genfun.cc

   1 #include <iostream>
   2 #include <iomanip>
   3 #include <vector>
   4 #include <assert.h>
   5 #include <barvinok/genfun.h>
   6 #include <barvinok/barvinok.h>
   7 #include "conversion.h"
   8 #include "counter.h"
   9 #include "genfun_constructor.h"
  10 #include "mat_util.h"
  11 #include "matrix_read.h"
  12 #include "remove_equalities.h"
  13
  14 using std::cout;
  15 using std::cerr;
  16 using std::endl;
  17 using std::pair;
  18 using std::vector;
  19
  20 bool short_rat_lex_smaller_denominator::operator()(const short_rat* r1,
  21                                                    const short_rat* r2) const
  22 {
  23     return lex_cmp(r1->d.power, r2->d.power) < 0;
  24 }
  25
  26 static void lex_order_terms(struct short_rat* rat)
  27 {
  28     for (int i = 0; i < rat->n.power.NumRows(); ++i) {
  29         int m = i;
  30         for (int j = i+1; j < rat->n.power.NumRows(); ++j)
  31             if (lex_cmp(rat->n.power[j], rat->n.power[m]) < 0)
  32                 m = j;
  33         if (m != i) {
  34             vec_ZZ tmp = rat->n.power[m];
  35             rat->n.power[m] = rat->n.power[i];
  36             rat->n.power[i] = tmp;
  37             QQ tmp_coeff = rat->n.coeff[m];
  38             rat->n.coeff[m] = rat->n.coeff[i];
  39             rat->n.coeff[i] = tmp_coeff;
  40         }
  41     }
  42 }
  43
  44 short_rat::short_rat(const short_rat& r)
  45 {
  46     n.coeff = r.n.coeff;
  47     n.power = r.n.power;
  48     d.power = r.d.power;
  49 }
  50
  51 short_rat::short_rat(Value c)
  52 {
  53     n.coeff.SetLength(1);
  54     value2zz(c, n.coeff[0].n);
  55     n.coeff[0].d = 1;
  56     n.power.SetDims(1, 0);
  57     d.power.SetDims(0, 0);
  58 }
  59
  60 short_rat::short_rat(const QQ& c, const vec_ZZ& num, const mat_ZZ& den)
  61 {
  62     n.coeff.SetLength(1);
  63     ZZ g = GCD(c.n, c.d);
  64     n.coeff[0].n = c.n/g;
  65     n.coeff[0].d = c.d/g;
  66     n.power.SetDims(1, num.length());
  67     n.power[0] = num;
  68     d.power = den;
  69     normalize();
  70 }
  71
  72 short_rat::short_rat(const vec_QQ& c, const mat_ZZ& num, const mat_ZZ& den)
  73 {
  74     n.coeff = c;
  75     n.power = num;
  76     d.power = den;
  77     normalize();
  78 }
  79
  80 void short_rat::normalize()
  81 {
  82     /* Make all powers in denominator reverse-lexico-positive */
  83     for (int i = 0; i < d.power.NumRows(); ++i) {
  84         int j;
  85         for (j = d.power.NumCols()-1; j >= 0; --j)
  86             if (!IsZero(d.power[i][j]))
  87                 break;
  88         assert(j >= 0);
  89         if (sign(d.power[i][j]) < 0) {
  90             negate(d.power[i], d.power[i]);
  91             for (int k = 0; k < n.coeff.length(); ++k) {
  92                 negate(n.coeff[k].n, n.coeff[k].n);
  93                 n.power[k] += d.power[i];
  94             }
  95         }
  96     }
  97
  98     /* Order powers in denominator */
  99     lex_order_rows(d.power);
 100 }
 101
 102 void short_rat::add(const short_rat *r)
 103 {
 104     for (int i = 0; i < r->n.power.NumRows(); ++i) {
 105         int len = n.coeff.length();
 106         int j;
 107         for (j = 0; j < len; ++j)
 108             if (r->n.power[i] == n.power[j])
 109                 break;
 110         if (j < len) {
 111             n.coeff[j] += r->n.coeff[i];
 112             if (n.coeff[j].n == 0) {
 113                 if (j < len-1) {
 114                     n.power[j] = n.power[len-1];
 115                     n.coeff[j] = n.coeff[len-1];
 116                 }
 117                 int dim = n.power.NumCols();
 118                 n.coeff.SetLength(len-1);
 119                 n.power.SetDims(len-1, dim);
 120             }
 121         } else {
 122             int dim = n.power.NumCols();
 123             n.coeff.SetLength(len+1);
 124             n.power.SetDims(len+1, dim);
 125             n.coeff[len] = r->n.coeff[i];
 126             n.power[len] = r->n.power[i];
 127         }
 128     }
 129 }
 130
 131 QQ short_rat::coefficient(Value* params, barvinok_options *options) const
 132 {
 133     unsigned nvar = d.power.NumRows();
 134     unsigned nparam = d.power.NumCols();
 135     Matrix *C = Matrix_Alloc(nparam + nvar, 1 + nvar + 1);
 136     Value tmp;
 137     value_init(tmp);
 138
 139     QQ c(0, 1);
 140
 141     for (int j = 0; j < n.coeff.length(); ++j) {
 142         C->NbRows = nparam+nvar;
 143         for (int r = 0; r < nparam; ++r) {
 144             value_set_si(C->p[r][0], 0);
 145             for (int c = 0; c < nvar; ++c) {
 146                 zz2value(d.power[c][r], C->p[r][1+c]);
 147             }
