2 * Copyright 2008-2009 Katholieke Universiteit Leuven
4 * Use of this software is governed by the GNU LGPLv2.1 license
6 * Written by Sven Verdoolaege, K.U.Leuven, Departement
7 * Computerwetenschappen, Celestijnenlaan 200A, B-3001 Leuven, Belgium
13 #include <isl_ctx_private.h>
14 #include <isl_map_private.h>
18 #include <isl/constraint.h>
19 #include <isl/polynomial.h>
20 #include <isl/union_map.h>
21 #include <isl_factorization.h>
22 #include <isl/schedule.h>
26 static char *get_filename(isl_ctx
*ctx
, const char *name
, const char *suffix
) {
29 char *pattern
= "%s/test_inputs/%s.%s";
31 length
= strlen(pattern
) - 6 + strlen(srcdir
) + strlen(name
)
33 filename
= isl_alloc_array(ctx
, char, length
);
38 sprintf(filename
, pattern
, srcdir
, name
, suffix
);
43 void test_parse_map(isl_ctx
*ctx
, const char *str
)
47 map
= isl_map_read_from_str(ctx
, str
, -1);
52 void test_parse_map_equal(isl_ctx
*ctx
, const char *str
, const char *str2
)
56 map
= isl_map_read_from_str(ctx
, str
, -1);
57 map2
= isl_map_read_from_str(ctx
, str2
, -1);
58 assert(map
&& map2
&& isl_map_is_equal(map
, map2
));
63 void test_parse_pwqp(isl_ctx
*ctx
, const char *str
)
65 isl_pw_qpolynomial
*pwqp
;
67 pwqp
= isl_pw_qpolynomial_read_from_str(ctx
, str
);
69 isl_pw_qpolynomial_free(pwqp
);
72 void test_parse(struct isl_ctx
*ctx
)
75 const char *str
, *str2
;
77 str
= "{ [i] -> [-i] }";
78 map
= isl_map_read_from_str(ctx
, str
, -1);
82 str
= "{ A[i] -> L[([i/3])] }";
83 map
= isl_map_read_from_str(ctx
, str
, -1);
87 test_parse_map(ctx
, "{[[s] -> A[i]] -> [[s+1] -> A[i]]}");
88 test_parse_map(ctx
, "{ [p1, y1, y2] -> [2, y1, y2] : "
89 "p1 = 1 && (y1 <= y2 || y2 = 0) }");
91 str
= "{ [x,y] : [([x/2]+y)/3] >= 1 }";
92 str2
= "{ [x, y] : 2y >= 6 - x }";
93 test_parse_map_equal(ctx
, str
, str2
);
95 test_parse_map_equal(ctx
, "{ [x,y] : x <= min(y, 2*y+3) }",
96 "{ [x,y] : x <= y, 2*y + 3 }");
97 str
= "{ [x, y] : (y <= x and y >= -3) or (2y <= -3 + x and y <= -4) }";
98 test_parse_map_equal(ctx
, "{ [x,y] : x >= min(y, 2*y+3) }", str
);
100 str
= "{[new,old] -> [new+1-2*[(new+1)/2],old+1-2*[(old+1)/2]]}";
101 map
= isl_map_read_from_str(ctx
, str
, -1);
102 str
= "{ [new, old] -> [o0, o1] : "
103 "exists (e0 = [(-1 - new + o0)/2], e1 = [(-1 - old + o1)/2]: "
104 "2e0 = -1 - new + o0 and 2e1 = -1 - old + o1 and o0 >= 0 and "
105 "o0 <= 1 and o1 >= 0 and o1 <= 1) }";
106 map2
= isl_map_read_from_str(ctx
, str
, -1);
107 assert(isl_map_is_equal(map
, map2
));
111 str
= "{[new,old] -> [new+1-2*[(new+1)/2],old+1-2*[(old+1)/2]]}";
112 map
= isl_map_read_from_str(ctx
, str
, -1);
113 str
= "{[new,old] -> [(new+1)%2,(old+1)%2]}";
114 map2
= isl_map_read_from_str(ctx
, str
, -1);
115 assert(isl_map_is_equal(map
, map2
));
119 str
= "[n] -> { [c1] : c1>=0 and c1<=floord(n-4,3) }";
120 str2
= "[n] -> { [c1] : c1 >= 0 and 3c1 <= -4 + n }";
121 test_parse_map_equal(ctx
, str
, str2
);
123 str
= "{ [i,j] -> [i] : i < j; [i,j] -> [j] : j <= i }";
124 str2
= "{ [i,j] -> [min(i,j)] }";
125 test_parse_map_equal(ctx
, str
, str2
);
127 str
= "{ [i,j] : i != j }";
128 str2
= "{ [i,j] : i < j or i > j }";
129 test_parse_map_equal(ctx
, str
, str2
);
131 str
= "{ [i,j] : (i+1)*2 >= j }";
132 str2
= "{ [i, j] : j <= 2 + 2i }";
133 test_parse_map_equal(ctx
, str
, str2
);
135 str
= "{ [i] -> [i > 0 ? 4 : 5] }";
136 str2
= "{ [i] -> [5] : i <= 0; [i] -> [4] : i >= 1 }";
137 test_parse_map_equal(ctx
, str
, str2
);
139 str
= "[N=2,M] -> { [i=[(M+N)/4]] }";
140 str2
= "[N, M] -> { [i] : N = 2 and 4i <= 2 + M and 4i >= -1 + M }";
141 test_parse_map_equal(ctx
, str
, str2
);
143 test_parse_pwqp(ctx
, "{ [i] -> i + [ (i + [i/3])/2 ] }");
144 test_parse_map(ctx
, "{ S1[i] -> [([i/10]),i%10] : 0 <= i <= 45 }");
147 void test_read(struct isl_ctx
*ctx
)
151 struct isl_basic_set
*bset1
, *bset2
;
152 const char *str
= "{[y]: Exists ( alpha : 2alpha = y)}";
154 filename
= get_filename(ctx
, "set", "omega");
156 input
= fopen(filename
, "r");
159 bset1
= isl_basic_set_read_from_file(ctx
, input
, 0);
160 bset2
= isl_basic_set_read_from_str(ctx
, str
, 0);
162 assert(isl_basic_set_is_equal(bset1
, bset2
) == 1);
164 isl_basic_set_free(bset1
);
165 isl_basic_set_free(bset2
);
171 void test_bounded(struct isl_ctx
*ctx
)
176 set
= isl_set_read_from_str(ctx
, "[n] -> {[i] : 0 <= i <= n }", -1);
177 bounded
= isl_set_is_bounded(set
);
181 set
= isl_set_read_from_str(ctx
, "{[n, i] : 0 <= i <= n }", -1);
182 bounded
= isl_set_is_bounded(set
);
186 set
= isl_set_read_from_str(ctx
, "[n] -> {[i] : i <= n }", -1);
187 bounded
= isl_set_is_bounded(set
);
192 /* Construct the basic set { [i] : 5 <= i <= N } */
193 void test_construction(struct isl_ctx
*ctx
)
197 struct isl_basic_set
*bset
;
198 struct isl_constraint
*c
;
202 dim
= isl_space_set_alloc(ctx
, 1, 1);
203 bset
= isl_basic_set_universe(dim
);
205 c
= isl_inequality_alloc(isl_basic_set_get_space(bset
));
206 isl_int_set_si(v
, -1);
207 isl_constraint_set_coefficient(c
, isl_dim_set
, 0, v
);
208 isl_int_set_si(v
, 1);
209 isl_constraint_set_coefficient(c
, isl_dim_param
, 0, v
);
210 bset
= isl_basic_set_add_constraint(bset
, c
);
212 c
= isl_inequality_alloc(isl_basic_set_get_space(bset
));
213 isl_int_set_si(v
, 1);
214 isl_constraint_set_coefficient(c
, isl_dim_set
, 0, v
);
215 isl_int_set_si(v
, -5);
216 isl_constraint_set_constant(c
, v
);
217 bset
= isl_basic_set_add_constraint(bset
, c
);
219 isl_basic_set_free(bset
);
224 void test_dim(struct isl_ctx
*ctx
)
227 isl_map
*map1
, *map2
;
229 map1
= isl_map_read_from_str(ctx
,
230 "[n] -> { [i] -> [j] : exists (a = [i/10] : i - 10a <= n ) }", -1);
231 map1
= isl_map_add_dims(map1
, isl_dim_in
, 1);
232 map2
= isl_map_read_from_str(ctx
,
233 "[n] -> { [i,k] -> [j] : exists (a = [i/10] : i - 10a <= n ) }", -1);
234 assert(isl_map_is_equal(map1
, map2
));
237 map1
= isl_map_project_out(map1
, isl_dim_in
, 0, 1);
238 map2
= isl_map_read_from_str(ctx
, "[n] -> { [i] -> [j] : n >= 0 }", -1);
239 assert(isl_map_is_equal(map1
, map2
));
244 str
= "[n] -> { [i] -> [] : exists a : 0 <= i <= n and i = 2 a }";
245 map1
= isl_map_read_from_str(ctx
, str
, -1);
246 str
= "{ [i] -> [j] : exists a : 0 <= i <= j and i = 2 a }";
247 map2
= isl_map_read_from_str(ctx
, str
, -1);
248 map1
= isl_map_move_dims(map1
, isl_dim_out
, 0, isl_dim_param
, 0, 1);
249 assert(isl_map_is_equal(map1
, map2
));
255 void test_div(struct isl_ctx
*ctx
)
259 struct isl_basic_set
*bset
;
260 struct isl_constraint
*c
;
265 dim
= isl_space_set_alloc(ctx
, 0, 3);
266 bset
= isl_basic_set_universe(dim
);
268 c
= isl_equality_alloc(isl_basic_set_get_space(bset
));
269 isl_int_set_si(v
, -1);
270 isl_constraint_set_constant(c
, v
);
271 isl_int_set_si(v
, 1);
272 isl_constraint_set_coefficient(c
, isl_dim_set
, 0, v
);
273 isl_int_set_si(v
, 3);
274 isl_constraint_set_coefficient(c
, isl_dim_set
, 1, v
);
275 bset
= isl_basic_set_add_constraint(bset
, c
);
277 c
= isl_equality_alloc(isl_basic_set_get_space(bset
));
278 isl_int_set_si(v
, 1);
279 isl_constraint_set_constant(c
, v
);
280 isl_int_set_si(v
, -1);
281 isl_constraint_set_coefficient(c
, isl_dim_set
, 0, v
);
282 isl_int_set_si(v
, 3);
283 isl_constraint_set_coefficient(c
, isl_dim_set
, 2, v
);
284 bset
= isl_basic_set_add_constraint(bset
, c
);
286 bset
= isl_basic_set_project_out(bset
, isl_dim_set
, 1, 2);
288 assert(bset
&& bset
->n_div
== 1);
289 isl_basic_set_free(bset
);
292 dim
= isl_space_set_alloc(ctx
, 0, 3);
293 bset
= isl_basic_set_universe(dim
);
295 c
= isl_equality_alloc(isl_basic_set_get_space(bset
));
296 isl_int_set_si(v
, 1);
297 isl_constraint_set_constant(c
, v
);
298 isl_int_set_si(v
, -1);
299 isl_constraint_set_coefficient(c
, isl_dim_set
, 0, v
);
300 isl_int_set_si(v
, 3);
301 isl_constraint_set_coefficient(c
, isl_dim_set
, 1, v
);
302 bset
= isl_basic_set_add_constraint(bset
, c
);
304 c
= isl_equality_alloc(isl_basic_set_get_space(bset
));
305 isl_int_set_si(v
, -1);
306 isl_constraint_set_constant(c
, v
);
307 isl_int_set_si(v
, 1);
308 isl_constraint_set_coefficient(c
, isl_dim_set
, 0, v
);
309 isl_int_set_si(v
, 3);
310 isl_constraint_set_coefficient(c
, isl_dim_set
, 2, v
);
311 bset
= isl_basic_set_add_constraint(bset
, c
);
313 bset
= isl_basic_set_project_out(bset
, isl_dim_set
, 1, 2);
315 assert(bset
&& bset
->n_div
== 1);
316 isl_basic_set_free(bset
);
319 dim
= isl_space_set_alloc(ctx
, 0, 3);
320 bset
= isl_basic_set_universe(dim
);
322 c
= isl_equality_alloc(isl_basic_set_get_space(bset
));
323 isl_int_set_si(v
, 1);
324 isl_constraint_set_constant(c
, v
);
325 isl_int_set_si(v
, -1);
326 isl_constraint_set_coefficient(c
, isl_dim_set
, 0, v
);
327 isl_int_set_si(v
, 3);
328 isl_constraint_set_coefficient(c
, isl_dim_set
, 1, v
);
329 bset
= isl_basic_set_add_constraint(bset
, c
);
331 c
= isl_equality_alloc(isl_basic_set_get_space(bset
));
332 isl_int_set_si(v
, -3);
333 isl_constraint_set_constant(c
, v
);
334 isl_int_set_si(v
, 1);
335 isl_constraint_set_coefficient(c
, isl_dim_set
, 0, v
);
336 isl_int_set_si(v
, 4);
337 isl_constraint_set_coefficient(c
, isl_dim_set
, 2, v
);
338 bset
= isl_basic_set_add_constraint(bset
, c
);
340 bset
= isl_basic_set_project_out(bset
, isl_dim_set
, 1, 2);
342 assert(bset
&& bset
->n_div
== 1);
343 isl_basic_set_free(bset
);
346 dim
= isl_space_set_alloc(ctx
, 0, 3);
347 bset
= isl_basic_set_universe(dim
);
349 c
= isl_equality_alloc(isl_basic_set_get_space(bset
));
350 isl_int_set_si(v
, 2);
351 isl_constraint_set_constant(c
, v
);
352 isl_int_set_si(v
, -1);
353 isl_constraint_set_coefficient(c
, isl_dim_set
, 0, v
);
354 isl_int_set_si(v
, 3);
355 isl_constraint_set_coefficient(c
, isl_dim_set
, 1, v
);
356 bset
= isl_basic_set_add_constraint(bset
, c
);
358 c
= isl_equality_alloc(isl_basic_set_get_space(bset
));
359 isl_int_set_si(v
, -1);
360 isl_constraint_set_constant(c
, v
);
361 isl_int_set_si(v
, 1);
362 isl_constraint_set_coefficient(c
, isl_dim_set
, 0, v
);
363 isl_int_set_si(v
, 6);
364 isl_constraint_set_coefficient(c
, isl_dim_set
, 2, v
);
365 bset
= isl_basic_set_add_constraint(bset
, c
);
367 bset
= isl_basic_set_project_out(bset
, isl_dim_set
, 1, 2);
369 assert(isl_basic_set_is_empty(bset
));
370 isl_basic_set_free(bset
);
373 dim
= isl_space_set_alloc(ctx
, 0, 3);
374 bset
= isl_basic_set_universe(dim
);
376 c
= isl_equality_alloc(isl_basic_set_get_space(bset
));
377 isl_int_set_si(v
, -1);
378 isl_constraint_set_coefficient(c
, isl_dim_set
, 0, v
);
379 isl_int_set_si(v
, 3);
380 isl_constraint_set_coefficient(c
, isl_dim_set
, 2, v
);
381 bset
= isl_basic_set_add_constraint(bset
, c
);
383 c
= isl_equality_alloc(isl_basic_set_get_space(bset
));
384 isl_int_set_si(v
, 1);
385 isl_constraint_set_coefficient(c
, isl_dim_set
, 0, v
);
386 isl_int_set_si(v
, -3);
387 isl_constraint_set_coefficient(c
, isl_dim_set
, 1, v
);
388 bset
= isl_basic_set_add_constraint(bset
, c
);
390 bset
= isl_basic_set_project_out(bset
, isl_dim_set
, 2, 1);
392 assert(bset
&& bset
->n_div
== 0);
393 isl_basic_set_free(bset
);
396 dim
= isl_space_set_alloc(ctx
, 0, 3);
397 bset
= isl_basic_set_universe(dim
);
399 c
= isl_equality_alloc(isl_basic_set_get_space(bset
));
400 isl_int_set_si(v
, -1);
401 isl_constraint_set_coefficient(c
, isl_dim_set
, 0, v
);
402 isl_int_set_si(v
, 6);
403 isl_constraint_set_coefficient(c
, isl_dim_set
, 2, v
);
404 bset
= isl_basic_set_add_constraint(bset
, c
);
406 c
= isl_equality_alloc(isl_basic_set_get_space(bset
));
407 isl_int_set_si(v
, 1);
408 isl_constraint_set_coefficient(c
, isl_dim_set
, 0, v
);
409 isl_int_set_si(v
, -3);
410 isl_constraint_set_coefficient(c
, isl_dim_set
, 1, v
);
411 bset
= isl_basic_set_add_constraint(bset
, c
);
413 bset
= isl_basic_set_project_out(bset
, isl_dim_set
, 2, 1);
415 assert(bset
&& bset
->n_div
== 1);
416 isl_basic_set_free(bset
);
419 /* This test is a bit tricky. We set up an equality
421 * Normalization of divs creates _two_ divs
424 * Afterwards e0 is removed again because it has coefficient -1
425 * and we end up with the original equality and div again.
