version.c: move barvinok_version from util.c

[barvinok.git] / util.c

#include <polylib/polylibgmp.h>
#include <stdlib.h>
#include <assert.h>
#include "config.h"

#ifndef HAVE_ENUMERATE4
#define Polyhedron_Enumerate(a,b,c,d) Polyhedron_Enumerate(a,b,c)
#endif

#define ALLOC(type) (type*)malloc(sizeof(type))
#define ALLOCN(type,n) (type*)malloc((n) * sizeof(type))

#ifdef __GNUC__
#define NALLOC(p,n) p = (typeof(p))malloc((n) * sizeof(*p))
#else
#define NALLOC(p,n) p = (void *)malloc((n) * sizeof(*p))
#endif

#ifndef HAVE_ENUMERATION_FREE
#define Enumeration_Free(en)    /* just leak some memory */
#endif

void manual_count(Polyhedron *P, Value* result)
{
    Polyhedron *U = Universe_Polyhedron(0);
    Enumeration *en = Polyhedron_Enumerate(P,U,1024,NULL);
    Value *v = compute_poly(en,NULL);
    value_assign(*result, *v);
    value_clear(*v);
    free(v);
    Enumeration_Free(en);
    Polyhedron_Free(U);
}

#ifndef HAVE_ENUMERATION_FREE
#undef Enumeration_Free
#endif

#include <barvinok/evalue.h>
#include <barvinok/util.h>
#include <barvinok/barvinok.h>

/* Return random value between 0 and max-1 inclusive
 */
int random_int(int max) {
    return (int) (((double)(max))*rand()/(RAND_MAX+1.0));
}

/* Inplace polarization
 */
void Polyhedron_Polarize(Polyhedron *P)
{
    unsigned NbRows = P->NbConstraints + P->NbRays;
    int i;
    Value **q;

    q = (Value **)malloc(NbRows * sizeof(Value *));
    assert(q);
    for (i = 0; i < P->NbRays; ++i)
        q[i] = P->Ray[i];
    for (; i < NbRows; ++i)
        q[i] = P->Constraint[i-P->NbRays];
    P->NbConstraints = NbRows - P->NbConstraints;
    P->NbRays = NbRows - P->NbRays;
    free(P->Constraint);
    P->Constraint = q;
    P->Ray = q + P->NbConstraints;
}

/*
 * Rather general polar
 * We can optimize it significantly if we assume that
 * P includes zero
 *
 * Also, we calculate the polar as defined in Schrijver
 * The opposite should probably work as well and would
 * eliminate the need for multiplying by -1
 */
Polyhedron* Polyhedron_Polar(Polyhedron *P, unsigned NbMaxRays)
{
    int i;
    Value mone;
    unsigned dim = P->Dimension + 2;
    Matrix *M = Matrix_Alloc(P->NbRays, dim);

    assert(M);
    value_init(mone);
    value_set_si(mone, -1);
    for (i = 0; i < P->NbRays; ++i) {
        Vector_Scale(P->Ray[i], M->p[i], mone, dim);
        value_multiply(M->p[i][0], M->p[i][0], mone);
        value_multiply(M->p[i][dim-1], M->p[i][dim-1], mone);
    }
    P = Constraints2Polyhedron(M, NbMaxRays);
    assert(P);
    Matrix_Free(M);
    value_clear(mone);
    return P;
}

/*
 * Returns the supporting cone of P at the vertex with index v
 */
Polyhedron* supporting_cone(Polyhedron *P, int v)
{
    Matrix *M;
    Value tmp;
    int i, n, j;
    unsigned char *supporting = (unsigned char *)malloc(P->NbConstraints);
    unsigned dim = P->Dimension + 2;

    assert(v >=0 && v < P->NbRays);
    assert(value_pos_p(P->Ray[v][dim-1]));
    assert(supporting);

    value_init(tmp);
    for (i = 0, n = 0; i < P->NbConstraints; ++i) {
        Inner_Product(P->Constraint[i] + 1, P->Ray[v] + 1, dim - 1, &tmp);
        if ((supporting[i] = value_zero_p(tmp)))
            ++n;
    }
    assert(n >= dim - 2);
    value_clear(tmp);
    M = Matrix_Alloc(n, dim);
    assert(M);
    for (i = 0, j = 0; i < P->NbConstraints; ++i)
        if (supporting[i]) {
            value_set_si(M->p[j][dim-1], 0);
            Vector_Copy(P->Constraint[i], M->p[j++], dim-1);
        }
    free(supporting);
    P = Constraints2Polyhedron(M, P->NbRays+1);
    assert(P);
    Matrix_Free(M);
    return P;
}

void value_lcm(Value i, Value j, Value* lcm)
{
    Value aux;
    value_init(aux);
    value_multiply(aux,i,j);
    Gcd(i,j,lcm);
    value_division(*lcm,aux,*lcm);
    value_clear(aux);
}

Polyhedron* supporting_cone_p(Polyhedron *P, Param_Vertices *v)
{
    Matrix *M;
    Value lcm, tmp, tmp2;
    unsigned char *supporting = (unsigned char *)malloc(P->NbConstraints);
    unsigned dim = P->Dimension + 2;
    unsigned nparam = v->Vertex->NbColumns - 2;
    unsigned nvar = dim - nparam - 2;
    int i, n, j;
    Vector *row;

