2 * Copyright 2008-2009 Katholieke Universiteit Leuven
4 * Use of this software is governed by the GNU LGPLv2.1 license
6 * Written by Sven Verdoolaege, K.U.Leuven, Departement
7 * Computerwetenschappen, Celestijnenlaan 200A, B-3001 Leuven, Belgium
13 #include <isl_ctx_private.h>
14 #include <isl_map_private.h>
18 #include <isl/constraint.h>
19 #include <isl/polynomial.h>
20 #include <isl/union_map.h>
21 #include <isl_factorization.h>
22 #include <isl/schedule.h>
23 #include <isl_options_private.h>
24 #include <isl/vertices.h>
28 static char *get_filename(isl_ctx
*ctx
, const char *name
, const char *suffix
) {
31 char *pattern
= "%s/test_inputs/%s.%s";
33 length
= strlen(pattern
) - 6 + strlen(srcdir
) + strlen(name
)
35 filename
= isl_alloc_array(ctx
, char, length
);
40 sprintf(filename
, pattern
, srcdir
, name
, suffix
);
45 void test_parse_map(isl_ctx
*ctx
, const char *str
)
49 map
= isl_map_read_from_str(ctx
, str
);
54 void test_parse_map_equal(isl_ctx
*ctx
, const char *str
, const char *str2
)
58 map
= isl_map_read_from_str(ctx
, str
);
59 map2
= isl_map_read_from_str(ctx
, str2
);
60 assert(map
&& map2
&& isl_map_is_equal(map
, map2
));
65 void test_parse_pwqp(isl_ctx
*ctx
, const char *str
)
67 isl_pw_qpolynomial
*pwqp
;
69 pwqp
= isl_pw_qpolynomial_read_from_str(ctx
, str
);
71 isl_pw_qpolynomial_free(pwqp
);
74 static void test_parse_pwaff(isl_ctx
*ctx
, const char *str
)
78 pwaff
= isl_pw_aff_read_from_str(ctx
, str
);
80 isl_pw_aff_free(pwaff
);
83 void test_parse(struct isl_ctx
*ctx
)
86 const char *str
, *str2
;
88 str
= "{ [i] -> [-i] }";
89 map
= isl_map_read_from_str(ctx
, str
);
93 str
= "{ A[i] -> L[([i/3])] }";
94 map
= isl_map_read_from_str(ctx
, str
);
98 test_parse_map(ctx
, "{[[s] -> A[i]] -> [[s+1] -> A[i]]}");
99 test_parse_map(ctx
, "{ [p1, y1, y2] -> [2, y1, y2] : "
100 "p1 = 1 && (y1 <= y2 || y2 = 0) }");
102 str
= "{ [x,y] : [([x/2]+y)/3] >= 1 }";
103 str2
= "{ [x, y] : 2y >= 6 - x }";
104 test_parse_map_equal(ctx
, str
, str2
);
106 test_parse_map_equal(ctx
, "{ [x,y] : x <= min(y, 2*y+3) }",
107 "{ [x,y] : x <= y, 2*y + 3 }");
108 str
= "{ [x, y] : (y <= x and y >= -3) or (2y <= -3 + x and y <= -4) }";
109 test_parse_map_equal(ctx
, "{ [x,y] : x >= min(y, 2*y+3) }", str
);
111 str
= "{[new,old] -> [new+1-2*[(new+1)/2],old+1-2*[(old+1)/2]]}";
112 map
= isl_map_read_from_str(ctx
, str
);
113 str
= "{ [new, old] -> [o0, o1] : "
114 "exists (e0 = [(-1 - new + o0)/2], e1 = [(-1 - old + o1)/2]: "
115 "2e0 = -1 - new + o0 and 2e1 = -1 - old + o1 and o0 >= 0 and "
116 "o0 <= 1 and o1 >= 0 and o1 <= 1) }";
117 map2
= isl_map_read_from_str(ctx
, str
);
118 assert(isl_map_is_equal(map
, map2
));
122 str
= "{[new,old] -> [new+1-2*[(new+1)/2],old+1-2*[(old+1)/2]]}";
123 map
= isl_map_read_from_str(ctx
, str
);
124 str
= "{[new,old] -> [(new+1)%2,(old+1)%2]}";
125 map2
= isl_map_read_from_str(ctx
, str
);
126 assert(isl_map_is_equal(map
, map2
));
130 str
= "[n] -> { [c1] : c1>=0 and c1<=floord(n-4,3) }";
131 str2
= "[n] -> { [c1] : c1 >= 0 and 3c1 <= -4 + n }";
132 test_parse_map_equal(ctx
, str
, str2
);
134 str
= "{ [i,j] -> [i] : i < j; [i,j] -> [j] : j <= i }";
135 str2
= "{ [i,j] -> [min(i,j)] }";
136 test_parse_map_equal(ctx
, str
, str2
);
138 str
= "{ [i,j] : i != j }";
139 str2
= "{ [i,j] : i < j or i > j }";
140 test_parse_map_equal(ctx
, str
, str2
);
142 str
= "{ [i,j] : (i+1)*2 >= j }";
143 str2
= "{ [i, j] : j <= 2 + 2i }";
144 test_parse_map_equal(ctx
, str
, str2
);
146 str
= "{ [i] -> [i > 0 ? 4 : 5] }";
147 str2
= "{ [i] -> [5] : i <= 0; [i] -> [4] : i >= 1 }";
148 test_parse_map_equal(ctx
, str
, str2
);
150 str
= "[N=2,M] -> { [i=[(M+N)/4]] }";
151 str2
= "[N, M] -> { [i] : N = 2 and 4i <= 2 + M and 4i >= -1 + M }";
152 test_parse_map_equal(ctx
, str
, str2
);
154 str
= "{ [x] : x >= 0 }";
155 str2
= "{ [x] : x-0 >= 0 }";
156 test_parse_map_equal(ctx
, str
, str2
);
158 str
= "{ [i] : ((i > 10)) }";
159 str2
= "{ [i] : i >= 11 }";
160 test_parse_map_equal(ctx
, str
, str2
);
162 str
= "{ [i] -> [0] }";
163 str2
= "{ [i] -> [0 * i] }";
164 test_parse_map_equal(ctx
, str
, str2
);
166 test_parse_pwqp(ctx
, "{ [i] -> i + [ (i + [i/3])/2 ] }");
167 test_parse_map(ctx
, "{ S1[i] -> [([i/10]),i%10] : 0 <= i <= 45 }");
168 test_parse_pwaff(ctx
, "{ [i] -> [i + 1] : i > 0; [a] -> [a] : a < 0 }");
169 test_parse_pwqp(ctx
, "{ [x] -> ([(x)/2] * [(x)/3]) }");
172 void test_read(struct isl_ctx
*ctx
)
176 struct isl_basic_set
*bset1
, *bset2
;
177 const char *str
= "{[y]: Exists ( alpha : 2alpha = y)}";
179 filename
= get_filename(ctx
, "set", "omega");
181 input
= fopen(filename
, "r");
184 bset1
= isl_basic_set_read_from_file(ctx
, input
);
185 bset2
= isl_basic_set_read_from_str(ctx
, str
);
187 assert(isl_basic_set_is_equal(bset1
, bset2
) == 1);
189 isl_basic_set_free(bset1
);
190 isl_basic_set_free(bset2
);
196 void test_bounded(struct isl_ctx
*ctx
)
201 set
= isl_set_read_from_str(ctx
, "[n] -> {[i] : 0 <= i <= n }");
202 bounded
= isl_set_is_bounded(set
);
206 set
= isl_set_read_from_str(ctx
, "{[n, i] : 0 <= i <= n }");
207 bounded
= isl_set_is_bounded(set
);
211 set
= isl_set_read_from_str(ctx
, "[n] -> {[i] : i <= n }");
212 bounded
= isl_set_is_bounded(set
);
217 /* Construct the basic set { [i] : 5 <= i <= N } */
218 void test_construction(struct isl_ctx
*ctx
)
223 struct isl_basic_set
*bset
;
224 struct isl_constraint
*c
;
228 dim
= isl_space_set_alloc(ctx
, 1, 1);
229 bset
= isl_basic_set_universe(isl_space_copy(dim
));
230 ls
= isl_local_space_from_space(dim
);
232 c
= isl_inequality_alloc(isl_local_space_copy(ls
));
233 isl_int_set_si(v
, -1);
234 isl_constraint_set_coefficient(c
, isl_dim_set
, 0, v
);
235 isl_int_set_si(v
, 1);
236 isl_constraint_set_coefficient(c
, isl_dim_param
, 0, v
);
237 bset
= isl_basic_set_add_constraint(bset
, c
);
239 c
= isl_inequality_alloc(isl_local_space_copy(ls
));
240 isl_int_set_si(v
, 1);
241 isl_constraint_set_coefficient(c
, isl_dim_set
, 0, v
);
242 isl_int_set_si(v
, -5);
243 isl_constraint_set_constant(c
, v
);
244 bset
= isl_basic_set_add_constraint(bset
, c
);
246 isl_local_space_free(ls
);
247 isl_basic_set_free(bset
);
252 void test_dim(struct isl_ctx
*ctx
)
255 isl_map
*map1
, *map2
;
257 map1
= isl_map_read_from_str(ctx
,
258 "[n] -> { [i] -> [j] : exists (a = [i/10] : i - 10a <= n ) }");
259 map1
= isl_map_add_dims(map1
, isl_dim_in
, 1);
260 map2
= isl_map_read_from_str(ctx
,
261 "[n] -> { [i,k] -> [j] : exists (a = [i/10] : i - 10a <= n ) }");
262 assert(isl_map_is_equal(map1
, map2
));
265 map1
= isl_map_project_out(map1
, isl_dim_in
, 0, 1);
266 map2
= isl_map_read_from_str(ctx
, "[n] -> { [i] -> [j] : n >= 0 }");
267 assert(isl_map_is_equal(map1
, map2
));
272 str
= "[n] -> { [i] -> [] : exists a : 0 <= i <= n and i = 2 a }";
273 map1
= isl_map_read_from_str(ctx
, str
);
274 str
= "{ [i] -> [j] : exists a : 0 <= i <= j and i = 2 a }";
275 map2
= isl_map_read_from_str(ctx
, str
);
276 map1
= isl_map_move_dims(map1
, isl_dim_out
, 0, isl_dim_param
, 0, 1);
277 assert(isl_map_is_equal(map1
, map2
));
283 void test_div(struct isl_ctx
*ctx
)
288 struct isl_basic_set
*bset
;
289 struct isl_constraint
*c
;
294 dim
= isl_space_set_alloc(ctx
, 0, 3);
295 bset
= isl_basic_set_universe(isl_space_copy(dim
));
296 ls
= isl_local_space_from_space(dim
);
298 c
= isl_equality_alloc(isl_local_space_copy(ls
));
299 isl_int_set_si(v
, -1);
300 isl_constraint_set_constant(c
, v
);
301 isl_int_set_si(v
, 1);
302 isl_constraint_set_coefficient(c
, isl_dim_set
, 0, v
);
303 isl_int_set_si(v
, 3);
304 isl_constraint_set_coefficient(c
, isl_dim_set
, 1, v
);
305 bset
= isl_basic_set_add_constraint(bset
, c
);
307 c
= isl_equality_alloc(isl_local_space_copy(ls
));
308 isl_int_set_si(v
, 1);
309 isl_constraint_set_constant(c
, v
);
310 isl_int_set_si(v
, -1);
311 isl_constraint_set_coefficient(c
, isl_dim_set
, 0, v
);
312 isl_int_set_si(v
, 3);
313 isl_constraint_set_coefficient(c
, isl_dim_set
, 2, v
);
314 bset
= isl_basic_set_add_constraint(bset
, c
);
316 bset
= isl_basic_set_project_out(bset
, isl_dim_set
, 1, 2);
318 assert(bset
&& bset
->n_div
== 1);
319 isl_local_space_free(ls
);
320 isl_basic_set_free(bset
);
323 dim
= isl_space_set_alloc(ctx
, 0, 3);
324 bset
= isl_basic_set_universe(isl_space_copy(dim
));
325 ls
= isl_local_space_from_space(dim
);
327 c
= isl_equality_alloc(isl_local_space_copy(ls
));
328 isl_int_set_si(v
, 1);
329 isl_constraint_set_constant(c
, v
);
330 isl_int_set_si(v
, -1);
331 isl_constraint_set_coefficient(c
, isl_dim_set
, 0, v
);
332 isl_int_set_si(v
, 3);
333 isl_constraint_set_coefficient(c
, isl_dim_set
, 1, v
);
334 bset
= isl_basic_set_add_constraint(bset
, c
);
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
, 2, v
);
343 bset
= isl_basic_set_add_constraint(bset
, c
);
345 bset
= isl_basic_set_project_out(bset
, isl_dim_set
, 1, 2);
347 assert(bset
&& bset
->n_div
== 1);
348 isl_local_space_free(ls
);
349 isl_basic_set_free(bset
);
352 dim
= isl_space_set_alloc(ctx
, 0, 3);
353 bset
= isl_basic_set_universe(isl_space_copy(dim
));
354 ls
= isl_local_space_from_space(dim
);
356 c
= isl_equality_alloc(isl_local_space_copy(ls
));
357 isl_int_set_si(v
, 1);
358 isl_constraint_set_constant(c
, v
);
359 isl_int_set_si(v
, -1);
360 isl_constraint_set_coefficient(c
, isl_dim_set
, 0, v
);
361 isl_int_set_si(v
, 3);
362 isl_constraint_set_coefficient(c
, isl_dim_set
, 1, v
);
363 bset
= isl_basic_set_add_constraint(bset
, c
);
365 c
= isl_equality_alloc(isl_local_space_copy(ls
));
366 isl_int_set_si(v
, -3);
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
, 4);
371 isl_constraint_set_coefficient(c
, isl_dim_set
, 2, v
);
372 bset
= isl_basic_set_add_constraint(bset
, c
);
374 bset
= isl_basic_set_project_out(bset
, isl_dim_set
, 1, 2);
376 assert(bset
&& bset
->n_div
== 1);
377 isl_local_space_free(ls
);
378 isl_basic_set_free(bset
);
381 dim
= isl_space_set_alloc(ctx
, 0, 3);
382 bset
= isl_basic_set_universe(isl_space_copy(dim
));
383 ls
= isl_local_space_from_space(dim
);
385 c
= isl_equality_alloc(isl_local_space_copy(ls
));
386 isl_int_set_si(v
, 2);
387 isl_constraint_set_constant(c
, v
);
388 isl_int_set_si(v
, -1);
389 isl_constraint_set_coefficient(c
, isl_dim_set
, 0, v
);
390 isl_int_set_si(v
, 3);
391 isl_constraint_set_coefficient(c
, isl_dim_set
, 1, v
);
392 bset
= isl_basic_set_add_constraint(bset
, c
);
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
, 6);
400 isl_constraint_set_coefficient(c
, isl_dim_set
, 2, v
);
401 bset
= isl_basic_set_add_constraint(bset
, c
);
403 bset
= isl_basic_set_project_out(bset
, isl_dim_set
, 1, 2);
405 assert(isl_basic_set_is_empty(bset
));
406 isl_local_space_free(ls
);
407 isl_basic_set_free(bset
);
410 dim
= isl_space_set_alloc(ctx
, 0, 3);
411 bset
= isl_basic_set_universe(isl_space_copy(dim
));
412 ls
= isl_local_space_from_space(dim
);
414 c
= isl_equality_alloc(isl_local_space_copy(ls
));
415 isl_int_set_si(v
, -1);
416 isl_constraint_set_coefficient(c
, isl_dim_set
, 0, v
);
417 isl_int_set_si(v
, 3);
418 isl_constraint_set_coefficient(c
, isl_dim_set
, 2, v
);
419 bset
= isl_basic_set_add_constraint(bset
, c
);
421 c
= isl_equality_alloc(isl_local_space_copy(ls
));
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 bset
= isl_basic_set_project_out(bset
, isl_dim_set
, 2, 1);
430 assert(bset
&& bset
->n_div
== 0);
431 isl_basic_set_free(bset
);
432 isl_local_space_free(ls
);
435 dim
= isl_space_set_alloc(ctx
, 0, 3);
436 bset
= isl_basic_set_universe(isl_space_copy(dim
));
437 ls
= isl_local_space_from_space(dim
);
439 c
= isl_equality_alloc(isl_local_space_copy(ls
));
440 isl_int_set_si(v
, -1);
441 isl_constraint_set_coefficient(c
, isl_dim_set
, 0, v
);
442 isl_int_set_si(v
, 6);
443 isl_constraint_set_coefficient(c
, isl_dim_set
, 2, v
);
444 bset
= isl_basic_set_add_constraint(bset
, c
);
446 c
= isl_equality_alloc(isl_local_space_copy(ls
));
447 isl_int_set_si(v
, 1);
448 isl_constraint_set_coefficient(c
, isl_dim_set
, 0, v
);
449 isl_int_set_si(v
, -3);
450 isl_constraint_set_coefficient(c
, isl_dim_set
, 1, v
);
451 bset
= isl_basic_set_add_constraint(bset
, c
);
453 bset
= isl_basic_set_project_out(bset
, isl_dim_set
, 2, 1);
455 assert(bset
&& bset
->n_div
== 1);
456 isl_basic_set_free(bset
);
457 isl_local_space_free(ls
);
460 /* This test is a bit tricky. We set up an equality
462 * Normalization of divs creates _two_ divs
465 * Afterwards e0 is removed again because it has coefficient -1
466 * and we end up with the original equality and div again.
