2 * Copyright 2008-2009 Katholieke Universiteit Leuven
4 * Use of this software is governed by the GNU LGPLv2.1 license
6 * Written by Sven Verdoolaege, K.U.Leuven, Departement
7 * Computerwetenschappen, Celestijnenlaan 200A, B-3001 Leuven, Belgium
13 #include <isl_ctx_private.h>
14 #include <isl_map_private.h>
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)
202 void test_read(struct isl_ctx
*ctx
)
206 struct isl_basic_set
*bset1
, *bset2
;
207 const char *str
= "{[y]: Exists ( alpha : 2alpha = y)}";
209 filename
= get_filename(ctx
, "set", "omega");
211 input
= fopen(filename
, "r");
214 bset1
= isl_basic_set_read_from_file(ctx
, input
);
215 bset2
= isl_basic_set_read_from_str(ctx
, str
);
217 assert(isl_basic_set_is_equal(bset1
, bset2
) == 1);
219 isl_basic_set_free(bset1
);
220 isl_basic_set_free(bset2
);
226 void test_bounded(struct isl_ctx
*ctx
)
231 set
= isl_set_read_from_str(ctx
, "[n] -> {[i] : 0 <= i <= n }");
232 bounded
= isl_set_is_bounded(set
);
236 set
= isl_set_read_from_str(ctx
, "{[n, i] : 0 <= i <= n }");
237 bounded
= isl_set_is_bounded(set
);
241 set
= isl_set_read_from_str(ctx
, "[n] -> {[i] : i <= n }");
242 bounded
= isl_set_is_bounded(set
);
247 /* Construct the basic set { [i] : 5 <= i <= N } */
248 void test_construction(struct isl_ctx
*ctx
)
253 struct isl_basic_set
*bset
;
254 struct isl_constraint
*c
;
258 dim
= isl_space_set_alloc(ctx
, 1, 1);
259 bset
= isl_basic_set_universe(isl_space_copy(dim
));
260 ls
= isl_local_space_from_space(dim
);
262 c
= isl_inequality_alloc(isl_local_space_copy(ls
));
263 isl_int_set_si(v
, -1);
264 isl_constraint_set_coefficient(c
, isl_dim_set
, 0, v
);
265 isl_int_set_si(v
, 1);
266 isl_constraint_set_coefficient(c
, isl_dim_param
, 0, v
);
267 bset
= isl_basic_set_add_constraint(bset
, c
);
269 c
= isl_inequality_alloc(isl_local_space_copy(ls
));
270 isl_int_set_si(v
, 1);
271 isl_constraint_set_coefficient(c
, isl_dim_set
, 0, v
);
272 isl_int_set_si(v
, -5);
273 isl_constraint_set_constant(c
, v
);
274 bset
= isl_basic_set_add_constraint(bset
, c
);
276 isl_local_space_free(ls
);
277 isl_basic_set_free(bset
);
282 void test_dim(struct isl_ctx
*ctx
)
285 isl_map
*map1
, *map2
;
287 map1
= isl_map_read_from_str(ctx
,
288 "[n] -> { [i] -> [j] : exists (a = [i/10] : i - 10a <= n ) }");
289 map1
= isl_map_add_dims(map1
, isl_dim_in
, 1);
290 map2
= isl_map_read_from_str(ctx
,
291 "[n] -> { [i,k] -> [j] : exists (a = [i/10] : i - 10a <= n ) }");
292 assert(isl_map_is_equal(map1
, map2
));
295 map1
= isl_map_project_out(map1
, isl_dim_in
, 0, 1);
296 map2
= isl_map_read_from_str(ctx
, "[n] -> { [i] -> [j] : n >= 0 }");
297 assert(isl_map_is_equal(map1
, map2
));
302 str
= "[n] -> { [i] -> [] : exists a : 0 <= i <= n and i = 2 a }";
303 map1
= isl_map_read_from_str(ctx
, str
);
304 str
= "{ [i] -> [j] : exists a : 0 <= i <= j and i = 2 a }";
305 map2
= isl_map_read_from_str(ctx
, str
);
306 map1
= isl_map_move_dims(map1
, isl_dim_out
, 0, isl_dim_param
, 0, 1);
307 assert(isl_map_is_equal(map1
, map2
));
313 static int test_div(isl_ctx
*ctx
)
322 struct isl_basic_set
*bset
;
323 struct isl_constraint
*c
;
328 dim
= isl_space_set_alloc(ctx
, 0, 3);
329 bset
= isl_basic_set_universe(isl_space_copy(dim
));
330 ls
= isl_local_space_from_space(dim
);
332 c
= isl_equality_alloc(isl_local_space_copy(ls
));
333 isl_int_set_si(v
, -1);
334 isl_constraint_set_constant(c
, v
);
335 isl_int_set_si(v
, 1);
336 isl_constraint_set_coefficient(c
, isl_dim_set
, 0, v
);
337 isl_int_set_si(v
, 3);
338 isl_constraint_set_coefficient(c
, isl_dim_set
, 1, v
);
339 bset
= isl_basic_set_add_constraint(bset
, c
);
341 c
= isl_equality_alloc(isl_local_space_copy(ls
));
342 isl_int_set_si(v
, 1);
343 isl_constraint_set_constant(c
, v
);
344 isl_int_set_si(v
, -1);
345 isl_constraint_set_coefficient(c
, isl_dim_set
, 0, v
);
346 isl_int_set_si(v
, 3);
347 isl_constraint_set_coefficient(c
, isl_dim_set
, 2, v
);
348 bset
= isl_basic_set_add_constraint(bset
, c
);
350 bset
= isl_basic_set_project_out(bset
, isl_dim_set
, 1, 2);
352 assert(bset
&& bset
->n_div
== 1);
353 isl_local_space_free(ls
);
354 isl_basic_set_free(bset
);
357 dim
= isl_space_set_alloc(ctx
, 0, 3);
358 bset
= isl_basic_set_universe(isl_space_copy(dim
));
359 ls
= isl_local_space_from_space(dim
);
361 c
= isl_equality_alloc(isl_local_space_copy(ls
));
362 isl_int_set_si(v
, 1);
363 isl_constraint_set_constant(c
, v
);
364 isl_int_set_si(v
, -1);
365 isl_constraint_set_coefficient(c
, isl_dim_set
, 0, v
);
366 isl_int_set_si(v
, 3);
367 isl_constraint_set_coefficient(c
, isl_dim_set
, 1, v
);
368 bset
= isl_basic_set_add_constraint(bset
, c
);
370 c
= isl_equality_alloc(isl_local_space_copy(ls
));
371 isl_int_set_si(v
, -1);
372 isl_constraint_set_constant(c
, v
);
373 isl_int_set_si(v
, 1);
374 isl_constraint_set_coefficient(c
, isl_dim_set
, 0, v
);
375 isl_int_set_si(v
, 3);
376 isl_constraint_set_coefficient(c
, isl_dim_set
, 2, v
);
377 bset
= isl_basic_set_add_constraint(bset
, c
);
379 bset
= isl_basic_set_project_out(bset
, isl_dim_set
, 1, 2);
381 assert(bset
&& bset
->n_div
== 1);
382 isl_local_space_free(ls
);
383 isl_basic_set_free(bset
);
386 dim
= isl_space_set_alloc(ctx
, 0, 3);
387 bset
= isl_basic_set_universe(isl_space_copy(dim
));
388 ls
= isl_local_space_from_space(dim
);
390 c
= isl_equality_alloc(isl_local_space_copy(ls
));
391 isl_int_set_si(v
, 1);
392 isl_constraint_set_constant(c
, v
);
393 isl_int_set_si(v
, -1);
394 isl_constraint_set_coefficient(c
, isl_dim_set
, 0, v
);
395 isl_int_set_si(v
, 3);
396 isl_constraint_set_coefficient(c
, isl_dim_set
, 1, v
);
397 bset
= isl_basic_set_add_constraint(bset
, c
);
399 c
= isl_equality_alloc(isl_local_space_copy(ls
));
400 isl_int_set_si(v
, -3);
401 isl_constraint_set_constant(c
, v
);
402 isl_int_set_si(v
, 1);
403 isl_constraint_set_coefficient(c
, isl_dim_set
, 0, v
);
404 isl_int_set_si(v
, 4);
405 isl_constraint_set_coefficient(c
, isl_dim_set
, 2, v
);
406 bset
= isl_basic_set_add_constraint(bset
, c
);
408 bset
= isl_basic_set_project_out(bset
, isl_dim_set
, 1, 2);
410 assert(bset
&& bset
->n_div
== 1);
411 isl_local_space_free(ls
);
412 isl_basic_set_free(bset
);
415 dim
= isl_space_set_alloc(ctx
, 0, 3);
416 bset
= isl_basic_set_universe(isl_space_copy(dim
));
417 ls
= isl_local_space_from_space(dim
);
419 c
= isl_equality_alloc(isl_local_space_copy(ls
));
420 isl_int_set_si(v
, 2);
421 isl_constraint_set_constant(c
, v
);
422 isl_int_set_si(v
, -1);
423 isl_constraint_set_coefficient(c
, isl_dim_set
, 0, v
);
424 isl_int_set_si(v
, 3);
425 isl_constraint_set_coefficient(c
, isl_dim_set
, 1, v
);
426 bset
= isl_basic_set_add_constraint(bset
, c
);
428 c
= isl_equality_alloc(isl_local_space_copy(ls
));
429 isl_int_set_si(v
, -1);
430 isl_constraint_set_constant(c
, v
);
431 isl_int_set_si(v
, 1);
432 isl_constraint_set_coefficient(c
, isl_dim_set
, 0, v
);
433 isl_int_set_si(v
, 6);
434 isl_constraint_set_coefficient(c
, isl_dim_set
, 2, v
);
435 bset
= isl_basic_set_add_constraint(bset
, c
);
437 bset
= isl_basic_set_project_out(bset
, isl_dim_set
, 1, 2);
439 assert(isl_basic_set_is_empty(bset
));
440 isl_local_space_free(ls
);
441 isl_basic_set_free(bset
);
444 dim
= isl_space_set_alloc(ctx
, 0, 3);
445 bset
= isl_basic_set_universe(isl_space_copy(dim
));
446 ls
= isl_local_space_from_space(dim
);
448 c
= isl_equality_alloc(isl_local_space_copy(ls
));
449 isl_int_set_si(v
, -1);
450 isl_constraint_set_coefficient(c
, isl_dim_set
, 0, v
);
451 isl_int_set_si(v
, 3);
452 isl_constraint_set_coefficient(c
, isl_dim_set
, 2, v
);
453 bset
= isl_basic_set_add_constraint(bset
, c
);
455 c
= isl_equality_alloc(isl_local_space_copy(ls
));
456 isl_int_set_si(v
, 1);
457 isl_constraint_set_coefficient(c
, isl_dim_set
, 0, v
);
458 isl_int_set_si(v
, -3);
459 isl_constraint_set_coefficient(c
, isl_dim_set
, 1, v
);
460 bset
= isl_basic_set_add_constraint(bset
, c
);
462 bset
= isl_basic_set_project_out(bset
, isl_dim_set
, 2, 1);
464 assert(bset
&& bset
->n_div
== 0);
465 isl_basic_set_free(bset
);
466 isl_local_space_free(ls
);
469 dim
= isl_space_set_alloc(ctx
, 0, 3);
470 bset
= isl_basic_set_universe(isl_space_copy(dim
));
471 ls
= isl_local_space_from_space(dim
);
473 c
= isl_equality_alloc(isl_local_space_copy(ls
));
474 isl_int_set_si(v
, -1);
475 isl_constraint_set_coefficient(c
, isl_dim_set
, 0, v
);
476 isl_int_set_si(v
, 6);
477 isl_constraint_set_coefficient(c
, isl_dim_set
, 2, v
);
478 bset
= isl_basic_set_add_constraint(bset
, c
);
480 c
= isl_equality_alloc(isl_local_space_copy(ls
));
481 isl_int_set_si(v
, 1);
482 isl_constraint_set_coefficient(c
, isl_dim_set
, 0, v
);
483 isl_int_set_si(v
, -3);
484 isl_constraint_set_coefficient(c
, isl_dim_set
, 1, v
);
485 bset
= isl_basic_set_add_constraint(bset
, c
);
487 bset
= isl_basic_set_project_out(bset
, isl_dim_set
, 2, 1);
489 assert(bset
&& bset
->n_div
== 1);
490 isl_basic_set_free(bset
);
491 isl_local_space_free(ls
);
494 /* This test is a bit tricky. We set up an equality
496 * Normalization of divs creates _two_ divs
499 * Afterwards e0 is removed again because it has coefficient -1
500 * and we end up with the original equality and div again.
501 * Perhaps we can avoid the introduction of this temporary div.
