2 * Copyright 2008-2009 Katholieke Universiteit Leuven
4 * Use of this software is governed by the GNU LGPLv2.1 license
6 * Written by Sven Verdoolaege, K.U.Leuven, Departement
7 * Computerwetenschappen, Celestijnenlaan 200A, B-3001 Leuven, Belgium
16 #include <isl_constraint.h>
17 #include <isl_polynomial.h>
18 #include <isl_union_map.h>
22 void test_parse_map(isl_ctx
*ctx
, const char *str
)
26 map
= isl_map_read_from_str(ctx
, str
, -1);
31 void test_parse_pwqp(isl_ctx
*ctx
, const char *str
)
33 isl_pw_qpolynomial
*pwqp
;
35 pwqp
= isl_pw_qpolynomial_read_from_str(ctx
, str
);
37 isl_pw_qpolynomial_free(pwqp
);
40 void test_parse(struct isl_ctx
*ctx
)
45 str
= "{ [i] -> [-i] }";
46 map
= isl_map_read_from_str(ctx
, str
, -1);
50 str
= "{ A[i] -> L[([i/3])] }";
51 map
= isl_map_read_from_str(ctx
, str
, -1);
55 test_parse_map(ctx
, "{[[s] -> A[i]] -> [[s+1] -> A[i]]}");
57 str
= "{[new,old] -> [new+1-2*[(new+1)/2],old+1-2*[(old+1)/2]]}";
58 map
= isl_map_read_from_str(ctx
, str
, -1);
59 str
= "{ [new, old] -> [o0, o1] : "
60 "exists (e0 = [(-1 - new + o0)/2], e1 = [(-1 - old + o1)/2]: "
61 "2e0 = -1 - new + o0 and 2e1 = -1 - old + o1 and o0 >= 0 and "
62 "o0 <= 1 and o1 >= 0 and o1 <= 1) }";
63 map2
= isl_map_read_from_str(ctx
, str
, -1);
64 assert(isl_map_is_equal(map
, map2
));
68 test_parse_pwqp(ctx
, "{ [i] -> i + [ (i + [i/3])/2 ] }");
71 void test_read(struct isl_ctx
*ctx
)
73 char filename
[PATH_MAX
];
76 struct isl_basic_set
*bset1
, *bset2
;
77 const char *str
= "{[y]: Exists ( alpha : 2alpha = y)}";
79 n
= snprintf(filename
, sizeof(filename
),
80 "%s/test_inputs/set.omega", srcdir
);
81 assert(n
< sizeof(filename
));
82 input
= fopen(filename
, "r");
85 bset1
= isl_basic_set_read_from_file(ctx
, input
, 0);
86 bset2
= isl_basic_set_read_from_str(ctx
, str
, 0);
88 assert(isl_basic_set_is_equal(bset1
, bset2
) == 1);
90 isl_basic_set_free(bset1
);
91 isl_basic_set_free(bset2
);
96 void test_bounded(struct isl_ctx
*ctx
)
101 set
= isl_set_read_from_str(ctx
, "[n] -> {[i] : 0 <= i <= n }", -1);
102 bounded
= isl_set_is_bounded(set
);
106 set
= isl_set_read_from_str(ctx
, "{[n, i] : 0 <= i <= n }", -1);
107 bounded
= isl_set_is_bounded(set
);
111 set
= isl_set_read_from_str(ctx
, "[n] -> {[i] : i <= n }", -1);
112 bounded
= isl_set_is_bounded(set
);
117 /* Construct the basic set { [i] : 5 <= i <= N } */
118 void test_construction(struct isl_ctx
*ctx
)
122 struct isl_basic_set
*bset
;
123 struct isl_constraint
*c
;
127 dim
= isl_dim_set_alloc(ctx
, 1, 1);
128 bset
= isl_basic_set_universe(dim
);
130 c
= isl_inequality_alloc(isl_basic_set_get_dim(bset
));
131 isl_int_set_si(v
, -1);
132 isl_constraint_set_coefficient(c
, isl_dim_set
, 0, v
);
133 isl_int_set_si(v
, 1);
134 isl_constraint_set_coefficient(c
, isl_dim_param
, 0, v
);
135 bset
= isl_basic_set_add_constraint(bset
, c
);
137 c
= isl_inequality_alloc(isl_basic_set_get_dim(bset
));
138 isl_int_set_si(v
, 1);
139 isl_constraint_set_coefficient(c
, isl_dim_set
, 0, v
);
140 isl_int_set_si(v
, -5);
141 isl_constraint_set_constant(c
, v
);
142 bset
= isl_basic_set_add_constraint(bset
, c
);
144 isl_basic_set_free(bset
);
149 void test_dim(struct isl_ctx
*ctx
)
152 isl_map
*map1
, *map2
;
154 map1
= isl_map_read_from_str(ctx
,
155 "[n] -> { [i] -> [j] : exists (a = [i/10] : i - 10a <= n ) }", -1);
156 map1
= isl_map_add_dims(map1
, isl_dim_in
, 1);
157 map2
= isl_map_read_from_str(ctx
,
158 "[n] -> { [i,k] -> [j] : exists (a = [i/10] : i - 10a <= n ) }", -1);
159 assert(isl_map_is_equal(map1
, map2
));
162 map1
= isl_map_project_out(map1
, isl_dim_in
, 0, 1);
163 map2
= isl_map_read_from_str(ctx
, "[n] -> { [i] -> [j] : n >= 0 }", -1);
164 assert(isl_map_is_equal(map1
, map2
));
169 str
= "[n] -> { [i] -> [] : exists a : 0 <= i <= n and i = 2 a }";
170 map1
= isl_map_read_from_str(ctx
, str
, -1);
171 str
= "{ [i] -> [j] : exists a : 0 <= i <= j and i = 2 a }";
172 map2
= isl_map_read_from_str(ctx
, str
, -1);
173 map1
= isl_map_move_dims(map1
, isl_dim_out
, 0, isl_dim_param
, 0, 1);
174 assert(isl_map_is_equal(map1
, map2
));
180 void test_div(struct isl_ctx
*ctx
)
186 struct isl_basic_set
*bset
;
187 struct isl_constraint
*c
;
192 dim
= isl_dim_set_alloc(ctx
, 0, 1);
193 bset
= isl_basic_set_universe(dim
);
195 c
= isl_equality_alloc(isl_basic_set_get_dim(bset
));
196 isl_int_set_si(v
, -1);
197 isl_constraint_set_constant(c
, v
);
198 isl_int_set_si(v
, 1);
199 isl_constraint_set_coefficient(c
, isl_dim_set
, 0, v
);
200 div
= isl_div_alloc(isl_basic_set_get_dim(bset
));
201 c
= isl_constraint_add_div(c
, div
, &pos
);
202 isl_int_set_si(v
, 3);
203 isl_constraint_set_coefficient(c
, isl_dim_div
, pos
, v
);
204 bset
= isl_basic_set_add_constraint(bset
, c
);
206 c
= isl_equality_alloc(isl_basic_set_get_dim(bset
));
207 isl_int_set_si(v
, 1);
208 isl_constraint_set_constant(c
, v
);
209 isl_int_set_si(v
, -1);
210 isl_constraint_set_coefficient(c
, isl_dim_set
, 0, v
);
211 div
= isl_div_alloc(isl_basic_set_get_dim(bset
));
212 c
= isl_constraint_add_div(c
, div
, &pos
);
213 isl_int_set_si(v
, 3);
214 isl_constraint_set_coefficient(c
, isl_dim_div
, pos
, v
);
215 bset
= isl_basic_set_add_constraint(bset
, c
);
217 assert(bset
&& bset
->n_div
== 1);
218 isl_basic_set_free(bset
);
221 dim
= isl_dim_set_alloc(ctx
, 0, 1);
222 bset
= isl_basic_set_universe(dim
);
224 c
= isl_equality_alloc(isl_basic_set_get_dim(bset
));
225 isl_int_set_si(v
, 1);
226 isl_constraint_set_constant(c
, v
);
227 isl_int_set_si(v
, -1);
228 isl_constraint_set_coefficient(c
, isl_dim_set
, 0, v
);
229 div
= isl_div_alloc(isl_basic_set_get_dim(bset
));
230 c
= isl_constraint_add_div(c
, div
, &pos
);
231 isl_int_set_si(v
, 3);
232 isl_constraint_set_coefficient(c
, isl_dim_div
, pos
, v
);
233 bset
= isl_basic_set_add_constraint(bset
, c
);
235 c
= isl_equality_alloc(isl_basic_set_get_dim(bset
));
236 isl_int_set_si(v
, -1);
