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 };
  27
  28 struct isl_tab_undo {
  29         enum isl_tab_undo_type  type;
  30         struct isl_tab_var      *var;
  31         struct isl_tab_undo     *next;
  32 };
  33
  34 /* The tableau maintains equality relations.
  35  * Each column and each row is associated to a variable or a constraint.
  36  * The "value" of an inequality constraint is the value of the corresponding
  37  * slack variable.
  38  * The "row_var" and "col_var" arrays map column and row indices
  39  * to indices in the "var" and "con" arrays.  The elements of these
  40  * arrays maintain extra information about the variables and the constraints.
  41  * Each row expresses the corresponding row variable as an affine expression
  42  * of the column variables.
  43  * The first two columns in the matrix contain the common denominator of
  44  * the row and the numerator of the constant term.  The third column
  45  * in the matrix is called column 0 with respect to the col_var array.
  46  * The sample value of the tableau is the value that assigns zero
  47  * to all the column variables and the constant term of each affine
  48  * expression to the corresponding row variable.
  49  * The operations on the tableau maintain the property that the sample
  50  * value satisfies the non-negativity constraints (usually on the slack
  51  * variables).
  52  *
  53  * The first n_dead column variables have their values fixed to zero.
  54  * The corresponding tab_vars are flagged "is_zero".
  55  * Some of the rows that have have zero coefficients in all but
  56  * the dead columns are also flagged "is_zero".
  57  *
  58  * The first n_redundant rows correspond to inequality constraints
  59  * that are always satisfied for any value satisfying the non-redundant
  60  * rows.  The corresponding tab_vars are flagged "is_redundant".
  61  * A row variable that is flagged "is_zero" is also flagged "is_redundant"
  62  * since the constraint has been reduced to 0 = 0 and is therefore always
  63  * satisfied.
  64  *
  65  * Dead columns and redundant rows are detected on the fly.
  66  * However, the basic operations do not ensure that all dead columns
  67  * or all redundant rows are detected.
  68  * isl_tab_detect_equalities and isl_tab_detect_redundant can be used
  69  * to peform and exhaustive search for dead columns and redundant rows.
  70  */
  71 struct isl_tab {
  72         struct isl_mat *mat;
  73
  74         unsigned n_row;
  75         unsigned n_col;
  76         unsigned n_dead;
  77         unsigned n_redundant;
  78
  79         unsigned n_var;
  80         unsigned n_con;
  81         unsigned n_eq;
  82         unsigned max_con;
  83         struct isl_tab_var *var;
  84         struct isl_tab_var *con;
  85         int *row_var;   /* v >= 0 -> var v;     v < 0 -> con ~v */
  86         int *col_var;   /* v >= 0 -> var v;     v < 0 -> con ~v */
  87
  88         struct isl_tab_undo bottom;
  89         struct isl_tab_undo *top;
  90
  91         struct isl_vec *dual;
  92
  93         unsigned need_undo : 1;
  94         unsigned rational : 1;
  95         unsigned empty : 1;
  96 };
  97
  98 struct isl_tab *isl_tab_alloc(struct isl_ctx *ctx,
  99         unsigned n_row, unsigned n_var);
 100 void isl_tab_free(struct isl_ctx *ctx, struct isl_tab *tab);
 101
 102 struct isl_tab *isl_tab_from_basic_map(struct isl_basic_map *bmap);
 103 struct isl_tab *isl_tab_from_basic_set(struct isl_basic_set *bset);
 104 struct isl_tab *isl_tab_from_recession_cone(struct isl_basic_map *bmap);
 105 int isl_tab_cone_is_bounded(struct isl_ctx *ctx, struct isl_tab *tab);
 106 struct isl_basic_map *isl_basic_map_update_from_tab(struct isl_basic_map *bmap,
 107         struct isl_tab *tab);
 108 struct isl_basic_set *isl_basic_set_update_from_tab(struct isl_basic_set *bset,
 109         struct isl_tab *tab);
 110 struct isl_tab *isl_tab_detect_equalities(struct isl_ctx *ctx,
 111                                 struct isl_tab *tab);
 112 struct isl_tab *isl_tab_detect_redundant(struct isl_ctx *ctx,
 113                                 struct isl_tab *tab);
 114 #define ISL_TAB_SAVE_DUAL       (1 << 0)
 115 enum isl_lp_result isl_tab_min(struct isl_ctx *ctx, struct isl_tab *tab,
 116         isl_int *f, isl_int denom, isl_int *opt, isl_int *opt_denom,
 117         unsigned flags);
 118
 119 struct isl_tab *isl_tab_extend(struct isl_ctx *ctx, struct isl_tab *tab,
 120                                 unsigned n_new);
 121 struct isl_tab *isl_tab_add_ineq(struct isl_ctx *ctx,
 122         struct isl_tab *tab, isl_int *ineq);
 123 struct isl_tab *isl_tab_add_valid_eq(struct isl_ctx *ctx,
 124         struct isl_tab *tab, isl_int *eq);
 125
 126 int isl_tab_is_equality(struct isl_ctx *ctx, struct isl_tab *tab, int con);
 127 int isl_tab_is_redundant(struct isl_ctx *ctx, struct isl_tab *tab, int con);
 128
 129 struct isl_vec *isl_tab_get_sample_value(struct isl_ctx *ctx,
 130                                                 struct isl_tab *tab);
 131
 132 enum isl_ineq_type {
 133         isl_ineq_error = -1,
 134         isl_ineq_redundant,
 135         isl_ineq_separate,
 136         isl_ineq_cut,
 137         isl_ineq_adj_eq,
 138         isl_ineq_adj_ineq,
 139 };
 140
 141 enum isl_ineq_type isl_tab_ineq_type(struct isl_ctx *ctx, struct isl_tab *tab,
 142         isl_int *ineq);
 143
 144 struct isl_tab_undo *isl_tab_snap(struct isl_ctx *ctx, struct isl_tab *tab);
 145 int isl_tab_rollback(struct isl_ctx *ctx, struct isl_tab *tab,
 146         struct isl_tab_undo *snap);
 147
 148 struct isl_tab *isl_tab_relax(struct isl_ctx *ctx,
 149         struct isl_tab *tab, int con);
 150 struct isl_tab *isl_tab_select_facet(struct isl_ctx *ctx,
 151         struct isl_tab *tab, int con);
 152
 153 void isl_tab_dump(struct isl_ctx *ctx, struct isl_tab *tab,
 154                                 FILE *out, int indent);
 155
 156 #endif