467 * Perhaps we can avoid the introduction of this temporary div.
469 dim
= isl_space_set_alloc(ctx
, 0, 4);
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
, -3);
477 isl_constraint_set_coefficient(c
, isl_dim_set
, 1, v
);
478 isl_int_set_si(v
, -3);
479 isl_constraint_set_coefficient(c
, isl_dim_set
, 2, v
);
480 isl_int_set_si(v
, 6);
481 isl_constraint_set_coefficient(c
, isl_dim_set
, 3, v
);
482 bset
= isl_basic_set_add_constraint(bset
, c
);
484 bset
= isl_basic_set_project_out(bset
, isl_dim_set
, 3, 1);
486 /* Test disabled for now */
488 assert(bset && bset->n_div == 1);
490 isl_local_space_free(ls
);
491 isl_basic_set_free(bset
);
494 dim
= isl_space_set_alloc(ctx
, 0, 5);
495 bset
= isl_basic_set_universe(isl_space_copy(dim
));
496 ls
= isl_local_space_from_space(dim
);
498 c
= isl_equality_alloc(isl_local_space_copy(ls
));
499 isl_int_set_si(v
, -1);
500 isl_constraint_set_coefficient(c
, isl_dim_set
, 0, v
);
501 isl_int_set_si(v
, -3);
502 isl_constraint_set_coefficient(c
, isl_dim_set
, 1, v
);
503 isl_int_set_si(v
, -3);
504 isl_constraint_set_coefficient(c
, isl_dim_set
, 3, v
);
505 isl_int_set_si(v
, 6);
506 isl_constraint_set_coefficient(c
, isl_dim_set
, 4, v
);
507 bset
= isl_basic_set_add_constraint(bset
, c
);
509 c
= isl_equality_alloc(isl_local_space_copy(ls
));
510 isl_int_set_si(v
, -1);
511 isl_constraint_set_coefficient(c
, isl_dim_set
, 0, v
);
512 isl_int_set_si(v
, 1);
513 isl_constraint_set_coefficient(c
, isl_dim_set
, 2, v
);
514 isl_int_set_si(v
, 1);
515 isl_constraint_set_constant(c
, v
);
516 bset
= isl_basic_set_add_constraint(bset
, c
);
518 bset
= isl_basic_set_project_out(bset
, isl_dim_set
, 4, 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, 4);
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
, -1);
536 isl_constraint_set_coefficient(c
, isl_dim_set
, 1, v
);
537 isl_int_set_si(v
, -2);
538 isl_constraint_set_coefficient(c
, isl_dim_set
, 2, v
);
539 bset
= isl_basic_set_add_constraint(bset
, c
);
541 c
= isl_equality_alloc(isl_local_space_copy(ls
));
542 isl_int_set_si(v
, -1);
543 isl_constraint_set_coefficient(c
, isl_dim_set
, 0, v
);
544 isl_int_set_si(v
, 3);
545 isl_constraint_set_coefficient(c
, isl_dim_set
, 3, v
);
546 isl_int_set_si(v
, 2);
547 isl_constraint_set_constant(c
, v
);
548 bset
= isl_basic_set_add_constraint(bset
, c
);
550 bset
= isl_basic_set_project_out(bset
, isl_dim_set
, 2, 2);
552 bset
= isl_basic_set_fix_si(bset
, isl_dim_set
, 0, 2);
554 assert(!isl_basic_set_is_empty(bset
));
556 isl_local_space_free(ls
);
557 isl_basic_set_free(bset
);
560 dim
= isl_space_set_alloc(ctx
, 0, 3);
561 bset
= isl_basic_set_universe(isl_space_copy(dim
));
562 ls
= isl_local_space_from_space(dim
);
564 c
= isl_equality_alloc(isl_local_space_copy(ls
));
565 isl_int_set_si(v
, 1);
566 isl_constraint_set_coefficient(c
, isl_dim_set
, 0, v
);
567 isl_int_set_si(v
, -2);
568 isl_constraint_set_coefficient(c
, isl_dim_set
, 2, v
);
569 bset
= isl_basic_set_add_constraint(bset
, c
);
571 bset
= isl_basic_set_project_out(bset
, isl_dim_set
, 2, 1);
573 bset
= isl_basic_set_fix_si(bset
, isl_dim_set
, 0, 2);
575 isl_local_space_free(ls
);
576 isl_basic_set_free(bset
);
581 void test_application_case(struct isl_ctx
*ctx
, const char *name
)
585 struct isl_basic_set
*bset1
, *bset2
;
586 struct isl_basic_map
*bmap
;
588 filename
= get_filename(ctx
, name
, "omega");
590 input
= fopen(filename
, "r");
593 bset1
= isl_basic_set_read_from_file(ctx
, input
);
594 bmap
= isl_basic_map_read_from_file(ctx
, input
);
596 bset1
= isl_basic_set_apply(bset1
, bmap
);
598 bset2
= isl_basic_set_read_from_file(ctx
, input
);
600 assert(isl_basic_set_is_equal(bset1
, bset2
) == 1);
602 isl_basic_set_free(bset1
);
603 isl_basic_set_free(bset2
);
609 void test_application(struct isl_ctx
*ctx
)
611 test_application_case(ctx
, "application");
612 test_application_case(ctx
, "application2");
615 void test_affine_hull_case(struct isl_ctx
*ctx
, const char *name
)
619 struct isl_basic_set
*bset1
, *bset2
;
621 filename
= get_filename(ctx
, name
, "polylib");
623 input
= fopen(filename
, "r");
626 bset1
= isl_basic_set_read_from_file(ctx
, input
);
627 bset2
= isl_basic_set_read_from_file(ctx
, input
);
629 bset1
= isl_basic_set_affine_hull(bset1
);
631 assert(isl_basic_set_is_equal(bset1
, bset2
) == 1);
633 isl_basic_set_free(bset1
);
634 isl_basic_set_free(bset2
);
640 void test_affine_hull(struct isl_ctx
*ctx
)
642 test_affine_hull_case(ctx
, "affine2");
643 test_affine_hull_case(ctx
, "affine");
644 test_affine_hull_case(ctx
, "affine3");
647 void test_convex_hull_case(struct isl_ctx
*ctx
, const char *name
)
651 struct isl_basic_set
*bset1
, *bset2
;
654 filename
= get_filename(ctx
, name
, "polylib");
656 input
= fopen(filename
, "r");
659 bset1
= isl_basic_set_read_from_file(ctx
, input
);
660 bset2
= isl_basic_set_read_from_file(ctx
, input
);
662 set
= isl_basic_set_union(bset1
, bset2
);
663 bset1
= isl_set_convex_hull(set
);
665 bset2
= isl_basic_set_read_from_file(ctx
, input
);
667 assert(isl_basic_set_is_equal(bset1
, bset2
) == 1);
669 isl_basic_set_free(bset1
);
670 isl_basic_set_free(bset2
);
676 void test_convex_hull_algo(struct isl_ctx
*ctx
, int convex
)
678 const char *str1
, *str2
;
679 isl_set
*set1
, *set2
;
680 int orig_convex
= ctx
->opt
->convex
;
681 ctx
->opt
->convex
= convex
;
683 test_convex_hull_case(ctx
, "convex0");
684 test_convex_hull_case(ctx
, "convex1");
685 test_convex_hull_case(ctx
, "convex2");
686 test_convex_hull_case(ctx
, "convex3");
687 test_convex_hull_case(ctx
, "convex4");
688 test_convex_hull_case(ctx
, "convex5");
689 test_convex_hull_case(ctx
, "convex6");
690 test_convex_hull_case(ctx
, "convex7");
691 test_convex_hull_case(ctx
, "convex8");
692 test_convex_hull_case(ctx
, "convex9");
693 test_convex_hull_case(ctx
, "convex10");
694 test_convex_hull_case(ctx
, "convex11");
695 test_convex_hull_case(ctx
, "convex12");
696 test_convex_hull_case(ctx
, "convex13");
697 test_convex_hull_case(ctx
, "convex14");
698 test_convex_hull_case(ctx
, "convex15");
700 str1
= "{ [i0, i1, i2] : (i2 = 1 and i0 = 0 and i1 >= 0) or "
701 "(i0 = 1 and i1 = 0 and i2 = 1) or "
702 "(i0 = 0 and i1 = 0 and i2 = 0) }";
703 str2
= "{ [i0, i1, i2] : i0 >= 0 and i2 >= i0 and i2 <= 1 and i1 >= 0 }";
704 set1
= isl_set_read_from_str(ctx
, str1
);
705 set2
= isl_set_read_from_str(ctx
, str2
);
706 set1
= isl_set_from_basic_set(isl_set_convex_hull(set1
));
707 assert(isl_set_is_equal(set1
, set2
));
711 ctx
->opt
->convex
= orig_convex
;
714 void test_convex_hull(struct isl_ctx
*ctx
)
716 test_convex_hull_algo(ctx
, ISL_CONVEX_HULL_FM
);
717 test_convex_hull_algo(ctx
, ISL_CONVEX_HULL_WRAP
);
720 void test_gist_case(struct isl_ctx
*ctx
, const char *name
)
724 struct isl_basic_set
*bset1
, *bset2
;
726 filename
= get_filename(ctx
, name
, "polylib");
728 input
= fopen(filename
, "r");
731 bset1
= isl_basic_set_read_from_file(ctx
, input
);
732 bset2
= isl_basic_set_read_from_file(ctx
, input
);
734 bset1
= isl_basic_set_gist(bset1
, bset2
);
736 bset2
= isl_basic_set_read_from_file(ctx
, input
);
738 assert(isl_basic_set_is_equal(bset1
, bset2
) == 1);
740 isl_basic_set_free(bset1
);
741 isl_basic_set_free(bset2
);
747 void test_gist(struct isl_ctx
*ctx
)
750 isl_basic_set
*bset1
, *bset2
;
752 test_gist_case(ctx
, "gist1");
754 str
= "[p0, p2, p3, p5, p6, p10] -> { [] : "
755 "exists (e0 = [(15 + p0 + 15p6 + 15p10)/16], e1 = [(p5)/8], "
756 "e2 = [(p6)/128], e3 = [(8p2 - p5)/128], "
757 "e4 = [(128p3 - p6)/4096]: 8e1 = p5 and 128e2 = p6 and "
758 "128e3 = 8p2 - p5 and 4096e4 = 128p3 - p6 and p2 >= 0 and "
759 "16e0 >= 16 + 16p6 + 15p10 and p2 <= 15 and p3 >= 0 and "
760 "p3 <= 31 and p6 >= 128p3 and p5 >= 8p2 and p10 >= 0 and "
761 "16e0 <= 15 + p0 + 15p6 + 15p10 and 16e0 >= p0 + 15p6 + 15p10 and "
762 "p10 <= 15 and p10 <= -1 + p0 - p6) }";
763 bset1
= isl_basic_set_read_from_str(ctx
, str
);
764 str
= "[p0, p2, p3, p5, p6, p10] -> { [] : exists (e0 = [(p5)/8], "
765 "e1 = [(p6)/128], e2 = [(8p2 - p5)/128], "
766 "e3 = [(128p3 - p6)/4096]: 8e0 = p5 and 128e1 = p6 and "
767 "128e2 = 8p2 - p5 and 4096e3 = 128p3 - p6 and p5 >= -7 and "
768 "p2 >= 0 and 8p2 <= -1 + p0 and p2 <= 15 and p3 >= 0 and "
769 "p3 <= 31 and 128p3 <= -1 + p0 and p6 >= -127 and "
770 "p5 <= -1 + p0 and p6 <= -1 + p0 and p6 >= 128p3 and "
771 "p0 >= 1 and p5 >= 8p2 and p10 >= 0 and p10 <= 15 ) }";
772 bset2
= isl_basic_set_read_from_str(ctx
, str
);
773 bset1
= isl_basic_set_gist(bset1
, bset2
);
774 assert(bset1
&& bset1
->n_div
== 0);
775 isl_basic_set_free(bset1
);
778 int test_coalesce_set(isl_ctx
*ctx
, const char *str
, int check_one
)
784 set
= isl_set_read_from_str(ctx
, str
);
785 set
= isl_set_coalesce(set
);
786 set2
= isl_set_read_from_str(ctx
, str
);
787 equal
= isl_set_is_equal(set
, set2
);
788 one
= set
&& set
->n
== 1;
795 isl_die(ctx
, isl_error_unknown
,
796 "coalesced set not equal to input", return -1);
797 if (check_one
&& !one
)
798 isl_die(ctx
, isl_error_unknown
,
799 "coalesced set should not be a union", return -1);
804 int test_coalesce(struct isl_ctx
*ctx
)
807 struct isl_set
*set
, *set2
;
808 struct isl_map
*map
, *map2
;
810 set
= isl_set_read_from_str(ctx
,
811 "{[x,y]: x >= 0 & x <= 10 & y >= 0 & y <= 10 or "
812 "y >= x & x >= 2 & 5 >= y }");
813 set
= isl_set_coalesce(set
);
814 assert(set
&& set
->n
== 1);
817 set
= isl_set_read_from_str(ctx
,
818 "{[x,y]: y >= 0 & 2x + y <= 30 & y <= 10 & x >= 0 or "
819 "x + y >= 10 & y <= x & x + y <= 20 & y >= 0}");
820 set
= isl_set_coalesce(set
