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
2812 #include <isl_union_templ.c>
2813
2814 int isl_pw_qpolynomial_is_one(__isl_keep isl_pw_qpolynomial *pwqp)
2815 {
2816         if (!pwqp)
2817                 return -1;
2818
2819         if (pwqp->n != -1)
2820                 return 0;
2821
2822         if (!isl_set_plain_is_universe(pwqp->p[0].set))
2823                 return 0;
2824
2825         return isl_qpolynomial_is_one(pwqp->p[0].qp);
2826 }
2827
2828 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_add(
2829         __isl_take isl_pw_qpolynomial *pwqp1,
2830         __isl_take isl_pw_qpolynomial *pwqp2)
2831 {
2832         return isl_pw_qpolynomial_union_add_(pwqp1, pwqp2);
2833 }
2834
2835 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_mul(
2836         __isl_take isl_pw_qpolynomial *pwqp1,
2837         __isl_take isl_pw_qpolynomial *pwqp2)
2838 {
2839         int i, j, n;
2840         struct isl_pw_qpolynomial *res;
2841
2842         if (!pwqp1 || !pwqp2)
2843                 goto error;
2844
2845         isl_assert(pwqp1->dim->ctx, isl_space_is_equal(pwqp1->dim, pwqp2->dim),
2846                         goto error);
2847
2848         if (isl_pw_qpolynomial_is_zero(pwqp1)) {
2849                 isl_pw_qpolynomial_free(pwqp2);
2850                 return pwqp1;
2851         }
2852
2853         if (isl_pw_qpolynomial_is_zero(pwqp2)) {
2854                 isl_pw_qpolynomial_free(pwqp1);
2855                 return pwqp2;
2856         }
2857
2858         if (isl_pw_qpolynomial_is_one(pwqp1)) {
2859                 isl_pw_qpolynomial_free(pwqp1);
2860                 return pwqp2;
2861         }
2862
2863         if (isl_pw_qpolynomial_is_one(pwqp2)) {
2864                 isl_pw_qpolynomial_free(pwqp2);
2865                 return pwqp1;
2866         }
2867
2868         n = pwqp1->n * pwqp2->n;
2869         res = isl_pw_qpolynomial_alloc_size(isl_space_copy(pwqp1->dim), n);
2870
2871         for (i = 0; i < pwqp1->n; ++i) {
2872                 for (j = 0; j < pwqp2->n; ++j) {
2873                         struct isl_set *common;
2874                         struct isl_qpolynomial *prod;
2875                         common = isl_set_intersect(isl_set_copy(pwqp1->p[i].set),
2876                                                 isl_set_copy(pwqp2->p[j].set));
2877                         if (isl_set_plain_is_empty(common)) {
2878                                 isl_set_free(common);
2879                                 continue;
2880                         }
2881
2882                         prod = isl_qpolynomial_mul(
2883                                 isl_qpolynomial_copy(pwqp1->p[i].qp),
2884                                 isl_qpolynomial_copy(pwqp2->p[j].qp));
2885
2886                         res = isl_pw_qpolynomial_add_piece(res, common, prod);
2887                 }
2888         }
2889
2890         isl_pw_qpolynomial_free(pwqp1);
2891         isl_pw_qpolynomial_free(pwqp2);
2892
2893         return res;
2894 error:
2895         isl_pw_qpolynomial_free(pwqp1);
2896         isl_pw_qpolynomial_free(pwqp2);
2897         return NULL;
2898 }
2899
2900 __isl_give isl_val *isl_upoly_eval(__isl_take struct isl_upoly *up,
2901         __isl_take isl_vec *vec)
2902 {
2903         int i;
2904         struct isl_upoly_rec *rec;
2905         isl_val *res;
2906         isl_val *base;
2907
2908         if (isl_upoly_is_cst(up)) {
2909                 isl_vec_free(vec);
2910                 res = isl_upoly_get_constant_val(up);
2911                 isl_upoly_free(up);
2912                 return res;
2913         }
2914
2915         rec = isl_upoly_as_rec(up);
2916         if (!rec)
2917                 goto error;
2918
2919         isl_assert(up->ctx, rec->n >= 1, goto error);
2920
2921         base = isl_val_rat_from_isl_int(up->ctx,
2922                                         vec->el[1 + up->var], vec->el[0]);
2923
2924         res = isl_upoly_eval(isl_upoly_copy(rec->p[rec->n - 1]),
2925                                 isl_vec_copy(vec));
2926
2927         for (i = rec->n - 2; i >= 0; --i) {
2928                 res = isl_val_mul(res, isl_val_copy(base));
2929                 res = isl_val_add(res,
2930                             isl_upoly_eval(isl_upoly_copy(rec->p[i]),
2931                                                             isl_vec_copy(vec)));
2932         }
2933
2934         isl_val_free(base);
2935         isl_upoly_free(up);
2936         isl_vec_free(vec);
2937         return res;
2938 error:
2939         isl_upoly_free(up);
2940         isl_vec_free(vec);
2941         return NULL;
2942 }
2943
2944 __isl_give isl_val *isl_qpolynomial_eval(__isl_take isl_qpolynomial *qp,
2945         __isl_take isl_point *pnt)
2946 {
2947         isl_vec *ext;
2948         isl_val *v;
2949
2950         if (!qp || !pnt)
2951                 goto error;
2952         isl_assert(pnt->dim->ctx, isl_space_is_equal(pnt->dim, qp->dim), goto error);
2953
2954         if (qp->div->n_row == 0)
2955                 ext = isl_vec_copy(pnt->vec);
2956         else {
2957                 int i;
2958                 unsigned dim = isl_space_dim(qp->dim, isl_dim_all);
2959                 ext = isl_vec_alloc(qp->dim->ctx, 1 + dim + qp->div->n_row);
2960                 if (!ext)
2961                         goto error;
2962
2963                 isl_seq_cpy(ext->el, pnt->vec->el, pnt->vec->size);
2964                 for (i = 0; i < qp->div->n_row; ++i) {
2965                         isl_seq_inner_product(qp->div->row[i] + 1, ext->el,
2966                                                 1 + dim + i, &ext->el[1+dim+i]);
2967                         isl_int_fdiv_q(ext->el[1+dim+i], ext->el[1+dim+i],
2968                                         qp->div->row[i][0]);
2969                 }
2970         }
2971
2972         v = isl_upoly_eval(isl_upoly_copy(qp->upoly), ext);
2973
2974         isl_qpolynomial_free(qp);
2975         isl_point_free(pnt);
2976
2977         return v;
2978 error:
2979         isl_qpolynomial_free(qp);
2980         isl_point_free(pnt);
2981         return NULL;
2982 }
2983
2984 int isl_upoly_cmp(__isl_keep struct isl_upoly_cst *cst1,
2985         __isl_keep struct isl_upoly_cst *cst2)
2986 {
2987         int cmp;
2988         isl_int t;
2989         isl_int_init(t);
2990         isl_int_mul(t, cst1->n, cst2->d);
2991         isl_int_submul(t, cst2->n, cst1->d);
2992         cmp = isl_int_sgn(t);
2993         isl_int_clear(t);
2994         return cmp;
2995 }
2996
2997 __isl_give isl_qpolynomial *isl_qpolynomial_insert_dims(
2998         __isl_take isl_qpolynomial *qp, enum isl_dim_type type,
2999         unsigned first, unsigned n)
3000 {
3001         unsigned total;
3002         unsigned g_pos;
3003         int *exp;
3004
3005         if (!qp)
3006                 return NULL;
3007         if (type == isl_dim_out)
3008                 isl_die(qp->div->ctx, isl_error_invalid,
3009                         "cannot insert output/set dimensions",
3010                         goto error);
3011         if (type == isl_dim_in)
3012                 type = isl_dim_set;
3013         if (n == 0 && !isl_space_is_named_or_nested(qp->dim, type))
3014                 return qp;
3015
3016         qp = isl_qpolynomial_cow(qp);
3017         if (!qp)
3018                 return NULL;
3019
3020         isl_assert(qp->div->ctx, first <= isl_space_dim(qp->dim, type),
3021                     goto error);
3022
3023         g_pos = pos(qp->dim, type) + first;
3024
3025         qp->div = isl_mat_insert_zero_cols(qp->div, 2 + g_pos, n);
3026         if (!qp->div)
3027                 goto error;
3028
3029         total = qp->div->n_col - 2;
3030         if (total > g_pos) {
3031                 int i;
3032                 exp = isl_alloc_array(qp->div->ctx, int, total - g_pos);
3033                 if (!exp)
3034                         goto error;
3035                 for (i = 0; i < total - g_pos; ++i)
3036                         exp[i] = i + n;
3037                 qp->upoly = expand(qp->upoly, exp, g_pos);
3038                 free(exp);
3039                 if (!qp->upoly)
3040                         goto error;
3041         }
3042
3043         qp->dim = isl_space_insert_dims(qp->dim, type, first, n);
3044         if (!qp->dim)
3045                 goto error;
3046
3047         return qp;
3048 error:
3049         isl_qpolynomial_free(qp);
3050         return NULL;
3051 }
3052
3053 __isl_give isl_qpolynomial *isl_qpolynomial_add_dims(
3054         __isl_take isl_qpolynomial *qp, enum isl_dim_type type, unsigned n)
3055 {
3056         unsigned pos;
3057
3058         pos = isl_qpolynomial_dim(qp, type);
3059
3060         return isl_qpolynomial_insert_dims(qp, type, pos, n);
3061 }
3062