503 dim
= isl_space_set_alloc(ctx
, 0, 4);
504 bset
= isl_basic_set_universe(isl_space_copy(dim
));
505 ls
= isl_local_space_from_space(dim
);
507 c
= isl_equality_alloc(isl_local_space_copy(ls
));
508 isl_int_set_si(v
, -1);
509 isl_constraint_set_coefficient(c
, isl_dim_set
, 0, v
);
510 isl_int_set_si(v
, -3);
511 isl_constraint_set_coefficient(c
, isl_dim_set
, 1, v
);
512 isl_int_set_si(v
, -3);
513 isl_constraint_set_coefficient(c
, isl_dim_set
, 2, v
);
514 isl_int_set_si(v
, 6);
515 isl_constraint_set_coefficient(c
, isl_dim_set
, 3, v
);
516 bset
= isl_basic_set_add_constraint(bset
, c
);
518 bset
= isl_basic_set_project_out(bset
, isl_dim_set
, 3, 1);
520 /* Test disabled for now */
522 assert(bset && bset->n_div == 1);
524 isl_local_space_free(ls
);
525 isl_basic_set_free(bset
);
528 dim
= isl_space_set_alloc(ctx
, 0, 5);
529 bset
= isl_basic_set_universe(isl_space_copy(dim
));
530 ls
= isl_local_space_from_space(dim
);
532 c
= isl_equality_alloc(isl_local_space_copy(ls
));
533 isl_int_set_si(v
, -1);
534 isl_constraint_set_coefficient(c
, isl_dim_set
, 0, v
);
535 isl_int_set_si(v
, -3);
536 isl_constraint_set_coefficient(c
, isl_dim_set
, 1, v
);
537 isl_int_set_si(v
, -3);
538 isl_constraint_set_coefficient(c
, isl_dim_set
, 3, v
);
539 isl_int_set_si(v
, 6);
540 isl_constraint_set_coefficient(c
, isl_dim_set
, 4, v
);
541 bset
= isl_basic_set_add_constraint(bset
, c
);
543 c
= isl_equality_alloc(isl_local_space_copy(ls
));
544 isl_int_set_si(v
, -1);
545 isl_constraint_set_coefficient(c
, isl_dim_set
, 0, v
);
546 isl_int_set_si(v
, 1);
547 isl_constraint_set_coefficient(c
, isl_dim_set
, 2, v
);
548 isl_int_set_si(v
, 1);
549 isl_constraint_set_constant(c
, v
);
550 bset
= isl_basic_set_add_constraint(bset
, c
);
552 bset
= isl_basic_set_project_out(bset
, isl_dim_set
, 4, 1);
554 /* Test disabled for now */
556 assert(bset && bset->n_div == 1);
558 isl_local_space_free(ls
);
559 isl_basic_set_free(bset
);
562 dim
= isl_space_set_alloc(ctx
, 0, 4);
563 bset
= isl_basic_set_universe(isl_space_copy(dim
));
564 ls
= isl_local_space_from_space(dim
);
566 c
= isl_equality_alloc(isl_local_space_copy(ls
));
567 isl_int_set_si(v
, 1);
568 isl_constraint_set_coefficient(c
, isl_dim_set
, 0, v
);
569 isl_int_set_si(v
, -1);
570 isl_constraint_set_coefficient(c
, isl_dim_set
, 1, v
);
571 isl_int_set_si(v
, -2);
572 isl_constraint_set_coefficient(c
, isl_dim_set
, 2, v
);
573 bset
= isl_basic_set_add_constraint(bset
, c
);
575 c
= isl_equality_alloc(isl_local_space_copy(ls
));
576 isl_int_set_si(v
, -1);
577 isl_constraint_set_coefficient(c
, isl_dim_set
, 0, v
);
578 isl_int_set_si(v
, 3);
579 isl_constraint_set_coefficient(c
, isl_dim_set
, 3, v
);
580 isl_int_set_si(v
, 2);
581 isl_constraint_set_constant(c
, v
);
582 bset
= isl_basic_set_add_constraint(bset
, c
);
584 bset
= isl_basic_set_project_out(bset
, isl_dim_set
, 2, 2);
586 bset
= isl_basic_set_fix_si(bset
, isl_dim_set
, 0, 2);
588 assert(!isl_basic_set_is_empty(bset
));
590 isl_local_space_free(ls
);
591 isl_basic_set_free(bset
);
594 dim
= isl_space_set_alloc(ctx
, 0, 3);
595 bset
= isl_basic_set_universe(isl_space_copy(dim
));
596 ls
= isl_local_space_from_space(dim
);
598 c
= isl_equality_alloc(isl_local_space_copy(ls
));
599 isl_int_set_si(v
, 1);
600 isl_constraint_set_coefficient(c
, isl_dim_set
, 0, v
);
601 isl_int_set_si(v
, -2);
602 isl_constraint_set_coefficient(c
, isl_dim_set
, 2, v
);
603 bset
= isl_basic_set_add_constraint(bset
, c
);
605 bset
= isl_basic_set_project_out(bset
, isl_dim_set
, 2, 1);
607 bset
= isl_basic_set_fix_si(bset
, isl_dim_set
, 0, 2);
609 isl_local_space_free(ls
);
610 isl_basic_set_free(bset
);
614 str
= "{ [i] : exists (e0, e1: 3e1 >= 1 + 2e0 and "
615 "8e1 <= -1 + 5i - 5e0 and 2e1 >= 1 + 2i - 5e0) }";
616 set
= isl_set_read_from_str(ctx
, str
);
617 set
= isl_set_compute_divs(set
);
622 str
= "{ [i,j] : 2*[i/2] + 3 * [j/4] <= 10 and 2 i = j }";
623 bset
= isl_basic_set_read_from_str(ctx
, str
);
624 n
= isl_basic_set_dim(bset
, isl_dim_div
);
625 isl_basic_set_free(bset
);
629 isl_die(ctx
, isl_error_unknown
,
630 "expecting no existentials", return -1);
632 str
= "{ [i,j,k] : 3 + i + 2j >= 0 and 2 * [(i+2j)/4] <= k }";
633 set
= isl_set_read_from_str(ctx
, str
);
634 set
= isl_set_remove_divs_involving_dims(set
, isl_dim_set
, 0, 2);
635 set
= isl_set_fix_si(set
, isl_dim_set
, 2, -3);
636 empty
= isl_set_is_empty(set
);
641 isl_die(ctx
, isl_error_unknown
,
642 "result not as accurate as expected", return -1);
647 void test_application_case(struct isl_ctx
*ctx
, const char *name
)
651 struct isl_basic_set
*bset1
, *bset2
;
652 struct isl_basic_map
*bmap
;
654 filename
= get_filename(ctx
, name
, "omega");
656 input
= fopen(filename
, "r");
659 bset1
= isl_basic_set_read_from_file(ctx
, input
);
660 bmap
= isl_basic_map_read_from_file(ctx
, input
);
662 bset1
= isl_basic_set_apply(bset1
, bmap
);
664 bset2
= isl_basic_set_read_from_file(ctx
, input
);
666 assert(isl_basic_set_is_equal(bset1
, bset2
) == 1);
668 isl_basic_set_free(bset1
);
669 isl_basic_set_free(bset2
);
675 void test_application(struct isl_ctx
*ctx
)
677 test_application_case(ctx
, "application");
678 test_application_case(ctx
, "application2");
681 void test_affine_hull_case(struct isl_ctx
*ctx
, const char *name
)
685 struct isl_basic_set
*bset1
, *bset2
;
687 filename
= get_filename(ctx
, name
, "polylib");
689 input
= fopen(filename
, "r");
692 bset1
= isl_basic_set_read_from_file(ctx
, input
);
693 bset2
= isl_basic_set_read_from_file(ctx
, input
);
695 bset1
= isl_basic_set_affine_hull(bset1
);
697 assert(isl_basic_set_is_equal(bset1
, bset2
) == 1);
699 isl_basic_set_free(bset1
);
700 isl_basic_set_free(bset2
);
706 int test_affine_hull(struct isl_ctx
*ctx
)
713 test_affine_hull_case(ctx
, "affine2");
714 test_affine_hull_case(ctx
, "affine");
715 test_affine_hull_case(ctx
, "affine3");
717 str
= "[m] -> { [i0] : exists (e0, e1: e1 <= 1 + i0 and "
718 "m >= 3 and 4i0 <= 2 + m and e1 >= i0 and "
719 "e1 >= 0 and e1 <= 2 and e1 >= 1 + 2e0 and "
720 "2e1 <= 1 + m + 4e0 and 2e1 >= 2 - m + 4i0 - 4e0) }";
721 set
= isl_set_read_from_str(ctx
, str
);
722 bset
= isl_set_affine_hull(set
);
723 n
= isl_basic_set_dim(bset
, isl_dim_div
);
724 isl_basic_set_free(bset
);
726 isl_die(ctx
, isl_error_unknown
, "not expecting any divs",
732 void test_convex_hull_case(struct isl_ctx
*ctx
, const char *name
)
736 struct isl_basic_set
*bset1
, *bset2
;
739 filename
= get_filename(ctx
, name
, "polylib");
741 input
= fopen(filename
, "r");
744 bset1
= isl_basic_set_read_from_file(ctx
, input
);
745 bset2
= isl_basic_set_read_from_file(ctx
, input
);
747 set
= isl_basic_set_union(bset1
, bset2
);
748 bset1
= isl_set_convex_hull(set
);
750 bset2
= isl_basic_set_read_from_file(ctx
, input
);
752 assert(isl_basic_set_is_equal(bset1
, bset2
) == 1);
754 isl_basic_set_free(bset1
);
755 isl_basic_set_free(bset2
);
761 void test_convex_hull_algo(struct isl_ctx
*ctx
, int convex
)
763 const char *str1
, *str2
;
764 isl_set
*set1
, *set2
;
765 int orig_convex
= ctx
->opt
->convex
;
766 ctx
->opt
->convex
= convex
;
768 test_convex_hull_case(ctx
, "convex0");
769 test_convex_hull_case(ctx
, "convex1");
770 test_convex_hull_case(ctx
, "convex2");
771 test_convex_hull_case(ctx
, "convex3");
772 test_convex_hull_case(ctx
, "convex4");
773 test_convex_hull_case(ctx
, "convex5");
774 test_convex_hull_case(ctx
, "convex6");
775 test_convex_hull_case(ctx
, "convex7");
776 test_convex_hull_case(ctx
, "convex8");
777 test_convex_hull_case(ctx
, "convex9");
778 test_convex_hull_case(ctx
, "convex10");
779 test_convex_hull_case(ctx
, "convex11");
780 test_convex_hull_case(ctx
, "convex12");
781 test_convex_hull_case(ctx
, "convex13");
782 test_convex_hull_case(ctx
, "convex14");
783 test_convex_hull_case(ctx
, "convex15");
785 str1
= "{ [i0, i1, i2] : (i2 = 1 and i0 = 0 and i1 >= 0) or "
786 "(i0 = 1 and i1 = 0 and i2 = 1) or "
787 "(i0 = 0 and i1 = 0 and i2 = 0) }";
788 str2
= "{ [i0, i1, i2] : i0 >= 0 and i2 >= i0 and i2 <= 1 and i1 >= 0 }";
789 set1
= isl_set_read_from_str(ctx
, str1
);
790 set2
= isl_set_read_from_str(ctx
, str2
);
791 set1
= isl_set_from_basic_set(isl_set_convex_hull(set1
));
792 assert(isl_set_is_equal(set1
, set2
));
796 ctx
->opt
->convex
= orig_convex
;
799 void test_convex_hull(struct isl_ctx
*ctx
)
801 test_convex_hull_algo(ctx
, ISL_CONVEX_HULL_FM
);
802 test_convex_hull_algo(ctx
, ISL_CONVEX_HULL_WRAP
);
805 void test_gist_case(struct isl_ctx
*ctx
, const char *name
)
809 struct isl_basic_set
*bset1
, *bset2
;
811 filename
= get_filename(ctx
, name
, "polylib");
813 input
= fopen(filename
, "r");
816 bset1
= isl_basic_set_read_from_file(ctx
, input
);
817 bset2
= isl_basic_set_read_from_file(ctx
, input
);
819 bset1
= isl_basic_set_gist(bset1
, bset2
);
821 bset2
= isl_basic_set_read_from_file(ctx
, input
);
823 assert(isl_basic_set_is_equal(bset1
, bset2
) == 1);
825 isl_basic_set_free(bset1
);
826 isl_basic_set_free(bset2
);
832 void test_gist(struct isl_ctx
*ctx
)
835 isl_basic_set
*bset1
, *bset2
;
837 test_gist_case(ctx
, "gist1");
839 str
= "[p0, p2, p3, p5, p6, p10] -> { [] : "
840 "exists (e0 = [(15 + p0 + 15p6 + 15p10)/16], e1 = [(p5)/8], "
841 "e2 = [(p6)/128], e3 = [(8p2 - p5)/128], "
842 "e4 = [(128p3 - p6)/4096]: 8e1 = p5 and 128e2 = p6 and "
843 "128e3 = 8p2 - p5 and 4096e4 = 128p3 - p6 and p2 >= 0 and "
844 "16e0 >= 16 + 16p6 + 15p10 and p2 <= 15 and p3 >= 0 and "
845 "p3 <= 31 and p6 >= 128p3 and p5 >= 8p2 and p10 >= 0 and "
846 "16e0 <= 15 + p0 + 15p6 + 15p10 and 16e0 >= p0 + 15p6 + 15p10 and "
847 "p10 <= 15 and p10 <= -1 + p0 - p6) }";
848 bset1
= isl_basic_set_read_from_str(ctx
, str
);
849 str
= "[p0, p2, p3, p5, p6, p10] -> { [] : exists (e0 = [(p5)/8], "
850 "e1 = [(p6)/128], e2 = [(8p2 - p5)/128], "
851 "e3 = [(128p3 - p6)/4096]: 8e0 = p5 and 128e1 = p6 and "
852 "128e2 = 8p2 - p5 and 4096e3 = 128p3 - p6 and p5 >= -7 and "
853 "p2 >= 0 and 8p2 <= -1 + p0 and p2 <= 15 and p3 >= 0 and "
854 "p3 <= 31 and 128p3 <= -1 + p0 and p6 >= -127 and "
855 "p5 <= -1 + p0 and p6 <= -1 + p0 and p6 >= 128p3 and "
856 "p0 >= 1 and p5 >= 8p2 and p10 >= 0 and p10 <= 15 ) }";
857 bset2
= isl_basic_set_read_from_str(ctx
, str
);
858 bset1
= isl_basic_set_gist(bset1
, bset2
);
859 assert(bset1
&& bset1
->n_div
== 0);
860 isl_basic_set_free(bset1
);
863 int test_coalesce_set(isl_ctx
*ctx
, const char *str
, int check_one
)
869 set
= isl_set_read_from_str(ctx
, str
);
870 set
= isl_set_coalesce(set
);
871 set2
= isl_set_read_from_str(ctx
, str
);
872 equal
= isl_set_is_equal(set
, set2
);
873 one
= set
&& set
->n
== 1;
880 isl_die(ctx
, isl_error_unknown
,
881 "coalesced set not equal to input", return -1);
882 if (check_one
&& !one
)
883 isl_die(ctx
, isl_error_unknown
,
884 "coalesced set should not be a union", return -1);
889 int test_coalesce_unbounded_wrapping(isl_ctx
*ctx
)
894 bounded
= isl_options_get_coalesce_bounded_wrapping(ctx
);
895 isl_options_set_coalesce_bounded_wrapping(ctx
, 0);
897 if (test_coalesce_set(ctx
,
898 "{[x,y,z] : y + 2 >= 0 and x - y + 1 >= 0 and "
899 "-x - y + 1 >= 0 and -3 <= z <= 3;"
