2 * Copyright 2008-2009 Katholieke Universiteit Leuven
4 * Use of this software is governed by the MIT license
6 * Written by Sven Verdoolaege, K.U.Leuven, Departement
7 * Computerwetenschappen, Celestijnenlaan 200A, B-3001 Leuven, Belgium
13 #include <isl_ctx_private.h>
14 #include <isl_map_private.h>
15 #include <isl_aff_private.h>
18 #include <isl/constraint.h>
19 #include <isl/polynomial.h>
20 #include <isl/union_map.h>
21 #include <isl_factorization.h>
22 #include <isl/schedule.h>
23 #include <isl_options_private.h>
24 #include <isl/vertices.h>
25 #include <isl/ast_build.h>
27 #define ARRAY_SIZE(array) (sizeof(array)/sizeof(*array))
31 static char *get_filename(isl_ctx
*ctx
, const char *name
, const char *suffix
) {
34 char *pattern
= "%s/test_inputs/%s.%s";
36 length
= strlen(pattern
) - 6 + strlen(srcdir
) + strlen(name
)
38 filename
= isl_alloc_array(ctx
, char, length
);
43 sprintf(filename
, pattern
, srcdir
, name
, suffix
);
48 void test_parse_map(isl_ctx
*ctx
, const char *str
)
52 map
= isl_map_read_from_str(ctx
, str
);
57 int test_parse_map_equal(isl_ctx
*ctx
, const char *str
, const char *str2
)
62 map
= isl_map_read_from_str(ctx
, str
);
63 map2
= isl_map_read_from_str(ctx
, str2
);
64 equal
= isl_map_is_equal(map
, map2
);
71 isl_die(ctx
, isl_error_unknown
, "maps not equal",
77 void test_parse_pwqp(isl_ctx
*ctx
, const char *str
)
79 isl_pw_qpolynomial
*pwqp
;
81 pwqp
= isl_pw_qpolynomial_read_from_str(ctx
, str
);
83 isl_pw_qpolynomial_free(pwqp
);
86 static void test_parse_pwaff(isl_ctx
*ctx
, const char *str
)
90 pwaff
= isl_pw_aff_read_from_str(ctx
, str
);
92 isl_pw_aff_free(pwaff
);
95 int test_parse(struct isl_ctx
*ctx
)
98 const char *str
, *str2
;
100 str
= "{ [i] -> [-i] }";
101 map
= isl_map_read_from_str(ctx
, str
);
105 str
= "{ A[i] -> L[([i/3])] }";
106 map
= isl_map_read_from_str(ctx
, str
);
110 test_parse_map(ctx
, "{[[s] -> A[i]] -> [[s+1] -> A[i]]}");
111 test_parse_map(ctx
, "{ [p1, y1, y2] -> [2, y1, y2] : "
112 "p1 = 1 && (y1 <= y2 || y2 = 0) }");
114 str
= "{ [x,y] : [([x/2]+y)/3] >= 1 }";
115 str2
= "{ [x, y] : 2y >= 6 - x }";
116 if (test_parse_map_equal(ctx
, str
, str2
) < 0)
119 if (test_parse_map_equal(ctx
, "{ [x,y] : x <= min(y, 2*y+3) }",
120 "{ [x,y] : x <= y, 2*y + 3 }") < 0)
122 str
= "{ [x, y] : (y <= x and y >= -3) or (2y <= -3 + x and y <= -4) }";
123 if (test_parse_map_equal(ctx
, "{ [x,y] : x >= min(y, 2*y+3) }",
127 str
= "{[new,old] -> [new+1-2*[(new+1)/2],old+1-2*[(old+1)/2]]}";
128 map
= isl_map_read_from_str(ctx
, str
);
129 str
= "{ [new, old] -> [o0, o1] : "
130 "exists (e0 = [(-1 - new + o0)/2], e1 = [(-1 - old + o1)/2]: "
131 "2e0 = -1 - new + o0 and 2e1 = -1 - old + o1 and o0 >= 0 and "
132 "o0 <= 1 and o1 >= 0 and o1 <= 1) }";
133 map2
= isl_map_read_from_str(ctx
, str
);
134 assert(isl_map_is_equal(map
, map2
));
138 str
= "{[new,old] -> [new+1-2*[(new+1)/2],old+1-2*[(old+1)/2]]}";
139 map
= isl_map_read_from_str(ctx
, str
);
140 str
= "{[new,old] -> [(new+1)%2,(old+1)%2]}";
141 map2
= isl_map_read_from_str(ctx
, str
);
142 assert(isl_map_is_equal(map
, map2
));
146 str
= "[n] -> { [c1] : c1>=0 and c1<=floord(n-4,3) }";
147 str2
= "[n] -> { [c1] : c1 >= 0 and 3c1 <= -4 + n }";
148 if (test_parse_map_equal(ctx
, str
, str2
) < 0)
151 str
= "{ [i,j] -> [i] : i < j; [i,j] -> [j] : j <= i }";
152 str2
= "{ [i,j] -> [min(i,j)] }";
153 if (test_parse_map_equal(ctx
, str
, str2
) < 0)
156 str
= "{ [i,j] : i != j }";
157 str2
= "{ [i,j] : i < j or i > j }";
158 if (test_parse_map_equal(ctx
, str
, str2
) < 0)
161 str
= "{ [i,j] : (i+1)*2 >= j }";
162 str2
= "{ [i, j] : j <= 2 + 2i }";
163 if (test_parse_map_equal(ctx
, str
, str2
) < 0)
166 str
= "{ [i] -> [i > 0 ? 4 : 5] }";
167 str2
= "{ [i] -> [5] : i <= 0; [i] -> [4] : i >= 1 }";
168 if (test_parse_map_equal(ctx
, str
, str2
) < 0)
171 str
= "[N=2,M] -> { [i=[(M+N)/4]] }";
172 str2
= "[N, M] -> { [i] : N = 2 and 4i <= 2 + M and 4i >= -1 + M }";
173 if (test_parse_map_equal(ctx
, str
, str2
) < 0)
176 str
= "{ [x] : x >= 0 }";
177 str2
= "{ [x] : x-0 >= 0 }";
178 if (test_parse_map_equal(ctx
, str
, str2
) < 0)
181 str
= "{ [i] : ((i > 10)) }";
182 str2
= "{ [i] : i >= 11 }";
183 if (test_parse_map_equal(ctx
, str
, str2
) < 0)
186 str
= "{ [i] -> [0] }";
187 str2
= "{ [i] -> [0 * i] }";
188 if (test_parse_map_equal(ctx
, str
, str2
) < 0)
191 test_parse_pwqp(ctx
, "{ [i] -> i + [ (i + [i/3])/2 ] }");
192 test_parse_map(ctx
, "{ S1[i] -> [([i/10]),i%10] : 0 <= i <= 45 }");
193 test_parse_pwaff(ctx
, "{ [i] -> [i + 1] : i > 0; [a] -> [a] : a < 0 }");
194 test_parse_pwqp(ctx
, "{ [x] -> ([(x)/2] * [(x)/3]) }");
196 if (test_parse_map_equal(ctx
, "{ [a] -> [b] : (not false) }",
197 "{ [a] -> [b] : true }") < 0)
200 if (test_parse_map_equal(ctx
, "{ [i] : i/2 <= 5 }",
201 "{ [i] : i <= 10 }") < 0)
204 if (test_parse_map_equal(ctx
, "{Sym=[n] [i] : i <= n }",
205 "[n] -> { [i] : i <= n }") < 0)
211 void test_read(struct isl_ctx
*ctx
)
215 struct isl_basic_set
*bset1
, *bset2
;
216 const char *str
= "{[y]: Exists ( alpha : 2alpha = y)}";
218 filename
= get_filename(ctx
, "set", "omega");
220 input
= fopen(filename
, "r");
223 bset1
= isl_basic_set_read_from_file(ctx
, input
);
224 bset2
= isl_basic_set_read_from_str(ctx
, str
);
226 assert(isl_basic_set_is_equal(bset1
, bset2
) == 1);
228 isl_basic_set_free(bset1
);
229 isl_basic_set_free(bset2
);
235 void test_bounded(struct isl_ctx
*ctx
)
240 set
= isl_set_read_from_str(ctx
, "[n] -> {[i] : 0 <= i <= n }");
241 bounded
= isl_set_is_bounded(set
);
245 set
= isl_set_read_from_str(ctx
, "{[n, i] : 0 <= i <= n }");
246 bounded
= isl_set_is_bounded(set
);
250 set
= isl_set_read_from_str(ctx
, "[n] -> {[i] : i <= n }");
251 bounded
= isl_set_is_bounded(set
);
256 /* Construct the basic set { [i] : 5 <= i <= N } */
257 void test_construction(struct isl_ctx
*ctx
)
262 struct isl_basic_set
*bset
;
263 struct isl_constraint
*c
;
267 dim
= isl_space_set_alloc(ctx
, 1, 1);
268 bset
= isl_basic_set_universe(isl_space_copy(dim
));
269 ls
= isl_local_space_from_space(dim
);
271 c
= isl_inequality_alloc(isl_local_space_copy(ls
));
272 isl_int_set_si(v
, -1);
273 isl_constraint_set_coefficient(c
, isl_dim_set
, 0, v
);
274 isl_int_set_si(v
, 1);
275 isl_constraint_set_coefficient(c
, isl_dim_param
, 0, v
);
276 bset
= isl_basic_set_add_constraint(bset
, c
);
278 c
= isl_inequality_alloc(isl_local_space_copy(ls
));
279 isl_int_set_si(v
, 1);
280 isl_constraint_set_coefficient(c
, isl_dim_set
, 0, v
);
281 isl_int_set_si(v
, -5);
282 isl_constraint_set_constant(c
, v
);
283 bset
= isl_basic_set_add_constraint(bset
, c
);
285 isl_local_space_free(ls
);
286 isl_basic_set_free(bset
);
291 void test_dim(struct isl_ctx
*ctx
)
294 isl_map
*map1
, *map2
;
296 map1
= isl_map_read_from_str(ctx
,
297 "[n] -> { [i] -> [j] : exists (a = [i/10] : i - 10a <= n ) }");
298 map1
= isl_map_add_dims(map1
, isl_dim_in
, 1);
299 map2
= isl_map_read_from_str(ctx
,
300 "[n] -> { [i,k] -> [j] : exists (a = [i/10] : i - 10a <= n ) }");
301 assert(isl_map_is_equal(map1
, map2
));
304 map1
= isl_map_project_out(map1
, isl_dim_in
, 0, 1);
305 map2
= isl_map_read_from_str(ctx
, "[n] -> { [i] -> [j] : n >= 0 }");
306 assert(isl_map_is_equal(map1
, map2
));
311 str
= "[n] -> { [i] -> [] : exists a : 0 <= i <= n and i = 2 a }";
312 map1
= isl_map_read_from_str(ctx
, str
);
313 str
= "{ [i] -> [j] : exists a : 0 <= i <= j and i = 2 a }";
314 map2
= isl_map_read_from_str(ctx
, str
);
315 map1
= isl_map_move_dims(map1
, isl_dim_out
, 0, isl_dim_param
, 0, 1);
316 assert(isl_map_is_equal(map1
, map2
));
322 static int test_div(isl_ctx
*ctx
)
331 struct isl_basic_set
*bset
;
332 struct isl_constraint
*c
;
337 dim
= isl_space_set_alloc(ctx
, 0, 3);
338 bset
= isl_basic_set_universe(isl_space_copy(dim
));
339 ls
= isl_local_space_from_space(dim
);
341 c
= isl_equality_alloc(isl_local_space_copy(ls
));
342 isl_int_set_si(v
, -1);
343 isl_constraint_set_constant(c
, v
);
344 isl_int_set_si(v
, 1);
345 isl_constraint_set_coefficient(c
, isl_dim_set
, 0, v
);
346 isl_int_set_si(v
, 3);
347 isl_constraint_set_coefficient(c
, isl_dim_set
, 1, v
);
348 bset
= isl_basic_set_add_constraint(bset
, c
);
350 c
= isl_equality_alloc(isl_local_space_copy(ls
));
351 isl_int_set_si(v
, 1);
352 isl_constraint_set_constant(c
, v
);
353 isl_int_set_si(v
, -1);
354 isl_constraint_set_coefficient(c
, isl_dim_set
, 0, v
);
355 isl_int_set_si(v
, 3);
356 isl_constraint_set_coefficient(c
, isl_dim_set
, 2, v
);
357 bset
= isl_basic_set_add_constraint(bset
, c
);
359 bset
= isl_basic_set_project_out(bset
, isl_dim_set
, 1, 2);
361 assert(bset
&& bset
->n_div
== 1);
362 isl_local_space_free(ls
);
363 isl_basic_set_free(bset
);
366 dim
= isl_space_set_alloc(ctx
, 0, 3);
367 bset
= isl_basic_set_universe(isl_space_copy(dim
));
368 ls
= isl_local_space_from_space(dim
);
370 c
= isl_equality_alloc(isl_local_space_copy(ls
));
371 isl_int_set_si(v
, 1);
372 isl_constraint_set_constant(c
, v
);
373 isl_int_set_si(v
, -1);
374 isl_constraint_set_coefficient(c
, isl_dim_set
, 0, v
);
375 isl_int_set_si(v
, 3);
376 isl_constraint_set_coefficient(c
, isl_dim_set
, 1, v
);
377 bset
= isl_basic_set_add_constraint(bset
, c
);
379 c
= isl_equality_alloc(isl_local_space_copy(ls
));
380 isl_int_set_si(v
, -1);
381 isl_constraint_set_constant(c
, v
);
382 isl_int_set_si(v
, 1);
383 isl_constraint_set_coefficient(c
, isl_dim_set
, 0, v
);
384 isl_int_set_si(v
, 3);
385 isl_constraint_set_coefficient(c
, isl_dim_set
, 2, v
);
386 bset
= isl_basic_set_add_constraint(bset
, c
);
388 bset
= isl_basic_set_project_out(bset
, isl_dim_set
, 1, 2);
390 assert(bset
&& bset
->n_div
== 1);
391 isl_local_space_free(ls
);
392 isl_basic_set_free(bset
);
395 dim
= isl_space_set_alloc(ctx
, 0, 3);
396 bset
= isl_basic_set_universe(isl_space_copy(dim
));
397 ls
= isl_local_space_from_space(dim
);
399 c
= isl_equality_alloc(isl_local_space_copy(ls
));
400 isl_int_set_si(v
, 1);
401 isl_constraint_set_constant(c
, v
);
402 isl_int_set_si(v
, -1);
403 isl_constraint_set_coefficient(c
, isl_dim_set
, 0, v
);
404 isl_int_set_si(v
, 3);
405 isl_constraint_set_coefficient(c
, isl_dim_set
, 1, v
);
406 bset
= isl_basic_set_add_constraint(bset
, c
);
408 c
= isl_equality_alloc(isl_local_space_copy(ls
));
409 isl_int_set_si(v
, -3);
410 isl_constraint_set_constant(c
, v
);
411 isl_int_set_si(v
, 1);
412 isl_constraint_set_coefficient(c
, isl_dim_set
, 0, v
);
413 isl_int_set_si(v
, 4);
414 isl_constraint_set_coefficient(c
, isl_dim_set
, 2, v
);
415 bset
= isl_basic_set_add_constraint(bset
, c
);
417 bset
= isl_basic_set_project_out(bset
, isl_dim_set
, 1, 2);
419 assert(bset
&& bset
->n_div
== 1);
420 isl_local_space_free(ls
);
421 isl_basic_set_free(bset
);
424 dim
= isl_space_set_alloc(ctx
, 0, 3);
425 bset
= isl_basic_set_universe(isl_space_copy(dim
));
426 ls
= isl_local_space_from_space(dim
);
428 c
= isl_equality_alloc(isl_local_space_copy(ls
));
429 isl_int_set_si(v
, 2);
430 isl_constraint_set_constant(c
, v
);
431 isl_int_set_si(v
, -1);
432 isl_constraint_set_coefficient(c
, isl_dim_set
, 0, v
);
433 isl_int_set_si(v
, 3);
434 isl_constraint_set_coefficient(c
, isl_dim_set
, 1, v
);
435 bset
= isl_basic_set_add_constraint(bset
, c
);
437 c
= isl_equality_alloc(isl_local_space_copy(ls
));
438 isl_int_set_si(v
, -1);
439 isl_constraint_set_constant(c
, v
);
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 bset
= isl_basic_set_project_out(bset
, isl_dim_set
, 1, 2);
448 assert(isl_basic_set_is_empty(bset
));
449 isl_local_space_free(ls
);
450 isl_basic_set_free(bset
);
453 dim
= isl_space_set_alloc(ctx
, 0, 3);
454 bset
= isl_basic_set_universe(isl_space_copy(dim
));
455 ls
= isl_local_space_from_space(dim
);
457 c
= isl_equality_alloc(isl_local_space_copy(ls
));
458 isl_int_set_si(v
, -1);
459 isl_constraint_set_coefficient(c
, isl_dim_set
, 0, v
);
460 isl_int_set_si(v
, 3);
461 isl_constraint_set_coefficient(c
, isl_dim_set
, 2, v
);
462 bset
= isl_basic_set_add_constraint(bset
, c
);
464 c
= isl_equality_alloc(isl_local_space_copy(ls
));
465 isl_int_set_si(v
, 1);
466 isl_constraint_set_coefficient(c
, isl_dim_set
, 0, v
);
467 isl_int_set_si(v
, -3);
468 isl_constraint_set_coefficient(c
, isl_dim_set
, 1, v
);
469 bset
= isl_basic_set_add_constraint(bset
, c
);
471 bset
= isl_basic_set_project_out(bset
, isl_dim_set
, 2, 1);
473 assert(bset
&& bset
->n_div
== 0);
474 isl_basic_set_free(bset
);
475 isl_local_space_free(ls
);
478 dim
= isl_space_set_alloc(ctx
, 0, 3);
479 bset
= isl_basic_set_universe(isl_space_copy(dim
));
480 ls
= isl_local_space_from_space(dim
);
482 c
= isl_equality_alloc(isl_local_space_copy(ls
));
483 isl_int_set_si(v
, -1);
484 isl_constraint_set_coefficient(c
, isl_dim_set
, 0, v
);
485 isl_int_set_si(v
, 6);
486 isl_constraint_set_coefficient(c
, isl_dim_set
, 2, v
);
487 bset
= isl_basic_set_add_constraint(bset
, c
);
489 c
= isl_equality_alloc(isl_local_space_copy(ls
));
490 isl_int_set_si(v
, 1);
491 isl_constraint_set_coefficient(c
, isl_dim_set
, 0, v
);
492 isl_int_set_si(v
, -3);
493 isl_constraint_set_coefficient(c
, isl_dim_set
, 1, v
);
494 bset
= isl_basic_set_add_constraint(bset
, c
);
496 bset
= isl_basic_set_project_out(bset
, isl_dim_set
, 2, 1);
498 assert(bset
&& bset
->n_div
== 1);
499 isl_basic_set_free(bset
);
500 isl_local_space_free(ls
);
503 /* This test is a bit tricky. We set up an equality
505 * Normalization of divs creates _two_ divs
508 * Afterwards e0 is removed again because it has coefficient -1
509 * and we end up with the original equality and div again.
510 * Perhaps we can avoid the introduction of this temporary div.
