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 "genfun_constructor.h"
   9 #include "mat_util.h"
  10 #include "matrix_read.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 struct parallel_polytopes {
 331     gf_base *red;
 332     Polyhedron *context;
 333     Matrix *Constraints;
 334     Matrix *CP, *T;
 335     int dim;
 336     int nparam;
 337     vector<parallel_cones>    cones;
 338     barvinok_options    *options;
 339
 340     parallel_polytopes(int n, Polyhedron *context, int nparam,
 341                        barvinok_options *options) :
 342                         context(context), dim(-1), nparam(nparam),
 343                         options(options) {
 344         red = NULL;
 345         Constraints = NULL;
 346         CP = NULL;
 347         T = NULL;
 348     }
 349     bool add(const QQ& c, Polyhedron *P) {
 350         int i;
 351
 352         for (i = 0; i < P->NbEq; ++i)
 353             if (First_Non_Zero(P->Constraint[i]+1,
 354                                P->Dimension-nparam) == -1)
 355                 break;
 356         if (i < P->NbEq)
 357             return false;
 358
 359         Polyhedron *Q = remove_equalities_p(Polyhedron_Copy(P), P->Dimension-nparam,
 360                                             NULL, options->MaxRays);
 361         POL_ENSURE_VERTICES(Q);
 362         if (emptyQ(Q)) {
 363             Polyhedron_Free(Q);
 364             return true;
 365         }
 366
 367         if (Q->NbEq != 0) {
 368             Polyhedron *R;
 369             if (!CP) {
 370                 Matrix *M;
 371                 M = Matrix_Alloc(Q->NbEq, Q->Dimension+2);
 372                 Vector_Copy(Q->Constraint[0], M->p[0], Q->NbEq * (Q->Dimension+2));
 373                 CP = compress_parms(M, nparam);
 374                 T = align_matrix(CP, Q->Dimension+1);
 375                 Matrix_Free(M);
 376             }
 377             R = Polyhedron_Preimage(Q, T, options->MaxRays);
 378             Polyhedron_Free(Q);
 379             Q = remove_equalities_p(R, R->Dimension-nparam, NULL,
 380                                     options->MaxRays);
 381         }
 382         assert(Q->NbEq == 0);
 383
 384         if (First_Non_Zero(Q->Constraint[Q->NbConstraints-1]+1, Q->Dimension) == -1)
 385             Q->NbConstraints--;
 386
 387         if (!Constraints) {
 388             dim = Q->Dimension;
 389             red = gf_base::create(Polyhedron_Copy(context), dim, nparam, options);
 390             red->base->init(Q);
 391             Constraints = Matrix_Alloc(Q->NbConstraints, Q->Dimension);
 392             for (int i = 0; i < Q->NbConstraints; ++i) {
 393                 Vector_Copy(Q->Constraint[i]+1, Constraints->p[i], Q->Dimension);
 394             }
 395         } else {
 396             assert(Q->Dimension == dim);
 397             for (int i = 0; i < Q->NbConstraints; ++i) {
 398                 int j;
 399                 for (j = 0; j < Constraints->NbRows; ++j)
 400                     if (Vector_Equal(Q->Constraint[i]+1, Constraints->p[j],
 401                                         Q->Dimension))
 402                         break;
 403                 assert(j < Constraints->NbRows);
 404             }
 405         }
 406
 407         for (int i = 0; i < Q->NbRays; ++i) {
 408             if (!value_pos_p(Q->Ray[i][dim+1]))
 409                 continue;
 410
 411             Polyhedron *C = supporting_cone(Q, i);
 412
 413             if (First_Non_Zero(C->Constraint[C->NbConstraints-1]+1,
 414                                C->Dimension) == -1)
 415                 C->NbConstraints--;
 416
 417             int *pos = new int[1+C->NbConstraints];
