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_freeze,
  26         isl_tab_undo_zero,
  27         isl_tab_undo_allocate,
  28         isl_tab_undo_relax,
  29         isl_tab_undo_bset_ineq,
  30         isl_tab_undo_bset_eq,
  31         isl_tab_undo_bset_div,
  32         isl_tab_undo_saved_basis,
  33         isl_tab_undo_drop_sample,
  34         isl_tab_undo_saved_samples,
  35         isl_tab_undo_callback,
  36 };
  37
  38 struct isl_tab_callback {
  39         int (*run)(struct isl_tab_callback *cb);
  40 };
  41
  42 union isl_tab_undo_val {
  43         int             var_index;
  44         int             *col_var;
  45         int             n;
  46         struct isl_tab_callback *callback;
  47 };
  48
  49 struct isl_tab_undo {
  50         enum isl_tab_undo_type  type;
  51         union isl_tab_undo_val  u;
  52         struct isl_tab_undo     *next;
  53 };
  54
  55 /* The tableau maintains equality relations.
  56  * Each column and each row is associated to a variable or a constraint.
  57  * The "value" of an inequality constraint is the value of the corresponding
  58  * slack variable.
  59  * The "row_var" and "col_var" arrays map column and row indices
  60  * to indices in the "var" and "con" arrays.  The elements of these
  61  * arrays maintain extra information about the variables and the constraints.
  62  * Each row expresses the corresponding row variable as an affine expression
  63  * of the column variables.
  64  * The first two columns in the matrix contain the common denominator of
  65  * the row and the numerator of the constant term.
  66  * If "M" is set, then the third column represents the "big parameter".
  67  * The third (M = 0) or fourth (M = 1) column
  68  * in the matrix is called column 0 with respect to the col_var array.
  69  * The sample value of the tableau is the value that assigns zero
  70  * to all the column variables and the constant term of each affine
  71  * expression to the corresponding row variable.
  72  * The operations on the tableau maintain the property that the sample
  73  * value satisfies the non-negativity constraints (usually on the slack
  74  * variables).
  75  *
  76  * The big parameter represents an arbitrarily big (and divisible)
  77  * positive number.  If present, then the sign of a row is determined
  78  * lexicographically, with the sign of the big parameter coefficient
  79  * considered first.  The big parameter is only used while
  80  * solving PILP problems.
  81  *
  82  * The first n_dead column variables have their values fixed to zero.
  83  * The corresponding tab_vars are flagged "is_zero".
  84  * Some of the rows that have have zero coefficients in all but
  85  * the dead columns are also flagged "is_zero".
  86  *
  87  * The first n_redundant rows correspond to inequality constraints
  88  * that are always satisfied for any value satisfying the non-redundant
  89  * rows.  The corresponding tab_vars are flagged "is_redundant".
  90  * A row variable that is flagged "is_zero" is also flagged "is_redundant"
  91  * since the constraint has been reduced to 0 = 0 and is therefore always
  92  * satisfied.
  93  *
  94  * There are "n_var" variables in total.  The first "n_param" of these
  95  * are called parameters and the last "n_div" of these are called divs.
  96  * The basic tableau operations makes no distinction between different
  97  * kinds of variables.  These special variables are only used while
  98  * solving PILP problems.
  99  *
 100  * Dead columns and redundant rows are detected on the fly.
 101  * However, the basic operations do not ensure that all dead columns
 102  * or all redundant rows are detected.
 103  * isl_tab_detect_implicit_equalities and isl_tab_detect_redundant can be used
 104  * to perform and exhaustive search for dead columns and redundant rows.
 105  *
 106  * The samples matrix contains "n_sample" integer points that have at some
 107  * point been elements satisfying the tableau.  The first "n_outside"
 108  * of them no longer satisfy the tableau.  They are kept because they
 109  * can be reinstated during rollback when the constraint that cut them
 110  * out is removed.  These samples are only maintained for the context
 111  * tableau while solving PILP problems.