237 isl_constraint_set_constant(c
, v
);
238 isl_int_set_si(v
, 1);
239 isl_constraint_set_coefficient(c
, isl_dim_set
, 0, v
);
240 div
= isl_div_alloc(isl_basic_set_get_dim(bset
));
241 c
= isl_constraint_add_div(c
, div
, &pos
);
242 isl_int_set_si(v
, 3);
243 isl_constraint_set_coefficient(c
, isl_dim_div
, pos
, v
);
244 bset
= isl_basic_set_add_constraint(bset
, c
);
246 assert(bset
&& bset
->n_div
== 1);
247 isl_basic_set_free(bset
);
250 dim
= isl_dim_set_alloc(ctx
, 0, 1);
251 bset
= isl_basic_set_universe(dim
);
253 c
= isl_equality_alloc(isl_basic_set_get_dim(bset
));
254 isl_int_set_si(v
, 1);
255 isl_constraint_set_constant(c
, v
);
256 isl_int_set_si(v
, -1);
257 isl_constraint_set_coefficient(c
, isl_dim_set
, 0, v
);
258 div
= isl_div_alloc(isl_basic_set_get_dim(bset
));
259 c
= isl_constraint_add_div(c
, div
, &pos
);
260 isl_int_set_si(v
, 3);
261 isl_constraint_set_coefficient(c
, isl_dim_div
, pos
, v
);
262 bset
= isl_basic_set_add_constraint(bset
, c
);
264 c
= isl_equality_alloc(isl_basic_set_get_dim(bset
));
265 isl_int_set_si(v
, -3);
266 isl_constraint_set_constant(c
, v
);
267 isl_int_set_si(v
, 1);
268 isl_constraint_set_coefficient(c
, isl_dim_set
, 0, v
);
269 div
= isl_div_alloc(isl_basic_set_get_dim(bset
));
270 c
= isl_constraint_add_div(c
, div
, &pos
);
271 isl_int_set_si(v
, 4);
272 isl_constraint_set_coefficient(c
, isl_dim_div
, pos
, v
);
273 bset
= isl_basic_set_add_constraint(bset
, c
);
275 assert(bset
&& bset
->n_div
== 1);
276 isl_basic_set_free(bset
);
279 dim
= isl_dim_set_alloc(ctx
, 0, 1);
280 bset
= isl_basic_set_universe(dim
);
282 c
= isl_equality_alloc(isl_basic_set_get_dim(bset
));
283 isl_int_set_si(v
, 2);
284 isl_constraint_set_constant(c
, v
);
285 isl_int_set_si(v
, -1);
286 isl_constraint_set_coefficient(c
, isl_dim_set
, 0, v
);
287 div
= isl_div_alloc(isl_basic_set_get_dim(bset
));
288 c
= isl_constraint_add_div(c
, div
, &pos
);
289 isl_int_set_si(v
, 3);
290 isl_constraint_set_coefficient(c
, isl_dim_div
, pos
, v
);
291 bset
= isl_basic_set_add_constraint(bset
, c
);
293 c
= isl_equality_alloc(isl_basic_set_get_dim(bset
));
294 isl_int_set_si(v
, -1);
295 isl_constraint_set_constant(c
, v
);
296 isl_int_set_si(v
, 1);
297 isl_constraint_set_coefficient(c
, isl_dim_set
, 0, v
);
298 div
= isl_div_alloc(isl_basic_set_get_dim(bset
));
299 c
= isl_constraint_add_div(c
, div
, &pos
);
300 isl_int_set_si(v
, 6);
301 isl_constraint_set_coefficient(c
, isl_dim_div
, pos
, v
);
302 bset
= isl_basic_set_add_constraint(bset
, c
);
304 assert(isl_basic_set_is_empty(bset
));
305 isl_basic_set_free(bset
);
308 dim
= isl_dim_set_alloc(ctx
, 0, 2);
309 bset
= isl_basic_set_universe(dim
);
311 c
= isl_equality_alloc(isl_basic_set_get_dim(bset
));
312 isl_int_set_si(v
, -1);
313 isl_constraint_set_coefficient(c
, isl_dim_set
, 0, v
);
314 div
= isl_div_alloc(isl_basic_set_get_dim(bset
));
315 c
= isl_constraint_add_div(c
, div
, &pos
);
316 isl_int_set_si(v
, 3);
317 isl_constraint_set_coefficient(c
, isl_dim_div
, pos
, v
);
318 bset
= isl_basic_set_add_constraint(bset
, c
);
320 c
= isl_equality_alloc(isl_basic_set_get_dim(bset
));
321 isl_int_set_si(v
, 1);
322 isl_constraint_set_coefficient(c
, isl_dim_set
, 0, v
);
323 isl_int_set_si(v
, -3);
324 isl_constraint_set_coefficient(c
, isl_dim_set
, 1, v
);
325 bset
= isl_basic_set_add_constraint(bset
, c
);
327 assert(bset
&& bset
->n_div
== 0);
328 isl_basic_set_free(bset
);
331 dim
= isl_dim_set_alloc(ctx
, 0, 2);
332 bset
= isl_basic_set_universe(dim
);
334 c
= isl_equality_alloc(isl_basic_set_get_dim(bset
));
335 isl_int_set_si(v
, -1);
336 isl_constraint_set_coefficient(c
, isl_dim_set
, 0, v
);
337 div
= isl_div_alloc(isl_basic_set_get_dim(bset
));
338 c
= isl_constraint_add_div(c
, div
, &pos
);
339 isl_int_set_si(v
, 6);
340 isl_constraint_set_coefficient(c
, isl_dim_div
, pos
, v
);
341 bset
= isl_basic_set_add_constraint(bset
, c
);
343 c
= isl_equality_alloc(isl_basic_set_get_dim(bset
));
344 isl_int_set_si(v
, 1);
345 isl_constraint_set_coefficient(c
, isl_dim_set
, 0, v
);
346 isl_int_set_si(v
, -3);
347 isl_constraint_set_coefficient(c
, isl_dim_set
, 1, v
);
348 bset
= isl_basic_set_add_constraint(bset
, c
);
350 assert(bset
&& bset
->n_div
== 1);
351 isl_basic_set_free(bset
);
354 /* This test is a bit tricky. We set up an equality
356 * Normalization of divs creates _two_ divs
359 * Afterwards e0 is removed again because it has coefficient -1
360 * and we end up with the original equality and div again.
361 * Perhaps we can avoid the introduction of this temporary div.
363 dim
= isl_dim_set_alloc(ctx
, 0, 3);
364 bset
= isl_basic_set_universe(dim
);
366 c
= isl_equality_alloc(isl_basic_set_get_dim(bset
));
367 isl_int_set_si(v
, -1);
368 isl_constraint_set_coefficient(c
, isl_dim_set
, 0, v
);
369 isl_int_set_si(v
, -3);
370 isl_constraint_set_coefficient(c
, isl_dim_set
, 1, v
);
371 isl_int_set_si(v
, -3);
372 isl_constraint_set_coefficient(c
, isl_dim_set
, 2, v
);
373 div
= isl_div_alloc(isl_basic_set_get_dim(bset
));
374 c
= isl_constraint_add_div(c
, div
, &pos
);
375 isl_int_set_si(v
, 6);
376 isl_constraint_set_coefficient(c
, isl_dim_div
, pos
, v
);
377 bset
= isl_basic_set_add_constraint(bset
, c
);
379 /* Test disabled for now */
381 assert(bset && bset->n_div == 1);
383 isl_basic_set_free(bset
);
386 dim
= isl_dim_set_alloc(ctx
, 0, 4);
387 bset
= isl_basic_set_universe(dim
);
389 c
= isl_equality_alloc(isl_basic_set_get_dim(bset
));
390 isl_int_set_si(v
, -1);
391 isl_constraint_set_coefficient(c
, isl_dim_set
, 0, v
);
392 isl_int_set_si(v
, -3);
393 isl_constraint_set_coefficient(c
, isl_dim_set
, 1, v
);
394 isl_int_set_si(v
, -3);
395 isl_constraint_set_coefficient(c
, isl_dim_set
, 3, v
);
396 div
= isl_div_alloc(isl_basic_set_get_dim(bset
));
397 c
= isl_constraint_add_div(c
, div
, &pos
);
398 isl_int_set_si(v
, 6);
399 isl_constraint_set_coefficient(c
, isl_dim_div