 148             zz2value(n.power[j][r], C->p[r][1+nvar]);
 149             value_subtract(C->p[r][1+nvar], C->p[r][1+nvar], params[r]);
 150         }
 151         for (int r = 0; r < nvar; ++r) {
 152             value_set_si(C->p[nparam+r][0], 1);
 153             Vector_Set(&C->p[nparam+r][1], 0, nvar + 1);
 154             value_set_si(C->p[nparam+r][1+r], 1);
 155         }
 156         Polyhedron *P = Constraints2Polyhedron(C, options->MaxRays);
 157         if (emptyQ2(P)) {
 158             Polyhedron_Free(P);
 159             continue;
 160         }
 161         barvinok_count_with_options(P, &tmp, options);
 162         Polyhedron_Free(P);
 163         if (value_zero_p(tmp))
 164             continue;
 165         QQ c2(0, 1);
 166         value2zz(tmp, c2.n);
 167         c2 *= n.coeff[j];
 168         c += c2;
 169     }
 170     Matrix_Free(C);
 171     value_clear(tmp);
 172     return c;
 173 }
 174
 175 bool short_rat::reduced()
 176 {
 177     int dim = n.power.NumCols();
 178     lex_order_terms(this);
 179     if (n.power.NumRows() % 2 == 0) {
 180         if (n.coeff[0].n == -n.coeff[1].n &&
 181             n.coeff[0].d == n.coeff[1].d) {
 182             vec_ZZ step = n.power[1] - n.power[0];
 183             int k;
 184             for (k = 1; k < n.power.NumRows()/2; ++k) {
 185                 if (n.coeff[2*k].n != -n.coeff[2*k+1].n ||
 186                     n.coeff[2*k].d != n.coeff[2*k+1].d)
 187                     break;
 188                 if (step != n.power[2*k+1] - n.power[2*k])
 189                     break;
 190             }
 191             if (k == n.power.NumRows()/2) {
 192                 for (k = 0; k < d.power.NumRows(); ++k)
 193                     if (d.power[k] == step)
 194                         break;
 195                 if (k < d.power.NumRows()) {
 196                     for (++k; k < d.power.NumRows(); ++k)
 197                         d.power[k-1] = d.power[k];
 198                     d.power.SetDims(k-1, dim);
 199                     for (k = 1; k < n.power.NumRows()/2; ++k) {
 200                         n.coeff[k] = n.coeff[2*k];
 201                         n.power[k] = n.power[2*k];
 202                     }
 203                     n.coeff.SetLength(k);
 204                     n.power.SetDims(k, dim);
 205                     return true;
 206                 }
 207             }
 208         }
 209     }
 210     return false;
 211 }
 212
 213 gen_fun::gen_fun(Value c)
 214 {
 215     short_rat *r = new short_rat(c);
 216     context = Universe_Polyhedron(0);
 217     term.insert(r);
 218 }
 219
 220 void gen_fun::add(const QQ& c, const vec_ZZ& num, const mat_ZZ& den)
 221 {
 222     if (c.n == 0)
 223         return;
 224
 225     add(new short_rat(c, num, den));
 226 }
 227
 228 void gen_fun::add(short_rat *r)
 229 {
 230     short_rat_list::iterator i = term.find(r);
 231     while (i != term.end()) {
 232         (*i)->add(r);
 233         if ((*i)->n.coeff.length() == 0) {
 234             delete *i;
 235             term.erase(i);
 236         } else if ((*i)->reduced()) {
 237             delete r;
 238             /* we've modified term[i], so remove it
 239              * and add it back again
 240              */
 241             r = *i;
 242             term.erase(i);
 243             i = term.find(r);
 244             continue;
 245         }
 246         delete r;
 247         return;
 248     }
 249
 250     term.insert(r);
 251 }
 252
 253 void gen_fun::add(const QQ& c, const gen_fun *gf, barvinok_options *options)
 254 {
 255     Polyhedron *U = DomainUnion(context, gf->context, options->MaxRays);
 256     Polyhedron *C = DomainConvex(U, options->MaxRays);
 257     Domain_Free(U);
 258     Domain_Free(context);
 259     context = C;
 260
 261     add(c, gf);
 262 }
 263
 264 void gen_fun::add(const QQ& c, const gen_fun *gf)
 265 {
 266     QQ p;
 267     for (short_rat_list::iterator i = gf->term.begin(); i != gf->term.end(); ++i) {
 268         for (int j = 0; j < (*i)->n.power.NumRows(); ++j) {
 269             p = c;
 270             p *= (*i)->n.coeff[j];
 271             add(p, (*i)->n.power[j], (*i)->d.power);
 272         }
 273     }
 274 }
 275
 276 static void split_param_compression(Matrix *CP, mat_ZZ& map, vec_ZZ& offset)
 277 {
 278     Matrix *T = Transpose(CP);
 279     matrix2zz(T, map, T->NbRows-1, T->NbColumns-1);
 280     values2zz(T->p[T->NbRows-1], offset, T->NbColumns-1);
 281     Matrix_Free(T);
 282 }
 283
 284 /*
 285  * Perform the substitution specified by CP
 286  *
 287  * CP is a homogeneous matrix that maps a set of "compressed parameters"
 288  * to the original set of parameters.