426 * Perhaps we can avoid the introduction of this temporary div.
428 dim
= isl_space_set_alloc(ctx
, 0, 4);
429 bset
= isl_basic_set_universe(dim
);
431 c
= isl_equality_alloc(isl_basic_set_get_space(bset
));
432 isl_int_set_si(v
, -1);
433 isl_constraint_set_coefficient(c
, isl_dim_set
, 0, v
);
434 isl_int_set_si(v
, -3);
435 isl_constraint_set_coefficient(c
, isl_dim_set
, 1, v
);
436 isl_int_set_si(v
, -3);
437 isl_constraint_set_coefficient(c
, isl_dim_set
, 2, v
);
438 isl_int_set_si(v
, 6);
439 isl_constraint_set_coefficient(c
, isl_dim_set
, 3, v
);
440 bset
= isl_basic_set_add_constraint(bset
, c
);
442 bset
= isl_basic_set_project_out(bset
, isl_dim_set
, 3, 1);
444 /* Test disabled for now */
446 assert(bset && bset->n_div == 1);
448 isl_basic_set_free(bset
);
451 dim
= isl_space_set_alloc(ctx
, 0, 5);
452 bset
= isl_basic_set_universe(dim
);
454 c
= isl_equality_alloc(isl_basic_set_get_space(bset
));
455 isl_int_set_si(v
, -1);
456 isl_constraint_set_coefficient(c
, isl_dim_set
, 0, v
);
457 isl_int_set_si(v
, -3);
458 isl_constraint_set_coefficient(c
, isl_dim_set
, 1, v
);
459 isl_int_set_si(v
, -3);
460 isl_constraint_set_coefficient(c
, isl_dim_set
, 3, v
);
461 isl_int_set_si(v
, 6);
462 isl_constraint_set_coefficient(c
, isl_dim_set
, 4, v
);
463 bset
= isl_basic_set_add_constraint(bset
, c
);
465 c
= isl_equality_alloc(isl_basic_set_get_space(bset
));
466 isl_int_set_si(v
, -1);
467 isl_constraint_set_coefficient(c
, isl_dim_set
, 0, v
);
468 isl_int_set_si(v
, 1);
469 isl_constraint_set_coefficient(c
, isl_dim_set
, 2, v
);
470 isl_int_set_si(v
, 1);
471 isl_constraint_set_constant(c
, v
);
472 bset
= isl_basic_set_add_constraint(bset
, c
);
474 bset
= isl_basic_set_project_out(bset
, isl_dim_set
, 4, 1);
476 /* Test disabled for now */
478 assert(bset && bset->n_div == 1);
480 isl_basic_set_free(bset
);
483 dim
= isl_space_set_alloc(ctx
, 0, 4);
484 bset
= isl_basic_set_universe(dim
);
486 c
= isl_equality_alloc(isl_basic_set_get_space(bset
));
487 isl_int_set_si(v
, 1);
488 isl_constraint_set_coefficient(c
, isl_dim_set
, 0, v
);
489 isl_int_set_si(v
, -1);
490 isl_constraint_set_coefficient(c
, isl_dim_set
, 1, v
);
491 isl_int_set_si(v
, -2);
492 isl_constraint_set_coefficient(c
, isl_dim_set
, 2, v
);
493 bset
= isl_basic_set_add_constraint(bset
, c
);
495 c
= isl_equality_alloc(isl_basic_set_get_space(bset
));
496 isl_int_set_si(v
, -1);
497 isl_constraint_set_coefficient(c
, isl_dim_set
, 0, v
);
498 isl_int_set_si(v
, 3);
499 isl_constraint_set_coefficient(c
, isl_dim_set
, 3, v
);
500 isl_int_set_si(v
, 2);
501 isl_constraint_set_constant(c
, v
);
502 bset
= isl_basic_set_add_constraint(bset
, c
);
504 bset
= isl_basic_set_project_out(bset
, isl_dim_set
, 2, 2);
506 bset
= isl_basic_set_fix_si(bset
, isl_dim_set
, 0, 2);
508 assert(!isl_basic_set_is_empty(bset
));
510 isl_basic_set_free(bset
);
513 dim
= isl_space_set_alloc(ctx
, 0, 3);
514 bset
= isl_basic_set_universe(dim
);
516 c
= isl_equality_alloc(isl_basic_set_get_space(bset
));
517 isl_int_set_si(v
, 1);
518 isl_constraint_set_coefficient(c
, isl_dim_set
, 0, v
);
519 isl_int_set_si(v
, -2);
520 isl_constraint_set_coefficient(c
, isl_dim_set
, 2, v
);
521 bset
= isl_basic_set_add_constraint(bset
, c
);
523 bset
= isl_basic_set_project_out(bset
, isl_dim_set
, 2, 1);
525 bset
= isl_basic_set_fix_si(bset
, isl_dim_set
, 0, 2);
527 isl_basic_set_free(bset
);
532 void test_application_case(struct isl_ctx
*ctx
, const char *name
)
536 struct isl_basic_set
*bset1
, *bset2
;
537 struct isl_basic_map
*bmap
;
539 filename
= get_filename(ctx
, name
, "omega");
541 input
= fopen(filename
, "r");
544 bset1
= isl_basic_set_read_from_file(ctx
, input
, 0);
545 bmap
= isl_basic_map_read_from_file(ctx
, input
, 0);
547 bset1
= isl_basic_set_apply(bset1
, bmap
);
549 bset2
= isl_basic_set_read_from_file(ctx
, input
, 0);
551 assert(isl_basic_set_is_equal(bset1
, bset2
) == 1);
553 isl_basic_set_free(bset1
);
554 isl_basic_set_free(bset2
);
560 void test_application(struct isl_ctx
*ctx
)
562 test_application_case(ctx
, "application");
563 test_application_case(ctx
, "application2");
566 void test_affine_hull_case(struct isl_ctx
*ctx
, const char *name
)
570 struct isl_basic_set
*bset1
, *bset2
;
572 filename
= get_filename(ctx
, name
, "polylib");
574 input
= fopen(filename
, "r");
577 bset1
= isl_basic_set_read_from_file(ctx
, input
, 0);
578 bset2
= isl_basic_set_read_from_file(ctx
, input
, 0);
580 bset1
= isl_basic_set_affine_hull(bset1
);
582 assert(isl_basic_set_is_equal(bset1
, bset2
) == 1);
584 isl_basic_set_free(bset1
);
585 isl_basic_set_free(bset2
);
591 void test_affine_hull(struct isl_ctx
*ctx
)
593 test_affine_hull_case(ctx
, "affine2");
594 test_affine_hull_case(ctx
, "affine");
595 test_affine_hull_case(ctx
, "affine3");
598 void test_convex_hull_case(struct isl_ctx
*ctx
, const char *name
)
602 struct isl_basic_set
*bset1
, *bset2
;
605 filename
= get_filename(ctx
, name
, "polylib");
607 input
= fopen(filename
, "r");
610 bset1
= isl_basic_set_read_from_file(ctx
, input
, 0);
611 bset2
= isl_basic_set_read_from_file(ctx
, input
, 0);
613 set
= isl_basic_set_union(bset1
, bset2
);
614 bset1
= isl_set_convex_hull(set
);
616 bset2
= isl_basic_set_read_from_file(ctx
, input
, 0);
618 assert(isl_basic_set_is_equal(bset1
, bset2
) == 1);
620 isl_basic_set_free(bset1
);
621 isl_basic_set_free(bset2
);
627 void test_convex_hull_algo(struct isl_ctx
*ctx
, int convex
)
629 const char *str1
, *str2
;
630 isl_set
*set1
, *set2
;
631 int orig_convex
= ctx
->opt
->convex
;
632 ctx
->opt
->convex
= convex
;
634 test_convex_hull_case(ctx
, "convex0");
635 test_convex_hull_case(ctx
, "convex1");
636 test_convex_hull_case(ctx
, "convex2");
637 test_convex_hull_case(ctx
, "convex3");
638 test_convex_hull_case(ctx
, "convex4");
639 test_convex_hull_case(ctx
, "convex5");
640 test_convex_hull_case(ctx
, "convex6");
641 test_convex_hull_case(ctx
, "convex7");
642 test_convex_hull_case(ctx
, "convex8");
643 test_convex_hull_case(ctx
, "convex9");
644 test_convex_hull_case(ctx
, "convex10");
645 test_convex_hull_case(ctx
, "convex11");
646 test_convex_hull_case(ctx
, "convex12");
647 test_convex_hull_case(ctx
, "convex13");
648 test_convex_hull_case(ctx
, "convex14");
649 test_convex_hull_case(ctx
, "convex15");
651 str1
= "{ [i0, i1, i2] : (i2 = 1 and i0 = 0 and i1 >= 0) or "
652 "(i0 = 1 and i1 = 0 and i2 = 1) or "
653 "(i0 = 0 and i1 = 0 and i2 = 0) }";
654 str2
= "{ [i0, i1, i2] : i0 >= 0 and i2 >= i0 and i2 <= 1 and i1 >= 0 }";
655 set1
= isl_set_read_from_str(ctx
, str1
, -1);
656 set2
= isl_set_read_from_str(ctx
, str2
, -1);
657 set1
= isl_set_from_basic_set(isl_set_convex_hull(set1
));
658 assert(isl_set_is_equal(set1
, set2
));
662 ctx
->opt
->convex
= orig_convex
;
665 void test_convex_hull(struct isl_ctx
*ctx
)
667 test_convex_hull_algo(ctx
, ISL_CONVEX_HULL_FM
);
668 test_convex_hull_algo(ctx
, ISL_CONVEX_HULL_WRAP
);
671 void test_gist_case(struct isl_ctx
*ctx
, const char *name
)
675 struct isl_basic_set
*bset1
, *bset2
;
677 filename
= get_filename(ctx
, name
, "polylib");
679 input
= fopen(filename
, "r");
682 bset1
= isl_basic_set_read_from_file(ctx
, input
, 0);
683 bset2
= isl_basic_set_read_from_file(ctx
, input
, 0);
685 bset1
= isl_basic_set_gist(bset1
, bset2
);
687 bset2
= isl_basic_set_read_from_file(ctx
, input
, 0);
689 assert(isl_basic_set_is_equal(bset1
, bset2
) == 1);
691 isl_basic_set_free(bset1
);
692 isl_basic_set_free(bset2
);
698 void test_gist(struct isl_ctx
*ctx
)
701 isl_basic_set
*bset1
, *bset2
;
703 test_gist_case(ctx
, "gist1");
705 str
= "[p0, p2, p3, p5, p6, p10] -> { [] : "
706 "exists (e0 = [(15 + p0 + 15p6 + 15p10)/16], e1 = [(p5)/8], "
707 "e2 = [(p6)/128], e3 = [(8p2 - p5)/128], "
708 "e4 = [(128p3 - p6)/4096]: 8e1 = p5 and 128e2 = p6 and "
709 "128e3 = 8p2 - p5 and 4096e4 = 128p3 - p6 and p2 >= 0 and "
710 "16e0 >= 16 + 16p6 + 15p10 and p2 <= 15 and p3 >= 0 and "
711 "p3 <= 31 and p6 >= 128p3 and p5 >= 8p2 and p10 >= 0 and "
712 "16e0 <= 15 + p0 + 15p6 + 15p10 and 16e0 >= p0 + 15p6 + 15p10 and "
713 "p10 <= 15 and p10 <= -1 + p0 - p6) }";
714 bset1
= isl_basic_set_read_from_str(ctx
, str
, -1);
715 str
= "[p0, p2, p3, p5, p6, p10] -> { [] : exists (e0 = [(p5)/8], "
716 "e1 = [(p6)/128], e2 = [(8p2 - p5)/128], "
717 "e3 = [(128p3 - p6)/4096]: 8e0 = p5 and 128e1 = p6 and "
718 "128e2 = 8p2 - p5 and 4096e3 = 128p3 - p6 and p5 >= -7 and "
719 "p2 >= 0 and 8p2 <= -1 + p0 and p2 <= 15 and p3 >= 0 and "
720 "p3 <= 31 and 128p3 <= -1 + p0 and p6 >= -127 and "
721 "p5 <= -1 + p0 and p6 <= -1 + p0 and p6 >= 128p3 and "
722 "p0 >= 1 and p5 >= 8p2 and p10 >= 0 and p10 <= 15 ) }";
723 bset2
= isl_basic_set_read_from_str(ctx
, str
, -1);
724 bset1
= isl_basic_set_gist(bset1
, bset2
);
725 assert(bset1
&& bset1
->n_div
== 0);
726 isl_basic_set_free(bset1
);
729 void test_coalesce_set(isl_ctx
*ctx
, const char *str
, int check_one
)
733 set
= isl_set_read_from_str(ctx
, str
, -1);
734 set
= isl_set_coalesce(set
);
735 set2
= isl_set_read_from_str(ctx
, str
, -1);
736 assert(isl_set_is_equal(set
, set2
));
738 assert(set
&& set
->n
== 1);
743 void test_coalesce(struct isl_ctx