3063 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_add_dims(
3064         __isl_take isl_pw_qpolynomial *pwqp,
3065         enum isl_dim_type type, unsigned n)
3066 {
3067         unsigned pos;
3068
3069         pos = isl_pw_qpolynomial_dim(pwqp, type);
3070
3071         return isl_pw_qpolynomial_insert_dims(pwqp, type, pos, n);
3072 }
3073
3074 static int *reordering_move(isl_ctx *ctx,
3075         unsigned len, unsigned dst, unsigned src, unsigned n)
3076 {
3077         int i;
3078         int *reordering;
3079
3080         reordering = isl_alloc_array(ctx, int, len);
3081         if (!reordering)
3082                 return NULL;
3083
3084         if (dst <= src) {
3085                 for (i = 0; i < dst; ++i)
3086                         reordering[i] = i;
3087                 for (i = 0; i < n; ++i)
3088                         reordering[src + i] = dst + i;
3089                 for (i = 0; i < src - dst; ++i)
3090                         reordering[dst + i] = dst + n + i;
3091                 for (i = 0; i < len - src - n; ++i)
3092                         reordering[src + n + i] = src + n + i;
3093         } else {
3094                 for (i = 0; i < src; ++i)
3095                         reordering[i] = i;
3096                 for (i = 0; i < n; ++i)
3097                         reordering[src + i] = dst + i;
3098                 for (i = 0; i < dst - src; ++i)
3099                         reordering[src + n + i] = src + i;
3100                 for (i = 0; i < len - dst - n; ++i)
3101                         reordering[dst + n + i] = dst + n + i;
3102         }
3103
3104         return reordering;
3105 }
3106
3107 __isl_give isl_qpolynomial *isl_qpolynomial_move_dims(
3108         __isl_take isl_qpolynomial *qp,
3109         enum isl_dim_type dst_type, unsigned dst_pos,
3110         enum isl_dim_type src_type, unsigned src_pos, unsigned n)
3111 {
3112         unsigned g_dst_pos;
3113         unsigned g_src_pos;
3114         int *reordering;
3115
3116         if (n == 0)
3117                 return qp;
3118
3119         qp = isl_qpolynomial_cow(qp);
3120         if (!qp)
3121                 return NULL;
3122
3123         if (dst_type == isl_dim_out || src_type == isl_dim_out)
3124                 isl_die(qp->dim->ctx, isl_error_invalid,
3125                         "cannot move output/set dimension",
3126                         goto error);
3127         if (dst_type == isl_dim_in)
3128                 dst_type = isl_dim_set;
3129         if (src_type == isl_dim_in)
3130                 src_type = isl_dim_set;
3131
3132         isl_assert(qp->dim->ctx, src_pos + n <= isl_space_dim(qp->dim, src_type),
3133                 goto error);
3134
3135         g_dst_pos = pos(qp->dim, dst_type) + dst_pos;
3136         g_src_pos = pos(qp->dim, src_type) + src_pos;
3137         if (dst_type > src_type)
3138                 g_dst_pos -= n;
3139
3140         qp->div = isl_mat_move_cols(qp->div, 2 + g_dst_pos, 2 + g_src_pos, n);
3141         if (!qp->div)
3142                 goto error;
3143         qp = sort_divs(qp);
3144         if (!qp)
3145                 goto error;
3146
3147         reordering = reordering_move(qp->dim->ctx,
3148                                 qp->div->n_col - 2, g_dst_pos, g_src_pos, n);
3149         if (!reordering)
3150                 goto error;
3151
3152         qp->upoly = reorder(qp->upoly, reordering);
3153         free(reordering);
3154         if (!qp->upoly)
3155                 goto error;
3156
3157         qp->dim = isl_space_move_dims(qp->dim, dst_type, dst_pos, src_type, src_pos, n);
3158         if (!qp->dim)
3159                 goto error;
3160
3161         return qp;
3162 error:
3163         isl_qpolynomial_free(qp);
3164         return NULL;
3165 }
3166
3167 __isl_give isl_qpolynomial *isl_qpolynomial_from_affine(__isl_take isl_space *dim,
3168         isl_int *f, isl_int denom)
3169 {
3170         struct isl_upoly *up;
3171
3172         dim = isl_space_domain(dim);
3173         if (!dim)
3174                 return NULL;
3175
3176         up = isl_upoly_from_affine(dim->ctx, f, denom,
3177                                         1 + isl_space_dim(dim, isl_dim_all));
3178
3179         return isl_qpolynomial_alloc(dim, 0, up);
3180 }
3181
3182 __isl_give isl_qpolynomial *isl_qpolynomial_from_aff(__isl_take isl_aff *aff)
3183 {
3184         isl_ctx *ctx;
3185         struct isl_upoly *up;
3186         isl_qpolynomial *qp;
3187
3188         if (!aff)
3189                 return NULL;
3190
3191         ctx = isl_aff_get_ctx(aff);
3192         up = isl_upoly_from_affine(ctx, aff->v->el + 1, aff->v->el[0],
3193                                     aff->v->size - 1);
3194
3195         qp = isl_qpolynomial_alloc(isl_aff_get_domain_space(aff),
3196                                     aff->ls->div->n_row, up);
3197         if (!qp)
3198                 goto error;
3199
3200         isl_mat_free(qp->div);
3201         qp->div = isl_mat_copy(aff->ls->div);
3202         qp->div = isl_mat_cow(qp->div);
3203         if (!qp->div)
3204                 goto error;
3205
3206         isl_aff_free(aff);
3207         qp = reduce_divs(qp);
3208         qp = remove_redundant_divs(qp);
3209         return qp;
3210 error:
3211         isl_aff_free(aff);
3212         return isl_qpolynomial_free(qp);
3213 }
3214
3215 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_from_pw_aff(
3216         __isl_take isl_pw_aff *pwaff)
3217 {
3218         int i;
3219         isl_pw_qpolynomial *pwqp;
3220
3221         if (!pwaff)
3222                 return NULL;
3223
3224         pwqp = isl_pw_qpolynomial_alloc_size(isl_pw_aff_get_space(pwaff),
3225                                                 pwaff->n);
3226
3227         for (i = 0; i < pwaff->n; ++i) {
3228                 isl_set *dom;
3229                 isl_qpolynomial *qp;
3230
3231                 dom = isl_set_copy(pwaff->p[i].set);
3232                 qp = isl_qpolynomial_from_aff(isl_aff_copy(pwaff->p[i].aff));
3233                 pwqp = isl_pw_qpolynomial_add_piece(pwqp,  dom, qp);
3234         }
3235
3236         isl_pw_aff_free(pwaff);
3237         return pwqp;
3238 }
3239
3240 __isl_give isl_qpolynomial *isl_qpolynomial_from_constraint(
3241         __isl_take isl_constraint *c, enum isl_dim_type type, unsigned pos)
3242 {
3243         isl_aff *aff;
3244
3245         aff = isl_constraint_get_bound(c, type, pos);
3246         isl_constraint_free(c);
3247         return isl_qpolynomial_from_aff(aff);
3248 }
3249
3250 /* For each 0 <= i < "n", replace variable "first" + i of type "type"
3251  * in "qp" by subs[i].
3252  */
3253 __isl_give isl_qpolynomial *isl_qpolynomial_substitute(
3254         __isl_take isl_qpolynomial *qp,
3255         enum isl_dim_type type, unsigned first, unsigned n,
3256         __isl_keep isl_qpolynomial **subs)
3257 {
3258         int i;
3259         struct isl_upoly **ups;
3260
3261         if (n == 0)
3262                 return qp;
3263
3264         qp = isl_qpolynomial_cow(qp);
3265         if (!qp)
3266                 return NULL;
3267
3268         if (type == isl_dim_out)
3269                 isl_die(qp->dim->ctx, isl_error_invalid,
3270                         "cannot substitute output/set dimension",
3271                         goto error);
3272         if (type == isl_dim_in)
3273                 type = isl_dim_set;
3274
3275         for (i = 0; i < n; ++i)
3276                 if (!subs[i])
3277                         goto error;
3278
3279         isl_assert(qp->dim->ctx, first + n <= isl_space_dim(qp->dim, type),
3280                         goto error);
3281
3282         for (i = 0; i < n; ++i)
3283                 isl_assert(qp->dim->ctx, isl_space_is_equal(qp->dim, subs[i]->dim),
3284                                 goto error);
3285
3286         isl_assert(qp->dim->ctx, qp->div->n_row == 0, goto error);
3287         for (i = 0; i < n; ++i)
3288                 isl_assert(qp->dim->ctx, subs[i]->div->n_row == 0, goto error);
3289
3290         first += pos(qp->dim, type);
3291
3292         ups = isl_alloc_array(qp->dim->ctx, struct isl_upoly *, n);
3293         if (!ups)
3294                 goto error;
3295         for (i = 0; i < n; ++i)
3296                 ups[i] = subs[i]->upoly;
3297
3298         qp->upoly = isl_upoly_subs(qp->upoly, first, n, ups);
3299
3300         free(ups);
3301
3302         if (!qp->upoly)
3303                 goto error;
3304
3305         return qp;
3306 error:
3307         isl_qpolynomial_free(qp);
3308         return NULL;
3309 }
3310
3311 /* Extend "bset" with extra set dimensions for each integer division
3312  * in "qp" and then call "fn" with the extended bset and the polynomial
3313  * that results from replacing each of the integer divisions by the
3314  * corresponding extra set dimension.