 289  *
 290  * This function is applied to a gen_fun computed with the compressed parameters
 291  * and adapts it to refer to the original parameters.
 292  *
 293  * That is, if y are the compressed parameters and x = A y + b are the original
 294  * parameters, then we want the coefficient of the monomial t^y in the original
 295  * generating function to be the coefficient of the monomial u^x in the resulting
 296  * generating function.
 297  * The original generating function has the form
 298  *
 299  *        a t^m/(1-t^n) = a t^m + a t^{m+n} + a t^{m+2n} + ...
 300  *
 301  * Since each term t^y should correspond to a term u^x, with x = A y + b, we want
 302  *
 303  *         a u^{A m + b} + a u^{A (m+n) + b} + a u^{A (m+2n) +b} + ... =
 304  *
 305  *         = a u^{A m + b}/(1-u^{A n})
 306  *
 307  * Therefore, we multiply the powers m and n in both numerator and denominator by A
 308  * and add b to the power in the numerator.
 309  * Since the above powers are stored as row vectors m^T and n^T,
 310  * we compute, say, m'^T = m^T A^T to obtain m' = A m.
 311  *
 312  * The pair (map, offset) contains the same information as CP.
 313  * map is the transpose of the linear part of CP, while offset is the constant part.
 314  */
 315 void gen_fun::substitute(Matrix *CP)
 316 {
 317     mat_ZZ map;
 318     vec_ZZ offset;
 319     split_param_compression(CP, map, offset);
 320     Polyhedron *C = Polyhedron_Image(context, CP, 0);
 321     Polyhedron_Free(context);
 322     context = C;
 323
 324     short_rat_list new_term;
 325     for (short_rat_list::iterator i = term.begin(); i != term.end(); ++i) {
 326         short_rat *r = (*i);
 327         r->d.power *= map;
 328         r->n.power *= map;
 329         for (int j = 0; j < r->n.power.NumRows(); ++j)
 330             r->n.power[j] += offset;
 331         r->normalize();
 332         new_term.insert(r);
 333     }
 334     term.swap(new_term);
 335 }
 336
 337 static int Matrix_Equal(Matrix *M1, Matrix *M2)
 338 {
 339     int i, j;
 340
 341     if (M1->NbRows != M2->NbRows)
 342         return 0;
 343     if (M1->NbColumns != M2->NbColumns)
 344         return 0;
 345     for (i = 0; i < M1->NbRows; ++i)
 346         for (j = 0; j < M1->NbColumns; ++j)
 347             if (value_ne(M1->p[i][j], M2->p[i][j]))
 348                 return 0;
 349
 350     return 1;
 351 }
 352
 353 struct parallel_cones {
 354     int     *pos;
 355     vector<pair<Vector *, QQ> >     vertices;
 356     parallel_cones(int *pos) : pos(pos) {}
 357 };
 358
 359 /* This structure helps in computing the generating functions
 360  * of polytopes with pairwise parallel hyperplanes more efficiently.
 361  * These occur when computing hadamard products of pairs of generating
 362  * functions with the same denominators.
 363  * If there are many such pairs then the same vertex cone
 364  * may appear more than once.  We therefore keep a list of all
 365  * vertex cones and only compute the corresponding generating function
 366  * once.
 367  * However, even HPs of generating functions with the same denominators
 368  * can result in polytopes of different "shapes", making them incomparable.
 369  * In particular, they can have different equalities among the parameters
 370  * and the variables.  In such cases, only polytopes of the first "shape"
 371  * that is encountered are kept in this way.  The others are handled
 372  * in the usual, non-optimized way.
