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 void test_parse(struct isl_ctx
*ctx
)
75 const char *str
, *str2
;
77 str
= "{ [i] -> [-i] }";
78 map
= isl_map_read_from_str(ctx
, str
);
82 str
= "{ A[i] -> L[([i/3])] }";
83 map
= isl_map_read_from_str(ctx
, str
);
87 test_parse_map(ctx
, "{[[s] -> A[i]] -> [[s+1] -> A[i]]}");
88 test_parse_map(ctx
, "{ [p1, y1, y2] -> [2, y1, y2] : "
89 "p1 = 1 && (y1 <= y2 || y2 = 0) }");
91 str
= "{ [x,y] : [([x/2]+y)/3] >= 1 }";
92 str2
= "{ [x, y] : 2y >= 6 - x }";
93 test_parse_map_equal(ctx
, str
, str2
);
95 test_parse_map_equal(ctx
, "{ [x,y] : x <= min(y, 2*y+3) }",
96 "{ [x,y] : x <= y, 2*y + 3 }");
97 str
= "{ [x, y] : (y <= x and y >= -3) or (2y <= -3 + x and y <= -4) }";
98 test_parse_map_equal(ctx
, "{ [x,y] : x >= min(y, 2*y+3) }", str
);
100 str
= "{[new,old] -> [new+1-2*[(new+1)/2],old+1-2*[(old+1)/2]]}";
101 map
= isl_map_read_from_str(ctx
, str
);
102 str
= "{ [new, old] -> [o0, o1] : "
103 "exists (e0 = [(-1 - new + o0)/2], e1 = [(-1 - old + o1)/2]: "
104 "2e0 = -1 - new + o0 and 2e1 = -1 - old + o1 and o0 >= 0 and "
105 "o0 <= 1 and o1 >= 0 and o1 <= 1) }";
106 map2
= isl_map_read_from_str(ctx
, str
);
107 assert(isl_map_is_equal(map
, map2
));
111 str
= "{[new,old] -> [new+1-2*[(new+1)/2],old+1-2*[(old+1)/2]]}";
112 map
= isl_map_read_from_str(ctx
, str
);
113 str
= "{[new,old] -> [(new+1)%2,(old+1)%2]}";
114 map2
= isl_map_read_from_str(ctx
, str
);
115 assert(isl_map_is_equal(map
, map2
));
119 str
= "[n] -> { [c1] : c1>=0 and c1<=floord(n-4,3) }";
120 str2
= "[n] -> { [c1] : c1 >= 0 and 3c1 <= -4 + n }";
121 test_parse_map_equal(ctx
, str
, str2
);
123 str
= "{ [i,j] -> [i] : i < j; [i,j] -> [j] : j <= i }";
124 str2
= "{ [i,j] -> [min(i,j)] }";
125 test_parse_map_equal(ctx
, str
, str2
);
127 str
= "{ [i,j] : i != j }";
128 str2
= "{ [i,j] : i < j or i > j }";
129 test_parse_map_equal(ctx
, str
, str2
);
131 str
= "{ [i,j] : (i+1)*2 >= j }";
132 str2
= "{ [i, j] : j <= 2 + 2i }";
133 test_parse_map_equal(ctx
, str
, str2
);
135 str
= "{ [i] -> [i > 0 ? 4 : 5] }";
136 str2
= "{ [i] -> [5] : i <= 0; [i] -> [4] : i >= 1 }";
137 test_parse_map_equal(ctx
, str
, str2
);
139 str
= "[N=2,M] -> { [i=[(M+N)/4]] }";
140 str2
= "[N, M] -> { [i] : N = 2 and 4i <= 2 + M and 4i >= -1 + M }";
141 test_parse_map_equal(ctx
, str
, str2
);
143 str
= "{ [x] : x >= 0 }";
144 str2
= "{ [x] : x-0 >= 0 }";
145 test_parse_map_equal(ctx
, str
, str2
);
147 test_parse_pwqp(ctx
, "{ [i] -> i + [ (i + [i/3])/2 ] }");
148 test_parse_map(ctx
, "{ S1[i] -> [([i/10]),i%10] : 0 <= i <= 45 }");
151 void test_read(struct isl_ctx
*ctx
)
155 struct isl_basic_set
*bset1
, *bset2
;
156 const char *str
= "{[y]: Exists ( alpha : 2alpha = y)}";
158 filename
= get_filename(ctx
, "set", "omega");
160 input
= fopen(filename
, "r");
163 bset1
= isl_basic_set_read_from_file(ctx
, input
);
164 bset2
= isl_basic_set_read_from_str(ctx
, str
);
166 assert(isl_basic_set_is_equal(bset1
, bset2
) == 1);
168 isl_basic_set_free(bset1
);
169 isl_basic_set_free(bset2
);
175 void test_bounded(struct isl_ctx
*ctx
)
180 set
= isl_set_read_from_str(ctx
, "[n] -> {[i] : 0 <= i <= n }");
181 bounded
= isl_set_is_bounded(set
);
185 set
= isl_set_read_from_str(ctx
, "{[n, i] : 0 <= i <= n }");
186 bounded
= isl_set_is_bounded(set
);
190 set
= isl_set_read_from_str(ctx
, "[n] -> {[i] : i <= n }");
191 bounded
= isl_set_is_bounded(set
);
196 /* Construct the basic set { [i] : 5 <= i <= N } */
197 void test_construction(struct isl_ctx
*ctx
)
202 struct isl_basic_set
*bset
;
203 struct isl_constraint
*c
;
207 dim
= isl_space_set_alloc(ctx
, 1, 1);
208 bset
= isl_basic_set_universe(isl_space_copy(dim
));
209 ls
= isl_local_space_from_space(dim
);
211 c
= isl_inequality_alloc(isl_local_space_copy(ls
));
212 isl_int_set_si(v
, -1);
213 isl_constraint_set_coefficient(c
, isl_dim_set
, 0, v
);
214 isl_int_set_si(v
, 1);
215 isl_constraint_set_coefficient(c
, isl_dim_param
, 0, v
);
216 bset
= isl_basic_set_add_constraint(bset
, c
);
218 c
= isl_inequality_alloc(isl_local_space_copy(ls
));
219 isl_int_set_si(v
, 1);
220 isl_constraint_set_coefficient(c
, isl_dim_set
, 0, v
);
221 isl_int_set_si(v
, -5);
222 isl_constraint_set_constant(c
, v
);
223 bset
= isl_basic_set_add_constraint(bset
, c
);
225 isl_local_space_free(ls
);
226 isl_basic_set_free(bset
);
231 void test_dim(struct isl_ctx
*ctx
)
234 isl_map
*map1
, *map2
;
236 map1
= isl_map_read_from_str(ctx
,
237 "[n] -> { [i] -> [j] : exists (a = [i/10] : i - 10a <= n ) }");
238 map1
= isl_map_add_dims(map1
, isl_dim_in
, 1);
239 map2
= isl_map_read_from_str(ctx
,
240 "[n] -> { [i,k] -> [j] : exists (a = [i/10] : i - 10a <= n ) }");
241 assert(isl_map_is_equal(map1
, map2
));
244 map1
= isl_map_project_out(map1
, isl_dim_in
, 0, 1);
245 map2
= isl_map_read_from_str(ctx
, "[n] -> { [i] -> [j] : n >= 0 }");
246 assert(isl_map_is_equal(map1
, map2
));
251 str
= "[n] -> { [i] -> [] : exists a : 0 <= i <= n and i = 2 a }";
252 map1
= isl_map_read_from_str(ctx
, str
);
253 str
= "{ [i] -> [j] : exists a : 0 <= i <= j and i = 2 a }";
254 map2
= isl_map_read_from_str(ctx
, str
);
255 map1
= isl_map_move_dims(map1
, isl_dim_out
, 0, isl_dim_param
, 0, 1);
256 assert(isl_map_is_equal(map1
, map2
));
262 void test_div(struct isl_ctx
*ctx
)
267 struct isl_basic_set
*bset
;
268 struct isl_constraint
*c
;
273 dim
= isl_space_set_alloc(ctx
, 0, 3);
274 bset
= isl_basic_set_universe(isl_space_copy(dim
));
275 ls
= isl_local_space_from_space(dim
);
277 c
= isl_equality_alloc(isl_local_space_copy(ls
));
278 isl_int_set_si(v
, -1);
279 isl_constraint_set_constant(c
, v
);
280 isl_int_set_si(v
, 1);
281 isl_constraint_set_coefficient(c
, isl_dim_set
, 0, v
);
282 isl_int_set_si(v
, 3);
283 isl_constraint_set_coefficient(c
, isl_dim_set
, 1, v
);
284 bset
= isl_basic_set_add_constraint(bset
, c
);
286 c
= isl_equality_alloc(isl_local_space_copy(ls
));
287 isl_int_set_si(v
, 1);
288 isl_constraint_set_constant(c
, v
);
289 isl_int_set_si(v
, -1);
290 isl_constraint_set_coefficient(c
, isl_dim_set
, 0, v
);
291 isl_int_set_si(v
, 3);
292 isl_constraint_set_coefficient(c
, isl_dim_set
, 2, v
);
293 bset
= isl_basic_set_add_constraint(bset
, c
);
295 bset
= isl_basic_set_project_out(bset
, isl_dim_set
, 1, 2);
297 assert(bset
&& bset
->n_div
== 1);
298 isl_local_space_free(ls
);
299 isl_basic_set_free(bset
);
302 dim
= isl_space_set_alloc(ctx
, 0, 3);
303 bset
= isl_basic_set_universe(isl_space_copy(dim
));
304 ls
= isl_local_space_from_space(dim
);
306 c
= isl_equality_alloc(isl_local_space_copy(ls
));
307 isl_int_set_si(v
, 1);
308 isl_constraint_set_constant(c
, v
);
309 isl_int_set_si(v
, -1);
310 isl_constraint_set_coefficient(c
, isl_dim_set
, 0, v
);
311 isl_int_set_si(v
, 3);
312 isl_constraint_set_coefficient(c
, isl_dim_set
, 1, v
);
313 bset
= isl_basic_set_add_constraint(bset
, c
);
315 c
= isl_equality_alloc(isl_local_space_copy(ls
));
316 isl_int_set_si(v
, -1);
317 isl_constraint_set_constant(c
, v
);
318 isl_int_set_si(v
, 1);
319 isl_constraint_set_coefficient(c
, isl_dim_set
, 0, v
);
320 isl_int_set_si(v
, 3);
321 isl_constraint_set_coefficient(c
, isl_dim_set
, 2, v
);
322 bset
= isl_basic_set_add_constraint(bset
, c
);
324 bset
= isl_basic_set_project_out(bset
, isl_dim_set
, 1, 2);
326 assert(bset
&& bset
->n_div
== 1);
327 isl_local_space_free(ls
);
328 isl_basic_set_free(bset
);
331 dim
= isl_space_set_alloc(ctx
, 0, 3);
332 bset
= isl_basic_set_universe(isl_space_copy(dim
));
333 ls
= isl_local_space_from_space(dim
);
335 c
= isl_equality_alloc(isl_local_space_copy(ls
));
336 isl_int_set_si(v
, 1);
337 isl_constraint_set_constant(c
, v
);
338 isl_int_set_si(v
, -1);
339 isl_constraint_set_coefficient(c
, isl_dim_set
, 0, v
);
340 isl_int_set_si(v
, 3);
341 isl_constraint_set_coefficient(c
, isl_dim_set
, 1, v
);
342 bset
= isl_basic_set_add_constraint(bset
, c
);
344 c
= isl_equality_alloc(isl_local_space_copy(ls
));
345 isl_int_set_si(v
, -3);
346 isl_constraint_set_constant(c
, v
);
347 isl_int_set_si(v
, 1);
348 isl_constraint_set_coefficient(c
, isl_dim_set
, 0, v
);
349 isl_int_set_si(v
, 4);
350 isl_constraint_set_coefficient(c
, isl_dim_set
, 2, v
);
351 bset
= isl_basic_set_add_constraint(bset
, c
);
353 bset
= isl_basic_set_project_out(bset
, isl_dim_set
, 1, 2);
355 assert(bset
&& bset
->n_div
== 1);
356 isl_local_space_free(ls
);
357 isl_basic_set_free(bset
);
360 dim
= isl_space_set_alloc(ctx
, 0, 3);
361 bset
= isl_basic_set_universe(isl_space_copy(dim
));
362 ls
= isl_local_space_from_space(dim
);
364 c
= isl_equality_alloc(isl_local_space_copy(ls
));
365 isl_int_set_si(v
, 2);
366 isl_constraint_set_constant(c
, v
);
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 bset
= isl_basic_set_add_constraint(bset
, c
);
373 c
= isl_equality_alloc(isl_local_space_copy(ls
));
374 isl_int_set_si(v
, -1);
375 isl_constraint_set_constant(c
, v
);
376 isl_int_set_si(v
, 1);
377 isl_constraint_set_coefficient(c
, isl_dim_set
, 0, v
);
378 isl_int_set_si(v
, 6);
379 isl_constraint_set_coefficient(c
, isl_dim_set
, 2, v
);
380 bset
= isl_basic_set_add_constraint(bset
, c
);
382 bset
= isl_basic_set_project_out(bset
, isl_dim_set
, 1, 2);
384 assert(isl_basic_set_is_empty(bset
));
385 isl_local_space_free(ls
);
386 isl_basic_set_free(bset
);
389 dim
= isl_space_set_alloc(ctx
, 0, 3);
390 bset
= isl_basic_set_universe(isl_space_copy(dim
));
391 ls
= isl_local_space_from_space(dim
);
393 c
= isl_equality_alloc(isl_local_space_copy(ls
));
394 isl_int_set_si(v
, -1);
395 isl_constraint_set_coefficient(c
, isl_dim_set
, 0, v
);
396 isl_int_set_si(v
, 3);
397 isl_constraint_set_coefficient(c
, isl_dim_set
, 2, v
);
398 bset
= isl_basic_set_add_constraint(bset
, c
);
400 c
= isl_equality_alloc(isl_local_space_copy(ls
));
401 isl_int_set_si(v
, 1);
402 isl_constraint_set_coefficient(c
, isl_dim_set
, 0, v
);
403 isl_int_set_si(v
, -3);
404 isl_constraint_set_coefficient(c
, isl_dim_set
, 1, v
);
405 bset
= isl_basic_set_add_constraint(bset
, c
);
407 bset
= isl_basic_set_project_out(bset
, isl_dim_set
, 2, 1);
409 assert(bset
&& bset
->n_div
== 0);
410 isl_basic_set_free(bset
);
411 isl_local_space_free(ls
);
414 dim
= isl_space_set_alloc(ctx
, 0, 3);
415 bset
= isl_basic_set_universe(isl_space_copy(dim
));
416 ls
= isl_local_space_from_space(dim
);
418 c
= isl_equality_alloc(isl_local_space_copy(ls
));
419 isl_int_set_si(v
, -1);
420 isl_constraint_set_coefficient(c
, isl_dim_set
, 0, v
);
421 isl_int_set_si(v
, 6);
422 isl_constraint_set_coefficient(c
, isl_dim_set
, 2, v
);
423 bset
= isl_basic_set_add_constraint(bset
, c
);
425 c
= isl_equality_alloc(isl_local_space_copy(ls
));
426 isl_int_set_si(v
, 1);
427 isl_constraint_set_coefficient(c
, isl_dim_set
, 0, v
);
428 isl_int_set_si(v
, -3);
429 isl_constraint_set_coefficient(c
, isl_dim_set
, 1, v
);
430 bset
= isl_basic_set_add_constraint(bset
, c
);
432 bset
= isl_basic_set_project_out(bset
, isl_dim_set
, 2, 1);
434 assert(bset
&& bset
->n_div
== 1);
435 isl_basic_set_free(bset
);
436 isl_local_space_free(ls
);
439 /* This test is a bit tricky. We set up an equality
441 * Normalization of divs creates _two_ divs
444 * Afterwards e0 is removed again because it has coefficient -1
445 * and we end up with the original equality and div again.
