2 * Copyright 2008-2009 Katholieke Universiteit Leuven
4 * Use of this software is governed by the MIT 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>
15 #include <isl_aff_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>
24 #include <isl/vertices.h>
26 #define ARRAY_SIZE(array) (sizeof(array)/sizeof(*array))
30 static char *get_filename(isl_ctx
*ctx
, const char *name
, const char *suffix
) {
33 char *pattern
= "%s/test_inputs/%s.%s";
35 length
= strlen(pattern
) - 6 + strlen(srcdir
) + strlen(name
)
37 filename
= isl_alloc_array(ctx
, char, length
);
42 sprintf(filename
, pattern
, srcdir
, name
, suffix
);
47 void test_parse_map(isl_ctx
*ctx
, const char *str
)
51 map
= isl_map_read_from_str(ctx
, str
);
56 int test_parse_map_equal(isl_ctx
*ctx
, const char *str
, const char *str2
)
61 map
= isl_map_read_from_str(ctx
, str
);
62 map2
= isl_map_read_from_str(ctx
, str2
);
63 equal
= isl_map_is_equal(map
, map2
);
70 isl_die(ctx
, isl_error_unknown
, "maps not equal",
76 void test_parse_pwqp(isl_ctx
*ctx
, const char *str
)
78 isl_pw_qpolynomial
*pwqp
;
80 pwqp
= isl_pw_qpolynomial_read_from_str(ctx
, str
);
82 isl_pw_qpolynomial_free(pwqp
);
85 static void test_parse_pwaff(isl_ctx
*ctx
, const char *str
)
89 pwaff
= isl_pw_aff_read_from_str(ctx
, str
);
91 isl_pw_aff_free(pwaff
);
94 int test_parse(struct isl_ctx
*ctx
)
97 const char *str
, *str2
;
99 str
= "{ [i] -> [-i] }";
100 map
= isl_map_read_from_str(ctx
, str
);
104 str
= "{ A[i] -> L[([i/3])] }";
105 map
= isl_map_read_from_str(ctx
, str
);
109 test_parse_map(ctx
, "{[[s] -> A[i]] -> [[s+1] -> A[i]]}");
110 test_parse_map(ctx
, "{ [p1, y1, y2] -> [2, y1, y2] : "
111 "p1 = 1 && (y1 <= y2 || y2 = 0) }");
113 str
= "{ [x,y] : [([x/2]+y)/3] >= 1 }";
114 str2
= "{ [x, y] : 2y >= 6 - x }";
115 if (test_parse_map_equal(ctx
, str
, str2
) < 0)
118 if (test_parse_map_equal(ctx
, "{ [x,y] : x <= min(y, 2*y+3) }",
119 "{ [x,y] : x <= y, 2*y + 3 }") < 0)
121 str
= "{ [x, y] : (y <= x and y >= -3) or (2y <= -3 + x and y <= -4) }";
122 if (test_parse_map_equal(ctx
, "{ [x,y] : x >= min(y, 2*y+3) }",
126 str
= "{[new,old] -> [new+1-2*[(new+1)/2],old+1-2*[(old+1)/2]]}";
127 map
= isl_map_read_from_str(ctx
, str
);
128 str
= "{ [new, old] -> [o0, o1] : "
129 "exists (e0 = [(-1 - new + o0)/2], e1 = [(-1 - old + o1)/2]: "
130 "2e0 = -1 - new + o0 and 2e1 = -1 - old + o1 and o0 >= 0 and "
131 "o0 <= 1 and o1 >= 0 and o1 <= 1) }";
132 map2
= isl_map_read_from_str(ctx
, str
);
133 assert(isl_map_is_equal(map
, map2
));
137 str
= "{[new,old] -> [new+1-2*[(new+1)/2],old+1-2*[(old+1)/2]]}";
138 map
= isl_map_read_from_str(ctx
, str
);
139 str
= "{[new,old] -> [(new+1)%2,(old+1)%2]}";
140 map2
= isl_map_read_from_str(ctx
, str
);
141 assert(isl_map_is_equal(map
, map2
));
145 str
= "[n] -> { [c1] : c1>=0 and c1<=floord(n-4,3) }";
146 str2
= "[n] -> { [c1] : c1 >= 0 and 3c1 <= -4 + n }";
147 if (test_parse_map_equal(ctx
, str
, str2
) < 0)
150 str
= "{ [i,j] -> [i] : i < j; [i,j] -> [j] : j <= i }";
151 str2
= "{ [i,j] -> [min(i,j)] }";
152 if (test_parse_map_equal(ctx
, str
, str2
) < 0)
155 str
= "{ [i,j] : i != j }";
156 str2
= "{ [i,j] : i < j or i > j }";
157 if (test_parse_map_equal(ctx
, str
, str2
) < 0)
160 str
= "{ [i,j] : (i+1)*2 >= j }";
161 str2
= "{ [i, j] : j <= 2 + 2i }";
162 if (test_parse_map_equal(ctx
, str
, str2
) < 0)
165 str
= "{ [i] -> [i > 0 ? 4 : 5] }";
166 str2
= "{ [i] -> [5] : i <= 0; [i] -> [4] : i >= 1 }";
167 if (test_parse_map_equal(ctx
, str
, str2
) < 0)
170 str
= "[N=2,M] -> { [i=[(M+N)/4]] }";
171 str2
= "[N, M] -> { [i] : N = 2 and 4i <= 2 + M and 4i >= -1 + M }";
172 if (test_parse_map_equal(ctx
, str
, str2
) < 0)
175 str
= "{ [x] : x >= 0 }";
176 str2
= "{ [x] : x-0 >= 0 }";
177 if (test_parse_map_equal(ctx
, str
, str2
) < 0)
180 str
= "{ [i] : ((i > 10)) }";
181 str2
= "{ [i] : i >= 11 }";
182 if (test_parse_map_equal(ctx
, str
, str2
) < 0)
185 str
= "{ [i] -> [0] }";
186 str2
= "{ [i] -> [0 * i] }";
187 if (test_parse_map_equal(ctx
, str
, str2
) < 0)
190 test_parse_pwqp(ctx
, "{ [i] -> i + [ (i + [i/3])/2 ] }");
191 test_parse_map(ctx
, "{ S1[i] -> [([i/10]),i%10] : 0 <= i <= 45 }");
192 test_parse_pwaff(ctx
, "{ [i] -> [i + 1] : i > 0; [a] -> [a] : a < 0 }");
193 test_parse_pwqp(ctx
, "{ [x] -> ([(x)/2] * [(x)/3]) }");
195 if (test_parse_map_equal(ctx
, "{ [a] -> [b] : (not false) }",
196 "{ [a] -> [b] : true }") < 0)
199 if (test_parse_map_equal(ctx
, "{ [i] : i/2 <= 5 }",
200 "{ [i] : i <= 10 }") < 0)
206 void test_read(struct isl_ctx
*ctx
)
210 struct isl_basic_set
*bset1
, *bset2
;
211 const char *str
= "{[y]: Exists ( alpha : 2alpha = y)}";
213 filename
= get_filename(ctx
, "set", "omega");
215 input
= fopen(filename
, "r");
218 bset1
= isl_basic_set_read_from_file(ctx
, input
);
219 bset2
= isl_basic_set_read_from_str(ctx
, str
);
221 assert(isl_basic_set_is_equal(bset1
, bset2
) == 1);
223 isl_basic_set_free(bset1
);
224 isl_basic_set_free(bset2
);
230 void test_bounded(struct isl_ctx
*ctx
)
235 set
= isl_set_read_from_str(ctx
, "[n] -> {[i] : 0 <= i <= n }");
236 bounded
= isl_set_is_bounded(set
);
240 set
= isl_set_read_from_str(ctx
, "{[n, i] : 0 <= i <= n }");
241 bounded
= isl_set_is_bounded(set
);
245 set
= isl_set_read_from_str(ctx
, "[n] -> {[i] : i <= n }");
246 bounded
= isl_set_is_bounded(set
);
251 /* Construct the basic set { [i] : 5 <= i <= N } */
252 void test_construction(struct isl_ctx
*ctx
)
257 struct isl_basic_set
*bset
;
258 struct isl_constraint
*c
;
262 dim
= isl_space_set_alloc(ctx
, 1, 1);
263 bset
= isl_basic_set_universe(isl_space_copy(dim
));
264 ls
= isl_local_space_from_space(dim
);
266 c
= isl_inequality_alloc(isl_local_space_copy(ls
));
267 isl_int_set_si(v
, -1);
268 isl_constraint_set_coefficient(c
, isl_dim_set
, 0, v
);
269 isl_int_set_si(v
, 1);
270 isl_constraint_set_coefficient(c
, isl_dim_param
, 0, v
);
271 bset
= isl_basic_set_add_constraint(bset
, c
);
273 c
= isl_inequality_alloc(isl_local_space_copy(ls
));
274 isl_int_set_si(v
, 1);
275 isl_constraint_set_coefficient(c
, isl_dim_set
, 0, v
);
276 isl_int_set_si(v
, -5);
277 isl_constraint_set_constant(c
, v
);
278 bset
= isl_basic_set_add_constraint(bset
, c
);
280 isl_local_space_free(ls
);
281 isl_basic_set_free(bset
);
286 void test_dim(struct isl_ctx
*ctx
)
289 isl_map
*map1
, *map2
;
291 map1
= isl_map_read_from_str(ctx
,
292 "[n] -> { [i] -> [j] : exists (a = [i/10] : i - 10a <= n ) }");
293 map1
= isl_map_add_dims(map1
, isl_dim_in
, 1);
294 map2
= isl_map_read_from_str(ctx
,
295 "[n] -> { [i,k] -> [j] : exists (a = [i/10] : i - 10a <= n ) }");
296 assert(isl_map_is_equal(map1
, map2
));
299 map1
= isl_map_project_out(map1
, isl_dim_in
, 0, 1);
300 map2
= isl_map_read_from_str(ctx
, "[n] -> { [i] -> [j] : n >= 0 }");
301 assert(isl_map_is_equal(map1
, map2
));
306 str
= "[n] -> { [i] -> [] : exists a : 0 <= i <= n and i = 2 a }";
307 map1
= isl_map_read_from_str(ctx
, str
);
308 str
= "{ [i] -> [j] : exists a : 0 <= i <= j and i = 2 a }";
309 map2
= isl_map_read_from_str(ctx
, str
);
310 map1
= isl_map_move_dims(map1
, isl_dim_out
, 0, isl_dim_param
, 0, 1);
311 assert(isl_map_is_equal(map1
, map2
));
317 static int test_div(isl_ctx
*ctx
)
326 struct isl_basic_set
*bset
;
327 struct isl_constraint
*c
;
332 dim
= isl_space_set_alloc(ctx
, 0, 3);
333 bset
= isl_basic_set_universe(isl_space_copy(dim
));
334 ls
= isl_local_space_from_space(dim
);
336 c
= isl_equality_alloc(isl_local_space_copy(ls
));
337 isl_int_set_si(v
, -1);
338 isl_constraint_set_constant(c
, v
);
339 isl_int_set_si(v
, 1);
340 isl_constraint_set_coefficient(c
, isl_dim_set
, 0, v
);
341 isl_int_set_si(v
, 3);
342 isl_constraint_set_coefficient(c
, isl_dim_set
, 1, v
);
343 bset
= isl_basic_set_add_constraint(bset
, c
);
345 c
= isl_equality_alloc(isl_local_space_copy(ls
));
346 isl_int_set_si(v
, 1);
347 isl_constraint_set_constant(c
, v
);
348 isl_int_set_si(v
, -1);
349 isl_constraint_set_coefficient(c
, isl_dim_set
, 0, v
);
350 isl_int_set_si(v
, 3);
351 isl_constraint_set_coefficient(c
, isl_dim_set
, 2, v
);
352 bset
= isl_basic_set_add_constraint(bset
, c
);
354 bset
= isl_basic_set_project_out(bset
, isl_dim_set
, 1, 2);
356 assert(bset
&& bset
->n_div
== 1);
357 isl_local_space_free(ls
);
358 isl_basic_set_free(bset
);
361 dim
= isl_space_set_alloc(ctx
, 0, 3);
362 bset
= isl_basic_set_universe(isl_space_copy(dim
));
363 ls
= isl_local_space_from_space(dim
);
365 c
= isl_equality_alloc(isl_local_space_copy(ls
));
366 isl_int_set_si(v
, 1);
367 isl_constraint_set_constant(c
, v
);
368 isl_int_set_si(v
, -1);
369 isl_constraint_set_coefficient(c
, isl_dim_set
, 0, v
);
370 isl_int_set_si(v
, 3);
371 isl_constraint_set_coefficient(c
, isl_dim_set
, 1, v
);
372 bset
= isl_basic_set_add_constraint(bset
, c
);
374 c
= isl_equality_alloc(isl_local_space_copy(ls
));
375 isl_int_set_si(v
, -1);
376 isl_constraint_set_constant(c
, v
);
377 isl_int_set_si(v
, 1);
378 isl_constraint_set_coefficient(c
, isl_dim_set
, 0, v
);
379 isl_int_set_si(v
, 3);
380 isl_constraint_set_coefficient(c
, isl_dim_set
, 2, v
);
381 bset
= isl_basic_set_add_constraint(bset
, c
);
383 bset
= isl_basic_set_project_out(bset
, isl_dim_set
, 1, 2);
385 assert(bset
&& bset
->n_div
== 1);
386 isl_local_space_free(ls
);
387 isl_basic_set_free(bset
);
390 dim
= isl_space_set_alloc(ctx
, 0, 3);
391 bset
= isl_basic_set_universe(isl_space_copy(dim
));
392 ls
= isl_local_space_from_space(dim
);
394 c
= isl_equality_alloc(isl_local_space_copy(ls
));
395 isl_int_set_si(v
, 1);
396 isl_constraint_set_constant(c
, v
);
397 isl_int_set_si(v
, -1);
398 isl_constraint_set_coefficient(c
, isl_dim_set
, 0, v
);
399 isl_int_set_si(v
, 3);
400 isl_constraint_set_coefficient(c
, isl_dim_set
, 1, v
);
401 bset
= isl_basic_set_add_constraint(bset
, c
);
403 c
= isl_equality_alloc(isl_local_space_copy(ls
));
404 isl_int_set_si(v
, -3);
405 isl_constraint_set_constant(c
, v
);
406 isl_int_set_si(v
, 1);
407 isl_constraint_set_coefficient(c
, isl_dim_set
, 0, v
);
408 isl_int_set_si(v
, 4);
409 isl_constraint_set_coefficient(c
, isl_dim_set
, 2, v
);
410 bset
= isl_basic_set_add_constraint(bset
, c
);
412 bset
= isl_basic_set_project_out(bset
, isl_dim_set
, 1, 2);
414 assert(bset
&& bset
->n_div
== 1);
415 isl_local_space_free(ls
);
416 isl_basic_set_free(bset
);
419 dim
= isl_space_set_alloc(ctx
, 0, 3);
420 bset
= isl_basic_set_universe(isl_space_copy(dim
));
421 ls
= isl_local_space_from_space(dim
);
423 c
= isl_equality_alloc(isl_local_space_copy(ls
));
424 isl_int_set_si(v
, 2);
425 isl_constraint_set_constant(c
, v
);
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 c
= isl_equality_alloc(isl_local_space_copy(ls
));
433 isl_int_set_si(v
, -1);
434 isl_constraint_set_constant(c
, v
);
435 isl_int_set_si(v
, 1);
436 isl_constraint_set_coefficient(c
, isl_dim_set
, 0, v
);
437 isl_int_set_si(v
, 6);
438 isl_constraint_set_coefficient(c
, isl_dim_set
, 2, v
);
439 bset
= isl_basic_set_add_constraint(bset
, c
);
441 bset
= isl_basic_set_project_out(bset
, isl_dim_set
, 1, 2);
443 assert(isl_basic_set_is_empty(bset
));
444 isl_local_space_free(ls
);
445 isl_basic_set_free(bset
);
448 dim
= isl_space_set_alloc(ctx
, 0, 3);
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
, 2, v
);
457 bset
= isl_basic_set_add_constraint(bset
, c
);
459 c
= isl_equality_alloc(isl_local_space_copy(ls
));
460 isl_int_set_si(v
, 1);
461 isl_constraint_set_coefficient(c
, isl_dim_set
, 0, v
);
462 isl_int_set_si(v
, -3);
463 isl_constraint_set_coefficient(c
, isl_dim_set
, 1, v
);
464 bset
= isl_basic_set_add_constraint(bset
, c
);
466 bset
= isl_basic_set_project_out(bset
, isl_dim_set
, 2, 1);
468 assert(bset
&& bset
->n_div
== 0);
469 isl_basic_set_free(bset
);
470 isl_local_space_free(ls
);
473 dim
= isl_space_set_alloc(ctx
, 0, 3);
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
, 6);
481 isl_constraint_set_coefficient(c
, isl_dim_set
, 2, v
);
482 bset
= isl_basic_set_add_constraint(bset
, c
);
484 c
= isl_equality_alloc(isl_local_space_copy(ls
));
485 isl_int_set_si(v
, 1);
486 isl_constraint_set_coefficient(c
, isl_dim_set
, 0, v
);
487 isl_int_set_si(v
, -3);
488 isl_constraint_set_coefficient(c
, isl_dim_set
, 1, v
);
489 bset
= isl_basic_set_add_constraint(bset
, c
);
491 bset
= isl_basic_set_project_out(bset
, isl_dim_set
, 2, 1);
493 assert(bset
&& bset
->n_div
== 1);
494 isl_basic_set_free(bset
);
495 isl_local_space_free(ls
);
498 /* This test is a bit tricky. We set up an equality
500 * Normalization of divs creates _two_ divs
503 * Afterwards e0 is removed again because it has coefficient -1
504 * and we end up with the original equality and div again.
