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
13 #include <isl_ctx_private.h>
14 #include <isl_map_private.h>
18 #include <isl/constraint.h>
19 #include <isl/polynomial.h>
20 #include <isl/union_map.h>
21 #include <isl_factorization.h>
22 #include <isl/schedule.h>
26 static char *get_filename(isl_ctx
*ctx
, const char *name
, const char *suffix
) {
29 char *pattern
= "%s/test_inputs/%s.%s";
31 length
= strlen(pattern
) - 6 + strlen(srcdir
) + strlen(name
)
33 filename
= isl_alloc_array(ctx
, char, length
);
38 sprintf(filename
, pattern
, srcdir
, name
, suffix
);
43 void test_parse_map(isl_ctx
*ctx
, const char *str
)
47 map
= isl_map_read_from_str(ctx
, str
);
52 void test_parse_map_equal(isl_ctx
*ctx
, const char *str
, const char *str2
)
56 map
= isl_map_read_from_str(ctx
, str
);
57 map2
= isl_map_read_from_str(ctx
, str2
);
58 assert(map
&& map2
&& isl_map_is_equal(map
, map2
));
63 void test_parse_pwqp(isl_ctx
*ctx
, const char *str
)
65 isl_pw_qpolynomial
*pwqp
;
67 pwqp
= isl_pw_qpolynomial_read_from_str(ctx
, str
);
69 isl_pw_qpolynomial_free(pwqp
);
72 static void test_parse_pwaff(isl_ctx
*ctx
, const char *str
)
76 pwaff
= isl_pw_aff_read_from_str(ctx
, str
);
78 isl_pw_aff_free(pwaff
);
81 void test_parse(struct isl_ctx
*ctx
)
84 const char *str
, *str2
;
86 str
= "{ [i] -> [-i] }";
87 map
= isl_map_read_from_str(ctx
, str
);
91 str
= "{ A[i] -> L[([i/3])] }";
92 map
= isl_map_read_from_str(ctx
, str
);
96 test_parse_map(ctx
, "{[[s] -> A[i]] -> [[s+1] -> A[i]]}");
97 test_parse_map(ctx
, "{ [p1, y1, y2] -> [2, y1, y2] : "
98 "p1 = 1 && (y1 <= y2 || y2 = 0) }");
100 str
= "{ [x,y] : [([x/2]+y)/3] >= 1 }";
101 str2
= "{ [x, y] : 2y >= 6 - x }";
102 test_parse_map_equal(ctx
, str
, str2
);
104 test_parse_map_equal(ctx
, "{ [x,y] : x <= min(y, 2*y+3) }",
105 "{ [x,y] : x <= y, 2*y + 3 }");
106 str
= "{ [x, y] : (y <= x and y >= -3) or (2y <= -3 + x and y <= -4) }";
107 test_parse_map_equal(ctx
, "{ [x,y] : x >= min(y, 2*y+3) }", str
);
109 str
= "{[new,old] -> [new+1-2*[(new+1)/2],old+1-2*[(old+1)/2]]}";
110 map
= isl_map_read_from_str(ctx
, str
);
111 str
= "{ [new, old] -> [o0, o1] : "
112 "exists (e0 = [(-1 - new + o0)/2], e1 = [(-1 - old + o1)/2]: "
113 "2e0 = -1 - new + o0 and 2e1 = -1 - old + o1 and o0 >= 0 and "
114 "o0 <= 1 and o1 >= 0 and o1 <= 1) }";
115 map2
= isl_map_read_from_str(ctx
, str
);
116 assert(isl_map_is_equal(map
, map2
));
120 str
= "{[new,old] -> [new+1-2*[(new+1)/2],old+1-2*[(old+1)/2]]}";
121 map
= isl_map_read_from_str(ctx
, str
);
122 str
= "{[new,old] -> [(new+1)%2,(old+1)%2]}";
123 map2
= isl_map_read_from_str(ctx
, str
);
124 assert(isl_map_is_equal(map
, map2
));
128 str
= "[n] -> { [c1] : c1>=0 and c1<=floord(n-4,3) }";
129 str2
= "[n] -> { [c1] : c1 >= 0 and 3c1 <= -4 + n }";
130 test_parse_map_equal(ctx
, str
, str2
);
132 str
= "{ [i,j] -> [i] : i < j; [i,j] -> [j] : j <= i }";
133 str2
= "{ [i,j] -> [min(i,j)] }";
134 test_parse_map_equal(ctx
, str
, str2
);
136 str
= "{ [i,j] : i != j }";
137 str2
= "{ [i,j] : i < j or i > j }";
138 test_parse_map_equal(ctx
, str
, str2
);
140 str
= "{ [i,j] : (i+1)*2 >= j }";
141 str2
= "{ [i, j] : j <= 2 + 2i }";
142 test_parse_map_equal(ctx
, str
, str2
);
144 str
= "{ [i] -> [i > 0 ? 4 : 5] }";
145 str2
= "{ [i] -> [5] : i <= 0; [i] -> [4] : i >= 1 }";
146 test_parse_map_equal(ctx
, str
, str2
);
148 str
= "[N=2,M] -> { [i=[(M+N)/4]] }";
149 str2
= "[N, M] -> { [i] : N = 2 and 4i <= 2 + M and 4i >= -1 + M }";
150 test_parse_map_equal(ctx
, str
, str2
);
152 str
= "{ [x] : x >= 0 }";
153 str2
= "{ [x] : x-0 >= 0 }";
154 test_parse_map_equal(ctx
, str
, str2
);
156 str
= "{ [i] : ((i > 10)) }";
157 str2
= "{ [i] : i >= 11 }";
158 test_parse_map_equal(ctx
, str
, str2
);
160 test_parse_pwqp(ctx
, "{ [i] -> i + [ (i + [i/3])/2 ] }");
161 test_parse_map(ctx
, "{ S1[i] -> [([i/10]),i%10] : 0 <= i <= 45 }");
162 test_parse_pwaff(ctx
, "{ [i] -> [i + 1] : i > 0; [a] -> [a] : a < 0 }");
165 void test_read(struct isl_ctx
*ctx
)
169 struct isl_basic_set
*bset1
, *bset2
;
170 const char *str
= "{[y]: Exists ( alpha : 2alpha = y)}";
172 filename
= get_filename(ctx
, "set", "omega");
174 input
= fopen(filename
, "r");
177 bset1
= isl_basic_set_read_from_file(ctx
, input
);
178 bset2
= isl_basic_set_read_from_str(ctx
, str
);
180 assert(isl_basic_set_is_equal(bset1
, bset2
) == 1);
182 isl_basic_set_free(bset1
);
183 isl_basic_set_free(bset2
);
189 void test_bounded(struct isl_ctx
*ctx
)
194 set
= isl_set_read_from_str(ctx
, "[n] -> {[i] : 0 <= i <= n }");
195 bounded
= isl_set_is_bounded(set
);
199 set
= isl_set_read_from_str(ctx
, "{[n, i] : 0 <= i <= n }");
200 bounded
= isl_set_is_bounded(set
);
204 set
= isl_set_read_from_str(ctx
, "[n] -> {[i] : i <= n }");
205 bounded
= isl_set_is_bounded(set
);
210 /* Construct the basic set { [i] : 5 <= i <= N } */
211 void test_construction(struct isl_ctx
*ctx
)
216 struct isl_basic_set
*bset
;
217 struct isl_constraint
*c
;
221 dim
= isl_space_set_alloc(ctx
, 1, 1);
222 bset
= isl_basic_set_universe(isl_space_copy(dim
));
223 ls
= isl_local_space_from_space(dim
);
225 c
= isl_inequality_alloc(isl_local_space_copy(ls
));
226 isl_int_set_si(v
, -1);
227 isl_constraint_set_coefficient(c
, isl_dim_set
, 0, v
);
228 isl_int_set_si(v
, 1);
229 isl_constraint_set_coefficient(c
, isl_dim_param
, 0, v
);
230 bset
= isl_basic_set_add_constraint(bset
, c
);
232 c
= isl_inequality_alloc(isl_local_space_copy(ls
));
233 isl_int_set_si(v
, 1);
234 isl_constraint_set_coefficient(c
, isl_dim_set
, 0, v
);
235 isl_int_set_si(v
, -5);
236 isl_constraint_set_constant(c
, v
);
237 bset
= isl_basic_set_add_constraint(bset
, c
);
239 isl_local_space_free(ls
);
240 isl_basic_set_free(bset
);
245 void test_dim(struct isl_ctx
*ctx
)
248 isl_map
*map1
, *map2
;
250 map1
= isl_map_read_from_str(ctx
,
251 "[n] -> { [i] -> [j] : exists (a = [i/10] : i - 10a <= n ) }");
252 map1
= isl_map_add_dims(map1
, isl_dim_in
, 1);
253 map2
= isl_map_read_from_str(ctx
,
254 "[n] -> { [i,k] -> [j] : exists (a = [i/10] : i - 10a <= n ) }");
255 assert(isl_map_is_equal(map1
, map2
));
258 map1
= isl_map_project_out(map1
, isl_dim_in
, 0, 1);
259 map2
= isl_map_read_from_str(ctx
, "[n] -> { [i] -> [j] : n >= 0 }");
260 assert(isl_map_is_equal(map1
, map2
));
265 str
= "[n] -> { [i] -> [] : exists a : 0 <= i <= n and i = 2 a }";
266 map1
= isl_map_read_from_str(ctx
, str
);
267 str
= "{ [i] -> [j] : exists a : 0 <= i <= j and i = 2 a }";
268 map2
= isl_map_read_from_str(ctx
, str
);
269 map1
= isl_map_move_dims(map1
, isl_dim_out
, 0, isl_dim_param
, 0, 1);
270 assert(isl_map_is_equal(map1
, map2
));
276 void test_div(struct isl_ctx
*ctx
)
281 struct isl_basic_set
*bset
;
282 struct isl_constraint
*c
;
287 dim
= isl_space_set_alloc(ctx
, 0, 3);
288 bset
= isl_basic_set_universe(isl_space_copy(dim
));
289 ls
= isl_local_space_from_space(dim
);
291 c
= isl_equality_alloc(isl_local_space_copy(ls
));
292 isl_int_set_si(v
, -1);
293 isl_constraint_set_constant(c
, v
);
294 isl_int_set_si(v
, 1);
295 isl_constraint_set_coefficient(c
, isl_dim_set
, 0, v
);
296 isl_int_set_si(v
, 3);
297 isl_constraint_set_coefficient(c
, isl_dim_set
, 1, v
);
298 bset
= isl_basic_set_add_constraint(bset
, c
);
300 c
= isl_equality_alloc(isl_local_space_copy(ls
));
301 isl_int_set_si(v
, 1);
302 isl_constraint_set_constant(c
, v
);
303 isl_int_set_si(v
, -1);
304 isl_constraint_set_coefficient(c
, isl_dim_set
, 0, v
);
305 isl_int_set_si(v
, 3);
306 isl_constraint_set_coefficient(c
, isl_dim_set
, 2, v
);
307 bset
= isl_basic_set_add_constraint(bset
, c
);
309 bset
= isl_basic_set_project_out(bset
, isl_dim_set
, 1, 2);
311 assert(bset
&& bset
->n_div
== 1);
312 isl_local_space_free(ls
);
313 isl_basic_set_free(bset
);
316 dim
= isl_space_set_alloc(ctx
, 0, 3);
317 bset
= isl_basic_set_universe(isl_space_copy(dim
));
318 ls
= isl_local_space_from_space(dim
);
320 c
= isl_equality_alloc(isl_local_space_copy(ls
));
321 isl_int_set_si(v
, 1);
322 isl_constraint_set_constant(c
, v
);
323 isl_int_set_si(v
, -1);
324 isl_constraint_set_coefficient(c
, isl_dim_set
, 0, v
);
325 isl_int_set_si(v
, 3);
326 isl_constraint_set_coefficient(c
, isl_dim_set
, 1, v
);
327 bset
= isl_basic_set_add_constraint(bset
, c
);
329 c
= isl_equality_alloc(isl_local_space_copy(ls
));
330 isl_int_set_si(v
, -1);
331 isl_constraint_set_constant(c
, v
);
332 isl_int_set_si(v
, 1);
333 isl_constraint_set_coefficient(c
, isl_dim_set
, 0, v
);
334 isl_int_set_si(v
, 3);
335 isl_constraint_set_coefficient(c
, isl_dim_set
, 2, v
);
336 bset
= isl_basic_set_add_constraint(bset
, c
);
338 bset
= isl_basic_set_project_out(bset
, isl_dim_set
, 1, 2);
340 assert(bset
&& bset
->n_div
== 1);
341 isl_local_space_free(ls
);
342 isl_basic_set_free(bset
);
345 dim
= isl_space_set_alloc(ctx
, 0, 3);
346 bset
= isl_basic_set_universe(isl_space_copy(dim
));
347 ls
= isl_local_space_from_space(dim
);
349 c
= isl_equality_alloc(isl_local_space_copy(ls
));
350 isl_int_set_si(v
, 1);
351 isl_constraint_set_constant(c
, v
);
352 isl_int_set_si(v
, -1);
353 isl_constraint_set_coefficient(c
, isl_dim_set
, 0, v
);
354 isl_int_set_si(v
, 3);
355 isl_constraint_set_coefficient(c
, isl_dim_set
, 1, v
);
356 bset
= isl_basic_set_add_constraint(bset
, c
);
358 c
= isl_equality_alloc(isl_local_space_copy(ls
));
359 isl_int_set_si(v
, -3);
360 isl_constraint_set_constant(c
, v
);
361 isl_int_set_si(v
, 1);
362 isl_constraint_set_coefficient(c
, isl_dim_set
, 0, v
);
363 isl_int_set_si(v
, 4);
364 isl_constraint_set_coefficient(c
, isl_dim_set
, 2, v
);
365 bset
= isl_basic_set_add_constraint(bset
, c
);
367 bset
= isl_basic_set_project_out(bset
, isl_dim_set
, 1, 2);
369 assert(bset
&& bset
->n_div
== 1);
370 isl_local_space_free(ls
);
371 isl_basic_set_free(bset
);
374 dim
= isl_space_set_alloc(ctx
, 0, 3);
375 bset
= isl_basic_set_universe(isl_space_copy(dim
));
376 ls
= isl_local_space_from_space(dim
);
378 c
= isl_equality_alloc(isl_local_space_copy(ls
));
379 isl_int_set_si(v
, 2);
380 isl_constraint_set_constant(c
, v
);
381 isl_int_set_si(v
, -1);
382 isl_constraint_set_coefficient(c
, isl_dim_set
, 0, v
);
383 isl_int_set_si(v
, 3);
384 isl_constraint_set_coefficient(c
, isl_dim_set
, 1, v
);
385 bset
= isl_basic_set_add_constraint(bset
, c
);
387 c
= isl_equality_alloc(isl_local_space_copy(ls
));
388 isl_int_set_si(v
, -1);
389 isl_constraint_set_constant(c
, v
);
390 isl_int_set_si(v
, 1);
391 isl_constraint_set_coefficient(c
, isl_dim_set
, 0, v
);
392 isl_int_set_si(v
, 6);
393 isl_constraint_set_coefficient(c
, isl_dim_set
, 2, v
);
394 bset
= isl_basic_set_add_constraint(bset
, c
);
396 bset
= isl_basic_set_project_out(bset
, isl_dim_set
, 1, 2);
398 assert(isl_basic_set_is_empty(bset
));
399 isl_local_space_free(ls
);
400 isl_basic_set_free(bset
);
403 dim
= isl_space_set_alloc(ctx
, 0, 3);
404 bset
= isl_basic_set_universe(isl_space_copy(dim
));
405 ls
= isl_local_space_from_space(dim
);
407 c
= isl_equality_alloc(isl_local_space_copy(ls
));
408 isl_int_set_si(v
, -1);
409 isl_constraint_set_coefficient(c
, isl_dim_set
, 0, v
);
410 isl_int_set_si(v
, 3);
411 isl_constraint_set_coefficient(c
, isl_dim_set
, 2, v
);
412 bset
= isl_basic_set_add_constraint(bset
, c
);
414 c
= isl_equality_alloc(isl_local_space_copy(ls
));
415 isl_int_set_si(v
, 1);
416 isl_constraint_set_coefficient(c
, isl_dim_set
, 0, v
);
417 isl_int_set_si(v
, -3);
418 isl_constraint_set_coefficient(c
, isl_dim_set
, 1, v
);
419 bset
= isl_basic_set_add_constraint(bset
, c
);
421 bset
= isl_basic_set_project_out(bset
, isl_dim_set
, 2, 1);
423 assert(bset
&& bset
->n_div
== 0);
424 isl_basic_set_free(bset
);
425 isl_local_space_free(ls
);
428 dim
= isl_space_set_alloc(ctx
, 0, 3);
429 bset
= isl_basic_set_universe(isl_space_copy(dim
));
430 ls
= isl_local_space_from_space(dim
);
432 c
= isl_equality_alloc(isl_local_space_copy(ls
));
433 isl_int_set_si(v
, -1);
434 isl_constraint_set_coefficient(c
, isl_dim_set
, 0, v
);
435 isl_int_set_si(v
, 6);
436 isl_constraint_set_coefficient(c
, isl_dim_set
, 2, v
);
437 bset
= isl_basic_set_add_constraint(bset
, c
);
439 c
= isl_equality_alloc(isl_local_space_copy(ls
));
440 isl_int_set_si(v
, 1);
441 isl_constraint_set_coefficient(c
, isl_dim_set
, 0, v
);
442 isl_int_set_si(v
, -3);
443 isl_constraint_set_coefficient(c
, isl_dim_set
, 1, v
);
444 bset
= isl_basic_set_add_constraint(bset
, c
);
446 bset
= isl_basic_set_project_out(bset
, isl_dim_set
, 2, 1);
448 assert(bset
&& bset
->n_div
== 1);
449 isl_basic_set_free(bset
);
450 isl_local_space_free(ls
);
453 /* This test is a bit tricky. We set up an equality
455 * Normalization of divs creates _two_ divs
458 * Afterwards e0 is removed again because it has coefficient -1
459 * and we end up with the original equality and div again.
