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>
23 #include <isl_options_private.h>
27 static char *get_filename(isl_ctx
*ctx
, const char *name
, const char *suffix
) {
30 char *pattern
= "%s/test_inputs/%s.%s";
32 length
= strlen(pattern
) - 6 + strlen(srcdir
) + strlen(name
)
34 filename
= isl_alloc_array(ctx
, char, length
);
39 sprintf(filename
, pattern
, srcdir
, name
, suffix
);
44 void test_parse_map(isl_ctx
*ctx
, const char *str
)
48 map
= isl_map_read_from_str(ctx
, str
);
53 void test_parse_map_equal(isl_ctx
*ctx
, const char *str
, const char *str2
)
57 map
= isl_map_read_from_str(ctx
, str
);
58 map2
= isl_map_read_from_str(ctx
, str2
);
59 assert(map
&& map2
&& isl_map_is_equal(map
, map2
));
64 void test_parse_pwqp(isl_ctx
*ctx
, const char *str
)
66 isl_pw_qpolynomial
*pwqp
;
68 pwqp
= isl_pw_qpolynomial_read_from_str(ctx
, str
);
70 isl_pw_qpolynomial_free(pwqp
);
73 static void test_parse_pwaff(isl_ctx
*ctx
, const char *str
)
77 pwaff
= isl_pw_aff_read_from_str(ctx
, str
);
79 isl_pw_aff_free(pwaff
);
82 void test_parse(struct isl_ctx
*ctx
)
85 const char *str
, *str2
;
87 str
= "{ [i] -> [-i] }";
88 map
= isl_map_read_from_str(ctx
, str
);
92 str
= "{ A[i] -> L[([i/3])] }";
93 map
= isl_map_read_from_str(ctx
, str
);
97 test_parse_map(ctx
, "{[[s] -> A[i]] -> [[s+1] -> A[i]]}");
98 test_parse_map(ctx
, "{ [p1, y1, y2] -> [2, y1, y2] : "
99 "p1 = 1 && (y1 <= y2 || y2 = 0) }");
101 str
= "{ [x,y] : [([x/2]+y)/3] >= 1 }";
102 str2
= "{ [x, y] : 2y >= 6 - x }";
103 test_parse_map_equal(ctx
, str
, str2
);
105 test_parse_map_equal(ctx
, "{ [x,y] : x <= min(y, 2*y+3) }",
106 "{ [x,y] : x <= y, 2*y + 3 }");
107 str
= "{ [x, y] : (y <= x and y >= -3) or (2y <= -3 + x and y <= -4) }";
108 test_parse_map_equal(ctx
, "{ [x,y] : x >= min(y, 2*y+3) }", str
);
110 str
= "{[new,old] -> [new+1-2*[(new+1)/2],old+1-2*[(old+1)/2]]}";
111 map
= isl_map_read_from_str(ctx
, str
);
112 str
= "{ [new, old] -> [o0, o1] : "
113 "exists (e0 = [(-1 - new + o0)/2], e1 = [(-1 - old + o1)/2]: "
114 "2e0 = -1 - new + o0 and 2e1 = -1 - old + o1 and o0 >= 0 and "
115 "o0 <= 1 and o1 >= 0 and o1 <= 1) }";
116 map2
= isl_map_read_from_str(ctx
, str
);
117 assert(isl_map_is_equal(map
, map2
));
121 str
= "{[new,old] -> [new+1-2*[(new+1)/2],old+1-2*[(old+1)/2]]}";
122 map
= isl_map_read_from_str(ctx
, str
);
123 str
= "{[new,old] -> [(new+1)%2,(old+1)%2]}";
124 map2
= isl_map_read_from_str(ctx
, str
);
125 assert(isl_map_is_equal(map
, map2
));
129 str
= "[n] -> { [c1] : c1>=0 and c1<=floord(n-4,3) }";
130 str2
= "[n] -> { [c1] : c1 >= 0 and 3c1 <= -4 + n }";
131 test_parse_map_equal(ctx
, str
, str2
);
133 str
= "{ [i,j] -> [i] : i < j; [i,j] -> [j] : j <= i }";
134 str2
= "{ [i,j] -> [min(i,j)] }";
135 test_parse_map_equal(ctx
, str
, str2
);
137 str
= "{ [i,j] : i != j }";
138 str2
= "{ [i,j] : i < j or i > j }";
139 test_parse_map_equal(ctx
, str
, str2
);
141 str
= "{ [i,j] : (i+1)*2 >= j }";
142 str2
= "{ [i, j] : j <= 2 + 2i }";
143 test_parse_map_equal(ctx
, str
, str2
);
145 str
= "{ [i] -> [i > 0 ? 4 : 5] }";
146 str2
= "{ [i] -> [5] : i <= 0; [i] -> [4] : i >= 1 }";
147 test_parse_map_equal(ctx
, str
, str2
);
149 str
= "[N=2,M] -> { [i=[(M+N)/4]] }";
150 str2
= "[N, M] -> { [i] : N = 2 and 4i <= 2 + M and 4i >= -1 + M }";
151 test_parse_map_equal(ctx
, str
, str2
);
153 str
= "{ [x] : x >= 0 }";
154 str2
= "{ [x] : x-0 >= 0 }";
155 test_parse_map_equal(ctx
, str
, str2
);
157 str
= "{ [i] : ((i > 10)) }";
158 str2
= "{ [i] : i >= 11 }";
159 test_parse_map_equal(ctx
, str
, str2
);
161 test_parse_pwqp(ctx
, "{ [i] -> i + [ (i + [i/3])/2 ] }");
162 test_parse_map(ctx
, "{ S1[i] -> [([i/10]),i%10] : 0 <= i <= 45 }");
163 test_parse_pwaff(ctx
, "{ [i] -> [i + 1] : i > 0; [a] -> [a] : a < 0 }");
166 void test_read(struct isl_ctx
*ctx
)
170 struct isl_basic_set
*bset1
, *bset2
;
171 const char *str
= "{[y]: Exists ( alpha : 2alpha = y)}";
173 filename
= get_filename(ctx
, "set", "omega");
175 input
= fopen(filename
, "r");
178 bset1
= isl_basic_set_read_from_file(ctx
, input
);
179 bset2
= isl_basic_set_read_from_str(ctx
, str
);
181 assert(isl_basic_set_is_equal(bset1
, bset2
) == 1);
183 isl_basic_set_free(bset1
);
184 isl_basic_set_free(bset2
);
190 void test_bounded(struct isl_ctx
*ctx
)
195 set
= isl_set_read_from_str(ctx
, "[n] -> {[i] : 0 <= i <= n }");
196 bounded
= isl_set_is_bounded(set
);
200 set
= isl_set_read_from_str(ctx
, "{[n, i] : 0 <= i <= n }");
201 bounded
= isl_set_is_bounded(set
);
205 set
= isl_set_read_from_str(ctx
, "[n] -> {[i] : i <= n }");
206 bounded
= isl_set_is_bounded(set
);
211 /* Construct the basic set { [i] : 5 <= i <= N } */
212 void test_construction(struct isl_ctx
*ctx
)
217 struct isl_basic_set
*bset
;
218 struct isl_constraint
*c
;
222 dim
= isl_space_set_alloc(ctx
, 1, 1);
223 bset
= isl_basic_set_universe(isl_space_copy(dim
));
224 ls
= isl_local_space_from_space(dim
);
226 c
= isl_inequality_alloc(isl_local_space_copy(ls
));
227 isl_int_set_si(v
, -1);
228 isl_constraint_set_coefficient(c
, isl_dim_set
, 0, v
);
229 isl_int_set_si(v
, 1);
230 isl_constraint_set_coefficient(c
, isl_dim_param
, 0, v
);
231 bset
= isl_basic_set_add_constraint(bset
, c
);
233 c
= isl_inequality_alloc(isl_local_space_copy(ls
));
234 isl_int_set_si(v
, 1);
235 isl_constraint_set_coefficient(c
, isl_dim_set
, 0, v
);
236 isl_int_set_si(v
, -5);
237 isl_constraint_set_constant(c
, v
);
238 bset
= isl_basic_set_add_constraint(bset
, c
);
240 isl_local_space_free(ls
);
241 isl_basic_set_free(bset
);
246 void test_dim(struct isl_ctx
*ctx
)
249 isl_map
*map1
, *map2
;
251 map1
= isl_map_read_from_str(ctx
,
252 "[n] -> { [i] -> [j] : exists (a = [i/10] : i - 10a <= n ) }");
253 map1
= isl_map_add_dims(map1
, isl_dim_in
, 1);
254 map2
= isl_map_read_from_str(ctx
,
255 "[n] -> { [i,k] -> [j] : exists (a = [i/10] : i - 10a <= n ) }");
256 assert(isl_map_is_equal(map1
, map2
));
259 map1
= isl_map_project_out(map1
, isl_dim_in
, 0, 1);
260 map2
= isl_map_read_from_str(ctx
, "[n] -> { [i] -> [j] : n >= 0 }");
261 assert(isl_map_is_equal(map1
, map2
));
266 str
= "[n] -> { [i] -> [] : exists a : 0 <= i <= n and i = 2 a }";
267 map1
= isl_map_read_from_str(ctx
, str
);
268 str
= "{ [i] -> [j] : exists a : 0 <= i <= j and i = 2 a }";
269 map2
= isl_map_read_from_str(ctx
, str
);
270 map1
= isl_map_move_dims(map1
, isl_dim_out
, 0, isl_dim_param
, 0, 1);
271 assert(isl_map_is_equal(map1
, map2
));
277 void test_div(struct isl_ctx
*ctx
)
282 struct isl_basic_set
*bset
;
283 struct isl_constraint
*c
;
288 dim
= isl_space_set_alloc(ctx
, 0, 3);
289 bset
= isl_basic_set_universe(isl_space_copy(dim
));
290 ls
= isl_local_space_from_space(dim
);
292 c
= isl_equality_alloc(isl_local_space_copy(ls
));
293 isl_int_set_si(v
, -1);
294 isl_constraint_set_constant(c
, v
);
295 isl_int_set_si(v
, 1);
296 isl_constraint_set_coefficient(c
, isl_dim_set
, 0, v
);
297 isl_int_set_si(v
, 3);
298 isl_constraint_set_coefficient(c
, isl_dim_set
, 1, v
);
299 bset
= isl_basic_set_add_constraint(bset
, c
);
301 c
= isl_equality_alloc(isl_local_space_copy(ls
));
302 isl_int_set_si(v
, 1);
303 isl_constraint_set_constant(c
, v
);
304 isl_int_set_si(v
, -1);
305 isl_constraint_set_coefficient(c
, isl_dim_set
, 0, v
);
306 isl_int_set_si(v
, 3);
307 isl_constraint_set_coefficient(c
, isl_dim_set
, 2, v
);
308 bset
= isl_basic_set_add_constraint(bset
, c
);
310 bset
= isl_basic_set_project_out(bset
, isl_dim_set
, 1, 2);
312 assert(bset
&& bset
->n_div
== 1);
313 isl_local_space_free(ls
);
314 isl_basic_set_free(bset
);
317 dim
= isl_space_set_alloc(ctx
, 0, 3);
318 bset
= isl_basic_set_universe(isl_space_copy(dim
));
319 ls
= isl_local_space_from_space(dim
);
321 c
= isl_equality_alloc(isl_local_space_copy(ls
));
322 isl_int_set_si(v
, 1);
323 isl_constraint_set_constant(c
, v
);
324 isl_int_set_si(v
, -1);
325 isl_constraint_set_coefficient(c
, isl_dim_set
, 0, v
);
326 isl_int_set_si(v
, 3);
327 isl_constraint_set_coefficient(c
, isl_dim_set
, 1, v
);
328 bset
= isl_basic_set_add_constraint(bset
, c
);
330 c
= isl_equality_alloc(isl_local_space_copy(ls
));
331 isl_int_set_si(v
, -1);
332 isl_constraint_set_constant(c
, v
);
333 isl_int_set_si(v
, 1);
334 isl_constraint_set_coefficient(c
, isl_dim_set
, 0, v
);
335 isl_int_set_si(v
, 3);
336 isl_constraint_set_coefficient(c
, isl_dim_set
, 2, v
);
337 bset
= isl_basic_set_add_constraint(bset
, c
);
339 bset
= isl_basic_set_project_out(bset
, isl_dim_set
, 1, 2);
341 assert(bset
&& bset
->n_div
== 1);
342 isl_local_space_free(ls
);
343 isl_basic_set_free(bset
);
346 dim
= isl_space_set_alloc(ctx
, 0, 3);
347 bset
= isl_basic_set_universe(isl_space_copy(dim
));
348 ls
= isl_local_space_from_space(dim
);
350 c
= isl_equality_alloc(isl_local_space_copy(ls
));
351 isl_int_set_si(v
, 1);
352 isl_constraint_set_constant(c
, v
);
353 isl_int_set_si(v
, -1);
354 isl_constraint_set_coefficient(c
, isl_dim_set
, 0, v
);
355 isl_int_set_si(v
, 3);
356 isl_constraint_set_coefficient(c
, isl_dim_set
, 1, v
);
357 bset
= isl_basic_set_add_constraint(bset
, c
);
359 c
= isl_equality_alloc(isl_local_space_copy(ls
));
360 isl_int_set_si(v
, -3);
361 isl_constraint_set_constant(c
, v
);
362 isl_int_set_si(v
, 1);
363 isl_constraint_set_coefficient(c
, isl_dim_set
, 0, v
);
364 isl_int_set_si(v
, 4);
365 isl_constraint_set_coefficient(c
, isl_dim_set
, 2, v
);
366 bset
= isl_basic_set_add_constraint(bset
, c
);
368 bset
= isl_basic_set_project_out(bset
, isl_dim_set
, 1, 2);
370 assert(bset
&& bset
->n_div
== 1);
371 isl_local_space_free(ls
);
372 isl_basic_set_free(bset
);
375 dim
= isl_space_set_alloc(ctx
, 0, 3);
376 bset
= isl_basic_set_universe(isl_space_copy(dim
));
377 ls
= isl_local_space_from_space(dim
);
379 c
= isl_equality_alloc(isl_local_space_copy(ls
));
380 isl_int_set_si(v
, 2);
381 isl_constraint_set_constant(c
, v
);
382 isl_int_set_si(v
, -1);
383 isl_constraint_set_coefficient(c
, isl_dim_set
, 0, v
);
384 isl_int_set_si(v
, 3);
385 isl_constraint_set_coefficient(c
, isl_dim_set
, 1, v
);
386 bset
= isl_basic_set_add_constraint(bset
, c
);
388 c
= isl_equality_alloc(isl_local_space_copy(ls
));
389 isl_int_set_si(v
, -1);
390 isl_constraint_set_constant(c
, v
);
391 isl_int_set_si(v
, 1);
392 isl_constraint_set_coefficient(c
, isl_dim_set
, 0, v
);
393 isl_int_set_si(v
, 6);
394 isl_constraint_set_coefficient(c
, isl_dim_set
, 2, v
);
395 bset
= isl_basic_set_add_constraint(bset
, c
);
397 bset
= isl_basic_set_project_out(bset
, isl_dim_set
, 1, 2);
399 assert(isl_basic_set_is_empty(bset
));
400 isl_local_space_free(ls
);
401 isl_basic_set_free(bset
);
404 dim
= isl_space_set_alloc(ctx
, 0, 3);
405 bset
= isl_basic_set_universe(isl_space_copy(dim
));
406 ls
= isl_local_space_from_space(dim
);
408 c
= isl_equality_alloc(isl_local_space_copy(ls
));
409 isl_int_set_si(v
, -1);
410 isl_constraint_set_coefficient(c
, isl_dim_set
, 0, v
);
411 isl_int_set_si(v
, 3);
412 isl_constraint_set_coefficient(c
, isl_dim_set
, 2, v
);
413 bset
= isl_basic_set_add_constraint(bset
, c
);
415 c
= isl_equality_alloc(isl_local_space_copy(ls
));
416 isl_int_set_si(v
, 1);
417 isl_constraint_set_coefficient(c
, isl_dim_set
, 0, v
);
418 isl_int_set_si(v
, -3);
419 isl_constraint_set_coefficient(c
, isl_dim_set
, 1, v
);
420 bset
= isl_basic_set_add_constraint(bset
, c
);
422 bset
= isl_basic_set_project_out(bset
, isl_dim_set
, 2, 1);
424 assert(bset
&& bset
->n_div
== 0);
425 isl_basic_set_free(bset
);
426 isl_local_space_free(ls
);
429 dim
= isl_space_set_alloc(ctx
, 0, 3);
430 bset
= isl_basic_set_universe(isl_space_copy(dim
));
431 ls
= isl_local_space_from_space(dim
);
433 c
= isl_equality_alloc(isl_local_space_copy(ls
));
434 isl_int_set_si(v
, -1);
435 isl_constraint_set_coefficient(c
, isl_dim_set
, 0, v
);
436 isl_int_set_si(v
, 6);
437 isl_constraint_set_coefficient(c
, isl_dim_set
, 2, v
);
438 bset
= isl_basic_set_add_constraint(bset
, c
);
440 c
= isl_equality_alloc(isl_local_space_copy(ls
));
441 isl_int_set_si(v
, 1);
442 isl_constraint_set_coefficient(c
, isl_dim_set
, 0, v
);
443 isl_int_set_si(v
, -3);
444 isl_constraint_set_coefficient(c
, isl_dim_set
, 1, v
);
445 bset
= isl_basic_set_add_constraint(bset
, c
);
447 bset
= isl_basic_set_project_out(bset
, isl_dim_set
, 2, 1);
449 assert(bset
&& bset
->n_div
== 1);
450 isl_basic_set_free(bset
);
451 isl_local_space_free(ls
);
454 /* This test is a bit tricky. We set up an equality
456 * Normalization of divs creates _two_ divs
459 * Afterwards e0 is removed again because it has coefficient -1
460 * and we end up with the original equality and div again.
