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isl_map_read: extract out read_var_def
[isl.git] / isl_test.c
blobdcb417d629cd0f33dfb8a4eb56a18ad08254655c
1 /*
2 * Copyright 2008-2009 Katholieke Universiteit Leuven
3 *
4 * Use of this software is governed by the GNU LGPLv2.1 license
5 *
6 * Written by Sven Verdoolaege, K.U.Leuven, Departement
7 * Computerwetenschappen, Celestijnenlaan 200A, B-3001 Leuven, Belgium
8 */
9
10 #include <assert.h>
11 #include <stdio.h>
12 #include <limits.h>
13 #include <isl_ctx.h>
14 #include <isl_set.h>
15 #include <isl_flow.h>
16 #include <isl_constraint.h>
17
18 static char *srcdir;
19
20 void test_read(struct isl_ctx *ctx)
21 {
22 char filename[PATH_MAX];
23 FILE *input;
24 int n;
25 struct isl_basic_set *bset1, *bset2;
26 const char *str = "{[y]: Exists ( alpha : 2alpha = y)}";
27
28 n = snprintf(filename, sizeof(filename),
29 "%s/test_inputs/set.omega", srcdir);
30 assert(n < sizeof(filename));
31 input = fopen(filename, "r");
32 assert(input);
33
34 bset1 = isl_basic_set_read_from_file(ctx, input, 0);
35 bset2 = isl_basic_set_read_from_str(ctx, str, 0);
36
37 assert(isl_basic_set_is_equal(bset1, bset2) == 1);
38
39 isl_basic_set_free(bset1);
40 isl_basic_set_free(bset2);
41
42 fclose(input);
43 }
44
45 void test_bounded(struct isl_ctx *ctx)
46 {
47 isl_set *set;
48 int bounded;
49
50 set = isl_set_read_from_str(ctx, "[n] -> {[i] : 0 <= i <= n }", -1);
51 bounded = isl_set_is_bounded(set);
52 assert(bounded);
53 isl_set_free(set);
54
55 set = isl_set_read_from_str(ctx, "{[n, i] : 0 <= i <= n }", -1);
56 bounded = isl_set_is_bounded(set);
57 assert(!bounded);
58 isl_set_free(set);
59
60 set = isl_set_read_from_str(ctx, "[n] -> {[i] : i <= n }", -1);
61 bounded = isl_set_is_bounded(set);
62 assert(!bounded);
63 isl_set_free(set);
64 }
65
66 /* Construct the basic set { [i] : 5 <= i <= N } */
67 void test_construction(struct isl_ctx *ctx)
68 {
69 isl_int v;
70 struct isl_dim *dim;
71 struct isl_basic_set *bset;
72 struct isl_constraint *c;
73
74 isl_int_init(v);
75
76 dim = isl_dim_set_alloc(ctx, 1, 1);
77 bset = isl_basic_set_universe(dim);
78
79 c = isl_inequality_alloc(isl_basic_set_get_dim(bset));
80 isl_int_set_si(v, -1);
81 isl_constraint_set_coefficient(c, isl_dim_set, 0, v);
82 isl_int_set_si(v, 1);
83 isl_constraint_set_coefficient(c, isl_dim_param, 0, v);
84 bset = isl_basic_set_add_constraint(bset, c);
85
86 c = isl_inequality_alloc(isl_basic_set_get_dim(bset));
87 isl_int_set_si(v, 1);
88 isl_constraint_set_coefficient(c, isl_dim_set, 0, v);
89 isl_int_set_si(v, -5);
90 isl_constraint_set_constant(c, v);
91 bset = isl_basic_set_add_constraint(bset, c);
92
93 isl_basic_set_free(bset);
94
95 isl_int_clear(v);
96 }
97
98 void test_dim(struct isl_ctx *ctx)
99 {
100 const char *str;
101 isl_map *map1, *map2;
102
103 map1 = isl_map_read_from_str(ctx,
104 "[n] -> { [i] -> [j] : exists (a = [i/10] : i - 10a <= n ) }", -1);
105 map1 = isl_map_add(map1, isl_dim_in, 1);
106 map2 = isl_map_read_from_str(ctx,
107 "[n] -> { [i,k] -> [j] : exists (a = [i/10] : i - 10a <= n ) }", -1);
108 assert(isl_map_is_equal(map1, map2));
109 isl_map_free(map2);
110
111 map1 = isl_map_project_out(map1, isl_dim_in, 0, 1);
112 map2 = isl_map_read_from_str(ctx, "[n] -> { [i] -> [j] : n >= 0 }", -1);
113 assert(isl_map_is_equal(map1, map2));
114
115 isl_map_free(map1);
116 isl_map_free(map2);
117
118 str = "[n] -> { [i] -> [] : exists a : 0 <= i <= n and i = 2 a }";
119 map1 = isl_map_read_from_str(ctx, str, -1);
120 str = "{ [i] -> [j] : exists a : 0 <= i <= j and i = 2 a }";
121 map2 = isl_map_read_from_str(ctx, str, -1);
122 map1 = isl_map_move_dims(map1, isl_dim_out, 0, isl_dim_param, 0, 1);
123 assert(isl_map_is_equal(map1, map2));
124
125 isl_map_free(map1);
126 isl_map_free(map2);
127 }
128
129 void test_div(struct isl_ctx *ctx)
130 {
131 isl_int v;
132 int pos;
133 struct isl_dim *dim;
134 struct isl_div *div;
135 struct isl_basic_set *bset;
136 struct isl_constraint *c;
137
138 isl_int_init(v);
139
140 /* test 1 */
141 dim = isl_dim_set_alloc(ctx, 0, 1);
142 bset = isl_basic_set_universe(dim);
143
144 c = isl_equality_alloc(isl_basic_set_get_dim(bset));
145 isl_int_set_si(v, -1);
146 isl_constraint_set_constant(c, v);
147 isl_int_set_si(v, 1);
148 isl_constraint_set_coefficient(c, isl_dim_set, 0, v);
149 div = isl_div_alloc(isl_basic_set_get_dim(bset));
150 c = isl_constraint_add_div(c, div, &pos);
151 isl_int_set_si(v, 3);
152 isl_constraint_set_coefficient(c, isl_dim_div, pos, v);
153 bset = isl_basic_set_add_constraint(bset, c);
154
155 c = isl_equality_alloc(isl_basic_set_get_dim(bset));
156 isl_int_set_si(v, 1);
157 isl_constraint_set_constant(c, v);
158 isl_int_set_si(v, -1);
159 isl_constraint_set_coefficient(c, isl_dim_set, 0, v);
160 div = isl_div_alloc(isl_basic_set_get_dim(bset));
161 c = isl_constraint_add_div(c, div, &pos);
162 isl_int_set_si(v, 3);
163 isl_constraint_set_coefficient(c, isl_dim_div, pos, v);
164 bset = isl_basic_set_add_constraint(bset, c);
165
166 assert(bset && bset->n_div == 1);
167 isl_basic_set_free(bset);
168
169 /* test 2 */
170 dim = isl_dim_set_alloc(ctx, 0, 1);
171 bset = isl_basic_set_universe(dim);
