/*

 * Copyright 2008-2009 Katholieke Universiteit Leuven

 * Copyright 2010      INRIA Saclay

 *

 * Use of this software is governed by the MIT license

 *

 * Written by Sven Verdoolaege, K.U.Leuven, Departement

 * Computerwetenschappen, Celestijnenlaan 200A, B-3001 Leuven, Belgium

 * and INRIA Saclay - Ile-de-France, Parc Club Orsay Universite,

 * ZAC des vignes, 4 rue Jacques Monod, 91893 Orsay, France

 */

#include <isl_mat_private.h>

#include <isl_vec_private.h>

#include <isl_seq.h>

#include "isl_map_private.h"

#include "isl_equalities.h"

#include <isl_val_private.h>

/* Given a set of modulo constraints

 *

 *    c + A y = 0 mod d

 *

 * this function computes a particular solution y_0

 *

 * The input is given as a matrix B = [ c A ] and a vector d.

 *

 * The output is matrix containing the solution y_0 or

 * a zero-column matrix if the constraints admit no integer solution.

 *

 * The given set of constrains is equivalent to

 *

 *    c + A y = -D x

 *

 * with D = diag d and x a fresh set of variables.

 * Reducing both c and A modulo d does not change the

 * value of y in the solution and may lead to smaller coefficients.

 * Let M = [ D A ] and [ H 0 ] = M U, the Hermite normal form of M.

 * Then

 *      [ x ]

 *    M [ y ] = - c

 * and so

 *                   [ x ]

 *    [ H 0 ] U^{-1} [ y ] = - c

 * Let

 *    [ A ]          [ x ]

 *    [ B ] = U^{-1} [ y ]

 * then

 *    H A + 0 B = -c

 *

 * so B may be chosen arbitrarily, e.g., B = 0, and then

 *

 *           [ x ] = [ -c ]

 *    U^{-1} [ y ] = [  0 ]

 * or

 *    [ x ]     [ -c ]

 *    [ y ] = U [  0 ]

 * specifically,

 *

 *    y = U_{2,1} (-c)

 *

 * If any of the coordinates of this y are non-integer

 * then the constraints admit no integer solution and

 * a zero-column matrix is returned.

 */

static struct isl_mat *particular_solution(struct isl_mat *B, struct isl_vec *d)

{

  int i, j;

  struct isl_mat *M = NULL;

  struct isl_mat *C = NULL;

  struct isl_mat *U = NULL;

  struct isl_mat *H = NULL;

  struct isl_mat *cst = NULL;

  struct isl_mat *T = NULL;

  M = isl_mat_alloc(B->ctx, B->n_row, B->n_row + B->n_col - 1);

  C = isl_mat_alloc(B->ctx, 1 + B->n_row, 1);

  if (!M || !C)

    goto error;

  isl_int_set_si(C->row[0][0], 1);

  for (i = 0; i < B->n_row; 
++i29.2k
) {

    isl_seq_clr(M->row[i], B->n_row);

    isl_int_set(M->row[i][i], d->block.data[i]);

    isl_int_neg(C->row[1 + i][0], B->row[i][0]);

    isl_int_fdiv_r(C->row[1+i][0], C->row[1+i][0], M->row[i][i]);

    for (j = 0; j < B->n_col - 1; 
++j132k
)

      isl_int_fdiv_r(M->row[i][B->n_row + j],

          B->row[i][1 + j], M->row[i][i]);

  }

  M = isl_mat_left_hermite(M, 0, &U, NULL);

  if (!M || !U)

    goto error;

  H = isl_mat_sub_alloc(M, 0, B->n_row, 0, B->n_row);

  H = isl_mat_lin_to_aff(H);

  C = isl_mat_inverse_product(H, C);

  if (!C)

    goto error;

  
for (i = 0; 23.4k
i < B->n_row; 
++i27.2k
) {

    if (!isl_int_is_divisible_by(C->row[1+i][0], C->row[0][0]))

      
break1.92k
;

    isl_int_divexact(C->row[1+i][0], C->row[1+i][0], C->row[0][0]);

