + total + div; ++i) {
2166                 if (isl_int_is_nonneg(qp->div->row[div][1 + i]) &&
2167                     isl_int_lt(qp->div->row[div][1 + i], qp->div->row[div][0]))
2168                         continue;
2169                 isl_int_fdiv_q(v, qp->div->row[div][1 + i], qp->div->row[div][0]);
2170                 isl_int_fdiv_r(qp->div->row[div][1 + i],
2171                                 qp->div->row[div][1 + i], qp->div->row[div][0]);
2172                 if (!isl_int_is_zero(aff->el[1 + total + div]))
2173                         isl_int_addmul(aff->el[i], v, aff->el[1 + total + div]);
2174                 for (j = div + 1; j < qp->div->n_row; ++j) {
2175                         if (isl_int_is_zero(qp->div->row[j][2 + total + div]))
2176                                 continue;
2177                         isl_int_addmul(qp->div->row[j][1 + i],
2178                                         v, qp->div->row[j][2 + total + div]);
2179                 }
2180         }
2181         isl_int_clear(v);
2182 }
2183
2184 /* Check if the last non-zero coefficient is bigger that half of the
2185  * denominator.  If so, we will invert the div to further reduce the number
2186  * of distinct divs that may appear.
2187  * If the last non-zero coefficient is exactly half the denominator,
2188  * then we continue looking for earlier coefficients that are bigger
2189  * than half the denominator.
2190  */
2191 static int needs_invert(__isl_keep isl_mat *div, int row)
2192 {
2193         int i;
2194         int cmp;
2195
2196         for (i = div->n_col - 1; i >= 1; --i) {
2197                 if (isl_int_is_zero(div->row[row][i]))
2198                         continue;
2199                 isl_int_mul_ui(div->row[row][i], div->row[row][i], 2);
2200                 cmp = isl_int_cmp(div->row[row][i], div->row[row][0]);
2201                 isl_int_divexact_ui(div->row[row][i], div->row[row][i], 2);
2202                 if (cmp)
2203                         return cmp > 0;
2204                 if (i == 1)
2205                         return 1;
2206         }
2207
2208         return 0;
2209 }
2210
2211 /* Replace div "div" q = [e/d] by -[(-e+(d-1))/d].
2212  * We only invert the coefficients of e (and the coefficient of q in
2213  * later divs and in "aff").  After calling this function, the
2214  * coefficients of e should be reduced again.
2215  */
2216 static void invert_div(__isl_keep isl_qpolynomial *qp, int div,
2217         __isl_keep isl_vec *aff)
2218 {
2219         unsigned total = qp->div->n_col - qp->div->n_row - 2;
2220
2221         isl_seq_neg(qp->div->row[div] + 1,
2222                     qp->div->row[div] + 1, qp->div->n_col - 1);
2223         isl_int_sub_ui(qp->div->row[div][1], qp->div->row[div][1], 1);
2224         isl_int_add(qp->div->row[div][1],
2225                     qp->div->row[div][1], qp->div->row[div][0]);
2226         if (!isl_int_is_zero(aff->el[1 + total + div]))
2227                 isl_int_neg(aff->el[1 + total + div], aff->el[1 + total + div]);
2228         isl_mat_col_mul(qp->div, 2 + total + div,
2229                         qp->div->ctx->negone, 2 + total + div);
2230 }
2231
2232 /* Assuming "qp" is a monomial, reduce all its divs to have coefficients
2233  * in the interval [0, d-1], with d the denominator and such that the
2234  * last non-zero coefficient that is not equal to d/2 is smaller than d/2.
2235  *
2236  * After the reduction, some divs may have become redundant or identical,
2237  * so we call substitute_non_divs and sort_divs.  If these functions
2238  * eliminate divs or merge two or more divs into one, the coefficients
2239  * of the enclosing divs may have to be reduced again, so we call
2240  * ourselves recursively if the number of divs decreases.
2241  */
2242 static __isl_give isl_qpolynomial *reduce_divs(__isl_take isl_qpolynomial *qp)
2243 {
2244         int i;
2245         isl_vec *aff = NULL;
2246         struct isl_upoly *s;
2247         unsigned n_div;
2248
2249         if (!qp)
2250                 return NULL;
2251
2252         aff = isl_vec_alloc(qp->div->ctx, qp->div->n_col - 1);
2253         aff = isl_vec_clr(aff);
2254         if (!aff)
2255                 goto error;
2256
2257         isl_int_set_si(aff->el[1 + qp->upoly->var], 1);
2258
2259         for (i = 0; i < qp->div->n_row; ++i) {
2260                 normalize_div(qp, i);
2261                 reduce_div(qp, i, aff);
2262                 if (needs_invert(qp->div, i)) {
2263                         invert_div(qp, i, aff);
2264                         reduce_div(qp, i, aff);
2265                 }
2266         }
2267
2268         s = isl_upoly_from_affine(qp->div->ctx, aff->el,
2269                                   qp->div->ctx->one, aff->size);
2270         qp->upoly = isl_upoly_subs(qp->upoly, qp->upoly->var, 1, &s);
2271         isl_upoly_free(s);
2272         if (!qp->upoly)
2273                 goto error;
2274
2275         isl_vec_free(aff);
2276
2277         n_div = qp->div->n_row;
2278         qp = substitute_non_divs(qp);
2279         qp = sort_divs(qp);
2280         if (qp && qp->div->n_row < n_div)
2281                 return reduce_divs(qp);
2282
2283         return qp;
2284 error:
2285         isl_qpolynomial_free(qp);
2286         isl_vec_free(aff);
2287         return NULL;
2288 }
2289
2290 __isl_give isl_qpolynomial *isl_qpolynomial_rat_cst_on_domain(
2291         __isl_take isl_space *dim, const isl_int n, const isl_int d)
2292 {
2293         struct isl_qpolynomial *qp;
2294         struct isl_upoly_cst *cst;
2295
2296         if (!dim)
2297                 return NULL;
2298
2299         qp = isl_qpolynomial_alloc(dim, 0, isl_upoly_zero(dim->ctx));
2300         if (!qp)
2301                 return NULL;
2302
2303         cst = isl_upoly_as_cst(qp->upoly);
2304         isl_int_set(cst->n, n);
2305         isl_int_set(cst->d, d);
2306
2307         return qp;
2308 }
2309
2310 /* Return an isl_qpolynomial that is equal to "val" on domain space "domain".
2311  */
2312 __isl_give isl_qpolynomial *isl_qpolynomial_val_on_domain(
2313         __isl_take isl_space *domain, __isl_take isl_val *val)
2314 {
2315         isl_qpolynomial *qp;
2316         struct isl_upoly_cst *cst;
2317
2318         if (!domain || !val)
2319                 goto error;
2320
2321         qp = isl_qpolynomial_alloc(isl_space_copy(domain), 0,
2322                                         isl_upoly_zero(domain->ctx));
2323         if (!qp)
2324                 goto error;
2325
2326         cst = isl_upoly_as_cst(qp->upoly);
2327         isl_int_set(cst->n, val->n);
2328         isl_int_set(cst->d, val->d);
2329
2330         isl_space_free(domain);
2331         isl_val_free(val);
2332         return qp;
2333 error:
2334         isl_space_free(domain);
2335         isl_val_free(val);
2336         return NULL;
2337 }
2338
2339 static int up_set_active(__isl_keep struct isl_upoly *up, int *active, int d)
2340 {
2341         struct isl_upoly_rec *rec;
2342         int i;
2343
2344         if (!up)
2345                 return -1;
2346
2347         if (isl_upoly_is_cst(up))
2348                 return 0;
2349
2350         if (up->var < d)
2351                 active[up->var] = 1;
2352
2353         rec = isl_upoly_as_rec(up);
2354         for (i = 0; i < rec->n; ++i)
2355                 if (up_set_active(rec->p[i], active, d) < 0)
2356                         return -1;
2357
2358         return 0;
2359 }
2360
2361 static int set_active(__isl_keep isl_qpolynomial *qp, int *active)
2362 {
2363         int i, j;
2364         int d = isl_space_dim(qp->dim, isl_dim_all);
2365
2366         if (!qp || !active)
2367                 return -1;
2368
2369         for (i = 0; i < d; ++i)
2370                 for (j = 0; j < qp->div->n_row; ++j) {
2371                         if (isl_int_is_zero(qp->div->row[j][2 + i]))
2372                                 continue;
2373                         active[i] = 1;
2374                         break;
2375                 }
2376
2377         return up_set_active(qp->upoly, active, d);
2378 }
2379
2380 int isl_qpolynomial_involves_dims(__isl_keep isl_qpolynomial *qp,
2381         enum isl_dim_type type, unsigned first, unsigned n)
2382 {
2383         int i;
2384         int *active = NULL;
2385         int involves = 0;
2386
2387         if (!qp)
2388                 return -1;
2389         if (n == 0)
2390                 return 0;
2391
2392         isl_assert(qp->dim->ctx,
2393                     first + n <= isl_qpolynomial_dim(qp, type), return -1);
2394         isl_assert(qp->dim->ctx, type == isl_dim_param ||
2395                                  type == isl_dim_in, return -1);
2396
2397         active = isl_calloc_array(qp->dim->ctx, int,
2398                                         isl_space_dim(qp->dim, isl_dim_all));
2399         if (set_active(qp, active) < 0)
2400                 goto error;
2401
2402         if (type == isl_dim_in)
2403                 first += isl_space_dim(qp->dim, isl_dim_param);
2404         for (i = 0; i < n; ++i)
2405                 if (active[first + i]) {
2406                         involves = 1;
2407                         break;
2408                 }
2409
2410         free(active);
2411
2412         return involves;
2413 error:
2414         free(active);
2415         return -1;
2416 }
2417
2418 /* Remove divs that do not appear in the quasi-polynomial, nor in any
2419  * of the divs that do appear in the quasi-polynomial.
