isl_tab.h

   1 #ifndef ISL_TAB_H
   2 #define ISL_TAB_H
   3
   4 #include "isl_lp.h"
   5 #include "isl_map.h"
   6 #include "isl_mat.h"
   7 #include "isl_set.h"
   8
   9 struct isl_tab_var {
  10         int index;
  11         unsigned is_row : 1;
  12         unsigned is_nonneg : 1;
  13         unsigned is_zero : 1;
  14         unsigned is_redundant : 1;
  15         unsigned marked : 1;
  16         unsigned frozen : 1;
  17 };
  18
  19 enum isl_tab_undo_type {
  20         isl_tab_undo_bottom,
  21         isl_tab_undo_empty,
  22         isl_tab_undo_nonneg,
  23         isl_tab_undo_redundant,
  24         isl_tab_undo_zero,
  25         isl_tab_undo_allocate,
  26         isl_tab_undo_relax,
  27         isl_tab_undo_bset_ineq,
  28         isl_tab_undo_bset_eq,
  29         isl_tab_undo_bset_div,
  30         isl_tab_undo_saved_basis,
  31         isl_tab_undo_drop_sample,
  32 };
  33
  34 union isl_tab_undo_val {
  35         int             var_index;
  36         int             *col_var;
  37 };
  38
  39 struct isl_tab_undo {
  40         enum isl_tab_undo_type  type;
  41         union isl_tab_undo_val  u;
  42         struct isl_tab_undo     *next;
  43 };
  44
  45 /* The tableau maintains equality relations.
  46  * Each column and each row is associated to a variable or a constraint.
  47  * The "value" of an inequality constraint is the value of the corresponding
  48  * slack variable.
  49  * The "row_var" and "col_var" arrays map column and row indices
  50  * to indices in the "var" and "con" arrays.  The elements of these
  51  * arrays maintain extra information about the variables and the constraints.
  52  * Each row expresses the corresponding row variable as an affine expression
  53  * of the column variables.
  54  * The first two columns in the matrix contain the common denominator of
  55  * the row and the numerator of the constant term.
  56  * If "M" is set, then the third column represents the "big parameter".
  57  * The third (M = 0) or fourth (M = 1) column
  58  * in the matrix is called column 0 with respect to the col_var array.
  59  * The sample value of the tableau is the value that assigns zero
  60  * to all the column variables and the constant term of each affine
  61  * expression to the corresponding row variable.
  62  * The operations on the tableau maintain the property that the sample
  63  * value satisfies the non-negativity constraints (usually on the slack
  64  * variables).
  65  *
  66  * The big parameter represents an arbitrarily big (and divisible)
  67  * positive number.  If present, then the sign of a row is determined
  68  * lexicographically, with the sign of the big parameter coefficient
  69  * considered first.  The big parameter is only used while
  70  * solving PILP problems.
  71  *
  72  * The first n_dead column variables have their values fixed to zero.
  73  * The corresponding tab_vars are flagged "is_zero".
  74  * Some of the rows that have have zero coefficients in all but
  75  * the dead columns are also flagged "is_zero".
  76  *
  77  * The first n_redundant rows correspond to inequality constraints
  78  * that are always satisfied for any value satisfying the non-redundant
  79  * rows.  The corresponding tab_vars are flagged "is_redundant".
  80  * A row variable that is flagged "is_zero" is also flagged "is_redundant"
  81  * since the constraint has been reduced to 0 = 0 and is therefore always
  82  * satisfied.
  83  *
  84  * There are "n_var" variables in total.  The first "n_param" of these
  85  * are called parameters and the last "n_div" of these are called divs.
  86  * The basic tableau operations makes no distinction between different
  87  * kinds of variables.  These special variables are only used while
  88  * solving PILP problems.
  89  *
  90  * Dead columns and redundant rows are detected on the fly.
  91  * However, the basic operations do not ensure that all dead columns
  92  * or all redundant rows are detected.
  93  * isl_tab_detect_equalities and isl_tab_detect_redundant can be used
  94  * to perform and exhaustive search for dead columns and redundant rows.
  95  *
  96  * The samples matrix contains "n_sample" integer points that have at some
  97  * point been elements satisfying the tableau.  The first "n_outside"
  98  * of them no longer satisfy the tableau.  They are kept because they
  99  * can be reinstated during rollback when the constraint that cut them
 100  * out is removed.  These samples are only maintained for the context
 101  * tableau while solving PILP problems.