446 * Perhaps we can avoid the introduction of this temporary div.
448 dim
= isl_space_set_alloc(ctx
, 0, 4);
449 bset
= isl_basic_set_universe(isl_space_copy(dim
));
450 ls
= isl_local_space_from_space(dim
);
452 c
= isl_equality_alloc(isl_local_space_copy(ls
));
453 isl_int_set_si(v
, -1);
454 isl_constraint_set_coefficient(c
, isl_dim_set
, 0, v
);
455 isl_int_set_si(v
, -3);
456 isl_constraint_set_coefficient(c
, isl_dim_set
, 1, v
);
457 isl_int_set_si(v
, -3);
458 isl_constraint_set_coefficient(c
, isl_dim_set
, 2, v
);
459 isl_int_set_si(v
, 6);
460 isl_constraint_set_coefficient(c
, isl_dim_set
, 3, v
);
461 bset
= isl_basic_set_add_constraint(bset
, c
);
463 bset
= isl_basic_set_project_out(bset
, isl_dim_set
, 3, 1);
465 /* Test disabled for now */
467 assert(bset && bset->n_div == 1);
469 isl_local_space_free(ls
);
470 isl_basic_set_free(bset
);
473 dim
= isl_space_set_alloc(ctx
, 0, 5);
474 bset
= isl_basic_set_universe(isl_space_copy(dim
));
475 ls
= isl_local_space_from_space(dim
);
477 c
= isl_equality_alloc(isl_local_space_copy(ls
));
478 isl_int_set_si(v
, -1);
479 isl_constraint_set_coefficient(c
, isl_dim_set
, 0, v
);
480 isl_int_set_si(v
, -3);
481 isl_constraint_set_coefficient(c
, isl_dim_set
, 1, v
);
482 isl_int_set_si(v
, -3);
483 isl_constraint_set_coefficient(c
, isl_dim_set
, 3, v
);
484 isl_int_set_si(v
, 6);
485 isl_constraint_set_coefficient(c
, isl_dim_set
, 4, v
);
486 bset
= isl_basic_set_add_constraint(bset
, c
);
488 c
= isl_equality_alloc(isl_local_space_copy(ls
));
489 isl_int_set_si(v
, -1);
490 isl_constraint_set_coefficient(c
, isl_dim_set
, 0, v
);
491 isl_int_set_si(v
, 1);
492 isl_constraint_set_coefficient(c
, isl_dim_set
, 2, v
);
493 isl_int_set_si(v
, 1);
494 isl_constraint_set_constant(c
, v
);
495 bset
= isl_basic_set_add_constraint(bset
, c
);
497 bset
= isl_basic_set_project_out(bset
, isl_dim_set
, 4, 1);
499 /* Test disabled for now */
501 assert(bset && bset->n_div == 1);
503 isl_local_space_free(ls
);
504 isl_basic_set_free(bset
);
507 dim
= isl_space_set_alloc(ctx
, 0, 4);
508 bset
= isl_basic_set_universe(isl_space_copy(dim
));
509 ls
= isl_local_space_from_space(dim
);
511 c
= isl_equality_alloc(isl_local_space_copy(ls
));
512 isl_int_set_si(v
, 1);
513 isl_constraint_set_coefficient(c
, isl_dim_set
, 0, v
);
514 isl_int_set_si(v
, -1);
515 isl_constraint_set_coefficient(c
, isl_dim_set
, 1, v
);
516 isl_int_set_si(v
, -2);
517 isl_constraint_set_coefficient(c
, isl_dim_set
, 2, v
);
518 bset
= isl_basic_set_add_constraint(bset
, c
);
520 c
= isl_equality_alloc(isl_local_space_copy(ls
));
521 isl_int_set_si(v
, -1);
522 isl_constraint_set_coefficient(c
, isl_dim_set
, 0, v
);
523 isl_int_set_si(v
, 3);
524 isl_constraint_set_coefficient(c
, isl_dim_set
, 3, v
);
525 isl_int_set_si(v
, 2);
526 isl_constraint_set_constant(c
, v
);
527 bset
= isl_basic_set_add_constraint(bset
, c
);
529 bset
= isl_basic_set_project_out(bset
, isl_dim_set
, 2, 2);
531 bset
= isl_basic_set_fix_si(bset
, isl_dim_set
, 0, 2);
533 assert(!isl_basic_set_is_empty(bset
));
535 isl_local_space_free(ls
);
536 isl_basic_set_free(bset
);
539 dim
= isl_space_set_alloc(ctx
, 0, 3);
540 bset
= isl_basic_set_universe(isl_space_copy(dim
));
541 ls
= isl_local_space_from_space(dim
);
543 c
= isl_equality_alloc(isl_local_space_copy(ls
));
544 isl_int_set_si(v
, 1);
545 isl_constraint_set_coefficient(c
, isl_dim_set
, 0, v
);
546 isl_int_set_si(v
, -2);
547 isl_constraint_set_coefficient(c
, isl_dim_set
, 2, v
);
548 bset
= isl_basic_set_add_constraint(bset
, c
);
550 bset
= isl_basic_set_project_out(bset
, isl_dim_set
, 2, 1);
552 bset
= isl_basic_set_fix_si(bset
, isl_dim_set
, 0, 2);
554 isl_local_space_free(ls
);
555 isl_basic_set_free(bset
);
560 void test_application_case(struct isl_ctx
*ctx
, const char *name
)
564 struct isl_basic_set
*bset1
, *bset2
;
565 struct isl_basic_map
*bmap
;
567 filename
= get_filename(ctx
, name
, "omega");
569 input
= fopen(filename
, "r");
572 bset1
= isl_basic_set_read_from_file(ctx
, input
);
573 bmap
= isl_basic_map_read_from_file(ctx
, input
);
575 bset1
= isl_basic_set_apply(bset1
, bmap
);
577 bset2
= isl_basic_set_read_from_file(ctx
, input
);
579 assert(isl_basic_set_is_equal(bset1
, bset2
) == 1);
581 isl_basic_set_free(bset1
);
582 isl_basic_set_free(bset2
);
588 void test_application(struct isl_ctx
*ctx
)
590 test_application_case(ctx
, "application");
591 test_application_case(ctx
, "application2");
594 void test_affine_hull_case(struct isl_ctx
*ctx
, const char *name
)
598 struct isl_basic_set
*bset1
, *bset2
;
600 filename
= get_filename(ctx
, name
, "polylib");
602 input
= fopen(filename
, "r");
605 bset1
= isl_basic_set_read_from_file(ctx
, input
);
606 bset2
= isl_basic_set_read_from_file(ctx
, input
);
608 bset1
= isl_basic_set_affine_hull(bset1
);
610 assert(isl_basic_set_is_equal(bset1
, bset2
) == 1);
612 isl_basic_set_free(bset1
);
613 isl_basic_set_free(bset2
);
619 void test_affine_hull(struct isl_ctx
*ctx
)
621 test_affine_hull_case(ctx
, "affine2");
622 test_affine_hull_case(ctx
, "affine");
623 test_affine_hull_case(ctx
, "affine3");
626 void test_convex_hull_case(struct isl_ctx
*ctx
, const char *name
)
630 struct isl_basic_set
*bset1
, *bset2
;
633 filename
= get_filename(ctx
, name
, "polylib");
635 input
= fopen(filename
, "r");
638 bset1
= isl_basic_set_read_from_file(ctx
, input
);
639 bset2
= isl_basic_set_read_from_file(ctx
, input
);
641 set
= isl_basic_set_union(bset1
, bset2
);
642 bset1
= isl_set_convex_hull(set
);
644 bset2
= isl_basic_set_read_from_file(ctx
, input
);
646 assert(isl_basic_set_is_equal(bset1
, bset2
) == 1);
648 isl_basic_set_free(bset1
);
649 isl_basic_set_free(bset2
);
655 void test_convex_hull_algo(struct isl_ctx
*ctx
, int convex
)
657 const char *str1
, *str2
;
658 isl_set
*set1
, *set2
;
659 int orig_convex
= ctx
->opt
->convex
;
660 ctx
->opt
->convex
= convex
;
662 test_convex_hull_case(ctx
, "convex0");
663 test_convex_hull_case(ctx
, "convex1");
664 test_convex_hull_case(ctx
, "convex2");
665 test_convex_hull_case(ctx
, "convex3");
666 test_convex_hull_case(ctx
, "convex4");
667 test_convex_hull_case(ctx
, "convex5");
668 test_convex_hull_case(ctx
, "convex6");
669 test_convex_hull_case(ctx
, "convex7");
670 test_convex_hull_case(ctx
, "convex8");
671 test_convex_hull_case(ctx
, "convex9");
672 test_convex_hull_case(ctx
, "convex10");
673 test_convex_hull_case(ctx
, "convex11");
674 test_convex_hull_case(ctx
, "convex12");
675 test_convex_hull_case(ctx
, "convex13");
676 test_convex_hull_case(ctx
, "convex14");
677 test_convex_hull_case(ctx
, "convex15");
679 str1
= "{ [i0, i1, i2] : (i2 = 1 and i0 = 0 and i1 >= 0) or "
680 "(i0 = 1 and i1 = 0 and i2 = 1) or "
681 "(i0 = 0 and i1 = 0 and i2 = 0) }";
682 str2
= "{ [i0, i1, i2] : i0 >= 0 and i2 >= i0 and i2 <= 1 and i1 >= 0 }";
683 set1
= isl_set_read_from_str(ctx
, str1
);
684 set2
= isl_set_read_from_str(ctx
, str2
);
685 set1
= isl_set_from_basic_set(isl_set_convex_hull(set1
));
686 assert(isl_set_is_equal(set1
, set2
));
690 ctx
->opt
->convex
= orig_convex
;
693 void test_convex_hull(struct isl_ctx
*ctx
)
695 test_convex_hull_algo(ctx
, ISL_CONVEX_HULL_FM
);
696 test_convex_hull_algo(ctx
, ISL_CONVEX_HULL_WRAP
);
699 void test_gist_case(struct isl_ctx
*ctx
, const char *name
)
703 struct isl_basic_set
*bset1
, *bset2
;
705 filename
= get_filename(ctx
, name
, "polylib");
707 input
= fopen(filename
, "r");
710 bset1
= isl_basic_set_read_from_file(ctx
, input
);
711 bset2
= isl_basic_set_read_from_file(ctx
, input
);
713 bset1
= isl_basic_set_gist(bset1
, bset2
);
715 bset2
= isl_basic_set_read_from_file(ctx
, input
);
717 assert(isl_basic_set_is_equal(bset1
, bset2
) == 1);
719 isl_basic_set_free(bset1
);
720 isl_basic_set_free(bset2
);
726 void test_gist(struct isl_ctx
*ctx
)
729 isl_basic_set
*bset1
, *bset2
;
731 test_gist_case(ctx
, "gist1");
733 str
= "[p0, p2, p3, p5, p6, p10] -> { [] : "
734 "exists (e0 = [(15 + p0 + 15p6 + 15p10)/16], e1 = [(p5)/8], "
735 "e2 = [(p6)/128], e3 = [(8p2 - p5)/128], "
736 "e4 = [(128p3 - p6)/4096]: 8e1 = p5 and 128e2 = p6 and "
737 "128e3 = 8p2 - p5 and 4096e4 = 128p3 - p6 and p2 >= 0 and "
738 "16e0 >= 16 + 16p6 + 15p10 and p2 <= 15 and p3 >= 0 and "
739 "p3 <= 31 and p6 >= 128p3 and p5 >= 8p2 and p10 >= 0 and "
740 "16e0 <= 15 + p0 + 15p6 + 15p10 and 16e0 >= p0 + 15p6 + 15p10 and "
741 "p10 <= 15 and p10 <= -1 + p0 - p6) }";
742 bset1
= isl_basic_set_read_from_str(ctx
, str
);
743 str
= "[p0, p2, p3, p5, p6, p10] -> { [] : exists (e0 = [(p5)/8], "
744 "e1 = [(p6)/128], e2 = [(8p2 - p5)/128], "
745 "e3 = [(128p3 - p6)/4096]: 8e0 = p5 and 128e1 = p6 and "
746 "128e2 = 8p2 - p5 and 4096e3 = 128p3 - p6 and p5 >= -7 and "
747 "p2 >= 0 and 8p2 <= -1 + p0 and p2 <= 15 and p3 >= 0 and "
748 "p3 <= 31 and 128p3 <= -1 + p0 and p6 >= -127 and "
749 "p5 <= -1 + p0 and p6 <= -1 + p0 and p6 >= 128p3 and "
750 "p0 >= 1 and p5 >= 8p2 and p10 >= 0 and p10 <= 15 ) }";
