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