512 dim
= isl_space_set_alloc(ctx
, 0, 4);
513 bset
= isl_basic_set_universe(isl_space_copy(dim
));
514 ls
= isl_local_space_from_space(dim
);
516 c
= isl_equality_alloc(isl_local_space_copy(ls
));
517 isl_int_set_si(v
, -1);
518 isl_constraint_set_coefficient(c
, isl_dim_set
, 0, v
);
519 isl_int_set_si(v
, -3);
520 isl_constraint_set_coefficient(c
, isl_dim_set
, 1, v
);
521 isl_int_set_si(v
, -3);
522 isl_constraint_set_coefficient(c
, isl_dim_set
, 2, v
);
523 isl_int_set_si(v
, 6);
524 isl_constraint_set_coefficient(c
, isl_dim_set
, 3, v
);
525 bset
= isl_basic_set_add_constraint(bset
, c
);
527 bset
= isl_basic_set_project_out(bset
, isl_dim_set
, 3, 1);
529 /* Test disabled for now */
531 assert(bset && bset->n_div == 1);
533 isl_local_space_free(ls
);
534 isl_basic_set_free(bset
);
537 dim
= isl_space_set_alloc(ctx
, 0, 5);
538 bset
= isl_basic_set_universe(isl_space_copy(dim
));
539 ls
= isl_local_space_from_space(dim
);
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
, 1, v
);
546 isl_int_set_si(v
, -3);
547 isl_constraint_set_coefficient(c
, isl_dim_set
, 3, v
);
548 isl_int_set_si(v
, 6);
549 isl_constraint_set_coefficient(c
, isl_dim_set
, 4, v
);
550 bset
= isl_basic_set_add_constraint(bset
, c
);
552 c
= isl_equality_alloc(isl_local_space_copy(ls
));
553 isl_int_set_si(v
, -1);
554 isl_constraint_set_coefficient(c
, isl_dim_set
, 0, v
);
555 isl_int_set_si(v
, 1);
556 isl_constraint_set_coefficient(c
, isl_dim_set
, 2, v
);
557 isl_int_set_si(v
, 1);
558 isl_constraint_set_constant(c
, v
);
559 bset
= isl_basic_set_add_constraint(bset
, c
);
561 bset
= isl_basic_set_project_out(bset
, isl_dim_set
, 4, 1);
563 /* Test disabled for now */
565 assert(bset && bset->n_div == 1);
567 isl_local_space_free(ls
);
568 isl_basic_set_free(bset
);
571 dim
= isl_space_set_alloc(ctx
, 0, 4);
572 bset
= isl_basic_set_universe(isl_space_copy(dim
));
573 ls
= isl_local_space_from_space(dim
);
575 c
= isl_equality_alloc(isl_local_space_copy(ls
));
576 isl_int_set_si(v
, 1);
577 isl_constraint_set_coefficient(c
, isl_dim_set
, 0, v
);
578 isl_int_set_si(v
, -1);
579 isl_constraint_set_coefficient(c
, isl_dim_set
, 1, v
);
580 isl_int_set_si(v
, -2);
581 isl_constraint_set_coefficient(c
, isl_dim_set
, 2, v
);
582 bset
= isl_basic_set_add_constraint(bset
, c
);
584 c
= isl_equality_alloc(isl_local_space_copy(ls
));
585 isl_int_set_si(v
, -1);
586 isl_constraint_set_coefficient(c
, isl_dim_set
, 0, v
);
587 isl_int_set_si(v
, 3);
588 isl_constraint_set_coefficient(c
, isl_dim_set
, 3, v
);
589 isl_int_set_si(v
, 2);
590 isl_constraint_set_constant(c
, v
);
591 bset
= isl_basic_set_add_constraint(bset
, c
);
593 bset
= isl_basic_set_project_out(bset
, isl_dim_set
, 2, 2);
595 bset
= isl_basic_set_fix_si(bset
, isl_dim_set
, 0, 2);
597 assert(!isl_basic_set_is_empty(bset
));
599 isl_local_space_free(ls
);
600 isl_basic_set_free(bset
);
603 dim
= isl_space_set_alloc(ctx
, 0, 3);
604 bset
= isl_basic_set_universe(isl_space_copy(dim
));
605 ls
= isl_local_space_from_space(dim
);
607 c
= isl_equality_alloc(isl_local_space_copy(ls
));
608 isl_int_set_si(v
, 1);
609 isl_constraint_set_coefficient(c
, isl_dim_set
, 0, v
);
610 isl_int_set_si(v
, -2);
611 isl_constraint_set_coefficient(c
, isl_dim_set
, 2, v
);
612 bset
= isl_basic_set_add_constraint(bset
, c
);
614 bset
= isl_basic_set_project_out(bset
, isl_dim_set
, 2, 1);
616 bset
= isl_basic_set_fix_si(bset
, isl_dim_set
, 0, 2);
618 isl_local_space_free(ls
);
619 isl_basic_set_free(bset
);
623 str
= "{ [i] : exists (e0, e1: 3e1 >= 1 + 2e0 and "
624 "8e1 <= -1 + 5i - 5e0 and 2e1 >= 1 + 2i - 5e0) }";
625 set
= isl_set_read_from_str(ctx
, str
);
626 set
= isl_set_compute_divs(set
);
631 str
= "{ [i,j] : 2*[i/2] + 3 * [j/4] <= 10 and 2 i = j }";
632 bset
= isl_basic_set_read_from_str(ctx
, str
);
633 n
= isl_basic_set_dim(bset
, isl_dim_div
);
634 isl_basic_set_free(bset
);
638 isl_die(ctx
, isl_error_unknown
,
639 "expecting no existentials", return -1);
641 str
= "{ [i,j,k] : 3 + i + 2j >= 0 and 2 * [(i+2j)/4] <= k }";
642 set
= isl_set_read_from_str(ctx
, str
);
643 set
= isl_set_remove_divs_involving_dims(set
, isl_dim_set
, 0, 2);
644 set
= isl_set_fix_si(set
, isl_dim_set
, 2, -3);
645 empty
= isl_set_is_empty(set
);
650 isl_die(ctx
, isl_error_unknown
,
651 "result not as accurate as expected", return -1);
656 void test_application_case(struct isl_ctx
*ctx
, const char *name
)
660 struct isl_basic_set
*bset1
, *bset2
;
661 struct isl_basic_map
*bmap
;
663 filename
= get_filename(ctx
, name
, "omega");
665 input
= fopen(filename
, "r");
668 bset1
= isl_basic_set_read_from_file(ctx
, input
);
669 bmap
= isl_basic_map_read_from_file(ctx
, input
);
671 bset1
= isl_basic_set_apply(bset1
, bmap
);
673 bset2
= isl_basic_set_read_from_file(ctx
, input
);
675 assert(isl_basic_set_is_equal(bset1
, bset2
) == 1);
677 isl_basic_set_free(bset1
);
678 isl_basic_set_free(bset2
);
684 void test_application(struct isl_ctx
*ctx
)
686 test_application_case(ctx
, "application");
687 test_application_case(ctx
, "application2");
690 void test_affine_hull_case(struct isl_ctx
*ctx
, const char *name
)
694 struct isl_basic_set
*bset1
, *bset2
;
696 filename
= get_filename(ctx
, name
, "polylib");
698 input
= fopen(filename
, "r");
701 bset1
= isl_basic_set_read_from_file(ctx
, input
);
702 bset2
= isl_basic_set_read_from_file(ctx
, input
);
704 bset1
= isl_basic_set_affine_hull(bset1
);
706 assert(isl_basic_set_is_equal(bset1
, bset2
) == 1);
708 isl_basic_set_free(bset1
);
709 isl_basic_set_free(bset2
);
715 int test_affine_hull(struct isl_ctx
*ctx
)
722 test_affine_hull_case(ctx
, "affine2");
723 test_affine_hull_case(ctx
, "affine");
724 test_affine_hull_case(ctx
, "affine3");
726 str
= "[m] -> { [i0] : exists (e0, e1: e1 <= 1 + i0 and "
727 "m >= 3 and 4i0 <= 2 + m and e1 >= i0 and "
728 "e1 >= 0 and e1 <= 2 and e1 >= 1 + 2e0 and "
729 "2e1 <= 1 + m + 4e0 and 2e1 >= 2 - m + 4i0 - 4e0) }";
730 set
= isl_set_read_from_str(ctx
, str
);
731 bset
= isl_set_affine_hull(set
);
732 n
= isl_basic_set_dim(bset
, isl_dim_div
);
733 isl_basic_set_free(bset
);
735 isl_die(ctx
, isl_error_unknown
, "not expecting any divs",
741 void test_convex_hull_case(struct isl_ctx
*ctx
, const char *name
)
745 struct isl_basic_set
*bset1
, *bset2
;
748 filename
= get_filename(ctx
, name
, "polylib");
750 input
= fopen(filename
, "r");
753 bset1
= isl_basic_set_read_from_file(ctx
, input
);
754 bset2
= isl_basic_set_read_from_file(ctx
, input
);
756 set
= isl_basic_set_union(bset1
, bset2
);
757 bset1
= isl_set_convex_hull(set
);
759 bset2
= isl_basic_set_read_from_file(ctx
, input
);
761 assert(isl_basic_set_is_equal(bset1
, bset2
) == 1);
763 isl_basic_set_free(bset1
);
764 isl_basic_set_free(bset2
);
770 void test_convex_hull_algo(struct isl_ctx
*ctx
, int convex
)
772 const char *str1
, *str2
;
773 isl_set
*set1
, *set2
;
774 int orig_convex
= ctx
->opt
->convex
;
775 ctx
->opt
->convex
= convex
;
777 test_convex_hull_case(ctx
, "convex0");
778 test_convex_hull_case(ctx
, "convex1");
779 test_convex_hull_case(ctx
, "convex2");
780 test_convex_hull_case(ctx
, "convex3");
781 test_convex_hull_case(ctx
, "convex4");
782 test_convex_hull_case(ctx
, "convex5");
783 test_convex_hull_case(ctx
, "convex6");
784 test_convex_hull_case(ctx
, "convex7");
785 test_convex_hull_case(ctx
, "convex8");
786 test_convex_hull_case(ctx
, "convex9");
787 test_convex_hull_case(ctx
, "convex10");
788 test_convex_hull_case(ctx
, "convex11");
789 test_convex_hull_case(ctx
, "convex12");
790 test_convex_hull_case(ctx
, "convex13");
791 test_convex_hull_case(ctx
, "convex14");
792 test_convex_hull_case(ctx
, "convex15");
794 str1
= "{ [i0, i1, i2] : (i2 = 1 and i0 = 0 and i1 >= 0) or "
795 "(i0 = 1 and i1 = 0 and i2 = 1) or "
796 "(i0 = 0 and i1 = 0 and i2 = 0) }";
797 str2
= "{ [i0, i1, i2] : i0 >= 0 and i2 >= i0 and i2 <= 1 and i1 >= 0 }";
798 set1
= isl_set_read_from_str(ctx
, str1
);
799 set2
= isl_set_read_from_str(ctx
, str2
);
800 set1
= isl_set_from_basic_set(isl_set_convex_hull(set1
));
801 assert(isl_set_is_equal(set1
, set2
));
805 ctx
->opt
->convex
= orig_convex
;
808 void test_convex_hull(struct isl_ctx
*ctx
)
810 test_convex_hull_algo(ctx
, ISL_CONVEX_HULL_FM
);
811 test_convex_hull_algo(ctx
, ISL_CONVEX_HULL_WRAP
);
814 void test_gist_case(struct isl_ctx
*ctx
, const char *name
)
818 struct isl_basic_set
*bset1
, *bset2
;
820 filename
= get_filename(ctx
, name
, "polylib");
822 input
= fopen(filename
, "r");
825 bset1
= isl_basic_set_read_from_file(ctx
, input
);
826 bset2
= isl_basic_set_read_from_file(ctx
, input
);
828 bset1
= isl_basic_set_gist(bset1
, bset2
);
830 bset2
= isl_basic_set_read_from_file(ctx
, input
);
832 assert(isl_basic_set_is_equal(bset1
, bset2
) == 1);
834 isl_basic_set_free(bset1
);
835 isl_basic_set_free(bset2
);
841 void test_gist(struct isl_ctx
*ctx
)
844 isl_basic_set
*bset1
, *bset2
;
846 test_gist_case(ctx
, "gist1");
848 str
= "[p0, p2, p3, p5, p6, p10] -> { [] : "
849 "exists (e0 = [(15 + p0 + 15p6 + 15p10)/16], e1 = [(p5)/8], "
850 "e2 = [(p6)/128], e3 = [(8p2 - p5)/128], "
851 "e4 = [(128p3 - p6)/4096]: 8e1 = p5 and 128e2 = p6 and "
852 "128e3 = 8p2 - p5 and 4096e4 = 128p3 - p6 and p2 >= 0 and "
853 "16e0 >= 16 + 16p6 + 15p10 and p2 <= 15 and p3 >= 0 and "
854 "p3 <= 31 and p6 >= 128p3 and p5 >= 8p2 and p10 >= 0 and "
855 "16e0 <= 15 + p0 + 15p6 + 15p10 and 16e0 >= p0 + 15p6 + 15p10 and "
856 "p10 <= 15 and p10 <= -1 + p0 - p6) }";
857 bset1
= isl_basic_set_read_from_str(ctx
, str
);
858 str
= "[p0, p2, p3, p5, p6, p10] -> { [] : exists (e0 = [(p5)/8], "
859 "e1 = [(p6)/128], e2 = [(8p2 - p5)/128], "
860 "e3 = [(128p3 - p6)/4096]: 8e0 = p5 and 128e1 = p6 and "
861 "128e2 = 8p2 - p5 and 4096e3 = 128p3 - p6 and p5 >= -7 and "
862 "p2 >= 0 and 8p2 <= -1 + p0 and p2 <= 15 and p3 >= 0 and "
863 "p3 <= 31 and 128p3 <= -1 + p0 and p6 >= -127 and "
864 "p5 <= -1 + p0 and p6 <= -1 + p0 and p6 >= 128p3 and "
865 "p0 >= 1 and p5 >= 8p2 and p10 >= 0 and p10 <= 15 ) }";
866 bset2
= isl_basic_set_read_from_str(ctx
, str
);
867 bset1
= isl_basic_set_gist(bset1
, bset2
);
868 assert(bset1
&& bset1
->n_div
== 0);
869 isl_basic_set_free(bset1
);
872 int test_coalesce_set(isl_ctx
*ctx
, const char *str
, int check_one
)
878 set
= isl_set_read_from_str(ctx
, str
);
879 set
= isl_set_coalesce(set
);
880 set2
= isl_set_read_from_str(ctx
, str
);
881 equal
= isl_set_is_equal(set
, set2
);
882 one
= set
&& set
->n
== 1;
889 isl_die(ctx
, isl_error_unknown
,
890 "coalesced set not equal to input", return -1);
891 if (check_one
&& !one
)
892 isl_die(ctx
, isl_error_unknown
,
893 "coalesced set should not be a union", return -1);
898 int test_coalesce_unbounded_wrapping(isl_ctx
*ctx
)
903 bounded
= isl_options_get_coalesce_bounded_wrapping(ctx
);
904 isl_options_set_coalesce_bounded_wrapping(ctx
, 0);
906 if (test_coalesce_set(ctx
,
907 "{[x,y,z] : y + 2 >= 0 and x - y + 1 >= 0 and "
908 "-x - y + 1 >= 0 and -3 <= z <= 3;"
909 "[x,y,z] : -x+z + 20 >= 0 and -x-z + 20 >= 0 and "
910 "x-z + 20 >= 0 and x+z + 20 >= 0 and "
911 "-10 <= y <= 0}", 1) < 0)
913 if (test_coalesce_set(ctx
,
914 "{[x,y] : 0 <= x,y <= 10; [5,y]: 4 <=y <= 11}", 1) < 0)
916 if (test_coalesce_set(ctx
,
917 "{[x,0,0] : -5 <= x <= 5; [0,y,1] : -5 <= y <= 5 }", 1) < 0)
925 isl_options_set_coalesce_bounded_wrapping(ctx
, bounded
);
930 int test_coalesce(struct isl_ctx
*ctx
)
933 struct isl_set
*set
, *set2
;
934 struct isl_map
*map
, *map2
;
936 set
= isl_set_read_from_str(ctx
,
937 "{[x,y]: x >= 0 & x <= 10 & y >= 0 & y <= 10 or "
938 "y >= x & x >= 2 & 5 >= y }");
939 set
= isl_set_coalesce(set
);
940 assert(set
&& set
->n
== 1);
943 set
= isl_set_read_from_str(ctx
,
944 "{[x,y]: y >= 0 & 2x + y <= 30 & y <= 10 & x >= 0 or "
945 "x + y >= 10 & y <= x & x + y <= 20 & y >= 0}");
946 set
= isl_set_coalesce(set
);
947 assert(set
&& set
->n
== 1);
950 set
= isl_set_read_from_str(ctx
,
951 "{[x,y]: y >= 0 & 2x + y <= 30 & y <= 10 & x >= 0 or "
952 "x + y >= 10 & y <= x & x + y <= 19 & y >= 0}");
953 set
= isl_set_coalesce(set
);
954 assert(set
&& set
->n
== 2);
957 set
= isl_set_read_from_str(ctx
,
958 "{[x,y]: y >= 0 & x <= 5 & y <= x or "
959 "y >= 0 & x >= 6 & x <= 10 & y <= x}");
960 set
= isl_set_coalesce(set
);
961 assert(set
&& set
->n
== 1);
964 set
= isl_set_read_from_str(ctx
,
965 "{[x,y]: y >= 0 & x <= 5 & y <= x or "
966 "y >= 0 & x >= 7 & x <= 10 & y <= x}");
967 set
= isl_set_coalesce(set
);
968 assert(set
&& set
->n
== 2);
971 set
= isl_set_read_from_str(ctx
,
972 "{[x,y]: y >= 0 & x <= 5 & y <= x or "
973 "y >= 0 & x >= 6 & x <= 10 & y + 1 <= x}");
974 set
= isl_set_coalesce(set
);
975 assert(set
&& set
->n
== 2);
978 set
= isl_set_read_from_str(ctx
,
979 "{[x,y]: y >= 0 & x <= 5 & y <= x or "
980 "y >= 0 & x = 6 & y <= 6}");
981 set
= isl_set_coalesce(set
);
982 assert(set
&& set
->n
== 1);
985 set
= isl_set_read_from_str(ctx
,
986 "{[x,y]: y >= 0 & x <= 5 & y <= x or "
987 "y >= 0 & x = 7 & y <= 6}");
988 set
= isl_set_coalesce(set
);
989 assert(set
&& set
->n
== 2);
992 set
= isl_set_read_from_str(ctx
,
993 "{[x,y]: y >= 0 & x <= 5 & y <= x or "
994 "y >= 0 & x = 6 & y <= 5}");
995 set
= isl_set_coalesce(set
);
996 assert(set
&& set
->n
== 1);
997 set2
= isl_set_read_from_str(ctx
,
998 "{[x,y]: y >= 0 & x <= 5 & y <= x or "
999 "y >= 0 & x = 6 & y <= 5}");
1000 assert(isl_set_is_equal(set
, set2
));
1004 set
= isl_set_read_from_str(ctx
,
1005 "{[x,y]: y >= 0 & x <= 5 & y <= x or "
1006 "y >= 0 & x = 6 & y <= 7}");
1007 set
= isl_set_coalesce(set
);
1008 assert(set
&& set
->n
== 2);
1011 set
= isl_set_read_from_str(ctx
,
1012 "[n] -> { [i] : i = 1 and n >= 2 or 2 <= i and i <= n }");
1013 set
= isl_set_coalesce(set
);
1014 assert(set
&& set
->n
== 1);
1015 set2
= isl_set_read_from_str(ctx
,
1016 "[n] -> { [i] : i = 1 and n >= 2 or 2 <= i and i <= n }");
1017 assert(isl_set_is_equal(set
, set2
));
1021 set
= isl_set_read_from_str(ctx
,