  }

  if (i < B->n_row)

    cst = isl_mat_alloc(B->ctx, B->n_row, 0);

  else

    cst = isl_mat_sub_alloc(C, 1, B->n_row, 0, 1);

  T = isl_mat_sub_alloc(U, B->n_row, B->n_col - 1, 0, B->n_row);

  cst = isl_mat_product(T, cst);

  isl_mat_free(M);

  isl_mat_free(C);

  isl_mat_free(U);

  return cst;

error:

  isl_mat_free(M);

  isl_mat_free(C);

  isl_mat_free(U);

  return NULL;

}

/* Compute and return the matrix

 *

 *    U_1^{-1} diag(d_1, 1, ..., 1)

 *

 * with U_1 the unimodular completion of the first (and only) row of B.

 * The columns of this matrix generate the lattice that satisfies

 * the single (linear) modulo constraint.

 */

static struct isl_mat *parameter_compression_1(

      struct isl_mat *B, struct isl_vec *d)

{

  struct isl_mat *U;

  U = isl_mat_alloc(B->ctx, B->n_col - 1, B->n_col - 1);

  if (!U)

    return NULL;

  isl_seq_cpy(U->row[0], B->row[0] + 1, B->n_col - 1);

  U = isl_mat_unimodular_complete(U, 1);

  U = isl_mat_right_inverse(U);

  if (!U)

    return NULL;

  isl_mat_col_mul(U, 0, d->block.data[0], 0);

  U = isl_mat_lin_to_aff(U);

  return U;

}

/* Compute a common lattice of solutions to the linear modulo

 * constraints specified by B and d.

 * See also the documentation of isl_mat_parameter_compression.

 * We put the matrix

 * 

 *    A = [ L_1^{-T} L_2^{-T} ... L_k^{-T} ]

 *

 * on a common denominator.  This denominator D is the lcm of modulos d.

 * Since L_i = U_i^{-1} diag(d_i, 1, ... 1), we have

 * L_i^{-T} = U_i^T diag(d_i, 1, ... 1)^{-T} = U_i^T diag(1/d_i, 1, ..., 1).

 * Putting this on the common denominator, we have

 * D * L_i^{-T} = U_i^T diag(D/d_i, D, ..., D).

 */

static struct isl_mat *parameter_compression_multi(

      struct isl_mat *B, struct isl_vec *d)

{

  int i, j, k;

  isl_int D;

  struct isl_mat *A = NULL, *U = NULL;

  struct isl_mat *T;

  unsigned size;

  isl_int_init(D);

  isl_vec_lcm(d, &D);

  size = B->n_col - 1;

  A = isl_mat_alloc(B->ctx, size, B->n_row * size);

  U = isl_mat_alloc(B->ctx, size, size);

  if (!U || !A)

    goto error;

  
for (i = 0; 3.94k
i < B->n_row; 
++i8.50k
) {

    isl_seq_cpy(U->row[0], B->row[i] + 1, size);

    U = isl_mat_unimodular_complete(U, 1);

    if (!U)

      goto error;

    isl_int_divexact(D, D, d->block.data[i]);

    for (k = 0; k < U->n_col; 
++k45.7k
)

      isl_int_mul(A->row[k][i*size+0], D, U->row[0][k]);

    isl_int_mul(D, D, d->block.data[i]);

    for (j = 1; j < U->n_row; 
++j37.2k
)

      
for (k = 0; 37.2k
k < U->n_col; 
++k262k
)

        isl_int_mul(A->row[k][i*size+j],

            D, U->row[j][k]);

  }

  A = isl_mat_left_hermite(A, 0, NULL, NULL);

  T = isl_mat_sub_alloc(A, 0, A->n_row, 0, A->n_row);

  T = isl_mat_lin_to_aff(T);

  if (!T)

    goto error;

  isl_int_set(T->row[0][0], D);

  T = isl_mat_right_inverse(T);

  if (!T)

    goto error;

  isl_assert(T->ctx, isl_int_is_one(T->row[0][0]), goto error);

  T = isl_mat_transpose(T);

  isl_mat_free(A);

  isl_mat_free(U);

  isl_int_clear(D);

  return T;

error:

  isl_mat_free(A);

  isl_mat_free(U);

  isl_int_clear(D);

  return NULL;

}

/* Given a set of modulo constraints

 *

 *    c + A y = 0 mod d

 *

 * this function returns an affine transformation T,

 *

 *    y = T y'

 *

 * that bijectively maps the integer vectors y' to integer

 * vectors y that satisfy the modulo constraints.

