2 * Copyright 2008-2009 Katholieke Universiteit Leuven
4 * Use of this software is governed by the GNU LGPLv2.1 license
6 * Written by Sven Verdoolaege, K.U.Leuven, Departement
7 * Computerwetenschappen, Celestijnenlaan 200A, B-3001 Leuven, Belgium
13 #include <isl_map_private.h>
17 #include <isl/constraint.h>
18 #include <isl/polynomial.h>
19 #include <isl/union_map.h>
20 #include <isl_factorization.h>
24 void test_parse_map(isl_ctx *ctx, const char *str)
28 map = isl_map_read_from_str(ctx, str, -1);
33 void test_parse_pwqp(isl_ctx *ctx, const char *str)
35 isl_pw_qpolynomial *pwqp;
37 pwqp = isl_pw_qpolynomial_read_from_str(ctx, str);
39 isl_pw_qpolynomial_free(pwqp);
42 void test_parse(struct isl_ctx *ctx)
47 str = "{ [i] -> [-i] }";
48 map = isl_map_read_from_str(ctx, str, -1);
52 str = "{ A[i] -> L[([i/3])] }";
53 map = isl_map_read_from_str(ctx, str, -1);
57 test_parse_map(ctx, "{[[s] -> A[i]] -> [[s+1] -> A[i]]}");
58 test_parse_map(ctx, "{ [p1, y1, y2] -> [2, y1, y2] : "
59 "p1 = 1 && (y1 <= y2 || y2 = 0) }");
61 str = "{[new,old] -> [new+1-2*[(new+1)/2],old+1-2*[(old+1)/2]]}";
62 map = isl_map_read_from_str(ctx, str, -1);
63 str = "{ [new, old] -> [o0, o1] : "
64 "exists (e0 = [(-1 - new + o0)/2], e1 = [(-1 - old + o1)/2]: "
65 "2e0 = -1 - new + o0 and 2e1 = -1 - old + o1 and o0 >= 0 and "
66 "o0 <= 1 and o1 >= 0 and o1 <= 1) }";
67 map2 = isl_map_read_from_str(ctx, str, -1);
68 assert(isl_map_is_equal(map, map2));
72 str = "{[new,old] -> [new+1-2*[(new+1)/2],old+1-2*[(old+1)/2]]}";
73 map = isl_map_read_from_str(ctx, str, -1);
74 str = "{[new,old] -> [(new+1)%2,(old+1)%2]}";
75 map2 = isl_map_read_from_str(ctx, str, -1);
76 assert(isl_map_is_equal(map, map2));
80 test_parse_pwqp(ctx, "{ [i] -> i + [ (i + [i/3])/2 ] }");
83 void test_read(struct isl_ctx *ctx)
85 char filename[PATH_MAX];
88 struct isl_basic_set *bset1, *bset2;
89 const char *str = "{[y]: Exists ( alpha : 2alpha = y)}";
91 n = snprintf(filename, sizeof(filename),
92 "%s/test_inputs/set.omega", srcdir);
93 assert(n < sizeof(filename));
94 input = fopen(filename, "r");
97 bset1 = isl_basic_set_read_from_file(ctx, input, 0);
98 bset2 = isl_basic_set_read_from_str(ctx, str, 0);
100 assert(isl_basic_set_is_equal(bset1, bset2) == 1);
102 isl_basic_set_free(bset1);
103 isl_basic_set_free(bset2);
108 void test_bounded(struct isl_ctx *ctx)
113 set = isl_set_read_from_str(ctx, "[n] -> {[i] : 0 <= i <= n }", -1);
114 bounded = isl_set_is_bounded(set);
118 set = isl_set_read_from_str(ctx, "{[n, i] : 0 <= i <= n }", -1);
119 bounded = isl_set_is_bounded(set);
123 set = isl_set_read_from_str(ctx, "[n] -> {[i] : i <= n }", -1);
124 bounded = isl_set_is_bounded(set);
129 /* Construct the basic set { [i] : 5 <= i <= N } */
130 void test_construction(struct isl_ctx *ctx)
134 struct isl_basic_set *bset;
135 struct isl_constraint *c;
139 dim = isl_dim_set_alloc(ctx, 1, 1);
140 bset = isl_basic_set_universe(dim);
142 c = isl_inequality_alloc(isl_basic_set_get_dim(bset));
143 isl_int_set_si(v, -1);
144 isl_constraint_set_coefficient(c, isl_dim_set, 0, v);
145 isl_int_set_si(v, 1);
146 isl_constraint_set_coefficient(c, isl_dim_param, 0, v);
147 bset = isl_basic_set_add_constraint(bset, c);
149 c = isl_inequality_alloc(isl_basic_set_get_dim(bset));
150 isl_int_set_si(v, 1);
151 isl_constraint_set_coefficient(c, isl_dim_set, 0, v);
152 isl_int_set_si(v, -5);
153 isl_constraint_set_constant(c, v);
154 bset = isl_basic_set_add_constraint(bset, c);
156 isl_basic_set_free(bset);
161 void test_dim(struct isl_ctx *ctx)
164 isl_map *map1, *map2;
166 map1 = isl_map_read_from_str(ctx,
167 "[n] -> { [i] -> [j] : exists (a = [i/10] : i - 10a <= n ) }", -1);
168 map1 = isl_map_add_dims(map1, isl_dim_in, 1);
169 map2 = isl_map_read_from_str(ctx,
170 "[n] -> { [i,k] -> [j] : exists (a = [i/10] : i - 10a <= n ) }", -1);
171 assert(isl_map_is_equal(map1, map2));
174 map1 = isl_map_project_out(map1, isl_dim_in, 0, 1);
175 map2 = isl_map_read_from_str(ctx, "[n] -> { [i] -> [j] : n >= 0 }", -1);
176 assert(isl_map_is_equal(map1, map2));
181 str = "[n] -> { [i] -> [] : exists a : 0 <= i <= n and i = 2 a }";
182 map1 = isl_map_read_from_str(ctx, str, -1);
183 str = "{ [i] -> [j] : exists a : 0 <= i <= j and i = 2 a }";
184 map2 = isl_map_read_from_str(ctx, str, -1);
185 map1 = isl_map_move_dims(map1, isl_dim_out, 0, isl_dim_param, 0, 1);
186 assert(isl_map_is_equal(map1, map2));
192 void test_div(struct isl_ctx *ctx)
198 struct isl_basic_set *bset;
199 struct isl_constraint *c;
204 dim = isl_dim_set_alloc(ctx, 0, 1);
205 bset = isl_basic_set_universe(dim);
207 c = isl_equality_alloc(isl_basic_set_get_dim(bset));
208 isl_int_set_si(v, -1);
209 isl_constraint_set_constant(c, v);
210 isl_int_set_si(v, 1);
211 isl_constraint_set_coefficient(c, isl_dim_set, 0, v);
212 div = isl_div_alloc(isl_basic_set_get_dim(bset));
213 c = isl_constraint_add_div(c, div, &pos);
214 isl_int_set_si(v, 3);
215 isl_constraint_set_coefficient(c, isl_dim_div, pos, v);
216 bset = isl_basic_set_add_constraint(bset, c);
218 c = isl_equality_alloc(isl_basic_set_get_dim(bset));
219 isl_int_set_si(v, 1);
220 isl_constraint_set_constant(c, v);
221 isl_int_set_si(v, -1);
222 isl_constraint_set_coefficient(c, isl_dim_set, 0, v);
223 div = isl_div_alloc(isl_basic_set_get_dim(bset));
224 c = isl_constraint_add_div(c, div, &pos);
225 isl_int_set_si(v, 3);
226 isl_constraint_set_coefficient(c, isl_dim_div, pos, v);
227 bset = isl_basic_set_add_constraint(bset, c);
229 assert(bset && bset->n_div == 1);
230 isl_basic_set_free(bset);
233 dim = isl_dim_set_alloc(ctx, 0, 1);
234 bset = isl_basic_set_universe(dim);
236 c = isl_equality_alloc(isl_basic_set_get_dim(bset));
237 isl_int_set_si(v, 1);
238 isl_constraint_set_constant(c, v);
239 isl_int_set_si(v, -1);
240 isl_constraint_set_coefficient(c, isl_dim_set, 0, v);
241 div = isl_div_alloc(isl_basic_set_get_dim(bset));
242 c = isl_constraint_add_div(c, div, &pos);
243 isl_int_set_si(v, 3);
244 isl_constraint_set_coefficient(c, isl_dim_div, pos, v);
245 bset = isl_basic_set_add_constraint(bset, c);
247 c = isl_equality_alloc(isl_basic_set_get_dim(bset));
248 isl_int_set_si(v, -1);
249 isl_constraint_set_constant(c, v);
250 isl_int_set_si(v, 1);
251 isl_constraint_set_coefficient(c, isl_dim_set, 0, v);
252 div = isl_div_alloc(isl_basic_set_get_dim(bset));
253 c = isl_constraint_add_div(c, div, &pos);
254 isl_int_set_si(v, 3);
255 isl_constraint_set_coefficient(c, isl_dim_div, pos, v);
256 bset = isl_basic_set_add_constraint(bset, c);
258 assert(bset && bset->n_div == 1);
259 isl_basic_set_free(bset);
262 dim = isl_dim_set_alloc(ctx, 0, 1);
263 bset = isl_basic_set_universe(dim);