2420  */
2421 static __isl_give isl_qpolynomial *remove_redundant_divs(
2422         __isl_take isl_qpolynomial *qp)
2423 {
2424         int i, j;
2425         int d;
2426         int len;
2427         int skip;
2428         int *active = NULL;
2429         int *reordering = NULL;
2430         int redundant = 0;
2431         int n_div;
2432         isl_ctx *ctx;
2433
2434         if (!qp)
2435                 return NULL;
2436         if (qp->div->n_row == 0)
2437                 return qp;
2438
2439         d = isl_space_dim(qp->dim, isl_dim_all);
2440         len = qp->div->n_col - 2;
2441         ctx = isl_qpolynomial_get_ctx(qp);
2442         active = isl_calloc_array(ctx, int, len);
2443         if (!active)
2444                 goto error;
2445
2446         if (up_set_active(qp->upoly, active, len) < 0)
2447                 goto error;
2448
2449         for (i = qp->div->n_row - 1; i >= 0; --i) {
2450                 if (!active[d + i]) {
2451                         redundant = 1;
2452                         continue;
2453                 }
2454                 for (j = 0; j < i; ++j) {
2455                         if (isl_int_is_zero(qp->div->row[i][2 + d + j]))
2456                                 continue;
2457                         active[d + j] = 1;
2458                         break;
2459                 }
2460         }
2461
2462         if (!redundant) {
2463                 free(active);
2464                 return qp;
2465         }
2466
2467         reordering = isl_alloc_array(qp->div->ctx, int, len);
2468         if (!reordering)
2469                 goto error;
2470
2471         for (i = 0; i < d; ++i)
2472                 reordering[i] = i;
2473
2474         skip = 0;
2475         n_div = qp->div->n_row;
2476         for (i = 0; i < n_div; ++i) {
2477                 if (!active[d + i]) {
2478                         qp->div = isl_mat_drop_rows(qp->div, i - skip, 1);
2479                         qp->div = isl_mat_drop_cols(qp->div,
2480                                                     2 + d + i - skip, 1);
2481                         skip++;
2482                 }
2483                 reordering[d + i] = d + i - skip;
2484         }
2485
2486         qp->upoly = reorder(qp->upoly, reordering);
2487
2488         if (!qp->upoly || !qp->div)
2489                 goto error;
2490
2491         free(active);
2492         free(reordering);
2493
2494         return qp;
2495 error:
2496         free(active);
2497         free(reordering);
2498         isl_qpolynomial_free(qp);
2499         return NULL;
2500 }
2501
2502 __isl_give struct isl_upoly *isl_upoly_drop(__isl_take struct isl_upoly *up,
2503         unsigned first, unsigned n)
2504 {
2505         int i;
2506         struct isl_upoly_rec *rec;
2507
2508         if (!up)
2509                 return NULL;
2510         if (n == 0 || up->var < 0 || up->var < first)
2511                 return up;
2512         if (up->var < first + n) {
2513                 up = replace_by_constant_term(up);
2514                 return isl_upoly_drop(up, first, n);
2515         }
2516         up = isl_upoly_cow(up);
2517         if (!up)
2518                 return NULL;
2519         up->var -= n;
2520         rec = isl_upoly_as_rec(up);
2521         if (!rec)
2522                 goto error;
2523
2524         for (i = 0; i < rec->n; ++i) {
2525                 rec->p[i] = isl_upoly_drop(rec->p[i], first, n);
2526                 if (!rec->p[i])
2527                         goto error;
2528         }
2529
2530         return up;
2531 error:
2532         isl_upoly_free(up);
2533         return NULL;
2534 }
2535
2536 __isl_give isl_qpolynomial *isl_qpolynomial_set_dim_name(
2537         __isl_take isl_qpolynomial *qp,
2538         enum isl_dim_type type, unsigned pos, const char *s)
2539 {
2540         qp = isl_qpolynomial_cow(qp);
2541         if (!qp)
2542                 return NULL;
2543         qp->dim = isl_space_set_dim_name(qp->dim, type, pos, s);
2544         if (!qp->dim)
2545                 goto error;
2546         return qp;
2547 error:
2548         isl_qpolynomial_free(qp);
2549         return NULL;
2550 }
2551
2552 __isl_give isl_qpolynomial *isl_qpolynomial_drop_dims(
2553         __isl_take isl_qpolynomial *qp,
2554         enum isl_dim_type type, unsigned first, unsigned n)
2555 {
2556         if (!qp)
2557                 return NULL;
2558         if (type == isl_dim_out)
2559                 isl_die(qp->dim->ctx, isl_error_invalid,
2560                         "cannot drop output/set dimension",
2561                         goto error);
2562         if (type == isl_dim_in)
2563                 type = isl_dim_set;
2564         if (n == 0 && !isl_space_is_named_or_nested(qp->dim, type))
2565                 return qp;
2566
2567         qp = isl_qpolynomial_cow(qp);
2568         if (!qp)
2569                 return NULL;
2570
2571         isl_assert(qp->dim->ctx, first + n <= isl_space_dim(qp->dim, type),
2572                         goto error);
2573         isl_assert(qp->dim->ctx, type == isl_dim_param ||
2574                                  type == isl_dim_set, goto error);
2575
2576         qp->dim = isl_space_drop_dims(qp->dim, type, first, n);
2577         if (!qp->dim)
2578                 goto error;
2579
2580         if (type == isl_dim_set)
2581                 first += isl_space_dim(qp->dim, isl_dim_param);
2582
2583         qp->div = isl_mat_drop_cols(qp->div, 2 + first, n);
2584         if (!qp->div)
2585                 goto error;
2586
2587         qp->upoly = isl_upoly_drop(qp->upoly, first, n);
2588         if (!qp->upoly)
2589                 goto error;
2590
2591         return qp;
2592 error:
2593         isl_qpolynomial_free(qp);
2594         return NULL;
2595 }
2596
2597 /* Project the domain of the quasi-polynomial onto its parameter space.
2598  * The quasi-polynomial may not involve any of the domain dimensions.
2599  */
2600 __isl_give isl_qpolynomial *isl_qpolynomial_project_domain_on_params(
2601         __isl_take isl_qpolynomial *qp)
2602 {
2603         isl_space *space;
2604         unsigned n;
2605         int involves;
2606
2607         n = isl_qpolynomial_dim(qp, isl_dim_in);
2608         involves = isl_qpolynomial_involves_dims(qp, isl_dim_in, 0, n);
2609         if (involves < 0)
2610                 return isl_qpolynomial_free(qp);
2611         if (involves)
2612                 isl_die(isl_qpolynomial_get_ctx(qp), isl_error_invalid,
2613                         "polynomial involves some of the domain dimensions",
2614                         return isl_qpolynomial_free(qp));
2615         qp = isl_qpolynomial_drop_dims(qp, isl_dim_in, 0, n);
2616         space = isl_qpolynomial_get_domain_space(qp);
2617         space = isl_space_params(space);
2618         qp = isl_qpolynomial_reset_domain_space(qp, space);
2619         return qp;
2620 }
2621
2622 static __isl_give isl_qpolynomial *isl_qpolynomial_substitute_equalities_lifted(
2623         __isl_take isl_qpolynomial *qp, __isl_take isl_basic_set *eq)
2624 {
2625         int i, j, k;
2626         isl_int denom;
2627         unsigned total;
2628         unsigned n_div;
2629         struct isl_upoly *up;
2630
2631         if (!eq)
2632                 goto error;
2633         if (eq->n_eq == 0) {
2634                 isl_basic_set_free(eq);
2635                 return qp;
2636         }
2637
2638         qp = isl_qpolynomial_cow(qp);
2639         if (!qp)
2640                 goto error;
2641         qp->div = isl_mat_cow(qp->div);
2642         if (!qp->div)
2643                 goto error;
2644
2645         total = 1 + isl_space_dim(eq->dim, isl_dim_all);
2646         n_div = eq->n_div;
2647         isl_int_init(denom);
2648         for (i = 0; i < eq->n_eq; ++i) {
2649                 j = isl_seq_last_non_zero(eq->eq[i], total + n_div);
2650                 if (j < 0 || j == 0 || j >= total)
2651                         continue;
2652
2653                 for (k = 0; k < qp->div->n_row; ++k) {
2654                         if (isl_int_is_zero(qp->div->row[k][1 + j]))
2655                                 continue;
2656                         isl_seq_elim(qp->div->row[k] + 1, eq->eq[i], j, total,
2657                                         &qp->div->row[k][0]);
2658                         normalize_div(qp, k);
2659                 }
2660
2661                 if (isl_int_is_pos(eq->eq[i][j]))
2662                         isl_seq_neg(eq->eq[i], eq->eq[i], total);
2663                 isl_int_abs(denom, eq->eq[i][j]);
2664                 isl_int_set_si(eq->eq[i][j], 0);
2665
2666                 up = isl_upoly_from_affine(qp->dim->ctx,
2667                                                    eq->eq[i], denom, total);
2668                 qp->upoly = isl_upoly_subs(qp->upoly, j - 1, 1, &up);
2669                 isl_upoly_free(up);
2670         }
2671         isl_int_clear(denom);
2672
2673         if (!qp->upoly)
2674                 goto error;
2675
2676         isl_basic_set_free(eq);
2677
2678         qp = substitute_non_divs(qp);
2679         qp = sort_divs(qp);
2680
2681         return qp;
2682 error:
2683         isl_basic_set_free(eq);
2684         isl_qpolynomial_free(qp);
2685         return NULL;
2686 }
2687
2688 /* Exploit the equalities in "eq" to simplify the quasi-polynomial.
2689  */
2690 __isl_give isl_qpolynomial *isl_qpolynomial_substitute_equalities(
2691         __isl_take isl_qpolynomial *qp, __isl_take isl_basic_set *eq)
2692 {
2693         if (!qp || !eq)
2694                 goto error;
2695         if (qp->div->n_row > 0)
2696                 eq = isl_basic_set_add_dims(eq, isl_dim_set, qp->div->n_row);
2697         return isl_qpolynomial_substitute_equalities_lifted(qp, eq);
2698 error:
2699         isl_basic_set_free(eq);
2700         isl_qpolynomial_free(qp);
2701         return NULL;
2702 }
2703
2704 static __isl_give isl_basic_set *add_div_constraints(
2705         __isl_take isl_basic_set *bset, __isl_take isl_mat *div)
2706 {
2707         int i;
2708         unsigned total;
2709
2710         if (!bset || !div)
2711                 goto error;
2712
2713         bset = isl_basic_set_extend_constraints(bset, 0, 2 * div->n_row);
2714         if (!bset)
2715                 goto error;
2716         total = isl_basic_set_total_dim(bset);
2717         for (i = 0; i < div->n_row; ++i)
2718                 if (isl_basic_set_add_div_constraints_var(bset,
2719                                     total - div->n_row + i, div->row[i]) < 0)
2720                         goto error;
2721
2722         isl_mat_free(div);
2723         return bset;
2724 error:
2725         isl_mat_free(div);
2726         isl_basic_set_free(bset);
2727         return NULL;
2728 }
2729
2730 /* Look for equalities among the variables shared by context and qp
2731  * and the integer divisions of qp, if any.
2732  * The equalities are then used to eliminate variables and/or integer
2733  * divisions from qp.
2734  */
2735 __isl_give isl_qpolynomial *isl_qpolynomial_gist(
2736         __isl_take isl_qpolynomial *qp, __isl_take isl_set *context)
2737 {
2738         isl_basic_set *aff;
2739
2740         if (!qp)
2741                 goto error;
2742         if (qp->div->n_row > 0) {
2743                 isl_basic_set *bset;
2744                 context = isl_set_add_dims(context, isl_dim_set,
2745                                             qp->div->n_row);
2746                 bset = isl_basic_set_universe(isl_set_get_space(context));
2747                 bset = add_div_constraints(bset, isl_mat_copy(qp->div));
2748                 context = isl_set_intersect(context,
2749                                             isl_set_from_basic_set(bset));
2750         }
2751
2752         aff = isl_set_affine_hull(context);
2753         return isl_qpolynomial_substitute_equalities_lifted(qp, aff);
2754 error:
2755         isl_qpolynomial_free(qp);
2756         isl_set_free(context);
2757         return NULL;
2758 }
2759
2760 __isl_give isl_qpolynomial *isl_qpolynomial_gist_params(
2761         __isl_take isl_qpolynomial *qp, __isl_take isl_set *context)
2762 {
2763         isl_space *space = isl_qpolynomial_get_domain_space(qp);
2764         isl_set *dom_context = isl_set_universe(space);
2765         dom_context = isl_set_intersect_params(dom_context, context);
2766         return isl_qpolynomial_gist(qp, dom_context);
2767 }
2768
2769 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_from_qpolynomial(
2770         __isl_take isl_qpolynomial *qp)
2771 {
2772         isl_set *dom;
2773
2774         if (!qp)
2775                 return NULL;
2776         if (isl_qpolynomial_is_zero(qp)) {
2777                 isl_space *dim = isl_qpolynomial_get_space(qp);
2778                 isl_qpolynomial_free(qp);
2779                 return isl_pw_qpolynomial_zero(dim);
2780         }
2781
2782         dom = isl_set_universe(isl_qpolynomial_get_domain_space(qp));
2783         return isl_pw_qpolynomial_alloc(dom, qp);
2784 }
2785
2786 #undef PW
2787 #define PW isl_pw_qpolynomial
2788 #undef EL
2789 #define EL isl_qpolynomial
2790 #undef EL_IS_ZERO
2791 #define EL_IS_ZERO is_zero
2792 #undef ZERO
2793 #define ZERO zero
2794 #undef IS_ZERO
2795 #define IS_ZERO is_zero
2796 #undef FIELD
2797 #define FIELD qp
2798 #undef DEFAULT_IS_ZERO
2799 #define DEFAULT_IS_ZERO 1
2800
2801 #define NO_PULLBACK
2802
2803 #include <isl_pw_templ.c>
2804
2805 #undef UNION
2806 #define UNION isl_union_pw_qpolynomial
2807 #undef PART
2808 #define PART isl_pw_qpolynomial
2809 #undef PARTS
2810 #define PARTS pw_qpolynomial
2811 #define ALIGN_DOMAIN
2812
2813 #include <isl_union_templ.c>
2814
2815 int isl_pw_qpolynomial_is_one(__isl_keep isl_pw_qpolynomial *pwqp)
2816 {
2817         if (!pwqp)
2818                 return -1;
2819
2820         if (pwqp->n != -1)
2821                 return 0;
2822
2823         if (!isl_set_plain_is_universe(pwqp->p[0].set))
2824                 return 0;
2825
2826         return isl_qpolynomial_is_one(pwqp->p[0].qp);
2827 }
2828
2829 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_add(
2830         __isl_take isl_pw_qpolynomial *pwqp1,
2831         __isl_take isl_pw_qpolynomial *pwqp2)
2832 {
2833         return isl_pw_qpolynomial_union_add_(pwqp1, pwqp2);
2834 }
2835
2836 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_mul(
2837         __isl_take isl_pw_qpolynomial *pwqp1,
2838         __isl_take isl_pw_qpolynomial *pwqp2)
2839 {
2840         int i, j, n;