460 * Perhaps we can avoid the introduction of this temporary div.
462 dim
= isl_space_set_alloc(ctx
, 0, 4);
463 bset
= isl_basic_set_universe(isl_space_copy(dim
));
464 ls
= isl_local_space_from_space(dim
);
466 c
= isl_equality_alloc(isl_local_space_copy(ls
));
467 isl_int_set_si(v
, -1);
468 isl_constraint_set_coefficient(c
, isl_dim_set
, 0, v
);
469 isl_int_set_si(v
, -3);
470 isl_constraint_set_coefficient(c
, isl_dim_set
, 1, v
);
471 isl_int_set_si(v
, -3);
472 isl_constraint_set_coefficient(c
, isl_dim_set
, 2, v
);
473 isl_int_set_si(v
, 6);
474 isl_constraint_set_coefficient(c
, isl_dim_set
, 3, v
);
475 bset
= isl_basic_set_add_constraint(bset
, c
);
477 bset
= isl_basic_set_project_out(bset
, isl_dim_set
, 3, 1);
479 /* Test disabled for now */
481 assert(bset && bset->n_div == 1);
483 isl_local_space_free(ls
);
484 isl_basic_set_free(bset
);
487 dim
= isl_space_set_alloc(ctx
, 0, 5);
488 bset
= isl_basic_set_universe(isl_space_copy(dim
));
489 ls
= isl_local_space_from_space(dim
);
491 c
= isl_equality_alloc(isl_local_space_copy(ls
));
492 isl_int_set_si(v
, -1);
493 isl_constraint_set_coefficient(c
, isl_dim_set
, 0, v
);
494 isl_int_set_si(v
, -3);
495 isl_constraint_set_coefficient(c
, isl_dim_set
, 1, v
);
496 isl_int_set_si(v
, -3);
497 isl_constraint_set_coefficient(c
, isl_dim_set
, 3, v
);
498 isl_int_set_si(v
, 6);
499 isl_constraint_set_coefficient(c
, isl_dim_set
, 4, v
);
500 bset
= isl_basic_set_add_constraint(bset
, c
);
502 c
= isl_equality_alloc(isl_local_space_copy(ls
));
503 isl_int_set_si(v
, -1);
504 isl_constraint_set_coefficient(c
, isl_dim_set
, 0, v
);
505 isl_int_set_si(v
, 1);
506 isl_constraint_set_coefficient(c
, isl_dim_set
, 2, v
);
507 isl_int_set_si(v
, 1);
508 isl_constraint_set_constant(c
, v
);
509 bset
= isl_basic_set_add_constraint(bset
, c
);
511 bset
= isl_basic_set_project_out(bset
, isl_dim_set
, 4, 1);
513 /* Test disabled for now */
515 assert(bset && bset->n_div == 1);
517 isl_local_space_free(ls
);
518 isl_basic_set_free(bset
);
521 dim
= isl_space_set_alloc(ctx
, 0, 4);
522 bset
= isl_basic_set_universe(isl_space_copy(dim
));
523 ls
= isl_local_space_from_space(dim
);
525 c
= isl_equality_alloc(isl_local_space_copy(ls
));
526 isl_int_set_si(v
, 1);
527 isl_constraint_set_coefficient(c
, isl_dim_set
, 0, v
);
528 isl_int_set_si(v
, -1);
529 isl_constraint_set_coefficient(c
, isl_dim_set
, 1, v
);
530 isl_int_set_si(v
, -2);
531 isl_constraint_set_coefficient(c
, isl_dim_set
, 2, v
);
532 bset
= isl_basic_set_add_constraint(bset
, c
);
534 c
= isl_equality_alloc(isl_local_space_copy(ls
));
535 isl_int_set_si(v
, -1);
536 isl_constraint_set_coefficient(c
, isl_dim_set
, 0, v
);
537 isl_int_set_si(v
, 3);
538 isl_constraint_set_coefficient(c
, isl_dim_set
, 3, v
);
539 isl_int_set_si(v
, 2);
540 isl_constraint_set_constant(c
, v
);
541 bset
= isl_basic_set_add_constraint(bset
, c
);
543 bset
= isl_basic_set_project_out(bset
, isl_dim_set
, 2, 2);
545 bset
= isl_basic_set_fix_si(bset
, isl_dim_set
, 0, 2);
547 assert(!isl_basic_set_is_empty(bset
));
549 isl_local_space_free(ls
);
550 isl_basic_set_free(bset
);
553 dim
= isl_space_set_alloc(ctx
, 0, 3);
554 bset
= isl_basic_set_universe(isl_space_copy(dim
));
555 ls
= isl_local_space_from_space(dim
);
557 c
= isl_equality_alloc(isl_local_space_copy(ls
));
558 isl_int_set_si(v
, 1);
559 isl_constraint_set_coefficient(c
, isl_dim_set
, 0, v
);
560 isl_int_set_si(v
, -2);
561 isl_constraint_set_coefficient(c
, isl_dim_set
, 2, v
);
562 bset
= isl_basic_set_add_constraint(bset
, c
);
564 bset
= isl_basic_set_project_out(bset
, isl_dim_set
, 2, 1);
566 bset
= isl_basic_set_fix_si(bset
, isl_dim_set
, 0, 2);
568 isl_local_space_free(ls
);
569 isl_basic_set_free(bset
);
574 void test_application_case(struct isl_ctx
*ctx
, const char *name
)
578 struct isl_basic_set
*bset1
, *bset2
;
579 struct isl_basic_map
*bmap
;
581 filename
= get_filename(ctx
, name
, "omega");
583 input
= fopen(filename
, "r");
586 bset1
= isl_basic_set_read_from_file(ctx
, input
);
587 bmap
= isl_basic_map_read_from_file(ctx
, input
);
589 bset1
= isl_basic_set_apply(bset1
, bmap
);
591 bset2
= isl_basic_set_read_from_file(ctx
, input
);
593 assert(isl_basic_set_is_equal(bset1
, bset2
) == 1);
595 isl_basic_set_free(bset1
);
596 isl_basic_set_free(bset2
);
602 void test_application(struct isl_ctx
*ctx
)
604 test_application_case(ctx
, "application");
605 test_application_case(ctx
, "application2");
608 void test_affine_hull_case(struct isl_ctx
*ctx
, const char *name
)
612 struct isl_basic_set
*bset1
, *bset2
;
614 filename
= get_filename(ctx
, name
, "polylib");
616 input
= fopen(filename
, "r");
619 bset1
= isl_basic_set_read_from_file(ctx
, input
);
620 bset2
= isl_basic_set_read_from_file(ctx
, input
);
622 bset1
= isl_basic_set_affine_hull(bset1
);
624 assert(isl_basic_set_is_equal(bset1
, bset2
) == 1);
626 isl_basic_set_free(bset1
);
627 isl_basic_set_free(bset2
);
633 void test_affine_hull(struct isl_ctx
*ctx
)
635 test_affine_hull_case(ctx
, "affine2");
636 test_affine_hull_case(ctx
, "affine");
637 test_affine_hull_case(ctx
, "affine3");
640 void test_convex_hull_case(struct isl_ctx
*ctx
, const char *name
)
644 struct isl_basic_set
*bset1
, *bset2
;
647 filename
= get_filename(ctx
, name
, "polylib");
649 input
= fopen(filename
, "r");
652 bset1
= isl_basic_set_read_from_file(ctx
, input
);
653 bset2
= isl_basic_set_read_from_file(ctx
, input
);
655 set
= isl_basic_set_union(bset1
, bset2
);
656 bset1
= isl_set_convex_hull(set
);
658 bset2
= isl_basic_set_read_from_file(ctx
, input
);
660 assert(isl_basic_set_is_equal(bset1
, bset2
) == 1);
662 isl_basic_set_free(bset1
);
663 isl_basic_set_free(bset2
);
669 void test_convex_hull_algo(struct isl_ctx
*ctx
, int convex
)
671 const char *str1
, *str2
;
672 isl_set
*set1
, *set2
;
673 int orig_convex
= ctx
->opt
->convex
;
674 ctx
->opt
->convex
= convex
;
676 test_convex_hull_case(ctx
, "convex0");
677 test_convex_hull_case(ctx
, "convex1");
678 test_convex_hull_case(ctx
, "convex2");
679 test_convex_hull_case(ctx
, "convex3");
680 test_convex_hull_case(ctx
, "convex4");
681 test_convex_hull_case(ctx
, "convex5");
682 test_convex_hull_case(ctx
, "convex6");
683 test_convex_hull_case(ctx
, "convex7");
684 test_convex_hull_case(ctx
, "convex8");
685 test_convex_hull_case(ctx
, "convex9");
686 test_convex_hull_case(ctx
, "convex10");
687 test_convex_hull_case(ctx
, "convex11");
688 test_convex_hull_case(ctx
, "convex12");
689 test_convex_hull_case(ctx
, "convex13");
690 test_convex_hull_case(ctx
, "convex14");
691 test_convex_hull_case(ctx
, "convex15");
693 str1
= "{ [i0, i1, i2] : (i2 = 1 and i0 = 0 and i1 >= 0) or "
694 "(i0 = 1 and i1 = 0 and i2 = 1) or "
695 "(i0 = 0 and i1 = 0 and i2 = 0) }";
696 str2
= "{ [i0, i1, i2] : i0 >= 0 and i2 >= i0 and i2 <= 1 and i1 >= 0 }";
697 set1
= isl_set_read_from_str(ctx
, str1
);
698 set2
= isl_set_read_from_str(ctx
, str2
);
699 set1
= isl_set_from_basic_set(isl_set_convex_hull(set1
));
700 assert(isl_set_is_equal(set1
, set2
));
704 ctx
->opt
->convex
= orig_convex
;
707 void test_convex_hull(struct isl_ctx
*ctx
)
709 test_convex_hull_algo(ctx
, ISL_CONVEX_HULL_FM
);
710 test_convex_hull_algo(ctx
, ISL_CONVEX_HULL_WRAP
);
713 void test_gist_case(struct isl_ctx
*ctx
, const char *name
)
717 struct isl_basic_set
*bset1
, *bset2
;
719 filename
= get_filename(ctx
, name
, "polylib");
721 input
= fopen(filename
, "r");
724 bset1
= isl_basic_set_read_from_file(ctx
, input
);
725 bset2
= isl_basic_set_read_from_file(ctx
, input
);
727 bset1
= isl_basic_set_gist(bset1
, bset2
);
729 bset2
= isl_basic_set_read_from_file(ctx
, input
);
731 assert(isl_basic_set_is_equal(bset1
, bset2
) == 1);
733 isl_basic_set_free(bset1
);
734 isl_basic_set_free(bset2
);
740 void test_gist(struct isl_ctx
*ctx
)
743 isl_basic_set
*bset1
, *bset2
;
745 test_gist_case(ctx
, "gist1");
747 str
= "[p0, p2, p3, p5, p6, p10] -> { [] : "
748 "exists (e0 = [(15 + p0 + 15p6 + 15p10)/16], e1 = [(p5)/8], "
749 "e2 = [(p6)/128], e3 = [(8p2 - p5)/128], "
750 "e4 = [(128p3 - p6)/4096]: 8e1 = p5 and 128e2 = p6 and "
751 "128e3 = 8p2 - p5 and 4096e4 = 128p3 - p6 and p2 >= 0 and "
752 "16e0 >= 16 + 16p6 + 15p10 and p2 <= 15 and p3 >= 0 and "
753 "p3 <= 31 and p6 >= 128p3 and p5 >= 8p2 and p10 >= 0 and "
754 "16e0 <= 15 + p0 + 15p6 + 15p10 and 16e0 >= p0 + 15p6 + 15p10 and "
755 "p10 <= 15 and p10 <= -1 + p0 - p6) }";
756 bset1
= isl_basic_set_read_from_str(ctx
, str
);
757 str
= "[p0, p2, p3, p5, p6, p10] -> { [] : exists (e0 = [(p5)/8], "
758 "e1 = [(p6)/128], e2 = [(8p2 - p5)/128], "
759 "e3 = [(128p3 - p6)/4096]: 8e0 = p5 and 128e1 = p6 and "
760 "128e2 = 8p2 - p5 and 4096e3 = 128p3 - p6 and p5 >= -7 and "
761 "p2 >= 0 and 8p2 <= -1 + p0 and p2 <= 15 and p3 >= 0 and "
762 "p3 <= 31 and 128p3 <= -1 + p0 and p6 >= -127 and "
763 "p5 <= -1 + p0 and p6 <= -1 + p0 and p6 >= 128p3 and "
764 "p0 >= 1 and p5 >= 8p2 and p10 >= 0 and p10 <= 15 ) }";
765 bset2
= isl_basic_set_read_from_str(ctx
, str
);
766 bset1
= isl_basic_set_gist(bset1
, bset2
);
767 assert(bset1
&& bset1
->n_div
== 0);
768 isl_basic_set_free(bset1
);
771 void test_coalesce_set(isl_ctx