, pos
, v
);
400 bset
= isl_basic_set_add_constraint(bset
, c
);
402 c
= isl_equality_alloc(isl_basic_set_get_dim(bset
));
403 isl_int_set_si(v
, -1);
404 isl_constraint_set_coefficient(c
, isl_dim_set
, 0, v
);
405 isl_int_set_si(v
, 1);
406 isl_constraint_set_coefficient(c
, isl_dim_set
, 2, v
);
407 isl_int_set_si(v
, 1);
408 isl_constraint_set_constant(c
, v
);
409 bset
= isl_basic_set_add_constraint(bset
, c
);
411 /* Test disabled for now */
413 assert(bset && bset->n_div == 1);
415 isl_basic_set_free(bset
);
418 dim
= isl_dim_set_alloc(ctx
, 0, 2);
419 bset
= isl_basic_set_universe(dim
);
421 c
= isl_equality_alloc(isl_basic_set_get_dim(bset
));
422 isl_int_set_si(v
, 1);
423 isl_constraint_set_coefficient(c
, isl_dim_set
, 0, v
);
424 isl_int_set_si(v
, -1);
425 isl_constraint_set_coefficient(c
, isl_dim_set
, 1, v
);
426 div
= isl_div_alloc(isl_basic_set_get_dim(bset
));
427 c
= isl_constraint_add_div(c
, div
, &pos
);
428 isl_int_set_si(v
, -2);
429 isl_constraint_set_coefficient(c
, isl_dim_div
, pos
, v
);
430 bset
= isl_basic_set_add_constraint(bset
, c
);
432 c
= isl_equality_alloc(isl_basic_set_get_dim(bset
));
433 isl_int_set_si(v
, -1);
434 isl_constraint_set_coefficient(c
, isl_dim_set
, 0, v
);
435 div
= isl_div_alloc(isl_basic_set_get_dim(bset
));
436 c
= isl_constraint_add_div(c
, div
, &pos
);
437 isl_int_set_si(v
, 3);
438 isl_constraint_set_coefficient(c
, isl_dim_div
, pos
, v
);
439 isl_int_set_si(v
, 2);
440 isl_constraint_set_constant(c
, v
);
441 bset
= isl_basic_set_add_constraint(bset
, c
);
443 bset
= isl_basic_set_fix_si(bset
, isl_dim_set
, 0, 2);
445 assert(!isl_basic_set_is_empty(bset
));
447 isl_basic_set_free(bset
);
450 dim
= isl_dim_set_alloc(ctx
, 0, 2);
451 bset
= isl_basic_set_universe(dim
);
453 c
= isl_equality_alloc(isl_basic_set_get_dim(bset
));
454 isl_int_set_si(v
, 1);
455 isl_constraint_set_coefficient(c
, isl_dim_set
, 0, v
);
456 div
= isl_div_alloc(isl_basic_set_get_dim(bset
));
457 c
= isl_constraint_add_div(c
, div
, &pos
);
458 isl_int_set_si(v
, -2);
459 isl_constraint_set_coefficient(c
, isl_dim_div
, pos
, v
);
460 bset
= isl_basic_set_add_constraint(bset
, c
);
462 bset
= isl_basic_set_fix_si(bset
, isl_dim_set
, 0, 2);
464 isl_basic_set_free(bset
);
469 void test_application_case(struct isl_ctx
*ctx
, const char *name
)
471 char filename
[PATH_MAX
];
474 struct isl_basic_set
*bset1
, *bset2
;
475 struct isl_basic_map
*bmap
;
477 n
= snprintf(filename
, sizeof(filename
),
478 "%s/test_inputs/%s.omega", srcdir
, name
);
479 assert(n
< sizeof(filename
));
480 input
= fopen(filename
, "r");
483 bset1
= isl_basic_set_read_from_file(ctx
, input
, 0);
484 bmap
= isl_basic_map_read_from_file(ctx
, input
, 0);
486 bset1
= isl_basic_set_apply(bset1
, bmap
);
488 bset2
= isl_basic_set_read_from_file(ctx
, input
, 0);
490 assert(isl_basic_set_is_equal(bset1
, bset2
) == 1);
492 isl_basic_set_free(bset1
);
493 isl_basic_set_free(bset2
);
498 void test_application(struct isl_ctx
*ctx
)
500 test_application_case(ctx
, "application");
501 test_application_case(ctx
, "application2");
504 void test_affine_hull_case(struct isl_ctx
*ctx
, const char *name
)
506 char filename
[PATH_MAX
];
509 struct isl_basic_set
*bset1
, *bset2
;
511 n
= snprintf(filename
, sizeof(filename
),
512 "%s/test_inputs/%s.polylib", srcdir
, name
);
513 assert(n
< sizeof(filename
));
514 input
= fopen(filename
, "r");
517 bset1
= isl_basic_set_read_from_file(ctx
, input
, 0);
518 bset2
= isl_basic_set_read_from_file(ctx
, input
, 0);
520 bset1
= isl_basic_set_affine_hull(bset1
);
522 assert(isl_basic_set_is_equal(bset1
, bset2
) == 1);
524 isl_basic_set_free(bset1
);
525 isl_basic_set_free(bset2
);
530 void test_affine_hull(struct isl_ctx
*ctx
)
532 test_affine_hull_case(ctx
, "affine2");
533 test_affine_hull_case(ctx
, "affine");
534 test_affine_hull_case(ctx
, "affine3");
537 void test_convex_hull_case(struct isl_ctx
*ctx
, const char *name
)
539 char filename
[PATH_MAX
];
542 struct isl_basic_set
*bset1
, *bset2
;
545 n
= snprintf(filename
, sizeof(filename
),
546 "%s/test_inputs/%s.polylib", srcdir
, name
);
547 assert(n
< sizeof(filename
));
548 input
= fopen(filename
, "r");
551 bset1
= isl_basic_set_read_from_file(ctx
, input
, 0);
552 bset2
= isl_basic_set_read_from_file(ctx
, input
, 0);
554 set
= isl_basic_set_union(bset1
, bset2
);
555 bset1
= isl_set_convex_hull(set
);
557 bset2
= isl_basic_set_read_from_file(ctx
, input
, 0);
559 assert(isl_basic_set_is_equal(bset1
, bset2
) == 1);
561 isl_basic_set_free(bset1
);
562 isl_basic_set_free(bset2
);
567 void test_convex_hull(struct isl_ctx
*ctx
)
569 const char *str1
, *str2
;
570 isl_set
*set1
, *set2
;
572 test_convex_hull_case(ctx
, "convex0");
573 test_convex_hull_case(ctx
, "convex1");
574 test_convex_hull_case(ctx
, "convex2");
575 test_convex_hull_case(ctx
, "convex3");
576 test_convex_hull_case(ctx
, "convex4");
577 test_convex_hull_case(ctx
, "convex5");
578 test_convex_hull_case(ctx
, "convex6");
579 test_convex_hull_case(ctx
, "convex7");
580 test_convex_hull_case(ctx
, "convex8");
581 test_convex_hull_case(ctx
, "convex9");
582 test_convex_hull_case(ctx
, "convex10");
583 test_convex_hull_case(ctx
, "convex11");
584 test_convex_hull_case(ctx
, "convex12");
585 test_convex_hull_case(ctx
, "convex13");
586 test_convex_hull_case(ctx
, "convex14");
587 test_convex_hull_case(ctx
, "convex15");
589 str1
= "{ [i0, i1, i2] : (i2 = 1 and i0 = 0 and i1 >= 0) or "
590 "(i0 = 1 and i1 = 0 and i2 = 1) or "
591 "(i0 = 0 and i1 = 0 and i2 = 0) }";
592 str2
= "{ [i0, i1, i2] : i0 >= 0 and i2 >= i0 and i2 <= 1 and i1 >= 0 }";
593 set1
= isl_set_read_from_str(ctx
, str1
, -1);
594 set2
= isl_set_read_from_str(ctx
, str2
, -1);
595 set1
= isl_set_from_basic_set(isl_set_convex_hull(set1
));
596 assert(isl_set_is_equal(set1
, set2
));
601 void test_gist_case(struct isl_ctx
*ctx
, const char *name
)
603 char filename