265 c = isl_equality_alloc(isl_basic_set_get_dim(bset));
266 isl_int_set_si(v, 1);
267 isl_constraint_set_constant(c, v);
268 isl_int_set_si(v, -1);
269 isl_constraint_set_coefficient(c, isl_dim_set, 0, v);
270 div = isl_div_alloc(isl_basic_set_get_dim(bset));
271 c = isl_constraint_add_div(c, div, &pos);
272 isl_int_set_si(v, 3);
273 isl_constraint_set_coefficient(c, isl_dim_div, pos, v);
274 bset = isl_basic_set_add_constraint(bset, c);
276 c = isl_equality_alloc(isl_basic_set_get_dim(bset));
277 isl_int_set_si(v, -3);
278 isl_constraint_set_constant(c, v);
279 isl_int_set_si(v, 1);
280 isl_constraint_set_coefficient(c, isl_dim_set, 0, v);
281 div = isl_div_alloc(isl_basic_set_get_dim(bset));
282 c = isl_constraint_add_div(c, div, &pos);
283 isl_int_set_si(v, 4);
284 isl_constraint_set_coefficient(c, isl_dim_div, pos, v);
285 bset = isl_basic_set_add_constraint(bset, c);
287 assert(bset && bset->n_div == 1);
288 isl_basic_set_free(bset);
291 dim = isl_dim_set_alloc(ctx, 0, 1);
292 bset = isl_basic_set_universe(dim);
294 c = isl_equality_alloc(isl_basic_set_get_dim(bset));
295 isl_int_set_si(v, 2);
296 isl_constraint_set_constant(c, v);
297 isl_int_set_si(v, -1);
298 isl_constraint_set_coefficient(c, isl_dim_set, 0, v);
299 div = isl_div_alloc(isl_basic_set_get_dim(bset));
300 c = isl_constraint_add_div(c, div, &pos);
301 isl_int_set_si(v, 3);
302 isl_constraint_set_coefficient(c, isl_dim_div, pos, v);
303 bset = isl_basic_set_add_constraint(bset, c);
305 c = isl_equality_alloc(isl_basic_set_get_dim(bset));
306 isl_int_set_si(v, -1);
307 isl_constraint_set_constant(c, v);
308 isl_int_set_si(v, 1);
309 isl_constraint_set_coefficient(c, isl_dim_set, 0, v);
310 div = isl_div_alloc(isl_basic_set_get_dim(bset));
311 c = isl_constraint_add_div(c, div, &pos);
312 isl_int_set_si(v, 6);
313 isl_constraint_set_coefficient(c, isl_dim_div, pos, v);
314 bset = isl_basic_set_add_constraint(bset, c);
316 assert(isl_basic_set_is_empty(bset));
317 isl_basic_set_free(bset);
320 dim = isl_dim_set_alloc(ctx, 0, 2);
321 bset = isl_basic_set_universe(dim);
323 c = isl_equality_alloc(isl_basic_set_get_dim(bset));
324 isl_int_set_si(v, -1);
325 isl_constraint_set_coefficient(c, isl_dim_set, 0, v);
326 div = isl_div_alloc(isl_basic_set_get_dim(bset));
327 c = isl_constraint_add_div(c, div, &pos);
328 isl_int_set_si(v, 3);
329 isl_constraint_set_coefficient(c, isl_dim_div, pos, v);
330 bset = isl_basic_set_add_constraint(bset, c);
332 c = isl_equality_alloc(isl_basic_set_get_dim(bset));
333 isl_int_set_si(v, 1);
334 isl_constraint_set_coefficient(c, isl_dim_set, 0, v);
335 isl_int_set_si(v, -3);
336 isl_constraint_set_coefficient(c, isl_dim_set, 1, v);
337 bset = isl_basic_set_add_constraint(bset, c);
339 assert(bset && bset->n_div == 0);
340 isl_basic_set_free(bset);
343 dim = isl_dim_set_alloc(ctx, 0, 2);
344 bset = isl_basic_set_universe(dim);
346 c = isl_equality_alloc(isl_basic_set_get_dim(bset));
347 isl_int_set_si(v, -1);
348 isl_constraint_set_coefficient(c, isl_dim_set, 0, v);
349 div = isl_div_alloc(isl_basic_set_get_dim(bset));
350 c = isl_constraint_add_div(c, div, &pos);
351 isl_int_set_si(v, 6);
352 isl_constraint_set_coefficient(c, isl_dim_div, pos, v);
353 bset = isl_basic_set_add_constraint(bset, c);
355 c = isl_equality_alloc(isl_basic_set_get_dim(bset));
356 isl_int_set_si(v, 1);
357 isl_constraint_set_coefficient(c, isl_dim_set, 0, v);
358 isl_int_set_si(v, -3);
359 isl_constraint_set_coefficient(c, isl_dim_set, 1, v);
360 bset = isl_basic_set_add_constraint(bset, c);
362 assert(bset && bset->n_div == 1);
363 isl_basic_set_free(bset);
366 /* This test is a bit tricky. We set up an equality
368 * Normalization of divs creates _two_ divs
371 * Afterwards e0 is removed again because it has coefficient -1
372 * and we end up with the original equality and div again.
373 * Perhaps we can avoid the introduction of this temporary div.
375 dim = isl_dim_set_alloc(ctx, 0, 3);
376 bset = isl_basic_set_universe(dim);
378 c = isl_equality_alloc(isl_basic_set_get_dim(bset));
379 isl_int_set_si(v, -1);
380 isl_constraint_set_coefficient(c, isl_dim_set, 0, v);
381 isl_int_set_si(v, -3);
382 isl_constraint_set_coefficient(c, isl_dim_set, 1, v);
383 isl_int_set_si(v, -3);
384 isl_constraint_set_coefficient(c, isl_dim_set, 2, v);
385 div = isl_div_alloc(isl_basic_set_get_dim(bset));
386 c = isl_constraint_add_div(c, div, &pos);
387 isl_int_set_si(v, 6);
388 isl_constraint_set_coefficient(c, isl_dim_div, pos, v);
389 bset = isl_basic_set_add_constraint(bset, c);
391 /* Test disabled for now */
393 assert(bset && bset->n_div == 1);
395 isl_basic_set_free(bset);
398 dim = isl_dim_set_alloc(ctx, 0, 4);
399 bset = isl_basic_set_universe(dim);
401 c = isl_equality_alloc(isl_basic_set_get_dim(bset));
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 isl_int_set_si(v, -3);
407 isl_constraint_set_coefficient(c, isl_dim_set, 3, v);
408 div = isl_div_alloc(isl_basic_set_get_dim(bset));
409 c = isl_constraint_add_div(c, div, &pos);
410 isl_int_set_si(v, 6);
411 isl_constraint_set_coefficient(c, isl_dim_div, pos, v);
412 bset = isl_basic_set_add_constraint(bset, c);
414 c = isl_equality_alloc(isl_basic_set_get_dim(bset));
415 isl_int_set_si(v, -1);
416 isl_constraint_set_coefficient(c, isl_dim_set, 0, v);
417 isl_int_set_si(v, 1);
418 isl_constraint_set_coefficient(c, isl_dim_set, 2, v);
419 isl_int_set_si(v, 1);
420 isl_constraint_set_constant(c, v);
421 bset = isl_basic_set_add_constraint(bset, c);
423 /* Test disabled for now */
425 assert(bset && bset->n_div == 1);
427 isl_basic_set_free(bset);
430 dim = isl_dim_set_alloc(ctx, 0, 2);
431 bset = isl_basic_set_universe(dim);
433 c = isl_equality_alloc(isl_basic_set_get_dim(bset));
434 isl_int_set_si(v, 1);
435 isl_constraint_set_coefficient(c, isl_dim_set, 0, v);
436 isl_int_set_si(v, -1);
437 isl_constraint_set_coefficient(c, isl_dim_set, 1, v);
438 div = isl_div_alloc(isl_basic_set_get_dim(bset));
439 c = isl_constraint_add_div(c, div, &pos);
440 isl_int_set_si(v, -2);
441 isl_constraint_set_coefficient(c, isl_dim_div, pos, v);
442 bset = isl_basic_set_add_constraint(bset, c);
444 c = isl_equality_alloc(isl_basic_set_get_dim(bset));
445 isl_int_set_si(v, -1);
446 isl_constraint_set_coefficient(c, isl_dim_set, 0, v);
447 div = isl_div_alloc(isl_basic_set_get_dim(bset));
448 c = isl_constraint_add_div(c, div, &pos);
449 isl_int_set_si(v, 3);
450 isl_constraint_set_coefficient(c, isl_dim_div, pos, v);
451 isl_int_set_si(v, 2);
452 isl_constraint_set_constant(c, v);
453 bset = isl_basic_set_add_constraint(bset, c);
455 bset = isl_basic_set_fix_si(bset, isl_dim_set, 0, 2);