1022 "{[x,y] : x >= 0 and y >= 0 or 0 <= y and y <= 5 and x = -1}");
1023 set
= isl_set_coalesce(set
);
1024 set2
= isl_set_read_from_str(ctx
,
1025 "{[x,y] : x >= 0 and y >= 0 or 0 <= y and y <= 5 and x = -1}");
1026 assert(isl_set_is_equal(set
, set2
));
1030 set
= isl_set_read_from_str(ctx
,
1031 "[n] -> { [i] : 1 <= i and i <= n - 1 or "
1032 "2 <= i and i <= n }");
1033 set
= isl_set_coalesce(set
);
1034 assert(set
&& set
->n
== 1);
1035 set2
= isl_set_read_from_str(ctx
,
1036 "[n] -> { [i] : 1 <= i and i <= n - 1 or "
1037 "2 <= i and i <= n }");
1038 assert(isl_set_is_equal(set
, set2
));
1042 map
= isl_map_read_from_str(ctx
,
1043 "[n] -> { [i0] -> [o0] : exists (e0 = [(i0)/4], e1 = [(o0)/4], "
1044 "e2 = [(n)/2], e3 = [(-2 + i0)/4], e4 = [(-2 + o0)/4], "
1045 "e5 = [(-2n + i0)/4]: 2e2 = n and 4e3 = -2 + i0 and "
1046 "4e4 = -2 + o0 and i0 >= 8 + 2n and o0 >= 2 + i0 and "
1047 "o0 <= 56 + 2n and o0 <= -12 + 4n and i0 <= 57 + 2n and "
1048 "i0 <= -11 + 4n and o0 >= 6 + 2n and 4e0 <= i0 and "
1049 "4e0 >= -3 + i0 and 4e1 <= o0 and 4e1 >= -3 + o0 and "
1050 "4e5 <= -2n + i0 and 4e5 >= -3 - 2n + i0);"
1051 "[i0] -> [o0] : exists (e0 = [(i0)/4], e1 = [(o0)/4], "
1052 "e2 = [(n)/2], e3 = [(-2 + i0)/4], e4 = [(-2 + o0)/4], "
1053 "e5 = [(-2n + i0)/4]: 2e2 = n and 4e3 = -2 + i0 and "
1054 "4e4 = -2 + o0 and 2e0 >= 3 + n and e0 <= -4 + n and "
1055 "2e0 <= 27 + n and e1 <= -4 + n and 2e1 <= 27 + n and "
1056 "2e1 >= 2 + n and e1 >= 1 + e0 and i0 >= 7 + 2n and "
1057 "i0 <= -11 + 4n and i0 <= 57 + 2n and 4e0 <= -2 + i0 and "
1058 "4e0 >= -3 + i0 and o0 >= 6 + 2n and o0 <= -11 + 4n and "
1059 "o0 <= 57 + 2n and 4e1 <= -2 + o0 and 4e1 >= -3 + o0 and "
1060 "4e5 <= -2n + i0 and 4e5 >= -3 - 2n + i0 ) }");
1061 map
= isl_map_coalesce(map
);
1062 map2
= isl_map_read_from_str(ctx
,
1063 "[n] -> { [i0] -> [o0] : exists (e0 = [(i0)/4], e1 = [(o0)/4], "
1064 "e2 = [(n)/2], e3 = [(-2 + i0)/4], e4 = [(-2 + o0)/4], "
1065 "e5 = [(-2n + i0)/4]: 2e2 = n and 4e3 = -2 + i0 and "
1066 "4e4 = -2 + o0 and i0 >= 8 + 2n and o0 >= 2 + i0 and "
1067 "o0 <= 56 + 2n and o0 <= -12 + 4n and i0 <= 57 + 2n and "
1068 "i0 <= -11 + 4n and o0 >= 6 + 2n and 4e0 <= i0 and "
1069 "4e0 >= -3 + i0 and 4e1 <= o0 and 4e1 >= -3 + o0 and "
1070 "4e5 <= -2n + i0 and 4e5 >= -3 - 2n + i0);"
1071 "[i0] -> [o0] : exists (e0 = [(i0)/4], e1 = [(o0)/4], "
1072 "e2 = [(n)/2], e3 = [(-2 + i0)/4], e4 = [(-2 + o0)/4], "
1073 "e5 = [(-2n + i0)/4]: 2e2 = n and 4e3 = -2 + i0 and "
1074 "4e4 = -2 + o0 and 2e0 >= 3 + n and e0 <= -4 + n and "
1075 "2e0 <= 27 + n and e1 <= -4 + n and 2e1 <= 27 + n and "
1076 "2e1 >= 2 + n and e1 >= 1 + e0 and i0 >= 7 + 2n and "
1077 "i0 <= -11 + 4n and i0 <= 57 + 2n and 4e0 <= -2 + i0 and "
1078 "4e0 >= -3 + i0 and o0 >= 6 + 2n and o0 <= -11 + 4n and "
1079 "o0 <= 57 + 2n and 4e1 <= -2 + o0 and 4e1 >= -3 + o0 and "
1080 "4e5 <= -2n + i0 and 4e5 >= -3 - 2n + i0 ) }");
1081 assert(isl_map_is_equal(map
, map2
));
1085 str
= "[n, m] -> { [] -> [o0, o2, o3] : (o3 = 1 and o0 >= 1 + m and "
1086 "o0 <= n + m and o2 <= m and o0 >= 2 + n and o2 >= 3) or "
1087 "(o0 >= 2 + n and o0 >= 1 + m and o0 <= n + m and n >= 1 and "
1088 "o3 <= -1 + o2 and o3 >= 1 - m + o2 and o3 >= 2 and o3 <= n) }";
1089 map
= isl_map_read_from_str(ctx
, str
);
1090 map
= isl_map_coalesce(map
);
1091 map2
= isl_map_read_from_str(ctx
, str
);
1092 assert(isl_map_is_equal(map
, map2
));
1096 str
= "[M, N] -> { [i0, i1, i2, i3, i4, i5, i6] -> "
1097 "[o0, o1, o2, o3, o4, o5, o6] : "
1098 "(o6 <= -4 + 2M - 2N + i0 + i1 - i2 + i6 - o0 - o1 + o2 and "
1099 "o3 <= -2 + i3 and o6 >= 2 + i0 + i3 + i6 - o0 - o3 and "
1100 "o6 >= 2 - M + N + i3 + i4 + i6 - o3 - o4 and o0 <= -1 + i0 and "
1101 "o4 >= 4 - 3M + 3N - i0 - i1 + i2 + 2i3 + i4 + o0 + o1 - o2 - 2o3 "
1102 "and o6 <= -3 + 2M - 2N + i3 + i4 - i5 + i6 - o3 - o4 + o5 and "
1103 "2o6 <= -5 + 5M - 5N + 2i0 + i1 - i2 - i5 + 2i6 - 2o0 - o1 + o2 + o5 "
1104 "and o6 >= 2i0 + i1 + i6 - 2o0 - o1 and "
1105 "3o6 <= -5 + 4M - 4N + 2i0 + i1 - i2 + 2i3 + i4 - i5 + 3i6 "
1106 "- 2o0 - o1 + o2 - 2o3 - o4 + o5) or "
1107 "(N >= 2 and o3 <= -1 + i3 and o0 <= -1 + i0 and "
1108 "o6 >= i3 + i6 - o3 and M >= 0 and "
1109 "2o6 >= 1 + i0 + i3 + 2i6 - o0 - o3 and "
1110 "o6 >= 1 - M + i0 + i6 - o0 and N >= 2M and o6 >= i0 + i6 - o0) }";
1111 map
= isl_map_read_from_str(ctx
, str
);
1112 map
= isl_map_coalesce(map
);
1113 map2
= isl_map_read_from_str(ctx
, str
);
1114 assert(isl_map_is_equal(map
, map2
));
1118 str
= "[M, N] -> { [] -> [o0] : (o0 = 0 and M >= 1 and N >= 2) or "
1119 "(o0 = 0 and M >= 1 and N >= 2M and N >= 2 + M) or "
1120 "(o0 = 0 and M >= 2 and N >= 3) or "
1121 "(M = 0 and o0 = 0 and N >= 3) }";
1122 map
= isl_map_read_from_str(ctx
, str
);
1123 map
= isl_map_coalesce(map
);
1124 map2
= isl_map_read_from_str(ctx
, str
);
1125 assert(isl_map_is_equal(map
, map2
));
1129 str
= "{ [i0, i1, i2, i3] : (i1 = 10i0 and i0 >= 1 and 10i0 <= 100 and "
1130 "i3 <= 9 + 10 i2 and i3 >= 1 + 10i2 and i3 >= 0) or "
1131 "(i1 <= 9 + 10i0 and i1 >= 1 + 10i0 and i2 >= 0 and "
1132 "i0 >= 0 and i1 <= 100 and i3 <= 9 + 10i2 and i3 >= 1 + 10i2) }";
1133 map
= isl_map_read_from_str(ctx
, str
);
1134 map
= isl_map_coalesce(map
);
1135 map2
= isl_map_read_from_str(ctx
, str
);
1136 assert(isl_map_is_equal(map
, map2
));
1140 test_coalesce_set(ctx
,
1141 "[M] -> { [i1] : (i1 >= 2 and i1 <= M) or "
1142 "(i1 = M and M >= 1) }", 0);
1143 test_coalesce_set(ctx
,
1144 "{[x,y] : x,y >= 0; [x,y] : 10 <= x <= 20 and y >= -1 }", 0);
1145 test_coalesce_set(ctx
,
1146 "{ [x, y] : (x >= 1 and y >= 1 and x <= 2 and y <= 2) or "
1147 "(y = 3 and x = 1) }", 1);
1148 test_coalesce_set(ctx
,
1149 "[M] -> { [i0, i1, i2, i3, i4] : (i1 >= 3 and i4 >= 2 + i2 and "
1150 "i2 >= 2 and i0 >= 2 and i3 >= 1 + i2 and i0 <= M and "
1151 "i1 <= M and i3 <= M and i4 <= M) or "
1152 "(i1 >= 2 and i4 >= 1 + i2 and i2 >= 2 and i0 >= 2 and "
1153 "i3 >= 1 + i2 and i0 <= M and i1 <= -1 + M and i3 <= M and "
1154 "i4 <= -1 + M) }", 1);
1155 test_coalesce_set(ctx
,
1156 "{ [x, y] : (x >= 0 and y >= 0 and x <= 10 and y <= 10) or "
1157 "(x >= 1 and y >= 1 and x <= 11 and y <= 11) }", 1);
1158 if (test_coalesce_unbounded_wrapping(ctx
) < 0)
1160 if (test_coalesce_set(ctx
, "{[x,0] : x >= 0; [x,1] : x <= 20}", 0) < 0)
1162 if (test_coalesce_set(ctx
, "{ [x, 1 - x] : 0 <= x <= 1; [0,0] }", 1) < 0)
1164 if (test_coalesce_set(ctx
, "{ [0,0]; [i,i] : 1 <= i <= 10 }", 1) < 0)
1166 if (test_coalesce_set(ctx
, "{ [0,0]; [i,j] : 1 <= i,j <= 10 }", 0) < 0)
1168 if (test_coalesce_set(ctx
, "{ [0,0]; [i,2i] : 1 <= i <= 10 }", 1) < 0)
1170 if (test_coalesce_set(ctx
, "{ [0,0]; [i,2i] : 2 <= i <= 10 }", 0) < 0)
1172 if (test_coalesce_set(ctx
, "{ [1,0]; [i,2i] : 1 <= i <= 10 }", 0) < 0)
1174 if (test_coalesce_set(ctx
, "{ [0,1]; [i,2i] : 1 <= i <= 10 }", 0) < 0)
1176 if (test_coalesce_set(ctx
, "{ [a, b] : exists e : 2e = a and "
1177 "a >= 0 and (a <= 3 or (b <= 0 and b >= -4 + a)) }", 0) < 0)
1179 if (test_coalesce_set(ctx
,
1180 "{ [i, j, i', j'] : i <= 2 and j <= 2 and "
1181 "j' >= -1 + 2i + j - 2i' and i' <= -1 + i and "
1182 "j >= 1 and j' <= i + j - i' and i >= 1; "
1183 "[1, 1, 1, 1] }", 0) < 0)
1185 if (test_coalesce_set(ctx
, "{ [i,j] : exists a,b : i = 2a and j = 3b; "
1186 "[i,j] : exists a : j = 3a }", 1) < 0)
1191 void test_closure(struct isl_ctx
*ctx
)
1195 isl_map
*up
, *right
;
1196 isl_map
*map
, *map2
;
1199 /* COCOA example 1 */
1200 map
= isl_map_read_from_str(ctx
,
1201 "[n] -> { [i,j] -> [i2,j2] : i2 = i + 1 and j2 = j + 1 and "
1202 "1 <= i and i < n and 1 <= j and j < n or "
1203 "i2 = i + 1 and j2 = j - 1 and "
1204 "1 <= i and i < n and 2 <= j and j <= n }");
1205 map
= isl_map_power(map
, &exact
);
1209 /* COCOA example 1 */
1210 map
= isl_map_read_from_str(ctx
,
1211 "[n] -> { [i,j] -> [i2,j2] : i2 = i + 1 and j2 = j + 1 and "
1212 "1 <= i and i < n and 1 <= j and j < n or "
1213 "i2 = i + 1 and j2 = j - 1 and "
1214 "1 <= i and i < n and 2 <= j and j <= n }");
1215 map
= isl_map_transitive_closure(map
, &exact
);
1217 map2
= isl_map_read_from_str(ctx
,
1218 "[n] -> { [i,j] -> [i2,j2] : exists (k1,k2,k : "
1219 "1 <= i and i < n and 1 <= j and j <= n and "
1220 "2 <= i2 and i2 <= n and 1 <= j2 and j2 <= n and "
1221 "i2 = i + k1 + k2 and j2 = j + k1 - k2 and "
1222 "k1 >= 0 and k2 >= 0 and k1 + k2 = k and k >= 1 )}");
1223 assert(isl_map_is_equal(map
, map2
));
1227 map
= isl_map_read_from_str(ctx
,
1228 "[n] -> { [x] -> [y] : y = x + 1 and 0 <= x and x <= n and "
1229 " 0 <= y and y <= n }");
1230 map
= isl_map_transitive_closure(map
, &exact
);
1231 map2
= isl_map_read_from_str(ctx
,
1232 "[n] -> { [x] -> [y] : y > x and 0 <= x and x <= n and "
1233 " 0 <= y and y <= n }");
1234 assert(isl_map_is_equal(map
, map2
));
1238 /* COCOA example 2 */
1239 map
= isl_map_read_from_str(ctx
,
1240 "[n] -> { [i,j] -> [i2,j2] : i2 = i + 2 and j2 = j + 2 and "
1241 "1 <= i and i < n - 1 and 1 <= j and j < n - 1 or "
1242 "i2 = i + 2 and j2 = j - 2 and "
1243 "1 <= i and i < n - 1 and 3 <= j and j <= n }");
1244 map
= isl_map_transitive_closure(map
, &exact
);
1246 map2
= isl_map_read_from_str(ctx
,
1247 "[n] -> { [i,j] -> [i2,j2] : exists (k1,k2,k : "
1248 "1 <= i and i < n - 1 and 1 <= j and j <= n and "
1249 "3 <= i2 and i2 <= n and 1 <= j2 and j2 <= n and "
1250 "i2 = i + 2 k1 + 2 k2 and j2 = j + 2 k1 - 2 k2 and "
1251 "k1 >= 0 and k2 >= 0 and k1 + k2 = k and k >= 1) }");
1252 assert(isl_map_is_equal(map
, map2
));
1256 /* COCOA Fig.2 left */
1257 map
= isl_map_read_from_str(ctx
,
1258 "[n] -> { [i,j] -> [i2,j2] : i2 = i + 2 and j2 = j and "
1259 "i <= 2 j - 3 and i <= n - 2 and j <= 2 i - 1 and "
1261 "i2 = i and j2 = j + 2 and i <= 2 j - 1 and i <= n and "
1262 "j <= 2 i - 3 and j <= n - 2 or "
1263 "i2 = i + 1 and j2 = j + 1 and i <= 2 j - 1 and "
1264 "i <= n - 1 and j <= 2 i - 1 and j <= n - 1 }");
1265 map
= isl_map_transitive_closure(map
, &exact
);
1269 /* COCOA Fig.2 right */
1270 map
= isl_map_read_from_str(ctx
,
1271 "[n] -> { [i,j] -> [i2,j2] : i2 = i + 3 and j2 = j and "
1272 "i <= 2 j - 4 and i <= n - 3 and j <= 2 i - 1 and "
1274 "i2 = i and j2 = j + 3 and i <= 2 j - 1 and i <= n and "
1275 "j <= 2 i - 4 and j <= n - 3 or "
1276 "i2 = i + 1 and j2 = j + 1 and i <= 2 j - 1 and "
1277 "i <= n - 1 and j <= 2 i - 1 and j <= n - 1 }");
1278 map
= isl_map_power(map
, &exact
);
1282 /* COCOA Fig.2 right */
1283 map
= isl_map_read_from_str(ctx
,
1284 "[n] -> { [i,j] -> [i2,j2] : i2 = i + 3 and j2 = j and "
1285 "i <= 2 j - 4 and i <= n - 3 and j <= 2 i - 1 and "
1287 "i2 = i and j2 = j + 3 and i <= 2 j - 1 and i <= n and "
1288 "j <= 2 i - 4 and j <= n - 3 or "
1289 "i2 = i + 1 and j2 = j + 1 and i <= 2 j - 1 and "
1290 "i <= n - 1 and j <= 2 i - 1 and j <= n - 1 }");
1291 map
= isl_map_transitive_closure(map
, &exact
);
1293 map2
= isl_map_read_from_str(ctx
,
1294 "[n] -> { [i,j] -> [i2,j2] : exists (k1,k2,k3,k : "
1295 "i <= 2 j - 1 and i <= n and j <= 2 i - 1 and "
1296 "j <= n and 3 + i + 2 j <= 3 n and "
1297 "3 + 2 i + j <= 3n and i2 <= 2 j2 -1 and i2 <= n and "
1298 "i2 <= 3 j2 - 4 and j2 <= 2 i2 -1 and j2 <= n and "
1299 "13 + 4 j2 <= 11 i2 and i2 = i + 3 k1 + k3 and "
1300 "j2 = j + 3 k2 + k3 and k1 >= 0 and k2 >= 0 and "
1301 "k3 >= 0 and k1 + k2 + k3 = k and k > 0) }");
1302 assert(isl_map_is_equal(map
, map2
));
1306 /* COCOA Fig.1 right */
1307 dom
= isl_set_read_from_str(ctx
,
1308 "{ [x,y] : x >= 0 and -2 x + 3 y >= 0 and x <= 3 and "
1309 "2 x - 3 y + 3 >= 0 }");
1310 right
= isl_map_read_from_str(ctx
,
1311 "{ [x,y] -> [x2,y2] : x2 = x + 1 and y2 = y }");
1312 up
= isl_map_read_from_str(ctx
,
1313 "{ [x,y] -> [x2,y2] : x2 = x and y2 = y + 1 }");
1314 right
= isl_map_intersect_domain(right
, isl_set_copy(dom
));
1315 right
= isl_map_intersect_range(right
, isl_set_copy(dom
));
1316 up
= isl_map_intersect_domain(up
, isl_set_copy(dom
));
1317 up
= isl_map_intersect_range(up
, dom
);
1318 map
= isl_map_union(up
, right
);
1319 map
= isl_map_transitive_closure(map
, &exact
);
1321 map2
= isl_map_read_from_str(ctx
,
1322 "{ [0,0] -> [0,1]; [0,0] -> [1,1]; [0,1] -> [1,1]; "
1323 " [2,2] -> [3,2]; [2,2] -> [3,3]; [3,2] -> [3,3] }");
1324 assert(isl_map_is_equal(map
, map2
));
1328 /* COCOA Theorem 1 counter example */
1329 map
= isl_map_read_from_str(ctx
,
1330 "{ [i,j] -> [i2,j2] : i = 0 and 0 <= j and j <= 1 and "
1331 "i2 = 1 and j2 = j or "
1332 "i = 0 and j = 0 and i2 = 0 and j2 = 1 }");
1333 map
= isl_map_transitive_closure(map
, &exact
);
1337 map
= isl_map_read_from_str(ctx
,
1338 "[m,n] -> { [i,j] -> [i2,j2] : i2 = i and j2 = j + 2 and "
1339 "1 <= i,i2 <= n and 1 <= j,j2 <= m or "
1340 "i2 = i + 1 and 3 <= j2 - j <= 4 and "
1341 "1 <= i,i2 <= n and 1 <= j,j2 <= m }");
1342 map
= isl_map_transitive_closure(map
, &exact
);
1346 /* Kelly et al 1996, fig 12 */
1347 map
= isl_map_read_from_str(ctx
,
1348 "[n] -> { [i,j] -> [i2,j2] : i2 = i and j2 = j + 1 and "
1349 "1 <= i,j,j+1 <= n or "
1350 "j = n and j2 = 1 and i2 = i + 1 and "
1351 "1 <= i,i+1 <= n }");
1352 map
= isl_map_transitive_closure(map
, &exact
);
1354 map2
= isl_map_read_from_str(ctx
,
1355 "[n] -> { [i,j] -> [i2,j2] : 1 <= j < j2 <= n and "
1356 "1 <= i <= n and i = i2 or "
1357 "1 <= i < i2 <= n and 1 <= j <= n and "
1359 assert(isl_map_is_equal(map
, map2
));
1363 /* Omega's closure4 */
1364 map
= isl_map_read_from_str(ctx
,
1365 "[m,n] -> { [x,y] -> [x2,y2] : x2 = x and y2 = y + 1 and "
1366 "1 <= x,y <= 10 or "
1367 "x2 = x + 1 and y2 = y and "
1368 "1 <= x <= 20 && 5 <= y <= 15 }");
1369 map
= isl_map_transitive_closure(map
, &exact
);
1373 map
= isl_map_read_from_str(ctx
,
1374 "[n] -> { [x] -> [y]: 1 <= n <= y - x <= 10 }");
1375 map
= isl_map_transitive_closure(map
, &exact
);
1377 map2
= isl_map_read_from_str(ctx
,
1378 "[n] -> { [x] -> [y] : 1 <= n <= 10 and y >= n + x }");
1379 assert(isl_map_is_equal(map
, map2
));
1383 str
= "[n, m] -> { [i0, i1, i2, i3] -> [o0, o1, o2, o3] : "
1384 "i3 = 1 and o0 = i0 and o1 = -1 + i1 and o2 = -1 + i2 and "
