/*

 * Copyright 2008-2009 Katholieke Universiteit Leuven

 * Copyright 2010      INRIA Saclay

 * Copyright 2014      Ecole Normale Superieure

 * Copyright 2017      Sven Verdoolaege

 *

 * 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

 * and Ecole Normale Superieure, 45 rue d'Ulm, 75230 Paris, France

 */

#include <isl_ctx_private.h>

#include <isl_map_private.h>

#include <isl/space.h>

#include <isl_seq.h>

#include <isl_mat_private.h>

#include <isl_vec_private.h>

#include <isl_space_private.h>

#include <isl_val_private.h>

isl_ctx *isl_mat_get_ctx(__isl_keep isl_mat *mat)

{

  return mat ? mat->ctx : NULL;

}

/* Return a hash value that digests "mat".

 */

uint32_t isl_mat_get_hash(__isl_keep isl_mat *mat)

{

  int i;

  uint32_t hash;

  if (!mat)

    return 0;

  hash = isl_hash_init();

  isl_hash_byte(hash, mat->n_row & 0xFF);

  isl_hash_byte(hash, mat->n_col & 0xFF);

  for (i = 0; i < mat->n_row; ++i) {

    uint32_t row_hash;

    row_hash = isl_seq_get_hash(mat->row[i], mat->n_col);

    isl_hash_hash(hash, row_hash);

  }

  return hash;

}

struct isl_mat *isl_mat_alloc(struct isl_ctx *ctx,

  unsigned n_row, unsigned n_col)

{

  int i;

  struct isl_mat *mat;

  mat = isl_alloc_type(ctx, struct isl_mat);

  if (!mat)

    return NULL;

  mat->row = NULL;

  mat->block = isl_blk_alloc(ctx, n_row * n_col);

  if (isl_blk_is_error(mat->block))

    goto error;

  mat->row = isl_alloc_array(ctx, isl_int *, n_row);

  if (n_row && 
!mat->row8.50M
)

    goto error;

  
for (i = 0; 11.2M
i < n_row; 
++i57.4M
)

    mat->row[i] = mat->block.data + i * n_col;

  mat->ctx = ctx;

  isl_ctx_ref(ctx);

  mat->ref = 1;

  mat->n_row = n_row;

  mat->n_col = n_col;

  mat->max_col = n_col;

  mat->flags = 0;

  return mat;

error:

  isl_blk_free(ctx, mat->block);

  free(mat);

  return NULL;

}

struct isl_mat *isl_mat_extend(struct isl_mat *mat,

  unsigned n_row, unsigned n_col)

{

  int i;

  isl_int *old;

  isl_int **row;

  if (!mat)

    return NULL;

  if (mat->max_col >= n_col && 
mat->n_row >= n_row207k
) {

    if (mat->n_col < n_col)

      mat->n_col = n_col;

    return mat;

  }

  if (mat->max_col < n_col) {

    struct isl_mat *new_mat;

    if (n_row < mat->n_row)

      n_row = mat->n_row;

    new_mat = isl_mat_alloc(mat->ctx, n_row, n_col);

    if (!new_mat)

      goto error;

    
for (i = 0; 4.40k
i < mat->n_row; 
++i37.6k
)

      isl_seq_cpy(new_mat->row[i], mat->row[i], mat->n_col);

    isl_mat_free(mat);

    return new_mat;

  }

  mat = isl_mat_cow(mat);

  if (!mat)

    goto error;

  old = mat->block.data;

  mat->block = isl_blk_extend(mat->ctx, mat->block, n_row * mat->max_col);

  if (isl_blk_is_error(mat->block))

    goto error;

  row = isl_realloc_array(mat->ctx, mat->row, isl_int *, n_row);

  if (n_row && !row)

    goto error;

  mat->row = row;

  for (i = 0; i < mat->n_row; 
++i2.40M
)

    mat->row[i] = mat->block.data + (mat->row[i] - old);

  for (i = mat->n_row; i < n_row; 
++i669k
)

    mat->row[i] = mat->block.data + i * mat->max_col;

  mat->n_row = n_row;

  if (mat->n_col < n_col)

    mat->n_col = n_col;

  return mat;

error:

  isl_mat_free(mat);

  return NULL;