461 * Perhaps we can avoid the introduction of this temporary div.
463 dim
= isl_space_set_alloc(ctx
, 0, 4);
464 bset
= isl_basic_set_universe(isl_space_copy(dim
));
465 ls
= isl_local_space_from_space(dim
);
467 c
= isl_equality_alloc(isl_local_space_copy(ls
));
468 isl_int_set_si(v
, -1);
469 isl_constraint_set_coefficient(c
, isl_dim_set
, 0, v
);
470 isl_int_set_si(v
, -3);
471 isl_constraint_set_coefficient(c
, isl_dim_set
, 1, v
);
472 isl_int_set_si(v
, -3);
473 isl_constraint_set_coefficient(c
, isl_dim_set
, 2, v
);
474 isl_int_set_si(v
, 6);
475 isl_constraint_set_coefficient(c
, isl_dim_set
, 3, v
);
476 bset
= isl_basic_set_add_constraint(bset
, c
);
478 bset
= isl_basic_set_project_out(bset
, isl_dim_set
, 3, 1);
480 /* Test disabled for now */
482 assert(bset && bset->n_div == 1);
484 isl_local_space_free(ls
);
485 isl_basic_set_free(bset
);
488 dim
= isl_space_set_alloc(ctx
, 0, 5);
489 bset
= isl_basic_set_universe(isl_space_copy(dim
));
490 ls
= isl_local_space_from_space(dim
);
492 c
= isl_equality_alloc(isl_local_space_copy(ls
));
493 isl_int_set_si(v
, -1);
494 isl_constraint_set_coefficient(c
, isl_dim_set
, 0, v
);
495 isl_int_set_si(v
, -3);
496 isl_constraint_set_coefficient(c
, isl_dim_set
, 1, v
);
497 isl_int_set_si(v
, -3);
498 isl_constraint_set_coefficient(c
, isl_dim_set
, 3, v
);
499 isl_int_set_si(v
, 6);
500 isl_constraint_set_coefficient(c
, isl_dim_set
, 4, v
);
501 bset
= isl_basic_set_add_constraint(bset
, c
);
503 c
= isl_equality_alloc(isl_local_space_copy(ls
));
504 isl_int_set_si(v
, -1);
505 isl_constraint_set_coefficient(c
, isl_dim_set
, 0, v
);
506 isl_int_set_si(v
, 1);
507 isl_constraint_set_coefficient(c
, isl_dim_set
, 2, v
);
508 isl_int_set_si(v
, 1);
509 isl_constraint_set_constant(c
, v
);
510 bset
= isl_basic_set_add_constraint(bset
, c
);
512 bset
= isl_basic_set_project_out(bset
, isl_dim_set
, 4, 1);
514 /* Test disabled for now */
516 assert(bset && bset->n_div == 1);
518 isl_local_space_free(ls
);
519 isl_basic_set_free(bset
);
522 dim
= isl_space_set_alloc(ctx
, 0, 4);
523 bset
= isl_basic_set_universe(isl_space_copy(dim
));
524 ls
= isl_local_space_from_space(dim
);
526 c
= isl_equality_alloc(isl_local_space_copy(ls
));
527 isl_int_set_si(v
, 1);
528 isl_constraint_set_coefficient(c
, isl_dim_set
, 0, v
);
529 isl_int_set_si(v
, -1);
530 isl_constraint_set_coefficient(c
, isl_dim_set
, 1, v
);
531 isl_int_set_si(v
, -2);
532 isl_constraint_set_coefficient(c
, isl_dim_set
, 2, v
);
533 bset
= isl_basic_set_add_constraint(bset
, c
);
535 c
= isl_equality_alloc(isl_local_space_copy(ls
));
536 isl_int_set_si(v
, -1);
537 isl_constraint_set_coefficient(c
, isl_dim_set
, 0, v
);
538 isl_int_set_si(v
, 3);
539 isl_constraint_set_coefficient(c
, isl_dim_set
, 3, v
);
540 isl_int_set_si(v
, 2);
541 isl_constraint_set_constant(c
, v
);
542 bset
= isl_basic_set_add_constraint(bset
, c
);
544 bset
= isl_basic_set_project_out(bset
, isl_dim_set
, 2, 2);
546 bset
= isl_basic_set_fix_si(bset
, isl_dim_set
, 0, 2);
548 assert(!isl_basic_set_is_empty(bset
));
550 isl_local_space_free(ls
);
551 isl_basic_set_free(bset
);
554 dim
= isl_space_set_alloc(ctx
, 0, 3);
555 bset
= isl_basic_set_universe(isl_space_copy(dim
));
556 ls
= isl_local_space_from_space(dim
);
558 c
= isl_equality_alloc(isl_local_space_copy(ls
));
559 isl_int_set_si(v
, 1);
560 isl_constraint_set_coefficient(c
, isl_dim_set
, 0, v
);
561 isl_int_set_si(v
, -2);
562 isl_constraint_set_coefficient(c
, isl_dim_set
, 2, v
);
563 bset
= isl_basic_set_add_constraint(bset
, c
);
565 bset
= isl_basic_set_project_out(bset
, isl_dim_set
, 2, 1);
567 bset
= isl_basic_set_fix_si(bset
, isl_dim_set
, 0, 2);
569 isl_local_space_free(ls
);
570 isl_basic_set_free(bset
);
575 void test_application_case(struct isl_ctx
*ctx
, const char *name
)
579 struct isl_basic_set
*bset1
, *bset2
;
580 struct isl_basic_map
*bmap
;
582 filename
= get_filename(ctx
, name
, "omega");
584 input
= fopen(filename
, "r");
587 bset1
= isl_basic_set_read_from_file(ctx
, input
);
588 bmap
= isl_basic_map_read_from_file(ctx
, input
);
590 bset1
= isl_basic_set_apply(bset1
, bmap
);
592 bset2
= isl_basic_set_read_from_file(ctx
, input
);
594 assert(isl_basic_set_is_equal(bset1
, bset2
) == 1);
596 isl_basic_set_free(bset1
);
597 isl_basic_set_free(bset2
);
603 void test_application(struct isl_ctx
*ctx
)
605 test_application_case(ctx
, "application");
606 test_application_case(ctx
, "application2");
609 void test_affine_hull_case(struct isl_ctx
*ctx
, const char *name
)
613 struct isl_basic_set
*bset1
, *bset2
;
615 filename
= get_filename(ctx
, name
, "polylib");
617 input
= fopen(filename
, "r");
620 bset1
= isl_basic_set_read_from_file(ctx
, input
);
621 bset2
= isl_basic_set_read_from_file(ctx
, input
);
623 bset1
= isl_basic_set_affine_hull(bset1
);
625 assert(isl_basic_set_is_equal(bset1
, bset2
) == 1);
627 isl_basic_set_free(bset1
);
628 isl_basic_set_free(bset2
);
634 void test_affine_hull(struct isl_ctx
*ctx
)
636 test_affine_hull_case(ctx
, "affine2");
637 test_affine_hull_case(ctx
, "affine");
638 test_affine_hull_case(ctx
, "affine3");
641 void test_convex_hull_case(struct isl_ctx
*ctx
, const char *name
)
645 struct isl_basic_set
*bset1
, *bset2
;
648 filename
= get_filename(ctx
, name
, "polylib");
650 input
= fopen(filename
, "r");
653 bset1
= isl_basic_set_read_from_file(ctx
, input
);
654 bset2
= isl_basic_set_read_from_file(ctx
, input
);
656 set
= isl_basic_set_union(bset1
, bset2
);
657 bset1
= isl_set_convex_hull(set
);
659 bset2
= isl_basic_set_read_from_file(ctx
, input
);
661 assert(isl_basic_set_is_equal(bset1
, bset2
) == 1);
663 isl_basic_set_free(bset1
);
664 isl_basic_set_free(bset2
);
670 void test_convex_hull_algo(struct isl_ctx
*ctx
, int convex
)
672 const char *str1
, *str2
;
673 isl_set
*set1
, *set2
;
674 int orig_convex
= ctx
->opt
->convex
;
675 ctx
->opt
->convex
= convex
;
677 test_convex_hull_case(ctx
, "convex0");
678 test_convex_hull_case(ctx
, "convex1");
679 test_convex_hull_case(ctx
, "convex2");
680 test_convex_hull_case(ctx
, "convex3");
681 test_convex_hull_case(ctx
, "convex4");
682 test_convex_hull_case(ctx
, "convex5");
683 test_convex_hull_case(ctx
, "convex6");
684 test_convex_hull_case(ctx
, "convex7");
685 test_convex_hull_case(ctx
, "convex8");
686 test_convex_hull_case(ctx
, "convex9");
687 test_convex_hull_case(ctx
, "convex10");
688 test_convex_hull_case(ctx
, "convex11");
689 test_convex_hull_case(ctx
, "convex12");
690 test_convex_hull_case(ctx
, "convex13");
691 test_convex_hull_case(ctx
, "convex14");
692 test_convex_hull_case(ctx
, "convex15");
694 str1
= "{ [i0, i1, i2] : (i2 = 1 and i0 = 0 and i1 >= 0) or "
695 "(i0 = 1 and i1 = 0 and i2 = 1) or "
696 "(i0 = 0 and i1 = 0 and i2 = 0) }";
697 str2
= "{ [i0, i1, i2] : i0 >= 0 and i2 >= i0 and i2 <= 1 and i1 >= 0 }";
698 set1
= isl_set_read_from_str(ctx
, str1
);
699 set2
= isl_set_read_from_str(ctx
, str2
);
700 set1
= isl_set_from_basic_set(isl_set_convex_hull(set1
));
701 assert(isl_set_is_equal(set1
, set2
));
705 ctx
->opt
->convex
= orig_convex
;
708 void test_convex_hull(struct isl_ctx
*ctx
)
710 test_convex_hull_algo(ctx
, ISL_CONVEX_HULL_FM
);
711 test_convex_hull_algo(ctx
, ISL_CONVEX_HULL_WRAP
);
714 void test_gist_case(struct isl_ctx
*ctx
, const char *name
)
718 struct isl_basic_set
*bset1
, *bset2
;
720 filename
= get_filename(ctx
, name
, "polylib");
722 input
= fopen(filename
, "r");
725 bset1
= isl_basic_set_read_from_file(ctx
, input
);
726 bset2
= isl_basic_set_read_from_file(ctx
, input
);
728 bset1
= isl_basic_set_gist(bset1
, bset2
);
730 bset2
= isl_basic_set_read_from_file(ctx
, input
);
732 assert(isl_basic_set_is_equal(bset1
, bset2
) == 1);
734 isl_basic_set_free(bset1
);
735 isl_basic_set_free(bset2
);
741 void test_gist(struct isl_ctx
*ctx
)
744 isl_basic_set
*bset1
, *bset2
;
746 test_gist_case(ctx
, "gist1");
748 str
= "[p0, p2, p3, p5, p6, p10] -> { [] : "
749 "exists (e0 = [(15 + p0 + 15p6 + 15p10)/16], e1 = [(p5)/8], "
750 "e2 = [(p6)/128], e3 = [(8p2 - p5)/128], "
751 "e4 = [(128p3 - p6)/4096]: 8e1 = p5 and 128e2 = p6 and "
752 "128e3 = 8p2 - p5 and 4096e4 = 128p3 - p6 and p2 >= 0 and "
753 "16e0 >= 16 + 16p6 + 15p10 and p2 <= 15 and p3 >= 0 and "
754 "p3 <= 31 and p6 >= 128p3 and p5 >= 8p2 and p10 >= 0 and "
755 "16e0 <= 15 + p0 + 15p6 + 15p10 and 16e0 >= p0 + 15p6 + 15p10 and "
756 "p10 <= 15 and p10 <= -1 + p0 - p6) }";
757 bset1
= isl_basic_set_read_from_str(ctx
, str
);
758 str
= "[p0, p2, p3, p5, p6, p10] -> { [] : exists (e0 = [(p5)/8], "
759 "e1 = [(p6)/128], e2 = [(8p2 - p5)/128], "
760 "e3 = [(128p3 - p6)/4096]: 8e0 = p5 and 128e1 = p6 and "
761 "128e2 = 8p2 - p5 and 4096e3 = 128p3 - p6 and p5 >= -7 and "
762 "p2 >= 0 and 8p2 <= -1 + p0 and p2 <= 15 and p3 >= 0 and "