1385 "o3 = -2 + i2 and i1 <= -1 + i0 and i1 >= 1 - m + i0 and "
1386 "i1 >= 2 and i1 <= n and i2 >= 3 and i2 <= 1 + n and i2 <= m }";
1387 map
= isl_map_read_from_str(ctx
, str
);
1388 map
= isl_map_transitive_closure(map
, &exact
);
1390 map2
= isl_map_read_from_str(ctx
, str
);
1391 assert(isl_map_is_equal(map
, map2
));
1395 str
= "{[0] -> [1]; [2] -> [3]}";
1396 map
= isl_map_read_from_str(ctx
, str
);
1397 map
= isl_map_transitive_closure(map
, &exact
);
1399 map2
= isl_map_read_from_str(ctx
, str
);
1400 assert(isl_map_is_equal(map
, map2
));
1404 str
= "[n] -> { [[i0, i1, 1, 0, i0] -> [i5, 1]] -> "
1405 "[[i0, -1 + i1, 2, 0, i0] -> [-1 + i5, 2]] : "
1406 "exists (e0 = [(3 - n)/3]: i5 >= 2 and i1 >= 2 and "
1407 "3i0 <= -1 + n and i1 <= -1 + n and i5 <= -1 + n and "
1408 "3e0 >= 1 - n and 3e0 <= 2 - n and 3i0 >= -2 + n); "
1409 "[[i0, i1, 2, 0, i0] -> [i5, 1]] -> "
1410 "[[i0, i1, 1, 0, i0] -> [-1 + i5, 2]] : "
1411 "exists (e0 = [(3 - n)/3]: i5 >= 2 and i1 >= 1 and "
1412 "3i0 <= -1 + n and i1 <= -1 + n and i5 <= -1 + n and "
1413 "3e0 >= 1 - n and 3e0 <= 2 - n and 3i0 >= -2 + n); "
1414 "[[i0, i1, 1, 0, i0] -> [i5, 2]] -> "
1415 "[[i0, -1 + i1, 2, 0, i0] -> [i5, 1]] : "
1416 "exists (e0 = [(3 - n)/3]: i1 >= 2 and i5 >= 1 and "
1417 "3i0 <= -1 + n and i1 <= -1 + n and i5 <= -1 + n and "
1418 "3e0 >= 1 - n and 3e0 <= 2 - n and 3i0 >= -2 + n); "
1419 "[[i0, i1, 2, 0, i0] -> [i5, 2]] -> "
1420 "[[i0, i1, 1, 0, i0] -> [i5, 1]] : "
1421 "exists (e0 = [(3 - n)/3]: i5 >= 1 and i1 >= 1 and "
1422 "3i0 <= -1 + n and i1 <= -1 + n and i5 <= -1 + n and "
1423 "3e0 >= 1 - n and 3e0 <= 2 - n and 3i0 >= -2 + n) }";
1424 map
= isl_map_read_from_str(ctx
, str
);
1425 map
= isl_map_transitive_closure(map
, NULL
);
1430 void test_lex(struct isl_ctx
*ctx
)
1435 dim
= isl_space_set_alloc(ctx
, 0, 0);
1436 map
= isl_map_lex_le(dim
);
1437 assert(!isl_map_is_empty(map
));
1441 void test_lexmin(struct isl_ctx
*ctx
)
1444 isl_basic_map
*bmap
;
1445 isl_map
*map
, *map2
;
1448 isl_pw_multi_aff
*pma
;
1450 str
= "[p0, p1] -> { [] -> [] : "
1451 "exists (e0 = [(2p1)/3], e1, e2, e3 = [(3 - p1 + 3e0)/3], "
1452 "e4 = [(p1)/3], e5 = [(p1 + 3e4)/3]: "
1453 "3e0 >= -2 + 2p1 and 3e0 >= p1 and 3e3 >= 1 - p1 + 3e0 and "
1454 "3e0 <= 2p1 and 3e3 >= -2 + p1 and 3e3 <= -1 + p1 and p1 >= 3 and "
1455 "3e5 >= -2 + 2p1 and 3e5 >= p1 and 3e5 <= -1 + p1 + 3e4 and "
1456 "3e4 <= p1 and 3e4 >= -2 + p1 and e3 <= -1 + e0 and "
1457 "3e4 >= 6 - p1 + 3e1 and 3e1 >= p1 and 3e5 >= -2 + p1 + 3e4 and "
1458 "2e4 >= 3 - p1 + 2e1 and e4 <= e1 and 3e3 <= 2 - p1 + 3e0 and "
1459 "e5 >= 1 + e1 and 3e4 >= 6 - 2p1 + 3e1 and "
1460 "p0 >= 2 and p1 >= p0 and 3e2 >= p1 and 3e4 >= 6 - p1 + 3e2 and "
1461 "e2 <= e1 and e3 >= 1 and e4 <= e2) }";
1462 map
= isl_map_read_from_str(ctx
, str
);
1463 map
= isl_map_lexmin(map
);
1466 str
= "[C] -> { [obj,a,b,c] : obj <= 38 a + 7 b + 10 c and "
1467 "a + b <= 1 and c <= 10 b and c <= C and a,b,c,C >= 0 }";
1468 set
= isl_set_read_from_str(ctx
, str
);
1469 set
= isl_set_lexmax(set
);
1470 str
= "[C] -> { [obj,a,b,c] : C = 8 }";
1471 set2
= isl_set_read_from_str(ctx
, str
);
1472 set
= isl_set_intersect(set
, set2
);
1473 assert(!isl_set_is_empty(set
));
1476 str
= "{ [x] -> [y] : x <= y <= 10; [x] -> [5] : -8 <= x <= 8 }";
1477 map
= isl_map_read_from_str(ctx
, str
);
1478 map
= isl_map_lexmin(map
);
1479 str
= "{ [x] -> [5] : 6 <= x <= 8; "
1480 "[x] -> [x] : x <= 5 or (9 <= x <= 10) }";
1481 map2
= isl_map_read_from_str(ctx
, str
);
1482 assert(isl_map_is_equal(map
, map2
));
1486 str
= "{ [x] -> [y] : 4y = x or 4y = -1 + x or 4y = -2 + x }";
1487 map
= isl_map_read_from_str(ctx
, str
);
1488 map2
= isl_map_copy(map
);
1489 map
= isl_map_lexmin(map
);
1490 assert(isl_map_is_equal(map
, map2
));
1494 str
= "{ [x] -> [y] : x = 4y; [x] -> [y] : x = 2y }";
1495 map
= isl_map_read_from_str(ctx
, str
);
1496 map
= isl_map_lexmin(map
);
1497 str
= "{ [x] -> [y] : (4y = x and x >= 0) or "
1498 "(exists (e0 = [(x)/4], e1 = [(-2 + x)/4]: 2y = x and "
1499 "4e1 = -2 + x and 4e0 <= -1 + x and 4e0 >= -3 + x)) or "
1500 "(exists (e0 = [(x)/4]: 2y = x and 4e0 = x and x <= -4)) }";
1501 map2
= isl_map_read_from_str(ctx
, str
);
1502 assert(isl_map_is_equal(map
, map2
));
1506 str
= "{ [i] -> [i', j] : j = i - 8i' and i' >= 0 and i' <= 7 and "
1507 " 8i' <= i and 8i' >= -7 + i }";
1508 bmap
= isl_basic_map_read_from_str(ctx
, str
);
1509 pma
= isl_basic_map_lexmin_pw_multi_aff(isl_basic_map_copy(bmap
));
1510 map2
= isl_map_from_pw_multi_aff(pma
);
1511 map
= isl_map_from_basic_map(bmap
);
1512 assert(isl_map_is_equal(map
, map2
));
1516 str
= "{ T[a] -> S[b, c] : a = 4b-2c and c >= b }";
1517 map
= isl_map_read_from_str(ctx
, str
);
1518 map
= isl_map_lexmin(map
);
1519 str
= "{ T[a] -> S[b, c] : 2b = a and 2c = a }";
1520 map2
= isl_map_read_from_str(ctx
, str
);
1521 assert(isl_map_is_equal(map
, map2
));
1531 static int collect_must_may(__isl_take isl_map
*dep
, int must
,
1532 void *dep_user
, void *user
)
1534 struct must_may
*mm
= (struct must_may
*)user
;
1537 mm
->must
= isl_map_union(mm
->must
, dep
);
1539 mm
->may
= isl_map_union(mm
->may
, dep
);
1544 static int common_space(void *first
, void *second
)
1546 int depth
= *(int *)first
;
1550 static int map_is_equal(__isl_keep isl_map
*map
, const char *str
)
1558 map2
= isl_map_read_from_str(map
->ctx
, str
);
1559 equal
= isl_map_is_equal(map
, map2
);
1565 static int map_check_equal(__isl_keep isl_map
*map
, const char *str
)
1569 equal
= map_is_equal(map
, str
);
1573 isl_die(isl_map_get_ctx(map
), isl_error_unknown
,
1574 "result not as expected", return -1);
1578 void test_dep(struct isl_ctx
*ctx
)
1583 isl_access_info
*ai
;
1590 str
= "{ [2,i,0] -> [i] : 0 <= i <= 10 }";
1591 map
= isl_map_read_from_str(ctx
, str
);
1592 ai
= isl_access_info_alloc(map
, &depth
, &common_space
, 2);
1594 str
= "{ [0,i,0] -> [i] : 0 <= i <= 10 }";
1595 map
= isl_map_read_from_str(ctx
, str
);
1596 ai
= isl_access_info_add_source(ai
, map
, 1, &depth
);
1598 str
= "{ [1,i,0] -> [5] : 0 <= i <= 10 }";
1599 map
= isl_map_read_from_str(ctx
, str
);
1600 ai
= isl_access_info_add_source(ai
, map
, 1, &depth
);
1602 flow
= isl_access_info_compute_flow(ai
);
1603 dim
= isl_space_alloc(ctx
, 0, 3, 3);
1604 mm
.must
= isl_map_empty(isl_space_copy(dim
));
1605 mm
.may
= isl_map_empty(dim
);
1607 isl_flow_foreach(flow
, collect_must_may
, &mm
);
1609 str
= "{ [0,i,0] -> [2,i,0] : (0 <= i <= 4) or (6 <= i <= 10); "
1610 " [1,10,0] -> [2,5,0] }";
1611 assert(map_is_equal(mm
.must
, str
));
1612 str
= "{ [i,j,k] -> [l,m,n] : 1 = 0 }";
1613 assert(map_is_equal(mm
.may
, str
));
1615 isl_map_free(mm
.must
);
1616 isl_map_free(mm
.may
);
1617 isl_flow_free(flow
);
1620 str
= "{ [2,i,0] -> [i] : 0 <= i <= 10 }";
1621 map
= isl_map_read_from_str(ctx
, str
);
1622 ai
= isl_access_info_alloc(map
, &depth
, &common_space
, 2);
1624 str
= "{ [0,i,0] -> [i] : 0 <= i <= 10 }";
1625 map
= isl_map_read_from_str(ctx
, str
);
1626 ai
= isl_access_info_add_source(ai
, map
, 1, &depth
);
1628 str
= "{ [1,i,0] -> [5] : 0 <= i <= 10 }";
1629 map
= isl_map_read_from_str(ctx
, str
);
1630 ai
= isl_access_info_add_source(ai
, map
, 0, &depth
);
1632 flow
= isl_access_info_compute_flow(ai
);
1633 dim
= isl_space_alloc(ctx
, 0, 3, 3);
1634 mm
.must
= isl_map_empty(isl_space_copy(dim
));
1635 mm
.may
= isl_map_empty(dim
);
1637 isl_flow_foreach(flow
, collect_must_may
, &mm
);
1639 str
= "{ [0,i,0] -> [2,i,0] : (0 <= i <= 4) or (6 <= i <= 10) }";
1640 assert(map_is_equal(mm
.must
, str
));
1641 str
= "{ [0,5,0] -> [2,5,0]; [1,i,0] -> [2,5,0] : 0 <= i <= 10 }";
1642 assert(map_is_equal(mm
.may
, str
));
1644 isl_map_free(mm
.must
);
1645 isl_map_free(mm
.may
);
1646 isl_flow_free(flow
);
1649 str
= "{ [2,i,0] -> [i] : 0 <= i <= 10 }";
1650 map
= isl_map_read_from_str(ctx
, str
);
1651 ai
= isl_access_info_alloc(map
, &depth
, &common_space
, 2);
1653 str
= "{ [0,i,0] -> [i] : 0 <= i <= 10 }";
1654 map
= isl_map_read_from_str(ctx
, str
);
1655 ai
= isl_access_info_add_source(ai
, map
, 0, &depth
);
1657 str
= "{ [1,i,0] -> [5] : 0 <= i <= 10 }";
1658 map
= isl_map_read_from_str(ctx
, str
);
1659 ai
= isl_access_info_add_source(ai
, map
, 0, &depth
);
1661 flow
= isl_access_info_compute_flow(ai
);
1662 dim
= isl_space_alloc(ctx
, 0, 3, 3);
1663 mm
.must
= isl_map_empty(isl_space_copy(dim
));
1664 mm
.may
= isl_map_empty(dim
);
1666 isl_flow_foreach(flow
, collect_must_may
, &mm
);
1668 str
= "{ [0,i,0] -> [2,i,0] : 0 <= i <= 10; "
1669 " [1,i,0] -> [2,5,0] : 0 <= i <= 10 }";
1670 assert(map_is_equal(mm
.may
, str
));
1671 str
= "{ [i,j,k] -> [l,m,n] : 1 = 0 }";
1672 assert(map_is_equal(mm
.must
, str
));
1674 isl_map_free(mm
.must
);
1675 isl_map_free(mm
.may
);
1676 isl_flow_free(flow
);
1679 str
= "{ [0,i,2] -> [i] : 0 <= i <= 10 }";
1680 map
= isl_map_read_from_str(ctx
, str
);
1681 ai
= isl_access_info_alloc(map
, &depth
, &common_space
, 2);
1683 str
= "{ [0,i,0] -> [i] : 0 <= i <= 10 }";
1684 map
= isl_map_read_from_str(ctx
, str
);
1685 ai
= isl_access_info_add_source(ai
, map
, 0, &depth
);
1687 str
= "{ [0,i,1] -> [5] : 0 <= i <= 10 }";
1688 map
= isl_map_read_from_str(ctx
, str
);
1689 ai
= isl_access_info_add_source(ai
, map
, 0, &depth
);
1691 flow
= isl_access_info_compute_flow(ai
);
1692 dim
= isl_space_alloc(ctx
, 0, 3, 3);
1693 mm
.must
= isl_map_empty(isl_space_copy(dim
));
1694 mm
.may
= isl_map_empty(dim
);
1696 isl_flow_foreach(flow
, collect_must_may
, &mm
);
1698 str
= "{ [0,i,0] -> [0,i,2] : 0 <= i <= 10; "
1699 " [0,i,1] -> [0,5,2] : 0 <= i <= 5 }";
1700 assert(map_is_equal(mm
.may
, str
));
1701 str
= "{ [i,j,k] -> [l,m,n] : 1 = 0 }";
1702 assert(map_is_equal(mm
.must
, str
));
1704 isl_map_free(mm
.must
);
1705 isl_map_free(mm
.may
);
1706 isl_flow_free(flow
);
1709 str
= "{ [0,i,1] -> [i] : 0 <= i <= 10 }";
1710 map
= isl_map_read_from_str(ctx
, str
);
1711 ai
= isl_access_info_alloc(map
, &depth
, &common_space
, 2);
1713 str
= "{ [0,i,0] -> [i] : 0 <= i <= 10 }";
1714 map
= isl_map_read_from_str(ctx
, str
);
1715 ai
= isl_access_info_add_source(ai
, map
, 0, &depth
);
1717 str
= "{ [0,i,2] -> [5] : 0 <= i <= 10 }";
1718 map
= isl_map_read_from_str(ctx
, str
);
1719 ai
= isl_access_info_add_source(ai
, map
, 0, &depth
);
1721 flow
= isl_access_info_compute_flow(ai
);
1722 dim
= isl_space_alloc(ctx
, 0, 3, 3);
1723 mm
.must
= isl_map_empty(isl_space_copy(dim
));
1724 mm
.may
= isl_map_empty(dim
);
1726 isl_flow_foreach(flow
, collect_must_may
, &mm
);
1728 str
= "{ [0,i,0] -> [0,i,1] : 0 <= i <= 10; "
1729 " [0,i,2] -> [0,5,1] : 0 <= i <= 4 }";
1730 assert(map_is_equal(mm
.may
, str
));
1731 str
= "{ [i,j,k] -> [l,m,n] : 1 = 0 }";
1732 assert(map_is_equal(mm
.must
, str
));
1734 isl_map_free(mm
.must
);
1735 isl_map_free(mm
.may
);
1736 isl_flow_free(flow
);
1741 str
= "{ [1,i,0,0,0] -> [i,j] : 0 <= i <= 10 and 0 <= j <= 10 }";
1742 map
= isl_map_read_from_str(ctx
, str
);
1743 ai
= isl_access_info_alloc(map
, &depth
, &common_space
, 1);
1745 str
= "{ [0,i,0,j,0] -> [i,j] : 0 <= i <= 10 and 0 <= j <= 10 }";
1746 map
= isl_map_read_from_str(ctx
, str
);
1747 ai
= isl_access_info_add_source(ai
, map
, 1, &depth
);
1749 flow
= isl_access_info_compute_flow(ai
);
1750 dim
= isl_space_alloc(ctx
, 0, 5, 5);
1751 mm
.must
= isl_map_empty(isl_space_copy(dim
));
1752 mm
.may
= isl_map_empty(dim
);
1754 isl_flow_foreach(flow
, collect_must_may
, &mm
);
1756 str
= "{ [0,i,0,j,0] -> [1,i,0,0,0] : 0 <= i,j <= 10 }";
1757 assert(map_is_equal(mm
.must
, str
));
1758 str
= "{ [0,0,0,0,0] -> [0,0,0,0,0] : 1 = 0 }";
1759 assert(map_is_equal(mm
.may
, str
));
1761 isl_map_free(mm
.must
);
1762 isl_map_free(mm
.may
);
1763 isl_flow_free(flow
);
1766 int test_sv(isl_ctx
*ctx
)
1770 isl_union_map
*umap
;
1773 str
= "[N] -> { [i] -> [f] : 0 <= i <= N and 0 <= i - 10 f <= 9 }";
1774 map
= isl_map_read_from_str(ctx
, str
);
1775 sv
= isl_map_is_single_valued(map
);
1780 isl_die(ctx
, isl_error_internal
,
1781 "map not detected as single valued", return -1);
1783 str
= "[N] -> { [i] -> [f] : 0 <= i <= N and 0 <= i - 10 f <= 10 }";
1784 map
= isl_map_read_from_str(ctx
, str
);
1785 sv
= isl_map_is_single_valued(map
);
1790 isl_die(ctx
, isl_error_internal
,
1791 "map detected as single valued", return -1);
1793 str
= "{ S1[i] -> [i] : 0 <= i <= 9; S2[i] -> [i] : 0 <= i <= 9 }";
1794 umap
= isl_union_map_read_from_str(ctx
, str
);
1795 sv
= isl_union_map_is_single_valued(umap
);
1796 isl_union_map_free(umap
);
1800 isl_die(ctx
, isl_error_internal
,
1801 "map not detected as single valued", return -1);
1803 str
= "{ [i] -> S1[i] : 0 <= i <= 9; [i] -> S2[i] : 0 <= i <= 9 }";
1804 umap
= isl_union_map_read_from_str(ctx
, str
);
1805 sv
= isl_union_map_is_single_valued(umap
);
1806 isl_union_map_free(umap
);
1810 isl_die(ctx
, isl_error_internal
,
1811 "map detected as single valued", return -1);
1816 void test_bijective_case(struct isl_ctx
*ctx
, const char *str
, int bijective
)
1820 map
= isl_map_read_from_str(ctx
, str
);
1822 assert(isl_map_is_bijective(map
));
1824 assert(!isl_map_is_bijective(map
));
1828 void test_bijective(struct isl_ctx
*ctx
)
1830 test_bijective_case(ctx
, "[N,M]->{[i,j] -> [i]}", 0);
1831 test_bijective_case(ctx
, "[N,M]->{[i,j] -> [i] : j=i}", 1);
1832 test_bijective_case(ctx
, "[N,M]->{[i,j] -> [i] : j=0}", 1);
1833 test_bijective_case(ctx
, "[N,M]->{[i,j] -> [i] : j=N}", 1);
1834 test_bijective_case(ctx
, "[N,M]->{[i,j] -> [j,i]}", 1);
1835 test_bijective_case(ctx
, "[N,M]->{[i,j] -> [i+j]}", 0);
1836 test_bijective_case(ctx
, "[N,M]->{[i,j] -> []}", 0);
1837 test_bijective_case(ctx
, "[N,M]->{[i,j] -> [i,j,N]}", 1);
1838 test_bijective_case(ctx
, "[N,M]->{[i,j] -> [2i]}", 0);
1839 test_bijective_case(ctx
, "[N,M]->{[i,j] -> [i,i]}", 0);
1840 test_bijective_case(ctx
, "[N,M]->{[i,j] -> [2i,i]}", 0);
1841 test_bijective_case(ctx
, "[N,M]->{[i,j] -> [2i,j]}", 1);
1842 test_bijective_case(ctx
, "[N,M]->{[i,j] -> [x,y] : 2x=i & y =j}", 1);