*ctx
, const char *str
, int check_one
)
775 set
= isl_set_read_from_str(ctx
, str
);
776 set
= isl_set_coalesce(set
);
777 set2
= isl_set_read_from_str(ctx
, str
);
778 assert(isl_set_is_equal(set
, set2
));
780 assert(set
&& set
->n
== 1);
785 void test_coalesce(struct isl_ctx
*ctx
)
788 struct isl_set
*set
, *set2
;
789 struct isl_map
*map
, *map2
;
791 set
= isl_set_read_from_str(ctx
,
792 "{[x,y]: x >= 0 & x <= 10 & y >= 0 & y <= 10 or "
793 "y >= x & x >= 2 & 5 >= y }");
794 set
= isl_set_coalesce(set
);
795 assert(set
&& set
->n
== 1);
798 set
= isl_set_read_from_str(ctx
,
799 "{[x,y]: y >= 0 & 2x + y <= 30 & y <= 10 & x >= 0 or "
800 "x + y >= 10 & y <= x & x + y <= 20 & y >= 0}");
801 set
= isl_set_coalesce(set
);
802 assert(set
&& set
->n
== 1);
805 set
= isl_set_read_from_str(ctx
,
806 "{[x,y]: y >= 0 & 2x + y <= 30 & y <= 10 & x >= 0 or "
807 "x + y >= 10 & y <= x & x + y <= 19 & y >= 0}");
808 set
= isl_set_coalesce(set
);
809 assert(set
&& set
->n
== 2);
812 set
= isl_set_read_from_str(ctx
,
813 "{[x,y]: y >= 0 & x <= 5 & y <= x or "
814 "y >= 0 & x >= 6 & x <= 10 & y <= x}");
815 set
= isl_set_coalesce(set
);
816 assert(set
&& set
->n
== 1);
819 set
= isl_set_read_from_str(ctx
,
820 "{[x,y]: y >= 0 & x <= 5 & y <= x or "
821 "y >= 0 & x >= 7 & x <= 10 & y <= x}");
822 set
= isl_set_coalesce(set
);
823 assert(set
&& set
->n
== 2);
826 set
= isl_set_read_from_str(ctx
,
827 "{[x,y]: y >= 0 & x <= 5 & y <= x or "
828 "y >= 0 & x >= 6 & x <= 10 & y + 1 <= x}");
829 set
= isl_set_coalesce(set
);
830 assert(set
&& set
->n
== 2);
833 set
= isl_set_read_from_str(ctx
,
834 "{[x,y]: y >= 0 & x <= 5 & y <= x or "
835 "y >= 0 & x = 6 & y <= 6}");
836 set
= isl_set_coalesce(set
);
837 assert(set
&& set
->n
== 1);
840 set
= isl_set_read_from_str(ctx
,
841 "{[x,y]: y >= 0 & x <= 5 & y <= x or "
842 "y >= 0 & x = 7 & y <= 6}");
843 set
= isl_set_coalesce(set
);
844 assert(set
&& set
->n
== 2);
847 set
= isl_set_read_from_str(ctx
,
848 "{[x,y]: y >= 0 & x <= 5 & y <= x or "
849 "y >= 0 & x = 6 & y <= 5}");
850 set
= isl_set_coalesce(set
);
851 assert(set
&& set
->n
== 1);
852 set2
= isl_set_read_from_str(ctx
,
853 "{[x,y]: y >= 0 & x <= 5 & y <= x or "
854 "y >= 0 & x = 6 & y <= 5}");
855 assert(isl_set_is_equal(set
, set2
));
859 set
= isl_set_read_from_str(ctx
,
860 "{[x,y]: y >= 0 & x <= 5 & y <= x or "
861 "y >= 0 & x = 6 & y <= 7}");
862 set
= isl_set_coalesce(set
);
863 assert(set
&& set
->n
== 2);
866 set
= isl_set_read_from_str(ctx
,
867 "[n] -> { [i] : i = 1 and n >= 2 or 2 <= i and i <= n }");
868 set
= isl_set_coalesce(set
);
869 assert(set
&& set
->n
== 1);
870 set2
= isl_set_read_from_str(ctx
,
871 "[n] -> { [i] : i = 1 and n >= 2 or 2 <= i and i <= n }");
872 assert(isl_set_is_equal(set
, set2
));
876 set
= isl_set_read_from_str(ctx
,
877 "{[x,y] : x >= 0 and y >= 0 or 0 <= y and y <= 5 and x = -1}");
878 set
= isl_set_coalesce(set
);
879 set2
= isl_set_read_from_str(ctx
,
880 "{[x,y] : x >= 0 and y >= 0 or 0 <= y and y <= 5 and x = -1}");
881 assert(isl_set_is_equal(set
, set2
));
885 set
= isl_set_read_from_str(ctx
,
886 "[n] -> { [i] : 1 <= i and i <= n - 1 or "
887 "2 <= i and i <= n }");
888 set
= isl_set_coalesce(set
);
889 assert(set
&& set
->n
== 1);
890 set2
= isl_set_read_from_str(ctx
,
891 "[n] -> { [i] : 1 <= i and i <= n - 1 or "
892 "2 <= i and i <= n }");
893 assert(isl_set_is_equal(set
, set2
));
897 map
= isl_map_read_from_str(ctx
,
898 "[n] -> { [i0] -> [o0] : exists (e0 = [(i0)/4], e1 = [(o0)/4], "
899 "e2 = [(n)/2], e3 = [(-2 + i0)/4], e4 = [(-2 + o0)/4], "
900 "e5 = [(-2n + i0)/4]: 2e2 = n and 4e3 = -2 + i0 and "
901 "4e4 = -2 + o0 and i0 >= 8 + 2n and o0 >= 2 + i0 and "
902 "o0 <= 56 + 2n and o0 <= -12 + 4n and i0 <= 57 + 2n and "
903 "i0 <= -11 + 4n and o0 >= 6 + 2n and 4e0 <= i0 and "
904 "4e0 >= -3 + i0 and 4e1 <= o0 and 4e1 >= -3 + o0 and "
905 "4e5 <= -2n + i0 and 4e5 >= -3 - 2n + i0);"
906 "[i0] -> [o0] : exists (e0 = [(i0)/4], e1 = [(o0)/4], "
907 "e2 = [(n)/2], e3 = [(-2 + i0)/4], e4 = [(-2 + o0)/4], "
908 "e5 = [(-2n + i0)/4]: 2e2 = n and 4e3 = -2 + i0 and "
909 "4e4 = -2 + o0 and 2e0 >= 3 + n and e0 <= -4 + n and "
910 "2e0 <= 27 + n and e1 <= -4 + n and 2e1 <= 27 + n and "
911 "2e1 >= 2 + n and e1 >= 1 + e0 and i0 >= 7 + 2n and "
912 "i0 <= -11 + 4n and i0 <= 57 + 2n and 4e0 <= -2 + i0 and "
913 "4e0 >= -3 + i0 and o0 >= 6 + 2n and o0 <= -11 + 4n and "
914 "o0 <= 57 + 2n and 4e1 <= -2 + o0 and 4e1 >= -3 + o0 and "
915 "4e5 <= -2n + i0 and 4e5 >= -3 - 2n + i0 ) }");
916 map
= isl_map_coalesce(map
);
917 map2
= isl_map_read_from_str(ctx
,
918 "[n] -> { [i0] -> [o0] : exists (e0 = [(i0)/4], e1 = [(o0)/4], "
919 "e2 = [(n)/2], e3 = [(-2 + i0)/4], e4 = [(-2 + o0)/4], "
920 "e5 = [(-2n + i0)/4]: 2e2 = n and 4e3 = -2 + i0 and "
921 "4e4 = -2 + o0 and i0 >= 8 + 2n and o0 >= 2 + i0 and "
922 "o0 <= 56 + 2n and o0 <= -12 + 4n and i0 <= 57 + 2n and "
923 "i0 <= -11 + 4n and o0 >= 6 + 2n and 4e0 <= i0 and "
924 "4e0 >= -3 + i0 and 4e1 <= o0 and 4e1 >= -3 + o0 and "
925 "4e5 <= -2n + i0 and 4e5 >= -3 - 2n + i0);"
926 "[i0] -> [o0] : exists (e0 = [(i0)/4], e1 = [(o0)/4], "
927 "e2 = [(n)/2], e3 = [(-2 + i0)/4], e4 = [(-2 + o0)/4], "
928 "e5 = [(-2n + i0)/4]: 2e2 = n and 4e3 = -2 + i0 and "
929 "4e4 = -2 + o0 and 2e0 >= 3 + n and e0 <= -4 + n and "
930 "2e0 <= 27 + n and e1 <= -4 + n and 2e1 <= 27 + n and "
931 "2e1 >= 2 + n and e1 >= 1 + e0 and i0 >= 7 + 2n and "
932 "i0 <= -11 + 4n and i0 <= 57 + 2n and 4e0 <= -2 + i0 and "
933 "4e0 >= -3 + i0 and o0 >= 6 + 2n and o0 <= -11 + 4n and "
934 "o0 <= 57 + 2n and 4e1 <= -2 + o0 and 4e1 >= -3 + o0 and "
935 "4e5 <= -2n + i0 and 4e5 >= -3 - 2n + i0 ) }");
936 assert(isl_map_is_equal(map
, map2
));
940 str
= "[n, m] -> { [] -> [o0, o2, o3] : (o3 = 1 and o0 >= 1 + m and "
941 "o0 <= n + m and o2 <= m and o0 >= 2 + n and o2 >= 3) or "
942 "(o0 >= 2 + n and o0 >= 1 + m and o0 <= n + m and n >= 1 and "
943 "o3 <= -1 + o2 and o3 >= 1 - m + o2 and o3 >= 2 and o3 <= n) }";
944 map
= isl_map_read_from_str(ctx
, str
);
945 map
= isl_map_coalesce(map
);
946 map2
= isl_map_read_from_str(ctx
, str
);
947 assert(isl_map_is_equal(map
, map2
));
951 str
= "[M, N] -> { [i0, i1, i2, i3, i4, i5, i6] -> "
952 "[o0, o1, o2, o3, o4, o5, o6] : "
953 "(o6 <= -4 + 2M - 2N + i0 + i1 - i2 + i6 - o0 - o1 + o2 and "
954 "o3 <= -2 + i3 and o6 >= 2 + i0 + i3 + i6 - o0 - o3 and "
955 "o6 >= 2 - M + N + i3 + i4 + i6 - o3 - o4 and o0 <= -1 + i0 and "
956 "o4 >= 4 - 3M + 3N - i0 - i1 + i2 + 2i3 + i4 + o0 + o1 - o2 - 2o3 "
957 "and o6 <= -3 + 2M - 2N + i3 + i4 - i5 + i6 - o3 - o4 + o5 and "
958 "2o6 <= -5 + 5M - 5N + 2i0 + i1 - i2 - i5 + 2i6 - 2o0 - o1 + o2 + o5 "
959 "and o6 >= 2i0 + i1 + i6 - 2o0 - o1 and "
960 "3o6 <= -5 + 4M - 4N + 2i0 + i1 - i2 + 2i3 + i4 - i5 + 3i6 "
961 "- 2o0 - o1 + o2 - 2o3 - o4 + o5) or "
962 "(N >= 2 and o3 <= -1 + i3 and o0 <= -1 + i0 and "
963 "o6 >= i3 + i6 - o3 and M >= 0 and "
964 "2o6 >= 1 + i0 + i3 + 2i6 - o0 - o3 and "
965 "o6 >= 1 - M + i0 + i6 - o0 and N >= 2M and o6 >= i0 + i6 - o0) }";
966 map
= isl_map_read_from_str(ctx
, str
);
967 map
= isl_map_coalesce(map
);
968 map2
= isl_map_read_from_str(ctx
, str
);
969 assert(isl_map_is_equal(map
, map2
));
973 str
= "[M, N] -> { [] -> [o0] : (o0 = 0 and M >= 1 and N >= 2) or "
974 "(o0 = 0 and M >= 1 and N >= 2M and N >= 2 + M) or "
975 "(o0 = 0 and M >= 2 and N >= 3) or "
976 "(M = 0 and o0 = 0 and N >= 3) }";
977 map
= isl_map_read_from_str(ctx
, str
);
978 map
= isl_map_coalesce(map
);
979 map2
= isl_map_read_from_str(ctx
, str
);
980 assert(isl_map_is_equal(map
, map2
));
984 str
= "{ [i0, i1, i2, i3] : (i1 = 10i0 and i0 >= 1 and 10i0 <= 100 and "
985 "i3 <= 9 + 10 i2 and i3 >= 1 + 10i2 and i3 >= 0) or "
986 "(i1 <= 9 + 10i0 and i1 >= 1 + 10i0 and i2 >= 0 and "
987 "i0 >= 0 and i1 <= 100 and i3 <= 9 + 10i2 and i3 >= 1 + 10i2) }";
988 map
= isl_map_read_from_str(ctx
, str
);
989 map
= isl_map_coalesce(map
);
990 map2
= isl_map_read_from_str(ctx
, str
);
991 assert(isl_map_is_equal(map
, map2
));
995 test_coalesce_set(ctx
,
996 "[M] -> { [i1] : (i1 >= 2 and i1 <= M) or "
997 "(i1 = M and M >= 1) }", 0);
998 test_coalesce_set(ctx
,
999 "{[x,y] : x,y >= 0; [x,y] : 10 <= x <= 20 and y >= -1 }", 0);
1000 test_coalesce_set(ctx
,
1001 "{ [x, y] : (x >= 1 and y >= 1 and x <= 2 and y <= 2) or "
1002 "(y = 3 and x = 1) }", 1);
1003 test_coalesce_set(ctx
,
1004 "[M] -> { [i0, i1, i2, i3, i4] : (i1 >= 3 and i4 >= 2 + i2 and "
1005 "i2 >= 2 and i0 >= 2 and i3 >= 1 + i2 and i0 <= M and "
1006 "i1 <= M and i3 <= M and i4 <= M) or "
1007 "(i1 >= 2 and i4 >= 1 + i2 and i2 >= 2 and i0 >= 2 and "
1008 "i3 >= 1 + i2 and i0 <= M and i1 <= -1 + M and i3 <= M and "
1009 "i4 <= -1 + M) }", 1);
1010 test_coalesce_set(ctx
,
1011 "{ [x, y] : (x >= 0 and y >= 0 and x <= 10 and y <= 10) or "
1012 "(x >= 1 and y >= 1 and x <= 11 and y <= 11) }", 1);
1013 test_coalesce_set(ctx
,
1014 "{[x,y,z] : y + 2 >= 0 and x - y + 1 >= 0 and "
1015 "-x - y + 1 >= 0 and -3 <= z <= 3;"
1016 "[x,y,z] : -x+z + 20 >= 0 and -x-z + 20 >= 0 and "
1017 "x-z + 20 >= 0 and x+z + 20 >= 0 and -10 <= y <= 0}", 1);
1018 test_coalesce_set(ctx
,