172
173 c = isl_equality_alloc(isl_basic_set_get_dim(bset));
174 isl_int_set_si(v, 1);
175 isl_constraint_set_constant(c, v);
176 isl_int_set_si(v, -1);
177 isl_constraint_set_coefficient(c, isl_dim_set, 0, v);
178 div = isl_div_alloc(isl_basic_set_get_dim(bset));
179 c = isl_constraint_add_div(c, div, &pos);
180 isl_int_set_si(v, 3);
181 isl_constraint_set_coefficient(c, isl_dim_div, pos, v);
182 bset = isl_basic_set_add_constraint(bset, c);
183
184 c = isl_equality_alloc(isl_basic_set_get_dim(bset));
185 isl_int_set_si(v, -1);
186 isl_constraint_set_constant(c, v);
187 isl_int_set_si(v, 1);
188 isl_constraint_set_coefficient(c, isl_dim_set, 0, v);
189 div = isl_div_alloc(isl_basic_set_get_dim(bset));
190 c = isl_constraint_add_div(c, div, &pos);
191 isl_int_set_si(v, 3);
192 isl_constraint_set_coefficient(c, isl_dim_div, pos, v);
193 bset = isl_basic_set_add_constraint(bset, c);
194
195 assert(bset && bset->n_div == 1);
196 isl_basic_set_free(bset);
197
198 /* test 3 */
199 dim = isl_dim_set_alloc(ctx, 0, 1);
200 bset = isl_basic_set_universe(dim);
201
202 c = isl_equality_alloc(isl_basic_set_get_dim(bset));
203 isl_int_set_si(v, 1);
204 isl_constraint_set_constant(c, v);
205 isl_int_set_si(v, -1);
206 isl_constraint_set_coefficient(c, isl_dim_set, 0, v);
207 div = isl_div_alloc(isl_basic_set_get_dim(bset));
208 c = isl_constraint_add_div(c, div, &pos);
209 isl_int_set_si(v, 3);
210 isl_constraint_set_coefficient(c, isl_dim_div, pos, v);
211 bset = isl_basic_set_add_constraint(bset, c);
212
213 c = isl_equality_alloc(isl_basic_set_get_dim(bset));
214 isl_int_set_si(v, -3);
215 isl_constraint_set_constant(c, v);
216 isl_int_set_si(v, 1);
217 isl_constraint_set_coefficient(c, isl_dim_set, 0, v);
218 div = isl_div_alloc(isl_basic_set_get_dim(bset));
219 c = isl_constraint_add_div(c, div, &pos);
220 isl_int_set_si(v, 4);
221 isl_constraint_set_coefficient(c, isl_dim_div, pos, v);
222 bset = isl_basic_set_add_constraint(bset, c);
223
224 assert(bset && bset->n_div == 1);
225 isl_basic_set_free(bset);
226
227 /* test 4 */
228 dim = isl_dim_set_alloc(ctx, 0, 1);
229 bset = isl_basic_set_universe(dim);
230
231 c = isl_equality_alloc(isl_basic_set_get_dim(bset));
232 isl_int_set_si(v, 2);
233 isl_constraint_set_constant(c, v);
234 isl_int_set_si(v, -1);
235 isl_constraint_set_coefficient(c, isl_dim_set, 0, v);
236 div = isl_div_alloc(isl_basic_set_get_dim(bset));
237 c = isl_constraint_add_div(c, div, &pos);
238 isl_int_set_si(v, 3);
239 isl_constraint_set_coefficient(c, isl_dim_div, pos, v);
240 bset = isl_basic_set_add_constraint(bset, c);
241
242 c = isl_equality_alloc(isl_basic_set_get_dim(bset));
243 isl_int_set_si(v, -1);
244 isl_constraint_set_constant(c, v);
245 isl_int_set_si(v, 1);
246 isl_constraint_set_coefficient(c, isl_dim_set, 0, v);
247 div = isl_div_alloc(isl_basic_set_get_dim(bset));
248 c = isl_constraint_add_div(c, div, &pos);
249 isl_int_set_si(v, 6);
250 isl_constraint_set_coefficient(c, isl_dim_div, pos, v);
251 bset = isl_basic_set_add_constraint(bset, c);
252
253 assert(isl_basic_set_is_empty(bset));
254 isl_basic_set_free(bset);
255
256 /* test 5 */
257 dim = isl_dim_set_alloc(ctx, 0, 2);
258 bset = isl_basic_set_universe(dim);
259
260 c = isl_equality_alloc(isl_basic_set_get_dim(bset));
261 isl_int_set_si(v, -1);
262 isl_constraint_set_coefficient(c, isl_dim_set, 0, v);
263 div = isl_div_alloc(isl_basic_set_get_dim(bset));
264 c = isl_constraint_add_div(c, div, &pos);
265 isl_int_set_si(v, 3);
266 isl_constraint_set_coefficient(c, isl_dim_div, pos, v);
267 bset = isl_basic_set_add_constraint(bset, c);
268
269 c = isl_equality_alloc(isl_basic_set_get_dim(bset));
270 isl_int_set_si(v, 1);
271 isl_constraint_set_coefficient(c, isl_dim_set, 0, v);
272 isl_int_set_si(v, -3);
273 isl_constraint_set_coefficient(c, isl_dim_set, 1, v);
274 bset = isl_basic_set_add_constraint(bset, c);
275
276 assert(bset && bset->n_div == 0);
277 isl_basic_set_free(bset);
278
279 /* test 6 */
280 dim = isl_dim_set_alloc(ctx, 0, 2);
281 bset = isl_basic_set_universe(dim);
282
283 c = isl_equality_alloc(isl_basic_set_get_dim(bset));
284 isl_int_set_si(v, -1);
285 isl_constraint_set_coefficient(c, isl_dim_set, 0, v);
286 div = isl_div_alloc(isl_basic_set_get_dim(bset));
287 c = isl_constraint_add_div(c, div, &pos);
288 isl_int_set_si(v, 6);
289 isl_constraint_set_coefficient(c, isl_dim_div, pos, v);
290 bset = isl_basic_set_add_constraint(bset, c);
291
292 c = isl_equality_alloc(isl_basic_set_get_dim(bset));
293 isl_int_set_si(v, 1);
294 isl_constraint_set_coefficient(c, isl_dim_set, 0, v);
295 isl_int_set_si(v, -3);
296 isl_constraint_set_coefficient(c, isl_dim_set, 1, v);
297 bset = isl_basic_set_add_constraint(bset, c);
298
299 assert(bset && bset->n_div == 1);
300 isl_basic_set_free(bset);
301
302 /* test 7 */
303 /* This test is a bit tricky. We set up an equality
304 * a + 3b + 3c = 6 e0
305 * Normalization of divs creates _two_ divs
306 * a = 3 e0
307 * c - b - e0 = 2 e1
308 * Afterwards e0 is removed again because it has coefficient -1
309 * and we end up with the original equality and div again.
310 * Perhaps we can avoid the introduction of this temporary div.