505 * Perhaps we can avoid the introduction of this temporary div.
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
, -3);
515 isl_constraint_set_coefficient(c
, isl_dim_set
, 1, v
);
516 isl_int_set_si(v
, -3);
517 isl_constraint_set_coefficient(c
, isl_dim_set
, 2, v
);
518 isl_int_set_si(v
, 6);
519 isl_constraint_set_coefficient(c
, isl_dim_set
, 3, v
);
520 bset
= isl_basic_set_add_constraint(bset
, c
);
522 bset
= isl_basic_set_project_out(bset
, isl_dim_set
, 3, 1);
524 /* Test disabled for now */
526 assert(bset && bset->n_div == 1);
528 isl_local_space_free(ls
);
529 isl_basic_set_free(bset
);
532 dim
= isl_space_set_alloc(ctx
, 0, 5);
533 bset
= isl_basic_set_universe(isl_space_copy(dim
));
534 ls
= isl_local_space_from_space(dim
);
536 c
= isl_equality_alloc(isl_local_space_copy(ls
));
537 isl_int_set_si(v
, -1);
538 isl_constraint_set_coefficient(c
, isl_dim_set
, 0, v
);
539 isl_int_set_si(v
, -3);
540 isl_constraint_set_coefficient(c
, isl_dim_set
, 1, v
);
541 isl_int_set_si(v
, -3);
542 isl_constraint_set_coefficient(c
, isl_dim_set
, 3, v
);
543 isl_int_set_si(v
, 6);
544 isl_constraint_set_coefficient(c
, isl_dim_set
, 4, v
);
545 bset
= isl_basic_set_add_constraint(bset
, c
);
547 c
= isl_equality_alloc(isl_local_space_copy(ls
));
548 isl_int_set_si(v
, -1);
549 isl_constraint_set_coefficient(c
, isl_dim_set
, 0, v
);
550 isl_int_set_si(v
, 1);
551 isl_constraint_set_coefficient(c
, isl_dim_set
, 2, v
);
552 isl_int_set_si(v
, 1);
553 isl_constraint_set_constant(c
, v
);
554 bset
= isl_basic_set_add_constraint(bset
, c
);
556 bset
= isl_basic_set_project_out(bset
, isl_dim_set
, 4, 1);
558 /* Test disabled for now */
560 assert(bset && bset->n_div == 1);
562 isl_local_space_free(ls
);
563 isl_basic_set_free(bset
);
566 dim
= isl_space_set_alloc(ctx
, 0, 4);
567 bset
= isl_basic_set_universe(isl_space_copy(dim
));
568 ls
= isl_local_space_from_space(dim
);
570 c
= isl_equality_alloc(isl_local_space_copy(ls
));
571 isl_int_set_si(v
, 1);
572 isl_constraint_set_coefficient(c
, isl_dim_set
, 0, v
);
573 isl_int_set_si(v
, -1);
574 isl_constraint_set_coefficient(c
, isl_dim_set
, 1, v
);
575 isl_int_set_si(v
, -2);
576 isl_constraint_set_coefficient(c
, isl_dim_set
, 2, v
);
577 bset
= isl_basic_set_add_constraint(bset
, c
);
579 c
= isl_equality_alloc(isl_local_space_copy(ls
));
580 isl_int_set_si(v
, -1);
581 isl_constraint_set_coefficient(c
, isl_dim_set
, 0, v
);
582 isl_int_set_si(v
, 3);
583 isl_constraint_set_coefficient(c
, isl_dim_set
, 3, v
);
584 isl_int_set_si(v
, 2);
585 isl_constraint_set_constant(c
, v
);
586 bset
= isl_basic_set_add_constraint(bset
, c
);
588 bset
= isl_basic_set_project_out(bset
, isl_dim_set
, 2, 2);
590 bset
= isl_basic_set_fix_si(bset
, isl_dim_set
, 0, 2);
592 assert(!isl_basic_set_is_empty(bset
));
594 isl_local_space_free(ls
);
595 isl_basic_set_free(bset
);
598 dim
= isl_space_set_alloc(ctx
, 0, 3);
599 bset
= isl_basic_set_universe(isl_space_copy(dim
));
600 ls
= isl_local_space_from_space(dim
);
602 c
= isl_equality_alloc(isl_local_space_copy(ls
));
603 isl_int_set_si(v
, 1);
604 isl_constraint_set_coefficient(c
, isl_dim_set
, 0, v
);
605 isl_int_set_si(v
, -2);
606 isl_constraint_set_coefficient(c
, isl_dim_set
, 2, v
);
607 bset
= isl_basic_set_add_constraint(bset
, c
);
609 bset
= isl_basic_set_project_out(bset
, isl_dim_set
, 2, 1);
611 bset
= isl_basic_set_fix_si(bset
, isl_dim_set
, 0, 2);
613 isl_local_space_free(ls
);
614 isl_basic_set_free(bset
);
618 str
= "{ [i] : exists (e0, e1: 3e1 >= 1 + 2e0 and "
619 "8e1 <= -1 + 5i - 5e0 and 2e1 >= 1 + 2i - 5e0) }";
620 set
= isl_set_read_from_str(ctx
, str
);
621 set
= isl_set_compute_divs(set
);
626 str
= "{ [i,j] : 2*[i/2] + 3 * [j/4] <= 10 and 2 i = j }";
627 bset
= isl_basic_set_read_from_str(ctx
, str
);
628 n
= isl_basic_set_dim(bset
, isl_dim_div
);
629 isl_basic_set_free(bset
);
633 isl_die(ctx
, isl_error_unknown
,
634 "expecting no existentials", return -1);
636 str
= "{ [i,j,k] : 3 + i + 2j >= 0 and 2 * [(i+2j)/4] <= k }";
637 set
= isl_set_read_from_str(ctx
, str
);
638 set
= isl_set_remove_divs_involving_dims(set
, isl_dim_set
, 0, 2);
639 set
= isl_set_fix_si(set
, isl_dim_set
, 2, -3);
640 empty
= isl_set_is_empty(set
);
645 isl_die(ctx
, isl_error_unknown
,
646 "result not as accurate as expected", return -1);
651 void test_application_case(struct isl_ctx
*ctx
, const char *name
)
655 struct isl_basic_set
*bset1
, *bset2
;
656 struct isl_basic_map
*bmap
;
658 filename
= get_filename(ctx
, name
, "omega");
660 input
= fopen(filename
, "r");
663 bset1
= isl_basic_set_read_from_file(ctx
, input
);
664 bmap
= isl_basic_map_read_from_file(ctx
, input
);
666 bset1
= isl_basic_set_apply(bset1
, bmap
);
668 bset2
= isl_basic_set_read_from_file(ctx
, input
);
670 assert(isl_basic_set_is_equal(bset1
, bset2
) == 1);
672 isl_basic_set_free(bset1
);
673 isl_basic_set_free(bset2
);
679 void test_application(struct isl_ctx
*ctx
)
681 test_application_case(ctx
, "application");
682 test_application_case(ctx
, "application2");
685 void test_affine_hull_case(struct isl_ctx
*ctx
, const char *name
)
689 struct isl_basic_set
*bset1
, *bset2
;
691 filename
= get_filename(ctx
, name
, "polylib");
693 input
= fopen(filename
, "r");
696 bset1
= isl_basic_set_read_from_file(ctx
, input
);
697 bset2
= isl_basic_set_read_from_file(ctx
, input
);
699 bset1
= isl_basic_set_affine_hull(bset1
);
701 assert(isl_basic_set_is_equal(bset1
, bset2
) == 1);
703 isl_basic_set_free(bset1
);
704 isl_basic_set_free(bset2
);
710 int test_affine_hull(struct isl_ctx
*ctx
)
717 test_affine_hull_case(ctx
, "affine2");
718 test_affine_hull_case(ctx
, "affine");
719 test_affine_hull_case(ctx
, "affine3");
721 str
= "[m] -> { [i0] : exists (e0, e1: e1 <= 1 + i0 and "
722 "m >= 3 and 4i0 <= 2 + m and e1 >= i0 and "
723 "e1 >= 0 and e1 <= 2 and e1 >= 1 + 2e0 and "
724 "2e1 <= 1 + m + 4e0 and 2e1 >= 2 - m + 4i0 - 4e0) }";
725 set
= isl_set_read_from_str(ctx
, str
);
726 bset
= isl_set_affine_hull(set
);
727 n
= isl_basic_set_dim(bset
, isl_dim_div
);
728 isl_basic_set_free(bset
);
730 isl_die(ctx
, isl_error_unknown
, "not expecting any divs",
736 void test_convex_hull_case(struct isl_ctx
*ctx
, const char *name
)
740 struct isl_basic_set
*bset1
, *bset2
;
743 filename
= get_filename(ctx
, name
, "polylib");
745 input
= fopen(filename
, "r");
748 bset1
= isl_basic_set_read_from_file(ctx
, input
);
749 bset2
= isl_basic_set_read_from_file(ctx
, input
);
751 set
= isl_basic_set_union(bset1
, bset2
);
752 bset1
= isl_set_convex_hull(set
);
754 bset2
= isl_basic_set_read_from_file(ctx
, input
);
756 assert(isl_basic_set_is_equal(bset1
, bset2
) == 1);
758 isl_basic_set_free(bset1
);
759 isl_basic_set_free(bset2
);
765 void test_convex_hull_algo(struct isl_ctx
*ctx
, int convex
)
767 const char *str1
, *str2
;
768 isl_set
*set1
, *set2
;
769 int orig_convex
= ctx
->opt
->convex
;
770 ctx
->opt
->convex
= convex
;
772 test_convex_hull_case(ctx
, "convex0");
773 test_convex_hull_case(ctx
, "convex1");
774 test_convex_hull_case(ctx
, "convex2");
775 test_convex_hull_case(ctx
, "convex3");
776 test_convex_hull_case(ctx
, "convex4");
777 test_convex_hull_case(ctx
, "convex5");
778 test_convex_hull_case(ctx
, "convex6");
779 test_convex_hull_case(ctx
, "convex7");
780 test_convex_hull_case(ctx
, "convex8");
781 test_convex_hull_case(ctx
, "convex9");
782 test_convex_hull_case(ctx
, "convex10");
783 test_convex_hull_case(ctx
, "convex11");
784 test_convex_hull_case(ctx
, "convex12");
785 test_convex_hull_case(ctx
, "convex13");
786 test_convex_hull_case(ctx
, "convex14");
787 test_convex_hull_case(ctx
, "convex15");
789 str1
= "{ [i0, i1, i2] : (i2 = 1 and i0 = 0 and i1 >= 0) or "
790 "(i0 = 1 and i1 = 0 and i2 = 1) or "
791 "(i0 = 0 and i1 = 0 and i2 = 0) }";
792 str2
= "{ [i0, i1, i2] : i0 >= 0 and i2 >= i0 and i2 <= 1 and i1 >= 0 }";
793 set1
= isl_set_read_from_str(ctx
, str1
);
794 set2
= isl_set_read_from_str(ctx
, str2
);
795 set1
= isl_set_from_basic_set(isl_set_convex_hull(set1
));
796 assert(isl_set_is_equal(set1
, set2
));
800 ctx
->opt
->convex
= orig_convex
;
803 void test_convex_hull(struct isl_ctx
*ctx
)
805 test_convex_hull_algo(ctx
, ISL_CONVEX_HULL_FM
);
806 test_convex_hull_algo(ctx
, ISL_CONVEX_HULL_WRAP
);
809 void test_gist_case(struct isl_ctx
*ctx
, const char *name
)
813 struct isl_basic_set
*bset1
, *bset2
;
815 filename
= get_filename(ctx
, name
, "polylib");
817 input
= fopen(filename
, "r");
820 bset1
= isl_basic_set_read_from_file(ctx
, input
);
821 bset2
= isl_basic_set_read_from_file(ctx
, input
);
823 bset1
= isl_basic_set_gist(bset1
, bset2
);
825 bset2
= isl_basic_set_read_from_file(ctx
, input
);
827 assert(isl_basic_set_is_equal(bset1
, bset2
) == 1);
829 isl_basic_set_free(bset1
);
830 isl_basic_set_free(bset2
);
836 void test_gist(struct isl_ctx
*ctx
)
839 isl_basic_set
*bset1
, *bset2
;
841 test_gist_case(ctx
, "gist1");
843 str
= "[p0, p2, p3, p5, p6, p10] -> { [] : "
844 "exists (e0 = [(15 + p0 + 15p6 + 15p10)/16], e1 = [(p5)/8], "
845 "e2 = [(p6)/128], e3 = [(8p2 - p5)/128], "
846 "e4 = [(128p3 - p6)/4096]: 8e1 = p5 and 128e2 = p6 and "
847 "128e3 = 8p2 - p5 and 4096e4 = 128p3 - p6 and p2 >= 0 and "
848 "16e0 >= 16 + 16p6 + 15p10 and p2 <= 15 and p3 >= 0 and "
849 "p3 <= 31 and p6 >= 128p3 and p5 >= 8p2 and p10 >= 0 and "
850 "16e0 <= 15 + p0 + 15p6 + 15p10 and 16e0 >= p0 + 15p6 + 15p10 and "
851 "p10 <= 15 and p10 <= -1 + p0 - p6) }";
852 bset1
= isl_basic_set_read_from_str(ctx
, str
);
853 str
= "[p0, p2, p3, p5, p6, p10] -> { [] : exists (e0 = [(p5)/8], "
854 "e1 = [(p6)/128], e2 = [(8p2 - p5)/128], "
855 "e3 = [(128p3 - p6)/4096]: 8e0 = p5 and 128e1 = p6 and "
856 "128e2 = 8p2 - p5 and 4096e3 = 128p3 - p6 and p5 >= -7 and "
857 "p2 >= 0 and 8p2 <= -1 + p0 and p2 <= 15 and p3 >= 0 and "
858 "p3 <= 31 and 128p3 <= -1 + p0 and p6 >= -127 and "
859 "p5 <= -1 + p0 and p6 <= -1 + p0 and p6 >= 128p3 and "
860 "p0 >= 1 and p5 >= 8p2 and p10 >= 0 and p10 <= 15 ) }";
861 bset2
= isl_basic_set_read_from_str(ctx
, str
);
862 bset1
= isl_basic_set_gist(bset1
, bset2
);
863 assert(bset1
&& bset1
->n_div
== 0);
864 isl_basic_set_free(bset1
);
867 int test_coalesce_set(isl_ctx
*ctx
, const char *str
, int check_one
)
873 set
= isl_set_read_from_str(ctx
, str
);
874 set
= isl_set_coalesce(set
);
875 set2
= isl_set_read_from_str(ctx
, str
);
876 equal
= isl_set_is_equal(set
, set2
);
877 one
= set
&& set
->n
== 1;
884 isl_die(ctx
, isl_error_unknown
,
885 "coalesced set not equal to input", return -1);
886 if (check_one
&& !one
)
887 isl_die(ctx
, isl_error_unknown
,
888 "coalesced set should not be a union", return -1);
893 int test_coalesce_unbounded_wrapping(isl_ctx
*ctx
)
898 bounded
= isl_options_get_coalesce_bounded_wrapping(ctx
);
899 isl_options_set_coalesce_bounded_wrapping(ctx
, 0);
901 if (test_coalesce_set(ctx
,
902 "{[x,y,z] : y + 2 >= 0 and x - y + 1 >= 0 and "
903 "-x - y + 1 >= 0 and -3 <= z <= 3;"
904 "[x,y,z] : -x+z + 20 >= 0 and -x-z + 20 >= 0 and "
905 "x-z + 20 >= 0 and x+z + 20 >= 0 and "
906 "-10 <= y <= 0}", 1) < 0)
908 if (test_coalesce_set(ctx
,
909 "{[x,y] : 0 <= x,y <= 10; [5,y]: 4 <=y <= 11}", 1) < 0)
911 if (test_coalesce_set(ctx
,
912 "{[x,0,0] : -5 <= x <= 5; [0,y,1] : -5 <= y <= 5 }", 1) < 0)
920 isl_options_set_coalesce_bounded_wrapping(ctx
, bounded
);
925 int test_coalesce(struct isl_ctx
*ctx
)
928 struct isl_set
*set
, *set2
;
929 struct isl_map
*map
, *map2
;
931 set
= isl_set_read_from_str(ctx
,
932 "{[x,y]: x >= 0 & x <= 10 & y >= 0 & y <= 10 or "
933 "y >= x & x >= 2 & 5 >= y }");
934 set