3315  */
3316 int isl_qpolynomial_as_polynomial_on_domain(__isl_keep isl_qpolynomial *qp,
3317         __isl_keep isl_basic_set *bset,
3318         int (*fn)(__isl_take isl_basic_set *bset,
3319                   __isl_take isl_qpolynomial *poly, void *user), void *user)
3320 {
3321         isl_space *dim;
3322         isl_mat *div;
3323         isl_qpolynomial *poly;
3324
3325         if (!qp || !bset)
3326                 goto error;
3327         if (qp->div->n_row == 0)
3328                 return fn(isl_basic_set_copy(bset), isl_qpolynomial_copy(qp),
3329                           user);
3330
3331         div = isl_mat_copy(qp->div);
3332         dim = isl_space_copy(qp->dim);
3333         dim = isl_space_add_dims(dim, isl_dim_set, qp->div->n_row);
3334         poly = isl_qpolynomial_alloc(dim, 0, isl_upoly_copy(qp->upoly));
3335         bset = isl_basic_set_copy(bset);
3336         bset = isl_basic_set_add_dims(bset, isl_dim_set, qp->div->n_row);
3337         bset = add_div_constraints(bset, div);
3338
3339         return fn(bset, poly, user);
3340 error:
3341         return -1;
3342 }
3343
3344 /* Return total degree in variables first (inclusive) up to last (exclusive).
3345  */
3346 int isl_upoly_degree(__isl_keep struct isl_upoly *up, int first, int last)
3347 {
3348         int deg = -1;
3349         int i;
3350         struct isl_upoly_rec *rec;
3351
3352         if (!up)
3353                 return -2;
3354         if (isl_upoly_is_zero(up))
3355                 return -1;
3356         if (isl_upoly_is_cst(up) || up->var < first)
3357                 return 0;
3358
3359         rec = isl_upoly_as_rec(up);
3360         if (!rec)
3361                 return -2;
3362
3363         for (i = 0; i < rec->n; ++i) {
3364                 int d;
3365
3366                 if (isl_upoly_is_zero(rec->p[i]))
3367                         continue;
3368                 d = isl_upoly_degree(rec->p[i], first, last);
3369                 if (up->var < last)
3370                         d += i;
3371                 if (d > deg)
3372                         deg = d;
3373         }
3374
3375         return deg;
3376 }
3377
3378 /* Return total degree in set variables.
3379  */
3380 int isl_qpolynomial_degree(__isl_keep isl_qpolynomial *poly)
3381 {
3382         unsigned ovar;
3383         unsigned nvar;
3384
3385         if (!poly)
3386                 return -2;
3387
3388         ovar = isl_space_offset(poly->dim, isl_dim_set);
3389         nvar = isl_space_dim(poly->dim, isl_dim_set);
3390         return isl_upoly_degree(poly->upoly, ovar, ovar + nvar);
3391 }
3392
3393 __isl_give struct isl_upoly *isl_upoly_coeff(__isl_keep struct isl_upoly *up,
3394         unsigned pos, int deg)
3395 {
3396         int i;
3397         struct isl_upoly_rec *rec;
3398
3399         if (!up)
3400                 return NULL;
3401
3402         if (isl_upoly_is_cst(up) || up->var < pos) {
3403                 if (deg == 0)
3404                         return isl_upoly_copy(up);
3405                 else
3406                         return isl_upoly_zero(up->ctx);
3407         }
3408
3409         rec = isl_upoly_as_rec(up);
3410         if (!rec)
3411                 return NULL;
3412
3413         if (up->var == pos) {
3414                 if (deg < rec->n)
3415                         return isl_upoly_copy(rec->p[deg]);
3416                 else
3417                         return isl_upoly_zero(up->ctx);
3418         }
3419
3420         up = isl_upoly_copy(up);
3421         up = isl_upoly_cow(up);
3422         rec = isl_upoly_as_rec(up);
3423         if (!rec)
3424                 goto error;
3425
3426         for (i = 0; i < rec->n; ++i) {
3427                 struct isl_upoly *t;
3428                 t = isl_upoly_coeff(rec->p[i], pos, deg);
3429                 if (!t)
3430                         goto error;
3431                 isl_upoly_free(rec->p[i]);
3432                 rec->p[i] = t;
3433         }
3434
3435         return up;
3436 error:
3437         isl_upoly_free(up);
3438         return NULL;
3439 }
3440
3441 /* Return coefficient of power "deg" of variable "t_pos" of type "type".
3442  */
3443 __isl_give isl_qpolynomial *isl_qpolynomial_coeff(
3444         __isl_keep isl_qpolynomial *qp,
3445         enum isl_dim_type type, unsigned t_pos, int deg)
3446 {
3447         unsigned g_pos;
3448         struct isl_upoly *up;
3449         isl_qpolynomial *c;
3450
3451         if (!qp)
3452                 return NULL;
3453
3454         if (type == isl_dim_out)
3455                 isl_die(qp->div->ctx, isl_error_invalid,
3456                         "output/set dimension does not have a coefficient",
3457                         return NULL);
3458         if (type == isl_dim_in)
3459                 type = isl_dim_set;
3460
3461         isl_assert(qp->div->ctx, t_pos < isl_space_dim(qp->dim, type),
3462                         return NULL);
3463
3464         g_pos = pos(qp->dim, type) + t_pos;
3465         up = isl_upoly_coeff(qp->upoly, g_pos, deg);
3466
3467         c = isl_qpolynomial_alloc(isl_space_copy(qp->dim), qp->div->n_row, up);
3468         if (!c)
3469                 return NULL;
3470         isl_mat_free(c->div);
3471         c->div = isl_mat_copy(qp->div);
3472         if (!c->div)
3473                 goto error;
3474         return c;
3475 error:
3476         isl_qpolynomial_free(c);
3477         return NULL;
3478 }
3479
3480 /* Homogenize the polynomial in the variables first (inclusive) up to
3481  * last (exclusive) by inserting powers of variable first.
3482  * Variable first is assumed not to appear in the input.
3483  */
3484 __isl_give struct isl_upoly *isl_upoly_homogenize(
3485         __isl_take struct isl_upoly *up, int deg, int target,
3486         int first, int last)
3487 {
3488         int i;
3489         struct isl_upoly_rec *rec;
3490
3491         if (!up)
3492                 return NULL;
3493         if (isl_upoly_is_zero(up))
3494                 return up;
3495         if (deg == target)
3496                 return up;
3497         if (isl_upoly_is_cst(up) || up->var < first) {
3498                 struct isl_upoly *hom;
3499
3500                 hom = isl_upoly_var_pow(up->ctx, first, target - deg);
3501                 if (!hom)
3502                         goto error;
3503                 rec = isl_upoly_as_rec(hom);
3504                 rec->p[target - deg] = isl_upoly_mul(rec->p[target - deg], up);
3505
3506                 return hom;
3507         }
3508
3509         up = isl_upoly_cow(up);
3510         rec = isl_upoly_as_rec(up);
3511         if (!rec)
3512                 goto error;
3513
3514         for (i = 0; i < rec->n; ++i) {
3515                 if (isl_upoly_is_zero(rec->p[i]))
3516                         continue;
3517                 rec->p[i] = isl_upoly_homogenize(rec->p[i],
3518                                 up->var < last ? deg + i : i, target,
3519                                 first, last);
3520                 if (!rec->p[i])
3521                         goto error;
3522         }
3523
3524         return up;
3525 error:
3526         isl_upoly_free(up);
3527         return NULL;
3528 }
3529
3530 /* Homogenize the polynomial in the set variables by introducing
3531  * powers of an extra set variable at position 0.