}

__isl_give isl_mat *isl_mat_sub_alloc6(isl_ctx *ctx, isl_int **row,

  unsigned first_row, unsigned n_row, unsigned first_col, unsigned n_col)

{

  int i;

  struct isl_mat *mat;

  mat = isl_alloc_type(ctx, struct isl_mat);

  if (!mat)

    return NULL;

  mat->row = isl_alloc_array(ctx, isl_int *, n_row);

  if (n_row && 
!mat->row3.18M
)

    goto error;

  
for (i = 0; 5.63M
i < n_row; 
++i15.9M
)

    mat->row[i] = row[first_row+i] + first_col;

  mat->ctx = ctx;

  isl_ctx_ref(ctx);

  mat->ref = 1;

  mat->n_row = n_row;

  mat->n_col = n_col;

  mat->block = isl_blk_empty();

  mat->flags = ISL_MAT_BORROWED;

  return mat;

error:

  free(mat);

  return NULL;

}

__isl_give isl_mat *isl_mat_sub_alloc(__isl_keep isl_mat *mat,

  unsigned first_row, unsigned n_row, unsigned first_col, unsigned n_col)

{

  if (!mat)

    return NULL;

  return isl_mat_sub_alloc6(mat->ctx, mat->row, first_row, n_row,

          first_col, n_col);

}

void isl_mat_sub_copy(struct isl_ctx *ctx, isl_int **dst, isl_int **src,

  unsigned n_row, unsigned dst_col, unsigned src_col, unsigned n_col)

{

  int i;

  for (i = 0; i < n_row; 
++i1.54M
)

    isl_seq_cpy(dst[i]+dst_col, src[i]+src_col, n_col);

}

void isl_mat_sub_neg(struct isl_ctx *ctx, isl_int **dst, isl_int **src,

  unsigned n_row, unsigned dst_col, unsigned src_col, unsigned n_col)

{

  int i;

  for (i = 0; i < n_row; 
++i760k
)

    isl_seq_neg(dst[i]+dst_col, src[i]+src_col, n_col);

}

__isl_give isl_mat *isl_mat_copy(__isl_keep isl_mat *mat)

{

  if (!mat)

    return NULL;

  mat->ref++;

  return mat;

}

__isl_give isl_mat *isl_mat_dup(__isl_keep isl_mat *mat)

{

  int i;

  struct isl_mat *mat2;

  if (!mat)

    return NULL;

  mat2 = isl_mat_alloc(mat->ctx, mat->n_row, mat->n_col);

  if (!mat2)

    return NULL;

  
for (i = 0; 694k
i < mat->n_row; 
++i1.86M
)

    isl_seq_cpy(mat2->row[i], mat->row[i], mat->n_col);

  return mat2;

}

__isl_give isl_mat *isl_mat_cow(__isl_take isl_mat *mat)

{

  struct isl_mat *mat2;

  if (!mat)

    return NULL;

  if (mat->ref == 1 && 
!8.54M
ISL_F_ISSET8.54M
(mat, ISL_MAT_BORROWED))

    
return mat7.89M
;

  mat2 = isl_mat_dup(mat);

  isl_mat_free(mat);

  return mat2;

}

__isl_null isl_mat *isl_mat_free(__isl_take isl_mat *mat)

{

  if (!mat)

    return NULL;

  if (--mat->ref > 0)

    return NULL;

  if (!ISL_F_ISSET(mat, ISL_MAT_BORROWED))

    
isl_blk_free(mat->ctx, mat->block)11.2M
;

  isl_ctx_deref(mat->ctx);

  free(mat->row);

  free(mat);

  return NULL;

}

int isl_mat_rows(__isl_keep isl_mat *mat)

{

  return mat ? mat->n_row : 
-10
;

}

int isl_mat_cols(__isl_keep isl_mat *mat)

{

  return mat ? mat->n_col : 
-10
;

}

/* Check that "col" is a valid column position for "mat".