311 */
312 dim = isl_dim_set_alloc(ctx, 0, 3);
313 bset = isl_basic_set_universe(dim);
314
315 c = isl_equality_alloc(isl_basic_set_get_dim(bset));
316 isl_int_set_si(v, -1);
317 isl_constraint_set_coefficient(c, isl_dim_set, 0, v);
318 isl_int_set_si(v, -3);
319 isl_constraint_set_coefficient(c, isl_dim_set, 1, v);
320 isl_int_set_si(v, -3);
321 isl_constraint_set_coefficient(c, isl_dim_set, 2, v);
322 div = isl_div_alloc(isl_basic_set_get_dim(bset));
323 c = isl_constraint_add_div(c, div, &pos);
324 isl_int_set_si(v, 6);
325 isl_constraint_set_coefficient(c, isl_dim_div, pos, v);
326 bset = isl_basic_set_add_constraint(bset, c);
327
328 /* Test disabled for now */
329 /*
330 assert(bset && bset->n_div == 1);
331 */
332 isl_basic_set_free(bset);
333
334 /* test 8 */
335 dim = isl_dim_set_alloc(ctx, 0, 4);
336 bset = isl_basic_set_universe(dim);
337
338 c = isl_equality_alloc(isl_basic_set_get_dim(bset));
339 isl_int_set_si(v, -1);
340 isl_constraint_set_coefficient(c, isl_dim_set, 0, v);
341 isl_int_set_si(v, -3);
342 isl_constraint_set_coefficient(c, isl_dim_set, 1, v);
343 isl_int_set_si(v, -3);
344 isl_constraint_set_coefficient(c, isl_dim_set, 3, v);
345 div = isl_div_alloc(isl_basic_set_get_dim(bset));
346 c = isl_constraint_add_div(c, div, &pos);
347 isl_int_set_si(v, 6);
348 isl_constraint_set_coefficient(c, isl_dim_div, pos, v);
349 bset = isl_basic_set_add_constraint(bset, c);
350
351 c = isl_equality_alloc(isl_basic_set_get_dim(bset));
352 isl_int_set_si(v, -1);
353 isl_constraint_set_coefficient(c, isl_dim_set, 0, v);
354 isl_int_set_si(v, 1);
355 isl_constraint_set_coefficient(c, isl_dim_set, 2, v);
356 isl_int_set_si(v, 1);
357 isl_constraint_set_constant(c, v);
358 bset = isl_basic_set_add_constraint(bset, c);
359
360 /* Test disabled for now */
361 /*
362 assert(bset && bset->n_div == 1);
363 */
364 isl_basic_set_free(bset);
365
366 /* test 9 */
367 dim = isl_dim_set_alloc(ctx, 0, 2);
368 bset = isl_basic_set_universe(dim);
369
370 c = isl_equality_alloc(isl_basic_set_get_dim(bset));
371 isl_int_set_si(v, 1);
372 isl_constraint_set_coefficient(c, isl_dim_set, 0, v);
373 isl_int_set_si(v, -1);
374 isl_constraint_set_coefficient(c, isl_dim_set, 1, v);
375 div = isl_div_alloc(isl_basic_set_get_dim(bset));
376 c = isl_constraint_add_div(c, div, &pos);
377 isl_int_set_si(v, -2);
378 isl_constraint_set_coefficient(c, isl_dim_div, pos, v);
379 bset = isl_basic_set_add_constraint(bset, c);
380
381 c = isl_equality_alloc(isl_basic_set_get_dim(bset));
382 isl_int_set_si(v, -1);
383 isl_constraint_set_coefficient(c, isl_dim_set, 0, v);
384 div = isl_div_alloc(isl_basic_set_get_dim(bset));
385 c = isl_constraint_add_div(c, div, &pos);
386 isl_int_set_si(v, 3);
387 isl_constraint_set_coefficient(c, isl_dim_div, pos, v);
388 isl_int_set_si(v, 2);
389 isl_constraint_set_constant(c, v);
390 bset = isl_basic_set_add_constraint(bset, c);
391
392 bset = isl_basic_set_fix_si(bset, isl_dim_set, 0, 2);
393
394 assert(!isl_basic_set_is_empty(bset));
395
396 isl_basic_set_free(bset);
397
398 /* test 10 */
399 dim = isl_dim_set_alloc(ctx, 0, 2);
400 bset = isl_basic_set_universe(dim);
401
402 c = isl_equality_alloc(isl_basic_set_get_dim(bset));
403 isl_int_set_si(v, 1);
404 isl_constraint_set_coefficient(c, isl_dim_set, 0, v);
405 div = isl_div_alloc(isl_basic_set_get_dim(bset));
406 c = isl_constraint_add_div(c, div, &pos);
407 isl_int_set_si(v, -2);
408 isl_constraint_set_coefficient(c, isl_dim_div, pos, v);
409 bset = isl_basic_set_add_constraint(bset, c);
410
411 bset = isl_basic_set_fix_si(bset, isl_dim_set, 0, 2);
412
413 isl_basic_set_free(bset);
414
415 isl_int_clear(v);
416 }
417
418 void test_application_case(struct isl_ctx *ctx, const char *name)
419 {
420 char filename[PATH_MAX];
421 FILE *input;
422 int n;
423 struct isl_basic_set *bset1, *bset2;
424 struct isl_basic_map *bmap;
425
426 n = snprintf(filename, sizeof(filename),
427 "%s/test_inputs/%s.omega", srcdir, name);
428 assert(n < sizeof(filename));
429 input = fopen(filename, "r");
430 assert(input);
431
432 bset1 = isl_basic_set_read_from_file(ctx, input, 0);
433 bmap = isl_basic_map_read_from_file(ctx, input, 0);
434
435 bset1 = isl_basic_set_apply(bset1, bmap);
436
437 bset2 = isl_basic_set_read_from_file(ctx, input, 0);
438
439 assert(isl_basic_set_is_equal(bset1, bset2) == 1);
440
441 isl_basic_set_free(bset1);
442 isl_basic_set_free(bset2);
443
444 fclose(input);
445 }
446
447 void test_application(struct isl_ctx *ctx)
448 {
449 test_application_case(ctx, "application");
450 test_application_case(ctx, "application2");
451 }
452
453 void test_affine_hull_case(struct isl_ctx *ctx, const char *name)
454 {
455 char filename[PATH_MAX];
456 FILE *input;
457 int n;
458 struct isl_basic_set *bset1, *bset2;
459
460 n = snprintf(filename, sizeof(filename),
461 "%s/test_inputs/%s.polylib", srcdir, name);
462 assert(n < sizeof(filename));
463 input = fopen(filename, "r");
464 assert(input);
465
466 bset1 = isl_basic_set_read_from_file(ctx, input, 0);
467 bset2 = isl_basic_set_read_from_file(ctx, input, 0);
468
469 bset1 = isl_basic_set_affine_hull(bset1);
470
471 assert(isl_basic_set_is_equal(bset1, bset2) == 1);
472
473 isl_basic_set_free(bset1);
474 isl_basic_set_free(bset2);
475
476 fclose(input);
477 }
478
479 void test_affine_hull(struct isl_ctx *ctx)
480 {
481 test_affine_hull_case(ctx, "affine2");
482 test_affine_hull_case(ctx, "affine");
483 test_affine_hull_case(ctx, "affine3");
484 }
485
486 void test_convex_hull_case(struct isl_ctx *ctx, const char *name)
487 {
488 char filename[PATH_MAX];
489 FILE *input;
490 int n;
491 struct isl_basic_set *bset1, *bset2;
492 struct isl_set *set;
493
494 n = snprintf(filename, sizeof(filename),