[PATH_MAX
];
606 struct isl_basic_set
*bset1
, *bset2
;
608 n
= snprintf(filename
, sizeof(filename
),
609 "%s/test_inputs/%s.polylib", srcdir
, name
);
610 assert(n
< sizeof(filename
));
611 input
= fopen(filename
, "r");
614 bset1
= isl_basic_set_read_from_file(ctx
, input
, 0);
615 bset2
= isl_basic_set_read_from_file(ctx
, input
, 0);
617 bset1
= isl_basic_set_gist(bset1
, bset2
);
619 bset2
= isl_basic_set_read_from_file(ctx
, input
, 0);
621 assert(isl_basic_set_is_equal(bset1
, bset2
) == 1);
623 isl_basic_set_free(bset1
);
624 isl_basic_set_free(bset2
);
629 void test_gist(struct isl_ctx
*ctx
)
631 test_gist_case(ctx
, "gist1");
634 void test_coalesce_set(isl_ctx
*ctx
, const char *str
, int check_one
)
638 set
= isl_set_read_from_str(ctx
, str
, -1);
639 set
= isl_set_coalesce(set
);
640 set2
= isl_set_read_from_str(ctx
, str
, -1);
641 assert(isl_set_is_equal(set
, set2
));
643 assert(set
&& set
->n
== 1);
648 void test_coalesce(struct isl_ctx
*ctx
)
651 struct isl_set
*set
, *set2
;
652 struct isl_map
*map
, *map2
;
654 set
= isl_set_read_from_str(ctx
,
655 "{[x,y]: x >= 0 & x <= 10 & y >= 0 & y <= 10 or "
656 "y >= x & x >= 2 & 5 >= y }", -1);
657 set
= isl_set_coalesce(set
);
658 assert(set
&& set
->n
== 1);
661 set
= isl_set_read_from_str(ctx
,
662 "{[x,y]: y >= 0 & 2x + y <= 30 & y <= 10 & x >= 0 or "
663 "x + y >= 10 & y <= x & x + y <= 20 & y >= 0}", -1);
664 set
= isl_set_coalesce(set
);
665 assert(set
&& set
->n
== 1);
668 set
= isl_set_read_from_str(ctx
,
669 "{[x,y]: y >= 0 & 2x + y <= 30 & y <= 10 & x >= 0 or "
670 "x + y >= 10 & y <= x & x + y <= 19 & y >= 0}", -1);
671 set
= isl_set_coalesce(set
);
672 assert(set
&& set
->n
== 2);
675 set
= isl_set_read_from_str(ctx
,
676 "{[x,y]: y >= 0 & x <= 5 & y <= x or "
677 "y >= 0 & x >= 6 & x <= 10 & y <= x}", -1);
678 set
= isl_set_coalesce(set
);
679 assert(set
&& set
->n
== 1);
682 set
= isl_set_read_from_str(ctx
,
683 "{[x,y]: y >= 0 & x <= 5 & y <= x or "
684 "y >= 0 & x >= 7 & x <= 10 & y <= x}", -1);
685 set
= isl_set_coalesce(set
);
686 assert(set
&& set
->n
== 2);
689 set
= isl_set_read_from_str(ctx
,
690 "{[x,y]: y >= 0 & x <= 5 & y <= x or "
691 "y >= 0 & x >= 6 & x <= 10 & y + 1 <= x}", -1);
692 set
= isl_set_coalesce(set
);
693 assert(set
&& set
->n
== 2);
696 set
= isl_set_read_from_str(ctx
,
697 "{[x,y]: y >= 0 & x <= 5 & y <= x or "
698 "y >= 0 & x = 6 & y <= 6}", -1);
699 set
= isl_set_coalesce(set
);
700 assert(set
&& set
->n
== 1);
703 set
= isl_set_read_from_str(ctx
,
704 "{[x,y]: y >= 0 & x <= 5 & y <= x or "
705 "y >= 0 & x = 7 & y <= 6}", -1);
706 set
= isl_set_coalesce(set
);
707 assert(set
&& set
->n
== 2);
710 set
= isl_set_read_from_str(ctx
,
711 "{[x,y]: y >= 0 & x <= 5 & y <= x or "
712 "y >= 0 & x = 6 & y <= 5}", -1);
713 set
= isl_set_coalesce(set
);
714 assert(set
&& set
->n
== 1);
715 set2
= isl_set_read_from_str(ctx
,
716 "{[x,y]: y >= 0 & x <= 5 & y <= x or "
717 "y >= 0 & x = 6 & y <= 5}", -1);
718 assert(isl_set_is_equal(set
, set2
));
722 set
= isl_set_read_from_str(ctx
,
723 "{[x,y]: y >= 0 & x <= 5 & y <= x or "
724 "y >= 0 & x = 6 & y <= 7}", -1);
725 set
= isl_set_coalesce(set
);
726 assert(set
&& set
->n
== 2);
729 set
= isl_set_read_from_str(ctx
,
730 "[n] -> { [i] : i = 1 and n >= 2 or 2 <= i and i <= n }", -1);
731 set
= isl_set_coalesce(set
);
732 assert(set
&& set
->n
== 1);
733 set2
= isl_set_read_from_str(ctx
,
734 "[n] -> { [i] : i = 1 and n >= 2 or 2 <= i and i <= n }", -1);
735 assert(isl_set_is_equal(set
, set2
));
739 set
= isl_set_read_from_str(ctx
,
740 "{[x,y] : x >= 0 and y >= 0 or 0 <= y and y <= 5 and x = -1}", -1);
741 set
= isl_set_coalesce(set
);
742 set2
= isl_set_read_from_str(ctx
,
743 "{[x,y] : x >= 0 and y >= 0 or 0 <= y and y <= 5 and x = -1}", -1);
744 assert(isl_set_is_equal(set
, set2
));
748 set
= isl_set_read_from_str(ctx
,
749 "[n] -> { [i] : 1 <= i and i <= n - 1 or "
750 "2 <= i and i <= n }", -1);
751 set
= isl_set_coalesce(set
);
752 assert(set
&& set
->n
== 1);
753 set2
= isl_set_read_from_str(ctx
,
754 "[n] -> { [i] : 1 <= i and i <= n - 1 or "
755 "2 <= i and i <= n }", -1);
756 assert(isl_set_is_equal(set
, set2
));
760 map
= isl_map_read_from_str(ctx
,
761 "[n] -> { [i0] -> [o0] : exists (e0 = [(i0)/4], e1 = [(o0)/4], "
762 "e2 = [(n)/2], e3 = [(-2 + i0)/4], e4 = [(-2 + o0)/4], "
763 "e5 = [(-2n + i0)/4]: 2e2 = n and 4e3 = -2 + i0 and "
764 "4e4 = -2 + o0 and i0 >= 8 + 2n and o0 >= 2 + i0 and "
765 "o0 <= 56 + 2n and o0 <= -12 + 4n and i0 <= 57 + 2n and "
766 "i0 <= -11 + 4n and o0 >= 6 + 2n and 4e0 <= i0 and "
767 "4e0 >= -3 + i0 and 4e1 <= o0 and 4e1 >= -3 + o0 and "
768 "4e5 <= -2n + i0 and 4e5 >= -3 - 2n + i0);"
769 "[i0] -> [o0] : exists (e0 = [(i0)/4], e1 = [(o0)/4], "
770 "e2 = [(n)/2], e3 = [(-2 + i0)/4], e4 = [(-2 + o0)/4], "
771 "e5 = [(-2n + i0)/4]: 2e2 = n and 4e3 = -2 + i0 and "
772 "4e4 = -2 + o0 and 2e0 >= 3 + n and e0 <= -4 + n and "
773 "2e0 <= 27 + n and e1 <= -4 + n and 2e1 <= 27 + n and "
774 "2e1 >= 2 + n and e1 >= 1 + e0 and i0 >= 7 + 2n and "
775 "i0 <= -11 + 4n and i0 <= 57 + 2n and 4e0 <= -2 + i0 and "
776 "4e0 >= -3 + i0 and o0 >= 6 + 2n and o0 <= -11 + 4n and "
777 "o0 <= 57 + 2n and 4e1 <= -2 + o0 and 4e1 >= -3 + o0 and "
778 "4e5 <= -2n + i0 and 4e5 >= -3 - 2n + i0 ) }", -1);
779 map
= isl_map_coalesce(map
);
780 map2
= isl_map_read_from_str(ctx
,
781 "[n] -> { [i0] -> [o0] : exists (e0 = [(i0)/4], e1 = [(o0)/4], "
782 "e2 = [(n)/2], e3 = [(-2 + i0)/4], e4 = [(-2 + o0)/4], "
783 "e5 = [(-2n + i0)/4]: 2e2 = n and 4e3 = -2 + i0 and "
784 "4e4 = -2 + o0 and i0 >= 8 + 2n and o0 >= 2 + i0 and "
785 "o0 <= 56 + 2n and o0 <= -12 + 4n and i0 <= 57 + 2n and "
786 "i0 <= -11 + 4n and o0 >= 6 + 2n and 4e0 <= i0 and "
787 "4e0 >= -3 + i0 and 4e1 <= o0 and 4e1 >= -3 + o0 and "
788 "4e5 <= -2n + i0 and 4e5 >= -3 - 2n + i0);"
789 "[i0] -> [o0] : exists (e0 = [(i0)/4], e1 = [(o0)/4], "
790 "e2 = [(n)/2], e3 = [(-2 + i0)/4], e4 = [(-2 + o0)/4], "