 */

static isl_stat check_col(__isl_keep isl_mat *mat, int col)

{

  if (!mat)

    return isl_stat_error;

  if (col < 0 || col >= mat->n_col)

    
isl_die0
(isl_mat_get_ctx(mat), isl_error_invalid,

      "column out of range", return isl_stat_error);

  return isl_stat_ok;

}

/* Check that "row" is a valid row position for "mat".

 */

static isl_stat check_row(__isl_keep isl_mat *mat, int row)

{

  if (!mat)

    return isl_stat_error;

  if (row < 0 || row >= mat->n_row)

    
isl_die0
(isl_mat_get_ctx(mat), isl_error_invalid,

      "row out of range", return isl_stat_error);

  return isl_stat_ok;

}

/* Check that there are "n" columns starting at position "first" in "mat".

 */

static isl_stat check_col_range(__isl_keep isl_mat *mat, unsigned first,

  unsigned n)

{

  if (!mat)

    return isl_stat_error;

  if (first + n > mat->n_col || first + n < first)

    
isl_die0
(isl_mat_get_ctx(mat), isl_error_invalid,

      "column position or range out of bounds",

      return isl_stat_error);

  return isl_stat_ok;

}

/* Check that there are "n" rows starting at position "first" in "mat".

 */

static isl_stat check_row_range(__isl_keep isl_mat *mat, unsigned first,

  unsigned n)

{

  if (!mat)

    return isl_stat_error;

  if (first + n > mat->n_row || first + n < first)

    
isl_die0
(isl_mat_get_ctx(mat), isl_error_invalid,

      "row position or range out of bounds",

      return isl_stat_error);

  return isl_stat_ok;

}

int isl_mat_get_element(__isl_keep isl_mat *mat, int row, int col, isl_int *v)

{

  if (check_row(mat, row) < 0)

    return -1;

  if (check_col(mat, col) < 0)

    return -1;

  isl_int_set(*v, mat->row[row][col]);

  return 0;

}

/* Extract the element at row "row", oolumn "col" of "mat".

 */

__isl_give isl_val *isl_mat_get_element_val(__isl_keep isl_mat *mat,

  int row, int col)

{

  isl_ctx *ctx;

  if (check_row(mat, row) < 0)

    return NULL;

  if (check_col(mat, col) < 0)

    return NULL;

  ctx = isl_mat_get_ctx(mat);

  return isl_val_int_from_isl_int(ctx, mat->row[row][col]);

}

__isl_give isl_mat *isl_mat_set_element(__isl_take isl_mat *mat,

  int row, int col, isl_int v)

{

  mat = isl_mat_cow(mat);

  if (check_row(mat, row) < 0)

    return isl_mat_free(mat);

  if (check_col(mat, col) < 0)

    return isl_mat_free(mat);

  isl_int_set(mat->row[row][col], v);

  return mat;

}

__isl_give isl_mat *isl_mat_set_element_si(__isl_take isl_mat *mat,

  int row, int col, int v)

{

  mat = isl_mat_cow(mat);

  if (check_row(mat, row) < 0)

    return isl_mat_free(mat);

  if (check_col(mat, col) < 0)

    return isl_mat_free(mat);

  isl_int_set_si(mat->row[row][col], v);

  return mat;

}

/* Replace the element at row "row", column "col" of "mat" by "v".