= isl_set_coalesce(set
);
935 assert(set
&& set
->n
== 1);
938 set
= isl_set_read_from_str(ctx
,
939 "{[x,y]: y >= 0 & 2x + y <= 30 & y <= 10 & x >= 0 or "
940 "x + y >= 10 & y <= x & x + y <= 20 & y >= 0}");
941 set
= isl_set_coalesce(set
);
942 assert(set
&& set
->n
== 1);
945 set
= isl_set_read_from_str(ctx
,
946 "{[x,y]: y >= 0 & 2x + y <= 30 & y <= 10 & x >= 0 or "
947 "x + y >= 10 & y <= x & x + y <= 19 & y >= 0}");
948 set
= isl_set_coalesce(set
);
949 assert(set
&& set
->n
== 2);
952 set
= isl_set_read_from_str(ctx
,
953 "{[x,y]: y >= 0 & x <= 5 & y <= x or "
954 "y >= 0 & x >= 6 & x <= 10 & y <= x}");
955 set
= isl_set_coalesce(set
);
956 assert(set
&& set
->n
== 1);
959 set
= isl_set_read_from_str(ctx
,
960 "{[x,y]: y >= 0 & x <= 5 & y <= x or "
961 "y >= 0 & x >= 7 & x <= 10 & y <= x}");
962 set
= isl_set_coalesce(set
);
963 assert(set
&& set
->n
== 2);
966 set
= isl_set_read_from_str(ctx
,
967 "{[x,y]: y >= 0 & x <= 5 & y <= x or "
968 "y >= 0 & x >= 6 & x <= 10 & y + 1 <= x}");
969 set
= isl_set_coalesce(set
);
970 assert(set
&& set
->n
== 2);
973 set
= isl_set_read_from_str(ctx
,
974 "{[x,y]: y >= 0 & x <= 5 & y <= x or "
975 "y >= 0 & x = 6 & y <= 6}");
976 set
= isl_set_coalesce(set
);
977 assert(set
&& set
->n
== 1);
980 set
= isl_set_read_from_str(ctx
,
981 "{[x,y]: y >= 0 & x <= 5 & y <= x or "
982 "y >= 0 & x = 7 & y <= 6}");
983 set
= isl_set_coalesce(set
);
984 assert(set
&& set
->n
== 2);
987 set
= isl_set_read_from_str(ctx
,
988 "{[x,y]: y >= 0 & x <= 5 & y <= x or "
989 "y >= 0 & x = 6 & y <= 5}");
990 set
= isl_set_coalesce(set
);
991 assert(set
&& set
->n
== 1);
992 set2
= isl_set_read_from_str(ctx
,
993 "{[x,y]: y >= 0 & x <= 5 & y <= x or "
994 "y >= 0 & x = 6 & y <= 5}");
995 assert(isl_set_is_equal(set
, set2
));
999 set
= isl_set_read_from_str(ctx
,
1000 "{[x,y]: y >= 0 & x <= 5 & y <= x or "
1001 "y >= 0 & x = 6 & y <= 7}");
1002 set
= isl_set_coalesce(set
);
1003 assert(set
&& set
->n
== 2);
1006 set
= isl_set_read_from_str(ctx
,
1007 "[n] -> { [i] : i = 1 and n >= 2 or 2 <= i and i <= n }");
1008 set
= isl_set_coalesce(set
);
1009 assert(set
&& set
->n
== 1);
1010 set2
= isl_set_read_from_str(ctx
,
1011 "[n] -> { [i] : i = 1 and n >= 2 or 2 <= i and i <= n }");
1012 assert(isl_set_is_equal(set
, set2
));
1016 set
= isl_set_read_from_str(ctx
,
1017 "{[x,y] : x >= 0 and y >= 0 or 0 <= y and y <= 5 and x = -1}");
1018 set
= isl_set_coalesce(set
);
1019 set2
= isl_set_read_from_str(ctx
,
1020 "{[x,y] : x >= 0 and y >= 0 or 0 <= y and y <= 5 and x = -1}");
1021 assert(isl_set_is_equal(set
, set2
));
1025 set
= isl_set_read_from_str(ctx
,
1026 "[n] -> { [i] : 1 <= i and i <= n - 1 or "
1027 "2 <= i and i <= n }");
1028 set
= isl_set_coalesce(set
);
1029 assert(set
&& set
->n
== 1);
1030 set2
= isl_set_read_from_str(ctx
,
1031 "[n] -> { [i] : 1 <= i and i <= n - 1 or "
1032 "2 <= i and i <= n }");
1033 assert(isl_set_is_equal(set
, set2
));
1037 map
= isl_map_read_from_str(ctx
,
1038 "[n] -> { [i0] -> [o0] : exists (e0 = [(i0)/4], e1 = [(o0)/4], "
1039 "e2 = [(n)/2], e3 = [(-2 + i0)/4], e4 = [(-2 + o0)/4], "
1040 "e5 = [(-2n + i0)/4]: 2e2 = n and 4e3 = -2 + i0 and "
1041 "4e4 = -2 + o0 and i0 >= 8 + 2n and o0 >= 2 + i0 and "
1042 "o0 <= 56 + 2n and o0 <= -12 + 4n and i0 <= 57 + 2n and "
1043 "i0 <= -11 + 4n and o0 >= 6 + 2n and 4e0 <= i0 and "
1044 "4e0 >= -3 + i0 and 4e1 <= o0 and 4e1 >= -3 + o0 and "
1045 "4e5 <= -2n + i0 and 4e5 >= -3 - 2n + i0);"
1046 "[i0] -> [o0] : exists (e0 = [(i0)/4], e1 = [(o0)/4], "
1047 "e2 = [(n)/2], e3 = [(-2 + i0)/4], e4 = [(-2 + o0)/4], "
1048 "e5 = [(-2n + i0)/4]: 2e2 = n and 4e3 = -2 + i0 and "
1049 "4e4 = -2 + o0 and 2e0 >= 3 + n and e0 <= -4 + n and "
1050 "2e0 <= 27 + n and e1 <= -4 + n and 2e1 <= 27 + n and "
1051 "2e1 >= 2 + n and e1 >= 1 + e0 and i0 >= 7 + 2n and "
1052 "i0 <= -11 + 4n and i0 <= 57 + 2n and 4e0 <= -2 + i0 and "
1053 "4e0 >= -3 + i0 and o0 >= 6 + 2n and o0 <= -11 + 4n and "
1054 "o0 <= 57 + 2n and 4e1 <= -2 + o0 and 4e1 >= -3 + o0 and "
1055 "4e5 <= -2n + i0 and 4e5 >= -3 - 2n + i0 ) }");
1056 map
= isl_map_coalesce(map
);
1057 map2
= isl_map_read_from_str(ctx
,
1058 "[n] -> { [i0] -> [o0] : exists (e0 = [(i0)/4], e1 = [(o0)/4], "
1059 "e2 = [(n)/2], e3 = [(-2 + i0)/4], e4 = [(-2 + o0)/4], "
1060 "e5 = [(-2n + i0)/4]: 2e2 = n and 4e3 = -2 + i0 and "
1061 "4e4 = -2 + o0 and i0 >= 8 + 2n and o0 >= 2 + i0 and "
1062 "o0 <= 56 + 2n and o0 <= -12 + 4n and i0 <= 57 + 2n and "
1063 "i0 <= -11 + 4n and o0 >= 6 + 2n and 4e0 <= i0 and "
1064 "4e0 >= -3 + i0 and 4e1 <= o0 and 4e1 >= -3 + o0 and "
1065 "4e5 <= -2n + i0 and 4e5 >= -3 - 2n + i0);"
1066 "[i0] -> [o0] : exists (e0 = [(i0)/4], e1 = [(o0)/4], "
1067 "e2 = [(n)/2], e3 = [(-2 + i0)/4], e4 = [(-2 + o0)/4], "
1068 "e5 = [(-2n + i0)/4]: 2e2 = n and 4e3 = -2 + i0 and "
1069 "4e4 = -2 + o0 and 2e0 >= 3 + n and e0 <= -4 + n and "
1070 "2e0 <= 27 + n and e1 <= -4 + n and 2e1 <= 27 + n and "
1071 "2e1 >= 2 + n and e1 >= 1 + e0 and i0 >= 7 + 2n and "
1072 "i0 <= -11 + 4n and i0 <= 57 + 2n and 4e0 <= -2 + i0 and "
1073 "4e0 >= -3 + i0 and o0 >= 6 + 2n and o0 <= -11 + 4n and "
1074 "o0 <= 57 + 2n and 4e1 <= -2 + o0 and 4e1 >= -3 + o0 and "
1075 "4e5 <= -2n + i0 and 4e5 >= -3 - 2n + i0 ) }");
1076 assert(isl_map_is_equal(map
, map2
));
1080 str
= "[n, m] -> { [] -> [o0, o2, o3] : (o3 = 1 and o0 >= 1 + m and "
1081 "o0 <= n + m and o2 <= m and o0 >= 2 + n and o2 >= 3) or "
1082 "(o0 >= 2 + n and o0 >= 1 + m and o0 <= n + m and n >= 1 and "
1083 "o3 <= -1 + o2 and o3 >= 1 - m + o2 and o3 >= 2 and o3 <= n) }";
1084 map
= isl_map_read_from_str(ctx
, str
);
1085 map
= isl_map_coalesce(map
);
1086 map2
= isl_map_read_from_str(ctx
, str
);
1087 assert(isl_map_is_equal(map
, map2
));
1091 str
= "[M, N] -> { [i0, i1, i2, i3, i4, i5, i6] -> "
1092 "[o0, o1, o2, o3, o4, o5, o6] : "
1093 "(o6 <= -4 + 2M - 2N + i0 + i1 - i2 + i6 - o0 - o1 + o2 and "
1094 "o3 <= -2 + i3 and o6 >= 2 + i0 + i3 + i6 - o0 - o3 and "
1095 "o6 >= 2 - M + N + i3 + i4 + i6 - o3 - o4 and o0 <= -1 + i0 and "
1096 "o4 >= 4 - 3M + 3N - i0 - i1 + i2 + 2i3 + i4 + o0 + o1 - o2 - 2o3 "
1097 "and o6 <= -3 + 2M - 2N + i3 + i4 - i5 + i6 - o3 - o4 + o5 and "
1098 "2o6 <= -5 + 5M - 5N + 2i0 + i1 - i2 - i5 + 2i6 - 2o0 - o1 + o2 + o5 "
1099 "and o6 >= 2i0 + i1 + i6 - 2o0 - o1 and "
1100 "3o6 <= -5 + 4M - 4N + 2i0 + i1 - i2 + 2i3 + i4 - i5 + 3i6 "
1101 "- 2o0 - o1 + o2 - 2o3 - o4 + o5) or "
1102 "(N >= 2 and o3 <= -1 + i3 and o0 <= -1 + i0 and "
1103 "o6 >= i3 + i6 - o3 and M >= 0 and "
1104 "2o6 >= 1 + i0 + i3 + 2i6 - o0 - o3 and "
1105 "o6 >= 1 - M + i0 + i6 - o0 and N >= 2M and o6 >= i0 + i6 - o0) }";
1106 map
= isl_map_read_from_str(ctx
, str
);
1107 map
= isl_map_coalesce(map
);
1108 map2
= isl_map_read_from_str(ctx
, str
);
1109 assert(isl_map_is_equal(map
, map2
));
1113 str
= "[M, N] -> { [] -> [o0] : (o0 = 0 and M >= 1 and N >= 2) or "
1114 "(o0 = 0 and M >= 1 and N >= 2M and N >= 2 + M) or "
1115 "(o0 = 0 and M >= 2 and N >= 3) or "
1116 "(M = 0 and o0 = 0 and N >= 3) }";
1117 map
= isl_map_read_from_str(ctx
, str
);
1118 map
= isl_map_coalesce(map
);
1119 map2
= isl_map_read_from_str(ctx
, str
);
1120 assert(isl_map_is_equal(map
, map2
));
1124 str
= "{ [i0, i1, i2, i3] : (i1 = 10i0 and i0 >= 1 and 10i0 <= 100 and "
1125 "i3 <= 9 + 10 i2 and i3 >= 1 + 10i2 and i3 >= 0) or "
1126 "(i1 <= 9 + 10i0 and i1 >= 1 + 10i0 and i2 >= 0 and "
1127 "i0 >= 0 and i1 <= 100 and i3 <= 9 + 10i2 and i3 >= 1 + 10i2) }";
1128 map
= isl_map_read_from_str(ctx
, str
);
1129 map
= isl_map_coalesce(map
);
1130 map2
= isl_map_read_from_str(ctx
, str
);
1131 assert(isl_map_is_equal(map
, map2
));
1135 test_coalesce_set(ctx
,
1136 "[M] -> { [i1] : (i1 >= 2 and i1 <= M) or "
1137 "(i1 = M and M >= 1) }", 0);
1138 test_coalesce_set(ctx
,
1139 "{[x,y] : x,y >= 0; [x,y] : 10 <= x <= 20 and y >= -1 }", 0);
1140 test_coalesce_set(ctx
,
1141 "{ [x, y] : (x >= 1 and y >= 1 and x <= 2 and y <= 2) or "
1142 "(y = 3 and x = 1) }", 1);
1143 test_coalesce_set(ctx
,
1144 "[M] -> { [i0, i1, i2, i3, i4] : (i1 >= 3 and i4 >= 2 + i2 and "
1145 "i2 >= 2 and i0 >= 2 and i3 >= 1 + i2 and i0 <= M and "
1146 "i1 <= M and i3 <= M and i4 <= M) or "
1147 "(i1 >= 2 and i4 >= 1 + i2 and i2 >= 2 and i0 >= 2 and "
1148 "i3 >= 1 + i2 and i0 <= M and i1 <= -1 + M and i3 <= M and "
1149 "i4 <= -1 + M) }", 1);
1150 test_coalesce_set(ctx
,
1151 "{ [x, y] : (x >= 0 and y >= 0 and x <= 10 and y <= 10) or "
1152 "(x >= 1 and y >= 1 and x <= 11 and y <= 11) }", 1);
1153 if (test_coalesce_unbounded_wrapping(ctx
) < 0)
1155 if (test_coalesce_set(ctx
, "{[x,0] : x >= 0; [x,1] : x <= 20}", 0) < 0)
1157 if (test_coalesce_set(ctx
, "{ [x, 1 - x] : 0 <= x <= 1; [0,0] }", 1) < 0)
1159 if (test_coalesce_set(ctx
, "{ [0,0]; [i,i] : 1 <= i <= 10 }", 1) < 0)
1161 if (test_coalesce_set(ctx
, "{ [0,0]; [i,j] : 1 <= i,j <= 10 }", 0) < 0)
1163 if (test_coalesce_set(ctx
, "{ [0,0]; [i,2i] : 1 <= i <= 10 }", 1) < 0)
1165 if (test_coalesce_set(ctx
, "{ [0,0]; [i,2i] : 2 <= i <= 10 }", 0) < 0)
1167 if (test_coalesce_set(ctx
, "{ [1,0]; [i,2i] : 1 <= i <= 10 }", 0) < 0)
1169 if (test_coalesce_set(ctx
, "{ [0,1]; [i,2i] : 1 <= i <= 10 }", 0) < 0)
1171 if (test_coalesce_set(ctx
, "{ [a, b] : exists e : 2e = a and "
1172 "a >= 0 and (a <= 3 or (b <= 0 and b >= -4 + a)) }", 0) < 0)
1174 if (test_coalesce_set(ctx
,
1175 "{ [i, j, i', j'] : i <= 2 and j <= 2 and "
1176 "j' >= -1 + 2i + j - 2i' and i' <= -1 + i and "
1177 "j >= 1 and j' <= i + j - i' and i >= 1; "
1178 "[1, 1, 1, 1] }", 0) < 0)
1180 if (test_coalesce_set(ctx
, "{ [i,j] : exists a,b : i = 2a and j = 3b; "
1181 "[i,j] : exists a : j = 3a }", 1) < 0)
1186 void test_closure(struct isl_ctx
*ctx
)
1190 isl_map
*up
, *right
;
1191 isl_map
*map
, *map2
;
1194 /* COCOA example 1 */
1195 map
= isl_map_read_from_str(ctx
,
1196 "[n] -> { [i,j] -> [i2,j2] : i2 = i + 1 and j2 = j + 1 and "
1197 "1 <= i and i < n and 1 <= j and j < n or "
1198 "i2 = i + 1 and j2 = j - 1 and "
1199 "1 <= i and i < n and 2 <= j and j <= n }");
1200 map
= isl_map_power(map
, &exact
);
1204 /* COCOA example 1 */
1205 map
= isl_map_read_from_str(ctx
,
1206 "[n] -> { [i,j] -> [i2,j2] : i2 = i + 1 and j2 = j + 1 and "
1207 "1 <= i and i < n and 1 <= j and j < n or "
1208 "i2 = i + 1 and j2 = j - 1 and "
1209 "1 <= i and i < n and 2 <= j and j <= n }");
1210 map
= isl_map_transitive_closure(map
, &exact
);
1212 map2
= isl_map_read_from_str(ctx
,
1213 "[n] -> { [i,j] -> [i2,j2] : exists (k1,k2,k : "
1214 "1 <= i and i < n and 1 <= j and j <= n and "
1215 "2 <= i2 and i2 <= n and 1 <= j2 and j2 <= n and "
1216 "i2 = i + k1 + k2 and j2 = j + k1 - k2 and "
1217 "k1 >= 0 and k2 >= 0 and k1 + k2 = k and k >= 1 )}");
1218 assert(isl_map_is_equal(map
, map2
));
1222 map
= isl_map_read_from_str(ctx
,
1223 "[n] -> { [x] -> [y] : y = x + 1 and 0 <= x and x <= n and "
1224 " 0 <= y and y <= n }");
1225 map
= isl_map_transitive_closure(map
, &exact
);
1226 map2
= isl_map_read_from_str(ctx
,
1227 "[n] -> { [x] -> [y] : y > x and 0 <= x and x <= n and "
1228 " 0 <= y and y <= n }");
1229 assert(isl_map_is_equal(map
, map2
));
1233 /* COCOA example 2 */
1234 map
= isl_map_read_from_str(ctx
,
1235 "[n] -> { [i,j] -> [i2,j2] : i2 = i + 2 and j2 = j + 2 and "
1236 "1 <= i and i < n - 1 and 1 <= j and j < n - 1 or "
1237 "i2 = i + 2 and j2 = j - 2 and "
1238 "1 <= i and i < n - 1 and 3 <= j and j <= n }");
1239 map
= isl_map_transitive_closure(map
, &exact
);
1241 map2
= isl_map_read_from_str(ctx
,
1242 "[n] -> { [i,j] -> [i2,j2] : exists (k1,k2,k : "
1243 "1 <= i and i < n - 1 and 1 <= j and j <= n and "