2841         struct isl_pw_qpolynomial *res;
2842
2843         if (!pwqp1 || !pwqp2)
2844                 goto error;
2845
2846         isl_assert(pwqp1->dim->ctx, isl_space_is_equal(pwqp1->dim, pwqp2->dim),
2847                         goto error);
2848
2849         if (isl_pw_qpolynomial_is_zero(pwqp1)) {
2850                 isl_pw_qpolynomial_free(pwqp2);
2851                 return pwqp1;
2852         }
2853
2854         if (isl_pw_qpolynomial_is_zero(pwqp2)) {
2855                 isl_pw_qpolynomial_free(pwqp1);
2856                 return pwqp2;
2857         }
2858
2859         if (isl_pw_qpolynomial_is_one(pwqp1)) {
2860                 isl_pw_qpolynomial_free(pwqp1);
2861                 return pwqp2;
2862         }
2863
2864         if (isl_pw_qpolynomial_is_one(pwqp2)) {
2865                 isl_pw_qpolynomial_free(pwqp2);
2866                 return pwqp1;
2867         }
2868
2869         n = pwqp1->n * pwqp2->n;
2870         res = isl_pw_qpolynomial_alloc_size(isl_space_copy(pwqp1->dim), n);
2871
2872         for (i = 0; i < pwqp1->n; ++i) {
2873                 for (j = 0; j < pwqp2->n; ++j) {
2874                         struct isl_set *common;
2875                         struct isl_qpolynomial *prod;
2876                         common = isl_set_intersect(isl_set_copy(pwqp1->p[i].set),
2877                                                 isl_set_copy(pwqp2->p[j].set));
2878                         if (isl_set_plain_is_empty(common)) {
2879                                 isl_set_free(common);
2880                                 continue;
2881                         }
2882
2883                         prod = isl_qpolynomial_mul(
2884                                 isl_qpolynomial_copy(pwqp1->p[i].qp),
2885                                 isl_qpolynomial_copy(pwqp2->p[j].qp));
2886
2887                         res = isl_pw_qpolynomial_add_piece(res, common, prod);
2888                 }
2889         }
2890
2891         isl_pw_qpolynomial_free(pwqp1);
2892         isl_pw_qpolynomial_free(pwqp2);
2893
2894         return res;
2895 error:
2896         isl_pw_qpolynomial_free(pwqp1);
2897         isl_pw_qpolynomial_free(pwqp2);
2898         return NULL;
2899 }
2900
2901 __isl_give isl_val *isl_upoly_eval(__isl_take struct isl_upoly *up,
2902         __isl_take isl_vec *vec)
2903 {
2904         int i;
2905         struct isl_upoly_rec *rec;
2906         isl_val *res;
2907         isl_val *base;
2908
2909         if (isl_upoly_is_cst(up)) {
2910                 isl_vec_free(vec);
2911                 res = isl_upoly_get_constant_val(up);
2912                 isl_upoly_free(up);
2913                 return res;
2914         }
2915
2916         rec = isl_upoly_as_rec(up);
2917         if (!rec)
2918                 goto error;
2919
2920         isl_assert(up->ctx, rec->n >= 1, goto error);
2921
2922         base = isl_val_rat_from_isl_int(up->ctx,
2923                                         vec->el[1 + up->var], vec->el[0]);
2924
2925         res = isl_upoly_eval(isl_upoly_copy(rec->p[rec->n - 1]),
2926                                 isl_vec_copy(vec));
2927
2928         for (i = rec->n - 2; i >= 0; --i) {
2929                 res = isl_val_mul(res, isl_val_copy(base));
2930                 res = isl_val_add(res,
2931                             isl_upoly_eval(isl_upoly_copy(rec->p[i]),
2932                                                             isl_vec_copy(vec)));
2933         }
2934
2935         isl_val_free(base);
2936         isl_upoly_free(up);
2937         isl_vec_free(vec);
2938         return res;
2939 error:
2940         isl_upoly_free(up);
2941         isl_vec_free(vec);
2942         return NULL;
2943 }
2944
2945 __isl_give isl_val *isl_qpolynomial_eval(__isl_take isl_qpolynomial *qp,
2946         __isl_take isl_point *pnt)
2947 {
2948         isl_vec *ext;
2949         isl_val *v;
2950
2951         if (!qp || !pnt)
2952                 goto error;
2953         isl_assert(pnt->dim->ctx, isl_space_is_equal(pnt->dim, qp->dim), goto error);
2954
2955         if (qp->div->n_row == 0)
2956                 ext = isl_vec_copy(pnt->vec);
2957         else {
2958                 int i;
2959                 unsigned dim = isl_space_dim(qp->dim, isl_dim_all);
2960                 ext = isl_vec_alloc(qp->dim->ctx, 1 + dim + qp->div->n_row);
2961                 if (!ext)
2962                         goto error;
2963
2964                 isl_seq_cpy(ext->el, pnt->vec->el, pnt->vec->size);
2965                 for (i = 0; i < qp->div->n_row; ++i) {
2966                         isl_seq_inner_product(qp->div->row[i] + 1, ext->el,
2967                                                 1 + dim + i, &ext->el[1+dim+i]);
2968                         isl_int_fdiv_q(ext->el[1+dim+i], ext->el[1+dim+i],
2969                                         qp->div->row[i][0]);
2970                 }
2971         }
2972
2973         v = isl_upoly_eval(isl_upoly_copy(qp->upoly), ext);
2974
2975         isl_qpolynomial_free(qp);
2976         isl_point_free(pnt);
2977
2978         return v;
2979 error:
2980         isl_qpolynomial_free(qp);
2981         isl_point_free(pnt);
2982         return NULL;
2983 }
2984
2985 int isl_upoly_cmp(__isl_keep struct isl_upoly_cst *cst1,
2986         __isl_keep struct isl_upoly_cst *cst2)
2987 {
2988         int cmp;
2989         isl_int t;
2990         isl_int_init(t);
2991         isl_int_mul(t, cst1->n, cst2->d);
2992         isl_int_submul(t, cst2->n, cst1->d);
2993         cmp = isl_int_sgn(t);
2994         isl_int_clear(t);
2995         return cmp;
2996 }
2997
2998 __isl_give isl_qpolynomial *isl_qpolynomial_insert_dims(
2999         __isl_take isl_qpolynomial *qp, enum isl_dim_type type,
3000         unsigned first, unsigned n)
3001 {
3002         unsigned total;
3003         unsigned g_pos;
3004         int *exp;
3005
3006         if (!qp)
3007                 return NULL;
3008         if (type == isl_dim_out)
3009                 isl_die(qp->div->ctx, isl_error_invalid,
3010                         "cannot insert output/set dimensions",
3011                         goto error);
3012         if (type == isl_dim_in)
3013                 type = isl_dim_set;
3014         if (n == 0 && !isl_space_is_named_or_nested(qp->dim, type))
3015                 return qp;
3016
3017         qp = isl_qpolynomial_cow(qp);
3018         if (!qp)
3019                 return NULL;
3020
3021         isl_assert(qp->div->ctx, first <= isl_space_dim(qp->dim, type),
3022                     goto error);
3023
3024         g_pos = pos(qp->dim, type) + first;
3025
3026         qp->div = isl_mat_insert_zero_cols(qp->div, 2 + g_pos, n);
3027         if (!qp->div)
3028                 goto error;
3029
3030         total = qp->div->n_col - 2;
3031         if (total > g_pos) {
3032                 int i;
3033                 exp = isl_alloc_array(qp->div->ctx, int, total - g_pos);
3034                 if (!exp)
3035                         goto error;
3036                 for (i = 0; i < total - g_pos; ++i)
3037                         exp[i] = i + n;
3038                 qp->upoly = expand(qp->upoly, exp, g_pos);
3039                 free(exp);
3040                 if (!qp->upoly)
3041                         goto error;
3042         }
3043
3044         qp->dim = isl_space_insert_dims(qp->dim, type, first, n);
3045         if (!qp->dim)
3046                 goto error;
3047
3048         return qp;
3049 error:
3050         isl_qpolynomial_free(qp);
3051         return NULL;
3052 }
3053
3054 __isl_give isl_qpolynomial *isl_qpolynomial_add_dims(
3055         __isl_take isl_qpolynomial *qp, enum isl_dim_type type, unsigned n)
3056 {
3057         unsigned pos;
3058
3059         pos = isl_qpolynomial_dim(qp, type);
3060
3061         return isl_qpolynomial_insert_dims(qp, type, pos, n);
3062 }
3063
3064 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_add_dims(
3065         __isl_take isl_pw_qpolynomial *pwqp,
3066         enum isl_dim_type type, unsigned n)
3067 {
3068         unsigned pos;
3069
3070         pos = isl_pw_qpolynomial_dim(pwqp, type);
3071
3072         return isl_pw_qpolynomial_insert_dims(pwqp, type, pos, n);
3073 }
3074
3075 static int *reordering_move(isl_ctx *ctx,
3076         unsigned len, unsigned dst, unsigned src, unsigned n)
3077 {
3078         int i;
3079         int *reordering;
3080
3081         reordering = isl_alloc_array(ctx, int, len);
3082         if (!reordering)
3083                 return NULL;
3084
3085         if (dst <= src) {
3086                 for (i = 0; i < dst; ++i)
3087                         reordering[i] = i;
3088                 for (i = 0; i < n; ++i)
3089                         reordering[src + i] = dst + i;
3090                 for (i = 0; i < src - dst; ++i)
3091                         reordering[dst + i] = dst + n + i;
3092                 for (i = 0; i < len - src - n; ++i)
3093                         reordering[src + n + i] = src + n + i;
3094         } else {
3095                 for (i = 0; i < src; ++i)
3096                         reordering[i] = i;
3097                 for (i = 0; i < n; ++i)
3098                         reordering[src + i] = dst + i;
3099                 for (i = 0; i < dst - src; ++i)
3100                         reordering[src + n + i] = src + i;
3101                 for (i = 0; i < len - dst - n; ++i)
3102                         reordering[dst + n + i] = dst + n + i;
3103         }
3104
3105         return reordering;
3106 }
3107
3108 __isl_give isl_qpolynomial *isl_qpolynomial_move_dims(
3109         __isl_take isl_qpolynomial *qp,
3110         enum isl_dim_type dst_type, unsigned dst_pos,
3111         enum isl_dim_type src_type, unsigned src_pos, unsigned n)
3112 {
3113         unsigned g_dst_pos;
3114         unsigned g_src_pos;
3115         int *reordering;
3116
3117         if (n == 0)
3118                 return qp;
3119
3120         qp = isl_qpolynomial_cow(qp);
3121         if (!qp)
3122                 return NULL;
3123
3124         if (dst_type == isl_dim_out || src_type == isl_dim_out)
3125                 isl_die(qp->dim->ctx, isl_error_invalid,
3126                         "cannot move output/set dimension",
3127                         goto error);
3128         if (dst_type == isl_dim_in)
3129                 dst_type = isl_dim_set;
3130         if (src_type == isl_dim_in)
3131                 src_type = isl_dim_set;
3132
3133         isl_assert(qp->dim->ctx, src_pos + n <= isl_space_dim(qp->dim, src_type),
3134                 goto error);
3135
3136         g_dst_pos = pos(qp->dim, dst_type) + dst_pos;
3137         g_src_pos = pos(qp->dim, src_type) + src_pos;
3138         if (dst_type > src_type)
3139                 g_dst_pos -= n;
3140
3141         qp->div = isl_mat_move_cols(qp->div, 2 + g_dst_pos, 2 + g_src_pos, n);
3142         if (!qp->div)
3143                 goto error;
3144         qp = sort_divs(qp);
3145         if (!qp)
3146                 goto error;
3147
3148         reordering = reordering_move(qp->dim->ctx,
3149                                 qp->div->n_col - 2, g_dst_pos, g_src_pos, n);
3150         if (!reordering)
3151                 goto error;
3152
3153         qp->upoly = reorder(qp->upoly, reordering);
3154         free(reordering);
3155         if (!qp->upoly)
3156                 goto error;
3157
3158         qp->dim = isl_space_move_dims(qp->dim, dst_type, dst_pos, src_type, src_pos, n);
3159         if (!qp->dim)
3160                 goto error;
3161
3162         return qp;
3163 error:
3164         isl_qpolynomial_free(qp);
3165         return NULL;
3166 }
3167
3168 __isl_give isl_qpolynomial *isl_qpolynomial_from_affine(__isl_take isl_space *dim,
3169         isl_int *f, isl_int denom)
3170 {
3171         struct isl_upoly *up;
3172
3173         dim = isl_space_domain(dim);
3174         if (!dim)
3175                 return NULL;
3176
3177         up = isl_upoly_from_affine(dim->ctx, f, denom,
3178                                         1 + isl_space_dim(dim, isl_dim_all));
3179
3180         return isl_qpolynomial_alloc(dim, 0, up);
3181 }
3182
3183 __isl_give isl_qpolynomial *isl_qpolynomial_from_aff(__isl_take isl_aff *aff)
3184 {
3185         isl_ctx *ctx;
3186         struct isl_upoly *up;
3187         isl_qpolynomial *qp;
3188
3189         if (!aff)
3190                 return NULL;
3191
3192         ctx = isl_aff_get_ctx(aff);
3193         up = isl_upoly_from_affine(ctx, aff->v->el + 1, aff->v->el[0],
3194                                     aff->v->size - 1);
3195
3196         qp = isl_qpolynomial_alloc(isl_aff_get_domain_space(aff),
3197                                     aff->ls->div->n_row, up);
3198         if (!qp)
3199                 goto error;
3200
3201         isl_mat_free(qp->div);
3202         qp->div = isl_mat_copy(aff->ls->div);
3203         qp->div = isl_mat_cow(qp->div);
3204         if (!qp->div)
3205                 goto error;
3206
3207         isl_aff_free(aff);
3208         qp = reduce_divs(qp);
3209         qp = remove_redundant_divs(qp);
3210         return qp;
3211 error:
3212         isl_aff_free(aff);
3213         return isl_qpolynomial_free(qp);
3214 }
3215
3216 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_from_pw_aff(
3217         __isl_take isl_pw_aff *pwaff)
3218 {
3219         int i;
3220         isl_pw_qpolynomial *pwqp;
3221
3222         if (!pwaff)
3223                 return NULL;
3224
3225         pwqp = isl_pw_qpolynomial_alloc_size(isl_pw_aff_get_space(pwaff),
3226                                                 pwaff->n);
3227
3228         for (i = 0; i < pwaff->n; ++i) {
3229                 isl_set *dom;
3230                 isl_qpolynomial *qp;
3231
3232                 dom = isl_set_copy(pwaff->p[i].set);
3233                 qp = isl_qpolynomial_from_aff(isl_aff_copy(pwaff->p[i].aff));
3234                 pwqp = isl_pw_qpolynomial_add_piece(pwqp,  dom, qp);
3235         }
3236
3237         isl_pw_aff_free(pwaff);
3238         return pwqp;
3239 }
3240
3241 __isl_give isl_qpolynomial *isl_qpolynomial_from_constraint(
3242         __isl_take isl_constraint *c, enum isl_dim_type type, unsigned pos)
3243 {
3244         isl_aff *aff;
3245
3246         aff = isl_constraint_get_bound(c, type, pos);
3247         isl_constraint_free(c);
3248         return isl_qpolynomial_from_aff(aff);
3249 }
3250
3251 /* For each 0 <= i < "n", replace variable "first" + i of type "type"
3252  * in "qp" by subs[i].