791 "e5 = [(-2n + i0)/4]: 2e2 = n and 4e3 = -2 + i0 and "
792 "4e4 = -2 + o0 and 2e0 >= 3 + n and e0 <= -4 + n and "
793 "2e0 <= 27 + n and e1 <= -4 + n and 2e1 <= 27 + n and "
794 "2e1 >= 2 + n and e1 >= 1 + e0 and i0 >= 7 + 2n and "
795 "i0 <= -11 + 4n and i0 <= 57 + 2n and 4e0 <= -2 + i0 and "
796 "4e0 >= -3 + i0 and o0 >= 6 + 2n and o0 <= -11 + 4n and "
797 "o0 <= 57 + 2n and 4e1 <= -2 + o0 and 4e1 >= -3 + o0 and "
798 "4e5 <= -2n + i0 and 4e5 >= -3 - 2n + i0 ) }", -1);
799 assert(isl_map_is_equal(map
, map2
));
803 str
= "[n, m] -> { [] -> [o0, o2, o3] : (o3 = 1 and o0 >= 1 + m and "
804 "o0 <= n + m and o2 <= m and o0 >= 2 + n and o2 >= 3) or "
805 "(o0 >= 2 + n and o0 >= 1 + m and o0 <= n + m and n >= 1 and "
806 "o3 <= -1 + o2 and o3 >= 1 - m + o2 and o3 >= 2 and o3 <= n) }";
807 map
= isl_map_read_from_str(ctx
, str
, -1);
808 map
= isl_map_coalesce(map
);
809 map2
= isl_map_read_from_str(ctx
, str
, -1);
810 assert(isl_map_is_equal(map
, map2
));
814 str
= "[M, N] -> { [i0, i1, i2, i3, i4, i5, i6] -> "
815 "[o0, o1, o2, o3, o4, o5, o6] : "
816 "(o6 <= -4 + 2M - 2N + i0 + i1 - i2 + i6 - o0 - o1 + o2 and "
817 "o3 <= -2 + i3 and o6 >= 2 + i0 + i3 + i6 - o0 - o3 and "
818 "o6 >= 2 - M + N + i3 + i4 + i6 - o3 - o4 and o0 <= -1 + i0 and "
819 "o4 >= 4 - 3M + 3N - i0 - i1 + i2 + 2i3 + i4 + o0 + o1 - o2 - 2o3 "
820 "and o6 <= -3 + 2M - 2N + i3 + i4 - i5 + i6 - o3 - o4 + o5 and "
821 "2o6 <= -5 + 5M - 5N + 2i0 + i1 - i2 - i5 + 2i6 - 2o0 - o1 + o2 + o5 "
822 "and o6 >= 2i0 + i1 + i6 - 2o0 - o1 and "
823 "3o6 <= -5 + 4M - 4N + 2i0 + i1 - i2 + 2i3 + i4 - i5 + 3i6 "
824 "- 2o0 - o1 + o2 - 2o3 - o4 + o5) or "
825 "(N >= 2 and o3 <= -1 + i3 and o0 <= -1 + i0 and "
826 "o6 >= i3 + i6 - o3 and M >= 0 and "
827 "2o6 >= 1 + i0 + i3 + 2i6 - o0 - o3 and "
828 "o6 >= 1 - M + i0 + i6 - o0 and N >= 2M and o6 >= i0 + i6 - o0) }";
829 map
= isl_map_read_from_str(ctx
, str
, -1);
830 map
= isl_map_coalesce(map
);
831 map2
= isl_map_read_from_str(ctx
, str
, -1);
832 assert(isl_map_is_equal(map
, map2
));
836 str
= "[M, N] -> { [] -> [o0] : (o0 = 0 and M >= 1 and N >= 2) or "
837 "(o0 = 0 and M >= 1 and N >= 2M and N >= 2 + M) or "
838 "(o0 = 0 and M >= 2 and N >= 3) or "
839 "(M = 0 and o0 = 0 and N >= 3) }";
840 map
= isl_map_read_from_str(ctx
, str
, -1);
841 map
= isl_map_coalesce(map
);
842 map2
= isl_map_read_from_str(ctx
, str
, -1);
843 assert(isl_map_is_equal(map
, map2
));
847 str
= "{ [i0, i1, i2, i3] : (i1 = 10i0 and i0 >= 1 and 10i0 <= 100 and "
848 "i3 <= 9 + 10 i2 and i3 >= 1 + 10i2 and i3 >= 0) or "
849 "(i1 <= 9 + 10i0 and i1 >= 1 + 10i0 and i2 >= 0 and "
850 "i0 >= 0 and i1 <= 100 and i3 <= 9 + 10i2 and i3 >= 1 + 10i2) }";
851 map
= isl_map_read_from_str(ctx
, str
, -1);
852 map
= isl_map_coalesce(map
);
853 map2
= isl_map_read_from_str(ctx
, str
, -1);
854 assert(isl_map_is_equal(map
, map2
));
858 test_coalesce_set(ctx
,
859 "[M] -> { [i1] : (i1 >= 2 and i1 <= M) or "
860 "(i1 = M and M >= 1) }", 0);
861 test_coalesce_set(ctx
,
862 "{[x,y] : x,y >= 0; [x,y] : 10 <= x <= 20 and y >= -1 }", 0);
863 test_coalesce_set(ctx
,
864 "{ [x, y] : (x >= 1 and y >= 1 and x <= 2 and y <= 2) or "
865 "(y = 3 and x = 1) }", 1);
866 test_coalesce_set(ctx
,
867 "[M] -> { [i0, i1, i2, i3, i4] : (i1 >= 3 and i4 >= 2 + i2 and "
868 "i2 >= 2 and i0 >= 2 and i3 >= 1 + i2 and i0 <= M and "
869 "i1 <= M and i3 <= M and i4 <= M) or "
870 "(i1 >= 2 and i4 >= 1 + i2 and i2 >= 2 and i0 >= 2 and "
871 "i3 >= 1 + i2 and i0 <= M and i1 <= -1 + M and i3 <= M and "
872 "i4 <= -1 + M) }", 1);
873 test_coalesce_set(ctx
,
874 "{ [x, y] : (x >= 0 and y >= 0 and x <= 10 and y <= 10) or "
875 "(x >= 1 and y >= 1 and x <= 11 and y <= 11) }", 1);
876 test_coalesce_set(ctx
,
877 "{[x,y,z] : y + 2 >= 0 and x - y + 1 >= 0 and "
878 "-x - y + 1 >= 0 and -3 <= z <= 3;"
879 "[x,y,z] : -x+z + 20 >= 0 and -x-z + 20 >= 0 and "
880 "x-z + 20 >= 0 and x+z + 20 >= 0 and -10 <= y <= 0}", 1);
881 test_coalesce_set(ctx
,
882 "{[x,y] : 0 <= x,y <= 10; [5,y]: 4 <=y <= 11}", 1);
883 test_coalesce_set(ctx
, "{[x,0] : x >= 0; [x,1] : x <= 20}", 0);
884 test_coalesce_set(ctx
,
885 "{[x,0,0] : -5 <= x <= 5; [0,y,1] : -5 <= y <= 5 }", 1);
886 test_coalesce_set(ctx
, "{ [x, 1 - x] : 0 <= x <= 1; [0,0] }", 1);
889 void test_closure(struct isl_ctx
*ctx
)
897 /* COCOA example 1 */
898 map
= isl_map_read_from_str(ctx
,
899 "[n,k] -> { [i,j] -> [i2,j2] : i2 = i + 1 and j2 = j + 1 and "
900 "1 <= i and i < n and 1 <= j and j < n or "
901 "i2 = i + 1 and j2 = j - 1 and "
902 "1 <= i and i < n and 2 <= j and j <= n }", -1);
903 map
= isl_map_power(map
, 1, &exact
);
907 /* COCOA example 1 */
908 map
= isl_map_read_from_str(ctx
,
909 "[n] -> { [i,j] -> [i2,j2] : i2 = i + 1 and j2 = j + 1 and "
910 "1 <= i and i < n and 1 <= j and j < n or "
911 "i2 = i + 1 and j2 = j - 1 and "
912 "1 <= i and i < n and 2 <= j and j <= n }", -1);
913 map
= isl_map_transitive_closure(map
, &exact
);
915 map2
= isl_map_read_from_str(ctx
,
916 "[n] -> { [i,j] -> [i2,j2] : exists (k1,k2,k : "
917 "1 <= i and i < n and 1 <= j and j <= n and "
918 "2 <= i2 and i2 <= n and 1 <= j2 and j2 <= n and "
919 "i2 = i + k1 + k2 and j2 = j + k1 - k2 and "
920 "k1 >= 0 and k2 >= 0 and k1 + k2 = k and k >= 1 )}", -1);
921 assert(isl_map_is_equal(map
, map2
));
925 map
= isl_map_read_from_str(ctx
,
926 "[n] -> { [x] -> [y] : y = x + 1 and 0 <= x and x <= n and "
927 " 0 <= y and y <= n }", -1);
928 map
= isl_map_transitive_closure(map
, &exact
);
929 map2
= isl_map_read_from_str(ctx
,
930 "[n] -> { [x] -> [y] : y > x and 0 <= x and x <= n and "
931 " 0 <= y and y <= n }", -1);
932 assert(isl_map_is_equal(map
, map2
));
936 /* COCOA example 2 */
937 map
= isl_map_read_from_str(ctx
,
938 "[n] -> { [i,j] -> [i2,j2] : i2 = i + 2 and j2 = j + 2 and "
939 "1 <= i and i < n - 1 and 1 <= j and j < n - 1 or "
940 "i2 = i + 2 and j2 = j - 2 and "