1244 "3 <= i2 and i2 <= n and 1 <= j2 and j2 <= n and "
1245 "i2 = i + 2 k1 + 2 k2 and j2 = j + 2 k1 - 2 k2 and "
1246 "k1 >= 0 and k2 >= 0 and k1 + k2 = k and k >= 1) }");
1247 assert(isl_map_is_equal(map
, map2
));
1251 /* COCOA Fig.2 left */
1252 map
= isl_map_read_from_str(ctx
,
1253 "[n] -> { [i,j] -> [i2,j2] : i2 = i + 2 and j2 = j and "
1254 "i <= 2 j - 3 and i <= n - 2 and j <= 2 i - 1 and "
1256 "i2 = i and j2 = j + 2 and i <= 2 j - 1 and i <= n and "
1257 "j <= 2 i - 3 and j <= n - 2 or "
1258 "i2 = i + 1 and j2 = j + 1 and i <= 2 j - 1 and "
1259 "i <= n - 1 and j <= 2 i - 1 and j <= n - 1 }");
1260 map
= isl_map_transitive_closure(map
, &exact
);
1264 /* COCOA Fig.2 right */
1265 map
= isl_map_read_from_str(ctx
,
1266 "[n] -> { [i,j] -> [i2,j2] : i2 = i + 3 and j2 = j and "
1267 "i <= 2 j - 4 and i <= n - 3 and j <= 2 i - 1 and "
1269 "i2 = i and j2 = j + 3 and i <= 2 j - 1 and i <= n and "
1270 "j <= 2 i - 4 and j <= n - 3 or "
1271 "i2 = i + 1 and j2 = j + 1 and i <= 2 j - 1 and "
1272 "i <= n - 1 and j <= 2 i - 1 and j <= n - 1 }");
1273 map
= isl_map_power(map
, &exact
);
1277 /* COCOA Fig.2 right */
1278 map
= isl_map_read_from_str(ctx
,
1279 "[n] -> { [i,j] -> [i2,j2] : i2 = i + 3 and j2 = j and "
1280 "i <= 2 j - 4 and i <= n - 3 and j <= 2 i - 1 and "
1282 "i2 = i and j2 = j + 3 and i <= 2 j - 1 and i <= n and "
1283 "j <= 2 i - 4 and j <= n - 3 or "
1284 "i2 = i + 1 and j2 = j + 1 and i <= 2 j - 1 and "
1285 "i <= n - 1 and j <= 2 i - 1 and j <= n - 1 }");
1286 map
= isl_map_transitive_closure(map
, &exact
);
1288 map2
= isl_map_read_from_str(ctx
,
1289 "[n] -> { [i,j] -> [i2,j2] : exists (k1,k2,k3,k : "
1290 "i <= 2 j - 1 and i <= n and j <= 2 i - 1 and "
1291 "j <= n and 3 + i + 2 j <= 3 n and "
1292 "3 + 2 i + j <= 3n and i2 <= 2 j2 -1 and i2 <= n and "
1293 "i2 <= 3 j2 - 4 and j2 <= 2 i2 -1 and j2 <= n and "
1294 "13 + 4 j2 <= 11 i2 and i2 = i + 3 k1 + k3 and "
1295 "j2 = j + 3 k2 + k3 and k1 >= 0 and k2 >= 0 and "
1296 "k3 >= 0 and k1 + k2 + k3 = k and k > 0) }");
1297 assert(isl_map_is_equal(map
, map2
));
1301 /* COCOA Fig.1 right */
1302 dom
= isl_set_read_from_str(ctx
,
1303 "{ [x,y] : x >= 0 and -2 x + 3 y >= 0 and x <= 3 and "
1304 "2 x - 3 y + 3 >= 0 }");
1305 right
= isl_map_read_from_str(ctx
,
1306 "{ [x,y] -> [x2,y2] : x2 = x + 1 and y2 = y }");
1307 up
= isl_map_read_from_str(ctx
,
1308 "{ [x,y] -> [x2,y2] : x2 = x and y2 = y + 1 }");
1309 right
= isl_map_intersect_domain(right
, isl_set_copy(dom
));
1310 right
= isl_map_intersect_range(right
, isl_set_copy(dom
));
1311 up
= isl_map_intersect_domain(up
, isl_set_copy(dom
));
1312 up
= isl_map_intersect_range(up
, dom
);
1313 map
= isl_map_union(up
, right
);
1314 map
= isl_map_transitive_closure(map
, &exact
);
1316 map2
= isl_map_read_from_str(ctx
,
1317 "{ [0,0] -> [0,1]; [0,0] -> [1,1]; [0,1] -> [1,1]; "
1318 " [2,2] -> [3,2]; [2,2] -> [3,3]; [3,2] -> [3,3] }");
1319 assert(isl_map_is_equal(map
, map2
));
1323 /* COCOA Theorem 1 counter example */
1324 map
= isl_map_read_from_str(ctx
,
1325 "{ [i,j] -> [i2,j2] : i = 0 and 0 <= j and j <= 1 and "
1326 "i2 = 1 and j2 = j or "
1327 "i = 0 and j = 0 and i2 = 0 and j2 = 1 }");
1328 map
= isl_map_transitive_closure(map
, &exact
);
1332 map
= isl_map_read_from_str(ctx
,
1333 "[m,n] -> { [i,j] -> [i2,j2] : i2 = i and j2 = j + 2 and "
1334 "1 <= i,i2 <= n and 1 <= j,j2 <= m or "
1335 "i2 = i + 1 and 3 <= j2 - j <= 4 and "
1336 "1 <= i,i2 <= n and 1 <= j,j2 <= m }");
1337 map
= isl_map_transitive_closure(map
, &exact
);
1341 /* Kelly et al 1996, fig 12 */
1342 map
= isl_map_read_from_str(ctx
,
1343 "[n] -> { [i,j] -> [i2,j2] : i2 = i and j2 = j + 1 and "
1344 "1 <= i,j,j+1 <= n or "
1345 "j = n and j2 = 1 and i2 = i + 1 and "
1346 "1 <= i,i+1 <= n }");
1347 map
= isl_map_transitive_closure(map
, &exact
);
1349 map2
= isl_map_read_from_str(ctx
,
1350 "[n] -> { [i,j] -> [i2,j2] : 1 <= j < j2 <= n and "
1351 "1 <= i <= n and i = i2 or "
1352 "1 <= i < i2 <= n and 1 <= j <= n and "
1354 assert(isl_map_is_equal(map
, map2
));
1358 /* Omega's closure4 */
1359 map
= isl_map_read_from_str(ctx
,
1360 "[m,n] -> { [x,y] -> [x2,y2] : x2 = x and y2 = y + 1 and "
1361 "1 <= x,y <= 10 or "
1362 "x2 = x + 1 and y2 = y and "
1363 "1 <= x <= 20 && 5 <= y <= 15 }");
1364 map
= isl_map_transitive_closure(map
, &exact
);
1368 map
= isl_map_read_from_str(ctx
,
1369 "[n] -> { [x] -> [y]: 1 <= n <= y - x <= 10 }");
1370 map
= isl_map_transitive_closure(map
, &exact
);
1372 map2
= isl_map_read_from_str(ctx
,
1373 "[n] -> { [x] -> [y] : 1 <= n <= 10 and y >= n + x }");
1374 assert(isl_map_is_equal(map
, map2
));
1378 str
= "[n, m] -> { [i0, i1, i2, i3] -> [o0, o1, o2, o3] : "
1379 "i3 = 1 and o0 = i0 and o1 = -1 + i1 and o2 = -1 + i2 and "
1380 "o3 = -2 + i2 and i1 <= -1 + i0 and i1 >= 1 - m + i0 and "
1381 "i1 >= 2 and i1 <= n and i2 >= 3 and i2 <= 1 + n and i2 <= m }";
1382 map
= isl_map_read_from_str(ctx
, str
);
1383 map
= isl_map_transitive_closure(map
, &exact
);
1385 map2
= isl_map_read_from_str(ctx
, str
);
1386 assert(isl_map_is_equal(map
, map2
));
1390 str
= "{[0] -> [1]; [2] -> [3]}";
1391 map
= isl_map_read_from_str(ctx
, str
);
1392 map
= isl_map_transitive_closure(map
, &exact
);
1394 map2
= isl_map_read_from_str(ctx
, str
);
1395 assert(isl_map_is_equal(map
, map2
));
1399 str
= "[n] -> { [[i0, i1, 1, 0, i0] -> [i5, 1]] -> "
1400 "[[i0, -1 + i1, 2, 0, i0] -> [-1 + i5, 2]] : "
1401 "exists (e0 = [(3 - n)/3]: i5 >= 2 and i1 >= 2 and "
1402 "3i0 <= -1 + n and i1 <= -1 + n and i5 <= -1 + n and "
1403 "3e0 >= 1 - n and 3e0 <= 2 - n and 3i0 >= -2 + n); "
1404 "[[i0, i1, 2, 0, i0] -> [i5, 1]] -> "
1405 "[[i0, i1, 1, 0, i0] -> [-1 + i5, 2]] : "
1406 "exists (e0 = [(3 - n)/3]: i5 >= 2 and i1 >= 1 and "
1407 "3i0 <= -1 + n and i1 <= -1 + n and i5 <= -1 + n and "
1408 "3e0 >= 1 - n and 3e0 <= 2 - n and 3i0 >= -2 + n); "
1409 "[[i0, i1, 1, 0, i0] -> [i5, 2]] -> "
1410 "[[i0, -1 + i1, 2, 0, i0] -> [i5, 1]] : "
1411 "exists (e0 = [(3 - n)/3]: i1 >= 2 and i5 >= 1 and "
1412 "3i0 <= -1 + n and i1 <= -1 + n and i5 <= -1 + n and "
1413 "3e0 >= 1 - n and 3e0 <= 2 - n and 3i0 >= -2 + n); "
1414 "[[i0, i1, 2, 0, i0] -> [i5, 2]] -> "
1415 "[[i0, i1, 1, 0, i0] -> [i5, 1]] : "
1416 "exists (e0 = [(3 - n)/3]: i5 >= 1 and i1 >= 1 and "
1417 "3i0 <= -1 + n and i1 <= -1 + n and i5 <= -1 + n and "
1418 "3e0 >= 1 - n and 3e0 <= 2 - n and 3i0 >= -2 + n) }";
1419 map
= isl_map_read_from_str(ctx
, str
);
1420 map
= isl_map_transitive_closure(map
, NULL
);
1425 void test_lex(struct isl_ctx
*ctx
)
1430 dim
= isl_space_set_alloc(ctx
, 0, 0);
1431 map
= isl_map_lex_le(dim
);
1432 assert(!isl_map_is_empty(map
));
1436 void test_lexmin(struct isl_ctx
*ctx
)
1439 isl_basic_map
*bmap
;
1440 isl_map
*map
, *map2
;
1443 isl_pw_multi_aff
*pma
;
1445 str
= "[p0, p1] -> { [] -> [] : "
1446 "exists (e0 = [(2p1)/3], e1, e2, e3 = [(3 - p1 + 3e0)/3], "
1447 "e4 = [(p1)/3], e5 = [(p1 + 3e4)/3]: "
1448 "3e0 >= -2 + 2p1 and 3e0 >= p1 and 3e3 >= 1 - p1 + 3e0 and "
1449 "3e0 <= 2p1 and 3e3 >= -2 + p1 and 3e3 <= -1 + p1 and p1 >= 3 and "
1450 "3e5 >= -2 + 2p1 and 3e5 >= p1 and 3e5 <= -1 + p1 + 3e4 and "
1451 "3e4 <= p1 and 3e4 >= -2 + p1 and e3 <= -1 + e0 and "
1452 "3e4 >= 6 - p1 + 3e1 and 3e1 >= p1 and 3e5 >= -2 + p1 + 3e4 and "
1453 "2e4 >= 3 - p1 + 2e1 and e4 <= e1 and 3e3 <= 2 - p1 + 3e0 and "
1454 "e5 >= 1 + e1 and 3e4 >= 6 - 2p1 + 3e1 and "
1455 "p0 >= 2 and p1 >= p0 and 3e2 >= p1 and 3e4 >= 6 - p1 + 3e2 and "
1456 "e2 <= e1 and e3 >= 1 and e4 <= e2) }";
1457 map
= isl_map_read_from_str(ctx
, str
);
1458 map
= isl_map_lexmin(map
);
1461 str
= "[C] -> { [obj,a,b,c] : obj <= 38 a + 7 b + 10 c and "
1462 "a + b <= 1 and c <= 10 b and c <= C and a,b,c,C >= 0 }";
1463 set
= isl_set_read_from_str(ctx
, str
);
1464 set
= isl_set_lexmax(set
);
1465 str
= "[C] -> { [obj,a,b,c] : C = 8 }";
1466 set2
= isl_set_read_from_str(ctx
, str
);
1467 set
= isl_set_intersect(set
, set2
);
1468 assert(!isl_set_is_empty(set
));
1471 str
= "{ [x] -> [y] : x <= y <= 10; [x] -> [5] : -8 <= x <= 8 }";
1472 map
= isl_map_read_from_str(ctx
, str
);
1473 map
= isl_map_lexmin(map
);
1474 str
= "{ [x] -> [5] : 6 <= x <= 8; "
1475 "[x] -> [x] : x <= 5 or (9 <= x <= 10) }";
1476 map2
= isl_map_read_from_str(ctx
, str
);
1477 assert(isl_map_is_equal(map
, map2
));
1481 str
= "{ [x] -> [y] : 4y = x or 4y = -1 + x or 4y = -2 + x }";
1482 map
= isl_map_read_from_str(ctx
, str
);
1483 map2
= isl_map_copy(map
);
1484 map
= isl_map_lexmin(map
);
1485 assert(isl_map_is_equal(map
, map2
));
1489 str
= "{ [x] -> [y] : x = 4y; [x] -> [y] : x = 2y }";
1490 map
= isl_map_read_from_str(ctx
, str
);
1491 map
= isl_map_lexmin(map
);
1492 str
= "{ [x] -> [y] : (4y = x and x >= 0) or "
1493 "(exists (e0 = [(x)/4], e1 = [(-2 + x)/4]: 2y = x and "
1494 "4e1 = -2 + x and 4e0 <= -1 + x and 4e0 >= -3 + x)) or "
1495 "(exists (e0 = [(x)/4]: 2y = x and 4e0 = x and x <= -4)) }";
1496 map2
= isl_map_read_from_str(ctx
, str
);
1497 assert(isl_map_is_equal(map
, map2
));
1501 str
= "{ [i] -> [i', j] : j = i - 8i' and i' >= 0 and i' <= 7 and "
1502 " 8i' <= i and 8i' >= -7 + i }";
1503 bmap
= isl_basic_map_read_from_str(ctx
, str
);
1504 pma
= isl_basic_map_lexmin_pw_multi_aff(isl_basic_map_copy(bmap
));
1505 map2
= isl_map_from_pw_multi_aff(pma
);
1506 map
= isl_map_from_basic_map(bmap
);
1507 assert(isl_map_is_equal(map
, map2
));
1511 str
= "{ T[a] -> S[b, c] : a = 4b-2c and c >= b }";
1512 map
= isl_map_read_from_str(ctx
, str
);
1513 map
= isl_map_lexmin(map
);
1514 str
= "{ T[a] -> S[b, c] : 2b = a and 2c = a }";
1515 map2
= isl_map_read_from_str(ctx
, str
);
1516 assert(isl_map_is_equal(map
, map2
));
1526 static int collect_must_may(__isl_take isl_map
*dep
, int must
,
1527 void *dep_user
, void *user
)
1529 struct must_may
*mm
= (struct must_may
*)user
;
1532 mm
->must
= isl_map_union(mm
->must
, dep
);
1534 mm
->may
= isl_map_union(mm
->may
, dep
);
1539 static int common_space(void *first
, void *second
)
1541 int depth
= *(int *)first
;
1545 static int map_is_equal(__isl_keep isl_map
*map
, const char *str
)
1553 map2
= isl_map_read_from_str(map
->ctx
, str
);
1554 equal
= isl_map_is_equal(map
, map2
);
1560 static int map_check_equal(__isl_keep isl_map
*map
, const char *str
)
1564 equal
= map_is_equal(map
, str
);
1568 isl_die(isl_map_get_ctx(map
), isl_error_unknown
,
1569 "result not as expected", return -1);
1573 void test_dep(struct isl_ctx
*ctx
)
1578 isl_access_info
*ai
;
1585 str
= "{ [2,i,0] -> [i] : 0 <= i <= 10 }";
1586 map
= isl_map_read_from_str(ctx
, str
);
1587 ai
= isl_access_info_alloc(map
, &depth
, &common_space
, 2);
1589 str
= "{ [0,i,0] -> [i] : 0 <= i <= 10 }";
1590 map
= isl_map_read_from_str(ctx
, str
);
1591 ai
= isl_access_info_add_source(ai
, map
, 1, &depth
);
1593 str
= "{ [1,i,0] -> [5] : 0 <= i <= 10 }";
1594 map
= isl_map_read_from_str(ctx
, str
);
1595 ai
= isl_access_info_add_source(ai
, map
, 1, &depth
);
1597 flow
= isl_access_info_compute_flow(ai
);
1598 dim
= isl_space_alloc(ctx
, 0, 3, 3);
1599 mm
.must
= isl_map_empty(isl_space_copy(dim
));
1600 mm
.may
= isl_map_empty(dim
);
1602 isl_flow_foreach(flow
, collect_must_may
, &mm
);
1604 str
= "{ [0,i,0] -> [2,i,0] : (0 <= i <= 4) or (6 <= i <= 10); "
1605 " [1,10,0] -> [2,5,0] }";
1606 assert(map_is_equal(mm
.must
, str
));
1607 str
= "{ [i,j,k] -> [l,m,n] : 1 = 0 }";
1608 assert(map_is_equal(mm
.may
, str
));
1610 isl_map_free(mm
.must
);
1611 isl_map_free(mm
.may
);
1612 isl_flow_free(flow
);
1615 str
= "{ [2,i,0] -> [i] : 0 <= i <= 10 }";
1616 map
= isl_map_read_from_str(ctx
, str
);
1617 ai
= isl_access_info_alloc(map
, &depth
