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         unsigned negated : 1;
  18 };
  19
  20 enum isl_tab_undo_type {
  21         isl_tab_undo_bottom,
  22         isl_tab_undo_empty,
  23         isl_tab_undo_nonneg,
  24         isl_tab_undo_redundant,
  25         isl_tab_undo_zero,
  26         isl_tab_undo_allocate,
  27         isl_tab_undo_relax,
  28         isl_tab_undo_bset_ineq,
  29         isl_tab_undo_bset_eq,
  30         isl_tab_undo_bset_div,
  31         isl_tab_undo_saved_basis,
  32         isl_tab_undo_drop_sample,
  33         isl_tab_undo_saved_samples,
  34 };
  35
  36 union isl_tab_undo_val {
  37         int             var_index;
  38         int             *col_var;
  39         int             n;
  40 };
  41
  42 struct isl_tab_undo {
  43         enum isl_tab_undo_type  type;
  44         union isl_tab_undo_val  u;
  45         struct isl_tab_undo     *next;
  46 };
  47
  48 /* The tableau maintains equality relations.
  49  * Each column and each row is associated to a variable or a constraint.
  50  * The "value" of an inequality constraint is the value of the corresponding
  51  * slack variable.
  52  * The "row_var" and "col_var" arrays map column and row indices
  53  * to indices in the "var" and "con" arrays.  The elements of these
  54  * arrays maintain extra information about the variables and the constraints.
  55  * Each row expresses the corresponding row variable as an affine expression
  56  * of the column variables.
  57  * The first two columns in the matrix contain the common denominator of
  58  * the row and the numerator of the constant term.
  59  * If "M" is set, then the third column represents the "big parameter".
  60  * The third (M = 0) or fourth (M = 1) column
  61  * in the matrix is called column 0 with respect to the col_var array.
  62  * The sample value of the tableau is the value that assigns zero
  63  * to all the column variables and the constant term of each affine
  64  * expression to the corresponding row variable.
  65  * The operations on the tableau maintain the property that the sample
  66  * value satisfies the non-negativity constraints (usually on the slack
  67  * variables).
  68  *
  69  * The big parameter represents an arbitrarily big (and divisible)
  70  * positive number.  If present, then the sign of a row is determined
  71  * lexicographically, with the sign of the big parameter coefficient
  72  * considered first.  The big parameter is only used while
  73  * solving PILP problems.
  74  *
  75  * The first n_dead column variables have their values fixed to zero.
  76  * The corresponding tab_vars are flagged "is_zero".
  77  * Some of the rows that have have zero coefficients in all but
  78  * the dead columns are also flagged "is_zero".
  79  *
  80  * The first n_redundant rows correspond to inequality constraints
  81  * that are always satisfied for any value satisfying the non-redundant
  82  * rows.  The corresponding tab_vars are flagged "is_redundant".
  83  * A row variable that is flagged "is_zero" is also flagged "is_redundant"
  84  * since the constraint has been reduced to 0 = 0 and is therefore always
  85  * satisfied.
  86  *
  87  * There are "n_var" variables in total.  The first "n_param" of these
  88  * are called parameters and the last "n_div" of these are called divs.
  89  * The basic tableau operations makes no distinction between different
  90  * kinds of variables.  These special variables are only used while
  91  * solving PILP problems.
  92  *
  93  * Dead columns and redundant rows are detected on the fly.
  94  * However, the basic operations do not ensure that all dead columns
  95  * or all redundant rows are detected.
  96  * isl_tab_detect_implicit_equalities and isl_tab_detect_redundant can be used
  97  * to perform and exhaustive search for dead columns and redundant rows.
  98  *
  99  * The samples matrix contains "n_sample" integer points that have at some
 100  * point been elements satisfying the tableau.  The first "n_outside"
 101  * of them no longer satisfy the tableau.  They are kept because they
 102  * can be reinstated during rollback when the constraint that cut them
 103  * out is removed.  These samples are only maintained for the context
 104  * tableau while solving PILP problems.