3253  */
3254 __isl_give isl_qpolynomial *isl_qpolynomial_substitute(
3255         __isl_take isl_qpolynomial *qp,
3256         enum isl_dim_type type, unsigned first, unsigned n,
3257         __isl_keep isl_qpolynomial **subs)
3258 {
3259         int i;
3260         struct isl_upoly **ups;
3261
3262         if (n == 0)
3263                 return qp;
3264
3265         qp = isl_qpolynomial_cow(qp);
3266         if (!qp)
3267                 return NULL;
3268
3269         if (type == isl_dim_out)
3270                 isl_die(qp->dim->ctx, isl_error_invalid,
3271                         "cannot substitute output/set dimension",
3272                         goto error);
3273         if (type == isl_dim_in)
3274                 type = isl_dim_set;
3275
3276         for (i = 0; i < n; ++i)
3277                 if (!subs[i])
3278                         goto error;
3279
3280         isl_assert(qp->dim->ctx, first + n <= isl_space_dim(qp->dim, type),
3281                         goto error);
3282
3283         for (i = 0; i < n; ++i)
3284                 isl_assert(qp->dim->ctx, isl_space_is_equal(qp->dim, subs[i]->dim),
3285                                 goto error);
3286
3287         isl_assert(qp->dim->ctx, qp->div->n_row == 0, goto error);
3288         for (i = 0; i < n; ++i)
3289                 isl_assert(qp->dim->ctx, subs[i]->div->n_row == 0, goto error);
3290
3291         first += pos(qp->dim, type);
3292
3293         ups = isl_alloc_array(qp->dim->ctx, struct isl_upoly *, n);
3294         if (!ups)
3295                 goto error;
3296         for (i = 0; i < n; ++i)
3297                 ups[i] = subs[i]->upoly;
3298
3299         qp->upoly = isl_upoly_subs(qp->upoly, first, n, ups);
3300
3301         free(ups);
3302
3303         if (!qp->upoly)
3304                 goto error;
3305
3306         return qp;
3307 error:
3308         isl_qpolynomial_free(qp);
3309         return NULL;
3310 }
3311
3312 /* Extend "bset" with extra set dimensions for each integer division
3313  * in "qp" and then call "fn" with the extended bset and the polynomial
3314  * that results from replacing each of the integer divisions by the
3315  * corresponding extra set dimension.
3316  */
3317 int isl_qpolynomial_as_polynomial_on_domain(__isl_keep isl_qpolynomial *qp,
3318         __isl_keep isl_basic_set *bset,
3319         int (*fn)(__isl_take isl_basic_set *bset,
3320                   __isl_take isl_qpolynomial *poly, void *user), void *user)
3321 {
3322         isl_space *dim;
3323         isl_mat *div;
3324         isl_qpolynomial *poly;
3325
3326         if (!qp || !bset)
3327                 goto error;
3328         if (qp->div->n_row == 0)
3329                 return fn(isl_basic_set_copy(bset), isl_qpolynomial_copy(qp),
3330                           user);
3331
3332         div = isl_mat_copy(qp->div);
3333         dim = isl_space_copy(qp->dim);
3334         dim = isl_space_add_dims(dim, isl_dim_set, qp->div->n_row);
3335         poly = isl_qpolynomial_alloc(dim, 0, isl_upoly_copy(qp->upoly));
3336         bset = isl_basic_set_copy(bset);
3337         bset = isl_basic_set_add_dims(bset, isl_dim_set, qp->div->n_row);
3338         bset = add_div_constraints(bset, div);
3339
3340         return fn(bset, poly, user);
3341 error:
3342         return -1;
3343 }
3344
3345 /* Return total degree in variables first (inclusive) up to last (exclusive).
3346  */
3347 int isl_upoly_degree(__isl_keep struct isl_upoly *up, int first, int last)
3348 {
3349         int deg = -1;
3350         int i;
3351         struct isl_upoly_rec *rec;
3352
3353         if (!up)
3354                 return -2;
3355         if (isl_upoly_is_zero(up))
3356                 return -1;
3357         if (isl_upoly_is_cst(up) || up->var < first)
3358                 return 0;
3359
3360         rec = isl_upoly_as_rec(up);
3361         if (!rec)
3362                 return -2;
3363
3364         for (i = 0; i < rec->n; ++i) {
3365                 int d;
3366
3367                 if (isl_upoly_is_zero(rec->p[i]))
3368                         continue;
3369                 d = isl_upoly_degree(rec->p[i], first, last);
3370                 if (up->var < last)
3371                         d += i;
3372                 if (d > deg)
3373                         deg = d;
3374         }
3375
3376         return deg;
3377 }
3378
3379 /* Return total degree in set variables.
3380  */
3381 int isl_qpolynomial_degree(__isl_keep isl_qpolynomial *poly)
3382 {
3383         unsigned ovar;
3384         unsigned nvar;
3385
3386         if (!poly)
3387                 return -2;
3388
3389         ovar = isl_space_offset(poly->dim, isl_dim_set);
3390         nvar = isl_space_dim(poly->dim, isl_dim_set);
3391         return isl_upoly_degree(poly->upoly, ovar, ovar + nvar);
3392 }
3393
3394 __isl_give struct isl_upoly *isl_upoly_coeff(__isl_keep struct isl_upoly *up,
3395         unsigned pos, int deg)
3396 {
3397         int i;
3398         struct isl_upoly_rec *rec;
3399
3400         if (!up)
3401                 return NULL;
3402
3403         if (isl_upoly_is_cst(up) || up->var < pos) {
3404                 if (deg == 0)
3405                         return isl_upoly_copy(up);
3406                 else
3407                         return isl_upoly_zero(up->ctx);
3408         }
3409
3410         rec = isl_upoly_as_rec(up);
3411         if (!rec)
3412                 return NULL;
3413
3414         if (up->var == pos) {
3415                 if (deg < rec->n)
3416                         return isl_upoly_copy(rec->p[deg]);
3417                 else
3418                         return isl_upoly_zero(up->ctx);
3419         }
3420
3421         up = isl_upoly_copy(up);
3422         up = isl_upoly_cow(up);
3423         rec = isl_upoly_as_rec(up);
3424         if (!rec)
3425                 goto error;
3426
3427         for (i = 0; i < rec->n; ++i) {
3428                 struct isl_upoly *t;
3429                 t = isl_upoly_coeff(rec->p[i], pos, deg);
3430                 if (!t)
3431                         goto error;
3432                 isl_upoly_free(rec->p[i]);
3433                 rec->p[i] = t;
3434         }
3435
3436         return up;
3437 error:
3438         isl_upoly_free(up);
3439         return NULL;
3440 }
3441
3442 /* Return coefficient of power "deg" of variable "t_pos" of type "type".
3443  */
3444 __isl_give isl_qpolynomial *isl_qpolynomial_coeff(
3445         __isl_keep isl_qpolynomial *qp,
3446         enum isl_dim_type type, unsigned t_pos, int deg)
3447 {
3448         unsigned g_pos;
3449         struct isl_upoly *up;
3450         isl_qpolynomial *c;
3451
3452         if (!qp)
3453                 return NULL;
3454
3455         if (type == isl_dim_out)
3456                 isl_die(qp->div->ctx, isl_error_invalid,
3457                         "output/set dimension does not have a coefficient",
3458                         return NULL);
3459         if (type == isl_dim_in)
3460                 type = isl_dim_set;
3461
3462         isl_assert(qp->div->ctx, t_pos < isl_space_dim(qp->dim, type),
3463                         return NULL);
3464
3465         g_pos = pos(qp->dim, type) + t_pos;
3466         up = isl_upoly_coeff(qp->upoly, g_pos, deg);
3467
3468         c = isl_qpolynomial_alloc(isl_space_copy(qp->dim), qp->div->n_row, up);
3469         if (!c)
3470                 return NULL;
3471         isl_mat_free(c->div);
3472         c->div = isl_mat_copy(qp->div);
3473         if (!c->div)
3474                 goto error;
3475         return c;
3476 error:
3477         isl_qpolynomial_free(c);
3478         return NULL;
3479 }
3480
3481 /* Homogenize the polynomial in the variables first (inclusive) up to
3482  * last (exclusive) by inserting powers of variable first.
3483  * Variable first is assumed not to appear in the input.
3484  */
3485 __isl_give struct isl_upoly *isl_upoly_homogenize(
3486         __isl_take struct isl_upoly *up, int deg, int target,
3487         int first, int last)
3488 {
3489         int i;
3490         struct isl_upoly_rec *rec;
3491
3492         if (!up)
3493                 return NULL;
3494         if (isl_upoly_is_zero(up))
3495                 return up;
3496         if (deg == target)
3497                 return up;
3498         if (isl_upoly_is_cst(up) || up->var < first) {
3499                 struct isl_upoly *hom;
3500
3501                 hom = isl_upoly_var_pow(up->ctx, first, target - deg);
3502                 if (!hom)
3503                         goto error;
3504                 rec = isl_upoly_as_rec(hom);
3505                 rec->p[target - deg] = isl_upoly_mul(rec->p[target - deg], up);
3506
3507                 return hom;
3508         }
3509
3510         up = isl_upoly_cow(up);
3511         rec = isl_upoly_as_rec(up);
3512         if (!rec)
3513                 goto error;
3514
3515         for (i = 0; i < rec->n; ++i) {
3516                 if (isl_upoly_is_zero(rec->p[i]))
3517                         continue;
3518                 rec->p[i] = isl_upoly_homogenize(rec->p[i],
3519                                 up->var < last ? deg + i : i, target,
3520                                 first, last);
3521                 if (!rec->p[i])
3522                         goto error;
3523         }
3524
3525         return up;
3526 error:
3527         isl_upoly_free(up);
3528         return NULL;
3529 }
3530
3531 /* Homogenize the polynomial in the set variables by introducing
3532  * powers of an extra set variable at position 0.