 */

__isl_give isl_mat *isl_mat_set_element_val(__isl_take isl_mat *mat,

  int row, int col, __isl_take isl_val *v)

{

  if (!v)

    return isl_mat_free(mat);

  if (!isl_val_is_int(v))

    isl_die(isl_val_get_ctx(v), isl_error_invalid,

      "expecting integer value", goto error);

  mat = isl_mat_set_element(mat, row, col, v->n);

  isl_val_free(v);

  return mat;

error:

  isl_val_free(v);

  return isl_mat_free(mat);

}

__isl_give isl_mat *isl_mat_diag(isl_ctx *ctx, unsigned n_row, isl_int d)

{

  int i;

  struct isl_mat *mat;

  mat = isl_mat_alloc(ctx, n_row, n_row);

  if (!mat)

    return NULL;

  
for (i = 0; 2.04M
i < n_row; 
++i10.3M
) {

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

    isl_int_set(mat->row[i][i], d);

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

  }

  return mat;

}

/* Create an "n_row" by "n_col" matrix with zero elements.

 */

__isl_give isl_mat *isl_mat_zero(isl_ctx *ctx, unsigned n_row, unsigned n_col)

{

  int i;

  isl_mat *mat;

  mat = isl_mat_alloc(ctx, n_row, n_col);

  if (!mat)

    return NULL;

  
for (i = 0; 149
i < n_row; 
++i41
)

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

  return mat;

}

__isl_give isl_mat *isl_mat_identity(isl_ctx *ctx, unsigned n_row)

{

  if (!ctx)

    return NULL;

  return isl_mat_diag(ctx, n_row, ctx->one);

}

/* Is "mat" a (possibly scaled) identity matrix?

 */

int isl_mat_is_scaled_identity(__isl_keep isl_mat *mat)

{

  int i;

  if (!mat)

    return -1;

  if (mat->n_row != mat->n_col)

    return 0;

  for (i = 0; i < mat->n_row; ++i) {

    if (isl_seq_first_non_zero(mat->row[i], i) != -1)

      return 0;

    if (isl_int_ne(mat->row[0][0], mat->row[i][i]))

      return 0;

    if (isl_seq_first_non_zero(mat->row[i] + i + 1,

              mat->n_col - (i + 1)) != -1)

      return 0;

  }

  return 1;

}

__isl_give isl_vec *isl_mat_vec_product(__isl_take isl_mat *mat,

  __isl_take isl_vec *vec)

{

  int i;

  struct isl_vec *prod;

  if (!mat || !vec)

    goto error;

  isl_assert(mat->ctx, mat->n_col == vec->size, goto error);

  prod = isl_vec_alloc(mat->ctx, mat->n_row);

  if (!prod)

    goto error;

  
for (i = 0; 671k
i < prod->size; 
++i5.08M
)

    isl_seq_inner_product(mat->row[i], vec->el, vec->size,

          &prod->block.data[i]);

  isl_mat_free(mat);

  isl_vec_free(vec);

  return prod;

error:

  isl_mat_free(mat);

  isl_vec_free(vec);

  return NULL;

}

__isl_give isl_vec *isl_mat_vec_inverse_product(__isl_take isl_mat *mat,

  __isl_take isl_vec *vec)

{

  struct isl_mat *vec_mat;

  int i;

  if (!mat || !vec)

    goto error;

  vec_mat = isl_mat_alloc(vec->ctx, vec->size, 1);

  if (!vec_mat)

    goto error;

  
for (i = 0; 437
i < vec->size; 
++i3.49k
)

    isl_int_set(vec_mat->row[i][0], vec->el[i]);

  vec_mat = isl_mat_inverse_product(mat, vec_mat);

  isl_vec_free(vec);

  if (!vec_mat)

    return NULL;

  vec = isl_vec_alloc(vec_mat->ctx, vec_mat->n_row);

  if (vec)

    
for (i = 0; 437
i < vec->size; 
++i3.49k
)

      isl_int_set(vec->el[i], vec_mat->row[i][0]);

  isl_mat_free(vec_mat);

  return vec;

error:

  isl_mat_free(mat);

  isl_vec_free(vec);

  return NULL;