);
821 assert(set
&& set
->n
== 1);
824 set
= isl_set_read_from_str(ctx
,
825 "{[x,y]: y >= 0 & 2x + y <= 30 & y <= 10 & x >= 0 or "
826 "x + y >= 10 & y <= x & x + y <= 19 & y >= 0}");
827 set
= isl_set_coalesce(set
);
828 assert(set
&& set
->n
== 2);
831 set
= isl_set_read_from_str(ctx
,
832 "{[x,y]: y >= 0 & x <= 5 & y <= x or "
833 "y >= 0 & x >= 6 & x <= 10 & y <= x}");
834 set
= isl_set_coalesce(set
);
835 assert(set
&& set
->n
== 1);
838 set
= isl_set_read_from_str(ctx
,
839 "{[x,y]: y >= 0 & x <= 5 & y <= x or "
840 "y >= 0 & x >= 7 & x <= 10 & y <= x}");
841 set
= isl_set_coalesce(set
);
842 assert(set
&& set
->n
== 2);
845 set
= isl_set_read_from_str(ctx
,
846 "{[x,y]: y >= 0 & x <= 5 & y <= x or "
847 "y >= 0 & x >= 6 & x <= 10 & y + 1 <= x}");
848 set
= isl_set_coalesce(set
);
849 assert(set
&& set
->n
== 2);
852 set
= isl_set_read_from_str(ctx
,
853 "{[x,y]: y >= 0 & x <= 5 & y <= x or "
854 "y >= 0 & x = 6 & y <= 6}");
855 set
= isl_set_coalesce(set
);
856 assert(set
&& set
->n
== 1);
859 set
= isl_set_read_from_str(ctx
,
860 "{[x,y]: y >= 0 & x <= 5 & y <= x or "
861 "y >= 0 & x = 7 & y <= 6}");
862 set
= isl_set_coalesce(set
);
863 assert(set
&& set
->n
== 2);
866 set
= isl_set_read_from_str(ctx
,
867 "{[x,y]: y >= 0 & x <= 5 & y <= x or "
868 "y >= 0 & x = 6 & y <= 5}");
869 set
= isl_set_coalesce(set
);
870 assert(set
&& set
->n
== 1);
871 set2
= isl_set_read_from_str(ctx
,
872 "{[x,y]: y >= 0 & x <= 5 & y <= x or "
873 "y >= 0 & x = 6 & y <= 5}");
874 assert(isl_set_is_equal(set
, set2
));
878 set
= isl_set_read_from_str(ctx
,
879 "{[x,y]: y >= 0 & x <= 5 & y <= x or "
880 "y >= 0 & x = 6 & y <= 7}");
881 set
= isl_set_coalesce(set
);
882 assert(set
&& set
->n
== 2);
885 set
= isl_set_read_from_str(ctx
,
886 "[n] -> { [i] : i = 1 and n >= 2 or 2 <= i and i <= n }");
887 set
= isl_set_coalesce(set
);
888 assert(set
&& set
->n
== 1);
889 set2
= isl_set_read_from_str(ctx
,
890 "[n] -> { [i] : i = 1 and n >= 2 or 2 <= i and i <= n }");
891 assert(isl_set_is_equal(set
, set2
));
895 set
= isl_set_read_from_str(ctx
,
896 "{[x,y] : x >= 0 and y >= 0 or 0 <= y and y <= 5 and x = -1}");
897 set
= isl_set_coalesce(set
);
898 set2
= isl_set_read_from_str(ctx
,
899 "{[x,y] : x >= 0 and y >= 0 or 0 <= y and y <= 5 and x = -1}");
900 assert(isl_set_is_equal(set
, set2
));
904 set
= isl_set_read_from_str(ctx
,
905 "[n] -> { [i] : 1 <= i and i <= n - 1 or "
906 "2 <= i and i <= n }");
907 set
= isl_set_coalesce(set
);
908 assert(set
&& set
->n
== 1);
909 set2
= isl_set_read_from_str(ctx
,
910 "[n] -> { [i] : 1 <= i and i <= n - 1 or "
911 "2 <= i and i <= n }");
912 assert(isl_set_is_equal(set
, set2
));
916 map
= isl_map_read_from_str(ctx
,
917 "[n] -> { [i0] -> [o0] : exists (e0 = [(i0)/4], e1 = [(o0)/4], "
918 "e2 = [(n)/2], e3 = [(-2 + i0)/4], e4 = [(-2 + o0)/4], "
919 "e5 = [(-2n + i0)/4]: 2e2 = n and 4e3 = -2 + i0 and "
920 "4e4 = -2 + o0 and i0 >= 8 + 2n and o0 >= 2 + i0 and "
921 "o0 <= 56 + 2n and o0 <= -12 + 4n and i0 <= 57 + 2n and "
922 "i0 <= -11 + 4n and o0 >= 6 + 2n and 4e0 <= i0 and "
923 "4e0 >= -3 + i0 and 4e1 <= o0 and 4e1 >= -3 + o0 and "
924 "4e5 <= -2n + i0 and 4e5 >= -3 - 2n + i0);"
925 "[i0] -> [o0] : exists (e0 = [(i0)/4], e1 = [(o0)/4], "
926 "e2 = [(n)/2], e3 = [(-2 + i0)/4], e4 = [(-2 + o0)/4], "
927 "e5 = [(-2n + i0)/4]: 2e2 = n and 4e3 = -2 + i0 and "
928 "4e4 = -2 + o0 and 2e0 >= 3 + n and e0 <= -4 + n and "
929 "2e0 <= 27 + n and e1 <= -4 + n and 2e1 <= 27 + n and "
930 "2e1 >= 2 + n and e1 >= 1 + e0 and i0 >= 7 + 2n and "
931 "i0 <= -11 + 4n and i0 <= 57 + 2n and 4e0 <= -2 + i0 and "
932 "4e0 >= -3 + i0 and o0 >= 6 + 2n and o0 <= -11 + 4n and "
933 "o0 <= 57 + 2n and 4e1 <= -2 + o0 and 4e1 >= -3 + o0 and "
934 "4e5 <= -2n + i0 and 4e5 >= -3 - 2n + i0 ) }");
935 map
= isl_map_coalesce(map
);
936 map2
= isl_map_read_from_str(ctx
,
937 "[n] -> { [i0] -> [o0] : exists (e0 = [(i0)/4], e1 = [(o0)/4], "
938 "e2 = [(n)/2], e3 = [(-2 + i0)/4], e4 = [(-2 + o0)/4], "
939 "e5 = [(-2n + i0)/4]: 2e2 = n and 4e3 = -2 + i0 and "
940 "4e4 = -2 + o0 and i0 >= 8 + 2n and o0 >= 2 + i0 and "
941 "o0 <= 56 + 2n and o0 <= -12 + 4n and i0 <= 57 + 2n and "
942 "i0 <= -11 + 4n and o0 >= 6 + 2n and 4e0 <= i0 and "
943 "4e0 >= -3 + i0 and 4e1 <= o0 and 4e1 >= -3 + o0 and "
944 "4e5 <= -2n + i0 and 4e5 >= -3 - 2n + i0);"
945 "[i0] -> [o0] : exists (e0 = [(i0)/4], e1 = [(o0)/4], "
946 "e2 = [(n)/2], e3 = [(-2 + i0)/4], e4 = [(-2 + o0)/4], "
947 "e5 = [(-2n + i0)/4]: 2e2 = n and 4e3 = -2 + i0 and "
948 "4e4 = -2 + o0 and 2e0 >= 3 + n and e0 <= -4 + n and "
949 "2e0 <= 27 + n and e1 <= -4 + n and 2e1 <= 27 + n and "
950 "2e1 >= 2 + n and e1 >= 1 + e0 and i0 >= 7 + 2n and "
951 "i0 <= -11 + 4n and i0 <= 57 + 2n and 4e0 <= -2 + i0 and "
952 "4e0 >= -3 + i0 and o0 >= 6 + 2n and o0 <= -11 + 4n and "
953 "o0 <= 57 + 2n and 4e1 <= -2 + o0 and 4e1 >= -3 + o0 and "
954 "4e5 <= -2n + i0 and 4e5 >= -3 - 2n + i0 ) }");
955 assert(isl_map_is_equal(map
, map2
));
959 str
= "[n, m] -> { [] -> [o0, o2, o3] : (o3 = 1 and o0 >= 1 + m and "
960 "o0 <= n + m and o2 <= m and o0 >= 2 + n and o2 >= 3) or "
961 "(o0 >= 2 + n and o0 >= 1 + m and o0 <= n + m and n >= 1 and "
962 "o3 <= -1 + o2 and o3 >= 1 - m + o2 and o3 >= 2 and o3 <= n) }";
963 map
= isl_map_read_from_str(ctx
, str
);
964 map
= isl_map_coalesce(map
);
965 map2
= isl_map_read_from_str(ctx
, str
);
966 assert(isl_map_is_equal(map
, map2
));
970 str
= "[M, N] -> { [i0, i1, i2, i3, i4, i5, i6] -> "
971 "[o0, o1, o2, o3, o4, o5, o6] : "
972 "(o6 <= -4 + 2M - 2N + i0 + i1 - i2 + i6 - o0 - o1 + o2 and "
973 "o3 <= -2 + i3 and o6 >= 2 + i0 + i3 + i6 - o0 - o3 and "
974 "o6 >= 2 - M + N + i3 + i4 + i6 - o3 - o4 and o0 <= -1 + i0 and "
975 "o4 >= 4 - 3M + 3N - i0 - i1 + i2 + 2i3 + i4 + o0 + o1 - o2 - 2o3 "
976 "and o6 <= -3 + 2M - 2N + i3 + i4 - i5 + i6 - o3 - o4 + o5 and "
977 "2o6 <= -5 + 5M - 5N + 2i0 + i1 - i2 - i5 + 2i6 - 2o0 - o1 + o2 + o5 "
978 "and o6 >= 2i0 + i1 + i6 - 2o0 - o1 and "
979 "3o6 <= -5 + 4M - 4N + 2i0 + i1 - i2 + 2i3 + i4 - i5 + 3i6 "
980 "- 2o0 - o1 + o2 - 2o3 - o4 + o5) or "
981 "(N >= 2 and o3 <= -1 + i3 and o0 <= -1 + i0 and "
982 "o6 >= i3 + i6 - o3 and M >= 0 and "
983 "2o6 >= 1 + i0 + i3 + 2i6 - o0 - o3 and "
984 "o6 >= 1 - M + i0 + i6 - o0 and N >= 2M and o6 >= i0 + i6 - o0) }";
985 map
= isl_map_read_from_str(ctx
, str
);
986 map
= isl_map_coalesce(map
);
987 map2
= isl_map_read_from_str(ctx
, str
);
988 assert(isl_map_is_equal(map
, map2
));
992 str
= "[M, N] -> { [] -> [o0] : (o0 = 0 and M >= 1 and N >= 2) or "
993 "(o0 = 0 and M >= 1 and N >= 2M and N >= 2 + M) or "
994 "(o0 = 0 and M >= 2 and N >= 3) or "
995 "(M = 0 and o0 = 0 and N >= 3) }";
996 map
= isl_map_read_from_str(ctx
, str
);
997 map
= isl_map_coalesce(map
);
998 map2
= isl_map_read_from_str(ctx
, str
);
999 assert(isl_map_is_equal(map
, map2
));
1003 str
= "{ [i0, i1, i2, i3] : (i1 = 10i0 and i0 >= 1 and 10i0 <= 100 and "
1004 "i3 <= 9 + 10 i2 and i3 >= 1 + 10i2 and i3 >= 0) or "
1005 "(i1 <= 9 + 10i0 and i1 >= 1 + 10i0 and i2 >= 0 and "
1006 "i0 >= 0 and i1 <= 100 and i3 <= 9 + 10i2 and i3 >= 1 + 10i2) }";
1007 map
= isl_map_read_from_str(ctx
, str
);
1008 map
= isl_map_coalesce(map
);
1009 map2
= isl_map_read_from_str(ctx
, str
);
1010 assert(isl_map_is_equal(map
, map2
));
1014 test_coalesce_set(ctx
,
1015 "[M] -> { [i1] : (i1 >= 2 and i1 <= M) or "
1016 "(i1 = M and M >= 1) }", 0);
1017 test_coalesce_set(ctx
,
1018 "{[x,y] : x,y >= 0; [x,y] : 10 <= x <= 20 and y >= -1 }", 0);
1019 test_coalesce_set(ctx
,
1020 "{ [x, y] : (x >= 1 and y >= 1 and x <= 2 and y <= 2) or "
1021 "(y = 3 and x = 1) }", 1);
1022 test_coalesce_set(ctx
,
1023 "[M] -> { [i0, i1, i2, i3, i4] : (i1 >= 3 and i4 >= 2 + i2 and "
1024 "i2 >= 2 and i0 >= 2 and i3 >= 1 + i2 and i0 <= M and "
1025 "i1 <= M and i3 <= M and i4 <= M) or "
1026 "(i1 >= 2 and i4 >= 1 + i2 and i2 >= 2 and i0 >= 2 and "
1027 "i3 >= 1 + i2 and i0 <= M and i1 <= -1 + M and i3 <= M and "
1028 "i4 <= -1 + M) }", 1);
1029 test_coalesce_set(ctx
,
1030 "{ [x, y] : (x >= 0 and y >= 0 and x <= 10 and y <= 10) or "
1031 "(x >= 1 and y >= 1 and x <= 11 and y <= 11) }", 1);
1032 test_coalesce_set(ctx
,
1033 "{[x,y,z] : y + 2 >= 0 and x - y + 1 >= 0 and "
1034 "-x - y + 1 >= 0 and -3 <= z <= 3;"
1035 "[x,y,z] : -x+z + 20 >= 0 and -x-z + 20 >= 0 and "
1036 "x-z + 20 >= 0 and x+z + 20 >= 0 and -10 <= y <= 0}", 1);
1037 if (test_coalesce_set(ctx
,
1038 "{[x,y] : 0 <= x,y <= 10; [5,y]: 4 <=y <= 11}", 1) < 0)
1040 if (test_coalesce_set(ctx
, "{[x,0] : x >= 0; [x,1] : x <= 20}", 0) < 0)
1042 if (test_coalesce_set(ctx
,
1043 "{[x,0,0] : -5 <= x <= 5; [0,y,1] : -5 <= y <= 5 }", 1) < 0)
1045 if (test_coalesce_set(ctx
, "{ [x, 1 - x] : 0 <= x <= 1; [0,0] }", 1) < 0)
1047 if (test_coalesce_set(ctx
, "{ [0,0]; [i,i] : 1 <= i <= 10 }", 1) < 0)
1049 if (test_coalesce_set(ctx
, "{ [0,0]; [i,j] : 1 <= i,j <= 10 }", 0) < 0)
1051 if (test_coalesce_set(ctx
, "{ [0,0]; [i,2i] : 1 <= i <= 10 }", 1) < 0)
1053 if (test_coalesce_set(ctx
, "{ [0,0]; [i,2i] : 2 <= i <= 10 }", 0) < 0)
1055 if (test_coalesce_set(ctx
, "{ [1,0]; [i,2i] : 1 <= i <= 10 }", 0) < 0)
1057 if (test_coalesce_set(ctx
, "{ [0,1]; [i,2i] : 1 <= i <= 10 }", 0) < 0)
1062 void test_closure(struct isl_ctx
*ctx
)
1066 isl_map
*up
, *right
;
1067 isl_map
*map
, *map2
;
1070 /* COCOA example 1 */
1071 map
= isl_map_read_from_str(ctx
,
1072 "[n] -> { [i,j] -> [i2,j2] : i2 = i + 1 and j2 = j + 1 and "
1073 "1 <= i and i < n and 1 <= j and j < n or "
1074 "i2 = i + 1 and j2 = j - 1 and "
1075 "1 <= i and i < n and 2 <= j and j <= n }");
1076 map
= isl_map_power(map