3533  */
3534 __isl_give isl_qpolynomial *isl_qpolynomial_homogenize(
3535         __isl_take isl_qpolynomial *poly)
3536 {
3537         unsigned ovar;
3538         unsigned nvar;
3539         int deg = isl_qpolynomial_degree(poly);
3540
3541         if (deg < -1)
3542                 goto error;
3543
3544         poly = isl_qpolynomial_insert_dims(poly, isl_dim_in, 0, 1);
3545         poly = isl_qpolynomial_cow(poly);
3546         if (!poly)
3547                 goto error;
3548
3549         ovar = isl_space_offset(poly->dim, isl_dim_set);
3550         nvar = isl_space_dim(poly->dim, isl_dim_set);
3551         poly->upoly = isl_upoly_homogenize(poly->upoly, 0, deg,
3552                                                 ovar, ovar + nvar);
3553         if (!poly->upoly)
3554                 goto error;
3555
3556         return poly;
3557 error:
3558         isl_qpolynomial_free(poly);
3559         return NULL;
3560 }
3561
3562 __isl_give isl_term *isl_term_alloc(__isl_take isl_space *dim,
3563         __isl_take isl_mat *div)
3564 {
3565         isl_term *term;
3566         int n;
3567
3568         if (!dim || !div)
3569                 goto error;
3570
3571         n = isl_space_dim(dim, isl_dim_all) + div->n_row;
3572
3573         term = isl_calloc(dim->ctx, struct isl_term,
3574                         sizeof(struct isl_term) + (n - 1) * sizeof(int));
3575         if (!term)
3576                 goto error;
3577
3578         term->ref = 1;
3579         term->dim = dim;
3580         term->div = div;
3581         isl_int_init(term->n);
3582         isl_int_init(term->d);
3583
3584         return term;
3585 error:
3586         isl_space_free(dim);
3587         isl_mat_free(div);
3588         return NULL;
3589 }
3590
3591 __isl_give isl_term *isl_term_copy(__isl_keep isl_term *term)
3592 {
3593         if (!term)
3594                 return NULL;
3595
3596         term->ref++;
3597         return term;
3598 }
3599
3600 __isl_give isl_term *isl_term_dup(__isl_keep isl_term *term)
3601 {
3602         int i;
3603         isl_term *dup;
3604         unsigned total;
3605
3606         if (!term)
3607                 return NULL;
3608
3609         total = isl_space_dim(term->dim, isl_dim_all) + term->div->n_row;
3610
3611         dup = isl_term_alloc(isl_space_copy(term->dim), isl_mat_copy(term->div));
3612         if (!dup)
3613                 return NULL;
3614
3615         isl_int_set(dup->n, term->n);
3616         isl_int_set(dup->d, term->d);
3617
3618         for (i = 0; i < total; ++i)
3619                 dup->pow[i] = term->pow[i];
3620
3621         return dup;
3622 }
3623
3624 __isl_give isl_term *isl_term_cow(__isl_take isl_term *term)
3625 {
3626         if (!term)
3627                 return NULL;
3628
3629         if (term->ref == 1)
3630                 return term;
3631         term->ref--;
3632         return isl_term_dup(term);
3633 }
3634
3635 void isl_term_free(__isl_take isl_term *term)
3636 {
3637         if (!term)
3638                 return;
3639
3640         if (--term->ref > 0)
3641                 return;
3642
3643         isl_space_free(term->dim);
3644         isl_mat_free(term->div);
3645         isl_int_clear(term->n);
3646         isl_int_clear(term->d);
3647         free(term);
3648 }
3649
3650 unsigned isl_term_dim(__isl_keep isl_term *term, enum isl_dim_type type)
3651 {
3652         if (!term)
3653                 return 0;
3654
3655         switch (type) {
3656         case isl_dim_param:
3657         case isl_dim_in:
3658         case isl_dim_out:       return isl_space_dim(term->dim, type);
3659         case isl_dim_div:       return term->div->n_row;
3660         case isl_dim_all:       return isl_space_dim(term->dim, isl_dim_all) +
3661                                                                 term->div->n_row;
3662         default:                return 0;
3663         }
3664 }
3665
3666 isl_ctx *isl_term_get_ctx(__isl_keep isl_term *term)
3667 {
3668         return term ? term->dim->ctx : NULL;
3669 }
3670
3671 void isl_term_get_num(__isl_keep isl_term *term, isl_int *n)
3672 {
3673         if (!term)
3674                 return;
3675         isl_int_set(*n, term->n);
3676 }
3677
3678 void isl_term_get_den(__isl_keep isl_term *term, isl_int *d)
3679 {
3680         if (!term)
3681                 return;
3682         isl_int_set(*d, term->d);
3683 }
3684
3685 /* Return the coefficient of the term "term".
3686  */
3687 __isl_give isl_val *isl_term_get_coefficient_val(__isl_keep isl_term *term)
3688 {
3689         if (!term)
3690                 return NULL;
3691
3692         return isl_val_rat_from_isl_int(isl_term_get_ctx(term),
3693                                         term->n, term->d);
3694 }
3695
3696 int isl_term_get_exp(__isl_keep isl_term *term,
3697         enum isl_dim_type type, unsigned pos)
3698 {
3699         if (!term)
3700                 return -1;
3701
3702         isl_assert(term->dim->ctx, pos < isl_term_dim(term, type), return -1);
3703
3704         if (type >= isl_dim_set)
3705                 pos += isl_space_dim(term->dim, isl_dim_param);
3706         if (type >= isl_dim_div)
3707                 pos += isl_space_dim(term->dim, isl_dim_set);
3708
3709         return term->pow[pos];
3710 }
3711
3712 __isl_give isl_aff *isl_term_get_div(__isl_keep isl_term *term, unsigned pos)
3713 {
3714         isl_local_space *ls;
3715         isl_aff *aff;
3716
3717         if (!term)
3718                 return NULL;
3719
3720         isl_assert(term->dim->ctx, pos < isl_term_dim(term, isl_dim_div),
3721                         return NULL);
3722
3723         ls = isl_local_space_alloc_div(isl_space_copy(term->dim),
3724                                         isl_mat_copy(term->div));
3725         aff = isl_aff_alloc(ls);
3726         if (!aff)
3727                 return NULL;
3728
3729         isl_seq_cpy(aff->v->el, term->div->row[pos], aff->v->size);
3730
3731         aff = isl_aff_normalize(aff);
3732
3733         return aff;
3734 }
3735
3736 __isl_give isl_term *isl_upoly_foreach_term(__isl_keep struct isl_upoly *up,
3737         int (*fn)(__isl_take isl_term *term, void *user),
3738         __isl_take isl_term *term, void *user)
3739 {
3740         int i;
3741         struct isl_upoly_rec *rec;
3742
3743         if (!up || !term)
3744                 goto error;
3745
3746         if (isl_upoly_is_zero(up))
3747                 return term;
3748
3749         isl_assert(up->ctx, !isl_upoly_is_nan(up), goto error);
3750         isl_assert(up->ctx, !isl_upoly_is_infty(up), goto error);
3751         isl_assert(up->ctx, !isl_upoly_is_neginfty(up), goto error);
3752
3753         if (isl_upoly_is_cst(up)) {
3754                 struct isl_upoly_cst *cst;
3755                 cst = isl_upoly_as_cst(up);
3756                 if (!cst)
3757                         goto error;
3758                 term = isl_term_cow(term);
3759                 if (!term)
3760                         goto error;
3761                 isl_int_set(term->n, cst->n);
3762                 isl_int_set(term->d, cst->d);
3763                 if (fn(isl_term_copy(term), user) < 0)
3764                         goto error;
3765                 return term;
3766         }
3767
3768         rec = isl_upoly_as_rec(up);
3769         if (!rec)
3770                 goto error;
3771
3772         for (i = 0; i < rec->n; ++i) {
3773                 term = isl_term_cow(term);
3774                 if (!term)
3775                         goto error;
3776                 term->pow[up->var] = i;
3777                 term = isl_upoly_foreach_term(rec->p[i], fn, term, user);
3778                 if (!term)
3779                         goto error;
3780         }
3781         term->pow[up->var] = 0;
3782
3783         return term;
3784 error:
3785         isl_term_free(term);
3786         return NULL;
3787 }
3788
3789 int isl_qpolynomial_foreach_term(__isl_keep isl_qpolynomial *qp,
3790         int (*fn)(__isl_take isl_term *term, void *user), void *user)
3791 {
3792         isl_term *term;
3793
3794         if (!qp)
3795                 return -1;
3796
3797         term = isl_term_alloc(isl_space_copy(qp->dim), isl_mat_copy(qp->div));
3798         if (!term)
3799                 return -1;
3800
3801         term = isl_upoly_foreach_term(qp->upoly, fn, term, user);
3802
3803         isl_term_free(term);
3804
3805         return term ? 0 : -1;
3806 }
3807
3808 __isl_give isl_qpolynomial *isl_qpolynomial_from_term(__isl_take isl_term *term)
3809 {
3810         struct isl_upoly *up;
3811         isl_qpolynomial *qp;
3812         int i, n;
3813
3814         if (!term)
3815                 return NULL;
3816
3817         n = isl_space_dim(term->dim, isl_dim_all) + term->div->n_row;
3818
3819         up = isl_upoly_rat_cst(term->dim->ctx, term->n, term->d);
3820         for (i = 0; i < n; ++i) {
3821                 if (!term->pow[i])
3822                         continue;
3823                 up = isl_upoly_mul(up,
3824                         isl_upoly_var_pow(term->dim->ctx, i, term->pow[i]));
3825         }
3826
3827         qp = isl_qpolynomial_alloc(isl_space_copy(term->dim), term->div->n_row, up);
3828         if (!qp)
3829                 goto error;
3830         isl_mat_free(qp->div);
3831         qp->div = isl_mat_copy(term->div);
3832         if (!qp->div)
3833                 goto error;
3834
3835         isl_term_free(term);
3836         return qp;
3837 error:
3838         isl_qpolynomial_free(qp);
3839         isl_term_free(term);
3840         return NULL;
3841 }
3842
3843 __isl_give isl_qpolynomial *isl_qpolynomial_lift(__isl_take isl_qpolynomial *qp,
3844         __isl_take isl_space *dim)
3845 {
3846         int i;
3847         int extra;
3848         unsigned total;
3849
3850         if (!qp || !dim)
3851                 goto error;
3852
3853         if (isl_space_is_equal(qp->dim, dim)) {
3854                 isl_space_free(dim);
3855                 return qp;
3856         }
3857
3858         qp = isl_qpolynomial_cow(qp);
3859         if (!qp)
3860                 goto error;
3861
3862         extra = isl_space_dim(dim, isl_dim_set) -
3863                         isl_space_dim(qp->dim, isl_dim_set);
3864         total = isl_space_dim(qp->dim, isl_dim_all);
3865         if (qp->div->n_row) {
3866                 int *exp;
3867
3868                 exp = isl_alloc_array(qp->div->ctx, int, qp->div->n_row);
3869                 if (!exp)
3870                         goto error;
3871                 for (i = 0; i < qp->div->n_row; ++i)
3872                         exp[i] = extra + i;
3873                 qp->upoly = expand(qp->upoly, exp, total);
3874                 free(exp);
3875                 if (!qp->upoly)
3876                         goto error;
3877         }
3878         qp->div = isl_mat_insert_cols(qp->div, 2 + total, extra);
3879         if (!qp->div)
3880                 goto error;
3881         for (i = 0; i < qp->div->n_row; ++i)
3882                 isl_seq_clr(qp->div->row[i] + 2 + total, extra);
3883
3884         isl_space_free(qp->dim);
3885         qp->dim = dim;
3886
3887         return qp;
3888 error:
3889         isl_space_free(dim);
3890         isl_qpolynomial_free(qp);
3891         return NULL;
3892 }
3893
3894 /* For each parameter or variable that does not appear in qp,
3895  * first eliminate the variable from all constraints and then set it to zero.