    assert(supporting);
    row = Vector_Alloc(nparam+1);
    assert(row);
    value_init(lcm);
    value_init(tmp);
    value_init(tmp2);
    value_set_si(lcm, 1);
    for (i = 0, n = 0; i < P->NbConstraints; ++i) {
        Vector_Set(row->p, 0, nparam+1);
        for (j = 0 ; j < nvar; ++j) {
            value_set_si(tmp, 1);
            value_assign(tmp2,  P->Constraint[i][j+1]);
            if (value_ne(lcm, v->Vertex->p[j][nparam+1])) {
                value_assign(tmp, lcm);
                value_lcm(lcm, v->Vertex->p[j][nparam+1], &lcm);
                value_division(tmp, lcm, tmp);
                value_multiply(tmp2, tmp2, lcm);
                value_division(tmp2, tmp2, v->Vertex->p[j][nparam+1]);
            }
            Vector_Combine(row->p, v->Vertex->p[j], row->p, 
                           tmp, tmp2, nparam+1);
        }
        value_set_si(tmp, 1);
        Vector_Combine(row->p, P->Constraint[i]+1+nvar, row->p, tmp, lcm, nparam+1);
        for (j = 0; j < nparam+1; ++j)
            if (value_notzero_p(row->p[j]))
                break;
        if ((supporting[i] = (j == nparam + 1)))
            ++n;
    }
    assert(n >= nvar);
    value_clear(tmp);
    value_clear(tmp2);
    value_clear(lcm);
    Vector_Free(row);
    M = Matrix_Alloc(n, nvar+2);
    assert(M);
    for (i = 0, j = 0; i < P->NbConstraints; ++i)
        if (supporting[i]) {
            value_set_si(M->p[j][nvar+1], 0);
            Vector_Copy(P->Constraint[i], M->p[j++], nvar+1);
        }
    free(supporting);
    P = Constraints2Polyhedron(M, P->NbRays+1);
    assert(P);
    Matrix_Free(M);
    return P;
}

Polyhedron* triangulate_cone(Polyhedron *P, unsigned NbMaxCons)
{
    const static int MAX_TRY=10;
    int i, j, r, n, t;
    Value tmp;
    unsigned dim = P->Dimension;
    Matrix *M = Matrix_Alloc(P->NbRays+1, dim+3);
    Matrix *M2, *M3;
    Polyhedron *L, *R, *T;
    assert(P->NbEq == 0);

    R = NULL;
    value_init(tmp);

    Vector_Set(M->p[0]+1, 0, dim+1);
    value_set_si(M->p[0][0], 1);
    value_set_si(M->p[0][dim+2], 1);
    Vector_Set(M->p[P->NbRays]+1, 0, dim+2);
    value_set_si(M->p[P->NbRays][0], 1);
    value_set_si(M->p[P->NbRays][dim+1], 1);

    /* Delaunay triangulation */
    for (i = 0, r = 1; i < P->NbRays; ++i) {
        if (value_notzero_p(P->Ray[i][dim+1]))
            continue;
        Vector_Copy(P->Ray[i], M->p[r], dim+1);
        Inner_Product(M->p[r]+1, M->p[r]+1, dim, &tmp);
        value_assign(M->p[r][dim+1], tmp);
        value_set_si(M->p[r][dim+2], 0);
        ++r;
    }

    M3 = Matrix_Copy(M);
    L = Rays2Polyhedron(M3, NbMaxCons);
    Matrix_Free(M3);

    M2 = Matrix_Alloc(dim+1, dim+2);

    t = 1;
    if (0) {
try_again:
        /* Usually R should still be 0 */
        Domain_Free(R);
        Polyhedron_Free(L);
        for (r = 1; r < P->NbRays; ++r) {
            value_set_si(M->p[r][dim+1], random_int((t+1)*dim)+1);
        }
        M3 = Matrix_Copy(M);
        L = Rays2Polyhedron(M3, NbMaxCons);
        Matrix_Free(M3);
        ++t;
    }
    assert(t <= MAX_TRY);

    R = NULL;
    n = 0;

    for (i = 0; i < L->NbConstraints; ++i) {
        /* Ignore perpendicular facets, i.e., facets with 0 z-coordinate */
        if (value_negz_p(L->Constraint[i][dim+1]))
            continue;
        if (value_notzero_p(L->Constraint[i][dim+2]))
            continue;
        for (j = 1, r = 1; j < M->NbRows; ++j) {
            Inner_Product(M->p[j]+1, L->Constraint[i]+1, dim+1, &tmp);
            if (value_notzero_p(tmp))
                continue;
            if (r > dim)
                goto try_again;
            Vector_Copy(M->p[j]+1, M2->p[r]+1, dim);
            value_set_si(M2->p[r][0], 1);
            value_set_si(M2->p[r][dim+1], 0);
            ++r;
        }
        assert(r == dim+1);
        Vector_Set(M2->p[0]+1, 0, dim);
        value_set_si(M2->p[0][0], 1);
        value_set_si(M2->p[0][dim+1], 1);
        T = Rays2Polyhedron(M2, P->NbConstraints+1);
        T->next = R;
        R = T;
        ++n;
    }
    Matrix_Free(M2);

    Polyhedron_Free(L);
    value_clear(tmp);
    Matrix_Free(M);

    return R;
}

void check_triangulization(Polyhedron *P, Polyhedron *T)
{
    Polyhedron *C, *D, *E, *F, *G, *U;
    for (C = T; C; C = C->next) {
        if (C == T)
            U = C;
        else 
            U = DomainConvex(DomainUnion(U, C, 100), 100);
        for (D = C->next; D; D = D->next) {
            F = C->next;
            G = D->next;
            C->next = NULL;
            D->next = NULL;
            E = DomainIntersection(C, D, 600);
            assert(E->NbRays == 0 || E->NbEq >= 1);
            Polyhedron_Free(E);
            C->next = F;
            D->next = G;
        }
    }
    assert(PolyhedronIncludes(U, P));
    assert(PolyhedronIncludes(P, U));
}

/* Computes x, y and g such that g = gcd(a,b) and a*x+b*y = g */
void Extended_Euclid(Value a, Value b, Value *x, Value *y, Value *g)
{
    Value c, d, e, f, tmp;

    value_init(c);
    value_init(d);
    value_init(e);
    value_init(f);
    value_init(tmp);
    value_absolute(c, a);
    value_absolute(d, b);
    value_set_si(e, 1);
    value_set_si(f, 0);
    while(value_pos_p(d)) {
        value_division(tmp, c, d);
        value_multiply(tmp, tmp, f);
        value_subtract(e, e, tmp);
        value_division(tmp, c, d);
        value_multiply(tmp, tmp, d);
        value_subtract(c, c, tmp);
        value_swap(c, d);
        value_swap(e, f);
    }
    value_assign(*g, c);
    if (value_zero_p(a))
        value_set_si(*x, 0);
    else if (value_pos_p(a))
        value_assign(*x, e);
    else value_oppose(*x, e);
    if (value_zero_p(b))
        value_set_si(*y, 0);
    else {
        value_multiply(tmp, a, *x);
        value_subtract(tmp, c, tmp);
        value_division(*y, tmp, b);
    }
    value_clear(c);
    value_clear(d);
    value_clear(e);
    value_clear(f);
    value_clear(tmp);
}

