/*

 * Copyright 2006-2007 Universiteit Leiden

 * Copyright 2008-2009 Katholieke Universiteit Leuven

 *

 * Use of this software is governed by the MIT license

 *

 * Written by Sven Verdoolaege, Leiden Institute of Advanced Computer Science,

 * Universiteit Leiden, Niels Bohrweg 1, 2333 CA Leiden, The Netherlands

 * and K.U.Leuven, Departement Computerwetenschappen, Celestijnenlaan 200A,

 * B-3001 Leuven, Belgium

 */

#include <stdlib.h>

#include <isl_ctx_private.h>

#include <isl_map_private.h>

#include <isl_vec_private.h>

#include <isl_options_private.h>

#include "isl_basis_reduction.h"

static void save_alpha(GBR_LP *lp, int first, int n, GBR_type *alpha)

{

  int i;

  for (i = 0; i < n; 
++i63.3k
)

    GBR_lp_get_alpha(lp, first + i, &alpha[i]);

}

/* Compute a reduced basis for the set represented by the tableau "tab".

 * tab->basis, which must be initialized by the calling function to an affine

 * unimodular basis, is updated to reflect the reduced basis.

 * The first tab->n_zero rows of the basis (ignoring the constant row)

 * are assumed to correspond to equalities and are left untouched.

 * tab->n_zero is updated to reflect any additional equalities that

 * have been detected in the first rows of the new basis.

 * The final tab->n_unbounded rows of the basis are assumed to correspond

 * to unbounded directions and are also left untouched.

 * In particular this means that the remaining rows are assumed to

 * correspond to bounded directions.

 *

 * This function implements the algorithm described in

 * "An Implementation of the Generalized Basis Reduction Algorithm

 *  for Integer Programming" of Cook el al. to compute a reduced basis.

 * We use \epsilon = 1/4.

 *

 * If ctx->opt->gbr_only_first is set, the user is only interested

 * in the first direction.  In this case we stop the basis reduction when

 * the width in the first direction becomes smaller than 2.

 */

struct isl_tab *isl_tab_compute_reduced_basis(struct isl_tab *tab)

{

  unsigned dim;

  struct isl_ctx *ctx;

  struct isl_mat *B;

  int i;

  GBR_LP *lp = NULL;

  GBR_type F_old, alpha, F_new;

  int row;

  isl_int tmp;

  struct isl_vec *b_tmp;

  GBR_type *F = NULL;

  GBR_type *alpha_buffer[2] = { NULL, NULL };

  GBR_type *alpha_saved;

  GBR_type F_saved;

  int use_saved = 0;

  isl_int mu[2];

  GBR_type mu_F[2];

  GBR_type two;

  GBR_type one;

  int empty = 0;

  int fixed = 0;

  int fixed_saved = 0;

  int mu_fixed[2];

  int n_bounded;

  int gbr_only_first;

  if (!tab)

    return NULL;

  if (tab->empty)

    return tab;

  ctx = tab->mat->ctx;

  gbr_only_first = ctx->opt->gbr_only_first;

  dim = tab->n_var;

  B = tab->basis;

  if (!B)

    return tab;

  n_bounded = dim - tab->n_unbounded;

  if (n_bounded <= tab->n_zero + 1)

    return tab;

  isl_int_init(tmp);

  isl_int_init(mu[0]);

  isl_int_init(mu[1]);

  GBR_init(alpha);

  GBR_init(F_old);

  GBR_init(F_new);

  GBR_init(F_saved);

  GBR_init(mu_F[0]);

  GBR_init(mu_F[1]);

  GBR_init(two);

  GBR_init(one);

  b_tmp = isl_vec_alloc(ctx, dim);

  if (!b_tmp)

    goto error;

  F = isl_alloc_array(ctx, GBR_type, n_bounded);

  alpha_buffer[0] = isl_alloc_array(ctx, GBR_type, n_bounded);

  alpha_buffer[1] = isl_alloc_array(ctx, GBR_type, n_bounded);

  alpha_saved = alpha_buffer[0];

  if (!F || !alpha_buffer[0] || !alpha_buffer[1])

    goto error;

  
for (i = 0; 3.09k
i < n_bounded; 
++i16.6k
) {

    GBR_init(F[i]);