941 "1 <= i and i < n - 1 and 3 <= j and j <= n }", -1);
942 map
= isl_map_transitive_closure(map
, &exact
);
944 map2
= isl_map_read_from_str(ctx
,
945 "[n] -> { [i,j] -> [i2,j2] : exists (k1,k2,k : "
946 "1 <= i and i < n - 1 and 1 <= j and j <= n and "
947 "3 <= i2 and i2 <= n and 1 <= j2 and j2 <= n and "
948 "i2 = i + 2 k1 + 2 k2 and j2 = j + 2 k1 - 2 k2 and "
949 "k1 >= 0 and k2 >= 0 and k1 + k2 = k and k >= 1) }", -1);
950 assert(isl_map_is_equal(map
, map2
));
954 /* COCOA Fig.2 left */
955 map
= isl_map_read_from_str(ctx
,
956 "[n] -> { [i,j] -> [i2,j2] : i2 = i + 2 and j2 = j and "
957 "i <= 2 j - 3 and i <= n - 2 and j <= 2 i - 1 and "
959 "i2 = i and j2 = j + 2 and i <= 2 j - 1 and i <= n and "
960 "j <= 2 i - 3 and j <= n - 2 or "
961 "i2 = i + 1 and j2 = j + 1 and i <= 2 j - 1 and "
962 "i <= n - 1 and j <= 2 i - 1 and j <= n - 1 }", -1);
963 map
= isl_map_transitive_closure(map
, &exact
);
967 /* COCOA Fig.2 right */
968 map
= isl_map_read_from_str(ctx
,
969 "[n,k] -> { [i,j] -> [i2,j2] : i2 = i + 3 and j2 = j and "
970 "i <= 2 j - 4 and i <= n - 3 and j <= 2 i - 1 and "
972 "i2 = i and j2 = j + 3 and i <= 2 j - 1 and i <= n and "
973 "j <= 2 i - 4 and j <= n - 3 or "
974 "i2 = i + 1 and j2 = j + 1 and i <= 2 j - 1 and "
975 "i <= n - 1 and j <= 2 i - 1 and j <= n - 1 }", -1);
976 map
= isl_map_power(map
, 1, &exact
);
980 /* COCOA Fig.2 right */
981 map
= isl_map_read_from_str(ctx
,
982 "[n] -> { [i,j] -> [i2,j2] : i2 = i + 3 and j2 = j and "
983 "i <= 2 j - 4 and i <= n - 3 and j <= 2 i - 1 and "
985 "i2 = i and j2 = j + 3 and i <= 2 j - 1 and i <= n and "
986 "j <= 2 i - 4 and j <= n - 3 or "
987 "i2 = i + 1 and j2 = j + 1 and i <= 2 j - 1 and "
988 "i <= n - 1 and j <= 2 i - 1 and j <= n - 1 }", -1);
989 map
= isl_map_transitive_closure(map
, &exact
);
991 map2
= isl_map_read_from_str(ctx
,
992 "[n] -> { [i,j] -> [i2,j2] : exists (k1,k2,k3,k : "
993 "i <= 2 j - 1 and i <= n and j <= 2 i - 1 and "
994 "j <= n and 3 + i + 2 j <= 3 n and "
995 "3 + 2 i + j <= 3n and i2 <= 2 j2 -1 and i2 <= n and "
996 "i2 <= 3 j2 - 4 and j2 <= 2 i2 -1 and j2 <= n and "
997 "13 + 4 j2 <= 11 i2 and i2 = i + 3 k1 + k3 and "
998 "j2 = j + 3 k2 + k3 and k1 >= 0 and k2 >= 0 and "
999 "k3 >= 0 and k1 + k2 + k3 = k and k > 0) }", -1);
1000 assert(isl_map_is_equal(map
, map2
));
1004 /* COCOA Fig.1 right */
1005 dom
= isl_set_read_from_str(ctx
,
1006 "{ [x,y] : x >= 0 and -2 x + 3 y >= 0 and x <= 3 and "
1007 "2 x - 3 y + 3 >= 0 }", -1);
1008 right
= isl_map_read_from_str(ctx
,
1009 "{ [x,y] -> [x2,y2] : x2 = x + 1 and y2 = y }", -1);
1010 up
= isl_map_read_from_str(ctx
,
1011 "{ [x,y] -> [x2,y2] : x2 = x and y2 = y + 1 }", -1);
1012 right
= isl_map_intersect_domain(right
, isl_set_copy(dom
));
1013 right
= isl_map_intersect_range(right
, isl_set_copy(dom
));
1014 up
= isl_map_intersect_domain(up
, isl_set_copy(dom
));
1015 up
= isl_map_intersect_range(up
, dom
);
1016 map
= isl_map_union(up
, right
);
1017 map
= isl_map_transitive_closure(map
, &exact
);
1019 map2
= isl_map_read_from_str(ctx
,
1020 "{ [0,0] -> [0,1]; [0,0] -> [1,1]; [0,1] -> [1,1]; "
1021 " [2,2] -> [3,2]; [2,2] -> [3,3]; [3,2] -> [3,3] }", -1);
1022 assert(isl_map_is_equal(map
, map2
));
1026 /* COCOA Theorem 1 counter example */
1027 map
= isl_map_read_from_str(ctx
,
1028 "{ [i,j] -> [i2,j2] : i = 0 and 0 <= j and j <= 1 and "
1029 "i2 = 1 and j2 = j or "
1030 "i = 0 and j = 0 and i2 = 0 and j2 = 1 }", -1);
1031 map
= isl_map_transitive_closure(map
, &exact
);
1035 map
= isl_map_read_from_str(ctx
,
1036 "[m,n] -> { [i,j] -> [i2,j2] : i2 = i and j2 = j + 2 and "
1037 "1 <= i,i2 <= n and 1 <= j,j2 <= m or "
1038 "i2 = i + 1 and 3 <= j2 - j <= 4 and "
1039 "1 <= i,i2 <= n and 1 <= j,j2 <= m }", -1);
1040 map
= isl_map_transitive_closure(map
, &exact
);
1044 /* Kelly et al 1996, fig 12 */
1045 map
= isl_map_read_from_str(ctx
,
1046 "[n] -> { [i,j] -> [i2,j2] : i2 = i and j2 = j + 1 and "
1047 "1 <= i,j,j+1 <= n or "
1048 "j = n and j2 = 1 and i2 = i + 1 and "
1049 "1 <= i,i+1 <= n }", -1);
1050 map
= isl_map_transitive_closure(map
, &exact
);
1052 map2
= isl_map_read_from_str(ctx
,
1053 "[n] -> { [i,j] -> [i2,j2] : 1 <= j < j2 <= n and "
1054 "1 <= i <= n and i = i2 or "
1055 "1 <= i < i2 <= n and 1 <= j <= n and "
1056 "1 <= j2 <= n }", -1);
1057 assert(isl_map_is_equal(map
, map2
));
1061 /* Omega's closure4 */
1062 map
= isl_map_read_from_str(ctx
,
1063 "[m,n] -> { [x,y] -> [x2,y2] : x2 = x and y2 = y + 1 and "
1064 "1 <= x,y <= 10 or "
1065 "x2 = x + 1 and y2 = y and "
1066 "1 <= x <= 20 && 5 <= y <= 15 }", -1);
1067 map
= isl_map_transitive_closure(map
, &exact
);
1071 map
= isl_map_read_from_str(ctx
,
1072 "[n] -> { [x] -> [y]: 1 <= n <= y - x <= 10 }", -1);
1073 map
= isl_map_transitive_closure(map
, &exact
);
1075 map2
= isl_map_read_from_str(ctx
,
1076 "[n] -> { [x] -> [y] : 1 <= n <= 10 and y >= n + x }", -1);
1077 assert(isl_map_is_equal(map
, map2
));
1081 str
= "[n, m] -> { [i0, i1, i2, i3] -> [o0, o1, o2, o3] : "
1082 "i3 = 1 and o0 = i0 and o1 = -1 + i1 and o2 = -1 + i2 and "
1083 "o3 = -2 + i2 and i1 <= -1 + i0 and i1 >= 1 - m + i0 and "
1084 "i1 >= 2 and i1 <= n and i2 >= 3 and i2 <= 1 + n and i2 <= m }";
1085 map
= isl_map_read_from_str(ctx
, str
, -1);
1086 map
= isl_map_transitive_closure(map
, &exact
);
1088 map2
= isl_map_read_from_str(ctx
, str
, -1);
1089 assert(isl_map_is_equal(map
, map2
));
1093 str
= "{[0] -> [1]; [2] -> [3]}";
1094 map
= isl_map_read_from_str(ctx
, str
, -1);
1095 map
= isl_map_transitive_closure(map
, &exact
);
1097 map2
= isl_map_read_from_str(ctx
, str
, -1);
1098 assert(isl_map_is_equal(map
, map2
));
1103 void test_lex(struct isl_ctx
*ctx
)
1108 dim
= isl_dim_alloc(ctx
, 0, 0, 0);
1109 map
= isl_map_lex_le(dim
);
1110 assert(!isl_map_is_empty(map
));
1114 void test_lexmin(struct isl_ctx
*ctx
)
1121 str
= "[p0, p1] -> { [] -> [] : "
1122 "exists (e0 = [(2p1)/3], e1, e2, e3 = [(3 - p1 + 3e0)/3], "
