isl_tab.h

   1 /*
   2  * Copyright 2008-2009 Katholieke Universiteit Leuven
   3  *
   4  * Use of this software is governed by the MIT 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_unrestrict,
  39         isl_tab_undo_bmap_ineq,
  40         isl_tab_undo_bmap_eq,
  41         isl_tab_undo_bmap_div,
  42         isl_tab_undo_saved_basis,
  43         isl_tab_undo_drop_sample,
  44         isl_tab_undo_saved_samples,
  45         isl_tab_undo_callback,
  46 };
  47
  48 struct isl_tab_callback {
  49         int (*run)(struct isl_tab_callback *cb);
  50 };
  51
  52 union isl_tab_undo_val {
  53         int             var_index;
  54         int             *col_var;
  55         int             n;
  56         struct isl_tab_callback *callback;
  57 };
  58
  59 struct isl_tab_undo {
  60         enum isl_tab_undo_type  type;
  61         union isl_tab_undo_val  u;
  62         struct isl_tab_undo     *next;
  63 };
  64
  65 /* The tableau maintains equality relations.
  66  * Each column and each row is associated to a variable or a constraint.
  67  * The "value" of an inequality constraint is the value of the corresponding
  68  * slack variable.
  69  * The "row_var" and "col_var" arrays map column and row indices
  70  * to indices in the "var" and "con" arrays.  The elements of these
  71  * arrays maintain extra information about the variables and the constraints.
  72  * Each row expresses the corresponding row variable as an affine expression
  73  * of the column variables.
  74  * The first two columns in the matrix contain the common denominator of
  75  * the row and the numerator of the constant term.
  76  * If "M" is set, then the third column represents the "big parameter".
  77  * The third (M = 0) or fourth (M = 1) column
  78  * in the matrix is called column 0 with respect to the col_var array.
  79  * The sample value of the tableau is the value that assigns zero
  80  * to all the column variables and the constant term of each affine
  81  * expression to the corresponding row variable.
  82  * The operations on the tableau maintain the property that the sample
  83  * value satisfies the non-negativity constraints (usually on the slack
  84  * variables).
  85  *
  86  * The big parameter represents an arbitrarily big (and divisible)
  87  * positive number.  If present, then the sign of a row is determined
  88  * lexicographically, with the sign of the big parameter coefficient
  89  * considered first.  The big parameter is only used while
  90  * solving PILP problems.
  91  *
  92  * The first n_dead column variables have their values fixed to zero.
  93  * The corresponding tab_vars are flagged "is_zero".
  94  * Some of the rows that have have zero coefficients in all but
  95  * the dead columns are also flagged "is_zero".
  96  *
  97  * The first n_redundant rows correspond to inequality constraints
  98  * that are always satisfied for any value satisfying the non-redundant
  99  * rows.  The corresponding tab_vars are flagged "is_redundant".
 100  * A row variable that is flagged "is_zero" is also flagged "is_redundant"
 101  * since the constraint has been reduced to 0 = 0 and is therefore always
 102  * satisfied.
 103  *
 104  * There are "n_var" variables in total.  The first "n_param" of these
 105  * are called parameters and the last "n_div" of these are called divs.
 106  * The basic tableau operations makes no distinction between different
 107  * kinds of variables.  These special variables are only used while
 108  * solving PILP problems.
 109  *
 110  * Dead columns and redundant rows are detected on the fly.
 111  * However, the basic operations do not ensure that all dead columns
 112  * or all redundant rows are detected.
 113  * isl_tab_detect_implicit_equalities and isl_tab_detect_redundant can be used
 114  * to perform and exhaustive search for dead columns and redundant rows.
 115  *
 116  * The samples matrix contains "n_sample" integer points that have at some
 117  * point been elements satisfying the tableau.  The first "n_outside"
 118  * of them no longer satisfy the tableau.  They are kept because they
 119  * can be reinstated during rollback when the constraint that cut them
 120  * out is removed.  These samples are only maintained for the context
 121  * tableau while solving PILP problems.
 122  *
 123  * If "preserve" is set, then we want to keep all constraints in the
 124  * tableau, even if they turn out to be redundant.