*ctx
)
746 struct isl_set
*set
, *set2
;
747 struct isl_map
*map
, *map2
;
749 set
= isl_set_read_from_str(ctx
,
750 "{[x,y]: x >= 0 & x <= 10 & y >= 0 & y <= 10 or "
751 "y >= x & x >= 2 & 5 >= y }", -1);
752 set
= isl_set_coalesce(set
);
753 assert(set
&& set
->n
== 1);
756 set
= isl_set_read_from_str(ctx
,
757 "{[x,y]: y >= 0 & 2x + y <= 30 & y <= 10 & x >= 0 or "
758 "x + y >= 10 & y <= x & x + y <= 20 & y >= 0}", -1);
759 set
= isl_set_coalesce(set
);
760 assert(set
&& set
->n
== 1);
763 set
= isl_set_read_from_str(ctx
,
764 "{[x,y]: y >= 0 & 2x + y <= 30 & y <= 10 & x >= 0 or "
765 "x + y >= 10 & y <= x & x + y <= 19 & y >= 0}", -1);
766 set
= isl_set_coalesce(set
);
767 assert(set
&& set
->n
== 2);
770 set
= isl_set_read_from_str(ctx
,
771 "{[x,y]: y >= 0 & x <= 5 & y <= x or "
772 "y >= 0 & x >= 6 & x <= 10 & y <= x}", -1);
773 set
= isl_set_coalesce(set
);
774 assert(set
&& set
->n
== 1);
777 set
= isl_set_read_from_str(ctx
,
778 "{[x,y]: y >= 0 & x <= 5 & y <= x or "
779 "y >= 0 & x >= 7 & x <= 10 & y <= x}", -1);
780 set
= isl_set_coalesce(set
);
781 assert(set
&& set
->n
== 2);
784 set
= isl_set_read_from_str(ctx
,
785 "{[x,y]: y >= 0 & x <= 5 & y <= x or "
786 "y >= 0 & x >= 6 & x <= 10 & y + 1 <= x}", -1);
787 set
= isl_set_coalesce(set
);
788 assert(set
&& set
->n
== 2);
791 set
= isl_set_read_from_str(ctx
,
792 "{[x,y]: y >= 0 & x <= 5 & y <= x or "
793 "y >= 0 & x = 6 & y <= 6}", -1);
794 set
= isl_set_coalesce(set
);
795 assert(set
&& set
->n
== 1);
798 set
= isl_set_read_from_str(ctx
,
799 "{[x,y]: y >= 0 & x <= 5 & y <= x or "
800 "y >= 0 & x = 7 & y <= 6}", -1);
801 set
= isl_set_coalesce(set
);
802 assert(set
&& set
->n
== 2);
805 set
= isl_set_read_from_str(ctx
,
806 "{[x,y]: y >= 0 & x <= 5 & y <= x or "
807 "y >= 0 & x = 6 & y <= 5}", -1);
808 set
= isl_set_coalesce(set
);
809 assert(set
&& set
->n
== 1);
810 set2
= isl_set_read_from_str(ctx
,
811 "{[x,y]: y >= 0 & x <= 5 & y <= x or "
812 "y >= 0 & x = 6 & y <= 5}", -1);
813 assert(isl_set_is_equal(set
, set2
));
817 set
= isl_set_read_from_str(ctx
,
818 "{[x,y]: y >= 0 & x <= 5 & y <= x or "
819 "y >= 0 & x = 6 & y <= 7}", -1);
820 set
= isl_set_coalesce(set
);
821 assert(set
&& set
->n
== 2);
824 set
= isl_set_read_from_str(ctx
,
825 "[n] -> { [i] : i = 1 and n >= 2 or 2 <= i and i <= n }", -1);
826 set
= isl_set_coalesce(set
);
827 assert(set
&& set
->n
== 1);
828 set2
= isl_set_read_from_str(ctx
,
829 "[n] -> { [i] : i = 1 and n >= 2 or 2 <= i and i <= n }", -1);
830 assert(isl_set_is_equal(set
, set2
));
834 set
= isl_set_read_from_str(ctx
,
835 "{[x,y] : x >= 0 and y >= 0 or 0 <= y and y <= 5 and x = -1}", -1);
836 set
= isl_set_coalesce(set
);
837 set2
= isl_set_read_from_str(ctx
,
838 "{[x,y] : x >= 0 and y >= 0 or 0 <= y and y <= 5 and x = -1}", -1);
839 assert(isl_set_is_equal(set
, set2
));
843 set
= isl_set_read_from_str(ctx
,
844 "[n] -> { [i] : 1 <= i and i <= n - 1 or "
845 "2 <= i and i <= n }", -1);
846 set
= isl_set_coalesce(set
);
847 assert(set
&& set
->n
== 1);
848 set2
= isl_set_read_from_str(ctx
,
849 "[n] -> { [i] : 1 <= i and i <= n - 1 or "
850 "2 <= i and i <= n }", -1);
851 assert(isl_set_is_equal(set
, set2
));
855 map
= isl_map_read_from_str(ctx
,
856 "[n] -> { [i0] -> [o0] : exists (e0 = [(i0)/4], e1 = [(o0)/4], "
857 "e2 = [(n)/2], e3 = [(-2 + i0)/4], e4 = [(-2 + o0)/4], "
858 "e5 = [(-2n + i0)/4]: 2e2 = n and 4e3 = -2 + i0 and "
859 "4e4 = -2 + o0 and i0 >= 8 + 2n and o0 >= 2 + i0 and "
860 "o0 <= 56 + 2n and o0 <= -12 + 4n and i0 <= 57 + 2n and "
861 "i0 <= -11 + 4n and o0 >= 6 + 2n and 4e0 <= i0 and "
862 "4e0 >= -3 + i0 and 4e1 <= o0 and 4e1 >= -3 + o0 and "
863 "4e5 <= -2n + i0 and 4e5 >= -3 - 2n + i0);"
864 "[i0] -> [o0] : exists (e0 = [(i0)/4], e1 = [(o0)/4], "
865 "e2 = [(n)/2], e3 = [(-2 + i0)/4], e4 = [(-2 + o0)/4], "
866 "e5 = [(-2n + i0)/4]: 2e2 = n and 4e3 = -2 + i0 and "
867 "4e4 = -2 + o0 and 2e0 >= 3 + n and e0 <= -4 + n and "
868 "2e0 <= 27 + n and e1 <= -4 + n and 2e1 <= 27 + n and "
869 "2e1 >= 2 + n and e1 >= 1 + e0 and i0 >= 7 + 2n and "
870 "i0 <= -11 + 4n and i0 <= 57 + 2n and 4e0 <= -2 + i0 and "
871 "4e0 >= -3 + i0 and o0 >= 6 + 2n and o0 <= -11 + 4n and "
872 "o0 <= 57 + 2n and 4e1 <= -2 + o0 and 4e1 >= -3 + o0 and "
873 "4e5 <= -2n + i0 and 4e5 >= -3 - 2n + i0 ) }", -1);
874 map
= isl_map_coalesce(map
);
875 map2
= isl_map_read_from_str(ctx
,
876 "[n] -> { [i0] -> [o0] : exists (e0 = [(i0)/4], e1 = [(o0)/4], "
877 "e2 = [(n)/2], e3 = [(-2 + i0)/4], e4 = [(-2 + o0)/4], "
878 "e5 = [(-2n + i0)/4]: 2e2 = n and 4e3 = -2 + i0 and "
879 "4e4 = -2 + o0 and i0 >= 8 + 2n and o0 >= 2 + i0 and "
880 "o0 <= 56 + 2n and o0 <= -12 + 4n and i0 <= 57 + 2n and "
881 "i0 <= -11 + 4n and o0 >= 6 + 2n and 4e0 <= i0 and "
882 "4e0 >= -3 + i0 and 4e1 <= o0 and 4e1 >= -3 + o0 and "
883 "4e5 <= -2n + i0 and 4e5 >= -3 - 2n + i0);"
884 "[i0] -> [o0] : exists (e0 = [(i0)/4], e1 = [(o0)/4], "
885 "e2 = [(n)/2], e3 = [(-2 + i0)/4], e4 = [(-2 + o0)/4], "
886 "e5 = [(-2n + i0)/4]: 2e2 = n and 4e3 = -2 + i0 and "
887 "4e4 = -2 + o0 and 2e0 >= 3 + n and e0 <= -4 + n and "
888 "2e0 <= 27 + n and e1 <= -4 + n and 2e1 <= 27 + n and "
889 "2e1 >= 2 + n and e1 >= 1 + e0 and i0 >= 7 + 2n and "
890 "i0 <= -11 + 4n and i0 <= 57 + 2n and 4e0 <= -2 + i0 and "
891 "4e0 >= -3 + i0 and o0 >= 6 + 2n and o0 <= -11 + 4n and "
892 "o0 <= 57 + 2n and 4e1 <= -2 + o0 and 4e1 >= -3 + o0 and "
893 "4e5 <= -2n + i0 and 4e5 >= -3 - 2n + i0 ) }", -1);
894 assert(isl_map_is_equal(map
, map2
));
898 str
= "[n, m] -> { [] -> [o0, o2, o3] : (o3 = 1 and o0 >= 1 + m and "
899 "o0 <= n + m and o2 <= m and o0 >= 2 + n and o2 >= 3) or "
900 "(o0 >= 2 + n and o0 >= 1 + m and o0 <= n + m and n >= 1 and "
901 "o3 <= -1 + o2 and o3 >= 1 - m + o2 and o3 >= 2 and o3 <= n) }";
902 map
= isl_map_read_from_str(ctx
, str
, -1);
903 map
= isl_map_coalesce(map
);
904 map2
= isl_map_read_from_str(ctx
, str
, -1);
905 assert(isl_map_is_equal(map
, map2
));
909 str
= "[M, N] -> { [i0, i1, i2, i3, i4, i5, i6] -> "
910 "[o0, o1, o2, o3, o4, o5, o6] : "
911 "(o6 <= -4 + 2M - 2N + i0 + i1 - i2 + i6 - o0 - o1 + o2 and "
912 "o3 <= -2 + i3 and o6 >= 2 + i0 + i3 + i6 - o0 - o3 and "
913 "o6 >= 2 - M + N + i3 + i4 + i6 - o3 - o4 and o0 <= -1 + i0 and "
914 "o4 >= 4 - 3M + 3N - i0 - i1 + i2 + 2i3 + i4 + o0 + o1 - o2 - 2o3 "
915 "and o6 <= -3 + 2M - 2N + i3 + i4 - i5 + i6 - o3 - o4 + o5 and "
916 "2o6 <= -5 + 5M - 5N + 2i0 + i1 - i2 - i5 + 2i6 - 2o0 - o1 + o2 + o5 "
917 "and o6 >= 2i0 + i1 + i6 - 2o0 - o1 and "
918 "3o6 <= -5 + 4M - 4N + 2i0 + i1 - i2 + 2i3 + i4 - i5 + 3i6 "
919 "- 2o0 - o1 + o2 - 2o3 - o4 + o5) or "
920 "(N >= 2 and o3 <= -1 + i3 and o0 <= -1 + i0 and "
921 "o6 >= i3 + i6 - o3 and M >= 0 and "
922 "2o6 >= 1 + i0 + i3 + 2i6 - o0 - o3 and "
923 "o6 >= 1 - M + i0 + i6 - o0 and N >= 2M and o6 >= i0 + i6 - o0) }";
924 map
= isl_map_read_from_str(ctx
, str
, -1);
925 map
= isl_map_coalesce(map
);
926 map2
= isl_map_read_from_str(ctx
, str
, -1);
927 assert(isl_map_is_equal(map
, map2
));
931 str
= "[M, N] -> { [] -> [o0] : (o0 = 0 and M >= 1 and N >= 2) or "
932 "(o0 = 0 and M >= 1 and N >= 2M and N >= 2 + M) or "
933 "(o0 = 0 and M >= 2 and N >= 3) or "
934 "(M = 0 and o0 = 0 and N >= 3) }";
935 map
= isl_map_read_from_str(ctx
, str
, -1);
936 map
= isl_map_coalesce(map
);
937 map2
= isl_map_read_from_str(ctx
, str
, -1);
938 assert(isl_map_is_equal(map
, map2
));
942 str
= "{ [i0, i1, i2, i3] : (i1 = 10i0 and i0 >= 1 and 10i0 <= 100 and "
943 "i3 <= 9 + 10 i2 and i3 >= 1 + 10i2 and i3 >= 0) or "
944 "(i1 <= 9 + 10i0 and i1 >= 1 + 10i0 and i2 >= 0 and "
945 "i0 >= 0 and i1 <= 100 and i3 <= 9 + 10i2 and i3 >= 1 + 10i2) }";
946 map
= isl_map_read_from_str(ctx
, str
, -1);
947 map
= isl_map_coalesce(map
);
948 map2
= isl_map_read_from_str(ctx
, str
, -1);
949 assert(isl_map_is_equal(map
, map2
));
953 test_coalesce_set(ctx
,
954 "[M] -> { [i1] : (i1 >= 2 and i1 <= M) or "
955 "(i1 = M and M >= 1) }", 0);
956 test_coalesce_set(ctx
,
957 "{[x,y] : x,y >= 0; [x,y] : 10 <= x <= 20 and y >= -1 }", 0);
958 test_coalesce_set(ctx
,
959 "{ [x, y] : (x >= 1 and y >= 1 and x <= 2 and y <= 2) or "
960 "(y = 3 and x = 1) }", 1);
961 test_coalesce_set(ctx
,
962 "[M] -> { [i0, i1, i2, i3, i4] : (i1 >= 3 and i4 >= 2 + i2 and "
963 "i2 >= 2 and i0 >= 2 and i3 >= 1 + i2 and i0 <= M and "
964 "i1 <= M and i3 <= M and i4 <= M) or "
965 "(i1 >= 2 and i4 >= 1 + i2 and i2 >= 2 and i0 >= 2 and "
966 "i3 >= 1 + i2 and i0 <= M and i1 <= -1 + M and i3 <= M and "
967 "i4 <= -1 + M) }", 1);
968 test_coalesce_set(ctx
,
969 "{ [x, y] : (x >= 0 and y >= 0 and x <= 10 and y <= 10) or "
970 "(x >= 1 and y >= 1 and x <= 11 and y <= 11) }", 1);
971 test_coalesce_set(ctx
,
972 "{[x,y,z] : y + 2 >= 0 and x - y + 1 >= 0 and "
973 "-x - y + 1 >= 0 and -3 <= z <= 3;"
974 "[x,y,z] : -x+z + 20 >= 0 and -x-z + 20 >= 0 and "
975 "x-z + 20 >= 0 and x+z + 20 >= 0 and -10 <= y <= 0}", 1);
976 test_coalesce_set(ctx
,
977 "{[x,y] : 0 <= x,y <= 10; [5,y]: 4 <=y <= 11}", 1);
978 test_coalesce_set(ctx
, "{[x,0] : x >= 0; [x,1] : x <= 20}", 0);
979 test_coalesce_set(ctx
,
980 "{[x,0,0] : -5 <= x <= 5; [0,y,1] : -5 <= y <= 5 }", 1);
981 test_coalesce_set(ctx