1845 void test_pwqp(struct isl_ctx
*ctx
)
1849 isl_pw_qpolynomial
*pwqp1
, *pwqp2
;
1851 str
= "{ [i,j,k] -> 1 + 9 * [i/5] + 7 * [j/11] + 4 * [k/13] }";
1852 pwqp1
= isl_pw_qpolynomial_read_from_str(ctx
, str
);
1854 pwqp1
= isl_pw_qpolynomial_move_dims(pwqp1
, isl_dim_param
, 0,
1857 str
= "[j] -> { [i,k] -> 1 + 9 * [i/5] + 7 * [j/11] + 4 * [k/13] }";
1858 pwqp2
= isl_pw_qpolynomial_read_from_str(ctx
, str
);
1860 pwqp1
= isl_pw_qpolynomial_sub(pwqp1
, pwqp2
);
1862 assert(isl_pw_qpolynomial_is_zero(pwqp1
));
1864 isl_pw_qpolynomial_free(pwqp1
);
1866 str
= "{ [i] -> i }";
1867 pwqp1
= isl_pw_qpolynomial_read_from_str(ctx
, str
);
1868 str
= "{ [k] : exists a : k = 2a }";
1869 set
= isl_set_read_from_str(ctx
, str
);
1870 pwqp1
= isl_pw_qpolynomial_gist(pwqp1
, set
);
1871 str
= "{ [i] -> i }";
1872 pwqp2
= isl_pw_qpolynomial_read_from_str(ctx
, str
);
1874 pwqp1
= isl_pw_qpolynomial_sub(pwqp1
, pwqp2
);
1876 assert(isl_pw_qpolynomial_is_zero(pwqp1
));
1878 isl_pw_qpolynomial_free(pwqp1
);
1880 str
= "{ [i] -> i + [ (i + [i/3])/2 ] }";
1881 pwqp1
= isl_pw_qpolynomial_read_from_str(ctx
, str
);
1883 set
= isl_set_read_from_str(ctx
, str
);
1884 pwqp1
= isl_pw_qpolynomial_gist(pwqp1
, set
);
1885 str
= "{ [i] -> 16 }";
1886 pwqp2
= isl_pw_qpolynomial_read_from_str(ctx
, str
);
1888 pwqp1
= isl_pw_qpolynomial_sub(pwqp1
, pwqp2
);
1890 assert(isl_pw_qpolynomial_is_zero(pwqp1
));
1892 isl_pw_qpolynomial_free(pwqp1
);
1894 str
= "{ [i] -> ([(i)/2]) }";
1895 pwqp1
= isl_pw_qpolynomial_read_from_str(ctx
, str
);
1896 str
= "{ [k] : exists a : k = 2a+1 }";
1897 set
= isl_set_read_from_str(ctx
, str
);
1898 pwqp1
= isl_pw_qpolynomial_gist(pwqp1
, set
);
1899 str
= "{ [i] -> -1/2 + 1/2 * i }";
1900 pwqp2
= isl_pw_qpolynomial_read_from_str(ctx
, str
);
1902 pwqp1
= isl_pw_qpolynomial_sub(pwqp1
, pwqp2
);
1904 assert(isl_pw_qpolynomial_is_zero(pwqp1
));
1906 isl_pw_qpolynomial_free(pwqp1
);
1908 str
= "{ [i] -> ([([i/2] + [i/2])/5]) }";
1909 pwqp1
= isl_pw_qpolynomial_read_from_str(ctx
, str
);
1910 str
= "{ [i] -> ([(2 * [i/2])/5]) }";
1911 pwqp2
= isl_pw_qpolynomial_read_from_str(ctx
, str
);
1913 pwqp1
= isl_pw_qpolynomial_sub(pwqp1
, pwqp2
);
1915 assert(isl_pw_qpolynomial_is_zero(pwqp1
));
1917 isl_pw_qpolynomial_free(pwqp1
);
1919 str
= "{ [x] -> ([x/2] + [(x+1)/2]) }";
1920 pwqp1
= isl_pw_qpolynomial_read_from_str(ctx
, str
);
1921 str
= "{ [x] -> x }";
1922 pwqp2
= isl_pw_qpolynomial_read_from_str(ctx
, str
);
1924 pwqp1
= isl_pw_qpolynomial_sub(pwqp1
, pwqp2
);
1926 assert(isl_pw_qpolynomial_is_zero(pwqp1
));
1928 isl_pw_qpolynomial_free(pwqp1
);
1930 str
= "{ [i] -> ([i/2]) : i >= 0; [i] -> ([i/3]) : i < 0 }";
1931 pwqp1
= isl_pw_qpolynomial_read_from_str(ctx
, str
);
1932 pwqp2
= isl_pw_qpolynomial_read_from_str(ctx
, str
);
1933 pwqp1
= isl_pw_qpolynomial_coalesce(pwqp1
);
1934 pwqp1
= isl_pw_qpolynomial_sub(pwqp1
, pwqp2
);
1935 assert(isl_pw_qpolynomial_is_zero(pwqp1
));
1936 isl_pw_qpolynomial_free(pwqp1
);
1939 void test_split_periods(isl_ctx
*ctx
)
1942 isl_pw_qpolynomial
*pwqp
;
1944 str
= "{ [U,V] -> 1/3 * U + 2/3 * V - [(U + 2V)/3] + [U/2] : "
1945 "U + 2V + 3 >= 0 and - U -2V >= 0 and - U + 10 >= 0 and "
1946 "U >= 0; [U,V] -> U^2 : U >= 100 }";
1947 pwqp
= isl_pw_qpolynomial_read_from_str(ctx
, str
);
1949 pwqp
= isl_pw_qpolynomial_split_periods(pwqp
, 2);
1952 isl_pw_qpolynomial_free(pwqp
);
1955 void test_union(isl_ctx
*ctx
)
1958 isl_union_set
*uset1
, *uset2
;
1959 isl_union_map
*umap1
, *umap2
;
1961 str
= "{ [i] : 0 <= i <= 1 }";
1962 uset1
= isl_union_set_read_from_str(ctx
, str
);
1963 str
= "{ [1] -> [0] }";
1964 umap1
= isl_union_map_read_from_str(ctx
, str
);
1966 umap2
= isl_union_set_lex_gt_union_set(isl_union_set_copy(uset1
), uset1
);
1967 assert(isl_union_map_is_equal(umap1
, umap2
));
1969 isl_union_map_free(umap1
);
1970 isl_union_map_free(umap2
);
1972 str
= "{ A[i] -> B[i]; B[i] -> C[i]; A[0] -> C[1] }";
1973 umap1
= isl_union_map_read_from_str(ctx
, str
);
1974 str
= "{ A[i]; B[i] }";
1975 uset1
= isl_union_set_read_from_str(ctx
, str
);
1977 uset2
= isl_union_map_domain(umap1
);
1979 assert(isl_union_set_is_equal(uset1
, uset2
));
1981 isl_union_set_free(uset1
);
1982 isl_union_set_free(uset2
);
1985 void test_bound(isl_ctx
*ctx
)
1988 isl_pw_qpolynomial
*pwqp
;
1989 isl_pw_qpolynomial_fold
*pwf
;
1991 str
= "{ [[a, b, c, d] -> [e]] -> 0 }";
1992 pwqp
= isl_pw_qpolynomial_read_from_str(ctx
, str
);
1993 pwf
= isl_pw_qpolynomial_bound(pwqp
, isl_fold_max
, NULL
);
1994 assert(isl_pw_qpolynomial_fold_dim(pwf
, isl_dim_in
) == 4);
1995 isl_pw_qpolynomial_fold_free(pwf
);
1997 str
= "{ [[x]->[x]] -> 1 : exists a : x = 2 a }";
1998 pwqp
= isl_pw_qpolynomial_read_from_str(ctx
, str
);
1999 pwf
= isl_pw_qpolynomial_bound(pwqp
, isl_fold_max
, NULL
);
2000 assert(isl_pw_qpolynomial_fold_dim(pwf
, isl_dim_in
) == 1);
2001 isl_pw_qpolynomial_fold_free(pwf
);
2004 void test_lift(isl_ctx
*ctx
)
2007 isl_basic_map
*bmap
;
2008 isl_basic_set
*bset
;
2010 str
= "{ [i0] : exists e0 : i0 = 4e0 }";
2011 bset
= isl_basic_set_read_from_str(ctx
, str
);
2012 bset
= isl_basic_set_lift(bset
);
2013 bmap
= isl_basic_map_from_range(bset
);
2014 bset
= isl_basic_map_domain(bmap
);
2015 isl_basic_set_free(bset
);
2022 } subset_tests
[] = {
2024 "{ [i0, i1] : exists (e0 = [(i0 - i1)/16], e1: "
2025 "16e0 <= i0 - i1 and 16e0 >= -15 + i0 - i1 and "
2026 "16e1 <= i1 and 16e0 >= -i1 and 16e1 >= -i0 + i1) }", 1 },
2028 "{ [i] : exists (e0 = [(255i)/256], e1 = [(127i + 65e0)/191], "
2029 "e2 = [(3i + 61e1)/65], e3 = [(52i + 12e2)/61], "
2030 "e4 = [(2i + e3)/3], e5 = [(4i + e3)/4], e6 = [(8i + e3)/12]: "
2031 "3e4 = 2i + e3 and 4e5 = 4i + e3 and 12e6 = 8i + e3 and "
2032 "i <= 255 and 64e3 >= -45 + 67i and i >= 0 and "
2033 "256e0 <= 255i and 256e0 >= -255 + 255i and "
2034 "191e1 <= 127i + 65e0 and 191e1 >= -190 + 127i + 65e0 and "
2035 "65e2 <= 3i + 61e1 and 65e2 >= -64 + 3i + 61e1 and "
2036 "61e3 <= 52i + 12e2 and 61e3 >= -60 + 52i + 12e2) }", 1 },
2037 { "{ [i] : 0 <= i <= 10 }", "{ rat: [i] : 0 <= i <= 10 }", 1 },
2038 { "{ rat: [i] : 0 <= i <= 10 }", "{ [i] : 0 <= i <= 10 }", 0 },
2039 { "{ rat: [0] }", "{ [i] : 0 <= i <= 10 }", 1 },
2040 { "{ rat: [(1)/2] }", "{ [i] : 0 <= i <= 10 }", 0 },
2043 static int test_subset(isl_ctx
*ctx
)
2046 isl_set
*set1
, *set2
;
2049 for (i
= 0; i
< ARRAY_SIZE(subset_tests
); ++i
) {
2050 set1
= isl_set_read_from_str(ctx
, subset_tests
[i
].set1
);
2051 set2
= isl_set_read_from_str(ctx
, subset_tests
[i
].set2
);
2052 subset
= isl_set_is_subset(set1
, set2
);
2057 if (subset
!= subset_tests
[i
].subset
)
2058 isl_die(ctx
, isl_error_unknown
,
2059 "incorrect subset result", return -1);
2066 const char *minuend
;
2067 const char *subtrahend
;
2068 const char *difference
;
2069 } subtract_domain_tests
[] = {
2070 { "{ A[i] -> B[i] }", "{ A[i] }", "{ }" },
2071 { "{ A[i] -> B[i] }", "{ B[i] }", "{ A[i] -> B[i] }" },
2072 { "{ A[i] -> B[i] }", "{ A[i] : i > 0 }", "{ A[i] -> B[i] : i <= 0 }" },
2075 static int test_subtract(isl_ctx
*ctx
)
2078 isl_union_map
*umap1
, *umap2
;
2079 isl_union_set
*uset
;
2082 for (i
= 0; i
< ARRAY_SIZE(subtract_domain_tests
); ++i
) {
2083 umap1
= isl_union_map_read_from_str(ctx
,
2084 subtract_domain_tests
[i
].minuend
);
2085 uset
= isl_union_set_read_from_str(ctx
,
2086 subtract_domain_tests
[i
].subtrahend
);
2087 umap2
= isl_union_map_read_from_str(ctx
,
2088 subtract_domain_tests
[i
].difference
);
2089 umap1
= isl_union_map_subtract_domain(umap1
, uset
);
2090 equal
= isl_union_map_is_equal(umap1
, umap2
);
2091 isl_union_map_free(umap1
);
2092 isl_union_map_free(umap2
);
2096 isl_die(ctx
, isl_error_unknown
,
2097 "incorrect subtract domain result", return -1);
2103 int test_factorize(isl_ctx
*ctx
)
2106 isl_basic_set
*bset
;
2109 str
= "{ [i0, i1, i2, i3, i4, i5, i6, i7] : 3i5 <= 2 - 2i0 and "
2110 "i0 >= -2 and i6 >= 1 + i3 and i7 >= 0 and 3i5 >= -2i0 and "
2111 "2i4 <= i2 and i6 >= 1 + 2i0 + 3i1 and i4 <= -1 and "
2112 "i6 >= 1 + 2i0 + 3i5 and i6 <= 2 + 2i0 + 3i5 and "
2113 "3i5 <= 2 - 2i0 - i2 + 3i4 and i6 <= 2 + 2i0 + 3i1 and "
2114 "i0 <= -1 and i7 <= i2 + i3 - 3i4 - i6 and "
2115 "3i5 >= -2i0 - i2 + 3i4 }";
2116 bset
= isl_basic_set_read_from_str(ctx
, str
);
2117 f
= isl_basic_set_factorizer(bset
);
2118 isl_basic_set_free(bset
);
2119 isl_factorizer_free(f
);
2121 isl_die(ctx
, isl_error_unknown
,
2122 "failed to construct factorizer", return -1);
2124 str
= "{ [i0, i1, i2, i3, i4, i5, i6, i7, i8, i9, i10, i11, i12] : "
2125 "i12 <= 2 + i0 - i11 and 2i8 >= -i4 and i11 >= i1 and "
2126 "3i5 <= -i2 and 2i11 >= -i4 - 2i7 and i11 <= 3 + i0 + 3i9 and "
2127 "i11 <= -i4 - 2i7 and i12 >= -i10 and i2 >= -2 and "
2128 "i11 >= i1 + 3i10 and i11 >= 1 + i0 + 3i9 and "
2129 "i11 <= 1 - i4 - 2i8 and 6i6 <= 6 - i2 and 3i6 >= 1 - i2 and "
2130 "i11 <= 2 + i1 and i12 <= i4 + i11 and i12 >= i0 - i11 and "
2131 "3i5 >= -2 - i2 and i12 >= -1 + i4 + i11 and 3i3 <= 3 - i2 and "
2132 "9i6 <= 11 - i2 + 6i5 and 3i3 >= 1 - i2 and "
2133 "9i6 <= 5 - i2 + 6i3 and i12 <= -1 and i2 <= 0 }";
2134 bset
= isl_basic_set_read_from_str(ctx
, str
);
2135 f
= isl_basic_set_factorizer(bset
);
2136 isl_basic_set_free(bset
);
2137 isl_factorizer_free(f
);
2139 isl_die(ctx
, isl_error_unknown
,
2140 "failed to construct factorizer", return -1);
2145 static int check_injective(__isl_take isl_map
*map
, void *user
)
2147 int *injective
= user
;
2149 *injective
= isl_map_is_injective(map
);
2152 if (*injective
< 0 || !*injective
)
2158 int test_one_schedule(isl_ctx
*ctx
, const char *d
, const char *w
,
2159 const char *r
, const char *s
, int tilable
, int parallel
)
2163 isl_union_map
*W
, *R
, *S
;
2164 isl_union_map
*empty
;
2165 isl_union_map
*dep_raw
, *dep_war
, *dep_waw
, *dep
;
2166 isl_union_map
*validity
, *proximity
;
2167 isl_union_map
*schedule
;
2168 isl_union_map
*test
;
2169 isl_union_set
*delta
;
2170 isl_union_set
*domain
;
2174 isl_schedule
*sched
;
2175 int is_nonneg
, is_parallel
, is_tilable
, is_injection
, is_complete
;
2177 D
= isl_union_set_read_from_str(ctx
, d
);
2178 W
= isl_union_map_read_from_str(ctx
, w
);
2179 R
= isl_union_map_read_from_str(ctx
, r
);
2180 S
= isl_union_map_read_from_str(ctx
, s
);
2182 W
= isl_union_map_intersect_domain(W
, isl_union_set_copy(D
));
2183 R
= isl_union_map_intersect_domain(R
, isl_union_set_copy(D
));
2185 empty
= isl_union_map_empty(isl_union_map_get_space(S
));
2186 isl_union_map_compute_flow(isl_union_map_copy(R
),
2187 isl_union_map_copy(W
), empty
,
2188 isl_union_map_copy(S
),
2189 &dep_raw
, NULL
, NULL
, NULL
);
2190 isl_union_map_compute_flow(isl_union_map_copy(W
),
2191 isl_union_map_copy(W
),
2192 isl_union_map_copy(R
),
2193 isl_union_map_copy(S
),
2194 &dep_waw
, &dep_war
, NULL
, NULL
);
2196 dep
= isl_union_map_union(dep_waw
, dep_war
);
2197 dep
= isl_union_map_union(dep
, dep_raw
);
2198 validity
= isl_union_map_copy(dep
);
2199 proximity
= isl_union_map_copy(dep
);
2201 sched
= isl_union_set_compute_schedule(isl_union_set_copy(D
),
2202 validity
, proximity
);
2203 schedule
= isl_schedule_get_map(sched
);
2204 isl_schedule_free(sched
);
2205 isl_union_map_free(W
);
2206 isl_union_map_free(R
);
2207 isl_union_map_free(S
);
2210 isl_union_map_foreach_map(schedule
, &check_injective
, &is_injection
);
2212 domain
= isl_union_map_domain(isl_union_map_copy(schedule
));
2213 is_complete
= isl_union_set_is_subset(D
, domain
);
2214 isl_union_set_free(D
);
2215 isl_union_set_free(domain
);
2217 test
= isl_union_map_reverse(isl_union_map_copy(schedule
));
2218 test
= isl_union_map_apply_range(test
, dep
);
2219 test
= isl_union_map_apply_range(test
, schedule
);
2221 delta
= isl_union_map_deltas(test
);
2222 if (isl_union_set_n_set(delta
) == 0) {
2226 isl_union_set_free(delta
);
2228 delta_set
= isl_set_from_union_set(delta
);
2230 slice
= isl_set_universe(isl_set_get_space(delta_set
));
2231 for (i
= 0; i
< tilable
; ++i
)
2232 slice
= isl_set_lower_bound_si(slice
, isl_dim_set
, i
, 0);
2233 is_tilable
= isl_set_is_subset(delta_set
, slice
);
2234 isl_set_free(slice
);
2236 slice
= isl_set_universe(isl_set_get_space(delta_set
));
2237 for (i
= 0; i
< parallel
; ++i
)
2238 slice
= isl_set_fix_si(slice
, isl_dim_set
, i
, 0);
2239 is_parallel
= isl_set_is_subset(delta_set
, slice
);
2240 isl_set_free(slice
);
2242 origin
= isl_set_universe(isl_set_get_space(delta_set
));
2243 for (i
= 0; i
< isl_set_dim(origin
, isl_dim_set
); ++i
)
2244 origin
= isl_set_fix_si(origin
, isl_dim_set
, i
, 0);
2246 delta_set
= isl_set_union(delta_set
, isl_set_copy(origin
));
2247 delta_set
= isl_set_lexmin(delta_set
);
2249 is_nonneg
= isl_set_is_equal(delta_set
, origin
);
2251 isl_set_free(origin
);
2252 isl_set_free(delta_set
);
2255 if (is_nonneg
< 0 || is_parallel
< 0 || is_tilable
< 0 ||
2256 is_injection
< 0 || is_complete
< 0)
2259 isl_die(ctx
, isl_error_unknown
,
2260 "generated schedule incomplete", return -1);
2262 isl_die(ctx
, isl_error_unknown
,
2263 "generated schedule not injective on each statement",
2266 isl_die(ctx
, isl_error_unknown
,
2267 "negative dependences in generated schedule",
2270 isl_die(ctx
, isl_error_unknown
,
2271 "generated schedule not as tilable as expected",
2274 isl_die(ctx
, isl_error_unknown
,
2275 "generated schedule not as parallel as expected",
2281 static __isl_give isl_union_map
*compute_schedule(isl_ctx
*ctx
,
2282 const char *domain
, const char *validity
, const char *proximity
)
2286 isl_union_map
*prox
;
2287 isl_schedule
*schedule
;
2288 isl_union_map
*sched
;
2290 dom
= isl_union_set_read_from_str(ctx
, domain
);
2291 dep
= isl_union_map_read_from_str(ctx
, validity
);
2292 prox
= isl_union_map_read_from_str(ctx
, proximity
);
2293 schedule
= isl_union_set_compute_schedule(dom
, dep
, prox
);
2294 sched
= isl_schedule_get_map(schedule
);
2295 isl_schedule_free(schedule
);
2300 /* Check that a schedule can be constructed on the given domain
2301 * with the given validity and proximity constraints.