, &exact
);
1080 /* COCOA example 1 */
1081 map
= isl_map_read_from_str(ctx
,
1082 "[n] -> { [i,j] -> [i2,j2] : i2 = i + 1 and j2 = j + 1 and "
1083 "1 <= i and i < n and 1 <= j and j < n or "
1084 "i2 = i + 1 and j2 = j - 1 and "
1085 "1 <= i and i < n and 2 <= j and j <= n }");
1086 map
= isl_map_transitive_closure(map
, &exact
);
1088 map2
= isl_map_read_from_str(ctx
,
1089 "[n] -> { [i,j] -> [i2,j2] : exists (k1,k2,k : "
1090 "1 <= i and i < n and 1 <= j and j <= n and "
1091 "2 <= i2 and i2 <= n and 1 <= j2 and j2 <= n and "
1092 "i2 = i + k1 + k2 and j2 = j + k1 - k2 and "
1093 "k1 >= 0 and k2 >= 0 and k1 + k2 = k and k >= 1 )}");
1094 assert(isl_map_is_equal(map
, map2
));
1098 map
= isl_map_read_from_str(ctx
,
1099 "[n] -> { [x] -> [y] : y = x + 1 and 0 <= x and x <= n and "
1100 " 0 <= y and y <= n }");
1101 map
= isl_map_transitive_closure(map
, &exact
);
1102 map2
= isl_map_read_from_str(ctx
,
1103 "[n] -> { [x] -> [y] : y > x and 0 <= x and x <= n and "
1104 " 0 <= y and y <= n }");
1105 assert(isl_map_is_equal(map
, map2
));
1109 /* COCOA example 2 */
1110 map
= isl_map_read_from_str(ctx
,
1111 "[n] -> { [i,j] -> [i2,j2] : i2 = i + 2 and j2 = j + 2 and "
1112 "1 <= i and i < n - 1 and 1 <= j and j < n - 1 or "
1113 "i2 = i + 2 and j2 = j - 2 and "
1114 "1 <= i and i < n - 1 and 3 <= j and j <= n }");
1115 map
= isl_map_transitive_closure(map
, &exact
);
1117 map2
= isl_map_read_from_str(ctx
,
1118 "[n] -> { [i,j] -> [i2,j2] : exists (k1,k2,k : "
1119 "1 <= i and i < n - 1 and 1 <= j and j <= n and "
1120 "3 <= i2 and i2 <= n and 1 <= j2 and j2 <= n and "
1121 "i2 = i + 2 k1 + 2 k2 and j2 = j + 2 k1 - 2 k2 and "
1122 "k1 >= 0 and k2 >= 0 and k1 + k2 = k and k >= 1) }");
1123 assert(isl_map_is_equal(map
, map2
));
1127 /* COCOA Fig.2 left */
1128 map
= isl_map_read_from_str(ctx
,
1129 "[n] -> { [i,j] -> [i2,j2] : i2 = i + 2 and j2 = j and "
1130 "i <= 2 j - 3 and i <= n - 2 and j <= 2 i - 1 and "
1132 "i2 = i and j2 = j + 2 and i <= 2 j - 1 and i <= n and "
1133 "j <= 2 i - 3 and j <= n - 2 or "
1134 "i2 = i + 1 and j2 = j + 1 and i <= 2 j - 1 and "
1135 "i <= n - 1 and j <= 2 i - 1 and j <= n - 1 }");
1136 map
= isl_map_transitive_closure(map
, &exact
);
1140 /* COCOA Fig.2 right */
1141 map
= isl_map_read_from_str(ctx
,
1142 "[n] -> { [i,j] -> [i2,j2] : i2 = i + 3 and j2 = j and "
1143 "i <= 2 j - 4 and i <= n - 3 and j <= 2 i - 1 and "
1145 "i2 = i and j2 = j + 3 and i <= 2 j - 1 and i <= n and "
1146 "j <= 2 i - 4 and j <= n - 3 or "
1147 "i2 = i + 1 and j2 = j + 1 and i <= 2 j - 1 and "
1148 "i <= n - 1 and j <= 2 i - 1 and j <= n - 1 }");
1149 map
= isl_map_power(map
, &exact
);
1153 /* COCOA Fig.2 right */
1154 map
= isl_map_read_from_str(ctx
,
1155 "[n] -> { [i,j] -> [i2,j2] : i2 = i + 3 and j2 = j and "
1156 "i <= 2 j - 4 and i <= n - 3 and j <= 2 i - 1 and "
1158 "i2 = i and j2 = j + 3 and i <= 2 j - 1 and i <= n and "
1159 "j <= 2 i - 4 and j <= n - 3 or "
1160 "i2 = i + 1 and j2 = j + 1 and i <= 2 j - 1 and "
1161 "i <= n - 1 and j <= 2 i - 1 and j <= n - 1 }");
1162 map
= isl_map_transitive_closure(map
, &exact
);
1164 map2
= isl_map_read_from_str(ctx
,
1165 "[n] -> { [i,j] -> [i2,j2] : exists (k1,k2,k3,k : "
1166 "i <= 2 j - 1 and i <= n and j <= 2 i - 1 and "
1167 "j <= n and 3 + i + 2 j <= 3 n and "
1168 "3 + 2 i + j <= 3n and i2 <= 2 j2 -1 and i2 <= n and "
1169 "i2 <= 3 j2 - 4 and j2 <= 2 i2 -1 and j2 <= n and "
1170 "13 + 4 j2 <= 11 i2 and i2 = i + 3 k1 + k3 and "
1171 "j2 = j + 3 k2 + k3 and k1 >= 0 and k2 >= 0 and "
1172 "k3 >= 0 and k1 + k2 + k3 = k and k > 0) }");
1173 assert(isl_map_is_equal(map
, map2
));
1177 /* COCOA Fig.1 right */
1178 dom
= isl_set_read_from_str(ctx
,
1179 "{ [x,y] : x >= 0 and -2 x + 3 y >= 0 and x <= 3 and "
1180 "2 x - 3 y + 3 >= 0 }");
1181 right
= isl_map_read_from_str(ctx
,
1182 "{ [x,y] -> [x2,y2] : x2 = x + 1 and y2 = y }");
1183 up
= isl_map_read_from_str(ctx
,
1184 "{ [x,y] -> [x2,y2] : x2 = x and y2 = y + 1 }");
1185 right
= isl_map_intersect_domain(right
, isl_set_copy(dom
));
1186 right
= isl_map_intersect_range(right
, isl_set_copy(dom
));
1187 up
= isl_map_intersect_domain(up
, isl_set_copy(dom
));
1188 up
= isl_map_intersect_range(up
, dom
);
1189 map
= isl_map_union(up
, right
);
1190 map
= isl_map_transitive_closure(map
, &exact
);
1192 map2
= isl_map_read_from_str(ctx
,
1193 "{ [0,0] -> [0,1]; [0,0] -> [1,1]; [0,1] -> [1,1]; "
1194 " [2,2] -> [3,2]; [2,2] -> [3,3]; [3,2] -> [3,3] }");
1195 assert(isl_map_is_equal(map
, map2
));
1199 /* COCOA Theorem 1 counter example */
1200 map
= isl_map_read_from_str(ctx
,
1201 "{ [i,j] -> [i2,j2] : i = 0 and 0 <= j and j <= 1 and "
1202 "i2 = 1 and j2 = j or "
1203 "i = 0 and j = 0 and i2 = 0 and j2 = 1 }");
1204 map
= isl_map_transitive_closure(map
, &exact
);
1208 map
= isl_map_read_from_str(ctx
,
1209 "[m,n] -> { [i,j] -> [i2,j2] : i2 = i and j2 = j + 2 and "
1210 "1 <= i,i2 <= n and 1 <= j,j2 <= m or "
1211 "i2 = i + 1 and 3 <= j2 - j <= 4 and "
1212 "1 <= i,i2 <= n and 1 <= j,j2 <= m }");
1213 map
= isl_map_transitive_closure(map
, &exact
);
1217 /* Kelly et al 1996, fig 12 */
1218 map
= isl_map_read_from_str(ctx
,
1219 "[n] -> { [i,j] -> [i2,j2] : i2 = i and j2 = j + 1 and "
1220 "1 <= i,j,j+1 <= n or "
1221 "j = n and j2 = 1 and i2 = i + 1 and "
1222 "1 <= i,i+1 <= n }");
1223 map
= isl_map_transitive_closure(map
, &exact
);
1225 map2
= isl_map_read_from_str(ctx
,
1226 "[n] -> { [i,j] -> [i2,j2] : 1 <= j < j2 <= n and "
1227 "1 <= i <= n and i = i2 or "
1228 "1 <= i < i2 <= n and 1 <= j <= n and "
1230 assert(isl_map_is_equal(map
, map2
));
1234 /* Omega's closure4 */
1235 map
= isl_map_read_from_str(ctx
,
1236 "[m,n] -> { [x,y] -> [x2,y2] : x2 = x and y2 = y + 1 and "
1237 "1 <= x,y <= 10 or "
1238 "x2 = x + 1 and y2 = y and "
1239 "1 <= x <= 20 && 5 <= y <= 15 }");
1240 map
= isl_map_transitive_closure(map
, &exact
);
1244 map
= isl_map_read_from_str(ctx
,
1245 "[n] -> { [x] -> [y]: 1 <= n <= y - x <= 10 }");
1246 map
= isl_map_transitive_closure(map
, &exact
);
1248 map2
= isl_map_read_from_str(ctx
,
1249 "[n] -> { [x] -> [y] : 1 <= n <= 10 and y >= n + x }");
1250 assert(isl_map_is_equal(map
, map2
));
1254 str
= "[n, m] -> { [i0, i1, i2, i3] -> [o0, o1, o2, o3] : "
1255 "i3 = 1 and o0 = i0 and o1 = -1 + i1 and o2 = -1 + i2 and "
1256 "o3 = -2 + i2 and i1 <= -1 + i0 and i1 >= 1 - m + i0 and "
1257 "i1 >= 2 and i1 <= n and i2 >= 3 and i2 <= 1 + n and i2 <= m }";
1258 map
= isl_map_read_from_str(ctx
, str
);
1259 map
= isl_map_transitive_closure(map
, &exact
);
1261 map2
= isl_map_read_from_str(ctx
, str
);
1262 assert(isl_map_is_equal(map
, map2
));
1266 str
= "{[0] -> [1]; [2] -> [3]}";
1267 map
= isl_map_read_from_str(ctx
, str
);
1268 map
= isl_map_transitive_closure(map
, &exact
);
1270 map2
= isl_map_read_from_str(ctx
, str
);
1271 assert(isl_map_is_equal(map
, map2
));
1275 str
= "[n] -> { [[i0, i1, 1, 0, i0] -> [i5, 1]] -> "
1276 "[[i0, -1 + i1, 2, 0, i0] -> [-1 + i5, 2]] : "
1277 "exists (e0 = [(3 - n)/3]: i5 >= 2 and i1 >= 2 and "
1278 "3i0 <= -1 + n and i1 <= -1 + n and i5 <= -1 + n and "
1279 "3e0 >= 1 - n and 3e0 <= 2 - n and 3i0 >= -2 + n); "
1280 "[[i0, i1, 2, 0, i0] -> [i5, 1]] -> "
1281 "[[i0, i1, 1, 0, i0] -> [-1 + i5, 2]] : "
1282 "exists (e0 = [(3 - n)/3]: i5 >= 2 and i1 >= 1 and "
1283 "3i0 <= -1 + n and i1 <= -1 + n and i5 <= -1 + n and "
1284 "3e0 >= 1 - n and 3e0 <= 2 - n and 3i0 >= -2 + n); "
1285 "[[i0, i1, 1, 0, i0] -> [i5, 2]] -> "
1286 "[[i0, -1 + i1, 2, 0, i0] -> [i5, 1]] : "
1287 "exists (e0 = [(3 - n)/3]: i1 >= 2 and i5 >= 1 and "
1288 "3i0 <= -1 + n and i1 <= -1 + n and i5 <= -1 + n and "
1289 "3e0 >= 1 - n and 3e0 <= 2 - n and 3i0 >= -2 + n); "
1290 "[[i0, i1, 2, 0, i0] -> [i5, 2]] -> "
1291 "[[i0, i1, 1, 0, i0] -> [i5, 1]] : "
1292 "exists (e0 = [(3 - n)/3]: i5 >= 1 and i1 >= 1 and "
1293 "3i0 <= -1 + n and i1 <= -1 + n and i5 <= -1 + n and "
1294 "3e0 >= 1 - n and 3e0 <= 2 - n and 3i0 >= -2 + n) }";
1295 map
= isl_map_read_from_str(ctx
, str
);
1296 map
= isl_map_transitive_closure(map
, NULL
);
1301 void test_lex(struct isl_ctx
*ctx
)
1306 dim
= isl_space_set_alloc(ctx
, 0, 0);
1307 map
= isl_map_lex_le(dim
);
1308 assert(!isl_map_is_empty(map
));
1312 void test_lexmin(struct isl_ctx
*ctx
)
1315 isl_basic_map
*bmap
;
1316 isl_map
*map
, *map2
;
1319 isl_pw_multi_aff
*pma
;
1321 str
= "[p0, p1] -> { [] -> [] : "
1322 "exists (e0 = [(2p1)/3], e1, e2, e3 = [(3 - p1 + 3e0)/3], "
1323 "e4 = [(p1)/3], e5 = [(p1 + 3e4)/3]: "
1324 "3e0 >= -2 + 2p1 and 3e0 >= p1 and 3e3 >= 1 - p1 + 3e0 and "
1325 "3e0 <= 2p1 and 3e3 >= -2 + p1 and 3e3 <= -1 + p1 and p1 >= 3 and "
1326 "3e5 >= -2 + 2p1 and 3e5 >= p1 and 3e5 <= -1 + p1 + 3e4 and "
1327 "3e4 <= p1 and 3e4 >= -2 + p1 and e3 <= -1 + e0 and "
1328 "3e4 >= 6 - p1 + 3e1 and 3e1 >= p1 and 3e5 >= -2 + p1 + 3e4 and "
1329 "2e4 >= 3 - p1 + 2e1 and e4 <= e1 and 3e3 <= 2 - p1 + 3e0 and "
1330 "e5 >= 1 + e1 and 3e4 >= 6 - 2p1 + 3e1 and "
1331 "p0 >= 2 and p1 >= p0 and 3e2 >= p1 and 3e4 >= 6 - p1 + 3e2 and "
1332 "e2 <= e1 and e3 >= 1 and e4 <= e2) }";
1333 map
= isl_map_read_from_str(ctx
, str
);
1334 map
= isl_map_lexmin(map
);
1337 str
= "[C] -> { [obj,a,b,c] : obj <= 38 a + 7 b + 10 c and "
1338 "a + b <= 1 and c <= 10 b and c <= C and a,b,c,C >= 0 }";
1339 set
= isl_set_read_from_str(ctx
, str
);
1340 set
= isl_set_lexmax(set
);
1341 str
= "[C] -> { [obj,a,b,c] : C = 8 }";
1342 set2
= isl_set_read_from_str(ctx
, str
);
1343 set
= isl_set_intersect(set
, set2
);
1344 assert(!isl_set_is_empty(set
));
1347 str
= "{ [x] -> [y] : x <= y <= 10; [x] -> [5] : -8 <= x <= 8 }";