751 bset2
= isl_basic_set_read_from_str(ctx
, str
);
752 bset1
= isl_basic_set_gist(bset1
, bset2
);
753 assert(bset1
&& bset1
->n_div
== 0);
754 isl_basic_set_free(bset1
);
757 void test_coalesce_set(isl_ctx
*ctx
, const char *str
, int check_one
)
761 set
= isl_set_read_from_str(ctx
, str
);
762 set
= isl_set_coalesce(set
);
763 set2
= isl_set_read_from_str(ctx
, str
);
764 assert(isl_set_is_equal(set
, set2
));
766 assert(set
&& set
->n
== 1);
771 void test_coalesce(struct isl_ctx
*ctx
)
774 struct isl_set
*set
, *set2
;
775 struct isl_map
*map
, *map2
;
777 set
= isl_set_read_from_str(ctx
,
778 "{[x,y]: x >= 0 & x <= 10 & y >= 0 & y <= 10 or "
779 "y >= x & x >= 2 & 5 >= y }");
780 set
= isl_set_coalesce(set
);
781 assert(set
&& set
->n
== 1);
784 set
= isl_set_read_from_str(ctx
,
785 "{[x,y]: y >= 0 & 2x + y <= 30 & y <= 10 & x >= 0 or "
786 "x + y >= 10 & y <= x & x + y <= 20 & y >= 0}");
787 set
= isl_set_coalesce(set
);
788 assert(set
&& set
->n
== 1);
791 set
= isl_set_read_from_str(ctx
,
792 "{[x,y]: y >= 0 & 2x + y <= 30 & y <= 10 & x >= 0 or "
793 "x + y >= 10 & y <= x & x + y <= 19 & y >= 0}");
794 set
= isl_set_coalesce(set
);
795 assert(set
&& set
->n
== 2);
798 set
= isl_set_read_from_str(ctx
,
799 "{[x,y]: y >= 0 & x <= 5 & y <= x or "
800 "y >= 0 & x >= 6 & x <= 10 & y <= x}");
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 & x <= 5 & y <= x or "
807 "y >= 0 & x >= 7 & x <= 10 & y <= x}");
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 + 1 <= x}");
815 set
= isl_set_coalesce(set
);
816 assert(set
&& set
->n
== 2);
819 set
= isl_set_read_from_str(ctx
,
820 "{[x,y]: y >= 0 & x <= 5 & y <= x or "
821 "y >= 0 & x = 6 & y <= 6}");
822 set
= isl_set_coalesce(set
);
823 assert(set
&& set
->n
== 1);
826 set
= isl_set_read_from_str(ctx
,
827 "{[x,y]: y >= 0 & x <= 5 & y <= x or "
828 "y >= 0 & x = 7 & y <= 6}");
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 <= 5}");
836 set
= isl_set_coalesce(set
);
837 assert(set
&& set
->n
== 1);
838 set2
= isl_set_read_from_str(ctx
,
839 "{[x,y]: y >= 0 & x <= 5 & y <= x or "
840 "y >= 0 & x = 6 & y <= 5}");
841 assert(isl_set_is_equal(set
, set2
));
845 set
= isl_set_read_from_str(ctx
,
846 "{[x,y]: y >= 0 & x <= 5 & y <= x or "
847 "y >= 0 & x = 6 & y <= 7}");
848 set
= isl_set_coalesce(set
);
849 assert(set
&& set
->n
== 2);
852 set
= isl_set_read_from_str(ctx
,
853 "[n] -> { [i] : i = 1 and n >= 2 or 2 <= i and i <= n }");
854 set
= isl_set_coalesce(set
);
855 assert(set
&& set
->n
== 1);
856 set2
= isl_set_read_from_str(ctx
,
857 "[n] -> { [i] : i = 1 and n >= 2 or 2 <= i and i <= n }");
858 assert(isl_set_is_equal(set
, set2
));
862 set
= isl_set_read_from_str(ctx
,
863 "{[x,y] : x >= 0 and y >= 0 or 0 <= y and y <= 5 and x = -1}");
864 set
= isl_set_coalesce(set
);
865 set2
= isl_set_read_from_str(ctx
,
866 "{[x,y] : x >= 0 and y >= 0 or 0 <= y and y <= 5 and x = -1}");
867 assert(isl_set_is_equal(set
, set2
));
871 set
= isl_set_read_from_str(ctx
,
872 "[n] -> { [i] : 1 <= i and i <= n - 1 or "
873 "2 <= i and i <= n }");
874 set
= isl_set_coalesce(set
);
875 assert(set
&& set
->n
== 1);
876 set2
= isl_set_read_from_str(ctx
,
877 "[n] -> { [i] : 1 <= i and i <= n - 1 or "
878 "2 <= i and i <= n }");
879 assert(isl_set_is_equal(set
, set2
));
883 map
= isl_map_read_from_str(ctx
,
884 "[n] -> { [i0] -> [o0] : exists (e0 = [(i0)/4], e1 = [(o0)/4], "
885 "e2 = [(n)/2], e3 = [(-2 + i0)/4], e4 = [(-2 + o0)/4], "
886 "e5 = [(-2n + i0)/4]: 2e2 = n and 4e3 = -2 + i0 and "
887 "4e4 = -2 + o0 and i0 >= 8 + 2n and o0 >= 2 + i0 and "
888 "o0 <= 56 + 2n and o0 <= -12 + 4n and i0 <= 57 + 2n and "
889 "i0 <= -11 + 4n and o0 >= 6 + 2n and 4e0 <= i0 and "
890 "4e0 >= -3 + i0 and 4e1 <= o0 and 4e1 >= -3 + o0 and "
891 "4e5 <= -2n + i0 and 4e5 >= -3 - 2n + i0);"
892 "[i0] -> [o0] : exists (e0 = [(i0)/4], e1 = [(o0)/4], "
893 "e2 = [(n)/2], e3 = [(-2 + i0)/4], e4 = [(-2 + o0)/4], "
894 "e5 = [(-2n + i0)/4]: 2e2 = n and 4e3 = -2 + i0 and "
895 "4e4 = -2 + o0 and 2e0 >= 3 + n and e0 <= -4 + n and "
896 "2e0 <= 27 + n and e1 <= -4 + n and 2e1 <= 27 + n and "
897 "2e1 >= 2 + n and e1 >= 1 + e0 and i0 >= 7 + 2n and "
898 "i0 <= -11 + 4n and i0 <= 57 + 2n and 4e0 <= -2 + i0 and "
899 "4e0 >= -3 + i0 and o0 >= 6 + 2n and o0 <= -11 + 4n and "
900 "o0 <= 57 + 2n and 4e1 <= -2 + o0 and 4e1 >= -3 + o0 and "
901 "4e5 <= -2n + i0 and 4e5 >= -3 - 2n + i0 ) }");
902 map
= isl_map_coalesce(map
);
903 map2
= isl_map_read_from_str(ctx
,
904 "[n] -> { [i0] -> [o0] : exists (e0 = [(i0)/4], e1 = [(o0)/4], "
905 "e2 = [(n)/2], e3 = [(-2 + i0)/4], e4 = [(-2 + o0)/4], "
906 "e5 = [(-2n + i0)/4]: 2e2 = n and 4e3 = -2 + i0 and "
907 "4e4 = -2 + o0 and i0 >= 8 + 2n and o0 >= 2 + i0 and "
908 "o0 <= 56 + 2n and o0 <= -12 + 4n and i0 <= 57 + 2n and "
909 "i0 <= -11 + 4n and o0 >= 6 + 2n and 4e0 <= i0 and "
910 "4e0 >= -3 + i0 and 4e1 <= o0 and 4e1 >= -3 + o0 and "
911 "4e5 <= -2n + i0 and 4e5 >= -3 - 2n + i0);"
912 "[i0] -> [o0] : exists (e0 = [(i0)/4], e1 = [(o0)/4], "
913 "e2 = [(n)/2], e3 = [(-2 + i0)/4], e4 = [(-2 + o0)/4], "
914 "e5 = [(-2n + i0)/4]: 2e2 = n and 4e3 = -2 + i0 and "
915 "4e4 = -2 + o0 and 2e0 >= 3 + n and e0 <= -4 + n and "
916 "2e0 <= 27 + n and e1 <= -4 + n and 2e1 <= 27 + n and "
917 "2e1 >= 2 + n and e1 >= 1 + e0 and i0 >= 7 + 2n and "
918 "i0 <= -11 + 4n and i0 <= 57 + 2n and 4e0 <= -2 + i0 and "
919 "4e0 >= -3 + i0 and o0 >= 6 + 2n and o0 <= -11 + 4n and "
920 "o0 <= 57 + 2n and 4e1 <= -2 + o0 and 4e1 >= -3 + o0 and "
921 "4e5 <= -2n + i0 and 4e5 >= -3 - 2n + i0 ) }");
922 assert(isl_map_is_equal(map
, map2
));
926 str
= "[n, m] -> { [] -> [o0, o2, o3] : (o3 = 1 and o0 >= 1 + m and "
927 "o0 <= n + m and o2 <= m and o0 >= 2 + n and o2 >= 3) or "
928 "(o0 >= 2 + n and o0 >= 1 + m and o0 <= n + m and n >= 1 and "
929 "o3 <= -1 + o2 and o3 >= 1 - m + o2 and o3 >= 2 and o3 <= n) }";
930 map
= isl_map_read_from_str(ctx
, str
);
931 map
= isl_map_coalesce(map
);
932 map2
= isl_map_read_from_str(ctx
, str
);
933 assert(isl_map_is_equal(map
, map2
));
937 str
= "[M, N] -> { [i0, i1, i2, i3, i4, i5, i6] -> "
938 "[o0, o1, o2, o3, o4, o5, o6] : "
939 "(o6 <= -4 + 2M - 2N + i0 + i1 - i2 + i6 - o0 - o1 + o2 and "
940 "o3 <= -2 + i3 and o6 >= 2 + i0 + i3 + i6 - o0 - o3 and "
941 "o6 >= 2 - M + N + i3 + i4 + i6 - o3 - o4 and o0 <= -1 + i0 and "
942 "o4 >= 4 - 3M + 3N - i0 - i1 + i2 + 2i3 + i4 + o0 + o1 - o2 - 2o3 "
943 "and o6 <= -3 + 2M - 2N + i3 + i4 - i5 + i6 - o3 - o4 + o5 and "
944 "2o6 <= -5 + 5M - 5N + 2i0 + i1 - i2 - i5 + 2i6 - 2o0 - o1 + o2 + o5 "
945 "and o6 >= 2i0 + i1 + i6 - 2o0 - o1 and "
946 "3o6 <= -5 + 4M - 4N + 2i0 + i1 - i2 + 2i3 + i4 - i5 + 3i6 "
947 "- 2o0 - o1 + o2 - 2o3 - o4 + o5) or "
948 "(N >= 2 and o3 <= -1 + i3 and o0 <= -1 + i0 and "
949 "o6 >= i3 + i6 - o3 and M >= 0 and "
950 "2o6 >= 1 + i0 + i3 + 2i6 - o0 - o3 and "
951 "o6 >= 1 - M + i0 + i6 - o0 and N >= 2M and o6 >= i0 + i6 - o0) }";
952 map
= isl_map_read_from_str(ctx
, str
);
953 map
= isl_map_coalesce(map
);
954 map2
= isl_map_read_from_str(ctx
, str
);
955 assert(isl_map_is_equal(map
, map2
));
959 str
= "[M, N] -> { [] -> [o0] : (o0 = 0 and M >= 1 and N >= 2) or "
960 "(o0 = 0 and M >= 1 and N >= 2M and N >= 2 + M) or "
961 "(o0 = 0 and M >= 2 and N >= 3) or "
962 "(M = 0 and o0 = 0 and N >= 3) }";
963 map
= isl_map_read_from_str(ctx
, str
);
964 map
= isl_map_coalesce(map
);
965 map2
= isl_map_read_from_str(ctx
, str
);
966 assert(isl_map_is_equal(map
, map2
));
970 str
= "{ [i0, i1, i2, i3] : (i1 = 10i0 and i0 >= 1 and 10i0 <= 100 and "
971 "i3 <= 9 + 10 i2 and i3 >= 1 + 10i2 and i3 >= 0) or "
972 "(i1 <= 9 + 10i0 and i1 >= 1 + 10i0 and i2 >= 0 and "
973 "i0 >= 0 and i1 <= 100 and i3 <= 9 + 10i2 and i3 >= 1 + 10i2) }";
974 map
= isl_map_read_from_str(ctx
, str
);
975 map
= isl_map_coalesce(map
);
976 map2
= isl_map_read_from_str(ctx
, str
);
977 assert(isl_map_is_equal(map
, map2
));
981 test_coalesce_set(ctx
,
982 "[M] -> { [i1] : (i1 >= 2 and i1 <= M) or "
983 "(i1 = M and M >= 1) }", 0);
984 test_coalesce_set(ctx
,
985 "{[x,y] : x,y >= 0; [x,y] : 10 <= x <= 20 and y >= -1 }", 0);
986 test_coalesce_set(ctx
,
987 "{ [x, y] : (x >= 1 and y >= 1 and x <= 2 and y <= 2) or "
988 "(y = 3 and x = 1) }", 1);
989 test_coalesce_set(ctx
,
990 "[M] -> { [i0, i1, i2, i3, i4] : (i1 >= 3 and i4 >= 2 + i2 and "
991 "i2 >= 2 and i0 >= 2 and i3 >= 1 + i2 and i0 <= M and "
992 "i1 <= M and i3 <= M and i4 <= M) or "
993 "(i1 >= 2 and i4 >= 1 + i2 and i2 >= 2 and i0 >= 2 and "
994 "i3 >= 1 + i2 and i0 <= M and i1 <= -1 + M and i3 <= M and "
995 "i4 <= -1 + M) }", 1);
996 test_coalesce_set(ctx
,
997 "{ [x, y] : (x >= 0 and y >= 0 and x <= 10 and y <= 10) or "
998 "(x >= 1 and y >= 1 and x <= 11 and y <= 11) }", 1);
999 test_coalesce_set(ctx
,
1000 "{[x,y,z] : y + 2 >= 0 and x - y + 1 >= 0 and "
1001 "-x - y + 1 >= 0 and -3 <= z <= 3;"
1002 "[x,y,z] : -x+z + 20 >= 0 and -x-z + 20 >= 0 and "