457 assert(!isl_basic_set_is_empty(bset));
459 isl_basic_set_free(bset);
462 dim = isl_dim_set_alloc(ctx, 0, 2);
463 bset = isl_basic_set_universe(dim);
465 c = isl_equality_alloc(isl_basic_set_get_dim(bset));
466 isl_int_set_si(v, 1);
467 isl_constraint_set_coefficient(c, isl_dim_set, 0, v);
468 div = isl_div_alloc(isl_basic_set_get_dim(bset));
469 c = isl_constraint_add_div(c, div, &pos);
470 isl_int_set_si(v, -2);
471 isl_constraint_set_coefficient(c, isl_dim_div, pos, v);
472 bset = isl_basic_set_add_constraint(bset, c);
474 bset = isl_basic_set_fix_si(bset, isl_dim_set, 0, 2);
476 isl_basic_set_free(bset);
481 void test_application_case(struct isl_ctx *ctx, const char *name)
483 char filename[PATH_MAX];
486 struct isl_basic_set *bset1, *bset2;
487 struct isl_basic_map *bmap;
489 n = snprintf(filename, sizeof(filename),
490 "%s/test_inputs/%s.omega", srcdir, name);
491 assert(n < sizeof(filename));
492 input = fopen(filename, "r");
495 bset1 = isl_basic_set_read_from_file(ctx, input, 0);
496 bmap = isl_basic_map_read_from_file(ctx, input, 0);
498 bset1 = isl_basic_set_apply(bset1, bmap);
500 bset2 = isl_basic_set_read_from_file(ctx, input, 0);
502 assert(isl_basic_set_is_equal(bset1, bset2) == 1);
504 isl_basic_set_free(bset1);
505 isl_basic_set_free(bset2);
510 void test_application(struct isl_ctx *ctx)
512 test_application_case(ctx, "application");
513 test_application_case(ctx, "application2");
516 void test_affine_hull_case(struct isl_ctx *ctx, const char *name)
518 char filename[PATH_MAX];
521 struct isl_basic_set *bset1, *bset2;
523 n = snprintf(filename, sizeof(filename),
524 "%s/test_inputs/%s.polylib", srcdir, name);
525 assert(n < sizeof(filename));
526 input = fopen(filename, "r");
529 bset1 = isl_basic_set_read_from_file(ctx, input, 0);
530 bset2 = isl_basic_set_read_from_file(ctx, input, 0);
532 bset1 = isl_basic_set_affine_hull(bset1);
534 assert(isl_basic_set_is_equal(bset1, bset2) == 1);
536 isl_basic_set_free(bset1);
537 isl_basic_set_free(bset2);
542 void test_affine_hull(struct isl_ctx *ctx)
544 test_affine_hull_case(ctx, "affine2");
545 test_affine_hull_case(ctx, "affine");
546 test_affine_hull_case(ctx, "affine3");
549 void test_convex_hull_case(struct isl_ctx *ctx, const char *name)
551 char filename[PATH_MAX];
554 struct isl_basic_set *bset1, *bset2;
557 n = snprintf(filename, sizeof(filename),
558 "%s/test_inputs/%s.polylib", srcdir, name);
559 assert(n < sizeof(filename));
560 input = fopen(filename, "r");
563 bset1 = isl_basic_set_read_from_file(ctx, input, 0);
564 bset2 = isl_basic_set_read_from_file(ctx, input, 0);
566 set = isl_basic_set_union(bset1, bset2);
567 bset1 = isl_set_convex_hull(set);
569 bset2 = isl_basic_set_read_from_file(ctx, input, 0);
571 assert(isl_basic_set_is_equal(bset1, bset2) == 1);
573 isl_basic_set_free(bset1);
574 isl_basic_set_free(bset2);
579 void test_convex_hull_algo(struct isl_ctx *ctx, int convex)
581 const char *str1, *str2;
582 isl_set *set1, *set2;
583 int orig_convex = ctx->opt->convex;
584 ctx->opt->convex = convex;
586 test_convex_hull_case(ctx, "convex0");
587 test_convex_hull_case(ctx, "convex1");
588 test_convex_hull_case(ctx, "convex2");
589 test_convex_hull_case(ctx, "convex3");
590 test_convex_hull_case(ctx, "convex4");
591 test_convex_hull_case(ctx, "convex5");
592 test_convex_hull_case(ctx, "convex6");
593 test_convex_hull_case(ctx, "convex7");
594 test_convex_hull_case(ctx, "convex8");
595 test_convex_hull_case(ctx, "convex9");
596 test_convex_hull_case(ctx, "convex10");
597 test_convex_hull_case(ctx, "convex11");
598 test_convex_hull_case(ctx, "convex12");
599 test_convex_hull_case(ctx, "convex13");
600 test_convex_hull_case(ctx, "convex14");
601 test_convex_hull_case(ctx, "convex15");
603 str1 = "{ [i0, i1, i2] : (i2 = 1 and i0 = 0 and i1 >= 0) or "
604 "(i0 = 1 and i1 = 0 and i2 = 1) or "
605 "(i0 = 0 and i1 = 0 and i2 = 0) }";
606 str2 = "{ [i0, i1, i2] : i0 >= 0 and i2 >= i0 and i2 <= 1 and i1 >= 0 }";
607 set1 = isl_set_read_from_str(ctx, str1, -1);
608 set2 = isl_set_read_from_str(ctx, str2, -1);
609 set1 = isl_set_from_basic_set(isl_set_convex_hull(set1));
610 assert(isl_set_is_equal(set1, set2));
614 ctx->opt->convex = orig_convex;
617 void test_convex_hull(struct isl_ctx *ctx)
619 test_convex_hull_algo(ctx, ISL_CONVEX_HULL_FM);
620 test_convex_hull_algo(ctx, ISL_CONVEX_HULL_WRAP);
623 void test_gist_case(struct isl_ctx *ctx, const char *name)
625 char filename[PATH_MAX];
628 struct isl_basic_set *bset1, *bset2;
630 n = snprintf(filename, sizeof(filename),
631 "%s/test_inputs/%s.polylib", srcdir, name);
632 assert(n < sizeof(filename));
633 input = fopen(filename, "r");
636 bset1 = isl_basic_set_read_from_file(ctx, input, 0);
637 bset2 = isl_basic_set_read_from_file(ctx, input, 0);
639 bset1 = isl_basic_set_gist(bset1, bset2);
641 bset2 = isl_basic_set_read_from_file(ctx, input, 0);
643 assert(isl_basic_set_is_equal(bset1, bset2) == 1);
645 isl_basic_set_free(bset1);
646 isl_basic_set_free(bset2);
651 void test_gist(struct isl_ctx *ctx)
653 test_gist_case(ctx, "gist1");
656 void test_coalesce_set(isl_ctx *ctx, const char *str, int check_one)
660 set = isl_set_read_from_str(ctx, str, -1);
661 set = isl_set_coalesce(set);
662 set2 = isl_set_read_from_str(ctx, str, -1);
663 assert(isl_set_is_equal(set, set2));
665 assert(set && set->n == 1);
670 void test_coalesce(struct isl_ctx *ctx)
673 struct isl_set *set, *set2;
674 struct isl_map *map, *map2;
676 set = isl_set_read_from_str(ctx,
677 "{[x,y]: x >= 0 & x <= 10 & y >= 0 & y <= 10 or "
678 "y >= x & x >= 2 & 5 >= y }", -1);
679 set = isl_set_coalesce(set);
680 assert(set && set->n == 1);
683 set = isl_set_read_from_str(ctx,
684 "{[x,y]: y >= 0 & 2x + y <= 30 & y <= 10 & x >= 0 or "
685 "x + y >= 10 & y <= x & x + y <= 20 & y >= 0}", -1);
686 set = isl_set_coalesce(set);
687 assert(set && set->n == 1);
690 set = isl_set_read_from_str(ctx,
691 "{[x,y]: y >= 0 & 2x + y <= 30 & y <= 10 & x >= 0 or "
692 "x + y >= 10 & y <= x & x + y <= 19 & y >= 0}", -1);
693 set = isl_set_coalesce(set);
694 assert(set && set->n == 2);
697 set = isl_set_read_from_str(ctx,
698 "{[x,y]: y >= 0 & x <= 5 & y <= x or "
699 "y >= 0 & x >= 6 & x <= 10 & y <= x}", -1);
700 set = isl_set_coalesce(set);
701 assert(set && set->n == 1);
704 set = isl_set_read_from_str(ctx,
705 "{[x,y]: y >= 0 & x <= 5 & y <= x or "
706 "y >= 0 & x >= 7 & x <= 10 & y <= x}", -1);
707 set = isl_set_coalesce(set);
708 assert(set && set->n == 2);
711 set = isl_set_read_from_str(ctx,
712 "{[x,y]: y >= 0 & x <= 5 & y <= x or "
713 "y >= 0 & x >= 6 & x <= 10 & y + 1 <= x}", -1);
714 set = isl_set_coalesce(set);