 112  */
 113 enum isl_tab_row_sign {
 114         isl_tab_row_unknown = 0,
 115         isl_tab_row_pos,
 116         isl_tab_row_neg,
 117         isl_tab_row_any,
 118 };
 119 struct isl_tab {
 120         struct isl_mat *mat;
 121
 122         unsigned n_row;
 123         unsigned n_col;
 124         unsigned n_dead;
 125         unsigned n_redundant;
 126
 127         unsigned n_var;
 128         unsigned n_param;
 129         unsigned n_div;
 130         unsigned max_var;
 131         unsigned n_con;
 132         unsigned n_eq;
 133         unsigned max_con;
 134         struct isl_tab_var *var;
 135         struct isl_tab_var *con;
 136         int *row_var;   /* v >= 0 -> var v;     v < 0 -> con ~v */
 137         int *col_var;   /* v >= 0 -> var v;     v < 0 -> con ~v */
 138         enum isl_tab_row_sign *row_sign;
 139
 140         struct isl_tab_undo bottom;
 141         struct isl_tab_undo *top;
 142
 143         struct isl_vec *dual;
 144         struct isl_basic_set *bset;
 145
 146         unsigned n_sample;
 147         unsigned n_outside;
 148         int *sample_index;
 149         struct isl_mat *samples;
 150
 151         int n_zero;
 152         int n_unbounded;
 153         struct isl_mat *basis;
 154
 155         unsigned need_undo : 1;
 156         unsigned rational : 1;
 157         unsigned empty : 1;
 158         unsigned in_undo : 1;
 159         unsigned M : 1;
 160         unsigned cone : 1;
 161 };
 162
 163 struct isl_tab *isl_tab_alloc(struct isl_ctx *ctx,
 164         unsigned n_row, unsigned n_var, unsigned M);
 165 void isl_tab_free(struct isl_tab *tab);
 166
 167 struct isl_tab *isl_tab_from_basic_map(struct isl_basic_map *bmap);
 168 struct isl_tab *isl_tab_from_basic_set(struct isl_basic_set *bset);
 169 struct isl_tab *isl_tab_from_recession_cone(struct isl_basic_set *bset);
 170 int isl_tab_cone_is_bounded(struct isl_tab *tab);
 171 struct isl_basic_map *isl_basic_map_update_from_tab(struct isl_basic_map *bmap,
 172         struct isl_tab *tab);
 173 struct isl_basic_set *isl_basic_set_update_from_tab(struct isl_basic_set *bset,
 174         struct isl_tab *tab);
 175 struct isl_tab *isl_tab_detect_implicit_equalities(struct isl_tab *tab) WARN_UNUSED;
 176 int isl_tab_detect_redundant(struct isl_tab *tab) WARN_UNUSED;
 177 #define ISL_TAB_SAVE_DUAL       (1 << 0)
 178 enum isl_lp_result isl_tab_min(struct isl_tab *tab,
 179         isl_int *f, isl_int denom, isl_int *opt, isl_int *opt_denom,
 180         unsigned flags) WARN_UNUSED;
 181
 182 struct isl_tab *isl_tab_extend(struct isl_tab *tab, unsigned n_new) WARN_UNUSED;
 183 int isl_tab_add_ineq(struct isl_tab *tab, isl_int *ineq) WARN_UNUSED;
 184 struct isl_tab *isl_tab_add_eq(struct isl_tab *tab, isl_int *eq) WARN_UNUSED;
 185 struct isl_tab *isl_tab_add_valid_eq(struct isl_tab *tab, isl_int *eq) WARN_UNUSED;
 186
 187 int isl_tab_freeze_constraint(struct isl_tab *tab, int con) WARN_UNUSED;
 188
 189 int isl_tab_is_equality(struct isl_tab *tab, int con);