 418             pos[0] = C->NbConstraints;
 419             int l = 0;
 420             for (int k = 0; k < Constraints->NbRows; ++k) {
 421                 for (int j = 0; j < C->NbConstraints; ++j) {
 422                     if (Vector_Equal(C->Constraint[j]+1, Constraints->p[k],
 423                                      C->Dimension)) {
 424                         pos[1+l++] = k;
 425                         break;
 426                     }
 427                 }
 428             }
 429             assert(l == C->NbConstraints);
 430
 431             int j;
 432             for (j = 0; j < cones.size(); ++j)
 433                 if (!memcmp(pos, cones[j].pos, (1+C->NbConstraints)*sizeof(int)))
 434                     break;
 435             if (j == cones.size())
 436                 cones.push_back(parallel_cones(pos));
 437             else
 438                 delete [] pos;
 439
 440             Polyhedron_Free(C);
 441
 442             int k;
 443             for (k = 0; k < cones[j].vertices.size(); ++k)
 444                 if (Vector_Equal(Q->Ray[i]+1, cones[j].vertices[k].first->p,
 445                                  Q->Dimension+1))
 446                     break;
 447
 448             if (k == cones[j].vertices.size()) {
 449                 Vector *vertex = Vector_Alloc(Q->Dimension+1);
 450                 Vector_Copy(Q->Ray[i]+1, vertex->p, Q->Dimension+1);
 451                 cones[j].vertices.push_back(pair<Vector*,QQ>(vertex, c));
 452             } else {
 453                 cones[j].vertices[k].second += c;
 454                 if (cones[j].vertices[k].second.n == 0) {
 455                     int size = cones[j].vertices.size();
 456                     Vector_Free(cones[j].vertices[k].first);
 457                     if (k < size-1)
 458                         cones[j].vertices[k] = cones[j].vertices[size-1];
 459                     cones[j].vertices.pop_back();
 460                 }
 461             }
 462         }
 463
 464         Polyhedron_Free(Q);
 465         return true;
 466     }
 467     gen_fun *compute() {
 468         if (!red)
 469             return NULL;
 470         for (int i = 0; i < cones.size(); ++i) {
 471             Matrix *M = Matrix_Alloc(cones[i].pos[0], 1+Constraints->NbColumns+1);
 472             Polyhedron *Cone;
 473             for (int j = 0; j <cones[i].pos[0]; ++j) {
 474                 value_set_si(M->p[j][0], 1);
 475                 Vector_Copy(Constraints->p[cones[i].pos[1+j]], M->p[j]+1,
 476                             Constraints->NbColumns);
 477             }
 478             Cone = Constraints2Polyhedron(M, options->MaxRays);
 479             Matrix_Free(M);
 480             for (int j = 0; j < cones[i].vertices.size(); ++j) {
 481                 red->base->do_vertex_cone(cones[i].vertices[j].second,
 482                                           Polyhedron_Copy(Cone),
 483                                           cones[i].vertices[j].first->p, options);
 484             }
 485             Polyhedron_Free(Cone);
 486         }
 487         if (CP)
 488             red->gf->substitute(CP);
 489         return red->gf;
 490     }
 491     void print(std::ostream& os) const {
 492         for (int i = 0; i < cones.size(); ++i) {
 493             os << "[";
 494             for (int j = 0; j < cones[i].pos[0]; ++j) {
 495                 if (j)
 496                     os << ", ";
 497                 os << cones[i].pos[1+j];
 498             }
 499             os << "]" << endl;
 500             for (int j = 0; j < cones[i].vertices.size(); ++j) {
 501                 Vector_Print(stderr, P_VALUE_FMT, cones[i].vertices[j].first);