 373  */
 374 struct parallel_polytopes {
 375     gf_base *red;
 376     Polyhedron *context;
 377     Matrix *Constraints;
 378     Matrix *CP, *T;
 379     int dim;
 380     int nparam;
 381     unsigned reduced_nparam;
 382     vector<parallel_cones>    cones;
 383     barvinok_options    *options;
 384
 385     parallel_polytopes(int n, Polyhedron *context, int nparam,
 386                        barvinok_options *options) :
 387                         context(context), dim(-1), nparam(nparam),
 388                         options(options) {
 389         red = NULL;
 390         Constraints = NULL;
 391         CP = NULL;
 392         T = NULL;
 393     }
 394     bool add(const QQ& c, Polyhedron *P) {
 395         int i;
 396
 397         for (i = 0; i < P->NbEq; ++i)
 398             if (First_Non_Zero(P->Constraint[i]+1,
 399                                P->Dimension-nparam) == -1)
 400                 break;
 401         if (i < P->NbEq)
 402             return false;
 403
 404         Polyhedron *Q = remove_equalities_p(Polyhedron_Copy(P), P->Dimension-nparam,
 405                                             NULL, options->MaxRays);
 406         POL_ENSURE_VERTICES(Q);
 407         if (emptyQ(Q)) {
 408             Polyhedron_Free(Q);
 409             return true;
 410         }
 411
 412         if (Q->Dimension == 0) {
 413             Polyhedron_Free(Q);
 414             return false;
 415         }
 416
 417         if (Q->NbEq != 0) {
 418             Matrix *Q_CP;
 419             Polyhedron *R = Q;
 420
 421             remove_all_equalities(&Q, NULL, &Q_CP, NULL, nparam,
 422                                   options->MaxRays);
 423
 424             POL_ENSURE_VERTICES(Q);
 425             if (emptyQ(Q) || Q->NbEq > 0 || Q->Dimension == 0) {
 426                 if (Q_CP)
 427                     Matrix_Free(Q_CP);
 428                 Polyhedron_Free(R);
 429                 Polyhedron_Free(Q);
 430                 return emptyQ(Q);
 431             }
 432
 433             if (red) {
 434                 if ((!CP ^ !Q_CP) || (CP && !Matrix_Equal(CP, Q_CP))) {
 435                     Matrix_Free(Q_CP);
 436                     Polyhedron_Free(R);
 437                     Polyhedron_Free(Q);
 438                     return false;
 439                 }
 440                 Matrix_Free(Q_CP);
 441             } else {
 442                 CP = Q_CP;
 443                 T = align_matrix(CP, R->Dimension+1);
 444             }
 445
 446             reduced_nparam = CP->NbColumns-1;
 447             Polyhedron_Free(R);
 448         } else {
 449             if (red && CP) {
 450                 Polyhedron_Free(Q);
 451                 return false;
 452             }
 453             reduced_nparam = nparam;
 454         }
 455
 456         if (First_Non_Zero(Q->Constraint[Q->NbConstraints-1]+1, Q->Dimension) == -1)
 457             Q->NbConstraints--;
 458
 459         if (!Constraints) {
 460             Polyhedron *reduced_context;
 461             dim = Q->Dimension;
 462             if (CP)
 463                 reduced_context = Polyhedron_Preimage(context, CP, options->MaxRays);
 464             else
 465                 reduced_context = Polyhedron_Copy(context);
 466             red = gf_base::create(reduced_context, dim, reduced_nparam, options);
 467             red->base->init(Q, 0);
 468             Constraints = Matrix_Alloc(Q->NbConstraints, Q->Dimension);
 469             for (int i = 0; i < Q->NbConstraints; ++i) {
 470                 Vector_Copy(Q->Constraint[i]+1, Constraints->p[i], Q->Dimension);
 471             }
 472         } else {
 473             if (Q->Dimension != dim) {
 474                 Polyhedron_Free(Q);
 475                 return false;
 476             }
 477             assert(Q->Dimension == dim);
 478             for (int i = 0; i < Q->NbConstraints; ++i) {
 479                 int j;
 480                 for (j = 0; j < Constraints->NbRows; ++j)
 481                     if (Vector_Equal(Q->Constraint[i]+1, Constraints->p[j],
 482                                         Q->Dimension))
 483                         break;
 484                 if (j >= Constraints->NbRows) {
 485                     Matrix_Extend(Constraints, Constraints->NbRows+1);
 486                     Vector_Copy(Q->Constraint[i]+1,
 487                                 Constraints->p[Constraints->NbRows-1],
 488                                 Q->Dimension);
 489                 }
 490             }
 491         }
 492
 493         for (int i = 0; i < Q->NbRays; ++i) {
 494             if (!value_pos_p(Q->Ray[i][dim+1]))
