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