715 assert(set && set->n == 2);
718 set = isl_set_read_from_str(ctx,
719 "{[x,y]: y >= 0 & x <= 5 & y <= x or "
720 "y >= 0 & x = 6 & y <= 6}", -1);
721 set = isl_set_coalesce(set);
722 assert(set && set->n == 1);
725 set = isl_set_read_from_str(ctx,
726 "{[x,y]: y >= 0 & x <= 5 & y <= x or "
727 "y >= 0 & x = 7 & y <= 6}", -1);
728 set = isl_set_coalesce(set);
729 assert(set && set->n == 2);
732 set = isl_set_read_from_str(ctx,
733 "{[x,y]: y >= 0 & x <= 5 & y <= x or "
734 "y >= 0 & x = 6 & y <= 5}", -1);
735 set = isl_set_coalesce(set);
736 assert(set && set->n == 1);
737 set2 = isl_set_read_from_str(ctx,
738 "{[x,y]: y >= 0 & x <= 5 & y <= x or "
739 "y >= 0 & x = 6 & y <= 5}", -1);
740 assert(isl_set_is_equal(set, set2));
744 set = isl_set_read_from_str(ctx,
745 "{[x,y]: y >= 0 & x <= 5 & y <= x or "
746 "y >= 0 & x = 6 & y <= 7}", -1);
747 set = isl_set_coalesce(set);
748 assert(set && set->n == 2);
751 set = isl_set_read_from_str(ctx,
752 "[n] -> { [i] : i = 1 and n >= 2 or 2 <= i and i <= n }", -1);
753 set = isl_set_coalesce(set);
754 assert(set && set->n == 1);
755 set2 = isl_set_read_from_str(ctx,
756 "[n] -> { [i] : i = 1 and n >= 2 or 2 <= i and i <= n }", -1);
757 assert(isl_set_is_equal(set, set2));
761 set = isl_set_read_from_str(ctx,
762 "{[x,y] : x >= 0 and y >= 0 or 0 <= y and y <= 5 and x = -1}", -1);
763 set = isl_set_coalesce(set);
764 set2 = isl_set_read_from_str(ctx,
765 "{[x,y] : x >= 0 and y >= 0 or 0 <= y and y <= 5 and x = -1}", -1);
766 assert(isl_set_is_equal(set, set2));
770 set = isl_set_read_from_str(ctx,
771 "[n] -> { [i] : 1 <= i and i <= n - 1 or "
772 "2 <= i and i <= n }", -1);
773 set = isl_set_coalesce(set);
774 assert(set && set->n == 1);
775 set2 = isl_set_read_from_str(ctx,
776 "[n] -> { [i] : 1 <= i and i <= n - 1 or "
777 "2 <= i and i <= n }", -1);
778 assert(isl_set_is_equal(set, set2));
782 map = isl_map_read_from_str(ctx,
783 "[n] -> { [i0] -> [o0] : exists (e0 = [(i0)/4], e1 = [(o0)/4], "
784 "e2 = [(n)/2], e3 = [(-2 + i0)/4], e4 = [(-2 + o0)/4], "
785 "e5 = [(-2n + i0)/4]: 2e2 = n and 4e3 = -2 + i0 and "
786 "4e4 = -2 + o0 and i0 >= 8 + 2n and o0 >= 2 + i0 and "
787 "o0 <= 56 + 2n and o0 <= -12 + 4n and i0 <= 57 + 2n and "
788 "i0 <= -11 + 4n and o0 >= 6 + 2n and 4e0 <= i0 and "
789 "4e0 >= -3 + i0 and 4e1 <= o0 and 4e1 >= -3 + o0 and "
790 "4e5 <= -2n + i0 and 4e5 >= -3 - 2n + i0);"
791 "[i0] -> [o0] : exists (e0 = [(i0)/4], e1 = [(o0)/4], "
792 "e2 = [(n)/2], e3 = [(-2 + i0)/4], e4 = [(-2 + o0)/4], "
793 "e5 = [(-2n + i0)/4]: 2e2 = n and 4e3 = -2 + i0 and "
794 "4e4 = -2 + o0 and 2e0 >= 3 + n and e0 <= -4 + n and "
795 "2e0 <= 27 + n and e1 <= -4 + n and 2e1 <= 27 + n and "
796 "2e1 >= 2 + n and e1 >= 1 + e0 and i0 >= 7 + 2n and "
797 "i0 <= -11 + 4n and i0 <= 57 + 2n and 4e0 <= -2 + i0 and "
798 "4e0 >= -3 + i0 and o0 >= 6 + 2n and o0 <= -11 + 4n and "
799 "o0 <= 57 + 2n and 4e1 <= -2 + o0 and 4e1 >= -3 + o0 and "
800 "4e5 <= -2n + i0 and 4e5 >= -3 - 2n + i0 ) }", -1);
801 map = isl_map_coalesce(map);
802 map2 = isl_map_read_from_str(ctx,
803 "[n] -> { [i0] -> [o0] : exists (e0 = [(i0)/4], e1 = [(o0)/4], "
804 "e2 = [(n)/2], e3 = [(-2 + i0)/4], e4 = [(-2 + o0)/4], "
805 "e5 = [(-2n + i0)/4]: 2e2 = n and 4e3 = -2 + i0 and "
806 "4e4 = -2 + o0 and i0 >= 8 + 2n and o0 >= 2 + i0 and "
807 "o0 <= 56 + 2n and o0 <= -12 + 4n and i0 <= 57 + 2n and "
808 "i0 <= -11 + 4n and o0 >= 6 + 2n and 4e0 <= i0 and "
809 "4e0 >= -3 + i0 and 4e1 <= o0 and 4e1 >= -3 + o0 and "
810 "4e5 <= -2n + i0 and 4e5 >= -3 - 2n + i0);"
811 "[i0] -> [o0] : exists (e0 = [(i0)/4], e1 = [(o0)/4], "
812 "e2 = [(n)/2], e3 = [(-2 + i0)/4], e4 = [(-2 + o0)/4], "
813 "e5 = [(-2n + i0)/4]: 2e2 = n and 4e3 = -2 + i0 and "
814 "4e4 = -2 + o0 and 2e0 >= 3 + n and e0 <= -4 + n and "
815 "2e0 <= 27 + n and e1 <= -4 + n and 2e1 <= 27 + n and "
816 "2e1 >= 2 + n and e1 >= 1 + e0 and i0 >= 7 + 2n and "
817 "i0 <= -11 + 4n and i0 <= 57 + 2n and 4e0 <= -2 + i0 and "
818 "4e0 >= -3 + i0 and o0 >= 6 + 2n and o0 <= -11 + 4n and "
819 "o0 <= 57 + 2n and 4e1 <= -2 + o0 and 4e1 >= -3 + o0 and "
820 "4e5 <= -2n + i0 and 4e5 >= -3 - 2n + i0 ) }", -1);
821 assert(isl_map_is_equal(map, map2));
825 str = "[n, m] -> { [] -> [o0, o2, o3] : (o3 = 1 and o0 >= 1 + m and "
826 "o0 <= n + m and o2 <= m and o0 >= 2 + n and o2 >= 3) or "
827 "(o0 >= 2 + n and o0 >= 1 + m and o0 <= n + m and n >= 1 and "
828 "o3 <= -1 + o2 and o3 >= 1 - m + o2 and o3 >= 2 and o3 <= n) }";
829 map = isl_map_read_from_str(ctx, str, -1);
830 map = isl_map_coalesce(map);
831 map2 = isl_map_read_from_str(ctx, str, -1);
832 assert(isl_map_is_equal(map, map2));
836 str = "[M, N] -> { [i0, i1, i2, i3, i4, i5, i6] -> "
837 "[o0, o1, o2, o3, o4, o5, o6] : "
838 "(o6 <= -4 + 2M - 2N + i0 + i1 - i2 + i6 - o0 - o1 + o2 and "
839 "o3 <= -2 + i3 and o6 >= 2 + i0 + i3 + i6 - o0 - o3 and "
840 "o6 >= 2 - M + N + i3 + i4 + i6 - o3 - o4 and o0 <= -1 + i0 and "
841 "o4 >= 4 - 3M + 3N - i0 - i1 + i2 + 2i3 + i4 + o0 + o1 - o2 - 2o3 "
842 "and o6 <= -3 + 2M - 2N + i3 + i4 - i5 + i6 - o3 - o4 + o5 and "
843 "2o6 <= -5 + 5M - 5N + 2i0 + i1 - i2 - i5 + 2i6 - 2o0 - o1 + o2 + o5 "
844 "and o6 >= 2i0 + i1 + i6 - 2o0 - o1 and "
845 "3o6 <= -5 + 4M - 4N + 2i0 + i1 - i2 + 2i3 + i4 - i5 + 3i6 "
846 "- 2o0 - o1 + o2 - 2o3 - o4 + o5) or "
847 "(N >= 2 and o3 <= -1 + i3 and o0 <= -1 + i0 and "
848 "o6 >= i3 + i6 - o3 and M >= 0 and "
849 "2o6 >= 1 + i0 + i3 + 2i6 - o0 - o3 and "
850 "o6 >= 1 - M + i0 + i6 - o0 and N >= 2M and o6 >= i0 + i6 - o0) }";
851 map = isl_map_read_from_str(ctx, str, -1);
852 map = isl_map_coalesce(map);
853 map2 = isl_map_read_from_str(ctx, str, -1);
854 assert(isl_map_is_equal(map, map2));
858 str = "[M, N] -> { [] -> [o0] : (o0 = 0 and M >= 1 and N >= 2) or "
859 "(o0 = 0 and M >= 1 and N >= 2M and N >= 2 + M) or "
860 "(o0 = 0 and M >= 2 and N >= 3) or "
861 "(M = 0 and o0 = 0 and N >= 3) }";
862 map = isl_map_read_from_str(ctx, str, -1);
863 map = isl_map_coalesce(map);
864 map2 = isl_map_read_from_str(ctx, str, -1);
865 assert(isl_map_is_equal(map, map2));
869 str = "{ [i0, i1, i2, i3] : (i1 = 10i0 and i0 >= 1 and 10i0 <= 100 and "
870 "i3 <= 9 + 10 i2 and i3 >= 1 + 10i2 and i3 >= 0) or "
871 "(i1 <= 9 + 10i0 and i1 >= 1 + 10i0 and i2 >= 0 and "
872 "i0 >= 0 and i1 <= 100 and i3 <= 9 + 10i2 and i3 >= 1 + 10i2) }";
873 map = isl_map_read_from_str(ctx, str, -1);
874 map = isl_map_coalesce(map);
875 map2 = isl_map_read_from_str(ctx, str, -1);
876 assert(isl_map_is_equal(map, map2));
880 test_coalesce_set(ctx,
881 "[M] -> { [i1] : (i1 >= 2 and i1 <= M) or "
882 "(i1 = M and M >= 1) }", 0);
883 test_coalesce_set(ctx,