 *

 * This function is inspired by Section 2.5.3

 * of B. Meister, "Stating and Manipulating Periodicity in the Polytope

 * Model.  Applications to Program Analysis and Optimization".

 * However, the implementation only follows the algorithm of that

 * section for computing a particular solution and not for computing

 * a general homogeneous solution.  The latter is incomplete and

 * may remove some valid solutions.

 * Instead, we use an adaptation of the algorithm in Section 7 of

 * B. Meister, S. Verdoolaege, "Polynomial Approximations in the Polytope

 * Model: Bringing the Power of Quasi-Polynomials to the Masses".

 *

 * The input is given as a matrix B = [ c A ] and a vector d.

 * Each element of the vector d corresponds to a row in B.

 * The output is a lower triangular matrix.

 * If no integer vector y satisfies the given constraints then

 * a matrix with zero columns is returned.

 *

 * We first compute a particular solution y_0 to the given set of

 * modulo constraints in particular_solution.  If no such solution

 * exists, then we return a zero-columned transformation matrix.

 * Otherwise, we compute the generic solution to

 *

 *    A y = 0 mod d

 *

 * That is we want to compute G such that

 *

 *    y = G y''

 *

 * with y'' integer, describes the set of solutions.

 *

 * We first remove the common factors of each row.

 * In particular if gcd(A_i,d_i) != 1, then we divide the whole

 * row i (including d_i) by this common factor.  If afterwards gcd(A_i) != 1,

 * then we divide this row of A by the common factor, unless gcd(A_i) = 0.

 * In the later case, we simply drop the row (in both A and d).

 *

 * If there are no rows left in A, then G is the identity matrix. Otherwise,

 * for each row i, we now determine the lattice of integer vectors

 * that satisfies this row.  Let U_i be the unimodular extension of the

 * row A_i.  This unimodular extension exists because gcd(A_i) = 1.

 * The first component of

 *

 *    y' = U_i y

 *

 * needs to be a multiple of d_i.  Let y' = diag(d_i, 1, ..., 1) y''.

 * Then,

 *

 *    y = U_i^{-1} diag(d_i, 1, ..., 1) y''

 *

 * for arbitrary integer vectors y''.  That is, y belongs to the lattice

 * generated by the columns of L_i = U_i^{-1} diag(d_i, 1, ..., 1).

 * If there is only one row, then G = L_1.

 *

 * If there is more than one row left, we need to compute the intersection

 * of the lattices.  That is, we need to compute an L such that

 *

 *    L = L_i L_i'  for all i

 *

 * with L_i' some integer matrices.  Let A be constructed as follows

 *

 *    A = [ L_1^{-T} L_2^{-T} ... L_k^{-T} ]

 *

 * and computed the Hermite Normal Form of A = [ H 0 ] U

 * Then,

 *

 *    L_i^{-T} = H U_{1,i}

 *

 * or

 *

 *    H^{-T} = L_i U_{1,i}^T

 *

 * In other words G = L = H^{-T}.

 * To ensure that G is lower triangular, we compute and use its Hermite

 * normal form.

 *

 * The affine transformation matrix returned is then

 *

 *    [  1   0  ]

 *    [ y_0  G  ]

 *

 * as any y = y_0 + G y' with y' integer is a solution to the original

 * modulo constraints.