, "{ [x, 1 - x] : 0 <= x <= 1; [0,0] }", 1);
982 test_coalesce_set(ctx
, "{ [0,0]; [i,i] : 1 <= i <= 10 }", 1);
983 test_coalesce_set(ctx
, "{ [0,0]; [i,j] : 1 <= i,j <= 10 }", 0);
984 test_coalesce_set(ctx
, "{ [0,0]; [i,2i] : 1 <= i <= 10 }", 1);
985 test_coalesce_set(ctx
, "{ [0,0]; [i,2i] : 2 <= i <= 10 }", 0);
986 test_coalesce_set(ctx
, "{ [1,0]; [i,2i] : 1 <= i <= 10 }", 0);
987 test_coalesce_set(ctx
, "{ [0,1]; [i,2i] : 1 <= i <= 10 }", 0);
990 void test_closure(struct isl_ctx
*ctx
)
998 /* COCOA example 1 */
999 map
= isl_map_read_from_str(ctx
,
1000 "[n] -> { [i,j] -> [i2,j2] : i2 = i + 1 and j2 = j + 1 and "
1001 "1 <= i and i < n and 1 <= j and j < n or "
1002 "i2 = i + 1 and j2 = j - 1 and "
1003 "1 <= i and i < n and 2 <= j and j <= n }", -1);
1004 map
= isl_map_power(map
, &exact
);
1008 /* COCOA example 1 */
1009 map
= isl_map_read_from_str(ctx
,
1010 "[n] -> { [i,j] -> [i2,j2] : i2 = i + 1 and j2 = j + 1 and "
1011 "1 <= i and i < n and 1 <= j and j < n or "
1012 "i2 = i + 1 and j2 = j - 1 and "
1013 "1 <= i and i < n and 2 <= j and j <= n }", -1);
1014 map
= isl_map_transitive_closure(map
, &exact
);
1016 map2
= isl_map_read_from_str(ctx
,
1017 "[n] -> { [i,j] -> [i2,j2] : exists (k1,k2,k : "
1018 "1 <= i and i < n and 1 <= j and j <= n and "
1019 "2 <= i2 and i2 <= n and 1 <= j2 and j2 <= n and "
1020 "i2 = i + k1 + k2 and j2 = j + k1 - k2 and "
1021 "k1 >= 0 and k2 >= 0 and k1 + k2 = k and k >= 1 )}", -1);
1022 assert(isl_map_is_equal(map
, map2
));
1026 map
= isl_map_read_from_str(ctx
,
1027 "[n] -> { [x] -> [y] : y = x + 1 and 0 <= x and x <= n and "
1028 " 0 <= y and y <= n }", -1);
1029 map
= isl_map_transitive_closure(map
, &exact
);
1030 map2
= isl_map_read_from_str(ctx
,
1031 "[n] -> { [x] -> [y] : y > x and 0 <= x and x <= n and "
1032 " 0 <= y and y <= n }", -1);
1033 assert(isl_map_is_equal(map
, map2
));
1037 /* COCOA example 2 */
1038 map
= isl_map_read_from_str(ctx
,
1039 "[n] -> { [i,j] -> [i2,j2] : i2 = i + 2 and j2 = j + 2 and "
1040 "1 <= i and i < n - 1 and 1 <= j and j < n - 1 or "
1041 "i2 = i + 2 and j2 = j - 2 and "
1042 "1 <= i and i < n - 1 and 3 <= j and j <= n }", -1);
1043 map
= isl_map_transitive_closure(map
, &exact
);
1045 map2
= isl_map_read_from_str(ctx
,
1046 "[n] -> { [i,j] -> [i2,j2] : exists (k1,k2,k : "
1047 "1 <= i and i < n - 1 and 1 <= j and j <= n and "
1048 "3 <= i2 and i2 <= n and 1 <= j2 and j2 <= n and "
1049 "i2 = i + 2 k1 + 2 k2 and j2 = j + 2 k1 - 2 k2 and "
1050 "k1 >= 0 and k2 >= 0 and k1 + k2 = k and k >= 1) }", -1);
1051 assert(isl_map_is_equal(map
, map2
));
1055 /* COCOA Fig.2 left */
1056 map
= isl_map_read_from_str(ctx
,
1057 "[n] -> { [i,j] -> [i2,j2] : i2 = i + 2 and j2 = j and "
1058 "i <= 2 j - 3 and i <= n - 2 and j <= 2 i - 1 and "
1060 "i2 = i and j2 = j + 2 and i <= 2 j - 1 and i <= n and "
1061 "j <= 2 i - 3 and j <= n - 2 or "
1062 "i2 = i + 1 and j2 = j + 1 and i <= 2 j - 1 and "
1063 "i <= n - 1 and j <= 2 i - 1 and j <= n - 1 }", -1);
1064 map
= isl_map_transitive_closure(map
, &exact
);
1068 /* COCOA Fig.2 right */
1069 map
= isl_map_read_from_str(ctx
,
1070 "[n] -> { [i,j] -> [i2,j2] : i2 = i + 3 and j2 = j and "
1071 "i <= 2 j - 4 and i <= n - 3 and j <= 2 i - 1 and "
1073 "i2 = i and j2 = j + 3 and i <= 2 j - 1 and i <= n and "
1074 "j <= 2 i - 4 and j <= n - 3 or "
1075 "i2 = i + 1 and j2 = j + 1 and i <= 2 j - 1 and "
1076 "i <= n - 1 and j <= 2 i - 1 and j <= n - 1 }", -1);
1077 map
= isl_map_power(map
, &exact
);
1081 /* COCOA Fig.2 right */
1082 map
= isl_map_read_from_str(ctx
,
1083 "[n] -> { [i,j] -> [i2,j2] : i2 = i + 3 and j2 = j and "
1084 "i <= 2 j - 4 and i <= n - 3 and j <= 2 i - 1 and "
1086 "i2 = i and j2 = j + 3 and i <= 2 j - 1 and i <= n and "
1087 "j <= 2 i - 4 and j <= n - 3 or "
1088 "i2 = i + 1 and j2 = j + 1 and i <= 2 j - 1 and "
1089 "i <= n - 1 and j <= 2 i - 1 and j <= n - 1 }", -1);
1090 map
= isl_map_transitive_closure(map
, &exact
);
1092 map2
= isl_map_read_from_str(ctx
,
1093 "[n] -> { [i,j] -> [i2,j2] : exists (k1,k2,k3,k : "
1094 "i <= 2 j - 1 and i <= n and j <= 2 i - 1 and "
1095 "j <= n and 3 + i + 2 j <= 3 n and "
1096 "3 + 2 i + j <= 3n and i2 <= 2 j2 -1 and i2 <= n and "
1097 "i2 <= 3 j2 - 4 and j2 <= 2 i2 -1 and j2 <= n and "
1098 "13 + 4 j2 <= 11 i2 and i2 = i + 3 k1 + k3 and "
1099 "j2 = j + 3 k2 + k3 and k1 >= 0 and k2 >= 0 and "
1100 "k3 >= 0 and k1 + k2 + k3 = k and k > 0) }", -1);
1101 assert(isl_map_is_equal(map
, map2
));
1105 /* COCOA Fig.1 right */
1106 dom
= isl_set_read_from_str(ctx
,
1107 "{ [x,y] : x >= 0 and -2 x + 3 y >= 0 and x <= 3 and "
1108 "2 x - 3 y + 3 >= 0 }", -1);
1109 right
= isl_map_read_from_str(ctx
,
1110 "{ [x,y] -> [x2,y2] : x2 = x + 1 and y2 = y }", -1);
1111 up
= isl_map_read_from_str(ctx
,
1112 "{ [x,y] -> [x2,y2] : x2 = x and y2 = y + 1 }", -1);
1113 right
= isl_map_intersect_domain(right
, isl_set_copy(dom
));
1114 right
= isl_map_intersect_range(right
, isl_set_copy(dom
));
1115 up
= isl_map_intersect_domain(up
, isl_set_copy(dom
));
1116 up
= isl_map_intersect_range(up
, dom
);
1117 map
= isl_map_union(up
, right
);
1118 map
= isl_map_transitive_closure(map
, &exact
);
1120 map2
= isl_map_read_from_str(ctx
,
1121 "{ [0,0] -> [0,1]; [0,0] -> [1,1]; [0,1] -> [1,1]; "
1122 " [2,2] -> [3,2]; [2,2] -> [3,3]; [3,2] -> [3,3] }", -1);
1123 assert(isl_map_is_equal(map
, map2
));
1127 /* COCOA Theorem 1 counter example */
1128 map
= isl_map_read_from_str(ctx
,
1129 "{ [i,j] -> [i2,j2] : i = 0 and 0 <= j and j <= 1 and "
1130 "i2 = 1 and j2 = j or "
1131 "i = 0 and j = 0 and i2 = 0 and j2 = 1 }", -1);
1132 map
= isl_map_transitive_closure(map
, &exact
);
1136 map
= isl_map_read_from_str(ctx
,
1137 "[m,n] -> { [i,j] -> [i2,j2] : i2 = i and j2 = j + 2 and "
1138 "1 <= i,i2 <= n and 1 <= j,j2 <= m or "
1139 "i2 = i + 1 and 3 <= j2 - j <= 4 and "
1140 "1 <= i,i2 <= n and 1 <= j,j2 <= m }", -1);
1141 map
= isl_map_transitive_closure(map
, &exact
);
1145 /* Kelly et al 1996, fig 12 */
1146 map
= isl_map_read_from_str(ctx
,
1147 "[n] -> { [i,j] -> [i2,j2] : i2 = i and j2 = j + 1 and "
1148 "1 <= i,j,j+1 <= n or "
1149 "j = n and j2 = 1 and i2 = i + 1 and "
1150 "1 <= i,i+1 <= n }", -1);
1151 map
= isl_map_transitive_closure(map
, &exact
);
1153 map2
= isl_map_read_from_str(ctx
,
1154 "[n] -> { [i,j] -> [i2,j2] : 1 <= j < j2 <= n and "
1155 "1 <= i <= n and i = i2 or "
1156 "1 <= i < i2 <= n and 1 <= j <= n and "
1157 "1 <= j2 <= n }", -1);
1158 assert(isl_map_is_equal(map
, map2
));
1162 /* Omega's closure4 */
1163 map
= isl_map_read_from_str(ctx
,
1164 "[m,n] -> { [x,y] -> [x2,y2] : x2 = x and y2 = y + 1 and "
1165 "1 <= x,y <= 10 or "
1166 "x2 = x + 1 and y2 = y and "
1167 "1 <= x <= 20 && 5 <= y <= 15 }", -1);
1168 map
= isl_map_transitive_closure(map
, &exact
);
1172 map
= isl_map_read_from_str(ctx
,
1173 "[n] -> { [x] -> [y]: 1 <= n <= y - x <= 10 }", -1);
1174 map
= isl_map_transitive_closure(map
, &exact
);
1176 map2
= isl_map_read_from_str(ctx
,
1177 "[n] -> { [x] -> [y] : 1 <= n <= 10 and y >= n + x }", -1);
1178 assert(isl_map_is_equal(map
, map2
));
1182 str
= "[n, m] -> { [i0, i1, i2, i3] -> [o0, o1, o2, o3] : "
1183 "i3 = 1 and o0 = i0 and o1 = -1 + i1 and o2 = -1 + i2 and "
1184 "o3 = -2 + i2 and i1 <= -1 + i0 and i1 >= 1 - m + i0 and "
1185 "i1 >= 2 and i1 <= n and i2 >= 3 and i2 <= 1 + n and i2 <= m }";
1186 map
= isl_map_read_from_str(ctx
, str
, -1);
1187 map
= isl_map_transitive_closure(map
, &exact
);
1189 map2
= isl_map_read_from_str(ctx
, str
, -1);
1190 assert(isl_map_is_equal(map
, map2
));
1194 str
= "{[0] -> [1]; [2] -> [3]}";
1195 map
= isl_map_read_from_str(ctx
, str
, -1);
1196 map
= isl_map_transitive_closure(map
, &exact
);
1198 map2
= isl_map_read_from_str(ctx
, str
, -1);
1199 assert(isl_map_is_equal(map
, map2
));
1203 str
= "[n] -> { [[i0, i1, 1, 0, i0] -> [i5, 1]] -> "
1204 "[[i0, -1 + i1, 2, 0, i0] -> [-1 + i5, 2]] : "
1205 "exists (e0 = [(3 - n)/3]: i5 >= 2 and i1 >= 2 and "
1206 "3i0 <= -1 + n and i1 <= -1 + n and i5 <= -1 + n and "
1207 "3e0 >= 1 - n and 3e0 <= 2 - n and 3i0 >= -2 + n); "
1208 "[[i0, i1, 2, 0, i0] -> [i5, 1]] -> "
1209 "[[i0, i1, 1, 0, i0] -> [-1 + i5, 2]] : "
1210 "exists (e0 = [(3 - n)/3]: i5 >= 2 and i1 >= 1 and "
1211 "3i0 <= -1 + n and i1 <= -1 + n and i5 <= -1 + n and "
1212 "3e0 >= 1 - n and 3e0 <= 2 - n and 3i0 >= -2 + n); "
1213 "[[i0, i1, 1, 0, i0] -> [i5, 2]] -> "
1214 "[[i0, -1 + i1, 2, 0, i0] -> [i5, 1]] : "
1215 "exists (e0 = [(3 - n)/3]: i1 >= 2 and i5 >= 1 and "
1216 "3i0 <= -1 + n and i1 <= -1 + n and i5 <= -1 + n and "
1217 "3e0 >= 1 - n and 3e0 <= 2 - n and 3i0 >= -2 + n); "
1218 "[[i0, i1, 2, 0, i0] -> [i5, 2]] -> "
1219 "[[i0, i1, 1, 0, i0] -> [i5, 1]] : "
1220 "exists (e0 = [(3 - n)/3]: i5 >= 1 and i1 >= 1 and "
1221 "3i0 <= -1 + n and i1 <= -1 + n and i5 <= -1 + n and "
1222 "3e0 >= 1 - n and 3e0 <= 2 - n and 3i0 >= -2 + n) }";
1223 map
= isl_map_read_from_str(ctx
, str
, -1);
1224 map
= isl_map_transitive_closure(map
, NULL
);
1229 void test_lex(struct isl_ctx
*ctx
)
1234 dim
= isl_space_alloc(ctx
, 0, 0, 0);
1235 map
= isl_map_lex_le(dim
);
1236 assert(!isl_map_is_empty(map
));
1240 static int consume_lexmin(__isl_take isl_basic_set
*dom
,