884 "{[x,y] : x,y >= 0; [x,y] : 10 <= x <= 20 and y >= -1 }", 0);
885 test_coalesce_set(ctx,
886 "{ [x, y] : (x >= 1 and y >= 1 and x <= 2 and y <= 2) or "
887 "(y = 3 and x = 1) }", 1);
888 test_coalesce_set(ctx,
889 "[M] -> { [i0, i1, i2, i3, i4] : (i1 >= 3 and i4 >= 2 + i2 and "
890 "i2 >= 2 and i0 >= 2 and i3 >= 1 + i2 and i0 <= M and "
891 "i1 <= M and i3 <= M and i4 <= M) or "
892 "(i1 >= 2 and i4 >= 1 + i2 and i2 >= 2 and i0 >= 2 and "
893 "i3 >= 1 + i2 and i0 <= M and i1 <= -1 + M and i3 <= M and "
894 "i4 <= -1 + M) }", 1);
895 test_coalesce_set(ctx,
896 "{ [x, y] : (x >= 0 and y >= 0 and x <= 10 and y <= 10) or "
897 "(x >= 1 and y >= 1 and x <= 11 and y <= 11) }", 1);
898 test_coalesce_set(ctx,
899 "{[x,y,z] : y + 2 >= 0 and x - y + 1 >= 0 and "
900 "-x - y + 1 >= 0 and -3 <= z <= 3;"
901 "[x,y,z] : -x+z + 20 >= 0 and -x-z + 20 >= 0 and "
902 "x-z + 20 >= 0 and x+z + 20 >= 0 and -10 <= y <= 0}", 1);
903 test_coalesce_set(ctx,
904 "{[x,y] : 0 <= x,y <= 10; [5,y]: 4 <=y <= 11}", 1);
905 test_coalesce_set(ctx, "{[x,0] : x >= 0; [x,1] : x <= 20}", 0);
906 test_coalesce_set(ctx,
907 "{[x,0,0] : -5 <= x <= 5; [0,y,1] : -5 <= y <= 5 }", 1);
908 test_coalesce_set(ctx, "{ [x, 1 - x] : 0 <= x <= 1; [0,0] }", 1);
909 test_coalesce_set(ctx, "{ [0,0]; [i,i] : 1 <= i <= 10 }", 1);
910 test_coalesce_set(ctx, "{ [0,0]; [i,j] : 1 <= i,j <= 10 }", 0);
913 void test_closure(struct isl_ctx *ctx)
921 /* COCOA example 1 */
922 map = isl_map_read_from_str(ctx,
923 "[n,k] -> { [i,j] -> [i2,j2] : i2 = i + 1 and j2 = j + 1 and "
924 "1 <= i and i < n and 1 <= j and j < n or "
925 "i2 = i + 1 and j2 = j - 1 and "
926 "1 <= i and i < n and 2 <= j and j <= n }", -1);
927 map = isl_map_power(map, 1, &exact);
931 /* COCOA example 1 */
932 map = isl_map_read_from_str(ctx,
933 "[n] -> { [i,j] -> [i2,j2] : i2 = i + 1 and j2 = j + 1 and "
934 "1 <= i and i < n and 1 <= j and j < n or "
935 "i2 = i + 1 and j2 = j - 1 and "
936 "1 <= i and i < n and 2 <= j and j <= n }", -1);
937 map = isl_map_transitive_closure(map, &exact);
939 map2 = isl_map_read_from_str(ctx,
940 "[n] -> { [i,j] -> [i2,j2] : exists (k1,k2,k : "
941 "1 <= i and i < n and 1 <= j and j <= n and "
942 "2 <= i2 and i2 <= n and 1 <= j2 and j2 <= n and "
943 "i2 = i + k1 + k2 and j2 = j + k1 - k2 and "
944 "k1 >= 0 and k2 >= 0 and k1 + k2 = k and k >= 1 )}", -1);
945 assert(isl_map_is_equal(map, map2));
949 map = isl_map_read_from_str(ctx,
950 "[n] -> { [x] -> [y] : y = x + 1 and 0 <= x and x <= n and "
951 " 0 <= y and y <= n }", -1);
952 map = isl_map_transitive_closure(map, &exact);
953 map2 = isl_map_read_from_str(ctx,
954 "[n] -> { [x] -> [y] : y > x and 0 <= x and x <= n and "
955 " 0 <= y and y <= n }", -1);
956 assert(isl_map_is_equal(map, map2));
960 /* COCOA example 2 */
961 map = isl_map_read_from_str(ctx,
962 "[n] -> { [i,j] -> [i2,j2] : i2 = i + 2 and j2 = j + 2 and "
963 "1 <= i and i < n - 1 and 1 <= j and j < n - 1 or "
964 "i2 = i + 2 and j2 = j - 2 and "
965 "1 <= i and i < n - 1 and 3 <= j and j <= n }", -1);
966 map = isl_map_transitive_closure(map, &exact);
968 map2 = isl_map_read_from_str(ctx,
969 "[n] -> { [i,j] -> [i2,j2] : exists (k1,k2,k : "
970 "1 <= i and i < n - 1 and 1 <= j and j <= n and "
971 "3 <= i2 and i2 <= n and 1 <= j2 and j2 <= n and "
972 "i2 = i + 2 k1 + 2 k2 and j2 = j + 2 k1 - 2 k2 and "
973 "k1 >= 0 and k2 >= 0 and k1 + k2 = k and k >= 1) }", -1);
974 assert(isl_map_is_equal(map, map2));
978 /* COCOA Fig.2 left */
979 map = isl_map_read_from_str(ctx,
980 "[n] -> { [i,j] -> [i2,j2] : i2 = i + 2 and j2 = j and "
981 "i <= 2 j - 3 and i <= n - 2 and j <= 2 i - 1 and "
983 "i2 = i and j2 = j + 2 and i <= 2 j - 1 and i <= n and "
984 "j <= 2 i - 3 and j <= n - 2 or "
985 "i2 = i + 1 and j2 = j + 1 and i <= 2 j - 1 and "
986 "i <= n - 1 and j <= 2 i - 1 and j <= n - 1 }", -1);
987 map = isl_map_transitive_closure(map, &exact);
991 /* COCOA Fig.2 right */
992 map = isl_map_read_from_str(ctx,
993 "[n,k] -> { [i,j] -> [i2,j2] : i2 = i + 3 and j2 = j and "
994 "i <= 2 j - 4 and i <= n - 3 and j <= 2 i - 1 and "
996 "i2 = i and j2 = j + 3 and i <= 2 j - 1 and i <= n and "
997 "j <= 2 i - 4 and j <= n - 3 or "
998 "i2 = i + 1 and j2 = j + 1 and i <= 2 j - 1 and "
999 "i <= n - 1 and j <= 2 i - 1 and j <= n - 1 }", -1);
1000 map = isl_map_power(map, 1, &exact);
1004 /* COCOA Fig.2 right */
1005 map = isl_map_read_from_str(ctx,
1006 "[n] -> { [i,j] -> [i2,j2] : i2 = i + 3 and j2 = j and "
1007 "i <= 2 j - 4 and i <= n - 3 and j <= 2 i - 1 and "
1009 "i2 = i and j2 = j + 3 and i <= 2 j - 1 and i <= n and "
1010 "j <= 2 i - 4 and j <= n - 3 or "
1011 "i2 = i + 1 and j2 = j + 1 and i <= 2 j - 1 and "
1012 "i <= n - 1 and j <= 2 i - 1 and j <= n - 1 }", -1);
1013 map = isl_map_transitive_closure(map, &exact);
1015 map2 = isl_map_read_from_str(ctx,
1016 "[n] -> { [i,j] -> [i2,j2] : exists (k1,k2,k3,k : "
1017 "i <= 2 j - 1 and i <= n and j <= 2 i - 1 and "
1018 "j <= n and 3 + i + 2 j <= 3 n and "
1019 "3 + 2 i + j <= 3n and i2 <= 2 j2 -1 and i2 <= n and "
1020 "i2 <= 3 j2 - 4 and j2 <= 2 i2 -1 and j2 <= n and "
1021 "13 + 4 j2 <= 11 i2 and i2 = i + 3 k1 + k3 and "
1022 "j2 = j + 3 k2 + k3 and k1 >= 0 and k2 >= 0 and "
1023 "k3 >= 0 and k1 + k2 + k3 = k and k > 0) }", -1);
1024 assert(isl_map_is_equal(map, map2));
1028 /* COCOA Fig.1 right */
1029 dom = isl_set_read_from_str(ctx,
1030 "{ [x,y] : x >= 0 and -2 x + 3 y >= 0 and x <= 3 and "
1031 "2 x - 3 y + 3 >= 0 }", -1);
1032 right = isl_map_read_from_str(ctx,
1033 "{ [x,y] -> [x2,y2] : x2 = x + 1 and y2 = y }", -1);
1034 up = isl_map_read_from_str(ctx,
1035 "{ [x,y] -> [x2,y2] : x2 = x and y2 = y + 1 }", -1);
1036 right = isl_map_intersect_domain(right, isl_set_copy(dom));
1037 right = isl_map_intersect_range(right, isl_set_copy(dom));
1038 up = isl_map_intersect_domain(up, isl_set_copy(dom));
1039 up = isl_map_intersect_range(up, dom);
1040 map = isl_map_union(up, right);
1041 map = isl_map_transitive_closure(map, &exact);
1043 map2 = isl_map_read_from_str(ctx,
1044 "{ [0,0] -> [0,1]; [0,0] -> [1,1]; [0,1] -> [1,1]; "
1045 " [2,2] -> [3,2]; [2,2] -> [3,3]; [3,2] -> [3,3] }", -1);
1046 assert(isl_map_is_equal(map, map2));
1050 /* COCOA Theorem 1 counter example */
1051 map = isl_map_read_from_str(ctx,
1052 "{ [i,j] -> [i2,j2] : i = 0 and 0 <= j and j <= 1 and "
1053 "i2 = 1 and j2 = j or "
1054 "i = 0 and j = 0 and i2 = 0 and j2 = 1 }", -1);
1055 map = isl_map_transitive_closure(map, &exact);
1059 map = isl_map_read_from_str(ctx,
1060 "[m,n] -> { [i,j] -> [i2,j2] : i2 = i and j2 = j + 2 and "
1061 "1 <= i,i2 <= n and 1 <= j,j2 <= m or "
1062 "i2 = i + 1 and 3 <= j2 - j <= 4 and "