1003 "x-z + 20 >= 0 and x+z + 20 >= 0 and -10 <= y <= 0}", 1);
1004 test_coalesce_set(ctx
,
1005 "{[x,y] : 0 <= x,y <= 10; [5,y]: 4 <=y <= 11}", 1);
1006 test_coalesce_set(ctx
, "{[x,0] : x >= 0; [x,1] : x <= 20}", 0);
1007 test_coalesce_set(ctx
,
1008 "{[x,0,0] : -5 <= x <= 5; [0,y,1] : -5 <= y <= 5 }", 1);
1009 test_coalesce_set(ctx
, "{ [x, 1 - x] : 0 <= x <= 1; [0,0] }", 1);
1010 test_coalesce_set(ctx
, "{ [0,0]; [i,i] : 1 <= i <= 10 }", 1);
1011 test_coalesce_set(ctx
, "{ [0,0]; [i,j] : 1 <= i,j <= 10 }", 0);
1012 test_coalesce_set(ctx
, "{ [0,0]; [i,2i] : 1 <= i <= 10 }", 1);
1013 test_coalesce_set(ctx
, "{ [0,0]; [i,2i] : 2 <= i <= 10 }", 0);
1014 test_coalesce_set(ctx
, "{ [1,0]; [i,2i] : 1 <= i <= 10 }", 0);
1015 test_coalesce_set(ctx
, "{ [0,1]; [i,2i] : 1 <= i <= 10 }", 0);
1018 void test_closure(struct isl_ctx
*ctx
)
1022 isl_map
*up
, *right
;
1023 isl_map
*map
, *map2
;
1026 /* COCOA example 1 */
1027 map
= isl_map_read_from_str(ctx
,
1028 "[n] -> { [i,j] -> [i2,j2] : i2 = i + 1 and j2 = j + 1 and "
1029 "1 <= i and i < n and 1 <= j and j < n or "
1030 "i2 = i + 1 and j2 = j - 1 and "
1031 "1 <= i and i < n and 2 <= j and j <= n }");
1032 map
= isl_map_power(map
, &exact
);
1036 /* COCOA example 1 */
1037 map
= isl_map_read_from_str(ctx
,
1038 "[n] -> { [i,j] -> [i2,j2] : i2 = i + 1 and j2 = j + 1 and "
1039 "1 <= i and i < n and 1 <= j and j < n or "
1040 "i2 = i + 1 and j2 = j - 1 and "
1041 "1 <= i and i < n and 2 <= j and j <= n }");
1042 map
= isl_map_transitive_closure(map
, &exact
);
1044 map2
= isl_map_read_from_str(ctx
,
1045 "[n] -> { [i,j] -> [i2,j2] : exists (k1,k2,k : "
1046 "1 <= i and i < n and 1 <= j and j <= n and "
1047 "2 <= i2 and i2 <= n and 1 <= j2 and j2 <= n and "
1048 "i2 = i + k1 + k2 and j2 = j + k1 - k2 and "
1049 "k1 >= 0 and k2 >= 0 and k1 + k2 = k and k >= 1 )}");
1050 assert(isl_map_is_equal(map
, map2
));
1054 map
= isl_map_read_from_str(ctx
,
1055 "[n] -> { [x] -> [y] : y = x + 1 and 0 <= x and x <= n and "
1056 " 0 <= y and y <= n }");
1057 map
= isl_map_transitive_closure(map
, &exact
);
1058 map2
= isl_map_read_from_str(ctx
,
1059 "[n] -> { [x] -> [y] : y > x and 0 <= x and x <= n and "
1060 " 0 <= y and y <= n }");
1061 assert(isl_map_is_equal(map
, map2
));
1065 /* COCOA example 2 */
1066 map
= isl_map_read_from_str(ctx
,
1067 "[n] -> { [i,j] -> [i2,j2] : i2 = i + 2 and j2 = j + 2 and "
1068 "1 <= i and i < n - 1 and 1 <= j and j < n - 1 or "
1069 "i2 = i + 2 and j2 = j - 2 and "
1070 "1 <= i and i < n - 1 and 3 <= j and j <= n }");
1071 map
= isl_map_transitive_closure(map
, &exact
);
1073 map2
= isl_map_read_from_str(ctx
,
1074 "[n] -> { [i,j] -> [i2,j2] : exists (k1,k2,k : "
1075 "1 <= i and i < n - 1 and 1 <= j and j <= n and "
1076 "3 <= i2 and i2 <= n and 1 <= j2 and j2 <= n and "
1077 "i2 = i + 2 k1 + 2 k2 and j2 = j + 2 k1 - 2 k2 and "
1078 "k1 >= 0 and k2 >= 0 and k1 + k2 = k and k >= 1) }");
1079 assert(isl_map_is_equal(map
, map2
));
1083 /* COCOA Fig.2 left */
1084 map
= isl_map_read_from_str(ctx
,
1085 "[n] -> { [i,j] -> [i2,j2] : i2 = i + 2 and j2 = j and "
1086 "i <= 2 j - 3 and i <= n - 2 and j <= 2 i - 1 and "
1088 "i2 = i and j2 = j + 2 and i <= 2 j - 1 and i <= n and "
1089 "j <= 2 i - 3 and j <= n - 2 or "
1090 "i2 = i + 1 and j2 = j + 1 and i <= 2 j - 1 and "
1091 "i <= n - 1 and j <= 2 i - 1 and j <= n - 1 }");
1092 map
= isl_map_transitive_closure(map
, &exact
);
1096 /* COCOA Fig.2 right */
1097 map
= isl_map_read_from_str(ctx
,
1098 "[n] -> { [i,j] -> [i2,j2] : i2 = i + 3 and j2 = j and "
1099 "i <= 2 j - 4 and i <= n - 3 and j <= 2 i - 1 and "
1101 "i2 = i and j2 = j + 3 and i <= 2 j - 1 and i <= n and "
1102 "j <= 2 i - 4 and j <= n - 3 or "
1103 "i2 = i + 1 and j2 = j + 1 and i <= 2 j - 1 and "
1104 "i <= n - 1 and j <= 2 i - 1 and j <= n - 1 }");
1105 map
= isl_map_power(map
, &exact
);
1109 /* COCOA Fig.2 right */
1110 map
= isl_map_read_from_str(ctx
,
1111 "[n] -> { [i,j] -> [i2,j2] : i2 = i + 3 and j2 = j and "
1112 "i <= 2 j - 4 and i <= n - 3 and j <= 2 i - 1 and "
1114 "i2 = i and j2 = j + 3 and i <= 2 j - 1 and i <= n and "
1115 "j <= 2 i - 4 and j <= n - 3 or "
1116 "i2 = i + 1 and j2 = j + 1 and i <= 2 j - 1 and "
1117 "i <= n - 1 and j <= 2 i - 1 and j <= n - 1 }");
1118 map
= isl_map_transitive_closure(map
, &exact
);
1120 map2
= isl_map_read_from_str(ctx
,
1121 "[n] -> { [i,j] -> [i2,j2] : exists (k1,k2,k3,k : "
1122 "i <= 2 j - 1 and i <= n and j <= 2 i - 1 and "
1123 "j <= n and 3 + i + 2 j <= 3 n and "
1124 "3 + 2 i + j <= 3n and i2 <= 2 j2 -1 and i2 <= n and "
1125 "i2 <= 3 j2 - 4 and j2 <= 2 i2 -1 and j2 <= n and "
1126 "13 + 4 j2 <= 11 i2 and i2 = i + 3 k1 + k3 and "
1127 "j2 = j + 3 k2 + k3 and k1 >= 0 and k2 >= 0 and "
1128 "k3 >= 0 and k1 + k2 + k3 = k and k > 0) }");
1129 assert(isl_map_is_equal(map
, map2
));
1133 /* COCOA Fig.1 right */
1134 dom
= isl_set_read_from_str(ctx
,
1135 "{ [x,y] : x >= 0 and -2 x + 3 y >= 0 and x <= 3 and "
1136 "2 x - 3 y + 3 >= 0 }");
1137 right
= isl_map_read_from_str(ctx
,
1138 "{ [x,y] -> [x2,y2] : x2 = x + 1 and y2 = y }");
1139 up
= isl_map_read_from_str(ctx
,
1140 "{ [x,y] -> [x2,y2] : x2 = x and y2 = y + 1 }");
1141 right
= isl_map_intersect_domain(right
, isl_set_copy(dom
));
1142 right
= isl_map_intersect_range(right
, isl_set_copy(dom
));
1143 up
= isl_map_intersect_domain(up
, isl_set_copy(dom
));
1144 up
= isl_map_intersect_range(up
, dom
);
1145 map
= isl_map_union(up
, right
);
1146 map
= isl_map_transitive_closure(map
, &exact
);
1148 map2
= isl_map_read_from_str(ctx
,
1149 "{ [0,0] -> [0,1]; [0,0] -> [1,1]; [0,1] -> [1,1]; "
1150 " [2,2] -> [3,2]; [2,2] -> [3,3]; [3,2] -> [3,3] }");
1151 assert(isl_map_is_equal(map
, map2
));
1155 /* COCOA Theorem 1 counter example */
1156 map
= isl_map_read_from_str(ctx
,
1157 "{ [i,j] -> [i2,j2] : i = 0 and 0 <= j and j <= 1 and "
1158 "i2 = 1 and j2 = j or "
1159 "i = 0 and j = 0 and i2 = 0 and j2 = 1 }");
1160 map
= isl_map_transitive_closure(map
, &exact
);
1164 map
= isl_map_read_from_str(ctx
,
1165 "[m,n] -> { [i,j] -> [i2,j2] : i2 = i and j2 = j + 2 and "
1166 "1 <= i,i2 <= n and 1 <= j,j2 <= m or "
1167 "i2 = i + 1 and 3 <= j2 - j <= 4 and "
1168 "1 <= i,i2 <= n and 1 <= j,j2 <= m }");
1169 map
= isl_map_transitive_closure(map
, &exact
);
1173 /* Kelly et al 1996, fig 12 */
1174 map
= isl_map_read_from_str(ctx
,
1175 "[n] -> { [i,j] -> [i2,j2] : i2 = i and j2 = j + 1 and "
1176 "1 <= i,j,j+1 <= n or "
1177 "j = n and j2 = 1 and i2 = i + 1 and "
1178 "1 <= i,i+1 <= n }");
1179 map
= isl_map_transitive_closure(map
, &exact
);
1181 map2
= isl_map_read_from_str(ctx
,
1182 "[n] -> { [i,j] -> [i2,j2] : 1 <= j < j2 <= n and "
1183 "1 <= i <= n and i = i2 or "
1184 "1 <= i < i2 <= n and 1 <= j <= n and "
1186 assert(isl_map_is_equal(map
, map2
));
1190 /* Omega's closure4 */
1191 map
= isl_map_read_from_str(ctx
,
1192 "[m,n] -> { [x,y] -> [x2,y2] : x2 = x and y2 = y + 1 and "
1193 "1 <= x,y <= 10 or "
1194 "x2 = x + 1 and y2 = y and "
1195 "1 <= x <= 20 && 5 <= y <= 15 }");
1196 map
= isl_map_transitive_closure(map
, &exact
);
1200 map
= isl_map_read_from_str(ctx
,
1201 "[n] -> { [x] -> [y]: 1 <= n <= y - x <= 10 }");
1202 map
= isl_map_transitive_closure(map
, &exact
);
1204 map2
= isl_map_read_from_str(ctx
,
1205 "[n] -> { [x] -> [y] : 1 <= n <= 10 and y >= n + x }");
1206 assert(isl_map_is_equal(map
, map2
));
1210 str
= "[n, m] -> { [i0, i1, i2, i3] -> [o0, o1, o2, o3] : "
1211 "i3 = 1 and o0 = i0 and o1 = -1 + i1 and o2 = -1 + i2 and "
1212 "o3 = -2 + i2 and i1 <= -1 + i0 and i1 >= 1 - m + i0 and "
1213 "i1 >= 2 and i1 <= n and i2 >= 3 and i2 <= 1 + n and i2 <= m }";
1214 map
= isl_map_read_from_str(ctx
, str
);
1215 map
= isl_map_transitive_closure(map
, &exact
);
1217 map2
= isl_map_read_from_str(ctx
, str
);
1218 assert(isl_map_is_equal(map
, map2
));
1222 str
= "{[0] -> [1]; [2] -> [3]}";
1223 map
= isl_map_read_from_str(ctx
, str
);
1224 map
= isl_map_transitive_closure(map
, &exact
);
1226 map2
= isl_map_read_from_str(ctx
, str
);
1227 assert(isl_map_is_equal(map
, map2
));
1231 str
= "[n] -> { [[i0, i1, 1, 0, i0] -> [i5, 1]] -> "
1232 "[[i0, -1 + i1, 2, 0, i0] -> [-1 + i5, 2]] : "
1233 "exists (e0 = [(3 - n)/3]: i5 >= 2 and i1 >= 2 and "
1234 "3i0 <= -1 + n and i1 <= -1 + n and i5 <= -1 + n and "
1235 "3e0 >= 1 - n and 3e0 <= 2 - n and 3i0 >= -2 + n); "
1236 "[[i0, i1, 2, 0, i0] -> [i5, 1]] -> "
1237 "[[i0, i1, 1, 0, i0] -> [-1 + i5, 2]] : "
1238 "exists (e0 = [(3 - n)/3]: i5 >= 2 and i1 >= 1 and "
1239 "3i0 <= -1 + n and i1 <= -1 + n and i5 <= -1 + n and "
1240 "3e0 >= 1 - n and 3e0 <= 2 - n and 3i0 >= -2 + n); "
1241 "[[i0, i1, 1, 0, i0] -> [i5, 2]] -> "
1242 "[[i0, -1 + i1, 2, 0, i0] -> [i5, 1]] : "
1243 "exists (e0 = [(3 - n)/3]: i1 >= 2 and i5 >= 1 and "
1244 "3i0 <= -1 + n and i1 <= -1 + n and i5 <= -1 + n and "
1245 "3e0 >= 1 - n and 3e0 <= 2 - n and 3i0 >= -2 + n); "
1246 "[[i0, i1, 2, 0, i0] -> [i5, 2]] -> "
1247 "[[i0, i1, 1, 0, i0] -> [i5, 1]] : "