Matrix * unimodular_complete(Vector *row) 
{
    Value g, b, c, old, tmp;
    Matrix *m;
    unsigned i, j;

    value_init(b);
    value_init(c);
    value_init(g);
    value_init(old);
    value_init(tmp);
    m = Matrix_Alloc(row->Size, row->Size);
    for (j = 0; j < row->Size; ++j) {
        value_assign(m->p[0][j], row->p[j]);
    }
    value_assign(g, row->p[0]);
    for (i = 1; value_zero_p(g) && i < row->Size; ++i) {
        for (j = 0; j < row->Size; ++j) {
            if (j == i-1)
                value_set_si(m->p[i][j], 1);
            else
                value_set_si(m->p[i][j], 0);
        }
        value_assign(g, row->p[i]);
    }
    for (; i < row->Size; ++i) {
        value_assign(old, g);
        Extended_Euclid(old, row->p[i], &c, &b, &g);
        value_oppose(b, b);
        for (j = 0; j < row->Size; ++j) {
            if (j < i) {
                value_multiply(tmp, row->p[j], b);
                value_division(m->p[i][j], tmp, old);
            } else if (j == i)
                value_assign(m->p[i][j], c);
            else
                value_set_si(m->p[i][j], 0);
        }
    }
    value_clear(b);
    value_clear(c);
    value_clear(g);
    value_clear(old);
    value_clear(tmp);
    return m;
}

/*
 * Returns a full-dimensional polyhedron with the same number
 * of integer points as P
 */
Polyhedron *remove_equalities(Polyhedron *P)
{
    Value g;
    Vector *v;
    Polyhedron *p = Polyhedron_Copy(P), *q;
    unsigned dim = p->Dimension;
    Matrix *m1, *m2;
    int i;

    value_init(g);
    while (!emptyQ2(p) && p->NbEq > 0) {
        assert(dim > 0);
        Vector_Gcd(p->Constraint[0]+1, dim+1, &g);
        Vector_AntiScale(p->Constraint[0]+1, p->Constraint[0]+1, g, dim+1);
        Vector_Gcd(p->Constraint[0]+1, dim, &g);
        if (value_notone_p(g) && value_notmone_p(g)) {
            Polyhedron_Free(p);
            p = Empty_Polyhedron(0);
            break;
        }
        v = Vector_Alloc(dim);
        Vector_Copy(p->Constraint[0]+1, v->p, dim);
        m1 = unimodular_complete(v);
        m2 = Matrix_Alloc(dim, dim+1);
        for (i = 0; i < dim-1 ; ++i) {
            Vector_Copy(m1->p[i+1], m2->p[i], dim);
            value_set_si(m2->p[i][dim], 0);
        }
        Vector_Set(m2->p[dim-1], 0, dim);
        value_set_si(m2->p[dim-1][dim], 1);
        q = Polyhedron_Image(p, m2, p->NbConstraints+1+p->NbRays);
        Vector_Free(v);
        Matrix_Free(m1);
        Matrix_Free(m2);
        Polyhedron_Free(p);
        p = q;
        --dim;
    }
    value_clear(g);
    return p;
}

/*
 * Returns a full-dimensional polyhedron with the same number
 * of integer points as P
 * nvar specifies the number of variables
 * The remaining dimensions are assumed to be parameters
 * Destroys P
 * factor is NbEq x (nparam+2) matrix, containing stride constraints
 * on the parameters; column nparam is the constant;
 * column nparam+1 is the stride
 *
 * if factor is NULL, only remove equalities that don't affect
 * the number of points
 */
Polyhedron *remove_equalities_p(Polyhedron *P, unsigned nvar, Matrix **factor)
{
    Value g;
    Vector *v;
    Polyhedron *p = P, *q;
    unsigned dim = p->Dimension;
    Matrix *m1, *m2, *f;
    int i, j, skip;

    value_init(g);
    if (factor) {
        f = Matrix_Alloc(p->NbEq, dim-nvar+2);
        *factor = f;
    }
    j = 0;
    skip = 0;
    while (nvar > 0 && p->NbEq - skip > 0) {
        assert(dim > 0);

        while (skip < p->NbEq &&
               First_Non_Zero(p->Constraint[skip]+1, nvar) == -1)
            ++skip;
        if (p->NbEq == skip)
            break;

        Vector_Gcd(p->Constraint[skip]+1, dim+1, &g);
        Vector_AntiScale(p->Constraint[skip]+1, p->Constraint[skip]+1, g, dim+1);
        Vector_Gcd(p->Constraint[skip]+1, nvar, &g);
        if (!factor && value_notone_p(g) && value_notmone_p(g)) {
            ++skip;
            continue;
        }
        if (factor) {
            Vector_Copy(p->Constraint[skip]+1+nvar, f->p[j], dim-nvar+1);
            value_assign(f->p[j][dim-nvar+1], g);
        }
        v = Vector_Alloc(dim);
        Vector_AntiScale(p->Constraint[skip]+1, v->p, g, nvar);
        Vector_Set(v->p+nvar, 0, dim-nvar);
        m1 = unimodular_complete(v);
        m2 = Matrix_Alloc(dim, dim+1);
        for (i = 0; i < dim-1 ; ++i) {
            Vector_Copy(m1->p[i+1], m2->p[i], dim);
            value_set_si(m2->p[i][dim], 0);
        }
        Vector_Set(m2->p[dim-1], 0, dim);
        value_set_si(m2->p[dim-1][dim], 1);
        q = Polyhedron_Image(p, m2, p->NbConstraints+1+p->NbRays);
        Vector_Free(v);
        Matrix_Free(m1);
        Matrix_Free(m2);
        Polyhedron_Free(p);
        p = q;
        --dim;
        --nvar;
        ++j;
    }
    value_clear(g);
    return p;
}

void Line_Length(Polyhedron *P, Value *len)
{
    Value tmp, pos, neg;
    int p = 0, n = 0;
    int i;

    assert(P->Dimension == 1);