 125  */
 126 enum isl_tab_row_sign {
 127         isl_tab_row_unknown = 0,
 128         isl_tab_row_pos,
 129         isl_tab_row_neg,
 130         isl_tab_row_any,
 131 };
 132 struct isl_tab {
 133         struct isl_mat *mat;
 134
 135         unsigned n_row;
 136         unsigned n_col;
 137         unsigned n_dead;
 138         unsigned n_redundant;
 139
 140         unsigned n_var;
 141         unsigned n_param;
 142         unsigned n_div;
 143         unsigned max_var;
 144         unsigned n_con;
 145         unsigned n_eq;
 146         unsigned max_con;
 147         struct isl_tab_var *var;
 148         struct isl_tab_var *con;
 149         int *row_var;   /* v >= 0 -> var v;     v < 0 -> con ~v */
 150         int *col_var;   /* v >= 0 -> var v;     v < 0 -> con ~v */
 151         enum isl_tab_row_sign *row_sign;
 152
 153         struct isl_tab_undo bottom;
 154         struct isl_tab_undo *top;
 155
 156         struct isl_vec *dual;
 157         struct isl_basic_map *bmap;
 158
 159         unsigned n_sample;
 160         unsigned n_outside;
 161         int *sample_index;
 162         struct isl_mat *samples;
 163
 164         int n_zero;
 165         int n_unbounded;
 166         struct isl_mat *basis;
 167
 168         int (*conflict)(int con, void *user);
 169         void *conflict_user;
 170
 171         unsigned strict_redundant : 1;
 172         unsigned need_undo : 1;
 173         unsigned preserve : 1;
 174         unsigned rational : 1;
 175         unsigned empty : 1;
 176         unsigned in_undo : 1;
 177         unsigned M : 1;
 178         unsigned cone : 1;
 179 };
 180
 181 struct isl_tab *isl_tab_alloc(struct isl_ctx *ctx,
 182         unsigned n_row, unsigned n_var, unsigned M);
 183 void isl_tab_free(struct isl_tab *tab);
 184
 185 isl_ctx *isl_tab_get_ctx(struct isl_tab *tab);
 186
 187 __isl_give struct isl_tab *isl_tab_from_basic_map(
 188         __isl_keep isl_basic_map *bmap, int track);
 189 __isl_give struct isl_tab *isl_tab_from_basic_set(
 190         __isl_keep isl_basic_set *bset, int track);
 191 struct isl_tab *isl_tab_from_recession_cone(struct isl_basic_set *bset,
 192         int parametric);
 193 int isl_tab_cone_is_bounded(struct isl_tab *tab);
 194 struct isl_basic_map *isl_basic_map_update_from_tab(struct isl_basic_map *bmap,
 195         struct isl_tab *tab);
 196 struct isl_basic_set *isl_basic_set_update_from_tab(struct isl_basic_set *bset,
 197         struct isl_tab *tab);
 198 int isl_tab_detect_implicit_equalities(struct isl_tab *tab) WARN_UNUSED;
 199 __isl_give isl_basic_map *isl_tab_make_equalities_explicit(struct isl_tab *tab,
 200         __isl_take isl_basic_map *bmap);
 201 int isl_tab_detect_redundant(struct isl_tab *tab) WARN_UNUSED;
 202 #define ISL_TAB_SAVE_DUAL       (1 << 0)
 203 enum isl_lp_result isl_tab_min(struct isl_tab *tab,
 204         isl_int *f, isl_int denom, isl_int *opt, isl_int *opt_denom,
 205         unsigned flags) WARN_UNUSED;
 206
 207 struct isl_tab *isl_tab_extend(struct isl_tab *tab, unsigned n_new) WARN_UNUSED;
 208 int isl_tab_add_ineq(struct isl_tab *tab, isl_int *ineq) WARN_UNUSED;
 209 int isl_tab_add_eq(struct isl_tab *tab, isl_int *eq) WARN_UNUSED;
 210 int isl_tab_add_valid_eq(struct isl_tab *tab, isl_int *eq) WARN_UNUSED;
 211
 212 int isl_tab_freeze_constraint(struct isl_tab *tab, int con) WARN_UNUSED;
 213
 214 int isl_tab_track_bmap(struct isl_tab *tab, __isl_take isl_basic_map *bmap) WARN_UNUSED;
 215 int isl_tab_track_bset(struct isl_tab *tab, __isl_take isl_basic_set *bset) WARN_UNUSED;
 216 __isl_keep isl_basic_set *isl_tab_peek_bset(struct isl_tab *tab);
 217
 218 int isl_tab_is_equality(struct isl_tab *tab, int con);
 219 int isl_tab_is_redundant(struct isl_tab *tab, int con);
 220
 221 int isl_tab_sample_is_integer(struct isl_tab *tab);
 222 struct isl_vec *isl_tab_get_sample_value(struct isl_tab *tab);
 223
 224 enum isl_ineq_type {
 225         isl_ineq_error = -1,
 226         isl_ineq_redundant,
 227         isl_ineq_separate,
 228         isl_ineq_cut,
 229         isl_ineq_adj_eq,
 230         isl_ineq_adj_ineq,
 231 };
 232
 233 enum isl_ineq_type isl_tab_ineq_type(struct isl_tab *tab, isl_int *ineq);
 234
 235 struct isl_tab_undo *isl_tab_snap(struct isl_tab *tab);
 236 int isl_tab_rollback(struct isl_tab *tab, struct isl_tab_undo *snap) WARN_UNUSED;
 237
 238 struct isl_tab *isl_tab_relax(struct isl_tab *tab, int con) WARN_UNUSED;
 239 int isl_tab_select_facet(struct isl_tab *tab, int con) WARN_UNUSED;
 240 int isl_tab_unrestrict(struct isl_tab *tab, int con) WARN_UNUSED;
 241
 242 void isl_tab_dump(__isl_keep struct isl_tab *tab);
 243
 244 struct isl_map *isl_tab_basic_map_partial_lexopt(
 245                 struct isl_basic_map *bmap, struct isl_basic_set *dom,
 246                 struct isl_set **empty, int max);
 247 __isl_give isl_pw_multi_aff *isl_basic_map_partial_lexopt_pw_multi_aff(
 248         __isl_take isl_basic_map *bmap, __isl_take isl_basic_set *dom,
 249         __isl_give isl_set **empty, int max);
 250
 251 /* An isl_region represents a sequence of consecutive variables.