3532  */
3533 __isl_give isl_qpolynomial *isl_qpolynomial_homogenize(
3534         __isl_take isl_qpolynomial *poly)
3535 {
3536         unsigned ovar;
3537         unsigned nvar;
3538         int deg = isl_qpolynomial_degree(poly);
3539
3540         if (deg < -1)
3541                 goto error;
3542
3543         poly = isl_qpolynomial_insert_dims(poly, isl_dim_in, 0, 1);
3544         poly = isl_qpolynomial_cow(poly);
3545         if (!poly)
3546                 goto error;
3547
3548         ovar = isl_space_offset(poly->dim, isl_dim_set);
3549         nvar = isl_space_dim(poly->dim, isl_dim_set);
3550         poly->upoly = isl_upoly_homogenize(poly->upoly, 0, deg,
3551                                                 ovar, ovar + nvar);
3552         if (!poly->upoly)
3553                 goto error;
3554
3555         return poly;
3556 error:
3557         isl_qpolynomial_free(poly);
3558         return NULL;
3559 }
3560
3561 __isl_give isl_term *isl_term_alloc(__isl_take isl_space *dim,
3562         __isl_take isl_mat *div)
3563 {
3564         isl_term *term;
3565         int n;
3566
3567         if (!dim || !div)
3568                 goto error;
3569
3570         n = isl_space_dim(dim, isl_dim_all) + div->n_row;
3571
3572         term = isl_calloc(dim->ctx, struct isl_term,
3573                         sizeof(struct isl_term) + (n - 1) * sizeof(int));
3574         if (!term)
3575                 goto error;
3576
3577         term->ref = 1;
3578         term->dim = dim;
3579         term->div = div;
3580         isl_int_init(term->n);
3581         isl_int_init(term->d);
3582
3583         return term;
3584 error:
3585         isl_space_free(dim);
3586         isl_mat_free(div);
3587         return NULL;
3588 }
3589
3590 __isl_give isl_term *isl_term_copy(__isl_keep isl_term *term)
3591 {
3592         if (!term)
3593                 return NULL;
3594
3595         term->ref++;
3596         return term;
3597 }
3598
3599 __isl_give isl_term *isl_term_dup(__isl_keep isl_term *term)
3600 {
3601         int i;
3602         isl_term *dup;
3603         unsigned total;
3604
3605         if (!term)
3606                 return NULL;
3607
3608         total = isl_space_dim(term->dim, isl_dim_all) + term->div->n_row;
3609
3610         dup = isl_term_alloc(isl_space_copy(term->dim), isl_mat_copy(term->div));
3611         if (!dup)
3612                 return NULL;
3613
3614         isl_int_set(dup->n, term->n);
3615         isl_int_set(dup->d, term->d);
3616
3617         for (i = 0; i < total; ++i)
3618                 dup->pow[i] = term->pow[i];
3619
3620         return dup;
3621 }
3622
3623 __isl_give isl_term *isl_term_cow(__isl_take isl_term *term)
3624 {
3625         if (!term)
3626                 return NULL;
3627
3628         if (term->ref == 1)
3629                 return term;
3630         term->ref--;
3631         return isl_term_dup(term);
3632 }
3633
3634 void isl_term_free(__isl_take isl_term *term)
3635 {
3636         if (!term)
3637                 return;
3638
3639         if (--term->ref > 0)
3640                 return;
3641
3642         isl_space_free(term->dim);
3643         isl_mat_free(term->div);
3644         isl_int_clear(term->n);
3645         isl_int_clear(term->d);
3646         free(term);
3647 }
3648
3649 unsigned isl_term_dim(__isl_keep isl_term *term, enum isl_dim_type type)
3650 {
3651         if (!term)
3652                 return 0;
3653
3654         switch (type) {
3655         case isl_dim_param:
3656         case isl_dim_in:
3657         case isl_dim_out:       return isl_space_dim(term->dim, type);
3658         case isl_dim_div:       return term->div->n_row;
3659         case isl_dim_all:       return isl_space_dim(term->dim, isl_dim_all) +
3660                                                                 term->div->n_row;
3661         default:                return 0;
3662         }
3663 }
3664
3665 isl_ctx *isl_term_get_ctx(__isl_keep isl_term *term)
3666 {
3667         return term ? term->dim->ctx : NULL;
3668 }
3669
3670 void isl_term_get_num(__isl_keep isl_term *term, isl_int *n)
3671 {
3672         if (!term)
3673                 return;
3674         isl_int_set(*n, term->n);
3675 }
3676
3677 void isl_term_get_den(__isl_keep isl_term *term, isl_int *d)
3678 {
3679         if (!term)
3680                 return;
3681         isl_int_set(*d, term->d);
3682 }
3683
3684 /* Return the coefficient of the term "term".
3685  */
3686 __isl_give isl_val *isl_term_get_coefficient_val(__isl_keep isl_term *term)
3687 {
3688         if (!term)
3689                 return NULL;
3690
3691         return isl_val_rat_from_isl_int(isl_term_get_ctx(term),
3692                                         term->n, term->d);
3693 }
3694
3695 int isl_term_get_exp(__isl_keep isl_term *term,
3696         enum isl_dim_type type, unsigned pos)
3697 {
3698         if (!term)
3699                 return -1;
3700
3701         isl_assert(term->dim->ctx, pos < isl_term_dim(term, type), return -1);
3702
3703         if (type >= isl_dim_set)
3704                 pos += isl_space_dim(term->dim, isl_dim_param);
3705         if (type >= isl_dim_div)
3706                 pos += isl_space_dim(term->dim, isl_dim_set);
3707
3708         return term->pow[pos];
3709 }
3710
3711 __isl_give isl_aff *isl_term_get_div(__isl_keep isl_term *term, unsigned pos)
3712 {
3713         isl_local_space *ls;
3714         isl_aff *aff;
3715
3716         if (!term)
3717                 return NULL;
3718
3719         isl_assert(term->dim->ctx, pos < isl_term_dim(term, isl_dim_div),
3720                         return NULL);
3721
3722         ls = isl_local_space_alloc_div(isl_space_copy(term->dim),
3723                                         isl_mat_copy(term->div));
3724         aff = isl_aff_alloc(ls);
3725         if (!aff)
3726                 return NULL;
3727
3728         isl_seq_cpy(aff->v->el, term->div->row[pos], aff->v->size);
3729
3730         aff = isl_aff_normalize(aff);
3731
3732         return aff;
3733 }
3734
3735 __isl_give isl_term *isl_upoly_foreach_term(__isl_keep struct isl_upoly *up,
3736         int (*fn)(__isl_take isl_term *term, void *user),
3737         __isl_take isl_term *term, void *user)
3738 {
3739         int i;
3740         struct isl_upoly_rec *rec;
3741
3742         if (!up || !term)
3743                 goto error;
3744
3745         if (isl_upoly_is_zero(up))
3746                 return term;
3747
3748         isl_assert(up->ctx, !isl_upoly_is_nan(up), goto error);
3749         isl_assert(up->ctx, !isl_upoly_is_infty(up), goto error);
3750         isl_assert(up->ctx, !isl_upoly_is_neginfty(up), goto error);
3751
3752         if (isl_upoly_is_cst(up)) {
3753                 struct isl_upoly_cst *cst;
3754                 cst = isl_upoly_as_cst(up);
3755                 if (!cst)
3756                         goto error;
3757                 term = isl_term_cow(term);
3758                 if (!term)
3759                         goto error;
3760                 isl_int_set(term->n, cst->n);
3761                 isl_int_set(term->d, cst->d);
3762                 if (fn(isl_term_copy(term), user) < 0)
3763                         goto error;
3764                 return term;
3765         }
3766
3767         rec = isl_upoly_as_rec(up);
3768         if (!rec)
3769                 goto error;
3770
3771         for (i = 0; i < rec->n; ++i) {
3772                 term = isl_term_cow(term);
3773                 if (!term)
3774                         goto error;
3775                 term->pow[up->var] = i;
3776                 term = isl_upoly_foreach_term(rec->p[i], fn, term, user);
3777                 if (!term)
3778                         goto error;
3779         }
3780         term->pow[up->var] = 0;
3781
3782         return term;
3783 error:
3784         isl_term_free(term);
3785         return NULL;
3786 }
3787
3788 int isl_qpolynomial_foreach_term(__isl_keep isl_qpolynomial *qp,
3789         int (*fn)(__isl_take isl_term *term, void *user), void *user)
3790 {
3791         isl_term *term;
3792
3793         if (!qp)
3794                 return -1;
3795
3796         term = isl_term_alloc(isl_space_copy(qp->dim), isl_mat_copy(qp->div));
3797         if (!term)
3798                 return -1;
3799
3800         term = isl_upoly_foreach_term(qp->upoly, fn, term, user);
3801
3802         isl_term_free(term);
3803
3804         return term ? 0 : -1;
3805 }
3806
3807 __isl_give isl_qpolynomial *isl_qpolynomial_from_term(__isl_take isl_term *term)
3808 {
3809         struct isl_upoly *up;
3810         isl_qpolynomial *qp;
3811         int i, n;
3812
3813         if (!term)
3814                 return NULL;
3815
3816         n = isl_space_dim(term->dim, isl_dim_all) + term->div->n_row;
3817
3818         up = isl_upoly_rat_cst(term->dim->ctx, term->n, term->d);
3819         for (i = 0; i < n; ++i) {
3820                 if (!term->pow[i])
3821                         continue;
3822                 up = isl_upoly_mul(up,
3823                         isl_upoly_var_pow(term->dim->ctx, i, term->pow[i]));
3824         }
3825
3826         qp = isl_qpolynomial_alloc(isl_space_copy(term->dim), term->div->n_row, up);
3827         if (!qp)
3828                 goto error;
3829         isl_mat_free(qp->div);
3830         qp->div = isl_mat_copy(term->div);
3831         if (!qp->div)
3832                 goto error;
3833
3834         isl_term_free(term);
3835         return qp;
3836 error:
3837         isl_qpolynomial_free(qp);
3838         isl_term_free(term);
3839         return NULL;
3840 }
3841
3842 __isl_give isl_qpolynomial *isl_qpolynomial_lift(__isl_take isl_qpolynomial *qp,
3843         __isl_take isl_space *dim)
3844 {
3845         int i;
3846         int extra;
3847         unsigned total;
3848
3849         if (!qp || !dim)
3850                 goto error;
3851
3852         if (isl_space_is_equal(qp->dim, dim)) {
3853                 isl_space_free(dim);
3854                 return qp;
3855         }
3856
3857         qp = isl_qpolynomial_cow(qp);
3858         if (!qp)
3859                 goto error;
3860
3861         extra = isl_space_dim(dim, isl_dim_set) -
3862                         isl_space_dim(qp->dim, isl_dim_set);
3863         total = isl_space_dim(qp->dim, isl_dim_all);
3864         if (qp->div->n_row) {
3865                 int *exp;
3866
3867                 exp = isl_alloc_array(qp->div->ctx, int, qp->div->n_row);
3868                 if (!exp)
3869                         goto error;
3870                 for (i = 0; i < qp->div->n_row; ++i)
3871                         exp[i] = extra + i;
3872                 qp->upoly = expand(qp->upoly, exp, total);
3873                 free(exp);
3874                 if (!qp->upoly)
3875                         goto error;
3876         }
3877         qp->div = isl_mat_insert_cols(qp->div, 2 + total, extra);
3878         if (!qp->div)
3879                 goto error;
3880         for (i = 0; i < qp->div->n_row; ++i)
3881                 isl_seq_clr(qp->div->row[i] + 2 + total, extra);
3882
3883         isl_space_free(qp->dim);
3884         qp->dim = dim;
3885
3886         return qp;
3887 error:
3888         isl_space_free(dim);
3889         isl_qpolynomial_free(qp);
3890         return NULL;
3891 }
3892
3893 /* For each parameter or variable that does not appear in qp,
3894  * first eliminate the variable from all constraints and then set it to zero.