900 "[x,y,z] : -x+z + 20 >= 0 and -x-z + 20 >= 0 and "
901 "x-z + 20 >= 0 and x+z + 20 >= 0 and "
902 "-10 <= y <= 0}", 1) < 0)
904 if (test_coalesce_set(ctx
,
905 "{[x,y] : 0 <= x,y <= 10; [5,y]: 4 <=y <= 11}", 1) < 0)
907 if (test_coalesce_set(ctx
,
908 "{[x,0,0] : -5 <= x <= 5; [0,y,1] : -5 <= y <= 5 }", 1) < 0)
916 isl_options_set_coalesce_bounded_wrapping(ctx
, bounded
);
921 int test_coalesce(struct isl_ctx
*ctx
)
924 struct isl_set
*set
, *set2
;
925 struct isl_map
*map
, *map2
;
927 set
= isl_set_read_from_str(ctx
,
928 "{[x,y]: x >= 0 & x <= 10 & y >= 0 & y <= 10 or "
929 "y >= x & x >= 2 & 5 >= y }");
930 set
= isl_set_coalesce(set
);
931 assert(set
&& set
->n
== 1);
934 set
= isl_set_read_from_str(ctx
,
935 "{[x,y]: y >= 0 & 2x + y <= 30 & y <= 10 & x >= 0 or "
936 "x + y >= 10 & y <= x & x + y <= 20 & y >= 0}");
937 set
= isl_set_coalesce(set
);
938 assert(set
&& set
->n
== 1);
941 set
= isl_set_read_from_str(ctx
,
942 "{[x,y]: y >= 0 & 2x + y <= 30 & y <= 10 & x >= 0 or "
943 "x + y >= 10 & y <= x & x + y <= 19 & y >= 0}");
944 set
= isl_set_coalesce(set
);
945 assert(set
&& set
->n
== 2);
948 set
= isl_set_read_from_str(ctx
,
949 "{[x,y]: y >= 0 & x <= 5 & y <= x or "
950 "y >= 0 & x >= 6 & x <= 10 & y <= x}");
951 set
= isl_set_coalesce(set
);
952 assert(set
&& set
->n
== 1);
955 set
= isl_set_read_from_str(ctx
,
956 "{[x,y]: y >= 0 & x <= 5 & y <= x or "
957 "y >= 0 & x >= 7 & x <= 10 & y <= x}");
958 set
= isl_set_coalesce(set
);
959 assert(set
&& set
->n
== 2);
962 set
= isl_set_read_from_str(ctx
,
963 "{[x,y]: y >= 0 & x <= 5 & y <= x or "
964 "y >= 0 & x >= 6 & x <= 10 & y + 1 <= x}");
965 set
= isl_set_coalesce(set
);
966 assert(set
&& set
->n
== 2);
969 set
= isl_set_read_from_str(ctx
,
970 "{[x,y]: y >= 0 & x <= 5 & y <= x or "
971 "y >= 0 & x = 6 & y <= 6}");
972 set
= isl_set_coalesce(set
);
973 assert(set
&& set
->n
== 1);
976 set
= isl_set_read_from_str(ctx
,
977 "{[x,y]: y >= 0 & x <= 5 & y <= x or "
978 "y >= 0 & x = 7 & y <= 6}");
979 set
= isl_set_coalesce(set
);
980 assert(set
&& set
->n
== 2);
983 set
= isl_set_read_from_str(ctx
,
984 "{[x,y]: y >= 0 & x <= 5 & y <= x or "
985 "y >= 0 & x = 6 & y <= 5}");
986 set
= isl_set_coalesce(set
);
987 assert(set
&& set
->n
== 1);
988 set2
= isl_set_read_from_str(ctx
,
989 "{[x,y]: y >= 0 & x <= 5 & y <= x or "
990 "y >= 0 & x = 6 & y <= 5}");
991 assert(isl_set_is_equal(set
, set2
));
995 set
= isl_set_read_from_str(ctx
,
996 "{[x,y]: y >= 0 & x <= 5 & y <= x or "
997 "y >= 0 & x = 6 & y <= 7}");
998 set
= isl_set_coalesce(set
);
999 assert(set
&& set
->n
== 2);
1002 set
= isl_set_read_from_str(ctx
,
1003 "[n] -> { [i] : i = 1 and n >= 2 or 2 <= i and i <= n }");
1004 set
= isl_set_coalesce(set
);
1005 assert(set
&& set
->n
== 1);
1006 set2
= isl_set_read_from_str(ctx
,
1007 "[n] -> { [i] : i = 1 and n >= 2 or 2 <= i and i <= n }");
1008 assert(isl_set_is_equal(set
, set2
));
1012 set
= isl_set_read_from_str(ctx
,
1013 "{[x,y] : x >= 0 and y >= 0 or 0 <= y and y <= 5 and x = -1}");
1014 set
= isl_set_coalesce(set
);
1015 set2
= isl_set_read_from_str(ctx
,
1016 "{[x,y] : x >= 0 and y >= 0 or 0 <= y and y <= 5 and x = -1}");
1017 assert(isl_set_is_equal(set
, set2
));
1021 set
= isl_set_read_from_str(ctx
,
1022 "[n] -> { [i] : 1 <= i and i <= n - 1 or "
1023 "2 <= i and i <= n }");
1024 set
= isl_set_coalesce(set
);
1025 assert(set
&& set
->n
== 1);
1026 set2
= isl_set_read_from_str(ctx
,
1027 "[n] -> { [i] : 1 <= i and i <= n - 1 or "
1028 "2 <= i and i <= n }");
1029 assert(isl_set_is_equal(set
, set2
));
1033 map
= isl_map_read_from_str(ctx
,
1034 "[n] -> { [i0] -> [o0] : exists (e0 = [(i0)/4], e1 = [(o0)/4], "
1035 "e2 = [(n)/2], e3 = [(-2 + i0)/4], e4 = [(-2 + o0)/4], "
1036 "e5 = [(-2n + i0)/4]: 2e2 = n and 4e3 = -2 + i0 and "
1037 "4e4 = -2 + o0 and i0 >= 8 + 2n and o0 >= 2 + i0 and "
1038 "o0 <= 56 + 2n and o0 <= -12 + 4n and i0 <= 57 + 2n and "
1039 "i0 <= -11 + 4n and o0 >= 6 + 2n and 4e0 <= i0 and "
1040 "4e0 >= -3 + i0 and 4e1 <= o0 and 4e1 >= -3 + o0 and "
1041 "4e5 <= -2n + i0 and 4e5 >= -3 - 2n + i0);"
1042 "[i0] -> [o0] : exists (e0 = [(i0)/4], e1 = [(o0)/4], "
1043 "e2 = [(n)/2], e3 = [(-2 + i0)/4], e4 = [(-2 + o0)/4], "
1044 "e5 = [(-2n + i0)/4]: 2e2 = n and 4e3 = -2 + i0 and "
1045 "4e4 = -2 + o0 and 2e0 >= 3 + n and e0 <= -4 + n and "
1046 "2e0 <= 27 + n and e1 <= -4 + n and 2e1 <= 27 + n and "
1047 "2e1 >= 2 + n and e1 >= 1 + e0 and i0 >= 7 + 2n and "
1048 "i0 <= -11 + 4n and i0 <= 57 + 2n and 4e0 <= -2 + i0 and "
1049 "4e0 >= -3 + i0 and o0 >= 6 + 2n and o0 <= -11 + 4n and "
1050 "o0 <= 57 + 2n and 4e1 <= -2 + o0 and 4e1 >= -3 + o0 and "
1051 "4e5 <= -2n + i0 and 4e5 >= -3 - 2n + i0 ) }");
1052 map
= isl_map_coalesce(map
);
1053 map2
= isl_map_read_from_str(ctx
,
1054 "[n] -> { [i0] -> [o0] : exists (e0 = [(i0)/4], e1 = [(o0)/4], "
1055 "e2 = [(n)/2], e3 = [(-2 + i0)/4], e4 = [(-2 + o0)/4], "
1056 "e5 = [(-2n + i0)/4]: 2e2 = n and 4e3 = -2 + i0 and "
1057 "4e4 = -2 + o0 and i0 >= 8 + 2n and o0 >= 2 + i0 and "
1058 "o0 <= 56 + 2n and o0 <= -12 + 4n and i0 <= 57 + 2n and "
1059 "i0 <= -11 + 4n and o0 >= 6 + 2n and 4e0 <= i0 and "
1060 "4e0 >= -3 + i0 and 4e1 <= o0 and 4e1 >= -3 + o0 and "
1061 "4e5 <= -2n + i0 and 4e5 >= -3 - 2n + i0);"
1062 "[i0] -> [o0] : exists (e0 = [(i0)/4], e1 = [(o0)/4], "
1063 "e2 = [(n)/2], e3 = [(-2 + i0)/4], e4 = [(-2 + o0)/4], "
1064 "e5 = [(-2n + i0)/4]: 2e2 = n and 4e3 = -2 + i0 and "
1065 "4e4 = -2 + o0 and 2e0 >= 3 + n and e0 <= -4 + n and "
1066 "2e0 <= 27 + n and e1 <= -4 + n and 2e1 <= 27 + n and "
1067 "2e1 >= 2 + n and e1 >= 1 + e0 and i0 >= 7 + 2n and "
1068 "i0 <= -11 + 4n and i0 <= 57 + 2n and 4e0 <= -2 + i0 and "
1069 "4e0 >= -3 + i0 and o0 >= 6 + 2n and o0 <= -11 + 4n and "
1070 "o0 <= 57 + 2n and 4e1 <= -2 + o0 and 4e1 >= -3 + o0 and "
1071 "4e5 <= -2n + i0 and 4e5 >= -3 - 2n + i0 ) }");
1072 assert(isl_map_is_equal(map
, map2
));
1076 str
= "[n, m] -> { [] -> [o0, o2, o3] : (o3 = 1 and o0 >= 1 + m and "
1077 "o0 <= n + m and o2 <= m and o0 >= 2 + n and o2 >= 3) or "
1078 "(o0 >= 2 + n and o0 >= 1 + m and o0 <= n + m and n >= 1 and "
1079 "o3 <= -1 + o2 and o3 >= 1 - m + o2 and o3 >= 2 and o3 <= n) }";
1080 map
= isl_map_read_from_str(ctx
, str
);
1081 map
= isl_map_coalesce(map
);
1082 map2
= isl_map_read_from_str(ctx
, str
);
1083 assert(isl_map_is_equal(map
, map2
));
1087 str
= "[M, N] -> { [i0, i1, i2, i3, i4, i5, i6] -> "
1088 "[o0, o1, o2, o3, o4, o5, o6] : "
1089 "(o6 <= -4 + 2M - 2N + i0 + i1 - i2 + i6 - o0 - o1 + o2 and "
1090 "o3 <= -2 + i3 and o6 >= 2 + i0 + i3 + i6 - o0 - o3 and "
1091 "o6 >= 2 - M + N + i3 + i4 + i6 - o3 - o4 and o0 <= -1 + i0 and "
1092 "o4 >= 4 - 3M + 3N - i0 - i1 + i2 + 2i3 + i4 + o0 + o1 - o2 - 2o3 "
1093 "and o6 <= -3 + 2M - 2N + i3 + i4 - i5 + i6 - o3 - o4 + o5 and "
1094 "2o6 <= -5 + 5M - 5N + 2i0 + i1 - i2 - i5 + 2i6 - 2o0 - o1 + o2 + o5 "
1095 "and o6 >= 2i0 + i1 + i6 - 2o0 - o1 and "
1096 "3o6 <= -5 + 4M - 4N + 2i0 + i1 - i2 + 2i3 + i4 - i5 + 3i6 "
1097 "- 2o0 - o1 + o2 - 2o3 - o4 + o5) or "
1098 "(N >= 2 and o3 <= -1 + i3 and o0 <= -1 + i0 and "
1099 "o6 >= i3 + i6 - o3 and M >= 0 and "
1100 "2o6 >= 1 + i0 + i3 + 2i6 - o0 - o3 and "
1101 "o6 >= 1 - M + i0 + i6 - o0 and N >= 2M and o6 >= i0 + i6 - o0) }";
1102 map
= isl_map_read_from_str(ctx
, str
);
1103 map
= isl_map_coalesce(map
);
1104 map2
= isl_map_read_from_str(ctx
, str
);
1105 assert(isl_map_is_equal(map
, map2
));
1109 str
= "[M, N] -> { [] -> [o0] : (o0 = 0 and M >= 1 and N >= 2) or "
1110 "(o0 = 0 and M >= 1 and N >= 2M and N >= 2 + M) or "
1111 "(o0 = 0 and M >= 2 and N >= 3) or "
1112 "(M = 0 and o0 = 0 and N >= 3) }";
1113 map
= isl_map_read_from_str(ctx
, str
);
1114 map
= isl_map_coalesce(map
);
1115 map2
= isl_map_read_from_str(ctx
, str
);
1116 assert(isl_map_is_equal(map
, map2
));
1120 str
= "{ [i0, i1, i2, i3] : (i1 = 10i0 and i0 >= 1 and 10i0 <= 100 and "
1121 "i3 <= 9 + 10 i2 and i3 >= 1 + 10i2 and i3 >= 0) or "
1122 "(i1 <= 9 + 10i0 and i1 >= 1 + 10i0 and i2 >= 0 and "
1123 "i0 >= 0 and i1 <= 100 and i3 <= 9 + 10i2 and i3 >= 1 + 10i2) }";
1124 map
= isl_map_read_from_str(ctx
, str
);
1125 map
= isl_map_coalesce(map
);
1126 map2
= isl_map_read_from_str(ctx
, str
);
1127 assert(isl_map_is_equal(map
, map2
));
1131 test_coalesce_set(ctx
,
1132 "[M] -> { [i1] : (i1 >= 2 and i1 <= M) or "
1133 "(i1 = M and M >= 1) }", 0);
1134 test_coalesce_set(ctx
,
1135 "{[x,y] : x,y >= 0; [x,y] : 10 <= x <= 20 and y >= -1 }", 0);
1136 test_coalesce_set(ctx
,
1137 "{ [x, y] : (x >= 1 and y >= 1 and x <= 2 and y <= 2) or "
1138 "(y = 3 and x = 1) }", 1);
1139 test_coalesce_set(ctx
,
1140 "[M] -> { [i0, i1, i2, i3, i4] : (i1 >= 3 and i4 >= 2 + i2 and "
1141 "i2 >= 2 and i0 >= 2 and i3 >= 1 + i2 and i0 <= M and "
1142 "i1 <= M and i3 <= M and i4 <= M) or "
1143 "(i1 >= 2 and i4 >= 1 + i2 and i2 >= 2 and i0 >= 2 and "
1144 "i3 >= 1 + i2 and i0 <= M and i1 <= -1 + M and i3 <= M and "
1145 "i4 <= -1 + M) }", 1);
1146 test_coalesce_set(ctx
,
1147 "{ [x, y] : (x >= 0 and y >= 0 and x <= 10 and y <= 10) or "
1148 "(x >= 1 and y >= 1 and x <= 11 and y <= 11) }", 1);
1149 if (test_coalesce_unbounded_wrapping(ctx
) < 0)
1151 if (test_coalesce_set(ctx
, "{[x,0] : x >= 0; [x,1] : x <= 20}", 0) < 0)
1153 if (test_coalesce_set(ctx
, "{ [x, 1 - x] : 0 <= x <= 1; [0,0] }", 1) < 0)
1155 if (test_coalesce_set(ctx
, "{ [0,0]; [i,i] : 1 <= i <= 10 }", 1) < 0)
1157 if (test_coalesce_set(ctx
, "{ [0,0]; [i,j] : 1 <= i,j <= 10 }", 0) < 0)
1159 if (test_coalesce_set(ctx
, "{ [0,0]; [i,2i] : 1 <= i <= 10 }", 1) < 0)
1161 if (test_coalesce_set(ctx
, "{ [0,0]; [i,2i] : 2 <= i <= 10 }", 0) < 0)
1163 if (test_coalesce_set(ctx
, "{ [1,0]; [i,2i] : 1 <= i <= 10 }", 0) < 0)
1165 if (test_coalesce_set(ctx
, "{ [0,1]; [i,2i] : 1 <= i <= 10 }", 0) < 0)
1167 if (test_coalesce_set(ctx
, "{ [a, b] : exists e : 2e = a and "
1168 "a >= 0 and (a <= 3 or (b <= 0 and b >= -4 + a)) }", 0) < 0)
1170 if (test_coalesce_set(ctx
,
1171 "{ [i, j, i', j'] : i <= 2 and j <= 2 and "
1172 "j' >= -1 + 2i + j - 2i' and i' <= -1 + i and "
1173 "j >= 1 and j' <= i + j - i' and i >= 1; "
1174 "[1, 1, 1, 1] }", 0) < 0)
1176 if (test_coalesce_set(ctx
, "{ [i,j] : exists a,b : i = 2a and j = 3b; "
1177 "[i,j] : exists a : j = 3a }", 1) < 0)
1182 void test_closure(struct isl_ctx
*ctx
)
1186 isl_map
*up
, *right
;
1187 isl_map
*map
, *map2
;
1190 /* COCOA example 1 */
1191 map
= isl_map_read_from_str(ctx
,
1192 "[n] -> { [i,j] -> [i2,j2] : i2 = i + 1 and j2 = j + 1 and "
1193 "1 <= i and i < n and 1 <= j and j < n or "
1194 "i2 = i + 1 and j2 = j - 1 and "
1195 "1 <= i and i < n and 2 <= j and j <= n }");
1196 map
= isl_map_power(map
, &exact
);
1200 /* COCOA example 1 */
1201 map
= isl_map_read_from_str(ctx
,
1202 "[n] -> { [i,j] -> [i2,j2] : i2 = i + 1 and j2 = j + 1 and "
1203 "1 <= i and i < n and 1 <= j and j < n or "
1204 "i2 = i + 1 and j2 = j - 1 and "
1205 "1 <= i and i < n and 2 <= j and j <= n }");
1206 map
= isl_map_transitive_closure(map
, &exact
);
1208 map2
= isl_map_read_from_str(ctx
,
1209 "[n] -> { [i,j] -> [i2,j2] : exists (k1,k2,k : "
1210 "1 <= i and i < n and 1 <= j and j <= n and "