    GBR_init(alpha_buffer[0][i]);

    GBR_init(alpha_buffer[1][i]);

  }

  GBR_set_ui(two, 2);

  GBR_set_ui(one, 1);

  lp = GBR_lp_init(tab);

  if (!lp)

    goto error;

  i = tab->n_zero;

  GBR_lp_set_obj(lp, B->row[1+i]+1, dim);

  ctx->stats->gbr_solved_lps++;

  if (GBR_lp_solve(lp) < 0)

    goto error;

  GBR_lp_get_obj_val(lp, &F[i]);

  if (GBR_lt(F[i], one)) {

    if (!GBR_is_zero(F[i])) {

      empty = GBR_lp_cut(lp, B->row[1+i]+1);

      if (empty)

        goto done;

      GBR_set_ui(F[i], 0);

    }

    tab->n_zero++;

  }

  
do 3.09k
{

    if (i+1 == tab->n_zero) {

      GBR_lp_set_obj(lp, B->row[1+i+1]+1, dim);

      ctx->stats->gbr_solved_lps++;

      if (GBR_lp_solve(lp) < 0)

        goto error;

      GBR_lp_get_obj_val(lp, &F_new);

      fixed = GBR_lp_is_fixed(lp);

      GBR_set_ui(alpha, 0);

    } else

    if (use_saved) {

      row = GBR_lp_next_row(lp);

      GBR_set(F_new, F_saved);

      fixed = fixed_saved;

      GBR_set(alpha, alpha_saved[i]);

    } else {

      row = GBR_lp_add_row(lp, B->row[1+i]+1, dim);

      GBR_lp_set_obj(lp, B->row[1+i+1]+1, dim);

      ctx->stats->gbr_solved_lps++;

      if (GBR_lp_solve(lp) < 0)

        goto error;

      GBR_lp_get_obj_val(lp, &F_new);

      fixed = GBR_lp_is_fixed(lp);

      GBR_lp_get_alpha(lp, row, &alpha);

      if (i > 0)

        save_alpha(lp, row-i, i, alpha_saved);

      if (GBR_lp_del_row(lp) < 0)

        goto error;

    }

    GBR_set(F[i+1], F_new);

    GBR_floor(mu[0], alpha);

    GBR_ceil(mu[1], alpha);

    if (isl_int_eq(mu[0], mu[1]))

      
isl_int_set24.7k
(tmp, mu[0]);

    else {

      int j;

      for (j = 0; j <= 1; 
++j12.5k
) {

        isl_int_set(tmp, mu[j]);

        isl_seq_combine(b_tmp->el,

            ctx->one, B->row[1+i+1]+1,

            tmp, B->row[1+i]+1, dim);

        GBR_lp_set_obj(lp, b_tmp->el, dim);

        ctx->stats->gbr_solved_lps++;

        if (GBR_lp_solve(lp) < 0)

          goto error;

        GBR_lp_get_obj_val(lp, &mu_F[j]);

        mu_fixed[j] = GBR_lp_is_fixed(lp);

        if (i > 0)

          save_alpha(lp, row-i, i, alpha_buffer[j]);

      }

      if (GBR_lt(mu_F[0], mu_F[1]))

        
j = 03.24k
;

      else

        j = 1;

      isl_int_set(tmp, mu[j]);

      GBR_set(F_new, mu_F[j]);

      fixed = mu_fixed[j];

      alpha_saved = alpha_buffer[j];

    }

    isl_seq_combine(B->row[1+i+1]+1, ctx->one, B->row[1+i+1]+1,

        tmp, B->row[1+i]+1, dim);

    if (i+1 == tab->n_zero && 
fixed0
) {

      if (!GBR_is_zero(F[i+1])) {

        empty = GBR_lp_cut(lp, B->row[1+i+1]+1);

        if (empty)

          goto done;

        GBR_set_ui(F[i+1], 0);

      }

      tab->n_zero++;

    }

    GBR_set(F_old, F[i]);

    use_saved = 0;