1241 __isl_take isl_aff_list
*list
, void *user
)
1244 isl_basic_map
*bmap
;
1245 isl_map
**map
= user
;
1247 dim
= isl_basic_set_get_space(dom
);
1248 bmap
= isl_basic_map_from_aff_list(dim
, list
);
1249 bmap
= isl_basic_map_intersect_domain(bmap
, dom
);
1251 *map
= isl_map_union(*map
, isl_map_from_basic_map(bmap
));
1256 void test_lexmin(struct isl_ctx
*ctx
)
1259 isl_basic_map
*bmap
;
1260 isl_map
*map
, *map2
;
1264 str
= "[p0, p1] -> { [] -> [] : "
1265 "exists (e0 = [(2p1)/3], e1, e2, e3 = [(3 - p1 + 3e0)/3], "
1266 "e4 = [(p1)/3], e5 = [(p1 + 3e4)/3]: "
1267 "3e0 >= -2 + 2p1 and 3e0 >= p1 and 3e3 >= 1 - p1 + 3e0 and "
1268 "3e0 <= 2p1 and 3e3 >= -2 + p1 and 3e3 <= -1 + p1 and p1 >= 3 and "
1269 "3e5 >= -2 + 2p1 and 3e5 >= p1 and 3e5 <= -1 + p1 + 3e4 and "
1270 "3e4 <= p1 and 3e4 >= -2 + p1 and e3 <= -1 + e0 and "
1271 "3e4 >= 6 - p1 + 3e1 and 3e1 >= p1 and 3e5 >= -2 + p1 + 3e4 and "
1272 "2e4 >= 3 - p1 + 2e1 and e4 <= e1 and 3e3 <= 2 - p1 + 3e0 and "
1273 "e5 >= 1 + e1 and 3e4 >= 6 - 2p1 + 3e1 and "
1274 "p0 >= 2 and p1 >= p0 and 3e2 >= p1 and 3e4 >= 6 - p1 + 3e2 and "
1275 "e2 <= e1 and e3 >= 1 and e4 <= e2) }";
1276 map
= isl_map_read_from_str(ctx
, str
, -1);
1277 map
= isl_map_lexmin(map
);
1280 str
= "[C] -> { [obj,a,b,c] : obj <= 38 a + 7 b + 10 c and "
1281 "a + b <= 1 and c <= 10 b and c <= C and a,b,c,C >= 0 }";
1282 set
= isl_set_read_from_str(ctx
, str
, -1);
1283 set
= isl_set_lexmax(set
);
1284 str
= "[C] -> { [obj,a,b,c] : C = 8 }";
1285 set2
= isl_set_read_from_str(ctx
, str
, -1);
1286 set
= isl_set_intersect(set
, set2
);
1287 assert(!isl_set_is_empty(set
));
1290 str
= "{ [x] -> [y] : x <= y <= 10; [x] -> [5] : -8 <= x <= 8 }";
1291 map
= isl_map_read_from_str(ctx
, str
, -1);
1292 map
= isl_map_lexmin(map
);
1293 str
= "{ [x] -> [5] : 6 <= x <= 8; "
1294 "[x] -> [x] : x <= 5 or (9 <= x <= 10) }";
1295 map2
= isl_map_read_from_str(ctx
, str
, -1);
1296 assert(isl_map_is_equal(map
, map2
));
1300 str
= "{ [x] -> [y] : 4y = x or 4y = -1 + x or 4y = -2 + x }";
1301 map
= isl_map_read_from_str(ctx
, str
, -1);
1302 map2
= isl_map_copy(map
);
1303 map
= isl_map_lexmin(map
);
1304 assert(isl_map_is_equal(map
, map2
));
1308 str
= "{ [x] -> [y] : x = 4y; [x] -> [y] : x = 2y }";
1309 map
= isl_map_read_from_str(ctx
, str
, -1);
1310 map
= isl_map_lexmin(map
);
1311 str
= "{ [x] -> [y] : (4y = x and x >= 0) or "
1312 "(exists (e0 = [(x)/4], e1 = [(-2 + x)/4]: 2y = x and "
1313 "4e1 = -2 + x and 4e0 <= -1 + x and 4e0 >= -3 + x)) or "
1314 "(exists (e0 = [(x)/4]: 2y = x and 4e0 = x and x <= -4)) }";
1315 map2
= isl_map_read_from_str(ctx
, str
, -1);
1316 assert(isl_map_is_equal(map
, map2
));
1320 str
= "{ [i] -> [i', j] : j = i - 8i' and i' >= 0 and i' <= 7 and "
1321 " 8i' <= i and 8i' >= -7 + i }";
1322 bmap
= isl_basic_map_read_from_str(ctx
, str
, -1);
1323 map2
= isl_map_empty(isl_basic_map_get_space(bmap
));
1324 isl_basic_map_foreach_lexmin(bmap
, &consume_lexmin
, &map2
);
1325 map
= isl_map_from_basic_map(bmap
);
1326 assert(isl_map_is_equal(map
, map2
));
1336 static int collect_must_may(__isl_take isl_map
*dep
, int must
,
1337 void *dep_user
, void *user
)
1339 struct must_may
*mm
= (struct must_may
*)user
;
1342 mm
->must
= isl_map_union(mm
->must
, dep
);
1344 mm
->may
= isl_map_union(mm
->may
, dep
);
1349 static int common_space(void *first
, void *second
)
1351 int depth
= *(int *)first
;
1355 static int map_is_equal(__isl_keep isl_map
*map
, const char *str
)
1363 map2
= isl_map_read_from_str(map
->ctx
, str
, -1);
1364 equal
= isl_map_is_equal(map
, map2
);
1370 void test_dep(struct isl_ctx
*ctx
)
1375 isl_access_info
*ai
;
1382 str
= "{ [2,i,0] -> [i] : 0 <= i <= 10 }";
1383 map
= isl_map_read_from_str(ctx
, str
, -1);
1384 ai
= isl_access_info_alloc(map
, &depth
, &common_space
, 2);
1386 str
= "{ [0,i,0] -> [i] : 0 <= i <= 10 }";
1387 map
= isl_map_read_from_str(ctx
, str
, -1);
1388 ai
= isl_access_info_add_source(ai
, map
, 1, &depth
);
1390 str
= "{ [1,i,0] -> [5] : 0 <= i <= 10 }";
1391 map
= isl_map_read_from_str(ctx
, str
, -1);
1392 ai
= isl_access_info_add_source(ai
, map
, 1, &depth
);
1394 flow
= isl_access_info_compute_flow(ai
);
1395 dim
= isl_space_alloc(ctx
, 0, 3, 3);
1396 mm
.must
= isl_map_empty(isl_space_copy(dim
));
1397 mm
.may
= isl_map_empty(dim
);
1399 isl_flow_foreach(flow
, collect_must_may
, &mm
);
1401 str
= "{ [0,i,0] -> [2,i,0] : (0 <= i <= 4) or (6 <= i <= 10); "
1402 " [1,10,0] -> [2,5,0] }";
1403 assert(map_is_equal(mm
.must
, str
));
1404 str
= "{ [i,j,k] -> [l,m,n] : 1 = 0 }";
1405 assert(map_is_equal(mm
.may
, str
));
1407 isl_map_free(mm
.must
);
1408 isl_map_free(mm
.may
);
1409 isl_flow_free(flow
);
1412 str
= "{ [2,i,0] -> [i] : 0 <= i <= 10 }";
1413 map
= isl_map_read_from_str(ctx
, str
, -1);
1414 ai
= isl_access_info_alloc(map
, &depth
, &common_space
, 2);
1416 str
= "{ [0,i,0] -> [i] : 0 <= i <= 10 }";
1417 map
= isl_map_read_from_str(ctx
, str
, -1);
1418 ai
= isl_access_info_add_source(ai
, map
, 1, &depth
);
1420 str
= "{ [1,i,0] -> [5] : 0 <= i <= 10 }";
1421 map
= isl_map_read_from_str(ctx
, str
, -1);
1422 ai
= isl_access_info_add_source(ai
, map
, 0, &depth
);
1424 flow
= isl_access_info_compute_flow(ai
);
1425 dim
= isl_space_alloc(ctx
, 0, 3, 3);
1426 mm
.must
= isl_map_empty(isl_space_copy(dim
));
1427 mm
.may
= isl_map_empty(dim
);
1429 isl_flow_foreach(flow
, collect_must_may
, &mm
);
1431 str
= "{ [0,i,0] -> [2,i,0] : (0 <= i <= 4) or (6 <= i <= 10) }";
1432 assert(map_is_equal(mm
.must
, str
));
1433 str
= "{ [0,5,0] -> [2,5,0]; [1,i,0] -> [2,5,0] : 0 <= i <= 10 }";
1434 assert(map_is_equal(mm
.may
, str
));
1436 isl_map_free(mm
.must
);
1437 isl_map_free(mm
.may
);
1438 isl_flow_free(flow
);
1441 str
= "{ [2,i,0] -> [i] : 0 <= i <= 10 }";
1442 map
= isl_map_read_from_str(ctx
, str
, -1);
1443 ai
= isl_access_info_alloc(map
, &depth
, &common_space
, 2);
1445 str
= "{ [0,i,0] -> [i] : 0 <= i <= 10 }";
1446 map
= isl_map_read_from_str(ctx
, str
, -1);
1447 ai
= isl_access_info_add_source(ai
, map
, 0, &depth
);
1449 str
= "{ [1,i,0] -> [5] : 0 <= i <= 10 }";
1450 map
= isl_map_read_from_str(ctx
, str
, -1);
1451 ai
= isl_access_info_add_source(ai
, map
, 0, &depth
);
1453 flow
= isl_access_info_compute_flow(ai
);
1454 dim
= isl_space_alloc(ctx
, 0, 3, 3);
1455 mm
.must
= isl_map_empty(isl_space_copy(dim
));
1456 mm
.may
= isl_map_empty(dim
);
1458 isl_flow_foreach(flow
, collect_must_may
, &mm
);
1460 str
= "{ [0,i,0] -> [2,i,0] : 0 <= i <= 10; "
1461 " [1,i,0] -> [2,5,0] : 0 <= i <= 10 }";
1462 assert(map_is_equal(mm
.may
, str
));
1463 str
= "{ [i,j,k] -> [l,m,n] : 1 = 0 }";
1464 assert(map_is_equal(mm
.must
, str
));
1466 isl_map_free(mm
.must
);
1467 isl_map_free(mm
.may
);
1468 isl_flow_free(flow
);
1471 str
= "{ [0,i,2] -> [i] : 0 <= i <= 10 }";
1472 map
= isl_map_read_from_str(ctx
, str
, -1);
1473 ai
= isl_access_info_alloc(map
, &depth
, &common_space
, 2);
1475 str
= "{ [0,i,0] -> [i] : 0 <= i <= 10 }";
1476 map
= isl_map_read_from_str(ctx
, str
, -1);
1477 ai
= isl_access_info_add_source(ai
, map
, 0, &depth
);
1479 str
= "{ [0,i,1] -> [5] : 0 <= i <= 10 }";
1480 map
= isl_map_read_from_str(ctx
, str
, -1);
1481 ai
= isl_access_info_add_source(ai
, map
, 0, &depth
);
1483 flow
= isl_access_info_compute_flow(ai
);
1484 dim
= isl_space_alloc(ctx
, 0, 3, 3);
1485 mm
.must
= isl_map_empty(isl_space_copy(dim
));
1486 mm
.may
= isl_map_empty(dim
);
1488 isl_flow_foreach(flow
, collect_must_may
, &mm
);
1490 str
= "{ [0,i,0] -> [0,i,2] : 0 <= i <= 10; "
1491 " [0,i,1] -> [0,5,2] : 0 <= i <= 5 }";
1492 assert(map_is_equal(mm
.may
, str
));
1493 str
= "{ [i,j,k] -> [l,m,n] : 1 = 0 }";
1494 assert(map_is_equal(mm
.must
, str
));
1496 isl_map_free(mm
.must
);
1497 isl_map_free(mm
.may
);
1498 isl_flow_free(flow
);
1501 str
= "{ [0,i,1] -> [i] : 0 <= i <= 10 }";
1502 map
= isl_map_read_from_str(ctx
, str
, -1);
1503 ai
= isl_access_info_alloc(map
, &depth
, &common_space
, 2);
1505 str
= "{ [0,i,0] -> [i] : 0 <= i <= 10 }";
1506 map
= isl_map_read_from_str(ctx
, str
, -1);
1507 ai
= isl_access_info_add_source(ai
, map
, 0, &depth
);
1509 str
= "{ [0,i,2] -> [5] : 0 <= i <= 10 }";
1510 map
= isl_map_read_from_str(ctx
, str
, -1);
1511 ai
= isl_access_info_add_source(ai
, map
, 0, &depth
);
1513 flow
= isl_access_info_compute_flow(ai
);
1514 dim
= isl_space_alloc(ctx
, 0, 3, 3);
1515 mm
.must
= isl_map_empty(isl_space_copy(dim
));
1516 mm
.may
= isl_map_empty(dim
);
1518 isl_flow_foreach(flow
, collect_must_may
, &mm
);
1520 str
= "{ [0,i,0] -> [0,i,1] : 0 <= i <= 10; "
1521 " [0,i,2] -> [0,5,1] : 0 <= i <= 4 }";
1522 assert(map_is_equal(mm
.may
, str
));
1523 str
= "{ [i,j,k] -> [l,m,n] : 1 = 0 }";
1524 assert(map_is_equal(mm
.must
, str
));
1526 isl_map_free(mm
.must
);
1527 isl_map_free(mm
.may
);
1528 isl_flow_free(flow
);
1533 str
= "{ [1,i,0,0,0] -> [i,j] : 0 <= i <= 10 and 0 <= j <= 10 }";
1534 map
= isl_map_read_from_str(ctx
, str
, -1);
1535 ai
= isl_access_info_alloc(map
, &depth
, &common_space
, 1);
1537 str
= "{ [0,i,0,j,0] -> [i,j] : 0 <= i <= 10 and 0 <= j <= 10 }";
1538 map
= isl_map_read_from_str(ctx
, str
, -1);
1539 ai
= isl_access_info_add_source(ai
, map
, 1, &depth
