genfun.cc

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