 252  * pos is the location (starting at 0) of the first variable in the sequence.
 253  */
 254 struct isl_region {
 255         int pos;
 256         int len;
 257 };
 258
 259 __isl_give isl_vec *isl_tab_basic_set_non_trivial_lexmin(
 260         __isl_take isl_basic_set *bset, int n_op, int n_region,
 261         struct isl_region *region,
 262         int (*conflict)(int con, void *user), void *user);
 263 __isl_give isl_vec *isl_tab_basic_set_non_neg_lexmin(
 264         __isl_take isl_basic_set *bset);
 265
 266 /* private */
 267
 268 struct isl_tab_var *isl_tab_var_from_row(struct isl_tab *tab, int i);
 269 int isl_tab_mark_redundant(struct isl_tab *tab, int row) WARN_UNUSED;
 270 int isl_tab_mark_empty(struct isl_tab *tab) WARN_UNUSED;
 271 struct isl_tab *isl_tab_dup(struct isl_tab *tab);
 272 struct isl_tab *isl_tab_product(struct isl_tab *tab1, struct isl_tab *tab2);
 273 int isl_tab_extend_cons(struct isl_tab *tab, unsigned n_new) WARN_UNUSED;
 274 int isl_tab_allocate_con(struct isl_tab *tab) WARN_UNUSED;
 275 int isl_tab_extend_vars(struct isl_tab *tab, unsigned n_new) WARN_UNUSED;
 276 int isl_tab_allocate_var(struct isl_tab *tab) WARN_UNUSED;
 277 int isl_tab_pivot(struct isl_tab *tab, int row, int col) WARN_UNUSED;
 278 int isl_tab_add_row(struct isl_tab *tab, isl_int *line) WARN_UNUSED;
 279 int isl_tab_row_is_redundant(struct isl_tab *tab, int row);
 280 int isl_tab_min_at_most_neg_one(struct isl_tab *tab, struct isl_tab_var *var);
 281 int isl_tab_sign_of_max(struct isl_tab *tab, int con);
 282 int isl_tab_kill_col(struct isl_tab *tab, int col) WARN_UNUSED;
 283
 284 int isl_tab_push(struct isl_tab *tab, enum isl_tab_undo_type type) WARN_UNUSED;
 285 int isl_tab_push_var(struct isl_tab *tab,
 286         enum isl_tab_undo_type type, struct isl_tab_var *var) WARN_UNUSED;
 287 int isl_tab_push_basis(struct isl_tab *tab) WARN_UNUSED;
 288
 289 struct isl_tab *isl_tab_init_samples(struct isl_tab *tab) WARN_UNUSED;
 290 int isl_tab_add_sample(struct isl_tab *tab,
 291         __isl_take isl_vec *sample) WARN_UNUSED;
 292 struct isl_tab *isl_tab_drop_sample(struct isl_tab *tab, int s);
 293 int isl_tab_save_samples(struct isl_tab *tab) WARN_UNUSED;
 294
 295 struct isl_tab *isl_tab_detect_equalities(struct isl_tab *tab,
 296         struct isl_tab *tab_cone) WARN_UNUSED;
 297
 298 int isl_tab_push_callback(struct isl_tab *tab,
 299         struct isl_tab_callback *callback) WARN_UNUSED;
 300
 301 int isl_tab_add_div(struct isl_tab *tab, __isl_keep isl_vec *div,
 302         int (*add_ineq)(void *user, isl_int *), void *user);
 303
 304 #endif