1211 "2 <= i2 and i2 <= n and 1 <= j2 and j2 <= n and "
1212 "i2 = i + k1 + k2 and j2 = j + k1 - k2 and "
1213 "k1 >= 0 and k2 >= 0 and k1 + k2 = k and k >= 1 )}");
1214 assert(isl_map_is_equal(map
, map2
));
1218 map
= isl_map_read_from_str(ctx
,
1219 "[n] -> { [x] -> [y] : y = x + 1 and 0 <= x and x <= n and "
1220 " 0 <= y and y <= n }");
1221 map
= isl_map_transitive_closure(map
, &exact
);
1222 map2
= isl_map_read_from_str(ctx
,
1223 "[n] -> { [x] -> [y] : y > x and 0 <= x and x <= n and "
1224 " 0 <= y and y <= n }");
1225 assert(isl_map_is_equal(map
, map2
));
1229 /* COCOA example 2 */
1230 map
= isl_map_read_from_str(ctx
,
1231 "[n] -> { [i,j] -> [i2,j2] : i2 = i + 2 and j2 = j + 2 and "
1232 "1 <= i and i < n - 1 and 1 <= j and j < n - 1 or "
1233 "i2 = i + 2 and j2 = j - 2 and "
1234 "1 <= i and i < n - 1 and 3 <= j and j <= n }");
1235 map
= isl_map_transitive_closure(map
, &exact
);
1237 map2
= isl_map_read_from_str(ctx
,
1238 "[n] -> { [i,j] -> [i2,j2] : exists (k1,k2,k : "
1239 "1 <= i and i < n - 1 and 1 <= j and j <= n and "
1240 "3 <= i2 and i2 <= n and 1 <= j2 and j2 <= n and "
1241 "i2 = i + 2 k1 + 2 k2 and j2 = j + 2 k1 - 2 k2 and "
1242 "k1 >= 0 and k2 >= 0 and k1 + k2 = k and k >= 1) }");
1243 assert(isl_map_is_equal(map
, map2
));
1247 /* COCOA Fig.2 left */
1248 map
= isl_map_read_from_str(ctx
,
1249 "[n] -> { [i,j] -> [i2,j2] : i2 = i + 2 and j2 = j and "
1250 "i <= 2 j - 3 and i <= n - 2 and j <= 2 i - 1 and "
1252 "i2 = i and j2 = j + 2 and i <= 2 j - 1 and i <= n and "
1253 "j <= 2 i - 3 and j <= n - 2 or "
1254 "i2 = i + 1 and j2 = j + 1 and i <= 2 j - 1 and "
1255 "i <= n - 1 and j <= 2 i - 1 and j <= n - 1 }");
1256 map
= isl_map_transitive_closure(map
, &exact
);
1260 /* COCOA Fig.2 right */
1261 map
= isl_map_read_from_str(ctx
,
1262 "[n] -> { [i,j] -> [i2,j2] : i2 = i + 3 and j2 = j and "
1263 "i <= 2 j - 4 and i <= n - 3 and j <= 2 i - 1 and "
1265 "i2 = i and j2 = j + 3 and i <= 2 j - 1 and i <= n and "
1266 "j <= 2 i - 4 and j <= n - 3 or "
1267 "i2 = i + 1 and j2 = j + 1 and i <= 2 j - 1 and "
1268 "i <= n - 1 and j <= 2 i - 1 and j <= n - 1 }");
1269 map
= isl_map_power(map
, &exact
);
1273 /* COCOA Fig.2 right */
1274 map
= isl_map_read_from_str(ctx
,
1275 "[n] -> { [i,j] -> [i2,j2] : i2 = i + 3 and j2 = j and "
1276 "i <= 2 j - 4 and i <= n - 3 and j <= 2 i - 1 and "
1278 "i2 = i and j2 = j + 3 and i <= 2 j - 1 and i <= n and "
1279 "j <= 2 i - 4 and j <= n - 3 or "
1280 "i2 = i + 1 and j2 = j + 1 and i <= 2 j - 1 and "
1281 "i <= n - 1 and j <= 2 i - 1 and j <= n - 1 }");
1282 map
= isl_map_transitive_closure(map
, &exact
);
1284 map2
= isl_map_read_from_str(ctx
,
1285 "[n] -> { [i,j] -> [i2,j2] : exists (k1,k2,k3,k : "
1286 "i <= 2 j - 1 and i <= n and j <= 2 i - 1 and "
1287 "j <= n and 3 + i + 2 j <= 3 n and "
1288 "3 + 2 i + j <= 3n and i2 <= 2 j2 -1 and i2 <= n and "
1289 "i2 <= 3 j2 - 4 and j2 <= 2 i2 -1 and j2 <= n and "
1290 "13 + 4 j2 <= 11 i2 and i2 = i + 3 k1 + k3 and "
1291 "j2 = j + 3 k2 + k3 and k1 >= 0 and k2 >= 0 and "
1292 "k3 >= 0 and k1 + k2 + k3 = k and k > 0) }");
1293 assert(isl_map_is_equal(map
, map2
));
1297 /* COCOA Fig.1 right */
1298 dom
= isl_set_read_from_str(ctx
,
1299 "{ [x,y] : x >= 0 and -2 x + 3 y >= 0 and x <= 3 and "
1300 "2 x - 3 y + 3 >= 0 }");
1301 right
= isl_map_read_from_str(ctx
,
1302 "{ [x,y] -> [x2,y2] : x2 = x + 1 and y2 = y }");
1303 up
= isl_map_read_from_str(ctx
,
1304 "{ [x,y] -> [x2,y2] : x2 = x and y2 = y + 1 }");
1305 right
= isl_map_intersect_domain(right
, isl_set_copy(dom
));
1306 right
= isl_map_intersect_range(right
, isl_set_copy(dom
));
1307 up
= isl_map_intersect_domain(up
, isl_set_copy(dom
));
1308 up
= isl_map_intersect_range(up
, dom
);
1309 map
= isl_map_union(up
, right
);
1310 map
= isl_map_transitive_closure(map
, &exact
);
1312 map2
= isl_map_read_from_str(ctx
,
1313 "{ [0,0] -> [0,1]; [0,0] -> [1,1]; [0,1] -> [1,1]; "
1314 " [2,2] -> [3,2]; [2,2] -> [3,3]; [3,2] -> [3,3] }");
1315 assert(isl_map_is_equal(map
, map2
));
1319 /* COCOA Theorem 1 counter example */
1320 map
= isl_map_read_from_str(ctx
,
1321 "{ [i,j] -> [i2,j2] : i = 0 and 0 <= j and j <= 1 and "
1322 "i2 = 1 and j2 = j or "
1323 "i = 0 and j = 0 and i2 = 0 and j2 = 1 }");
1324 map
= isl_map_transitive_closure(map
, &exact
);
1328 map
= isl_map_read_from_str(ctx
,
1329 "[m,n] -> { [i,j] -> [i2,j2] : i2 = i and j2 = j + 2 and "
1330 "1 <= i,i2 <= n and 1 <= j,j2 <= m or "
1331 "i2 = i + 1 and 3 <= j2 - j <= 4 and "
1332 "1 <= i,i2 <= n and 1 <= j,j2 <= m }");
1333 map
= isl_map_transitive_closure(map
, &exact
);
1337 /* Kelly et al 1996, fig 12 */
1338 map
= isl_map_read_from_str(ctx
,
1339 "[n] -> { [i,j] -> [i2,j2] : i2 = i and j2 = j + 1 and "
1340 "1 <= i,j,j+1 <= n or "
1341 "j = n and j2 = 1 and i2 = i + 1 and "
1342 "1 <= i,i+1 <= n }");
1343 map
= isl_map_transitive_closure(map
, &exact
);
1345 map2
= isl_map_read_from_str(ctx
,
1346 "[n] -> { [i,j] -> [i2,j2] : 1 <= j < j2 <= n and "
1347 "1 <= i <= n and i = i2 or "
1348 "1 <= i < i2 <= n and 1 <= j <= n and "
1350 assert(isl_map_is_equal(map
, map2
));
1354 /* Omega's closure4 */
1355 map
= isl_map_read_from_str(ctx
,
1356 "[m,n] -> { [x,y] -> [x2,y2] : x2 = x and y2 = y + 1 and "
1357 "1 <= x,y <= 10 or "
1358 "x2 = x + 1 and y2 = y and "
1359 "1 <= x <= 20 && 5 <= y <= 15 }");
1360 map
= isl_map_transitive_closure(map
, &exact
);
1364 map
= isl_map_read_from_str(ctx
,
1365 "[n] -> { [x] -> [y]: 1 <= n <= y - x <= 10 }");
1366 map
= isl_map_transitive_closure(map
, &exact
);
1368 map2
= isl_map_read_from_str(ctx
,
1369 "[n] -> { [x] -> [y] : 1 <= n <= 10 and y >= n + x }");
1370 assert(isl_map_is_equal(map
, map2
));
1374 str
= "[n, m] -> { [i0, i1, i2, i3] -> [o0, o1, o2, o3] : "
1375 "i3 = 1 and o0 = i0 and o1 = -1 + i1 and o2 = -1 + i2 and "
1376 "o3 = -2 + i2 and i1 <= -1 + i0 and i1 >= 1 - m + i0 and "
1377 "i1 >= 2 and i1 <= n and i2 >= 3 and i2 <= 1 + n and i2 <= m }";
1378 map
= isl_map_read_from_str(ctx
, str
);
1379 map
= isl_map_transitive_closure(map
, &exact
);
1381 map2
= isl_map_read_from_str(ctx
, str
);
1382 assert(isl_map_is_equal(map
, map2
));
1386 str
= "{[0] -> [1]; [2] -> [3]}";
1387 map
= isl_map_read_from_str(ctx
, str
);
1388 map
= isl_map_transitive_closure(map
, &exact
);
1390 map2
= isl_map_read_from_str(ctx
, str
);
1391 assert(isl_map_is_equal(map
, map2
));
1395 str
= "[n] -> { [[i0, i1, 1, 0, i0] -> [i5, 1]] -> "
1396 "[[i0, -1 + i1, 2, 0, i0] -> [-1 + i5, 2]] : "
1397 "exists (e0 = [(3 - n)/3]: i5 >= 2 and i1 >= 2 and "
1398 "3i0 <= -1 + n and i1 <= -1 + n and i5 <= -1 + n and "
1399 "3e0 >= 1 - n and 3e0 <= 2 - n and 3i0 >= -2 + n); "
1400 "[[i0, i1, 2, 0, i0] -> [i5, 1]] -> "
1401 "[[i0, i1, 1, 0, i0] -> [-1 + i5, 2]] : "
1402 "exists (e0 = [(3 - n)/3]: i5 >= 2 and i1 >= 1 and "
1403 "3i0 <= -1 + n and i1 <= -1 + n and i5 <= -1 + n and "
1404 "3e0 >= 1 - n and 3e0 <= 2 - n and 3i0 >= -2 + n); "
1405 "[[i0, i1, 1, 0, i0] -> [i5, 2]] -> "
1406 "[[i0, -1 + i1, 2, 0, i0] -> [i5, 1]] : "
1407 "exists (e0 = [(3 - n)/3]: i1 >= 2 and i5 >= 1 and "
1408 "3i0 <= -1 + n and i1 <= -1 + n and i5 <= -1 + n and "
1409 "3e0 >= 1 - n and 3e0 <= 2 - n and 3i0 >= -2 + n); "
1410 "[[i0, i1, 2, 0, i0] -> [i5, 2]] -> "
1411 "[[i0, i1, 1, 0, i0] -> [i5, 1]] : "
1412 "exists (e0 = [(3 - n)/3]: i5 >= 1 and i1 >= 1 and "
1413 "3i0 <= -1 + n and i1 <= -1 + n and i5 <= -1 + n and "
1414 "3e0 >= 1 - n and 3e0 <= 2 - n and 3i0 >= -2 + n) }";
1415 map
= isl_map_read_from_str(ctx
, str
);
1416 map
= isl_map_transitive_closure(map
, NULL
);
1421 void test_lex(struct isl_ctx
*ctx
)
1426 dim
= isl_space_set_alloc(ctx
, 0, 0);
1427 map
= isl_map_lex_le(dim
);
1428 assert(!isl_map_is_empty(map
));
1432 void test_lexmin(struct isl_ctx
*ctx
)
1435 isl_basic_map
*bmap
;
1436 isl_map
*map
, *map2
;
1439 isl_pw_multi_aff
*pma
;
1441 str
= "[p0, p1] -> { [] -> [] : "
1442 "exists (e0 = [(2p1)/3], e1, e2, e3 = [(3 - p1 + 3e0)/3], "
1443 "e4 = [(p1)/3], e5 = [(p1 + 3e4)/3]: "
1444 "3e0 >= -2 + 2p1 and 3e0 >= p1 and 3e3 >= 1 - p1 + 3e0 and "
1445 "3e0 <= 2p1 and 3e3 >= -2 + p1 and 3e3 <= -1 + p1 and p1 >= 3 and "
1446 "3e5 >= -2 + 2p1 and 3e5 >= p1 and 3e5 <= -1 + p1 + 3e4 and "
1447 "3e4 <= p1 and 3e4 >= -2 + p1 and e3 <= -1 + e0 and "
1448 "3e4 >= 6 - p1 + 3e1 and 3e1 >= p1 and 3e5 >= -2 + p1 + 3e4 and "
1449 "2e4 >= 3 - p1 + 2e1 and e4 <= e1 and 3e3 <= 2 - p1 + 3e0 and "
1450 "e5 >= 1 + e1 and 3e4 >= 6 - 2p1 + 3e1 and "
1451 "p0 >= 2 and p1 >= p0 and 3e2 >= p1 and 3e4 >= 6 - p1 + 3e2 and "
1452 "e2 <= e1 and e3 >= 1 and e4 <= e2) }";
1453 map
= isl_map_read_from_str(ctx
, str
);
1454 map
= isl_map_lexmin(map
);
1457 str
= "[C] -> { [obj,a,b,c] : obj <= 38 a + 7 b + 10 c and "
1458 "a + b <= 1 and c <= 10 b and c <= C and a,b,c,C >= 0 }";
1459 set
= isl_set_read_from_str(ctx
, str
);
1460 set
= isl_set_lexmax(set
);
1461 str
= "[C] -> { [obj,a,b,c] : C = 8 }";
1462 set2
= isl_set_read_from_str(ctx
, str
);
1463 set
= isl_set_intersect(set
, set2
);
1464 assert(!isl_set_is_empty(set
));
1467 str
= "{ [x] -> [y] : x <= y <= 10; [x] -> [5] : -8 <= x <= 8 }";
1468 map
= isl_map_read_from_str(ctx
, str
);
1469 map
= isl_map_lexmin(map
);
1470 str
= "{ [x] -> [5] : 6 <= x <= 8; "
1471 "[x] -> [x] : x <= 5 or (9 <= x <= 10) }";
1472 map2
= isl_map_read_from_str(ctx
, str
);
1473 assert(isl_map_is_equal(map
, map2
));
1477 str
= "{ [x] -> [y] : 4y = x or 4y = -1 + x or 4y = -2 + x }";
1478 map
= isl_map_read_from_str(ctx
, str
);
1479 map2
= isl_map_copy(map
);
1480 map
= isl_map_lexmin(map
);
1481 assert(isl_map_is_equal(map
, map2
));
1485 str
= "{ [x] -> [y] : x = 4y; [x] -> [y] : x = 2y }";
1486 map
= isl_map_read_from_str(ctx
, str
);
1487 map
= isl_map_lexmin(map
);
1488 str
= "{ [x] -> [y] : (4y = x and x >= 0) or "
1489 "(exists (e0 = [(x)/4], e1 = [(-2 + x)/4]: 2y = x and "
1490 "4e1 = -2 + x and 4e0 <= -1 + x and 4e0 >= -3 + x)) or "
1491 "(exists (e0 = [(x)/4]: 2y = x and 4e0 = x and x <= -4)) }";
1492 map2
= isl_map_read_from_str(ctx
, str
);
1493 assert(isl_map_is_equal(map
, map2
));
1497 str
= "{ [i] -> [i', j] : j = i - 8i' and i' >= 0 and i' <= 7 and "
1498 " 8i' <= i and 8i' >= -7 + i }";
1499 bmap
= isl_basic_map_read_from_str(ctx
, str
);
1500 pma
= isl_basic_map_lexmin_pw_multi_aff(isl_basic_map_copy(bmap
));
1501 map2
= isl_map_from_pw_multi_aff(pma
);
1502 map
= isl_map_from_basic_map(bmap
);
1503 assert(isl_map_is_equal(map
, map2
));
1507 str
= "{ T[a] -> S[b, c] : a = 4b-2c and c >= b }";
1508 map
= isl_map_read_from_str(ctx
, str
);
1509 map
= isl_map_lexmin(map
);
1510 str
= "{ T[a] -> S[b, c] : 2b = a and 2c = a }";
1511 map2
= isl_map_read_from_str(ctx
, str
);
1512 assert(isl_map_is_equal(map
, map2
));
1522 static int collect_must_may(__isl_take isl_map
*dep
, int must
,
1523 void *dep_user
, void *user
)
1525 struct must_may
*mm
= (struct must_may
*)user
;
1528 mm
->must
= isl_map_union(mm
->must
, dep
);
1530 mm
->may
= isl_map_union(mm
->may
, dep
);
1535 static int common_space(void *first
, void *second
)
1537 int depth
= *(int *)first
;
1541 static int map_is_equal(__isl_keep isl_map
*map
, const char *str
