isl_tab.h

   1 /*
   2  * Copyright 2008-2009 Katholieke Universiteit Leuven
   3  *
   4  * Use of this software is governed by the GNU LGPLv2.1 license
   5  *
   6  * Written by Sven Verdoolaege, K.U.Leuven, Departement
   7  * Computerwetenschappen, Celestijnenlaan 200A, B-3001 Leuven, Belgium
   8  */
   9
  10 #ifndef ISL_TAB_H
  11 #define ISL_TAB_H
  12
  13 #include "isl_lp.h"
  14 #include "isl_map.h"
  15 #include "isl_mat.h"
  16 #include "isl_set.h"
  17
  18 struct isl_tab_var {
  19         int index;
  20         unsigned is_row : 1;
  21         unsigned is_nonneg : 1;
  22         unsigned is_zero : 1;
  23         unsigned is_redundant : 1;
  24         unsigned marked : 1;
  25         unsigned frozen : 1;
  26         unsigned negated : 1;
  27 };
  28
  29 enum isl_tab_undo_type {
  30         isl_tab_undo_bottom,
  31         isl_tab_undo_empty,
  32         isl_tab_undo_nonneg,
  33         isl_tab_undo_redundant,
  34         isl_tab_undo_freeze,
  35         isl_tab_undo_zero,
  36         isl_tab_undo_allocate,
  37         isl_tab_undo_relax,
  38         isl_tab_undo_bmap_ineq,
  39         isl_tab_undo_bmap_eq,
  40         isl_tab_undo_bmap_div,
  41         isl_tab_undo_saved_basis,
  42         isl_tab_undo_drop_sample,
  43         isl_tab_undo_saved_samples,
  44         isl_tab_undo_callback,
  45 };
  46
  47 struct isl_tab_callback {
  48         int (*run)(struct isl_tab_callback *cb);
  49 };
  50
  51 union isl_tab_undo_val {
  52         int             var_index;
  53         int             *col_var;
  54         int             n;
  55         struct isl_tab_callback *callback;
  56 };
  57
  58 struct isl_tab_undo {
  59         enum isl_tab_undo_type  type;
  60         union isl_tab_undo_val  u;
  61         struct isl_tab_undo     *next;
  62 };
  63
  64 /* The tableau maintains equality relations.
  65  * Each column and each row is associated to a variable or a constraint.
  66  * The "value" of an inequality constraint is the value of the corresponding
  67  * slack variable.
  68  * The "row_var" and "col_var" arrays map column and row indices
  69  * to indices in the "var" and "con" arrays.  The elements of these
  70  * arrays maintain extra information about the variables and the constraints.
  71  * Each row expresses the corresponding row variable as an affine expression
  72  * of the column variables.
  73  * The first two columns in the matrix contain the common denominator of
  74  * the row and the numerator of the constant term.
  75  * If "M" is set, then the third column represents the "big parameter".
  76  * The third (M = 0) or fourth (M = 1) column
  77  * in the matrix is called column 0 with respect to the col_var array.
  78  * The sample value of the tableau is the value that assigns zero
  79  * to all the column variables and the constant term of each affine
  80  * expression to the corresponding row variable.
  81  * The operations on the tableau maintain the property that the sample
  82  * value satisfies the non-negativity constraints (usually on the slack
  83  * variables).
  84  *
  85  * The big parameter represents an arbitrarily big (and divisible)
  86  * positive number.  If present, then the sign of a row is determined
  87  * lexicographically, with the sign of the big parameter coefficient
  88  * considered first.  The big parameter is only used while
  89  * solving PILP problems.
  90  *
  91  * The first n_dead column variables have their values fixed to zero.
  92  * The corresponding tab_vars are flagged "is_zero".
  93  * Some of the rows that have have zero coefficients in all but
  94  * the dead columns are also flagged "is_zero".
  95  *
  96  * The first n_redundant rows correspond to inequality constraints
  97  * that are always satisfied for any value satisfying the non-redundant
  98  * rows.  The corresponding tab_vars are flagged "is_redundant".
  99  * A row variable that is flagged "is_zero" is also flagged "is_redundant"
 100  * since the constraint has been reduced to 0 = 0 and is therefore always
 101  * satisfied.
 102  *
 103  * There are "n_var" variables in total.  The first "n_param" of these
 104  * are called parameters and the last "n_div" of these are called divs.
 105  * The basic tableau operations makes no distinction between different
 106  * kinds of variables.  These special variables are only used while
 107  * solving PILP problems.
 108  *
 109  * Dead columns and redundant rows are detected on the fly.