1063 "1 <= i,i2 <= n and 1 <= j,j2 <= m }", -1);
1064 map = isl_map_transitive_closure(map, &exact);
1068 /* Kelly et al 1996, fig 12 */
1069 map = isl_map_read_from_str(ctx,
1070 "[n] -> { [i,j] -> [i2,j2] : i2 = i and j2 = j + 1 and "
1071 "1 <= i,j,j+1 <= n or "
1072 "j = n and j2 = 1 and i2 = i + 1 and "
1073 "1 <= i,i+1 <= n }", -1);
1074 map = isl_map_transitive_closure(map, &exact);
1076 map2 = isl_map_read_from_str(ctx,
1077 "[n] -> { [i,j] -> [i2,j2] : 1 <= j < j2 <= n and "
1078 "1 <= i <= n and i = i2 or "
1079 "1 <= i < i2 <= n and 1 <= j <= n and "
1080 "1 <= j2 <= n }", -1);
1081 assert(isl_map_is_equal(map, map2));
1085 /* Omega's closure4 */
1086 map = isl_map_read_from_str(ctx,
1087 "[m,n] -> { [x,y] -> [x2,y2] : x2 = x and y2 = y + 1 and "
1088 "1 <= x,y <= 10 or "
1089 "x2 = x + 1 and y2 = y and "
1090 "1 <= x <= 20 && 5 <= y <= 15 }", -1);
1091 map = isl_map_transitive_closure(map, &exact);
1095 map = isl_map_read_from_str(ctx,
1096 "[n] -> { [x] -> [y]: 1 <= n <= y - x <= 10 }", -1);
1097 map = isl_map_transitive_closure(map, &exact);
1099 map2 = isl_map_read_from_str(ctx,
1100 "[n] -> { [x] -> [y] : 1 <= n <= 10 and y >= n + x }", -1);
1101 assert(isl_map_is_equal(map, map2));
1105 str = "[n, m] -> { [i0, i1, i2, i3] -> [o0, o1, o2, o3] : "
1106 "i3 = 1 and o0 = i0 and o1 = -1 + i1 and o2 = -1 + i2 and "
1107 "o3 = -2 + i2 and i1 <= -1 + i0 and i1 >= 1 - m + i0 and "
1108 "i1 >= 2 and i1 <= n and i2 >= 3 and i2 <= 1 + n and i2 <= m }";
1109 map = isl_map_read_from_str(ctx, str, -1);
1110 map = isl_map_transitive_closure(map, &exact);
1112 map2 = isl_map_read_from_str(ctx, str, -1);
1113 assert(isl_map_is_equal(map, map2));
1117 str = "{[0] -> [1]; [2] -> [3]}";
1118 map = isl_map_read_from_str(ctx, str, -1);
1119 map = isl_map_transitive_closure(map, &exact);
1121 map2 = isl_map_read_from_str(ctx, str, -1);
1122 assert(isl_map_is_equal(map, map2));
1126 str = "[n] -> { [[i0, i1, 1, 0, i0] -> [i5, 1]] -> "
1127 "[[i0, -1 + i1, 2, 0, i0] -> [-1 + i5, 2]] : "
1128 "exists (e0 = [(3 - n)/3]: i5 >= 2 and i1 >= 2 and "
1129 "3i0 <= -1 + n and i1 <= -1 + n and i5 <= -1 + n and "
1130 "3e0 >= 1 - n and 3e0 <= 2 - n and 3i0 >= -2 + n); "
1131 "[[i0, i1, 2, 0, i0] -> [i5, 1]] -> "
1132 "[[i0, i1, 1, 0, i0] -> [-1 + i5, 2]] : "
1133 "exists (e0 = [(3 - n)/3]: i5 >= 2 and i1 >= 1 and "
1134 "3i0 <= -1 + n and i1 <= -1 + n and i5 <= -1 + n and "
1135 "3e0 >= 1 - n and 3e0 <= 2 - n and 3i0 >= -2 + n); "
1136 "[[i0, i1, 1, 0, i0] -> [i5, 2]] -> "
1137 "[[i0, -1 + i1, 2, 0, i0] -> [i5, 1]] : "
1138 "exists (e0 = [(3 - n)/3]: i1 >= 2 and i5 >= 1 and "
1139 "3i0 <= -1 + n and i1 <= -1 + n and i5 <= -1 + n and "
1140 "3e0 >= 1 - n and 3e0 <= 2 - n and 3i0 >= -2 + n); "
1141 "[[i0, i1, 2, 0, i0] -> [i5, 2]] -> "
1142 "[[i0, i1, 1, 0, i0] -> [i5, 1]] : "
1143 "exists (e0 = [(3 - n)/3]: i5 >= 1 and i1 >= 1 and "
1144 "3i0 <= -1 + n and i1 <= -1 + n and i5 <= -1 + n and "
1145 "3e0 >= 1 - n and 3e0 <= 2 - n and 3i0 >= -2 + n) }";
1146 map = isl_map_read_from_str(ctx, str, -1);
1147 map = isl_map_transitive_closure(map, NULL);
1152 void test_lex(struct isl_ctx *ctx)
1157 dim = isl_dim_alloc(ctx, 0, 0, 0);
1158 map = isl_map_lex_le(dim);
1159 assert(!isl_map_is_empty(map));
1163 void test_lexmin(struct isl_ctx *ctx)
1166 isl_map *map, *map2;
1170 str = "[p0, p1] -> { [] -> [] : "
1171 "exists (e0 = [(2p1)/3], e1, e2, e3 = [(3 - p1 + 3e0)/3], "
1172 "e4 = [(p1)/3], e5 = [(p1 + 3e4)/3]: "
1173 "3e0 >= -2 + 2p1 and 3e0 >= p1 and 3e3 >= 1 - p1 + 3e0 and "
1174 "3e0 <= 2p1 and 3e3 >= -2 + p1 and 3e3 <= -1 + p1 and p1 >= 3 and "
1175 "3e5 >= -2 + 2p1 and 3e5 >= p1 and 3e5 <= -1 + p1 + 3e4 and "
1176 "3e4 <= p1 and 3e4 >= -2 + p1 and e3 <= -1 + e0 and "
1177 "3e4 >= 6 - p1 + 3e1 and 3e1 >= p1 and 3e5 >= -2 + p1 + 3e4 and "
1178 "2e4 >= 3 - p1 + 2e1 and e4 <= e1 and 3e3 <= 2 - p1 + 3e0 and "
1179 "e5 >= 1 + e1 and 3e4 >= 6 - 2p1 + 3e1 and "
1180 "p0 >= 2 and p1 >= p0 and 3e2 >= p1 and 3e4 >= 6 - p1 + 3e2 and "
1181 "e2 <= e1 and e3 >= 1 and e4 <= e2) }";
1182 map = isl_map_read_from_str(ctx, str, -1);
1183 map = isl_map_lexmin(map);
1186 str = "[C] -> { [obj,a,b,c] : obj <= 38 a + 7 b + 10 c and "
1187 "a + b <= 1 and c <= 10 b and c <= C and a,b,c,C >= 0 }";
1188 set = isl_set_read_from_str(ctx, str, -1);
1189 set = isl_set_lexmax(set);
1190 str = "[C] -> { [obj,a,b,c] : C = 8 }";
1191 set2 = isl_set_read_from_str(ctx, str, -1);
1192 set = isl_set_intersect(set, set2);
1193 assert(!isl_set_is_empty(set));
1196 str = "{ [x] -> [y] : x <= y <= 10; [x] -> [5] : -8 <= x <= 8 }";
1197 map = isl_map_read_from_str(ctx, str, -1);
1198 map = isl_map_lexmin(map);
1199 str = "{ [x] -> [5] : 6 <= x <= 8; "
1200 "[x] -> [x] : x <= 5 or (9 <= x <= 10) }";
1201 map2 = isl_map_read_from_str(ctx, str, -1);
1202 assert(isl_map_is_equal(map, map2));
1206 str = "{ [x] -> [y] : 4y = x or 4y = -1 + x or 4y = -2 + x }";
1207 map = isl_map_read_from_str(ctx, str, -1);
1208 map2 = isl_map_copy(map);
1209 map = isl_map_lexmin(map);
1210 assert(isl_map_is_equal(map, map2));
1214 str = "{ [x] -> [y] : x = 4y; [x] -> [y] : x = 2y }";
1215 map = isl_map_read_from_str(ctx, str, -1);
1216 map = isl_map_lexmin(map);
1217 str = "{ [x] -> [y] : (4y = x and x >= 0) or "
1218 "(exists (e0 = [(x)/4], e1 = [(-2 + x)/4]: 2y = x and "
1219 "4e1 = -2 + x and 4e0 <= -1 + x and 4e0 >= -3 + x)) or "
1220 "(exists (e0 = [(x)/4]: 2y = x and 4e0 = x and x <= -4)) }";
1221 map2 = isl_map_read_from_str(ctx, str, -1);
1222 assert(isl_map_is_equal(map, map2));
1232 static int collect_must_may(__isl_take isl_map *dep, int must,
1233 void *dep_user, void *user)
1235 struct must_may *mm = (struct must_may *)user;
1238 mm->must = isl_map_union(mm->must, dep);
1240 mm->may = isl_map_union(mm->may, dep);
1245 static int common_space(void *first, void *second)
1247 int depth = *(int *)first;
1251 static int map_is_equal(__isl_keep isl_map *map, const char *str)
1259 map2 = isl_map_read_from_str(map->ctx, str, -1);
1260 equal = isl_map_is_equal(map, map2);
1266 void test_dep(struct isl_ctx *ctx)
1271 isl_access_info *ai;
1278 str = "{ [2,i,0] -> [i] : 0 <= i <= 10 }";
1279 map = isl_map_read_from_str(ctx, str, -1);
1280 ai = isl_access_info_alloc(map, &depth, &common_space, 2);
1282 str = "{ [0,i,0] -> [i] : 0 <= i <= 10 }";
1283 map = isl_map_read_from_str(ctx, str, -1);
1284 ai = isl_access_info_add_source(ai, map, 1, &depth);
1286 str = "{ [1,i,0] -> [5] : 0 <= i <= 10 }";
1287 map = isl_map_read_from_str(ctx, str, -1);
1288 ai = isl_access_info_add_source(ai, map, 1, &depth);
1290 flow = isl_access_info_compute_flow(ai);
1291 dim = isl_dim_alloc(ctx, 0, 3, 3);