 495                 continue;
 496
 497             Polyhedron *C = supporting_cone(Q, i);
 498
 499             if (First_Non_Zero(C->Constraint[C->NbConstraints-1]+1,
 500                                C->Dimension) == -1)
 501                 C->NbConstraints--;
 502
 503             int *pos = new int[1+C->NbConstraints];
 504             int l = 0;
 505             for (int k = 0; k < Constraints->NbRows; ++k) {
 506                 for (int j = 0; j < C->NbConstraints; ++j) {
 507                     if (Vector_Equal(C->Constraint[j]+1, Constraints->p[k],
 508                                      C->Dimension)) {
 509                         pos[1+l++] = k;
 510                         break;
 511                     }
 512                 }
 513             }
 514             pos[0] = l;
 515
 516             int j;
 517             for (j = 0; j < cones.size(); ++j)
 518                 if (!memcmp(pos, cones[j].pos, (1+C->NbConstraints)*sizeof(int)))
 519                     break;
 520             if (j == cones.size())
 521                 cones.push_back(parallel_cones(pos));
 522             else
 523                 delete [] pos;
 524
 525             Polyhedron_Free(C);
 526
 527             int k;
 528             for (k = 0; k < cones[j].vertices.size(); ++k)
 529                 if (Vector_Equal(Q->Ray[i]+1, cones[j].vertices[k].first->p,
 530                                  Q->Dimension+1))
 531                     break;
 532
 533             if (k == cones[j].vertices.size()) {
 534                 Vector *vertex = Vector_Alloc(Q->Dimension+1);
 535                 Vector_Copy(Q->Ray[i]+1, vertex->p, Q->Dimension+1);
 536                 cones[j].vertices.push_back(pair<Vector*,QQ>(vertex, c));
 537             } else {
 538                 cones[j].vertices[k].second += c;
 539                 if (cones[j].vertices[k].second.n == 0) {
 540                     int size = cones[j].vertices.size();
 541                     Vector_Free(cones[j].vertices[k].first);
 542                     if (k < size-1)
 543                         cones[j].vertices[k] = cones[j].vertices[size-1];
 544                     cones[j].vertices.pop_back();
 545                 }
 546             }
 547         }
 548
 549         Polyhedron_Free(Q);
 550         return true;
 551     }
 552     gen_fun *compute() {
 553         if (!red)
 554             return NULL;
 555         for (int i = 0; i < cones.size(); ++i) {
 556             Matrix *M = Matrix_Alloc(cones[i].pos[0], 1+Constraints->NbColumns+1);
 557             Polyhedron *Cone;
 558             for (int j = 0; j <cones[i].pos[0]; ++j) {
 559                 value_set_si(M->p[j][0], 1);
 560                 Vector_Copy(Constraints->p[cones[i].pos[1+j]], M->p[j]+1,
 561                             Constraints->NbColumns);
 562             }
 563             Cone = Constraints2Polyhedron(M, options->MaxRays);
 564             Matrix_Free(M);
 565             for (int j = 0; j < cones[i].vertices.size(); ++j) {
 566                 red->base->do_vertex_cone(cones[i].vertices[j].second,
 567                                           Polyhedron_Copy(Cone),
 568                                           cones[i].vertices[j].first->p, options);
 569             }
 570             Polyhedron_Free(Cone);
 571         }
 572         if (CP)
 573             red->gf->substitute(CP);
 574         return red->gf;
 575     }
 576     void print(std::ostream& os) const {
 577         for (int i = 0; i < cones.size(); ++i) {
 578             os << "[";
 579             for (int j = 0; j < cones[i].pos[0]; ++j) {
 580                 if (j)
 581                     os << ", ";
 582                 os << cones[i].pos[1+j];
 583             }
 584             os << "]" << endl;
 585             for (int j = 0; j < cones[i].vertices.size(); ++j) {
 586                 Vector_Print(stderr, P_VALUE_FMT, cones[i].vertices[j].first);
 587                 os << cones[i].vertices[j].second << endl;
 588             }
 589         }
 590     }
 591     ~parallel_polytopes() {
 592         for (int i = 0; i < cones.size(); ++i) {
 593             delete [] cones[i].pos;
 594             for (int j = 0; j < cones[i].vertices.size(); ++j)
 595                 Vector_Free(cones[i].vertices[j].first);
 596         }
 597         if (Constraints)
 598             Matrix_Free(Constraints);
 599         if (CP)
 600             Matrix_Free(CP);
 601         if (T)
 602             Matrix_Free(T);
 603         delete red;
 604     }
 605 };
 606
 607 gen_fun *gen_fun::Hadamard_product(const gen_fun *gf, barvinok_options *options)
