genfun.cc

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