2303 static int test_has_schedule(isl_ctx
*ctx
, const char *domain
,
2304 const char *validity
, const char *proximity
)
2306 isl_union_map
*sched
;
2308 sched
= compute_schedule(ctx
, domain
, validity
, proximity
);
2312 isl_union_map_free(sched
);
2316 int test_special_schedule(isl_ctx
*ctx
, const char *domain
,
2317 const char *validity
, const char *proximity
, const char *expected_sched
)
2319 isl_union_map
*sched1
, *sched2
;
2322 sched1
= compute_schedule(ctx
, domain
, validity
, proximity
);
2323 sched2
= isl_union_map_read_from_str(ctx
, expected_sched
);
2325 equal
= isl_union_map_is_equal(sched1
, sched2
);
2326 isl_union_map_free(sched1
);
2327 isl_union_map_free(sched2
);
2332 isl_die(ctx
, isl_error_unknown
, "unexpected schedule",
2338 int test_schedule(isl_ctx
*ctx
)
2340 const char *D
, *W
, *R
, *V
, *P
, *S
;
2342 /* Handle resulting schedule with zero bands. */
2343 if (test_one_schedule(ctx
, "{[]}", "{}", "{}", "{[] -> []}", 0, 0) < 0)
2347 D
= "[T,N] -> { S1[t,i] : 1 <= t <= T and 2 <= i <= N - 1 }";
2348 W
= "{ S1[t,i] -> a[t,i] }";
2349 R
= "{ S1[t,i] -> a[t-1,i]; S1[t,i] -> a[t-1,i-1]; "
2350 "S1[t,i] -> a[t-1,i+1] }";
2351 S
= "{ S1[t,i] -> [t,i] }";
2352 if (test_one_schedule(ctx
, D
, W
, R
, S
, 2, 0) < 0)
2355 /* Fig. 5 of CC2008 */
2356 D
= "[N] -> { S_0[i, j] : i >= 0 and i <= -1 + N and j >= 2 and "
2358 W
= "[N] -> { S_0[i, j] -> a[i, j] : i >= 0 and i <= -1 + N and "
2359 "j >= 2 and j <= -1 + N }";
2360 R
= "[N] -> { S_0[i, j] -> a[j, i] : i >= 0 and i <= -1 + N and "
2361 "j >= 2 and j <= -1 + N; "
2362 "S_0[i, j] -> a[i, -1 + j] : i >= 0 and i <= -1 + N and "
2363 "j >= 2 and j <= -1 + N }";
2364 S
= "[N] -> { S_0[i, j] -> [0, i, 0, j, 0] }";
2365 if (test_one_schedule(ctx
, D
, W
, R
, S
, 2, 0) < 0)
2368 D
= "{ S1[i] : 0 <= i <= 10; S2[i] : 0 <= i <= 9 }";
2369 W
= "{ S1[i] -> a[i] }";
2370 R
= "{ S2[i] -> a[i+1] }";
2371 S
= "{ S1[i] -> [0,i]; S2[i] -> [1,i] }";
2372 if (test_one_schedule(ctx
, D
, W
, R
, S
, 1, 1) < 0)
2375 D
= "{ S1[i] : 0 <= i < 10; S2[i] : 0 <= i < 10 }";
2376 W
= "{ S1[i] -> a[i] }";
2377 R
= "{ S2[i] -> a[9-i] }";
2378 S
= "{ S1[i] -> [0,i]; S2[i] -> [1,i] }";
2379 if (test_one_schedule(ctx
, D
, W
, R
, S
, 1, 1) < 0)
2382 D
= "[N] -> { S1[i] : 0 <= i < N; S2[i] : 0 <= i < N }";
2383 W
= "{ S1[i] -> a[i] }";
2384 R
= "[N] -> { S2[i] -> a[N-1-i] }";
2385 S
= "{ S1[i] -> [0,i]; S2[i] -> [1,i] }";
2386 if (test_one_schedule(ctx
, D
, W
, R
, S
, 1, 1) < 0)
2389 D
= "{ S1[i] : 0 < i < 10; S2[i] : 0 <= i < 10 }";
2390 W
= "{ S1[i] -> a[i]; S2[i] -> b[i] }";
2391 R
= "{ S2[i] -> a[i]; S1[i] -> b[i-1] }";
2392 S
= "{ S1[i] -> [i,0]; S2[i] -> [i,1] }";
2393 if (test_one_schedule(ctx
, D
, W
, R
, S
, 0, 0) < 0)
2396 D
= "[N] -> { S1[i] : 1 <= i <= N; S2[i,j] : 1 <= i,j <= N }";
2397 W
= "{ S1[i] -> a[0,i]; S2[i,j] -> a[i,j] }";
2398 R
= "{ S2[i,j] -> a[i-1,j] }";
2399 S
= "{ S1[i] -> [0,i,0]; S2[i,j] -> [1,i,j] }";
2400 if (test_one_schedule(ctx
, D
, W
, R
, S
, 2, 1) < 0)
2403 D
= "[N] -> { S1[i] : 1 <= i <= N; S2[i,j] : 1 <= i,j <= N }";
2404 W
= "{ S1[i] -> a[i,0]; S2[i,j] -> a[i,j] }";
2405 R
= "{ S2[i,j] -> a[i,j-1] }";
2406 S
= "{ S1[i] -> [0,i,0]; S2[i,j] -> [1,i,j] }";
2407 if (test_one_schedule(ctx
, D
, W
, R
, S
, 2, 1) < 0)
2410 D
= "[N] -> { S_0[]; S_1[i] : i >= 0 and i <= -1 + N; S_2[] }";
2411 W
= "[N] -> { S_0[] -> a[0]; S_2[] -> b[0]; "
2412 "S_1[i] -> a[1 + i] : i >= 0 and i <= -1 + N }";
2413 R
= "[N] -> { S_2[] -> a[N]; S_1[i] -> a[i] : i >= 0 and i <= -1 + N }";
2414 S
= "[N] -> { S_1[i] -> [1, i, 0]; S_2[] -> [2, 0, 1]; "
2415 "S_0[] -> [0, 0, 0] }";
2416 if (test_one_schedule(ctx
, D
, W
, R
, S
, 1, 0) < 0)
2418 ctx
->opt
->schedule_parametric
= 0;
2419 if (test_one_schedule(ctx
, D
, W
, R
, S
, 0, 0) < 0)
2421 ctx
->opt
->schedule_parametric
= 1;
2423 D
= "[N] -> { S1[i] : 1 <= i <= N; S2[i] : 1 <= i <= N; "
2424 "S3[i,j] : 1 <= i,j <= N; S4[i] : 1 <= i <= N }";
2425 W
= "{ S1[i] -> a[i,0]; S2[i] -> a[0,i]; S3[i,j] -> a[i,j] }";
2426 R
= "[N] -> { S3[i,j] -> a[i-1,j]; S3[i,j] -> a[i,j-1]; "
2427 "S4[i] -> a[i,N] }";
2428 S
= "{ S1[i] -> [0,i,0]; S2[i] -> [1,i,0]; S3[i,j] -> [2,i,j]; "
2429 "S4[i] -> [4,i,0] }";
2430 if (test_one_schedule(ctx
, D
, W
, R
, S
, 2, 0) < 0)
2433 D
= "[N] -> { S_0[i, j] : i >= 1 and i <= N and j >= 1 and j <= N }";
2434 W
= "[N] -> { S_0[i, j] -> s[0] : i >= 1 and i <= N and j >= 1 and "
2436 R
= "[N] -> { S_0[i, j] -> s[0] : i >= 1 and i <= N and j >= 1 and "
2438 "S_0[i, j] -> a[i, j] : i >= 1 and i <= N and j >= 1 and "
2440 S
= "[N] -> { S_0[i, j] -> [0, i, 0, j, 0] }";
2441 if (test_one_schedule(ctx
, D
, W
, R
, S
, 0, 0) < 0)
2444 D
= "[N] -> { S_0[t] : t >= 0 and t <= -1 + N; "
2445 " S_2[t] : t >= 0 and t <= -1 + N; "
2446 " S_1[t, i] : t >= 0 and t <= -1 + N and i >= 0 and "
2448 W
= "[N] -> { S_0[t] -> a[t, 0] : t >= 0 and t <= -1 + N; "
2449 " S_2[t] -> b[t] : t >= 0 and t <= -1 + N; "
2450 " S_1[t, i] -> a[t, 1 + i] : t >= 0 and t <= -1 + N and "
2451 "i >= 0 and i <= -1 + N }";
2452 R
= "[N] -> { S_1[t, i] -> a[t, i] : t >= 0 and t <= -1 + N and "
2453 "i >= 0 and i <= -1 + N; "
2454 " S_2[t] -> a[t, N] : t >= 0 and t <= -1 + N }";
2455 S
= "[N] -> { S_2[t] -> [0, t, 2]; S_1[t, i] -> [0, t, 1, i, 0]; "
2456 " S_0[t] -> [0, t, 0] }";
2458 if (test_one_schedule(ctx
, D
, W
, R
, S
, 2, 1) < 0)
2460 ctx
->opt
->schedule_parametric
= 0;
2461 if (test_one_schedule(ctx
, D
, W
, R
, S
, 0, 0) < 0)
2463 ctx
->opt
->schedule_parametric
= 1;
2465 D
= "[N] -> { S1[i,j] : 0 <= i,j < N; S2[i,j] : 0 <= i,j < N }";
2466 S
= "{ S1[i,j] -> [0,i,j]; S2[i,j] -> [1,i,j] }";
2467 if (test_one_schedule(ctx
, D
, "{}", "{}", S
, 2, 2) < 0)
2470 D
= "[M, N] -> { S_1[i] : i >= 0 and i <= -1 + M; "
2471 "S_0[i, j] : i >= 0 and i <= -1 + M and j >= 0 and j <= -1 + N }";
2472 W
= "[M, N] -> { S_0[i, j] -> a[j] : i >= 0 and i <= -1 + M and "
2473 "j >= 0 and j <= -1 + N; "
2474 "S_1[i] -> b[0] : i >= 0 and i <= -1 + M }";
2475 R
= "[M, N] -> { S_0[i, j] -> a[0] : i >= 0 and i <= -1 + M and "
2476 "j >= 0 and j <= -1 + N; "
2477 "S_1[i] -> b[0] : i >= 0 and i <= -1 + M }";
2478 S
= "[M, N] -> { S_1[i] -> [1, i, 0]; S_0[i, j] -> [0, i, 0, j, 0] }";
2479 if (test_one_schedule(ctx
, D
, W
, R
, S
, 0, 0) < 0)
2482 D
= "{ S_0[i] : i >= 0 }";
2483 W
= "{ S_0[i] -> a[i] : i >= 0 }";
2484 R
= "{ S_0[i] -> a[0] : i >= 0 }";
2485 S
= "{ S_0[i] -> [0, i, 0] }";
2486 if (test_one_schedule(ctx
, D
, W
, R
, S
, 0, 0) < 0)
2489 D
= "{ S_0[i] : i >= 0; S_1[i] : i >= 0 }";
2490 W
= "{ S_0[i] -> a[i] : i >= 0; S_1[i] -> b[i] : i >= 0 }";
2491 R
= "{ S_0[i] -> b[0] : i >= 0; S_1[i] -> a[i] : i >= 0 }";
2492 S
= "{ S_1[i] -> [0, i, 1]; S_0[i] -> [0, i, 0] }";
2493 if (test_one_schedule(ctx
, D
, W
, R
, S
, 0, 0) < 0)
2496 D
= "[n] -> { S_0[j, k] : j <= -1 + n and j >= 0 and "
2497 "k <= -1 + n and k >= 0 }";
2498 W
= "[n] -> { S_0[j, k] -> B[j] : j <= -1 + n and j >= 0 and " "k <= -1 + n and k >= 0 }";
2499 R
= "[n] -> { S_0[j, k] -> B[j] : j <= -1 + n and j >= 0 and "
2500 "k <= -1 + n and k >= 0; "
2501 "S_0[j, k] -> B[k] : j <= -1 + n and j >= 0 and "
2502 "k <= -1 + n and k >= 0; "
2503 "S_0[j, k] -> A[k] : j <= -1 + n and j >= 0 and "
2504 "k <= -1 + n and k >= 0 }";
2505 S
= "[n] -> { S_0[j, k] -> [2, j, k] }";
2506 ctx
->opt
->schedule_outer_zero_distance
= 1;
2507 if (test_one_schedule(ctx
, D
, W
, R
, S
, 0, 0) < 0)
2509 ctx
->opt
->schedule_outer_zero_distance
= 0;
2511 D
= "{Stmt_for_body24[i0, i1, i2, i3]:"
2512 "i0 >= 0 and i0 <= 1 and i1 >= 0 and i1 <= 6 and i2 >= 2 and "
2513 "i2 <= 6 - i1 and i3 >= 0 and i3 <= -1 + i2;"
2514 "Stmt_for_body24[i0, i1, 1, 0]:"
2515 "i0 >= 0 and i0 <= 1 and i1 >= 0 and i1 <= 5;"
2516 "Stmt_for_body7[i0, i1, i2]:"
2517 "i0 >= 0 and i0 <= 1 and i1 >= 0 and i1 <= 7 and i2 >= 0 and "
2520 V
= "{Stmt_for_body24[0, i1, i2, i3] -> "
2521 "Stmt_for_body24[1, i1, i2, i3]:"
2522 "i3 >= 0 and i3 <= -1 + i2 and i1 >= 0 and i2 <= 6 - i1 and "
2524 "Stmt_for_body24[0, i1, i2, i3] -> "
2525 "Stmt_for_body7[1, 1 + i1 + i3, 1 + i1 + i2]:"
2526 "i3 <= -1 + i2 and i2 <= 6 - i1 and i2 >= 1 and i1 >= 0 and "
2528 "Stmt_for_body24[0, i1, i2, i3] ->"
2529 "Stmt_for_body7[1, i1, 1 + i1 + i3]:"
2530 "i3 >= 0 and i2 <= 6 - i1 and i1 >= 0 and i3 <= -1 + i2;"
2531 "Stmt_for_body7[0, i1, i2] -> Stmt_for_body7[1, i1, i2]:"
2532 "(i2 >= 1 + i1 and i2 <= 6 and i1 >= 0 and i1 <= 4) or "
2533 "(i2 >= 3 and i2 <= 7 and i1 >= 1 and i2 >= 1 + i1) or "
2534 "(i2 >= 0 and i2 <= i1 and i2 >= -7 + i1 and i1 <= 7);"
2535 "Stmt_for_body7[0, i1, 1 + i1] -> Stmt_for_body7[1, i1, 1 + i1]:"
2536 "i1 <= 6 and i1 >= 0;"
2537 "Stmt_for_body7[0, 0, 7] -> Stmt_for_body7[1, 0, 7];"
2538 "Stmt_for_body7[i0, i1, i2] -> "
2539 "Stmt_for_body24[i0, o1, -1 + i2 - o1, -1 + i1 - o1]:"
2540 "i0 >= 0 and i0 <= 1 and o1 >= 0 and i2 >= 1 + i1 and "
2541 "o1 <= -2 + i2 and i2 <= 7 and o1 <= -1 + i1;"
2542 "Stmt_for_body7[i0, i1, i2] -> "
2543 "Stmt_for_body24[i0, i1, o2, -1 - i1 + i2]:"
2544 "i0 >= 0 and i0 <= 1 and i1 >= 0 and o2 >= -i1 + i2 and "
2545 "o2 >= 1 and o2 <= 6 - i1 and i2 >= 1 + i1 }";
2547 S
= "{ Stmt_for_body24[i0, i1, i2, i3] -> "
2548 "[i0, 5i0 + i1, 6i0 + i1 + i2, 1 + 6i0 + i1 + i2 + i3, 1];"
2549 "Stmt_for_body7[i0, i1, i2] -> [0, 5i0, 6i0 + i1, 6i0 + i2, 0] }";
2551 if (test_special_schedule(ctx
, D
, V
, P
, S
) < 0)
2554 D
= "{ S_0[i, j] : i >= 1 and i <= 10 and j >= 1 and j <= 8 }";
2555 V
= "{ S_0[i, j] -> S_0[i, 1 + j] : i >= 1 and i <= 10 and "
2556 "j >= 1 and j <= 7;"
2557 "S_0[i, j] -> S_0[1 + i, j] : i >= 1 and i <= 9 and "
2558 "j >= 1 and j <= 8 }";
2560 S
= "{ S_0[i, j] -> [i + j, j] }";
2561 ctx
->opt
->schedule_algorithm
= ISL_SCHEDULE_ALGORITHM_FEAUTRIER
;
2562 if (test_special_schedule(ctx
, D
, V
, P
, S
) < 0)
2564 ctx
->opt
->schedule_algorithm
= ISL_SCHEDULE_ALGORITHM_ISL
;
2566 /* Fig. 1 from Feautrier's "Some Efficient Solutions..." pt. 2, 1992 */
2567 D
= "[N] -> { S_0[i, j] : i >= 0 and i <= -1 + N and "
2568 "j >= 0 and j <= -1 + i }";
2569 V
= "[N] -> { S_0[i, j] -> S_0[i, 1 + j] : j <= -2 + i and "
2570 "i <= -1 + N and j >= 0;"
2571 "S_0[i, -1 + i] -> S_0[1 + i, 0] : i >= 1 and "
2574 S
= "{ S_0[i, j] -> [i, j] }";
2575 ctx
->opt
->schedule_algorithm
= ISL_SCHEDULE_ALGORITHM_FEAUTRIER
;
2576 if (test_special_schedule(ctx
, D
, V
, P
, S
) < 0)
2578 ctx
->opt
->schedule_algorithm
= ISL_SCHEDULE_ALGORITHM_ISL
;
2580 /* Test both algorithms on a case with only proximity dependences. */
2581 D
= "{ S[i,j] : 0 <= i <= 10 }";
2583 P
= "{ S[i,j] -> S[i+1,j] : 0 <= i,j <= 10 }";
2584 S
= "{ S[i, j] -> [j, i] }";
2585 ctx
->opt
->schedule_algorithm
= ISL_SCHEDULE_ALGORITHM_FEAUTRIER
;
2586 if (test_special_schedule(ctx
, D
, V
, P
, S
) < 0)
2588 ctx
->opt
->schedule_algorithm
= ISL_SCHEDULE_ALGORITHM_ISL
;
2589 if (test_special_schedule(ctx
, D
, V
, P
, S
) < 0)
2592 D
= "{ A[a]; B[] }";
2594 P
= "{ A[a] -> B[] }";
2595 if (test_has_schedule(ctx
, D
, V
, P
) < 0)
2601 int test_plain_injective(isl_ctx
*ctx
, const char *str
, int injective
)
2603 isl_union_map
*umap
;
2606 umap
= isl_union_map_read_from_str(ctx
, str
);
2607 test
= isl_union_map_plain_is_injective(umap
);
2608 isl_union_map_free(umap
);
2611 if (test
== injective
)
2614 isl_die(ctx
, isl_error_unknown
,
2615 "map not detected as injective", return -1);
2617 isl_die(ctx
, isl_error_unknown
,
2618 "map detected as injective", return -1);
2621 int test_injective(isl_ctx
*ctx
)
2625 if (test_plain_injective(ctx
, "{S[i,j] -> A[0]; T[i,j] -> B[1]}", 0))
2627 if (test_plain_injective(ctx
, "{S[] -> A[0]; T[] -> B[0]}", 1))
2629 if (test_plain_injective(ctx
, "{S[] -> A[0]; T[] -> A[1]}", 1))
2631 if (test_plain_injective(ctx
, "{S[] -> A[0]; T[] -> A[0]}", 0))
2633 if (test_plain_injective(ctx
, "{S[i] -> A[i,0]; T[i] -> A[i,1]}", 1))
2635 if (test_plain_injective(ctx
, "{S[i] -> A[i]; T[i] -> A[i]}", 0))
2637 if (test_plain_injective(ctx
, "{S[] -> A[0,0]; T[] -> A[0,1]}", 1))
2639 if (test_plain_injective(ctx
, "{S[] -> A[0,0]; T[] -> A[1,0]}", 1))
2642 str
= "{S[] -> A[0,0]; T[] -> A[0,1]; U[] -> A[1,0]}";
2643 if (test_plain_injective(ctx
, str
, 1))
2645 str
= "{S[] -> A[0,0]; T[] -> A[0,1]; U[] -> A[0,0]}";
2646 if (test_plain_injective(ctx
, str
, 0))
2652 static int aff_plain_is_equal(__isl_keep isl_aff
*aff
, const char *str
)
2660 aff2
= isl_aff_read_from_str(isl_aff_get_ctx(aff
), str
);
2661 equal
= isl_aff_plain_is_equal(aff
, aff2
);
2667 static int aff_check_plain_equal(__isl_keep isl_aff
*aff
, const char *str
)
2671 equal
= aff_plain_is_equal(aff
, str
);
2675 isl_die(isl_aff_get_ctx(aff
), isl_error_unknown
,
2676 "result not as expected", return -1);
2680 int test_aff(isl_ctx
*ctx
)
2685 isl_local_space
*ls
;
2689 space
= isl_space_set_alloc(ctx
, 0, 1);
2690 ls
= isl_local_space_from_space(space
);
2691 aff
= isl_aff_zero_on_domain(ls
);
2693 aff
= isl_aff_add_coefficient_si(aff
, isl_dim_in
, 0, 1);
2694 aff
= isl_aff_scale_down_ui(aff
, 3);
2695 aff
= isl_aff_floor(aff
);
2696 aff
= isl_aff_add_coefficient_si(aff
, isl_dim_in
, 0, 1);
2697 aff
= isl_aff_scale_down_ui(aff
, 2);