    value_init(tmp);
    value_init(pos);
    value_init(neg);

    for (i = 0; i < P->NbConstraints; ++i) {
        value_oppose(tmp, P->Constraint[i][2]);
        if (value_pos_p(P->Constraint[i][1])) {
            mpz_cdiv_q(tmp, tmp, P->Constraint[i][1]);
            if (!p || value_gt(tmp, pos))
                value_assign(pos, tmp);
            p = 1;
        } else {
            mpz_fdiv_q(tmp, tmp, P->Constraint[i][1]);
            if (!n || value_lt(tmp, neg))
                value_assign(neg, tmp);
            n = 1;
        }
        if (n && p) {
            value_subtract(tmp, neg, pos);
            value_increment(*len, tmp);
        } else
            value_set_si(*len, -1);
    }

    value_clear(tmp);
    value_clear(pos);
    value_clear(neg);
}

/*
 * Factors the polyhedron P into polyhedra Q_i such that
 * the number of integer points in P is equal to the product
 * of the number of integer points in the individual Q_i
 *
 * If no factors can be found, NULL is returned.
 * Otherwise, a linked list of the factors is returned.
 *
 * The algorithm works by first computing the Hermite normal form
 * and then grouping columns linked by one or more constraints together,
 * where a constraints "links" two or more columns if the constraint
 * has nonzero coefficients in the columns.
 */
Polyhedron* Polyhedron_Factor(Polyhedron *P, unsigned nparam, 
                              unsigned NbMaxRays)
{
    int i, j, k;
    Matrix *M, *H, *Q, *U;
    int *pos;           /* for each column: row position of pivot */
    int *group;         /* group to which a column belongs */
    int *cnt;           /* number of columns in the group */
    int *rowgroup;      /* group to which a constraint belongs */
    int nvar = P->Dimension - nparam;
    Polyhedron *F = NULL;

    if (nvar <= 1)
        return NULL;

    NALLOC(pos, nvar);
    NALLOC(group, nvar);
    NALLOC(cnt, nvar);
    NALLOC(rowgroup, P->NbConstraints);

    M = Matrix_Alloc(P->NbConstraints, nvar);
    for (i = 0; i < P->NbConstraints; ++i)
        Vector_Copy(P->Constraint[i]+1, M->p[i], nvar);
    left_hermite(M, &H, &Q, &U);
    Matrix_Free(M);
    Matrix_Free(Q);
    Matrix_Free(U);

    for (i = 0; i < P->NbConstraints; ++i)
        rowgroup[i] = -1;
    for (i = 0, j = 0; i < H->NbColumns; ++i) {
        for ( ; j < H->NbRows; ++j)
            if (value_notzero_p(H->p[j][i]))
                break;
        assert (j < H->NbRows);
        pos[i] = j;
    }
    for (i = 0; i < nvar; ++i) {
        group[i] = i;
        cnt[i] = 1;
    }
    for (i = 0; i < H->NbColumns && cnt[0] < nvar; ++i) {
        if (rowgroup[pos[i]] == -1)
            rowgroup[pos[i]] = i;
        for (j = pos[i]+1; j <  H->NbRows; ++j) {
            if (value_zero_p(H->p[j][i]))
                continue;
            if (rowgroup[j] != -1)
                continue;
            rowgroup[j] = group[i];
            for (k = i+1; k < H->NbColumns && j >= pos[k]; ++k) {
                int g = group[k];
                while (cnt[g] == 0)
                    g = group[g];
                group[k] = g;
                if (group[k] != group[i] && value_notzero_p(H->p[j][k])) {
                    assert(cnt[group[k]] != 0);
                    assert(cnt[group[i]] != 0);
                    if (group[i] < group[k]) {
                        cnt[group[i]] += cnt[group[k]];
                        cnt[group[k]] = 0;
                        group[k] = group[i];
                    } else {
                        cnt[group[k]] += cnt[group[i]];
                        cnt[group[i]] = 0;
                        group[i] = group[k];
                    }
                }
            }
        }
    }

    if (cnt[0] != nvar) {
        /* Extract out pure context constraints separately */
        Polyhedron **next = &F;
        for (i = nparam ? -1 : 0; i < nvar; ++i) {
            int d;

            if (i == -1) {
                for (j = 0, k = 0; j < P->NbConstraints; ++j)
                    if (rowgroup[j] == -1) {
                        if (First_Non_Zero(P->Constraint[j]+1+nvar, 
                                           nparam) == -1)
                            rowgroup[j] = -2;
                        else 
                            ++k;
                    }
                if (k == 0)
                    continue;
                d = 0;
            } else {
                if (cnt[i] == 0)
                    continue;
                d = cnt[i];
                for (j = 0, k = 0; j < P->NbConstraints; ++j)
                    if (rowgroup[j] >= 0 && group[rowgroup[j]] == i) {
                        rowgroup[j] = i;
                        ++k;
                    }
            }

            M = Matrix_Alloc(k, d+nparam+2);
            for (j = 0, k = 0; j < P->NbConstraints; ++j) {
                int l, m;
                if (rowgroup[j] != i)
                    continue;
                value_assign(M->p[k][0], P->Constraint[j][0]);
                for (l = 0, m = 0; m < d; ++l) {
                    if (group[l] != i)
                        continue;
                    value_assign(M->p[k][1+m++], H->p[j][l]);
                }
                Vector_Copy(P->Constraint[j]+1+nvar, M->p[k]+1+m, nparam+1);
                ++k;
            }
            *next = Constraints2Polyhedron(M, NbMaxRays);
            next = &(*next)->next;
            Matrix_Free(M);
        }
    }
    Matrix_Free(H);
    free(pos);
    free(group);
    free(cnt);
    free(rowgroup);
    return F;
}

/*
 * Project on final dim dimensions
 */
Polyhedron* Polyhedron_Project(Polyhedron *P, int dim)
{
    int i;
    int remove = P->Dimension - dim;
    Matrix *T;
    Polyhedron *I;

    if (P->Dimension == dim)
        return Polyhedron_Copy(P);

    T = Matrix_Alloc(dim+1, P->Dimension+1);
    for (i = 0; i < dim+1; ++i)
        value_set_si(T->p[i][i+remove], 1);
    I = Polyhedron_Image(P, T, P->NbConstraints);
    Matrix_Free(T);
    return I;
}