1292 mm.must = isl_map_empty(isl_dim_copy(dim));
1293 mm.may = isl_map_empty(dim);
1295 isl_flow_foreach(flow, collect_must_may, &mm);
1297 str = "{ [0,i,0] -> [2,i,0] : (0 <= i <= 4) or (6 <= i <= 10); "
1298 " [1,10,0] -> [2,5,0] }";
1299 assert(map_is_equal(mm.must, str));
1300 str = "{ [i,j,k] -> [l,m,n] : 1 = 0 }";
1301 assert(map_is_equal(mm.may, str));
1303 isl_map_free(mm.must);
1304 isl_map_free(mm.may);
1305 isl_flow_free(flow);
1308 str = "{ [2,i,0] -> [i] : 0 <= i <= 10 }";
1309 map = isl_map_read_from_str(ctx, str, -1);
1310 ai = isl_access_info_alloc(map, &depth, &common_space, 2);
1312 str = "{ [0,i,0] -> [i] : 0 <= i <= 10 }";
1313 map = isl_map_read_from_str(ctx, str, -1);
1314 ai = isl_access_info_add_source(ai, map, 1, &depth);
1316 str = "{ [1,i,0] -> [5] : 0 <= i <= 10 }";
1317 map = isl_map_read_from_str(ctx, str, -1);
1318 ai = isl_access_info_add_source(ai, map, 0, &depth);
1320 flow = isl_access_info_compute_flow(ai);
1321 dim = isl_dim_alloc(ctx, 0, 3, 3);
1322 mm.must = isl_map_empty(isl_dim_copy(dim));
1323 mm.may = isl_map_empty(dim);
1325 isl_flow_foreach(flow, collect_must_may, &mm);
1327 str = "{ [0,i,0] -> [2,i,0] : (0 <= i <= 4) or (6 <= i <= 10) }";
1328 assert(map_is_equal(mm.must, str));
1329 str = "{ [0,5,0] -> [2,5,0]; [1,i,0] -> [2,5,0] : 0 <= i <= 10 }";
1330 assert(map_is_equal(mm.may, str));
1332 isl_map_free(mm.must);
1333 isl_map_free(mm.may);
1334 isl_flow_free(flow);
1337 str = "{ [2,i,0] -> [i] : 0 <= i <= 10 }";
1338 map = isl_map_read_from_str(ctx, str, -1);
1339 ai = isl_access_info_alloc(map, &depth, &common_space, 2);
1341 str = "{ [0,i,0] -> [i] : 0 <= i <= 10 }";
1342 map = isl_map_read_from_str(ctx, str, -1);
1343 ai = isl_access_info_add_source(ai, map, 0, &depth);
1345 str = "{ [1,i,0] -> [5] : 0 <= i <= 10 }";
1346 map = isl_map_read_from_str(ctx, str, -1);
1347 ai = isl_access_info_add_source(ai, map, 0, &depth);
1349 flow = isl_access_info_compute_flow(ai);
1350 dim = isl_dim_alloc(ctx, 0, 3, 3);
1351 mm.must = isl_map_empty(isl_dim_copy(dim));
1352 mm.may = isl_map_empty(dim);
1354 isl_flow_foreach(flow, collect_must_may, &mm);
1356 str = "{ [0,i,0] -> [2,i,0] : 0 <= i <= 10; "
1357 " [1,i,0] -> [2,5,0] : 0 <= i <= 10 }";
1358 assert(map_is_equal(mm.may, str));
1359 str = "{ [i,j,k] -> [l,m,n] : 1 = 0 }";
1360 assert(map_is_equal(mm.must, str));
1362 isl_map_free(mm.must);
1363 isl_map_free(mm.may);
1364 isl_flow_free(flow);
1367 str = "{ [0,i,2] -> [i] : 0 <= i <= 10 }";
1368 map = isl_map_read_from_str(ctx, str, -1);
1369 ai = isl_access_info_alloc(map, &depth, &common_space, 2);
1371 str = "{ [0,i,0] -> [i] : 0 <= i <= 10 }";
1372 map = isl_map_read_from_str(ctx, str, -1);
1373 ai = isl_access_info_add_source(ai, map, 0, &depth);
1375 str = "{ [0,i,1] -> [5] : 0 <= i <= 10 }";
1376 map = isl_map_read_from_str(ctx, str, -1);
1377 ai = isl_access_info_add_source(ai, map, 0, &depth);
1379 flow = isl_access_info_compute_flow(ai);
1380 dim = isl_dim_alloc(ctx, 0, 3, 3);
1381 mm.must = isl_map_empty(isl_dim_copy(dim));
1382 mm.may = isl_map_empty(dim);
1384 isl_flow_foreach(flow, collect_must_may, &mm);
1386 str = "{ [0,i,0] -> [0,i,2] : 0 <= i <= 10; "
1387 " [0,i,1] -> [0,5,2] : 0 <= i <= 5 }";
1388 assert(map_is_equal(mm.may, str));
1389 str = "{ [i,j,k] -> [l,m,n] : 1 = 0 }";
1390 assert(map_is_equal(mm.must, str));
1392 isl_map_free(mm.must);
1393 isl_map_free(mm.may);
1394 isl_flow_free(flow);
1397 str = "{ [0,i,1] -> [i] : 0 <= i <= 10 }";
1398 map = isl_map_read_from_str(ctx, str, -1);
1399 ai = isl_access_info_alloc(map, &depth, &common_space, 2);
1401 str = "{ [0,i,0] -> [i] : 0 <= i <= 10 }";
1402 map = isl_map_read_from_str(ctx, str, -1);
1403 ai = isl_access_info_add_source(ai, map, 0, &depth);
1405 str = "{ [0,i,2] -> [5] : 0 <= i <= 10 }";
1406 map = isl_map_read_from_str(ctx, str, -1);
1407 ai = isl_access_info_add_source(ai, map, 0, &depth);
1409 flow = isl_access_info_compute_flow(ai);
1410 dim = isl_dim_alloc(ctx, 0, 3, 3);
1411 mm.must = isl_map_empty(isl_dim_copy(dim));
1412 mm.may = isl_map_empty(dim);
1414 isl_flow_foreach(flow, collect_must_may, &mm);
1416 str = "{ [0,i,0] -> [0,i,1] : 0 <= i <= 10; "
1417 " [0,i,2] -> [0,5,1] : 0 <= i <= 4 }";
1418 assert(map_is_equal(mm.may, str));
1419 str = "{ [i,j,k] -> [l,m,n] : 1 = 0 }";
1420 assert(map_is_equal(mm.must, str));
1422 isl_map_free(mm.must);
1423 isl_map_free(mm.may);
1424 isl_flow_free(flow);
1429 str = "{ [1,i,0,0,0] -> [i,j] : 0 <= i <= 10 and 0 <= j <= 10 }";
1430 map = isl_map_read_from_str(ctx, str, -1);
1431 ai = isl_access_info_alloc(map, &depth, &common_space, 1);
1433 str = "{ [0,i,0,j,0] -> [i,j] : 0 <= i <= 10 and 0 <= j <= 10 }";
1434 map = isl_map_read_from_str(ctx, str, -1);
1435 ai = isl_access_info_add_source(ai, map, 1, &depth);
1437 flow = isl_access_info_compute_flow(ai);
1438 dim = isl_dim_alloc(ctx, 0, 5, 5);
1439 mm.must = isl_map_empty(isl_dim_copy(dim));
1440 mm.may = isl_map_empty(dim);
1442 isl_flow_foreach(flow, collect_must_may, &mm);
1444 str = "{ [0,i,0,j,0] -> [1,i,0,0,0] : 0 <= i,j <= 10 }";
1445 assert(map_is_equal(mm.must, str));
1446 str = "{ [0,0,0,0,0] -> [0,0,0,0,0] : 1 = 0 }";
1447 assert(map_is_equal(mm.may, str));
1449 isl_map_free(mm.must);
1450 isl_map_free(mm.may);
1451 isl_flow_free(flow);
1454 void test_sv(struct isl_ctx *ctx)
1459 str = "[N] -> { [i] -> [f] : 0 <= i <= N and 0 <= i - 10 f <= 9 }";
1460 map = isl_map_read_from_str(ctx, str, -1);
1461 assert(isl_map_is_single_valued(map));
1464 str = "[N] -> { [i] -> [f] : 0 <= i <= N and 0 <= i - 10 f <= 10 }";
1465 map = isl_map_read_from_str(ctx, str, -1);
1466 assert(!isl_map_is_single_valued(map));
1470 void test_bijective_case(struct isl_ctx *ctx, const char *str, int bijective)
1474 map = isl_map_read_from_str(ctx, str, -1);
1476 assert(isl_map_is_bijective(map));
1478 assert(!isl_map_is_bijective(map));
1482 void test_bijective(struct isl_ctx *ctx)
1484 test_bijective_case(ctx, "[N,M]->{[i,j] -> [i]}", 0);
1485 test_bijective_case(ctx, "[N,M]->{[i,j] -> [i] : j=i}", 1);
1486 test_bijective_case(ctx, "[N,M]->{[i,j] -> [i] : j=0}", 1);
1487 test_bijective_case(ctx, "[N,M]->{[i,j] -> [i] : j=N}", 1);
1488 test_bijective_case(ctx, "[N,M]->{[i,j] -> [j,i]}", 1);
1489 test_bijective_case(ctx, "[N,M]->{[i,j] -> [i+j]}", 0);
1490 test_bijective_case(ctx, "[N,M]->{[i,j] -> []}", 0);
1491 test_bijective_case(ctx, "[N,M]->{[i,j] -> [i,j,N]}", 1);
1492 test_bijective_case(ctx, "[N,M]->{[i,j] -> [2i]}", 0);
1493 test_bijective_case(ctx, "[N,M]->{[i,j] -> [i,i]}", 0);
1494 test_bijective_case(ctx, "[N,M]->{[i,j] -> [2i,i]}", 0);
1495 test_bijective_case(ctx, "[N,M]->{[i,j] -> [2i,j]}", 1);