 502                 os << cones[i].vertices[j].second << endl;
 503             }
 504         }
 505     }
 506     ~parallel_polytopes() {
 507         for (int i = 0; i < cones.size(); ++i) {
 508             delete [] cones[i].pos;
 509             for (int j = 0; j < cones[i].vertices.size(); ++j)
 510                 Vector_Free(cones[i].vertices[j].first);
 511         }
 512         if (Constraints)
 513             Matrix_Free(Constraints);
 514         if (CP)
 515             Matrix_Free(CP);
 516         if (T)
 517             Matrix_Free(T);
 518         delete red;
 519     }
 520 };
 521
 522 gen_fun *gen_fun::Hadamard_product(const gen_fun *gf, barvinok_options *options)
 523 {
 524     QQ one(1, 1);
 525     Polyhedron *C = DomainIntersection(context, gf->context, options->MaxRays);
 526     Polyhedron *U = Universe_Polyhedron(C->Dimension);
 527     gen_fun *sum = new gen_fun(C);
 528     for (short_rat_list::iterator i = term.begin(); i != term.end(); ++i) {
 529         for (short_rat_list::iterator i2 = gf->term.begin(); i2 != gf->term.end();
 530                                                              ++i2) {
 531             int d = (*i)->d.power.NumCols();
 532             int k1 = (*i)->d.power.NumRows();
 533             int k2 = (*i2)->d.power.NumRows();
 534             assert((*i)->d.power.NumCols() == (*i2)->d.power.NumCols());
 535
 536             parallel_polytopes pp((*i)->n.power.NumRows() *
 537                                   (*i2)->n.power.NumRows(),
 538                                   sum->context, d, options);
 539
 540             for (int j = 0; j < (*i)->n.power.NumRows(); ++j) {
 541                 for (int j2 = 0; j2 < (*i2)->n.power.NumRows(); ++j2) {
 542                     Matrix *M = Matrix_Alloc(k1+k2+d+d, 1+k1+k2+d+1);
 543                     for (int k = 0; k < k1+k2; ++k) {
 544                         value_set_si(M->p[k][0], 1);
 545                         value_set_si(M->p[k][1+k], 1);
 546                     }
 547                     for (int k = 0; k < d; ++k) {
 548                         value_set_si(M->p[k1+k2+k][1+k1+k2+k], -1);
 549                         zz2value((*i)->n.power[j][k], M->p[k1+k2+k][1+k1+k2+d]);
 550                         for (int l = 0; l < k1; ++l)
 551                             zz2value((*i)->d.power[l][k], M->p[k1+k2+k][1+l]);
 552                     }
 553                     for (int k = 0; k < d; ++k) {
 554                         value_set_si(M->p[k1+k2+d+k][1+k1+k2+k], -1);
 555                         zz2value((*i2)->n.power[j2][k],
 556                                  M->p[k1+k2+d+k][1+k1+k2+d]);
 557                         for (int l = 0; l < k2; ++l)
 558                             zz2value((*i2)->d.power[l][k],
 559                                      M->p[k1+k2+d+k][1+k1+l]);
 560                     }
 561                     Polyhedron *P = Constraints2Polyhedron(M, options->MaxRays);
 562                     Matrix_Free(M);
 563
 564                     QQ c = (*i)->n.coeff[j];
 565                     c *= (*i2)->n.coeff[j2];
 566                     if (!pp.add(c, P)) {
 567                         gen_fun *t = barvinok_series_with_options(P, U, options);
 568                         sum->add(c, t);
 569                         delete t;
 570                     }
 571
 572                     Polyhedron_Free(P);
 573                 }
 574             }
 575
 576             gen_fun *t = pp.compute();
 577             if (t) {
 578                 sum->add(one, t);
 579                 delete t;
 580             }
 581         }
 582     }
 583     Polyhedron_Free(U);