2698 aff
= isl_aff_floor(aff
);
2699 aff
= isl_aff_add_coefficient_si(aff
, isl_dim_in
, 0, 1);
2702 set
= isl_set_read_from_str(ctx
, str
);
2703 aff
= isl_aff_gist(aff
, set
);
2705 aff
= isl_aff_add_constant_si(aff
, -16);
2706 zero
= isl_aff_plain_is_zero(aff
);
2712 isl_die(ctx
, isl_error_unknown
, "unexpected result", return -1);
2714 aff
= isl_aff_read_from_str(ctx
, "{ [-1] }");
2715 aff
= isl_aff_scale_down_ui(aff
, 64);
2716 aff
= isl_aff_floor(aff
);
2717 equal
= aff_check_plain_equal(aff
, "{ [-1] }");
2725 int test_dim_max(isl_ctx
*ctx
)
2729 isl_set
*set1
, *set2
;
2734 str
= "[N] -> { [i] : 0 <= i <= min(N,10) }";
2735 set
= isl_set_read_from_str(ctx
, str
);
2736 pwaff
= isl_set_dim_max(set
, 0);
2737 set1
= isl_set_from_pw_aff(pwaff
);
2738 str
= "[N] -> { [10] : N >= 10; [N] : N <= 9 and N >= 0 }";
2739 set2
= isl_set_read_from_str(ctx
, str
);
2740 equal
= isl_set_is_equal(set1
, set2
);
2746 isl_die(ctx
, isl_error_unknown
, "unexpected result", return -1);
2748 str
= "[N] -> { [i] : 0 <= i <= max(2N,N+6) }";
2749 set
= isl_set_read_from_str(ctx
, str
);
2750 pwaff
= isl_set_dim_max(set
, 0);
2751 set1
= isl_set_from_pw_aff(pwaff
);
2752 str
= "[N] -> { [6 + N] : -6 <= N <= 5; [2N] : N >= 6 }";
2753 set2
= isl_set_read_from_str(ctx
, str
);
2754 equal
= isl_set_is_equal(set1
, set2
);
2760 isl_die(ctx
, isl_error_unknown
, "unexpected result", return -1);
2762 str
= "[N] -> { [i] : 0 <= i <= 2N or 0 <= i <= N+6 }";
2763 set
= isl_set_read_from_str(ctx
, str
);
2764 pwaff
= isl_set_dim_max(set
, 0);
2765 set1
= isl_set_from_pw_aff(pwaff
);
2766 str
= "[N] -> { [6 + N] : -6 <= N <= 5; [2N] : N >= 6 }";
2767 set2
= isl_set_read_from_str(ctx
, str
);
2768 equal
= isl_set_is_equal(set1
, set2
);
2774 isl_die(ctx
, isl_error_unknown
, "unexpected result", return -1);
2776 str
= "[N,M] -> { [i,j] -> [([i/16]), i%16, ([j/16]), j%16] : "
2777 "0 <= i < N and 0 <= j < M }";
2778 map
= isl_map_read_from_str(ctx
, str
);
2779 set
= isl_map_range(map
);
2781 pwaff
= isl_set_dim_max(isl_set_copy(set
), 0);
2782 set1
= isl_set_from_pw_aff(pwaff
);
2783 str
= "[N,M] -> { [([(N-1)/16])] : M,N > 0 }";
2784 set2
= isl_set_read_from_str(ctx
, str
);
2785 equal
= isl_set_is_equal(set1
, set2
);
2789 pwaff
= isl_set_dim_max(isl_set_copy(set
), 3);
2790 set1
= isl_set_from_pw_aff(pwaff
);
2791 str
= "[N,M] -> { [t] : t = min(M-1,15) and M,N > 0 }";
2792 set2
= isl_set_read_from_str(ctx
, str
);
2793 if (equal
>= 0 && equal
)
2794 equal
= isl_set_is_equal(set1
, set2
);
2803 isl_die(ctx
, isl_error_unknown
, "unexpected result", return -1);
2808 int test_product(isl_ctx
*ctx
)
2812 isl_union_set
*uset1
, *uset2
;
2816 set
= isl_set_read_from_str(ctx
, str
);
2817 set
= isl_set_product(set
, isl_set_copy(set
));
2818 ok
= isl_set_is_wrapping(set
);
2823 isl_die(ctx
, isl_error_unknown
, "unexpected result", return -1);
2826 uset1
= isl_union_set_read_from_str(ctx
, str
);
2827 uset1
= isl_union_set_product(uset1
, isl_union_set_copy(uset1
));
2828 str
= "{ [[] -> []] }";
2829 uset2
= isl_union_set_read_from_str(ctx
, str
);
2830 ok
= isl_union_set_is_equal(uset1
, uset2
);
2831 isl_union_set_free(uset1
);
2832 isl_union_set_free(uset2
);
2836 isl_die(ctx
, isl_error_unknown
, "unexpected result", return -1);
2841 int test_equal(isl_ctx
*ctx
)
2844 isl_set
*set
, *set2
;
2848 set
= isl_set_read_from_str(ctx
, str
);
2850 set2
= isl_set_read_from_str(ctx
, str
);
2851 equal
= isl_set_is_equal(set
, set2
);
2857 isl_die(ctx
, isl_error_unknown
, "unexpected result", return -1);
2862 static int test_plain_fixed(isl_ctx
*ctx
, __isl_take isl_map
*map
,
2863 enum isl_dim_type type
, unsigned pos
, int fixed
)
2867 test
= isl_map_plain_is_fixed(map
, type
, pos
, NULL
);
2874 isl_die(ctx
, isl_error_unknown
,
2875 "map not detected as fixed", return -1);
2877 isl_die(ctx
, isl_error_unknown
,
2878 "map detected as fixed", return -1);
2881 int test_fixed(isl_ctx
*ctx
)
2886 str
= "{ [i] -> [i] }";
2887 map
= isl_map_read_from_str(ctx
, str
);
2888 if (test_plain_fixed(ctx
, map
, isl_dim_out
, 0, 0))
2890 str
= "{ [i] -> [1] }";
2891 map
= isl_map_read_from_str(ctx
, str
);
2892 if (test_plain_fixed(ctx
, map
, isl_dim_out
, 0, 1))
2894 str
= "{ S_1[p1] -> [o0] : o0 = -2 and p1 >= 1 and p1 <= 7 }";
2895 map
= isl_map_read_from_str(ctx
, str
);
2896 if (test_plain_fixed(ctx
, map
, isl_dim_out
, 0, 1))
2898 map
= isl_map_read_from_str(ctx
, str
);
2899 map
= isl_map_neg(map
);
2900 if (test_plain_fixed(ctx
, map
, isl_dim_out
, 0, 1))
2906 int test_vertices(isl_ctx
*ctx
)
2909 isl_basic_set
*bset
;
2910 isl_vertices
*vertices
;
2912 str
= "{ A[t, i] : t = 12 and i >= 4 and i <= 12 }";
2913 bset
= isl_basic_set_read_from_str(ctx
, str
);
2914 vertices
= isl_basic_set_compute_vertices(bset
);
2915 isl_basic_set_free(bset
);
2916 isl_vertices_free(vertices
);
2920 str
= "{ A[t, i] : t = 14 and i = 1 }";
2921 bset
= isl_basic_set_read_from_str(ctx
, str
);
2922 vertices
= isl_basic_set_compute_vertices(bset
);
2923 isl_basic_set_free(bset
);
2924 isl_vertices_free(vertices
);
2931 int test_union_pw(isl_ctx
*ctx
)
2935 isl_union_set
*uset
;
2936 isl_union_pw_qpolynomial
*upwqp1
, *upwqp2
;
2938 str
= "{ [x] -> x^2 }";
2939 upwqp1
= isl_union_pw_qpolynomial_read_from_str(ctx
, str
);
2940 upwqp2
= isl_union_pw_qpolynomial_copy(upwqp1
);
2941 uset
= isl_union_pw_qpolynomial_domain(upwqp1
);
2942 upwqp1
= isl_union_pw_qpolynomial_copy(upwqp2
);
2943 upwqp1
= isl_union_pw_qpolynomial_intersect_domain(upwqp1
, uset
);
2944 equal
= isl_union_pw_qpolynomial_plain_is_equal(upwqp1
, upwqp2
);
2945 isl_union_pw_qpolynomial_free(upwqp1
);
2946 isl_union_pw_qpolynomial_free(upwqp2
);
2950 isl_die(ctx
, isl_error_unknown
, "unexpected result", return -1);
2955 int test_output(isl_ctx
*ctx
)
2963 str
= "[x] -> { [1] : x % 4 <= 2; [2] : x = 3 }";
2964 pa
= isl_pw_aff_read_from_str(ctx
, str
);
2966 p
= isl_printer_to_str(ctx
);
2967 p
= isl_printer_set_output_format(p
, ISL_FORMAT_C
);
2968 p
= isl_printer_print_pw_aff(p
, pa
);
2969 s
= isl_printer_get_str(p
);
2970 isl_printer_free(p
);
2971 isl_pw_aff_free(pa
);
2975 equal
= !strcmp(s
, "(2 - x + 4*floord(x, 4) >= 0) ? (1) : 2");
2980 isl_die(ctx
, isl_error_unknown
, "unexpected result", return -1);
2985 int test_sample(isl_ctx
*ctx
)
2988 isl_basic_set
*bset1
, *bset2
;
2991 str
= "{ [a, b, c, d, e, f, g, h, i, j, k] : "
2992 "3i >= 1073741823b - c - 1073741823e + f and c >= 0 and "
2993 "3i >= -1 + 3221225466b + c + d - 3221225466e - f and "
2994 "2e >= a - b and 3e <= 2a and 3k <= -a and f <= -1 + a and "
2995 "3i <= 4 - a + 4b + 2c - e - 2f and 3k <= -a + c - f and "
2996 "3h >= -2 + a and 3g >= -3 - a and 3k >= -2 - a and "
2997 "3i >= -2 - a - 2c + 3e + 2f and 3h <= a + c - f and "
2998 "3h >= a + 2147483646b + 2c - 2147483646e - 2f and "
2999 "3g <= -1 - a and 3i <= 1 + c + d - f and a <= 1073741823 and "
3000 "f >= 1 - a + 1073741822b + c + d - 1073741822e and "
3001 "3i >= 1 + 2b - 2c + e + 2f + 3g and "
3002 "1073741822f <= 1073741822 - a + 1073741821b + 1073741822c +"
3003 "d - 1073741821e and "
3004 "3j <= 3 - a + 3b and 3g <= -2 - 2b + c + d - e - f and "
3005 "3j >= 1 - a + b + 2e and "
3006 "3f >= -3 + a + 3221225462b + 3c + d - 3221225465e and "
3007 "3i <= 4 - a + 4b - e and "
3008 "f <= 1073741822 + 1073741822b - 1073741822e and 3h <= a and "
3009 "f >= 0 and 2e <= 4 - a + 5b - d and 2e <= a - b + d and "
3010 "c <= -1 + a and 3i >= -2 - a + 3e and "
3011 "1073741822e <= 1073741823 - a + 1073741822b + c and "
3012 "3g >= -4 + 3221225464b + 3c + d - 3221225467e - 3f and "
3013 "3i >= -1 + 3221225466b + 3c + d - 3221225466e - 3f and "
3014 "1073741823e >= 1 + 1073741823b - d and "
3015 "3i >= 1073741823b + c - 1073741823e - f and "
3016 "3i >= 1 + 2b + e + 3g }";
3017 bset1
= isl_basic_set_read_from_str(ctx
, str
);
3018 bset2
= isl_basic_set_sample(isl_basic_set_copy(bset1
));
3019 empty
= isl_basic_set_is_empty(bset2
);
3020 subset
= isl_basic_set_is_subset(bset2
, bset1
);
3021 isl_basic_set_free(bset1
);
3022 isl_basic_set_free(bset2
);
3023 if (empty
< 0 || subset
< 0)
3026 isl_die(ctx
, isl_error_unknown
, "point not found", return -1);
3028 isl_die(ctx
, isl_error_unknown
, "bad point found", return -1);
3033 int test_fixed_power(isl_ctx
*ctx
)
3041 str
= "{ [i] -> [i + 1] }";
3042 map
= isl_map_read_from_str(ctx
, str
);
3043 isl_int_set_si(exp
, 23);
3044 map
= isl_map_fixed_power(map
, exp
);
3045 equal
= map_check_equal(map
, "{ [i] -> [i + 23] }");
3054 int test_slice(isl_ctx
*ctx
)
3060 str
= "{ [i] -> [j] }";
3061 map
= isl_map_read_from_str(ctx
, str
);
3062 map
= isl_map_equate(map
, isl_dim_in
, 0, isl_dim_out
, 0);
3063 equal
= map_check_equal(map
, "{ [i] -> [i] }");
3068 str
= "{ [i] -> [j] }";
3069 map
= isl_map_read_from_str(ctx
, str
);
3070 map
= isl_map_equate(map
, isl_dim_in
, 0, isl_dim_in
, 0);
3071 equal
= map_check_equal(map
, "{ [i] -> [j] }");
3076 str
= "{ [i] -> [j] }";
3077 map
= isl_map_read_from_str(ctx
, str
);
3078 map
= isl_map_oppose(map
, isl_dim_in
, 0, isl_dim_out
, 0);
3079 equal
= map_check_equal(map
, "{ [i] -> [-i] }");
3084 str
= "{ [i] -> [j] }";
3085 map
= isl_map_read_from_str(ctx
, str
);
3086 map
= isl_map_oppose(map
, isl_dim_in
, 0, isl_dim_in
, 0);
3087 equal
= map_check_equal(map
, "{ [0] -> [j] }");
3092 str
= "{ [i] -> [j] }";
3093 map
= isl_map_read_from_str(ctx
, str
);
3094 map
= isl_map_order_gt(map
, isl_dim_in
, 0, isl_dim_out
, 0);
3095 equal
= map_check_equal(map
, "{ [i] -> [j] : i > j }");
3100 str
= "{ [i] -> [j] }";
3101 map
= isl_map_read_from_str(ctx
, str
);
3102 map
= isl_map_order_gt(map
, isl_dim_in
, 0, isl_dim_in
, 0);
3103 equal
= map_check_equal(map
, "{ [i] -> [j] : false }");
3111 int test_eliminate(isl_ctx
*ctx
)
3117 str
= "{ [i] -> [j] : i = 2j }";
3118 map
= isl_map_read_from_str(ctx
, str
);
3119 map
= isl_map_eliminate(map
, isl_dim_out
, 0, 1);
3120 equal
= map_check_equal(map
, "{ [i] -> [j] : exists a : i = 2a }");
3128 /* Check that isl_set_dim_residue_class detects that the values of j
3129 * in the set below are all odd and that it does not detect any spurious
3132 static int test_residue_class(isl_ctx
*ctx
)
3139 str
= "{ [i,j] : j = 4 i + 1 and 0 <= i <= 100; "
3140 "[i,j] : j = 4 i + 3 and 500 <= i <= 600 }";
3141 set
= isl_set_read_from_str(ctx
, str
);
3144 res
= isl_set_dim_residue_class(set
, 1, &m
, &r
);
3146 (isl_int_cmp_si(m
, 2) != 0 || isl_int_cmp_si(r
, 1) != 0))
3147 isl_die(ctx
, isl_error_unknown
, "incorrect residue class",
3156 int test_align_parameters(isl_ctx
*ctx
)
3160 isl_multi_aff
*ma1
, *ma2
;
3163 str
= "{ A[B[] -> C[]] -> D[E[] -> F[]] }";
3164 ma1
= isl_multi_aff_read_from_str(ctx
, str
);
3166 space
= isl_space_params_alloc(ctx
, 1);
3167 space
= isl_space_set_dim_name(space
, isl_dim_param
, 0, "N");
3168 ma1
= isl_multi_aff_align_params(ma1
, space
);
3170 str
= "[N] -> { A[B[] -> C[]] -> D[E[] -> F[]] }";
3171 ma2
= isl_multi_aff_read_from_str(ctx
, str
);
3173 equal
= isl_multi_aff_plain_is_equal(ma1
, ma2
);
3175 isl_multi_aff_free(ma1
);
3176 isl_multi_aff_free(ma2
);
3181 isl_die(ctx
, isl_error_unknown
,
3182 "result not as expected", return -1);
3187 static int test_list(isl_ctx
*ctx
)
3189 isl_id
*a
, *b
, *c
, *d
, *id
;
3193 a
= isl_id_alloc(ctx
, "a", NULL
);
3194 b
= isl_id_alloc(ctx
, "b", NULL
);
3195 c
= isl_id_alloc(ctx
, "c", NULL
);
3196 d
= isl_id_alloc(ctx
, "d", NULL
);
3198 list
= isl_id_list_alloc(ctx
, 4);
3199 list
= isl_id_list_add(list
, a
);
3200 list
= isl_id_list_add(list
, b
);
3201 list
= isl_id_list_add(list
, c
);
3202 list
= isl_id_list_add(list
, d
);
3203 list
= isl_id_list_drop(list
, 1, 1);
3205 if (isl_id_list_n_id(list
) != 3) {
3206 isl_id_list_free(list
);
3207 isl_die(ctx
, isl_error_unknown
,
3208 "unexpected number of elements in list", return -1);
3211 id
= isl_id_list_get_id(list
, 0);
3214 id
= isl_id_list_get_id(list
, 1);
3217 id
= isl_id_list_get_id(list
, 2);
3221 isl_id_list_free(list
);
3224 isl_die(ctx
, isl_error_unknown
,
3225 "unexpected elements in list", return -1);
3230 const char *set_conversion_tests
[] = {
3231 "[N] -> { [i] : N - 1 <= 2 i <= N }",
3232 "[N] -> { [i] : exists a : i = 4 a and N - 1 <= i <= N }",
3233 "[N] -> { [i,j] : exists a : i = 4 a and N - 1 <= i, 2j <= N }",
3234 "[N] -> { [[i]->[j]] : exists a : i = 4 a and N - 1 <= i, 2j <= N }",
3237 /* Check that converting from isl_set to isl_pw_multi_aff and back
3238 * to isl_set produces the original isl_set.
3240 static int test_set_conversion(isl_ctx
*ctx
)
3244 isl_set
*set1
, *set2
;
3245 isl_pw_multi_aff
*pma
;
3248 for (i
= 0; i
< ARRAY_SIZE(set_conversion_tests
); ++i
) {
3249 str
= set_conversion_tests
[i
];
3250 set1
= isl_set_read_from_str(ctx
, str
);
3251 pma
= isl_pw_multi_aff_from_set(isl_set_copy(set1
));
3252 set2
= isl_set_from_pw_multi_aff(pma
);
3253 equal
= isl_set_is_equal(set1
, set2
);
3260 isl_die(ctx
, isl_error_unknown
, "bad conversion",
3267 /* Check that converting from isl_map to isl_pw_multi_aff and back
3268 * to isl_map produces the original isl_map.