495 "%s/test_inputs/%s.polylib", srcdir, name);
496 assert(n < sizeof(filename));
497 input = fopen(filename, "r");
498 assert(input);
499
500 bset1 = isl_basic_set_read_from_file(ctx, input, 0);
501 bset2 = isl_basic_set_read_from_file(ctx, input, 0);
502
503 set = isl_basic_set_union(bset1, bset2);
504 bset1 = isl_set_convex_hull(set);
505
506 bset2 = isl_basic_set_read_from_file(ctx, input, 0);
507
508 assert(isl_basic_set_is_equal(bset1, bset2) == 1);
509
510 isl_basic_set_free(bset1);
511 isl_basic_set_free(bset2);
512
513 fclose(input);
514 }
515
516 void test_convex_hull(struct isl_ctx *ctx)
517 {
518 const char *str1, *str2;
519 isl_set *set1, *set2;
520
521 test_convex_hull_case(ctx, "convex0");
522 test_convex_hull_case(ctx, "convex1");
523 test_convex_hull_case(ctx, "convex2");
524 test_convex_hull_case(ctx, "convex3");
525 test_convex_hull_case(ctx, "convex4");
526 test_convex_hull_case(ctx, "convex5");
527 test_convex_hull_case(ctx, "convex6");
528 test_convex_hull_case(ctx, "convex7");
529 test_convex_hull_case(ctx, "convex8");
530 test_convex_hull_case(ctx, "convex9");
531 test_convex_hull_case(ctx, "convex10");
532 test_convex_hull_case(ctx, "convex11");
533 test_convex_hull_case(ctx, "convex12");
534 test_convex_hull_case(ctx, "convex13");
535 test_convex_hull_case(ctx, "convex14");
536 test_convex_hull_case(ctx, "convex15");
537
538 str1 = "{ [i0, i1, i2] : (i2 = 1 and i0 = 0 and i1 >= 0) or "
539 "(i0 = 1 and i1 = 0 and i2 = 1) or "
540 "(i0 = 0 and i1 = 0 and i2 = 0) }";
541 str2 = "{ [i0, i1, i2] : i0 >= 0 and i2 >= i0 and i2 <= 1 and i1 >= 0 }";
542 set1 = isl_set_read_from_str(ctx, str1, -1);
543 set2 = isl_set_read_from_str(ctx, str2, -1);
544 set1 = isl_set_from_basic_set(isl_set_convex_hull(set1));
545 assert(isl_set_is_equal(set1, set2));
546 isl_set_free(set1);
547 isl_set_free(set2);
548 }
549
550 void test_gist_case(struct isl_ctx *ctx, const char *name)
551 {
552 char filename[PATH_MAX];
553 FILE *input;
554 int n;
555 struct isl_basic_set *bset1, *bset2;
556
557 n = snprintf(filename, sizeof(filename),
558 "%s/test_inputs/%s.polylib", srcdir, name);
559 assert(n < sizeof(filename));
560 input = fopen(filename, "r");
561 assert(input);
562
563 bset1 = isl_basic_set_read_from_file(ctx, input, 0);
564 bset2 = isl_basic_set_read_from_file(ctx, input, 0);
565
566 bset1 = isl_basic_set_gist(bset1, bset2);
567
568 bset2 = isl_basic_set_read_from_file(ctx, input, 0);
569
570 assert(isl_basic_set_is_equal(bset1, bset2) == 1);
571
572 isl_basic_set_free(bset1);
573 isl_basic_set_free(bset2);
574
575 fclose(input);
576 }
577
578 void test_gist(struct isl_ctx *ctx)
579 {
580 test_gist_case(ctx, "gist1");
581 }
582
583 void test_coalesce_set(isl_ctx *ctx, const char *str, int check_one)
584 {
585 isl_set *set, *set2;
586
587 set = isl_set_read_from_str(ctx, str, -1);
588 set = isl_set_coalesce(set);
589 set2 = isl_set_read_from_str(ctx, str, -1);
590 assert(isl_set_is_equal(set, set2));
591 if (check_one)
592 assert(set && set->n == 1);
593 isl_set_free(set);
594 isl_set_free(set2);
595 }
596
597 void test_coalesce(struct isl_ctx *ctx)
598 {
599 const char *str;
600 struct isl_set *set, *set2;
601 struct isl_map *map, *map2;
602
603 set = isl_set_read_from_str(ctx,
604 "{[x,y]: x >= 0 & x <= 10 & y >= 0 & y <= 10 or "
605 "y >= x & x >= 2 & 5 >= y }", -1);
606 set = isl_set_coalesce(set);
607 assert(set && set->n == 1);
608 isl_set_free(set);
609
610 set = isl_set_read_from_str(ctx,
611 "{[x,y]: y >= 0 & 2x + y <= 30 & y <= 10 & x >= 0 or "
612 "x + y >= 10 & y <= x & x + y <= 20 & y >= 0}", -1);
613 set = isl_set_coalesce(set);
614 assert(set && set->n == 1);
615 isl_set_free(set);
616
617 set = isl_set_read_from_str(ctx,
618 "{[x,y]: y >= 0 & 2x + y <= 30 & y <= 10 & x >= 0 or "
619 "x + y >= 10 & y <= x & x + y <= 19 & y >= 0}", -1);
620 set = isl_set_coalesce(set);
621 assert(set && set->n == 2);
622 isl_set_free(set);
623
624 set = isl_set_read_from_str(ctx,
625 "{[x,y]: y >= 0 & x <= 5 & y <= x or "
626 "y >= 0 & x >= 6 & x <= 10 & y <= x}", -1);
627 set = isl_set_coalesce(set);
628 assert(set && set->n == 1);
629 isl_set_free(set);
630
631 set = isl_set_read_from_str(ctx,
632 "{[x,y]: y >= 0 & x <= 5 & y <= x or "
633 "y >= 0 & x >= 7 & x <= 10 & y <= x}", -1);
634 set = isl_set_coalesce(set);
635 assert(set && set->n == 2);
636 isl_set_free(set);
637
638 set = isl_set_read_from_str(ctx,
639 "{[x,y]: y >= 0 & x <= 5 & y <= x or "
640 "y >= 0 & x >= 6 & x <= 10 & y + 1 <= x}", -1);
641 set = isl_set_coalesce(set);
642 assert(set && set->n == 2);
643 isl_set_free(set);
644
645 set = isl_set_read_from_str(ctx,
646 "{[x,y]: y >= 0 & x <= 5 & y <= x or "
647 "y >= 0 & x = 6 & y <= 6}", -1);
648 set = isl_set_coalesce(set);
649 assert(set && set->n == 1);
650 isl_set_free(set);
651
652 set = isl_set_read_from_str(ctx,
653 "{[x,y]: y >= 0 & x <= 5 & y <= x or "
654 "y >= 0 & x = 7 & y <= 6}", -1);
655 set = isl_set_coalesce(set);
656 assert(set && set->n == 2);
657 isl_set_free(set);
658
659 set = isl_set_read_from_str(ctx,
660 "{[x,y]: y >= 0 & x <= 5 & y <= x or "
661 "y >= 0 & x = 6 & y <= 5}", -1);
662 set = isl_set_coalesce(set);
663 assert(set && set->n == 1);
664 set2 = isl_set_read_from_str(ctx,
665 "{[x,y]: y >= 0 & x <= 5 & y <= x or "
666 "y >= 0 & x = 6 & y <= 5}", -1);
667 assert(isl_set_is_equal(set, set2));
668 isl_set_free(set);
669 isl_set_free(set2);
670
671 set = isl_set_read_from_str(ctx,
672 "{[x,y]: y >= 0 & x <= 5 & y <= x or "
673 "y >= 0 & x = 6 & y <= 7}", -1);
674 set = isl_set_coalesce(set);
675 assert(set && set->n == 2);
676 isl_set_free(set);
677
678 set = isl_set_read_from_str(ctx,
679 "[n] -> { [i] : i = 1 and n >= 2 or 2 <= i and i <= n }", -1);
680 set = isl_set_coalesce(set);
