basis_reduction_templ.c

   1 #include <stdlib.h>
   2 #include "isl_basis_reduction.h"
   3
   4 static void save_alpha(GBR_LP *lp, int first, int n, GBR_type *alpha)
   5 {
   6         int i;
   7
   8         for (i = 0; i < n; ++i)
   9                 GBR_lp_get_alpha(lp, first + i, &alpha[i]);
  10 }
  11
  12 /* This function implements the algorithm described in
  13  * "An Implementation of the Generalized Basis Reduction Algorithm
  14  *  for Integer Programming" of Cook el al. to compute a reduced basis.
  15  * We use \epsilon = 1/4.
  16  *
  17  * If ctx->gbr_only_first is set, the user is only interested
  18  * in the first direction.  In this case we stop the basis reduction when
  19  * the width in the first direction becomes smaller than 2.
  20  */
  21 struct isl_mat *isl_basic_set_reduced_basis(struct isl_basic_set *bset)
  22 {
  23         unsigned dim;
  24         struct isl_mat *basis;
  25         int unbounded;
  26         int i;
  27         GBR_LP *lp = NULL;
  28         GBR_type F_old, alpha, F_new;
  29         int row;
  30         isl_int tmp;
  31         struct isl_vec *b_tmp;
  32         GBR_type *F = NULL;
  33         GBR_type *alpha_buffer[2] = { NULL, NULL };
  34         GBR_type *alpha_saved;
  35         GBR_type F_saved;
  36         int use_saved = 0;
  37         isl_int mu[2];
  38         GBR_type mu_F[2];
  39         GBR_type two;
  40
  41         if (!bset)
  42                 return NULL;
  43
  44         dim = isl_basic_set_total_dim(bset);
  45         basis = isl_mat_identity(bset->ctx, dim);
  46         if (!basis)
  47                 return NULL;
  48
  49         if (dim == 1)
  50                 return basis;
  51
  52         isl_int_init(tmp);
  53         isl_int_init(mu[0]);
  54         isl_int_init(mu[1]);
  55
  56         GBR_init(alpha);
  57         GBR_init(F_old);
  58         GBR_init(F_new);
  59         GBR_init(F_saved);
  60         GBR_init(mu_F[0]);
  61         GBR_init(mu_F[1]);
  62         GBR_init(two);
  63
  64         b_tmp = isl_vec_alloc(bset->ctx, dim);
  65         if (!b_tmp)
  66                 goto error;
  67
  68         F = isl_alloc_array(bset->ctx, GBR_type, dim);
  69         alpha_buffer[0] = isl_alloc_array(bset->ctx, GBR_type, dim);
  70         alpha_buffer[1] = isl_alloc_array(bset->ctx, GBR_type, dim);
  71         alpha_saved = alpha_buffer[0];
  72
  73         if (!F || !alpha_buffer[0] || !alpha_buffer[1])
  74                 goto error;
  75
  76         for (i = 0; i < dim; ++i) {
  77                 GBR_init(F[i]);
  78                 GBR_init(alpha_buffer[0][i]);
  79                 GBR_init(alpha_buffer[1][i]);
  80         }
  81
  82         GBR_set_ui(two, 2);
  83
  84         lp = GBR_lp_init(bset);
  85         if (!lp)
  86                 goto error;
  87
  88         i = 0;
  89
  90         GBR_lp_set_obj(lp, basis->row[0], dim);
  91         bset->ctx->stats->gbr_solved_lps++;
  92         unbounded = GBR_lp_solve(lp);
  93         isl_assert(bset->ctx, !unbounded, goto error);
  94         GBR_lp_get_obj_val(lp, &F[0]);
  95
  96         do {
  97                 if (use_saved) {
  98                         row = GBR_lp_next_row(lp);
  99                         GBR_set(F_new, F_saved);
 100                         GBR_set(alpha, alpha_saved[i]);
 101                 } else {
 102                         row = GBR_lp_add_row(lp, basis->row[i], dim);
 103                         GBR_lp_set_obj(lp, basis->row[i+1], dim);
 104                         bset->ctx->stats->gbr_solved_lps++;
 105                         unbounded = GBR_lp_solve(lp);
 106                         isl_assert(bset->ctx, !unbounded, goto error);
 107                         GBR_lp_get_obj_val(lp, &F_new);
 108
 109                         GBR_lp_get_alpha(lp, row, &alpha);
 110
 111                         if (i > 0)
 112                                 save_alpha(lp, row-i, i, alpha_saved);
 113