);
1541 flow
= isl_access_info_compute_flow(ai
);
1542 dim
= isl_space_alloc(ctx
, 0, 5, 5);
1543 mm
.must
= isl_map_empty(isl_space_copy(dim
));
1544 mm
.may
= isl_map_empty(dim
);
1546 isl_flow_foreach(flow
, collect_must_may
, &mm
);
1548 str
= "{ [0,i,0,j,0] -> [1,i,0,0,0] : 0 <= i,j <= 10 }";
1549 assert(map_is_equal(mm
.must
, str
));
1550 str
= "{ [0,0,0,0,0] -> [0,0,0,0,0] : 1 = 0 }";
1551 assert(map_is_equal(mm
.may
, str
));
1553 isl_map_free(mm
.must
);
1554 isl_map_free(mm
.may
);
1555 isl_flow_free(flow
);
1558 int test_sv(isl_ctx
*ctx
)
1562 isl_union_map
*umap
;
1565 str
= "[N] -> { [i] -> [f] : 0 <= i <= N and 0 <= i - 10 f <= 9 }";
1566 map
= isl_map_read_from_str(ctx
, str
, -1);
1567 sv
= isl_map_is_single_valued(map
);
1572 isl_die(ctx
, isl_error_internal
,
1573 "map not detected as single valued", return -1);
1575 str
= "[N] -> { [i] -> [f] : 0 <= i <= N and 0 <= i - 10 f <= 10 }";
1576 map
= isl_map_read_from_str(ctx
, str
, -1);
1577 sv
= isl_map_is_single_valued(map
);
1582 isl_die(ctx
, isl_error_internal
,
1583 "map detected as single valued", return -1);
1585 str
= "{ S1[i] -> [i] : 0 <= i <= 9; S2[i] -> [i] : 0 <= i <= 9 }";
1586 umap
= isl_union_map_read_from_str(ctx
, str
);
1587 sv
= isl_union_map_is_single_valued(umap
);
1588 isl_union_map_free(umap
);
1592 isl_die(ctx
, isl_error_internal
,
1593 "map not detected as single valued", return -1);
1595 str
= "{ [i] -> S1[i] : 0 <= i <= 9; [i] -> S2[i] : 0 <= i <= 9 }";
1596 umap
= isl_union_map_read_from_str(ctx
, str
);
1597 sv
= isl_union_map_is_single_valued(umap
);
1598 isl_union_map_free(umap
);
1602 isl_die(ctx
, isl_error_internal
,
1603 "map detected as single valued", return -1);
1608 void test_bijective_case(struct isl_ctx
*ctx
, const char *str
, int bijective
)
1612 map
= isl_map_read_from_str(ctx
, str
, -1);
1614 assert(isl_map_is_bijective(map
));
1616 assert(!isl_map_is_bijective(map
));
1620 void test_bijective(struct isl_ctx
*ctx
)
1622 test_bijective_case(ctx
, "[N,M]->{[i,j] -> [i]}", 0);
1623 test_bijective_case(ctx
, "[N,M]->{[i,j] -> [i] : j=i}", 1);
1624 test_bijective_case(ctx
, "[N,M]->{[i,j] -> [i] : j=0}", 1);
1625 test_bijective_case(ctx
, "[N,M]->{[i,j] -> [i] : j=N}", 1);
1626 test_bijective_case(ctx
, "[N,M]->{[i,j] -> [j,i]}", 1);
1627 test_bijective_case(ctx
, "[N,M]->{[i,j] -> [i+j]}", 0);
1628 test_bijective_case(ctx
, "[N,M]->{[i,j] -> []}", 0);
1629 test_bijective_case(ctx
, "[N,M]->{[i,j] -> [i,j,N]}", 1);
1630 test_bijective_case(ctx
, "[N,M]->{[i,j] -> [2i]}", 0);
1631 test_bijective_case(ctx
, "[N,M]->{[i,j] -> [i,i]}", 0);
1632 test_bijective_case(ctx
, "[N,M]->{[i,j] -> [2i,i]}", 0);
1633 test_bijective_case(ctx
, "[N,M]->{[i,j] -> [2i,j]}", 1);
1634 test_bijective_case(ctx
, "[N,M]->{[i,j] -> [x,y] : 2x=i & y =j}", 1);
1637 void test_pwqp(struct isl_ctx
*ctx
)
1641 isl_pw_qpolynomial
*pwqp1
, *pwqp2
;
1643 str
= "{ [i,j,k] -> 1 + 9 * [i/5] + 7 * [j/11] + 4 * [k/13] }";
1644 pwqp1
= isl_pw_qpolynomial_read_from_str(ctx
, str
);
1646 pwqp1
= isl_pw_qpolynomial_move_dims(pwqp1
, isl_dim_param
, 0,
1649 str
= "[j] -> { [i,k] -> 1 + 9 * [i/5] + 7 * [j/11] + 4 * [k/13] }";
1650 pwqp2
= isl_pw_qpolynomial_read_from_str(ctx
, str
);
1652 pwqp1
= isl_pw_qpolynomial_sub(pwqp1
, pwqp2
);
1654 assert(isl_pw_qpolynomial_is_zero(pwqp1
));
1656 isl_pw_qpolynomial_free(pwqp1
);
1658 str
= "{ [i] -> i }";
1659 pwqp1
= isl_pw_qpolynomial_read_from_str(ctx
, str
);
1660 str
= "{ [k] : exists a : k = 2a }";
1661 set
= isl_set_read_from_str(ctx
, str
, 0);
1662 pwqp1
= isl_pw_qpolynomial_gist(pwqp1
, set
);
1663 str
= "{ [i] -> i }";
1664 pwqp2
= isl_pw_qpolynomial_read_from_str(ctx
, str
);
1666 pwqp1
= isl_pw_qpolynomial_sub(pwqp1
, pwqp2
);
1668 assert(isl_pw_qpolynomial_is_zero(pwqp1
));
1670 isl_pw_qpolynomial_free(pwqp1
);
1672 str
= "{ [i] -> i + [ (i + [i/3])/2 ] }";
1673 pwqp1
= isl_pw_qpolynomial_read_from_str(ctx
, str
);
1675 set
= isl_set_read_from_str(ctx
, str
, 0);
1676 pwqp1
= isl_pw_qpolynomial_gist(pwqp1
, set
);
1677 str
= "{ [i] -> 16 }";
1678 pwqp2
= isl_pw_qpolynomial_read_from_str(ctx
, str
);
1680 pwqp1
= isl_pw_qpolynomial_sub(pwqp1
, pwqp2
);
1682 assert(isl_pw_qpolynomial_is_zero(pwqp1
));
1684 isl_pw_qpolynomial_free(pwqp1
);
1686 str
= "{ [i] -> ([(i)/2]) }";
1687 pwqp1
= isl_pw_qpolynomial_read_from_str(ctx
, str
);
1688 str
= "{ [k] : exists a : k = 2a+1 }";
1689 set
= isl_set_read_from_str(ctx
, str
, 0);
1690 pwqp1
= isl_pw_qpolynomial_gist(pwqp1
, set
);
1691 str
= "{ [i] -> -1/2 + 1/2 * i }";
1692 pwqp2
= isl_pw_qpolynomial_read_from_str(ctx
, str
);
1694 pwqp1
= isl_pw_qpolynomial_sub(pwqp1
, pwqp2
);
1696 assert(isl_pw_qpolynomial_is_zero(pwqp1
));
1698 isl_pw_qpolynomial_free(pwqp1
);
1700 str
= "{ [i] -> ([([i/2] + [i/2])/5]) }";
1701 pwqp1
= isl_pw_qpolynomial_read_from_str(ctx
, str
);
1702 str
= "{ [i] -> ([(2 * [i/2])/5]) }";
1703 pwqp2
= isl_pw_qpolynomial_read_from_str(ctx
, str
);
1705 pwqp1
= isl_pw_qpolynomial_sub(pwqp1
, pwqp2
);
1707 assert(isl_pw_qpolynomial_is_zero(pwqp1
));
1709 isl_pw_qpolynomial_free(pwqp1
);
1711 str
= "{ [x] -> ([x/2] + [(x+1)/2]) }";
1712 pwqp1
= isl_pw_qpolynomial_read_from_str(ctx
, str
);
1713 str
= "{ [x] -> x }";
1714 pwqp2
= isl_pw_qpolynomial_read_from_str(ctx
, str
);
1716 pwqp1
= isl_pw_qpolynomial_sub(pwqp1
, pwqp2
);
1718 assert(isl_pw_qpolynomial_is_zero(pwqp1
));
1720 isl_pw_qpolynomial_free(pwqp1
);
1722 str
= "{ [i] -> ([i/2]) : i >= 0; [i] -> ([i/3]) : i < 0 }";
1723 pwqp1
= isl_pw_qpolynomial_read_from_str(ctx
, str
);
1724 pwqp2
= isl_pw_qpolynomial_read_from_str(ctx
, str
);
1725 pwqp1
= isl_pw_qpolynomial_coalesce(pwqp1
);
1726 pwqp1
= isl_pw_qpolynomial_sub(pwqp1
, pwqp2
);
1727 assert(isl_pw_qpolynomial_is_zero(pwqp1
));
1728 isl_pw_qpolynomial_free(pwqp1
);
1731 void test_split_periods(isl_ctx
*ctx
)
1734 isl_pw_qpolynomial
*pwqp
;
1736 str
= "{ [U,V] -> 1/3 * U + 2/3 * V - [(U + 2V)/3] + [U/2] : "
1737 "U + 2V + 3 >= 0 and - U -2V >= 0 and - U + 10 >= 0 and "
1738 "U >= 0; [U,V] -> U^2 : U >= 100 }";
1739 pwqp
= isl_pw_qpolynomial_read_from_str(ctx
, str
);
1741 pwqp
= isl_pw_qpolynomial_split_periods(pwqp
, 2);
1744 isl_pw_qpolynomial_free(pwqp
);
1747 void test_union(isl_ctx
*ctx
)
1750 isl_union_set
*uset1
, *uset2
;
1751 isl_union_map
*umap1
, *umap2
;
1753 str
= "{ [i] : 0 <= i <= 1 }";
1754 uset1
= isl_union_set_read_from_str(ctx
, str
);
1755 str
= "{ [1] -> [0] }";
1756 umap1
= isl_union_map_read_from_str(ctx
, str
);
1758 umap2
= isl_union_set_lex_gt_union_set(isl_union_set_copy(uset1
), uset1
);
1759 assert(isl_union_map_is_equal(umap1
, umap2
));
1761 isl_union_map_free(umap1
);
1762 isl_union_map_free(umap2
);
1764 str
= "{ A[i] -> B[i]; B[i] -> C[i]; A[0] -> C[1] }";
1765 umap1
= isl_union_map_read_from_str(ctx
, str
);
1766 str
= "{ A[i]; B[i] }";
1767 uset1
= isl_union_set_read_from_str(ctx
, str
);
1769 uset2
= isl_union_map_domain(umap1
);
1771 assert(isl_union_set_is_equal(uset1
, uset2
));
1773 isl_union_set_free(uset1
);
1774 isl_union_set_free(uset2
);
1777 void test_bound(isl_ctx
*ctx
)
1780 isl_pw_qpolynomial
*pwqp
;
1781 isl_pw_qpolynomial_fold
*pwf
;
1783 str
= "{ [[a, b, c, d] -> [e]] -> 0 }";
1784 pwqp
= isl_pw_qpolynomial_read_from_str(ctx
, str
);
1785 pwf
= isl_pw_qpolynomial_bound(pwqp
, isl_fold_max
, NULL
);
1786 assert(isl_pw_qpolynomial_fold_dim(pwf
, isl_dim_set
) == 4);
1787 isl_pw_qpolynomial_fold_free(pwf
);
1789 str
= "{ [[x]->[x]] -> 1 : exists a : x = 2 a }";
1790 pwqp
= isl_pw_qpolynomial_read_from_str(ctx
, str
);
1791 pwf
= isl_pw_qpolynomial_bound(pwqp
, isl_fold_max
, NULL
);
1792 assert(isl_pw_qpolynomial_fold_dim(pwf
, isl_dim_set
) == 1);
1793 isl_pw_qpolynomial_fold_free(pwf
);
1796 void test_lift(isl_ctx
*ctx
)
1799 isl_basic_map
*bmap
;
1800 isl_basic_set
*bset
;
1802 str
= "{ [i0] : exists e0 : i0 = 4e0 }";
1803 bset
= isl_basic_set_read_from_str(ctx
, str
, 0);
1804 bset
= isl_basic_set_lift(bset
);
1805 bmap
= isl_basic_map_from_range(bset
);
1806 bset
= isl_basic_map_domain(bmap
);
1807 isl_basic_set_free(bset
);
1810 void test_subset(isl_ctx
*ctx
)
1813 isl_set
*set1
, *set2
;
1815 str
= "{ [112, 0] }";
1816 set1
= isl_set_read_from_str(ctx
, str
, 0);
1817 str
= "{ [i0, i1] : exists (e0 = [(i0 - i1)/16], e1: "
1818 "16e0 <= i0 - i1 and 16e0 >= -15 + i0 - i1 and "
1819 "16e1 <= i1 and 16e0 >= -i1 and 16e1 >= -i0 + i1) }";
1820 set2
= isl_set_read_from_str(ctx
, str
, 0);
1821 assert(isl_set_is_subset(set1
, set2
));
1826 void test_factorize(isl_ctx
*ctx
)
1829 isl_basic_set
*bset
;
1832 str
= "{ [i0, i1, i2, i3, i4, i5, i6, i7] : 3i5 <= 2 - 2i0 and "
1833 "i0 >= -2 and i6 >= 1 + i3 and i7 >= 0 and 3i5 >= -2i0 and "
1834 "2i4 <= i2 and i6 >= 1 + 2i0 + 3i1 and i4 <= -1 and "
1835 "i6 >= 1 + 2i0 + 3i5 and i6 <= 2 + 2i0 + 3i5 and "
1836 "3i5 <= 2 - 2i0 - i2 + 3i4 and i6 <= 2 + 2i0 + 3i1 and "
1837 "i0 <= -1 and i7 <= i2 + i3 - 3i4 - i6 and "
1838 "3i5 >= -2i0 - i2 + 3i4 }";
1839 bset
= isl_basic_set_read_from_str(ctx
, str
, 0);
1840 f
= isl_basic_set_factorizer(bset
);
1842 isl_basic_set_free(bset
);
1843 isl_factorizer_free(f
);
1845 str
= "{ [i0, i1, i2, i3, i4, i5, i6, i7, i8, i9, i10, i11, i12] : "