)
1549 map2
= isl_map_read_from_str(map
->ctx
, str
);
1550 equal
= isl_map_is_equal(map
, map2
);
1556 static int map_check_equal(__isl_keep isl_map
*map
, const char *str
)
1560 equal
= map_is_equal(map
, str
);
1564 isl_die(isl_map_get_ctx(map
), isl_error_unknown
,
1565 "result not as expected", return -1);
1569 void test_dep(struct isl_ctx
*ctx
)
1574 isl_access_info
*ai
;
1581 str
= "{ [2,i,0] -> [i] : 0 <= i <= 10 }";
1582 map
= isl_map_read_from_str(ctx
, str
);
1583 ai
= isl_access_info_alloc(map
, &depth
, &common_space
, 2);
1585 str
= "{ [0,i,0] -> [i] : 0 <= i <= 10 }";
1586 map
= isl_map_read_from_str(ctx
, str
);
1587 ai
= isl_access_info_add_source(ai
, map
, 1, &depth
);
1589 str
= "{ [1,i,0] -> [5] : 0 <= i <= 10 }";
1590 map
= isl_map_read_from_str(ctx
, str
);
1591 ai
= isl_access_info_add_source(ai
, map
, 1, &depth
);
1593 flow
= isl_access_info_compute_flow(ai
);
1594 dim
= isl_space_alloc(ctx
, 0, 3, 3);
1595 mm
.must
= isl_map_empty(isl_space_copy(dim
));
1596 mm
.may
= isl_map_empty(dim
);
1598 isl_flow_foreach(flow
, collect_must_may
, &mm
);
1600 str
= "{ [0,i,0] -> [2,i,0] : (0 <= i <= 4) or (6 <= i <= 10); "
1601 " [1,10,0] -> [2,5,0] }";
1602 assert(map_is_equal(mm
.must
, str
));
1603 str
= "{ [i,j,k] -> [l,m,n] : 1 = 0 }";
1604 assert(map_is_equal(mm
.may
, str
));
1606 isl_map_free(mm
.must
);
1607 isl_map_free(mm
.may
);
1608 isl_flow_free(flow
);
1611 str
= "{ [2,i,0] -> [i] : 0 <= i <= 10 }";
1612 map
= isl_map_read_from_str(ctx
, str
);
1613 ai
= isl_access_info_alloc(map
, &depth
, &common_space
, 2);
1615 str
= "{ [0,i,0] -> [i] : 0 <= i <= 10 }";
1616 map
= isl_map_read_from_str(ctx
, str
);
1617 ai
= isl_access_info_add_source(ai
, map
, 1, &depth
);
1619 str
= "{ [1,i,0] -> [5] : 0 <= i <= 10 }";
1620 map
= isl_map_read_from_str(ctx
, str
);
1621 ai
= isl_access_info_add_source(ai
, map
, 0, &depth
);
1623 flow
= isl_access_info_compute_flow(ai
);
1624 dim
= isl_space_alloc(ctx
, 0, 3, 3);
1625 mm
.must
= isl_map_empty(isl_space_copy(dim
));
1626 mm
.may
= isl_map_empty(dim
);
1628 isl_flow_foreach(flow
, collect_must_may
, &mm
);
1630 str
= "{ [0,i,0] -> [2,i,0] : (0 <= i <= 4) or (6 <= i <= 10) }";
1631 assert(map_is_equal(mm
.must
, str
));
1632 str
= "{ [0,5,0] -> [2,5,0]; [1,i,0] -> [2,5,0] : 0 <= i <= 10 }";
1633 assert(map_is_equal(mm
.may
, str
));
1635 isl_map_free(mm
.must
);
1636 isl_map_free(mm
.may
);
1637 isl_flow_free(flow
);
1640 str
= "{ [2,i,0] -> [i] : 0 <= i <= 10 }";
1641 map
= isl_map_read_from_str(ctx
, str
);
1642 ai
= isl_access_info_alloc(map
, &depth
, &common_space
, 2);
1644 str
= "{ [0,i,0] -> [i] : 0 <= i <= 10 }";
1645 map
= isl_map_read_from_str(ctx
, str
);
1646 ai
= isl_access_info_add_source(ai
, map
, 0, &depth
);
1648 str
= "{ [1,i,0] -> [5] : 0 <= i <= 10 }";
1649 map
= isl_map_read_from_str(ctx
, str
);
1650 ai
= isl_access_info_add_source(ai
, map
, 0, &depth
);
1652 flow
= isl_access_info_compute_flow(ai
);
1653 dim
= isl_space_alloc(ctx
, 0, 3, 3);
1654 mm
.must
= isl_map_empty(isl_space_copy(dim
));
1655 mm
.may
= isl_map_empty(dim
);
1657 isl_flow_foreach(flow
, collect_must_may
, &mm
);
1659 str
= "{ [0,i,0] -> [2,i,0] : 0 <= i <= 10; "
1660 " [1,i,0] -> [2,5,0] : 0 <= i <= 10 }";
1661 assert(map_is_equal(mm
.may
, str
));
1662 str
= "{ [i,j,k] -> [l,m,n] : 1 = 0 }";
1663 assert(map_is_equal(mm
.must
, str
));
1665 isl_map_free(mm
.must
);
1666 isl_map_free(mm
.may
);
1667 isl_flow_free(flow
);
1670 str
= "{ [0,i,2] -> [i] : 0 <= i <= 10 }";
1671 map
= isl_map_read_from_str(ctx
, str
);
1672 ai
= isl_access_info_alloc(map
, &depth
, &common_space
, 2);
1674 str
= "{ [0,i,0] -> [i] : 0 <= i <= 10 }";
1675 map
= isl_map_read_from_str(ctx
, str
);
1676 ai
= isl_access_info_add_source(ai
, map
, 0, &depth
);
1678 str
= "{ [0,i,1] -> [5] : 0 <= i <= 10 }";
1679 map
= isl_map_read_from_str(ctx
, str
);
1680 ai
= isl_access_info_add_source(ai
, map
, 0, &depth
);
1682 flow
= isl_access_info_compute_flow(ai
);
1683 dim
= isl_space_alloc(ctx
, 0, 3, 3);
1684 mm
.must
= isl_map_empty(isl_space_copy(dim
));
1685 mm
.may
= isl_map_empty(dim
);
1687 isl_flow_foreach(flow
, collect_must_may
, &mm
);
1689 str
= "{ [0,i,0] -> [0,i,2] : 0 <= i <= 10; "
1690 " [0,i,1] -> [0,5,2] : 0 <= i <= 5 }";
1691 assert(map_is_equal(mm
.may
, str
));
1692 str
= "{ [i,j,k] -> [l,m,n] : 1 = 0 }";
1693 assert(map_is_equal(mm
.must
, str
));
1695 isl_map_free(mm
.must
);
1696 isl_map_free(mm
.may
);
1697 isl_flow_free(flow
);
1700 str
= "{ [0,i,1] -> [i] : 0 <= i <= 10 }";
1701 map
= isl_map_read_from_str(ctx
, str
);
1702 ai
= isl_access_info_alloc(map
, &depth
, &common_space
, 2);
1704 str
= "{ [0,i,0] -> [i] : 0 <= i <= 10 }";
1705 map
= isl_map_read_from_str(ctx
, str
);
1706 ai
= isl_access_info_add_source(ai
, map
, 0, &depth
);
1708 str
= "{ [0,i,2] -> [5] : 0 <= i <= 10 }";
1709 map
= isl_map_read_from_str(ctx
, str
);
1710 ai
= isl_access_info_add_source(ai
, map
, 0, &depth
);
1712 flow
= isl_access_info_compute_flow(ai
);
1713 dim
= isl_space_alloc(ctx
, 0, 3, 3);
1714 mm
.must
= isl_map_empty(isl_space_copy(dim
));
1715 mm
.may
= isl_map_empty(dim
);
1717 isl_flow_foreach(flow
, collect_must_may
, &mm
);
1719 str
= "{ [0,i,0] -> [0,i,1] : 0 <= i <= 10; "
1720 " [0,i,2] -> [0,5,1] : 0 <= i <= 4 }";
1721 assert(map_is_equal(mm
.may
, str
));
1722 str
= "{ [i,j,k] -> [l,m,n] : 1 = 0 }";
1723 assert(map_is_equal(mm
.must
, str
));
1725 isl_map_free(mm
.must
);
1726 isl_map_free(mm
.may
);
1727 isl_flow_free(flow
);
1732 str
= "{ [1,i,0,0,0] -> [i,j] : 0 <= i <= 10 and 0 <= j <= 10 }";
1733 map
= isl_map_read_from_str(ctx
, str
);
1734 ai
= isl_access_info_alloc(map
, &depth
, &common_space
, 1);
1736 str
= "{ [0,i,0,j,0] -> [i,j] : 0 <= i <= 10 and 0 <= j <= 10 }";
1737 map
= isl_map_read_from_str(ctx
, str
);
1738 ai
= isl_access_info_add_source(ai
, map
, 1, &depth
);
1740 flow
= isl_access_info_compute_flow(ai
);
1741 dim
= isl_space_alloc(ctx
, 0, 5, 5);
1742 mm
.must
= isl_map_empty(isl_space_copy(dim
));
1743 mm
.may
= isl_map_empty(dim
);
1745 isl_flow_foreach(flow
, collect_must_may
, &mm
);
1747 str
= "{ [0,i,0,j,0] -> [1,i,0,0,0] : 0 <= i,j <= 10 }";
1748 assert(map_is_equal(mm
.must
, str
));
1749 str
= "{ [0,0,0,0,0] -> [0,0,0,0,0] : 1 = 0 }";
1750 assert(map_is_equal(mm
.may
, str
));
1752 isl_map_free(mm
.must
);
1753 isl_map_free(mm
.may
);
1754 isl_flow_free(flow
);
1757 int test_sv(isl_ctx
*ctx
)
1761 isl_union_map
*umap
;
1764 str
= "[N] -> { [i] -> [f] : 0 <= i <= N and 0 <= i - 10 f <= 9 }";
1765 map
= isl_map_read_from_str(ctx
, str
);
1766 sv
= isl_map_is_single_valued(map
);
1771 isl_die(ctx
, isl_error_internal
,
1772 "map not detected as single valued", return -1);
1774 str
= "[N] -> { [i] -> [f] : 0 <= i <= N and 0 <= i - 10 f <= 10 }";
1775 map
= isl_map_read_from_str(ctx
, str
);
1776 sv
= isl_map_is_single_valued(map
);
1781 isl_die(ctx
, isl_error_internal
,
1782 "map detected as single valued", return -1);
1784 str
= "{ S1[i] -> [i] : 0 <= i <= 9; S2[i] -> [i] : 0 <= i <= 9 }";
1785 umap
= isl_union_map_read_from_str(ctx
, str
);
1786 sv
= isl_union_map_is_single_valued(umap
);
1787 isl_union_map_free(umap
);
1791 isl_die(ctx
, isl_error_internal
,
1792 "map not detected as single valued", return -1);
1794 str
= "{ [i] -> S1[i] : 0 <= i <= 9; [i] -> S2[i] : 0 <= i <= 9 }";
1795 umap
= isl_union_map_read_from_str(ctx
, str
);
1796 sv
= isl_union_map_is_single_valued(umap
);
1797 isl_union_map_free(umap
);
1801 isl_die(ctx
, isl_error_internal
,
1802 "map detected as single valued", return -1);
1807 void test_bijective_case(struct isl_ctx
*ctx
, const char *str
, int bijective
)
1811 map
= isl_map_read_from_str(ctx
, str
);
1813 assert(isl_map_is_bijective(map
));
1815 assert(!isl_map_is_bijective(map
));
1819 void test_bijective(struct isl_ctx
*ctx
)
1821 test_bijective_case(ctx
, "[N,M]->{[i,j] -> [i]}", 0);
1822 test_bijective_case(ctx
, "[N,M]->{[i,j] -> [i] : j=i}", 1);
1823 test_bijective_case(ctx
, "[N,M]->{[i,j] -> [i] : j=0}", 1);
1824 test_bijective_case(ctx
, "[N,M]->{[i,j] -> [i] : j=N}", 1);
1825 test_bijective_case(ctx
, "[N,M]->{[i,j] -> [j,i]}", 1);
1826 test_bijective_case(ctx
, "[N,M]->{[i,j] -> [i+j]}", 0);
1827 test_bijective_case(ctx
, "[N,M]->{[i,j] -> []}", 0);
1828 test_bijective_case(ctx
, "[N,M]->{[i,j] -> [i,j,N]}", 1);
1829 test_bijective_case(ctx
, "[N,M]->{[i,j] -> [2i]}", 0);
1830 test_bijective_case(ctx
, "[N,M]->{[i,j] -> [i,i]}", 0);
1831 test_bijective_case(ctx
, "[N,M]->{[i,j] -> [2i,i]}", 0);
1832 test_bijective_case(ctx
, "[N,M]->{[i,j] -> [2i,j]}", 1);
1833 test_bijective_case(ctx
, "[N,M]->{[i,j] -> [x,y] : 2x=i & y =j}", 1);
1836 void test_pwqp(struct isl_ctx
*ctx
)
1840 isl_pw_qpolynomial
*pwqp1
, *pwqp2
;
1842 str
= "{ [i,j,k] -> 1 + 9 * [i/5] + 7 * [j/11] + 4 * [k/13] }";
1843 pwqp1
= isl_pw_qpolynomial_read_from_str(ctx
, str
);
1845 pwqp1
= isl_pw_qpolynomial_move_dims(pwqp1
, isl_dim_param
, 0,
1848 str
= "[j] -> { [i,k] -> 1 + 9 * [i/5] + 7 * [j/11] + 4 * [k/13] }";
1849 pwqp2
= isl_pw_qpolynomial_read_from_str(ctx
, str
);
1851 pwqp1
= isl_pw_qpolynomial_sub(pwqp1
, pwqp2
);
1853 assert(isl_pw_qpolynomial_is_zero(pwqp1
));
1855 isl_pw_qpolynomial_free(pwqp1
);
1857 str
= "{ [i] -> i }";
1858 pwqp1
= isl_pw_qpolynomial_read_from_str(ctx
, str
);
1859 str
= "{ [k] : exists a : k = 2a }";
1860 set
= isl_set_read_from_str(ctx
, str
);
1861 pwqp1
= isl_pw_qpolynomial_gist(pwqp1
, set
);
1862 str
= "{ [i] -> i }";
1863 pwqp2
= isl_pw_qpolynomial_read_from_str(ctx
, str
);
1865 pwqp1
= isl_pw_qpolynomial_sub(pwqp1
, pwqp2
);
1867 assert(isl_pw_qpolynomial_is_zero(pwqp1
));
1869 isl_pw_qpolynomial_free(pwqp1
);
1871 str
= "{ [i] -> i + [ (i + [i/3])/2 ] }";
1872 pwqp1
= isl_pw_qpolynomial_read_from_str(ctx
, str
);
1874 set
= isl_set_read_from_str(ctx
, str
);
1875 pwqp1
= isl_pw_qpolynomial_gist(pwqp1
, set
);
1876 str
= "{ [i] -> 16 }";
1877 pwqp2
= isl_pw_qpolynomial_read_from_str(ctx
, str
);
1879 pwqp1
= isl_pw_qpolynomial_sub(pwqp1
, pwqp2
);
1881 assert(isl_pw_qpolynomial_is_zero(pwqp1
));
1883 isl_pw_qpolynomial_free(pwqp1
);
1885 str
= "{ [i] -> ([(i)/2]) }";
1886 pwqp1
= isl_pw_qpolynomial_read_from_str(ctx
, str
);
1887 str
= "{ [k] : exists a : k = 2a+1 }";
1888 set
= isl_set_read_from_str(ctx
, str
);
1889 pwqp1
= isl_pw_qpolynomial_gist(pwqp1
, set
);
1890 str
= "{ [i] -> -1/2 + 1/2 * i }";
1891 pwqp2
= isl_pw_qpolynomial_read_from_str(ctx
, str
);
1893 pwqp1
= isl_pw_qpolynomial_sub(pwqp1
, pwqp2
);
1895 assert(isl_pw_qpolynomial_is_zero(pwqp1
));
1897 isl_pw_qpolynomial_free(pwqp1
);
1899 str
= "{ [i] -> ([([i/2] + [i/2])/5]) }";
1900 pwqp1
= isl_pw_qpolynomial_read_from_str(ctx
, str
);
1901 str
= "{ [i] -> ([(2 * [i/2])/5]) }";
1902 pwqp2
= isl_pw_qpolynomial_read_from_str(ctx
, str
);
1904 pwqp1
= isl_pw_qpolynomial_sub(pwqp1
, pwqp2
);
1906 assert(isl_pw_qpolynomial_is_zero(pwqp1
));
1908 isl_pw_qpolynomial_free(pwqp1
);
1910 str
= "{ [x] -> ([x/2] + [(x+1)/2]) }";
1911 pwqp1
= isl_pw_qpolynomial_read_from_str(ctx
, str
);
1912 str
= "{ [x] -> x }";
1913 pwqp2
= isl_pw_qpolynomial_read_from_str(ctx
, str
);
1915 pwqp1