681 assert(set && set->n == 1);
682 set2 = isl_set_read_from_str(ctx,
683 "[n] -> { [i] : i = 1 and n >= 2 or 2 <= i and i <= n }", -1);
684 assert(isl_set_is_equal(set, set2));
685 isl_set_free(set);
686 isl_set_free(set2);
687
688 set = isl_set_read_from_str(ctx,
689 "{[x,y] : x >= 0 and y >= 0 or 0 <= y and y <= 5 and x = -1}", -1);
690 set = isl_set_coalesce(set);
691 set2 = isl_set_read_from_str(ctx,
692 "{[x,y] : x >= 0 and y >= 0 or 0 <= y and y <= 5 and x = -1}", -1);
693 assert(isl_set_is_equal(set, set2));
694 isl_set_free(set);
695 isl_set_free(set2);
696
697 set = isl_set_read_from_str(ctx,
698 "[n] -> { [i] : 1 <= i and i <= n - 1 or "
699 "2 <= i and i <= n }", -1);
700 set = isl_set_coalesce(set);
701 assert(set && set->n == 1);
702 set2 = isl_set_read_from_str(ctx,
703 "[n] -> { [i] : 1 <= i and i <= n - 1 or "
704 "2 <= i and i <= n }", -1);
705 assert(isl_set_is_equal(set, set2));
706 isl_set_free(set);
707 isl_set_free(set2);
708
709 map = isl_map_read_from_str(ctx,
710 "[n] -> { [i0] -> [o0] : exists (e0 = [(i0)/4], e1 = [(o0)/4], "
711 "e2 = [(n)/2], e3 = [(-2 + i0)/4], e4 = [(-2 + o0)/4], "
712 "e5 = [(-2n + i0)/4]: 2e2 = n and 4e3 = -2 + i0 and "
713 "4e4 = -2 + o0 and i0 >= 8 + 2n and o0 >= 2 + i0 and "
714 "o0 <= 56 + 2n and o0 <= -12 + 4n and i0 <= 57 + 2n and "
715 "i0 <= -11 + 4n and o0 >= 6 + 2n and 4e0 <= i0 and "
716 "4e0 >= -3 + i0 and 4e1 <= o0 and 4e1 >= -3 + o0 and "
717 "4e5 <= -2n + i0 and 4e5 >= -3 - 2n + i0);"
718 "[i0] -> [o0] : exists (e0 = [(i0)/4], e1 = [(o0)/4], "
719 "e2 = [(n)/2], e3 = [(-2 + i0)/4], e4 = [(-2 + o0)/4], "
720 "e5 = [(-2n + i0)/4]: 2e2 = n and 4e3 = -2 + i0 and "
721 "4e4 = -2 + o0 and 2e0 >= 3 + n and e0 <= -4 + n and "
722 "2e0 <= 27 + n and e1 <= -4 + n and 2e1 <= 27 + n and "
723 "2e1 >= 2 + n and e1 >= 1 + e0 and i0 >= 7 + 2n and "
724 "i0 <= -11 + 4n and i0 <= 57 + 2n and 4e0 <= -2 + i0 and "
725 "4e0 >= -3 + i0 and o0 >= 6 + 2n and o0 <= -11 + 4n and "
726 "o0 <= 57 + 2n and 4e1 <= -2 + o0 and 4e1 >= -3 + o0 and "
727 "4e5 <= -2n + i0 and 4e5 >= -3 - 2n + i0 ) }", -1);
728 map = isl_map_coalesce(map);
729 map2 = isl_map_read_from_str(ctx,
730 "[n] -> { [i0] -> [o0] : exists (e0 = [(i0)/4], e1 = [(o0)/4], "
731 "e2 = [(n)/2], e3 = [(-2 + i0)/4], e4 = [(-2 + o0)/4], "
732 "e5 = [(-2n + i0)/4]: 2e2 = n and 4e3 = -2 + i0 and "
733 "4e4 = -2 + o0 and i0 >= 8 + 2n and o0 >= 2 + i0 and "
734 "o0 <= 56 + 2n and o0 <= -12 + 4n and i0 <= 57 + 2n and "
735 "i0 <= -11 + 4n and o0 >= 6 + 2n and 4e0 <= i0 and "
736 "4e0 >= -3 + i0 and 4e1 <= o0 and 4e1 >= -3 + o0 and "
737 "4e5 <= -2n + i0 and 4e5 >= -3 - 2n + i0);"
738 "[i0] -> [o0] : exists (e0 = [(i0)/4], e1 = [(o0)/4], "
739 "e2 = [(n)/2], e3 = [(-2 + i0)/4], e4 = [(-2 + o0)/4], "
740 "e5 = [(-2n + i0)/4]: 2e2 = n and 4e3 = -2 + i0 and "
741 "4e4 = -2 + o0 and 2e0 >= 3 + n and e0 <= -4 + n and "
742 "2e0 <= 27 + n and e1 <= -4 + n and 2e1 <= 27 + n and "
743 "2e1 >= 2 + n and e1 >= 1 + e0 and i0 >= 7 + 2n and "
744 "i0 <= -11 + 4n and i0 <= 57 + 2n and 4e0 <= -2 + i0 and "
745 "4e0 >= -3 + i0 and o0 >= 6 + 2n and o0 <= -11 + 4n and "
746 "o0 <= 57 + 2n and 4e1 <= -2 + o0 and 4e1 >= -3 + o0 and "
747 "4e5 <= -2n + i0 and 4e5 >= -3 - 2n + i0 ) }", -1);
748 assert(isl_map_is_equal(map, map2));
749 isl_map_free(map);
750 isl_map_free(map2);
751
752 str = "[n, m] -> { [] -> [o0, o2, o3] : (o3 = 1 and o0 >= 1 + m and "
753 "o0 <= n + m and o2 <= m and o0 >= 2 + n and o2 >= 3) or "
754 "(o0 >= 2 + n and o0 >= 1 + m and o0 <= n + m and n >= 1 and "
755 "o3 <= -1 + o2 and o3 >= 1 - m + o2 and o3 >= 2 and o3 <= n) }";
756 map = isl_map_read_from_str(ctx, str, -1);
757 map = isl_map_coalesce(map);
758 map2 = isl_map_read_from_str(ctx, str, -1);
759 assert(isl_map_is_equal(map, map2));
760 isl_map_free(map);
761 isl_map_free(map2);
762
763 str = "[M, N] -> { [i0, i1, i2, i3, i4, i5, i6] -> "
764 "[o0, o1, o2, o3, o4, o5, o6] : "
765 "(o6 <= -4 + 2M - 2N + i0 + i1 - i2 + i6 - o0 - o1 + o2 and "
766 "o3 <= -2 + i3 and o6 >= 2 + i0 + i3 + i6 - o0 - o3 and "
767 "o6 >= 2 - M + N + i3 + i4 + i6 - o3 - o4 and o0 <= -1 + i0 and "
768 "o4 >= 4 - 3M + 3N - i0 - i1 + i2 + 2i3 + i4 + o0 + o1 - o2 - 2o3 "
769 "and o6 <= -3 + 2M - 2N + i3 + i4 - i5 + i6 - o3 - o4 + o5 and "
770 "2o6 <= -5 + 5M - 5N + 2i0 + i1 - i2 - i5 + 2i6 - 2o0 - o1 + o2 + o5 "
771 "and o6 >= 2i0 + i1 + i6 - 2o0 - o1 and "
772 "3o6 <= -5 + 4M - 4N + 2i0 + i1 - i2 + 2i3 + i4 - i5 + 3i6 "
773 "- 2o0 - o1 + o2 - 2o3 - o4 + o5) or "
774 "(N >= 2 and o3 <= -1 + i3 and o0 <= -1 + i0 and "
775 "o6 >= i3 + i6 - o3 and M >= 0 and "
776 "2o6 >= 1 + i0 + i3 + 2i6 - o0 - o3 and "
777 "o6 >= 1 - M + i0 + i6 - o0 and N >= 2M and o6 >= i0 + i6 - o0) }";
778 map = isl_map_read_from_str(ctx, str, -1);
779 map = isl_map_coalesce(map);
780 map2 = isl_map_read_from_str(ctx, str, -1);
781 assert(isl_map_is_equal(map, map2));
782 isl_map_free(map);
783 isl_map_free(map2);
784
785 str = "[M, N] -> { [] -> [o0] : (o0 = 0 and M >= 1 and N >= 2) or "
786 "(o0 = 0 and M >= 1 and N >= 2M and N >= 2 + M) or "
787 "(o0 = 0 and M >= 2 and N >= 3) or "
788 "(M = 0 and o0 = 0 and N >= 3) }";
789 map = isl_map_read_from_str(ctx, str, -1);
790 map = isl_map_coalesce(map);
791 map2 = isl_map_read_from_str(ctx, str, -1);
792 assert(isl_map_is_equal(map, map2));
793 isl_map_free(map);
794 isl_map_free(map2);
795
796 str = "{ [i0, i1, i2, i3] : (i1 = 10i0 and i0 >= 1 and 10i0 <= 100 and "
797 "i3 <= 9 + 10 i2 and i3 >= 1 + 10i2 and i3 >= 0) or "
798 "(i1 <= 9 + 10i0 and i1 >= 1 + 10i0 and i2 >= 0 and "
799 "i0 >= 0 and i1 <= 100 and i3 <= 9 + 10i2 and i3 >= 1 + 10i2) }";
800 map = isl_map_read_from_str(ctx, str, -1);
801 map = isl_map_coalesce(map);
802 map2 = isl_map_read_from_str(ctx, str, -1);