1846 "i12 <= 2 + i0 - i11 and 2i8 >= -i4 and i11 >= i1 and "
1847 "3i5 <= -i2 and 2i11 >= -i4 - 2i7 and i11 <= 3 + i0 + 3i9 and "
1848 "i11 <= -i4 - 2i7 and i12 >= -i10 and i2 >= -2 and "
1849 "i11 >= i1 + 3i10 and i11 >= 1 + i0 + 3i9 and "
1850 "i11 <= 1 - i4 - 2i8 and 6i6 <= 6 - i2 and 3i6 >= 1 - i2 and "
1851 "i11 <= 2 + i1 and i12 <= i4 + i11 and i12 >= i0 - i11 and "
1852 "3i5 >= -2 - i2 and i12 >= -1 + i4 + i11 and 3i3 <= 3 - i2 and "
1853 "9i6 <= 11 - i2 + 6i5 and 3i3 >= 1 - i2 and "
1854 "9i6 <= 5 - i2 + 6i3 and i12 <= -1 and i2 <= 0 }";
1855 bset
= isl_basic_set_read_from_str(ctx
, str
, 0);
1856 f
= isl_basic_set_factorizer(bset
);
1858 isl_basic_set_free(bset
);
1859 isl_factorizer_free(f
);
1862 static int check_injective(__isl_take isl_map
*map
, void *user
)
1864 int *injective
= user
;
1866 *injective
= isl_map_is_injective(map
);
1869 if (*injective
< 0 || !*injective
)
1875 int test_one_schedule(isl_ctx
*ctx
, const char *d
, const char *w
,
1876 const char *r
, const char *s
, int tilable
, int parallel
)
1880 isl_union_map
*W
, *R
, *S
;
1881 isl_union_map
*empty
;
1882 isl_union_map
*dep_raw
, *dep_war
, *dep_waw
, *dep
;
1883 isl_union_map
*validity
, *proximity
;
1884 isl_union_map
*schedule
;
1885 isl_union_map
*test
;
1886 isl_union_set
*delta
;
1887 isl_union_set
*domain
;
1891 isl_schedule
*sched
;
1892 int is_nonneg
, is_parallel
, is_tilable
, is_injection
, is_complete
;
1894 D
= isl_union_set_read_from_str(ctx
, d
);
1895 W
= isl_union_map_read_from_str(ctx
, w
);
1896 R
= isl_union_map_read_from_str(ctx
, r
);
1897 S
= isl_union_map_read_from_str(ctx
, s
);
1899 W
= isl_union_map_intersect_domain(W
, isl_union_set_copy(D
));
1900 R
= isl_union_map_intersect_domain(R
, isl_union_set_copy(D
));
1902 empty
= isl_union_map_empty(isl_union_map_get_space(S
));
1903 isl_union_map_compute_flow(isl_union_map_copy(R
),
1904 isl_union_map_copy(W
), empty
,
1905 isl_union_map_copy(S
),
1906 &dep_raw
, NULL
, NULL
, NULL
);
1907 isl_union_map_compute_flow(isl_union_map_copy(W
),
1908 isl_union_map_copy(W
),
1909 isl_union_map_copy(R
),
1910 isl_union_map_copy(S
),
1911 &dep_waw
, &dep_war
, NULL
, NULL
);
1913 dep
= isl_union_map_union(dep_waw
, dep_war
);
1914 dep
= isl_union_map_union(dep
, dep_raw
);
1915 validity
= isl_union_map_copy(dep
);
1916 proximity
= isl_union_map_copy(dep
);
1918 sched
= isl_union_set_compute_schedule(isl_union_set_copy(D
),
1919 validity
, proximity
);
1920 schedule
= isl_schedule_get_map(sched
);
1921 isl_schedule_free(sched
);
1922 isl_union_map_free(W
);
1923 isl_union_map_free(R
);
1924 isl_union_map_free(S
);
1927 isl_union_map_foreach_map(schedule
, &check_injective
, &is_injection
);
1929 domain
= isl_union_map_domain(isl_union_map_copy(schedule
));
1930 is_complete
= isl_union_set_is_subset(D
, domain
);
1931 isl_union_set_free(D
);
1932 isl_union_set_free(domain
);
1934 test
= isl_union_map_reverse(isl_union_map_copy(schedule
));
1935 test
= isl_union_map_apply_range(test
, dep
);
1936 test
= isl_union_map_apply_range(test
, schedule
);
1938 delta
= isl_union_map_deltas(test
);
1939 if (isl_union_set_n_set(delta
) == 0) {
1943 isl_union_set_free(delta
);
1945 delta_set
= isl_set_from_union_set(delta
);
1947 slice
= isl_set_universe(isl_set_get_space(delta_set
));
1948 for (i
= 0; i
< tilable
; ++i
)
1949 slice
= isl_set_lower_bound_si(slice
, isl_dim_set
, i
, 0);
1950 is_tilable
= isl_set_is_subset(delta_set
, slice
);
1951 isl_set_free(slice
);
1953 slice
= isl_set_universe(isl_set_get_space(delta_set
));
1954 for (i
= 0; i
< parallel
; ++i
)
1955 slice
= isl_set_fix_si(slice
, isl_dim_set
, i
, 0);
1956 is_parallel
= isl_set_is_subset(delta_set
, slice
);
1957 isl_set_free(slice
);
1959 origin
= isl_set_universe(isl_set_get_space(delta_set
));
1960 for (i
= 0; i
< isl_set_dim(origin
, isl_dim_set
); ++i
)
1961 origin
= isl_set_fix_si(origin
, isl_dim_set
, i
, 0);
1963 delta_set
= isl_set_union(delta_set
, isl_set_copy(origin
));
1964 delta_set
= isl_set_lexmin(delta_set
);
1966 is_nonneg
= isl_set_is_equal(delta_set
, origin
);
1968 isl_set_free(origin
);
1969 isl_set_free(delta_set
);
1972 if (is_nonneg
< 0 || is_parallel
< 0 || is_tilable
< 0 ||
1973 is_injection
< 0 || is_complete
< 0)
1976 isl_die(ctx
, isl_error_unknown
,
1977 "generated schedule incomplete", return -1);
1979 isl_die(ctx
, isl_error_unknown
,
1980 "generated schedule not injective on each statement",
1983 isl_die(ctx
, isl_error_unknown
,
1984 "negative dependences in generated schedule",
1987 isl_die(ctx
, isl_error_unknown
,
1988 "generated schedule not as tilable as expected",
1991 isl_die(ctx
, isl_error_unknown
,
1992 "generated schedule not as parallel as expected",
1998 int test_special_schedule(isl_ctx
*ctx
)
2002 isl_union_map
*empty
;
2004 isl_union_map
*sched1
, *sched2
;
2005 isl_schedule
*schedule
;
2008 str
= "{ S[i,j] : 0 <= i <= 10 }";
2009 dom
= isl_union_set_read_from_str(ctx
, str
);
2010 str
= "{ S[i,j] -> S[i+1,j] : 0 <= i,j <= 10 }";
2011 dep
= isl_union_map_read_from_str(ctx
, str
);
2012 empty
= isl_union_map_read_from_str(ctx
, "{}");
2013 schedule
= isl_union_set_compute_schedule(dom
, empty
, dep
);
2014 sched1
= isl_schedule_get_map(schedule
);
2015 isl_schedule_free(schedule
);
2017 str
= "{ S[i, j] -> [j, i] }";
2018 sched2
= isl_union_map_read_from_str(ctx
, str
);
2020 equal
= isl_union_map_is_equal(sched1
, sched2
);
2021 isl_union_map_free(sched1
);
2022 isl_union_map_free(sched2
);
2027 isl_die(ctx
, isl_error_unknown
, "unexpected schedule",
2033 int test_schedule(isl_ctx
*ctx
)
2035 const char *D
, *W
, *R
, *S
;
2038 D
= "[T,N] -> { S1[t,i] : 1 <= t <= T and 2 <= i <= N - 1 }";
2039 W
= "{ S1[t,i] -> a[t,i] }";
2040 R
= "{ S1[t,i] -> a[t-1,i]; S1[t,i] -> a[t-1,i-1]; "
2041 "S1[t,i] -> a[t-1,i+1] }";
2042 S
= "{ S1[t,i] -> [t,i] }";
2043 if (test_one_schedule(ctx
, D
, W
, R
, S
, 2, 0) < 0)
2046 /* Fig. 5 of CC2008 */
2047 D
= "[N] -> { S_0[i, j] : i >= 0 and i <= -1 + N and j >= 2 and "
2049 W
= "[N] -> { S_0[i, j] -> a[i, j] : i >= 0 and i <= -1 + N and "
2050 "j >= 2 and j <= -1 + N }";
2051 R
= "[N] -> { S_0[i, j] -> a[j, i] : i >= 0 and i <= -1 + N and "
2052 "j >= 2 and j <= -1 + N; "
2053 "S_0[i, j] -> a[i, -1 + j] : i >= 0 and i <= -1 + N and "
2054 "j >= 2 and j <= -1 + N }";
2055 S
= "[N] -> { S_0[i, j] -> [0, i, 0, j, 0] }";
2056 if (test_one_schedule(ctx
, D
, W
, R
, S
, 2, 0) < 0)
2059 D
= "{ S1[i] : 0 <= i <= 10; S2[i] : 0 <= i <= 9 }";
2060 W
= "{ S1[i] -> a[i] }";
2061 R
= "{ S2[i] -> a[i+1] }";
2062 S
= "{ S1[i] -> [0,i]; S2[i] -> [1,i] }";
2063 if (test_one_schedule(ctx
, D
, W
, R
, S
, 1, 1) < 0)
2066 D
= "{ S1[i] : 0 <= i < 10; S2[i] : 0 <= i < 10 }";
2067 W
= "{ S1[i] -> a[i] }";
2068 R
= "{ S2[i] -> a[9-i] }";
2069 S
= "{ S1[i] -> [0,i]; S2[i] -> [1,i] }";
2070 if (test_one_schedule(ctx
, D
, W
, R
, S
, 1, 1) < 0)
2073 D
= "[N] -> { S1[i] : 0 <= i < N; S2[i] : 0 <= i < N }";
2074 W
= "{ S1[i] -> a[i] }";
2075 R
= "[N] -> { S2[i] -> a[N-1-i] }";
2076 S
= "{ S1[i] -> [0,i]; S2[i] -> [1,i] }";
2077 if (test_one_schedule(ctx
, D
, W
, R
, S
, 1, 1) < 0)
2080 D
= "{ S1[i] : 0 < i < 10; S2[i] : 0 <= i < 10 }";
2081 W
= "{ S1[i] -> a[i]; S2[i] -> b[i] }";
2082 R
= "{ S2[i] -> a[i]; S1[i] -> b[i-1] }";
2083 S
= "{ S1[i] -> [i,0]; S2[i] -> [i,1] }";
2084 if (test_one_schedule(ctx
, D
, W
, R
, S
, 0, 0) < 0)
2087 D
= "[N] -> { S1[i] : 1 <= i <= N; S2[i,j] : 1 <= i,j <= N }";
2088 W
= "{ S1[i] -> a[0,i]; S2[i,j] -> a[i,j] }";
2089 R
= "{ S2[i,j] -> a[i-1,j] }";
2090 S
= "{ S1[i] -> [0,i,0]; S2[i,j] -> [1,i,j] }";
2091 if (test_one_schedule(ctx
, D
, W
, R
, S
, 2, 1) < 0)
2094 D
= "[N] -> { S1[i] : 1 <= i <= N; S2[i,j] : 1 <= i,j <= N }";
2095 W
= "{ S1[i] -> a[i,0]; S2[i,j] -> a[i,j] }";
2096 R
= "{ S2[i,j] -> a[i,j-1] }";
2097 S
= "{ S1[i] -> [0,i,0]; S2[i,j] -> [1,i,j] }";
2098 if (test_one_schedule(ctx
, D
, W
, R
, S
, 2, 1) < 0)
2101 D
= "[N] -> { S_0[]; S_1[i] : i >= 0 and i <= -1 + N; S_2[] }";
2102 W
= "[N] -> { S_0[] -> a[0]; S_2[] -> b[0]; "
2103 "S_1[i] -> a[1 + i] : i >= 0 and i <= -1 + N }";
2104 R
= "[N] -> { S_2[] -> a[N]; S_1[i] -> a[i] : i >= 0 and i <= -1 + N }";
2105 S
= "[N] -> { S_1[i] -> [1, i, 0]; S_2[] -> [2, 0, 1]; "
2106 "S_0[] -> [0, 0, 0] }";
2107 if (test_one_schedule(ctx
, D
, W
, R
, S
, 1, 0) < 0)
2109 ctx
->opt
->schedule_parametric
= 0;
2110 if (test_one_schedule(ctx
, D
, W
, R
, S
, 0, 0) < 0)
2112 ctx
->opt
->schedule_parametric
= 1;
2114 D
= "[N] -> { S1[i] : 1 <= i <= N; S2[i] : 1 <= i <= N; "
2115 "S3[i,j] : 1 <= i,j <= N; S4[i] : 1 <= i <= N }";
2116 W
= "{ S1[i] -> a[i,0]; S2[i] -> a[0,i]; S3[i,j] -> a[i,j] }";
2117 R
= "[N] -> { S3[i,j] -> a[i-1,j]; S3[i,j] -> a[i,j-1]; "
2118 "S4[i] -> a[i,N] }";
2119 S
= "{ S1[i] -> [0,i,0]; S2[i] -> [1,i,0]; S3[i,j] -> [2,i,j]; "
2120 "S4[i] -> [4,i,0] }";
2121 if (test_one_schedule(ctx
, D
, W
, R
, S
, 2, 0) < 0)
2124 D
= "[N] -> { S_0[i, j] : i >= 1 and i <= N and j >= 1 and j <= N }";
2125 W
= "[N] -> { S_0[i, j] -> s[0] : i >= 1 and i <= N and j >= 1 and "
2127 R
= "[N] -> { S_0[i, j] -> s[0] : i >= 1 and i <= N and j >= 1 and "
2129 "S_0[i, j] -> a[i, j] : i >= 1 and i <= N and j >= 1 and "
2131 S