/* Constructs a new constraint that ensures that
 * the first constraint is (strictly) smaller than
 * the second.
 */
static void smaller_constraint(Value *a, Value *b, Value *c, int pos, int shift,
                        int len, int strict, Value *tmp)
{
    value_oppose(*tmp, b[pos+1]);
    value_set_si(c[0], 1);
    Vector_Combine(a+1+shift, b+1+shift, c+1, *tmp, a[pos+1], len-shift-1);
    if (strict)
        value_decrement(c[len-shift-1], c[len-shift-1]);
    ConstraintSimplify(c, c, len-shift, tmp);
}

struct section { Polyhedron * D; evalue E; };

evalue * ParamLine_Length_mod(Polyhedron *P, Polyhedron *C, int MaxRays)
{
    unsigned dim = P->Dimension;
    unsigned nvar = dim - C->Dimension;
    int *pos;
    int i, j, p, n, z;
    struct section *s;
    Matrix *M, *M2;
    int nd = 0;
    int k, l, k2, l2, q;
    evalue *L, *U;
    evalue *F;
    Value g;
    Polyhedron *T;
    evalue mone;

    assert(nvar == 1);

    NALLOC(pos, P->NbConstraints);
    value_init(g);
    value_init(mone.d);
    evalue_set_si(&mone, -1, 1);

    for (i = 0, z = 0; i < P->NbConstraints; ++i)
        if (value_zero_p(P->Constraint[i][1]))
            ++z;
    /* put those with positive coefficients first; number: p */
    for (i = 0, p = 0, n = P->NbConstraints-z-1; i < P->NbConstraints; ++i)
        if (value_pos_p(P->Constraint[i][1]))
            pos[p++] = i;
        else if (value_neg_p(P->Constraint[i][1]))
            pos[n--] = i;
    n = P->NbConstraints-z-p;
    assert (p >= 1 && n >= 1);
    s = (struct section *) malloc(p * n * sizeof(struct section));
    M = Matrix_Alloc((p-1) + (n-1), dim-nvar+2);
    for (k = 0; k < p; ++k) {
        for (k2 = 0; k2 < p; ++k2) {
            if (k2 == k)
                continue;
            q = k2 - (k2 > k);
            smaller_constraint(
                P->Constraint[pos[k]],
                P->Constraint[pos[k2]],
                M->p[q], 0, nvar, dim+2, k2 > k, &g);
        }
        for (l = p; l < p+n; ++l) {
            for (l2 = p; l2 < p+n; ++l2) {
                if (l2 == l)
                    continue;
                q = l2-1 - (l2 > l);
                smaller_constraint(
                    P->Constraint[pos[l2]],
                    P->Constraint[pos[l]],
                    M->p[q], 0, nvar, dim+2, l2 > l, &g);
            }
            M2 = Matrix_Copy(M);
            T = Constraints2Polyhedron(M2, P->NbRays);
            Matrix_Free(M2);
            s[nd].D = DomainIntersection(T, C, MaxRays);
            Domain_Free(T);
            POL_ENSURE_VERTICES(s[nd].D);
            if (emptyQ(s[nd].D)) {
                Polyhedron_Free(s[nd].D);
                continue;
            }
            L = bv_ceil3(P->Constraint[pos[k]]+1+nvar, 
                      dim-nvar+1,
                      P->Constraint[pos[k]][0+1], s[nd].D);
            U = bv_ceil3(P->Constraint[pos[l]]+1+nvar, 
                      dim-nvar+1,
                      P->Constraint[pos[l]][0+1], s[nd].D);
            eadd(L, U);
            eadd(&mone, U);
            emul(&mone, U);
            s[nd].E = *U;
            free_evalue_refs(L); 
            free(L);
            free(U);
            ++nd;
        }
    }

    Matrix_Free(M);

    F = ALLOC(evalue);
    value_init(F->d);
    value_set_si(F->d, 0);
    F->x.p = new_enode(partition, 2*nd, dim-nvar);
    for (k = 0; k < nd; ++k) {
        EVALUE_SET_DOMAIN(F->x.p->arr[2*k], s[k].D);
        value_clear(F->x.p->arr[2*k+1].d);
        F->x.p->arr[2*k+1] = s[k].E;
    }
    free(s);

    free_evalue_refs(&mone); 
    value_clear(g);
    free(pos);

    return F;
}

#ifdef USE_MODULO
evalue* ParamLine_Length(Polyhedron *P, Polyhedron *C, unsigned MaxRays)
{
    return ParamLine_Length_mod(P, C, MaxRays);
}
#else
evalue* ParamLine_Length(Polyhedron *P, Polyhedron *C, unsigned MaxRays)
{
    evalue* tmp;
    tmp = ParamLine_Length_mod(P, C, MaxRays);
    evalue_mod2table(tmp, C->Dimension);
    reduce_evalue(tmp);
    return tmp;
}
#endif

Bool isIdentity(Matrix *M)
{
    unsigned i, j;
    if (M->NbRows != M->NbColumns)
        return False;

    for (i = 0;i < M->NbRows; i ++)
        for (j = 0; j < M->NbColumns; j ++)
            if (i == j) {
                if(value_notone_p(M->p[i][j]))
                    return False;
            } else {
                if(value_notzero_p(M->p[i][j]))
                    return False;
            }
    return True;
}

void Param_Polyhedron_Print(FILE* DST, Param_Polyhedron *PP, char **param_names)
{
  Param_Domain *P;
  Param_Vertices *V;

  for(P=PP->D;P;P=P->next) {
    
    /* prints current val. dom. */
    printf( "---------------------------------------\n" );
    printf( "Domain :\n");
    Print_Domain( stdout, P->Domain, param_names );
    
    /* scan the vertices */
    printf( "Vertices :\n");
    FORALL_PVertex_in_ParamPolyhedron(V,P,PP) {
        