, &common_space
, 2);
1619 str
= "{ [0,i,0] -> [i] : 0 <= i <= 10 }";
1620 map
= isl_map_read_from_str(ctx
, str
);
1621 ai
= isl_access_info_add_source(ai
, map
, 1, &depth
);
1623 str
= "{ [1,i,0] -> [5] : 0 <= i <= 10 }";
1624 map
= isl_map_read_from_str(ctx
, str
);
1625 ai
= isl_access_info_add_source(ai
, map
, 0, &depth
);
1627 flow
= isl_access_info_compute_flow(ai
);
1628 dim
= isl_space_alloc(ctx
, 0, 3, 3);
1629 mm
.must
= isl_map_empty(isl_space_copy(dim
));
1630 mm
.may
= isl_map_empty(dim
);
1632 isl_flow_foreach(flow
, collect_must_may
, &mm
);
1634 str
= "{ [0,i,0] -> [2,i,0] : (0 <= i <= 4) or (6 <= i <= 10) }";
1635 assert(map_is_equal(mm
.must
, str
));
1636 str
= "{ [0,5,0] -> [2,5,0]; [1,i,0] -> [2,5,0] : 0 <= i <= 10 }";
1637 assert(map_is_equal(mm
.may
, str
));
1639 isl_map_free(mm
.must
);
1640 isl_map_free(mm
.may
);
1641 isl_flow_free(flow
);
1644 str
= "{ [2,i,0] -> [i] : 0 <= i <= 10 }";
1645 map
= isl_map_read_from_str(ctx
, str
);
1646 ai
= isl_access_info_alloc(map
, &depth
, &common_space
, 2);
1648 str
= "{ [0,i,0] -> [i] : 0 <= i <= 10 }";
1649 map
= isl_map_read_from_str(ctx
, str
);
1650 ai
= isl_access_info_add_source(ai
, map
, 0, &depth
);
1652 str
= "{ [1,i,0] -> [5] : 0 <= i <= 10 }";
1653 map
= isl_map_read_from_str(ctx
, str
);
1654 ai
= isl_access_info_add_source(ai
, map
, 0, &depth
);
1656 flow
= isl_access_info_compute_flow(ai
);
1657 dim
= isl_space_alloc(ctx
, 0, 3, 3);
1658 mm
.must
= isl_map_empty(isl_space_copy(dim
));
1659 mm
.may
= isl_map_empty(dim
);
1661 isl_flow_foreach(flow
, collect_must_may
, &mm
);
1663 str
= "{ [0,i,0] -> [2,i,0] : 0 <= i <= 10; "
1664 " [1,i,0] -> [2,5,0] : 0 <= i <= 10 }";
1665 assert(map_is_equal(mm
.may
, str
));
1666 str
= "{ [i,j,k] -> [l,m,n] : 1 = 0 }";
1667 assert(map_is_equal(mm
.must
, str
));
1669 isl_map_free(mm
.must
);
1670 isl_map_free(mm
.may
);
1671 isl_flow_free(flow
);
1674 str
= "{ [0,i,2] -> [i] : 0 <= i <= 10 }";
1675 map
= isl_map_read_from_str(ctx
, str
);
1676 ai
= isl_access_info_alloc(map
, &depth
, &common_space
, 2);
1678 str
= "{ [0,i,0] -> [i] : 0 <= i <= 10 }";
1679 map
= isl_map_read_from_str(ctx
, str
);
1680 ai
= isl_access_info_add_source(ai
, map
, 0, &depth
);
1682 str
= "{ [0,i,1] -> [5] : 0 <= i <= 10 }";
1683 map
= isl_map_read_from_str(ctx
, str
);
1684 ai
= isl_access_info_add_source(ai
, map
, 0, &depth
);
1686 flow
= isl_access_info_compute_flow(ai
);
1687 dim
= isl_space_alloc(ctx
, 0, 3, 3);
1688 mm
.must
= isl_map_empty(isl_space_copy(dim
));
1689 mm
.may
= isl_map_empty(dim
);
1691 isl_flow_foreach(flow
, collect_must_may
, &mm
);
1693 str
= "{ [0,i,0] -> [0,i,2] : 0 <= i <= 10; "
1694 " [0,i,1] -> [0,5,2] : 0 <= i <= 5 }";
1695 assert(map_is_equal(mm
.may
, str
));
1696 str
= "{ [i,j,k] -> [l,m,n] : 1 = 0 }";
1697 assert(map_is_equal(mm
.must
, str
));
1699 isl_map_free(mm
.must
);
1700 isl_map_free(mm
.may
);
1701 isl_flow_free(flow
);
1704 str
= "{ [0,i,1] -> [i] : 0 <= i <= 10 }";
1705 map
= isl_map_read_from_str(ctx
, str
);
1706 ai
= isl_access_info_alloc(map
, &depth
, &common_space
, 2);
1708 str
= "{ [0,i,0] -> [i] : 0 <= i <= 10 }";
1709 map
= isl_map_read_from_str(ctx
, str
);
1710 ai
= isl_access_info_add_source(ai
, map
, 0, &depth
);
1712 str
= "{ [0,i,2] -> [5] : 0 <= i <= 10 }";
1713 map
= isl_map_read_from_str(ctx
, str
);
1714 ai
= isl_access_info_add_source(ai
, map
, 0, &depth
);
1716 flow
= isl_access_info_compute_flow(ai
);
1717 dim
= isl_space_alloc(ctx
, 0, 3, 3);
1718 mm
.must
= isl_map_empty(isl_space_copy(dim
));
1719 mm
.may
= isl_map_empty(dim
);
1721 isl_flow_foreach(flow
, collect_must_may
, &mm
);
1723 str
= "{ [0,i,0] -> [0,i,1] : 0 <= i <= 10; "
1724 " [0,i,2] -> [0,5,1] : 0 <= i <= 4 }";
1725 assert(map_is_equal(mm
.may
, str
));
1726 str
= "{ [i,j,k] -> [l,m,n] : 1 = 0 }";
1727 assert(map_is_equal(mm
.must
, str
));
1729 isl_map_free(mm
.must
);
1730 isl_map_free(mm
.may
);
1731 isl_flow_free(flow
);
1736 str
= "{ [1,i,0,0,0] -> [i,j] : 0 <= i <= 10 and 0 <= j <= 10 }";
1737 map
= isl_map_read_from_str(ctx
, str
);
1738 ai
= isl_access_info_alloc(map
, &depth
, &common_space
, 1);
1740 str
= "{ [0,i,0,j,0] -> [i,j] : 0 <= i <= 10 and 0 <= j <= 10 }";
1741 map
= isl_map_read_from_str(ctx
, str
);
1742 ai
= isl_access_info_add_source(ai
, map
, 1, &depth
);
1744 flow
= isl_access_info_compute_flow(ai
);
1745 dim
= isl_space_alloc(ctx
, 0, 5, 5);
1746 mm
.must
= isl_map_empty(isl_space_copy(dim
));
1747 mm
.may
= isl_map_empty(dim
);
1749 isl_flow_foreach(flow
, collect_must_may
, &mm
);
1751 str
= "{ [0,i,0,j,0] -> [1,i,0,0,0] : 0 <= i,j <= 10 }";
1752 assert(map_is_equal(mm
.must
, str
));
1753 str
= "{ [0,0,0,0,0] -> [0,0,0,0,0] : 1 = 0 }";
1754 assert(map_is_equal(mm
.may
, str
));
1756 isl_map_free(mm
.must
);
1757 isl_map_free(mm
.may
);
1758 isl_flow_free(flow
);
1761 int test_sv(isl_ctx
*ctx
)
1765 isl_union_map
*umap
;
1768 str
= "[N] -> { [i] -> [f] : 0 <= i <= N and 0 <= i - 10 f <= 9 }";
1769 map
= isl_map_read_from_str(ctx
, str
);
1770 sv
= isl_map_is_single_valued(map
);
1775 isl_die(ctx
, isl_error_internal
,
1776 "map not detected as single valued", return -1);
1778 str
= "[N] -> { [i] -> [f] : 0 <= i <= N and 0 <= i - 10 f <= 10 }";
1779 map
= isl_map_read_from_str(ctx
, str
);
1780 sv
= isl_map_is_single_valued(map
);
1785 isl_die(ctx
, isl_error_internal
,
1786 "map detected as single valued", return -1);
1788 str
= "{ S1[i] -> [i] : 0 <= i <= 9; S2[i] -> [i] : 0 <= i <= 9 }";
1789 umap
= isl_union_map_read_from_str(ctx
, str
);
1790 sv
= isl_union_map_is_single_valued(umap
);
1791 isl_union_map_free(umap
);
1795 isl_die(ctx
, isl_error_internal
,
1796 "map not detected as single valued", return -1);
1798 str
= "{ [i] -> S1[i] : 0 <= i <= 9; [i] -> S2[i] : 0 <= i <= 9 }";
1799 umap
= isl_union_map_read_from_str(ctx
, str
);
1800 sv
= isl_union_map_is_single_valued(umap
);
1801 isl_union_map_free(umap
);
1805 isl_die(ctx
, isl_error_internal
,
1806 "map detected as single valued", return -1);
1811 void test_bijective_case(struct isl_ctx
*ctx
, const char *str
, int bijective
)
1815 map
= isl_map_read_from_str(ctx
, str
);
1817 assert(isl_map_is_bijective(map
));
1819 assert(!isl_map_is_bijective(map
));
1823 void test_bijective(struct isl_ctx
*ctx
)
1825 test_bijective_case(ctx
, "[N,M]->{[i,j] -> [i]}", 0);
1826 test_bijective_case(ctx
, "[N,M]->{[i,j] -> [i] : j=i}", 1);
1827 test_bijective_case(ctx
, "[N,M]->{[i,j] -> [i] : j=0}", 1);
1828 test_bijective_case(ctx
, "[N,M]->{[i,j] -> [i] : j=N}", 1);
1829 test_bijective_case(ctx
, "[N,M]->{[i,j] -> [j,i]}", 1);
1830 test_bijective_case(ctx
, "[N,M]->{[i,j] -> [i+j]}", 0);
1831 test_bijective_case(ctx
, "[N,M]->{[i,j] -> []}", 0);
1832 test_bijective_case(ctx
, "[N,M]->{[i,j] -> [i,j,N]}", 1);
1833 test_bijective_case(ctx
, "[N,M]->{[i,j] -> [2i]}", 0);
1834 test_bijective_case(ctx
, "[N,M]->{[i,j] -> [i,i]}", 0);
1835 test_bijective_case(ctx
, "[N,M]->{[i,j] -> [2i,i]}", 0);
1836 test_bijective_case(ctx
, "[N,M]->{[i,j] -> [2i,j]}", 1);
1837 test_bijective_case(ctx
, "[N,M]->{[i,j] -> [x,y] : 2x=i & y =j}", 1);
1840 void test_pwqp(struct isl_ctx
*ctx
)
1844 isl_pw_qpolynomial
*pwqp1
, *pwqp2
;
1846 str
= "{ [i,j,k] -> 1 + 9 * [i/5] + 7 * [j/11] + 4 * [k/13] }";
1847 pwqp1
= isl_pw_qpolynomial_read_from_str(ctx
, str
);
1849 pwqp1
= isl_pw_qpolynomial_move_dims(pwqp1
, isl_dim_param
, 0,
1852 str
= "[j] -> { [i,k] -> 1 + 9 * [i/5] + 7 * [j/11] + 4 * [k/13] }";
1853 pwqp2
= isl_pw_qpolynomial_read_from_str(ctx
, str
);
1855 pwqp1
= isl_pw_qpolynomial_sub(pwqp1
, pwqp2
);
1857 assert(isl_pw_qpolynomial_is_zero(pwqp1
));
1859 isl_pw_qpolynomial_free(pwqp1
);
1861 str
= "{ [i] -> i }";
1862 pwqp1
= isl_pw_qpolynomial_read_from_str(ctx
, str
);
1863 str
= "{ [k] : exists a : k = 2a }";
1864 set
= isl_set_read_from_str(ctx
, str
);
1865 pwqp1
= isl_pw_qpolynomial_gist(pwqp1
, set
);
1866 str
= "{ [i] -> i }";
1867 pwqp2
= isl_pw_qpolynomial_read_from_str(ctx
, str
);
1869 pwqp1
= isl_pw_qpolynomial_sub(pwqp1
, pwqp2
);
1871 assert(isl_pw_qpolynomial_is_zero(pwqp1
));
1873 isl_pw_qpolynomial_free(pwqp1
);
1875 str
= "{ [i] -> i + [ (i + [i/3])/2 ] }";
1876 pwqp1
= isl_pw_qpolynomial_read_from_str(ctx
, str
);
1878 set
= isl_set_read_from_str(ctx
, str
);
1879 pwqp1
= isl_pw_qpolynomial_gist(pwqp1
, set
);
1880 str
= "{ [i] -> 16 }";
1881 pwqp2
= isl_pw_qpolynomial_read_from_str(ctx
, str
);
1883 pwqp1
= isl_pw_qpolynomial_sub(pwqp1
, pwqp2
);
1885 assert(isl_pw_qpolynomial_is_zero(pwqp1
));
1887 isl_pw_qpolynomial_free(pwqp1
);
1889 str
= "{ [i] -> ([(i)/2]) }";
1890 pwqp1
= isl_pw_qpolynomial_read_from_str(ctx
, str
);
1891 str
= "{ [k] : exists a : k = 2a+1 }";
1892 set
= isl_set_read_from_str(ctx
, str
);
1893 pwqp1
= isl_pw_qpolynomial_gist(pwqp1
, set
);
1894 str
= "{ [i] -> -1/2 + 1/2 * i }";
1895 pwqp2
= isl_pw_qpolynomial_read_from_str(ctx
, str
);
1897 pwqp1
= isl_pw_qpolynomial_sub(pwqp1
, pwqp2
);
1899 assert(isl_pw_qpolynomial_is_zero(pwqp1
));
1901 isl_pw_qpolynomial_free(pwqp1
);
1903 str
= "{ [i] -> ([([i/2] + [i/2])/5]) }";
1904 pwqp1
= isl_pw_qpolynomial_read_from_str(ctx
, str
);
1905 str
= "{ [i] -> ([(2 * [i/2])/5]) }";
1906 pwqp2
= isl_pw_qpolynomial_read_from_str(ctx
, str
);
1908 pwqp1
= isl_pw_qpolynomial_sub(pwqp1
, pwqp2
);
1910 assert(isl_pw_qpolynomial_is_zero(pwqp1
));
1912 isl_pw_qpolynomial_free(pwqp1
);
1914 str
= "{ [x] -> ([x/2] + [(x+1)/2]) }";
1915 pwqp1
= isl_pw_qpolynomial_read_from_str(ctx
, str
);
1916 str
= "{ [x] -> x }";
1917 pwqp2
= isl_pw_qpolynomial_read_from_str(ctx
, str
);
1919 pwqp1
= isl_pw_qpolynomial_sub(pwqp1
, pwqp2
);
1921 assert(isl_pw_qpolynomial_is_zero(pwqp1
));
1923 isl_pw_qpolynomial_free(pwqp1
);
1925 str
= "{ [i] -> ([i/2]) : i >= 0; [i] -> ([i/3]) : i < 0 }";
1926 pwqp1
= isl_pw_qpolynomial_read_from_str(ctx
, str
);
1927 pwqp2
= isl_pw_qpolynomial_read_from_str(ctx
, str
);
1928 pwqp1
= isl_pw_qpolynomial_coalesce(pwqp1
);
1929 pwqp1
= isl_pw_qpolynomial_sub(pwqp1
, pwqp2
);
1930 assert(isl_pw_qpolynomial_is_zero(pwqp1
));
1931 isl_pw_qpolynomial_free(pwqp1
);
1934 void test_split_periods(isl_ctx
*ctx
)
1937 isl_pw_qpolynomial
*pwqp
;
1939 str
= "{ [U,V] -> 1/3 * U + 2/3 * V - [(U + 2V)/3] + [U/2] : "
1940 "U + 2V + 3 >= 0 and - U -2V >= 0 and - U + 10 >= 0 and "
1941 "U >= 0; [U,V] -> U^2 : U >= 100 }";
1942 pwqp
= isl_pw_qpolynomial_read_from_str(ctx
, str
);
1944 pwqp
= isl_pw_qpolynomial_split_periods(pwqp
, 2);
1947 isl_pw_qpolynomial_free(pwqp
);
1950 void test_union(isl_ctx
*ctx
)
1953 isl_union_set
*uset1
, *uset2
;
1954 isl_union_map
*umap1
, *umap2
;
1956 str
= "{ [i] : 0 <= i <= 1 }";
1957 uset1
= isl_union_set_read_from_str(ctx
, str
);
1958 str
= "{ [1] -> [0] }";
1959 umap1
= isl_union_map_read_from_str(ctx
, str
);
1961 umap2
= isl_union_set_lex_gt_union_set(isl_union_set_copy(uset1
), uset1
);
1962 assert(isl_union_map_is_equal(umap1
, umap2
));
1964 isl_union_map_free(umap1
);
1965 isl_union_map_free(umap2
);
1967 str
= "{ A[i] -> B[i]; B[i] -> C[i]; A[0] -> C[1] }";
1968 umap1
= isl_union_map_read_from_str(ctx
, str
);
1969 str
= "{ A[i]; B[i] }";
1970 uset1
= isl_union_set_read_from_str(ctx
, str
);
1972 uset2
= isl_union_map_domain(umap1
);
1974 assert(isl_union_set_is_equal(uset1
, uset2
));
1976 isl_union_set_free(uset1
);
1977 isl_union_set_free(uset2
);
1980 void test_bound(isl_ctx
*ctx
)
1983 isl_pw_qpolynomial
*pwqp
;
1984 isl_pw_qpolynomial_fold
*pwf
;
1986 str
= "{ [[a, b, c, d] -> [e]] -> 0 }";
1987 pwqp
= isl_pw_qpolynomial_read_from_str(ctx
, str
);
1988 pwf
= isl_pw_qpolynomial_bound(pwqp
, isl_fold_max
, NULL