}

__isl_give isl_vec *isl_vec_mat_product(__isl_take isl_vec *vec,

  __isl_take isl_mat *mat)

{

  int i, j;

  struct isl_vec *prod;

  if (!mat || !vec)

    goto error;

  isl_assert(mat->ctx, mat->n_row == vec->size, goto error);

  prod = isl_vec_alloc(mat->ctx, mat->n_col);

  if (!prod)

    goto error;

  
for (i = 0; 186k
i < prod->size; 
++i1.94M
) {

    isl_int_set_si(prod->el[i], 0);

    for (j = 0; j < vec->size; 
++j21.9M
)

      isl_int_addmul(prod->el[i], vec->el[j], mat->row[j][i]);

  }

  isl_mat_free(mat);

  isl_vec_free(vec);

  return prod;

error:

  isl_mat_free(mat);

  isl_vec_free(vec);

  return NULL;

}

__isl_give isl_mat *isl_mat_aff_direct_sum(__isl_take isl_mat *left,

  __isl_take isl_mat *right)

{

  int i;

  struct isl_mat *sum;

  if (!left || !right)

    goto error;

  isl_assert(left->ctx, left->n_row == right->n_row, goto error);

  isl_assert(left->ctx, left->n_row >= 1, goto error);

  isl_assert(left->ctx, left->n_col >= 1, goto error);

  isl_assert(left->ctx, right->n_col >= 1, goto error);

  isl_assert(left->ctx,

      isl_seq_first_non_zero(left->row[0]+1, left->n_col-1) == -1,

      goto error);

  isl_assert(left->ctx,

      isl_seq_first_non_zero(right->row[0]+1, right->n_col-1) == -1,

      goto error);

  sum = isl_mat_alloc(left->ctx, left->n_row, left->n_col + right->n_col - 1);

  if (!sum)

    goto error;

  isl_int_lcm(sum->row[0][0], left->row[0][0], right->row[0][0]);

  isl_int_divexact(left->row[0][0], sum->row[0][0], left->row[0][0]);

  isl_int_divexact(right->row[0][0], sum->row[0][0], right->row[0][0]);

  isl_seq_clr(sum->row[0]+1, sum->n_col-1);

  for (i = 1; i < sum->n_row; 
++i2.61M
) {

    isl_int_mul(sum->row[i][0], left->row[0][0], left->row[i][0]);

    isl_int_addmul(sum->row[i][0],

        right->row[0][0], right->row[i][0]);

    isl_seq_scale(sum->row[i]+1, left->row[i]+1, left->row[0][0],

        left->n_col-1);

    isl_seq_scale(sum->row[i]+left->n_col,

        right->row[i]+1, right->row[0][0],

        right->n_col-1);

  }

  isl_int_divexact(left->row[0][0], sum->row[0][0], left->row[0][0]);

  isl_int_divexact(right->row[0][0], sum->row[0][0], right->row[0][0]);

  isl_mat_free(left);

  isl_mat_free(right);

  return sum;

error:

  isl_mat_free(left);

  isl_mat_free(right);

  return NULL;

}

static void exchange(struct isl_mat *M, struct isl_mat **U,

  struct isl_mat **Q, unsigned row, unsigned i, unsigned j)

{

  int r;

  for (r = row; r < M->n_row; 
++r8.63M
)

    isl_int_swap(M->row[r][i], M->row[r][j]);

  if (U) {

    for (r = 0; r < (*U)->n_row; 
++r15.1M
)

      isl_int_swap((*U)->row[r][i], (*U)->row[r][j]);

  }

  if (Q)

    isl_mat_swap_rows(*Q, i, j);

}

static void subtract(struct isl_mat *M, struct isl_mat **U,

  struct isl_mat **Q, unsigned row, unsigned i, unsigned j, isl_int m)