      /* prints each vertex */
      Print_Vertex( stdout, V->Vertex, param_names );
      printf( "\n" );
    }
    END_FORALL_PVertex_in_ParamPolyhedron;
  }
}

void Enumeration_Print(FILE *Dst, Enumeration *en, char **params)
{
    for (; en; en = en->next) {
        Print_Domain(Dst, en->ValidityDomain, params);
        print_evalue(Dst, &en->EP, params);
    }
}

void Enumeration_Free(Enumeration *en)
{
  Enumeration *ee;

  while( en )
  {
          free_evalue_refs( &(en->EP) );
          Domain_Free( en->ValidityDomain );
          ee = en ->next;
          free( en );
          en = ee;
  }
}

void Enumeration_mod2table(Enumeration *en, unsigned nparam)
{
    for (; en; en = en->next) {
        evalue_mod2table(&en->EP, nparam);
        reduce_evalue(&en->EP);
    }
}

size_t Enumeration_size(Enumeration *en)
{
    size_t s = 0;

    for (; en; en = en->next) {
        s += domain_size(en->ValidityDomain);
        s += evalue_size(&en->EP);
    }
    return s;
}

void Free_ParamNames(char **params, int m)
{
    while (--m >= 0)
        free(params[m]);
    free(params);
}

int DomainIncludes(Polyhedron *Pol1, Polyhedron *Pol2)
{
    Polyhedron *P2;
    for ( ; Pol1; Pol1 = Pol1->next) {
        for (P2 = Pol2; P2; P2 = P2->next)
            if (!PolyhedronIncludes(Pol1, P2))
                break;
        if (!P2)
            return 1;
    }
    return 0;
}

int line_minmax(Polyhedron *I, Value *min, Value *max)
{
    int i;

    if (I->NbEq >= 1) {
        value_oppose(I->Constraint[0][2], I->Constraint[0][2]);
        /* There should never be a remainder here */
        if (value_pos_p(I->Constraint[0][1]))
            mpz_fdiv_q(*min, I->Constraint[0][2], I->Constraint[0][1]);
        else
            mpz_fdiv_q(*min, I->Constraint[0][2], I->Constraint[0][1]);
        value_assign(*max, *min);
    } else for (i = 0; i < I->NbConstraints; ++i) {
        if (value_zero_p(I->Constraint[i][1])) {
            Polyhedron_Free(I);
            return 0;
        }

        value_oppose(I->Constraint[i][2], I->Constraint[i][2]);
        if (value_pos_p(I->Constraint[i][1]))
            mpz_cdiv_q(*min, I->Constraint[i][2], I->Constraint[i][1]);
        else
            mpz_fdiv_q(*max, I->Constraint[i][2], I->Constraint[i][1]);
    }
    Polyhedron_Free(I);
    return 1;
}

/** 

PROCEDURES TO COMPUTE ENUMERATION. recursive procedure, recurse for
each imbriquation

@param pos index position of current loop index (1..hdim-1)
@param P loop domain
@param context context values for fixed indices 
@param exist    number of existential variables
@return the number of integer points in this
polyhedron 

*/
void count_points_e (int pos, Polyhedron *P, int exist, int nparam,
                     Value *context, Value *res)
{
    Value LB, UB, k, c;

    if (emptyQ(P)) {
        value_set_si(*res, 0);
        return;
    }

    value_init(LB); value_init(UB); value_init(k);
    value_set_si(LB,0);
    value_set_si(UB,0);

    if (lower_upper_bounds(pos,P,context,&LB,&UB) !=0) {
        /* Problem if UB or LB is INFINITY */
        value_clear(LB); value_clear(UB); value_clear(k);
        if (pos > P->Dimension - nparam - exist)
            value_set_si(*res, 1);
        else 
            value_set_si(*res, -1);
        return;
    }
  
#ifdef EDEBUG1
    if (!P->next) {
        int i;
        for (value_assign(k,LB); value_le(k,UB); value_increment(k,k)) {
            fprintf(stderr, "(");
            for (i=1; i<pos; i++) {
                value_print(stderr,P_VALUE_FMT,context[i]);
                fprintf(stderr,",");
            }
            value_print(stderr,P_VALUE_FMT,k);
            fprintf(stderr,")\n");
        }
    }
#endif
  
    value_set_si(context[pos],0);
    if (value_lt(UB,LB)) {
        value_clear(LB); value_clear(UB); value_clear(k);
        value_set_si(*res, 0);
        return;  
    }  
    if (!P->next) {
        if (exist)
            value_set_si(*res, 1);
        else {
            value_subtract(k,UB,LB);
            value_add_int(k,k,1);
            value_assign(*res, k);
        }
        value_clear(LB); value_clear(UB); value_clear(k);
        return;
    } 

    /*-----------------------------------------------------------------*/
    /* Optimization idea                                               */
    /*   If inner loops are not a function of k (the current index)    */
    /*   i.e. if P->Constraint[i][pos]==0 for all P following this and */
    /*        for all i,                                               */
    /*   Then CNT = (UB-LB+1)*count_points(pos+1, P->next, context)    */
    /*   (skip the for loop)                                           */
    /*-----------------------------------------------------------------*/
  
    value_init(c);
    value_set_si(*res, 0);
    for (value_assign(k,LB);value_le(k,UB);value_increment(k,k)) {
        /* Insert k in context */
        value_assign(context[pos],k);
        count_points_e(pos+1, P->next, exist, nparam, context, &c);
        if(value_notmone_p(c))
            value_addto(*res, *res, c);
        else {
            value_set_si(*res, -1);
            break;
        }
        if (pos > P->Dimension - nparam - exist &&
                value_pos_p(*res))
            break;
    }
    value_clear(c);
  
