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