 105  */
 106 enum isl_tab_row_sign {
 107         isl_tab_row_unknown = 0,
 108         isl_tab_row_pos,
 109         isl_tab_row_neg,
 110         isl_tab_row_any,
 111 };
 112 struct isl_tab {
 113         struct isl_mat *mat;
 114
 115         unsigned n_row;
 116         unsigned n_col;
 117         unsigned n_dead;
 118         unsigned n_redundant;
 119
 120         unsigned n_var;
 121         unsigned n_param;
 122         unsigned n_div;
 123         unsigned max_var;
 124         unsigned n_con;
 125         unsigned n_eq;
 126         unsigned max_con;
 127         struct isl_tab_var *var;
 128         struct isl_tab_var *con;
 129         int *row_var;   /* v >= 0 -> var v;     v < 0 -> con ~v */
 130         int *col_var;   /* v >= 0 -> var v;     v < 0 -> con ~v */
 131         enum isl_tab_row_sign *row_sign;
 132
 133         struct isl_tab_undo bottom;
 134         struct isl_tab_undo *top;
 135
 136         struct isl_vec *dual;
 137         struct isl_basic_set *bset;
 138
 139         unsigned n_sample;
 140         unsigned n_outside;
 141         int *sample_index;
 142         struct isl_mat *samples;
 143
 144         int n_zero;
 145         int n_unbounded;
 146         struct isl_mat *basis;
 147
 148         unsigned need_undo : 1;
 149         unsigned rational : 1;
 150         unsigned empty : 1;
 151         unsigned in_undo : 1;
 152         unsigned M : 1;
 153 };
 154
 155 struct isl_tab *isl_tab_alloc(struct isl_ctx *ctx,
 156         unsigned n_row, unsigned n_var, unsigned M);
 157 void isl_tab_free(struct isl_tab *tab);
 158
 159 struct isl_tab *isl_tab_from_basic_map(struct isl_basic_map *bmap);
 160 struct isl_tab *isl_tab_from_basic_set(struct isl_basic_set *bset);
 161 struct isl_tab *isl_tab_from_recession_cone(struct isl_basic_set *bset);
 162 int isl_tab_cone_is_bounded(struct isl_tab *tab);
 163 struct isl_basic_map *isl_basic_map_update_from_tab(struct isl_basic_map *bmap,
 164         struct isl_tab *tab);
 165 struct isl_basic_set *isl_basic_set_update_from_tab(struct isl_basic_set *bset,
 166         struct isl_tab *tab);
 167 struct isl_tab *isl_tab_detect_implicit_equalities(struct isl_tab *tab);
 168 struct isl_tab *isl_tab_detect_redundant(struct isl_tab *tab);
 169 #define ISL_TAB_SAVE_DUAL       (1 << 0)
 170 enum isl_lp_result isl_tab_min(struct isl_tab *tab,
 171         isl_int *f, isl_int denom, isl_int *opt, isl_int *opt_denom,
 172         unsigned flags);
 173
 174 struct isl_tab *isl_tab_extend(struct isl_tab *tab, unsigned n_new);
 175 struct isl_tab *isl_tab_add_ineq(struct isl_tab *tab, isl_int *ineq);
 176 struct isl_tab *isl_tab_add_eq(struct isl_tab *tab, isl_int *eq);
 177 struct isl_tab *isl_tab_add_valid_eq(struct isl_tab *tab, isl_int *eq);
 178
 179 int isl_tab_is_equality(struct isl_tab *tab, int con);
 180 int isl_tab_is_redundant(struct isl_tab *tab, int con);
 181
 182 int isl_tab_sample_is_integer(struct isl_tab *tab);
 183 struct isl_vec *isl_tab_get_sample_value(struct isl_tab *tab);
 184
 185 enum isl_ineq_type {
 186         isl_ineq_error = -1,
 187         isl_ineq_redundant,
 188         isl_ineq_separate,
 189         isl_ineq_cut,
 190         isl_ineq_adj_eq,
 191         isl_ineq_adj_ineq,
 192 };
 193
 194 enum isl_ineq_type isl_tab_ineq_type(struct isl_tab *tab, isl_int *ineq);
 195
 196 struct isl_tab_undo *isl_tab_snap(struct isl_tab *tab);
 197 int isl_tab_rollback(struct isl_tab *tab, struct isl_tab_undo *snap);
 198
 199 struct isl_tab *isl_tab_relax(struct isl_tab *tab, int con);
 200 struct isl_tab *isl_tab_select_facet(struct isl_tab *tab, int con);
 201
 202 void isl_tab_dump(struct isl_tab *tab, FILE *out, int indent);
 203
 204 struct isl_map *isl_tab_basic_map_partial_lexopt(
 205                 struct isl_basic_map *bmap, struct isl_basic_set *dom,
 206                 struct isl_set **empty, int max);
 207
 208 /* private */
 209
 210 struct isl_tab_var *isl_tab_var_from_row(struct isl_tab *tab, int i);
 211 int isl_tab_mark_redundant(struct isl_tab *tab, int row);
 212 struct isl_tab *isl_tab_mark_empty(struct isl_tab *tab);
 213 struct isl_tab *isl_tab_dup(struct isl_tab *tab);
 214 struct isl_tab *isl_tab_product(struct isl_tab *tab1, struct isl_tab *tab2);
 215 int isl_tab_extend_cons(struct isl_tab *tab, unsigned n_new);
 216 int isl_tab_allocate_con(struct isl_tab *tab);
 217 int isl_tab_extend_vars(struct isl_tab *tab, unsigned n_new);
 218 int isl_tab_allocate_var(struct isl_tab *tab);
 219 void isl_tab_pivot(struct isl_tab *tab, int row, int col);
 220 int isl_tab_add_row(struct isl_tab *tab, isl_int *line);
 221 int isl_tab_row_is_redundant(struct isl_tab *tab, int row);
 222 int isl_tab_min_at_most_neg_one(struct isl_tab *tab, struct isl_tab_var *var);
 223 int isl_tab_kill_col(struct isl_tab *tab, int col);
 224
 225 void isl_tab_push(struct isl_tab *tab, enum isl_tab_undo_type type);
 226 void isl_tab_push_var(struct isl_tab *tab,
 227         enum isl_tab_undo_type type, struct isl_tab_var *var);
 228 void isl_tab_push_basis(struct isl_tab *tab);
 229
 230 struct isl_tab *isl_tab_init_samples(struct isl_tab *tab);
 231 struct isl_tab *isl_tab_add_sample(struct isl_tab *tab,
 232         __isl_take isl_vec *sample);
 233 struct isl_tab *isl_tab_drop_sample(struct isl_tab *tab, int s);
 234 void isl_tab_save_samples(struct isl_tab *tab);
 235
 236 #endif