1123 "e4 = [(p1)/3], e5 = [(p1 + 3e4)/3]: "
1124 "3e0 >= -2 + 2p1 and 3e0 >= p1 and 3e3 >= 1 - p1 + 3e0 and "
1125 "3e0 <= 2p1 and 3e3 >= -2 + p1 and 3e3 <= -1 + p1 and p1 >= 3 and "
1126 "3e5 >= -2 + 2p1 and 3e5 >= p1 and 3e5 <= -1 + p1 + 3e4 and "
1127 "3e4 <= p1 and 3e4 >= -2 + p1 and e3 <= -1 + e0 and "
1128 "3e4 >= 6 - p1 + 3e1 and 3e1 >= p1 and 3e5 >= -2 + p1 + 3e4 and "
1129 "2e4 >= 3 - p1 + 2e1 and e4 <= e1 and 3e3 <= 2 - p1 + 3e0 and "
1130 "e5 >= 1 + e1 and 3e4 >= 6 - 2p1 + 3e1 and "
1131 "p0 >= 2 and p1 >= p0 and 3e2 >= p1 and 3e4 >= 6 - p1 + 3e2 and "
1132 "e2 <= e1 and e3 >= 1 and e4 <= e2) }";
1133 map
= isl_map_read_from_str(ctx
, str
, -1);
1134 map
= isl_map_lexmin(map
);
1137 str
= "[C] -> { [obj,a,b,c] : obj <= 38 a + 7 b + 10 c and "
1138 "a + b <= 1 and c <= 10 b and c <= C and a,b,c,C >= 0 }";
1139 set
= isl_set_read_from_str(ctx
, str
, -1);
1140 set
= isl_set_lexmax(set
);
1141 str
= "[C] -> { [obj,a,b,c] : C = 8 }";
1142 set2
= isl_set_read_from_str(ctx
, str
, -1);
1143 set
= isl_set_intersect(set
, set2
);
1144 assert(!isl_set_is_empty(set
));
1153 static int collect_must_may(__isl_take isl_map
*dep
, int must
,
1154 void *dep_user
, void *user
)
1156 struct must_may
*mm
= (struct must_may
*)user
;
1159 mm
->must
= isl_map_union(mm
->must
, dep
);
1161 mm
->may
= isl_map_union(mm
->may
, dep
);
1166 static int common_space(void *first
, void *second
)
1168 int depth
= *(int *)first
;
1172 static int map_is_equal(__isl_keep isl_map
*map
, const char *str
)
1180 map2
= isl_map_read_from_str(map
->ctx
, str
, -1);
1181 equal
= isl_map_is_equal(map
, map2
);
1187 void test_dep(struct isl_ctx
*ctx
)
1192 isl_access_info
*ai
;
1199 str
= "{ [2,i,0] -> [i] : 0 <= i <= 10 }";
1200 map
= isl_map_read_from_str(ctx
, str
, -1);
1201 ai
= isl_access_info_alloc(map
, &depth
, &common_space
, 2);
1203 str
= "{ [0,i,0] -> [i] : 0 <= i <= 10 }";
1204 map
= isl_map_read_from_str(ctx
, str
, -1);
1205 ai
= isl_access_info_add_source(ai
, map
, 1, &depth
);
1207 str
= "{ [1,i,0] -> [5] : 0 <= i <= 10 }";
1208 map
= isl_map_read_from_str(ctx
, str
, -1);
1209 ai
= isl_access_info_add_source(ai
, map
, 1, &depth
);
1211 flow
= isl_access_info_compute_flow(ai
);
1212 dim
= isl_dim_alloc(ctx
, 0, 3, 3);
1213 mm
.must
= isl_map_empty(isl_dim_copy(dim
));
1214 mm
.may
= isl_map_empty(dim
);
1216 isl_flow_foreach(flow
, collect_must_may
, &mm
);
1218 str
= "{ [0,i,0] -> [2,i,0] : (0 <= i <= 4) or (6 <= i <= 10); "
1219 " [1,10,0] -> [2,5,0] }";
1220 assert(map_is_equal(mm
.must
, str
));
1221 str
= "{ [i,j,k] -> [l,m,n] : 1 = 0 }";
1222 assert(map_is_equal(mm
.may
, str
));
1224 isl_map_free(mm
.must
);
1225 isl_map_free(mm
.may
);
1226 isl_flow_free(flow
);
1229 str
= "{ [2,i,0] -> [i] : 0 <= i <= 10 }";
1230 map
= isl_map_read_from_str(ctx
, str
, -1);
1231 ai
= isl_access_info_alloc(map
, &depth
, &common_space
, 2);
1233 str
= "{ [0,i,0] -> [i] : 0 <= i <= 10 }";
1234 map
= isl_map_read_from_str(ctx
, str
, -1);
1235 ai
= isl_access_info_add_source(ai
, map
, 1, &depth
);
1237 str
= "{ [1,i,0] -> [5] : 0 <= i <= 10 }";
1238 map
= isl_map_read_from_str(ctx
, str
, -1);
1239 ai
= isl_access_info_add_source(ai
, map
, 0, &depth
);
1241 flow
= isl_access_info_compute_flow(ai
);
1242 dim
= isl_dim_alloc(ctx
, 0, 3, 3);
1243 mm
.must
= isl_map_empty(isl_dim_copy(dim
));
1244 mm
.may
= isl_map_empty(dim
);
1246 isl_flow_foreach(flow
, collect_must_may
, &mm
);
1248 str
= "{ [0,i,0] -> [2,i,0] : (0 <= i <= 4) or (6 <= i <= 10) }";
1249 assert(map_is_equal(mm
.must
, str
));
1250 str
= "{ [0,5,0] -> [2,5,0]; [1,i,0] -> [2,5,0] : 0 <= i <= 10 }";
1251 assert(map_is_equal(mm
.may
, str
));
1253 isl_map_free(mm
.must
);
1254 isl_map_free(mm
.may
);
1255 isl_flow_free(flow
);
1258 str
= "{ [2,i,0] -> [i] : 0 <= i <= 10 }";
1259 map
= isl_map_read_from_str(ctx
, str
, -1);
1260 ai
= isl_access_info_alloc(map
, &depth
, &common_space
, 2);
1262 str
= "{ [0,i,0] -> [i] : 0 <= i <= 10 }";
1263 map
= isl_map_read_from_str(ctx
, str
, -1);
1264 ai
= isl_access_info_add_source(ai
, map
, 0, &depth
);
1266 str
= "{ [1,i,0] -> [5] : 0 <= i <= 10 }";
1267 map
= isl_map_read_from_str(ctx
, str
, -1);
1268 ai
= isl_access_info_add_source(ai
, map
, 0, &depth
);
1270 flow
= isl_access_info_compute_flow(ai
);
1271 dim
= isl_dim_alloc(ctx
, 0, 3, 3);
1272 mm
.must
= isl_map_empty(isl_dim_copy(dim
));
1273 mm
.may
= isl_map_empty(dim
);
1275 isl_flow_foreach(flow
, collect_must_may
, &mm
);
1277 str
= "{ [0,i,0] -> [2,i,0] : 0 <= i <= 10; "
1278 " [1,i,0] -> [2,5,0] : 0 <= i <= 10 }";
1279 assert(map_is_equal(mm
.may
, str
));
1280 str
= "{ [i,j,k] -> [l,m,n] : 1 = 0 }";
1281 assert(map_is_equal(mm
.must
, str
));
1283 isl_map_free(mm
.must
);
1284 isl_map_free(mm
.may
);
1285 isl_flow_free(flow
);
1288 str
= "{ [0,i,2] -> [i] : 0 <= i <= 10 }";
1289 map
= isl_map_read_from_str(ctx
, str
, -1);
1290 ai
= isl_access_info_alloc(map
, &depth
, &common_space
, 2);
1292 str
= "{ [0,i,0] -> [i] : 0 <= i <= 10 }";
1293 map
= isl_map_read_from_str(ctx
, str
, -1);
1294 ai
= isl_access_info_add_source(ai
, map
, 0, &depth
);
1296 str
= "{ [0,i,1] -> [5] : 0 <= i <= 10 }";
1297 map
= isl_map_read_from_str(ctx
, str
, -1);
1298 ai
= isl_access_info_add_source(ai
, map
, 0, &depth
);
1300 flow
= isl_access_info_compute_flow(ai
);
1301 dim
= isl_dim_alloc(ctx
, 0, 3, 3);
1302 mm
.must
= isl_map_empty(isl_dim_copy(dim
));
1303 mm
.may
= isl_map_empty(dim
);
1305 isl_flow_foreach(flow
, collect_must_may
, &mm
);
1307 str
= "{ [0,i,0] -> [0,i,2] : 0 <= i <= 10; "
1308 " [0,i,1] -> [0,5,2] : 0 <= i <= 5 }";
1309 assert(map_is_equal(mm
.may
, str
));
1310 str
= "{ [i,j,k] -> [l,m,n] : 1 = 0 }";
1311 assert(map_is_equal(mm
.must
, str
));
1313 isl_map_free(mm
.must
);
1314 isl_map_free(mm
.may
);
1315 isl_flow_free(flow
);
1318 str
= "{ [0,i,1] -> [i] : 0 <= i <= 10 }";
1319 map
= isl_map_read_from_str(ctx
, str
, -1);
1320 ai