= isl_pw_qpolynomial_sub(pwqp1
, pwqp2
);
1917 assert(isl_pw_qpolynomial_is_zero(pwqp1
));
1919 isl_pw_qpolynomial_free(pwqp1
);
1921 str
= "{ [i] -> ([i/2]) : i >= 0; [i] -> ([i/3]) : i < 0 }";
1922 pwqp1
= isl_pw_qpolynomial_read_from_str(ctx
, str
);
1923 pwqp2
= isl_pw_qpolynomial_read_from_str(ctx
, str
);
1924 pwqp1
= isl_pw_qpolynomial_coalesce(pwqp1
);
1925 pwqp1
= isl_pw_qpolynomial_sub(pwqp1
, pwqp2
);
1926 assert(isl_pw_qpolynomial_is_zero(pwqp1
));
1927 isl_pw_qpolynomial_free(pwqp1
);
1930 void test_split_periods(isl_ctx
*ctx
)
1933 isl_pw_qpolynomial
*pwqp
;
1935 str
= "{ [U,V] -> 1/3 * U + 2/3 * V - [(U + 2V)/3] + [U/2] : "
1936 "U + 2V + 3 >= 0 and - U -2V >= 0 and - U + 10 >= 0 and "
1937 "U >= 0; [U,V] -> U^2 : U >= 100 }";
1938 pwqp
= isl_pw_qpolynomial_read_from_str(ctx
, str
);
1940 pwqp
= isl_pw_qpolynomial_split_periods(pwqp
, 2);
1943 isl_pw_qpolynomial_free(pwqp
);
1946 void test_union(isl_ctx
*ctx
)
1949 isl_union_set
*uset1
, *uset2
;
1950 isl_union_map
*umap1
, *umap2
;
1952 str
= "{ [i] : 0 <= i <= 1 }";
1953 uset1
= isl_union_set_read_from_str(ctx
, str
);
1954 str
= "{ [1] -> [0] }";
1955 umap1
= isl_union_map_read_from_str(ctx
, str
);
1957 umap2
= isl_union_set_lex_gt_union_set(isl_union_set_copy(uset1
), uset1
);
1958 assert(isl_union_map_is_equal(umap1
, umap2
));
1960 isl_union_map_free(umap1
);
1961 isl_union_map_free(umap2
);
1963 str
= "{ A[i] -> B[i]; B[i] -> C[i]; A[0] -> C[1] }";
1964 umap1
= isl_union_map_read_from_str(ctx
, str
);
1965 str
= "{ A[i]; B[i] }";
1966 uset1
= isl_union_set_read_from_str(ctx
, str
);
1968 uset2
= isl_union_map_domain(umap1
);
1970 assert(isl_union_set_is_equal(uset1
, uset2
));
1972 isl_union_set_free(uset1
);
1973 isl_union_set_free(uset2
);
1976 void test_bound(isl_ctx
*ctx
)
1979 isl_pw_qpolynomial
*pwqp
;
1980 isl_pw_qpolynomial_fold
*pwf
;
1982 str
= "{ [[a, b, c, d] -> [e]] -> 0 }";
1983 pwqp
= isl_pw_qpolynomial_read_from_str(ctx
, str
);
1984 pwf
= isl_pw_qpolynomial_bound(pwqp
, isl_fold_max
, NULL
);
1985 assert(isl_pw_qpolynomial_fold_dim(pwf
, isl_dim_in
) == 4);
1986 isl_pw_qpolynomial_fold_free(pwf
);
1988 str
= "{ [[x]->[x]] -> 1 : exists a : x = 2 a }";
1989 pwqp
= isl_pw_qpolynomial_read_from_str(ctx
, str
);
1990 pwf
= isl_pw_qpolynomial_bound(pwqp
, isl_fold_max
, NULL
);
1991 assert(isl_pw_qpolynomial_fold_dim(pwf
, isl_dim_in
) == 1);
1992 isl_pw_qpolynomial_fold_free(pwf
);
1995 void test_lift(isl_ctx
*ctx
)
1998 isl_basic_map
*bmap
;
1999 isl_basic_set
*bset
;
2001 str
= "{ [i0] : exists e0 : i0 = 4e0 }";
2002 bset
= isl_basic_set_read_from_str(ctx
, str
);
2003 bset
= isl_basic_set_lift(bset
);
2004 bmap
= isl_basic_map_from_range(bset
);
2005 bset
= isl_basic_map_domain(bmap
);
2006 isl_basic_set_free(bset
);
2009 void test_subset(isl_ctx
*ctx
)
2012 isl_set
*set1
, *set2
;
2014 str
= "{ [112, 0] }";
2015 set1
= isl_set_read_from_str(ctx
, str
);
2016 str
= "{ [i0, i1] : exists (e0 = [(i0 - i1)/16], e1: "
2017 "16e0 <= i0 - i1 and 16e0 >= -15 + i0 - i1 and "
2018 "16e1 <= i1 and 16e0 >= -i1 and 16e1 >= -i0 + i1) }";
2019 set2
= isl_set_read_from_str(ctx
, str
);
2020 assert(isl_set_is_subset(set1
, set2
));
2025 int test_factorize(isl_ctx
*ctx
)
2028 isl_basic_set
*bset
;
2031 str
= "{ [i0, i1, i2, i3, i4, i5, i6, i7] : 3i5 <= 2 - 2i0 and "
2032 "i0 >= -2 and i6 >= 1 + i3 and i7 >= 0 and 3i5 >= -2i0 and "
2033 "2i4 <= i2 and i6 >= 1 + 2i0 + 3i1 and i4 <= -1 and "
2034 "i6 >= 1 + 2i0 + 3i5 and i6 <= 2 + 2i0 + 3i5 and "
2035 "3i5 <= 2 - 2i0 - i2 + 3i4 and i6 <= 2 + 2i0 + 3i1 and "
2036 "i0 <= -1 and i7 <= i2 + i3 - 3i4 - i6 and "
2037 "3i5 >= -2i0 - i2 + 3i4 }";
2038 bset
= isl_basic_set_read_from_str(ctx
, str
);
2039 f
= isl_basic_set_factorizer(bset
);
2040 isl_basic_set_free(bset
);
2041 isl_factorizer_free(f
);
2043 isl_die(ctx
, isl_error_unknown
,
2044 "failed to construct factorizer", return -1);
2046 str
= "{ [i0, i1, i2, i3, i4, i5, i6, i7, i8, i9, i10, i11, i12] : "
2047 "i12 <= 2 + i0 - i11 and 2i8 >= -i4 and i11 >= i1 and "
2048 "3i5 <= -i2 and 2i11 >= -i4 - 2i7 and i11 <= 3 + i0 + 3i9 and "
2049 "i11 <= -i4 - 2i7 and i12 >= -i10 and i2 >= -2 and "
2050 "i11 >= i1 + 3i10 and i11 >= 1 + i0 + 3i9 and "
2051 "i11 <= 1 - i4 - 2i8 and 6i6 <= 6 - i2 and 3i6 >= 1 - i2 and "
2052 "i11 <= 2 + i1 and i12 <= i4 + i11 and i12 >= i0 - i11 and "
2053 "3i5 >= -2 - i2 and i12 >= -1 + i4 + i11 and 3i3 <= 3 - i2 and "
2054 "9i6 <= 11 - i2 + 6i5 and 3i3 >= 1 - i2 and "
2055 "9i6 <= 5 - i2 + 6i3 and i12 <= -1 and i2 <= 0 }";
2056 bset
= isl_basic_set_read_from_str(ctx
, str
);
2057 f
= isl_basic_set_factorizer(bset
);
2058 isl_basic_set_free(bset
);
2059 isl_factorizer_free(f
);
2061 isl_die(ctx
, isl_error_unknown
,
2062 "failed to construct factorizer", return -1);
2067 static int check_injective(__isl_take isl_map
*map
, void *user
)
2069 int *injective
= user
;
2071 *injective
= isl_map_is_injective(map
);
2074 if (*injective
< 0 || !*injective
)
2080 int test_one_schedule(isl_ctx
*ctx
, const char *d
, const char *w
,
2081 const char *r
, const char *s
, int tilable
, int parallel
)
2085 isl_union_map
*W
, *R
, *S
;
2086 isl_union_map
*empty
;
2087 isl_union_map
*dep_raw
, *dep_war
, *dep_waw
, *dep
;
2088 isl_union_map
*validity
, *proximity
;
2089 isl_union_map
*schedule
;
2090 isl_union_map
*test
;
2091 isl_union_set
*delta
;
2092 isl_union_set
*domain
;
2096 isl_schedule
*sched
;
2097 int is_nonneg
, is_parallel
, is_tilable
, is_injection
, is_complete
;
2099 D
= isl_union_set_read_from_str(ctx
, d
);
2100 W
= isl_union_map_read_from_str(ctx
, w
);
2101 R
= isl_union_map_read_from_str(ctx
, r
);
2102 S
= isl_union_map_read_from_str(ctx
, s
);
2104 W
= isl_union_map_intersect_domain(W
, isl_union_set_copy(D
));
2105 R
= isl_union_map_intersect_domain(R
, isl_union_set_copy(D
));
2107 empty
= isl_union_map_empty(isl_union_map_get_space(S
));
2108 isl_union_map_compute_flow(isl_union_map_copy(R
),
2109 isl_union_map_copy(W
), empty
,
2110 isl_union_map_copy(S
),
2111 &dep_raw
, NULL
, NULL
, NULL
);
2112 isl_union_map_compute_flow(isl_union_map_copy(W
),
2113 isl_union_map_copy(W
),
2114 isl_union_map_copy(R
),
2115 isl_union_map_copy(S
),
2116 &dep_waw
, &dep_war
, NULL
, NULL
);
2118 dep
= isl_union_map_union(dep_waw
, dep_war
);
2119 dep
= isl_union_map_union(dep
, dep_raw
);
2120 validity
= isl_union_map_copy(dep
);
2121 proximity
= isl_union_map_copy(dep
);
2123 sched
= isl_union_set_compute_schedule(isl_union_set_copy(D
),
2124 validity
, proximity
);
2125 schedule
= isl_schedule_get_map(sched
);
2126 isl_schedule_free(sched
);
2127 isl_union_map_free(W
);
2128 isl_union_map_free(R
);
2129 isl_union_map_free(S
);
2132 isl_union_map_foreach_map(schedule
, &check_injective
, &is_injection
);
2134 domain
= isl_union_map_domain(isl_union_map_copy(schedule
));
2135 is_complete
= isl_union_set_is_subset(D
, domain
);
2136 isl_union_set_free(D
);
2137 isl_union_set_free(domain
);
2139 test
= isl_union_map_reverse(isl_union_map_copy(schedule
));
2140 test
= isl_union_map_apply_range(test
, dep
);
2141 test
= isl_union_map_apply_range(test
, schedule
);
2143 delta
= isl_union_map_deltas(test
);
2144 if (isl_union_set_n_set(delta
) == 0) {
2148 isl_union_set_free(delta
);
2150 delta_set
= isl_set_from_union_set(delta
);
2152 slice
= isl_set_universe(isl_set_get_space(delta_set
));
2153 for (i
= 0; i
< tilable
; ++i
)
2154 slice
= isl_set_lower_bound_si(slice
, isl_dim_set
, i
, 0);
2155 is_tilable
= isl_set_is_subset(delta_set
, slice
);
2156 isl_set_free(slice
);
2158 slice
= isl_set_universe(isl_set_get_space(delta_set
));
2159 for (i
= 0; i
< parallel
; ++i
)
2160 slice
= isl_set_fix_si(slice
, isl_dim_set
, i
, 0);
2161 is_parallel
= isl_set_is_subset(delta_set
, slice
);
2162 isl_set_free(slice
);
2164 origin
= isl_set_universe(isl_set_get_space(delta_set
));
2165 for (i
= 0; i
< isl_set_dim(origin
, isl_dim_set
); ++i
)
2166 origin
= isl_set_fix_si(origin
, isl_dim_set
, i
, 0);
2168 delta_set
= isl_set_union(delta_set
, isl_set_copy(origin
));
2169 delta_set
= isl_set_lexmin(delta_set
);
2171 is_nonneg
= isl_set_is_equal(delta_set
, origin
);
2173 isl_set_free(origin
);
2174 isl_set_free(delta_set
);
2177 if (is_nonneg
< 0 || is_parallel
< 0 || is_tilable
< 0 ||
2178 is_injection
< 0 || is_complete
< 0)
2181 isl_die(ctx
, isl_error_unknown
,
2182 "generated schedule incomplete", return -1);
2184 isl_die(ctx
, isl_error_unknown
,
2185 "generated schedule not injective on each statement",
2188 isl_die(ctx
, isl_error_unknown
,
2189 "negative dependences in generated schedule",
2192 isl_die(ctx
, isl_error_unknown
,
2193 "generated schedule not as tilable as expected",
2196 isl_die(ctx
, isl_error_unknown
,
2197 "generated schedule not as parallel as expected",
2203 int test_special_schedule(isl_ctx
*ctx
, const char *domain
,
2204 const char *validity
, const char *proximity
, const char *expected_sched
)
2208 isl_union_map
*prox
;
2209 isl_union_map
*sched1
, *sched2
;
2210 isl_schedule
*schedule
;
2213 dom
= isl_union_set_read_from_str(ctx
, domain
);
2214 dep
= isl_union_map_read_from_str(ctx
, validity
);
2215 prox
= isl_union_map_read_from_str(ctx
, proximity
);
2216 schedule
= isl_union_set_compute_schedule(dom
, dep
, prox
);
2217 sched1
= isl_schedule_get_map(schedule
);
2218 isl_schedule_free(schedule
);
2220 sched2
= isl_union_map_read_from_str(ctx
, expected_sched
);
2222 equal
= isl_union_map_is_equal(sched1
, sched2
);
2223 isl_union_map_free(sched1
);
2224 isl_union_map_free(sched2
);
2229 isl_die(ctx
, isl_error_unknown
, "unexpected schedule",
2235 int test_schedule(isl_ctx
*ctx
)
2237 const char *D
, *W
, *R
, *V
, *P
, *S
;
2240 D
= "[T,N] -> { S1[t,i] : 1 <= t <= T and 2 <= i <= N - 1 }";
2241 W
= "{ S1[t,i] -> a[t,i] }";
2242 R
= "{ S1[t,i] -> a[t-1,i]; S1[t,i] -> a[t-1,i-1]; "
2243 "S1[t,i] -> a[t-1,i+1] }";
2244 S
= "{ S1[t,i] -> [t,i] }";
2245 if (test_one_schedule(ctx
, D
, W
, R
, S
, 2, 0) < 0)
2248 /* Fig. 5 of CC2008 */
2249 D
= "[N] -> { S_0[i, j] : i >= 0 and i <= -1 + N and j >= 2 and "
2251 W
= "[N] -> { S_0[i, j] -> a[i, j] : i >= 0 and i <= -1 + N and "
2252 "j >= 2 and j <= -1 + N }";
2253 R
= "[N] -> { S_0[i, j] -> a[j, i] : i >= 0 and i <= -1 + N and "
2254 "j >= 2 and j <= -1 + N; "
2255 "S_0[i, j] -> a[i, -1 + j] : i >= 0 and i <= -1 + N and "
2256 "j >= 2 and j <= -1 + N }";
2257 S
= "[N] -> { S_0[i, j] -> [0, i, 0, j, 0] }";
2258 if (test_one_schedule(ctx
, D
, W
, R
, S
, 2, 0) < 0)
2261 D
= "{ S1[i] : 0 <= i <= 10; S2[i] : 0 <= i <= 9 }";
2262 W
= "{ S1[i] -> a[i] }";
2263 R
= "{ S2[i] -> a[i+1] }";
2264 S
= "{ S1[i] -> [0,i]; S2[i] -> [1,i] }";
2265 if (test_one_schedule(ctx
, D
, W
, R
, S
, 1, 1) < 0)
2268 D
= "{ S1[i] : 0 <= i < 10; S2[i] : 0 <= i < 10 }";
2269 W
= "{ S1[i] -> a[i] }";
2270 R
= "{ S2[i] -> a[9-i] }";
2271 S
= "{ S1[i] -> [0,i]; S2[i] -> [1,i] }";
2272 if (test_one_schedule(ctx
, D
, W
, R
, S
, 1, 1) < 0)
2275 D
= "[N] -> { S1[i] : 0 <= i < N; S2[i] : 0 <= i < N }";
2276 W
= "{ S1[i] -> a[i] }";
2277 R
= "[N] -> { S2[i] -> a[N-1-i] }";
2278 S
= "{ S1[i] -> [0,i]; S2[i] -> [1,i] }";
2279 if (test_one_schedule(ctx
, D