{

  int r;

  for (r = row; r < M->n_row; 
++r2.32M
)

    isl_int_submul(M->row[r][j], m, M->row[r][i]);

  if (U) {

    for (r = 0; r < (*U)->n_row; 
++r4.62M
)

      isl_int_submul((*U)->row[r][j], m, (*U)->row[r][i]);

  }

  if (Q) {

    for (r = 0; r < (*Q)->n_col; 
++r1.63M
)

      isl_int_addmul((*Q)->row[i][r], m, (*Q)->row[j][r]);

  }

}

static void oppose(struct isl_mat *M, struct isl_mat **U,

  struct isl_mat **Q, unsigned row, unsigned col)

{

  int r;

  for (r = row; r < M->n_row; 
++r1.36M
)

    isl_int_neg(M->row[r][col], M->row[r][col]);

  if (U) {

    for (r = 0; r < (*U)->n_row; 
++r1.76M
)

      isl_int_neg((*U)->row[r][col], (*U)->row[r][col]);

  }

  if (Q)

    isl_seq_neg((*Q)->row[col], (*Q)->row[col], (*Q)->n_col);

}

/* Given matrix M, compute

 *

 *    M U = H

 *    M   = H Q

 *

 * with U and Q unimodular matrices and H a matrix in column echelon form

 * such that on each echelon row the entries in the non-echelon column

 * are non-negative (if neg == 0) or non-positive (if neg == 1)

 * and strictly smaller (in absolute value) than the entries in the echelon

 * column.

 * If U or Q are NULL, then these matrices are not computed.

 */

__isl_give isl_mat *isl_mat_left_hermite(__isl_take isl_mat *M, int neg,

  __isl_give isl_mat **U, __isl_give isl_mat **Q)

{

  isl_int c;

  int row, col;

  if (U)

    *U = NULL;

  if (Q)

    *Q = NULL;

  if (!M)

    goto error;

  M = isl_mat_cow(M);

  if (!M)

    goto error;

  if (U) {

    *U = isl_mat_identity(M->ctx, M->n_col);

    if (!*U)

      goto error;

  }

  if (Q) {

    *Q = isl_mat_identity(M->ctx, M->n_col);

    if (!*Q)

      goto error;

  }

  col = 0;

  isl_int_init(c);

  for (row = 0; row < M->n_row; 
++row3.33M
) {

    int first, i, off;

    first = isl_seq_abs_min_non_zero(M->row[row]+col, M->n_col-col);

    if (first == -1)

      continue;

    first += col;

    if (first != col)

      exchange(M, U, Q, row, first, col);

    if (isl_int_is_neg(M->row[row][col]))

      
oppose(M, U, Q, row, col)323k
;

    first = col+1;

    while ((off = isl_seq_first_non_zero(M->row[row]+first,

                   M->n_col-first)) != -1) {

      first += off;

      isl_int_fdiv_q(c, M->row[row][first], M->row[row][col]);

      subtract(M, U, Q, row, col, first, c);

      if (!isl_int_is_zero(M->row[row][first]))

        
exchange(M, U, Q, row, first, col)22.5k
;

      else

        ++first;

    }

    for (i = 0; i < col; 
++i5.80M
) {

      if (isl_int_is_zero(M->row[row][i]))

        
continue5.63M
;

      if (neg)

        
isl_int_cdiv_q0
(c, M->row[row][i], M->row[row][col]);

      else

        isl_int_fdiv_q(c, M->row[row][i], M->row[row][col]);

      if (isl_int_is_zero(c))

        
continue52.4k
;

      subtract(M, U, Q, row, col, i, c);

    }

    ++col;

  }

  isl_int_clear(c);

  return M;

error:

  if (Q) {

    isl_mat_free(*Q);

    *Q = NULL;

  }

  if (U) {

    isl_mat_free(*U);

    *U = NULL;

  }

  isl_mat_free(M);

  return NULL;

}

/* Use row "row" of "mat" to eliminate column "col" from all other rows.