 110  * However, the basic operations do not ensure that all dead columns
 111  * or all redundant rows are detected.
 112  * isl_tab_detect_implicit_equalities and isl_tab_detect_redundant can be used
 113  * to perform and exhaustive search for dead columns and redundant rows.
 114  *
 115  * The samples matrix contains "n_sample" integer points that have at some
 116  * point been elements satisfying the tableau.  The first "n_outside"
 117  * of them no longer satisfy the tableau.  They are kept because they
 118  * can be reinstated during rollback when the constraint that cut them
 119  * out is removed.  These samples are only maintained for the context
 120  * tableau while solving PILP problems.
 121  */
 122 enum isl_tab_row_sign {
 123         isl_tab_row_unknown = 0,
 124         isl_tab_row_pos,
 125         isl_tab_row_neg,
 126         isl_tab_row_any,
 127 };
 128 struct isl_tab {
 129         struct isl_mat *mat;
 130
 131         unsigned n_row;
 132         unsigned n_col;
 133         unsigned n_dead;
 134         unsigned n_redundant;
 135
 136         unsigned n_var;
 137         unsigned n_param;
 138         unsigned n_div;
 139         unsigned max_var;
 140         unsigned n_con;
 141         unsigned n_eq;
 142         unsigned max_con;
 143         struct isl_tab_var *var;
 144         struct isl_tab_var *con;
 145         int *row_var;   /* v >= 0 -> var v;     v < 0 -> con ~v */
 146         int *col_var;   /* v >= 0 -> var v;     v < 0 -> con ~v */
 147         enum isl_tab_row_sign *row_sign;
 148
 149         struct isl_tab_undo bottom;
 150         struct isl_tab_undo *top;
 151
 152         struct isl_vec *dual;
 153         struct isl_basic_map *bmap;
 154
 155         unsigned n_sample;
 156         unsigned n_outside;
 157         int *sample_index;
 158         struct isl_mat *samples;
 159
 160         int n_zero;
 161         int n_unbounded;
 162         struct isl_mat *basis;
 163
 164         unsigned strict_redundant : 1;
 165         unsigned need_undo : 1;
 166         unsigned rational : 1;
 167         unsigned empty : 1;
 168         unsigned in_undo : 1;
 169         unsigned M : 1;
 170         unsigned cone : 1;
 171 };
 172
 173 struct isl_tab *isl_tab_alloc(struct isl_ctx *ctx,
 174         unsigned n_row, unsigned n_var, unsigned M);
 175 void isl_tab_free(struct isl_tab *tab);
 176
 177 struct isl_tab *isl_tab_from_basic_map(struct isl_basic_map *bmap);
 178 struct isl_tab *isl_tab_from_basic_set(struct isl_basic_set *bset);
 179 struct isl_tab *isl_tab_from_recession_cone(struct isl_basic_set *bset,
 180         int parametric);
 181 int isl_tab_cone_is_bounded(struct isl_tab *tab);
 182 struct isl_basic_map *isl_basic_map_update_from_tab(struct isl_basic_map *bmap,
 183         struct isl_tab *tab);
 184 struct isl_basic_set *isl_basic_set_update_from_tab(struct isl_basic_set *bset,
 185         struct isl_tab *tab);
 186 int isl_tab_detect_implicit_equalities(struct isl_tab *tab) WARN_UNUSED;
 187 int isl_tab_detect_redundant(struct isl_tab *tab) WARN_UNUSED;
 188 #define ISL_TAB_SAVE_DUAL       (1 << 0)
 189 enum isl_lp_result isl_tab_min(struct isl_tab *tab,
 190         isl_int *f, isl_int denom, isl_int *opt, isl_int *opt_denom,
 191         unsigned flags) WARN_UNUSED;
 192
 193 struct isl_tab *isl_tab_extend(struct isl_tab *tab, unsigned n_new) WARN_UNUSED;
 194 int isl_tab_add_ineq(struct isl_tab *tab, isl_int *ineq) WARN_UNUSED;
 195 int isl_tab_add_eq(struct isl_tab *tab, isl_int *eq) WARN_UNUSED;
 196 struct isl_tab *isl_tab_add_valid_eq(struct isl_tab *tab, isl_int *eq) WARN_UNUSED;