3896  */
3897 static __isl_give isl_set *fix_inactive(__isl_take isl_set *set,
3898         __isl_keep isl_qpolynomial *qp)
3899 {
3900         int *active = NULL;
3901         int i;
3902         int d;
3903         unsigned nparam;
3904         unsigned nvar;
3905
3906         if (!set || !qp)
3907                 goto error;
3908
3909         d = isl_space_dim(set->dim, isl_dim_all);
3910         active = isl_calloc_array(set->ctx, int, d);
3911         if (set_active(qp, active) < 0)
3912                 goto error;
3913
3914         for (i = 0; i < d; ++i)
3915                 if (!active[i])
3916                         break;
3917
3918         if (i == d) {
3919                 free(active);
3920                 return set;
3921         }
3922
3923         nparam = isl_space_dim(set->dim, isl_dim_param);
3924         nvar = isl_space_dim(set->dim, isl_dim_set);
3925         for (i = 0; i < nparam; ++i) {
3926                 if (active[i])
3927                         continue;
3928                 set = isl_set_eliminate(set, isl_dim_param, i, 1);
3929                 set = isl_set_fix_si(set, isl_dim_param, i, 0);
3930         }
3931         for (i = 0; i < nvar; ++i) {
3932                 if (active[nparam + i])
3933                         continue;
3934                 set = isl_set_eliminate(set, isl_dim_set, i, 1);
3935                 set = isl_set_fix_si(set, isl_dim_set, i, 0);
3936         }
3937
3938         free(active);
3939
3940         return set;
3941 error:
3942         free(active);
3943         isl_set_free(set);
3944         return NULL;
3945 }
3946
3947 struct isl_opt_data {
3948         isl_qpolynomial *qp;
3949         int first;
3950         isl_val *opt;
3951         int max;
3952 };
3953
3954 static int opt_fn(__isl_take isl_point *pnt, void *user)
3955 {
3956         struct isl_opt_data *data = (struct isl_opt_data *)user;
3957         isl_val *val;
3958
3959         val = isl_qpolynomial_eval(isl_qpolynomial_copy(data->qp), pnt);
3960         if (data->first) {
3961                 data->first = 0;
3962                 data->opt = val;
3963         } else if (data->max) {
3964                 data->opt = isl_val_max(data->opt, val);
3965         } else {
3966                 data->opt = isl_val_min(data->opt, val);
3967         }
3968
3969         return 0;
3970 }
3971
3972 __isl_give isl_val *isl_qpolynomial_opt_on_domain(
3973         __isl_take isl_qpolynomial *qp, __isl_take isl_set *set, int max)
3974 {
3975         struct isl_opt_data data = { NULL, 1, NULL, max };
3976
3977         if (!set || !qp)
3978                 goto error;
3979
3980         if (isl_upoly_is_cst(qp->upoly)) {
3981                 isl_set_free(set);
3982                 data.opt = isl_qpolynomial_get_constant_val(qp);
3983                 isl_qpolynomial_free(qp);
3984                 return data.opt;
3985         }
3986
3987         set = fix_inactive(set, qp);
3988
3989         data.qp = qp;
3990         if (isl_set_foreach_point(set, opt_fn, &data) < 0)
3991                 goto error;
3992
3993         if (data.first)
3994                 data.opt = isl_val_zero(isl_set_get_ctx(set));
3995
3996         isl_set_free(set);
3997         isl_qpolynomial_free(qp);
3998         return data.opt;
3999 error:
4000         isl_set_free(set);
4001         isl_qpolynomial_free(qp);
4002         isl_val_free(data.opt);
4003         return NULL;
4004 }
4005
4006 __isl_give isl_qpolynomial *isl_qpolynomial_morph_domain(
4007         __isl_take isl_qpolynomial *qp, __isl_take isl_morph *morph)
4008 {
4009         int i;
4010         int n_sub;
4011         isl_ctx *ctx;
4012         struct isl_upoly **subs;
4013         isl_mat *mat, *diag;
4014
4015         qp = isl_qpolynomial_cow(qp);
4016         if (!qp || !morph)
4017                 goto error;
4018
4019         ctx = qp->dim->ctx;
4020         isl_assert(ctx, isl_space_is_equal(qp->dim, morph->dom->dim), goto error);
4021
4022         n_sub = morph->inv->n_row - 1;
4023         if (morph->inv->n_row != morph->inv->n_col)
4024                 n_sub += qp->div->n_row;
4025         subs = isl_calloc_array(ctx, struct isl_upoly *, n_sub);
4026         if (n_sub && !subs)
4027                 goto error;
4028
4029         for (i = 0; 1 + i < morph->inv->n_row; ++i)
4030                 subs[i] = isl_upoly_from_affine(ctx, morph->inv->row[1 + i],
4031                                         morph->inv->row[0][0], morph->inv->n_col);
4032         if (morph->inv->n_row != morph->inv->n_col)
4033                 for (i = 0; i < qp->div->n_row; ++i)
4034                         subs[morph->inv->n_row - 1 + i] =
4035                             isl_upoly_var_pow(ctx, morph->inv->n_col - 1 + i, 1);
4036
4037         qp->upoly = isl_upoly_subs(qp->upoly, 0, n_sub, subs);
4038
4039         for (i = 0; i < n_sub; ++i)
4040                 isl_upoly_free(subs[i]);
4041         free(subs);
4042
4043         diag = isl_mat_diag(ctx, 1, morph->inv->row[0][0]);
4044         mat = isl_mat_diagonal(diag, isl_mat_copy(morph->inv));
4045         diag = isl_mat_diag(ctx, qp->div->n_row, morph->inv->row[0][0]);
4046         mat = isl_mat_diagonal(mat, diag);
4047         qp->div = isl_mat_product(qp->div, mat);
4048         isl_space_free(qp->dim);
4049         qp->dim = isl_space_copy(morph->ran->dim);
4050
4051         if (!qp->upoly || !qp->div || !qp->dim)
4052                 goto error;
4053
4054         isl_morph_free(morph);
4055
4056         return qp;
4057 error:
4058         isl_qpolynomial_free(qp);
4059         isl_morph_free(morph);
4060         return NULL;
4061 }
4062
4063 static int neg_entry(void **entry, void *user)
4064 {
4065         isl_pw_qpolynomial **pwqp = (isl_pw_qpolynomial **)entry;
4066
4067         *pwqp = isl_pw_qpolynomial_neg(*pwqp);
4068
4069         return *pwqp ? 0 : -1;
4070 }
4071
4072 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_neg(
4073         __isl_take isl_union_pw_qpolynomial *upwqp)
4074 {
4075         upwqp = isl_union_pw_qpolynomial_cow(upwqp);
4076         if (!upwqp)
4077                 return NULL;
4078
4079         if (isl_hash_table_foreach(upwqp->space->ctx, &upwqp->table,
4080                                    &neg_entry, NULL) < 0)
4081                 goto error;
4082
4083         return upwqp;
4084 error:
4085         isl_union_pw_qpolynomial_free(upwqp);
4086         return NULL;
4087 }
4088
4089 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_mul(
4090         __isl_take isl_union_pw_qpolynomial *upwqp1,
4091         __isl_take isl_union_pw_qpolynomial *upwqp2)
4092 {
4093         return match_bin_op(upwqp1, upwqp2, &isl_pw_qpolynomial_mul);
4094 }
4095
4096 /* Reorder the columns of the given div definitions according to the
4097  * given reordering.
4098  */
4099 static __isl_give isl_mat *reorder_divs(__isl_take isl_mat *div,
4100         __isl_take isl_reordering *r)
4101 {
4102         int i, j;
4103         isl_mat *mat;
4104         int extra;
4105
4106         if (!div || !r)
4107                 goto error;
4108
4109         extra = isl_space_dim(r->dim, isl_dim_all) + div->n_row - r->len;
4110         mat = isl_mat_alloc(div->ctx, div->n_row, div->n_col + extra);
4111         if (!mat)
4112                 goto error;
4113
4114         for (i = 0; i < div->n_row; ++i) {
4115                 isl_seq_cpy(mat->row[i], div->row[i], 2);
4116                 isl_seq_clr(mat->row[i] + 2, mat->n_col - 2);
4117                 for (j = 0; j < r->len; ++j)
4118                         isl_int_set(mat->row[i][2 + r->pos[j]],
4119                                     div->row[i][2 + j]);
4120         }
4121
4122         isl_reordering_free(r);
4123         isl_mat_free(div);
4124         return mat;
4125 error:
4126         isl_reordering_free(r);
4127         isl_mat_free(div);
4128         return NULL;
4129 }
4130
4131 /* Reorder the dimension of "qp" according to the given reordering.
4132  */
4133 __isl_give isl_qpolynomial *isl_qpolynomial_realign_domain(
4134         __isl_take isl_qpolynomial *qp, __isl_take isl_reordering *r)
4135 {
4136         qp = isl_qpolynomial_cow(qp);
4137         if (!qp)
4138                 goto error;
4139
4140         r = isl_reordering_extend(r, qp->div->n_row);
4141         if (!r)
4142                 goto error;
4143
4144         qp->div = reorder_divs(qp->div, isl_reordering_copy(r));
4145         if (!qp->div)
4146                 goto error;
4147
4148         qp->upoly = reorder(qp->upoly, r->pos);
4149         if (!qp->upoly)
4150                 goto error;
4151
4152         qp = isl_qpolynomial_reset_domain_space(qp, isl_space_copy(r->dim));
4153
4154         isl_reordering_free(r);
4155         return qp;
4156 error:
4157         isl_qpolynomial_free(qp);
4158         isl_reordering_free(r);
4159         return NULL;
4160 }
4161
4162 __isl_give isl_qpolynomial *isl_qpolynomial_align_params(
4163         __isl_take isl_qpolynomial *qp, __isl_take isl_space *model)
4164 {
4165         if (!qp || !model)
4166                 goto error;
4167
4168         if (!isl_space_match(qp->dim, isl_dim_param, model, isl_dim_param)) {
4169                 isl_reordering *exp;
4170
4171                 model = isl_space_drop_dims(model, isl_dim_in,
4172                                         0, isl_space_dim(model, isl_dim_in));
4173                 model = isl_space_drop_dims(model, isl_dim_out,
4174                                         0, isl_space_dim(model, isl_dim_out));
4175                 exp = isl_parameter_alignment_reordering(qp->dim, model);
4176                 exp = isl_reordering_extend_space(exp,
4177                                         isl_qpolynomial_get_domain_space(qp));
4178                 qp = isl_qpolynomial_realign_domain(qp, exp);
4179         }
4180
4181         isl_space_free(model);
4182         return qp;
4183 error:
4184         isl_space_free(model);
4185         isl_qpolynomial_free(qp);
4186         return NULL;
4187 }
4188
4189 struct isl_split_periods_data {
4190         int max_periods;
4191         isl_pw_qpolynomial *res;
4192 };
4193
4194 /* Create a slice where the integer division "div" has the fixed value "v".
4195  * In particular, if "div" refers to floor(f/m), then create a slice
4196  *
4197  *      m v <= f <= m v + (m - 1)
4198  *
4199  * or
4200  *
4201  *      f - m v >= 0
4202  *      -f + m v + (m - 1) >= 0
4203  */
4204 static __isl_give isl_set *set_div_slice(__isl_take isl_space *dim,
4205         __isl_keep isl_qpolynomial *qp, int div, isl_int v)
4206 {
4207         int total;
4208         isl_basic_set *bset = NULL;
4209         int k;
4210
4211         if (!dim || !qp)
4212                 goto error;
4213
4214         total = isl_space_dim(dim, isl_dim_all);
4215         bset = isl_basic_set_alloc_space(isl_space_copy(dim), 0, 0, 2);
4216
4217         k = isl_basic_set_alloc_inequality(bset);
4218         if (k < 0)
4219                 goto error;
4220         isl_seq_cpy(bset->ineq[k], qp->div->row[div] + 1, 1 + total);
4221         isl_int_submul(bset->ineq[k][0], v, qp->div->row[div][0]);
4222
4223         k = isl_basic_set_alloc_inequality(bset);
4224         if (k < 0)
4225                 goto error;
4226         isl_seq_neg(bset->ineq[k], qp->div->row[div] + 1, 1 + total);
4227         isl_int_addmul(bset->ineq[k][0], v, qp->div->row[div][0]);
4228         isl_int_add(bset->ineq[k][0], bset->ineq[k][0], qp->div->row[div][0]);
4229         isl_int_sub_ui(bset->ineq[k][0], bset->ineq[k][0], 1);
4230
4231         isl_space_free(dim);
4232         return isl_set_from_basic_set(bset);
4233 error:
4234         isl_basic_set_free(bset);
4235         isl_space_free(dim);
4236         return NULL;
4237 }
4238
4239 static int split_periods(__isl_take isl_set *set,
4240         __isl_take isl_qpolynomial *qp, void *user);
4241
4242 /* Create a slice of the domain "set" such that integer division "div"
4243  * has the fixed value "v" and add the results to data->res,
4244  * replacing the integer division by "v" in "qp".