, W
, R
, S
, 1, 1) < 0)
2282 D
= "{ S1[i] : 0 < i < 10; S2[i] : 0 <= i < 10 }";
2283 W
= "{ S1[i] -> a[i]; S2[i] -> b[i] }";
2284 R
= "{ S2[i] -> a[i]; S1[i] -> b[i-1] }";
2285 S
= "{ S1[i] -> [i,0]; S2[i] -> [i,1] }";
2286 if (test_one_schedule(ctx
, D
, W
, R
, S
, 0, 0) < 0)
2289 D
= "[N] -> { S1[i] : 1 <= i <= N; S2[i,j] : 1 <= i,j <= N }";
2290 W
= "{ S1[i] -> a[0,i]; S2[i,j] -> a[i,j] }";
2291 R
= "{ S2[i,j] -> a[i-1,j] }";
2292 S
= "{ S1[i] -> [0,i,0]; S2[i,j] -> [1,i,j] }";
2293 if (test_one_schedule(ctx
, D
, W
, R
, S
, 2, 1) < 0)
2296 D
= "[N] -> { S1[i] : 1 <= i <= N; S2[i,j] : 1 <= i,j <= N }";
2297 W
= "{ S1[i] -> a[i,0]; S2[i,j] -> a[i,j] }";
2298 R
= "{ S2[i,j] -> a[i,j-1] }";
2299 S
= "{ S1[i] -> [0,i,0]; S2[i,j] -> [1,i,j] }";
2300 if (test_one_schedule(ctx
, D
, W
, R
, S
, 2, 1) < 0)
2303 D
= "[N] -> { S_0[]; S_1[i] : i >= 0 and i <= -1 + N; S_2[] }";
2304 W
= "[N] -> { S_0[] -> a[0]; S_2[] -> b[0]; "
2305 "S_1[i] -> a[1 + i] : i >= 0 and i <= -1 + N }";
2306 R
= "[N] -> { S_2[] -> a[N]; S_1[i] -> a[i] : i >= 0 and i <= -1 + N }";
2307 S
= "[N] -> { S_1[i] -> [1, i, 0]; S_2[] -> [2, 0, 1]; "
2308 "S_0[] -> [0, 0, 0] }";
2309 if (test_one_schedule(ctx
, D
, W
, R
, S
, 1, 0) < 0)
2311 ctx
->opt
->schedule_parametric
= 0;
2312 if (test_one_schedule(ctx
, D
, W
, R
, S
, 0, 0) < 0)
2314 ctx
->opt
->schedule_parametric
= 1;
2316 D
= "[N] -> { S1[i] : 1 <= i <= N; S2[i] : 1 <= i <= N; "
2317 "S3[i,j] : 1 <= i,j <= N; S4[i] : 1 <= i <= N }";
2318 W
= "{ S1[i] -> a[i,0]; S2[i] -> a[0,i]; S3[i,j] -> a[i,j] }";
2319 R
= "[N] -> { S3[i,j] -> a[i-1,j]; S3[i,j] -> a[i,j-1]; "
2320 "S4[i] -> a[i,N] }";
2321 S
= "{ S1[i] -> [0,i,0]; S2[i] -> [1,i,0]; S3[i,j] -> [2,i,j]; "
2322 "S4[i] -> [4,i,0] }";
2323 if (test_one_schedule(ctx
, D
, W
, R
, S
, 2, 0) < 0)
2326 D
= "[N] -> { S_0[i, j] : i >= 1 and i <= N and j >= 1 and j <= N }";
2327 W
= "[N] -> { S_0[i, j] -> s[0] : i >= 1 and i <= N and j >= 1 and "
2329 R
= "[N] -> { S_0[i, j] -> s[0] : i >= 1 and i <= N and j >= 1 and "
2331 "S_0[i, j] -> a[i, j] : i >= 1 and i <= N and j >= 1 and "
2333 S
= "[N] -> { S_0[i, j] -> [0, i, 0, j, 0] }";
2334 if (test_one_schedule(ctx
, D
, W
, R
, S
, 0, 0) < 0)
2337 D
= "[N] -> { S_0[t] : t >= 0 and t <= -1 + N; "
2338 " S_2[t] : t >= 0 and t <= -1 + N; "
2339 " S_1[t, i] : t >= 0 and t <= -1 + N and i >= 0 and "
2341 W
= "[N] -> { S_0[t] -> a[t, 0] : t >= 0 and t <= -1 + N; "
2342 " S_2[t] -> b[t] : t >= 0 and t <= -1 + N; "
2343 " S_1[t, i] -> a[t, 1 + i] : t >= 0 and t <= -1 + N and "
2344 "i >= 0 and i <= -1 + N }";
2345 R
= "[N] -> { S_1[t, i] -> a[t, i] : t >= 0 and t <= -1 + N and "
2346 "i >= 0 and i <= -1 + N; "
2347 " S_2[t] -> a[t, N] : t >= 0 and t <= -1 + N }";
2348 S
= "[N] -> { S_2[t] -> [0, t, 2]; S_1[t, i] -> [0, t, 1, i, 0]; "
2349 " S_0[t] -> [0, t, 0] }";
2351 if (test_one_schedule(ctx
, D
, W
, R
, S
, 2, 1) < 0)
2353 ctx
->opt
->schedule_parametric
= 0;
2354 if (test_one_schedule(ctx
, D
, W
, R
, S
, 0, 0) < 0)
2356 ctx
->opt
->schedule_parametric
= 1;
2358 D
= "[N] -> { S1[i,j] : 0 <= i,j < N; S2[i,j] : 0 <= i,j < N }";
2359 S
= "{ S1[i,j] -> [0,i,j]; S2[i,j] -> [1,i,j] }";
2360 if (test_one_schedule(ctx
, D
, "{}", "{}", S
, 2, 2) < 0)
2363 D
= "[M, N] -> { S_1[i] : i >= 0 and i <= -1 + M; "
2364 "S_0[i, j] : i >= 0 and i <= -1 + M and j >= 0 and j <= -1 + N }";
2365 W
= "[M, N] -> { S_0[i, j] -> a[j] : i >= 0 and i <= -1 + M and "
2366 "j >= 0 and j <= -1 + N; "
2367 "S_1[i] -> b[0] : i >= 0 and i <= -1 + M }";
2368 R
= "[M, N] -> { S_0[i, j] -> a[0] : i >= 0 and i <= -1 + M and "
2369 "j >= 0 and j <= -1 + N; "
2370 "S_1[i] -> b[0] : i >= 0 and i <= -1 + M }";
2371 S
= "[M, N] -> { S_1[i] -> [1, i, 0]; S_0[i, j] -> [0, i, 0, j, 0] }";
2372 if (test_one_schedule(ctx
, D
, W
, R
, S
, 0, 0) < 0)
2375 D
= "{ S_0[i] : i >= 0 }";
2376 W
= "{ S_0[i] -> a[i] : i >= 0 }";
2377 R
= "{ S_0[i] -> a[0] : i >= 0 }";
2378 S
= "{ S_0[i] -> [0, i, 0] }";
2379 if (test_one_schedule(ctx
, D
, W
, R
, S
, 0, 0) < 0)
2382 D
= "{ S_0[i] : i >= 0; S_1[i] : i >= 0 }";
2383 W
= "{ S_0[i] -> a[i] : i >= 0; S_1[i] -> b[i] : i >= 0 }";
2384 R
= "{ S_0[i] -> b[0] : i >= 0; S_1[i] -> a[i] : i >= 0 }";
2385 S
= "{ S_1[i] -> [0, i, 1]; S_0[i] -> [0, i, 0] }";
2386 if (test_one_schedule(ctx
, D
, W
, R
, S
, 0, 0) < 0)
2389 D
= "[n] -> { S_0[j, k] : j <= -1 + n and j >= 0 and "
2390 "k <= -1 + n and k >= 0 }";
2391 W
= "[n] -> { S_0[j, k] -> B[j] : j <= -1 + n and j >= 0 and " "k <= -1 + n and k >= 0 }";
2392 R
= "[n] -> { S_0[j, k] -> B[j] : j <= -1 + n and j >= 0 and "
2393 "k <= -1 + n and k >= 0; "
2394 "S_0[j, k] -> B[k] : j <= -1 + n and j >= 0 and "
2395 "k <= -1 + n and k >= 0; "
2396 "S_0[j, k] -> A[k] : j <= -1 + n and j >= 0 and "
2397 "k <= -1 + n and k >= 0 }";
2398 S
= "[n] -> { S_0[j, k] -> [2, j, k] }";
2399 ctx
->opt
->schedule_outer_zero_distance
= 1;
2400 if (test_one_schedule(ctx
, D
, W
, R
, S
, 0, 0) < 0)
2402 ctx
->opt
->schedule_outer_zero_distance
= 0;
2404 D
= "{Stmt_for_body24[i0, i1, i2, i3]:"
2405 "i0 >= 0 and i0 <= 1 and i1 >= 0 and i1 <= 6 and i2 >= 2 and "
2406 "i2 <= 6 - i1 and i3 >= 0 and i3 <= -1 + i2;"
2407 "Stmt_for_body24[i0, i1, 1, 0]:"
2408 "i0 >= 0 and i0 <= 1 and i1 >= 0 and i1 <= 5;"
2409 "Stmt_for_body7[i0, i1, i2]:"
2410 "i0 >= 0 and i0 <= 1 and i1 >= 0 and i1 <= 7 and i2 >= 0 and "
2413 V
= "{Stmt_for_body24[0, i1, i2, i3] -> "
2414 "Stmt_for_body24[1, i1, i2, i3]:"
2415 "i3 >= 0 and i3 <= -1 + i2 and i1 >= 0 and i2 <= 6 - i1 and "
2417 "Stmt_for_body24[0, i1, i2, i3] -> "
2418 "Stmt_for_body7[1, 1 + i1 + i3, 1 + i1 + i2]:"
2419 "i3 <= -1 + i2 and i2 <= 6 - i1 and i2 >= 1 and i1 >= 0 and "
2421 "Stmt_for_body24[0, i1, i2, i3] ->"
2422 "Stmt_for_body7[1, i1, 1 + i1 + i3]:"
2423 "i3 >= 0 and i2 <= 6 - i1 and i1 >= 0 and i3 <= -1 + i2;"
2424 "Stmt_for_body7[0, i1, i2] -> Stmt_for_body7[1, i1, i2]:"
2425 "(i2 >= 1 + i1 and i2 <= 6 and i1 >= 0 and i1 <= 4) or "
2426 "(i2 >= 3 and i2 <= 7 and i1 >= 1 and i2 >= 1 + i1) or "
2427 "(i2 >= 0 and i2 <= i1 and i2 >= -7 + i1 and i1 <= 7);"
2428 "Stmt_for_body7[0, i1, 1 + i1] -> Stmt_for_body7[1, i1, 1 + i1]:"
2429 "i1 <= 6 and i1 >= 0;"
2430 "Stmt_for_body7[0, 0, 7] -> Stmt_for_body7[1, 0, 7];"
2431 "Stmt_for_body7[i0, i1, i2] -> "
2432 "Stmt_for_body24[i0, o1, -1 + i2 - o1, -1 + i1 - o1]:"
2433 "i0 >= 0 and i0 <= 1 and o1 >= 0 and i2 >= 1 + i1 and "
2434 "o1 <= -2 + i2 and i2 <= 7 and o1 <= -1 + i1;"
2435 "Stmt_for_body7[i0, i1, i2] -> "
2436 "Stmt_for_body24[i0, i1, o2, -1 - i1 + i2]:"
2437 "i0 >= 0 and i0 <= 1 and i1 >= 0 and o2 >= -i1 + i2 and "
2438 "o2 >= 1 and o2 <= 6 - i1 and i2 >= 1 + i1 }";
2440 S
= "{ Stmt_for_body24[i0, i1, i2, i3] -> "
2441 "[i0, 5i0 + i1, 6i0 + i1 + i2, 1 + 6i0 + i1 + i2 + i3, 1];"
2442 "Stmt_for_body7[i0, i1, i2] -> [0, 5i0, 6i0 + i1, 6i0 + i2, 0] }";
2444 if (test_special_schedule(ctx
, D
, V
, P
, S
) < 0)
2447 D
= "{ S_0[i, j] : i >= 1 and i <= 10 and j >= 1 and j <= 8 }";
2448 V
= "{ S_0[i, j] -> S_0[i, 1 + j] : i >= 1 and i <= 10 and "
2449 "j >= 1 and j <= 7;"
2450 "S_0[i, j] -> S_0[1 + i, j] : i >= 1 and i <= 9 and "
2451 "j >= 1 and j <= 8 }";
2453 S
= "{ S_0[i, j] -> [i + j, j] }";
2454 ctx
->opt
->schedule_algorithm
= ISL_SCHEDULE_ALGORITHM_FEAUTRIER
;
2455 if (test_special_schedule(ctx
, D
, V
, P
, S
) < 0)
2457 ctx
->opt
->schedule_algorithm
= ISL_SCHEDULE_ALGORITHM_ISL
;
2459 /* Fig. 1 from Feautrier's "Some Efficient Solutions..." pt. 2, 1992 */
2460 D
= "[N] -> { S_0[i, j] : i >= 0 and i <= -1 + N and "
2461 "j >= 0 and j <= -1 + i }";
2462 V
= "[N] -> { S_0[i, j] -> S_0[i, 1 + j] : j <= -2 + i and "
2463 "i <= -1 + N and j >= 0;"
2464 "S_0[i, -1 + i] -> S_0[1 + i, 0] : i >= 1 and "
2467 S
= "{ S_0[i, j] -> [i, j] }";
2468 ctx
->opt
->schedule_algorithm
= ISL_SCHEDULE_ALGORITHM_FEAUTRIER
;
2469 if (test_special_schedule(ctx
, D
, V
, P
, S
) < 0)
2471 ctx
->opt
->schedule_algorithm
= ISL_SCHEDULE_ALGORITHM_ISL
;
2473 /* Test both algorithms on a case with only proximity dependences. */
2474 D
= "{ S[i,j] : 0 <= i <= 10 }";
2476 P
= "{ S[i,j] -> S[i+1,j] : 0 <= i,j <= 10 }";
2477 S
= "{ S[i, j] -> [j, i] }";
2478 ctx
->opt
->schedule_algorithm
= ISL_SCHEDULE_ALGORITHM_FEAUTRIER
;
2479 if (test_special_schedule(ctx
, D
, V
, P
, S
) < 0)
2481 ctx
->opt
->schedule_algorithm
= ISL_SCHEDULE_ALGORITHM_ISL
;
2482 return test_special_schedule(ctx
, D
, V
, P
, S
);
2485 int test_plain_injective(isl_ctx
*ctx
, const char *str
, int injective
)
2487 isl_union_map
*umap
;
2490 umap
= isl_union_map_read_from_str(ctx
, str
);
2491 test
= isl_union_map_plain_is_injective(umap
);
2492 isl_union_map_free(umap
);
2495 if (test
== injective
)
2498 isl_die(ctx
, isl_error_unknown
,
2499 "map not detected as injective", return -1);
2501 isl_die(ctx
, isl_error_unknown
,
2502 "map detected as injective", return -1);
2505 int test_injective(isl_ctx
*ctx
)
2509 if (test_plain_injective(ctx
, "{S[i,j] -> A[0]; T[i,j] -> B[1]}", 0))
2511 if (test_plain_injective(ctx
, "{S[] -> A[0]; T[] -> B[0]}", 1))
2513 if (test_plain_injective(ctx
, "{S[] -> A[0]; T[] -> A[1]}", 1))
2515 if (test_plain_injective(ctx
, "{S[] -> A[0]; T[] -> A[0]}", 0))
2517 if (test_plain_injective(ctx
, "{S[i] -> A[i,0]; T[i] -> A[i,1]}", 1))
2519 if (test_plain_injective(ctx
, "{S[i] -> A[i]; T[i] -> A[i]}", 0))
2521 if (test_plain_injective(ctx
, "{S[] -> A[0,0]; T[] -> A[0,1]}", 1))
2523 if (test_plain_injective(ctx
, "{S[] -> A[0,0]; T[] -> A[1,0]}", 1))
2526 str
= "{S[] -> A[0,0]; T[] -> A[0,1]; U[] -> A[1,0]}";
2527 if (test_plain_injective(ctx
, str
, 1))
2529 str
= "{S[] -> A[0,0]; T[] -> A[0,1]; U[] -> A[0,0]}";
2530 if (test_plain_injective(ctx
, str
, 0))
2536 static int aff_plain_is_equal(__isl_keep isl_aff
*aff
, const char *str
)
2544 aff2
= isl_aff_read_from_str(isl_aff_get_ctx(aff
), str
);
2545 equal
= isl_aff_plain_is_equal(aff
, aff2
);
2551 static int aff_check_plain_equal(__isl_keep isl_aff
*aff
, const char *str
)
2555 equal
= aff_plain_is_equal(aff
, str
);
2559 isl_die(isl_aff_get_ctx(aff
), isl_error_unknown
,
2560 "result not as expected", return -1);
2564 int test_aff(isl_ctx
*ctx
)
2569 isl_local_space
*ls
;
2573 space
= isl_space_set_alloc(ctx
, 0, 1);
2574 ls
= isl_local_space_from_space(space
);
2575 aff
= isl_aff_zero_on_domain(ls
);
2577 aff
= isl_aff_add_coefficient_si(aff
, isl_dim_in
, 0, 1);
2578 aff
= isl_aff_scale_down_ui(aff
, 3);
2579 aff
= isl_aff_floor(aff
);
2580 aff
= isl_aff_add_coefficient_si(aff
, isl_dim_in
, 0, 1);
2581 aff
= isl_aff_scale_down_ui(aff
, 2);
2582 aff
= isl_aff_floor(aff
);
2583 aff
= isl_aff_add_coefficient_si(aff
, isl_dim_in
, 0, 1);
2586 set
= isl_set_read_from_str(ctx
, str
);
2587 aff
= isl_aff_gist(aff
, set
);
2589 aff
= isl_aff_add_constant_si(aff
, -16);
2590 zero
= isl_aff_plain_is_zero(aff
);
2596 isl_die(ctx
, isl_error_unknown
, "unexpected result", return -1);
2598 aff
= isl_aff_read_from_str(ctx
, "{ [-1] }");
2599 aff
= isl_aff_scale_down_ui(aff
, 64);
2600 aff
= isl_aff_floor(aff
);
2601 equal
= aff_check_plain_equal(aff
, "{ [-1] }");
2609 int test_dim_max(isl_ctx
*ctx
)
2613 isl_set
*set1
, *set2
;
2618 str