1496 test_bijective_case(ctx, "[N,M]->{[i,j] -> [x,y] : 2x=i & y =j}", 1);
1499 void test_pwqp(struct isl_ctx *ctx)
1503 isl_pw_qpolynomial *pwqp1, *pwqp2;
1505 str = "{ [i,j,k] -> 1 + 9 * [i/5] + 7 * [j/11] + 4 * [k/13] }";
1506 pwqp1 = isl_pw_qpolynomial_read_from_str(ctx, str);
1508 pwqp1 = isl_pw_qpolynomial_move_dims(pwqp1, isl_dim_param, 0,
1511 str = "[j] -> { [i,k] -> 1 + 9 * [i/5] + 7 * [j/11] + 4 * [k/13] }";
1512 pwqp2 = isl_pw_qpolynomial_read_from_str(ctx, str);
1514 pwqp1 = isl_pw_qpolynomial_sub(pwqp1, pwqp2);
1516 assert(isl_pw_qpolynomial_is_zero(pwqp1));
1518 isl_pw_qpolynomial_free(pwqp1);
1520 str = "{ [i] -> i }";
1521 pwqp1 = isl_pw_qpolynomial_read_from_str(ctx, str);
1522 str = "{ [k] : exists a : k = 2a }";
1523 set = isl_set_read_from_str(ctx, str, 0);
1524 pwqp1 = isl_pw_qpolynomial_gist(pwqp1, set);
1525 str = "{ [i] -> i }";
1526 pwqp2 = isl_pw_qpolynomial_read_from_str(ctx, str);
1528 pwqp1 = isl_pw_qpolynomial_sub(pwqp1, pwqp2);
1530 assert(isl_pw_qpolynomial_is_zero(pwqp1));
1532 isl_pw_qpolynomial_free(pwqp1);
1534 str = "{ [i] -> i + [ (i + [i/3])/2 ] }";
1535 pwqp1 = isl_pw_qpolynomial_read_from_str(ctx, str);
1537 set = isl_set_read_from_str(ctx, str, 0);
1538 pwqp1 = isl_pw_qpolynomial_gist(pwqp1, set);
1539 str = "{ [i] -> 16 }";
1540 pwqp2 = isl_pw_qpolynomial_read_from_str(ctx, str);
1542 pwqp1 = isl_pw_qpolynomial_sub(pwqp1, pwqp2);
1544 assert(isl_pw_qpolynomial_is_zero(pwqp1));
1546 isl_pw_qpolynomial_free(pwqp1);
1548 str = "{ [i] -> ([(i)/2]) }";
1549 pwqp1 = isl_pw_qpolynomial_read_from_str(ctx, str);
1550 str = "{ [k] : exists a : k = 2a+1 }";
1551 set = isl_set_read_from_str(ctx, str, 0);
1552 pwqp1 = isl_pw_qpolynomial_gist(pwqp1, set);
1553 str = "{ [i] -> -1/2 + 1/2 * i }";
1554 pwqp2 = isl_pw_qpolynomial_read_from_str(ctx, str);
1556 pwqp1 = isl_pw_qpolynomial_sub(pwqp1, pwqp2);
1558 assert(isl_pw_qpolynomial_is_zero(pwqp1));
1560 isl_pw_qpolynomial_free(pwqp1);
1562 str = "{ [i] -> ([([i/2] + [i/2])/5]) }";
1563 pwqp1 = isl_pw_qpolynomial_read_from_str(ctx, str);
1564 str = "{ [i] -> ([(2 * [i/2])/5]) }";
1565 pwqp2 = isl_pw_qpolynomial_read_from_str(ctx, str);
1567 pwqp1 = isl_pw_qpolynomial_sub(pwqp1, pwqp2);
1569 assert(isl_pw_qpolynomial_is_zero(pwqp1));
1571 isl_pw_qpolynomial_free(pwqp1);
1573 str = "{ [x] -> ([x/2] + [(x+1)/2]) }";
1574 pwqp1 = isl_pw_qpolynomial_read_from_str(ctx, str);
1575 str = "{ [x] -> x }";
1576 pwqp2 = isl_pw_qpolynomial_read_from_str(ctx, str);
1578 pwqp1 = isl_pw_qpolynomial_sub(pwqp1, pwqp2);
1580 assert(isl_pw_qpolynomial_is_zero(pwqp1));
1582 isl_pw_qpolynomial_free(pwqp1);
1585 void test_split_periods(isl_ctx *ctx)
1588 isl_pw_qpolynomial *pwqp;
1590 str = "{ [U,V] -> 1/3 * U + 2/3 * V - [(U + 2V)/3] + [U/2] : "
1591 "U + 2V + 3 >= 0 and - U -2V >= 0 and - U + 10 >= 0 and "
1592 "U >= 0; [U,V] -> U^2 : U >= 100 }";
1593 pwqp = isl_pw_qpolynomial_read_from_str(ctx, str);
1595 pwqp = isl_pw_qpolynomial_split_periods(pwqp, 2);
1598 isl_pw_qpolynomial_free(pwqp);
1601 void test_union(isl_ctx *ctx)
1604 isl_union_set *uset1, *uset2;
1605 isl_union_map *umap1, *umap2;
1607 str = "{ [i] : 0 <= i <= 1 }";
1608 uset1 = isl_union_set_read_from_str(ctx, str);
1609 str = "{ [1] -> [0] }";
1610 umap1 = isl_union_map_read_from_str(ctx, str);
1612 umap2 = isl_union_set_lex_gt_union_set(isl_union_set_copy(uset1), uset1);
1613 assert(isl_union_map_is_equal(umap1, umap2));
1615 isl_union_map_free(umap1);
1616 isl_union_map_free(umap2);
1618 str = "{ A[i] -> B[i]; B[i] -> C[i]; A[0] -> C[1] }";
1619 umap1 = isl_union_map_read_from_str(ctx, str);
1620 str = "{ A[i]; B[i] }";
1621 uset1 = isl_union_set_read_from_str(ctx, str);
1623 uset2 = isl_union_map_domain(umap1);
1625 assert(isl_union_set_is_equal(uset1, uset2));
1627 isl_union_set_free(uset1);
1628 isl_union_set_free(uset2);
1631 void test_bound(isl_ctx *ctx)
1634 isl_pw_qpolynomial *pwqp;
1635 isl_pw_qpolynomial_fold *pwf;
1637 str = "{ [[a, b, c, d] -> [e]] -> 0 }";
1638 pwqp = isl_pw_qpolynomial_read_from_str(ctx, str);
1639 pwf = isl_pw_qpolynomial_bound(pwqp, isl_fold_max, NULL);
1640 assert(isl_pw_qpolynomial_fold_dim(pwf, isl_dim_set) == 4);
1641 isl_pw_qpolynomial_fold_free(pwf);
1644 void test_lift(isl_ctx *ctx)
1647 isl_basic_map *bmap;
1648 isl_basic_set *bset;
1650 str = "{ [i0] : exists e0 : i0 = 4e0 }";
1651 bset = isl_basic_set_read_from_str(ctx, str, 0);
1652 bset = isl_basic_set_lift(bset);
1653 bmap = isl_basic_map_from_range(bset);
1654 bset = isl_basic_map_domain(bmap);
1655 isl_basic_set_free(bset);
1658 void test_subset(isl_ctx *ctx)
1661 isl_set *set1, *set2;
1663 str = "{ [112, 0] }";
1664 set1 = isl_set_read_from_str(ctx, str, 0);
1665 str = "{ [i0, i1] : exists (e0 = [(i0 - i1)/16], e1: "
1666 "16e0 <= i0 - i1 and 16e0 >= -15 + i0 - i1 and "
1667 "16e1 <= i1 and 16e0 >= -i1 and 16e1 >= -i0 + i1) }";
1668 set2 = isl_set_read_from_str(ctx, str, 0);
1669 assert(isl_set_is_subset(set1, set2));
1674 void test_factorize(isl_ctx *ctx)
1677 isl_basic_set *bset;
1680 str = "{ [i0, i1, i2, i3, i4, i5, i6, i7] : 3i5 <= 2 - 2i0 and "
1681 "i0 >= -2 and i6 >= 1 + i3 and i7 >= 0 and 3i5 >= -2i0 and "
1682 "2i4 <= i2 and i6 >= 1 + 2i0 + 3i1 and i4 <= -1 and "
1683 "i6 >= 1 + 2i0 + 3i5 and i6 <= 2 + 2i0 + 3i5 and "
1684 "3i5 <= 2 - 2i0 - i2 + 3i4 and i6 <= 2 + 2i0 + 3i1 and "
1685 "i0 <= -1 and i7 <= i2 + i3 - 3i4 - i6 and "
1686 "3i5 >= -2i0 - i2 + 3i4 }";
1687 bset = isl_basic_set_read_from_str(ctx, str, 0);
1688 f = isl_basic_set_factorizer(bset);
1690 isl_basic_set_free(bset);
1691 isl_factorizer_free(f);
1693 str = "{ [i0, i1, i2, i3, i4, i5, i6, i7, i8, i9, i10, i11, i12] : "
1694 "i12 <= 2 + i0 - i11 and 2i8 >= -i4 and i11 >= i1 and "
1695 "3i5 <= -i2 and 2i11 >= -i4 - 2i7 and i11 <= 3 + i0 + 3i9 and "
1696 "i11 <= -i4 - 2i7 and i12 >= -i10 and i2 >= -2 and "
1697 "i11 >= i1 + 3i10 and i11 >= 1 + i0 + 3i9 and "
1698 "i11 <= 1 - i4 - 2i8 and 6i6 <= 6 - i2 and 3i6 >= 1 - i2 and "
1699 "i11 <= 2 + i1 and i12 <= i4 + i11 and i12 >= i0 - i11 and "
1700 "3i5 >= -2 - i2 and i12 >= -1 + i4 + i11 and 3i3 <= 3 - i2 and "
1701 "9i6 <= 11 - i2 + 6i5 and 3i3 >= 1 - i2 and "
1702 "9i6 <= 5 - i2 + 6i3 and i12 <= -1 and i2 <= 0 }";
1703 bset = isl_basic_set_read_from_str(ctx, str, 0);
1704 f = isl_basic_set_factorizer(bset);
1706 isl_basic_set_free(bset);
1707 isl_factorizer_free(f);
1712 struct isl_ctx *ctx;
1714 srcdir = getenv("srcdir");
1717 ctx = isl_ctx_alloc();
1718 test_factorize(ctx);
1723 test_split_periods(ctx);
1728 test_bijective(ctx);
1732 test_construction(ctx);
1735 test_application(ctx);
1736 test_affine_hull(ctx);
1737 test_convex_hull(ctx);