);
1989 assert(isl_pw_qpolynomial_fold_dim(pwf
, isl_dim_in
) == 4);
1990 isl_pw_qpolynomial_fold_free(pwf
);
1992 str
= "{ [[x]->[x]] -> 1 : exists a : x = 2 a }";
1993 pwqp
= isl_pw_qpolynomial_read_from_str(ctx
, str
);
1994 pwf
= isl_pw_qpolynomial_bound(pwqp
, isl_fold_max
, NULL
);
1995 assert(isl_pw_qpolynomial_fold_dim(pwf
, isl_dim_in
) == 1);
1996 isl_pw_qpolynomial_fold_free(pwf
);
1999 void test_lift(isl_ctx
*ctx
)
2002 isl_basic_map
*bmap
;
2003 isl_basic_set
*bset
;
2005 str
= "{ [i0] : exists e0 : i0 = 4e0 }";
2006 bset
= isl_basic_set_read_from_str(ctx
, str
);
2007 bset
= isl_basic_set_lift(bset
);
2008 bmap
= isl_basic_map_from_range(bset
);
2009 bset
= isl_basic_map_domain(bmap
);
2010 isl_basic_set_free(bset
);
2017 } subset_tests
[] = {
2019 "{ [i0, i1] : exists (e0 = [(i0 - i1)/16], e1: "
2020 "16e0 <= i0 - i1 and 16e0 >= -15 + i0 - i1 and "
2021 "16e1 <= i1 and 16e0 >= -i1 and 16e1 >= -i0 + i1) }", 1 },
2023 "{ [i] : exists (e0 = [(255i)/256], e1 = [(127i + 65e0)/191], "
2024 "e2 = [(3i + 61e1)/65], e3 = [(52i + 12e2)/61], "
2025 "e4 = [(2i + e3)/3], e5 = [(4i + e3)/4], e6 = [(8i + e3)/12]: "
2026 "3e4 = 2i + e3 and 4e5 = 4i + e3 and 12e6 = 8i + e3 and "
2027 "i <= 255 and 64e3 >= -45 + 67i and i >= 0 and "
2028 "256e0 <= 255i and 256e0 >= -255 + 255i and "
2029 "191e1 <= 127i + 65e0 and 191e1 >= -190 + 127i + 65e0 and "
2030 "65e2 <= 3i + 61e1 and 65e2 >= -64 + 3i + 61e1 and "
2031 "61e3 <= 52i + 12e2 and 61e3 >= -60 + 52i + 12e2) }", 1 },
2034 static int test_subset(isl_ctx
*ctx
)
2037 isl_set
*set1
, *set2
;
2040 for (i
= 0; i
< ARRAY_SIZE(subset_tests
); ++i
) {
2041 set1
= isl_set_read_from_str(ctx
, subset_tests
[i
].set1
);
2042 set2
= isl_set_read_from_str(ctx
, subset_tests
[i
].set2
);
2043 subset
= isl_set_is_subset(set1
, set2
);
2048 if (subset
!= subset_tests
[i
].subset
)
2049 isl_die(ctx
, isl_error_unknown
,
2050 "incorrect subset result", return -1);
2057 const char *minuend
;
2058 const char *subtrahend
;
2059 const char *difference
;
2060 } subtract_domain_tests
[] = {
2061 { "{ A[i] -> B[i] }", "{ A[i] }", "{ }" },
2062 { "{ A[i] -> B[i] }", "{ B[i] }", "{ A[i] -> B[i] }" },
2063 { "{ A[i] -> B[i] }", "{ A[i] : i > 0 }", "{ A[i] -> B[i] : i <= 0 }" },
2066 static int test_subtract(isl_ctx
*ctx
)
2069 isl_union_map
*umap1
, *umap2
;
2070 isl_union_set
*uset
;
2073 for (i
= 0; i
< ARRAY_SIZE(subtract_domain_tests
); ++i
) {
2074 umap1
= isl_union_map_read_from_str(ctx
,
2075 subtract_domain_tests
[i
].minuend
);
2076 uset
= isl_union_set_read_from_str(ctx
,
2077 subtract_domain_tests
[i
].subtrahend
);
2078 umap2
= isl_union_map_read_from_str(ctx
,
2079 subtract_domain_tests
[i
].difference
);
2080 umap1
= isl_union_map_subtract_domain(umap1
, uset
);
2081 equal
= isl_union_map_is_equal(umap1
, umap2
);
2082 isl_union_map_free(umap1
);
2083 isl_union_map_free(umap2
);
2087 isl_die(ctx
, isl_error_unknown
,
2088 "incorrect subtract domain result", return -1);
2094 int test_factorize(isl_ctx
*ctx
)
2097 isl_basic_set
*bset
;
2100 str
= "{ [i0, i1, i2, i3, i4, i5, i6, i7] : 3i5 <= 2 - 2i0 and "
2101 "i0 >= -2 and i6 >= 1 + i3 and i7 >= 0 and 3i5 >= -2i0 and "
2102 "2i4 <= i2 and i6 >= 1 + 2i0 + 3i1 and i4 <= -1 and "
2103 "i6 >= 1 + 2i0 + 3i5 and i6 <= 2 + 2i0 + 3i5 and "
2104 "3i5 <= 2 - 2i0 - i2 + 3i4 and i6 <= 2 + 2i0 + 3i1 and "
2105 "i0 <= -1 and i7 <= i2 + i3 - 3i4 - i6 and "
2106 "3i5 >= -2i0 - i2 + 3i4 }";
2107 bset
= isl_basic_set_read_from_str(ctx
, str
);
2108 f
= isl_basic_set_factorizer(bset
);
2109 isl_basic_set_free(bset
);
2110 isl_factorizer_free(f
);
2112 isl_die(ctx
, isl_error_unknown
,
2113 "failed to construct factorizer", return -1);
2115 str
= "{ [i0, i1, i2, i3, i4, i5, i6, i7, i8, i9, i10, i11, i12] : "
2116 "i12 <= 2 + i0 - i11 and 2i8 >= -i4 and i11 >= i1 and "
2117 "3i5 <= -i2 and 2i11 >= -i4 - 2i7 and i11 <= 3 + i0 + 3i9 and "
2118 "i11 <= -i4 - 2i7 and i12 >= -i10 and i2 >= -2 and "
2119 "i11 >= i1 + 3i10 and i11 >= 1 + i0 + 3i9 and "
2120 "i11 <= 1 - i4 - 2i8 and 6i6 <= 6 - i2 and 3i6 >= 1 - i2 and "
2121 "i11 <= 2 + i1 and i12 <= i4 + i11 and i12 >= i0 - i11 and "
2122 "3i5 >= -2 - i2 and i12 >= -1 + i4 + i11 and 3i3 <= 3 - i2 and "
2123 "9i6 <= 11 - i2 + 6i5 and 3i3 >= 1 - i2 and "
2124 "9i6 <= 5 - i2 + 6i3 and i12 <= -1 and i2 <= 0 }";
2125 bset
= isl_basic_set_read_from_str(ctx
, str
);
2126 f
= isl_basic_set_factorizer(bset
);
2127 isl_basic_set_free(bset
);
2128 isl_factorizer_free(f
);
2130 isl_die(ctx
, isl_error_unknown
,
2131 "failed to construct factorizer", return -1);
2136 static int check_injective(__isl_take isl_map
*map
, void *user
)
2138 int *injective
= user
;
2140 *injective
= isl_map_is_injective(map
);
2143 if (*injective
< 0 || !*injective
)
2149 int test_one_schedule(isl_ctx
*ctx
, const char *d
, const char *w
,
2150 const char *r
, const char *s
, int tilable
, int parallel
)
2154 isl_union_map
*W
, *R
, *S
;
2155 isl_union_map
*empty
;
2156 isl_union_map
*dep_raw
, *dep_war
, *dep_waw
, *dep
;
2157 isl_union_map
*validity
, *proximity
;
2158 isl_union_map
*schedule
;
2159 isl_union_map
*test
;
2160 isl_union_set
*delta
;
2161 isl_union_set
*domain
;
2165 isl_schedule
*sched
;
2166 int is_nonneg
, is_parallel
, is_tilable
, is_injection
, is_complete
;
2168 D
= isl_union_set_read_from_str(ctx
, d
);
2169 W
= isl_union_map_read_from_str(ctx
, w
);
2170 R
= isl_union_map_read_from_str(ctx
, r
);
2171 S
= isl_union_map_read_from_str(ctx
, s
);
2173 W
= isl_union_map_intersect_domain(W
, isl_union_set_copy(D
));
2174 R
= isl_union_map_intersect_domain(R
, isl_union_set_copy(D
));
2176 empty
= isl_union_map_empty(isl_union_map_get_space(S
));
2177 isl_union_map_compute_flow(isl_union_map_copy(R
),
2178 isl_union_map_copy(W
), empty
,
2179 isl_union_map_copy(S
),
2180 &dep_raw
, NULL
, NULL
, NULL
);
2181 isl_union_map_compute_flow(isl_union_map_copy(W
),
2182 isl_union_map_copy(W
),
2183 isl_union_map_copy(R
),
2184 isl_union_map_copy(S
),
2185 &dep_waw
, &dep_war
, NULL
, NULL
);
2187 dep
= isl_union_map_union(dep_waw
, dep_war
);
2188 dep
= isl_union_map_union(dep
, dep_raw
);
2189 validity
= isl_union_map_copy(dep
);
2190 proximity
= isl_union_map_copy(dep
);
2192 sched
= isl_union_set_compute_schedule(isl_union_set_copy(D
),
2193 validity
, proximity
);
2194 schedule
= isl_schedule_get_map(sched
);
2195 isl_schedule_free(sched
);
2196 isl_union_map_free(W
);
2197 isl_union_map_free(R
);
2198 isl_union_map_free(S
);
2201 isl_union_map_foreach_map(schedule
, &check_injective
, &is_injection
);
2203 domain
= isl_union_map_domain(isl_union_map_copy(schedule
));
2204 is_complete
= isl_union_set_is_subset(D
, domain
);
2205 isl_union_set_free(D
);
2206 isl_union_set_free(domain
);
2208 test
= isl_union_map_reverse(isl_union_map_copy(schedule
));
2209 test
= isl_union_map_apply_range(test
, dep
);
2210 test
= isl_union_map_apply_range(test
, schedule
);
2212 delta
= isl_union_map_deltas(test
);
2213 if (isl_union_set_n_set(delta
) == 0) {
2217 isl_union_set_free(delta
);
2219 delta_set
= isl_set_from_union_set(delta
);
2221 slice
= isl_set_universe(isl_set_get_space(delta_set
));
2222 for (i
= 0; i
< tilable
; ++i
)
2223 slice
= isl_set_lower_bound_si(slice
, isl_dim_set
, i
, 0);
2224 is_tilable
= isl_set_is_subset(delta_set
, slice
);
2225 isl_set_free(slice
);
2227 slice
= isl_set_universe(isl_set_get_space(delta_set
));
2228 for (i
= 0; i
< parallel
; ++i
)
2229 slice
= isl_set_fix_si(slice
, isl_dim_set
, i
, 0);
2230 is_parallel
= isl_set_is_subset(delta_set
, slice
);
2231 isl_set_free(slice
);
2233 origin
= isl_set_universe(isl_set_get_space(delta_set
));
2234 for (i
= 0; i
< isl_set_dim(origin
, isl_dim_set
); ++i
)
2235 origin
= isl_set_fix_si(origin
, isl_dim_set
, i
, 0);
2237 delta_set
= isl_set_union(delta_set
, isl_set_copy(origin
));
2238 delta_set
= isl_set_lexmin(delta_set
);
2240 is_nonneg
= isl_set_is_equal(delta_set
, origin
);
2242 isl_set_free(origin
);
2243 isl_set_free(delta_set
);
2246 if (is_nonneg
< 0 || is_parallel
< 0 || is_tilable
< 0 ||
2247 is_injection
< 0 || is_complete
< 0)
2250 isl_die(ctx
, isl_error_unknown
,
2251 "generated schedule incomplete", return -1);
2253 isl_die(ctx
, isl_error_unknown
,
2254 "generated schedule not injective on each statement",
2257 isl_die(ctx
, isl_error_unknown
,
2258 "negative dependences in generated schedule",
2261 isl_die(ctx
, isl_error_unknown
,
2262 "generated schedule not as tilable as expected",
2265 isl_die(ctx
, isl_error_unknown
,
2266 "generated schedule not as parallel as expected",
2272 int test_special_schedule(isl_ctx
*ctx
, const char *domain
,
2273 const char *validity
, const char *proximity
, const char *expected_sched
)
2277 isl_union_map
*prox
;
2278 isl_union_map
*sched1
, *sched2
;
2279 isl_schedule
*schedule
;
2282 dom
= isl_union_set_read_from_str(ctx
, domain
);
2283 dep
= isl_union_map_read_from_str(ctx
, validity
);
2284 prox
= isl_union_map_read_from_str(ctx
, proximity
);
2285 schedule
= isl_union_set_compute_schedule(dom
, dep
, prox
);
2286 sched1
= isl_schedule_get_map(schedule
);
2287 isl_schedule_free(schedule
);
2289 sched2
= isl_union_map_read_from_str(ctx
, expected_sched
);
2291 equal
= isl_union_map_is_equal(sched1
, sched2
);
2292 isl_union_map_free(sched1
);
2293 isl_union_map_free(sched2
);
2298 isl_die(ctx
, isl_error_unknown
, "unexpected schedule",
2304 int test_schedule(isl_ctx
*ctx
)
2306 const char *D
, *W
, *R
, *V
, *P
, *S
;
2309 D
= "[T,N] -> { S1[t,i] : 1 <= t <= T and 2 <= i <= N - 1 }";
2310 W
= "{ S1[t,i] -> a[t,i] }";
2311 R
= "{ S1[t,i] -> a[t-1,i]; S1[t,i] -> a[t-1,i-1]; "
2312 "S1[t,i] -> a[t-1,i+1] }";
2313 S
= "{ S1[t,i] -> [t,i] }";
2314 if (test_one_schedule(ctx
, D
, W
, R
, S
, 2, 0) < 0)
2317 /* Fig. 5 of CC2008 */
2318 D
= "[N] -> { S_0[i, j] : i >= 0 and i <= -1 + N and j >= 2 and "
2320 W
= "[N] -> { S_0[i, j] -> a[i, j] : i >= 0 and i <= -1 + N and "
2321 "j >= 2 and j <= -1 + N }";
2322 R
= "[N] -> { S_0[i, j] -> a[j, i] : i >= 0 and i <= -1 + N and "
2323 "j >= 2 and j <= -1 + N; "
2324 "S_0[i, j] -> a[i, -1 + j] : i >= 0 and i <= -1 + N and "
2325 "j >= 2 and j <= -1 + N }";
2326 S
= "[N] -> { S_0[i, j] -> [0, i, 0, j, 0] }";
2327 if (test_one_schedule(ctx
, D
, W
, R
, S
, 2, 0) < 0)
2330 D
= "{ S1[i] : 0 <= i <= 10; S2[i] : 0 <= i <= 9 }";
2331 W
= "{ S1[i] -> a[i] }";
2332 R
= "{ S2[i] -> a[i+1] }";
2333 S
= "{ S1[i] -> [0,i]; S2[i] -> [1,i] }";
2334 if (test_one_schedule(ctx
, D
, W
, R
, S
, 1, 1) < 0)
2337 D
= "{ S1[i] : 0 <= i < 10; S2[i] : 0 <= i < 10 }";
2338 W
= "{ S1[i] -> a[i] }";
2339 R
= "{ S2[i] -> a[9-i] }";
2340 S
= "{ S1[i] -> [0,i]; S2[i] -> [1,i] }";
2341 if (test_one_schedule(ctx
, D
, W
, R
, S
, 1, 1) < 0)
2344 D
= "[N] -> { S1[i] : 0 <= i < N; S2[i] : 0 <= i < N }";
2345 W
= "{ S1[i] -> a[i] }";
2346 R
= "[N] -> { S2[i] -> a[N-1-i] }";
2347 S
= "{ S1[i] -> [0,i]; S2[i] -> [1,i] }";
2348 if (test_one_schedule(ctx
, D
, W
, R
, S
, 1, 1) < 0)
2351 D
= "{ S1[i] : 0 < i < 10; S2[i] : 0 <= i < 10 }";
2352 W
= "{ S1[i] -> a[i]; S2[i] -> b[i] }";
2353 R
= "{ S2[i] -> a[i]; S1[i] -> b[i-1] }";
2354 S
= "{ S1[i] -> [i,0]; S2[i] -> [i,1] }";
2355 if (test_one_schedule(ctx
, D
, W
, R
, S
, 0, 0) < 0)
2358 D
= "[N] -> { S1[i] : 1 <= i <= N; S2[i,j] : 1 <= i,j <= N }";
2359 W
= "{ S1[i] -> a[0,i]; S2[i,j] -> a[i,j] }";
2360 R
= "{ S2[i,j] -> a[i-1,j] }";
2361 S
= "{ S1[i] -> [0,i,0]; S2[i,j] -> [1,i,j] }";
2362 if (test_one_schedule(ctx
, D
, W
, R
, S
, 2, 1) < 0)
2365 D
= "[N] -> { S1[i] : 1 <= i <= N; S2[i,j] : 1 <= i,j <= N }";
2366 W
= "{ S1[i] -> a[i,0]; S2[i,j] -> a[i,j] }";