1019 "{[x,y] : 0 <= x,y <= 10; [5,y]: 4 <=y <= 11}", 1);
1020 test_coalesce_set(ctx
, "{[x,0] : x >= 0; [x,1] : x <= 20}", 0);
1021 test_coalesce_set(ctx
,
1022 "{[x,0,0] : -5 <= x <= 5; [0,y,1] : -5 <= y <= 5 }", 1);
1023 test_coalesce_set(ctx
, "{ [x, 1 - x] : 0 <= x <= 1; [0,0] }", 1);
1024 test_coalesce_set(ctx
, "{ [0,0]; [i,i] : 1 <= i <= 10 }", 1);
1025 test_coalesce_set(ctx
, "{ [0,0]; [i,j] : 1 <= i,j <= 10 }", 0);
1026 test_coalesce_set(ctx
, "{ [0,0]; [i,2i] : 1 <= i <= 10 }", 1);
1027 test_coalesce_set(ctx
, "{ [0,0]; [i,2i] : 2 <= i <= 10 }", 0);
1028 test_coalesce_set(ctx
, "{ [1,0]; [i,2i] : 1 <= i <= 10 }", 0);
1029 test_coalesce_set(ctx
, "{ [0,1]; [i,2i] : 1 <= i <= 10 }", 0);
1032 void test_closure(struct isl_ctx
*ctx
)
1036 isl_map
*up
, *right
;
1037 isl_map
*map
, *map2
;
1040 /* COCOA example 1 */
1041 map
= isl_map_read_from_str(ctx
,
1042 "[n] -> { [i,j] -> [i2,j2] : i2 = i + 1 and j2 = j + 1 and "
1043 "1 <= i and i < n and 1 <= j and j < n or "
1044 "i2 = i + 1 and j2 = j - 1 and "
1045 "1 <= i and i < n and 2 <= j and j <= n }");
1046 map
= isl_map_power(map
, &exact
);
1050 /* COCOA example 1 */
1051 map
= isl_map_read_from_str(ctx
,
1052 "[n] -> { [i,j] -> [i2,j2] : i2 = i + 1 and j2 = j + 1 and "
1053 "1 <= i and i < n and 1 <= j and j < n or "
1054 "i2 = i + 1 and j2 = j - 1 and "
1055 "1 <= i and i < n and 2 <= j and j <= n }");
1056 map
= isl_map_transitive_closure(map
, &exact
);
1058 map2
= isl_map_read_from_str(ctx
,
1059 "[n] -> { [i,j] -> [i2,j2] : exists (k1,k2,k : "
1060 "1 <= i and i < n and 1 <= j and j <= n and "
1061 "2 <= i2 and i2 <= n and 1 <= j2 and j2 <= n and "
1062 "i2 = i + k1 + k2 and j2 = j + k1 - k2 and "
1063 "k1 >= 0 and k2 >= 0 and k1 + k2 = k and k >= 1 )}");
1064 assert(isl_map_is_equal(map
, map2
));
1068 map
= isl_map_read_from_str(ctx
,
1069 "[n] -> { [x] -> [y] : y = x + 1 and 0 <= x and x <= n and "
1070 " 0 <= y and y <= n }");
1071 map
= isl_map_transitive_closure(map
, &exact
);
1072 map2
= isl_map_read_from_str(ctx
,
1073 "[n] -> { [x] -> [y] : y > x and 0 <= x and x <= n and "
1074 " 0 <= y and y <= n }");
1075 assert(isl_map_is_equal(map
, map2
));
1079 /* COCOA example 2 */
1080 map
= isl_map_read_from_str(ctx
,
1081 "[n] -> { [i,j] -> [i2,j2] : i2 = i + 2 and j2 = j + 2 and "
1082 "1 <= i and i < n - 1 and 1 <= j and j < n - 1 or "
1083 "i2 = i + 2 and j2 = j - 2 and "
1084 "1 <= i and i < n - 1 and 3 <= j and j <= n }");
1085 map
= isl_map_transitive_closure(map
, &exact
);
1087 map2
= isl_map_read_from_str(ctx
,
1088 "[n] -> { [i,j] -> [i2,j2] : exists (k1,k2,k : "
1089 "1 <= i and i < n - 1 and 1 <= j and j <= n and "
1090 "3 <= i2 and i2 <= n and 1 <= j2 and j2 <= n and "
1091 "i2 = i + 2 k1 + 2 k2 and j2 = j + 2 k1 - 2 k2 and "
1092 "k1 >= 0 and k2 >= 0 and k1 + k2 = k and k >= 1) }");
1093 assert(isl_map_is_equal(map
, map2
));
1097 /* COCOA Fig.2 left */
1098 map
= isl_map_read_from_str(ctx
,
1099 "[n] -> { [i,j] -> [i2,j2] : i2 = i + 2 and j2 = j and "
1100 "i <= 2 j - 3 and i <= n - 2 and j <= 2 i - 1 and "
1102 "i2 = i and j2 = j + 2 and i <= 2 j - 1 and i <= n and "
1103 "j <= 2 i - 3 and j <= n - 2 or "
1104 "i2 = i + 1 and j2 = j + 1 and i <= 2 j - 1 and "
1105 "i <= n - 1 and j <= 2 i - 1 and j <= n - 1 }");
1106 map
= isl_map_transitive_closure(map
, &exact
);
1110 /* COCOA Fig.2 right */
1111 map
= isl_map_read_from_str(ctx
,
1112 "[n] -> { [i,j] -> [i2,j2] : i2 = i + 3 and j2 = j and "
1113 "i <= 2 j - 4 and i <= n - 3 and j <= 2 i - 1 and "
1115 "i2 = i and j2 = j + 3 and i <= 2 j - 1 and i <= n and "
1116 "j <= 2 i - 4 and j <= n - 3 or "
1117 "i2 = i + 1 and j2 = j + 1 and i <= 2 j - 1 and "
1118 "i <= n - 1 and j <= 2 i - 1 and j <= n - 1 }");
1119 map
= isl_map_power(map
, &exact
);
1123 /* COCOA Fig.2 right */
1124 map
= isl_map_read_from_str(ctx
,
1125 "[n] -> { [i,j] -> [i2,j2] : i2 = i + 3 and j2 = j and "
1126 "i <= 2 j - 4 and i <= n - 3 and j <= 2 i - 1 and "
1128 "i2 = i and j2 = j + 3 and i <= 2 j - 1 and i <= n and "
1129 "j <= 2 i - 4 and j <= n - 3 or "
1130 "i2 = i + 1 and j2 = j + 1 and i <= 2 j - 1 and "
1131 "i <= n - 1 and j <= 2 i - 1 and j <= n - 1 }");
1132 map
= isl_map_transitive_closure(map
, &exact
);
1134 map2
= isl_map_read_from_str(ctx
,
1135 "[n] -> { [i,j] -> [i2,j2] : exists (k1,k2,k3,k : "
1136 "i <= 2 j - 1 and i <= n and j <= 2 i - 1 and "
1137 "j <= n and 3 + i + 2 j <= 3 n and "
1138 "3 + 2 i + j <= 3n and i2 <= 2 j2 -1 and i2 <= n and "
1139 "i2 <= 3 j2 - 4 and j2 <= 2 i2 -1 and j2 <= n and "
1140 "13 + 4 j2 <= 11 i2 and i2 = i + 3 k1 + k3 and "
1141 "j2 = j + 3 k2 + k3 and k1 >= 0 and k2 >= 0 and "
1142 "k3 >= 0 and k1 + k2 + k3 = k and k > 0) }");
1143 assert(isl_map_is_equal(map
, map2
));
1147 /* COCOA Fig.1 right */
1148 dom
= isl_set_read_from_str(ctx
,
1149 "{ [x,y] : x >= 0 and -2 x + 3 y >= 0 and x <= 3 and "
1150 "2 x - 3 y + 3 >= 0 }");
1151 right
= isl_map_read_from_str(ctx
,
1152 "{ [x,y] -> [x2,y2] : x2 = x + 1 and y2 = y }");
1153 up
= isl_map_read_from_str(ctx
,
1154 "{ [x,y] -> [x2,y2] : x2 = x and y2 = y + 1 }");
1155 right
= isl_map_intersect_domain(right
, isl_set_copy(dom
));
1156 right
= isl_map_intersect_range(right
, isl_set_copy(dom
));
1157 up
= isl_map_intersect_domain(up
, isl_set_copy(dom
));
1158 up
= isl_map_intersect_range(up
, dom
);
1159 map
= isl_map_union(up
, right
);
1160 map
= isl_map_transitive_closure(map
, &exact
);
1162 map2
= isl_map_read_from_str(ctx
,
1163 "{ [0,0] -> [0,1]; [0,0] -> [1,1]; [0,1] -> [1,1]; "
1164 " [2,2] -> [3,2]; [2,2] -> [3,3]; [3,2] -> [3,3] }");
1165 assert(isl_map_is_equal(map
, map2
));
1169 /* COCOA Theorem 1 counter example */
1170 map
= isl_map_read_from_str(ctx
,
1171 "{ [i,j] -> [i2,j2] : i = 0 and 0 <= j and j <= 1 and "
1172 "i2 = 1 and j2 = j or "
1173 "i = 0 and j = 0 and i2 = 0 and j2 = 1 }");
1174 map
= isl_map_transitive_closure(map
, &exact
);
1178 map
= isl_map_read_from_str(ctx
,
1179 "[m,n] -> { [i,j] -> [i2,j2] : i2 = i and j2 = j + 2 and "
1180 "1 <= i,i2 <= n and 1 <= j,j2 <= m or "
1181 "i2 = i + 1 and 3 <= j2 - j <= 4 and "
1182 "1 <= i,i2 <= n and 1 <= j,j2 <= m }");
1183 map
= isl_map_transitive_closure(map
, &exact
);
1187 /* Kelly et al 1996, fig 12 */
1188 map
= isl_map_read_from_str(ctx
,
1189 "[n] -> { [i,j] -> [i2,j2] : i2 = i and j2 = j + 1 and "
1190 "1 <= i,j,j+1 <= n or "
1191 "j = n and j2 = 1 and i2 = i + 1 and "
1192 "1 <= i,i+1 <= n }");
1193 map
= isl_map_transitive_closure(map
, &exact
);
1195 map2
= isl_map_read_from_str(ctx
,
1196 "[n] -> { [i,j] -> [i2,j2] : 1 <= j < j2 <= n and "
1197 "1 <= i <= n and i = i2 or "
1198 "1 <= i < i2 <= n and 1 <= j <= n and "
1200 assert(isl_map_is_equal(map
, map2
));
1204 /* Omega's closure4 */
1205 map
= isl_map_read_from_str(ctx
,
1206 "[m,n] -> { [x,y] -> [x2,y2] : x2 = x and y2 = y + 1 and "
1207 "1 <= x,y <= 10 or "
1208 "x2 = x + 1 and y2 = y and "
1209 "1 <= x <= 20 && 5 <= y <= 15 }");
1210 map
= isl_map_transitive_closure(map
, &exact
);
1214 map
= isl_map_read_from_str(ctx
,
1215 "[n] -> { [x] -> [y]: 1 <= n <= y - x <= 10 }");
1216 map
= isl_map_transitive_closure(map
, &exact
);
1218 map2
= isl_map_read_from_str(ctx
,
1219 "[n] -> { [x] -> [y] : 1 <= n <= 10 and y >= n + x }");
1220 assert(isl_map_is_equal(map
, map2
));
1224 str
= "[n, m] -> { [i0, i1, i2, i3] -> [o0, o1, o2, o3] : "
1225 "i3 = 1 and o0 = i0 and o1 = -1 + i1 and o2 = -1 + i2 and "
1226 "o3 = -2 + i2 and i1 <= -1 + i0 and i1 >= 1 - m + i0 and "
1227 "i1 >= 2 and i1 <= n and i2 >= 3 and i2 <= 1 + n and i2 <= m }";
1228 map
= isl_map_read_from_str(ctx
, str
);
1229 map
= isl_map_transitive_closure(map
, &exact
);
1231 map2
= isl_map_read_from_str(ctx
, str
);
1232 assert(isl_map_is_equal(map
, map2
));
1236 str
= "{[0] -> [1]; [2] -> [3]}";
1237 map
= isl_map_read_from_str(ctx
, str
);
1238 map
= isl_map_transitive_closure(map
, &exact
);
1240 map2
= isl_map_read_from_str(ctx
, str
);
1241 assert(isl_map_is_equal(map
, map2
));
1245 str
= "[n] -> { [[i0, i1, 1, 0, i0] -> [i5, 1]] -> "
1246 "[[i0, -1 + i1, 2, 0, i0] -> [-1 + i5, 2]] : "
1247 "exists (e0 = [(3 - n)/3]: i5 >= 2 and i1 >= 2 and "
1248 "3i0 <= -1 + n and i1 <= -1 + n and i5 <= -1 + n and "
1249 "3e0 >= 1 - n and 3e0 <= 2 - n and 3i0 >= -2 + n); "
1250 "[[i0, i1, 2, 0, i0] -> [i5, 1]] -> "
1251 "[[i0, i1, 1, 0, i0] -> [-1 + i5, 2]] : "
1252 "exists (e0 = [(3 - n)/3]: i5 >= 2 and i1 >= 1 and "
1253 "3i0 <= -1 + n and i1 <= -1 + n and i5 <= -1 + n and "
1254 "3e0 >= 1 - n and 3e0 <= 2 - n and 3i0 >= -2 + n); "
1255 "[[i0, i1, 1, 0, i0] -> [i5, 2]] -> "
1256 "[[i0, -1 + i1, 2, 0, i0] -> [i5, 1]] : "
1257 "exists (e0 = [(3 - n)/3]: i1 >= 2 and i5 >= 1 and "
1258 "3i0 <= -1 + n and i1 <= -1 + n and i5 <= -1 + n and "
1259 "3e0 >= 1 - n and 3e0 <= 2 - n and 3i0 >= -2 + n); "
1260 "[[i0, i1, 2, 0, i0] -> [i5, 2]] -> "
1261 "[[i0, i1, 1, 0, i0] -> [i5, 1]] : "
1262 "exists (e0 = [(3 - n)/3]: i5 >= 1 and i1 >= 1 and "
1263 "3i0 <= -1 + n and i1 <= -1 + n and i5 <= -1 + n and "
1264 "3e0 >= 1 - n and 3e0 <= 2 - n and 3i0 >= -2 + n) }";
1265 map
= isl_map_read_from_str(ctx
, str
);
1266 map
= isl_map_transitive_closure(map
, NULL
);
1271 void test_lex(struct isl_ctx
*ctx
)
1276 dim