1348 map
= isl_map_read_from_str(ctx
, str
);
1349 map
= isl_map_lexmin(map
);
1350 str
= "{ [x] -> [5] : 6 <= x <= 8; "
1351 "[x] -> [x] : x <= 5 or (9 <= x <= 10) }";
1352 map2
= isl_map_read_from_str(ctx
, str
);
1353 assert(isl_map_is_equal(map
, map2
));
1357 str
= "{ [x] -> [y] : 4y = x or 4y = -1 + x or 4y = -2 + x }";
1358 map
= isl_map_read_from_str(ctx
, str
);
1359 map2
= isl_map_copy(map
);
1360 map
= isl_map_lexmin(map
);
1361 assert(isl_map_is_equal(map
, map2
));
1365 str
= "{ [x] -> [y] : x = 4y; [x] -> [y] : x = 2y }";
1366 map
= isl_map_read_from_str(ctx
, str
);
1367 map
= isl_map_lexmin(map
);
1368 str
= "{ [x] -> [y] : (4y = x and x >= 0) or "
1369 "(exists (e0 = [(x)/4], e1 = [(-2 + x)/4]: 2y = x and "
1370 "4e1 = -2 + x and 4e0 <= -1 + x and 4e0 >= -3 + x)) or "
1371 "(exists (e0 = [(x)/4]: 2y = x and 4e0 = x and x <= -4)) }";
1372 map2
= isl_map_read_from_str(ctx
, str
);
1373 assert(isl_map_is_equal(map
, map2
));
1377 str
= "{ [i] -> [i', j] : j = i - 8i' and i' >= 0 and i' <= 7 and "
1378 " 8i' <= i and 8i' >= -7 + i }";
1379 bmap
= isl_basic_map_read_from_str(ctx
, str
);
1380 pma
= isl_basic_map_lexmin_pw_multi_aff(isl_basic_map_copy(bmap
));
1381 map2
= isl_map_from_pw_multi_aff(pma
);
1382 map
= isl_map_from_basic_map(bmap
);
1383 assert(isl_map_is_equal(map
, map2
));
1387 str
= "{ T[a] -> S[b, c] : a = 4b-2c and c >= b }";
1388 map
= isl_map_read_from_str(ctx
, str
);
1389 map
= isl_map_lexmin(map
);
1390 str
= "{ T[a] -> S[b, c] : 2b = a and 2c = a }";
1391 map2
= isl_map_read_from_str(ctx
, str
);
1392 assert(isl_map_is_equal(map
, map2
));
1402 static int collect_must_may(__isl_take isl_map
*dep
, int must
,
1403 void *dep_user
, void *user
)
1405 struct must_may
*mm
= (struct must_may
*)user
;
1408 mm
->must
= isl_map_union(mm
->must
, dep
);
1410 mm
->may
= isl_map_union(mm
->may
, dep
);
1415 static int common_space(void *first
, void *second
)
1417 int depth
= *(int *)first
;
1421 static int map_is_equal(__isl_keep isl_map
*map
, const char *str
)
1429 map2
= isl_map_read_from_str(map
->ctx
, str
);
1430 equal
= isl_map_is_equal(map
, map2
);
1436 void test_dep(struct isl_ctx
*ctx
)
1441 isl_access_info
*ai
;
1448 str
= "{ [2,i,0] -> [i] : 0 <= i <= 10 }";
1449 map
= isl_map_read_from_str(ctx
, str
);
1450 ai
= isl_access_info_alloc(map
, &depth
, &common_space
, 2);
1452 str
= "{ [0,i,0] -> [i] : 0 <= i <= 10 }";
1453 map
= isl_map_read_from_str(ctx
, str
);
1454 ai
= isl_access_info_add_source(ai
, map
, 1, &depth
);
1456 str
= "{ [1,i,0] -> [5] : 0 <= i <= 10 }";
1457 map
= isl_map_read_from_str(ctx
, str
);
1458 ai
= isl_access_info_add_source(ai
, map
, 1, &depth
);
1460 flow
= isl_access_info_compute_flow(ai
);
1461 dim
= isl_space_alloc(ctx
, 0, 3, 3);
1462 mm
.must
= isl_map_empty(isl_space_copy(dim
));
1463 mm
.may
= isl_map_empty(dim
);
1465 isl_flow_foreach(flow
, collect_must_may
, &mm
);
1467 str
= "{ [0,i,0] -> [2,i,0] : (0 <= i <= 4) or (6 <= i <= 10); "
1468 " [1,10,0] -> [2,5,0] }";
1469 assert(map_is_equal(mm
.must
, str
));
1470 str
= "{ [i,j,k] -> [l,m,n] : 1 = 0 }";
1471 assert(map_is_equal(mm
.may
, str
));
1473 isl_map_free(mm
.must
);
1474 isl_map_free(mm
.may
);
1475 isl_flow_free(flow
);
1478 str
= "{ [2,i,0] -> [i] : 0 <= i <= 10 }";
1479 map
= isl_map_read_from_str(ctx
, str
);
1480 ai
= isl_access_info_alloc(map
, &depth
, &common_space
, 2);
1482 str
= "{ [0,i,0] -> [i] : 0 <= i <= 10 }";
1483 map
= isl_map_read_from_str(ctx
, str
);
1484 ai
= isl_access_info_add_source(ai
, map
, 1, &depth
);
1486 str
= "{ [1,i,0] -> [5] : 0 <= i <= 10 }";
1487 map
= isl_map_read_from_str(ctx
, str
);
1488 ai
= isl_access_info_add_source(ai
, map
, 0, &depth
);
1490 flow
= isl_access_info_compute_flow(ai
);
1491 dim
= isl_space_alloc(ctx
, 0, 3, 3);
1492 mm
.must
= isl_map_empty(isl_space_copy(dim
));
1493 mm
.may
= isl_map_empty(dim
);
1495 isl_flow_foreach(flow
, collect_must_may
, &mm
);
1497 str
= "{ [0,i,0] -> [2,i,0] : (0 <= i <= 4) or (6 <= i <= 10) }";
1498 assert(map_is_equal(mm
.must
, str
));
1499 str
= "{ [0,5,0] -> [2,5,0]; [1,i,0] -> [2,5,0] : 0 <= i <= 10 }";
1500 assert(map_is_equal(mm
.may
, str
));
1502 isl_map_free(mm
.must
);
1503 isl_map_free(mm
.may
);
1504 isl_flow_free(flow
);
1507 str
= "{ [2,i,0] -> [i] : 0 <= i <= 10 }";
1508 map
= isl_map_read_from_str(ctx
, str
);
1509 ai
= isl_access_info_alloc(map
, &depth
, &common_space
, 2);
1511 str
= "{ [0,i,0] -> [i] : 0 <= i <= 10 }";
1512 map
= isl_map_read_from_str(ctx
, str
);
1513 ai
= isl_access_info_add_source(ai
, map
, 0, &depth
);
1515 str
= "{ [1,i,0] -> [5] : 0 <= i <= 10 }";
1516 map
= isl_map_read_from_str(ctx
, str
);
1517 ai
= isl_access_info_add_source(ai
, map
, 0, &depth
);
1519 flow
= isl_access_info_compute_flow(ai
);
1520 dim
= isl_space_alloc(ctx
, 0, 3, 3);
1521 mm
.must
= isl_map_empty(isl_space_copy(dim
));
1522 mm
.may
= isl_map_empty(dim
);
1524 isl_flow_foreach(flow
, collect_must_may
, &mm
);
1526 str
= "{ [0,i,0] -> [2,i,0] : 0 <= i <= 10; "
1527 " [1,i,0] -> [2,5,0] : 0 <= i <= 10 }";
1528 assert(map_is_equal(mm
.may
, str
));
1529 str
= "{ [i,j,k] -> [l,m,n] : 1 = 0 }";
1530 assert(map_is_equal(mm
.must
, str
));
1532 isl_map_free(mm
.must
);
1533 isl_map_free(mm
.may
);
1534 isl_flow_free(flow
);
1537 str
= "{ [0,i,2] -> [i] : 0 <= i <= 10 }";
1538 map
= isl_map_read_from_str(ctx
, str
);
1539 ai
= isl_access_info_alloc(map
, &depth
, &common_space
, 2);
1541 str
= "{ [0,i,0] -> [i] : 0 <= i <= 10 }";
1542 map
= isl_map_read_from_str(ctx
, str
);
1543 ai
= isl_access_info_add_source(ai
, map
, 0, &depth
);
1545 str
= "{ [0,i,1] -> [5] : 0 <= i <= 10 }";
1546 map
= isl_map_read_from_str(ctx
, str
);
1547 ai
= isl_access_info_add_source(ai
, map
, 0, &depth
);
1549 flow
= isl_access_info_compute_flow(ai
);
1550 dim
= isl_space_alloc(ctx
, 0, 3, 3);
1551 mm
.must
= isl_map_empty(isl_space_copy(dim
));
1552 mm
.may
= isl_map_empty(dim
);
1554 isl_flow_foreach(flow
, collect_must_may
, &mm
);
1556 str
= "{ [0,i,0] -> [0,i,2] : 0 <= i <= 10; "
1557 " [0,i,1] -> [0,5,2] : 0 <= i <= 5 }";
1558 assert(map_is_equal(mm
.may
, str
));
1559 str
= "{ [i,j,k] -> [l,m,n] : 1 = 0 }";
1560 assert(map_is_equal(mm
.must
, str
));
1562 isl_map_free(mm
.must
);
1563 isl_map_free(mm
.may
);
1564 isl_flow_free(flow
);
1567 str
= "{ [0,i,1] -> [i] : 0 <= i <= 10 }";
1568 map
= isl_map_read_from_str(ctx
, str
);
1569 ai
= isl_access_info_alloc(map
, &depth
, &common_space
, 2);
1571 str
= "{ [0,i,0] -> [i] : 0 <= i <= 10 }";
1572 map
= isl_map_read_from_str(ctx
, str
);
1573 ai
= isl_access_info_add_source(ai
, map
, 0, &depth
);
1575 str
= "{ [0,i,2] -> [5] : 0 <= i <= 10 }";
1576 map
= isl_map_read_from_str(ctx
, str
);
1577 ai
= isl_access_info_add_source(ai
, map
, 0, &depth
);
1579 flow
= isl_access_info_compute_flow(ai
);
1580 dim
= isl_space_alloc(ctx
, 0, 3, 3);
1581 mm
.must
= isl_map_empty(isl_space_copy(dim
));
1582 mm
.may
= isl_map_empty(dim
);
1584 isl_flow_foreach(flow
, collect_must_may
, &mm
);
1586 str
= "{ [0,i,0] -> [0,i,1] : 0 <= i <= 10; "
1587 " [0,i,2] -> [0,5,1] : 0 <= i <= 4 }";
1588 assert(map_is_equal(mm
.may
, str
));
1589 str
= "{ [i,j,k] -> [l,m,n] : 1 = 0 }";
1590 assert(map_is_equal(mm
.must
, str
));
1592 isl_map_free(mm
.must
);
1593 isl_map_free(mm
.may
);
1594 isl_flow_free(flow
);
1599 str
= "{ [1,i,0,0,0] -> [i,j] : 0 <= i <= 10 and 0 <= j <= 10 }";
1600 map
= isl_map_read_from_str(ctx
, str
);
1601 ai
= isl_access_info_alloc(map
, &depth
, &common_space
, 1);
1603 str
= "{ [0,i,0,j,0] -> [i,j] : 0 <= i <= 10 and 0 <= j <= 10 }";
1604 map
= isl_map_read_from_str(ctx
, str
);
1605 ai
= isl_access_info_add_source(ai
, map
, 1, &depth
);
1607 flow
= isl_access_info_compute_flow(ai
);
1608 dim
= isl_space_alloc(ctx
, 0, 5, 5);
1609 mm
.must
= isl_map_empty(isl_space_copy(dim
));
1610 mm
.may
= isl_map_empty(dim
);
1612 isl_flow_foreach(flow
, collect_must_may
, &mm
);
1614 str
= "{ [0,i,0,j,0] -> [1,i,0,0,0] : 0 <= i,j <= 10 }";
1615 assert(map_is_equal(mm
.must
, str
));
1616 str
= "{ [0,0,0,0,0] -> [0,0,0,0,0] : 1 = 0 }";
1617 assert(map_is_equal(mm
.may
, str
));
1619 isl_map_free(mm
.must
);
1620 isl_map_free(mm
.may
);
1621 isl_flow_free(flow
);
1624 int test_sv(isl_ctx
*ctx
)
1628 isl_union_map
*umap
;
1631 str
= "[N] -> { [i] -> [f] : 0 <= i <= N and 0 <= i - 10 f <= 9 }";
1632 map
= isl_map_read_from_str(ctx
, str
);
1633 sv
= isl_map_is_single_valued(map
);
1638 isl_die(ctx
, isl_error_internal
,
1639 "map not detected as single valued", return -1);
1641 str
= "[N] -> { [i] -> [f] : 0 <= i <= N and 0 <= i - 10 f <= 10 }";
1642 map
= isl_map_read_from_str(ctx
, str
);
1643 sv
= isl_map_is_single_valued(map
);
1648 isl_die(ctx
, isl_error_internal
,
1649 "map detected as single valued", return -1);
1651 str
= "{ S1[i] -> [i] : 0 <= i <= 9; S2[i] -> [i] : 0 <= i <= 9 }";
1652 umap
= isl_union_map_read_from_str(ctx
, str
);
1653 sv
= isl_union_map_is_single_valued(umap
);
1654 isl_union_map_free(umap
);
1658 isl_die(ctx
, isl_error_internal
,
1659 "map not detected as single valued", return -1);
1661 str
= "{ [i] -> S1[i] : 0 <= i <= 9; [i] -> S2[i] : 0 <= i <= 9 }";
1662 umap
= isl_union_map_read_from_str(ctx
, str
);
1663 sv
= isl_union_map_is_single_valued(umap
);
1664 isl_union_map_free(umap
);
1668 isl_die(ctx
, isl_error_internal
,
1669 "map detected as single valued", return -1);
1674 void test_bijective_case(struct isl_ctx
*ctx
, const char *str
, int bijective
)
1678 map
= isl_map_read_from_str(ctx
, str
);
1680 assert(isl_map_is_bijective(map
));
1682 assert(!isl_map_is_bijective(map