803 assert(isl_map_is_equal(map, map2));
804 isl_map_free(map);
805 isl_map_free(map2);
806
807 test_coalesce_set(ctx,
808 "[M] -> { [i1] : (i1 >= 2 and i1 <= M) or "
809 "(i1 = M and M >= 1) }", 0);
810 test_coalesce_set(ctx,
811 "{[x,y] : x,y >= 0; [x,y] : 10 <= x <= 20 and y >= -1 }", 0);
812 test_coalesce_set(ctx,
813 "{ [x, y] : (x >= 1 and y >= 1 and x <= 2 and y <= 2) or "
814 "(y = 3 and x = 1) }", 1);
815 test_coalesce_set(ctx,
816 "[M] -> { [i0, i1, i2, i3, i4] : (i1 >= 3 and i4 >= 2 + i2 and "
817 "i2 >= 2 and i0 >= 2 and i3 >= 1 + i2 and i0 <= M and "
818 "i1 <= M and i3 <= M and i4 <= M) or "
819 "(i1 >= 2 and i4 >= 1 + i2 and i2 >= 2 and i0 >= 2 and "
820 "i3 >= 1 + i2 and i0 <= M and i1 <= -1 + M and i3 <= M and "
821 "i4 <= -1 + M) }", 1);
822 test_coalesce_set(ctx,
823 "{ [x, y] : (x >= 0 and y >= 0 and x <= 10 and y <= 10) or "
824 "(x >= 1 and y >= 1 and x <= 11 and y <= 11) }", 1);
825 test_coalesce_set(ctx,
826 "{[x,y,z] : y + 2 >= 0 and x - y + 1 >= 0 and "
827 "-x - y + 1 >= 0 and -3 <= z <= 3;"
828 "[x,y,z] : -x+z + 20 >= 0 and -x-z + 20 >= 0 and "
829 "x-z + 20 >= 0 and x+z + 20 >= 0 and -10 <= y <= 0}", 1);
830 test_coalesce_set(ctx,
831 "{[x,y] : 0 <= x,y <= 10; [5,y]: 4 <=y <= 11}", 1);
832 }
833
834 void test_closure(struct isl_ctx *ctx)
835 {
836 const char *str;
837 isl_set *dom;
838 isl_map *up, *right;
839 isl_map *map, *map2;
840 int exact;
841
842 /* COCOA example 1 */
843 map = isl_map_read_from_str(ctx,
844 "[n,k] -> { [i,j] -> [i2,j2] : i2 = i + 1 and j2 = j + 1 and "
845 "1 <= i and i < n and 1 <= j and j < n or "
846 "i2 = i + 1 and j2 = j - 1 and "
847 "1 <= i and i < n and 2 <= j and j <= n }", -1);
848 map = isl_map_power(map, 1, &exact);
849 assert(exact);
850 isl_map_free(map);
851
852 /* COCOA example 1 */
853 map = isl_map_read_from_str(ctx,
854 "[n] -> { [i,j] -> [i2,j2] : i2 = i + 1 and j2 = j + 1 and "
855 "1 <= i and i < n and 1 <= j and j < n or "
856 "i2 = i + 1 and j2 = j - 1 and "
857 "1 <= i and i < n and 2 <= j and j <= n }", -1);
858 map = isl_map_transitive_closure(map, &exact);
859 assert(exact);
860 map2 = isl_map_read_from_str(ctx,
861 "[n] -> { [i,j] -> [i2,j2] : exists (k1,k2,k : "
862 "1 <= i and i < n and 1 <= j and j <= n and "
863 "2 <= i2 and i2 <= n and 1 <= j2 and j2 <= n and "
864 "i2 = i + k1 + k2 and j2 = j + k1 - k2 and "
865 "k1 >= 0 and k2 >= 0 and k1 + k2 = k and k >= 1 )}", -1);
866 assert(isl_map_is_equal(map, map2));
867 isl_map_free(map2);
868 isl_map_free(map);
869
870 map = isl_map_read_from_str(ctx,
871 "[n] -> { [x] -> [y] : y = x + 1 and 0 <= x and x <= n and "
872 " 0 <= y and y <= n }", -1);
873 map = isl_map_transitive_closure(map, &exact);
874 map2 = isl_map_read_from_str(ctx,
875 "[n] -> { [x] -> [y] : y > x and 0 <= x and x <= n and "
876 " 0 <= y and y <= n }", -1);
877 assert(isl_map_is_equal(map, map2));
878 isl_map_free(map2);
879 isl_map_free(map);
880
881 /* COCOA example 2 */
882 map = isl_map_read_from_str(ctx,
883 "[n] -> { [i,j] -> [i2,j2] : i2 = i + 2 and j2 = j + 2 and "
884 "1 <= i and i < n - 1 and 1 <= j and j < n - 1 or "
885 "i2 = i + 2 and j2 = j - 2 and "
886 "1 <= i and i < n - 1 and 3 <= j and j <= n }", -1);
887 map = isl_map_transitive_closure(map, &exact);
888 assert(exact);
889 map2 = isl_map_read_from_str(ctx,
890 "[n] -> { [i,j] -> [i2,j2] : exists (k1,k2,k : "
891 "1 <= i and i < n - 1 and 1 <= j and j <= n and "
892 "3 <= i2 and i2 <= n and 1 <= j2 and j2 <= n and "
893 "i2 = i + 2 k1 + 2 k2 and j2 = j + 2 k1 - 2 k2 and "
894 "k1 >= 0 and k2 >= 0 and k1 + k2 = k and k >= 1) }", -1);
895 assert(isl_map_is_equal(map, map2));
896 isl_map_free(map);
897 isl_map_free(map2);
898
899 /* COCOA Fig.2 left */
900 map = isl_map_read_from_str(ctx,
901 "[n] -> { [i,j] -> [i2,j2] : i2 = i + 2 and j2 = j and "
902 "i <= 2 j - 3 and i <= n - 2 and j <= 2 i - 1 and "
903 "j <= n or "
904 "i2 = i and j2 = j + 2 and i <= 2 j - 1 and i <= n and "
905 "j <= 2 i - 3 and j <= n - 2 or "
906 "i2 = i + 1 and j2 = j + 1 and i <= 2 j - 1 and "
907 "i <= n - 1 and j <= 2 i - 1 and j <= n - 1 }", -1);
908 map = isl_map_transitive_closure(map, &exact);
909 assert(exact);
910 isl_map_free(map);
911
912 /* COCOA Fig.2 right */
913 map = isl_map_read_from_str(ctx,
914 "[n,k] -> { [i,j] -> [i2,j2] : i2 = i + 3 and j2 = j and "
915 "i <= 2 j - 4 and i <= n - 3 and j <= 2 i - 1 and "
916 "j <= n or "
917 "i2 = i and j2 = j + 3 and i <= 2 j - 1 and i <= n and "
918 "j <= 2 i - 4 and j <= n - 3 or "
919 "i2 = i + 1 and j2 = j + 1 and i <= 2 j - 1 and "
920 "i <= n - 1 and j <= 2 i - 1 and j <= n - 1 }", -1);
921 map = isl_map_power(map, 1, &exact);
922 assert(exact);
923 isl_map_free(map);
924
925 /* COCOA Fig.2 right */
926 map = isl_map_read_from_str(ctx,
927 "[n] -> { [i,j] -> [i2,j2] : i2 = i + 3 and j2 = j and "
928 "i <= 2 j - 4 and i <= n - 3 and j <= 2 i - 1 and "
929 "j <= n or "
930 "i2 = i and j2 = j + 3 and i <= 2 j - 1 and i <= n and "
931 "j <= 2 i - 4 and j <= n - 3 or "
932 "i2 = i + 1 and j2 = j + 1 and i <= 2 j - 1 and "
933 "i <= n - 1 and j <= 2 i - 1 and j <= n - 1 }", -1);
934 map = isl_map_transitive_closure(map, &exact);
935 assert(exact);
936 map2 = isl_map_read_from_str(ctx,
937 "[n] -> { [i,j] -> [i2,j2] : exists (k1,k2,k3,k : "
938 "i <= 2 j - 1 and i <= n and j <= 2 i - 1 and "
939 "j <= n and 3 + i + 2 j <= 3 n and "
940 "3 + 2 i + j <= 3n and i2 <= 2 j2 -1 and i2 <= n and "
941 "i2 <= 3 j2 - 4 and j2 <= 2 i2 -1 and j2 <= n and "
942 "13 + 4 j2 <= 11 i2 and i2 = i + 3 k1 + k3 and "
943 "j2 = j + 3 k2 + k3 and k1 >= 0 and k2 >= 0 and "
944 "k3 >= 0 and k1 + k2 + k3 = k and k > 0) }", -1);
945 assert(isl_map_is_equal(map, map2));
946 isl_map_free(map2);
947 isl_map_free(map);
948
949 /* COCOA Fig.1 right */