1248 "exists (e0 = [(3 - n)/3]: i5 >= 1 and i1 >= 1 and "
1249 "3i0 <= -1 + n and i1 <= -1 + n and i5 <= -1 + n and "
1250 "3e0 >= 1 - n and 3e0 <= 2 - n and 3i0 >= -2 + n) }";
1251 map
= isl_map_read_from_str(ctx
, str
);
1252 map
= isl_map_transitive_closure(map
, NULL
);
1257 void test_lex(struct isl_ctx
*ctx
)
1262 dim
= isl_space_set_alloc(ctx
, 0, 0);
1263 map
= isl_map_lex_le(dim
);
1264 assert(!isl_map_is_empty(map
));
1268 static int consume_lexmin(__isl_take isl_basic_set
*dom
,
1269 __isl_take isl_aff_list
*list
, void *user
)
1272 isl_basic_map
*bmap
;
1273 isl_map
**map
= user
;
1275 dim
= isl_basic_set_get_space(dom
);
1276 bmap
= isl_basic_map_from_aff_list(dim
, list
);
1277 bmap
= isl_basic_map_intersect_domain(bmap
, dom
);
1279 *map
= isl_map_union(*map
, isl_map_from_basic_map(bmap
));
1284 void test_lexmin(struct isl_ctx
*ctx
)
1287 isl_basic_map
*bmap
;
1288 isl_map
*map
, *map2
;
1292 str
= "[p0, p1] -> { [] -> [] : "
1293 "exists (e0 = [(2p1)/3], e1, e2, e3 = [(3 - p1 + 3e0)/3], "
1294 "e4 = [(p1)/3], e5 = [(p1 + 3e4)/3]: "
1295 "3e0 >= -2 + 2p1 and 3e0 >= p1 and 3e3 >= 1 - p1 + 3e0 and "
1296 "3e0 <= 2p1 and 3e3 >= -2 + p1 and 3e3 <= -1 + p1 and p1 >= 3 and "
1297 "3e5 >= -2 + 2p1 and 3e5 >= p1 and 3e5 <= -1 + p1 + 3e4 and "
1298 "3e4 <= p1 and 3e4 >= -2 + p1 and e3 <= -1 + e0 and "
1299 "3e4 >= 6 - p1 + 3e1 and 3e1 >= p1 and 3e5 >= -2 + p1 + 3e4 and "
1300 "2e4 >= 3 - p1 + 2e1 and e4 <= e1 and 3e3 <= 2 - p1 + 3e0 and "
1301 "e5 >= 1 + e1 and 3e4 >= 6 - 2p1 + 3e1 and "
1302 "p0 >= 2 and p1 >= p0 and 3e2 >= p1 and 3e4 >= 6 - p1 + 3e2 and "
1303 "e2 <= e1 and e3 >= 1 and e4 <= e2) }";
1304 map
= isl_map_read_from_str(ctx
, str
);
1305 map
= isl_map_lexmin(map
);
1308 str
= "[C] -> { [obj,a,b,c] : obj <= 38 a + 7 b + 10 c and "
1309 "a + b <= 1 and c <= 10 b and c <= C and a,b,c,C >= 0 }";
1310 set
= isl_set_read_from_str(ctx
, str
);
1311 set
= isl_set_lexmax(set
);
1312 str
= "[C] -> { [obj,a,b,c] : C = 8 }";
1313 set2
= isl_set_read_from_str(ctx
, str
);
1314 set
= isl_set_intersect(set
, set2
);
1315 assert(!isl_set_is_empty(set
));
1318 str
= "{ [x] -> [y] : x <= y <= 10; [x] -> [5] : -8 <= x <= 8 }";
1319 map
= isl_map_read_from_str(ctx
, str
);
1320 map
= isl_map_lexmin(map
);
1321 str
= "{ [x] -> [5] : 6 <= x <= 8; "
1322 "[x] -> [x] : x <= 5 or (9 <= x <= 10) }";
1323 map2
= isl_map_read_from_str(ctx
, str
);
1324 assert(isl_map_is_equal(map
, map2
));
1328 str
= "{ [x] -> [y] : 4y = x or 4y = -1 + x or 4y = -2 + x }";
1329 map
= isl_map_read_from_str(ctx
, str
);
1330 map2
= isl_map_copy(map
);
1331 map
= isl_map_lexmin(map
);
1332 assert(isl_map_is_equal(map
, map2
));
1336 str
= "{ [x] -> [y] : x = 4y; [x] -> [y] : x = 2y }";
1337 map
= isl_map_read_from_str(ctx
, str
);
1338 map
= isl_map_lexmin(map
);
1339 str
= "{ [x] -> [y] : (4y = x and x >= 0) or "
1340 "(exists (e0 = [(x)/4], e1 = [(-2 + x)/4]: 2y = x and "
1341 "4e1 = -2 + x and 4e0 <= -1 + x and 4e0 >= -3 + x)) or "
1342 "(exists (e0 = [(x)/4]: 2y = x and 4e0 = x and x <= -4)) }";
1343 map2
= isl_map_read_from_str(ctx
, str
);
1344 assert(isl_map_is_equal(map
, map2
));
1348 str
= "{ [i] -> [i', j] : j = i - 8i' and i' >= 0 and i' <= 7 and "
1349 " 8i' <= i and 8i' >= -7 + i }";
1350 bmap
= isl_basic_map_read_from_str(ctx
, str
);
1351 map2
= isl_map_empty(isl_basic_map_get_space(bmap
));
1352 isl_basic_map_foreach_lexmin(bmap
, &consume_lexmin
, &map2
);
1353 map
= isl_map_from_basic_map(bmap
);
1354 assert(isl_map_is_equal(map
, map2
));
1364 static int collect_must_may(__isl_take isl_map
*dep
, int must
,
1365 void *dep_user
, void *user
)
1367 struct must_may
*mm
= (struct must_may
*)user
;
1370 mm
->must
= isl_map_union(mm
->must
, dep
);
1372 mm
->may
= isl_map_union(mm
->may
, dep
);
1377 static int common_space(void *first
, void *second
)
1379 int depth
= *(int *)first
;
1383 static int map_is_equal(__isl_keep isl_map
*map
, const char *str
)
1391 map2
= isl_map_read_from_str(map
->ctx
, str
);
1392 equal
= isl_map_is_equal(map
, map2
);
1398 void test_dep(struct isl_ctx
*ctx
)
1403 isl_access_info
*ai
;
1410 str
= "{ [2,i,0] -> [i] : 0 <= i <= 10 }";
1411 map
= isl_map_read_from_str(ctx
, str
);
1412 ai
= isl_access_info_alloc(map
, &depth
, &common_space
, 2);
1414 str
= "{ [0,i,0] -> [i] : 0 <= i <= 10 }";
1415 map
= isl_map_read_from_str(ctx
, str
);
1416 ai
= isl_access_info_add_source(ai
, map
, 1, &depth
);
1418 str
= "{ [1,i,0] -> [5] : 0 <= i <= 10 }";
1419 map
= isl_map_read_from_str(ctx
, str
);
1420 ai
= isl_access_info_add_source(ai
, map
, 1, &depth
);
1422 flow
= isl_access_info_compute_flow(ai
);
1423 dim
= isl_space_alloc(ctx
, 0, 3, 3);
1424 mm
.must
= isl_map_empty(isl_space_copy(dim
));
1425 mm
.may
= isl_map_empty(dim
);
1427 isl_flow_foreach(flow
, collect_must_may
, &mm
);
1429 str
= "{ [0,i,0] -> [2,i,0] : (0 <= i <= 4) or (6 <= i <= 10); "
1430 " [1,10,0] -> [2,5,0] }";
1431 assert(map_is_equal(mm
.must
, str
));
1432 str
= "{ [i,j,k] -> [l,m,n] : 1 = 0 }";
1433 assert(map_is_equal(mm
.may
, str
));
1435 isl_map_free(mm
.must
);
1436 isl_map_free(mm
.may
);
1437 isl_flow_free(flow
);
1440 str
= "{ [2,i,0] -> [i] : 0 <= i <= 10 }";
1441 map
= isl_map_read_from_str(ctx
, str
);
1442 ai
= isl_access_info_alloc(map
, &depth
, &common_space
, 2);
1444 str
= "{ [0,i,0] -> [i] : 0 <= i <= 10 }";
1445 map
= isl_map_read_from_str(ctx
, str
);
1446 ai
= isl_access_info_add_source(ai
, map
, 1, &depth
);
1448 str
= "{ [1,i,0] -> [5] : 0 <= i <= 10 }";
1449 map
= isl_map_read_from_str(ctx
, str
);
1450 ai
= isl_access_info_add_source(ai
, map
, 0, &depth
);
1452 flow
= isl_access_info_compute_flow(ai
);
1453 dim
= isl_space_alloc(ctx
, 0, 3, 3);
1454 mm
.must
= isl_map_empty(isl_space_copy(dim
));
1455 mm
.may
= isl_map_empty(dim
);
1457 isl_flow_foreach(flow
, collect_must_may
, &mm
);
1459 str
= "{ [0,i,0] -> [2,i,0] : (0 <= i <= 4) or (6 <= i <= 10) }";
1460 assert(map_is_equal(mm
.must
, str
));
1461 str
= "{ [0,5,0] -> [2,5,0]; [1,i,0] -> [2,5,0] : 0 <= i <= 10 }";
1462 assert(map_is_equal(mm
.may
, str
));
1464 isl_map_free(mm
.must
);
1465 isl_map_free(mm
.may
);
1466 isl_flow_free(flow
);
1469 str
= "{ [2,i,0] -> [i] : 0 <= i <= 10 }";
1470 map
= isl_map_read_from_str(ctx
, str
);
1471 ai
= isl_access_info_alloc(map
, &depth
, &common_space
, 2);
1473 str
= "{ [0,i,0] -> [i] : 0 <= i <= 10 }";
1474 map
= isl_map_read_from_str(ctx
, str
);
1475 ai
= isl_access_info_add_source(ai
, map
, 0, &depth
);
1477 str
= "{ [1,i,0] -> [5] : 0 <= i <= 10 }";
1478 map
= isl_map_read_from_str(ctx
, str
);
1479 ai
= isl_access_info_add_source(ai
, map
, 0, &depth
);
1481 flow
= isl_access_info_compute_flow(ai
);
1482 dim
= isl_space_alloc(ctx
, 0, 3, 3);
1483 mm
.must
= isl_map_empty(isl_space_copy(dim
));
1484 mm
.may
= isl_map_empty(dim
);
1486 isl_flow_foreach(flow
, collect_must_may
, &mm
);
1488 str
= "{ [0,i,0] -> [2,i,0] : 0 <= i <= 10; "
1489 " [1,i,0] -> [2,5,0] : 0 <= i <= 10 }";
1490 assert(map_is_equal(mm
.may
, str
));
1491 str
= "{ [i,j,k] -> [l,m,n] : 1 = 0 }";
1492 assert(map_is_equal(mm
.must
, str
));
1494 isl_map_free(mm
.must
);
1495 isl_map_free(mm
.may
);
1496 isl_flow_free(flow
);
1499 str
= "{ [0,i,2] -> [i] : 0 <= i <= 10 }";
1500 map
= isl_map_read_from_str(ctx
, str
);
1501 ai
= isl_access_info_alloc(map
, &depth
, &common_space
, 2);
1503 str
= "{ [0,i,0] -> [i] : 0 <= i <= 10 }";
1504 map
= isl_map_read_from_str(ctx
, str
);
1505 ai
= isl_access_info_add_source(ai
, map
, 0, &depth
);
1507 str
= "{ [0,i,1] -> [5] : 0 <= i <= 10 }";
1508 map
= isl_map_read_from_str(ctx
, str
);
1509 ai
= isl_access_info_add_source(ai
, map
, 0, &depth
);
1511 flow
= isl_access_info_compute_flow(ai
);
1512 dim
= isl_space_alloc(ctx
, 0, 3, 3);
1513 mm
.must
= isl_map_empty(isl_space_copy(dim
));
1514 mm
.may
= isl_map_empty(dim
);
1516 isl_flow_foreach(flow
, collect_must_may
, &mm
);
1518 str
= "{ [0,i,0] -> [0,i,2] : 0 <= i <= 10; "
1519 " [0,i,1] -> [0,5,2] : 0 <= i <= 5 }";
1520 assert(map_is_equal(mm
.may
, str
));
1521 str
= "{ [i,j,k] -> [l,m,n] : 1 = 0 }";
1522 assert(map_is_equal(mm
.must
, str
));
1524 isl_map_free(mm
.must
);
1525 isl_map_free(mm
.may
);
1526 isl_flow_free(flow
);
1529 str
= "{ [0,i,1] -> [i] : 0 <= i <= 10 }";
1530 map
= isl_map_read_from_str(ctx
, str
);
1531 ai
= isl_access_info_alloc(map
, &depth
, &common_space
, 2);
1533 str
= "{ [0,i,0] -> [i] : 0 <= i <= 10 }";
1534 map
= isl_map_read_from_str(ctx
, str
);
1535 ai
= isl_access_info_add_source(ai
, map
, 0, &depth
);
1537 str
= "{ [0,i,2] -> [5] : 0 <= i <= 10 }";
1538 map
= isl_map_read_from_str(ctx
, str
);
1539 ai
= isl_access_info_add_source(ai
, map
, 0, &depth
);
1541 flow
= isl_access_info_compute_flow(ai
);
1542 dim
= isl_space_alloc(ctx
, 0, 3, 3);
1543 mm
.must
= isl_map_empty(isl_space_copy(dim
));
1544 mm
.may
= isl_map_empty(dim
);
1546 isl_flow_foreach(flow
, collect_must_may
, &mm
);
1548 str
= "{ [0,i,0] -> [0,i,1] : 0 <= i <= 10; "