2367 R
= "{ S2[i,j] -> a[i,j-1] }";
2368 S
= "{ S1[i] -> [0,i,0]; S2[i,j] -> [1,i,j] }";
2369 if (test_one_schedule(ctx
, D
, W
, R
, S
, 2, 1) < 0)
2372 D
= "[N] -> { S_0[]; S_1[i] : i >= 0 and i <= -1 + N; S_2[] }";
2373 W
= "[N] -> { S_0[] -> a[0]; S_2[] -> b[0]; "
2374 "S_1[i] -> a[1 + i] : i >= 0 and i <= -1 + N }";
2375 R
= "[N] -> { S_2[] -> a[N]; S_1[i] -> a[i] : i >= 0 and i <= -1 + N }";
2376 S
= "[N] -> { S_1[i] -> [1, i, 0]; S_2[] -> [2, 0, 1]; "
2377 "S_0[] -> [0, 0, 0] }";
2378 if (test_one_schedule(ctx
, D
, W
, R
, S
, 1, 0) < 0)
2380 ctx
->opt
->schedule_parametric
= 0;
2381 if (test_one_schedule(ctx
, D
, W
, R
, S
, 0, 0) < 0)
2383 ctx
->opt
->schedule_parametric
= 1;
2385 D
= "[N] -> { S1[i] : 1 <= i <= N; S2[i] : 1 <= i <= N; "
2386 "S3[i,j] : 1 <= i,j <= N; S4[i] : 1 <= i <= N }";
2387 W
= "{ S1[i] -> a[i,0]; S2[i] -> a[0,i]; S3[i,j] -> a[i,j] }";
2388 R
= "[N] -> { S3[i,j] -> a[i-1,j]; S3[i,j] -> a[i,j-1]; "
2389 "S4[i] -> a[i,N] }";
2390 S
= "{ S1[i] -> [0,i,0]; S2[i] -> [1,i,0]; S3[i,j] -> [2,i,j]; "
2391 "S4[i] -> [4,i,0] }";
2392 if (test_one_schedule(ctx
, D
, W
, R
, S
, 2, 0) < 0)
2395 D
= "[N] -> { S_0[i, j] : i >= 1 and i <= N and j >= 1 and j <= N }";
2396 W
= "[N] -> { S_0[i, j] -> s[0] : i >= 1 and i <= N and j >= 1 and "
2398 R
= "[N] -> { S_0[i, j] -> s[0] : i >= 1 and i <= N and j >= 1 and "
2400 "S_0[i, j] -> a[i, j] : i >= 1 and i <= N and j >= 1 and "
2402 S
= "[N] -> { S_0[i, j] -> [0, i, 0, j, 0] }";
2403 if (test_one_schedule(ctx
, D
, W
, R
, S
, 0, 0) < 0)
2406 D
= "[N] -> { S_0[t] : t >= 0 and t <= -1 + N; "
2407 " S_2[t] : t >= 0 and t <= -1 + N; "
2408 " S_1[t, i] : t >= 0 and t <= -1 + N and i >= 0 and "
2410 W
= "[N] -> { S_0[t] -> a[t, 0] : t >= 0 and t <= -1 + N; "
2411 " S_2[t] -> b[t] : t >= 0 and t <= -1 + N; "
2412 " S_1[t, i] -> a[t, 1 + i] : t >= 0 and t <= -1 + N and "
2413 "i >= 0 and i <= -1 + N }";
2414 R
= "[N] -> { S_1[t, i] -> a[t, i] : t >= 0 and t <= -1 + N and "
2415 "i >= 0 and i <= -1 + N; "
2416 " S_2[t] -> a[t, N] : t >= 0 and t <= -1 + N }";
2417 S
= "[N] -> { S_2[t] -> [0, t, 2]; S_1[t, i] -> [0, t, 1, i, 0]; "
2418 " S_0[t] -> [0, t, 0] }";
2420 if (test_one_schedule(ctx
, D
, W
, R
, S
, 2, 1) < 0)
2422 ctx
->opt
->schedule_parametric
= 0;
2423 if (test_one_schedule(ctx
, D
, W
, R
, S
, 0, 0) < 0)
2425 ctx
->opt
->schedule_parametric
= 1;
2427 D
= "[N] -> { S1[i,j] : 0 <= i,j < N; S2[i,j] : 0 <= i,j < N }";
2428 S
= "{ S1[i,j] -> [0,i,j]; S2[i,j] -> [1,i,j] }";
2429 if (test_one_schedule(ctx
, D
, "{}", "{}", S
, 2, 2) < 0)
2432 D
= "[M, N] -> { S_1[i] : i >= 0 and i <= -1 + M; "
2433 "S_0[i, j] : i >= 0 and i <= -1 + M and j >= 0 and j <= -1 + N }";
2434 W
= "[M, N] -> { S_0[i, j] -> a[j] : i >= 0 and i <= -1 + M and "
2435 "j >= 0 and j <= -1 + N; "
2436 "S_1[i] -> b[0] : i >= 0 and i <= -1 + M }";
2437 R
= "[M, N] -> { S_0[i, j] -> a[0] : i >= 0 and i <= -1 + M and "
2438 "j >= 0 and j <= -1 + N; "
2439 "S_1[i] -> b[0] : i >= 0 and i <= -1 + M }";
2440 S
= "[M, N] -> { S_1[i] -> [1, i, 0]; S_0[i, j] -> [0, i, 0, j, 0] }";
2441 if (test_one_schedule(ctx
, D
, W
, R
, S
, 0, 0) < 0)
2444 D
= "{ S_0[i] : i >= 0 }";
2445 W
= "{ S_0[i] -> a[i] : i >= 0 }";
2446 R
= "{ S_0[i] -> a[0] : i >= 0 }";
2447 S
= "{ S_0[i] -> [0, i, 0] }";
2448 if (test_one_schedule(ctx
, D
, W
, R
, S
, 0, 0) < 0)
2451 D
= "{ S_0[i] : i >= 0; S_1[i] : i >= 0 }";
2452 W
= "{ S_0[i] -> a[i] : i >= 0; S_1[i] -> b[i] : i >= 0 }";
2453 R
= "{ S_0[i] -> b[0] : i >= 0; S_1[i] -> a[i] : i >= 0 }";
2454 S
= "{ S_1[i] -> [0, i, 1]; S_0[i] -> [0, i, 0] }";
2455 if (test_one_schedule(ctx
, D
, W
, R
, S
, 0, 0) < 0)
2458 D
= "[n] -> { S_0[j, k] : j <= -1 + n and j >= 0 and "
2459 "k <= -1 + n and k >= 0 }";
2460 W
= "[n] -> { S_0[j, k] -> B[j] : j <= -1 + n and j >= 0 and " "k <= -1 + n and k >= 0 }";
2461 R
= "[n] -> { S_0[j, k] -> B[j] : j <= -1 + n and j >= 0 and "
2462 "k <= -1 + n and k >= 0; "
2463 "S_0[j, k] -> B[k] : j <= -1 + n and j >= 0 and "
2464 "k <= -1 + n and k >= 0; "
2465 "S_0[j, k] -> A[k] : j <= -1 + n and j >= 0 and "
2466 "k <= -1 + n and k >= 0 }";
2467 S
= "[n] -> { S_0[j, k] -> [2, j, k] }";
2468 ctx
->opt
->schedule_outer_zero_distance
= 1;
2469 if (test_one_schedule(ctx
, D
, W
, R
, S
, 0, 0) < 0)
2471 ctx
->opt
->schedule_outer_zero_distance
= 0;
2473 D
= "{Stmt_for_body24[i0, i1, i2, i3]:"
2474 "i0 >= 0 and i0 <= 1 and i1 >= 0 and i1 <= 6 and i2 >= 2 and "
2475 "i2 <= 6 - i1 and i3 >= 0 and i3 <= -1 + i2;"
2476 "Stmt_for_body24[i0, i1, 1, 0]:"
2477 "i0 >= 0 and i0 <= 1 and i1 >= 0 and i1 <= 5;"
2478 "Stmt_for_body7[i0, i1, i2]:"
2479 "i0 >= 0 and i0 <= 1 and i1 >= 0 and i1 <= 7 and i2 >= 0 and "
2482 V
= "{Stmt_for_body24[0, i1, i2, i3] -> "
2483 "Stmt_for_body24[1, i1, i2, i3]:"
2484 "i3 >= 0 and i3 <= -1 + i2 and i1 >= 0 and i2 <= 6 - i1 and "
2486 "Stmt_for_body24[0, i1, i2, i3] -> "
2487 "Stmt_for_body7[1, 1 + i1 + i3, 1 + i1 + i2]:"
2488 "i3 <= -1 + i2 and i2 <= 6 - i1 and i2 >= 1 and i1 >= 0 and "
2490 "Stmt_for_body24[0, i1, i2, i3] ->"
2491 "Stmt_for_body7[1, i1, 1 + i1 + i3]:"
2492 "i3 >= 0 and i2 <= 6 - i1 and i1 >= 0 and i3 <= -1 + i2;"
2493 "Stmt_for_body7[0, i1, i2] -> Stmt_for_body7[1, i1, i2]:"
2494 "(i2 >= 1 + i1 and i2 <= 6 and i1 >= 0 and i1 <= 4) or "
2495 "(i2 >= 3 and i2 <= 7 and i1 >= 1 and i2 >= 1 + i1) or "
2496 "(i2 >= 0 and i2 <= i1 and i2 >= -7 + i1 and i1 <= 7);"
2497 "Stmt_for_body7[0, i1, 1 + i1] -> Stmt_for_body7[1, i1, 1 + i1]:"
2498 "i1 <= 6 and i1 >= 0;"
2499 "Stmt_for_body7[0, 0, 7] -> Stmt_for_body7[1, 0, 7];"
2500 "Stmt_for_body7[i0, i1, i2] -> "
2501 "Stmt_for_body24[i0, o1, -1 + i2 - o1, -1 + i1 - o1]:"
2502 "i0 >= 0 and i0 <= 1 and o1 >= 0 and i2 >= 1 + i1 and "
2503 "o1 <= -2 + i2 and i2 <= 7 and o1 <= -1 + i1;"
2504 "Stmt_for_body7[i0, i1, i2] -> "
2505 "Stmt_for_body24[i0, i1, o2, -1 - i1 + i2]:"
2506 "i0 >= 0 and i0 <= 1 and i1 >= 0 and o2 >= -i1 + i2 and "
2507 "o2 >= 1 and o2 <= 6 - i1 and i2 >= 1 + i1 }";
2509 S
= "{ Stmt_for_body24[i0, i1, i2, i3] -> "
2510 "[i0, 5i0 + i1, 6i0 + i1 + i2, 1 + 6i0 + i1 + i2 + i3, 1];"
2511 "Stmt_for_body7[i0, i1, i2] -> [0, 5i0, 6i0 + i1, 6i0 + i2, 0] }";
2513 if (test_special_schedule(ctx
, D
, V
, P
, S
) < 0)
2516 D
= "{ S_0[i, j] : i >= 1 and i <= 10 and j >= 1 and j <= 8 }";
2517 V
= "{ S_0[i, j] -> S_0[i, 1 + j] : i >= 1 and i <= 10 and "
2518 "j >= 1 and j <= 7;"
2519 "S_0[i, j] -> S_0[1 + i, j] : i >= 1 and i <= 9 and "
2520 "j >= 1 and j <= 8 }";
2522 S
= "{ S_0[i, j] -> [i + j, j] }";
2523 ctx
->opt
->schedule_algorithm
= ISL_SCHEDULE_ALGORITHM_FEAUTRIER
;
2524 if (test_special_schedule(ctx
, D
, V
, P
, S
) < 0)
2526 ctx
->opt
->schedule_algorithm
= ISL_SCHEDULE_ALGORITHM_ISL
;
2528 /* Fig. 1 from Feautrier's "Some Efficient Solutions..." pt. 2, 1992 */
2529 D
= "[N] -> { S_0[i, j] : i >= 0 and i <= -1 + N and "
2530 "j >= 0 and j <= -1 + i }";
2531 V
= "[N] -> { S_0[i, j] -> S_0[i, 1 + j] : j <= -2 + i and "
2532 "i <= -1 + N and j >= 0;"
2533 "S_0[i, -1 + i] -> S_0[1 + i, 0] : i >= 1 and "
2536 S
= "{ S_0[i, j] -> [i, j] }";
2537 ctx
->opt
->schedule_algorithm
= ISL_SCHEDULE_ALGORITHM_FEAUTRIER
;
2538 if (test_special_schedule(ctx
, D
, V
, P
, S
) < 0)
2540 ctx
->opt
->schedule_algorithm
= ISL_SCHEDULE_ALGORITHM_ISL
;
2542 /* Test both algorithms on a case with only proximity dependences. */
2543 D
= "{ S[i,j] : 0 <= i <= 10 }";
2545 P
= "{ S[i,j] -> S[i+1,j] : 0 <= i,j <= 10 }";
2546 S
= "{ S[i, j] -> [j, i] }";
2547 ctx
->opt
->schedule_algorithm
= ISL_SCHEDULE_ALGORITHM_FEAUTRIER
;
2548 if (test_special_schedule(ctx
, D
, V
, P
, S
) < 0)
2550 ctx
->opt
->schedule_algorithm
= ISL_SCHEDULE_ALGORITHM_ISL
;
2551 return test_special_schedule(ctx
, D
, V
, P
, S
);
2554 int test_plain_injective(isl_ctx
*ctx
, const char *str
, int injective
)
2556 isl_union_map
*umap
;
2559 umap
= isl_union_map_read_from_str(ctx
, str
);
2560 test
= isl_union_map_plain_is_injective(umap
);
2561 isl_union_map_free(umap
);
2564 if (test
== injective
)
2567 isl_die(ctx
, isl_error_unknown
,
2568 "map not detected as injective", return -1);
2570 isl_die(ctx
, isl_error_unknown
,
2571 "map detected as injective", return -1);
2574 int test_injective(isl_ctx
*ctx
)
2578 if (test_plain_injective(ctx
, "{S[i,j] -> A[0]; T[i,j] -> B[1]}", 0))
2580 if (test_plain_injective(ctx
, "{S[] -> A[0]; T[] -> B[0]}", 1))
2582 if (test_plain_injective(ctx
, "{S[] -> A[0]; T[] -> A[1]}", 1))
2584 if (test_plain_injective(ctx
, "{S[] -> A[0]; T[] -> A[0]}", 0))
2586 if (test_plain_injective(ctx
, "{S[i] -> A[i,0]; T[i] -> A[i,1]}", 1))
2588 if (test_plain_injective(ctx
, "{S[i] -> A[i]; T[i] -> A[i]}", 0))
2590 if (test_plain_injective(ctx
, "{S[] -> A[0,0]; T[] -> A[0,1]}", 1))
2592 if (test_plain_injective(ctx
, "{S[] -> A[0,0]; T[] -> A[1,0]}", 1))
2595 str
= "{S[] -> A[0,0]; T[] -> A[0,1]; U[] -> A[1,0]}";
2596 if (test_plain_injective(ctx
, str
, 1))
2598 str
= "{S[] -> A[0,0]; T[] -> A[0,1]; U[] -> A[0,0]}";
2599 if (test_plain_injective(ctx
, str
, 0))
2605 static int aff_plain_is_equal(__isl_keep isl_aff
*aff
, const char *str
)
2613 aff2
= isl_aff_read_from_str(isl_aff_get_ctx(aff
), str
);
2614 equal
= isl_aff_plain_is_equal(aff
, aff2
);
2620 static int aff_check_plain_equal(__isl_keep isl_aff
*aff
, const char *str
)
2624 equal
= aff_plain_is_equal(aff
, str
);
2628 isl_die(isl_aff_get_ctx(aff
), isl_error_unknown
,
2629 "result not as expected", return -1);
2633 int test_aff(isl_ctx
*ctx
)
2638 isl_local_space
*ls
;
2642 space
= isl_space_set_alloc(ctx
, 0, 1);
2643 ls
= isl_local_space_from_space(space
);
2644 aff
= isl_aff_zero_on_domain(ls
);
2646 aff
= isl_aff_add_coefficient_si(aff
, isl_dim_in
, 0, 1);
2647 aff
= isl_aff_scale_down_ui(aff
, 3);
2648 aff
= isl_aff_floor(aff
);
2649 aff
= isl_aff_add_coefficient_si(aff
, isl_dim_in
, 0, 1);
2650 aff
= isl_aff_scale_down_ui(aff
, 2);
2651 aff
= isl_aff_floor(aff
);
2652 aff
= isl_aff_add_coefficient_si(aff
, isl_dim_in
, 0, 1);
2655 set
= isl_set_read_from_str(ctx
, str
);
2656 aff
= isl_aff_gist(aff
, set
);
2658 aff
= isl_aff_add_constant_si(aff
, -16);
2659 zero
= isl_aff_plain_is_zero(aff
);
2665 isl_die(ctx
, isl_error_unknown
, "unexpected result", return -1);
2667 aff
= isl_aff_read_from_str(ctx
, "{ [-1] }");
2668 aff
= isl_aff_scale_down_ui(aff
, 64);
2669 aff
= isl_aff_floor(aff
);
2670 equal
= aff_check_plain_equal(aff
, "{ [-1] }");
2678 int test_dim_max(isl_ctx
*ctx
)
2682 isl_set
*set1
, *set2
;
2687 str
= "[N] -> { [i] : 0 <= i <= min(N,10) }";
2688 set
= isl_set_read_from_str(ctx
, str
);
2689 pwaff
= isl_set_dim_max(set
, 0);
2690 set1
= isl_set_from_pw_aff(pwaff
);
2691 str
= "[N] -> { [10] : N >= 10; [N] : N <= 9 and N >= 0 }";
2692 set2
= isl_set_read_from_str(ctx
, str
);
2693 equal
= isl_set_is_equal(set1
, set2
);
2699 isl_die(ctx
, isl_error_unknown
, "unexpected result", return -1);
2701 str
= "[N] -> { [i] : 0 <= i <= max(2N,N+6) }";
2702 set
= isl_set_read_from_str(ctx
, str
);
2703 pwaff
= isl_set_dim_max(set
, 0);
2704 set1
= isl_set_from_pw_aff(pwaff
);
2705 str
= "[N] -> { [6 + N] : -6 <= N <= 5; [2N] : N >= 6 }";
2706 set2
= isl_set_read_from_str(ctx
, str
);
2707 equal
= isl_set_is_equal(set1
, set2
);
2713 isl_die(ctx
, isl_error_unknown
, "unexpected result", return -1);
2715 str
= "[N] -> { [i] : 0 <= i <= 2N or 0 <= i <= N+6 }";
2716 set
= isl_set_read_from_str(ctx
, str
);
2717 pwaff
= isl_set_dim_max(set
, 0);
2718 set1
= isl_set_from_pw_aff(pwaff
);
2719 str
= "[N] -> { [6 + N] : -6 <= N <= 5; [2N] : N >= 6 }";
2720 set2
= isl_set_read_from_str(ctx
, str
);
2721 equal
= isl_set_is_equal(set1