 */

static __isl_give isl_mat *eliminate(__isl_take isl_mat *mat, int row, int col)

{

  int k, nr, nc;

  isl_ctx *ctx;

  if (!mat)

    return NULL;

  ctx = isl_mat_get_ctx(mat);

  nr = isl_mat_rows(mat);

  nc = isl_mat_cols(mat);

  for (k = 0; k < nr; 
++k2.12k
) {

    if (k == row)

      continue;

    if (isl_int_is_zero(mat->row[k][col]))

      continue;

    mat = isl_mat_cow(mat);

    if (!mat)

      return NULL;

    isl_seq_elim(mat->row[k], mat->row[row], col, nc, NULL);

    isl_seq_normalize(ctx, mat->row[k], nc);

  }

  return mat;

}

/* Perform Gaussian elimination on the rows of "mat", but start

 * from the final row and the final column.

 * Any zero rows that result from the elimination are removed.

 *

 * In particular, for each column from last to first,

 * look for the last row with a non-zero coefficient in that column,

 * move it last (but before other rows moved last in previous steps) and

 * use it to eliminate the column from the other rows.

 */

__isl_give isl_mat *isl_mat_reverse_gauss(__isl_take isl_mat *mat)

{

  int k, row, last, nr, nc;

  if (!mat)

    return NULL;

  nr = isl_mat_rows(mat);

  nc = isl_mat_cols(mat);

  last = nc - 1;

  for (row = nr - 1; row >= 0; 
--row1.19k
) {

    for (; last >= 0; 
--last391
) {

      for (k = row; k >= 0; 
--k471
)

        if (!isl_int_is_zero(mat->row[k][last]))

          
break1.19k
;

      if (k >= 0)

        break;

    }

    if (last < 0)

      break;

    if (k != row)

      mat = isl_mat_swap_rows(mat, k, row);

    if (!mat)

      return NULL;

    if (isl_int_is_neg(mat->row[row][last]))

      
mat = isl_mat_row_neg(mat, row)4
;

    mat = eliminate(mat, row, last);

    if (!mat)

      return NULL;

  }

  mat = isl_mat_drop_rows(mat, 0, row + 1);

  return mat;

}

/* Negate the lexicographically negative rows of "mat" such that

 * all rows in the result are lexicographically non-negative.

 */

__isl_give isl_mat *isl_mat_lexnonneg_rows(__isl_take isl_mat *mat)

{

  int i, nr, nc;

  if (!mat)

    return NULL;

  nr = isl_mat_rows(mat);

  nc = isl_mat_cols(mat);

  for (i = 0; i < nr; 
++i1.19k
) {

    int pos;

    pos = isl_seq_first_non_zero(mat->row[i], nc);

    if (pos < 0)

      continue;

    if (isl_int_is_nonneg(mat->row[i][pos]))

      
continue1.18k
;

    mat = isl_mat_row_neg(mat, i);

    if (!mat)

      return NULL;

  }

  return mat;

}

/* Given a matrix "H" is column echelon form, what is the first

 * zero column?  That is how many initial columns are non-zero?

 * Start looking at column "first_col" and only consider

 * the columns to be of size "n_row".

 * "H" is assumed to be non-NULL.

 *

 * Since "H" is in column echelon form, the first non-zero entry

 * in a column is always in a later position compared to the previous column.

 */

static int hermite_first_zero_col(__isl_keep isl_mat *H, int first_col,

  int n_row)

{

  int row, col;

  for (col = first_col, row = 0; col < H->n_col; 
++col147
) {

    for (; row < n_row; 
++row127
)

      if (!isl_int_is_zero(H->row[row][col]))

        
break147
;

    if (row == n_row)

      return col;

  }

  
return H->n_col26
;

}

/* Return the rank of "mat", or -1 in case of error.