));
1686 void test_bijective(struct isl_ctx
*ctx
)
1688 test_bijective_case(ctx
, "[N,M]->{[i,j] -> [i]}", 0);
1689 test_bijective_case(ctx
, "[N,M]->{[i,j] -> [i] : j=i}", 1);
1690 test_bijective_case(ctx
, "[N,M]->{[i,j] -> [i] : j=0}", 1);
1691 test_bijective_case(ctx
, "[N,M]->{[i,j] -> [i] : j=N}", 1);
1692 test_bijective_case(ctx
, "[N,M]->{[i,j] -> [j,i]}", 1);
1693 test_bijective_case(ctx
, "[N,M]->{[i,j] -> [i+j]}", 0);
1694 test_bijective_case(ctx
, "[N,M]->{[i,j] -> []}", 0);
1695 test_bijective_case(ctx
, "[N,M]->{[i,j] -> [i,j,N]}", 1);
1696 test_bijective_case(ctx
, "[N,M]->{[i,j] -> [2i]}", 0);
1697 test_bijective_case(ctx
, "[N,M]->{[i,j] -> [i,i]}", 0);
1698 test_bijective_case(ctx
, "[N,M]->{[i,j] -> [2i,i]}", 0);
1699 test_bijective_case(ctx
, "[N,M]->{[i,j] -> [2i,j]}", 1);
1700 test_bijective_case(ctx
, "[N,M]->{[i,j] -> [x,y] : 2x=i & y =j}", 1);
1703 void test_pwqp(struct isl_ctx
*ctx
)
1707 isl_pw_qpolynomial
*pwqp1
, *pwqp2
;
1709 str
= "{ [i,j,k] -> 1 + 9 * [i/5] + 7 * [j/11] + 4 * [k/13] }";
1710 pwqp1
= isl_pw_qpolynomial_read_from_str(ctx
, str
);
1712 pwqp1
= isl_pw_qpolynomial_move_dims(pwqp1
, isl_dim_param
, 0,
1715 str
= "[j] -> { [i,k] -> 1 + 9 * [i/5] + 7 * [j/11] + 4 * [k/13] }";
1716 pwqp2
= isl_pw_qpolynomial_read_from_str(ctx
, str
);
1718 pwqp1
= isl_pw_qpolynomial_sub(pwqp1
, pwqp2
);
1720 assert(isl_pw_qpolynomial_is_zero(pwqp1
));
1722 isl_pw_qpolynomial_free(pwqp1
);
1724 str
= "{ [i] -> i }";
1725 pwqp1
= isl_pw_qpolynomial_read_from_str(ctx
, str
);
1726 str
= "{ [k] : exists a : k = 2a }";
1727 set
= isl_set_read_from_str(ctx
, str
);
1728 pwqp1
= isl_pw_qpolynomial_gist(pwqp1
, set
);
1729 str
= "{ [i] -> i }";
1730 pwqp2
= isl_pw_qpolynomial_read_from_str(ctx
, str
);
1732 pwqp1
= isl_pw_qpolynomial_sub(pwqp1
, pwqp2
);
1734 assert(isl_pw_qpolynomial_is_zero(pwqp1
));
1736 isl_pw_qpolynomial_free(pwqp1
);
1738 str
= "{ [i] -> i + [ (i + [i/3])/2 ] }";
1739 pwqp1
= isl_pw_qpolynomial_read_from_str(ctx
, str
);
1741 set
= isl_set_read_from_str(ctx
, str
);
1742 pwqp1
= isl_pw_qpolynomial_gist(pwqp1
, set
);
1743 str
= "{ [i] -> 16 }";
1744 pwqp2
= isl_pw_qpolynomial_read_from_str(ctx
, str
);
1746 pwqp1
= isl_pw_qpolynomial_sub(pwqp1
, pwqp2
);
1748 assert(isl_pw_qpolynomial_is_zero(pwqp1
));
1750 isl_pw_qpolynomial_free(pwqp1
);
1752 str
= "{ [i] -> ([(i)/2]) }";
1753 pwqp1
= isl_pw_qpolynomial_read_from_str(ctx
, str
);
1754 str
= "{ [k] : exists a : k = 2a+1 }";
1755 set
= isl_set_read_from_str(ctx
, str
);
1756 pwqp1
= isl_pw_qpolynomial_gist(pwqp1
, set
);
1757 str
= "{ [i] -> -1/2 + 1/2 * i }";
1758 pwqp2
= isl_pw_qpolynomial_read_from_str(ctx
, str
);
1760 pwqp1
= isl_pw_qpolynomial_sub(pwqp1
, pwqp2
);
1762 assert(isl_pw_qpolynomial_is_zero(pwqp1
));
1764 isl_pw_qpolynomial_free(pwqp1
);
1766 str
= "{ [i] -> ([([i/2] + [i/2])/5]) }";
1767 pwqp1
= isl_pw_qpolynomial_read_from_str(ctx
, str
);
1768 str
= "{ [i] -> ([(2 * [i/2])/5]) }";
1769 pwqp2
= isl_pw_qpolynomial_read_from_str(ctx
, str
);
1771 pwqp1
= isl_pw_qpolynomial_sub(pwqp1
, pwqp2
);
1773 assert(isl_pw_qpolynomial_is_zero(pwqp1
));
1775 isl_pw_qpolynomial_free(pwqp1
);
1777 str
= "{ [x] -> ([x/2] + [(x+1)/2]) }";
1778 pwqp1
= isl_pw_qpolynomial_read_from_str(ctx
, str
);
1779 str
= "{ [x] -> x }";
1780 pwqp2
= isl_pw_qpolynomial_read_from_str(ctx
, str
);
1782 pwqp1
= isl_pw_qpolynomial_sub(pwqp1
, pwqp2
);
1784 assert(isl_pw_qpolynomial_is_zero(pwqp1
));
1786 isl_pw_qpolynomial_free(pwqp1
);
1788 str
= "{ [i] -> ([i/2]) : i >= 0; [i] -> ([i/3]) : i < 0 }";
1789 pwqp1
= isl_pw_qpolynomial_read_from_str(ctx
, str
);
1790 pwqp2
= isl_pw_qpolynomial_read_from_str(ctx
, str
);
1791 pwqp1
= isl_pw_qpolynomial_coalesce(pwqp1
);
1792 pwqp1
= isl_pw_qpolynomial_sub(pwqp1
, pwqp2
);
1793 assert(isl_pw_qpolynomial_is_zero(pwqp1
));
1794 isl_pw_qpolynomial_free(pwqp1
);
1797 void test_split_periods(isl_ctx
*ctx
)
1800 isl_pw_qpolynomial
*pwqp
;
1802 str
= "{ [U,V] -> 1/3 * U + 2/3 * V - [(U + 2V)/3] + [U/2] : "
1803 "U + 2V + 3 >= 0 and - U -2V >= 0 and - U + 10 >= 0 and "
1804 "U >= 0; [U,V] -> U^2 : U >= 100 }";
1805 pwqp
= isl_pw_qpolynomial_read_from_str(ctx
, str
);
1807 pwqp
= isl_pw_qpolynomial_split_periods(pwqp
, 2);
1810 isl_pw_qpolynomial_free(pwqp
);
1813 void test_union(isl_ctx
*ctx
)
1816 isl_union_set
*uset1
, *uset2
;
1817 isl_union_map
*umap1
, *umap2
;
1819 str
= "{ [i] : 0 <= i <= 1 }";
1820 uset1
= isl_union_set_read_from_str(ctx
, str
);
1821 str
= "{ [1] -> [0] }";
1822 umap1
= isl_union_map_read_from_str(ctx
, str
);
1824 umap2
= isl_union_set_lex_gt_union_set(isl_union_set_copy(uset1
), uset1
);
1825 assert(isl_union_map_is_equal(umap1
, umap2
));
1827 isl_union_map_free(umap1
);
1828 isl_union_map_free(umap2
);
1830 str
= "{ A[i] -> B[i]; B[i] -> C[i]; A[0] -> C[1] }";
1831 umap1
= isl_union_map_read_from_str(ctx
, str
);
1832 str
= "{ A[i]; B[i] }";
1833 uset1
= isl_union_set_read_from_str(ctx
, str
);
1835 uset2
= isl_union_map_domain(umap1
);
1837 assert(isl_union_set_is_equal(uset1
, uset2
));
1839 isl_union_set_free(uset1
);
1840 isl_union_set_free(uset2
);
1843 void test_bound(isl_ctx
*ctx
)
1846 isl_pw_qpolynomial
*pwqp
;
1847 isl_pw_qpolynomial_fold
*pwf
;
1849 str
= "{ [[a, b, c, d] -> [e]] -> 0 }";
1850 pwqp
= isl_pw_qpolynomial_read_from_str(ctx
, str
);
1851 pwf
= isl_pw_qpolynomial_bound(pwqp
, isl_fold_max
, NULL
);
1852 assert(isl_pw_qpolynomial_fold_dim(pwf
, isl_dim_in
) == 4);
1853 isl_pw_qpolynomial_fold_free(pwf
);
1855 str
= "{ [[x]->[x]] -> 1 : exists a : x = 2 a }";
1856 pwqp
= isl_pw_qpolynomial_read_from_str(ctx
, str
);
1857 pwf
= isl_pw_qpolynomial_bound(pwqp
, isl_fold_max
, NULL
);
1858 assert(isl_pw_qpolynomial_fold_dim(pwf
, isl_dim_in
) == 1);
1859 isl_pw_qpolynomial_fold_free(pwf
);
1862 void test_lift(isl_ctx
*ctx
)
1865 isl_basic_map
*bmap
;
1866 isl_basic_set
*bset
;
1868 str
= "{ [i0] : exists e0 : i0 = 4e0 }";
1869 bset
= isl_basic_set_read_from_str(ctx
, str
);
1870 bset
= isl_basic_set_lift(bset
);
1871 bmap
= isl_basic_map_from_range(bset
);
1872 bset
= isl_basic_map_domain(bmap
);
1873 isl_basic_set_free(bset
);
1876 void test_subset(isl_ctx
*ctx
)
1879 isl_set
*set1
, *set2
;
1881 str
= "{ [112, 0] }";
1882 set1
= isl_set_read_from_str(ctx
, str
);
1883 str
= "{ [i0, i1] : exists (e0 = [(i0 - i1)/16], e1: "
1884 "16e0 <= i0 - i1 and 16e0 >= -15 + i0 - i1 and "
1885 "16e1 <= i1 and 16e0 >= -i1 and 16e1 >= -i0 + i1) }";
1886 set2
= isl_set_read_from_str(ctx
, str
);
1887 assert(isl_set_is_subset(set1
, set2
));
1892 void test_factorize(isl_ctx
*ctx
)
1895 isl_basic_set
*bset
;
1898 str
= "{ [i0, i1, i2, i3, i4, i5, i6, i7] : 3i5 <= 2 - 2i0 and "
1899 "i0 >= -2 and i6 >= 1 + i3 and i7 >= 0 and 3i5 >= -2i0 and "
1900 "2i4 <= i2 and i6 >= 1 + 2i0 + 3i1 and i4 <= -1 and "
1901 "i6 >= 1 + 2i0 + 3i5 and i6 <= 2 + 2i0 + 3i5 and "
1902 "3i5 <= 2 - 2i0 - i2 + 3i4 and i6 <= 2 + 2i0 + 3i1 and "
1903 "i0 <= -1 and i7 <= i2 + i3 - 3i4 - i6 and "
1904 "3i5 >= -2i0 - i2 + 3i4 }";
1905 bset
= isl_basic_set_read_from_str(ctx
, str
);
1906 f
= isl_basic_set_factorizer(bset
);
1908 isl_basic_set_free(bset
);
1909 isl_factorizer_free(f
);
1911 str
= "{ [i0, i1, i2, i3, i4, i5, i6, i7, i8, i9, i10, i11, i12] : "
1912 "i12 <= 2 + i0 - i11 and 2i8 >= -i4 and i11 >= i1 and "
1913 "3i5 <= -i2 and 2i11 >= -i4 - 2i7 and i11 <= 3 + i0 + 3i9 and "
1914 "i11 <= -i4 - 2i7 and i12 >= -i10 and i2 >= -2 and "
1915 "i11 >= i1 + 3i10 and i11 >= 1 + i0 + 3i9 and "
1916 "i11 <= 1 - i4 - 2i8 and 6i6 <= 6 - i2 and 3i6 >= 1 - i2 and "
1917 "i11 <= 2 + i1 and i12 <= i4 + i11 and i12 >= i0 - i11 and "
1918 "3i5 >= -2 - i2 and i12 >= -1 + i4 + i11 and 3i3 <= 3 - i2 and "
1919 "9i6 <= 11 - i2 + 6i5 and 3i3 >= 1 - i2 and "
1920 "9i6 <= 5 - i2 + 6i3 and i12 <= -1 and i2 <= 0 }";
1921 bset
= isl_basic_set_read_from_str(ctx
, str
);
1922 f
= isl_basic_set_factorizer(bset
);
1924 isl_basic_set_free(bset
);
1925 isl_factorizer_free(f
);
1928 static int check_injective(__isl_take isl_map
*map
, void *user
)
1930 int *injective
= user
;
1932 *injective
= isl_map_is_injective(map
);
1935 if (*injective
< 0 || !*injective
)
1941 int test_one_schedule(isl_ctx
*ctx
, const char *d
, const char *w
,
1942 const char *r
, const char *s
, int tilable
, int parallel
)
1946 isl_union_map
*W
, *R
, *S
;
1947 isl_union_map
*empty
;
1948 isl_union_map
*dep_raw
, *dep_war
, *dep_waw
, *dep
;
1949 isl_union_map
*validity
, *proximity
;
1950 isl_union_map
*schedule
;
1951 isl_union_map
*test
;
1952 isl_union_set
*delta
;
1953 isl_union_set
*domain
;
1957 isl_schedule
*sched
;
1958 int is_nonneg
, is_parallel
, is_tilable
, is_injection
, is_complete
;
1960 D
= isl_union_set_read_from_str(ctx
, d
);
1961 W
= isl_union_map_read_from_str(ctx
, w
);
1962 R
= isl_union_map_read_from_str(ctx
, r
);
1963 S
= isl_union_map_read_from_str(ctx
, s
);
1965 W
= isl_union_map_intersect_domain(W
, isl_union_set_copy(D
));
1966 R
= isl_union_map_intersect_domain(R
, isl_union_set_copy(D
));
1968 empty
= isl_union_map_empty(isl_union_map_get_space(S
));
1969 isl_union_map_compute_flow(isl_union_map_copy(R
),
1970 isl_union_map_copy(W
), empty
,
1971 isl_union_map_copy(S
),
1972 &dep_raw
, NULL
, NULL
, NULL
);
1973 isl_union_map_compute_flow(isl_union_map_copy(W
),
1974 isl_union_map_copy(W
),
1975 isl_union_map_copy(R
),
1976 isl_union_map_copy(S
),
1977 &dep_waw
, &dep_war
, NULL
, NULL
);
1979 dep
= isl_union_map_union(dep_waw
, dep_war
);
1980 dep
= isl_union_map_union(dep
, dep_raw
);
1981 validity
= isl_union_map_copy(dep
);
1982 proximity
= isl_union_map_copy(dep