3895  */
3896 static __isl_give isl_set *fix_inactive(__isl_take isl_set *set,
3897         __isl_keep isl_qpolynomial *qp)
3898 {
3899         int *active = NULL;
3900         int i;
3901         int d;
3902         unsigned nparam;
3903         unsigned nvar;
3904
3905         if (!set || !qp)
3906                 goto error;
3907
3908         d = isl_space_dim(set->dim, isl_dim_all);
3909         active = isl_calloc_array(set->ctx, int, d);
3910         if (set_active(qp, active) < 0)
3911                 goto error;
3912
3913         for (i = 0; i < d; ++i)
3914                 if (!active[i])
3915                         break;
3916
3917         if (i == d) {
3918                 free(active);
3919                 return set;
3920         }
3921
3922         nparam = isl_space_dim(set->dim, isl_dim_param);
3923         nvar = isl_space_dim(set->dim, isl_dim_set);
3924         for (i = 0; i < nparam; ++i) {
3925                 if (active[i])
3926                         continue;
3927                 set = isl_set_eliminate(set, isl_dim_param, i, 1);
3928                 set = isl_set_fix_si(set, isl_dim_param, i, 0);
3929         }
3930         for (i = 0; i < nvar; ++i) {
3931                 if (active[nparam + i])
3932                         continue;
3933                 set = isl_set_eliminate(set, isl_dim_set, i, 1);
3934                 set = isl_set_fix_si(set, isl_dim_set, i, 0);
3935         }
3936
3937         free(active);
3938
3939         return set;
3940 error:
3941         free(active);
3942         isl_set_free(set);
3943         return NULL;
3944 }
3945
3946 struct isl_opt_data {
3947         isl_qpolynomial *qp;
3948         int first;
3949         isl_val *opt;
3950         int max;
3951 };
3952
3953 static int opt_fn(__isl_take isl_point *pnt, void *user)
3954 {
3955         struct isl_opt_data *data = (struct isl_opt_data *)user;
3956         isl_val *val;
3957
3958         val = isl_qpolynomial_eval(isl_qpolynomial_copy(data->qp), pnt);
3959         if (data->first) {
3960                 data->first = 0;
3961                 data->opt = val;
3962         } else if (data->max) {
3963                 data->opt = isl_val_max(data->opt, val);
3964         } else {
3965                 data->opt = isl_val_min(data->opt, val);
3966         }
3967
3968         return 0;
3969 }
3970
3971 __isl_give isl_val *isl_qpolynomial_opt_on_domain(
3972         __isl_take isl_qpolynomial *qp, __isl_take isl_set *set, int max)
3973 {
3974         struct isl_opt_data data = { NULL, 1, NULL, max };
3975
3976         if (!set || !qp)
3977                 goto error;
3978
3979         if (isl_upoly_is_cst(qp->upoly)) {
3980                 isl_set_free(set);
3981                 data.opt = isl_qpolynomial_get_constant_val(qp);
3982                 isl_qpolynomial_free(qp);
3983                 return data.opt;
3984         }
3985
3986         set = fix_inactive(set, qp);
3987
3988         data.qp = qp;
3989         if (isl_set_foreach_point(set, opt_fn, &data) < 0)
3990                 goto error;
3991
3992         if (data.first)
3993                 data.opt = isl_val_zero(isl_set_get_ctx(set));
3994
3995         isl_set_free(set);
3996         isl_qpolynomial_free(qp);
3997         return data.opt;
3998 error:
3999         isl_set_free(set);
4000         isl_qpolynomial_free(qp);
4001         isl_val_free(data.opt);
4002         return NULL;
4003 }
4004
4005 __isl_give isl_qpolynomial *isl_qpolynomial_morph_domain(
4006         __isl_take isl_qpolynomial *qp, __isl_take isl_morph *morph)
4007 {
4008         int i;
4009         int n_sub;
4010         isl_ctx *ctx;
4011         struct isl_upoly **subs;
4012         isl_mat *mat, *diag;
4013
4014         qp = isl_qpolynomial_cow(qp);
4015         if (!qp || !morph)
4016                 goto error;
4017
4018         ctx = qp->dim->ctx;
4019         isl_assert(ctx, isl_space_is_equal(qp->dim, morph->dom->dim), goto error);
4020
4021         n_sub = morph->inv->n_row - 1;
4022         if (morph->inv->n_row != morph->inv->n_col)
4023                 n_sub += qp->div->n_row;
4024         subs = isl_calloc_array(ctx, struct isl_upoly *, n_sub);
4025         if (n_sub && !subs)
4026                 goto error;
4027
4028         for (i = 0; 1 + i < morph->inv->n_row; ++i)
4029                 subs[i] = isl_upoly_from_affine(ctx, morph->inv->row[1 + i],
4030                                         morph->inv->row[0][0], morph->inv->n_col);
4031         if (morph->inv->n_row != morph->inv->n_col)
4032                 for (i = 0; i < qp->div->n_row; ++i)
4033                         subs[morph->inv->n_row - 1 + i] =
4034                             isl_upoly_var_pow(ctx, morph->inv->n_col - 1 + i, 1);
4035
4036         qp->upoly = isl_upoly_subs(qp->upoly, 0, n_sub, subs);
4037
4038         for (i = 0; i < n_sub; ++i)
4039                 isl_upoly_free(subs[i]);
4040         free(subs);
4041
4042         diag = isl_mat_diag(ctx, 1, morph->inv->row[0][0]);
4043         mat = isl_mat_diagonal(diag, isl_mat_copy(morph->inv));
4044         diag = isl_mat_diag(ctx, qp->div->n_row, morph->inv->row[0][0]);
4045         mat = isl_mat_diagonal(mat, diag);
4046         qp->div = isl_mat_product(qp->div, mat);
4047         isl_space_free(qp->dim);
4048         qp->dim = isl_space_copy(morph->ran->dim);
4049
4050         if (!qp->upoly || !qp->div || !qp->dim)
4051                 goto error;
4052
4053         isl_morph_free(morph);
4054
4055         return qp;
4056 error:
4057         isl_qpolynomial_free(qp);
4058         isl_morph_free(morph);
4059         return NULL;
4060 }
4061
4062 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_mul(
4063         __isl_take isl_union_pw_qpolynomial *upwqp1,
4064         __isl_take isl_union_pw_qpolynomial *upwqp2)
4065 {
4066         return isl_union_pw_qpolynomial_match_bin_op(upwqp1, upwqp2,
4067                                                 &isl_pw_qpolynomial_mul);
4068 }
4069
4070 /* Reorder the columns of the given div definitions according to the
4071  * given reordering.
4072  */
4073 static __isl_give isl_mat *reorder_divs(__isl_take isl_mat *div,
4074         __isl_take isl_reordering *r)
4075 {
4076         int i, j;
4077         isl_mat *mat;
4078         int extra;
4079
4080         if (!div || !r)
4081                 goto error;
4082
4083         extra = isl_space_dim(r->dim, isl_dim_all) + div->n_row - r->len;
4084         mat = isl_mat_alloc(div->ctx, div->n_row, div->n_col + extra);
4085         if (!mat)
4086                 goto error;
4087
4088         for (i = 0; i < div->n_row; ++i) {
4089                 isl_seq_cpy(mat->row[i], div->row[i], 2);
4090                 isl_seq_clr(mat->row[i] + 2, mat->n_col - 2);
4091                 for (j = 0; j < r->len; ++j)
4092                         isl_int_set(mat->row[i][2 + r->pos[j]],
4093                                     div->row[i][2 + j]);
4094         }
4095
4096         isl_reordering_free(r);
4097         isl_mat_free(div);
4098         return mat;
4099 error:
4100         isl_reordering_free(r);
4101         isl_mat_free(div);
4102         return NULL;
4103 }
4104
4105 /* Reorder the dimension of "qp" according to the given reordering.
4106  */
4107 __isl_give isl_qpolynomial *isl_qpolynomial_realign_domain(
4108         __isl_take isl_qpolynomial *qp, __isl_take isl_reordering *r)
4109 {
4110         qp = isl_qpolynomial_cow(qp);
4111         if (!qp)
4112                 goto error;
4113
4114         r = isl_reordering_extend(r, qp->div->n_row);
4115         if (!r)
4116                 goto error;
4117
4118         qp->div = reorder_divs(qp->div, isl_reordering_copy(r));
4119         if (!qp->div)
4120                 goto error;
4121
4122         qp->upoly = reorder(qp->upoly, r->pos);
4123         if (!qp->upoly)
4124                 goto error;
4125
4126         qp = isl_qpolynomial_reset_domain_space(qp, isl_space_copy(r->dim));
4127
4128         isl_reordering_free(r);
4129         return qp;
4130 error:
4131         isl_qpolynomial_free(qp);
4132         isl_reordering_free(r);
4133         return NULL;
4134 }
4135
4136 __isl_give isl_qpolynomial *isl_qpolynomial_align_params(
4137         __isl_take isl_qpolynomial *qp, __isl_take isl_space *model)
4138 {
4139         if (!qp || !model)
4140                 goto error;
4141
4142         if (!isl_space_match(qp->dim, isl_dim_param, model, isl_dim_param)) {
4143                 isl_reordering *exp;
4144
4145                 model = isl_space_drop_dims(model, isl_dim_in,
4146                                         0, isl_space_dim(model, isl_dim_in));
4147                 model = isl_space_drop_dims(model, isl_dim_out,
4148                                         0, isl_space_dim(model, isl_dim_out));
4149                 exp = isl_parameter_alignment_reordering(qp->dim, model);
4150                 exp = isl_reordering_extend_space(exp,
4151                                         isl_qpolynomial_get_domain_space(qp));
4152                 qp = isl_qpolynomial_realign_domain(qp, exp);
4153         }
4154
4155         isl_space_free(model);
4156         return qp;
4157 error:
4158         isl_space_free(model);
4159         isl_qpolynomial_free(qp);
4160         return NULL;
4161 }
4162
4163 struct isl_split_periods_data {
4164         int max_periods;
4165         isl_pw_qpolynomial *res;
4166 };
4167
4168 /* Create a slice where the integer division "div" has the fixed value "v".