 102  */
 103 enum isl_tab_row_sign {
 104         isl_tab_row_unknown = 0,
 105         isl_tab_row_pos,
 106         isl_tab_row_neg,
 107         isl_tab_row_any,
 108 };
 109 struct isl_tab {
 110         struct isl_mat *mat;
 111
 112         unsigned n_row;
 113         unsigned n_col;
 114         unsigned n_dead;
 115         unsigned n_redundant;
 116
 117         unsigned n_var;
 118         unsigned n_param;
 119         unsigned n_div;
 120         unsigned max_var;
 121         unsigned n_con;
 122         unsigned n_eq;
 123         unsigned max_con;
 124         struct isl_tab_var *var;
 125         struct isl_tab_var *con;
 126         int *row_var;   /* v >= 0 -> var v;     v < 0 -> con ~v */
 127         int *col_var;   /* v >= 0 -> var v;     v < 0 -> con ~v */
 128         enum isl_tab_row_sign *row_sign;
 129
 130         struct isl_tab_undo bottom;
 131         struct isl_tab_undo *top;
 132
 133         struct isl_vec *dual;
 134         struct isl_basic_set *bset;
 135
 136         unsigned n_sample;
 137         unsigned n_outside;
 138         struct isl_mat *samples;
 139
 140         unsigned need_undo : 1;
 141         unsigned rational : 1;
 142         unsigned empty : 1;
 143         unsigned in_undo : 1;
 144         unsigned M : 1;
 145 };
 146
 147 struct isl_tab *isl_tab_alloc(struct isl_ctx *ctx,
 148         unsigned n_row, unsigned n_var, unsigned M);
 149 void isl_tab_free(struct isl_tab *tab);
 150
 151 struct isl_tab *isl_tab_from_basic_map(struct isl_basic_map *bmap);
 152 struct isl_tab *isl_tab_from_basic_set(struct isl_basic_set *bset);
 153 struct isl_tab *isl_tab_from_recession_cone(struct isl_basic_map *bmap);
 154 int isl_tab_cone_is_bounded(struct isl_tab *tab);
 155 struct isl_basic_map *isl_basic_map_update_from_tab(struct isl_basic_map *bmap,
 156         struct isl_tab *tab);
 157 struct isl_basic_set *isl_basic_set_update_from_tab(struct isl_basic_set *bset,
 158         struct isl_tab *tab);
 159 struct isl_tab *isl_tab_detect_equalities(struct isl_tab *tab);
 160 struct isl_tab *isl_tab_detect_redundant(struct isl_tab *tab);
 161 #define ISL_TAB_SAVE_DUAL       (1 << 0)
 162 enum isl_lp_result isl_tab_min(struct isl_tab *tab,
 163         isl_int *f, isl_int denom, isl_int *opt, isl_int *opt_denom,
 164         unsigned flags);
 165
 166 struct isl_tab *isl_tab_extend(struct isl_tab *tab, unsigned n_new);
 167 struct isl_tab *isl_tab_add_ineq(struct isl_tab *tab, isl_int *ineq);
 168 struct isl_tab *isl_tab_add_valid_eq(struct isl_tab *tab, isl_int *eq);
 169
 170 int isl_tab_is_equality(struct isl_tab *tab, int con);
 171 int isl_tab_is_redundant(struct isl_tab *tab, int con);
 172
 173 int isl_tab_sample_is_integer(struct isl_tab *tab);
 174 struct isl_vec *isl_tab_get_sample_value(struct isl_tab *tab);
 175
 176 enum isl_ineq_type {
 177         isl_ineq_error = -1,
 178         isl_ineq_redundant,
 179         isl_ineq_separate,
 180         isl_ineq_cut,
 181         isl_ineq_adj_eq,
 182         isl_ineq_adj_ineq,
 183 };
 184
 185 enum isl_ineq_type isl_tab_ineq_type(struct isl_tab *tab, isl_int *ineq);
 186
 187 struct isl_tab_undo *isl_tab_snap(struct isl_tab *tab);
 188 int isl_tab_rollback(struct isl_tab *tab, struct isl_tab_undo *snap);
 189
 190 struct isl_tab *isl_tab_relax(struct isl_tab *tab, int con);
 191 struct isl_tab *isl_tab_select_facet(struct isl_tab *tab, int con);
 192
 193 void isl_tab_dump(struct isl_tab *tab, FILE *out, int indent);
 194
 195 struct isl_map *isl_tab_basic_map_partial_lexopt(
 196                 struct isl_basic_map *bmap, struct isl_basic_set *dom,
 197                 struct isl_set **empty, int max);
 198
 199 /* private */
 200
 201 struct isl_tab_var *isl_tab_var_from_row(struct isl_tab *tab, int i);
 202 int isl_tab_mark_redundant(struct isl_tab *tab, int row);
 203 struct isl_tab *isl_tab_mark_empty(struct isl_tab *tab);
 204 struct isl_tab *isl_tab_dup(struct isl_tab *tab);
 205 int isl_tab_extend_cons(struct isl_tab *tab, unsigned n_new);
 206 int isl_tab_allocate_con(struct isl_tab *tab);
 207 int isl_tab_extend_vars(struct isl_tab *tab, unsigned n_new);
 208 int isl_tab_allocate_var(struct isl_tab *tab);
 209 void isl_tab_pivot(struct isl_tab *tab, int row, int col);
 210 int isl_tab_add_row(struct isl_tab *tab, isl_int *line);
 211 int isl_tab_row_is_redundant(struct isl_tab *tab, int row);
 212 int isl_tab_min_at_most_neg_one(struct isl_tab *tab, struct isl_tab_var *var);
 213
 214 void isl_tab_push(struct isl_tab *tab, enum isl_tab_undo_type type);
 215 void isl_tab_push_var(struct isl_tab *tab,
 216         enum isl_tab_undo_type type, struct isl_tab_var *var);
 217 void isl_tab_push_basis(struct isl_tab *tab);
 218
 219 #endif