);
1984 sched
= isl_union_set_compute_schedule(isl_union_set_copy(D
),
1985 validity
, proximity
);
1986 schedule
= isl_schedule_get_map(sched
);
1987 isl_schedule_free(sched
);
1988 isl_union_map_free(W
);
1989 isl_union_map_free(R
);
1990 isl_union_map_free(S
);
1993 isl_union_map_foreach_map(schedule
, &check_injective
, &is_injection
);
1995 domain
= isl_union_map_domain(isl_union_map_copy(schedule
));
1996 is_complete
= isl_union_set_is_subset(D
, domain
);
1997 isl_union_set_free(D
);
1998 isl_union_set_free(domain
);
2000 test
= isl_union_map_reverse(isl_union_map_copy(schedule
));
2001 test
= isl_union_map_apply_range(test
, dep
);
2002 test
= isl_union_map_apply_range(test
, schedule
);
2004 delta
= isl_union_map_deltas(test
);
2005 if (isl_union_set_n_set(delta
) == 0) {
2009 isl_union_set_free(delta
);
2011 delta_set
= isl_set_from_union_set(delta
);
2013 slice
= isl_set_universe(isl_set_get_space(delta_set
));
2014 for (i
= 0; i
< tilable
; ++i
)
2015 slice
= isl_set_lower_bound_si(slice
, isl_dim_set
, i
, 0);
2016 is_tilable
= isl_set_is_subset(delta_set
, slice
);
2017 isl_set_free(slice
);
2019 slice
= isl_set_universe(isl_set_get_space(delta_set
));
2020 for (i
= 0; i
< parallel
; ++i
)
2021 slice
= isl_set_fix_si(slice
, isl_dim_set
, i
, 0);
2022 is_parallel
= isl_set_is_subset(delta_set
, slice
);
2023 isl_set_free(slice
);
2025 origin
= isl_set_universe(isl_set_get_space(delta_set
));
2026 for (i
= 0; i
< isl_set_dim(origin
, isl_dim_set
); ++i
)
2027 origin
= isl_set_fix_si(origin
, isl_dim_set
, i
, 0);
2029 delta_set
= isl_set_union(delta_set
, isl_set_copy(origin
));
2030 delta_set
= isl_set_lexmin(delta_set
);
2032 is_nonneg
= isl_set_is_equal(delta_set
, origin
);
2034 isl_set_free(origin
);
2035 isl_set_free(delta_set
);
2038 if (is_nonneg
< 0 || is_parallel
< 0 || is_tilable
< 0 ||
2039 is_injection
< 0 || is_complete
< 0)
2042 isl_die(ctx
, isl_error_unknown
,
2043 "generated schedule incomplete", return -1);
2045 isl_die(ctx
, isl_error_unknown
,
2046 "generated schedule not injective on each statement",
2049 isl_die(ctx
, isl_error_unknown
,
2050 "negative dependences in generated schedule",
2053 isl_die(ctx
, isl_error_unknown
,
2054 "generated schedule not as tilable as expected",
2057 isl_die(ctx
, isl_error_unknown
,
2058 "generated schedule not as parallel as expected",
2064 int test_special_schedule(isl_ctx
*ctx
, const char *domain
,
2065 const char *validity
, const char *proximity
, const char *expected_sched
)
2069 isl_union_map
*prox
;
2070 isl_union_map
*sched1
, *sched2
;
2071 isl_schedule
*schedule
;
2074 dom
= isl_union_set_read_from_str(ctx
, domain
);
2075 dep
= isl_union_map_read_from_str(ctx
, validity
);
2076 prox
= isl_union_map_read_from_str(ctx
, proximity
);
2077 schedule
= isl_union_set_compute_schedule(dom
, dep
, prox
);
2078 sched1
= isl_schedule_get_map(schedule
);
2079 isl_schedule_free(schedule
);
2081 sched2
= isl_union_map_read_from_str(ctx
, expected_sched
);
2083 equal
= isl_union_map_is_equal(sched1
, sched2
);
2084 isl_union_map_free(sched1
);
2085 isl_union_map_free(sched2
);
2090 isl_die(ctx
, isl_error_unknown
, "unexpected schedule",
2096 int test_schedule(isl_ctx
*ctx
)
2098 const char *D
, *W
, *R
, *V
, *P
, *S
;
2101 D
= "[T,N] -> { S1[t,i] : 1 <= t <= T and 2 <= i <= N - 1 }";
2102 W
= "{ S1[t,i] -> a[t,i] }";
2103 R
= "{ S1[t,i] -> a[t-1,i]; S1[t,i] -> a[t-1,i-1]; "
2104 "S1[t,i] -> a[t-1,i+1] }";
2105 S
= "{ S1[t,i] -> [t,i] }";
2106 if (test_one_schedule(ctx
, D
, W
, R
, S
, 2, 0) < 0)
2109 /* Fig. 5 of CC2008 */
2110 D
= "[N] -> { S_0[i, j] : i >= 0 and i <= -1 + N and j >= 2 and "
2112 W
= "[N] -> { S_0[i, j] -> a[i, j] : i >= 0 and i <= -1 + N and "
2113 "j >= 2 and j <= -1 + N }";
2114 R
= "[N] -> { S_0[i, j] -> a[j, i] : i >= 0 and i <= -1 + N and "
2115 "j >= 2 and j <= -1 + N; "
2116 "S_0[i, j] -> a[i, -1 + j] : i >= 0 and i <= -1 + N and "
2117 "j >= 2 and j <= -1 + N }";
2118 S
= "[N] -> { S_0[i, j] -> [0, i, 0, j, 0] }";
2119 if (test_one_schedule(ctx
, D
, W
, R
, S
, 2, 0) < 0)
2122 D
= "{ S1[i] : 0 <= i <= 10; S2[i] : 0 <= i <= 9 }";
2123 W
= "{ S1[i] -> a[i] }";
2124 R
= "{ S2[i] -> a[i+1] }";
2125 S
= "{ S1[i] -> [0,i]; S2[i] -> [1,i] }";
2126 if (test_one_schedule(ctx
, D
, W
, R
, S
, 1, 1) < 0)
2129 D
= "{ S1[i] : 0 <= i < 10; S2[i] : 0 <= i < 10 }";
2130 W
= "{ S1[i] -> a[i] }";
2131 R
= "{ S2[i] -> a[9-i] }";
2132 S
= "{ S1[i] -> [0,i]; S2[i] -> [1,i] }";
2133 if (test_one_schedule(ctx
, D
, W
, R
, S
, 1, 1) < 0)
2136 D
= "[N] -> { S1[i] : 0 <= i < N; S2[i] : 0 <= i < N }";
2137 W
= "{ S1[i] -> a[i] }";
2138 R
= "[N] -> { S2[i] -> a[N-1-i] }";
2139 S
= "{ S1[i] -> [0,i]; S2[i] -> [1,i] }";
2140 if (test_one_schedule(ctx
, D
, W
, R
, S
, 1, 1) < 0)
2143 D
= "{ S1[i] : 0 < i < 10; S2[i] : 0 <= i < 10 }";
2144 W
= "{ S1[i] -> a[i]; S2[i] -> b[i] }";
2145 R
= "{ S2[i] -> a[i]; S1[i] -> b[i-1] }";
2146 S
= "{ S1[i] -> [i,0]; S2[i] -> [i,1] }";
2147 if (test_one_schedule(ctx
, D
, W
, R
, S
, 0, 0) < 0)
2150 D
= "[N] -> { S1[i] : 1 <= i <= N; S2[i,j] : 1 <= i,j <= N }";
2151 W
= "{ S1[i] -> a[0,i]; S2[i,j] -> a[i,j] }";
2152 R
= "{ S2[i,j] -> a[i-1,j] }";
2153 S
= "{ S1[i] -> [0,i,0]; S2[i,j] -> [1,i,j] }";
2154 if (test_one_schedule(ctx
, D
, W
, R
, S
, 2, 1) < 0)
2157 D
= "[N] -> { S1[i] : 1 <= i <= N; S2[i,j] : 1 <= i,j <= N }";
2158 W
= "{ S1[i] -> a[i,0]; S2[i,j] -> a[i,j] }";
2159 R
= "{ S2[i,j] -> a[i,j-1] }";
2160 S
= "{ S1[i] -> [0,i,0]; S2[i,j] -> [1,i,j] }";
2161 if (test_one_schedule(ctx
, D
, W
, R
, S
, 2, 1) < 0)
2164 D
= "[N] -> { S_0[]; S_1[i] : i >= 0 and i <= -1 + N; S_2[] }";
2165 W
= "[N] -> { S_0[] -> a[0]; S_2[] -> b[0]; "
2166 "S_1[i] -> a[1 + i] : i >= 0 and i <= -1 + N }";
2167 R
= "[N] -> { S_2[] -> a[N]; S_1[i] -> a[i] : i >= 0 and i <= -1 + N }";
2168 S
= "[N] -> { S_1[i] -> [1, i, 0]; S_2[] -> [2, 0, 1]; "
2169 "S_0[] -> [0, 0, 0] }";
2170 if (test_one_schedule(ctx
, D
, W
, R
, S
, 1, 0) < 0)
2172 ctx
->opt
->schedule_parametric
= 0;
2173 if (test_one_schedule(ctx
, D
, W
, R
, S
, 0, 0) < 0)
2175 ctx
->opt
->schedule_parametric
= 1;
2177 D
= "[N] -> { S1[i] : 1 <= i <= N; S2[i] : 1 <= i <= N; "
2178 "S3[i,j] : 1 <= i,j <= N; S4[i] : 1 <= i <= N }";
2179 W
= "{ S1[i] -> a[i,0]; S2[i] -> a[0,i]; S3[i,j] -> a[i,j] }";
2180 R
= "[N] -> { S3[i,j] -> a[i-1,j]; S3[i,j] -> a[i,j-1]; "
2181 "S4[i] -> a[i,N] }";
2182 S
= "{ S1[i] -> [0,i,0]; S2[i] -> [1,i,0]; S3[i,j] -> [2,i,j]; "
2183 "S4[i] -> [4,i,0] }";
2184 if (test_one_schedule(ctx
, D
, W
, R
, S
, 2, 0) < 0)
2187 D
= "[N] -> { S_0[i, j] : i >= 1 and i <= N and j >= 1 and j <= N }";
2188 W
= "[N] -> { S_0[i, j] -> s[0] : i >= 1 and i <= N and j >= 1 and "
2190 R
= "[N] -> { S_0[i, j] -> s[0] : i >= 1 and i <= N and j >= 1 and "
2192 "S_0[i, j] -> a[i, j] : i >= 1 and i <= N and j >= 1 and "
2194 S
= "[N] -> { S_0[i, j] -> [0, i, 0, j, 0] }";
2195 if (test_one_schedule(ctx
, D
, W
, R
, S
, 0, 0) < 0)
2198 D
= "[N] -> { S_0[t] : t >= 0 and t <= -1 + N; "
2199 " S_2[t] : t >= 0 and t <= -1 + N; "
2200 " S_1[t, i] : t >= 0 and t <= -1 + N and i >= 0 and "
2202 W
= "[N] -> { S_0[t] -> a[t, 0] : t >= 0 and t <= -1 + N; "
2203 " S_2[t] -> b[t] : t >= 0 and t <= -1 + N; "
2204 " S_1[t, i] -> a[t, 1 + i] : t >= 0 and t <= -1 + N and "
2205 "i >= 0 and i <= -1 + N }";
2206 R
= "[N] -> { S_1[t, i] -> a[t, i] : t >= 0 and t <= -1 + N and "
2207 "i >= 0 and i <= -1 + N; "
2208 " S_2[t] -> a[t, N] : t >= 0 and t <= -1 + N }";
2209 S
= "[N] -> { S_2[t] -> [0, t, 2]; S_1[t, i] -> [0, t, 1, i, 0]; "
2210 " S_0[t] -> [0, t, 0] }";
2212 if (test_one_schedule(ctx
, D
, W
, R
, S
, 2, 1) < 0)
2214 ctx
->opt
->schedule_parametric
= 0;
2215 if (test_one_schedule(ctx
, D
, W
, R
, S
, 0, 0) < 0)
2217 ctx
->opt
->schedule_parametric
= 1;
2219 D
= "[N] -> { S1[i,j] : 0 <= i,j < N; S2[i,j] : 0 <= i,j < N }";
2220 S
= "{ S1[i,j] -> [0,i,j]; S2[i,j] -> [1,i,j] }";
2221 if (test_one_schedule(ctx
, D
, "{}", "{}", S
, 2, 2) < 0)
2224 D
= "[M, N] -> { S_1[i] : i >= 0 and i <= -1 + M; "
2225 "S_0[i, j] : i >= 0 and i <= -1 + M and j >= 0 and j <= -1 + N }";
2226 W
= "[M, N] -> { S_0[i, j] -> a[j] : i >= 0 and i <= -1 + M and "
2227 "j >= 0 and j <= -1 + N; "
2228 "S_1[i] -> b[0] : i >= 0 and i <= -1 + M }";
2229 R
= "[M, N] -> { S_0[i, j] -> a[0] : i >= 0 and i <= -1 + M and "
2230 "j >= 0 and j <= -1 + N; "
2231 "S_1[i] -> b[0] : i >= 0 and i <= -1 + M }";
2232 S
= "[M, N] -> { S_1[i] -> [1, i, 0]; S_0[i, j] -> [0, i, 0, j, 0] }";
2233 if (test_one_schedule(ctx
, D
, W
, R
, S
, 0, 0) < 0)
2236 D
= "{ S_0[i] : i >= 0 }";
2237 W
= "{ S_0[i] -> a[i] : i >= 0 }";
2238 R
= "{ S_0[i] -> a[0] : i >= 0 }";
2239 S
= "{ S_0[i] -> [0, i, 0] }";
2240 if (test_one_schedule(ctx
, D
, W
, R
, S
, 0, 0) < 0)
2243 D
= "{ S_0[i] : i >= 0; S_1[i] : i >= 0 }";
2244 W
= "{ S_0[i] -> a[i] : i >= 0; S_1[i] -> b[i] : i >= 0 }";
2245 R
= "{ S_0[i] -> b[0] : i >= 0; S_1[i] -> a[i] : i >= 0 }";
2246 S
= "{ S_1[i] -> [0, i, 1]; S_0[i] -> [0, i, 0] }";
2247 if (test_one_schedule(ctx
, D
, W
, R
, S
, 0, 0) < 0)
2250 D
= "[n] -> { S_0[j, k] : j <= -1 + n and j >= 0 and "
2251 "k <= -1 + n and k >= 0 }";
2252 W
= "[n] -> { S_0[j, k] -> B[j] : j <= -1 + n and j >= 0 and " "k <= -1 + n and k >= 0 }";
2253 R
= "[n] -> { S_0[j, k] -> B[j] : j <= -1 + n and j >= 0 and "
2254 "k <= -1 + n and k >= 0; "
2255 "S_0[j, k] -> B[k] : j <= -1 + n and j >= 0 and "
2256 "k <= -1 + n and k >= 0; "
2257 "S_0[j, k] -> A[k] : j <= -1 + n and j >= 0 and "
2258 "k <= -1 + n and k >= 0 }";
2259 S
= "[n] -> { S_0[j, k] -> [2, j, k] }";
2260 ctx
->opt