 190 int isl_tab_is_redundant(struct isl_tab *tab, int con);
 191
 192 int isl_tab_sample_is_integer(struct isl_tab *tab);
 193 struct isl_vec *isl_tab_get_sample_value(struct isl_tab *tab);
 194
 195 enum isl_ineq_type {
 196         isl_ineq_error = -1,
 197         isl_ineq_redundant,
 198         isl_ineq_separate,
 199         isl_ineq_cut,
 200         isl_ineq_adj_eq,
 201         isl_ineq_adj_ineq,
 202 };
 203
 204 enum isl_ineq_type isl_tab_ineq_type(struct isl_tab *tab, isl_int *ineq);
 205
 206 struct isl_tab_undo *isl_tab_snap(struct isl_tab *tab);
 207 int isl_tab_rollback(struct isl_tab *tab, struct isl_tab_undo *snap) WARN_UNUSED;
 208
 209 struct isl_tab *isl_tab_relax(struct isl_tab *tab, int con) WARN_UNUSED;
 210 struct isl_tab *isl_tab_select_facet(struct isl_tab *tab, int con) WARN_UNUSED;
 211
 212 void isl_tab_dump(struct isl_tab *tab, FILE *out, int indent);
 213
 214 struct isl_map *isl_tab_basic_map_partial_lexopt(
 215                 struct isl_basic_map *bmap, struct isl_basic_set *dom,
 216                 struct isl_set **empty, int max);
 217
 218 /* private */
 219
 220 struct isl_tab_var *isl_tab_var_from_row(struct isl_tab *tab, int i);
 221 int isl_tab_mark_redundant(struct isl_tab *tab, int row) WARN_UNUSED;
 222 int isl_tab_mark_empty(struct isl_tab *tab) WARN_UNUSED;
 223 struct isl_tab *isl_tab_dup(struct isl_tab *tab);
 224 struct isl_tab *isl_tab_product(struct isl_tab *tab1, struct isl_tab *tab2);
 225 int isl_tab_extend_cons(struct isl_tab *tab, unsigned n_new) WARN_UNUSED;
 226 int isl_tab_allocate_con(struct isl_tab *tab) WARN_UNUSED;
 227 int isl_tab_extend_vars(struct isl_tab *tab, unsigned n_new) WARN_UNUSED;
 228 int isl_tab_allocate_var(struct isl_tab *tab) WARN_UNUSED;
 229 int isl_tab_pivot(struct isl_tab *tab, int row, int col) WARN_UNUSED;
 230 int isl_tab_add_row(struct isl_tab *tab, isl_int *line) WARN_UNUSED;
 231 int isl_tab_row_is_redundant(struct isl_tab *tab, int row);
 232 int isl_tab_min_at_most_neg_one(struct isl_tab *tab, struct isl_tab_var *var);
 233 int isl_tab_kill_col(struct isl_tab *tab, int col) WARN_UNUSED;
 234
 235 int isl_tab_push(struct isl_tab *tab, enum isl_tab_undo_type type) WARN_UNUSED;
 236 int isl_tab_push_var(struct isl_tab *tab,
 237         enum isl_tab_undo_type type, struct isl_tab_var *var) WARN_UNUSED;
 238 int isl_tab_push_basis(struct isl_tab *tab) WARN_UNUSED;
 239
 240 struct isl_tab *isl_tab_init_samples(struct isl_tab *tab) WARN_UNUSED;
 241 struct isl_tab *isl_tab_add_sample(struct isl_tab *tab,
 242         __isl_take isl_vec *sample) WARN_UNUSED;
 243 struct isl_tab *isl_tab_drop_sample(struct isl_tab *tab, int s);
 244 int isl_tab_save_samples(struct isl_tab *tab) WARN_UNUSED;
 245
 246 struct isl_tab *isl_tab_detect_equalities(struct isl_tab *tab,
 247         struct isl_tab *tab_cone) WARN_UNUSED;
 248
 249 int isl_tab_push_callback(struct isl_tab *tab,
 250         struct isl_tab_callback *callback) WARN_UNUSED;
 251
 252 #endif