 */

__isl_give isl_mat *isl_mat_parameter_compression(__isl_take isl_mat *B,

  __isl_take isl_vec *d)

{

  int i;

  struct isl_mat *cst = NULL;

  struct isl_mat *T = NULL;

  isl_int D;

  if (!B || !d)

    goto error;

  isl_assert(B->ctx, B->n_row == d->size, goto error);

  cst = particular_solution(B, d);

  if (!cst)

    goto error;

  if (cst->n_col == 0) {

    T = isl_mat_alloc(B->ctx, B->n_col, 0);

    isl_mat_free(cst);

    isl_mat_free(B);

    isl_vec_free(d);

    return T;

  }

  isl_int_init(D);

  /* Replace a*g*row = 0 mod g*m by row = 0 mod m */

  for (i = 0; i < B->n_row; 
++i26.2k
) {

    isl_seq_gcd(B->row[i] + 1, B->n_col - 1, &D);

    if (isl_int_is_one(D))

      
continue24.7k
;

    if (isl_int_is_zero(D)) {

      B = isl_mat_drop_rows(B, i, 1);

      d = isl_vec_cow(d);

      if (!B || !d)

        goto error2;

      isl_seq_cpy(d->block.data+i, d->block.data+i+1,

              d->size - (i+1));

      d->size--;

      i--;

      continue;

    }

    B = isl_mat_cow(B);

    if (!B)

      goto error2;

    isl_seq_scale_down(B->row[i] + 1, B->row[i] + 1, D, B->n_col-1);

    isl_int_gcd(D, D, d->block.data[i]);

    d = isl_vec_cow(d);

    if (!d)

      goto error2;

    isl_int_divexact(d->block.data[i], d->block.data[i], D);

  }

  isl_int_clear(D);

  if (B->n_row == 0)

    T = isl_mat_identity(B->ctx, B->n_col);

  else if (B->n_row == 1)

    T = parameter_compression_1(B, d);

  else

    T = parameter_compression_multi(B, d);

  T = isl_mat_left_hermite(T, 0, NULL, NULL);

  if (!T)

    goto error;

  isl_mat_sub_copy(T->ctx, T->row + 1, cst->row, cst->n_row, 0, 0, 1);

  isl_mat_free(cst);

  isl_mat_free(B);

  isl_vec_free(d);

  return T;

error2:

  isl_int_clear(D);

error:

  isl_mat_free(cst);

  isl_mat_free(B);

  isl_vec_free(d);

  return NULL;

}

/* Given a set of equalities

 *

 *    B(y) + A x = 0            (*)

 *

 * compute and return an affine transformation T,

 *

 *    y = T y'

 *

 * that bijectively maps the integer vectors y' to integer

 * vectors y that satisfy the modulo constraints for some value of x.

 *

 * Let [H 0] be the Hermite Normal Form of A, i.e.,

 *

 *    A = [H 0] Q

 *

 * Then y is a solution of (*) iff

 *

 *    H^-1 B(y) (= - [I 0] Q x)

 *

 * is an integer vector.  Let d be the common denominator of H^-1.

 * We impose

 *

 *    d H^-1 B(y) = 0 mod d

 *

 * and compute the solution using isl_mat_parameter_compression.

 */

__isl_give isl_mat *isl_mat_parameter_compression_ext(__isl_take isl_mat *B,

  __isl_take isl_mat *A)

{

  isl_ctx *ctx;

  isl_vec *d;

  int n_row, n_col;

  if (!A)

    return isl_mat_free(B);

  ctx = isl_mat_get_ctx(A);

  n_row = A->n_row;

  n_col = A->n_col;

  A = isl_mat_left_hermite(A, 0, NULL, NULL);

  A = isl_mat_drop_cols(A, n_row, n_col - n_row);

  A = isl_mat_lin_to_aff(A);

  A = isl_mat_right_inverse(A);

  d = isl_vec_alloc(ctx, n_row);

  if (A)

    d = isl_vec_set(d, A->row[0][0]);

  A = isl_mat_drop_rows(A, 0, 1);

  A = isl_mat_drop_cols(A, 0, 1);

  B = isl_mat_product(A, B);

  return isl_mat_parameter_compression(B, d);

}

/* Return a compression matrix that indicates that there are no solutions

 * to the original constraints.  In particular, return a zero-column

 * matrix with 1 + dim rows.  If "T2" is not NULL, then assign *T2

 * the inverse of this matrix.  *T2 may already have been assigned

 * matrix, so free it first.

 * "free1", "free2" and "free3" are temporary matrices that are

 * not useful when an empty compression is returned.  They are

 * simply freed.