= "[N] -> { [i] : 0 <= i <= min(N,10) }";
2619 set
= isl_set_read_from_str(ctx
, str
);
2620 pwaff
= isl_set_dim_max(set
, 0);
2621 set1
= isl_set_from_pw_aff(pwaff
);
2622 str
= "[N] -> { [10] : N >= 10; [N] : N <= 9 and N >= 0 }";
2623 set2
= isl_set_read_from_str(ctx
, str
);
2624 equal
= isl_set_is_equal(set1
, set2
);
2630 isl_die(ctx
, isl_error_unknown
, "unexpected result", return -1);
2632 str
= "[N] -> { [i] : 0 <= i <= max(2N,N+6) }";
2633 set
= isl_set_read_from_str(ctx
, str
);
2634 pwaff
= isl_set_dim_max(set
, 0);
2635 set1
= isl_set_from_pw_aff(pwaff
);
2636 str
= "[N] -> { [6 + N] : -6 <= N <= 5; [2N] : N >= 6 }";
2637 set2
= isl_set_read_from_str(ctx
, str
);
2638 equal
= isl_set_is_equal(set1
, set2
);
2644 isl_die(ctx
, isl_error_unknown
, "unexpected result", return -1);
2646 str
= "[N] -> { [i] : 0 <= i <= 2N or 0 <= i <= N+6 }";
2647 set
= isl_set_read_from_str(ctx
, str
);
2648 pwaff
= isl_set_dim_max(set
, 0);
2649 set1
= isl_set_from_pw_aff(pwaff
);
2650 str
= "[N] -> { [6 + N] : -6 <= N <= 5; [2N] : N >= 6 }";
2651 set2
= isl_set_read_from_str(ctx
, str
);
2652 equal
= isl_set_is_equal(set1
, set2
);
2658 isl_die(ctx
, isl_error_unknown
, "unexpected result", return -1);
2660 str
= "[N,M] -> { [i,j] -> [([i/16]), i%16, ([j/16]), j%16] : "
2661 "0 <= i < N and 0 <= j < M }";
2662 map
= isl_map_read_from_str(ctx
, str
);
2663 set
= isl_map_range(map
);
2665 pwaff
= isl_set_dim_max(isl_set_copy(set
), 0);
2666 set1
= isl_set_from_pw_aff(pwaff
);
2667 str
= "[N,M] -> { [([(N-1)/16])] : M,N > 0 }";
2668 set2
= isl_set_read_from_str(ctx
, str
);
2669 equal
= isl_set_is_equal(set1
, set2
);
2673 pwaff
= isl_set_dim_max(isl_set_copy(set
), 3);
2674 set1
= isl_set_from_pw_aff(pwaff
);
2675 str
= "[N,M] -> { [t] : t = min(M-1,15) and M,N > 0 }";
2676 set2
= isl_set_read_from_str(ctx
, str
);
2677 if (equal
>= 0 && equal
)
2678 equal
= isl_set_is_equal(set1
, set2
);
2687 isl_die(ctx
, isl_error_unknown
, "unexpected result", return -1);
2692 int test_product(isl_ctx
*ctx
)
2696 isl_union_set
*uset1
, *uset2
;
2700 set
= isl_set_read_from_str(ctx
, str
);
2701 set
= isl_set_product(set
, isl_set_copy(set
));
2702 ok
= isl_set_is_wrapping(set
);
2707 isl_die(ctx
, isl_error_unknown
, "unexpected result", return -1);
2710 uset1
= isl_union_set_read_from_str(ctx
, str
);
2711 uset1
= isl_union_set_product(uset1
, isl_union_set_copy(uset1
));
2712 str
= "{ [[] -> []] }";
2713 uset2
= isl_union_set_read_from_str(ctx
, str
);
2714 ok
= isl_union_set_is_equal(uset1
, uset2
);
2715 isl_union_set_free(uset1
);
2716 isl_union_set_free(uset2
);
2720 isl_die(ctx
, isl_error_unknown
, "unexpected result", return -1);
2725 int test_equal(isl_ctx
*ctx
)
2728 isl_set
*set
, *set2
;
2732 set
= isl_set_read_from_str(ctx
, str
);
2734 set2
= isl_set_read_from_str(ctx
, str
);
2735 equal
= isl_set_is_equal(set
, set2
);
2741 isl_die(ctx
, isl_error_unknown
, "unexpected result", return -1);
2746 static int test_plain_fixed(isl_ctx
*ctx
, __isl_take isl_map
*map
,
2747 enum isl_dim_type type
, unsigned pos
, int fixed
)
2751 test
= isl_map_plain_is_fixed(map
, type
, pos
, NULL
);
2758 isl_die(ctx
, isl_error_unknown
,
2759 "map not detected as fixed", return -1);
2761 isl_die(ctx
, isl_error_unknown
,
2762 "map detected as fixed", return -1);
2765 int test_fixed(isl_ctx
*ctx
)
2770 str
= "{ [i] -> [i] }";
2771 map
= isl_map_read_from_str(ctx
, str
);
2772 if (test_plain_fixed(ctx
, map
, isl_dim_out
, 0, 0))
2774 str
= "{ [i] -> [1] }";
2775 map
= isl_map_read_from_str(ctx
, str
);
2776 if (test_plain_fixed(ctx
, map
, isl_dim_out
, 0, 1))
2778 str
= "{ S_1[p1] -> [o0] : o0 = -2 and p1 >= 1 and p1 <= 7 }";
2779 map
= isl_map_read_from_str(ctx
, str
);
2780 if (test_plain_fixed(ctx
, map
, isl_dim_out
, 0, 1))
2782 map
= isl_map_read_from_str(ctx
, str
);
2783 map
= isl_map_neg(map
);
2784 if (test_plain_fixed(ctx
, map
, isl_dim_out
, 0, 1))
2790 int test_vertices(isl_ctx
*ctx
)
2793 isl_basic_set
*bset
;
2794 isl_vertices
*vertices
;
2796 str
= "{ A[t, i] : t = 12 and i >= 4 and i <= 12 }";
2797 bset
= isl_basic_set_read_from_str(ctx
, str
);
2798 vertices
= isl_basic_set_compute_vertices(bset
);
2799 isl_basic_set_free(bset
);
2800 isl_vertices_free(vertices
);
2804 str
= "{ A[t, i] : t = 14 and i = 1 }";
2805 bset
= isl_basic_set_read_from_str(ctx
, str
);
2806 vertices
= isl_basic_set_compute_vertices(bset
);
2807 isl_basic_set_free(bset
);
2808 isl_vertices_free(vertices
);
2815 int test_union_pw(isl_ctx
*ctx
)
2819 isl_union_set
*uset
;
2820 isl_union_pw_qpolynomial
*upwqp1
, *upwqp2
;
2822 str
= "{ [x] -> x^2 }";
2823 upwqp1
= isl_union_pw_qpolynomial_read_from_str(ctx
, str
);
2824 upwqp2
= isl_union_pw_qpolynomial_copy(upwqp1
);
2825 uset
= isl_union_pw_qpolynomial_domain(upwqp1
);
2826 upwqp1
= isl_union_pw_qpolynomial_copy(upwqp2
);
2827 upwqp1
= isl_union_pw_qpolynomial_intersect_domain(upwqp1
, uset
);
2828 equal
= isl_union_pw_qpolynomial_plain_is_equal(upwqp1
, upwqp2
);
2829 isl_union_pw_qpolynomial_free(upwqp1
);
2830 isl_union_pw_qpolynomial_free(upwqp2
);
2834 isl_die(ctx
, isl_error_unknown
, "unexpected result", return -1);
2839 int test_output(isl_ctx
*ctx
)
2847 str
= "[x] -> { [1] : x % 4 <= 2; [2] : x = 3 }";
2848 pa
= isl_pw_aff_read_from_str(ctx
, str
);
2850 p
= isl_printer_to_str(ctx
);
2851 p
= isl_printer_set_output_format(p
, ISL_FORMAT_C
);
2852 p
= isl_printer_print_pw_aff(p
, pa
);
2853 s
= isl_printer_get_str(p
);
2854 isl_printer_free(p
);
2855 isl_pw_aff_free(pa
);
2856 equal
= !strcmp(s
, "(2 - x + 4*floord(x, 4) >= 0) ? (1) : 2");
2861 isl_die(ctx
, isl_error_unknown
, "unexpected result", return -1);
2866 int test_sample(isl_ctx
*ctx
)
2869 isl_basic_set
*bset1
, *bset2
;
2872 str
= "{ [a, b, c, d, e, f, g, h, i, j, k] : "
2873 "3i >= 1073741823b - c - 1073741823e + f and c >= 0 and "
2874 "3i >= -1 + 3221225466b + c + d - 3221225466e - f and "
2875 "2e >= a - b and 3e <= 2a and 3k <= -a and f <= -1 + a and "
2876 "3i <= 4 - a + 4b + 2c - e - 2f and 3k <= -a + c - f and "
2877 "3h >= -2 + a and 3g >= -3 - a and 3k >= -2 - a and "
2878 "3i >= -2 - a - 2c + 3e + 2f and 3h <= a + c - f and "
2879 "3h >= a + 2147483646b + 2c - 2147483646e - 2f and "
2880 "3g <= -1 - a and 3i <= 1 + c + d - f and a <= 1073741823 and "
2881 "f >= 1 - a + 1073741822b + c + d - 1073741822e and "
2882 "3i >= 1 + 2b - 2c + e + 2f + 3g and "
2883 "1073741822f <= 1073741822 - a + 1073741821b + 1073741822c +"
2884 "d - 1073741821e and "
2885 "3j <= 3 - a + 3b and 3g <= -2 - 2b + c + d - e - f and "
2886 "3j >= 1 - a + b + 2e and "
2887 "3f >= -3 + a + 3221225462b + 3c + d - 3221225465e and "
2888 "3i <= 4 - a + 4b - e and "
2889 "f <= 1073741822 + 1073741822b - 1073741822e and 3h <= a and "
2890 "f >= 0 and 2e <= 4 - a + 5b - d and 2e <= a - b + d and "
2891 "c <= -1 + a and 3i >= -2 - a + 3e and "
2892 "1073741822e <= 1073741823 - a + 1073741822b + c and "
2893 "3g >= -4 + 3221225464b + 3c + d - 3221225467e - 3f and "
2894 "3i >= -1 + 3221225466b + 3c + d - 3221225466e - 3f and "
2895 "1073741823e >= 1 + 1073741823b - d and "
2896 "3i >= 1073741823b + c - 1073741823e - f and "
2897 "3i >= 1 + 2b + e + 3g }";
2898 bset1
= isl_basic_set_read_from_str(ctx
, str
);
2899 bset2
= isl_basic_set_sample(isl_basic_set_copy(bset1
));
2900 empty
= isl_basic_set_is_empty(bset2
);
2901 subset
= isl_basic_set_is_subset(bset2
, bset1
);
2902 isl_basic_set_free(bset1
);
2903 isl_basic_set_free(bset2
);
2905 isl_die(ctx
, isl_error_unknown
, "point not found", return -1);
2907 isl_die(ctx
, isl_error_unknown
, "bad point found", return -1);
2912 int test_fixed_power(isl_ctx
*ctx
)
2920 str
= "{ [i] -> [i + 1] }";
2921 map
= isl_map_read_from_str(ctx
, str
);
2922 isl_int_set_si(exp
, 23);
2923 map
= isl_map_fixed_power(map
, exp
);
2924 equal
= map_check_equal(map
, "{ [i] -> [i + 23] }");
2933 int test_slice(isl_ctx
*ctx
)
2939 str
= "{ [i] -> [j] }";
2940 map
= isl_map_read_from_str(ctx
, str
);
2941 map
= isl_map_equate(map
, isl_dim_in
, 0, isl_dim_out
, 0);
2942 equal
= map_check_equal(map
, "{ [i] -> [i] }");
2947 str
= "{ [i] -> [j] }";
2948 map
= isl_map_read_from_str(ctx
, str
);
2949 map
= isl_map_equate(map
, isl_dim_in
, 0, isl_dim_in
, 0);
2950 equal
= map_check_equal(map
, "{ [i] -> [j] }");
2955 str
= "{ [i] -> [j] }";
2956 map
= isl_map_read_from_str(ctx
, str
);
2957 map
= isl_map_oppose(map
, isl_dim_in
, 0, isl_dim_out
, 0);
2958 equal
= map_check_equal(map
, "{ [i] -> [-i] }");
2963 str
= "{ [i] -> [j] }";
2964 map
= isl_map_read_from_str(ctx
, str
);
2965 map
= isl_map_oppose(map
, isl_dim_in
, 0, isl_dim_in
, 0);
2966 equal
= map_check_equal(map
, "{ [0] -> [j] }");
2971 str
= "{ [i] -> [j] }";
2972 map
= isl_map_read_from_str(ctx
, str
);
2973 map
= isl_map_order_gt(map
, isl_dim_in
, 0, isl_dim_out
, 0);
2974 equal
= map_check_equal(map
, "{ [i] -> [j] : i > j }");
2979 str
= "{ [i] -> [j] }";
2980 map
= isl_map_read_from_str(ctx
, str
);
2981 map
= isl_map_order_gt(map
, isl_dim_in
, 0, isl_dim_in
, 0);
2982 equal
= map_check_equal(map
, "{ [i] -> [j] : false }");
2990 int test_eliminate(isl_ctx
*ctx
)
2996 str
= "{ [i] -> [j] : i = 2j }";
2997 map
= isl_map_read_from_str(ctx
, str
);
2998 map
= isl_map_eliminate(map
, isl_dim_out
, 0, 1);
2999 equal
= map_check_equal(map
, "{ [i] -> [j] : exists a : i = 2a }");
3007 int test_align_parameters(isl_ctx
*ctx
)
3011 isl_multi_aff
*ma1
, *ma2
;
3014 str
= "{ A[B[] -> C[]] -> D[E[] -> F[]] }";
3015 ma1
= isl_multi_aff_read_from_str(ctx
, str
);
3017 space
= isl_space_params_alloc(ctx
, 1);
3018 space
= isl_space_set_dim_name(space
, isl_dim_param
, 0, "N");
3019 ma1
= isl_multi_aff_align_params(ma1
, space
);
3021 str
= "[N] -> { A[B[] -> C[]] -> D[E[] -> F[]] }";
3022 ma2
= isl_multi_aff_read_from_str(ctx
, str
);
3024 equal
= isl_multi_aff_plain_is_equal(ma1
, ma2
);
3026 isl_multi_aff_free(ma1
);
3027 isl_multi_aff_free(ma2
);
3032 isl_die(ctx
, isl_error_unknown
,
3033 "result not as expected", return -1);
3040 int (*fn
)(isl_ctx
*ctx
);
3042 { "align parameters", &test_align_parameters
},
3043 { "eliminate", &test_eliminate
},
3044 { "div", &test_div
},
3045 { "slice", &test_slice
},
3046 { "fixed power", &test_fixed_power
},
3047 { "sample", &test_sample
},
3048 { "output", &test_output
},
3049 { "vertices", &test_vertices
},
3050 { "fixed", &test_fixed
},
3051 { "equal", &test_equal
},
3052 { "product", &test_product
},
3053 { "dim_max", &test_dim_max
},
3054 { "affine", &test_aff
},
3055 { "injective", &test_injective
},
3056 { "schedule", &test_schedule
},
3057 { "union_pw", &test_union_pw
},
3058 { "parse", &test_parse
},
3059 { "single-valued", &test_sv
},
3060 { "affine hull", &test_affine_hull
},
3061 { "coalesce", &test_coalesce
},
3062 { "factorize", &test_factorize
},
3068 struct isl_ctx
*ctx
;
3070 srcdir
= getenv("srcdir");
3073 ctx
= isl_ctx_alloc();
3074 for (i
= 0; i
< ARRAY_SIZE(tests
); ++i
) {
3075 printf("%s\n", tests
[i
].name
);
3076 if (tests
[i
].fn(ctx
) < 0)
3083 test_split_periods(ctx
);
3086 test_bijective(ctx
);
3090 test_construction(ctx
);
3092 test_application(ctx
);
3093 test_convex_hull(ctx
);