 584     return sum;
 585 }
 586
 587 void gen_fun::add_union(gen_fun *gf, barvinok_options *options)
 588 {
 589     QQ one(1, 1), mone(-1, 1);
 590
 591     gen_fun *hp = Hadamard_product(gf, options);
 592     add(one, gf);
 593     add(mone, hp);
 594     delete hp;
 595 }
 596
 597 static void Polyhedron_Shift(Polyhedron *P, Vector *offset)
 598 {
 599     Value tmp;
 600     value_init(tmp);
 601     for (int i = 0; i < P->NbConstraints; ++i) {
 602         Inner_Product(P->Constraint[i]+1, offset->p, P->Dimension, &tmp);
 603         value_subtract(P->Constraint[i][1+P->Dimension],
 604                        P->Constraint[i][1+P->Dimension], tmp);
 605     }
 606     for (int i = 0; i < P->NbRays; ++i) {
 607         if (value_notone_p(P->Ray[i][0]))
 608             continue;
 609         if (value_zero_p(P->Ray[i][1+P->Dimension]))
 610             continue;
 611         Vector_Combine(P->Ray[i]+1, offset->p, P->Ray[i]+1,
 612                        P->Ray[i][0], P->Ray[i][1+P->Dimension], P->Dimension);
 613     }
 614     value_clear(tmp);
 615 }
 616
 617 void gen_fun::shift(const vec_ZZ& offset)
 618 {
 619     for (short_rat_list::iterator i = term.begin(); i != term.end(); ++i)
 620         for (int j = 0; j < (*i)->n.power.NumRows(); ++j)
 621             (*i)->n.power[j] += offset;
 622
 623     Vector *v = Vector_Alloc(offset.length());
 624     zz2values(offset, v->p);
 625     Polyhedron_Shift(context, v);
 626     Vector_Free(v);
 627 }
 628
 629 /* Divide the generating functin by 1/(1-z^power).
 630  * The effect on the corresponding explicit function f(x) is
 631  * f'(x) = \sum_{i=0}^\infty f(x - i * power)
 632  */
 633 void gen_fun::divide(const vec_ZZ& power)
 634 {
 635     for (short_rat_list::iterator i = term.begin(); i != term.end(); ++i) {
 636         int r = (*i)->d.power.NumRows();
 637         int c = (*i)->d.power.NumCols();
 638         (*i)->d.power.SetDims(r+1, c);
 639         (*i)->d.power[r] = power;
 640     }
 641
 642     Vector *v = Vector_Alloc(1+power.length()+1);
 643     value_set_si(v->p[0], 1);
 644     zz2values(power, v->p+1);
 645     Polyhedron *C = AddRays(v->p, 1, context, context->NbConstraints+1);
 646     Vector_Free(v);
 647     Polyhedron_Free(context);
 648     context = C;
 649 }
 650
 651 static void print_power(std::ostream& os, const QQ& c, const vec_ZZ& p,
 652                         unsigned int nparam, char **param_name)
 653 {
 654     bool first = true;
 655
 656     for (int i = 0; i < p.length(); ++i) {
 657         if (p[i] == 0)
 658             continue;
 659         if (first) {
 660             if (c.n == -1 && c.d == 1)
 661                 os << "-";
 662             else if (c.n != 1 || c.d != 1) {
 663                 os << c.n;
 664                 if (c.d != 1)
 665                     os << " / " << c.d;
 666                 os << "*";
 667             }
 668             first = false;
 669         } else
 670             os << "*";
 671         if (i < nparam)
 672             os << param_name[i];
 673         else
 674             os << "x" << i;
 675         if (p[i] == 1)
 676             continue;
 677         if (p[i] < 0)
 678             os << "^(" << p[i] << ")";
 679         else
 680             os << "^" << p[i];
 681     }
 682     if (first) {
 683         os << c.n;
 684         if (c.d != 1)
 685             os << " / " << c.d;
 686     }
 687 }
 688
 689 void short_rat::print(std::ostream& os, unsigned int nparam, char **param_name) const
 690 {
 691     QQ mone(-1, 1);
 692     os << "(";
 693     for (int j = 0; j < n.coeff.length(); ++j) {
 694         if (j != 0 && n.coeff[j].n >= 0)
 695             os << "+";