 */

static __isl_give isl_mat *empty_compression(isl_ctx *ctx, unsigned dim,

  __isl_give isl_mat **T2, __isl_take isl_mat *free1,

  __isl_take isl_mat *free2, __isl_take isl_mat *free3)

{

  isl_mat_free(free1);

  isl_mat_free(free2);

  isl_mat_free(free3);

  if (T2) {

    isl_mat_free(*T2);

    *T2 = isl_mat_alloc(ctx, 0, 1 + dim);

  }

  return isl_mat_alloc(ctx, 1 + dim, 0);

}

/* Given a matrix that maps a (possibly) parametric domain to

 * a parametric domain, add in rows that map the "nparam" parameters onto

 * themselves.

 */

static __isl_give isl_mat *insert_parameter_rows(__isl_take isl_mat *mat,

  unsigned nparam)

{

  int i;

  if (nparam == 0)

    return mat;

  if (!mat)

    return NULL;

  mat = isl_mat_insert_rows(mat, 1, nparam);

  if (!mat)

    return NULL;

  
for (i = 0; 1
i < nparam; 
++i1
) {

    isl_seq_clr(mat->row[1 + i], mat->n_col);

    isl_int_set(mat->row[1 + i][1 + i], mat->row[0][0]);

  }

  return mat;

}

/* Given a set of equalities

 *

 *    -C(y) + M x = 0

 *

 * this function computes a unimodular transformation from a lower-dimensional

 * space to the original space that bijectively maps the integer points x'

 * in the lower-dimensional space to the integer points x in the original

 * space that satisfy the equalities.

 *

 * The input is given as a matrix B = [ -C M ] and the output is a

 * matrix that maps [1 x'] to [1 x].

 * The number of equality constraints in B is assumed to be smaller than

 * or equal to the number of variables x.

 * "first" is the position of the first x variable.

 * The preceding variables are considered to be y-variables.

 * If T2 is not NULL, then *T2 is set to a matrix mapping [1 x] to [1 x'].

 *

 * First compute the (left) Hermite normal form of M,

 *

 *    M [U1 U2] = M U = H = [H1 0]

 * or

 *                  M = H Q = [H1 0] [Q1]

 *                                             [Q2]

 *

 * with U, Q unimodular, Q = U^{-1} (and H lower triangular).

 * Define the transformed variables as

 *

 *    x = [U1 U2] [ x1' ] = [U1 U2] [Q1] x

 *                [ x2' ]           [Q2]

 *

 * The equalities then become

 *

 *    -C(y) + H1 x1' = 0   or   x1' = H1^{-1} C(y) = C'(y)

 *

 * If the denominator of the constant term does not divide the

 * the common denominator of the coefficients of y, then every

 * integer point is mapped to a non-integer point and then the original set

 * has no integer solutions (since the x' are a unimodular transformation

 * of the x).  In this case, a zero-column matrix is returned.

 * Otherwise, the transformation is given by

 *

 *    x = U1 H1^{-1} C(y) + U2 x2'

 *

 * The inverse transformation is simply

 *

 *    x2' = Q2 x

 */

__isl_give isl_mat *isl_mat_final_variable_compression(__isl_take isl_mat *B,

  int first, __isl_give isl_mat **T2)

{

  int i, n;

  isl_ctx *ctx;

  isl_mat *H = NULL, *C, *H1, *U = NULL, *U1, *U2;

  unsigned dim;

  if (T2)

    *T2 = NULL;

  if (!B)

    goto error;

  ctx = isl_mat_get_ctx(B);

  dim = B->n_col - 1;

  n = dim - first;

  if (n < B->n_row)

    
isl_die0
(ctx, isl_error_invalid, "too many equality constraints",

      goto error);

  H = isl_mat_sub_alloc(B, 0, B->n_row, 1 + first, n);

  H = isl_mat_left_hermite(H, 0, &U, T2);

  if (!H || !U || (T2 && 
!*T2147k
))

    goto error;

  if (T2) {

    *T2 = isl_mat_drop_rows(*T2, 0, B->n_row);

    *T2 = isl_mat_diagonal(isl_mat_identity(ctx, 1 + first), *T2);

    if (!*T2)

      goto error;