 608 {
 609     QQ one(1, 1);
 610     Polyhedron *C = DomainIntersection(context, gf->context, options->MaxRays);
 611     gen_fun *sum = new gen_fun(C);
 612
 613     int j = 0;
 614     for (short_rat_list::iterator i = term.begin(); i != term.end(); ++i, j++) {
 615         int k = 0;
 616         for (short_rat_list::iterator i2 = gf->term.begin();
 617                 i2 != gf->term.end();
 618                 ++i2, k++) {
 619             int d = (*i)->d.power.NumCols();
 620             int k1 = (*i)->d.power.NumRows();
 621             int k2 = (*i2)->d.power.NumRows();
 622             assert((*i)->d.power.NumCols() == (*i2)->d.power.NumCols());
 623
 624             if (options->verbose)
 625                 fprintf(stderr, "HP: %d/%d %d/%d \r",
 626                                     j, term.size(), k, gf->term.size());
 627
 628             parallel_polytopes pp((*i)->n.power.NumRows() *
 629                                   (*i2)->n.power.NumRows(),
 630                                   sum->context, d, options);
 631
 632             for (int j = 0; j < (*i)->n.power.NumRows(); ++j) {
 633                 for (int j2 = 0; j2 < (*i2)->n.power.NumRows(); ++j2) {
 634                     Matrix *M = Matrix_Alloc(k1+k2+d+d, 1+k1+k2+d+1);
 635                     for (int k = 0; k < k1+k2; ++k) {
 636                         value_set_si(M->p[k][0], 1);
 637                         value_set_si(M->p[k][1+k], 1);
 638                     }
 639                     for (int k = 0; k < d; ++k) {
 640                         value_set_si(M->p[k1+k2+k][1+k1+k2+k], -1);
 641                         zz2value((*i)->n.power[j][k], M->p[k1+k2+k][1+k1+k2+d]);
 642                         for (int l = 0; l < k1; ++l)
 643                             zz2value((*i)->d.power[l][k], M->p[k1+k2+k][1+l]);
 644                     }
 645                     for (int k = 0; k < d; ++k) {
 646                         value_set_si(M->p[k1+k2+d+k][1+k1+k2+k], -1);
 647                         zz2value((*i2)->n.power[j2][k],
 648                                  M->p[k1+k2+d+k][1+k1+k2+d]);
 649                         for (int l = 0; l < k2; ++l)
 650                             zz2value((*i2)->d.power[l][k],
 651                                      M->p[k1+k2+d+k][1+k1+l]);
 652                     }
 653                     Polyhedron *P = Constraints2Polyhedron(M, options->MaxRays);
 654                     Matrix_Free(M);
 655
 656                     QQ c = (*i)->n.coeff[j];
 657                     c *= (*i2)->n.coeff[j2];
 658                     if (!pp.add(c, P)) {
 659                         gen_fun *t = barvinok_enumerate_series(P, C->Dimension, options);
 660                         sum->add(c, t);
 661                         delete t;
 662                     }
 663
 664                     Polyhedron_Free(P);
 665                 }
 666             }
 667
 668             gen_fun *t = pp.compute();
 669             if (t) {
 670                 sum->add(one, t);
 671                 delete t;
 672             }
 673         }
 674     }
 675     return sum;
 676 }
 677
 678 void gen_fun::add_union(gen_fun *gf, barvinok_options *options)
 679 {
 680     QQ one(1, 1), mone(-1, 1);
 681
 682     gen_fun *hp = Hadamard_product(gf, options);
 683     add(one, gf);
 684     add(mone, hp);
 685     delete hp;
 686 }
 687
 688 static void Polyhedron_Shift(Polyhedron *P, Vector *offset)
 689 {
 690     Value tmp;
 691     value_init(tmp);
 692     for (int i = 0; i < P->NbConstraints; ++i) {
 693         Inner_Product(P->Constraint[i]+1, offset->p, P->Dimension, &tmp);
 694         value_subtract(P->Constraint[i][1+P->Dimension],
 695                        P->Constraint[i][1+P->Dimension], tmp);
 696     }
 697     for (int i = 0; i < P->NbRays; ++i) {
 698         if (value_notone_p(P->Ray[i][0]))
 699             continue;
 700         if (value_zero_p(P->Ray[i][1+P->Dimension]))
 701             continue;
 702         Vector_Combine(P->Ray[i]+1, offset->p, P->Ray[i]+1,
 703                        P->Ray[i][0], P->Ray[i][1+P->Dimension], P->Dimension);
 704     }
 705     value_clear(tmp);
 706 }
 707
 708 void gen_fun::shift(const vec_ZZ& offset)
 709 {
 710     for (short_rat_list::iterator i = term.begin(); i != term.end(); ++i)
 711         for (int j = 0; j < (*i)->n.power.NumRows(); ++j)
 712             (*i)->n.power[j] += offset;
 713
 714     Vector *v = Vector_Alloc(offset.length());
 715     zz2values(offset, v->p);
 716     Polyhedron_Shift(context, v);
 717     Vector_Free(v);
 718 }
 719
 720 /* Divide the generating functin by 1/(1-z^power).
