1 /*
2 * Copyright 2011 INRIA Saclay
3 * Copyright 2012 Ecole Normale Superieure
4 *
5 * Use of this software is governed by the MIT license
6 *
7 * Written by Sven Verdoolaege, INRIA Saclay - Ile-de-France,
8 * Parc Club Orsay Universite, ZAC des vignes, 4 rue Jacques Monod,
9 * 91893 Orsay, France
10 * and Ecole Normale Superieure, 45 rue d'Ulm, 75230 Paris, France
11 */
12
13 #include <isl_pw_macro.h>
14
15 /* Given a function "cmp" that returns the set of elements where
16 * "el1" is "better" than "el2", return this set.
17 */
FN(PW,better)18 static __isl_give isl_set *FN(PW,better)(__isl_keep EL *el1, __isl_keep EL *el2,
19 __isl_give isl_set *(*cmp)(__isl_take EL *el1, __isl_take EL *el2))
20 {
21 return cmp(FN(EL,copy)(el1), FN(EL,copy)(el2));
22 }
23
24 /* Return a list containing the domains of the pieces of "pw".
25 */
FN(PW,extract_domains)26 static __isl_give isl_set_list *FN(PW,extract_domains)(__isl_keep PW *pw)
27 {
28 int i;
29 isl_ctx *ctx;
30 isl_set_list *list;
31
32 if (!pw)
33 return NULL;
34 ctx = FN(PW,get_ctx)(pw);
35 list = isl_set_list_alloc(ctx, pw->n);
36 for (i = 0; i < pw->n; ++i)
37 list = isl_set_list_add(list, isl_set_copy(pw->p[i].set));
38
39 return list;
40 }
41
42 /* Given sets B ("set"), C ("better") and A' ("out"), return
43 *
44 * (B \cap C) \cup ((B \setminus C) \setminus A')
45 */
FN(PW,better_or_out)46 static __isl_give isl_set *FN(PW,better_or_out)(__isl_take isl_set *set,
47 __isl_take isl_set *better, __isl_take isl_set *out)
48 {
49 isl_set *set_better, *set_out;
50
51 set_better = isl_set_intersect(isl_set_copy(set), isl_set_copy(better));
52 set_out = isl_set_subtract(isl_set_subtract(set, better), out);
53
54 return isl_set_union(set_better, set_out);
55 }
56
57 /* Given sets A ("set"), C ("better") and B' ("out"), return
58 *
59 * (A \setminus C) \cup ((A \cap C) \setminus B')
60 */
FN(PW,worse_or_out)61 static __isl_give isl_set *FN(PW,worse_or_out)(__isl_take isl_set *set,
62 __isl_take isl_set *better, __isl_take isl_set *out)
63 {
64 isl_set *set_worse, *set_out;
65
66 set_worse = isl_set_subtract(isl_set_copy(set), isl_set_copy(better));
67 set_out = isl_set_subtract(isl_set_intersect(set, better), out);
68
69 return isl_set_union(set_worse, set_out);
70 }
71
72 /* Given two piecewise expressions "pw1" and "pw2", replace their domains
73 * by the sets in "list1" and "list2" and combine the results into
74 * a single piecewise expression.
75 * The pieces of "pw1" and "pw2" are assumed to have been sorted
76 * according to the function value expressions.
77 * The pieces of the result are also sorted in this way.
78 *
79 * Run through the pieces of "pw1" and "pw2" in order until they
80 * have both been exhausted, picking the piece from "pw1" or "pw2"
81 * depending on which should come first, together with the corresponding
82 * domain from "list1" or "list2". In cases where the next pieces
83 * in both "pw1" and "pw2" have the same function value expression,
84 * construct only a single piece in the result with as domain
85 * the union of the domains in "list1" and "list2".
86 */
FN(PW,merge)87 static __isl_give PW *FN(PW,merge)(__isl_take PW *pw1, __isl_take PW *pw2,
88 __isl_take isl_set_list *list1, __isl_take isl_set_list *list2)
89 {
90 int i, j;
91 PW *res;
92
93 if (!pw1 || !pw2)
94 goto error;
95
96 res = FN(PW,alloc_size)(isl_space_copy(pw1->dim), pw1->n + pw2->n);
97
98 i = 0; j = 0;
99 while (i < pw1->n || j < pw2->n) {
100 int cmp;
101 isl_set *set;
102 EL *el;
103
104 if (i < pw1->n && j < pw2->n)
105 cmp = FN(EL,plain_cmp)(pw1->p[i].FIELD,
106 pw2->p[j].FIELD);
107 else
108 cmp = i < pw1->n ? -1 : 1;
109
110 if (cmp < 0) {
111 set = isl_set_list_get_set(list1, i);
112 el = FN(EL,copy)(pw1->p[i].FIELD);
113 ++i;
114 } else if (cmp > 0) {
115 set = isl_set_list_get_set(list2, j);
116 el = FN(EL,copy)(pw2->p[j].FIELD);
117 ++j;
118 } else {
119 set = isl_set_union(isl_set_list_get_set(list1, i),
120 isl_set_list_get_set(list2, j));
121 el = FN(EL,copy)(pw1->p[i].FIELD);
122 ++i;
123 ++j;
124 }
125 res = FN(PW,add_piece)(res, set, el);
126 }
127
128 isl_set_list_free(list1);
129 isl_set_list_free(list2);
130 FN(PW,free)(pw1);
131 FN(PW,free)(pw2);
132 return res;
133 error:
134 isl_set_list_free(list1);
135 isl_set_list_free(list2);
136 FN(PW,free)(pw1);
137 FN(PW,free)(pw2);
138 return NULL;
139 }
140
141 /* Given a function "cmp" that returns the set of elements where
142 * "el1" is "better" than "el2", return a piecewise
143 * expression defined on the union of the definition domains
144 * of "pw1" and "pw2" that maps to the "best" of "pw1" and
145 * "pw2" on each cell. If only one of the two input functions
146 * is defined on a given cell, then it is considered the best.