763 "p3 <= 31 and 128p3 <= -1 + p0 and p6 >= -127 and "
764 "p5 <= -1 + p0 and p6 <= -1 + p0 and p6 >= 128p3 and "
765 "p0 >= 1 and p5 >= 8p2 and p10 >= 0 and p10 <= 15 ) }";
766 bset2
= isl_basic_set_read_from_str(ctx
, str
);
767 bset1
= isl_basic_set_gist(bset1
, bset2
);
768 assert(bset1
&& bset1
->n_div
== 0);
769 isl_basic_set_free(bset1
);
772 void test_coalesce_set(isl_ctx
*ctx
, const char *str
, int check_one
)
776 set
= isl_set_read_from_str(ctx
, str
);
777 set
= isl_set_coalesce(set
);
778 set2
= isl_set_read_from_str(ctx
, str
);
779 assert(isl_set_is_equal(set
, set2
));
781 assert(set
&& set
->n
== 1);
786 void test_coalesce(struct isl_ctx
*ctx
)
789 struct isl_set
*set
, *set2
;
790 struct isl_map
*map
, *map2
;
792 set
= isl_set_read_from_str(ctx
,
793 "{[x,y]: x >= 0 & x <= 10 & y >= 0 & y <= 10 or "
794 "y >= x & x >= 2 & 5 >= y }");
795 set
= isl_set_coalesce(set
);
796 assert(set
&& set
->n
== 1);
799 set
= isl_set_read_from_str(ctx
,
800 "{[x,y]: y >= 0 & 2x + y <= 30 & y <= 10 & x >= 0 or "
801 "x + y >= 10 & y <= x & x + y <= 20 & y >= 0}");
802 set
= isl_set_coalesce(set
);
803 assert(set
&& set
->n
== 1);
806 set
= isl_set_read_from_str(ctx
,
807 "{[x,y]: y >= 0 & 2x + y <= 30 & y <= 10 & x >= 0 or "
808 "x + y >= 10 & y <= x & x + y <= 19 & y >= 0}");
809 set
= isl_set_coalesce(set
);
810 assert(set
&& set
->n
== 2);
813 set
= isl_set_read_from_str(ctx
,
814 "{[x,y]: y >= 0 & x <= 5 & y <= x or "
815 "y >= 0 & x >= 6 & x <= 10 & y <= x}");
816 set
= isl_set_coalesce(set
);
817 assert(set
&& set
->n
== 1);
820 set
= isl_set_read_from_str(ctx
,
821 "{[x,y]: y >= 0 & x <= 5 & y <= x or "
822 "y >= 0 & x >= 7 & x <= 10 & y <= x}");
823 set
= isl_set_coalesce(set
);
824 assert(set
&& set
->n
== 2);
827 set
= isl_set_read_from_str(ctx
,
828 "{[x,y]: y >= 0 & x <= 5 & y <= x or "
829 "y >= 0 & x >= 6 & x <= 10 & y + 1 <= x}");
830 set
= isl_set_coalesce(set
);
831 assert(set
&& set
->n
== 2);
834 set
= isl_set_read_from_str(ctx
,
835 "{[x,y]: y >= 0 & x <= 5 & y <= x or "
836 "y >= 0 & x = 6 & y <= 6}");
837 set
= isl_set_coalesce(set
);
838 assert(set
&& set
->n
== 1);
841 set
= isl_set_read_from_str(ctx
,
842 "{[x,y]: y >= 0 & x <= 5 & y <= x or "
843 "y >= 0 & x = 7 & y <= 6}");
844 set
= isl_set_coalesce(set
);
845 assert(set
&& set
->n
== 2);
848 set
= isl_set_read_from_str(ctx
,
849 "{[x,y]: y >= 0 & x <= 5 & y <= x or "
850 "y >= 0 & x = 6 & y <= 5}");
851 set
= isl_set_coalesce(set
);
852 assert(set
&& set
->n
== 1);
853 set2
= isl_set_read_from_str(ctx
,
854 "{[x,y]: y >= 0 & x <= 5 & y <= x or "
855 "y >= 0 & x = 6 & y <= 5}");
856 assert(isl_set_is_equal(set
, set2
));
860 set
= isl_set_read_from_str(ctx
,
861 "{[x,y]: y >= 0 & x <= 5 & y <= x or "
862 "y >= 0 & x = 6 & y <= 7}");
863 set
= isl_set_coalesce(set
);
864 assert(set
&& set
->n
== 2);
867 set
= isl_set_read_from_str(ctx
,
868 "[n] -> { [i] : i = 1 and n >= 2 or 2 <= i and i <= n }");
869 set
= isl_set_coalesce(set
);
870 assert(set
&& set
->n
== 1);
871 set2
= isl_set_read_from_str(ctx
,
872 "[n] -> { [i] : i = 1 and n >= 2 or 2 <= i and i <= n }");
873 assert(isl_set_is_equal(set
, set2
));
877 set
= isl_set_read_from_str(ctx
,
878 "{[x,y] : x >= 0 and y >= 0 or 0 <= y and y <= 5 and x = -1}");
879 set
= isl_set_coalesce(set
);
880 set2
= isl_set_read_from_str(ctx
,
881 "{[x,y] : x >= 0 and y >= 0 or 0 <= y and y <= 5 and x = -1}");
882 assert(isl_set_is_equal(set
, set2
));
886 set
= isl_set_read_from_str(ctx
,
887 "[n] -> { [i] : 1 <= i and i <= n - 1 or "
888 "2 <= i and i <= n }");
889 set
= isl_set_coalesce(set
);
890 assert(set
&& set
->n
== 1);
891 set2
= isl_set_read_from_str(ctx
,
892 "[n] -> { [i] : 1 <= i and i <= n - 1 or "
893 "2 <= i and i <= n }");
894 assert(isl_set_is_equal(set
, set2
));
898 map
= isl_map_read_from_str(ctx
,
899 "[n] -> { [i0] -> [o0] : exists (e0 = [(i0)/4], e1 = [(o0)/4], "
900 "e2 = [(n)/2], e3 = [(-2 + i0)/4], e4 = [(-2 + o0)/4], "
901 "e5 = [(-2n + i0)/4]: 2e2 = n and 4e3 = -2 + i0 and "
902 "4e4 = -2 + o0 and i0 >= 8 + 2n and o0 >= 2 + i0 and "
903 "o0 <= 56 + 2n and o0 <= -12 + 4n and i0 <= 57 + 2n and "
904 "i0 <= -11 + 4n and o0 >= 6 + 2n and 4e0 <= i0 and "
905 "4e0 >= -3 + i0 and 4e1 <= o0 and 4e1 >= -3 + o0 and "
906 "4e5 <= -2n + i0 and 4e5 >= -3 - 2n + i0);"
907 "[i0] -> [o0] : exists (e0 = [(i0)/4], e1 = [(o0)/4], "
908 "e2 = [(n)/2], e3 = [(-2 + i0)/4], e4 = [(-2 + o0)/4], "
909 "e5 = [(-2n + i0)/4]: 2e2 = n and 4e3 = -2 + i0 and "
910 "4e4 = -2 + o0 and 2e0 >= 3 + n and e0 <= -4 + n and "
911 "2e0 <= 27 + n and e1 <= -4 + n and 2e1 <= 27 + n and "
912 "2e1 >= 2 + n and e1 >= 1 + e0 and i0 >= 7 + 2n and "
913 "i0 <= -11 + 4n and i0 <= 57 + 2n and 4e0 <= -2 + i0 and "
914 "4e0 >= -3 + i0 and o0 >= 6 + 2n and o0 <= -11 + 4n and "
915 "o0 <= 57 + 2n and 4e1 <= -2 + o0 and 4e1 >= -3 + o0 and "
916 "4e5 <= -2n + i0 and 4e5 >= -3 - 2n + i0 ) }");
917 map
= isl_map_coalesce(map
);
918 map2
= isl_map_read_from_str(ctx
,
919 "[n] -> { [i0] -> [o0] : exists (e0 = [(i0)/4], e1 = [(o0)/4], "
920 "e2 = [(n)/2], e3 = [(-2 + i0)/4], e4 = [(-2 + o0)/4], "
921 "e5 = [(-2n + i0)/4]: 2e2 = n and 4e3 = -2 + i0 and "
922 "4e4 = -2 + o0 and i0 >= 8 + 2n and o0 >= 2 + i0 and "
923 "o0 <= 56 + 2n and o0 <= -12 + 4n and i0 <= 57 + 2n and "
924 "i0 <= -11 + 4n and o0 >= 6 + 2n and 4e0 <= i0 and "
925 "4e0 >= -3 + i0 and 4e1 <= o0 and 4e1 >= -3 + o0 and "
926 "4e5 <= -2n + i0 and 4e5 >= -3 - 2n + i0);"
927 "[i0] -> [o0] : exists (e0 = [(i0)/4], e1 = [(o0)/4], "
928 "e2 = [(n)/2], e3 = [(-2 + i0)/4], e4 = [(-2 + o0)/4], "
929 "e5 = [(-2n + i0)/4]: 2e2 = n and 4e3 = -2 + i0 and "
930 "4e4 = -2 + o0 and 2e0 >= 3 + n and e0 <= -4 + n and "
931 "2e0 <= 27 + n and e1 <= -4 + n and 2e1 <= 27 + n and "
932 "2e1 >= 2 + n and e1 >= 1 + e0 and i0 >= 7 + 2n and "
933 "i0 <= -11 + 4n and i0 <= 57 + 2n and 4e0 <= -2 + i0 and "
934 "4e0 >= -3 + i0 and o0 >= 6 + 2n and o0 <= -11 + 4n and "
935 "o0 <= 57 + 2n and 4e1 <= -2 + o0 and 4e1 >= -3 + o0 and "
936 "4e5 <= -2n + i0 and 4e5 >= -3 - 2n + i0 ) }");
937 assert(isl_map_is_equal(map
, map2
));
941 str
= "[n, m] -> { [] -> [o0, o2, o3] : (o3 = 1 and o0 >= 1 + m and "
942 "o0 <= n + m and o2 <= m and o0 >= 2 + n and o2 >= 3) or "
943 "(o0 >= 2 + n and o0 >= 1 + m and o0 <= n + m and n >= 1 and "
944 "o3 <= -1 + o2 and o3 >= 1 - m + o2 and o3 >= 2 and o3 <= n) }";
945 map
= isl_map_read_from_str(ctx
, str
);
946 map
= isl_map_coalesce(map
);
947 map2
= isl_map_read_from_str(ctx
, str
);
948 assert(isl_map_is_equal(map
, map2
));
952 str
= "[M, N] -> { [i0, i1, i2, i3, i4, i5, i6] -> "
953 "[o0, o1, o2, o3, o4, o5, o6] : "
954 "(o6 <= -4 + 2M - 2N + i0 + i1 - i2 + i6 - o0 - o1 + o2 and "
955 "o3 <= -2 + i3 and o6 >= 2 + i0 + i3 + i6 - o0 - o3 and "
956 "o6 >= 2 - M + N + i3 + i4 + i6 - o3 - o4 and o0 <= -1 + i0 and "
957 "o4 >= 4 - 3M + 3N - i0 - i1 + i2 + 2i3 + i4 + o0 + o1 - o2 - 2o3 "
958 "and o6 <= -3 + 2M - 2N + i3 + i4 - i5 + i6 - o3 - o4 + o5 and "
959 "2o6 <= -5 + 5M - 5N + 2i0 + i1 - i2 - i5 + 2i6 - 2o0 - o1 + o2 + o5 "
960 "and o6 >= 2i0 + i1 + i6 - 2o0 - o1 and "
961 "3o6 <= -5 + 4M - 4N + 2i0 + i1 - i2 + 2i3 + i4 - i5 + 3i6 "
962 "- 2o0 - o1 + o2 - 2o3 - o4 + o5) or "
963 "(N >= 2 and o3 <= -1 + i3 and o0 <= -1 + i0 and "
964 "o6 >= i3 + i6 - o3 and M >= 0 and "
965 "2o6 >= 1 + i0 + i3 + 2i6 - o0 - o3 and "
966 "o6 >= 1 - M + i0 + i6 - o0 and N >= 2M and o6 >= i0 + i6 - o0) }";
967 map
= isl_map_read_from_str(ctx
, str
);
968 map
= isl_map_coalesce(map
);
969 map2
= isl_map_read_from_str(ctx
, str
);
970 assert(isl_map_is_equal(map
, map2
));
974 str
= "[M, N] -> { [] -> [o0] : (o0 = 0 and M >= 1 and N >= 2) or "
975 "(o0 = 0 and M >= 1 and N >= 2M and N >= 2 + M) or "
976 "(o0 = 0 and M >= 2 and N >= 3) or "
977 "(M = 0 and o0 = 0 and N >= 3) }";
978 map
= isl_map_read_from_str(ctx
, str
);
979 map
= isl_map_coalesce(map
);
980 map2
= isl_map_read_from_str(ctx
, str
);
981 assert(isl_map_is_equal(map
, map2
));
985 str
= "{ [i0, i1, i2, i3] : (i1 = 10i0 and i0 >= 1 and 10i0 <= 100 and "
986 "i3 <= 9 + 10 i2 and i3 >= 1 + 10i2 and i3 >= 0) or "
987 "(i1 <= 9 + 10i0 and i1 >= 1 + 10i0 and i2 >= 0 and "
988 "i0 >= 0 and i1 <= 100 and i3 <= 9 + 10i2 and i3 >= 1 + 10i2) }";
989 map
= isl_map_read_from_str(ctx
, str
);
990 map
= isl_map_coalesce(map
);
991 map2
= isl_map_read_from_str(ctx
, str
);
992 assert(isl_map_is_equal(map
, map2
));
996 test_coalesce_set(ctx
,
997 "[M] -> { [i1] : (i1 >= 2 and i1 <= M) or "
998 "(i1 = M and M >= 1) }", 0);
999 test_coalesce_set(ctx
,
1000 "{[x,y] : x,y >= 0; [x,y] : 10 <= x <= 20 and y >= -1 }", 0);
1001 test_coalesce_set(ctx
,
1002 "{ [x, y] : (x >= 1 and y >= 1 and x <= 2 and y <= 2) or "
1003 "(y = 3 and x = 1) }", 1);
1004 test_coalesce_set(ctx
,
1005 "[M] -> { [i0, i1, i2, i3, i4] : (i1 >= 3 and i4 >= 2 + i2 and "