= isl_space_set_alloc(ctx
, 0, 0);
1277 map
= isl_map_lex_le(dim
);
1278 assert(!isl_map_is_empty(map
));
1282 static int consume_lexmin(__isl_take isl_basic_set
*dom
,
1283 __isl_take isl_aff_list
*list
, void *user
)
1286 isl_basic_map
*bmap
;
1287 isl_map
**map
= user
;
1289 dim
= isl_basic_set_get_space(dom
);
1290 bmap
= isl_basic_map_from_aff_list(dim
, list
);
1291 bmap
= isl_basic_map_intersect_domain(bmap
, dom
);
1293 *map
= isl_map_union(*map
, isl_map_from_basic_map(bmap
));
1298 void test_lexmin(struct isl_ctx
*ctx
)
1301 isl_basic_map
*bmap
;
1302 isl_map
*map
, *map2
;
1306 str
= "[p0, p1] -> { [] -> [] : "
1307 "exists (e0 = [(2p1)/3], e1, e2, e3 = [(3 - p1 + 3e0)/3], "
1308 "e4 = [(p1)/3], e5 = [(p1 + 3e4)/3]: "
1309 "3e0 >= -2 + 2p1 and 3e0 >= p1 and 3e3 >= 1 - p1 + 3e0 and "
1310 "3e0 <= 2p1 and 3e3 >= -2 + p1 and 3e3 <= -1 + p1 and p1 >= 3 and "
1311 "3e5 >= -2 + 2p1 and 3e5 >= p1 and 3e5 <= -1 + p1 + 3e4 and "
1312 "3e4 <= p1 and 3e4 >= -2 + p1 and e3 <= -1 + e0 and "
1313 "3e4 >= 6 - p1 + 3e1 and 3e1 >= p1 and 3e5 >= -2 + p1 + 3e4 and "
1314 "2e4 >= 3 - p1 + 2e1 and e4 <= e1 and 3e3 <= 2 - p1 + 3e0 and "
1315 "e5 >= 1 + e1 and 3e4 >= 6 - 2p1 + 3e1 and "
1316 "p0 >= 2 and p1 >= p0 and 3e2 >= p1 and 3e4 >= 6 - p1 + 3e2 and "
1317 "e2 <= e1 and e3 >= 1 and e4 <= e2) }";
1318 map
= isl_map_read_from_str(ctx
, str
);
1319 map
= isl_map_lexmin(map
);
1322 str
= "[C] -> { [obj,a,b,c] : obj <= 38 a + 7 b + 10 c and "
1323 "a + b <= 1 and c <= 10 b and c <= C and a,b,c,C >= 0 }";
1324 set
= isl_set_read_from_str(ctx
, str
);
1325 set
= isl_set_lexmax(set
);
1326 str
= "[C] -> { [obj,a,b,c] : C = 8 }";
1327 set2
= isl_set_read_from_str(ctx
, str
);
1328 set
= isl_set_intersect(set
, set2
);
1329 assert(!isl_set_is_empty(set
));
1332 str
= "{ [x] -> [y] : x <= y <= 10; [x] -> [5] : -8 <= x <= 8 }";
1333 map
= isl_map_read_from_str(ctx
, str
);
1334 map
= isl_map_lexmin(map
);
1335 str
= "{ [x] -> [5] : 6 <= x <= 8; "
1336 "[x] -> [x] : x <= 5 or (9 <= x <= 10) }";
1337 map2
= isl_map_read_from_str(ctx
, str
);
1338 assert(isl_map_is_equal(map
, map2
));
1342 str
= "{ [x] -> [y] : 4y = x or 4y = -1 + x or 4y = -2 + x }";
1343 map
= isl_map_read_from_str(ctx
, str
);
1344 map2
= isl_map_copy(map
);
1345 map
= isl_map_lexmin(map
);
1346 assert(isl_map_is_equal(map
, map2
));
1350 str
= "{ [x] -> [y] : x = 4y; [x] -> [y] : x = 2y }";
1351 map
= isl_map_read_from_str(ctx
, str
);
1352 map
= isl_map_lexmin(map
);
1353 str
= "{ [x] -> [y] : (4y = x and x >= 0) or "
1354 "(exists (e0 = [(x)/4], e1 = [(-2 + x)/4]: 2y = x and "
1355 "4e1 = -2 + x and 4e0 <= -1 + x and 4e0 >= -3 + x)) or "
1356 "(exists (e0 = [(x)/4]: 2y = x and 4e0 = x and x <= -4)) }";
1357 map2
= isl_map_read_from_str(ctx
, str
);
1358 assert(isl_map_is_equal(map
, map2
));
1362 str
= "{ [i] -> [i', j] : j = i - 8i' and i' >= 0 and i' <= 7 and "
1363 " 8i' <= i and 8i' >= -7 + i }";
1364 bmap
= isl_basic_map_read_from_str(ctx
, str
);
1365 map2
= isl_map_empty(isl_basic_map_get_space(bmap
));
1366 isl_basic_map_foreach_lexmin(bmap
, &consume_lexmin
, &map2
);
1367 map
= isl_map_from_basic_map(bmap
);
1368 assert(isl_map_is_equal(map
, map2
));
1378 static int collect_must_may(__isl_take isl_map
*dep
, int must
,
1379 void *dep_user
, void *user
)
1381 struct must_may
*mm
= (struct must_may
*)user
;
1384 mm
->must
= isl_map_union(mm
->must
, dep
);
1386 mm
->may
= isl_map_union(mm
->may
, dep
);
1391 static int common_space(void *first
, void *second
)
1393 int depth
= *(int *)first
;
1397 static int map_is_equal(__isl_keep isl_map
*map
, const char *str
)
1405 map2
= isl_map_read_from_str(map
->ctx
, str
);
1406 equal
= isl_map_is_equal(map
, map2
);
1412 void test_dep(struct isl_ctx
*ctx
)
1417 isl_access_info
*ai
;
1424 str
= "{ [2,i,0] -> [i] : 0 <= i <= 10 }";
1425 map
= isl_map_read_from_str(ctx
, str
);
1426 ai
= isl_access_info_alloc(map
, &depth
, &common_space
, 2);
1428 str
= "{ [0,i,0] -> [i] : 0 <= i <= 10 }";
1429 map
= isl_map_read_from_str(ctx
, str
);
1430 ai
= isl_access_info_add_source(ai
, map
, 1, &depth
);
1432 str
= "{ [1,i,0] -> [5] : 0 <= i <= 10 }";
1433 map
= isl_map_read_from_str(ctx
, str
);
1434 ai
= isl_access_info_add_source(ai
, map
, 1, &depth
);
1436 flow
= isl_access_info_compute_flow(ai
);
1437 dim
= isl_space_alloc(ctx
, 0, 3, 3);
1438 mm
.must
= isl_map_empty(isl_space_copy(dim
));
1439 mm
.may
= isl_map_empty(dim
);
1441 isl_flow_foreach(flow
, collect_must_may
, &mm
);
1443 str
= "{ [0,i,0] -> [2,i,0] : (0 <= i <= 4) or (6 <= i <= 10); "
1444 " [1,10,0] -> [2,5,0] }";
1445 assert(map_is_equal(mm
.must
, str
));
1446 str
= "{ [i,j,k] -> [l,m,n] : 1 = 0 }";
1447 assert(map_is_equal(mm
.may
, str
));
1449 isl_map_free(mm
.must
);
1450 isl_map_free(mm
.may
);
1451 isl_flow_free(flow
);
1454 str
= "{ [2,i,0] -> [i] : 0 <= i <= 10 }";
1455 map
= isl_map_read_from_str(ctx
, str
);
1456 ai
= isl_access_info_alloc(map
, &depth
, &common_space
, 2);
1458 str
= "{ [0,i,0] -> [i] : 0 <= i <= 10 }";
1459 map
= isl_map_read_from_str(ctx
, str
);
1460 ai
= isl_access_info_add_source(ai
, map
, 1, &depth
);
1462 str
= "{ [1,i,0] -> [5] : 0 <= i <= 10 }";
1463 map
= isl_map_read_from_str(ctx
, str
);
1464 ai
= isl_access_info_add_source(ai
, map
, 0, &depth
);
1466 flow
= isl_access_info_compute_flow(ai
);
1467 dim
= isl_space_alloc(ctx
, 0, 3, 3);
1468 mm
.must
= isl_map_empty(isl_space_copy(dim
));
1469 mm
.may
= isl_map_empty(dim
);
1471 isl_flow_foreach(flow
, collect_must_may
, &mm
);
1473 str
= "{ [0,i,0] -> [2,i,0] : (0 <= i <= 4) or (6 <= i <= 10) }";
1474 assert(map_is_equal(mm
.must
, str
));
1475 str
= "{ [0,5,0] -> [2,5,0]; [1,i,0] -> [2,5,0] : 0 <= i <= 10 }";
1476 assert(map_is_equal(mm
.may
, str
));
1478 isl_map_free(mm
.must
);
1479 isl_map_free(mm
.may
);
1480 isl_flow_free(flow
);
1483 str
= "{ [2,i,0] -> [i] : 0 <= i <= 10 }";
1484 map
= isl_map_read_from_str(ctx
, str
);
1485 ai
= isl_access_info_alloc(map
, &depth
, &common_space
, 2);
1487 str
= "{ [0,i,0] -> [i] : 0 <= i <= 10 }";
1488 map
= isl_map_read_from_str(ctx
, str
);
1489 ai
= isl_access_info_add_source(ai
, map
, 0, &depth
);
1491 str
= "{ [1,i,0] -> [5] : 0 <= i <= 10 }";
1492 map
= isl_map_read_from_str(ctx
, str
);
1493 ai
= isl_access_info_add_source(ai
, map
, 0, &depth
);
1495 flow
= isl_access_info_compute_flow(ai
);
1496 dim
= isl_space_alloc(ctx
, 0, 3, 3);
1497 mm
.must
= isl_map_empty(isl_space_copy(dim
));
1498 mm
.may
= isl_map_empty(dim
);
1500 isl_flow_foreach(flow
, collect_must_may
, &mm
);
1502 str
= "{ [0,i,0] -> [2,i,0] : 0 <= i <= 10; "
1503 " [1,i,0] -> [2,5,0] : 0 <= i <= 10 }";
1504 assert(map_is_equal(mm
.may
, str
));
1505 str
= "{ [i,j,k] -> [l,m,n] : 1 = 0 }";
1506 assert(map_is_equal(mm
.must
, str
));
1508 isl_map_free(mm
.must
);
1509 isl_map_free(mm
.may
);
1510 isl_flow_free(flow
);
1513 str
= "{ [0,i,2] -> [i] : 0 <= i <= 10 }";
1514 map
= isl_map_read_from_str(ctx
, str
);
1515 ai
= isl_access_info_alloc(map
, &depth
, &common_space
, 2);
1517 str
= "{ [0,i,0] -> [i] : 0 <= i <= 10 }";
1518 map
= isl_map_read_from_str(ctx
, str
);
1519 ai
= isl_access_info_add_source(ai
, map
, 0, &depth
);
1521 str
= "{ [0,i,1] -> [5] : 0 <= i <= 10 }";
1522 map
= isl_map_read_from_str(ctx
, str
);
1523 ai
= isl_access_info_add_source(ai
, map
, 0, &depth
);
1525 flow
= isl_access_info_compute_flow(ai
);
1526 dim
= isl_space_alloc(ctx
, 0, 3, 3);
1527 mm
.must
= isl_map_empty(isl_space_copy(dim
));
1528 mm
.may
= isl_map_empty(dim
);
1530 isl_flow_foreach(flow
, collect_must_may
, &mm
);
1532 str
= "{ [0,i,0] -> [0,i,2] : 0 <= i <= 10; "
1533 " [0,i,1] -> [0,5,2] : 0 <= i <= 5 }";
1534 assert(map_is_equal(mm
.may
, str
));
1535 str
= "{ [i,j,k] -> [l,m,n] : 1 = 0 }";
1536 assert(map_is_equal(mm
.must
, str
));
1538 isl_map_free(mm
.must
);
1539 isl_map_free(mm
.may
);
1540 isl_flow_free(flow
);
1543 str
= "{ [0,i,1] -> [i] : 0 <= i <= 10 }";
1544 map
= isl_map_read_from_str(ctx
, str
);
1545 ai
= isl_access_info_alloc(map
, &depth
, &common_space
, 2);
1547 str
= "{ [0,i,0] -> [i] : 0 <= i <= 10 }";
1548 map
= isl_map_read_from_str(ctx
, str
);
1549 ai
= isl_access_info_add_source(ai
, map
, 0, &depth
);
1551 str
= "{ [0,i,2] -> [5] : 0 <= i <= 10 }";
1552 map
= isl_map_read_from_str(ctx
, str
);
1553 ai
= isl_access_info_add_source(ai
, map
, 0, &depth
);
1555 flow
= isl_access_info_compute_flow(ai
);
1556 dim
= isl_space_alloc(ctx
, 0, 3, 3);
1557 mm
.must
= isl_map_empty(isl_space_copy(dim
));
1558 mm
.may
= isl_map_empty(dim
);
1560 isl_flow_foreach(flow
, collect_must_may
, &mm
);
1562 str
= "{ [0,i,0] -> [0,i,1] : 0 <= i <= 10; "
1563 " [0,i,2] -> [0,5,1] : 0 <= i <= 4 }";
1564 assert(map_is_equal(mm
.may
, str
));
1565 str
= "{ [i,j,k] -> [l,m,n] : 1 = 0 }";
1566 assert(map_is_equal(mm
.must
, str
));
1568 isl_map_free(mm
.must
);
1569 isl_map_free(mm
.may
);
1570 isl_flow_free(flow
);
1575 str
= "{ [1,i,0,0,0] -> [i,j] : 0 <= i <= 10 and 0 <= j <= 10 }";
1576 map
= isl_map_read_from_str(ctx
, str
);
1577 ai
= isl_access_info_alloc(map
, &depth
, &common_space
, 1);
1579 str
= "{ [0,i,0,j,0] -> [i,j] : 0 <= i <= 10 and 0 <= j <= 10 }";
1580 map