4169  * In particular, if "div" refers to floor(f/m), then create a slice
4170  *
4171  *      m v <= f <= m v + (m - 1)
4172  *
4173  * or
4174  *
4175  *      f - m v >= 0
4176  *      -f + m v + (m - 1) >= 0
4177  */
4178 static __isl_give isl_set *set_div_slice(__isl_take isl_space *dim,
4179         __isl_keep isl_qpolynomial *qp, int div, isl_int v)
4180 {
4181         int total;
4182         isl_basic_set *bset = NULL;
4183         int k;
4184
4185         if (!dim || !qp)
4186                 goto error;
4187
4188         total = isl_space_dim(dim, isl_dim_all);
4189         bset = isl_basic_set_alloc_space(isl_space_copy(dim), 0, 0, 2);
4190
4191         k = isl_basic_set_alloc_inequality(bset);
4192         if (k < 0)
4193                 goto error;
4194         isl_seq_cpy(bset->ineq[k], qp->div->row[div] + 1, 1 + total);
4195         isl_int_submul(bset->ineq[k][0], v, qp->div->row[div][0]);
4196
4197         k = isl_basic_set_alloc_inequality(bset);
4198         if (k < 0)
4199                 goto error;
4200         isl_seq_neg(bset->ineq[k], qp->div->row[div] + 1, 1 + total);
4201         isl_int_addmul(bset->ineq[k][0], v, qp->div->row[div][0]);
4202         isl_int_add(bset->ineq[k][0], bset->ineq[k][0], qp->div->row[div][0]);
4203         isl_int_sub_ui(bset->ineq[k][0], bset->ineq[k][0], 1);
4204
4205         isl_space_free(dim);
4206         return isl_set_from_basic_set(bset);
4207 error:
4208         isl_basic_set_free(bset);
4209         isl_space_free(dim);
4210         return NULL;
4211 }
4212
4213 static int split_periods(__isl_take isl_set *set,
4214         __isl_take isl_qpolynomial *qp, void *user);
4215
4216 /* Create a slice of the domain "set" such that integer division "div"
4217  * has the fixed value "v" and add the results to data->res,
4218  * replacing the integer division by "v" in "qp".
4219  */
4220 static int set_div(__isl_take isl_set *set,
4221         __isl_take isl_qpolynomial *qp, int div, isl_int v,
4222         struct isl_split_periods_data *data)
4223 {
4224         int i;
4225         int total;
4226         isl_set *slice;
4227         struct isl_upoly *cst;
4228
4229         slice = set_div_slice(isl_set_get_space(set), qp, div, v);
4230         set = isl_set_intersect(set, slice);
4231
4232         if (!qp)
4233                 goto error;
4234
4235         total = isl_space_dim(qp->dim, isl_dim_all);
4236
4237         for (i = div + 1; i < qp->div->n_row; ++i) {
4238                 if (isl_int_is_zero(qp->div->row[i][2 + total + div]))
4239                         continue;
4240                 isl_int_addmul(qp->div->row[i][1],
4241                                 qp->div->row[i][2 + total + div], v);
4242                 isl_int_set_si(qp->div->row[i][2 + total + div], 0);
4243         }
4244
4245         cst = isl_upoly_rat_cst(qp->dim->ctx, v, qp->dim->ctx->one);
4246         qp = substitute_div(qp, div, cst);
4247
4248         return split_periods(set, qp, data);
4249 error:
4250         isl_set_free(set);
4251         isl_qpolynomial_free(qp);
4252         return -1;
4253 }
4254
4255 /* Split the domain "set" such that integer division "div"
4256  * has a fixed value (ranging from "min" to "max") on each slice
4257  * and add the results to data->res.
4258  */
4259 static int split_div(__isl_take isl_set *set,
4260         __isl_take isl_qpolynomial *qp, int div, isl_int min, isl_int max,
4261         struct isl_split_periods_data *data)
4262 {
4263         for (; isl_int_le(min, max); isl_int_add_ui(min, min, 1)) {
4264                 isl_set *set_i = isl_set_copy(set);
4265                 isl_qpolynomial *qp_i = isl_qpolynomial_copy(qp);
4266
4267                 if (set_div(set_i, qp_i, div, min, data) < 0)
4268                         goto error;
4269         }
4270         isl_set_free(set);
4271         isl_qpolynomial_free(qp);
4272         return 0;
4273 error:
4274         isl_set_free(set);
4275         isl_qpolynomial_free(qp);
4276         return -1;
4277 }
4278
4279 /* If "qp" refers to any integer division
4280  * that can only attain "max_periods" distinct values on "set"
4281  * then split the domain along those distinct values.
4282  * Add the results (or the original if no splitting occurs)
4283  * to data->res.
4284  */
4285 static int split_periods(__isl_take isl_set *set,
4286         __isl_take isl_qpolynomial *qp, void *user)
4287 {
4288         int i;
4289         isl_pw_qpolynomial *pwqp;
4290         struct isl_split_periods_data *data;
4291         isl_int min, max;
4292         int total;
4293         int r = 0;
4294
4295         data = (struct isl_split_periods_data *)user;
4296
4297         if (!set || !qp)
4298                 goto error;
4299
4300         if (qp->div->n_row == 0) {
4301                 pwqp = isl_pw_qpolynomial_alloc(set, qp);
4302                 data->res = isl_pw_qpolynomial_add_disjoint(data->res, pwqp);
4303                 return 0;
4304         }
4305
4306         isl_int_init(min);
4307         isl_int_init(max);
4308         total = isl_space_dim(qp->dim, isl_dim_all);
4309         for (i = 0; i < qp->div->n_row; ++i) {
4310                 enum isl_lp_result lp_res;
4311
4312                 if (isl_seq_first_non_zero(qp->div->row[i] + 2 + total,
4313                                                 qp->div->n_row) != -1)
4314                         continue;
4315
4316                 lp_res = isl_set_solve_lp(set, 0, qp->div->row[i] + 1,
4317                                           set->ctx->one, &min, NULL, NULL);
4318                 if (lp_res == isl_lp_error)
4319                         goto error2;
4320                 if (lp_res == isl_lp_unbounded || lp_res == isl_lp_empty)
4321                         continue;
4322                 isl_int_fdiv_q(min, min, qp->div->row[i][0]);
4323
4324                 lp_res = isl_set_solve_lp(set, 1, qp->div->row[i] + 1,
4325                                           set->ctx->one, &max, NULL, NULL);
4326                 if (lp_res == isl_lp_error)
4327                         goto error2;
4328                 if (lp_res == isl_lp_unbounded || lp_res == isl_lp_empty)
4329                         continue;
4330                 isl_int_fdiv_q(max, max, qp->div->row[i][0]);
4331
4332                 isl_int_sub(max, max, min);
4333                 if (isl_int_cmp_si(max, data->max_periods) < 0) {
4334                         isl_int_add(max, max, min);
4335                         break;
4336                 }
4337         }
4338
4339         if (i < qp->div->n_row) {
4340                 r = split_div(set, qp, i, min, max, data);
4341         } else {
4342                 pwqp = isl_pw_qpolynomial_alloc(set, qp);
4343                 data->res = isl_pw_qpolynomial_add_disjoint(data->res, pwqp);
4344         }
4345
4346         isl_int_clear(max);
4347         isl_int_clear(min);
4348
4349         return r;
4350 error2:
4351         isl_int_clear(max);
4352         isl_int_clear(min);
4353 error:
4354         isl_set_free(set);
4355         isl_qpolynomial_free(qp);
4356         return -1;
4357 }
4358
4359 /* If any quasi-polynomial in pwqp refers to any integer division
4360  * that can only attain "max_periods" distinct values on its domain
4361  * then split the domain along those distinct values.