= "[N] -> { S_0[i, j] -> [0, i, 0, j, 0] }";
2132 if (test_one_schedule(ctx
, D
, W
, R
, S
, 0, 0) < 0)
2135 D
= "[N] -> { S_0[t] : t >= 0 and t <= -1 + N; "
2136 " S_2[t] : t >= 0 and t <= -1 + N; "
2137 " S_1[t, i] : t >= 0 and t <= -1 + N and i >= 0 and "
2139 W
= "[N] -> { S_0[t] -> a[t, 0] : t >= 0 and t <= -1 + N; "
2140 " S_2[t] -> b[t] : t >= 0 and t <= -1 + N; "
2141 " S_1[t, i] -> a[t, 1 + i] : t >= 0 and t <= -1 + N and "
2142 "i >= 0 and i <= -1 + N }";
2143 R
= "[N] -> { S_1[t, i] -> a[t, i] : t >= 0 and t <= -1 + N and "
2144 "i >= 0 and i <= -1 + N; "
2145 " S_2[t] -> a[t, N] : t >= 0 and t <= -1 + N }";
2146 S
= "[N] -> { S_2[t] -> [0, t, 2]; S_1[t, i] -> [0, t, 1, i, 0]; "
2147 " S_0[t] -> [0, t, 0] }";
2149 if (test_one_schedule(ctx
, D
, W
, R
, S
, 2, 1) < 0)
2151 ctx
->opt
->schedule_parametric
= 0;
2152 if (test_one_schedule(ctx
, D
, W
, R
, S
, 0, 0) < 0)
2154 ctx
->opt
->schedule_parametric
= 1;
2156 D
= "[N] -> { S1[i,j] : 0 <= i,j < N; S2[i,j] : 0 <= i,j < N }";
2157 S
= "{ S1[i,j] -> [0,i,j]; S2[i,j] -> [1,i,j] }";
2158 if (test_one_schedule(ctx
, D
, "{}", "{}", S
, 2, 2) < 0)
2161 D
= "[M, N] -> { S_1[i] : i >= 0 and i <= -1 + M; "
2162 "S_0[i, j] : i >= 0 and i <= -1 + M and j >= 0 and j <= -1 + N }";
2163 W
= "[M, N] -> { S_0[i, j] -> a[j] : i >= 0 and i <= -1 + M and "
2164 "j >= 0 and j <= -1 + N; "
2165 "S_1[i] -> b[0] : i >= 0 and i <= -1 + M }";
2166 R
= "[M, N] -> { S_0[i, j] -> a[0] : i >= 0 and i <= -1 + M and "
2167 "j >= 0 and j <= -1 + N; "
2168 "S_1[i] -> b[0] : i >= 0 and i <= -1 + M }";
2169 S
= "[M, N] -> { S_1[i] -> [1, i, 0]; S_0[i, j] -> [0, i, 0, j, 0] }";
2170 if (test_one_schedule(ctx
, D
, W
, R
, S
, 0, 0) < 0)
2173 D
= "{ S_0[i] : i >= 0 }";
2174 W
= "{ S_0[i] -> a[i] : i >= 0 }";
2175 R
= "{ S_0[i] -> a[0] : i >= 0 }";
2176 S
= "{ S_0[i] -> [0, i, 0] }";
2177 if (test_one_schedule(ctx
, D
, W
, R
, S
, 0, 0) < 0)
2180 D
= "{ S_0[i] : i >= 0; S_1[i] : i >= 0 }";
2181 W
= "{ S_0[i] -> a[i] : i >= 0; S_1[i] -> b[i] : i >= 0 }";
2182 R
= "{ S_0[i] -> b[0] : i >= 0; S_1[i] -> a[i] : i >= 0 }";
2183 S
= "{ S_1[i] -> [0, i, 1]; S_0[i] -> [0, i, 0] }";
2184 if (test_one_schedule(ctx
, D
, W
, R
, S
, 0, 0) < 0)
2187 D
= "[n] -> { S_0[j, k] : j <= -1 + n and j >= 0 and "
2188 "k <= -1 + n and k >= 0 }";
2189 W
= "[n] -> { S_0[j, k] -> B[j] : j <= -1 + n and j >= 0 and " "k <= -1 + n and k >= 0 }";
2190 R
= "[n] -> { S_0[j, k] -> B[j] : j <= -1 + n and j >= 0 and "
2191 "k <= -1 + n and k >= 0; "
2192 "S_0[j, k] -> B[k] : j <= -1 + n and j >= 0 and "
2193 "k <= -1 + n and k >= 0; "
2194 "S_0[j, k] -> A[k] : j <= -1 + n and j >= 0 and "
2195 "k <= -1 + n and k >= 0 }";
2196 S
= "[n] -> { S_0[j, k] -> [2, j, k] }";
2197 ctx
->opt
->schedule_outer_zero_distance
= 1;
2198 if (test_one_schedule(ctx
, D
, W
, R
, S
, 0, 0) < 0)
2200 ctx
->opt
->schedule_outer_zero_distance
= 0;
2202 return test_special_schedule(ctx
);
2205 int test_plain_injective(isl_ctx
*ctx
, const char *str
, int injective
)
2207 isl_union_map
*umap
;
2210 umap
= isl_union_map_read_from_str(ctx
, str
);
2211 test
= isl_union_map_plain_is_injective(umap
);
2212 isl_union_map_free(umap
);
2215 if (test
== injective
)
2218 isl_die(ctx
, isl_error_unknown
,
2219 "map not detected as injective", return -1);
2221 isl_die(ctx
, isl_error_unknown
,
2222 "map detected as injective", return -1);
2225 int test_injective(isl_ctx
*ctx
)
2229 if (test_plain_injective(ctx
, "{S[i,j] -> A[0]; T[i,j] -> B[1]}", 0))
2231 if (test_plain_injective(ctx
, "{S[] -> A[0]; T[] -> B[0]}", 1))
2233 if (test_plain_injective(ctx
, "{S[] -> A[0]; T[] -> A[1]}", 1))
2235 if (test_plain_injective(ctx
, "{S[] -> A[0]; T[] -> A[0]}", 0))
2237 if (test_plain_injective(ctx
, "{S[i] -> A[i,0]; T[i] -> A[i,1]}", 1))
2239 if (test_plain_injective(ctx
, "{S[i] -> A[i]; T[i] -> A[i]}", 0))
2241 if (test_plain_injective(ctx
, "{S[] -> A[0,0]; T[] -> A[0,1]}", 1))
2243 if (test_plain_injective(ctx
, "{S[] -> A[0,0]; T[] -> A[1,0]}", 1))
2246 str
= "{S[] -> A[0,0]; T[] -> A[0,1]; U[] -> A[1,0]}";
2247 if (test_plain_injective(ctx
, str
, 1))
2249 str
= "{S[] -> A[0,0]; T[] -> A[0,1]; U[] -> A[0,0]}";
2250 if (test_plain_injective(ctx
, str
, 0))
2256 int test_aff(isl_ctx
*ctx
)
2261 isl_local_space
*ls
;
2265 dim
= isl_space_set_alloc(ctx
, 0, 1);
2266 ls
= isl_local_space_from_space(dim
);
2267 aff
= isl_aff_zero(ls
);
2269 aff
= isl_aff_add_coefficient_si(aff
, isl_dim_set
, 0, 1);
2270 aff
= isl_aff_scale_down_ui(aff
, 3);
2271 aff
= isl_aff_floor(aff
);
2272 aff
= isl_aff_add_coefficient_si(aff
, isl_dim_set
, 0, 1);
2273 aff
= isl_aff_scale_down_ui(aff
, 2);
2274 aff
= isl_aff_floor(aff
);
2275 aff
= isl_aff_add_coefficient_si(aff
, isl_dim_set
, 0, 1);
2278 set
= isl_set_read_from_str(ctx
, str
, 0);
2279 aff
= isl_aff_gist(aff
, set
);
2281 aff
= isl_aff_add_constant_si(aff
, -16);
2282 zero
= isl_aff_plain_is_zero(aff
);
2288 isl_die(ctx
, isl_error_unknown
, "unexpected result", return -1);
2293 int test_dim_max(isl_ctx
*ctx
)
2297 isl_map
*map
, *map2
;
2301 str
= "[N] -> { [i] : 0 <= i <= min(N,10) }";
2302 set
= isl_set_read_from_str(ctx
, str
, -1);
2303 pwaff
= isl_set_dim_max(set
, 0);
2304 map
= isl_map_from_pw_aff(pwaff
);
2305 str
= "[N] -> { [] -> [10] : N >= 10; [] -> [N] : N <= 9 and N >= 0 }";
2306 map2
= isl_map_read_from_str(ctx
, str
, -1);
2307 equal
= isl_map_is_equal(map
, map2
);
2313 isl_die(ctx
, isl_error_unknown
, "unexpected result", return -1);
2315 str
= "[N] -> { [i] : 0 <= i <= max(2N,N+6) }";
2316 set
= isl_set_read_from_str(ctx
, str
, -1);
2317 pwaff
= isl_set_dim_max(set
, 0);
2318 map
= isl_map_from_pw_aff(pwaff
);
2319 str
= "[N] -> { [] -> [6 + N] : -6 <= N <= 5; [] -> [2N] : N >= 6 }";
2320 map2
= isl_map_read_from_str(ctx
, str
, -1);
2321 equal
= isl_map_is_equal(map
, map2
);
2327 isl_die(ctx
, isl_error_unknown
, "unexpected result", return -1);
2329 str
= "[N] -> { [i] : 0 <= i <= 2N or 0 <= i <= N+6 }";
2330 set
= isl_set_read_from_str(ctx
, str
, -1);
2331 pwaff
= isl_set_dim_max(set
, 0);
2332 map
= isl_map_from_pw_aff(pwaff
);
2333 str
= "[N] -> { [] -> [6 + N] : -6 <= N <= 5; [] -> [2N] : N >= 6 }";
2334 map2
= isl_map_read_from_str(ctx
, str
, -1);
2335 equal
= isl_map_is_equal(map
, map2
);
2341 isl_die(ctx
, isl_error_unknown
, "unexpected result", return -1);
2343 str
= "[N,M] -> { [i,j] -> [([i/16]), i%16, ([j/16]), j%16] : "
2344 "0 <= i < N and 0 <= j < M }";
2345 map
= isl_map_read_from_str(ctx
, str
, -1);
2346 set
= isl_map_range(map
);
2348 pwaff
= isl_set_dim_max(isl_set_copy(set
), 0);
2349 map
= isl_map_from_pw_aff(pwaff
);
2350 str
= "[N,M] -> { [] -> [([(N-1)/16])] : M,N > 0 }";
2351 map2
= isl_map_read_from_str(ctx
, str
, -1);
2352 equal
= isl_map_is_equal(map
, map2
);
2356 pwaff
= isl_set_dim_max(isl_set_copy(set
), 3);
2357 map
= isl_map_from_pw_aff(pwaff
);
2358 str
= "[N,M] -> { [] -> [t] : t = min(M-1,15) and M,N > 0 }";
2359 map2
= isl_map_read_from_str(ctx
, str
, -1);
2360 if (equal
>= 0 && equal
)
2361 equal
= isl_map_is_equal(map
, map2
);
2370 isl_die(ctx
, isl_error_unknown
, "unexpected result", return -1);
2375 int test_product(isl_ctx
*ctx
)
2382 set
= isl_set_read_from_str(ctx
, str
, -1);
2383 set
= isl_set_product(set
, isl_set_copy(set
));
2384 ok
= isl_set_is_wrapping(set
);
2389 isl_die(ctx
, isl_error_unknown
, "unexpected result", return -1);
2394 int test_equal(isl_ctx
*ctx
)
2397 isl_set
*set
, *set2
;
2401 set
= isl_set_read_from_str(ctx
, str
, -1);
2403 set2
= isl_set_read_from_str(ctx
, str
, -1);
2404 equal
= isl_set_is_equal(set
, set2
);
2410 isl_die(ctx
, isl_error_unknown
, "unexpected result", return -1);
2415 static int test_plain_fixed(isl_ctx
*ctx
, __isl_take isl_map
*map
,
2416 enum isl_dim_type type
, unsigned pos
, int fixed
)
2420 test
= isl_map_plain_is_fixed(map
, type
, pos
, NULL
);
2427 isl_die(ctx
, isl_error_unknown
,
2428 "map not detected as fixed", return -1);
2430 isl_die(ctx
, isl_error_unknown
,
2431 "map detected as fixed", return -1);
2434 int test_fixed(isl_ctx
*ctx
)
2439 str
= "{ [i] -> [i] }";
2440 map
= isl_map_read_from_str(ctx
, str
, -1);
2441 if (test_plain_fixed(ctx
, map
, isl_dim_out
, 0, 0))
2443 str
= "{ [i] -> [1] }";
2444 map
= isl_map_read_from_str(ctx
, str
, -1);
2445 if (test_plain_fixed(ctx
, map
, isl_dim_out
, 0, 1))
2447 str
= "{ S_1[p1] -> [o0] : o0 = -2 and p1 >= 1 and p1 <= 7 }";
2448 map
= isl_map_read_from_str(ctx
, str
, -1);
2449 if (test_plain_fixed(ctx
, map
, isl_dim_out
, 0, 1))
2451 map
= isl_map_read_from_str(ctx
, str
, -1);
2452 map
= isl_map_neg(map
);
2453 if (test_plain_fixed(ctx
, map
, isl_dim_out
, 0, 1))
2461 struct isl_ctx
*ctx
;
2463 srcdir
= getenv("srcdir");
2466 ctx
= isl_ctx_alloc();
2467 if (test_fixed(ctx
) < 0)
2469 if (test_equal(ctx
) < 0)
2471 if (test_product(ctx
) < 0)
2473 if (test_dim_max(ctx
) < 0)
2475 if (test_aff(ctx
) < 0)
2477 if (test_injective(ctx
) < 0)
2479 if (test_schedule(ctx
) < 0)
2481 test_factorize(ctx
);
2486 test_split_periods(ctx
);
2490 if (test_sv(ctx
) < 0)
2492 test_bijective(ctx
);
2496 test_construction(ctx
);
2499 test_application(ctx
);
2500 test_affine_hull(ctx
);
2501 test_convex_hull(ctx
);