= isl_map_read_from_str(ctx
, str
);
1581 ai
= isl_access_info_add_source(ai
, map
, 1, &depth
);
1583 flow
= isl_access_info_compute_flow(ai
);
1584 dim
= isl_space_alloc(ctx
, 0, 5, 5);
1585 mm
.must
= isl_map_empty(isl_space_copy(dim
));
1586 mm
.may
= isl_map_empty(dim
);
1588 isl_flow_foreach(flow
, collect_must_may
, &mm
);
1590 str
= "{ [0,i,0,j,0] -> [1,i,0,0,0] : 0 <= i,j <= 10 }";
1591 assert(map_is_equal(mm
.must
, str
));
1592 str
= "{ [0,0,0,0,0] -> [0,0,0,0,0] : 1 = 0 }";
1593 assert(map_is_equal(mm
.may
, str
));
1595 isl_map_free(mm
.must
);
1596 isl_map_free(mm
.may
);
1597 isl_flow_free(flow
);
1600 int test_sv(isl_ctx
*ctx
)
1604 isl_union_map
*umap
;
1607 str
= "[N] -> { [i] -> [f] : 0 <= i <= N and 0 <= i - 10 f <= 9 }";
1608 map
= isl_map_read_from_str(ctx
, str
);
1609 sv
= isl_map_is_single_valued(map
);
1614 isl_die(ctx
, isl_error_internal
,
1615 "map not detected as single valued", return -1);
1617 str
= "[N] -> { [i] -> [f] : 0 <= i <= N and 0 <= i - 10 f <= 10 }";
1618 map
= isl_map_read_from_str(ctx
, str
);
1619 sv
= isl_map_is_single_valued(map
);
1624 isl_die(ctx
, isl_error_internal
,
1625 "map detected as single valued", return -1);
1627 str
= "{ S1[i] -> [i] : 0 <= i <= 9; S2[i] -> [i] : 0 <= i <= 9 }";
1628 umap
= isl_union_map_read_from_str(ctx
, str
);
1629 sv
= isl_union_map_is_single_valued(umap
);
1630 isl_union_map_free(umap
);
1634 isl_die(ctx
, isl_error_internal
,
1635 "map not detected as single valued", return -1);
1637 str
= "{ [i] -> S1[i] : 0 <= i <= 9; [i] -> S2[i] : 0 <= i <= 9 }";
1638 umap
= isl_union_map_read_from_str(ctx
, str
);
1639 sv
= isl_union_map_is_single_valued(umap
);
1640 isl_union_map_free(umap
);
1644 isl_die(ctx
, isl_error_internal
,
1645 "map detected as single valued", return -1);
1650 void test_bijective_case(struct isl_ctx
*ctx
, const char *str
, int bijective
)
1654 map
= isl_map_read_from_str(ctx
, str
);
1656 assert(isl_map_is_bijective(map
));
1658 assert(!isl_map_is_bijective(map
));
1662 void test_bijective(struct isl_ctx
*ctx
)
1664 test_bijective_case(ctx
, "[N,M]->{[i,j] -> [i]}", 0);
1665 test_bijective_case(ctx
, "[N,M]->{[i,j] -> [i] : j=i}", 1);
1666 test_bijective_case(ctx
, "[N,M]->{[i,j] -> [i] : j=0}", 1);
1667 test_bijective_case(ctx
, "[N,M]->{[i,j] -> [i] : j=N}", 1);
1668 test_bijective_case(ctx
, "[N,M]->{[i,j] -> [j,i]}", 1);
1669 test_bijective_case(ctx
, "[N,M]->{[i,j] -> [i+j]}", 0);
1670 test_bijective_case(ctx
, "[N,M]->{[i,j] -> []}", 0);
1671 test_bijective_case(ctx
, "[N,M]->{[i,j] -> [i,j,N]}", 1);
1672 test_bijective_case(ctx
, "[N,M]->{[i,j] -> [2i]}", 0);
1673 test_bijective_case(ctx
, "[N,M]->{[i,j] -> [i,i]}", 0);
1674 test_bijective_case(ctx
, "[N,M]->{[i,j] -> [2i,i]}", 0);
1675 test_bijective_case(ctx
, "[N,M]->{[i,j] -> [2i,j]}", 1);
1676 test_bijective_case(ctx
, "[N,M]->{[i,j] -> [x,y] : 2x=i & y =j}", 1);
1679 void test_pwqp(struct isl_ctx
*ctx
)
1683 isl_pw_qpolynomial
*pwqp1
, *pwqp2
;
1685 str
= "{ [i,j,k] -> 1 + 9 * [i/5] + 7 * [j/11] + 4 * [k/13] }";
1686 pwqp1
= isl_pw_qpolynomial_read_from_str(ctx
, str
);
1688 pwqp1
= isl_pw_qpolynomial_move_dims(pwqp1
, isl_dim_param
, 0,
1691 str
= "[j] -> { [i,k] -> 1 + 9 * [i/5] + 7 * [j/11] + 4 * [k/13] }";
1692 pwqp2
= isl_pw_qpolynomial_read_from_str(ctx
, str
);
1694 pwqp1
= isl_pw_qpolynomial_sub(pwqp1
, pwqp2
);
1696 assert(isl_pw_qpolynomial_is_zero(pwqp1
));
1698 isl_pw_qpolynomial_free(pwqp1
);
1700 str
= "{ [i] -> i }";
1701 pwqp1
= isl_pw_qpolynomial_read_from_str(ctx
, str
);
1702 str
= "{ [k] : exists a : k = 2a }";
1703 set
= isl_set_read_from_str(ctx
, str
);
1704 pwqp1
= isl_pw_qpolynomial_gist(pwqp1
, set
);
1705 str
= "{ [i] -> i }";
1706 pwqp2
= isl_pw_qpolynomial_read_from_str(ctx
, str
);
1708 pwqp1
= isl_pw_qpolynomial_sub(pwqp1
, pwqp2
);
1710 assert(isl_pw_qpolynomial_is_zero(pwqp1
));
1712 isl_pw_qpolynomial_free(pwqp1
);
1714 str
= "{ [i] -> i + [ (i + [i/3])/2 ] }";
1715 pwqp1
= isl_pw_qpolynomial_read_from_str(ctx
, str
);
1717 set
= isl_set_read_from_str(ctx
, str
);
1718 pwqp1
= isl_pw_qpolynomial_gist(pwqp1
, set
);
1719 str
= "{ [i] -> 16 }";
1720 pwqp2
= isl_pw_qpolynomial_read_from_str(ctx
, str
);
1722 pwqp1
= isl_pw_qpolynomial_sub(pwqp1
, pwqp2
);
1724 assert(isl_pw_qpolynomial_is_zero(pwqp1
));
1726 isl_pw_qpolynomial_free(pwqp1
);
1728 str
= "{ [i] -> ([(i)/2]) }";
1729 pwqp1
= isl_pw_qpolynomial_read_from_str(ctx
, str
);
1730 str
= "{ [k] : exists a : k = 2a+1 }";
1731 set
= isl_set_read_from_str(ctx
, str
);
1732 pwqp1
= isl_pw_qpolynomial_gist(pwqp1
, set
);
1733 str
= "{ [i] -> -1/2 + 1/2 * i }";
1734 pwqp2
= isl_pw_qpolynomial_read_from_str(ctx
, str
);
1736 pwqp1
= isl_pw_qpolynomial_sub(pwqp1
, pwqp2
);
1738 assert(isl_pw_qpolynomial_is_zero(pwqp1
));
1740 isl_pw_qpolynomial_free(pwqp1
);
1742 str
= "{ [i] -> ([([i/2] + [i/2])/5]) }";
1743 pwqp1
= isl_pw_qpolynomial_read_from_str(ctx
, str
);
1744 str
= "{ [i] -> ([(2 * [i/2])/5]) }";
1745 pwqp2
= isl_pw_qpolynomial_read_from_str(ctx
, str
);
1747 pwqp1
= isl_pw_qpolynomial_sub(pwqp1
, pwqp2
);
1749 assert(isl_pw_qpolynomial_is_zero(pwqp1
));
1751 isl_pw_qpolynomial_free(pwqp1
);
1753 str
= "{ [x] -> ([x/2] + [(x+1)/2]) }";
1754 pwqp1
= isl_pw_qpolynomial_read_from_str(ctx
, str
);
1755 str
= "{ [x] -> x }";
1756 pwqp2
= isl_pw_qpolynomial_read_from_str(ctx
, str
);
1758 pwqp1
= isl_pw_qpolynomial_sub(pwqp1
, pwqp2
);
1760 assert(isl_pw_qpolynomial_is_zero(pwqp1
));
1762 isl_pw_qpolynomial_free(pwqp1
);
1764 str
= "{ [i] -> ([i/2]) : i >= 0; [i] -> ([i/3]) : i < 0 }";
1765 pwqp1
= isl_pw_qpolynomial_read_from_str(ctx
, str
);
1766 pwqp2
= isl_pw_qpolynomial_read_from_str(ctx
, str
);
1767 pwqp1
= isl_pw_qpolynomial_coalesce(pwqp1
);
1768 pwqp1
= isl_pw_qpolynomial_sub(pwqp1
, pwqp2
);
1769 assert(isl_pw_qpolynomial_is_zero(pwqp1
));
1770 isl_pw_qpolynomial_free(pwqp1
);
1773 void test_split_periods(isl_ctx
*ctx
)
1776 isl_pw_qpolynomial
*pwqp
;
1778 str
= "{ [U,V] -> 1/3 * U + 2/3 * V - [(U + 2V)/3] + [U/2] : "
1779 "U + 2V + 3 >= 0 and - U -2V >= 0 and - U + 10 >= 0 and "
1780 "U >= 0; [U,V] -> U^2 : U >= 100 }";
1781 pwqp
= isl_pw_qpolynomial_read_from_str(ctx
, str
);
1783 pwqp
= isl_pw_qpolynomial_split_periods(pwqp
, 2);
1786 isl_pw_qpolynomial_free(pwqp
);
1789 void test_union(isl_ctx
*ctx
)
1792 isl_union_set
*uset1
, *uset2
;
1793 isl_union_map
*umap1
, *umap2
;
1795 str
= "{ [i] : 0 <= i <= 1 }";
1796 uset1
= isl_union_set_read_from_str(ctx
, str
);
1797 str
= "{ [1] -> [0] }";
1798 umap1
= isl_union_map_read_from_str(ctx
, str
);
1800 umap2
= isl_union_set_lex_gt_union_set(isl_union_set_copy(uset1
), uset1
);
1801 assert(isl_union_map_is_equal(umap1
, umap2
));
1803 isl_union_map_free(umap1
);
1804 isl_union_map_free(umap2
);
1806 str
= "{ A[i] -> B[i]; B[i] -> C[i]; A[0] -> C[1] }";
1807 umap1
= isl_union_map_read_from_str(ctx
, str
);
1808 str
= "{ A[i]; B[i] }";
1809 uset1
= isl_union_set_read_from_str(ctx
, str
);
1811 uset2
= isl_union_map_domain(umap1
);
1813 assert(isl_union_set_is_equal(uset1
, uset2
));
1815 isl_union_set_free(uset1
);
1816 isl_union_set_free(uset2
);
1819 void test_bound(isl_ctx
*ctx
)
1822 isl_pw_qpolynomial
*pwqp
;
1823 isl_pw_qpolynomial_fold
*pwf
;
1825 str
= "{ [[a, b, c, d] -> [e]] -> 0 }";
1826 pwqp
= isl_pw_qpolynomial_read_from_str(ctx
, str
);
1827 pwf
= isl_pw_qpolynomial_bound(pwqp
, isl_fold_max
, NULL
);
1828 assert(isl_pw_qpolynomial_fold_dim(pwf
, isl_dim_in
) == 4);
1829 isl_pw_qpolynomial_fold_free(pwf
);
1831 str
= "{ [[x]->[x]] -> 1 : exists a : x = 2 a }";
1832 pwqp
= isl_pw_qpolynomial_read_from_str(ctx
, str
);
1833 pwf
= isl_pw_qpolynomial_bound(pwqp
, isl_fold_max
, NULL
);
1834 assert(isl_pw_qpolynomial_fold_dim(pwf
, isl_dim_in
) == 1);
1835 isl_pw_qpolynomial_fold_free(pwf
);
1838 void test_lift(isl_ctx
*ctx
)
1841 isl_basic_map
*bmap
;
1842 isl_basic_set
*bset
;
1844 str
= "{ [i0] : exists e0 : i0 = 4e0 }";
1845 bset
= isl_basic_set_read_from_str(ctx
, str
);
1846 bset
= isl_basic_set_lift(bset
);
1847 bmap
= isl_basic_map_from_range(bset
);
1848 bset
= isl_basic_map_domain(bmap
);
1849 isl_basic_set_free(bset
);
1852 void test_subset(isl_ctx
*ctx
)
1855 isl_set
*set1
, *set2
;
1857 str
= "{ [112, 0] }";
1858 set1
= isl_set_read_from_str(ctx
, str
);
1859 str
= "{ [i0, i1] : exists (e0 = [(i0 - i1)/16], e1: "
1860 "16e0 <= i0 - i1 and 16e0 >= -15 + i0 - i1 and "
1861 "16e1 <= i1 and 16e0 >= -i1 and 16e1 >= -i0 + i1) }";
1862 set2
= isl_set_read_from_str(ctx
, str
);
1863 assert(isl_set_is_subset(set1
, set2
));
1868 void test_factorize(isl_ctx
*ctx
)
1871 isl_basic_set
*bset
;
1874 str
= "{ [i0, i1, i2, i3, i4, i5, i6, i7] : 3i5 <= 2 - 2i0 and "
1875 "i0 >= -2 and i6 >= 1 + i3 and i7 >= 0 and 3i5 >= -2i0 and "
1876 "2i4 <= i2 and i6 >= 1 + 2i0 + 3i1 and i4 <= -1 and "
1877 "i6 >= 1 + 2i0 + 3i5 and i6 <= 2 + 2i0 + 3i5 and "
1878 "3i5 <= 2 - 2i0 - i2 + 3i4 and i6 <= 2 + 2i0 + 3i1 and "
1879 "i0 <= -1 and i7 <= i2 + i3 - 3i4 - i6 and "
1880 "3i5 >= -2i0 - i2 + 3i4 }";
1881 bset
= isl_basic_set_read_from_str(ctx
, str
);
1882 f
= isl_basic_set_factorizer(bset
);
1884 isl_basic_set_free(bset
);
1885 isl_factorizer_free(f
);
1887 str