 696         print_power(os, n.coeff[j], n.power[j], nparam, param_name);
 697     }
 698     os << ")/(";
 699     for (int j = 0; j < d.power.NumRows(); ++j) {
 700         if (j != 0)
 701             os << " * ";
 702         os << "(1";
 703         print_power(os, mone, d.power[j], nparam, param_name);
 704         os << ")";
 705     }
 706     os << ")";
 707 }
 708
 709 void gen_fun::print(std::ostream& os, unsigned int nparam, char **param_name) const
 710 {
 711     for (short_rat_list::iterator i = term.begin(); i != term.end(); ++i) {
 712         if (i != term.begin())
 713             os << " + ";
 714         (*i)->print(os, nparam, param_name);
 715     }
 716 }
 717
 718 std::ostream & operator<< (std::ostream & os, const short_rat& r)
 719 {
 720     os << r.n.coeff << endl;
 721     os << r.n.power << endl;
 722     os << r.d.power << endl;
 723     return os;
 724 }
 725
 726 std::ostream & operator<< (std::ostream & os, const Polyhedron& P)
 727 {
 728     char *str;
 729     void (*gmp_free)(void *, size_t);
 730     mp_get_memory_functions(NULL, NULL, &gmp_free);
 731     os << P.NbConstraints << " " << P.Dimension+2 << endl;
 732     for (int i = 0; i < P.NbConstraints; ++i) {
 733         for (int j = 0; j < P.Dimension+2; ++j) {
 734             str = mpz_get_str(0, 10, P.Constraint[i][j]);
 735             os << std::setw(4) << str << " ";
 736             (*gmp_free)(str, strlen(str)+1);
 737         }
 738         os << endl;
 739     }
 740     return os;
 741 }
 742
 743 std::ostream & operator<< (std::ostream & os, const gen_fun& gf)
 744 {
 745     os << *gf.context << endl;
 746     os << endl;
 747     os << gf.term.size() << endl;
 748     for (short_rat_list::iterator i = gf.term.begin(); i != gf.term.end(); ++i)
 749         os << **i;
 750     return os;
 751 }
 752
 753 gen_fun *gen_fun::read(std::istream& is, barvinok_options *options)
 754 {
 755     Matrix *M = Matrix_Read(is);
 756     Polyhedron *C = Constraints2Polyhedron(M, options->MaxRays);
 757     Matrix_Free(M);
 758
 759     gen_fun *gf = new gen_fun(C);
 760
 761     int n;
 762     is >> n;
 763
 764     vec_QQ c;
 765     mat_ZZ num;
 766     mat_ZZ den;
 767     for (int i = 0; i < n; ++i) {
 768         is >> c >> num >> den;
 769         gf->add(new short_rat(c, num, den));
 770     }
 771
 772     return gf;
 773 }
 774
 775 gen_fun::operator evalue *() const
 776 {
 777     evalue *EP = NULL;
 778     evalue factor;
 779     value_init(factor.d);
 780     value_init(factor.x.n);
 781     for (short_rat_list::iterator i = term.begin(); i != term.end(); ++i) {
 782         unsigned nvar = (*i)->d.power.NumRows();
 783         unsigned nparam = (*i)->d.power.NumCols();
 784         Matrix *C = Matrix_Alloc(nparam + nvar, 1 + nvar + nparam + 1);
 785         mat_ZZ& d = (*i)->d.power;
 786         Polyhedron *U = context ? context : Universe_Polyhedron(nparam);
 787
 788         for (int j = 0; j < (*i)->n.coeff.length(); ++j) {
 789             for (int r = 0; r < nparam; ++r) {
 790                 value_set_si(C->p[r][0], 0);
 791                 for (int c = 0; c < nvar; ++c) {
 792                     zz2value(d[c][r], C->p[r][1+c]);
 793                 }
 794                 Vector_Set(&C->p[r][1+nvar], 0, nparam);
 795                 value_set_si(C->p[r][1+nvar+r], -1);
 796                 zz2value((*i)->n.power[j][r], C->p[r][1+nvar+nparam]);
 797             }
 798             for (int r = 0; r < nvar; ++r) {
 799                 value_set_si(C->p[nparam+r][0], 1);
 800                 Vector_Set(&C->p[nparam+r][1], 0, nvar + nparam + 1);
 801                 value_set_si(C->p[nparam+r][1+r], 1);