    /* mu_F[0] = 4 * F_new; mu_F[1] = 3 * F_old */

    GBR_set_ui(mu_F[0], 4);

    GBR_mul(mu_F[0], mu_F[0], F_new);

    GBR_set_ui(mu_F[1], 3);

    GBR_mul(mu_F[1], mu_F[1], F_old);

    if (GBR_lt(mu_F[0], mu_F[1])) {

      B = isl_mat_swap_rows(B, 1 + i, 1 + i + 1);

      if (i > tab->n_zero) {

        use_saved = 1;

        GBR_set(F_saved, F_new);

        fixed_saved = fixed;

        if (GBR_lp_del_row(lp) < 0)

          goto error;

        --i;

      } else {

        GBR_set(F[tab->n_zero], F_new);

        if (gbr_only_first && GBR_lt(F[tab->n_zero], two))

          
break2.07k
;

        if (fixed) {

          if (!GBR_is_zero(F[tab->n_zero])) {

            empty = GBR_lp_cut(lp, B->row[1+tab->n_zero]+1);

            if (empty)

              goto done;

            GBR_set_ui(F[tab->n_zero], 0);

          }

          tab->n_zero++;

        }

      }

    } else {

      GBR_lp_add_row(lp, B->row[1+i]+1, dim);

      ++i;

    }

  } while (
i < n_bounded - 128.8k
);

  if (0) {

done:

    if (empty < 0) {

error:

      isl_mat_free(B);

      B = NULL;

    }

  }

  GBR_lp_delete(lp);

  if (alpha_buffer[1])

    
for (i = 0; 3.09k
i < n_bounded; 
++i16.6k
) {

      GBR_clear(F[i]);

      GBR_clear(alpha_buffer[0][i]);

      GBR_clear(alpha_buffer[1][i]);

    }

  free(F);

  free(alpha_buffer[0]);

  free(alpha_buffer[1]);

  isl_vec_free(b_tmp);

  GBR_clear(alpha);

  GBR_clear(F_old);

  GBR_clear(F_new);

  GBR_clear(F_saved);

  GBR_clear(mu_F[0]);

  GBR_clear(mu_F[1]);

  GBR_clear(two);

  GBR_clear(one);

  isl_int_clear(tmp);

  isl_int_clear(mu[0]);

  isl_int_clear(mu[1]);

  tab->basis = B;

  return tab;

}

/* Compute an affine form of a reduced basis of the given basic

 * non-parametric set, which is assumed to be bounded and not

 * include any integer divisions.

 * The first column and the first row correspond to the constant term.

 *

 * If the input contains any equalities, we first create an initial

 * basis with the equalities first.  Otherwise, we start off with

 * the identity matrix.

 */

__isl_give isl_mat *isl_basic_set_reduced_basis(__isl_keep isl_basic_set *bset)

{

  struct isl_mat *basis;

  struct isl_tab *tab;

  if (!bset)

    return NULL;

  if (isl_basic_set_dim(bset, isl_dim_div) != 0)

    isl_die(bset->ctx, isl_error_invalid,

      "no integer division allowed", return NULL);

  if (isl_basic_set_dim(bset, isl_dim_param) != 0)

    isl_die(bset->ctx, isl_error_invalid,

      "no parameters allowed", return NULL);

  tab = isl_tab_from_basic_set(bset, 0);

  if (!tab)

    return NULL;

  if (bset->n_eq == 0)

    tab->basis = isl_mat_identity(bset->ctx, 1 + tab->n_var);

  else {

    isl_mat *eq;

    unsigned nvar = isl_basic_set_total_dim(bset);

    eq = isl_mat_sub_alloc6(bset->ctx, bset->eq, 0, bset->n_eq,

          1, nvar);

    eq = isl_mat_left_hermite(eq, 0, NULL, &tab->basis);

    tab->basis = isl_mat_lin_to_aff(tab->basis);

    tab->n_zero = bset->n_eq;

    isl_mat_free(eq);

  }

  tab = isl_tab_compute_reduced_basis(tab);

  if (!tab)

    return NULL;

  basis = isl_mat_copy(tab->basis);

  isl_tab_free(tab);

  return basis;

}