4362  */
4363 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_split_periods(
4364         __isl_take isl_pw_qpolynomial *pwqp, int max_periods)
4365 {
4366         struct isl_split_periods_data data;
4367
4368         data.max_periods = max_periods;
4369         data.res = isl_pw_qpolynomial_zero(isl_pw_qpolynomial_get_space(pwqp));
4370
4371         if (isl_pw_qpolynomial_foreach_piece(pwqp, &split_periods, &data) < 0)
4372                 goto error;
4373
4374         isl_pw_qpolynomial_free(pwqp);
4375
4376         return data.res;
4377 error:
4378         isl_pw_qpolynomial_free(data.res);
4379         isl_pw_qpolynomial_free(pwqp);
4380         return NULL;
4381 }
4382
4383 /* Construct a piecewise quasipolynomial that is constant on the given
4384  * domain.  In particular, it is
4385  *      0       if cst == 0
4386  *      1       if cst == 1
4387  *  infinity    if cst == -1
4388  */
4389 static __isl_give isl_pw_qpolynomial *constant_on_domain(
4390         __isl_take isl_basic_set *bset, int cst)
4391 {
4392         isl_space *dim;
4393         isl_qpolynomial *qp;
4394
4395         if (!bset)
4396                 return NULL;
4397
4398         bset = isl_basic_set_params(bset);
4399         dim = isl_basic_set_get_space(bset);
4400         if (cst < 0)
4401                 qp = isl_qpolynomial_infty_on_domain(dim);
4402         else if (cst == 0)
4403                 qp = isl_qpolynomial_zero_on_domain(dim);
4404         else
4405                 qp = isl_qpolynomial_one_on_domain(dim);
4406         return isl_pw_qpolynomial_alloc(isl_set_from_basic_set(bset), qp);
4407 }
4408
4409 /* Factor bset, call fn on each of the factors and return the product.
4410  *
4411  * If no factors can be found, simply call fn on the input.
4412  * Otherwise, construct the factors based on the factorizer,
4413  * call fn on each factor and compute the product.
4414  */
4415 static __isl_give isl_pw_qpolynomial *compressed_multiplicative_call(
4416         __isl_take isl_basic_set *bset,
4417         __isl_give isl_pw_qpolynomial *(*fn)(__isl_take isl_basic_set *bset))
4418 {
4419         int i, n;
4420         isl_space *dim;
4421         isl_set *set;
4422         isl_factorizer *f;
4423         isl_qpolynomial *qp;
4424         isl_pw_qpolynomial *pwqp;
4425         unsigned nparam;
4426         unsigned nvar;
4427
4428         f = isl_basic_set_factorizer(bset);
4429         if (!f)
4430                 goto error;
4431         if (f->n_group == 0) {
4432                 isl_factorizer_free(f);
4433                 return fn(bset);
4434         }
4435
4436         nparam = isl_basic_set_dim(bset, isl_dim_param);
4437         nvar = isl_basic_set_dim(bset, isl_dim_set);
4438
4439         dim = isl_basic_set_get_space(bset);
4440         dim = isl_space_domain(dim);
4441         set = isl_set_universe(isl_space_copy(dim));
4442         qp = isl_qpolynomial_one_on_domain(dim);
4443         pwqp = isl_pw_qpolynomial_alloc(set, qp);
4444
4445         bset = isl_morph_basic_set(isl_morph_copy(f->morph), bset);
4446
4447         for (i = 0, n = 0; i < f->n_group; ++i) {
4448                 isl_basic_set *bset_i;
4449                 isl_pw_qpolynomial *pwqp_i;
4450
4451                 bset_i = isl_basic_set_copy(bset);
4452                 bset_i = isl_basic_set_drop_constraints_involving(bset_i,
4453                             nparam + n + f->len[i], nvar - n - f->len[i]);
4454                 bset_i = isl_basic_set_drop_constraints_involving(bset_i,
4455                             nparam, n);
4456                 bset_i = isl_basic_set_drop(bset_i, isl_dim_set,
4457                             n + f->len[i], nvar - n - f->len[i]);
4458                 bset_i = isl_basic_set_drop(bset_i, isl_dim_set, 0, n);
4459
4460                 pwqp_i = fn(bset_i);
4461                 pwqp = isl_pw_qpolynomial_mul(pwqp, pwqp_i);
4462
4463                 n += f->len[i];
4464         }
4465
4466         isl_basic_set_free(bset);
4467         isl_factorizer_free(f);
4468
4469         return pwqp;
4470 error:
4471         isl_basic_set_free(bset);
4472         return NULL;
4473 }
4474
4475 /* Factor bset, call fn on each of the factors and return the product.
4476  * The function is assumed to evaluate to zero on empty domains,
4477  * to one on zero-dimensional domains and to infinity on unbounded domains
4478  * and will not be called explicitly on zero-dimensional or unbounded domains.
4479  *
4480  * We first check for some special cases and remove all equalities.
4481  * Then we hand over control to compressed_multiplicative_call.
4482  */
4483 __isl_give isl_pw_qpolynomial *isl_basic_set_multiplicative_call(
4484         __isl_take isl_basic_set *bset,
4485         __isl_give isl_pw_qpolynomial *(*fn)(__isl_take isl_basic_set *bset))
4486 {
4487         int bounded;
4488         isl_morph *morph;
4489         isl_pw_qpolynomial *pwqp;
4490
4491         if (!bset)
4492                 return NULL;
4493
4494         if (isl_basic_set_plain_is_empty(bset))
4495                 return constant_on_domain(bset, 0);
4496
4497         if (isl_basic_set_dim(bset, isl_dim_set) == 0)
4498                 return constant_on_domain(bset, 1);
4499
4500         bounded = isl_basic_set_is_bounded(bset);
4501         if (bounded < 0)
4502                 goto error;
4503         if (!bounded)
4504                 return constant_on_domain(bset, -1);
4505
4506         if (bset->n_eq == 0)
4507                 return compressed_multiplicative_call(bset, fn);
4508
4509         morph = isl_basic_set_full_compression(bset);
4510         bset = isl_morph_basic_set(isl_morph_copy(morph), bset);
4511
4512         pwqp = compressed_multiplicative_call(bset, fn);
4513
4514         morph = isl_morph_dom_params(morph);
4515         morph = isl_morph_ran_params(morph);
4516         morph = isl_morph_inverse(morph);
4517
4518         pwqp = isl_pw_qpolynomial_morph_domain(pwqp, morph);
4519
4520         return pwqp;
4521 error:
4522         isl_basic_set_free(bset);
4523         return NULL;
4524 }
4525
4526 /* Drop all floors in "qp", turning each integer division [a/m] into
4527  * a rational division a/m.  If "down" is set, then the integer division
4528  * is replaced by (a-(m-1))/m instead.
4529  */
4530 static __isl_give isl_qpolynomial *qp_drop_floors(
4531         __isl_take isl_qpolynomial *qp, int down)
4532 {
4533         int i;
4534         struct isl_upoly *s;
4535
4536         if (!qp)
4537                 return NULL;
4538         if (qp->div->n_row == 0)
4539                 return qp;
4540
4541         qp = isl_qpolynomial_cow(qp);
4542         if (!qp)
4543                 return NULL;
4544
4545         for (i = qp->div->n_row - 1; i >= 0; --i) {
4546                 if (down) {
4547                         isl_int_sub(qp->div->row[i][1],
4548                                     qp->div->row[i][1], qp->div->row[i][0]);
4549                         isl_int_add_ui(qp->div->row[i][1],
4550                                        qp->div->row[i][1], 1);
4551                 }
4552                 s = isl_upoly_from_affine(qp->dim->ctx, qp->div->row[i] + 1,
4553                                         qp->div->row[i][0], qp->div->n_col - 1);
4554                 qp = substitute_div(qp, i, s);
4555                 if (!qp)
4556                         return NULL;
4557         }
4558
4559         return qp;
4560 }
4561
4562 /* Drop all floors in "pwqp", turning each integer division [a/m] into
4563  * a rational division a/m.
4564  */
4565 static __isl_give isl_pw_qpolynomial *pwqp_drop_floors(
4566         __isl_take isl_pw_qpolynomial *pwqp)
4567 {
4568         int i;
4569
4570         if (!pwqp)
4571                 return NULL;
4572
4573         if (isl_pw_qpolynomial_is_zero(pwqp))
4574                 return pwqp;
4575
4576         pwqp = isl_pw_qpolynomial_cow(pwqp);
4577         if (!pwqp)
4578                 return NULL;
4579
4580         for (i = 0; i < pwqp->n; ++i) {
4581                 pwqp->p[i].qp = qp_drop_floors(pwqp->p[i].qp, 0);
4582                 if (!pwqp->p[i].qp)
4583                         goto error;
4584         }
4585
4586         return pwqp;
4587 error:
4588         isl_pw_qpolynomial_free(pwqp);
4589         return NULL;
4590 }
4591
4592 /* Adjust all the integer divisions in "qp" such that they are at least
4593  * one over the given orthant (identified by "signs").  This ensures
4594  * that they will still be non-negative even after subtracting (m-1)/m.
4595  *
4596  * In particular, f is replaced by f' + v, changing f = [a/m]
4597  * to f' = [(a - m v)/m].
4598  * If the constant term k in a is smaller than m,
4599  * the constant term of v is set to floor(k/m) - 1.
4600  * For any other term, if the coefficient c and the variable x have
4601  * the same sign, then no changes are needed.
4602  * Otherwise, if the variable is positive (and c is negative),
4603  * then the coefficient of x in v is set to floor(c/m).
4604  * If the variable is negative (and c is positive),
4605  * then the coefficient of x in v is set to ceil(c/m).
