1 /*
2 * Copyright 2008-2009 Katholieke Universiteit Leuven
3 * Copyright 2010 INRIA Saclay
4 * Copyright 2011 Sven Verdoolaege
5 *
6 * Use of this software is governed by the MIT license
7 *
8 * Written by Sven Verdoolaege, K.U.Leuven, Departement
9 * Computerwetenschappen, Celestijnenlaan 200A, B-3001 Leuven, Belgium
10 * and INRIA Saclay - Ile-de-France, Parc Club Orsay Universite,
11 * ZAC des vignes, 4 rue Jacques Monod, 91893 Orsay, France
12 */
13
14 #define xSF(TYPE,SUFFIX) TYPE ## SUFFIX
15 #define SF(TYPE,SUFFIX) xSF(TYPE,SUFFIX)
16
17 /* Given a basic map with at least two parallel constraints (as found
18 * by the function parallel_constraints), first look for more constraints
19 * parallel to the two constraint and replace the found list of parallel
20 * constraints by a single constraint with as "input" part the minimum
21 * of the input parts of the list of constraints. Then, recursively call
22 * basic_map_partial_lexopt (possibly finding more parallel constraints)
23 * and plug in the definition of the minimum in the result.
24 *
25 * As in parallel_constraints, only inequality constraints that only
26 * involve input variables that do not occur in any other inequality
27 * constraints are considered.
28 *
29 * More specifically, given a set of constraints
30 *
31 * a x + b_i(p) >= 0
32 *
33 * Replace this set by a single constraint
34 *
35 * a x + u >= 0
36 *
37 * with u a new parameter with constraints
38 *
39 * u <= b_i(p)
40 *
41 * Any solution to the new system is also a solution for the original system
42 * since
43 *
44 * a x >= -u >= -b_i(p)
45 *
46 * Moreover, m = min_i(b_i(p)) satisfies the constraints on u and can
47 * therefore be plugged into the solution.
48 */
SF(basic_map_partial_lexopt_symm,SUFFIX)49 static TYPE *SF(basic_map_partial_lexopt_symm,SUFFIX)(
50 __isl_take isl_basic_map *bmap, __isl_take isl_basic_set *dom,
51 __isl_give isl_set **empty, int max, int first, int second)
52 {
53 int i, n, k;
54 int *list = NULL;
55 unsigned n_in, n_out, n_div;
56 isl_ctx *ctx;
57 isl_vec *var = NULL;
58 isl_mat *cst = NULL;
59 isl_space *map_space, *set_space;
60
61 map_space = isl_basic_map_get_space(bmap);
62 set_space = empty ? isl_basic_set_get_space(dom) : NULL;
63
64 n_in = isl_basic_map_dim(bmap, isl_dim_param) +
65 isl_basic_map_dim(bmap, isl_dim_in);
66 n_out = isl_basic_map_dim(bmap, isl_dim_all) - n_in;
67
68 ctx = isl_basic_map_get_ctx(bmap);
69 list = isl_alloc_array(ctx, int, bmap->n_ineq);
70 var = isl_vec_alloc(ctx, n_out);
71 if ((bmap->n_ineq && !list) || (n_out && !var))
72 goto error;
73
74 list[0] = first;
75 list[1] = second;
76 isl_seq_cpy(var->el, bmap->ineq[first] + 1 + n_in, n_out);
77 for (i = second + 1, n = 2; i < bmap->n_ineq; ++i) {
78 if (isl_seq_eq(var->el, bmap->ineq[i] + 1 + n_in, n_out) &&
79 all_single_occurrence(bmap, i, n_in))
80 list[n++] = i;
81 }
82
83 cst = isl_mat_alloc(ctx, n, 1 + n_in);
84 if (!cst)
85 goto error;
86
87 for (i = 0; i < n; ++i)
88 isl_seq_cpy(cst->row[i], bmap->ineq[list[i]], 1 + n_in);
89
90 bmap = isl_basic_map_cow(bmap);
91 if (!bmap)
92 goto error;
93 for (i = n - 1; i >= 0; --i)
94 if (isl_basic_map_drop_inequality(bmap, list[i]) < 0)
95 goto error;
96
97 bmap = isl_basic_map_add_dims(bmap, isl_dim_in, 1);
98 bmap = isl_basic_map_extend_constraints(bmap, 0, 1);
99 k = isl_basic_map_alloc_inequality(bmap);
100 if (k < 0)
101 goto error;
102 isl_seq_clr(bmap->ineq[k], 1 + n_in);
103 isl_int_set_si(bmap->ineq[k][1 + n_in], 1);
104 isl_seq_cpy(bmap->ineq[k] + 1 + n_in + 1, var->el, n_out);
105 bmap = isl_basic_map_finalize(bmap);
106
107 n_div = isl_basic_set_dim(dom, isl_dim_div);
108 dom = isl_basic_set_add_dims(dom, isl_dim_set, 1);
109 dom = isl_basic_set_extend_constraints(dom, 0, n);
110 for (i = 0; i < n; ++i) {
111 k = isl_basic_set_alloc_inequality(dom);
112 if (k < 0)
113 goto error;
114 isl_seq_cpy(dom->ineq[k], cst->row[i], 1 + n_in);
115 isl_int_set_si(dom->ineq[k][1 + n_in], -1);
116 isl_seq_clr(dom->ineq[k] + 1 + n_in + 1, n_div);
117 }
118
119 isl_vec_free(var);
120 free(list);
121
122 return SF(basic_map_partial_lexopt_symm_core,SUFFIX)(bmap, dom, empty,
123 max, cst, map_space, set_space);
124 error:
125 isl_space_free(map_space);
126 isl_space_free(set_space);
127 isl_mat_free(cst);
128 isl_vec_free(var);
129 free(list);
130 isl_basic_set_free(dom);
131 isl_basic_map_free(bmap);
132 return NULL;
133 }
134
135 /* Recursive part of isl_tab_basic_map_partial_lexopt*, after detecting
136 * equalities and removing redundant constraints.