950 dom = isl_set_read_from_str(ctx,
951 "{ [x,y] : x >= 0 and -2 x + 3 y >= 0 and x <= 3 and "
952 "2 x - 3 y + 3 >= 0 }", -1);
953 right = isl_map_read_from_str(ctx,
954 "{ [x,y] -> [x2,y2] : x2 = x + 1 and y2 = y }", -1);
955 up = isl_map_read_from_str(ctx,
956 "{ [x,y] -> [x2,y2] : x2 = x and y2 = y + 1 }", -1);
957 right = isl_map_intersect_domain(right, isl_set_copy(dom));
958 right = isl_map_intersect_range(right, isl_set_copy(dom));
959 up = isl_map_intersect_domain(up, isl_set_copy(dom));
960 up = isl_map_intersect_range(up, dom);
961 map = isl_map_union(up, right);
962 map = isl_map_transitive_closure(map, &exact);
963 assert(exact);
964 map2 = isl_map_read_from_str(ctx,
965 "{ [0,0] -> [0,1]; [0,0] -> [1,1]; [0,1] -> [1,1]; "
966 " [2,2] -> [3,2]; [2,2] -> [3,3]; [3,2] -> [3,3] }", -1);
967 assert(isl_map_is_equal(map, map2));
968 isl_map_free(map2);
969 isl_map_free(map);
970
971 /* COCOA Theorem 1 counter example */
972 map = isl_map_read_from_str(ctx,
973 "{ [i,j] -> [i2,j2] : i = 0 and 0 <= j and j <= 1 and "
974 "i2 = 1 and j2 = j or "
975 "i = 0 and j = 0 and i2 = 0 and j2 = 1 }", -1);
976 map = isl_map_transitive_closure(map, &exact);
977 assert(exact);
978 isl_map_free(map);
979
980 map = isl_map_read_from_str(ctx,
981 "[m,n] -> { [i,j] -> [i2,j2] : i2 = i and j2 = j + 2 and "
982 "1 <= i,i2 <= n and 1 <= j,j2 <= m or "
983 "i2 = i + 1 and 3 <= j2 - j <= 4 and "
984 "1 <= i,i2 <= n and 1 <= j,j2 <= m }", -1);
985 map = isl_map_transitive_closure(map, &exact);
986 assert(exact);
987 isl_map_free(map);
988
989 /* Kelly et al 1996, fig 12 */
990 map = isl_map_read_from_str(ctx,
991 "[n] -> { [i,j] -> [i2,j2] : i2 = i and j2 = j + 1 and "
992 "1 <= i,j,j+1 <= n or "
993 "j = n and j2 = 1 and i2 = i + 1 and "
994 "1 <= i,i+1 <= n }", -1);
995 map = isl_map_transitive_closure(map, &exact);
996 assert(exact);
997 map2 = isl_map_read_from_str(ctx,
998 "[n] -> { [i,j] -> [i2,j2] : 1 <= j < j2 <= n and "
999 "1 <= i <= n and i = i2 or "
1000 "1 <= i < i2 <= n and 1 <= j <= n and "
1001 "1 <= j2 <= n }", -1);
1002 assert(isl_map_is_equal(map, map2));
1003 isl_map_free(map2);
1004 isl_map_free(map);
1005
1006 /* Omega's closure4 */
1007 map = isl_map_read_from_str(ctx,
1008 "[m,n] -> { [x,y] -> [x2,y2] : x2 = x and y2 = y + 1 and "
1009 "1 <= x,y <= 10 or "
1010 "x2 = x + 1 and y2 = y and "
1011 "1 <= x <= 20 && 5 <= y <= 15 }", -1);
1012 map = isl_map_transitive_closure(map, &exact);
1013 assert(exact);
1014 isl_map_free(map);
1015
1016 map = isl_map_read_from_str(ctx,
1017 "[n] -> { [x] -> [y]: 1 <= n <= y - x <= 10 }", -1);
1018 map = isl_map_transitive_closure(map, &exact);
1019 assert(!exact);
1020 map2 = isl_map_read_from_str(ctx,
1021 "[n] -> { [x] -> [y] : 1 <= n <= 10 and y >= n + x }", -1);
1022 assert(isl_map_is_equal(map, map2));
1023 isl_map_free(map);
1024 isl_map_free(map2);
1025
1026 str = "[n, m] -> { [i0, i1, i2, i3] -> [o0, o1, o2, o3] : "
1027 "i3 = 1 and o0 = i0 and o1 = -1 + i1 and o2 = -1 + i2 and "
1028 "o3 = -2 + i2 and i1 <= -1 + i0 and i1 >= 1 - m + i0 and "
1029 "i1 >= 2 and i1 <= n and i2 >= 3 and i2 <= 1 + n and i2 <= m }";
1030 map = isl_map_read_from_str(ctx, str, -1);
1031 map = isl_map_transitive_closure(map, &exact);
1032 assert(exact);
1033 map2 = isl_map_read_from_str(ctx, str, -1);
1034 assert(isl_map_is_equal(map, map2));
1035 isl_map_free(map);
1036 isl_map_free(map2);
1037
1038 str = "{[0] -> [1]; [2] -> [3]}";
1039 map = isl_map_read_from_str(ctx, str, -1);
1040 map = isl_map_transitive_closure(map, &exact);
1041 assert(exact);
1042 map2 = isl_map_read_from_str(ctx, str, -1);
1043 assert(isl_map_is_equal(map, map2));
1044 isl_map_free(map);
1045 isl_map_free(map2);
1046 }
1047
1048 void test_lex(struct isl_ctx *ctx)
1049 {
1050 isl_dim *dim;
1051 isl_map *map;
1052
1053 dim = isl_dim_alloc(ctx, 0, 0, 0);
1054 map = isl_map_lex_le(dim);
1055 assert(!isl_map_is_empty(map));
1056 isl_map_free(map);
1057 }
1058
1059 void test_lexmin(struct isl_ctx *ctx)
1060 {
1061 const char *str;
1062 isl_map *map;
1063 isl_set *set;
1064 isl_set *set2;
1065
1066 str = "[p0, p1] -> { [] -> [] : "
1067 "exists (e0 = [(2p1)/3], e1, e2, e3 = [(3 - p1 + 3e0)/3], "
1068 "e4 = [(p1)/3], e5 = [(p1 + 3e4)/3]: "
1069 "3e0 >= -2 + 2p1 and 3e0 >= p1 and 3e3 >= 1 - p1 + 3e0 and "
1070 "3e0 <= 2p1 and 3e3 >= -2 + p1 and 3e3 <= -1 + p1 and p1 >= 3 and "
1071 "3e5 >= -2 + 2p1 and 3e5 >= p1 and 3e5 <= -1 + p1 + 3e4 and "
1072 "3e4 <= p1 and 3e4 >= -2 + p1 and e3 <= -1 + e0 and "
1073 "3e4 >= 6 - p1 + 3e1 and 3e1 >= p1 and 3e5 >= -2 + p1 + 3e4 and "
1074 "2e4 >= 3 - p1 + 2e1 and e4 <= e1 and 3e3 <= 2 - p1 + 3e0 and "
1075 "e5 >= 1 + e1 and 3e4 >= 6 - 2p1 + 3e1 and "
1076 "p0 >= 2 and p1 >= p0 and 3e2 >= p1 and 3e4 >= 6 - p1 + 3e2 and "
1077 "e2 <= e1 and e3 >= 1 and e4 <= e2) }";
1078 map = isl_map_read_from_str(ctx, str, -1);
1079 map = isl_map_lexmin(map);
1080 isl_map_free(map);
1081
1082 str = "[C] -> { [obj,a,b,c] : obj <= 38 a + 7 b + 10 c and "
1083 "a + b <= 1 and c <= 10 b and c <= C and a,b,c,C >= 0 }";
1084 set = isl_set_read_from_str(ctx, str, -1);
1085 set = isl_set_lexmax(set);
1086 str = "[C] -> { [obj,a,b,c] : C = 8 }";
1087 set2 = isl_set_read_from_str(ctx, str, -1);
1088 set = isl_set_intersect(set, set2);
1089 assert(!isl_set_is_empty(set));
1090 isl_set_free(set);
1091 }
1092
1093 struct must_may {
1094 isl_map *must;
1095 isl_map *may;
1096 };
1097
1098 static int collect_must_may(__isl_take isl_map *dep, int must,
1099 void *dep_user, void *user)
1100 {
1101 struct must_may *mm = (struct must_may *)user;
1102
1103 if (must)
1104 mm->must = isl_map_union(mm->must, dep);
1105 else
1106 mm->may = isl_map_union(mm->may, dep);
1107
1108 return 0;
1109 }
1110
1111 static int common_space(void *first, void *second)