1006 "i2 >= 2 and i0 >= 2 and i3 >= 1 + i2 and i0 <= M and "
1007 "i1 <= M and i3 <= M and i4 <= M) or "
1008 "(i1 >= 2 and i4 >= 1 + i2 and i2 >= 2 and i0 >= 2 and "
1009 "i3 >= 1 + i2 and i0 <= M and i1 <= -1 + M and i3 <= M and "
1010 "i4 <= -1 + M) }", 1);
1011 test_coalesce_set(ctx
,
1012 "{ [x, y] : (x >= 0 and y >= 0 and x <= 10 and y <= 10) or "
1013 "(x >= 1 and y >= 1 and x <= 11 and y <= 11) }", 1);
1014 test_coalesce_set(ctx
,
1015 "{[x,y,z] : y + 2 >= 0 and x - y + 1 >= 0 and "
1016 "-x - y + 1 >= 0 and -3 <= z <= 3;"
1017 "[x,y,z] : -x+z + 20 >= 0 and -x-z + 20 >= 0 and "
1018 "x-z + 20 >= 0 and x+z + 20 >= 0 and -10 <= y <= 0}", 1);
1019 test_coalesce_set(ctx
,
1020 "{[x,y] : 0 <= x,y <= 10; [5,y]: 4 <=y <= 11}", 1);
1021 test_coalesce_set(ctx
, "{[x,0] : x >= 0; [x,1] : x <= 20}", 0);
1022 test_coalesce_set(ctx
,
1023 "{[x,0,0] : -5 <= x <= 5; [0,y,1] : -5 <= y <= 5 }", 1);
1024 test_coalesce_set(ctx
, "{ [x, 1 - x] : 0 <= x <= 1; [0,0] }", 1);
1025 test_coalesce_set(ctx
, "{ [0,0]; [i,i] : 1 <= i <= 10 }", 1);
1026 test_coalesce_set(ctx
, "{ [0,0]; [i,j] : 1 <= i,j <= 10 }", 0);
1027 test_coalesce_set(ctx
, "{ [0,0]; [i,2i] : 1 <= i <= 10 }", 1);
1028 test_coalesce_set(ctx
, "{ [0,0]; [i,2i] : 2 <= i <= 10 }", 0);
1029 test_coalesce_set(ctx
, "{ [1,0]; [i,2i] : 1 <= i <= 10 }", 0);
1030 test_coalesce_set(ctx
, "{ [0,1]; [i,2i] : 1 <= i <= 10 }", 0);
1033 void test_closure(struct isl_ctx
*ctx
)
1037 isl_map
*up
, *right
;
1038 isl_map
*map
, *map2
;
1041 /* COCOA example 1 */
1042 map
= isl_map_read_from_str(ctx
,
1043 "[n] -> { [i,j] -> [i2,j2] : i2 = i + 1 and j2 = j + 1 and "
1044 "1 <= i and i < n and 1 <= j and j < n or "
1045 "i2 = i + 1 and j2 = j - 1 and "
1046 "1 <= i and i < n and 2 <= j and j <= n }");
1047 map
= isl_map_power(map
, &exact
);
1051 /* COCOA example 1 */
1052 map
= isl_map_read_from_str(ctx
,
1053 "[n] -> { [i,j] -> [i2,j2] : i2 = i + 1 and j2 = j + 1 and "
1054 "1 <= i and i < n and 1 <= j and j < n or "
1055 "i2 = i + 1 and j2 = j - 1 and "
1056 "1 <= i and i < n and 2 <= j and j <= n }");
1057 map
= isl_map_transitive_closure(map
, &exact
);
1059 map2
= isl_map_read_from_str(ctx
,
1060 "[n] -> { [i,j] -> [i2,j2] : exists (k1,k2,k : "
1061 "1 <= i and i < n and 1 <= j and j <= n and "
1062 "2 <= i2 and i2 <= n and 1 <= j2 and j2 <= n and "
1063 "i2 = i + k1 + k2 and j2 = j + k1 - k2 and "
1064 "k1 >= 0 and k2 >= 0 and k1 + k2 = k and k >= 1 )}");
1065 assert(isl_map_is_equal(map
, map2
));
1069 map
= isl_map_read_from_str(ctx
,
1070 "[n] -> { [x] -> [y] : y = x + 1 and 0 <= x and x <= n and "
1071 " 0 <= y and y <= n }");
1072 map
= isl_map_transitive_closure(map
, &exact
);
1073 map2
= isl_map_read_from_str(ctx
,
1074 "[n] -> { [x] -> [y] : y > x and 0 <= x and x <= n and "
1075 " 0 <= y and y <= n }");
1076 assert(isl_map_is_equal(map
, map2
));
1080 /* COCOA example 2 */
1081 map
= isl_map_read_from_str(ctx
,
1082 "[n] -> { [i,j] -> [i2,j2] : i2 = i + 2 and j2 = j + 2 and "
1083 "1 <= i and i < n - 1 and 1 <= j and j < n - 1 or "
1084 "i2 = i + 2 and j2 = j - 2 and "
1085 "1 <= i and i < n - 1 and 3 <= j and j <= n }");
1086 map
= isl_map_transitive_closure(map
, &exact
);
1088 map2
= isl_map_read_from_str(ctx
,
1089 "[n] -> { [i,j] -> [i2,j2] : exists (k1,k2,k : "
1090 "1 <= i and i < n - 1 and 1 <= j and j <= n and "
1091 "3 <= i2 and i2 <= n and 1 <= j2 and j2 <= n and "
1092 "i2 = i + 2 k1 + 2 k2 and j2 = j + 2 k1 - 2 k2 and "
1093 "k1 >= 0 and k2 >= 0 and k1 + k2 = k and k >= 1) }");
1094 assert(isl_map_is_equal(map
, map2
));
1098 /* COCOA Fig.2 left */
1099 map
= isl_map_read_from_str(ctx
,
1100 "[n] -> { [i,j] -> [i2,j2] : i2 = i + 2 and j2 = j and "
1101 "i <= 2 j - 3 and i <= n - 2 and j <= 2 i - 1 and "
1103 "i2 = i and j2 = j + 2 and i <= 2 j - 1 and i <= n and "
1104 "j <= 2 i - 3 and j <= n - 2 or "
1105 "i2 = i + 1 and j2 = j + 1 and i <= 2 j - 1 and "
1106 "i <= n - 1 and j <= 2 i - 1 and j <= n - 1 }");
1107 map
= isl_map_transitive_closure(map
, &exact
);
1111 /* COCOA Fig.2 right */
1112 map
= isl_map_read_from_str(ctx
,
1113 "[n] -> { [i,j] -> [i2,j2] : i2 = i + 3 and j2 = j and "
1114 "i <= 2 j - 4 and i <= n - 3 and j <= 2 i - 1 and "
1116 "i2 = i and j2 = j + 3 and i <= 2 j - 1 and i <= n and "
1117 "j <= 2 i - 4 and j <= n - 3 or "
1118 "i2 = i + 1 and j2 = j + 1 and i <= 2 j - 1 and "
1119 "i <= n - 1 and j <= 2 i - 1 and j <= n - 1 }");
1120 map
= isl_map_power(map
, &exact
);
1124 /* COCOA Fig.2 right */
1125 map
= isl_map_read_from_str(ctx
,
1126 "[n] -> { [i,j] -> [i2,j2] : i2 = i + 3 and j2 = j and "
1127 "i <= 2 j - 4 and i <= n - 3 and j <= 2 i - 1 and "
1129 "i2 = i and j2 = j + 3 and i <= 2 j - 1 and i <= n and "
1130 "j <= 2 i - 4 and j <= n - 3 or "
1131 "i2 = i + 1 and j2 = j + 1 and i <= 2 j - 1 and "
1132 "i <= n - 1 and j <= 2 i - 1 and j <= n - 1 }");
1133 map
= isl_map_transitive_closure(map
, &exact
);
1135 map2
= isl_map_read_from_str(ctx
,
1136 "[n] -> { [i,j] -> [i2,j2] : exists (k1,k2,k3,k : "
1137 "i <= 2 j - 1 and i <= n and j <= 2 i - 1 and "
1138 "j <= n and 3 + i + 2 j <= 3 n and "
1139 "3 + 2 i + j <= 3n and i2 <= 2 j2 -1 and i2 <= n and "
1140 "i2 <= 3 j2 - 4 and j2 <= 2 i2 -1 and j2 <= n and "
1141 "13 + 4 j2 <= 11 i2 and i2 = i + 3 k1 + k3 and "
1142 "j2 = j + 3 k2 + k3 and k1 >= 0 and k2 >= 0 and "
1143 "k3 >= 0 and k1 + k2 + k3 = k and k > 0) }");
1144 assert(isl_map_is_equal(map
, map2
));
1148 /* COCOA Fig.1 right */
1149 dom
= isl_set_read_from_str(ctx
,
1150 "{ [x,y] : x >= 0 and -2 x + 3 y >= 0 and x <= 3 and "
1151 "2 x - 3 y + 3 >= 0 }");
1152 right
= isl_map_read_from_str(ctx
,
1153 "{ [x,y] -> [x2,y2] : x2 = x + 1 and y2 = y }");
1154 up
= isl_map_read_from_str(ctx
,
1155 "{ [x,y] -> [x2,y2] : x2 = x and y2 = y + 1 }");
1156 right
= isl_map_intersect_domain(right
, isl_set_copy(dom
));
1157 right
= isl_map_intersect_range(right
, isl_set_copy(dom
));
1158 up
= isl_map_intersect_domain(up
, isl_set_copy(dom
));
1159 up
= isl_map_intersect_range(up
, dom
);
1160 map
= isl_map_union(up
, right
);
1161 map
= isl_map_transitive_closure(map
, &exact
);
1163 map2
= isl_map_read_from_str(ctx
,
1164 "{ [0,0] -> [0,1]; [0,0] -> [1,1]; [0,1] -> [1,1]; "
1165 " [2,2] -> [3,2]; [2,2] -> [3,3]; [3,2] -> [3,3] }");
1166 assert(isl_map_is_equal(map
, map2
));
1170 /* COCOA Theorem 1 counter example */
1171 map
= isl_map_read_from_str(ctx
,
1172 "{ [i,j] -> [i2,j2] : i = 0 and 0 <= j and j <= 1 and "
1173 "i2 = 1 and j2 = j or "
1174 "i = 0 and j = 0 and i2 = 0 and j2 = 1 }");
1175 map
= isl_map_transitive_closure(map
, &exact
);
1179 map
= isl_map_read_from_str(ctx
,
1180 "[m,n] -> { [i,j] -> [i2,j2] : i2 = i and j2 = j + 2 and "
1181 "1 <= i,i2 <= n and 1 <= j,j2 <= m or "
1182 "i2 = i + 1 and 3 <= j2 - j <= 4 and "
1183 "1 <= i,i2 <= n and 1 <= j,j2 <= m }");
1184 map
= isl_map_transitive_closure(map
, &exact
);
1188 /* Kelly et al 1996, fig 12 */
1189 map
= isl_map_read_from_str(ctx
,
1190 "[n] -> { [i,j] -> [i2,j2] : i2 = i and j2 = j + 1 and "
1191 "1 <= i,j,j+1 <= n or "
1192 "j = n and j2 = 1 and i2 = i + 1 and "
1193 "1 <= i,i+1 <= n }");
1194 map
= isl_map_transitive_closure(map
, &exact
);
1196 map2
= isl_map_read_from_str(ctx
,
1197 "[n] -> { [i,j] -> [i2,j2] : 1 <= j < j2 <= n and "
1198 "1 <= i <= n and i = i2 or "
1199 "1 <= i < i2 <= n and 1 <= j <= n and "
1201 assert(isl_map_is_equal(map
, map2
));
1205 /* Omega's closure4 */
1206 map
= isl_map_read_from_str(ctx
,
1207 "[m,n] -> { [x,y] -> [x2,y2] : x2 = x and y2 = y + 1 and "
1208 "1 <= x,y <= 10 or "
1209 "x2 = x + 1 and y2 = y and "
1210 "1 <= x <= 20 && 5 <= y <= 15 }");
1211 map
= isl_map_transitive_closure(map
, &exact
);
1215 map
= isl_map_read_from_str(ctx
,
1216 "[n] -> { [x] -> [y]: 1 <= n <= y - x <= 10 }");
1217 map
= isl_map_transitive_closure(map
, &exact
);
1219 map2
= isl_map_read_from_str(ctx
,
1220 "[n] -> { [x] -> [y] : 1 <= n <= 10 and y >= n + x }");
1221 assert(isl_map_is_equal(map
, map2
));
1225 str
= "[n, m] -> { [i0, i1, i2, i3] -> [o0, o1, o2, o3] : "
1226 "i3 = 1 and o0 = i0 and o1 = -1 + i1 and o2 = -1 + i2 and "
1227 "o3 = -2 + i2 and i1 <= -1 + i0 and i1 >= 1 - m + i0 and "
1228 "i1 >= 2 and i1 <= n and i2 >= 3 and i2 <= 1 + n and i2 <= m }";
1229 map
= isl_map_read_from_str(ctx
, str
);
1230 map
= isl_map_transitive_closure(map
, &exact
);
1232 map2
= isl_map_read_from_str(ctx
, str
);
1233 assert(isl_map_is_equal(map
, map2
));
1237 str
= "{[0] -> [1]; [2] -> [3]}";
1238 map
= isl_map_read_from_str(ctx
, str
);
1239 map
= isl_map_transitive_closure(map
, &exact
);
1241 map2
= isl_map_read_from_str(ctx
, str
);
1242 assert(isl_map_is_equal(map
, map2
));
1246 str
= "[n] -> { [[i0, i1, 1, 0, i0] -> [i5, 1]] -> "
1247 "[[i0, -1 + i1, 2, 0, i0] -> [-1 + i5, 2]] : "