 721  * The effect on the corresponding explicit function f(x) is
 722  * f'(x) = \sum_{i=0}^\infty f(x - i * power)
 723  */
 724 void gen_fun::divide(const vec_ZZ& power)
 725 {
 726     for (short_rat_list::iterator i = term.begin(); i != term.end(); ++i) {
 727         int r = (*i)->d.power.NumRows();
 728         int c = (*i)->d.power.NumCols();
 729         (*i)->d.power.SetDims(r+1, c);
 730         (*i)->d.power[r] = power;
 731     }
 732
 733     Vector *v = Vector_Alloc(1+power.length()+1);
 734     value_set_si(v->p[0], 1);
 735     zz2values(power, v->p+1);
 736     Polyhedron *C = AddRays(v->p, 1, context, context->NbConstraints+1);
 737     Vector_Free(v);
 738     Polyhedron_Free(context);
 739     context = C;
 740 }
 741
 742 static void print_power(std::ostream& os, const QQ& c, const vec_ZZ& p,
 743                         unsigned int nparam, const char **param_name)
 744 {
 745     bool first = true;
 746
 747     for (int i = 0; i < p.length(); ++i) {
 748         if (p[i] == 0)
 749             continue;
 750         if (first) {
 751             if (c.n == -1 && c.d == 1)
 752                 os << "-";
 753             else if (c.n != 1 || c.d != 1) {
 754                 os << c.n;
 755                 if (c.d != 1)
 756                     os << "/" << c.d;
 757                 os << "*";
 758             }
 759             first = false;
 760         } else
 761             os << "*";
 762         if (i < nparam)
 763             os << param_name[i];
 764         else
 765             os << "x" << i;
 766         if (p[i] == 1)
 767             continue;
 768         if (p[i] < 0)
 769             os << "^(" << p[i] << ")";
 770         else
 771             os << "^" << p[i];
 772     }
 773     if (first) {
 774         os << c.n;
 775         if (c.d != 1)
 776             os << "/" << c.d;
 777     }
 778 }
 779
 780 void short_rat::print(std::ostream& os, unsigned int nparam,
 781                         const char **param_name) const
 782 {
 783     QQ mone(-1, 1);
 784     os << "(";
 785     for (int j = 0; j < n.coeff.length(); ++j) {
 786         if (j != 0 && n.coeff[j].n >= 0)
 787             os << "+";
 788         print_power(os, n.coeff[j], n.power[j], nparam, param_name);
 789     }
 790     os << ")";
 791     if (d.power.NumRows() == 0)
 792         return;
 793     os << "/(";
 794     for (int j = 0; j < d.power.NumRows(); ++j) {
 795         if (j != 0)
 796             os << " * ";
 797         os << "(1";
 798         print_power(os, mone, d.power[j], nparam, param_name);
 799         os << ")";
 800     }
 801     os << ")";
 802 }
 803
 804 void gen_fun::print(std::ostream& os, unsigned int nparam,
 805                         const char **param_name) const
 806 {
 807     for (short_rat_list::iterator i = term.begin(); i != term.end(); ++i) {
 808         if (i != term.begin())
 809             os << " + ";
 810         (*i)->print(os, nparam, param_name);
 811     }
 812 }
 813
 814 std::ostream & operator<< (std::ostream & os, const short_rat& r)
 815 {
 816     os << r.n.coeff << endl;
 817     os << r.n.power << endl;
 818     os << r.d.power << endl;
 819     return os;
 820 }
 821
 822 extern "C" { typedef void (*gmp_free_t)(void *, size_t); }
 823
 824 std::ostream & operator<< (std::ostream & os, const Polyhedron& P)
 825 {
 826     char *str;
 827     gmp_free_t gmp_free;
 828     mp_get_memory_functions(NULL, NULL, &gmp_free);
 829     os << P.NbConstraints << " " << P.Dimension+2 << endl;
 830     for (int i = 0; i < P.NbConstraints; ++i) {
 831         for (int j = 0; j < P.Dimension+2; ++j) {
 832             str = mpz_get_str(0, 10, P.Constraint[i][j]);
 833             os << std::setw(4) << str << " ";
 834             (*gmp_free)(str, strlen(str)+1);
 835         }
 836         os << endl;
 837     }
 838     return os;
 839 }
 840
 841 std::ostream & operator<< (std::ostream & os, const gen_fun& gf)
 842 {
 843     os << *gf.context << endl;
 844     os << endl;
 845     os << gf.term.size() << endl;
 846     for (short_rat_list::iterator i = gf.term.begin(); i != gf.term.end(); ++i)
 847         os << **i;
 848     return os;
 849 }
 850
 851 gen_fun *gen_fun::read(std::istream& is, barvinok_options *options)
 852 {
 853     Matrix *M = Matrix_Read(is);
 854     Polyhedron *C = Constraints2Polyhedron(M, options->MaxRays);
 855     Matrix_Free(M);
 856
 857     gen_fun *gf = new gen_fun(C);
 858
 859     int n;
 860     is >> n;
 861
 862     vec_QQ c;
 863     mat_ZZ num;
 864     mat_ZZ den;
 865     for (int i = 0; i < n; ++i) {
 866         is >> c >> num >> den;
 867         gf->add(new short_rat(c, num, den));
 868     }
 869
 870     return gf;
 871 }
 872
 873 gen_fun::operator evalue *() const
 874 {
 875     evalue *EP = NULL;
 876     evalue factor;
 877     value_init(factor.d);
 878     value_init(factor.x.n);
 879     for (short_rat_list::iterator i = term.begin(); i != term.end(); ++i) {
 880         unsigned nvar = (*i)->d.power.NumRows();