4606  */
4607 static __isl_give isl_qpolynomial *make_divs_pos(__isl_take isl_qpolynomial *qp,
4608         int *signs)
4609 {
4610         int i, j;
4611         int total;
4612         isl_vec *v = NULL;
4613         struct isl_upoly *s;
4614
4615         qp = isl_qpolynomial_cow(qp);
4616         if (!qp)
4617                 return NULL;
4618         qp->div = isl_mat_cow(qp->div);
4619         if (!qp->div)
4620                 goto error;
4621
4622         total = isl_space_dim(qp->dim, isl_dim_all);
4623         v = isl_vec_alloc(qp->div->ctx, qp->div->n_col - 1);
4624
4625         for (i = 0; i < qp->div->n_row; ++i) {
4626                 isl_int *row = qp->div->row[i];
4627                 v = isl_vec_clr(v);
4628                 if (!v)
4629                         goto error;
4630                 if (isl_int_lt(row[1], row[0])) {
4631                         isl_int_fdiv_q(v->el[0], row[1], row[0]);
4632                         isl_int_sub_ui(v->el[0], v->el[0], 1);
4633                         isl_int_submul(row[1], row[0], v->el[0]);
4634                 }
4635                 for (j = 0; j < total; ++j) {
4636                         if (isl_int_sgn(row[2 + j]) * signs[j] >= 0)
4637                                 continue;
4638                         if (signs[j] < 0)
4639                                 isl_int_cdiv_q(v->el[1 + j], row[2 + j], row[0]);
4640                         else
4641                                 isl_int_fdiv_q(v->el[1 + j], row[2 + j], row[0]);
4642                         isl_int_submul(row[2 + j], row[0], v->el[1 + j]);
4643                 }
4644                 for (j = 0; j < i; ++j) {
4645                         if (isl_int_sgn(row[2 + total + j]) >= 0)
4646                                 continue;
4647                         isl_int_fdiv_q(v->el[1 + total + j],
4648                                         row[2 + total + j], row[0]);
4649                         isl_int_submul(row[2 + total + j],
4650                                         row[0], v->el[1 + total + j]);
4651                 }
4652                 for (j = i + 1; j < qp->div->n_row; ++j) {
4653                         if (isl_int_is_zero(qp->div->row[j][2 + total + i]))
4654                                 continue;
4655                         isl_seq_combine(qp->div->row[j] + 1,
4656                                 qp->div->ctx->one, qp->div->row[j] + 1,
4657                                 qp->div->row[j][2 + total + i], v->el, v->size);
4658                 }
4659                 isl_int_set_si(v->el[1 + total + i], 1);
4660                 s = isl_upoly_from_affine(qp->dim->ctx, v->el,
4661                                         qp->div->ctx->one, v->size);
4662                 qp->upoly = isl_upoly_subs(qp->upoly, total + i, 1, &s);
4663                 isl_upoly_free(s);
4664                 if (!qp->upoly)
4665                         goto error;
4666         }
4667
4668         isl_vec_free(v);
4669         return qp;
4670 error:
4671         isl_vec_free(v);
4672         isl_qpolynomial_free(qp);
4673         return NULL;
4674 }
4675
4676 struct isl_to_poly_data {
4677         int sign;
4678         isl_pw_qpolynomial *res;
4679         isl_qpolynomial *qp;
4680 };
4681
4682 /* Appoximate data->qp by a polynomial on the orthant identified by "signs".
4683  * We first make all integer divisions positive and then split the
4684  * quasipolynomials into terms with sign data->sign (the direction
4685  * of the requested approximation) and terms with the opposite sign.
4686  * In the first set of terms, each integer division [a/m] is
4687  * overapproximated by a/m, while in the second it is underapproximated
4688  * by (a-(m-1))/m.
4689  */
4690 static int to_polynomial_on_orthant(__isl_take isl_set *orthant, int *signs,
4691         void *user)
4692 {
4693         struct isl_to_poly_data *data = user;
4694         isl_pw_qpolynomial *t;
4695         isl_qpolynomial *qp, *up, *down;
4696
4697         qp = isl_qpolynomial_copy(data->qp);
4698         qp = make_divs_pos(qp, signs);
4699
4700         up = isl_qpolynomial_terms_of_sign(qp, signs, data->sign);
4701         up = qp_drop_floors(up, 0);
4702         down = isl_qpolynomial_terms_of_sign(qp, signs, -data->sign);
4703         down = qp_drop_floors(down, 1);
4704
4705         isl_qpolynomial_free(qp);
4706         qp = isl_qpolynomial_add(up, down);
4707
4708         t = isl_pw_qpolynomial_alloc(orthant, qp);
4709         data->res = isl_pw_qpolynomial_add_disjoint(data->res, t);
4710
4711         return 0;
4712 }
4713
4714 /* Approximate each quasipolynomial by a polynomial.  If "sign" is positive,
4715  * the polynomial will be an overapproximation.  If "sign" is negative,
4716  * it will be an underapproximation.  If "sign" is zero, the approximation
4717  * will lie somewhere in between.
4718  *
4719  * In particular, is sign == 0, we simply drop the floors, turning
4720  * the integer divisions into rational divisions.
4721  * Otherwise, we split the domains into orthants, make all integer divisions
4722  * positive and then approximate each [a/m] by either a/m or (a-(m-1))/m,
4723  * depending on the requested sign and the sign of the term in which
4724  * the integer division appears.
4725  */
4726 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_to_polynomial(
4727         __isl_take isl_pw_qpolynomial *pwqp, int sign)
4728 {
4729         int i;
4730         struct isl_to_poly_data data;
4731
4732         if (sign == 0)
4733                 return pwqp_drop_floors(pwqp);
4734
4735         if (!pwqp)
4736                 return NULL;
4737
4738         data.sign = sign;
4739         data.res = isl_pw_qpolynomial_zero(isl_pw_qpolynomial_get_space(pwqp));
4740
4741         for (i = 0; i < pwqp->n; ++i) {
4742                 if (pwqp->p[i].qp->div->n_row == 0) {
4743                         isl_pw_qpolynomial *t;
4744                         t = isl_pw_qpolynomial_alloc(
4745                                         isl_set_copy(pwqp->p[i].set),
4746                                         isl_qpolynomial_copy(pwqp->p[i].qp));
4747                         data.res = isl_pw_qpolynomial_add_disjoint(data.res, t);
4748                         continue;
4749                 }
4750                 data.qp = pwqp->p[i].qp;
4751                 if (isl_set_foreach_orthant(pwqp->p[i].set,
4752                                         &to_polynomial_on_orthant, &data) < 0)
4753                         goto error;
4754         }
4755
4756         isl_pw_qpolynomial_free(pwqp);
4757
4758         return data.res;
4759 error:
4760         isl_pw_qpolynomial_free(pwqp);
4761         isl_pw_qpolynomial_free(data.res);
4762         return NULL;
4763 }
4764
4765 static int poly_entry(void **entry, void *user)
4766 {
4767         int *sign = user;
4768         isl_pw_qpolynomial **pwqp = (isl_pw_qpolynomial **)entry;
4769
4770         *pwqp = isl_pw_qpolynomial_to_polynomial(*pwqp, *sign);
4771
4772         return *pwqp ? 0 : -1;
4773 }
4774
4775 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_to_polynomial(
4776         __isl_take isl_union_pw_qpolynomial *upwqp, int sign)
4777 {
4778         upwqp = isl_union_pw_qpolynomial_cow(upwqp);
4779         if (!upwqp)
4780                 return NULL;
4781
4782         if (isl_hash_table_foreach(upwqp->space->ctx, &upwqp->table,
4783                                    &poly_entry, &sign) < 0)
4784                 goto error;
4785
4786         return upwqp;
4787 error:
4788         isl_union_pw_qpolynomial_free(upwqp);
4789         return NULL;
4790 }
4791
4792 __isl_give isl_basic_map *isl_basic_map_from_qpolynomial(
4793         __isl_take isl_qpolynomial *qp)
4794 {
4795         int i, k;
4796         isl_space *dim;
4797         isl_vec *aff = NULL;
4798         isl_basic_map *bmap = NULL;
4799         unsigned pos;
4800         unsigned n_div;
4801
4802         if (!qp)
4803                 return NULL;
4804         if (!isl_upoly_is_affine(qp->upoly))
4805                 isl_die(qp->dim->ctx, isl_error_invalid,
4806                         "input quasi-polynomial not affine", goto error);
4807         aff = isl_qpolynomial_extract_affine(qp);
4808         if (!aff)
4809                 goto error;
4810         dim = isl_qpolynomial_get_space(qp);
4811         pos = 1 + isl_space_offset(dim, isl_dim_out);
4812         n_div = qp->div->n_row;
4813         bmap = isl_basic_map_alloc_space(dim, n_div, 1, 2 * n_div);
4814
4815         for (i = 0; i < n_div; ++i) {
4816                 k = isl_basic_map_alloc_div(bmap);
4817                 if (k < 0)
4818                         goto error;
4819                 isl_seq_cpy(bmap->div[k], qp->div->row[i], qp->div->n_col);
4820                 isl_int_set_si(bmap->div[k][qp->div->n_col], 0);
4821                 if (isl_basic_map_add_div_constraints(bmap, k) < 0)
4822                         goto error;
4823         }
4824         k = isl_basic_map_alloc_equality(bmap);
4825         if (k < 0)
4826                 goto error;
4827         isl_int_neg(bmap->eq[k][pos], aff->el[0]);
4828         isl_seq_cpy(bmap->eq[k], aff->el + 1, pos);
4829         isl_seq_cpy(bmap->eq[k] + pos + 1, aff->el + 1 + pos, n_div);
4830
4831         isl_vec_free(aff);
4832         isl_qpolynomial_free(qp);
4833         bmap = isl_basic_map_finalize(bmap);
4834         return bmap;
4835 error:
4836         isl_vec_free(aff);
4837         isl_qpolynomial_free(qp);
4838         isl_basic_map_free(bmap);
4839         return NULL;
4840 }