#ifdef EDEBUG11
    fprintf(stderr,"%d\n",CNT);
#endif
  
    /* Reset context */
    value_set_si(context[pos],0);
    value_clear(LB); value_clear(UB); value_clear(k);
    return;
} /* count_points_e */

int DomainContains(Polyhedron *P, Value *list_args, int len, 
                   unsigned MaxRays, int set)
{
    int i;
    Value m;

    if (P->Dimension == len)
        return in_domain(P, list_args);

    assert(set); // assume list_args is large enough
    assert((P->Dimension - len) % 2 == 0);
    value_init(m);
    for (i = 0; i < P->Dimension - len; i += 2) {
        int j, k;
        for (j = 0 ; j < P->NbEq; ++j)
            if (value_notzero_p(P->Constraint[j][1+len+i]))
                break;
        assert(j < P->NbEq);
        value_absolute(m, P->Constraint[j][1+len+i]);
        k = First_Non_Zero(P->Constraint[j]+1, len);
        assert(k != -1);
        assert(First_Non_Zero(P->Constraint[j]+1+k+1, len - k - 1) == -1);
        mpz_fdiv_q(list_args[len+i], list_args[k], m);
        mpz_fdiv_r(list_args[len+i+1], list_args[k], m);
    }
    value_clear(m);

    return in_domain(P, list_args);
}

Polyhedron *DomainConcat(Polyhedron *head, Polyhedron *tail)
{
    Polyhedron *S;
    if (!head)
        return tail;
    for (S = head; S->next; S = S->next)
        ;
    S->next = tail;
    return head;
}

#ifndef HAVE_LEXSMALLER

evalue *barvinok_lexsmaller_ev(Polyhedron *P, Polyhedron *D, unsigned dim,
                               Polyhedron *C, unsigned MaxRays)
{
    assert(0);
}

#else
#include <polylib/ranking.h>

evalue *barvinok_lexsmaller_ev(Polyhedron *P, Polyhedron *D, unsigned dim,
                               Polyhedron *C, unsigned MaxRays)
{
    evalue *ranking;
    Polyhedron *RC, *RD, *Q;
    unsigned nparam = dim + C->Dimension;
    unsigned exist;
    Polyhedron *CA;

    RC = LexSmaller(P, D, dim, C, MaxRays);
    RD = RC->next;
    RC->next = NULL;

    exist = RD->Dimension - nparam - dim;
    CA = align_context(RC, RD->Dimension, MaxRays);
    Q = DomainIntersection(RD, CA, MaxRays);
    Polyhedron_Free(CA);
    Domain_Free(RD);
    Polyhedron_Free(RC);
    RD = Q;

    for (Q = RD; Q; Q = Q->next) {
        evalue *t;
        Polyhedron *next = Q->next;
        Q->next = 0;

        t = barvinok_enumerate_e(Q, exist, nparam, MaxRays);

        if (Q == RD)
            ranking = t;
        else {
            eadd(t, ranking);
            free_evalue_refs(t);
            free(t);
        }

        Q->next = next;
    }

    Domain_Free(RD);

    return ranking;
}

Enumeration *barvinok_lexsmaller(Polyhedron *P, Polyhedron *D, unsigned dim,
                                 Polyhedron *C, unsigned MaxRays)
{
    evalue *EP = barvinok_lexsmaller_ev(P, D, dim, C, MaxRays);

    return partition2enumeration(EP);
}
#endif

/* "align" matrix to have nrows by inserting
 * the necessary number of rows and an equal number of columns in front
 */
Matrix *align_matrix(Matrix *M, int nrows)
{
    int i;
    int newrows = nrows - M->NbRows;
    Matrix *M2 = Matrix_Alloc(nrows, newrows + M->NbColumns);
    for (i = 0; i < newrows; ++i)
        value_set_si(M2->p[i][i], 1);
    for (i = 0; i < M->NbRows; ++i)
        Vector_Copy(M->p[i], M2->p[newrows+i]+newrows, M->NbColumns);
    return M2;
}

static void print_varlist(FILE *out, int n, char **names)
{
    int i;
    fprintf(out, "[");
    for (i = 0; i < n; ++i) {
        if (i)
            fprintf(out, ",");
        fprintf(out, "%s", names[i]);
    }
    fprintf(out, "]");
}

static void print_term(FILE *out, Value v, int pos, int dim, int nparam,
                       char **iter_names, char **param_names, int *first)
{
    if (value_zero_p(v)) {
        if (first && *first && pos >= dim + nparam)
            fprintf(out, "0");
        return;
    }

    if (first) {
        if (!*first && value_pos_p(v))
            fprintf(out, "+");
        *first = 0;
    }
    if (pos < dim + nparam) {
        if (value_mone_p(v))
            fprintf(out, "-");
        else if (!value_one_p(v))
            value_print(out, VALUE_FMT, v);
        if (pos < dim)
            fprintf(out, "%s", iter_names[pos]);
        else
            fprintf(out, "%s", param_names[pos-dim]);
    } else
        value_print(out, VALUE_FMT, v);
}

char **util_generate_names(int n, char *prefix)
{
    int i;
    int len = (prefix ? strlen(prefix) : 0) + 10;
    char **names = ALLOCN(char*, n);
    if (!names) {
        fprintf(stderr, "ERROR: memory overflow.\n");
        exit(1);
    }
    for (i = 0; i < n; ++i) {
        names[i] = ALLOCN(char, len);
        if (!names[i]) {
            fprintf(stderr, "ERROR: memory overflow.\n");
            exit(1);
        }
        if (!prefix)
            snprintf(names[i], len, "%d", i);
        else
            snprintf(names[i], len, "%s%d", prefix, i);
    }

    return names;
}

void util_free_names(int n, char **names)
{
    int i;
    for (i = 0; i < n; ++i)
        free(names[i]);
    free(names);
}

void Polyhedron_pprint(FILE *out, Polyhedron *P, int dim, int nparam,
                       char **iter_names, char **param_names)
{
    int i, j;
    Value tmp;

    assert(dim + nparam == P->Dimension);

    value_init(tmp);

    fprintf(out, "{ ");
    if (nparam) {
        print_varlist(out, nparam, param_names);
        fprintf(out, " -> ");
    }
    print_varlist(out, dim, iter_names);
    fprintf(out, " : ");