  }

  C = isl_mat_alloc(ctx, 1 + B->n_row, 1 + first);

  if (!C)

    goto error;

  isl_int_set_si(C->row[0][0], 1);

  isl_seq_clr(C->row[0] + 1, first);

  isl_mat_sub_neg(ctx, C->row + 1, B->row, B->n_row, 0, 0, 1 + first);

  H1 = isl_mat_sub_alloc(H, 0, H->n_row, 0, H->n_row);

  H1 = isl_mat_lin_to_aff(H1);

  C = isl_mat_inverse_product(H1, C);

  if (!C)

    goto error;

  isl_mat_free(H);

  if (!isl_int_is_one(C->row[0][0])) {

    isl_int g;

    isl_int_init(g);

    for (i = 0; i < B->n_row; 
++i3.69k
) {

      isl_seq_gcd(C->row[1 + i] + 1, first, &g);

      isl_int_gcd(g, g, C->row[0][0]);

      if (!isl_int_is_divisible_by(C->row[1 + i][0], g))

        
break6
;

    }

    isl_int_clear(g);

    if (i < B->n_row)

      return empty_compression(ctx, dim, T2, B, C, U);

    C = isl_mat_normalize(C);

  }

  U1 = isl_mat_sub_alloc(U, 0, U->n_row, 0, B->n_row);

  U1 = isl_mat_lin_to_aff(U1);

  U2 = isl_mat_sub_alloc(U, 0, U->n_row, B->n_row, U->n_row - B->n_row);

  U2 = isl_mat_lin_to_aff(U2);

  isl_mat_free(U);

  C = isl_mat_product(U1, C);

  C = isl_mat_aff_direct_sum(C, U2);

  C = insert_parameter_rows(C, first);

  isl_mat_free(B);

  return C;

error:

  isl_mat_free(B);

  isl_mat_free(H);

  isl_mat_free(U);

  if (T2) {

    isl_mat_free(*T2);

    *T2 = NULL;

  }

  return NULL;

}

/* Given a set of equalities

 *

 *    M x - c = 0

 *

 * this function computes a unimodular transformation from a lower-dimensional

 * space to the original space that bijectively maps the integer points x'

 * in the lower-dimensional space to the integer points x in the original

 * space that satisfy the equalities.

 *

 * The input is given as a matrix B = [ -c M ] and the output is a

 * matrix that maps [1 x'] to [1 x].

 * The number of equality constraints in B is assumed to be smaller than

 * or equal to the number of variables x.

 * If T2 is not NULL, then *T2 is set to a matrix mapping [1 x] to [1 x'].

 */

__isl_give isl_mat *isl_mat_variable_compression(__isl_take isl_mat *B,

  __isl_give isl_mat **T2)

{

  return isl_mat_final_variable_compression(B, 0, T2);

}

/* Return "bset" and set *T and *T2 to the identity transformation

 * on "bset" (provided T and T2 are not NULL).

 */

static __isl_give isl_basic_set *return_with_identity(

  __isl_take isl_basic_set *bset, __isl_give isl_mat **T,

  __isl_give isl_mat **T2)

{

  unsigned dim;

  isl_mat *id;

  if (!bset)

    return NULL;

  if (!T && 
!T20
)

    return bset;

  dim = isl_basic_set_dim(bset, isl_dim_set);

  id = isl_mat_identity(isl_basic_map_get_ctx(bset), 1 + dim);

  if (T)

    *T = isl_mat_copy(id);

  if (T2)

    *T2 = isl_mat_copy(id);

  isl_mat_free(id);

  return bset;

}

/* Use the n equalities of bset to unimodularly transform the

 * variables x such that n transformed variables x1' have a constant value

 * and rewrite the constraints of bset in terms of the remaining

 * transformed variables x2'.  The matrix pointed to by T maps

 * the new variables x2' back to the original variables x, while T2

 * maps the original variables to the new variables.

