12 unsigned is_nonneg
: 1;
14 unsigned is_redundant
: 1;
20 enum isl_tab_undo_type
{
24 isl_tab_undo_redundant
,
27 isl_tab_undo_allocate
,
29 isl_tab_undo_bset_ineq
,
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
,
38 struct isl_tab_callback
{
39 int (*run
)(struct isl_tab_callback
*cb
);
42 union isl_tab_undo_val
{
46 struct isl_tab_callback
*callback
;
50 enum isl_tab_undo_type type
;
51 union isl_tab_undo_val u
;
52 struct isl_tab_undo
*next
;
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
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
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.
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".
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
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.
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.
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.
113 enum isl_tab_row_sign
{
114 isl_tab_row_unknown
= 0,
125 unsigned n_redundant
;
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
;
140 struct isl_tab_undo bottom
;
141 struct isl_tab_undo
*top
;
143 struct isl_vec
*dual
;
144 struct isl_basic_set
*bset
;
149 struct isl_mat
*samples
;
153 struct isl_mat
*basis
;
155 unsigned need_undo
: 1;
156 unsigned rational
: 1;
158 unsigned in_undo
: 1;
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
);
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
;
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
;
187 int isl_tab_freeze_constraint(struct isl_tab
*tab
, int con
) WARN_UNUSED
;
189 int isl_tab_is_equality(struct isl_tab
*tab
, int con
);
190 int isl_tab_is_redundant(struct isl_tab
*tab
, int con
);
192 int isl_tab_sample_is_integer(struct isl_tab
*tab
);
193 struct isl_vec
*isl_tab_get_sample_value(struct isl_tab
*tab
);
204 enum isl_ineq_type
isl_tab_ineq_type(struct isl_tab
*tab
, isl_int
*ineq
);
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
;
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
;
212 void isl_tab_dump(struct isl_tab
*tab
, FILE *out
, int indent
);
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
);
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
;
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
;
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
;
246 struct isl_tab
*isl_tab_detect_equalities(struct isl_tab
*tab
,
247 struct isl_tab
*tab_cone
) WARN_UNUSED
;
249 int isl_tab_push_callback(struct isl_tab
*tab
,
250 struct isl_tab_callback
*callback
) WARN_UNUSED
;