1549 " [0,i,2] -> [0,5,1] : 0 <= i <= 4 }";
1550 assert(map_is_equal(mm
.may
, str
));
1551 str
= "{ [i,j,k] -> [l,m,n] : 1 = 0 }";
1552 assert(map_is_equal(mm
.must
, str
));
1554 isl_map_free(mm
.must
);
1555 isl_map_free(mm
.may
);
1556 isl_flow_free(flow
);
1561 str
= "{ [1,i,0,0,0] -> [i,j] : 0 <= i <= 10 and 0 <= j <= 10 }";
1562 map
= isl_map_read_from_str(ctx
, str
);
1563 ai
= isl_access_info_alloc(map
, &depth
, &common_space
, 1);
1565 str
= "{ [0,i,0,j,0] -> [i,j] : 0 <= i <= 10 and 0 <= j <= 10 }";
1566 map
= isl_map_read_from_str(ctx
, str
);
1567 ai
= isl_access_info_add_source(ai
, map
, 1, &depth
);
1569 flow
= isl_access_info_compute_flow(ai
);
1570 dim
= isl_space_alloc(ctx
, 0, 5, 5);
1571 mm
.must
= isl_map_empty(isl_space_copy(dim
));
1572 mm
.may
= isl_map_empty(dim
);
1574 isl_flow_foreach(flow
, collect_must_may
, &mm
);
1576 str
= "{ [0,i,0,j,0] -> [1,i,0,0,0] : 0 <= i,j <= 10 }";
1577 assert(map_is_equal(mm
.must
, str
));
1578 str
= "{ [0,0,0,0,0] -> [0,0,0,0,0] : 1 = 0 }";
1579 assert(map_is_equal(mm
.may
, str
));
1581 isl_map_free(mm
.must
);
1582 isl_map_free(mm
.may
);
1583 isl_flow_free(flow
);
1586 int test_sv(isl_ctx
*ctx
)
1590 isl_union_map
*umap
;
1593 str
= "[N] -> { [i] -> [f] : 0 <= i <= N and 0 <= i - 10 f <= 9 }";
1594 map
= isl_map_read_from_str(ctx
, str
);
1595 sv
= isl_map_is_single_valued(map
);
1600 isl_die(ctx
, isl_error_internal
,
1601 "map not detected as single valued", return -1);
1603 str
= "[N] -> { [i] -> [f] : 0 <= i <= N and 0 <= i - 10 f <= 10 }";
1604 map
= isl_map_read_from_str(ctx
, str
);
1605 sv
= isl_map_is_single_valued(map
);
1610 isl_die(ctx
, isl_error_internal
,
1611 "map detected as single valued", return -1);
1613 str
= "{ S1[i] -> [i] : 0 <= i <= 9; S2[i] -> [i] : 0 <= i <= 9 }";
1614 umap
= isl_union_map_read_from_str(ctx
, str
);
1615 sv
= isl_union_map_is_single_valued(umap
);
1616 isl_union_map_free(umap
);
1620 isl_die(ctx
, isl_error_internal
,
1621 "map not detected as single valued", return -1);
1623 str
= "{ [i] -> S1[i] : 0 <= i <= 9; [i] -> S2[i] : 0 <= i <= 9 }";
1624 umap
= isl_union_map_read_from_str(ctx
, str
);
1625 sv
= isl_union_map_is_single_valued(umap
);
1626 isl_union_map_free(umap
);
1630 isl_die(ctx
, isl_error_internal
,
1631 "map detected as single valued", return -1);
1636 void test_bijective_case(struct isl_ctx
*ctx
, const char *str
, int bijective
)
1640 map
= isl_map_read_from_str(ctx
, str
);
1642 assert(isl_map_is_bijective(map
));
1644 assert(!isl_map_is_bijective(map
));
1648 void test_bijective(struct isl_ctx
*ctx
)
1650 test_bijective_case(ctx
, "[N,M]->{[i,j] -> [i]}", 0);
1651 test_bijective_case(ctx
, "[N,M]->{[i,j] -> [i] : j=i}", 1);
1652 test_bijective_case(ctx
, "[N,M]->{[i,j] -> [i] : j=0}", 1);
1653 test_bijective_case(ctx
, "[N,M]->{[i,j] -> [i] : j=N}", 1);
1654 test_bijective_case(ctx
, "[N,M]->{[i,j] -> [j,i]}", 1);
1655 test_bijective_case(ctx
, "[N,M]->{[i,j] -> [i+j]}", 0);
1656 test_bijective_case(ctx
, "[N,M]->{[i,j] -> []}", 0);
1657 test_bijective_case(ctx
, "[N,M]->{[i,j] -> [i,j,N]}", 1);
1658 test_bijective_case(ctx
, "[N,M]->{[i,j] -> [2i]}", 0);
1659 test_bijective_case(ctx
, "[N,M]->{[i,j] -> [i,i]}", 0);
1660 test_bijective_case(ctx
, "[N,M]->{[i,j] -> [2i,i]}", 0);
1661 test_bijective_case(ctx
, "[N,M]->{[i,j] -> [2i,j]}", 1);
1662 test_bijective_case(ctx
, "[N,M]->{[i,j] -> [x,y] : 2x=i & y =j}", 1);
1665 void test_pwqp(struct isl_ctx
*ctx
)
1669 isl_pw_qpolynomial
*pwqp1
, *pwqp2
;
1671 str
= "{ [i,j,k] -> 1 + 9 * [i/5] + 7 * [j/11] + 4 * [k/13] }";
1672 pwqp1
= isl_pw_qpolynomial_read_from_str(ctx
, str
);
1674 pwqp1
= isl_pw_qpolynomial_move_dims(pwqp1
, isl_dim_param
, 0,
1677 str
= "[j] -> { [i,k] -> 1 + 9 * [i/5] + 7 * [j/11] + 4 * [k/13] }";
1678 pwqp2
= isl_pw_qpolynomial_read_from_str(ctx
, str
);
1680 pwqp1
= isl_pw_qpolynomial_sub(pwqp1
, pwqp2
);
1682 assert(isl_pw_qpolynomial_is_zero(pwqp1
));
1684 isl_pw_qpolynomial_free(pwqp1
);
1686 str
= "{ [i] -> i }";
1687 pwqp1
= isl_pw_qpolynomial_read_from_str(ctx
, str
);
1688 str
= "{ [k] : exists a : k = 2a }";
1689 set
= isl_set_read_from_str(ctx
, str
);
1690 pwqp1
= isl_pw_qpolynomial_gist(pwqp1
, set
);
1691 str
= "{ [i] -> i }";
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 + [ (i + [i/3])/2 ] }";
1701 pwqp1
= isl_pw_qpolynomial_read_from_str(ctx
, str
);
1703 set
= isl_set_read_from_str(ctx
, str
);
1704 pwqp1
= isl_pw_qpolynomial_gist(pwqp1
, set
);
1705 str
= "{ [i] -> 16 }";
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)/2]) }";
1715 pwqp1
= isl_pw_qpolynomial_read_from_str(ctx
, str
);
1716 str
= "{ [k] : exists a : k = 2a+1 }";
1717 set
= isl_set_read_from_str(ctx
, str
);
1718 pwqp1
= isl_pw_qpolynomial_gist(pwqp1
, set
);
1719 str
= "{ [i] -> -1/2 + 1/2 * i }";
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] + [i/2])/5]) }";
1729 pwqp1
= isl_pw_qpolynomial_read_from_str(ctx
, str
);
1730 str
= "{ [i] -> ([(2 * [i/2])/5]) }";
1731 pwqp2
= isl_pw_qpolynomial_read_from_str(ctx
, str
);
1733 pwqp1
= isl_pw_qpolynomial_sub(pwqp1
, pwqp2
);
1735 assert(isl_pw_qpolynomial_is_zero(pwqp1
));
1737 isl_pw_qpolynomial_free(pwqp1
);
1739 str
= "{ [x] -> ([x/2] + [(x+1)/2]) }";
1740 pwqp1
= isl_pw_qpolynomial_read_from_str(ctx
, str
);
1741 str
= "{ [x] -> x }";
1742 pwqp2
= isl_pw_qpolynomial_read_from_str(ctx
, str
);
1744 pwqp1
= isl_pw_qpolynomial_sub(pwqp1
, pwqp2
);
1746 assert(isl_pw_qpolynomial_is_zero(pwqp1
));
1748 isl_pw_qpolynomial_free(pwqp1
);
1750 str
= "{ [i] -> ([i/2]) : i >= 0; [i] -> ([i/3]) : i < 0 }";
1751 pwqp1
= isl_pw_qpolynomial_read_from_str(ctx
, str
);
1752 pwqp2
= isl_pw_qpolynomial_read_from_str(ctx
, str
);
1753 pwqp1
= isl_pw_qpolynomial_coalesce(pwqp1
);
1754 pwqp1
= isl_pw_qpolynomial_sub(pwqp1
, pwqp2
);
1755 assert(isl_pw_qpolynomial_is_zero(pwqp1
));
1756 isl_pw_qpolynomial_free(pwqp1
);
1759 void test_split_periods(isl_ctx
*ctx
)
1762 isl_pw_qpolynomial
*pwqp
;
1764 str
= "{ [U,V] -> 1/3 * U + 2/3 * V - [(U + 2V)/3] + [U/2] : "
1765 "U + 2V + 3 >= 0 and - U -2V >= 0 and - U + 10 >= 0 and "
1766 "U >= 0; [U,V] -> U^2 : U >= 100 }";
1767 pwqp
= isl_pw_qpolynomial_read_from_str(ctx
, str
);
1769 pwqp
= isl_pw_qpolynomial_split_periods(pwqp
, 2);
1772 isl_pw_qpolynomial_free(pwqp
);
1775 void test_union(isl_ctx
*ctx
)
1778 isl_union_set
*uset1
, *uset2
;
1779 isl_union_map
*umap1
, *umap2
;
1781 str
= "{ [i] : 0 <= i <= 1 }";
1782 uset1
= isl_union_set_read_from_str(ctx
, str
);
1783 str
= "{ [1] -> [0] }";
1784 umap1
= isl_union_map_read_from_str(ctx
, str
);
1786 umap2
= isl_union_set_lex_gt_union_set(isl_union_set_copy(uset1
), uset1
);
1787 assert(isl_union_map_is_equal(umap1
, umap2
));
1789 isl_union_map_free(umap1
);
1790 isl_union_map_free(umap2
);
1792 str
= "{ A[i] -> B[i]; B[i] -> C[i]; A[0] -> C[1] }";
1793 umap1
= isl_union_map_read_from_str(ctx
, str
);
1794 str
= "{ A[i]; B[i] }";
1795 uset1
= isl_union_set_read_from_str(ctx
, str
);
1797 uset2
= isl_union_map_domain(umap1
);
1799 assert(isl_union_set_is_equal(uset1
, uset2
));
1801 isl_union_set_free(uset1
);
1802 isl_union_set_free(uset2
);
1805 void test_bound(isl_ctx
*ctx
)
1808 isl_pw_qpolynomial
*pwqp
;
1809 isl_pw_qpolynomial_fold
*pwf
;
1811 str
= "{ [[a, b, c, d] -> [e]] -> 0 }";
1812 pwqp
= isl_pw_qpolynomial_read_from_str(ctx
, str
);
1813 pwf
= isl_pw_qpolynomial_bound(pwqp
, isl_fold_max
, NULL
);
1814 assert(isl_pw_qpolynomial_fold_dim(pwf
, isl_dim_in
) == 4);
1815 isl_pw_qpolynomial_fold_free(pwf
);
1817 str
= "{ [[x]->[x]] -> 1 : exists a : x = 2 a }";
1818 pwqp
= isl_pw_qpolynomial_read_from_str(ctx
, str
);
1819 pwf
= isl_pw_qpolynomial_bound(pwqp
, isl_fold_max
, NULL
);
1820 assert(isl_pw_qpolynomial_fold_dim(pwf
, isl_dim_in
) == 1);
1821 isl_pw_qpolynomial_fold_free(pwf
);
1824 void test_lift(isl_ctx
*ctx
)
1827 isl_basic_map
*bmap
;
1828 isl_basic_set
*bset
;
1830 str
= "{ [i0] : exists e0 : i0 = 4e0 }";
1831 bset
= isl_basic_set_read_from_str(ctx
, str
);
1832 bset
= isl_basic_set_lift(bset
);
1833 bmap
= isl_basic_map_from_range(bset
);
1834 bset
= isl_basic_map_domain(bmap
);
1835 isl_basic_set_free(bset
);
1838 void test_subset(isl_ctx
*ctx
)
1841 isl_set
*set1
, *set2
;
1843 str
= "{ [112, 0] }";
1844 set1
= isl_set_read_from_str(ctx
, str
);
1845 str
= "{ [i0, i1] : exists (e0 = [(i0 - i1)/16], e1: "
1846 "16e0 <= i0 - i1 and 16e0 >= -15 + i0 - i1 and "
1847 "16e1 <= i1 and 16e0 >= -i1 and 16e1 >= -i0 + i1) }";
1848 set2
= isl_set_read_from_str(ctx
, str
);
1849 assert(isl_set_is_subset(set1
, set2
));
1854 void test_factorize(isl_ctx
*ctx
)
1857 isl_basic_set
*bset
;
1860 str
= "{ [i0, i1, i2, i3, i4, i5, i6, i7] : 3i5 <= 2 - 2i0 and "
1861 "i0 >= -2 and i6 >= 1 + i3 and i7 >= 0 and 3i5 >= -2i0 and "
1862 "2i4 <= i2 and i6 >= 1 + 2i0 + 3i1 and i4 <= -1 and "
1863 "i6 >= 1 + 2i0 + 3i5 and i6 <= 2 + 2i0 + 3i5 and "
1864 "3i5 <= 2 - 2i0 - i2 + 3i4 and i6 <= 2 + 2i0 + 3i1 and "