 */

static struct isl_basic_set *compress_variables(

  struct isl_basic_set *bset, struct isl_mat **T, struct isl_mat **T2)

{

  struct isl_mat *B, *TC;

  unsigned dim;

  if (T)

    *T = NULL;

  if (T2)

    *T2 = NULL;

  if (!bset)

    goto error;

  isl_assert(bset->ctx, isl_basic_set_n_param(bset) == 0, goto error);

  isl_assert(bset->ctx, bset->n_div == 0, goto error);

  dim = isl_basic_set_n_dim(bset);

  isl_assert(bset->ctx, bset->n_eq <= dim, goto error);

  if (bset->n_eq == 0)

    return return_with_identity(bset, T, T2);

  B = isl_mat_sub_alloc6(bset->ctx, bset->eq, 0, bset->n_eq, 0, 1 + dim);

  TC = isl_mat_variable_compression(B, T2);

  if (!TC)

    goto error;

  if (TC->n_col == 0) {

    isl_mat_free(TC);

    if (T2) {

      isl_mat_free(*T2);

      *T2 = NULL;

    }

    bset = isl_basic_set_set_to_empty(bset);

    return return_with_identity(bset, T, T2);

  }

  bset = isl_basic_set_preimage(bset, T ? isl_mat_copy(TC) : 
TC0
);

  if (T)

    *T = TC;

  return bset;

error:

  isl_basic_set_free(bset);

  return NULL;

}

struct isl_basic_set *isl_basic_set_remove_equalities(

  struct isl_basic_set *bset, struct isl_mat **T, struct isl_mat **T2)

{

  if (T)

    *T = NULL;

  if (T2)

    *T2 = NULL;

  if (!bset)

    return NULL;

  isl_assert(bset->ctx, isl_basic_set_n_param(bset) == 0, goto error);

  bset = isl_basic_set_gauss(bset, NULL);

  if (ISL_F_ISSET(bset, ISL_BASIC_SET_EMPTY))

    
return return_with_identity(bset, T, T2)0
;

  bset = compress_variables(bset, T, T2);

  return bset;

error:

  isl_basic_set_free(bset);

  *T = NULL;

  return NULL;

}

/* Check if dimension dim belongs to a residue class

 *    i_dim \equiv r mod m

 * with m != 1 and if so return m in *modulo and r in *residue.

 * As a special case, when i_dim has a fixed value v, then

 * *modulo is set to 0 and *residue to v.

 *

 * If i_dim does not belong to such a residue class, then *modulo

 * is set to 1 and *residue is set to 0.

 */

isl_stat isl_basic_set_dim_residue_class(__isl_keep isl_basic_set *bset,

  int pos, isl_int *modulo, isl_int *residue)

{

  isl_bool fixed;

  struct isl_ctx *ctx;

  struct isl_mat *H = NULL, *U = NULL, *C, *H1, *U1;

  unsigned total;

  unsigned nparam;

  if (!bset || !modulo || !residue)

    return isl_stat_error;

  fixed = isl_basic_set_plain_dim_is_fixed(bset, pos, residue);

  if (fixed < 0)

    return isl_stat_error;

  if (fixed) {

    isl_int_set_si(*modulo, 0);

    return isl_stat_ok;

  }

  ctx = isl_basic_set_get_ctx(bset);

  total = isl_basic_set_total_dim(bset);

  nparam = isl_basic_set_n_param(bset);

  H = isl_mat_sub_alloc6(ctx, bset->eq, 0, bset->n_eq, 1, total);

  H = isl_mat_left_hermite(H, 0, &U, NULL);

  if (!H)

    return isl_stat_error;

  isl_seq_gcd(U->row[nparam + pos]+bset->n_eq,

      total-bset->n_eq, modulo);

  if (isl_int_is_zero(*modulo))

    
isl_int_set_si0
(*modulo, 1);

  if (isl_int_is_one(*modulo)) {

    isl_int_set_si(*residue, 0);

    isl_mat_free(H);

    isl_mat_free(U);

    return isl_stat_ok;

  }

  C = isl_mat_alloc(ctx, 1 + bset->n_eq, 1);

  if (!C)

    goto error;

  isl_int_set_si(C->row[0][0], 1);

  isl_mat_sub_neg(ctx, C->row + 1, bset->eq, bset->n_eq, 0, 0, 1);

  H1 = isl_mat_sub_alloc(H, 0, H->n_row, 0, H->n_row);