, set2
);
2727 isl_die(ctx
, isl_error_unknown
, "unexpected result", return -1);
2729 str
= "[N,M] -> { [i,j] -> [([i/16]), i%16, ([j/16]), j%16] : "
2730 "0 <= i < N and 0 <= j < M }";
2731 map
= isl_map_read_from_str(ctx
, str
);
2732 set
= isl_map_range(map
);
2734 pwaff
= isl_set_dim_max(isl_set_copy(set
), 0);
2735 set1
= isl_set_from_pw_aff(pwaff
);
2736 str
= "[N,M] -> { [([(N-1)/16])] : M,N > 0 }";
2737 set2
= isl_set_read_from_str(ctx
, str
);
2738 equal
= isl_set_is_equal(set1
, set2
);
2742 pwaff
= isl_set_dim_max(isl_set_copy(set
), 3);
2743 set1
= isl_set_from_pw_aff(pwaff
);
2744 str
= "[N,M] -> { [t] : t = min(M-1,15) and M,N > 0 }";
2745 set2
= isl_set_read_from_str(ctx
, str
);
2746 if (equal
>= 0 && equal
)
2747 equal
= isl_set_is_equal(set1
, set2
);
2756 isl_die(ctx
, isl_error_unknown
, "unexpected result", return -1);
2761 int test_product(isl_ctx
*ctx
)
2765 isl_union_set
*uset1
, *uset2
;
2769 set
= isl_set_read_from_str(ctx
, str
);
2770 set
= isl_set_product(set
, isl_set_copy(set
));
2771 ok
= isl_set_is_wrapping(set
);
2776 isl_die(ctx
, isl_error_unknown
, "unexpected result", return -1);
2779 uset1
= isl_union_set_read_from_str(ctx
, str
);
2780 uset1
= isl_union_set_product(uset1
, isl_union_set_copy(uset1
));
2781 str
= "{ [[] -> []] }";
2782 uset2
= isl_union_set_read_from_str(ctx
, str
);
2783 ok
= isl_union_set_is_equal(uset1
, uset2
);
2784 isl_union_set_free(uset1
);
2785 isl_union_set_free(uset2
);
2789 isl_die(ctx
, isl_error_unknown
, "unexpected result", return -1);
2794 int test_equal(isl_ctx
*ctx
)
2797 isl_set
*set
, *set2
;
2801 set
= isl_set_read_from_str(ctx
, str
);
2803 set2
= isl_set_read_from_str(ctx
, str
);
2804 equal
= isl_set_is_equal(set
, set2
);
2810 isl_die(ctx
, isl_error_unknown
, "unexpected result", return -1);
2815 static int test_plain_fixed(isl_ctx
*ctx
, __isl_take isl_map
*map
,
2816 enum isl_dim_type type
, unsigned pos
, int fixed
)
2820 test
= isl_map_plain_is_fixed(map
, type
, pos
, NULL
);
2827 isl_die(ctx
, isl_error_unknown
,
2828 "map not detected as fixed", return -1);
2830 isl_die(ctx
, isl_error_unknown
,
2831 "map detected as fixed", return -1);
2834 int test_fixed(isl_ctx
*ctx
)
2839 str
= "{ [i] -> [i] }";
2840 map
= isl_map_read_from_str(ctx
, str
);
2841 if (test_plain_fixed(ctx
, map
, isl_dim_out
, 0, 0))
2843 str
= "{ [i] -> [1] }";
2844 map
= isl_map_read_from_str(ctx
, str
);
2845 if (test_plain_fixed(ctx
, map
, isl_dim_out
, 0, 1))
2847 str
= "{ S_1[p1] -> [o0] : o0 = -2 and p1 >= 1 and p1 <= 7 }";
2848 map
= isl_map_read_from_str(ctx
, str
);
2849 if (test_plain_fixed(ctx
, map
, isl_dim_out
, 0, 1))
2851 map
= isl_map_read_from_str(ctx
, str
);
2852 map
= isl_map_neg(map
);
2853 if (test_plain_fixed(ctx
, map
, isl_dim_out
, 0, 1))
2859 int test_vertices(isl_ctx
*ctx
)
2862 isl_basic_set
*bset
;
2863 isl_vertices
*vertices
;
2865 str
= "{ A[t, i] : t = 12 and i >= 4 and i <= 12 }";
2866 bset
= isl_basic_set_read_from_str(ctx
, str
);
2867 vertices
= isl_basic_set_compute_vertices(bset
);
2868 isl_basic_set_free(bset
);
2869 isl_vertices_free(vertices
);
2873 str
= "{ A[t, i] : t = 14 and i = 1 }";
2874 bset
= isl_basic_set_read_from_str(ctx
, str
);
2875 vertices
= isl_basic_set_compute_vertices(bset
);
2876 isl_basic_set_free(bset
);
2877 isl_vertices_free(vertices
);
2884 int test_union_pw(isl_ctx
*ctx
)
2888 isl_union_set
*uset
;
2889 isl_union_pw_qpolynomial
*upwqp1
, *upwqp2
;
2891 str
= "{ [x] -> x^2 }";
2892 upwqp1
= isl_union_pw_qpolynomial_read_from_str(ctx
, str
);
2893 upwqp2
= isl_union_pw_qpolynomial_copy(upwqp1
);
2894 uset
= isl_union_pw_qpolynomial_domain(upwqp1
);
2895 upwqp1
= isl_union_pw_qpolynomial_copy(upwqp2
);
2896 upwqp1
= isl_union_pw_qpolynomial_intersect_domain(upwqp1
, uset
);
2897 equal
= isl_union_pw_qpolynomial_plain_is_equal(upwqp1
, upwqp2
);
2898 isl_union_pw_qpolynomial_free(upwqp1
);
2899 isl_union_pw_qpolynomial_free(upwqp2
);
2903 isl_die(ctx
, isl_error_unknown
, "unexpected result", return -1);
2908 int test_output(isl_ctx
*ctx
)
2916 str
= "[x] -> { [1] : x % 4 <= 2; [2] : x = 3 }";
2917 pa
= isl_pw_aff_read_from_str(ctx
, str
);
2919 p
= isl_printer_to_str(ctx
);
2920 p
= isl_printer_set_output_format(p
, ISL_FORMAT_C
);
2921 p
= isl_printer_print_pw_aff(p
, pa
);
2922 s
= isl_printer_get_str(p
);
2923 isl_printer_free(p
);
2924 isl_pw_aff_free(pa
);
2925 equal
= !strcmp(s
, "(2 - x + 4*floord(x, 4) >= 0) ? (1) : 2");
2930 isl_die(ctx
, isl_error_unknown
, "unexpected result", return -1);
2935 int test_sample(isl_ctx
*ctx
)
2938 isl_basic_set
*bset1
, *bset2
;
2941 str
= "{ [a, b, c, d, e, f, g, h, i, j, k] : "
2942 "3i >= 1073741823b - c - 1073741823e + f and c >= 0 and "
2943 "3i >= -1 + 3221225466b + c + d - 3221225466e - f and "
2944 "2e >= a - b and 3e <= 2a and 3k <= -a and f <= -1 + a and "
2945 "3i <= 4 - a + 4b + 2c - e - 2f and 3k <= -a + c - f and "
2946 "3h >= -2 + a and 3g >= -3 - a and 3k >= -2 - a and "
2947 "3i >= -2 - a - 2c + 3e + 2f and 3h <= a + c - f and "
2948 "3h >= a + 2147483646b + 2c - 2147483646e - 2f and "
2949 "3g <= -1 - a and 3i <= 1 + c + d - f and a <= 1073741823 and "
2950 "f >= 1 - a + 1073741822b + c + d - 1073741822e and "
2951 "3i >= 1 + 2b - 2c + e + 2f + 3g and "
2952 "1073741822f <= 1073741822 - a + 1073741821b + 1073741822c +"
2953 "d - 1073741821e and "
2954 "3j <= 3 - a + 3b and 3g <= -2 - 2b + c + d - e - f and "
2955 "3j >= 1 - a + b + 2e and "
2956 "3f >= -3 + a + 3221225462b + 3c + d - 3221225465e and "
2957 "3i <= 4 - a + 4b - e and "
2958 "f <= 1073741822 + 1073741822b - 1073741822e and 3h <= a and "
2959 "f >= 0 and 2e <= 4 - a + 5b - d and 2e <= a - b + d and "
2960 "c <= -1 + a and 3i >= -2 - a + 3e and "
2961 "1073741822e <= 1073741823 - a + 1073741822b + c and "
2962 "3g >= -4 + 3221225464b + 3c + d - 3221225467e - 3f and "
2963 "3i >= -1 + 3221225466b + 3c + d - 3221225466e - 3f and "
2964 "1073741823e >= 1 + 1073741823b - d and "
2965 "3i >= 1073741823b + c - 1073741823e - f and "
2966 "3i >= 1 + 2b + e + 3g }";
2967 bset1
= isl_basic_set_read_from_str(ctx
, str
);
2968 bset2
= isl_basic_set_sample(isl_basic_set_copy(bset1
));
2969 empty
= isl_basic_set_is_empty(bset2
);
2970 subset
= isl_basic_set_is_subset(bset2
, bset1
);
2971 isl_basic_set_free(bset1
);
2972 isl_basic_set_free(bset2
);
2974 isl_die(ctx
, isl_error_unknown
, "point not found", return -1);
2976 isl_die(ctx
, isl_error_unknown
, "bad point found", return -1);
2981 int test_fixed_power(isl_ctx
*ctx
)
2989 str
= "{ [i] -> [i + 1] }";
2990 map
= isl_map_read_from_str(ctx
, str
);
2991 isl_int_set_si(exp
, 23);
2992 map
= isl_map_fixed_power(map
, exp
);
2993 equal
= map_check_equal(map
, "{ [i] -> [i + 23] }");
3002 int test_slice(isl_ctx
*ctx
)
3008 str
= "{ [i] -> [j] }";
3009 map
= isl_map_read_from_str(ctx
, str
);
3010 map
= isl_map_equate(map
, isl_dim_in
, 0, isl_dim_out
, 0);
3011 equal
= map_check_equal(map
, "{ [i] -> [i] }");
3016 str
= "{ [i] -> [j] }";
3017 map
= isl_map_read_from_str(ctx
, str
);
3018 map
= isl_map_equate(map
, isl_dim_in
, 0, isl_dim_in
, 0);
3019 equal
= map_check_equal(map
, "{ [i] -> [j] }");
3024 str
= "{ [i] -> [j] }";
3025 map
= isl_map_read_from_str(ctx
, str
);
3026 map
= isl_map_oppose(map
, isl_dim_in
, 0, isl_dim_out
, 0);
3027 equal
= map_check_equal(map
, "{ [i] -> [-i] }");
3032 str
= "{ [i] -> [j] }";
3033 map
= isl_map_read_from_str(ctx
, str
);
3034 map
= isl_map_oppose(map
, isl_dim_in
, 0, isl_dim_in
, 0);
3035 equal
= map_check_equal(map
, "{ [0] -> [j] }");
3040 str
= "{ [i] -> [j] }";
3041 map
= isl_map_read_from_str(ctx
, str
);
3042 map
= isl_map_order_gt(map
, isl_dim_in
, 0, isl_dim_out
, 0);
3043 equal
= map_check_equal(map
, "{ [i] -> [j] : i > j }");
3048 str
= "{ [i] -> [j] }";
3049 map
= isl_map_read_from_str(ctx
, str
);
3050 map
= isl_map_order_gt(map
, isl_dim_in
, 0, isl_dim_in
, 0);
3051 equal
= map_check_equal(map
, "{ [i] -> [j] : false }");
3059 int test_eliminate(isl_ctx
*ctx
)
3065 str
= "{ [i] -> [j] : i = 2j }";
3066 map
= isl_map_read_from_str(ctx
, str
);
3067 map
= isl_map_eliminate(map
, isl_dim_out
, 0, 1);
3068 equal
= map_check_equal(map
, "{ [i] -> [j] : exists a : i = 2a }");
3076 /* Check that isl_set_dim_residue_class detects that the values of j
3077 * in the set below are all odd and that it does not detect any spurious
3080 static int test_residue_class(isl_ctx
*ctx
)
3087 str
= "{ [i,j] : j = 4 i + 1 and 0 <= i <= 100; "
3088 "[i,j] : j = 4 i + 3 and 500 <= i <= 600 }";
3089 set
= isl_set_read_from_str(ctx
, str
);
3092 res
= isl_set_dim_residue_class(set
, 1, &m
, &r
);
3094 (isl_int_cmp_si(m
, 2) != 0 || isl_int_cmp_si(r
, 1) != 0))
3095 isl_die(ctx
, isl_error_unknown
, "incorrect residue class",
3104 int test_align_parameters(isl_ctx
*ctx
)
3108 isl_multi_aff
*ma1
, *ma2
;
3111 str
= "{ A[B[] -> C[]] -> D[E[] -> F[]] }";
3112 ma1
= isl_multi_aff_read_from_str(ctx
, str
);
3114 space
= isl_space_params_alloc(ctx
, 1);
3115 space
= isl_space_set_dim_name(space
, isl_dim_param
, 0, "N");
3116 ma1
= isl_multi_aff_align_params(ma1
, space
);
3118 str
= "[N] -> { A[B[] -> C[]] -> D[E[] -> F[]] }";
3119 ma2
= isl_multi_aff_read_from_str(ctx
, str
);
3121 equal
= isl_multi_aff_plain_is_equal(ma1
, ma2
);
3123 isl_multi_aff_free(ma1
);
3124 isl_multi_aff_free(ma2
);
3129 isl_die(ctx
, isl_error_unknown
,
3130 "result not as expected", return -1);
3135 static int test_list(isl_ctx
*ctx
)
3137 isl_id
*a
, *b
, *c
, *d
, *id
;
3141 a
= isl_id_alloc(ctx
, "a", NULL
);
3142 b
= isl_id_alloc(ctx
, "b", NULL
);
3143 c
= isl_id_alloc(ctx
, "c", NULL
);
3144 d
= isl_id_alloc(ctx
, "d", NULL
);
3146 list
= isl_id_list_alloc(ctx
, 4);
3147 list
= isl_id_list_add(list
, a
);
3148 list
= isl_id_list_add(list
, b
);
3149 list
= isl_id_list_add(list
, c
);
3150 list
= isl_id_list_add(list
, d
);
3151 list
= isl_id_list_drop(list
, 1, 1);
3153 if (isl_id_list_n_id(list
) != 3) {
3154 isl_id_list_free(list
);
3155 isl_die(ctx
, isl_error_unknown
,
3156 "unexpected number of elements in list", return -1);
3159 id
= isl_id_list_get_id(list
, 0);
3162 id
= isl_id_list_get_id(list
, 1);
3165 id
= isl_id_list_get_id(list
, 2);
3169 isl_id_list_free(list
);
3172 isl_die(ctx
, isl_error_unknown
,
3173 "unexpected elements in list", return -1);
3180 int (*fn
)(isl_ctx
*ctx
);
3182 { "list", &test_list
},
3183 { "align parameters", &test_align_parameters
},
3184 { "eliminate", &test_eliminate
},
3185 { "reisdue class", &test_residue_class
},
3186 { "div", &test_div
},
3187 { "slice", &test_slice
},
3188 { "fixed power", &test_fixed_power
},
3189 { "sample", &test_sample
},
3190 { "output", &test_output
},
3191 { "vertices", &test_vertices
},
3192 { "fixed", &test_fixed
},
3193 { "equal", &test_equal
},
3194 { "product", &test_product
},
3195 { "dim_max", &test_dim_max
},
3196 { "affine", &test_aff
},
3197 { "injective", &test_injective
},
3198 { "schedule", &test_schedule
},
3199 { "union_pw", &test_union_pw
},
3200 { "parse", &test_parse
},
3201 { "single-valued", &test_sv
},
3202 { "affine hull", &test_affine_hull
},
3203 { "coalesce", &test_coalesce
},
3204 { "factorize", &test_factorize
},
3205 { "subset", &test_subset
},
3206 { "subtract", &test_subtract
},
3212 struct isl_ctx
*ctx
;
3214 srcdir
= getenv("srcdir");
3217 ctx
= isl_ctx_alloc();
3218 for (i
= 0; i
< ARRAY_SIZE(tests
); ++i
) {
3219 printf("%s\n", tests
[i
].name
);
3220 if (tests
[i
].fn(ctx
) < 0)
3226 test_split_periods(ctx
);
3229 test_bijective(ctx
);
3233 test_construction(ctx
);
3235 test_application(ctx
);
3236 test_convex_hull(ctx
);