 114                         GBR_lp_del_row(lp);
 115                 }
 116                 GBR_set(F[i+1], F_new);
 117
 118                 GBR_floor(mu[0], alpha);
 119                 GBR_ceil(mu[1], alpha);
 120
 121                 if (isl_int_eq(mu[0], mu[1]))
 122                         isl_int_set(tmp, mu[0]);
 123                 else {
 124                         int j;
 125
 126                         for (j = 0; j <= 1; ++j) {
 127                                 isl_int_set(tmp, mu[j]);
 128                                 isl_seq_combine(b_tmp->el,
 129                                                 bset->ctx->one, basis->row[i+1],
 130                                                 tmp, basis->row[i], dim);
 131                                 GBR_lp_set_obj(lp, b_tmp->el, dim);
 132                                 bset->ctx->stats->gbr_solved_lps++;
 133                                 unbounded = GBR_lp_solve(lp);
 134                                 isl_assert(bset->ctx, !unbounded, goto error);
 135                                 GBR_lp_get_obj_val(lp, &mu_F[j]);
 136                                 if (i > 0)
 137                                         save_alpha(lp, row-i, i, alpha_buffer[j]);
 138                         }
 139
 140                         if (GBR_lt(mu_F[0], mu_F[1]))
 141                                 j = 0;
 142                         else
 143                                 j = 1;
 144
 145                         isl_int_set(tmp, mu[j]);
 146                         GBR_set(F_new, mu_F[j]);
 147                         alpha_saved = alpha_buffer[j];
 148                 }
 149                 isl_seq_combine(basis->row[i+1],
 150                                 bset->ctx->one, basis->row[i+1],
 151                                 tmp, basis->row[i], dim);
 152
 153                 GBR_set(F_old, F[i]);
 154
 155                 use_saved = 0;
 156                 /* mu_F[0] = 4 * F_new; mu_F[1] = 3 * F_old */
 157                 GBR_set_ui(mu_F[0], 4);
 158                 GBR_mul(mu_F[0], mu_F[0], F_new);
 159                 GBR_set_ui(mu_F[1], 3);
 160                 GBR_mul(mu_F[1], mu_F[1], F_old);
 161                 if (GBR_lt(mu_F[0], mu_F[1])) {
 162                         basis = isl_mat_swap_rows(basis, i, i + 1);
 163                         if (i > 0) {
 164                                 use_saved = 1;
 165                                 GBR_set(F_saved, F_new);
 166                                 GBR_lp_del_row(lp);
 167                                 --i;
 168                         } else {
 169                                 GBR_set(F[0], F_new);
 170                                 if (bset->ctx->gbr_only_first &&
 171                                     GBR_lt(F[0], two))
 172                                         break;
 173                         }
 174                 } else {
 175                         GBR_lp_add_row(lp, basis->row[i], dim);
 176                         ++i;
 177                 }
 178         } while (i < dim-1);
 179
 180         if (0) {
 181 error:
 182             isl_mat_free(basis);
 183             basis = NULL;
 184         }
 185
 186         GBR_lp_delete(lp);
 187
 188         if (alpha_buffer[1])
 189                 for (i = 0; i < dim; ++i) {
 190                         GBR_clear(F[i]);
 191                         GBR_clear(alpha_buffer[0][i]);
 192                         GBR_clear(alpha_buffer[1][i]);
 193                 }
 194         free(F);
 195         free(alpha_buffer[0]);
 196         free(alpha_buffer[1]);
 197
 198         isl_vec_free(b_tmp);
 199
 200         GBR_clear(alpha);
 201         GBR_clear(F_old);
 202         GBR_clear(F_new);
 203         GBR_clear(F_saved);
 204         GBR_clear(mu_F[0]);
 205         GBR_clear(mu_F[1]);
 206         GBR_clear(two);
 207
 208         isl_int_clear(tmp);
 209         isl_int_clear(mu[0]);
 210         isl_int_clear(mu[1]);
 211
 212         return basis;
 213 }