= "{ [i0, i1, i2, i3, i4, i5, i6, i7, i8, i9, i10, i11, i12] : "
1888 "i12 <= 2 + i0 - i11 and 2i8 >= -i4 and i11 >= i1 and "
1889 "3i5 <= -i2 and 2i11 >= -i4 - 2i7 and i11 <= 3 + i0 + 3i9 and "
1890 "i11 <= -i4 - 2i7 and i12 >= -i10 and i2 >= -2 and "
1891 "i11 >= i1 + 3i10 and i11 >= 1 + i0 + 3i9 and "
1892 "i11 <= 1 - i4 - 2i8 and 6i6 <= 6 - i2 and 3i6 >= 1 - i2 and "
1893 "i11 <= 2 + i1 and i12 <= i4 + i11 and i12 >= i0 - i11 and "
1894 "3i5 >= -2 - i2 and i12 >= -1 + i4 + i11 and 3i3 <= 3 - i2 and "
1895 "9i6 <= 11 - i2 + 6i5 and 3i3 >= 1 - i2 and "
1896 "9i6 <= 5 - i2 + 6i3 and i12 <= -1 and i2 <= 0 }";
1897 bset
= isl_basic_set_read_from_str(ctx
, str
);
1898 f
= isl_basic_set_factorizer(bset
);
1900 isl_basic_set_free(bset
);
1901 isl_factorizer_free(f
);
1904 static int check_injective(__isl_take isl_map
*map
, void *user
)
1906 int *injective
= user
;
1908 *injective
= isl_map_is_injective(map
);
1911 if (*injective
< 0 || !*injective
)
1917 int test_one_schedule(isl_ctx
*ctx
, const char *d
, const char *w
,
1918 const char *r
, const char *s
, int tilable
, int parallel
)
1922 isl_union_map
*W
, *R
, *S
;
1923 isl_union_map
*empty
;
1924 isl_union_map
*dep_raw
, *dep_war
, *dep_waw
, *dep
;
1925 isl_union_map
*validity
, *proximity
;
1926 isl_union_map
*schedule
;
1927 isl_union_map
*test
;
1928 isl_union_set
*delta
;
1929 isl_union_set
*domain
;
1933 isl_schedule
*sched
;
1934 int is_nonneg
, is_parallel
, is_tilable
, is_injection
, is_complete
;
1936 D
= isl_union_set_read_from_str(ctx
, d
);
1937 W
= isl_union_map_read_from_str(ctx
, w
);
1938 R
= isl_union_map_read_from_str(ctx
, r
);
1939 S
= isl_union_map_read_from_str(ctx
, s
);
1941 W
= isl_union_map_intersect_domain(W
, isl_union_set_copy(D
));
1942 R
= isl_union_map_intersect_domain(R
, isl_union_set_copy(D
));
1944 empty
= isl_union_map_empty(isl_union_map_get_space(S
));
1945 isl_union_map_compute_flow(isl_union_map_copy(R
),
1946 isl_union_map_copy(W
), empty
,
1947 isl_union_map_copy(S
),
1948 &dep_raw
, NULL
, NULL
, NULL
);
1949 isl_union_map_compute_flow(isl_union_map_copy(W
),
1950 isl_union_map_copy(W
),
1951 isl_union_map_copy(R
),
1952 isl_union_map_copy(S
),
1953 &dep_waw
, &dep_war
, NULL
, NULL
);
1955 dep
= isl_union_map_union(dep_waw
, dep_war
);
1956 dep
= isl_union_map_union(dep
, dep_raw
);
1957 validity
= isl_union_map_copy(dep
);
1958 proximity
= isl_union_map_copy(dep
);
1960 sched
= isl_union_set_compute_schedule(isl_union_set_copy(D
),
1961 validity
, proximity
);
1962 schedule
= isl_schedule_get_map(sched
);
1963 isl_schedule_free(sched
);
1964 isl_union_map_free(W
);
1965 isl_union_map_free(R
);
1966 isl_union_map_free(S
);
1969 isl_union_map_foreach_map(schedule
, &check_injective
, &is_injection
);
1971 domain
= isl_union_map_domain(isl_union_map_copy(schedule
));
1972 is_complete
= isl_union_set_is_subset(D
, domain
);
1973 isl_union_set_free(D
);
1974 isl_union_set_free(domain
);
1976 test
= isl_union_map_reverse(isl_union_map_copy(schedule
));
1977 test
= isl_union_map_apply_range(test
, dep
);
1978 test
= isl_union_map_apply_range(test
, schedule
);
1980 delta
= isl_union_map_deltas(test
);
1981 if (isl_union_set_n_set(delta
) == 0) {
1985 isl_union_set_free(delta
);
1987 delta_set
= isl_set_from_union_set(delta
);
1989 slice
= isl_set_universe(isl_set_get_space(delta_set
));
1990 for (i
= 0; i
< tilable
; ++i
)
1991 slice
= isl_set_lower_bound_si(slice
, isl_dim_set
, i
, 0);
1992 is_tilable
= isl_set_is_subset(delta_set
, slice
);
1993 isl_set_free(slice
);
1995 slice
= isl_set_universe(isl_set_get_space(delta_set
));
1996 for (i
= 0; i
< parallel
; ++i
)
1997 slice
= isl_set_fix_si(slice
, isl_dim_set
, i
, 0);
1998 is_parallel
= isl_set_is_subset(delta_set
, slice
);
1999 isl_set_free(slice
);
2001 origin
= isl_set_universe(isl_set_get_space(delta_set
));
2002 for (i
= 0; i
< isl_set_dim(origin
, isl_dim_set
); ++i
)
2003 origin
= isl_set_fix_si(origin
, isl_dim_set
, i
, 0);
2005 delta_set
= isl_set_union(delta_set
, isl_set_copy(origin
));
2006 delta_set
= isl_set_lexmin(delta_set
);
2008 is_nonneg
= isl_set_is_equal(delta_set
, origin
);
2010 isl_set_free(origin
);
2011 isl_set_free(delta_set
);
2014 if (is_nonneg
< 0 || is_parallel
< 0 || is_tilable
< 0 ||
2015 is_injection
< 0 || is_complete
< 0)
2018 isl_die(ctx
, isl_error_unknown
,
2019 "generated schedule incomplete", return -1);
2021 isl_die(ctx
, isl_error_unknown
,
2022 "generated schedule not injective on each statement",
2025 isl_die(ctx
, isl_error_unknown
,
2026 "negative dependences in generated schedule",
2029 isl_die(ctx
, isl_error_unknown
,
2030 "generated schedule not as tilable as expected",
2033 isl_die(ctx
, isl_error_unknown
,
2034 "generated schedule not as parallel as expected",
2040 int test_special_schedule(isl_ctx
*ctx
)
2044 isl_union_map
*empty
;
2046 isl_union_map
*sched1
, *sched2
;
2047 isl_schedule
*schedule
;
2050 str
= "{ S[i,j] : 0 <= i <= 10 }";
2051 dom
= isl_union_set_read_from_str(ctx
, str
);
2052 str
= "{ S[i,j] -> S[i+1,j] : 0 <= i,j <= 10 }";
2053 dep
= isl_union_map_read_from_str(ctx
, str
);
2054 empty
= isl_union_map_read_from_str(ctx
, "{}");
2055 schedule
= isl_union_set_compute_schedule(dom
, empty
, dep
);
2056 sched1
= isl_schedule_get_map(schedule
);
2057 isl_schedule_free(schedule
);
2059 str
= "{ S[i, j] -> [j, i] }";
2060 sched2
= isl_union_map_read_from_str(ctx
, str
);
2062 equal
= isl_union_map_is_equal(sched1
, sched2
);
2063 isl_union_map_free(sched1
);
2064 isl_union_map_free(sched2
);
2069 isl_die(ctx
, isl_error_unknown
, "unexpected schedule",
2075 int test_schedule(isl_ctx
*ctx
)
2077 const char *D
, *W
, *R
, *S
;
2080 D
= "[T,N] -> { S1[t,i] : 1 <= t <= T and 2 <= i <= N - 1 }";
2081 W
= "{ S1[t,i] -> a[t,i] }";
2082 R
= "{ S1[t,i] -> a[t-1,i]; S1[t,i] -> a[t-1,i-1]; "
2083 "S1[t,i] -> a[t-1,i+1] }";
2084 S
= "{ S1[t,i] -> [t,i] }";
2085 if (test_one_schedule(ctx
, D
, W
, R
, S
, 2, 0) < 0)
2088 /* Fig. 5 of CC2008 */
2089 D
= "[N] -> { S_0[i, j] : i >= 0 and i <= -1 + N and j >= 2 and "
2091 W
= "[N] -> { S_0[i, j] -> a[i, j] : i >= 0 and i <= -1 + N and "
2092 "j >= 2 and j <= -1 + N }";
2093 R
= "[N] -> { S_0[i, j] -> a[j, i] : i >= 0 and i <= -1 + N and "
2094 "j >= 2 and j <= -1 + N; "
2095 "S_0[i, j] -> a[i, -1 + j] : i >= 0 and i <= -1 + N and "
2096 "j >= 2 and j <= -1 + N }";
2097 S
= "[N] -> { S_0[i, j] -> [0, i, 0, j, 0] }";
2098 if (test_one_schedule(ctx
, D
, W
, R
, S
, 2, 0) < 0)
2101 D
= "{ S1[i] : 0 <= i <= 10; S2[i] : 0 <= i <= 9 }";
2102 W
= "{ S1[i] -> a[i] }";
2103 R
= "{ S2[i] -> a[i+1] }";
2104 S
= "{ S1[i] -> [0,i]; S2[i] -> [1,i] }";
2105 if (test_one_schedule(ctx
, D
, W
, R
, S
, 1, 1) < 0)
2108 D
= "{ S1[i] : 0 <= i < 10; S2[i] : 0 <= i < 10 }";
2109 W
= "{ S1[i] -> a[i] }";
2110 R
= "{ S2[i] -> a[9-i] }";
2111 S
= "{ S1[i] -> [0,i]; S2[i] -> [1,i] }";
2112 if (test_one_schedule(ctx
, D
, W
, R
, S
, 1, 1) < 0)
2115 D
= "[N] -> { S1[i] : 0 <= i < N; S2[i] : 0 <= i < N }";
2116 W
= "{ S1[i] -> a[i] }";
2117 R
= "[N] -> { S2[i] -> a[N-1-i] }";
2118 S
= "{ S1[i] -> [0,i]; S2[i] -> [1,i] }";
2119 if (test_one_schedule(ctx
, D
, W
, R
, S
, 1, 1) < 0)
2122 D
= "{ S1[i] : 0 < i < 10; S2[i] : 0 <= i < 10 }";
2123 W
= "{ S1[i] -> a[i]; S2[i] -> b[i] }";
2124 R
= "{ S2[i] -> a[i]; S1[i] -> b[i-1] }";
2125 S
= "{ S1[i] -> [i,0]; S2[i] -> [i,1] }";
2126 if (test_one_schedule(ctx
, D
, W
, R
, S
, 0, 0) < 0)
2129 D
= "[N] -> { S1[i] : 1 <= i <= N; S2[i,j] : 1 <= i,j <= N }";
2130 W
= "{ S1[i] -> a[0,i]; S2[i,j] -> a[i,j] }";
2131 R
= "{ S2[i,j] -> a[i-1,j] }";
2132 S
= "{ S1[i] -> [0,i,0]; S2[i,j] -> [1,i,j] }";
2133 if (test_one_schedule(ctx
, D
, W
, R
, S
, 2, 1) < 0)
2136 D
= "[N] -> { S1[i] : 1 <= i <= N; S2[i,j] : 1 <= i,j <= N }";
2137 W
= "{ S1[i] -> a[i,0]; S2[i,j] -> a[i,j] }";
2138 R
= "{ S2[i,j] -> a[i,j-1] }";
2139 S
= "{ S1[i] -> [0,i,0]; S2[i,j] -> [1,i,j] }";
2140 if (test_one_schedule(ctx
, D
, W
, R
, S
, 2, 1) < 0)
2143 D
= "[N] -> { S_0[]; S_1[i] : i >= 0 and i <= -1 + N; S_2[] }";
2144 W
= "[N] -> { S_0[] -> a[0]; S_2[] -> b[0]; "
2145 "S_1[i] -> a[1 + i] : i >= 0 and i <= -1 + N }";
2146 R
= "[N] -> { S_2[] -> a[N]; S_1[i] -> a[i] : i >= 0 and i <= -1 + N }";
2147 S
= "[N] -> { S_1[i] -> [1, i, 0]; S_2[] -> [2, 0, 1]; "
2148 "S_0[] -> [0, 0, 0] }";
2149 if (test_one_schedule(ctx
, D
, W
, R
, S
, 1, 0) < 0)
2151 ctx
->opt
->schedule_parametric
= 0;
2152 if (test_one_schedule(ctx
, D
, W
, R
, S
, 0, 0) < 0)
2154 ctx
->opt
->schedule_parametric
= 1;
2156 D
= "[N] -> { S1[i] : 1 <= i <= N; S2[i] : 1 <= i <= N; "
2157 "S3[i,j] : 1 <= i,j <= N; S4[i] : 1 <= i <= N }";
2158 W
= "{ S1[i] -> a[i,0]; S2[i] -> a[0,i]; S3[i,j] -> a[i,j] }";
2159 R
= "[N] -> { S3[i,j] -> a[i-1,j]; S3[i,j] -> a[i,j-1]; "
2160 "S4[i] -> a[i,N] }";
2161 S
= "{ S1[i] -> [0,i,0]; S2[i] -> [1,i,0]; S3[i,j] -> [2,i,j]; "
2162 "S4[i] -> [4,i,0] }";
2163 if (test_one_schedule(ctx
, D
, W
, R
, S
, 2, 0) < 0)
2166 D
= "[N] -> { S_0[i, j] : i >= 1 and i <= N and j >= 1 and j <= N }";
2167 W
= "[N] -> { S_0[i, j] -> s[0] : i >= 1 and i <= N and j >= 1 and "
2169 R
= "[N] -> { S_0[i, j] -> s[0] : i >= 1 and i <= N and j >= 1 and "
