12 unsigned is_nonneg : 1;
14 unsigned is_redundant : 1;
19 enum isl_tab_undo_type {
23 isl_tab_undo_redundant,
25 isl_tab_undo_allocate,
27 isl_tab_undo_bset_ineq,
29 isl_tab_undo_bset_div,
30 isl_tab_undo_saved_basis,
31 isl_tab_undo_drop_sample,
34 union isl_tab_undo_val {
40 enum isl_tab_undo_type type;
41 union isl_tab_undo_val u;
42 struct isl_tab_undo *next;
45 /* The tableau maintains equality relations.
46 * Each column and each row is associated to a variable or a constraint.
47 * The "value" of an inequality constraint is the value of the corresponding
49 * The "row_var" and "col_var" arrays map column and row indices
50 * to indices in the "var" and "con" arrays. The elements of these
51 * arrays maintain extra information about the variables and the constraints.
52 * Each row expresses the corresponding row variable as an affine expression
53 * of the column variables.
54 * The first two columns in the matrix contain the common denominator of
55 * the row and the numerator of the constant term.
56 * If "M" is set, then the third column represents the "big parameter".
57 * The third (M = 0) or fourth (M = 1) column
58 * in the matrix is called column 0 with respect to the col_var array.
59 * The sample value of the tableau is the value that assigns zero
60 * to all the column variables and the constant term of each affine
61 * expression to the corresponding row variable.
62 * The operations on the tableau maintain the property that the sample
63 * value satisfies the non-negativity constraints (usually on the slack
66 * The big parameter represents an arbitrarily big (and divisible)
67 * positive number. If present, then the sign of a row is determined
68 * lexicographically, with the sign of the big parameter coefficient
69 * considered first. The big parameter will only be used while
70 * solving PILP problems.
72 * The first n_dead column variables have their values fixed to zero.
73 * The corresponding tab_vars are flagged "is_zero".
74 * Some of the rows that have have zero coefficients in all but
75 * the dead columns are also flagged "is_zero".
77 * The first n_redundant rows correspond to inequality constraints
78 * that are always satisfied for any value satisfying the non-redundant
79 * rows. The corresponding tab_vars are flagged "is_redundant".
80 * A row variable that is flagged "is_zero" is also flagged "is_redundant"
81 * since the constraint has been reduced to 0 = 0 and is therefore always
84 * There are "n_var" variables in total. The first "n_param" of these
85 * are called parameters and the last "n_div" of these are called divs.
86 * The basic tableau operations makes no distinction between different
89 * Dead columns and redundant rows are detected on the fly.
90 * However, the basic operations do not ensure that all dead columns
91 * or all redundant rows are detected.
92 * isl_tab_detect_equalities and isl_tab_detect_redundant can be used
93 * to perform and exhaustive search for dead columns and redundant rows.
95 * The samples matrix contains "n_sample" integer points that have at some
96 * point been elements satisfying the tableau. The first "n_outside"
97 * of them no longer satisfy the tableau. They are kept because they
98 * can be reinstated during rollback when the constraint that cut them
101 enum isl_tab_row_sign {
102 isl_tab_row_unknown = 0,
113 unsigned n_redundant;
122 struct isl_tab_var *var;
123 struct isl_tab_var *con;
124 int *row_var; /* v >= 0 -> var v; v < 0 -> con ~v */
125 int *col_var; /* v >= 0 -> var v; v < 0 -> con ~v */
126 enum isl_tab_row_sign *row_sign;
128 struct isl_tab_undo bottom;
129 struct isl_tab_undo *top;
131 struct isl_vec *dual;
132 struct isl_basic_set *bset;
136 struct isl_mat *samples;
138 unsigned need_undo : 1;
139 unsigned rational : 1;
141 unsigned in_undo : 1;
145 struct isl_tab *isl_tab_alloc(struct isl_ctx *ctx,
146 unsigned n_row, unsigned n_var, unsigned M);
147 void isl_tab_free(struct isl_tab *tab);
149 struct isl_tab *isl_tab_from_basic_map(struct isl_basic_map *bmap);
150 struct isl_tab *isl_tab_from_basic_set(struct isl_basic_set *bset);
151 struct isl_tab *isl_tab_from_recession_cone(struct isl_basic_map *bmap);
152 int isl_tab_cone_is_bounded(struct isl_tab *tab);
153 struct isl_basic_map *isl_basic_map_update_from_tab(struct isl_basic_map *bmap,
154 struct isl_tab *tab);
155 struct isl_basic_set *isl_basic_set_update_from_tab(struct isl_basic_set *bset,
156 struct isl_tab *tab);
157 struct isl_tab *isl_tab_detect_equalities(struct isl_tab *tab);
158 struct isl_tab *isl_tab_detect_redundant(struct isl_tab *tab);
159 #define ISL_TAB_SAVE_DUAL (1 << 0)
160 enum isl_lp_result isl_tab_min(struct isl_tab *tab,
161 isl_int *f, isl_int denom, isl_int *opt, isl_int *opt_denom,
164 struct isl_tab *isl_tab_extend(struct isl_tab *tab, unsigned n_new);
165 struct isl_tab *isl_tab_add_ineq(struct isl_tab *tab, isl_int *ineq);
166 struct isl_tab *isl_tab_add_valid_eq(struct isl_tab *tab, isl_int *eq);
168 int isl_tab_is_equality(struct isl_tab *tab, int con);
169 int isl_tab_is_redundant(struct isl_tab *tab, int con);
171 int isl_tab_sample_is_integer(struct isl_tab *tab);
172 struct isl_vec *isl_tab_get_sample_value(struct isl_tab *tab);
183 enum isl_ineq_type isl_tab_ineq_type(struct isl_tab *tab, isl_int *ineq);
185 struct isl_tab_undo *isl_tab_snap(struct isl_tab *tab);
186 int isl_tab_rollback(struct isl_tab *tab, struct isl_tab_undo *snap);
188 struct isl_tab *isl_tab_relax(struct isl_tab *tab, int con);
189 struct isl_tab *isl_tab_select_facet(struct isl_tab *tab, int con);
191 void isl_tab_dump(struct isl_tab *tab, FILE *out, int indent);
195 struct isl_tab_var *isl_tab_var_from_row(struct isl_tab *tab, int i);
196 int isl_tab_mark_redundant(struct isl_tab *tab, int row);
197 struct isl_tab *isl_tab_mark_empty(struct isl_tab *tab);
198 struct isl_tab *isl_tab_dup(struct isl_tab *tab);
199 int isl_tab_extend_cons(struct isl_tab *tab, unsigned n_new);
200 int isl_tab_allocate_con(struct isl_tab *tab);
201 int isl_tab_extend_vars(struct isl_tab *tab, unsigned n_new);
202 int isl_tab_allocate_var(struct isl_tab *tab);
203 void isl_tab_pivot(struct isl_tab *tab, int row, int col);
204 int isl_tab_add_row(struct isl_tab *tab, isl_int *line);
205 int isl_tab_row_is_redundant(struct isl_tab *tab, int row);
206 int isl_tab_min_at_most_neg_one(struct isl_tab *tab, struct isl_tab_var *var);
208 void isl_tab_push(struct isl_tab *tab, enum isl_tab_undo_type type);
209 void isl_tab_push_var(struct isl_tab *tab,
210 enum isl_tab_undo_type type, struct isl_tab_var *var);
211 void isl_tab_push_basis(struct isl_tab *tab);