147 *
148 * Run through all pairs of pieces in "pw1" and "pw2".
149 * If the domains of these pieces intersect, then the intersection
150 * needs to be distributed over the two pieces based on "cmp".
151 * Let C be the set where the piece from "pw2" is better (according to "cmp")
152 * than the piece from "pw1". Let A be the domain of the piece from "pw1" and
153 * B the domain of the piece from "pw2".
154 *
155 * The elements in C need to be removed from A, except for those parts
156 * that lie outside of B. That is,
157 *
158 * A <- (A \setminus C) \cup ((A \cap C) \setminus B')
159 *
160 * Conversely, the elements in B need to be restricted to C, except
161 * for those parts that lie outside of A. That is
162 *
163 * B <- (B \cap C) \cup ((B \setminus C) \setminus A')
164 *
165 * Since all pairs of pieces are considered, the domains are updated
166 * several times. A and B refer to these updated domains
167 * (kept track of in "list1" and "list2"), while A' and B' refer
168 * to the original domains of the pieces. It is safe to use these
169 * original domains because the difference between, say, A' and A is
170 * the domains of pw2-pieces that have been removed before and
171 * those domains are disjoint from B. A' is used instead of A
172 * because the continued updating of A may result in this domain
173 * getting broken up into more disjuncts.
174 *
175 * After the updated domains have been computed, the result is constructed
176 * from "pw1", "pw2", "list1" and "list2". If there are any pieces
177 * in "pw1" and "pw2" with the same function value expression, then
178 * they are combined into a single piece in the result.
179 * In order to be able to do this efficiently, the pieces of "pw1" and
180 * "pw2" are first sorted according to their function value expressions.
181 */
FN(PW,union_opt_cmp)182 static __isl_give PW *FN(PW,union_opt_cmp)(
183 __isl_take PW *pw1, __isl_take PW *pw2,
184 __isl_give isl_set *(*cmp)(__isl_take EL *el1, __isl_take EL *el2))
185 {
186 int i, j;
187 PW *res = NULL;
188 isl_ctx *ctx;
189 isl_set *set = NULL;
190 isl_set_list *list1 = NULL, *list2 = NULL;
191
192 if (!pw1 || !pw2)
193 goto error;
194
195 ctx = isl_space_get_ctx(pw1->dim);
196 if (!isl_space_is_equal(pw1->dim, pw2->dim))
197 isl_die(ctx, isl_error_invalid,
198 "arguments should live in the same space", goto error);
199
200 if (FN(PW,is_empty)(pw1)) {
201 FN(PW,free)(pw1);
202 return pw2;
203 }
204
205 if (FN(PW,is_empty)(pw2)) {
206 FN(PW,free)(pw2);
207 return pw1;
208 }
209
210 pw1 = FN(PW,sort)(pw1);
211 pw2 = FN(PW,sort)(pw2);
212 if (!pw1 || !pw2)
213 goto error;
214
215 list1 = FN(PW,extract_domains)(pw1);
216 list2 = FN(PW,extract_domains)(pw2);
217
218 for (i = 0; i < pw1->n; ++i) {
219 for (j = 0; j < pw2->n; ++j) {
220 isl_bool disjoint;
221 isl_set *better, *set_i, *set_j;
222
223 disjoint = isl_set_is_disjoint(pw1->p[i].set,
224 pw2->p[j].set);
225 if (disjoint < 0)
226 goto error;
227 if (disjoint)
228 continue;
229 better = FN(PW,better)(pw2->p[j].FIELD,
230 pw1->p[i].FIELD, cmp);
231 set_i = isl_set_list_get_set(list1, i);
232 set_j = isl_set_copy(pw2->p[j].set);
233 set_i = FN(PW,worse_or_out)(set_i,
234 isl_set_copy(better), set_j);
235 list1 = isl_set_list_set_set(list1, i, set_i);
236 set_i = isl_set_copy(pw1->p[i].set);
237 set_j = isl_set_list_get_set(list2, j);
238 set_j = FN(PW,better_or_out)(set_j, better, set_i);
239 list2 = isl_set_list_set_set(list2, j, set_j);
240 }
241 }
242
243 res = FN(PW,merge)(pw1, pw2, list1, list2);
244
245 return res;
246 error:
247 isl_set_list_free(list1);
248 isl_set_list_free(list2);
249 FN(PW,free)(pw1);
250 FN(PW,free)(pw2);
251 isl_set_free(set);
252 return FN(PW,free)(res);
253 }
254