 */

int isl_mat_rank(__isl_keep isl_mat *mat)

{

  int rank;

  isl_mat *H;

  H = isl_mat_left_hermite(isl_mat_copy(mat), 0, NULL, NULL);

  if (!H)

    return -1;

  rank = hermite_first_zero_col(H, 0, H->n_row);

  isl_mat_free(H);

  return rank;

}

__isl_give isl_mat *isl_mat_right_kernel(__isl_take isl_mat *mat)

{

  int rank;

  struct isl_mat *U = NULL;

  struct isl_mat *K;

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

  if (!mat || !U)

    goto error;

  rank = hermite_first_zero_col(mat, 0, mat->n_row);

  K = isl_mat_alloc(U->ctx, U->n_row, U->n_col - rank);

  if (!K)

    goto error;

  isl_mat_sub_copy(K->ctx, K->row, U->row, U->n_row, 0, rank, U->n_col-rank);

  isl_mat_free(mat);

  isl_mat_free(U);

  return K;

error:

  isl_mat_free(mat);

  isl_mat_free(U);

  return NULL;

}

__isl_give isl_mat *isl_mat_lin_to_aff(__isl_take isl_mat *mat)

{

  int i;

  struct isl_mat *mat2;

  if (!mat)

    return NULL;

  mat2 = isl_mat_alloc(mat->ctx, 1+mat->n_row, 1+mat->n_col);

  if (!mat2)

    goto error;

  isl_int_set_si(mat2->row[0][0], 1);

  isl_seq_clr(mat2->row[0]+1, mat->n_col);

  for (i = 0; i < mat->n_row; 
++i8.99M
) {

    isl_int_set_si(mat2->row[1+i][0], 0);

    isl_seq_cpy(mat2->row[1+i]+1, mat->row[i], mat->n_col);

  }

  isl_mat_free(mat);

  return mat2;

error:

  isl_mat_free(mat);

  return NULL;

}

/* Given two matrices M1 and M2, return the block matrix

 *

 *  [ M1  0  ]

 *  [ 0   M2 ]

 */

__isl_give isl_mat *isl_mat_diagonal(__isl_take isl_mat *mat1,

  __isl_take isl_mat *mat2)

{

  int i;

  isl_mat *mat;

  if (!mat1 || !mat2)

    goto error;

  mat = isl_mat_alloc(mat1->ctx, mat1->n_row + mat2->n_row,

               mat1->n_col + mat2->n_col);

  if (!mat)

    goto error;

  
for (i = 0; 335k
i < mat1->n_row; 
++i335k
) {

    isl_seq_cpy(mat->row[i], mat1->row[i], mat1->n_col);

    isl_seq_clr(mat->row[i] + mat1->n_col, mat2->n_col);

  }

  for (i = 0; i < mat2->n_row; 
++i1.79M
) {

    isl_seq_clr(mat->row[mat1->n_row + i], mat1->n_col);

    isl_seq_cpy(mat->row[mat1->n_row + i] + mat1->n_col,

                mat2->row[i], mat2->n_col);

  }

  isl_mat_free(mat1);

  isl_mat_free(mat2);

  return mat;

error:

  isl_mat_free(mat1);

  isl_mat_free(mat2);

  return NULL;

}

static int row_first_non_zero(isl_int **row, unsigned n_row, unsigned col)

{

  int i;

  for (i = 0; i < n_row; 
++i1.61M
)

    if (!isl_int_is_zero(row[i][col]))

      
return i1.14M
;

  
return -11.13M
;

}

static int row_abs_min_non_zero(isl_int **row, unsigned n_row, unsigned col)

{

  int i, min = row_first_non_zero(row, n_row, col);

  if (min < 0)

    return -1;

  
for (i = min + 1; 1.13M
i < n_row; 
++i1.61M
) {

    if (isl_int_is_zero(row[i][col]))

      
continue1.60M
;

    if (isl_int_abs_lt(row[i][col], row[min][col]))

      
min = i683
;

  }

  return min;

}

static isl_stat inv_exchange(__isl_keep isl_mat **left,

  __isl_keep isl_mat **right, unsigned i, unsigned j)