1248 "exists (e0 = [(3 - n)/3]: i5 >= 2 and i1 >= 2 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 "[[i0, i1, 2, 0, i0] -> [i5, 1]] -> "
1252 "[[i0, i1, 1, 0, i0] -> [-1 + i5, 2]] : "
1253 "exists (e0 = [(3 - n)/3]: i5 >= 2 and i1 >= 1 and "
1254 "3i0 <= -1 + n and i1 <= -1 + n and i5 <= -1 + n and "
1255 "3e0 >= 1 - n and 3e0 <= 2 - n and 3i0 >= -2 + n); "
1256 "[[i0, i1, 1, 0, i0] -> [i5, 2]] -> "
1257 "[[i0, -1 + i1, 2, 0, i0] -> [i5, 1]] : "
1258 "exists (e0 = [(3 - n)/3]: i1 >= 2 and i5 >= 1 and "
1259 "3i0 <= -1 + n and i1 <= -1 + n and i5 <= -1 + n and "
1260 "3e0 >= 1 - n and 3e0 <= 2 - n and 3i0 >= -2 + n); "
1261 "[[i0, i1, 2, 0, i0] -> [i5, 2]] -> "
1262 "[[i0, i1, 1, 0, i0] -> [i5, 1]] : "
1263 "exists (e0 = [(3 - n)/3]: i5 >= 1 and i1 >= 1 and "
1264 "3i0 <= -1 + n and i1 <= -1 + n and i5 <= -1 + n and "
1265 "3e0 >= 1 - n and 3e0 <= 2 - n and 3i0 >= -2 + n) }";
1266 map
= isl_map_read_from_str(ctx
, str
);
1267 map
= isl_map_transitive_closure(map
, NULL
);
1272 void test_lex(struct isl_ctx
*ctx
)
1277 dim
= isl_space_set_alloc(ctx
, 0, 0);
1278 map
= isl_map_lex_le(dim
);
1279 assert(!isl_map_is_empty(map
));
1283 void test_lexmin(struct isl_ctx
*ctx
)
1286 isl_basic_map
*bmap
;
1287 isl_map
*map
, *map2
;
1290 isl_pw_multi_aff
*pma
;
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 pma
= isl_basic_map_lexmin_pw_multi_aff(isl_basic_map_copy(bmap
));
1352 map2
= isl_map_from_pw_multi_aff(pma
);
1353 map
= isl_map_from_basic_map(bmap
);
1354 assert(isl_map_is_equal(map
, map2
));
1358 str
= "{ T[a] -> S[b, c] : a = 4b-2c and c >= b }";
1359 map
= isl_map_read_from_str(ctx
, str
);
1360 map
= isl_map_lexmin(map
);
1361 str
= "{ T[a] -> S[b, c] : 2b = a and 2c = a }";
1362 map2
= isl_map_read_from_str(ctx
, str
);
1363 assert(isl_map_is_equal(map
, map2
));
1373 static int collect_must_may(__isl_take isl_map
*dep
, int must
,
1374 void *dep_user
, void *user
)
1376 struct must_may
*mm
= (struct must_may
*)user
;
1379 mm
->must
= isl_map_union(mm
->must
, dep
);
1381 mm
->may
= isl_map_union(mm
->may
, dep
);
1386 static int common_space(void *first
, void *second
)
1388 int depth
= *(int *)first
;
1392 static int map_is_equal(__isl_keep isl_map
*map
, const char *str
)
1400 map2
= isl_map_read_from_str(map
->ctx
, str
);
1401 equal
= isl_map_is_equal(map
, map2
);
1407 void test_dep(struct isl_ctx
*ctx
)
1412 isl_access_info
*ai
;
1419 str
= "{ [2,i,0] -> [i] : 0 <= i <= 10 }";
1420 map
= isl_map_read_from_str(ctx
, str
);
1421 ai
= isl_access_info_alloc(map
, &depth
, &common_space
, 2);
1423 str
= "{ [0,i,0] -> [i] : 0 <= i <= 10 }";
1424 map
= isl_map_read_from_str(ctx
, str
);
1425 ai
= isl_access_info_add_source(ai
, map
, 1, &depth
);
1427 str
= "{ [1,i,0] -> [5] : 0 <= i <= 10 }";
1428 map
= isl_map_read_from_str(ctx
, str
);
1429 ai
= isl_access_info_add_source(ai
, map
, 1, &depth
);
1431 flow
= isl_access_info_compute_flow(ai
);
1432 dim
= isl_space_alloc(ctx
, 0, 3, 3);
1433 mm
.must
= isl_map_empty(isl_space_copy(dim
));
1434 mm
.may
= isl_map_empty(dim
);
1436 isl_flow_foreach(flow
, collect_must_may
, &mm
);
1438 str
= "{ [0,i,0] -> [2,i,0] : (0 <= i <= 4) or (6 <= i <= 10); "
1439 " [1,10,0] -> [2,5,0] }";
1440 assert(map_is_equal(mm
.must
, str
));
1441 str
= "{ [i,j,k] -> [l,m,n] : 1 = 0 }";
1442 assert(map_is_equal(mm
.may
, str
));
1444 isl_map_free(mm
.must
);
1445 isl_map_free(mm
.may
);
1446 isl_flow_free(flow
);
1449 str
= "{ [2,i,0] -> [i] : 0 <= i <= 10 }";
1450 map
= isl_map_read_from_str(ctx
, str
);
1451 ai
= isl_access_info_alloc(map
, &depth
, &common_space
, 2);
1453 str
= "{ [0,i,0] -> [i] : 0 <= i <= 10 }";
1454 map
= isl_map_read_from_str(ctx
, str
);
1455 ai
= isl_access_info_add_source(ai
, map
, 1, &depth
);
1457 str
= "{ [1,i,0] -> [5] : 0 <= i <= 10 }";
1458 map
= isl_map_read_from_str(ctx
, str
);
1459 ai
= isl_access_info_add_source(ai
, map
, 0, &depth
);
1461 flow
= isl_access_info_compute_flow(ai
);
1462 dim
= isl_space_alloc(ctx
, 0, 3, 3);
1463 mm
.must
= isl_map_empty(isl_space_copy(dim
));
1464 mm
.may
= isl_map_empty(dim
);
1466 isl_flow_foreach(flow
, collect_must_may
, &mm
);
1468 str
= "{ [0,i,0] -> [2,i,0] : (0 <= i <= 4) or (6 <= i <= 10) }";
1469 assert(map_is_equal(mm
.must
, str
));
1470 str
= "{ [0,5,0] -> [2,5,0]; [1,i,0] -> [2,5,0] : 0 <= i <= 10 }";
1471 assert(map_is_equal(mm
.may
, str
));
1473 isl_map_free(mm
.must
);
1474 isl_map_free(mm
.may
);
1475 isl_flow_free(flow
);
1478 str
= "{ [2,i,0] -> [i] : 0 <= i <= 10 }";
1479 map
= isl_map_read_from_str(ctx
, str
);
1480 ai
= isl_access_info_alloc(map
, &depth
, &common_space
, 2);
1482 str
= "{ [0,i,0] -> [i] : 0 <= i <= 10 }";
1483 map
= isl_map_read_from_str(ctx
, str
);
1484 ai
= isl_access_info_add_source(ai
, map
, 0, &depth
);
1486 str
= "{ [1,i,0] -> [5] : 0 <= i <= 10 }";
1487 map
= isl_map_read_from_str(ctx
, str
);
1488 ai
= isl_access_info_add_source(ai
, map
, 0, &depth
);
1490 flow
= isl_access_info_compute_flow(ai
);
1491 dim
= isl_space_alloc(ctx
, 0, 3, 3);
1492 mm
.must
= isl_map_empty(isl_space_copy(dim
));
1493 mm
.may
= isl_map_empty(dim
);
1495 isl_flow_foreach(flow
, collect_must_may
, &mm
);
1497 str
= "{ [0,i,0] -> [2,i,0] : 0 <= i <= 10; "
1498 " [1,i,0] -> [2,5,0] : 0 <= i <= 10 }";
1499 assert(map_is_equal(mm
.may
, str
));
1500 str
= "{ [i,j,k] -> [l,m,n] : 1 = 0 }";
1501 assert(map_is_equal(mm
.must
, str
));
1503 isl_map_free(mm
.must
);
1504 isl_map_free(mm
.may
);
1505 isl_flow_free(flow
);
1508 str
= "{ [0,i,2] -> [i] : 0 <= i <= 10 }";
1509 map
= isl_map_read_from_str(ctx
, str
);
1510 ai
= isl_access_info_alloc(map
, &depth
, &common_space
, 2);
1512 str
= "{ [0,i,0] -> [i] : 0 <= i <= 10 }";
1513 map
= isl_map_read_from_str(ctx
, str
);
1514 ai
= isl_access_info_add_source(ai
, map
, 0, &depth
);
1516 str
= "{ [0,i,1] -> [5] : 0 <= i <= 10 }";
1517 map
= isl_map_read_from_str(ctx
, str
);
1518 ai
= isl_access_info_add_source(ai
, map
, 0, &depth
);
1520 flow
= isl_access_info_compute_flow(ai
);
1521 dim
= isl_space_alloc(ctx
, 0, 3, 3);
1522 mm
.must
= isl_map_empty(isl_space_copy(dim
));
1523 mm
.may
= isl_map_empty(dim
);
1525 isl_flow_foreach(flow
, collect_must_may
, &mm
);
1527 str
= "{ [0,i,0] -> [0,i,2] : 0 <= i <= 10; "
1528 " [0,i,1] -> [0,5,2] : 0 <= i <= 5 }";
1529 assert(map_is_equal(mm
.may
, str
));
1530 str
= "{ [i,j,k] -> [l,m,n] : 1 = 0 }";
1531 assert(map_is_equal(mm
.must
, str
));
1533 isl_map_free(mm
.must
);
1534 isl_map_free(mm
.may
);
1535 isl_flow_free(flow
);
1538 str
= "{ [0,i,1] -> [i] : 0 <= i <= 10 }";
1539 map
= isl_map_read_from_str(ctx
, str
);
1540 ai
= isl_access_info_alloc(map
, &depth
, &common_space
, 2);
1542 str
= "{ [0,i,0] -> [i] : 0 <= i <= 10 }";
1543 map
= isl_map_read_from_str(ctx
, str
);
1544 ai
= isl_access_info_add_source(ai
, map
, 0, &depth
);
1546 str
= "{ [0,i,2] -> [5] : 0 <= i <= 10 }";
1547 map
= isl_map_read_from_str(ctx
, str
);
1548 ai
= isl_access_info_add_source(ai
, map
, 0, &depth
);
1550 flow
= isl_access_info_compute_flow(ai
);
1551 dim
= isl_space_alloc(ctx
, 0, 3, 3);
1552 mm
.must
= isl_map_empty(isl_space_copy(dim
));
1553 mm
.may
= isl_map_empty(dim
);
1555 isl_flow_foreach(flow
, collect_must_may
, &mm
);
1557 str
= "{ [0,i,0] -> [0,i,1] : 0 <= i <= 10; "
1558 " [0,i,2] -> [0,5,1] : 0 <= i <= 4 }";
1559 assert(map_is_equal(mm
.may
, str
));
1560 str
= "{ [i,j,k] -> [l,m,n] : 1 = 0 }";
1561 assert(map_is_equal(mm
.must
, str
));
1563 isl_map_free(mm
.must
);
1564 isl_map_free(mm
.may
);
1565 isl_flow_free(flow
);
1570 str
= "{ [1,i,0,0,0] -> [i,j] : 0 <= i <= 10 and 0 <= j <= 10 }";
1571 map
= isl_map_read_from_str(ctx
, str
);
1572 ai
= isl_access_info_alloc(map
, &depth
, &common_space
, 1);
1574 str
= "{ [0,i,0,j,0] -> [i,j] : 0 <= i <= 10 and 0 <= j <= 10 }";
1575 map
= isl_map_read_from_str(ctx
, str
);
1576 ai
= isl_access_info_add_source(ai
, map
, 1, &depth
);
1578 flow
= isl_access_info_compute_flow(ai
);
1579 dim
= isl_space_alloc(ctx
, 0, 5, 5);
1580 mm
.must
= isl_map_empty(isl_space_copy(dim
));
1581 mm
.may
= isl_map_empty(dim
);
1583 isl_flow_foreach(flow
, collect_must_may
, &mm
);
1585 str
= "{ [0,i,0,j,0] -> [1,i,0,0,0] : 0 <= i,j <= 10 }";
1586 assert(map_is_equal(mm
.must
, str
));
1587 str
= "{ [0,0,0,0,0] -> [0,0,0,0,0] : 1 = 0 }";
1588 assert(map_is_equal(mm
.may
, str
));
1590 isl_map_free(mm
.must
);
1591 isl_map_free(mm
.may
);
1592 isl_flow_free(flow
);
1595 int test_sv(isl_ctx
*ctx
)
1599 isl_union_map
*umap
;
1602 str
= "[N] -> { [i] -> [f] : 0 <= i <= N and 0 <= i - 10 f <= 9 }";
1603 map
= isl_map_read_from_str(ctx
, str
);
1604 sv
= isl_map_is_single_valued(map
);
1609 isl_die(ctx
, isl_error_internal
,
1610 "map not detected as single valued", return -1);
1612 str
= "[N] -> { [i] -> [f] : 0 <= i <= N and 0 <= i - 10 f <= 10 }";
1613 map
= isl_map_read_from_str(ctx
, str
);
1614 sv