1865 "i0 <= -1 and i7 <= i2 + i3 - 3i4 - i6 and "
1866 "3i5 >= -2i0 - i2 + 3i4 }";
1867 bset
= isl_basic_set_read_from_str(ctx
, str
);
1868 f
= isl_basic_set_factorizer(bset
);
1870 isl_basic_set_free(bset
);
1871 isl_factorizer_free(f
);
1873 str
= "{ [i0, i1, i2, i3, i4, i5, i6, i7, i8, i9, i10, i11, i12] : "
1874 "i12 <= 2 + i0 - i11 and 2i8 >= -i4 and i11 >= i1 and "
1875 "3i5 <= -i2 and 2i11 >= -i4 - 2i7 and i11 <= 3 + i0 + 3i9 and "
1876 "i11 <= -i4 - 2i7 and i12 >= -i10 and i2 >= -2 and "
1877 "i11 >= i1 + 3i10 and i11 >= 1 + i0 + 3i9 and "
1878 "i11 <= 1 - i4 - 2i8 and 6i6 <= 6 - i2 and 3i6 >= 1 - i2 and "
1879 "i11 <= 2 + i1 and i12 <= i4 + i11 and i12 >= i0 - i11 and "
1880 "3i5 >= -2 - i2 and i12 >= -1 + i4 + i11 and 3i3 <= 3 - i2 and "
1881 "9i6 <= 11 - i2 + 6i5 and 3i3 >= 1 - i2 and "
1882 "9i6 <= 5 - i2 + 6i3 and i12 <= -1 and i2 <= 0 }";
1883 bset
= isl_basic_set_read_from_str(ctx
, str
);
1884 f
= isl_basic_set_factorizer(bset
);
1886 isl_basic_set_free(bset
);
1887 isl_factorizer_free(f
);
1890 static int check_injective(__isl_take isl_map
*map
, void *user
)
1892 int *injective
= user
;
1894 *injective
= isl_map_is_injective(map
);
1897 if (*injective
< 0 || !*injective
)
1903 int test_one_schedule(isl_ctx
*ctx
, const char *d
, const char *w
,
1904 const char *r
, const char *s
, int tilable
, int parallel
)
1908 isl_union_map
*W
, *R
, *S
;
1909 isl_union_map
*empty
;
1910 isl_union_map
*dep_raw
, *dep_war
, *dep_waw
, *dep
;
1911 isl_union_map
*validity
, *proximity
;
1912 isl_union_map
*schedule
;
1913 isl_union_map
*test
;
1914 isl_union_set
*delta
;
1915 isl_union_set
*domain
;
1919 isl_schedule
*sched
;
1920 int is_nonneg
, is_parallel
, is_tilable
, is_injection
, is_complete
;
1922 D
= isl_union_set_read_from_str(ctx
, d
);
1923 W
= isl_union_map_read_from_str(ctx
, w
);
1924 R
= isl_union_map_read_from_str(ctx
, r
);
1925 S
= isl_union_map_read_from_str(ctx
, s
);
1927 W
= isl_union_map_intersect_domain(W
, isl_union_set_copy(D
));
1928 R
= isl_union_map_intersect_domain(R
, isl_union_set_copy(D
));
1930 empty
= isl_union_map_empty(isl_union_map_get_space(S
));
1931 isl_union_map_compute_flow(isl_union_map_copy(R
),
1932 isl_union_map_copy(W
), empty
,
1933 isl_union_map_copy(S
),
1934 &dep_raw
, NULL
, NULL
, NULL
);
1935 isl_union_map_compute_flow(isl_union_map_copy(W
),
1936 isl_union_map_copy(W
),
1937 isl_union_map_copy(R
),
1938 isl_union_map_copy(S
),
1939 &dep_waw
, &dep_war
, NULL
, NULL
);
1941 dep
= isl_union_map_union(dep_waw
, dep_war
);
1942 dep
= isl_union_map_union(dep
, dep_raw
);
1943 validity
= isl_union_map_copy(dep
);
1944 proximity
= isl_union_map_copy(dep
);
1946 sched
= isl_union_set_compute_schedule(isl_union_set_copy(D
),
1947 validity
, proximity
);
1948 schedule
= isl_schedule_get_map(sched
);
1949 isl_schedule_free(sched
);
1950 isl_union_map_free(W
);
1951 isl_union_map_free(R
);
1952 isl_union_map_free(S
);
1955 isl_union_map_foreach_map(schedule
, &check_injective
, &is_injection
);
1957 domain
= isl_union_map_domain(isl_union_map_copy(schedule
));
1958 is_complete
= isl_union_set_is_subset(D
, domain
);
1959 isl_union_set_free(D
);
1960 isl_union_set_free(domain
);
1962 test
= isl_union_map_reverse(isl_union_map_copy(schedule
));
1963 test
= isl_union_map_apply_range(test
, dep
);
1964 test
= isl_union_map_apply_range(test
, schedule
);
1966 delta
= isl_union_map_deltas(test
);
1967 if (isl_union_set_n_set(delta
) == 0) {
1971 isl_union_set_free(delta
);
1973 delta_set
= isl_set_from_union_set(delta
);
1975 slice
= isl_set_universe(isl_set_get_space(delta_set
));
1976 for (i
= 0; i
< tilable
; ++i
)
1977 slice
= isl_set_lower_bound_si(slice
, isl_dim_set
, i
, 0);
1978 is_tilable
= isl_set_is_subset(delta_set
, slice
);
1979 isl_set_free(slice
);
1981 slice
= isl_set_universe(isl_set_get_space(delta_set
));
1982 for (i
= 0; i
< parallel
; ++i
)
1983 slice
= isl_set_fix_si(slice
, isl_dim_set
, i
, 0);
1984 is_parallel
= isl_set_is_subset(delta_set
, slice
);
1985 isl_set_free(slice
);
1987 origin
= isl_set_universe(isl_set_get_space(delta_set
));
1988 for (i
= 0; i
< isl_set_dim(origin
, isl_dim_set
); ++i
)
1989 origin
= isl_set_fix_si(origin
, isl_dim_set
, i
, 0);
1991 delta_set
= isl_set_union(delta_set
, isl_set_copy(origin
));
1992 delta_set
= isl_set_lexmin(delta_set
);
1994 is_nonneg
= isl_set_is_equal(delta_set
, origin
);
1996 isl_set_free(origin
);
1997 isl_set_free(delta_set
);
2000 if (is_nonneg
< 0 || is_parallel
< 0 || is_tilable
< 0 ||
2001 is_injection
< 0 || is_complete
< 0)
2004 isl_die(ctx
, isl_error_unknown
,
2005 "generated schedule incomplete", return -1);
2007 isl_die(ctx
, isl_error_unknown
,
2008 "generated schedule not injective on each statement",
2011 isl_die(ctx
, isl_error_unknown
,
2012 "negative dependences in generated schedule",
2015 isl_die(ctx
, isl_error_unknown
,
2016 "generated schedule not as tilable as expected",
2019 isl_die(ctx
, isl_error_unknown
,
2020 "generated schedule not as parallel as expected",
2026 int test_special_schedule(isl_ctx
*ctx
)
2030 isl_union_map
*empty
;
2032 isl_union_map
*sched1
, *sched2
;
2033 isl_schedule
*schedule
;
2036 str
= "{ S[i,j] : 0 <= i <= 10 }";
2037 dom
= isl_union_set_read_from_str(ctx
, str
);
2038 str
= "{ S[i,j] -> S[i+1,j] : 0 <= i,j <= 10 }";
2039 dep
= isl_union_map_read_from_str(ctx
, str
);
2040 empty
= isl_union_map_read_from_str(ctx
, "{}");
2041 schedule
= isl_union_set_compute_schedule(dom
, empty
, dep
);
2042 sched1
= isl_schedule_get_map(schedule
);
2043 isl_schedule_free(schedule
);
2045 str
= "{ S[i, j] -> [j, i] }";
2046 sched2
= isl_union_map_read_from_str(ctx
, str
);
2048 equal
= isl_union_map_is_equal(sched1
, sched2
);
2049 isl_union_map_free(sched1
);
2050 isl_union_map_free(sched2
);
2055 isl_die(ctx
, isl_error_unknown
, "unexpected schedule",
2061 int test_schedule(isl_ctx
*ctx
)
2063 const char *D
, *W
, *R
, *S
;
2066 D
= "[T,N] -> { S1[t,i] : 1 <= t <= T and 2 <= i <= N - 1 }";
2067 W
= "{ S1[t,i] -> a[t,i] }";
2068 R
= "{ S1[t,i] -> a[t-1,i]; S1[t,i] -> a[t-1,i-1]; "
2069 "S1[t,i] -> a[t-1,i+1] }";
2070 S
= "{ S1[t,i] -> [t,i] }";
2071 if (test_one_schedule(ctx
, D
, W
, R
, S
, 2, 0) < 0)
2074 /* Fig. 5 of CC2008 */
2075 D
= "[N] -> { S_0[i, j] : i >= 0 and i <= -1 + N and j >= 2 and "
2077 W
= "[N] -> { S_0[i, j] -> a[i, j] : i >= 0 and i <= -1 + N and "
2078 "j >= 2 and j <= -1 + N }";
2079 R
= "[N] -> { S_0[i, j] -> a[j, i] : i >= 0 and i <= -1 + N and "
2080 "j >= 2 and j <= -1 + N; "
2081 "S_0[i, j] -> a[i, -1 + j] : i >= 0 and i <= -1 + N and "
2082 "j >= 2 and j <= -1 + N }";
2083 S
= "[N] -> { S_0[i, j] -> [0, i, 0, j, 0] }";
2084 if (test_one_schedule(ctx
, D
, W
, R
, S
, 2, 0) < 0)
2087 D
= "{ S1[i] : 0 <= i <= 10; S2[i] : 0 <= i <= 9 }";
2088 W
= "{ S1[i] -> a[i] }";
2089 R
= "{ S2[i] -> a[i+1] }";
2090 S
= "{ S1[i] -> [0,i]; S2[i] -> [1,i] }";
2091 if (test_one_schedule(ctx
, D
, W
, R
, S
, 1, 1) < 0)
2094 D
= "{ S1[i] : 0 <= i < 10; S2[i] : 0 <= i < 10 }";
2095 W
= "{ S1[i] -> a[i] }";
2096 R
= "{ S2[i] -> a[9-i] }";
2097 S
= "{ S1[i] -> [0,i]; S2[i] -> [1,i] }";
2098 if (test_one_schedule(ctx
, D
, W
, R
, S
, 1, 1) < 0)
2101 D
= "[N] -> { S1[i] : 0 <= i < N; S2[i] : 0 <= i < N }";
2102 W
= "{ S1[i] -> a[i] }";
2103 R
= "[N] -> { S2[i] -> a[N-1-i] }";
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]; S2[i] -> b[i] }";
2110 R
= "{ S2[i] -> a[i]; S1[i] -> b[i-1] }";
2111 S
= "{ S1[i] -> [i,0]; S2[i] -> [i,1] }";
2112 if (test_one_schedule(ctx
, D
, W
, R
, S
, 0, 0) < 0)
2115 D
= "[N] -> { S1[i] : 1 <= i <= N; S2[i,j] : 1 <= i,j <= N }";
2116 W
= "{ S1[i] -> a[0,i]; S2[i,j] -> a[i,j] }";
2117 R
= "{ S2[i,j] -> a[i-1,j] }";
2118 S
= "{ S1[i] -> [0,i,0]; S2[i,j] -> [1,i,j] }";
2119 if (test_one_schedule(ctx
, D
, W
, R
, S
, 2, 1) < 0)
2122 D
= "[N] -> { S1[i] : 1 <= i <= N; S2[i,j] : 1 <= i,j <= N }";
2123 W
= "{ S1[i] -> a[i,0]; S2[i,j] -> a[i,j] }";
2124 R
= "{ S2[i,j] -> a[i,j-1] }";
2125 S
= "{ S1[i] -> [0,i,0]; S2[i,j] -> [1,i,j] }";
2126 if (test_one_schedule(ctx
, D
, W
, R
, S
, 2, 1) < 0)
2129 D
= "[N] -> { S_0[]; S_1[i] : i >= 0 and i <= -1 + N; S_2[] }";
2130 W
= "[N] -> { S_0[] -> a[0]; S_2[] -> b[0]; "
2131 "S_1[i] -> a[1 + i] : i >= 0 and i <= -1 + N }";
2132 R
= "[N] -> { S_2[] -> a[N]; S_1[i] -> a[i] : i >= 0 and i <= -1 + N }";
2133 S
= "[N] -> { S_1[i] -> [1, i, 0]; S_2[] -> [2, 0, 1]; "
2134 "S_0[] -> [0, 0, 0] }";
2135 if (test_one_schedule(ctx
, D
, W
, R
, S
, 1, 0) < 0)
2137 ctx
->opt
->schedule_parametric
= 0;
2138 if (test_one_schedule(ctx
, D
, W
, R
, S
, 0, 0) < 0)
2140 ctx
->opt
->schedule_parametric
= 1;
2142 D
= "[N] -> { S1[i] : 1 <= i <= N; S2[i] : 1 <= i <= N; "
2143 "S3[i,j] : 1 <= i,j <= N; S4[i] : 1 <= i <= N }";
2144 W
= "{ S1[i] -> a[i,0]; S2[i] -> a[0,i]; S3[i,j] -> a[i,j] }";
2145 R
= "[N] -> { S3[i,j] -> a[i-1,j]; S3[i,j] -> a[i,j-1]; "
2146 "S4[i] -> a[i,N] }";
2147 S
= "{ S1[i] -> [0,i,0]; S2[i] -> [1,i,0]; S3[i,j] -> [2,i,j]; "