 802             }
 803             Polyhedron *P = Constraints2Polyhedron(C, 0);
 804             evalue *E = barvinok_enumerate_ev(P, U, 0);
 805             Polyhedron_Free(P);
 806             if (EVALUE_IS_ZERO(*E)) {
 807                 evalue_free(E);
 808                 continue;
 809             }
 810             zz2value((*i)->n.coeff[j].n, factor.x.n);
 811             zz2value((*i)->n.coeff[j].d, factor.d);
 812             emul(&factor, E);
 813             /*
 814             Matrix_Print(stdout, P_VALUE_FMT, C);
 815             char *test[] = { "A", "B", "C", "D", "E", "F", "G" };
 816             print_evalue(stdout, E, test);
 817             */
 818             if (!EP)
 819                 EP = E;
 820             else {
 821                 eadd(E, EP);
 822                 evalue_free(E);
 823             }
 824         }
 825         Matrix_Free(C);
 826         if (!context)
 827             Polyhedron_Free(U);
 828     }
 829     value_clear(factor.d);
 830     value_clear(factor.x.n);
 831     return EP;
 832 }
 833
 834 ZZ gen_fun::coefficient(Value* params, barvinok_options *options) const
 835 {
 836     if (context && !in_domain(context, params))
 837         return ZZ::zero();
 838
 839     QQ sum(0, 1);
 840
 841     for (short_rat_list::iterator i = term.begin(); i != term.end(); ++i)
 842         sum += (*i)->coefficient(params, options);
 843
 844     assert(sum.d == 1);
 845     return sum.n;
 846 }
 847
 848 void gen_fun::coefficient(Value* params, Value* c) const
 849 {
 850     barvinok_options *options = barvinok_options_new_with_defaults();
 851
 852     ZZ coeff = coefficient(params, options);
 853
 854     zz2value(coeff, *c);
 855
 856     barvinok_options_free(options);
 857 }
 858
 859 gen_fun *gen_fun::summate(int nvar, barvinok_options *options) const
 860 {
 861     int dim = context->Dimension;
 862     int nparam = dim - nvar;
 863     reducer *red;
 864     gen_fun *gf;
 865
 866     if (options->incremental_specialization == 1) {
 867         red = new partial_ireducer(Polyhedron_Project(context, nparam), dim, nparam);
 868     } else
 869         red = new partial_reducer(Polyhedron_Project(context, nparam), dim, nparam);
 870     for (;;) {
 871         try {
 872             red->init(context);
 873             for (short_rat_list::iterator i = term.begin(); i != term.end(); ++i)
 874                 red->reduce((*i)->n.coeff, (*i)->n.power, (*i)->d.power);
 875             break;
 876         } catch (OrthogonalException &e) {
 877             red->reset();
 878         }
 879     }
 880     gf = red->get_gf();
 881     delete red;
 882     return gf;
 883 }
 884
 885 /* returns true if the set was finite and false otherwise */
 886 bool gen_fun::summate(Value *sum) const
 887 {
 888     if (term.size() == 0) {
 889         value_set_si(*sum, 0);
 890         return true;
 891     }
 892
 893     int maxlen = 0;
 894     for (short_rat_list::iterator i = term.begin(); i != term.end(); ++i)
 895         if ((*i)->d.power.NumRows() > maxlen)
 896             maxlen = (*i)->d.power.NumRows();
 897
 898     infinite_icounter cnt((*term.begin())->d.power.NumCols(), maxlen);
 899     for (short_rat_list::iterator i = term.begin(); i != term.end(); ++i)
 900         cnt.reduce((*i)->n.coeff, (*i)->n.power, (*i)->d.power);
 901
 902     for (int i = 1; i <= maxlen; ++i)
 903         if (value_notzero_p(mpq_numref(cnt.count[i]))) {
 904             value_set_si(*sum, -1);
 905             return false;
 906         }
 907
 908     assert(value_one_p(mpq_denref(cnt.count[0])));
 909     value_assign(*sum, mpq_numref(cnt.count[0]));
 910     return true;
 911 }