3270 static int test_map_conversion(isl_ctx
*ctx
)
3273 isl_map
*map1
, *map2
;
3274 isl_pw_multi_aff
*pma
;
3277 str
= "{ [a, b, c, d] -> s0[a, b, e, f] : "
3278 "exists (e0 = [(a - 2c)/3], e1 = [(-4 + b - 5d)/9], "
3279 "e2 = [(-d + f)/9]: 3e0 = a - 2c and 9e1 = -4 + b - 5d and "
3280 "9e2 = -d + f and f >= 0 and f <= 8 and 9e >= -5 - 2a and "
3282 map1
= isl_map_read_from_str(ctx
, str
);
3283 pma
= isl_pw_multi_aff_from_map(isl_map_copy(map1
));
3284 map2
= isl_map_from_pw_multi_aff(pma
);
3285 equal
= isl_map_is_equal(map1
, map2
);
3292 isl_die(ctx
, isl_error_unknown
, "bad conversion", return -1);
3297 static int test_conversion(isl_ctx
*ctx
)
3299 if (test_set_conversion(ctx
) < 0)
3301 if (test_map_conversion(ctx
) < 0)
3306 /* Check that isl_basic_map_curry does not modify input.
3308 static int test_curry(isl_ctx
*ctx
)
3311 isl_basic_map
*bmap1
, *bmap2
;
3314 str
= "{ [A[] -> B[]] -> C[] }";
3315 bmap1
= isl_basic_map_read_from_str(ctx
, str
);
3316 bmap2
= isl_basic_map_curry(isl_basic_map_copy(bmap1
));
3317 equal
= isl_basic_map_is_equal(bmap1
, bmap2
);
3318 isl_basic_map_free(bmap1
);
3319 isl_basic_map_free(bmap2
);
3324 isl_die(ctx
, isl_error_unknown
,
3325 "curried map should not be equal to original",
3335 } preimage_tests
[] = {
3336 { "{ B[i,j] : 0 <= i < 10 and 0 <= j < 100 }",
3337 "{ A[j,i] -> B[i,j] }",
3338 "{ A[j,i] : 0 <= i < 10 and 0 <= j < 100 }" },
3339 { "{ rat: B[i,j] : 0 <= i, j and 3 i + 5 j <= 100 }",
3340 "{ A[a,b] -> B[a/2,b/6] }",
3341 "{ rat: A[a,b] : 0 <= a, b and 9 a + 5 b <= 600 }" },
3342 { "{ B[i,j] : 0 <= i, j and 3 i + 5 j <= 100 }",
3343 "{ A[a,b] -> B[a/2,b/6] }",
3344 "{ A[a,b] : 0 <= a, b and 9 a + 5 b <= 600 and "
3345 "exists i,j : a = 2 i and b = 6 j }" },
3346 { "[n] -> { S[i] : 0 <= i <= 100 }", "[n] -> { S[n] }",
3347 "[n] -> { : 0 <= n <= 100 }" },
3348 { "{ B[i] : 0 <= i < 100 and exists a : i = 4 a }",
3349 "{ A[a] -> B[2a] }",
3350 "{ A[a] : 0 <= a < 50 and exists b : a = 2 b }" },
3351 { "{ B[i] : 0 <= i < 100 and exists a : i = 4 a }",
3352 "{ A[a] -> B[([a/2])] }",
3353 "{ A[a] : 0 <= a < 200 and exists b : [a/2] = 4 b }" },
3354 { "{ B[i,j,k] : 0 <= i,j,k <= 100 }",
3355 "{ A[a] -> B[a,a,a/3] }",
3356 "{ A[a] : 0 <= a <= 100 and exists b : a = 3 b }" },
3357 { "{ B[i,j] : j = [(i)/2] } ", "{ A[i,j] -> B[i/3,j] }",
3358 "{ A[i,j] : j = [(i)/6] and exists a : i = 3 a }" },
3361 int test_preimage(isl_ctx
*ctx
)
3364 isl_basic_set
*bset1
, *bset2
;
3368 for (i
= 0; i
< ARRAY_SIZE(preimage_tests
); ++i
) {
3369 bset1
= isl_basic_set_read_from_str(ctx
, preimage_tests
[i
].set
);
3370 ma
= isl_multi_aff_read_from_str(ctx
, preimage_tests
[i
].ma
);
3371 bset2
= isl_basic_set_read_from_str(ctx
, preimage_tests
[i
].res
);
3372 bset1
= isl_basic_set_preimage_multi_aff(bset1
, ma
);
3373 equal
= isl_basic_set_is_equal(bset1
, bset2
);
3374 isl_basic_set_free(bset1
);
3375 isl_basic_set_free(bset2
);
3379 isl_die(ctx
, isl_error_unknown
, "bad preimage",
3390 } pullback_tests
[] = {
3391 { "{ B[i,j] -> C[i + 2j] }" , "{ A[a,b] -> B[b,a] }",
3392 "{ A[a,b] -> C[b + 2a] }" },
3393 { "{ B[i] -> C[2i] }", "{ A[a] -> B[(a)/2] }", "{ A[a] -> C[a] }" },
3394 { "{ B[i] -> C[(i)/2] }", "{ A[a] -> B[2a] }", "{ A[a] -> C[a] }" },
3395 { "{ B[i] -> C[(i)/2] }", "{ A[a] -> B[(a)/3] }",
3396 "{ A[a] -> C[(a)/6] }" },
3397 { "{ B[i] -> C[2i] }", "{ A[a] -> B[5a] }", "{ A[a] -> C[10a] }" },
3398 { "{ B[i] -> C[2i] }", "{ A[a] -> B[(a)/3] }",
3399 "{ A[a] -> C[(2a)/3] }" },
3400 { "{ B[i,j] -> C[i + j] }", "{ A[a] -> B[a,a] }", "{ A[a] -> C[2a] }"},
3401 { "{ B[a] -> C[a,a] }", "{ A[i,j] -> B[i + j] }",
3402 "{ A[i,j] -> C[i + j, i + j] }"},
3403 { "{ B[i] -> C[([i/2])] }", "{ B[5] }", "{ C[2] }" },
3404 { "[n] -> { B[i,j] -> C[([i/2]) + 2j] }",
3405 "[n] -> { B[n,[n/3]] }", "[n] -> { C[([n/2]) + 2*[n/3]] }", },
3408 static int test_pullback(isl_ctx
*ctx
)
3411 isl_multi_aff
*ma1
, *ma2
;
3415 for (i
= 0; i
< ARRAY_SIZE(pullback_tests
); ++i
) {
3416 ma1
= isl_multi_aff_read_from_str(ctx
, pullback_tests
[i
].ma1
);
3417 ma
= isl_multi_aff_read_from_str(ctx
, pullback_tests
[i
].ma
);
3418 ma2
= isl_multi_aff_read_from_str(ctx
, pullback_tests
[i
].res
);
3419 ma1
= isl_multi_aff_pullback_multi_aff(ma1
, ma
);
3420 equal
= isl_multi_aff_plain_is_equal(ma1
, ma2
);
3421 isl_multi_aff_free(ma1
);
3422 isl_multi_aff_free(ma2
);
3426 isl_die(ctx
, isl_error_unknown
, "bad pullback",
3433 /* Check that negation is printed correctly.
3435 static int test_ast(isl_ctx
*ctx
)
3437 isl_ast_expr
*expr
, *expr1
, *expr2
, *expr3
;
3441 expr1
= isl_ast_expr_from_id(isl_id_alloc(ctx
, "A", NULL
));
3442 expr2
= isl_ast_expr_from_id(isl_id_alloc(ctx
, "B", NULL
));
3443 expr
= isl_ast_expr_add(expr1
, expr2
);
3444 expr
= isl_ast_expr_neg(expr
);
3445 str
= isl_ast_expr_to_str(expr
);
3446 ok
= str
? !strcmp(str
, "-(A + B)") : -1;
3448 isl_ast_expr_free(expr
);
3453 isl_die(ctx
, isl_error_unknown
,
3454 "isl_ast_expr printed incorrectly", return -1);
3456 expr1
= isl_ast_expr_from_id(isl_id_alloc(ctx
, "A", NULL
));
3457 expr2
= isl_ast_expr_from_id(isl_id_alloc(ctx
, "B", NULL
));
3458 expr
= isl_ast_expr_add(expr1
, expr2
);
3459 expr3
= isl_ast_expr_from_id(isl_id_alloc(ctx
, "C", NULL
));
3460 expr
= isl_ast_expr_sub(expr3
, expr
);
3461 str
= isl_ast_expr_to_str(expr
);
3462 ok
= str
? !strcmp(str
, "C - (A + B)") : -1;
3464 isl_ast_expr_free(expr
);
3469 isl_die(ctx
, isl_error_unknown
,
3470 "isl_ast_expr printed incorrectly", return -1);
3475 /* Internal data structure for before_for and after_for callbacks.
3477 * depth is the current depth
3478 * before is the number of times before_for has been called
3479 * after is the number of times after_for has been called
3481 struct isl_test_codegen_data
{
3487 /* This function is called before each for loop in the AST generated
3488 * from test_ast_gen1.
3490 * Increment the number of calls and the depth.
3491 * Check that the space returned by isl_ast_build_get_schedule_space
3492 * matches the target space of the schedule returned by
3493 * isl_ast_build_get_schedule.
3494 * Return an isl_id that is checked by the corresponding call
3497 static __isl_give isl_id
*before_for(__isl_keep isl_ast_build
*build
,
3500 struct isl_test_codegen_data
*data
= user
;
3503 isl_union_map
*schedule
;
3504 isl_union_set
*uset
;
3509 ctx
= isl_ast_build_get_ctx(build
);
3511 if (data
->before
>= 3)
3512 isl_die(ctx
, isl_error_unknown
,
3513 "unexpected number of for nodes", return NULL
);
3514 if (data
->depth
>= 2)
3515 isl_die(ctx
, isl_error_unknown
,
3516 "unexpected depth", return NULL
);
3518 snprintf(name
, sizeof(name
), "d%d", data
->depth
);
3522 schedule
= isl_ast_build_get_schedule(build
);
3523 uset
= isl_union_map_range(schedule
);
3526 if (isl_union_set_n_set(uset
) != 1) {
3527 isl_union_set_free(uset
);
3528 isl_die(ctx
, isl_error_unknown
,
3529 "expecting single range space", return NULL
);
3532 space
= isl_ast_build_get_schedule_space(build
);
3533 set
= isl_union_set_extract_set(uset
, space
);
3534 isl_union_set_free(uset
);
3535 empty
= isl_set_is_empty(set
);
3541 isl_die(ctx
, isl_error_unknown
,
3542 "spaces don't match", return NULL
);
3544 return isl_id_alloc(ctx
, name
, NULL
);
3547 /* This function is called after each for loop in the AST generated
3548 * from test_ast_gen1.
3550 * Increment the number of calls and decrement the depth.
3551 * Check that the annotation attached to the node matches
3552 * the isl_id returned by the corresponding call to before_for.
3554 static __isl_give isl_ast_node
*after_for(__isl_take isl_ast_node
*node
,
3555 __isl_keep isl_ast_build
*build
, void *user
)
3557 struct isl_test_codegen_data
*data
= user
;
3565 if (data
->after
> data
->before
)
3566 isl_die(isl_ast_node_get_ctx(node
), isl_error_unknown
,
3567 "mismatch in number of for nodes",
3568 return isl_ast_node_free(node
));
3570 id
= isl_ast_node_get_annotation(node
);
3572 isl_die(isl_ast_node_get_ctx(node
), isl_error_unknown
,
3573 "missing annotation", return isl_ast_node_free(node
));
3575 name
= isl_id_get_name(id
);
3576 valid
= name
&& atoi(name
+ 1) == data
->depth
;
3580 isl_die(isl_ast_node_get_ctx(node
), isl_error_unknown
,
3581 "wrong annotation", return isl_ast_node_free(node
));
3586 /* Check that the before_each_for and after_each_for callbacks
3587 * are called for each for loop in the generated code,
3588 * that they are called in the right order and that the isl_id
3589 * returned from the before_each_for callback is attached to
3590 * the isl_ast_node passed to the corresponding after_each_for call.
3592 static int test_ast_gen1(isl_ctx
*ctx
)
3596 isl_union_map
*schedule
;
3597 isl_ast_build
*build
;
3599 struct isl_test_codegen_data data
;
3601 str
= "[N] -> { : N >= 10 }";
3602 set
= isl_set_read_from_str(ctx
, str
);
3603 str
= "[N] -> { A[i,j] -> S[8,i,3,j] : 0 <= i,j <= N; "
3604 "B[i,j] -> S[8,j,9,i] : 0 <= i,j <= N }";
3605 schedule
= isl_union_map_read_from_str(ctx
, str
);
3610 build
= isl_ast_build_from_context(set
);
3611 build
= isl_ast_build_set_before_each_for(build
,
3612 &before_for
, &data
);
3613 build
= isl_ast_build_set_after_each_for(build
,
3615 tree
= isl_ast_build_ast_from_schedule(build
, schedule
);
3616 isl_ast_build_free(build
);
3620 isl_ast_node_free(tree
);
3622 if (data
.before
!= 3 || data
.after
!= 3)
3623 isl_die(ctx
, isl_error_unknown
,
3624 "unexpected number of for nodes", return -1);
3629 /* Check that the AST generator handles domains that are integrally disjoint
3630 * but not ratinoally disjoint.
3632 static int test_ast_gen2(isl_ctx
*ctx
)
3636 isl_union_map
*schedule
;
3637 isl_union_map
*options
;
3638 isl_ast_build
*build
;
3641 str
= "{ A[i,j] -> [i,j] : 0 <= i,j <= 1 }";
3642 schedule
= isl_union_map_read_from_str(ctx
, str
);
3643 set
= isl_set_universe(isl_space_params_alloc(ctx
, 0));
3644 build
= isl_ast_build_from_context(set
);
3646 str
= "{ [i,j] -> atomic[1] : i + j = 1; [i,j] -> unroll[1] : i = j }";
3647 options
= isl_union_map_read_from_str(ctx
, str
);
3648 build
= isl_ast_build_set_options(build
, options
);
3649 tree
= isl_ast_build_ast_from_schedule(build
, schedule
);
3650 isl_ast_build_free(build
);
3653 isl_ast_node_free(tree
);
3658 /* Increment *user on each call.
3660 static __isl_give isl_ast_node
*count_domains(__isl_take isl_ast_node
*node
,
3661 __isl_keep isl_ast_build
*build
, void *user
)
3670 /* Test that unrolling tries to minimize the number of instances.
3671 * In particular, for the schedule given below, make sure it generates
3672 * 3 nodes (rather than 101).
3674 static int test_ast_gen3(isl_ctx
*ctx
)
3678 isl_union_map
*schedule
;
3679 isl_union_map
*options
;
3680 isl_ast_build
*build
;
3684 str
= "[n] -> { A[i] -> [i] : 0 <= i <= 100 and n <= i <= n + 2 }";
3685 schedule
= isl_union_map_read_from_str(ctx
, str
);
3686 set
= isl_set_universe(isl_space_params_alloc(ctx
, 0));
3688 str
= "{ [i] -> unroll[0] }";
3689 options
= isl_union_map_read_from_str(ctx
, str
);
3691 build
= isl_ast_build_from_context(set
);
3692 build
= isl_ast_build_set_options(build
, options
);
3693 build
= isl_ast_build_set_at_each_domain(build
,
3694 &count_domains
, &n_domain
);
3695 tree
= isl_ast_build_ast_from_schedule(build
, schedule
);
3696 isl_ast_build_free(build
);
3700 isl_ast_node_free(tree
);
3703 isl_die(ctx
, isl_error_unknown
,
3704 "unexpected number of for nodes", return -1);
3709 /* Check that if the ast_build_exploit_nested_bounds options is set,
3710 * we do not get an outer if node in the generated AST,
3711 * while we do get such an outer if node if the options is not set.
3713 static int test_ast_gen4(isl_ctx
*ctx
)
3717 isl_union_map
*schedule
;
3718 isl_ast_build
*build
;
3720 enum isl_ast_node_type type
;
3723 enb
= isl_options_get_ast_build_exploit_nested_bounds(ctx
);
3724 str
= "[N,M] -> { A[i,j] -> [i,j] : 0 <= i <= N and 0 <= j <= M }";
3726 isl_options_set_ast_build_exploit_nested_bounds(ctx
, 1);
3728 schedule
= isl_union_map_read_from_str(ctx
, str
);
3729 set
= isl_set_universe(isl_space_params_alloc(ctx
, 0));
3730 build
= isl_ast_build_from_context(set
);
3731 tree
= isl_ast_build_ast_from_schedule(build
, schedule
);
3732 isl_ast_build_free(build
);
3736 type
= isl_ast_node_get_type(tree
);
3737 isl_ast_node_free(tree
);
3739 if (type
== isl_ast_node_if
)
3740 isl_die(ctx
, isl_error_unknown
,
3741 "not expecting if node", return -1);
3743 isl_options_set_ast_build_exploit_nested_bounds(ctx
, 0);
3745 schedule
= isl_union_map_read_from_str(ctx
, str
);
3746 set
= isl_set_universe(isl_space_params_alloc(ctx
, 0));
3747 build
= isl_ast_build_from_context(set
);
3748 tree
= isl_ast_build_ast_from_schedule(build
, schedule
);
3749 isl_ast_build_free(build
);
3753 type
= isl_ast_node_get_type(tree
);
3754 isl_ast_node_free(tree
);
3756 if (type
!= isl_ast_node_if
)
3757 isl_die(ctx
, isl_error_unknown
,
3758 "expecting if node", return -1);
3760 isl_options_set_ast_build_exploit_nested_bounds(ctx
, enb
);
3765 static int test_ast_gen(isl_ctx
*ctx
)
3767 if (test_ast_gen1(ctx
) < 0)
3769 if (test_ast_gen2(ctx
) < 0)
3771 if (test_ast_gen3(ctx
) < 0)
3773 if (test_ast_gen4(ctx
) < 0)
3778 /* Check if dropping output dimensions from an isl_pw_multi_aff
3781 static int test_pw_multi_aff(isl_ctx
*ctx
)
3784 isl_pw_multi_aff
*pma1
, *pma2
;
3787 str
= "{ [i,j] -> [i+j, 4i-j] }";
3788 pma1
= isl_pw_multi_aff_read_from_str(ctx
, str
);
3789 str
= "{ [i,j] -> [4i-j] }";
3790 pma2
= isl_pw_multi_aff_read_from_str(ctx
, str
);
3792 pma1
= isl_pw_multi_aff_drop_dims(pma1
, isl_dim_out
, 0, 1);
3794 equal
= isl_pw_multi_aff_plain_is_equal(pma1
, pma2
);
3796 isl_pw_multi_aff_free(pma1
);
3797 isl_pw_multi_aff_free(pma2
);
3801 isl_die(ctx
, isl_error_unknown
,
3802 "expressions not equal", return -1);
3809 int (*fn
)(isl_ctx
*ctx
);
3811 { "curry", &test_curry
},
3812 { "piecewise multi affine expressions", &test_pw_multi_aff
},
3813 { "conversion", &test_conversion
},
3814 { "list", &test_list
},
3815 { "align parameters", &test_align_parameters
},
3816 { "preimage", &test_preimage
},
3817 { "pullback", &test_pullback
},
3818 { "AST", &test_ast
},
3819 { "AST generation", &test_ast_gen
},
3820 { "eliminate", &test_eliminate
},
3821 { "residue class", &test_residue_class
},
3822 { "div", &test_div
},
3823 { "slice", &test_slice
},
3824 { "fixed power", &test_fixed_power
},
3825 { "sample", &test_sample
},
3826 { "output", &test_output
},
3827 { "vertices", &test_vertices
},
3828 { "fixed", &test_fixed
},
3829 { "equal", &test_equal
},
3830 { "product", &test_product
},
3831 { "dim_max", &test_dim_max
},
3832 { "affine", &test_aff
},
3833 { "injective", &test_injective
},
3834 { "schedule", &test_schedule
},
3835 { "union_pw", &test_union_pw
},
3836 { "parse", &test_parse
},
3837 { "single-valued", &test_sv
},
3838 { "affine hull", &test_affine_hull
},
3839 { "coalesce", &test_coalesce
},
3840 { "factorize", &test_factorize
},
3841 { "subset", &test_subset
},
3842 { "subtract", &test_subtract
},
3848 struct isl_ctx
*ctx
;
3850 srcdir
= getenv("srcdir");
3853 ctx
= isl_ctx_alloc();
3854 for (i
= 0; i
< ARRAY_SIZE(tests
); ++i
) {
3855 printf("%s\n", tests
[i
].name
);
3856 if (tests
[i
].fn(ctx
) < 0)
3862 test_split_periods(ctx
);
3865 test_bijective(ctx
);
3869 test_construction(ctx
);
3871 test_application(ctx
);
3872 test_convex_hull(ctx
);