2148 "S4[i] -> [4,i,0] }";
2149 if (test_one_schedule(ctx
, D
, W
, R
, S
, 2, 0) < 0)
2152 D
= "[N] -> { S_0[i, j] : i >= 1 and i <= N and j >= 1 and j <= N }";
2153 W
= "[N] -> { S_0[i, j] -> s[0] : i >= 1 and i <= N and j >= 1 and "
2155 R
= "[N] -> { S_0[i, j] -> s[0] : i >= 1 and i <= N and j >= 1 and "
2157 "S_0[i, j] -> a[i, j] : i >= 1 and i <= N and j >= 1 and "
2159 S
= "[N] -> { S_0[i, j] -> [0, i, 0, j, 0] }";
2160 if (test_one_schedule(ctx
, D
, W
, R
, S
, 0, 0) < 0)
2163 D
= "[N] -> { S_0[t] : t >= 0 and t <= -1 + N; "
2164 " S_2[t] : t >= 0 and t <= -1 + N; "
2165 " S_1[t, i] : t >= 0 and t <= -1 + N and i >= 0 and "
2167 W
= "[N] -> { S_0[t] -> a[t, 0] : t >= 0 and t <= -1 + N; "
2168 " S_2[t] -> b[t] : t >= 0 and t <= -1 + N; "
2169 " S_1[t, i] -> a[t, 1 + i] : t >= 0 and t <= -1 + N and "
2170 "i >= 0 and i <= -1 + N }";
2171 R
= "[N] -> { S_1[t, i] -> a[t, i] : t >= 0 and t <= -1 + N and "
2172 "i >= 0 and i <= -1 + N; "
2173 " S_2[t] -> a[t, N] : t >= 0 and t <= -1 + N }";
2174 S
= "[N] -> { S_2[t] -> [0, t, 2]; S_1[t, i] -> [0, t, 1, i, 0]; "
2175 " S_0[t] -> [0, t, 0] }";
2177 if (test_one_schedule(ctx
, D
, W
, R
, S
, 2, 1) < 0)
2179 ctx
->opt
->schedule_parametric
= 0;
2180 if (test_one_schedule(ctx
, D
, W
, R
, S
, 0, 0) < 0)
2182 ctx
->opt
->schedule_parametric
= 1;
2184 D
= "[N] -> { S1[i,j] : 0 <= i,j < N; S2[i,j] : 0 <= i,j < N }";
2185 S
= "{ S1[i,j] -> [0,i,j]; S2[i,j] -> [1,i,j] }";
2186 if (test_one_schedule(ctx
, D
, "{}", "{}", S
, 2, 2) < 0)
2189 D
= "[M, N] -> { S_1[i] : i >= 0 and i <= -1 + M; "
2190 "S_0[i, j] : i >= 0 and i <= -1 + M and j >= 0 and j <= -1 + N }";
2191 W
= "[M, N] -> { S_0[i, j] -> a[j] : i >= 0 and i <= -1 + M and "
2192 "j >= 0 and j <= -1 + N; "
2193 "S_1[i] -> b[0] : i >= 0 and i <= -1 + M }";
2194 R
= "[M, N] -> { S_0[i, j] -> a[0] : i >= 0 and i <= -1 + M and "
2195 "j >= 0 and j <= -1 + N; "
2196 "S_1[i] -> b[0] : i >= 0 and i <= -1 + M }";
2197 S
= "[M, N] -> { S_1[i] -> [1, i, 0]; S_0[i, j] -> [0, i, 0, j, 0] }";
2198 if (test_one_schedule(ctx
, D
, W
, R
, S
, 0, 0) < 0)
2201 D
= "{ S_0[i] : i >= 0 }";
2202 W
= "{ S_0[i] -> a[i] : i >= 0 }";
2203 R
= "{ S_0[i] -> a[0] : i >= 0 }";
2204 S
= "{ S_0[i] -> [0, i, 0] }";
2205 if (test_one_schedule(ctx
, D
, W
, R
, S
, 0, 0) < 0)
2208 D
= "{ S_0[i] : i >= 0; S_1[i] : i >= 0 }";
2209 W
= "{ S_0[i] -> a[i] : i >= 0; S_1[i] -> b[i] : i >= 0 }";
2210 R
= "{ S_0[i] -> b[0] : i >= 0; S_1[i] -> a[i] : i >= 0 }";
2211 S
= "{ S_1[i] -> [0, i, 1]; S_0[i] -> [0, i, 0] }";
2212 if (test_one_schedule(ctx
, D
, W
, R
, S
, 0, 0) < 0)
2215 D
= "[n] -> { S_0[j, k] : j <= -1 + n and j >= 0 and "
2216 "k <= -1 + n and k >= 0 }";
2217 W
= "[n] -> { S_0[j, k] -> B[j] : j <= -1 + n and j >= 0 and " "k <= -1 + n and k >= 0 }";
2218 R
= "[n] -> { S_0[j, k] -> B[j] : j <= -1 + n and j >= 0 and "
2219 "k <= -1 + n and k >= 0; "
2220 "S_0[j, k] -> B[k] : j <= -1 + n and j >= 0 and "
2221 "k <= -1 + n and k >= 0; "
2222 "S_0[j, k] -> A[k] : j <= -1 + n and j >= 0 and "
2223 "k <= -1 + n and k >= 0 }";
2224 S
= "[n] -> { S_0[j, k] -> [2, j, k] }";
2225 ctx
->opt
->schedule_outer_zero_distance
= 1;
2226 if (test_one_schedule(ctx
, D
, W
, R
, S
, 0, 0) < 0)
2228 ctx
->opt
->schedule_outer_zero_distance
= 0;
2230 return test_special_schedule(ctx
);
2233 int test_plain_injective(isl_ctx
*ctx
, const char *str
, int injective
)
2235 isl_union_map
*umap
;
2238 umap
= isl_union_map_read_from_str(ctx
, str
);
2239 test
= isl_union_map_plain_is_injective(umap
);
2240 isl_union_map_free(umap
);
2243 if (test
== injective
)
2246 isl_die(ctx
, isl_error_unknown
,
2247 "map not detected as injective", return -1);
2249 isl_die(ctx
, isl_error_unknown
,
2250 "map detected as injective", return -1);
2253 int test_injective(isl_ctx
*ctx
)
2257 if (test_plain_injective(ctx
, "{S[i,j] -> A[0]; T[i,j] -> B[1]}", 0))
2259 if (test_plain_injective(ctx
, "{S[] -> A[0]; T[] -> B[0]}", 1))
2261 if (test_plain_injective(ctx
, "{S[] -> A[0]; T[] -> A[1]}", 1))
2263 if (test_plain_injective(ctx
, "{S[] -> A[0]; T[] -> A[0]}", 0))
2265 if (test_plain_injective(ctx
, "{S[i] -> A[i,0]; T[i] -> A[i,1]}", 1))
2267 if (test_plain_injective(ctx
, "{S[i] -> A[i]; T[i] -> A[i]}", 0))
2269 if (test_plain_injective(ctx
, "{S[] -> A[0,0]; T[] -> A[0,1]}", 1))
2271 if (test_plain_injective(ctx
, "{S[] -> A[0,0]; T[] -> A[1,0]}", 1))
2274 str
= "{S[] -> A[0,0]; T[] -> A[0,1]; U[] -> A[1,0]}";
2275 if (test_plain_injective(ctx
, str
, 1))
2277 str
= "{S[] -> A[0,0]; T[] -> A[0,1]; U[] -> A[0,0]}";
2278 if (test_plain_injective(ctx
, str
, 0))
2284 int test_aff(isl_ctx
*ctx
)
2289 isl_local_space
*ls
;
2293 dim
= isl_space_set_alloc(ctx
, 0, 1);
2294 ls
= isl_local_space_from_space(dim
);
2295 aff
= isl_aff_zero_on_domain(ls
);
2297 aff
= isl_aff_add_coefficient_si(aff
, isl_dim_in
, 0, 1);
2298 aff
= isl_aff_scale_down_ui(aff
, 3);
2299 aff
= isl_aff_floor(aff
);
2300 aff
= isl_aff_add_coefficient_si(aff
, isl_dim_in
, 0, 1);
2301 aff
= isl_aff_scale_down_ui(aff
, 2);
2302 aff
= isl_aff_floor(aff
);
2303 aff
= isl_aff_add_coefficient_si(aff
, isl_dim_in
, 0, 1);
2306 set
= isl_set_read_from_str(ctx
, str
);
2307 aff
= isl_aff_gist(aff
, set
);
2309 aff
= isl_aff_add_constant_si(aff
, -16);
2310 zero
= isl_aff_plain_is_zero(aff
);
2316 isl_die(ctx
, isl_error_unknown
, "unexpected result", return -1);
2321 int test_dim_max(isl_ctx
*ctx
)
2325 isl_set
*set1
, *set2
;
2330 str
= "[N] -> { [i] : 0 <= i <= min(N,10) }";
2331 set
= isl_set_read_from_str(ctx
, str
);
2332 pwaff
= isl_set_dim_max(set
, 0);
2333 set1
= isl_set_from_pw_aff(pwaff
);
2334 str
= "[N] -> { [10] : N >= 10; [N] : N <= 9 and N >= 0 }";
2335 set2
= isl_set_read_from_str(ctx
, str
);
2336 equal
= isl_set_is_equal(set1
, set2
);
2342 isl_die(ctx
, isl_error_unknown
, "unexpected result", return -1);
2344 str
= "[N] -> { [i] : 0 <= i <= max(2N,N+6) }";
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] -> { [6 + N] : -6 <= N <= 5; [2N] : N >= 6 }";
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 <= 2N or 0 <= i <= 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,M] -> { [i,j] -> [([i/16]), i%16, ([j/16]), j%16] : "
2373 "0 <= i < N and 0 <= j < M }";
2374 map
= isl_map_read_from_str(ctx
, str
);
2375 set
= isl_map_range(map
);
2377 pwaff
= isl_set_dim_max(isl_set_copy(set
), 0);
2378 set1
= isl_set_from_pw_aff(pwaff
);
2379 str
= "[N,M] -> { [([(N-1)/16])] : M,N > 0 }";
2380 set2
= isl_set_read_from_str(ctx
, str
);
2381 equal
= isl_set_is_equal(set1
, set2
);
2385 pwaff
= isl_set_dim_max(isl_set_copy(set
), 3);
2386 set1
= isl_set_from_pw_aff(pwaff
);
2387 str
= "[N,M] -> { [t] : t = min(M-1,15) and M,N > 0 }";
2388 set2
= isl_set_read_from_str(ctx
, str
);
2389 if (equal
>= 0 && equal
)
2390 equal
= isl_set_is_equal(set1
, set2
);
2399 isl_die(ctx
, isl_error_unknown
, "unexpected result", return -1);
2404 int test_product(isl_ctx
*ctx
)
2411 set
= isl_set_read_from_str(ctx
, str
);
2412 set
= isl_set_product(set
, isl_set_copy(set
));
2413 ok
= isl_set_is_wrapping(set
);
2418 isl_die(ctx
, isl_error_unknown
, "unexpected result", return -1);
2423 int test_equal(isl_ctx
*ctx
)
2426 isl_set
*set
, *set2
;
2430 set
= isl_set_read_from_str(ctx
, str
);
2432 set2
= isl_set_read_from_str(ctx
, str
);
2433 equal
= isl_set_is_equal(set
, set2
);
2439 isl_die(ctx
, isl_error_unknown
, "unexpected result", return -1);
2444 static int test_plain_fixed(isl_ctx
*ctx
, __isl_take isl_map
*map
,
2445 enum isl_dim_type type
, unsigned pos
, int fixed
)
2449 test
= isl_map_plain_is_fixed(map
, type
, pos
, NULL
);
2456 isl_die(ctx
, isl_error_unknown
,
2457 "map not detected as fixed", return -1);
2459 isl_die(ctx
, isl_error_unknown
,
2460 "map detected as fixed", return -1);
2463 int test_fixed(isl_ctx
*ctx
)
2468 str
= "{ [i] -> [i] }";
2469 map
= isl_map_read_from_str(ctx
, str
);
2470 if (test_plain_fixed(ctx
, map
, isl_dim_out
, 0, 0))
2472 str
= "{ [i] -> [1] }";
2473 map
= isl_map_read_from_str(ctx
, str
);
2474 if (test_plain_fixed(ctx
, map
, isl_dim_out
, 0, 1))
2476 str
= "{ S_1[p1] -> [o0] : o0 = -2 and p1 >= 1 and p1 <= 7 }";
2477 map
= isl_map_read_from_str(ctx
, str
);
2478 if (test_plain_fixed(ctx
, map
, isl_dim_out
, 0, 1))
2480 map
= isl_map_read_from_str(ctx
, str
);
2481 map
= isl_map_neg(map
);
2482 if (test_plain_fixed(ctx
, map
, isl_dim_out
, 0, 1))
2490 struct isl_ctx
*ctx
;
2492 srcdir
= getenv("srcdir");
2495 ctx
= isl_ctx_alloc();
2496 if (test_fixed(ctx
) < 0)
2498 if (test_equal(ctx
) < 0)
2500 if (test_product(ctx
) < 0)
2502 if (test_dim_max(ctx
) < 0)
2504 if (test_aff(ctx
) < 0)
2506 if (test_injective(ctx
) < 0)
2508 if (test_schedule(ctx
) < 0)
2510 test_factorize(ctx
);
2515 test_split_periods(ctx
);
2519 if (test_sv(ctx
) < 0)
2521 test_bijective(ctx
);
2525 test_construction(ctx
);
2528 test_application(ctx
);
2529 test_affine_hull(ctx
);
2530 test_convex_hull(ctx
);