4245  */
4246 static int set_div(__isl_take isl_set *set,
4247         __isl_take isl_qpolynomial *qp, int div, isl_int v,
4248         struct isl_split_periods_data *data)
4249 {
4250         int i;
4251         int total;
4252         isl_set *slice;
4253         struct isl_upoly *cst;
4254
4255         slice = set_div_slice(isl_set_get_space(set), qp, div, v);
4256         set = isl_set_intersect(set, slice);
4257
4258         if (!qp)
4259                 goto error;
4260
4261         total = isl_space_dim(qp->dim, isl_dim_all);
4262
4263         for (i = div + 1; i < qp->div->n_row; ++i) {
4264                 if (isl_int_is_zero(qp->div->row[i][2 + total + div]))
4265                         continue;
4266                 isl_int_addmul(qp->div->row[i][1],
4267                                 qp->div->row[i][2 + total + div], v);
4268                 isl_int_set_si(qp->div->row[i][2 + total + div], 0);
4269         }
4270
4271         cst = isl_upoly_rat_cst(qp->dim->ctx, v, qp->dim->ctx->one);
4272         qp = substitute_div(qp, div, cst);
4273
4274         return split_periods(set, qp, data);
4275 error:
4276         isl_set_free(set);
4277         isl_qpolynomial_free(qp);
4278         return -1;
4279 }
4280
4281 /* Split the domain "set" such that integer division "div"
4282  * has a fixed value (ranging from "min" to "max") on each slice
4283  * and add the results to data->res.
4284  */
4285 static int split_div(__isl_take isl_set *set,
4286         __isl_take isl_qpolynomial *qp, int div, isl_int min, isl_int max,
4287         struct isl_split_periods_data *data)
4288 {
4289         for (; isl_int_le(min, max); isl_int_add_ui(min, min, 1)) {
4290                 isl_set *set_i = isl_set_copy(set);
4291                 isl_qpolynomial *qp_i = isl_qpolynomial_copy(qp);
4292
4293                 if (set_div(set_i, qp_i, div, min, data) < 0)
4294                         goto error;
4295         }
4296         isl_set_free(set);
4297         isl_qpolynomial_free(qp);
4298         return 0;
4299 error:
4300         isl_set_free(set);
4301         isl_qpolynomial_free(qp);
4302         return -1;
4303 }
4304
4305 /* If "qp" refers to any integer division
4306  * that can only attain "max_periods" distinct values on "set"
4307  * then split the domain along those distinct values.
4308  * Add the results (or the original if no splitting occurs)
4309  * to data->res.
4310  */
4311 static int split_periods(__isl_take isl_set *set,
4312         __isl_take isl_qpolynomial *qp, void *user)
4313 {
4314         int i;
4315         isl_pw_qpolynomial *pwqp;
4316         struct isl_split_periods_data *data;
4317         isl_int min, max;
4318         int total;
4319         int r = 0;
4320
4321         data = (struct isl_split_periods_data *)user;
4322
4323         if (!set || !qp)
4324                 goto error;
4325
4326         if (qp->div->n_row == 0) {
4327                 pwqp = isl_pw_qpolynomial_alloc(set, qp);
4328                 data->res = isl_pw_qpolynomial_add_disjoint(data->res, pwqp);
4329                 return 0;
4330         }
4331
4332         isl_int_init(min);
4333         isl_int_init(max);
4334         total = isl_space_dim(qp->dim, isl_dim_all);
4335         for (i = 0; i < qp->div->n_row; ++i) {
4336                 enum isl_lp_result lp_res;
4337
4338                 if (isl_seq_first_non_zero(qp->div->row[i] + 2 + total,
4339                                                 qp->div->n_row) != -1)
4340                         continue;
4341
4342                 lp_res = isl_set_solve_lp(set, 0, qp->div->row[i] + 1,
4343                                           set->ctx->one, &min, NULL, NULL);
4344                 if (lp_res == isl_lp_error)
4345                         goto error2;
4346                 if (lp_res == isl_lp_unbounded || lp_res == isl_lp_empty)
4347                         continue;
4348                 isl_int_fdiv_q(min, min, qp->div->row[i][0]);
4349
4350                 lp_res = isl_set_solve_lp(set, 1, qp->div->row[i] + 1,
4351                                           set->ctx->one, &max, NULL, NULL);
4352                 if (lp_res == isl_lp_error)
4353                         goto error2;
4354                 if (lp_res == isl_lp_unbounded || lp_res == isl_lp_empty)
4355                         continue;
4356                 isl_int_fdiv_q(max, max, qp->div->row[i][0]);
4357
4358                 isl_int_sub(max, max, min);
4359                 if (isl_int_cmp_si(max, data->max_periods) < 0) {
4360                         isl_int_add(max, max, min);
4361                         break;
4362                 }
4363         }
4364
4365         if (i < qp->div->n_row) {
4366                 r = split_div(set, qp, i, min, max, data);
4367         } else {
4368                 pwqp = isl_pw_qpolynomial_alloc(set, qp);
4369                 data->res = isl_pw_qpolynomial_add_disjoint(data->res, pwqp);
4370         }
4371
4372         isl_int_clear(max);
4373         isl_int_clear(min);
4374
4375         return r;
4376 error2:
4377         isl_int_clear(max);
4378         isl_int_clear(min);
4379 error:
4380         isl_set_free(set);
4381         isl_qpolynomial_free(qp);
4382         return -1;
4383 }
4384
4385 /* If any quasi-polynomial in pwqp refers to any integer division
4386  * that can only attain "max_periods" distinct values on its domain
4387  * then split the domain along those distinct values.
4388  */
4389 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_split_periods(
4390         __isl_take isl_pw_qpolynomial *pwqp, int max_periods)
4391 {
4392         struct isl_split_periods_data data;
4393
4394         data.max_periods = max_periods;
4395         data.res = isl_pw_qpolynomial_zero(isl_pw_qpolynomial_get_space(pwqp));
4396
4397         if (isl_pw_qpolynomial_foreach_piece(pwqp, &split_periods, &data) < 0)
4398                 goto error;
4399
4400         isl_pw_qpolynomial_free(pwqp);
4401
4402         return data.res;
4403 error:
4404         isl_pw_qpolynomial_free(data.res);
4405         isl_pw_qpolynomial_free(pwqp);
4406         return NULL;
4407 }
4408
4409 /* Construct a piecewise quasipolynomial that is constant on the given
4410  * domain.  In particular, it is
4411  *      0       if cst == 0
4412  *      1       if cst == 1
4413  *  infinity    if cst == -1
4414  */
4415 static __isl_give isl_pw_qpolynomial *constant_on_domain(
4416         __isl_take isl_basic_set *bset, int cst)
4417 {
4418         isl_space *dim;
4419         isl_qpolynomial *qp;
4420
4421         if (!bset)
4422                 return NULL;
4423
4424         bset = isl_basic_set_params(bset);
4425         dim = isl_basic_set_get_space(bset);
4426         if (cst < 0)
4427                 qp = isl_qpolynomial_infty_on_domain(dim);
4428         else if (cst == 0)
4429                 qp = isl_qpolynomial_zero_on_domain(dim);
4430         else
4431                 qp = isl_qpolynomial_one_on_domain(dim);
4432         return isl_pw_qpolynomial_alloc(isl_set_from_basic_set(bset), qp);
4433 }
4434
4435 /* Factor bset, call fn on each of the factors and return the product.
4436  *
4437  * If no factors can be found, simply call fn on the input.
4438  * Otherwise, construct the factors based on the factorizer,
4439  * call fn on each factor and compute the product.
4440  */
4441 static __isl_give isl_pw_qpolynomial *compressed_multiplicative_call(
4442         __isl_take isl_basic_set *bset,
4443         __isl_give isl_pw_qpolynomial *(*fn)(__isl_take isl_basic_set *bset))
4444 {
4445         int i, n;
4446         isl_space *dim;
4447         isl_set *set;
4448         isl_factorizer *f;
4449         isl_qpolynomial *qp;
4450         isl_pw_qpolynomial *pwqp;
4451         unsigned nparam;
4452         unsigned nvar;
4453
4454         f = isl_basic_set_factorizer(bset);
4455         if (!f)
4456                 goto error;
4457         if (f->n_group == 0) {
4458                 isl_factorizer_free(f);
4459                 return fn(bset);
4460         }
4461
4462         nparam = isl_basic_set_dim(bset, isl_dim_param);
4463         nvar = isl_basic_set_dim(bset, isl_dim_set);
4464
4465         dim = isl_basic_set_get_space(bset);
4466         dim = isl_space_domain(dim);
4467         set = isl_set_universe(isl_space_copy(dim));
4468         qp = isl_qpolynomial_one_on_domain(dim);
4469         pwqp = isl_pw_qpolynomial_alloc(set, qp);
4470
4471         bset = isl_morph_basic_set(isl_morph_copy(f->morph), bset);
4472
4473         for (i = 0, n = 0; i < f->n_group; ++i) {
4474                 isl_basic_set *bset_i;
4475                 isl_pw_qpolynomial *pwqp_i;
4476
4477                 bset_i = isl_basic_set_copy(bset);
4478                 bset_i = isl_basic_set_drop_constraints_involving(bset_i,
4479                             nparam + n + f->len[i], nvar - n - f->len[i]);
4480                 bset_i = isl_basic_set_drop_constraints_involving(bset_i,
4481                             nparam, n);
4482                 bset_i = isl_basic_set_drop(bset_i, isl_dim_set,
4483                             n + f->len[i], nvar - n - f->len[i]);
4484                 bset_i = isl_basic_set_drop(bset_i, isl_dim_set, 0, n);
4485
4486                 pwqp_i = fn(bset_i);
4487                 pwqp = isl_pw_qpolynomial_mul(pwqp, pwqp_i);
4488
4489                 n += f->len[i];
4490         }
4491
4492         isl_basic_set_free(bset);
4493         isl_factorizer_free(f);
4494
4495         return pwqp;
4496 error:
4497         isl_basic_set_free(bset);
4498         return NULL;
4499 }
4500
4501 /* Factor bset, call fn on each of the factors and return the product.
4502  * The function is assumed to evaluate to zero on empty domains,
4503  * to one on zero-dimensional domains and to infinity on unbounded domains
4504  * and will not be called explicitly on zero-dimensional or unbounded domains.
4505  *
4506  * We first check for some special cases and remove all equalities.
4507  * Then we hand over control to compressed_multiplicative_call.
4508  */
4509 __isl_give isl_pw_qpolynomial *isl_basic_set_multiplicative_call(
4510         __isl_take isl_basic_set *bset,
4511         __isl_give isl_pw_qpolynomial *(*fn)(__isl_take isl_basic_set *bset))
4512 {
4513         int bounded;
4514         isl_morph *morph;
4515         isl_pw_qpolynomial *pwqp;
4516
4517         if (!bset)
4518                 return NULL;
4519
4520         if (isl_basic_set_plain_is_empty(bset))
4521                 return constant_on_domain(bset, 0);
4522
4523         if (isl_basic_set_dim(bset, isl_dim_set) == 0)
4524                 return constant_on_domain(bset, 1);
4525
4526         bounded = isl_basic_set_is_bounded(bset);
4527         if (bounded < 0)
4528                 goto error;
4529         if (!bounded)
4530                 return constant_on_domain(bset, -1);
4531
4532         if (bset->n_eq == 0)
4533                 return compressed_multiplicative_call(bset, fn);
4534
4535         morph = isl_basic_set_full_compression(bset);
4536         bset = isl_morph_basic_set(isl_morph_copy(morph), bset);
4537
4538         pwqp = compressed_multiplicative_call(bset, fn);
4539
4540         morph = isl_morph_dom_params(morph);
4541         morph = isl_morph_ran_params(morph);
4542         morph = isl_morph_inverse(morph);
4543
4544         pwqp = isl_pw_qpolynomial_morph_domain(pwqp, morph);
4545
4546         return pwqp;
4547 error:
4548         isl_basic_set_free(bset);
4549         return NULL;
4550 }
4551
4552 /* Drop all floors in "qp", turning each integer division [a/m] into
4553  * a rational division a/m.  If "down" is set, then the integer division
4554  * is replaced by (a-(m-1))/m instead.