= isl_access_info_alloc(map
, &depth
, &common_space
, 2);
1322 str
= "{ [0,i,0] -> [i] : 0 <= i <= 10 }";
1323 map
= isl_map_read_from_str(ctx
, str
, -1);
1324 ai
= isl_access_info_add_source(ai
, map
, 0, &depth
);
1326 str
= "{ [0,i,2] -> [5] : 0 <= i <= 10 }";
1327 map
= isl_map_read_from_str(ctx
, str
, -1);
1328 ai
= isl_access_info_add_source(ai
, map
, 0, &depth
);
1330 flow
= isl_access_info_compute_flow(ai
);
1331 dim
= isl_dim_alloc(ctx
, 0, 3, 3);
1332 mm
.must
= isl_map_empty(isl_dim_copy(dim
));
1333 mm
.may
= isl_map_empty(dim
);
1335 isl_flow_foreach(flow
, collect_must_may
, &mm
);
1337 str
= "{ [0,i,0] -> [0,i,1] : 0 <= i <= 10; "
1338 " [0,i,2] -> [0,5,1] : 0 <= i <= 4 }";
1339 assert(map_is_equal(mm
.may
, str
));
1340 str
= "{ [i,j,k] -> [l,m,n] : 1 = 0 }";
1341 assert(map_is_equal(mm
.must
, str
));
1343 isl_map_free(mm
.must
);
1344 isl_map_free(mm
.may
);
1345 isl_flow_free(flow
);
1350 str
= "{ [1,i,0,0,0] -> [i,j] : 0 <= i <= 10 and 0 <= j <= 10 }";
1351 map
= isl_map_read_from_str(ctx
, str
, -1);
1352 ai
= isl_access_info_alloc(map
, &depth
, &common_space
, 1);
1354 str
= "{ [0,i,0,j,0] -> [i,j] : 0 <= i <= 10 and 0 <= j <= 10 }";
1355 map
= isl_map_read_from_str(ctx
, str
, -1);
1356 ai
= isl_access_info_add_source(ai
, map
, 1, &depth
);
1358 flow
= isl_access_info_compute_flow(ai
);
1359 dim
= isl_dim_alloc(ctx
, 0, 5, 5);
1360 mm
.must
= isl_map_empty(isl_dim_copy(dim
));
1361 mm
.may
= isl_map_empty(dim
);
1363 isl_flow_foreach(flow
, collect_must_may
, &mm
);
1365 str
= "{ [0,i,0,j,0] -> [1,i,0,0,0] : 0 <= i,j <= 10 }";
1366 assert(map_is_equal(mm
.must
, str
));
1367 str
= "{ [0,0,0,0,0] -> [0,0,0,0,0] : 1 = 0 }";
1368 assert(map_is_equal(mm
.may
, str
));
1370 isl_map_free(mm
.must
);
1371 isl_map_free(mm
.may
);
1372 isl_flow_free(flow
);
1375 void test_sv(struct isl_ctx
*ctx
)
1380 str
= "[N] -> { [i] -> [f] : 0 <= i <= N and 0 <= i - 10 f <= 9 }";
1381 map
= isl_map_read_from_str(ctx
, str
, -1);
1382 assert(isl_map_is_single_valued(map
));
1385 str
= "[N] -> { [i] -> [f] : 0 <= i <= N and 0 <= i - 10 f <= 10 }";
1386 map
= isl_map_read_from_str(ctx
, str
, -1);
1387 assert(!isl_map_is_single_valued(map
));
1391 void test_bijective_case(struct isl_ctx
*ctx
, const char *str
, int bijective
)
1395 map
= isl_map_read_from_str(ctx
, str
, -1);
1397 assert(isl_map_is_bijective(map
));
1399 assert(!isl_map_is_bijective(map
));
1403 void test_bijective(struct isl_ctx
*ctx
)
1405 test_bijective_case(ctx
, "[N,M]->{[i,j] -> [i]}", 0);
1406 test_bijective_case(ctx
, "[N,M]->{[i,j] -> [i] : j=i}", 1);
1407 test_bijective_case(ctx
, "[N,M]->{[i,j] -> [i] : j=0}", 1);
1408 test_bijective_case(ctx
, "[N,M]->{[i,j] -> [i] : j=N}", 1);
1409 test_bijective_case(ctx
, "[N,M]->{[i,j] -> [j,i]}", 1);
1410 test_bijective_case(ctx
, "[N,M]->{[i,j] -> [i+j]}", 0);
1411 test_bijective_case(ctx
, "[N,M]->{[i,j] -> []}", 0);
1412 test_bijective_case(ctx
, "[N,M]->{[i,j] -> [i,j,N]}", 1);
1413 test_bijective_case(ctx
, "[N,M]->{[i,j] -> [2i]}", 0);
1414 test_bijective_case(ctx
, "[N,M]->{[i,j] -> [i,i]}", 0);
1415 test_bijective_case(ctx
, "[N,M]->{[i,j] -> [2i,i]}", 0);
1416 test_bijective_case(ctx
, "[N,M]->{[i,j] -> [2i,j]}", 1);
1417 test_bijective_case(ctx
, "[N,M]->{[i,j] -> [x,y] : 2x=i & y =j}", 1);
1420 void test_pwqp(struct isl_ctx
*ctx
)
1424 isl_pw_qpolynomial
*pwqp1
, *pwqp2
;
1426 str
= "{ [i,j,k] -> 1 + 9 * [i/5] + 7 * [j/11] + 4 * [k/13] }";
1427 pwqp1
= isl_pw_qpolynomial_read_from_str(ctx
, str
);
1429 pwqp1
= isl_pw_qpolynomial_move_dims(pwqp1
, isl_dim_param
, 0,
1432 str
= "[j] -> { [i,k] -> 1 + 9 * [i/5] + 7 * [j/11] + 4 * [k/13] }";
1433 pwqp2
= isl_pw_qpolynomial_read_from_str(ctx
, str
);
1435 pwqp1
= isl_pw_qpolynomial_sub(pwqp1
, pwqp2
);
1437 assert(isl_pw_qpolynomial_is_zero(pwqp1
));
1439 isl_pw_qpolynomial_free(pwqp1
);
1441 str
= "{ [i] -> i }";
1442 pwqp1
= isl_pw_qpolynomial_read_from_str(ctx
, str
);
1443 str
= "{ [k] : exists a : k = 2a }";
1444 set
= isl_set_read_from_str(ctx
, str
, 0);
1445 pwqp1
= isl_pw_qpolynomial_gist(pwqp1
, set
);
1446 str
= "{ [i] -> i }";
1447 pwqp2
= isl_pw_qpolynomial_read_from_str(ctx
, str
);
1449 pwqp1
= isl_pw_qpolynomial_sub(pwqp1
, pwqp2
);
1451 assert(isl_pw_qpolynomial_is_zero(pwqp1
));
1453 isl_pw_qpolynomial_free(pwqp1
);
1455 str
= "{ [i] -> i + [ (i + [i/3])/2 ] }";
1456 pwqp1
= isl_pw_qpolynomial_read_from_str(ctx
, str
);
1458 set
= isl_set_read_from_str(ctx
, str
, 0);
1459 pwqp1
= isl_pw_qpolynomial_gist(pwqp1
, set
);
1460 str
= "{ [i] -> 16 }";
1461 pwqp2
= isl_pw_qpolynomial_read_from_str(ctx
, str
);
1463 pwqp1
= isl_pw_qpolynomial_sub(pwqp1
, pwqp2
);
1465 assert(isl_pw_qpolynomial_is_zero(pwqp1
));
1467 isl_pw_qpolynomial_free(pwqp1
);
1470 void test_split_periods(isl_ctx
*ctx
)
1473 isl_pw_qpolynomial
*pwqp
;
1475 str
= "{ [U,V] -> 1/3 * U + 2/3 * V - [(U + 2V)/3] + [U/2] : "
1476 "U + 2V + 3 >= 0 and - U -2V >= 0 and - U + 10 >= 0 and "
1477 "U >= 0; [U,V] -> U^2 : U >= 100 }";
1478 pwqp
= isl_pw_qpolynomial_read_from_str(ctx
, str
);
1480 pwqp
= isl_pw_qpolynomial_split_periods(pwqp
, 2);
1483 isl_pw_qpolynomial_free(pwqp
);
1486 void test_union(isl_ctx
*ctx
)
1489 isl_union_set
*uset
;
1490 isl_union_map
*umap1
, *umap2
;
1492 str
= "{ [i] : 0 <= i <= 1 }";
1493 uset
= isl_union_set_from_set(isl_set_read_from_str(ctx
, str
, -1));
1494 str
= "{ [1] -> [0] }";
1495 umap1
= isl_union_map_from_map(isl_map_read_from_str(ctx
, str
, -1));
1497 umap2
= isl_union_set_lex_gt_union_set(isl_union_set_copy(uset
), uset
);
1498 assert(isl_union_map_is_equal(umap1
, umap2
));
1500 isl_union_map_free(umap1
);
1501 isl_union_map_free(umap2
);
1506 struct isl_ctx
*ctx
;
1508 srcdir
= getenv("srcdir");
1511 ctx
= isl_ctx_alloc();
1513 test_split_periods(ctx
);
1518 test_bijective(ctx
);
1522 test_construction(ctx
);
1525 test_application(ctx
);
1526 test_affine_hull(ctx
);
1527 test_convex_hull(ctx
);