  H1 = isl_mat_lin_to_aff(H1);

  C = isl_mat_inverse_product(H1, C);

  isl_mat_free(H);

  U1 = isl_mat_sub_alloc(U, nparam+pos, 1, 0, bset->n_eq);

  U1 = isl_mat_lin_to_aff(U1);

  isl_mat_free(U);

  C = isl_mat_product(U1, C);

  if (!C)

    return isl_stat_error;

  if (!isl_int_is_divisible_by(C->row[1][0], C->row[0][0])) {

    bset = isl_basic_set_copy(bset);

    bset = isl_basic_set_set_to_empty(bset);

    isl_basic_set_free(bset);

    isl_int_set_si(*modulo, 1);

    isl_int_set_si(*residue, 0);

    return isl_stat_ok;

  }

  isl_int_divexact(*residue, C->row[1][0], C->row[0][0]);

  isl_int_fdiv_r(*residue, *residue, *modulo);

  isl_mat_free(C);

  return isl_stat_ok;

error:

  isl_mat_free(H);

  isl_mat_free(U);

  return isl_stat_error;

}

/* Check if dimension dim belongs to a residue class

 *    i_dim \equiv r mod m

 * with m != 1 and if so return m in *modulo and r in *residue.

 * As a special case, when i_dim has a fixed value v, then

 * *modulo is set to 0 and *residue to v.

 *

 * If i_dim does not belong to such a residue class, then *modulo

 * is set to 1 and *residue is set to 0.

 */

isl_stat isl_set_dim_residue_class(__isl_keep isl_set *set,

  int pos, isl_int *modulo, isl_int *residue)

{

  isl_int m;

  isl_int r;

  int i;

  if (!set || !modulo || !residue)

    return isl_stat_error;

  if (set->n == 0) {

    isl_int_set_si(*modulo, 0);

    isl_int_set_si(*residue, 0);

    return isl_stat_ok;

  }

  if (isl_basic_set_dim_residue_class(set->p[0], pos, modulo, residue)<0)

    return isl_stat_error;

  if (set->n == 1)

    return isl_stat_ok;

  if (isl_int_is_one(*modulo))

    
return isl_stat_ok9
;

  isl_int_init(m);

  isl_int_init(r);

  for (i = 1; i < set->n; 
++i1
) {

    if (isl_basic_set_dim_residue_class(set->p[i], pos, &m, &r) < 0)

      goto error;

    isl_int_gcd(*modulo, *modulo, m);

    isl_int_sub(m, *residue, r);

    isl_int_gcd(*modulo, *modulo, m);

    if (!isl_int_is_zero(*modulo))

      isl_int_fdiv_r(*residue, *residue, *modulo);

    if (isl_int_is_one(*modulo))

      
break0
;

  }

  isl_int_clear(m);

  isl_int_clear(r);

  return isl_stat_ok;

error:

  isl_int_clear(m);

  isl_int_clear(r);

  return isl_stat_error;

}

/* Check if dimension "dim" belongs to a residue class

 *    i_dim \equiv r mod m

 * with m != 1 and if so return m in *modulo and r in *residue.

 * As a special case, when i_dim has a fixed value v, then

 * *modulo is set to 0 and *residue to v.

 *

 * If i_dim does not belong to such a residue class, then *modulo

 * is set to 1 and *residue is set to 0.

 */

isl_stat isl_set_dim_residue_class_val(__isl_keep isl_set *set,

  int pos, __isl_give isl_val **modulo, __isl_give isl_val **residue)

{

  *modulo = NULL;

  *residue = NULL;

  if (!set)

    return isl_stat_error;

  *modulo = isl_val_alloc(isl_set_get_ctx(set));

  *residue = isl_val_alloc(isl_set_get_ctx(set));

  if (!*modulo || !*residue)

    goto error;

  if (isl_set_dim_residue_class(set, pos,

          &(*modulo)->n, &(*residue)->n) < 0)

    goto error;

  isl_int_set_si((*modulo)->d, 1);

  isl_int_set_si((*residue)->d, 1);

  return isl_stat_ok;

error:

  isl_val_free(*modulo);

  isl_val_free(*residue);

  return isl_stat_error;

}