->schedule_outer_zero_distance
= 1;
2261 if (test_one_schedule(ctx
, D
, W
, R
, S
, 0, 0) < 0)
2263 ctx
->opt
->schedule_outer_zero_distance
= 0;
2265 D
= "{ S_0[i, j] : i >= 1 and i <= 10 and j >= 1 and j <= 8 }";
2266 V
= "{ S_0[i, j] -> S_0[i, 1 + j] : i >= 1 and i <= 10 and "
2267 "j >= 1 and j <= 7;"
2268 "S_0[i, j] -> S_0[1 + i, j] : i >= 1 and i <= 9 and "
2269 "j >= 1 and j <= 8 }";
2271 S
= "{ S_0[i, j] -> [i + j, j] }";
2272 ctx
->opt
->schedule_algorithm
= ISL_SCHEDULE_ALGORITHM_FEAUTRIER
;
2273 if (test_special_schedule(ctx
, D
, V
, P
, S
) < 0)
2275 ctx
->opt
->schedule_algorithm
= ISL_SCHEDULE_ALGORITHM_ISL
;
2277 /* Fig. 1 from Feautrier's "Some Efficient Solutions..." pt. 2, 1992 */
2278 D
= "[N] -> { S_0[i, j] : i >= 0 and i <= -1 + N and "
2279 "j >= 0 and j <= -1 + i }";
2280 V
= "[N] -> { S_0[i, j] -> S_0[i, 1 + j] : j <= -2 + i and "
2281 "i <= -1 + N and j >= 0;"
2282 "S_0[i, -1 + i] -> S_0[1 + i, 0] : i >= 1 and "
2285 S
= "{ S_0[i, j] -> [i, j] }";
2286 ctx
->opt
->schedule_algorithm
= ISL_SCHEDULE_ALGORITHM_FEAUTRIER
;
2287 if (test_special_schedule(ctx
, D
, V
, P
, S
) < 0)
2289 ctx
->opt
->schedule_algorithm
= ISL_SCHEDULE_ALGORITHM_ISL
;
2291 /* Test both algorithms on a case with only proximity dependences. */
2292 D
= "{ S[i,j] : 0 <= i <= 10 }";
2294 P
= "{ S[i,j] -> S[i+1,j] : 0 <= i,j <= 10 }";
2295 S
= "{ S[i, j] -> [j, i] }";
2296 ctx
->opt
->schedule_algorithm
= ISL_SCHEDULE_ALGORITHM_FEAUTRIER
;
2297 if (test_special_schedule(ctx
, D
, V
, P
, S
) < 0)
2299 ctx
->opt
->schedule_algorithm
= ISL_SCHEDULE_ALGORITHM_ISL
;
2300 return test_special_schedule(ctx
, D
, V
, P
, S
);
2303 int test_plain_injective(isl_ctx
*ctx
, const char *str
, int injective
)
2305 isl_union_map
*umap
;
2308 umap
= isl_union_map_read_from_str(ctx
, str
);
2309 test
= isl_union_map_plain_is_injective(umap
);
2310 isl_union_map_free(umap
);
2313 if (test
== injective
)
2316 isl_die(ctx
, isl_error_unknown
,
2317 "map not detected as injective", return -1);
2319 isl_die(ctx
, isl_error_unknown
,
2320 "map detected as injective", return -1);
2323 int test_injective(isl_ctx
*ctx
)
2327 if (test_plain_injective(ctx
, "{S[i,j] -> A[0]; T[i,j] -> B[1]}", 0))
2329 if (test_plain_injective(ctx
, "{S[] -> A[0]; T[] -> B[0]}", 1))
2331 if (test_plain_injective(ctx
, "{S[] -> A[0]; T[] -> A[1]}", 1))
2333 if (test_plain_injective(ctx
, "{S[] -> A[0]; T[] -> A[0]}", 0))
2335 if (test_plain_injective(ctx
, "{S[i] -> A[i,0]; T[i] -> A[i,1]}", 1))
2337 if (test_plain_injective(ctx
, "{S[i] -> A[i]; T[i] -> A[i]}", 0))
2339 if (test_plain_injective(ctx
, "{S[] -> A[0,0]; T[] -> A[0,1]}", 1))
2341 if (test_plain_injective(ctx
, "{S[] -> A[0,0]; T[] -> A[1,0]}", 1))
2344 str
= "{S[] -> A[0,0]; T[] -> A[0,1]; U[] -> A[1,0]}";
2345 if (test_plain_injective(ctx
, str
, 1))
2347 str
= "{S[] -> A[0,0]; T[] -> A[0,1]; U[] -> A[0,0]}";
2348 if (test_plain_injective(ctx
, str
, 0))
2354 int test_aff(isl_ctx
*ctx
)
2359 isl_local_space
*ls
;
2363 dim
= isl_space_set_alloc(ctx
, 0, 1);
2364 ls
= isl_local_space_from_space(dim
);
2365 aff
= isl_aff_zero_on_domain(ls
);
2367 aff
= isl_aff_add_coefficient_si(aff
, isl_dim_in
, 0, 1);
2368 aff
= isl_aff_scale_down_ui(aff
, 3);
2369 aff
= isl_aff_floor(aff
);
2370 aff
= isl_aff_add_coefficient_si(aff
, isl_dim_in
, 0, 1);
2371 aff
= isl_aff_scale_down_ui(aff
, 2);
2372 aff
= isl_aff_floor(aff
);
2373 aff
= isl_aff_add_coefficient_si(aff
, isl_dim_in
, 0, 1);
2376 set
= isl_set_read_from_str(ctx
, str
);
2377 aff
= isl_aff_gist(aff
, set
);
2379 aff
= isl_aff_add_constant_si(aff
, -16);
2380 zero
= isl_aff_plain_is_zero(aff
);
2386 isl_die(ctx
, isl_error_unknown
, "unexpected result", return -1);
2391 int test_dim_max(isl_ctx
*ctx
)
2395 isl_set
*set1
, *set2
;
2400 str
= "[N] -> { [i] : 0 <= i <= min(N,10) }";
2401 set
= isl_set_read_from_str(ctx
, str
);
2402 pwaff
= isl_set_dim_max(set
, 0);
2403 set1
= isl_set_from_pw_aff(pwaff
);
2404 str
= "[N] -> { [10] : N >= 10; [N] : N <= 9 and N >= 0 }";
2405 set2
= isl_set_read_from_str(ctx
, str
);
2406 equal
= isl_set_is_equal(set1
, set2
);
2412 isl_die(ctx
, isl_error_unknown
, "unexpected result", return -1);
2414 str
= "[N] -> { [i] : 0 <= i <= max(2N,N+6) }";
2415 set
= isl_set_read_from_str(ctx
, str
);
2416 pwaff
= isl_set_dim_max(set
, 0);
2417 set1
= isl_set_from_pw_aff(pwaff
);
2418 str
= "[N] -> { [6 + N] : -6 <= N <= 5; [2N] : N >= 6 }";
2419 set2
= isl_set_read_from_str(ctx
, str
);
2420 equal
= isl_set_is_equal(set1
, set2
);
2426 isl_die(ctx
, isl_error_unknown
, "unexpected result", return -1);
2428 str
= "[N] -> { [i] : 0 <= i <= 2N or 0 <= i <= N+6 }";
2429 set
= isl_set_read_from_str(ctx
, str
);
2430 pwaff
= isl_set_dim_max(set
, 0);
2431 set1
= isl_set_from_pw_aff(pwaff
);
2432 str
= "[N] -> { [6 + N] : -6 <= N <= 5; [2N] : N >= 6 }";
2433 set2
= isl_set_read_from_str(ctx
, str
);
2434 equal
= isl_set_is_equal(set1
, set2
);
2440 isl_die(ctx
, isl_error_unknown
, "unexpected result", return -1);
2442 str
= "[N,M] -> { [i,j] -> [([i/16]), i%16, ([j/16]), j%16] : "
2443 "0 <= i < N and 0 <= j < M }";
2444 map
= isl_map_read_from_str(ctx
, str
);
2445 set
= isl_map_range(map
);
2447 pwaff
= isl_set_dim_max(isl_set_copy(set
), 0);
2448 set1
= isl_set_from_pw_aff(pwaff
);
2449 str
= "[N,M] -> { [([(N-1)/16])] : M,N > 0 }";
2450 set2
= isl_set_read_from_str(ctx
, str
);
2451 equal
= isl_set_is_equal(set1
, set2
);
2455 pwaff
= isl_set_dim_max(isl_set_copy(set
), 3);
2456 set1
= isl_set_from_pw_aff(pwaff
);
2457 str
= "[N,M] -> { [t] : t = min(M-1,15) and M,N > 0 }";
2458 set2
= isl_set_read_from_str(ctx
, str
);
2459 if (equal
>= 0 && equal
)
2460 equal
= isl_set_is_equal(set1
, set2
);
2469 isl_die(ctx
, isl_error_unknown
, "unexpected result", return -1);
2474 int test_product(isl_ctx
*ctx
)
2478 isl_union_set
*uset1
, *uset2
;
2482 set
= isl_set_read_from_str(ctx
, str
);
2483 set
= isl_set_product(set
, isl_set_copy(set
));
2484 ok
= isl_set_is_wrapping(set
);
2489 isl_die(ctx
, isl_error_unknown
, "unexpected result", return -1);
2492 uset1
= isl_union_set_read_from_str(ctx
, str
);
2493 uset1
= isl_union_set_product(uset1
, isl_union_set_copy(uset1
));
2494 str
= "{ [[] -> []] }";
2495 uset2
= isl_union_set_read_from_str(ctx
, str
);
2496 ok
= isl_union_set_is_equal(uset1
, uset2
);
2497 isl_union_set_free(uset1
);
2498 isl_union_set_free(uset2
);
2502 isl_die(ctx
, isl_error_unknown
, "unexpected result", return -1);
2507 int test_equal(isl_ctx
*ctx
)
2510 isl_set
*set
, *set2
;
2514 set
= isl_set_read_from_str(ctx
, str
);
2516 set2
= isl_set_read_from_str(ctx
, str
);
2517 equal
= isl_set_is_equal(set
, set2
);
2523 isl_die(ctx
, isl_error_unknown
, "unexpected result", return -1);
2528 static int test_plain_fixed(isl_ctx
*ctx
, __isl_take isl_map
*map
,
2529 enum isl_dim_type type
, unsigned pos
, int fixed
)
2533 test
= isl_map_plain_is_fixed(map
, type
, pos
, NULL
);
2540 isl_die(ctx
, isl_error_unknown
,
2541 "map not detected as fixed", return -1);
2543 isl_die(ctx
, isl_error_unknown
,
2544 "map detected as fixed", return -1);
2547 int test_fixed(isl_ctx
*ctx
)
2552 str
= "{ [i] -> [i] }";
2553 map
= isl_map_read_from_str(ctx
, str
);
2554 if (test_plain_fixed(ctx
, map
, isl_dim_out
, 0, 0))
2556 str
= "{ [i] -> [1] }";
2557 map
= isl_map_read_from_str(ctx
, str
);
2558 if (test_plain_fixed(ctx
, map
, isl_dim_out
, 0, 1))
2560 str
= "{ S_1[p1] -> [o0] : o0 = -2 and p1 >= 1 and p1 <= 7 }";
2561 map
= isl_map_read_from_str(ctx
, str
);
2562 if (test_plain_fixed(ctx
, map
, isl_dim_out
, 0, 1))
2564 map
= isl_map_read_from_str(ctx
, str
);
2565 map
= isl_map_neg(map
);
2566 if (test_plain_fixed(ctx
, map
, isl_dim_out
, 0, 1))
2572 int test_vertices(isl_ctx
*ctx
)
2575 isl_basic_set
*bset
;
2576 isl_vertices
*vertices
;
2578 str
= "{ A[t, i] : t = 12 and i >= 4 and i <= 12 }";
2579 bset
= isl_basic_set_read_from_str(ctx
, str
);
2580 vertices
= isl_basic_set_compute_vertices(bset
);
2581 isl_basic_set_free(bset
);
2582 isl_vertices_free(vertices
);
2586 str
= "{ A[t, i] : t = 14 and i = 1 }";
2587 bset
= isl_basic_set_read_from_str(ctx
, str
);
2588 vertices
= isl_basic_set_compute_vertices(bset
);
2589 isl_basic_set_free(bset
);
2590 isl_vertices_free(vertices
);
2597 int test_union_pw(isl_ctx
*ctx
)
2601 isl_union_set
*uset
;
2602 isl_union_pw_qpolynomial
*upwqp1
, *upwqp2
;
2604 str
= "{ [x] -> x^2 }";
2605 upwqp1
= isl_union_pw_qpolynomial_read_from_str(ctx
, str
);
2606 upwqp2
= isl_union_pw_qpolynomial_copy(upwqp1
);
2607 uset
= isl_union_pw_qpolynomial_domain(upwqp1
);
2608 upwqp1
= isl_union_pw_qpolynomial_copy(upwqp2
);
2609 upwqp1
= isl_union_pw_qpolynomial_intersect_domain(upwqp1
, uset
);
2610 equal
= isl_union_pw_qpolynomial_plain_is_equal(upwqp1
, upwqp2
);
2611 isl_union_pw_qpolynomial_free(upwqp1
);
2612 isl_union_pw_qpolynomial_free(upwqp2
);
2616 isl_die(ctx
, isl_error_unknown
, "unexpected result", return -1);
2623 struct isl_ctx
*ctx
;
2625 srcdir
= getenv("srcdir");
2628 ctx
= isl_ctx_alloc();
2629 if (test_vertices(ctx
) < 0)
2631 if (test_fixed(ctx
) < 0)
2633 if (test_equal(ctx
) < 0)
2635 if (test_product(ctx
) < 0)
2637 if (test_dim_max(ctx
) < 0)
2639 if (test_aff(ctx
) < 0)
2641 if (test_injective(ctx
) < 0)
2643 if (test_schedule(ctx
) < 0)
2645 if (test_union_pw(ctx
) < 0)
2647 test_factorize(ctx
);
2652 test_split_periods(ctx
);
2656 if (test_sv(ctx
) < 0)
2658 test_bijective(ctx
);
2662 test_construction(ctx
);
2665 test_application(ctx
);
2666 test_affine_hull(ctx
);
2667 test_convex_hull(ctx
);
2669 if (test_coalesce(ctx
) < 0)