    if (emptyQ2(P))
        fprintf(out, "FALSE");
    else for (i = 0; i < P->NbConstraints; ++i) {
        int first = 1;
        int v = First_Non_Zero(P->Constraint[i]+1, P->Dimension);
        if (v == -1 && value_pos_p(P->Constraint[i][0]))
            continue;
        if (i)
            fprintf(out, " && ");
        if (v == -1 && value_notzero_p(P->Constraint[i][1+P->Dimension]))
            fprintf(out, "FALSE");
        else if (value_pos_p(P->Constraint[i][v+1])) {
            print_term(out, P->Constraint[i][v+1], v, dim, nparam, 
                       iter_names, param_names, NULL);
            if (value_zero_p(P->Constraint[i][0]))
                fprintf(out, " = ");
            else
                fprintf(out, " >= ");
            for (j = v+1; j <= dim+nparam; ++j) {
                value_oppose(tmp, P->Constraint[i][1+j]);
                print_term(out, tmp, j, dim, nparam, 
                           iter_names, param_names, &first);
            }
        } else {
            value_oppose(tmp, P->Constraint[i][1+v]);
            print_term(out, tmp, v, dim, nparam, 
                       iter_names, param_names, NULL);
            fprintf(out, " <= ");
            for (j = v+1; j <= dim+nparam; ++j)
                print_term(out, P->Constraint[i][1+j], j, dim, nparam, 
                           iter_names, param_names, &first);
        }
    }

    fprintf(out, " }\n");

    value_clear(tmp);
}

/* Construct a cone over P with P placed at x_d = 1, with
 * x_d the coordinate of an extra dimension
 *
 * It's probably a mistake to depend so much on the internal
 * representation.  We should probably simply compute the
 * vertices/facets first.
 */
Polyhedron *Cone_over_Polyhedron(Polyhedron *P)
{
    unsigned NbConstraints = 0;
    unsigned NbRays = 0;
    Polyhedron *C;
    int i;

    if (POL_HAS(P, POL_INEQUALITIES))
        NbConstraints = P->NbConstraints + 1;
    if (POL_HAS(P, POL_POINTS))
        NbRays = P->NbRays + 1;

    C = Polyhedron_Alloc(P->Dimension+1, NbConstraints, NbRays);
    if (POL_HAS(P, POL_INEQUALITIES)) {
        C->NbEq = P->NbEq;
        for (i = 0; i < P->NbConstraints; ++i)
            Vector_Copy(P->Constraint[i], C->Constraint[i], P->Dimension+2);
        /* n >= 0 */
        value_set_si(C->Constraint[P->NbConstraints][0], 1);
        value_set_si(C->Constraint[P->NbConstraints][1+P->Dimension], 1);
    }
    if (POL_HAS(P, POL_POINTS)) {
        C->NbBid = P->NbBid;
        for (i = 0; i < P->NbRays; ++i)
            Vector_Copy(P->Ray[i], C->Ray[i], P->Dimension+2);
        /* vertex 0 */
        value_set_si(C->Ray[P->NbRays][0], 1);
        value_set_si(C->Ray[P->NbRays][1+C->Dimension], 1);
    }
    POL_SET(C, POL_VALID);
    if (POL_HAS(P, POL_INEQUALITIES))
        POL_SET(C, POL_INEQUALITIES);
    if (POL_HAS(P, POL_POINTS))
        POL_SET(C, POL_POINTS);
    if (POL_HAS(P, POL_VERTICES))
        POL_SET(C, POL_VERTICES);
    return C;
}

Matrix *compress_variables(Matrix *Equalities, unsigned nparam)
{
    unsigned dim = (Equalities->NbColumns-2) - nparam;
    Matrix *M, *H, *Q, *U, *C, *ratH, *invH, *Ul, *T1, *T2, *T;
    Value mone;
    int n, i;
    int ok;

    for (n = 0; n < Equalities->NbRows; ++n)
        if (First_Non_Zero(Equalities->p[n]+1, dim) == -1)
            break;
    if (n == 0)
        return Identity(dim+nparam+1);
    value_init(mone);
    value_set_si(mone, -1);
    M = Matrix_Alloc(n, dim);
    C = Matrix_Alloc(n+1, nparam+1);
    for (i = 0; i < n; ++i) {
        Vector_Copy(Equalities->p[i]+1, M->p[i], dim);
        Vector_Scale(Equalities->p[i]+1+dim, C->p[i], mone, nparam+1);
    }
    value_set_si(C->p[n][nparam], 1);
    left_hermite(M, &H, &Q, &U);
    Matrix_Free(M);
    Matrix_Free(Q);
    value_clear(mone);

    /* we will need to treat scalings later */
    if (nparam > 0)
        for (i = 0; i < n; ++i)
            assert(value_one_p(H->p[i][i]));

    ratH = Matrix_Alloc(n+1, n+1);
    invH = Matrix_Alloc(n+1, n+1);
    for (i = 0; i < n; ++i)
        Vector_Copy(H->p[i], ratH->p[i], n);
    value_set_si(ratH->p[n][n], 1);
    ok = Matrix_Inverse(ratH, invH);
    assert(ok);
    Matrix_Free(H);
    Matrix_Free(ratH);
    T1 = Matrix_Alloc(n+1, nparam+1);
    Matrix_Product(invH, C, T1);
    Matrix_Free(C);
    Matrix_Free(invH);
    if (nparam == 0 && value_notone_p(T1->p[n][nparam])) {
        for (i = 0; i < n; ++i) {
            if (!mpz_divisible_p(T1->p[i][nparam], T1->p[n][nparam])) {
                Matrix_Free(T1);
                Matrix_Free(U);
                return NULL;
            }
            value_division(T1->p[i][nparam], T1->p[i][nparam], T1->p[n][nparam]);
        }
        value_set_si(T1->p[n][nparam], 1);
    }
    Ul = Matrix_Alloc(dim+1, n+1);
    for (i = 0; i < dim; ++i)
        Vector_Copy(U->p[i], Ul->p[i], n);
    value_set_si(Ul->p[dim][n], 1);
    T2 = Matrix_Alloc(dim+1, nparam+1);
    Matrix_Product(Ul, T1, T2);
    Matrix_Free(Ul);
    Matrix_Free(T1);

    T = Matrix_Alloc(dim+nparam+1, (dim-n)+nparam+1);
    for (i = 0; i < dim; ++i) {
        Vector_Copy(U->p[i]+n, T->p[i], dim-n);
        Vector_Copy(T2->p[i], T->p[i]+dim-n, nparam+1);
    }
    for (i = 0; i < nparam+1; ++i)
        value_set_si(T->p[dim+i][(dim-n)+i], 1);
    assert(value_one_p(T2->p[dim][nparam]));
    Matrix_Free(U);
    Matrix_Free(T2);

    return T;
}