= isl_map_is_single_valued(map
);
1619 isl_die(ctx
, isl_error_internal
,
1620 "map detected as single valued", return -1);
1622 str
= "{ S1[i] -> [i] : 0 <= i <= 9; S2[i] -> [i] : 0 <= i <= 9 }";
1623 umap
= isl_union_map_read_from_str(ctx
, str
);
1624 sv
= isl_union_map_is_single_valued(umap
);
1625 isl_union_map_free(umap
);
1629 isl_die(ctx
, isl_error_internal
,
1630 "map not detected as single valued", return -1);
1632 str
= "{ [i] -> S1[i] : 0 <= i <= 9; [i] -> S2[i] : 0 <= i <= 9 }";
1633 umap
= isl_union_map_read_from_str(ctx
, str
);
1634 sv
= isl_union_map_is_single_valued(umap
);
1635 isl_union_map_free(umap
);
1639 isl_die(ctx
, isl_error_internal
,
1640 "map detected as single valued", return -1);
1645 void test_bijective_case(struct isl_ctx
*ctx
, const char *str
, int bijective
)
1649 map
= isl_map_read_from_str(ctx
, str
);
1651 assert(isl_map_is_bijective(map
));
1653 assert(!isl_map_is_bijective(map
));
1657 void test_bijective(struct isl_ctx
*ctx
)
1659 test_bijective_case(ctx
, "[N,M]->{[i,j] -> [i]}", 0);
1660 test_bijective_case(ctx
, "[N,M]->{[i,j] -> [i] : j=i}", 1);
1661 test_bijective_case(ctx
, "[N,M]->{[i,j] -> [i] : j=0}", 1);
1662 test_bijective_case(ctx
, "[N,M]->{[i,j] -> [i] : j=N}", 1);
1663 test_bijective_case(ctx
, "[N,M]->{[i,j] -> [j,i]}", 1);
1664 test_bijective_case(ctx
, "[N,M]->{[i,j] -> [i+j]}", 0);
1665 test_bijective_case(ctx
, "[N,M]->{[i,j] -> []}", 0);
1666 test_bijective_case(ctx
, "[N,M]->{[i,j] -> [i,j,N]}", 1);
1667 test_bijective_case(ctx
, "[N,M]->{[i,j] -> [2i]}", 0);
1668 test_bijective_case(ctx
, "[N,M]->{[i,j] -> [i,i]}", 0);
1669 test_bijective_case(ctx
, "[N,M]->{[i,j] -> [2i,i]}", 0);
1670 test_bijective_case(ctx
, "[N,M]->{[i,j] -> [2i,j]}", 1);
1671 test_bijective_case(ctx
, "[N,M]->{[i,j] -> [x,y] : 2x=i & y =j}", 1);
1674 void test_pwqp(struct isl_ctx
*ctx
)
1678 isl_pw_qpolynomial
*pwqp1
, *pwqp2
;
1680 str
= "{ [i,j,k] -> 1 + 9 * [i/5] + 7 * [j/11] + 4 * [k/13] }";
1681 pwqp1
= isl_pw_qpolynomial_read_from_str(ctx
, str
);
1683 pwqp1
= isl_pw_qpolynomial_move_dims(pwqp1
, isl_dim_param
, 0,
1686 str
= "[j] -> { [i,k] -> 1 + 9 * [i/5] + 7 * [j/11] + 4 * [k/13] }";
1687 pwqp2
= isl_pw_qpolynomial_read_from_str(ctx
, str
);
1689 pwqp1
= isl_pw_qpolynomial_sub(pwqp1
, pwqp2
);
1691 assert(isl_pw_qpolynomial_is_zero(pwqp1
));
1693 isl_pw_qpolynomial_free(pwqp1
);
1695 str
= "{ [i] -> i }";
1696 pwqp1
= isl_pw_qpolynomial_read_from_str(ctx
, str
);
1697 str
= "{ [k] : exists a : k = 2a }";
1698 set
= isl_set_read_from_str(ctx
, str
);
1699 pwqp1
= isl_pw_qpolynomial_gist(pwqp1
, set
);
1700 str
= "{ [i] -> i }";
1701 pwqp2
= isl_pw_qpolynomial_read_from_str(ctx
, str
);
1703 pwqp1
= isl_pw_qpolynomial_sub(pwqp1
, pwqp2
);
1705 assert(isl_pw_qpolynomial_is_zero(pwqp1
));
1707 isl_pw_qpolynomial_free(pwqp1
);
1709 str
= "{ [i] -> i + [ (i + [i/3])/2 ] }";
1710 pwqp1
= isl_pw_qpolynomial_read_from_str(ctx
, str
);
1712 set
= isl_set_read_from_str(ctx
, str
);
1713 pwqp1
= isl_pw_qpolynomial_gist(pwqp1
, set
);
1714 str
= "{ [i] -> 16 }";
1715 pwqp2
= isl_pw_qpolynomial_read_from_str(ctx
, str
);
1717 pwqp1
= isl_pw_qpolynomial_sub(pwqp1
, pwqp2
);
1719 assert(isl_pw_qpolynomial_is_zero(pwqp1
));
1721 isl_pw_qpolynomial_free(pwqp1
);
1723 str
= "{ [i] -> ([(i)/2]) }";
1724 pwqp1
= isl_pw_qpolynomial_read_from_str(ctx
, str
);
1725 str
= "{ [k] : exists a : k = 2a+1 }";
1726 set
= isl_set_read_from_str(ctx
, str
);
1727 pwqp1
= isl_pw_qpolynomial_gist(pwqp1
, set
);
1728 str
= "{ [i] -> -1/2 + 1/2 * i }";
1729 pwqp2
= isl_pw_qpolynomial_read_from_str(ctx
, str
);
1731 pwqp1
= isl_pw_qpolynomial_sub(pwqp1
, pwqp2
);
1733 assert(isl_pw_qpolynomial_is_zero(pwqp1
));
1735 isl_pw_qpolynomial_free(pwqp1
);
1737 str
= "{ [i] -> ([([i/2] + [i/2])/5]) }";
1738 pwqp1
= isl_pw_qpolynomial_read_from_str(ctx
, str
);
1739 str
= "{ [i] -> ([(2 * [i/2])/5]) }";
1740 pwqp2
= isl_pw_qpolynomial_read_from_str(ctx
, str
);
1742 pwqp1
= isl_pw_qpolynomial_sub(pwqp1
, pwqp2
);
1744 assert(isl_pw_qpolynomial_is_zero(pwqp1
));
1746 isl_pw_qpolynomial_free(pwqp1
);
1748 str
= "{ [x] -> ([x/2] + [(x+1)/2]) }";
1749 pwqp1
= isl_pw_qpolynomial_read_from_str(ctx
, str
);
1750 str
= "{ [x] -> x }";
1751 pwqp2
= isl_pw_qpolynomial_read_from_str(ctx
, str
);
1753 pwqp1
= isl_pw_qpolynomial_sub(pwqp1
, pwqp2
);
1755 assert(isl_pw_qpolynomial_is_zero(pwqp1
));
1757 isl_pw_qpolynomial_free(pwqp1
);
1759 str
= "{ [i] -> ([i/2]) : i >= 0; [i] -> ([i/3]) : i < 0 }";
1760 pwqp1
= isl_pw_qpolynomial_read_from_str(ctx
, str
);
1761 pwqp2
= isl_pw_qpolynomial_read_from_str(ctx
, str
);
1762 pwqp1
= isl_pw_qpolynomial_coalesce(pwqp1
);
1763 pwqp1
= isl_pw_qpolynomial_sub(pwqp1
, pwqp2
);
1764 assert(isl_pw_qpolynomial_is_zero(pwqp1
));
1765 isl_pw_qpolynomial_free(pwqp1
);
1768 void test_split_periods(isl_ctx
*ctx
)
1771 isl_pw_qpolynomial
*pwqp
;
1773 str
= "{ [U,V] -> 1/3 * U + 2/3 * V - [(U + 2V)/3] + [U/2] : "
1774 "U + 2V + 3 >= 0 and - U -2V >= 0 and - U + 10 >= 0 and "
1775 "U >= 0; [U,V] -> U^2 : U >= 100 }";
1776 pwqp
= isl_pw_qpolynomial_read_from_str(ctx
, str
);
1778 pwqp
= isl_pw_qpolynomial_split_periods(pwqp
, 2);
1781 isl_pw_qpolynomial_free(pwqp
);
1784 void test_union(isl_ctx
*ctx
)
1787 isl_union_set
*uset1
, *uset2
;
1788 isl_union_map
*umap1
, *umap2
;
1790 str
= "{ [i] : 0 <= i <= 1 }";
1791 uset1
= isl_union_set_read_from_str(ctx
, str
);
1792 str
= "{ [1] -> [0] }";
1793 umap1
= isl_union_map_read_from_str(ctx
, str
);
1795 umap2
= isl_union_set_lex_gt_union_set(isl_union_set_copy(uset1
), uset1
);
1796 assert(isl_union_map_is_equal(umap1
, umap2
));
1798 isl_union_map_free(umap1
);
1799 isl_union_map_free(umap2
);
1801 str
= "{ A[i] -> B[i]; B[i] -> C[i]; A[0] -> C[1] }";
1802 umap1
= isl_union_map_read_from_str(ctx
, str
);
1803 str
= "{ A[i]; B[i] }";
1804 uset1
= isl_union_set_read_from_str(ctx
, str
);
1806 uset2
= isl_union_map_domain(umap1
);
1808 assert(isl_union_set_is_equal(uset1
, uset2
));
1810 isl_union_set_free(uset1
);
1811 isl_union_set_free(uset2
);
1814 void test_bound(isl_ctx
*ctx
)
1817 isl_pw_qpolynomial
*pwqp
;
1818 isl_pw_qpolynomial_fold
*pwf
;
1820 str
= "{ [[a, b, c, d] -> [e]] -> 0 }";
1821 pwqp
= isl_pw_qpolynomial_read_from_str(ctx
, str
);
1822 pwf
= isl_pw_qpolynomial_bound(pwqp
, isl_fold_max
, NULL
);
1823 assert(isl_pw_qpolynomial_fold_dim(pwf
, isl_dim_in
) == 4);
1824 isl_pw_qpolynomial_fold_free(pwf
);
1826 str
= "{ [[x]->[x]] -> 1 : exists a : x = 2 a }";
1827 pwqp
= isl_pw_qpolynomial_read_from_str(ctx
, str
);
1828 pwf
= isl_pw_qpolynomial_bound(pwqp
, isl_fold_max
, NULL
);
1829 assert(isl_pw_qpolynomial_fold_dim(pwf
, isl_dim_in
) == 1);
1830 isl_pw_qpolynomial_fold_free(pwf
);
1833 void test_lift(isl_ctx
*ctx
)
1836 isl_basic_map
*bmap
;
1837 isl_basic_set
*bset
;
1839 str
= "{ [i0] : exists e0 : i0 = 4e0 }";
1840 bset
= isl_basic_set_read_from_str(ctx
, str
);
1841 bset
= isl_basic_set_lift(bset
);
1842 bmap
= isl_basic_map_from_range(bset
);
1843 bset
= isl_basic_map_domain(bmap
);
1844 isl_basic_set_free(bset
);
1847 void test_subset(isl_ctx
*ctx
)
1850 isl_set
*set1
, *set2
;
1852 str
= "{ [112, 0] }";
1853 set1
= isl_set_read_from_str(ctx
, str
);
1854 str
= "{ [i0, i1] : exists (e0 = [(i0 - i1)/16], e1: "
1855 "16e0 <= i0 - i1 and 16e0 >= -15 + i0 - i1 and "
1856 "16e1 <= i1 and 16e0 >= -i1 and 16e1 >= -i0 + i1) }";
1857 set2
= isl_set_read_from_str(ctx
, str
);
1858 assert(isl_set_is_subset(set1
, set2
));
1863 void test_factorize(isl_ctx
*ctx
)
1866 isl_basic_set
*bset
;
1869 str
= "{ [i0, i1, i2, i3, i4, i5, i6, i7] : 3i5 <= 2 - 2i0 and "
1870 "i0 >= -2 and i6 >= 1 + i3 and i7 >= 0 and 3i5 >= -2i0 and "
1871 "2i4 <= i2 and i6 >= 1 + 2i0 + 3i1 and i4 <= -1 and "
1872 "i6 >= 1 + 2i0 + 3i5 and i6 <= 2 + 2i0 + 3i5 and "
1873 "3i5 <= 2 - 2i0 - i2 + 3i4 and i6 <= 2 + 2i0 + 3i1 and "
1874 "i0 <= -1 and i7 <= i2 + i3 - 3i4 - i6 and "
1875 "3i5 >= -2i0 - i2 + 3i4 }";
1876 bset
= isl_basic_set_read_from_str(ctx
, str
);
1877 f
= isl_basic_set_factorizer(bset
);
1879 isl_basic_set_free(bset
);
1880 isl_factorizer_free(f
);
1882 str
= "{ [i0, i1, i2, i3, i4, i5, i6, i7, i8, i9, i10, i11, i12] : "
1883 "i12 <= 2 + i0 - i11 and 2i8 >= -i4 and i11 >= i1 and "
1884 "3i5 <= -i2 and 2i11 >= -i4 - 2i7 and i11 <= 3 + i0 + 3i9 and "
1885 "i11 <= -i4 - 2i7 and i12 >= -i10 and i2 >= -2 and "
1886 "i11 >= i1 + 3i10 and i11 >= 1 + i0 + 3i9 and "
1887 "i11 <= 1 - i4 - 2i8 and 6i6 <= 6 - i2 and 3i6 >= 1 - i2 and "
1888 "i11 <= 2 + i1 and i12 <= i4 + i11 and i12 >= i0 - i11 and "
1889 "3i5 >= -2 - i2 and i12 >= -1 + i4 + i11 and 3i3 <= 3 - i2 and "
1890 "9i6 <= 11 - i2 + 6i5 and 3i3 >= 1 - i2 and "
1891 "9i6 <= 5 - i2 + 6i3 and i12 <= -1 and i2 <= 0 }";
1892 bset
= isl_basic_set_read_from_str(ctx
, str
);
1893 f
= isl_basic_set_factorizer(bset
);