137 *
138 * We first check if there are any parallel constraints (left).
139 * If not, we are in the base case.
140 * If there are parallel constraints, we replace them by a single
141 * constraint in basic_map_partial_lexopt_symm_pma and then call
142 * this function recursively to look for more parallel constraints.
143 */
SF(basic_map_partial_lexopt,SUFFIX)144 static __isl_give TYPE *SF(basic_map_partial_lexopt,SUFFIX)(
145 __isl_take isl_basic_map *bmap, __isl_take isl_basic_set *dom,
146 __isl_give isl_set **empty, int max)
147 {
148 isl_bool par = isl_bool_false;
149 int first, second;
150
151 if (!bmap)
152 goto error;
153
154 if (bmap->ctx->opt->pip_symmetry)
155 par = parallel_constraints(bmap, &first, &second);
156 if (par < 0)
157 goto error;
158 if (!par)
159 return SF(basic_map_partial_lexopt_base,SUFFIX)(bmap, dom,
160 empty, max);
161
162 return SF(basic_map_partial_lexopt_symm,SUFFIX)(bmap, dom, empty, max,
163 first, second);
164 error:
165 isl_basic_set_free(dom);
166 isl_basic_map_free(bmap);
167 return NULL;
168 }
169
170 /* Compute the lexicographic minimum (or maximum if "flags" includes
171 * ISL_OPT_MAX) of "bmap" over the domain "dom" and return the result as
172 * either a map or a piecewise multi-affine expression depending on TYPE.
173 * If "empty" is not NULL, then *empty is assigned a set that
174 * contains those parts of the domain where there is no solution.
175 * If "flags" includes ISL_OPT_FULL, then "dom" is NULL and the optimum
176 * should be computed over the domain of "bmap". "empty" is also NULL
177 * in this case.
178 * If "bmap" is marked as rational (ISL_BASIC_MAP_RATIONAL),
179 * then we compute the rational optimum. Otherwise, we compute
180 * the integral optimum.
181 *
182 * We perform some preprocessing. As the PILP solver does not
183 * handle implicit equalities very well, we first make sure all
184 * the equalities are explicitly available.
185 *
186 * We also add context constraints to the basic map and remove
187 * redundant constraints. This is only needed because of the
188 * way we handle simple symmetries. In particular, we currently look
189 * for symmetries on the constraints, before we set up the main tableau.
190 * It is then no good to look for symmetries on possibly redundant constraints.
191 * If the domain was extracted from the basic map, then there is
192 * no need to add back those constraints again.
193 */
SF(isl_tab_basic_map_partial_lexopt,SUFFIX)194 __isl_give TYPE *SF(isl_tab_basic_map_partial_lexopt,SUFFIX)(
195 __isl_take isl_basic_map *bmap, __isl_take isl_basic_set *dom,
196 __isl_give isl_set **empty, unsigned flags)
197 {
198 int max, full;
199 isl_bool compatible;
200
201 if (empty)
202 *empty = NULL;
203
204 full = ISL_FL_ISSET(flags, ISL_OPT_FULL);
205 if (full)
206 dom = extract_domain(bmap, flags);
207 compatible = isl_basic_map_compatible_domain(bmap, dom);
208 if (compatible < 0)
209 goto error;
210 if (!compatible)
211 isl_die(isl_basic_map_get_ctx(bmap), isl_error_invalid,
212 "domain does not match input", goto error);
213
214 max = ISL_FL_ISSET(flags, ISL_OPT_MAX);
215 if (isl_basic_set_dim(dom, isl_dim_all) == 0)
216 return SF(basic_map_partial_lexopt,SUFFIX)(bmap, dom, empty,
217 max);
218
219 if (!full)
220 bmap = isl_basic_map_intersect_domain(bmap,
221 isl_basic_set_copy(dom));
222 bmap = isl_basic_map_detect_equalities(bmap);
223 bmap = isl_basic_map_remove_redundancies(bmap);
224
225 return SF(basic_map_partial_lexopt,SUFFIX)(bmap, dom, empty, max);
226 error:
227 isl_basic_set_free(dom);
228 isl_basic_map_free(bmap);
229 return NULL;
230 }
231