4555  */
4556 static __isl_give isl_qpolynomial *qp_drop_floors(
4557         __isl_take isl_qpolynomial *qp, int down)
4558 {
4559         int i;
4560         struct isl_upoly *s;
4561
4562         if (!qp)
4563                 return NULL;
4564         if (qp->div->n_row == 0)
4565                 return qp;
4566
4567         qp = isl_qpolynomial_cow(qp);
4568         if (!qp)
4569                 return NULL;
4570
4571         for (i = qp->div->n_row - 1; i >= 0; --i) {
4572                 if (down) {
4573                         isl_int_sub(qp->div->row[i][1],
4574                                     qp->div->row[i][1], qp->div->row[i][0]);
4575                         isl_int_add_ui(qp->div->row[i][1],
4576                                        qp->div->row[i][1], 1);
4577                 }
4578                 s = isl_upoly_from_affine(qp->dim->ctx, qp->div->row[i] + 1,
4579                                         qp->div->row[i][0], qp->div->n_col - 1);
4580                 qp = substitute_div(qp, i, s);
4581                 if (!qp)
4582                         return NULL;
4583         }
4584
4585         return qp;
4586 }
4587
4588 /* Drop all floors in "pwqp", turning each integer division [a/m] into
4589  * a rational division a/m.
4590  */
4591 static __isl_give isl_pw_qpolynomial *pwqp_drop_floors(
4592         __isl_take isl_pw_qpolynomial *pwqp)
4593 {
4594         int i;
4595
4596         if (!pwqp)
4597                 return NULL;
4598
4599         if (isl_pw_qpolynomial_is_zero(pwqp))
4600                 return pwqp;
4601
4602         pwqp = isl_pw_qpolynomial_cow(pwqp);
4603         if (!pwqp)
4604                 return NULL;
4605
4606         for (i = 0; i < pwqp->n; ++i) {
4607                 pwqp->p[i].qp = qp_drop_floors(pwqp->p[i].qp, 0);
4608                 if (!pwqp->p[i].qp)
4609                         goto error;
4610         }
4611
4612         return pwqp;
4613 error:
4614         isl_pw_qpolynomial_free(pwqp);
4615         return NULL;
4616 }
4617
4618 /* Adjust all the integer divisions in "qp" such that they are at least
4619  * one over the given orthant (identified by "signs").  This ensures
4620  * that they will still be non-negative even after subtracting (m-1)/m.
4621  *
4622  * In particular, f is replaced by f' + v, changing f = [a/m]
4623  * to f' = [(a - m v)/m].
4624  * If the constant term k in a is smaller than m,
4625  * the constant term of v is set to floor(k/m) - 1.
4626  * For any other term, if the coefficient c and the variable x have
4627  * the same sign, then no changes are needed.
4628  * Otherwise, if the variable is positive (and c is negative),
4629  * then the coefficient of x in v is set to floor(c/m).
4630  * If the variable is negative (and c is positive),
4631  * then the coefficient of x in v is set to ceil(c/m).
4632  */
4633 static __isl_give isl_qpolynomial *make_divs_pos(__isl_take isl_qpolynomial *qp,
4634         int *signs)
4635 {
4636         int i, j;
4637         int total;
4638         isl_vec *v = NULL;
4639         struct isl_upoly *s;
4640
4641         qp = isl_qpolynomial_cow(qp);
4642         if (!qp)
4643                 return NULL;
4644         qp->div = isl_mat_cow(qp->div);
4645         if (!qp->div)
4646                 goto error;
4647
4648         total = isl_space_dim(qp->dim, isl_dim_all);
4649         v = isl_vec_alloc(qp->div->ctx, qp->div->n_col - 1);
4650
4651         for (i = 0; i < qp->div->n_row; ++i) {
4652                 isl_int *row = qp->div->row[i];
4653                 v = isl_vec_clr(v);
4654                 if (!v)
4655                         goto error;
4656                 if (isl_int_lt(row[1], row[0])) {
4657                         isl_int_fdiv_q(v->el[0], row[1], row[0]);
4658                         isl_int_sub_ui(v->el[0], v->el[0], 1);
4659                         isl_int_submul(row[1], row[0], v->el[0]);
4660                 }
4661                 for (j = 0; j < total; ++j) {
4662                         if (isl_int_sgn(row[2 + j]) * signs[j] >= 0)
4663                                 continue;
4664                         if (signs[j] < 0)
4665                                 isl_int_cdiv_q(v->el[1 + j], row[2 + j], row[0]);
4666                         else
4667                                 isl_int_fdiv_q(v->el[1 + j], row[2 + j], row[0]);
4668                         isl_int_submul(row[2 + j], row[0], v->el[1 + j]);
4669                 }
4670                 for (j = 0; j < i; ++j) {
4671                         if (isl_int_sgn(row[2 + total + j]) >= 0)
4672                                 continue;
4673                         isl_int_fdiv_q(v->el[1 + total + j],
4674                                         row[2 + total + j], row[0]);
4675                         isl_int_submul(row[2 + total + j],
4676                                         row[0], v->el[1 + total + j]);
4677                 }
4678                 for (j = i + 1; j < qp->div->n_row; ++j) {
4679                         if (isl_int_is_zero(qp->div->row[j][2 + total + i]))
4680                                 continue;
4681                         isl_seq_combine(qp->div->row[j] + 1,
4682                                 qp->div->ctx->one, qp->div->row[j] + 1,
4683                                 qp->div->row[j][2 + total + i], v->el, v->size);
4684                 }
4685                 isl_int_set_si(v->el[1 + total + i], 1);
4686                 s = isl_upoly_from_affine(qp->dim->ctx, v->el,
4687                                         qp->div->ctx->one, v->size);
4688                 qp->upoly = isl_upoly_subs(qp->upoly, total + i, 1, &s);
4689                 isl_upoly_free(s);
4690                 if (!qp->upoly)
4691                         goto error;
4692         }
4693
4694         isl_vec_free(v);
4695         return qp;
4696 error:
4697         isl_vec_free(v);
4698         isl_qpolynomial_free(qp);
4699         return NULL;
4700 }
4701
4702 struct isl_to_poly_data {
4703         int sign;
4704         isl_pw_qpolynomial *res;
4705         isl_qpolynomial *qp;
4706 };
4707
4708 /* Appoximate data->qp by a polynomial on the orthant identified by "signs".
4709  * We first make all integer divisions positive and then split the
4710  * quasipolynomials into terms with sign data->sign (the direction
4711  * of the requested approximation) and terms with the opposite sign.
4712  * In the first set of terms, each integer division [a/m] is
4713  * overapproximated by a/m, while in the second it is underapproximated
4714  * by (a-(m-1))/m.
4715  */
4716 static int to_polynomial_on_orthant(__isl_take isl_set *orthant, int *signs,
4717         void *user)
4718 {
4719         struct isl_to_poly_data *data = user;
4720         isl_pw_qpolynomial *t;
4721         isl_qpolynomial *qp, *up, *down;
4722
4723         qp = isl_qpolynomial_copy(data->qp);
4724         qp = make_divs_pos(qp, signs);
4725
4726         up = isl_qpolynomial_terms_of_sign(qp, signs, data->sign);
4727         up = qp_drop_floors(up, 0);
4728         down = isl_qpolynomial_terms_of_sign(qp, signs, -data->sign);
4729         down = qp_drop_floors(down, 1);
4730
4731         isl_qpolynomial_free(qp);
4732         qp = isl_qpolynomial_add(up, down);
4733
4734         t = isl_pw_qpolynomial_alloc(orthant, qp);
4735         data->res = isl_pw_qpolynomial_add_disjoint(data->res, t);
4736
4737         return 0;
4738 }
4739
4740 /* Approximate each quasipolynomial by a polynomial.  If "sign" is positive,
4741  * the polynomial will be an overapproximation.  If "sign" is negative,
4742  * it will be an underapproximation.  If "sign" is zero, the approximation
4743  * will lie somewhere in between.
4744  *
4745  * In particular, is sign == 0, we simply drop the floors, turning
4746  * the integer divisions into rational divisions.
4747  * Otherwise, we split the domains into orthants, make all integer divisions
4748  * positive and then approximate each [a/m] by either a/m or (a-(m-1))/m,
4749  * depending on the requested sign and the sign of the term in which
4750  * the integer division appears.
4751  */
4752 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_to_polynomial(
4753         __isl_take isl_pw_qpolynomial *pwqp, int sign)
4754 {
4755         int i;
4756         struct isl_to_poly_data data;
4757
4758         if (sign == 0)
4759                 return pwqp_drop_floors(pwqp);
4760
4761         if (!pwqp)
4762                 return NULL;
4763
4764         data.sign = sign;
4765         data.res = isl_pw_qpolynomial_zero(isl_pw_qpolynomial_get_space(pwqp));
4766
4767         for (i = 0; i < pwqp->n; ++i) {
4768                 if (pwqp->p[i].qp->div->n_row == 0) {
4769                         isl_pw_qpolynomial *t;
4770                         t = isl_pw_qpolynomial_alloc(
4771                                         isl_set_copy(pwqp->p[i].set),
4772                                         isl_qpolynomial_copy(pwqp->p[i].qp));
4773                         data.res = isl_pw_qpolynomial_add_disjoint(data.res, t);
4774                         continue;
4775                 }
4776                 data.qp = pwqp->p[i].qp;
4777                 if (isl_set_foreach_orthant(pwqp->p[i].set,
4778                                         &to_polynomial_on_orthant, &data) < 0)
4779                         goto error;
4780         }
4781
4782         isl_pw_qpolynomial_free(pwqp);
4783
4784         return data.res;
4785 error:
4786         isl_pw_qpolynomial_free(pwqp);
4787         isl_pw_qpolynomial_free(data.res);
4788         return NULL;
4789 }
4790
4791 static int poly_entry(void **entry, void *user)
4792 {
4793         int *sign = user;
4794         isl_pw_qpolynomial **pwqp = (isl_pw_qpolynomial **)entry;
4795
4796         *pwqp = isl_pw_qpolynomial_to_polynomial(*pwqp, *sign);
4797
4798         return *pwqp ? 0 : -1;
4799 }
4800
4801 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_to_polynomial(
4802         __isl_take isl_union_pw_qpolynomial *upwqp, int sign)
4803 {
4804         upwqp = isl_union_pw_qpolynomial_cow(upwqp);
4805         if (!upwqp)
4806                 return NULL;
4807
4808         if (isl_hash_table_foreach(upwqp->space->ctx, &upwqp->table,
4809                                    &poly_entry, &sign) < 0)
4810                 goto error;
4811
4812         return upwqp;
4813 error:
4814         isl_union_pw_qpolynomial_free(upwqp);
4815         return NULL;
4816 }
4817
4818 __isl_give isl_basic_map *isl_basic_map_from_qpolynomial(
4819         __isl_take isl_qpolynomial *qp)
4820 {
4821         int i, k;
4822         isl_space *dim;
4823         isl_vec *aff = NULL;
4824         isl_basic_map *bmap = NULL;
4825         unsigned pos;
4826         unsigned n_div;
4827
4828         if (!qp)
4829                 return NULL;
4830         if (!isl_upoly_is_affine(qp->upoly))
4831                 isl_die(qp->dim->ctx, isl_error_invalid,
4832                         "input quasi-polynomial not affine", goto error);
4833         aff = isl_qpolynomial_extract_affine(qp);
4834         if (!aff)
4835                 goto error;
4836         dim = isl_qpolynomial_get_space(qp);
4837         pos = 1 + isl_space_offset(dim, isl_dim_out);
4838         n_div = qp->div->n_row;
4839         bmap = isl_basic_map_alloc_space(dim, n_div, 1, 2 * n_div);
4840
4841         for (i = 0; i < n_div; ++i) {
4842                 k = isl_basic_map_alloc_div(bmap);
4843                 if (k < 0)
4844                         goto error;
4845                 isl_seq_cpy(bmap->div[k], qp->div->row[i], qp->div->n_col);
4846                 isl_int_set_si(bmap->div[k][qp->div->n_col], 0);
4847                 if (isl_basic_map_add_div_constraints(bmap, k) < 0)
4848                         goto error;
4849         }
4850         k = isl_basic_map_alloc_equality(bmap);
4851         if (k < 0)
4852                 goto error;
4853         isl_int_neg(bmap->eq[k][pos], aff->el[0]);
4854         isl_seq_cpy(bmap->eq[k], aff->el + 1, pos);
4855         isl_seq_cpy(bmap->eq[k] + pos + 1, aff->el + 1 + pos, n_div);
4856
4857         isl_vec_free(aff);
4858         isl_qpolynomial_free(qp);
4859         bmap = isl_basic_map_finalize(bmap);
4860         return bmap;
4861 error:
4862         isl_vec_free(aff);
4863         isl_qpolynomial_free(qp);
4864         isl_basic_map_free(bmap);
4865         return NULL;
4866 }