1895 isl_basic_set_free(bset
);
1896 isl_factorizer_free(f
);
1899 static int check_injective(__isl_take isl_map
*map
, void *user
)
1901 int *injective
= user
;
1903 *injective
= isl_map_is_injective(map
);
1906 if (*injective
< 0 || !*injective
)
1912 int test_one_schedule(isl_ctx
*ctx
, const char *d
, const char *w
,
1913 const char *r
, const char *s
, int tilable
, int parallel
)
1917 isl_union_map
*W
, *R
, *S
;
1918 isl_union_map
*empty
;
1919 isl_union_map
*dep_raw
, *dep_war
, *dep_waw
, *dep
;
1920 isl_union_map
*validity
, *proximity
;
1921 isl_union_map
*schedule
;
1922 isl_union_map
*test
;
1923 isl_union_set
*delta
;
1924 isl_union_set
*domain
;
1928 isl_schedule
*sched
;
1929 int is_nonneg
, is_parallel
, is_tilable
, is_injection
, is_complete
;
1931 D
= isl_union_set_read_from_str(ctx
, d
);
1932 W
= isl_union_map_read_from_str(ctx
, w
);
1933 R
= isl_union_map_read_from_str(ctx
, r
);
1934 S
= isl_union_map_read_from_str(ctx
, s
);
1936 W
= isl_union_map_intersect_domain(W
, isl_union_set_copy(D
));
1937 R
= isl_union_map_intersect_domain(R
, isl_union_set_copy(D
));
1939 empty
= isl_union_map_empty(isl_union_map_get_space(S
));
1940 isl_union_map_compute_flow(isl_union_map_copy(R
),
1941 isl_union_map_copy(W
), empty
,
1942 isl_union_map_copy(S
),
1943 &dep_raw
, NULL
, NULL
, NULL
);
1944 isl_union_map_compute_flow(isl_union_map_copy(W
),
1945 isl_union_map_copy(W
),
1946 isl_union_map_copy(R
),
1947 isl_union_map_copy(S
),
1948 &dep_waw
, &dep_war
, NULL
, NULL
);
1950 dep
= isl_union_map_union(dep_waw
, dep_war
);
1951 dep
= isl_union_map_union(dep
, dep_raw
);
1952 validity
= isl_union_map_copy(dep
);
1953 proximity
= isl_union_map_copy(dep
);
1955 sched
= isl_union_set_compute_schedule(isl_union_set_copy(D
),
1956 validity
, proximity
);
1957 schedule
= isl_schedule_get_map(sched
);
1958 isl_schedule_free(sched
);
1959 isl_union_map_free(W
);
1960 isl_union_map_free(R
);
1961 isl_union_map_free(S
);
1964 isl_union_map_foreach_map(schedule
, &check_injective
, &is_injection
);
1966 domain
= isl_union_map_domain(isl_union_map_copy(schedule
));
1967 is_complete
= isl_union_set_is_subset(D
, domain
);
1968 isl_union_set_free(D
);
1969 isl_union_set_free(domain
);
1971 test
= isl_union_map_reverse(isl_union_map_copy(schedule
));
1972 test
= isl_union_map_apply_range(test
, dep
);
1973 test
= isl_union_map_apply_range(test
, schedule
);
1975 delta
= isl_union_map_deltas(test
);
1976 if (isl_union_set_n_set(delta
) == 0) {
1980 isl_union_set_free(delta
);
1982 delta_set
= isl_set_from_union_set(delta
);
1984 slice
= isl_set_universe(isl_set_get_space(delta_set
));
1985 for (i
= 0; i
< tilable
; ++i
)
1986 slice
= isl_set_lower_bound_si(slice
, isl_dim_set
, i
, 0);
1987 is_tilable
= isl_set_is_subset(delta_set
, slice
);
1988 isl_set_free(slice
);
1990 slice
= isl_set_universe(isl_set_get_space(delta_set
));
1991 for (i
= 0; i
< parallel
; ++i
)
1992 slice
= isl_set_fix_si(slice
, isl_dim_set
, i
, 0);
1993 is_parallel
= isl_set_is_subset(delta_set
, slice
);
1994 isl_set_free(slice
);
1996 origin
= isl_set_universe(isl_set_get_space(delta_set
));
1997 for (i
= 0; i
< isl_set_dim(origin
, isl_dim_set
); ++i
)
1998 origin
= isl_set_fix_si(origin
, isl_dim_set
, i
, 0);
2000 delta_set
= isl_set_union(delta_set
, isl_set_copy(origin
));
2001 delta_set
= isl_set_lexmin(delta_set
);
2003 is_nonneg
= isl_set_is_equal(delta_set
, origin
);
2005 isl_set_free(origin
);
2006 isl_set_free(delta_set
);
2009 if (is_nonneg
< 0 || is_parallel
< 0 || is_tilable
< 0 ||
2010 is_injection
< 0 || is_complete
< 0)
2013 isl_die(ctx
, isl_error_unknown
,
2014 "generated schedule incomplete", return -1);
2016 isl_die(ctx
, isl_error_unknown
,
2017 "generated schedule not injective on each statement",
2020 isl_die(ctx
, isl_error_unknown
,
2021 "negative dependences in generated schedule",
2024 isl_die(ctx
, isl_error_unknown
,
2025 "generated schedule not as tilable as expected",
2028 isl_die(ctx
, isl_error_unknown
,
2029 "generated schedule not as parallel as expected",
2035 int test_special_schedule(isl_ctx
*ctx
)
2039 isl_union_map
*empty
;
2041 isl_union_map
*sched1
, *sched2
;
2042 isl_schedule
*schedule
;
2045 str
= "{ S[i,j] : 0 <= i <= 10 }";
2046 dom
= isl_union_set_read_from_str(ctx
, str
);
2047 str
= "{ S[i,j] -> S[i+1,j] : 0 <= i,j <= 10 }";
2048 dep
= isl_union_map_read_from_str(ctx
, str
);
2049 empty
= isl_union_map_read_from_str(ctx
, "{}");
2050 schedule
= isl_union_set_compute_schedule(dom
, empty
, dep
);
2051 sched1
= isl_schedule_get_map(schedule
);
2052 isl_schedule_free(schedule
);
2054 str
= "{ S[i, j] -> [j, i] }";
2055 sched2
= isl_union_map_read_from_str(ctx
, str
);
2057 equal
= isl_union_map_is_equal(sched1
, sched2
);
2058 isl_union_map_free(sched1
);
2059 isl_union_map_free(sched2
);
2064 isl_die(ctx
, isl_error_unknown
, "unexpected schedule",
2070 int test_schedule(isl_ctx
*ctx
)
2072 const char *D
, *W
, *R
, *S
;
2075 D
= "[T,N] -> { S1[t,i] : 1 <= t <= T and 2 <= i <= N - 1 }";
2076 W
= "{ S1[t,i] -> a[t,i] }";
2077 R
= "{ S1[t,i] -> a[t-1,i]; S1[t,i] -> a[t-1,i-1]; "
2078 "S1[t,i] -> a[t-1,i+1] }";
2079 S
= "{ S1[t,i] -> [t,i] }";
2080 if (test_one_schedule(ctx
, D
, W
, R
, S
, 2, 0) < 0)
2083 /* Fig. 5 of CC2008 */
2084 D
= "[N] -> { S_0[i, j] : i >= 0 and i <= -1 + N and j >= 2 and "
2086 W
= "[N] -> { S_0[i, j] -> a[i, j] : i >= 0 and i <= -1 + N and "
2087 "j >= 2 and j <= -1 + N }";
2088 R
= "[N] -> { S_0[i, j] -> a[j, i] : i >= 0 and i <= -1 + N and "
2089 "j >= 2 and j <= -1 + N; "
2090 "S_0[i, j] -> a[i, -1 + j] : i >= 0 and i <= -1 + N and "
2091 "j >= 2 and j <= -1 + N }";
2092 S
= "[N] -> { S_0[i, j] -> [0, i, 0, j, 0] }";
2093 if (test_one_schedule(ctx
, D
, W
, R
, S
, 2, 0) < 0)
2096 D
= "{ S1[i] : 0 <= i <= 10; S2[i] : 0 <= i <= 9 }";
2097 W
= "{ S1[i] -> a[i] }";
2098 R
= "{ S2[i] -> a[i+1] }";
2099 S
= "{ S1[i] -> [0,i]; S2[i] -> [1,i] }";
2100 if (test_one_schedule(ctx
, D
, W
, R
, S
, 1, 1) < 0)
2103 D
= "{ S1[i] : 0 <= i < 10; S2[i] : 0 <= i < 10 }";
2104 W
= "{ S1[i] -> a[i] }";
2105 R
= "{ S2[i] -> a[9-i] }";
2106 S
= "{ S1[i] -> [0,i]; S2[i] -> [1,i] }";
2107 if (test_one_schedule(ctx
, D
, W
, R
, S
, 1, 1) < 0)
2110 D
= "[N] -> { S1[i] : 0 <= i < N; S2[i] : 0 <= i < N }";
2111 W
= "{ S1[i] -> a[i] }";
2112 R
= "[N] -> { S2[i] -> a[N-1-i] }";
2113 S
= "{ S1[i] -> [0,i]; S2[i] -> [1,i] }";
2114 if (test_one_schedule(ctx
, D
, W
, R
, S
, 1, 1) < 0)
2117 D
= "{ S1[i] : 0 < i < 10; S2[i] : 0 <= i < 10 }";
2118 W
= "{ S1[i] -> a[i]; S2[i] -> b[i] }";
2119 R
= "{ S2[i] -> a[i]; S1[i] -> b[i-1] }";
2120 S
= "{ S1[i] -> [i,0]; S2[i] -> [i,1] }";
2121 if (test_one_schedule(ctx
, D
, W
, R
, S
, 0, 0) < 0)
2124 D
= "[N] -> { S1[i] : 1 <= i <= N; S2[i,j] : 1 <= i,j <= N }";
2125 W
= "{ S1[i] -> a[0,i]; S2[i,j] -> a[i,j] }";
2126 R
= "{ S2[i,j] -> a[i-1,j] }";
2127 S
= "{ S1[i] -> [0,i,0]; S2[i,j] -> [1,i,j] }";
2128 if (test_one_schedule(ctx
, D
, W
, R
, S
, 2, 1) < 0)
2131 D
= "[N] -> { S1[i] : 1 <= i <= N; S2[i,j] : 1 <= i,j <= N }";
2132 W
= "{ S1[i] -> a[i,0]; S2[i,j] -> a[i,j] }";
2133 R
= "{ S2[i,j] -> a[i,j-1] }";
2134 S
= "{ S1[i] -> [0,i,0]; S2[i,j] -> [1,i,j] }";
2135 if (test_one_schedule(ctx
, D
, W
, R
, S
, 2, 1) < 0)
2138 D
= "[N] -> { S_0[]; S_1[i] : i >= 0 and i <= -1 + N; S_2[] }";
2139 W
= "[N] -> { S_0[] -> a[0]; S_2[] -> b[0]; "
2140 "S_1[i] -> a[1 + i] : i >= 0 and i <= -1 + N }";
2141 R
= "[N] -> { S_2[] -> a[N]; S_1[i] -> a[i] : i >= 0 and i <= -1 + N }";
2142 S
= "[N] -> { S_1[i] -> [1, i, 0]; S_2[] -> [2, 0, 1]; "
2143 "S_0[] -> [0, 0, 0] }";
2144 if (test_one_schedule(ctx
, D
, W
, R
, S
, 1, 0) < 0)
2146 ctx
->opt
->schedule_parametric
= 0;
2147 if (test_one_schedule(ctx
, D
, W
, R
, S
, 0, 0) < 0)
2149 ctx
->opt
->schedule_parametric
= 1;
2151 D
= "[N] -> { S1[i] : 1 <= i <= N; S2[i] : 1 <= i <= N; "
2152 "S3[i,j] : 1 <= i,j <= N; S4[i] : 1 <= i <= N }";
2153 W
= "{ S1[i] -> a[i,0]; S2[i] -> a[0,i]; S3[i,j] -> a[i,j] }";
2154 R
= "[N] -> { S3[i,j] -> a[i-1,j]; S3[i,j] -> a[i,j-1]; "
2155 "S4[i] -> a[i,N] }";
2156 S
= "{ S1[i] -> [0,i,0]; S2[i] -> [1,i,0]; S3[i,j] -> [2,i,j]; "
2157 "S4[i] -> [4,i,0] }";
2158 if (test_one_schedule(ctx
, D
, W
, R
, S
, 2, 0) < 0)
2161 D
= "[N] -> { S_0[i, j] : i >= 1 and i <= N and j >= 1 and j <= N }";
2162 W
= "[N] -> { S_0[i, j] -> s[0] : i >= 1 and i <= N and j >= 1 and "
2164 R
= "[N] -> { S_0[i, j] -> s[0] : i >= 1 and i <= N and j >= 1 and "
2166 "S_0[i, j] -> a[i, j] : i >= 1 and i <= N and j >= 1 and "
2168 S
= "[N] -> { S_0[i, j] -> [0, i, 0, j, 0] }";
2169 if (test_one_schedule(ctx
, D
, W
, R
, S
, 0, 0) < 0)
2172 D
= "[N] -> { S_0[t] : t >= 0 and t <= -1 + N; "
2173 " S_2[t] : t >= 0 and t <= -1 + N; "
2174 " S_1[t, i] : t >= 0 and t <= -1 + N and i >= 0 and "
2176 W