 881         unsigned nparam = (*i)->d.power.NumCols();
 882         Matrix *C = Matrix_Alloc(nparam + nvar, 1 + nvar + nparam + 1);
 883         mat_ZZ& d = (*i)->d.power;
 884         Polyhedron *U = context;
 885
 886         for (int j = 0; j < (*i)->n.coeff.length(); ++j) {
 887             for (int r = 0; r < nparam; ++r) {
 888                 value_set_si(C->p[r][0], 0);
 889                 for (int c = 0; c < nvar; ++c) {
 890                     zz2value(d[c][r], C->p[r][1+c]);
 891                 }
 892                 Vector_Set(&C->p[r][1+nvar], 0, nparam);
 893                 value_set_si(C->p[r][1+nvar+r], -1);
 894                 zz2value((*i)->n.power[j][r], C->p[r][1+nvar+nparam]);
 895             }
 896             for (int r = 0; r < nvar; ++r) {
 897                 value_set_si(C->p[nparam+r][0], 1);
 898                 Vector_Set(&C->p[nparam+r][1], 0, nvar + nparam + 1);
 899                 value_set_si(C->p[nparam+r][1+r], 1);
 900             }
 901             Polyhedron *P = Constraints2Polyhedron(C, 0);
 902             evalue *E = barvinok_enumerate_ev(P, U, 0);
 903             Polyhedron_Free(P);
 904             if (EVALUE_IS_ZERO(*E)) {
 905                 evalue_free(E);
 906                 continue;
 907             }
 908             zz2value((*i)->n.coeff[j].n, factor.x.n);
 909             zz2value((*i)->n.coeff[j].d, factor.d);
 910             emul(&factor, E);
 911             if (!EP)
 912                 EP = E;
 913             else {
 914                 eadd(E, EP);
 915                 evalue_free(E);
 916             }
 917         }
 918         Matrix_Free(C);
 919     }
 920     value_clear(factor.d);
 921     value_clear(factor.x.n);
 922     return EP ? EP : evalue_zero();
 923 }
 924
 925 ZZ gen_fun::coefficient(Value* params, barvinok_options *options) const
 926 {
 927     if (!in_domain(context, params))
 928         return ZZ::zero();
 929
 930     QQ sum(0, 1);
 931
 932     for (short_rat_list::iterator i = term.begin(); i != term.end(); ++i)
 933         sum += (*i)->coefficient(params, options);
 934
 935     assert(sum.d == 1);
 936     return sum.n;
 937 }
 938
 939 void gen_fun::coefficient(Value* params, Value* c) const
 940 {
 941     barvinok_options *options = barvinok_options_new_with_defaults();
 942
 943     ZZ coeff = coefficient(params, options);
 944
 945     zz2value(coeff, *c);
 946
 947     barvinok_options_free(options);
 948 }
 949
 950 gen_fun *gen_fun::summate(int nvar, barvinok_options *options) const
 951 {
 952     int dim = context->Dimension;
 953     int nparam = dim - nvar;
 954     reducer *red;
 955     gen_fun *gf;
 956
 957     if (nparam == 0) {
 958         bool finite;
 959         Value c;
 960         value_init(c);
 961         finite = summate(&c);
 962         assert(finite);
 963         gf = new gen_fun(c);
 964         value_clear(c);
 965         return gf;
 966     }
 967
 968     if (options->incremental_specialization == 1) {
 969         red = new partial_ireducer(Polyhedron_Project(context, nparam), dim, nparam);
 970     } else
 971         red = new partial_reducer(Polyhedron_Project(context, nparam), dim, nparam);
 972     for (;;) {
 973         int n_try = 0;
 974         try {
 975             red->init(context, n_try);
 976             for (short_rat_list::iterator i = term.begin(); i != term.end(); ++i)
 977                 red->reduce((*i)->n.coeff, (*i)->n.power, (*i)->d.power);
 978             break;
 979         } catch (OrthogonalException &e) {
 980             red->reset();
 981             n_try++;
 982         }
 983     }
 984     gf = red->get_gf();
 985     delete red;
 986     return gf;
 987 }
 988
 989 /* returns true if the set was finite and false otherwise */
 990 bool gen_fun::summate(Value *sum) const
 991 {
 992     if (term.size() == 0) {
 993         value_set_si(*sum, 0);
 994         return true;
 995     }
 996
 997     int maxlen = 0;
 998     for (short_rat_list::iterator i = term.begin(); i != term.end(); ++i)
 999         if ((*i)->d.power.NumRows() > maxlen)
1000             maxlen = (*i)->d.power.NumRows();
1001
1002     infinite_counter cnt((*term.begin())->d.power.NumCols(), maxlen);
1003     cnt.init(context, 0);
1004     for (short_rat_list::iterator i = term.begin(); i != term.end(); ++i)
1005         cnt.reduce((*i)->n.coeff, (*i)->n.power, (*i)->d.power);
1006
1007     for (int i = 1; i <= maxlen; ++i)
1008         if (value_notzero_p(mpq_numref(cnt.count[i]))) {
1009             value_set_si(*sum, -1);
1010             return false;
1011         }
1012
1013     assert(value_one_p(mpq_denref(cnt.count[0])));
1014     value_assign(*sum, mpq_numref(cnt.count[0]));
1015     return true;
1016 }
1017
1018 bool gen_fun::is_zero() const
1019 {
1020     bool empty;
1021     Value c;
1022
1023     value_init(c);
1024
1025     empty = summate(&c) && value_zero_p(c);
1026
1027     value_clear(c);
1028
1029     return empty;
1030 }