 197
 198 int isl_tab_freeze_constraint(struct isl_tab *tab, int con) WARN_UNUSED;
 199
 200 int isl_tab_track_bmap(struct isl_tab *tab, __isl_take isl_basic_map *bmap) WARN_UNUSED;
 201 int isl_tab_track_bset(struct isl_tab *tab, __isl_take isl_basic_set *bset) WARN_UNUSED;
 202 __isl_keep isl_basic_set *isl_tab_peek_bset(struct isl_tab *tab);
 203
 204 int isl_tab_is_equality(struct isl_tab *tab, int con);
 205 int isl_tab_is_redundant(struct isl_tab *tab, int con);
 206
 207 int isl_tab_sample_is_integer(struct isl_tab *tab);
 208 struct isl_vec *isl_tab_get_sample_value(struct isl_tab *tab);
 209
 210 enum isl_ineq_type {
 211         isl_ineq_error = -1,
 212         isl_ineq_redundant,
 213         isl_ineq_separate,
 214         isl_ineq_cut,
 215         isl_ineq_adj_eq,
 216         isl_ineq_adj_ineq,
 217 };
 218
 219 enum isl_ineq_type isl_tab_ineq_type(struct isl_tab *tab, isl_int *ineq);
 220
 221 struct isl_tab_undo *isl_tab_snap(struct isl_tab *tab);
 222 int isl_tab_rollback(struct isl_tab *tab, struct isl_tab_undo *snap) WARN_UNUSED;
 223
 224 struct isl_tab *isl_tab_relax(struct isl_tab *tab, int con) WARN_UNUSED;
 225 int isl_tab_select_facet(struct isl_tab *tab, int con) WARN_UNUSED;
 226
 227 void isl_tab_dump(struct isl_tab *tab, FILE *out, int indent);
 228
 229 struct isl_map *isl_tab_basic_map_partial_lexopt(
 230                 struct isl_basic_map *bmap, struct isl_basic_set *dom,
 231                 struct isl_set **empty, int max);
 232
 233 /* private */
 234
 235 struct isl_tab_var *isl_tab_var_from_row(struct isl_tab *tab, int i);
 236 int isl_tab_mark_redundant(struct isl_tab *tab, int row) WARN_UNUSED;
 237 int isl_tab_mark_empty(struct isl_tab *tab) WARN_UNUSED;
 238 struct isl_tab *isl_tab_dup(struct isl_tab *tab);
 239 struct isl_tab *isl_tab_product(struct isl_tab *tab1, struct isl_tab *tab2);
 240 int isl_tab_extend_cons(struct isl_tab *tab, unsigned n_new) WARN_UNUSED;
 241 int isl_tab_allocate_con(struct isl_tab *tab) WARN_UNUSED;
 242 int isl_tab_extend_vars(struct isl_tab *tab, unsigned n_new) WARN_UNUSED;
 243 int isl_tab_allocate_var(struct isl_tab *tab) WARN_UNUSED;
 244 int isl_tab_pivot(struct isl_tab *tab, int row, int col) WARN_UNUSED;
 245 int isl_tab_add_row(struct isl_tab *tab, isl_int *line) WARN_UNUSED;
 246 int isl_tab_row_is_redundant(struct isl_tab *tab, int row);
 247 int isl_tab_min_at_most_neg_one(struct isl_tab *tab, struct isl_tab_var *var);
 248 int isl_tab_sign_of_max(struct isl_tab *tab, int con);
 249 int isl_tab_kill_col(struct isl_tab *tab, int col) WARN_UNUSED;
 250
 251 int isl_tab_push(struct isl_tab *tab, enum isl_tab_undo_type type) WARN_UNUSED;
 252 int isl_tab_push_var(struct isl_tab *tab,
 253         enum isl_tab_undo_type type, struct isl_tab_var *var) WARN_UNUSED;
 254 int isl_tab_push_basis(struct isl_tab *tab) WARN_UNUSED;
 255
 256 struct isl_tab *isl_tab_init_samples(struct isl_tab *tab) WARN_UNUSED;
 257 struct isl_tab *isl_tab_add_sample(struct isl_tab *tab,
 258         __isl_take isl_vec *sample) WARN_UNUSED;
 259 struct isl_tab *isl_tab_drop_sample(struct isl_tab *tab, int s);
 260 int isl_tab_save_samples(struct isl_tab *tab) WARN_UNUSED;
 261
 262 struct isl_tab *isl_tab_detect_equalities(struct isl_tab *tab,
 263         struct isl_tab *tab_cone) WARN_UNUSED;
 264
 265 int isl_tab_push_callback(struct isl_tab *tab,
 266         struct isl_tab_callback *callback) WARN_UNUSED;
 267
 268 int isl_tab_add_div(struct isl_tab *tab, __isl_keep isl_vec *div,
 269         int (*add_ineq)(void *user, isl_int *), void *user);
 270
 271 #endif