= "[N] -> { S_0[t] -> a[t, 0] : t >= 0 and t <= -1 + N; "
2177 " S_2[t] -> b[t] : t >= 0 and t <= -1 + N; "
2178 " S_1[t, i] -> a[t, 1 + i] : t >= 0 and t <= -1 + N and "
2179 "i >= 0 and i <= -1 + N }";
2180 R
= "[N] -> { S_1[t, i] -> a[t, i] : t >= 0 and t <= -1 + N and "
2181 "i >= 0 and i <= -1 + N; "
2182 " S_2[t] -> a[t, N] : t >= 0 and t <= -1 + N }";
2183 S
= "[N] -> { S_2[t] -> [0, t, 2]; S_1[t, i] -> [0, t, 1, i, 0]; "
2184 " S_0[t] -> [0, t, 0] }";
2186 if (test_one_schedule(ctx
, D
, W
, R
, S
, 2, 1) < 0)
2188 ctx
->opt
->schedule_parametric
= 0;
2189 if (test_one_schedule(ctx
, D
, W
, R
, S
, 0, 0) < 0)
2191 ctx
->opt
->schedule_parametric
= 1;
2193 D
= "[N] -> { S1[i,j] : 0 <= i,j < N; S2[i,j] : 0 <= i,j < N }";
2194 S
= "{ S1[i,j] -> [0,i,j]; S2[i,j] -> [1,i,j] }";
2195 if (test_one_schedule(ctx
, D
, "{}", "{}", S
, 2, 2) < 0)
2198 D
= "[M, N] -> { S_1[i] : i >= 0 and i <= -1 + M; "
2199 "S_0[i, j] : i >= 0 and i <= -1 + M and j >= 0 and j <= -1 + N }";
2200 W
= "[M, N] -> { S_0[i, j] -> a[j] : i >= 0 and i <= -1 + M and "
2201 "j >= 0 and j <= -1 + N; "
2202 "S_1[i] -> b[0] : i >= 0 and i <= -1 + M }";
2203 R
= "[M, N] -> { S_0[i, j] -> a[0] : i >= 0 and i <= -1 + M and "
2204 "j >= 0 and j <= -1 + N; "
2205 "S_1[i] -> b[0] : i >= 0 and i <= -1 + M }";
2206 S
= "[M, N] -> { S_1[i] -> [1, i, 0]; S_0[i, j] -> [0, i, 0, j, 0] }";
2207 if (test_one_schedule(ctx
, D
, W
, R
, S
, 0, 0) < 0)
2210 D
= "{ S_0[i] : i >= 0 }";
2211 W
= "{ S_0[i] -> a[i] : i >= 0 }";
2212 R
= "{ S_0[i] -> a[0] : i >= 0 }";
2213 S
= "{ S_0[i] -> [0, i, 0] }";
2214 if (test_one_schedule(ctx
, D
, W
, R
, S
, 0, 0) < 0)
2217 D
= "{ S_0[i] : i >= 0; S_1[i] : i >= 0 }";
2218 W
= "{ S_0[i] -> a[i] : i >= 0; S_1[i] -> b[i] : i >= 0 }";
2219 R
= "{ S_0[i] -> b[0] : i >= 0; S_1[i] -> a[i] : i >= 0 }";
2220 S
= "{ S_1[i] -> [0, i, 1]; S_0[i] -> [0, i, 0] }";
2221 if (test_one_schedule(ctx
, D
, W
, R
, S
, 0, 0) < 0)
2224 D
= "[n] -> { S_0[j, k] : j <= -1 + n and j >= 0 and "
2225 "k <= -1 + n and k >= 0 }";
2226 W
= "[n] -> { S_0[j, k] -> B[j] : j <= -1 + n and j >= 0 and " "k <= -1 + n and k >= 0 }";
2227 R
= "[n] -> { S_0[j, k] -> B[j] : j <= -1 + n and j >= 0 and "
2228 "k <= -1 + n and k >= 0; "
2229 "S_0[j, k] -> B[k] : j <= -1 + n and j >= 0 and "
2230 "k <= -1 + n and k >= 0; "
2231 "S_0[j, k] -> A[k] : j <= -1 + n and j >= 0 and "
2232 "k <= -1 + n and k >= 0 }";
2233 S
= "[n] -> { S_0[j, k] -> [2, j, k] }";
2234 ctx
->opt
->schedule_outer_zero_distance
= 1;
2235 if (test_one_schedule(ctx
, D
, W
, R
, S
, 0, 0) < 0)
2237 ctx
->opt
->schedule_outer_zero_distance
= 0;
2239 return test_special_schedule(ctx
);
2242 int test_plain_injective(isl_ctx
*ctx
, const char *str
, int injective
)
2244 isl_union_map
*umap
;
2247 umap
= isl_union_map_read_from_str(ctx
, str
);
2248 test
= isl_union_map_plain_is_injective(umap
);
2249 isl_union_map_free(umap
);
2252 if (test
== injective
)
2255 isl_die(ctx
, isl_error_unknown
,
2256 "map not detected as injective", return -1);
2258 isl_die(ctx
, isl_error_unknown
,
2259 "map detected as injective", return -1);
2262 int test_injective(isl_ctx
*ctx
)
2266 if (test_plain_injective(ctx
, "{S[i,j] -> A[0]; T[i,j] -> B[1]}", 0))
2268 if (test_plain_injective(ctx
, "{S[] -> A[0]; T[] -> B[0]}", 1))
2270 if (test_plain_injective(ctx
, "{S[] -> A[0]; T[] -> A[1]}", 1))
2272 if (test_plain_injective(ctx
, "{S[] -> A[0]; T[] -> A[0]}", 0))
2274 if (test_plain_injective(ctx
, "{S[i] -> A[i,0]; T[i] -> A[i,1]}", 1))
2276 if (test_plain_injective(ctx
, "{S[i] -> A[i]; T[i] -> A[i]}", 0))
2278 if (test_plain_injective(ctx
, "{S[] -> A[0,0]; T[] -> A[0,1]}", 1))
2280 if (test_plain_injective(ctx
, "{S[] -> A[0,0]; T[] -> A[1,0]}", 1))
2283 str
= "{S[] -> A[0,0]; T[] -> A[0,1]; U[] -> A[1,0]}";
2284 if (test_plain_injective(ctx
, str
, 1))
2286 str
= "{S[] -> A[0,0]; T[] -> A[0,1]; U[] -> A[0,0]}";
2287 if (test_plain_injective(ctx
, str
, 0))
2293 int test_aff(isl_ctx
*ctx
)
2298 isl_local_space
*ls
;
2302 dim
= isl_space_set_alloc(ctx
, 0, 1);
2303 ls
= isl_local_space_from_space(dim
);
2304 aff
= isl_aff_zero_on_domain(ls
);
2306 aff
= isl_aff_add_coefficient_si(aff
, isl_dim_in
, 0, 1);
2307 aff
= isl_aff_scale_down_ui(aff
, 3);
2308 aff
= isl_aff_floor(aff
);
2309 aff
= isl_aff_add_coefficient_si(aff
, isl_dim_in
, 0, 1);
2310 aff
= isl_aff_scale_down_ui(aff
, 2);
2311 aff
= isl_aff_floor(aff
);
2312 aff
= isl_aff_add_coefficient_si(aff
, isl_dim_in
, 0, 1);
2315 set
= isl_set_read_from_str(ctx
, str
);
2316 aff
= isl_aff_gist(aff
, set
);
2318 aff
= isl_aff_add_constant_si(aff
, -16);
2319 zero
= isl_aff_plain_is_zero(aff
);
2325 isl_die(ctx
, isl_error_unknown
, "unexpected result", return -1);
2330 int test_dim_max(isl_ctx
*ctx
)
2334 isl_set
*set1
, *set2
;
2339 str
= "[N] -> { [i] : 0 <= i <= min(N,10) }";
2340 set
= isl_set_read_from_str(ctx
, str
);
2341 pwaff
= isl_set_dim_max(set
, 0);
2342 set1
= isl_set_from_pw_aff(pwaff
);
2343 str
= "[N] -> { [10] : N >= 10; [N] : N <= 9 and N >= 0 }";
2344 set2
= isl_set_read_from_str(ctx
, str
);
2345 equal
= isl_set_is_equal(set1
, set2
);
2351 isl_die(ctx
, isl_error_unknown
, "unexpected result", return -1);
2353 str
= "[N] -> { [i] : 0 <= i <= max(2N,N+6) }";
2354 set
= isl_set_read_from_str(ctx
, str
);
2355 pwaff
= isl_set_dim_max(set
, 0);
2356 set1
= isl_set_from_pw_aff(pwaff
);
2357 str
= "[N] -> { [6 + N] : -6 <= N <= 5; [2N] : N >= 6 }";
2358 set2
= isl_set_read_from_str(ctx
, str
);
2359 equal
= isl_set_is_equal(set1
, set2
);
2365 isl_die(ctx
, isl_error_unknown
, "unexpected result", return -1);
2367 str
= "[N] -> { [i] : 0 <= i <= 2N or 0 <= i <= N+6 }";
2368 set
= isl_set_read_from_str(ctx
, str
);
2369 pwaff
= isl_set_dim_max(set
, 0);
2370 set1
= isl_set_from_pw_aff(pwaff
);
2371 str
= "[N] -> { [6 + N] : -6 <= N <= 5; [2N] : N >= 6 }";
2372 set2
= isl_set_read_from_str(ctx
, str
);
2373 equal
= isl_set_is_equal(set1
, set2
);
2379 isl_die(ctx
, isl_error_unknown
, "unexpected result", return -1);
2381 str
= "[N,M] -> { [i,j] -> [([i/16]), i%16, ([j/16]), j%16] : "
2382 "0 <= i < N and 0 <= j < M }";
2383 map
= isl_map_read_from_str(ctx
, str
);
2384 set
= isl_map_range(map
);
2386 pwaff
= isl_set_dim_max(isl_set_copy(set
), 0);
2387 set1
= isl_set_from_pw_aff(pwaff
);
2388 str
= "[N,M] -> { [([(N-1)/16])] : M,N > 0 }";
2389 set2
= isl_set_read_from_str(ctx
, str
);
2390 equal
= isl_set_is_equal(set1
, set2
);
2394 pwaff
= isl_set_dim_max(isl_set_copy(set
), 3);
2395 set1
= isl_set_from_pw_aff(pwaff
);
2396 str
= "[N,M] -> { [t] : t = min(M-1,15) and M,N > 0 }";
2397 set2
= isl_set_read_from_str(ctx
, str
);
2398 if (equal
>= 0 && equal
)
2399 equal
= isl_set_is_equal(set1
, set2
);
2408 isl_die(ctx
, isl_error_unknown
, "unexpected result", return -1);
2413 int test_product(isl_ctx
*ctx
)
2420 set
= isl_set_read_from_str(ctx
, str
);
2421 set
= isl_set_product(set
, isl_set_copy(set
));
2422 ok
= isl_set_is_wrapping(set
);
2427 isl_die(ctx
, isl_error_unknown
, "unexpected result", return -1);
2432 int test_equal(isl_ctx
*ctx
)
2435 isl_set
*set
, *set2
;
2439 set
= isl_set_read_from_str(ctx
, str
);
2441 set2
= isl_set_read_from_str(ctx
, str
);
2442 equal
= isl_set_is_equal(set
, set2
);
2448 isl_die(ctx
, isl_error_unknown
, "unexpected result", return -1);
2453 static int test_plain_fixed(isl_ctx
*ctx
, __isl_take isl_map
*map
,
2454 enum isl_dim_type type
, unsigned pos
, int fixed
)
2458 test
= isl_map_plain_is_fixed(map
, type
, pos
, NULL
);
2465 isl_die(ctx
, isl_error_unknown
,
2466 "map not detected as fixed", return -1);
2468 isl_die(ctx
, isl_error_unknown
,
2469 "map detected as fixed", return -1);
2472 int test_fixed(isl_ctx
*ctx
)
2477 str
= "{ [i] -> [i] }";
2478 map
= isl_map_read_from_str(ctx
, str
);
2479 if (test_plain_fixed(ctx
, map
, isl_dim_out
, 0, 0))
2481 str
= "{ [i] -> [1] }";
2482 map
= isl_map_read_from_str(ctx
, str
);
2483 if (test_plain_fixed(ctx
, map
, isl_dim_out
, 0, 1))
2485 str
= "{ S_1[p1] -> [o0] : o0 = -2 and p1 >= 1 and p1 <= 7 }";
2486 map
= isl_map_read_from_str(ctx
, str
);
2487 if (test_plain_fixed(ctx
, map
, isl_dim_out
, 0, 1))
2489 map
= isl_map_read_from_str(ctx
, str
);
2490 map
= isl_map_neg(map
);
2491 if (test_plain_fixed(ctx
, map
, isl_dim_out
, 0, 1))
2499 struct isl_ctx
*ctx
;
2501 srcdir
= getenv("srcdir");
2504 ctx
= isl_ctx_alloc();
2505 if (test_fixed(ctx
) < 0)
2507 if (test_equal(ctx
) < 0)
2509 if (test_product(ctx
) < 0)
2511 if (test_dim_max(ctx
) < 0)
2513 if (test_aff(ctx
) < 0)
2515 if (test_injective(ctx
) < 0)
2517 if (test_schedule(ctx
) < 0)
2519 test_factorize(ctx
);
2524 test_split_periods(ctx
);
2528 if (test_sv(ctx
) < 0)
2530 test_bijective(ctx
);
2534 test_construction(ctx
);
2537 test_application(ctx
);
2538 test_affine_hull(ctx
);
2539 test_convex_hull(ctx
);