2171 "S_0[i, j] -> a[i, j] : i >= 1 and i <= N and j >= 1 and "
2173 S
= "[N] -> { S_0[i, j] -> [0, i, 0, j, 0] }";
2174 if (test_one_schedule(ctx
, D
, W
, R
, S
, 0, 0) < 0)
2177 D
= "[N] -> { S_0[t] : t >= 0 and t <= -1 + N; "
2178 " S_2[t] : t >= 0 and t <= -1 + N; "
2179 " S_1[t, i] : t >= 0 and t <= -1 + N and i >= 0 and "
2181 W
= "[N] -> { S_0[t] -> a[t, 0] : t >= 0 and t <= -1 + N; "
2182 " S_2[t] -> b[t] : t >= 0 and t <= -1 + N; "
2183 " S_1[t, i] -> a[t, 1 + i] : t >= 0 and t <= -1 + N and "
2184 "i >= 0 and i <= -1 + N }";
2185 R
= "[N] -> { S_1[t, i] -> a[t, i] : t >= 0 and t <= -1 + N and "
2186 "i >= 0 and i <= -1 + N; "
2187 " S_2[t] -> a[t, N] : t >= 0 and t <= -1 + N }";
2188 S
= "[N] -> { S_2[t] -> [0, t, 2]; S_1[t, i] -> [0, t, 1, i, 0]; "
2189 " S_0[t] -> [0, t, 0] }";
2191 if (test_one_schedule(ctx
, D
, W
, R
, S
, 2, 1) < 0)
2193 ctx
->opt
->schedule_parametric
= 0;
2194 if (test_one_schedule(ctx
, D
, W
, R
, S
, 0, 0) < 0)
2196 ctx
->opt
->schedule_parametric
= 1;
2198 D
= "[N] -> { S1[i,j] : 0 <= i,j < N; S2[i,j] : 0 <= i,j < N }";
2199 S
= "{ S1[i,j] -> [0,i,j]; S2[i,j] -> [1,i,j] }";
2200 if (test_one_schedule(ctx
, D
, "{}", "{}", S
, 2, 2) < 0)
2203 D
= "[M, N] -> { S_1[i] : i >= 0 and i <= -1 + M; "
2204 "S_0[i, j] : i >= 0 and i <= -1 + M and j >= 0 and j <= -1 + N }";
2205 W
= "[M, N] -> { S_0[i, j] -> a[j] : i >= 0 and i <= -1 + M and "
2206 "j >= 0 and j <= -1 + N; "
2207 "S_1[i] -> b[0] : i >= 0 and i <= -1 + M }";
2208 R
= "[M, N] -> { S_0[i, j] -> a[0] : i >= 0 and i <= -1 + M and "
2209 "j >= 0 and j <= -1 + N; "
2210 "S_1[i] -> b[0] : i >= 0 and i <= -1 + M }";
2211 S
= "[M, N] -> { S_1[i] -> [1, i, 0]; S_0[i, j] -> [0, i, 0, j, 0] }";
2212 if (test_one_schedule(ctx
, D
, W
, R
, S
, 0, 0) < 0)
2215 D
= "{ S_0[i] : i >= 0 }";
2216 W
= "{ S_0[i] -> a[i] : i >= 0 }";
2217 R
= "{ S_0[i] -> a[0] : i >= 0 }";
2218 S
= "{ S_0[i] -> [0, i, 0] }";
2219 if (test_one_schedule(ctx
, D
, W
, R
, S
, 0, 0) < 0)
2222 D
= "{ S_0[i] : i >= 0; S_1[i] : i >= 0 }";
2223 W
= "{ S_0[i] -> a[i] : i >= 0; S_1[i] -> b[i] : i >= 0 }";
2224 R
= "{ S_0[i] -> b[0] : i >= 0; S_1[i] -> a[i] : i >= 0 }";
2225 S
= "{ S_1[i] -> [0, i, 1]; S_0[i] -> [0, i, 0] }";
2226 if (test_one_schedule(ctx
, D
, W
, R
, S
, 0, 0) < 0)
2229 D
= "[n] -> { S_0[j, k] : j <= -1 + n and j >= 0 and "
2230 "k <= -1 + n and k >= 0 }";
2231 W
= "[n] -> { S_0[j, k] -> B[j] : j <= -1 + n and j >= 0 and " "k <= -1 + n and k >= 0 }";
2232 R
= "[n] -> { S_0[j, k] -> B[j] : j <= -1 + n and j >= 0 and "
2233 "k <= -1 + n and k >= 0; "
2234 "S_0[j, k] -> B[k] : j <= -1 + n and j >= 0 and "
2235 "k <= -1 + n and k >= 0; "
2236 "S_0[j, k] -> A[k] : j <= -1 + n and j >= 0 and "
2237 "k <= -1 + n and k >= 0 }";
2238 S
= "[n] -> { S_0[j, k] -> [2, j, k] }";
2239 ctx
->opt
->schedule_outer_zero_distance
= 1;
2240 if (test_one_schedule(ctx
, D
, W
, R
, S
, 0, 0) < 0)
2242 ctx
->opt
->schedule_outer_zero_distance
= 0;
2244 return test_special_schedule(ctx
);
2247 int test_plain_injective(isl_ctx
*ctx
, const char *str
, int injective
)
2249 isl_union_map
*umap
;
2252 umap
= isl_union_map_read_from_str(ctx
, str
);
2253 test
= isl_union_map_plain_is_injective(umap
);
2254 isl_union_map_free(umap
);
2257 if (test
== injective
)
2260 isl_die(ctx
, isl_error_unknown
,
2261 "map not detected as injective", return -1);
2263 isl_die(ctx
, isl_error_unknown
,
2264 "map detected as injective", return -1);
2267 int test_injective(isl_ctx
*ctx
)
2271 if (test_plain_injective(ctx
, "{S[i,j] -> A[0]; T[i,j] -> B[1]}", 0))
2273 if (test_plain_injective(ctx
, "{S[] -> A[0]; T[] -> B[0]}", 1))
2275 if (test_plain_injective(ctx
, "{S[] -> A[0]; T[] -> A[1]}", 1))
2277 if (test_plain_injective(ctx
, "{S[] -> A[0]; T[] -> A[0]}", 0))
2279 if (test_plain_injective(ctx
, "{S[i] -> A[i,0]; T[i] -> A[i,1]}", 1))
2281 if (test_plain_injective(ctx
, "{S[i] -> A[i]; T[i] -> A[i]}", 0))
2283 if (test_plain_injective(ctx
, "{S[] -> A[0,0]; T[] -> A[0,1]}", 1))
2285 if (test_plain_injective(ctx
, "{S[] -> A[0,0]; T[] -> A[1,0]}", 1))
2288 str
= "{S[] -> A[0,0]; T[] -> A[0,1]; U[] -> A[1,0]}";
2289 if (test_plain_injective(ctx
, str
, 1))
2291 str
= "{S[] -> A[0,0]; T[] -> A[0,1]; U[] -> A[0,0]}";
2292 if (test_plain_injective(ctx
, str
, 0))
2298 int test_aff(isl_ctx
*ctx
)
2303 isl_local_space
*ls
;
2307 dim
= isl_space_set_alloc(ctx
, 0, 1);
2308 ls
= isl_local_space_from_space(dim
);
2309 aff
= isl_aff_zero_on_domain(ls
);
2311 aff
= isl_aff_add_coefficient_si(aff
, isl_dim_in
, 0, 1);
2312 aff
= isl_aff_scale_down_ui(aff
, 3);
2313 aff
= isl_aff_floor(aff
);
2314 aff
= isl_aff_add_coefficient_si(aff
, isl_dim_in
, 0, 1);
2315 aff
= isl_aff_scale_down_ui(aff
, 2);
2316 aff
= isl_aff_floor(aff
);
2317 aff
= isl_aff_add_coefficient_si(aff
, isl_dim_in
, 0, 1);
2320 set
= isl_set_read_from_str(ctx
, str
);
2321 aff
= isl_aff_gist(aff
, set
);
2323 aff
= isl_aff_add_constant_si(aff
, -16);
2324 zero
= isl_aff_plain_is_zero(aff
);
2330 isl_die(ctx
, isl_error_unknown
, "unexpected result", return -1);
2335 int test_dim_max(isl_ctx
*ctx
)
2339 isl_set
*set1
, *set2
;
2344 str
= "[N] -> { [i] : 0 <= i <= min(N,10) }";
2345 set
= isl_set_read_from_str(ctx
, str
);
2346 pwaff
= isl_set_dim_max(set
, 0);
2347 set1
= isl_set_from_pw_aff(pwaff
);
2348 str
= "[N] -> { [10] : N >= 10; [N] : N <= 9 and N >= 0 }";
2349 set2
= isl_set_read_from_str(ctx
, str
);
2350 equal
= isl_set_is_equal(set1
, set2
);
2356 isl_die(ctx
, isl_error_unknown
, "unexpected result", return -1);
2358 str
= "[N] -> { [i] : 0 <= i <= max(2N,N+6) }";
2359 set
= isl_set_read_from_str(ctx
, str
);
2360 pwaff
= isl_set_dim_max(set
, 0);
2361 set1
= isl_set_from_pw_aff(pwaff
);
2362 str
= "[N] -> { [6 + N] : -6 <= N <= 5; [2N] : N >= 6 }";
2363 set2
= isl_set_read_from_str(ctx
, str
);
2364 equal
= isl_set_is_equal(set1
, set2
);
2370 isl_die(ctx
, isl_error_unknown
, "unexpected result", return -1);
2372 str
= "[N] -> { [i] : 0 <= i <= 2N or 0 <= i <= N+6 }";
2373 set
= isl_set_read_from_str(ctx
, str
);
2374 pwaff
= isl_set_dim_max(set
, 0);
2375 set1
= isl_set_from_pw_aff(pwaff
);
2376 str
= "[N] -> { [6 + N] : -6 <= N <= 5; [2N] : N >= 6 }";
2377 set2
= isl_set_read_from_str(ctx
, str
);
2378 equal
= isl_set_is_equal(set1
, set2
);
2384 isl_die(ctx
, isl_error_unknown
, "unexpected result", return -1);
2386 str
= "[N,M] -> { [i,j] -> [([i/16]), i%16, ([j/16]), j%16] : "
2387 "0 <= i < N and 0 <= j < M }";
2388 map
= isl_map_read_from_str(ctx
, str
);
2389 set
= isl_map_range(map
);
2391 pwaff
= isl_set_dim_max(isl_set_copy(set
), 0);
2392 set1
= isl_set_from_pw_aff(pwaff
);
2393 str
= "[N,M] -> { [([(N-1)/16])] : M,N > 0 }";
2394 set2
= isl_set_read_from_str(ctx
, str
);
2395 equal
= isl_set_is_equal(set1
, set2
);
2399 pwaff
= isl_set_dim_max(isl_set_copy(set
), 3);
2400 set1
= isl_set_from_pw_aff(pwaff
);
2401 str
= "[N,M] -> { [t] : t = min(M-1,15) and M,N > 0 }";
2402 set2
= isl_set_read_from_str(ctx
, str
);
2403 if (equal
>= 0 && equal
)
2404 equal
= isl_set_is_equal(set1
, set2
);
2413 isl_die(ctx
, isl_error_unknown
, "unexpected result", return -1);
2418 int test_product(isl_ctx
*ctx
)
2425 set
= isl_set_read_from_str(ctx
, str
);
2426 set
= isl_set_product(set
, isl_set_copy(set
));
2427 ok
= isl_set_is_wrapping(set
);
2432 isl_die(ctx
, isl_error_unknown
, "unexpected result", return -1);
2437 int test_equal(isl_ctx
*ctx
)
2440 isl_set
*set
, *set2
;
2444 set
= isl_set_read_from_str(ctx
, str
);
2446 set2
= isl_set_read_from_str(ctx
, str
);
2447 equal
= isl_set_is_equal(set
, set2
);
2453 isl_die(ctx
, isl_error_unknown
, "unexpected result", return -1);
2458 static int test_plain_fixed(isl_ctx
*ctx
, __isl_take isl_map
*map
,
2459 enum isl_dim_type type
, unsigned pos
, int fixed
)
2463 test
= isl_map_plain_is_fixed(map
, type
, pos
, NULL
);
2470 isl_die(ctx
, isl_error_unknown
,
2471 "map not detected as fixed", return -1);
2473 isl_die(ctx
, isl_error_unknown
,
2474 "map detected as fixed", return -1);
2477 int test_fixed(isl_ctx
*ctx
)
2482 str
= "{ [i] -> [i] }";
2483 map
= isl_map_read_from_str(ctx
, str
);
2484 if (test_plain_fixed(ctx
, map
, isl_dim_out
, 0, 0))
2486 str
= "{ [i] -> [1] }";
2487 map
= isl_map_read_from_str(ctx
, str
);
2488 if (test_plain_fixed(ctx
, map
, isl_dim_out
, 0, 1))
2490 str
= "{ S_1[p1] -> [o0] : o0 = -2 and p1 >= 1 and p1 <= 7 }";
2491 map
= isl_map_read_from_str(ctx
, str
);
2492 if (test_plain_fixed(ctx
, map
, isl_dim_out
, 0, 1))
2494 map
= isl_map_read_from_str(ctx
, str
);
2495 map
= isl_map_neg(map
);
2496 if (test_plain_fixed(ctx
, map
, isl_dim_out
, 0, 1))
2504 struct isl_ctx
*ctx
;
2506 srcdir
= getenv("srcdir");
2509 ctx
= isl_ctx_alloc();
2510 if (test_fixed(ctx
) < 0)
2512 if (test_equal(ctx
) < 0)
2514 if (test_product(ctx
) < 0)
2516 if (test_dim_max(ctx
) < 0)
2518 if (test_aff(ctx
) < 0)
2520 if (test_injective(ctx
) < 0)
2522 if (test_schedule(ctx
) < 0)
2524 test_factorize(ctx
);
2529 test_split_periods(ctx
);
2533 if (test_sv(ctx
) < 0)
2535 test_bijective(ctx
);
2539 test_construction(ctx
);
2542 test_application(ctx
);
2543 test_affine_hull(ctx
);
2544 test_convex_hull(ctx
);