1112 {
1113 int depth = *(int *)first;
1114 return 2 * depth;
1115 }
1116
1117 static int map_is_equal(__isl_keep isl_map *map, const char *str)
1118 {
1119 isl_map *map2;
1120 int equal;
1121
1122 if (!map)
1123 return -1;
1124
1125 map2 = isl_map_read_from_str(map->ctx, str, -1);
1126 equal = isl_map_is_equal(map, map2);
1127 isl_map_free(map2);
1128
1129 return equal;
1130 }
1131
1132 void test_dep(struct isl_ctx *ctx)
1133 {
1134 const char *str;
1135 isl_dim *dim;
1136 isl_map *map;
1137 isl_access_info *ai;
1138 isl_flow *flow;
1139 int depth;
1140 struct must_may mm;
1141
1142 depth = 3;
1143
1144 str = "{ [2,i,0] -> [i] : 0 <= i <= 10 }";
1145 map = isl_map_read_from_str(ctx, str, -1);
1146 ai = isl_access_info_alloc(map, &depth, &common_space, 2);
1147
1148 str = "{ [0,i,0] -> [i] : 0 <= i <= 10 }";
1149 map = isl_map_read_from_str(ctx, str, -1);
1150 ai = isl_access_info_add_source(ai, map, 1, &depth);
1151
1152 str = "{ [1,i,0] -> [5] : 0 <= i <= 10 }";
1153 map = isl_map_read_from_str(ctx, str, -1);
1154 ai = isl_access_info_add_source(ai, map, 1, &depth);
1155
1156 flow = isl_access_info_compute_flow(ai);
1157 dim = isl_dim_alloc(ctx, 0, 3, 3);
1158 mm.must = isl_map_empty(isl_dim_copy(dim));
1159 mm.may = isl_map_empty(dim);
1160
1161 isl_flow_foreach(flow, collect_must_may, &mm);
1162
1163 str = "{ [0,i,0] -> [2,i,0] : (0 <= i <= 4) or (6 <= i <= 10); "
1164 " [1,10,0] -> [2,5,0] }";
1165 assert(map_is_equal(mm.must, str));
1166 str = "{ [i,j,k] -> [l,m,n] : 1 = 0 }";
1167 assert(map_is_equal(mm.may, str));
1168
1169 isl_map_free(mm.must);
1170 isl_map_free(mm.may);
1171 isl_flow_free(flow);
1172
1173
1174 str = "{ [2,i,0] -> [i] : 0 <= i <= 10 }";
1175 map = isl_map_read_from_str(ctx, str, -1);
1176 ai = isl_access_info_alloc(map, &depth, &common_space, 2);
1177
1178 str = "{ [0,i,0] -> [i] : 0 <= i <= 10 }";
1179 map = isl_map_read_from_str(ctx, str, -1);
1180 ai = isl_access_info_add_source(ai, map, 1, &depth);
1181
1182 str = "{ [1,i,0] -> [5] : 0 <= i <= 10 }";
1183 map = isl_map_read_from_str(ctx, str, -1);
1184 ai = isl_access_info_add_source(ai, map, 0, &depth);
1185
1186 flow = isl_access_info_compute_flow(ai);
1187 dim = isl_dim_alloc(ctx, 0, 3, 3);
1188 mm.must = isl_map_empty(isl_dim_copy(dim));
1189 mm.may = isl_map_empty(dim);
1190
1191 isl_flow_foreach(flow, collect_must_may, &mm);
1192
1193 str = "{ [0,i,0] -> [2,i,0] : (0 <= i <= 4) or (6 <= i <= 10) }";
1194 assert(map_is_equal(mm.must, str));
1195 str = "{ [0,5,0] -> [2,5,0]; [1,i,0] -> [2,5,0] : 0 <= i <= 10 }";
1196 assert(map_is_equal(mm.may, str));
1197
1198 isl_map_free(mm.must);
1199 isl_map_free(mm.may);
1200 isl_flow_free(flow);
1201
1202
1203 str = "{ [2,i,0] -> [i] : 0 <= i <= 10 }";
1204 map = isl_map_read_from_str(ctx, str, -1);
1205 ai = isl_access_info_alloc(map, &depth, &common_space, 2);
1206
1207 str = "{ [0,i,0] -> [i] : 0 <= i <= 10 }";
1208 map = isl_map_read_from_str(ctx, str, -1);
1209 ai = isl_access_info_add_source(ai, map, 0, &depth);
1210
1211 str = "{ [1,i,0] -> [5] : 0 <= i <= 10 }";
1212 map = isl_map_read_from_str(ctx, str, -1);
1213 ai = isl_access_info_add_source(ai, map, 0, &depth);
1214
1215 flow = isl_access_info_compute_flow(ai);
1216 dim = isl_dim_alloc(ctx, 0, 3, 3);
1217 mm.must = isl_map_empty(isl_dim_copy(dim));
1218 mm.may = isl_map_empty(dim);
1219
1220 isl_flow_foreach(flow, collect_must_may, &mm);
1221
1222 str = "{ [0,i,0] -> [2,i,0] : 0 <= i <= 10; "
1223 " [1,i,0] -> [2,5,0] : 0 <= i <= 10 }";
1224 assert(map_is_equal(mm.may, str));
1225 str = "{ [i,j,k] -> [l,m,n] : 1 = 0 }";
1226 assert(map_is_equal(mm.must, str));
1227
1228 isl_map_free(mm.must);
1229 isl_map_free(mm.may);
1230 isl_flow_free(flow);
1231
1232
1233 str = "{ [0,i,2] -> [i] : 0 <= i <= 10 }";
1234 map = isl_map_read_from_str(ctx, str, -1);
1235 ai = isl_access_info_alloc(map, &depth, &common_space, 2);
1236
1237 str = "{ [0,i,0] -> [i] : 0 <= i <= 10 }";
1238 map = isl_map_read_from_str(ctx, str, -1);
1239 ai = isl_access_info_add_source(ai, map, 0, &depth);
1240
1241 str = "{ [0,i,1] -> [5] : 0 <= i <= 10 }";
1242 map = isl_map_read_from_str(ctx, str, -1);
1243 ai = isl_access_info_add_source(ai, map, 0, &depth);
1244
1245 flow = isl_access_info_compute_flow(ai);
1246 dim = isl_dim_alloc(ctx, 0, 3, 3);
1247 mm.must = isl_map_empty(isl_dim_copy(dim));
1248 mm.may = isl_map_empty(dim);
1249
1250 isl_flow_foreach(flow, collect_must_may, &mm);
1251
1252 str = "{ [0,i,0] -> [0,i,2] : 0 <= i <= 10; "
1253 " [0,i,1] -> [0,5,2] : 0 <= i <= 5 }";
1254 assert(map_is_equal(mm.may, str));
1255 str = "{ [i,j,k] -> [l,m,n] : 1 = 0 }";
1256 assert(map_is_equal(mm.must, str));
1257
1258 isl_map_free(mm.must);
1259 isl_map_free(mm.may);
1260 isl_flow_free(flow);
1261
1262
1263 str = "{ [0,i,1] -> [i] : 0 <= i <= 10 }";
1264 map = isl_map_read_from_str(ctx, str, -1);
1265 ai = isl_access_info_alloc(map, &depth, &common_space, 2);
1266
1267 str = "{ [0,i,0] -> [i] : 0 <= i <= 10 }";
1268 map = isl_map_read_from_str(ctx, str, -1);
1269 ai = isl_access_info_add_source(ai, map, 0, &depth);
1270
1271 str = "{ [0,i,2] -> [5] : 0 <= i <= 10 }";
1272 map = isl_map_read_from_str(ctx, str, -1);
1273 ai = isl_access_info_add_source(ai, map, 0, &depth);
1274
1275 flow = isl_access_info_compute_flow(ai);
1276 dim = isl_dim_alloc(ctx, 0, 3, 3);
1277 mm.must = isl_map_empty(isl_dim_copy(dim));
1278 mm.may = isl_map_empty(dim);
1279
1280 isl_flow_foreach(flow, collect_must_may, &mm);
1281
1282 str = "{ [0,i,0] -> [0,i,1] : 0 <= i <= 10; "
1283 " [0,i,2] -> [0,5,1] : 0 <= i <= 4 }";
1284 assert(map_is_equal(mm.may, str));
1285 str = "{ [i,j,k] -> [l,m,n] : 1 = 0 }";
1286 assert(map_is_equal(mm.must, str));
1287
1288 isl_map_free(mm.must);
1289 isl_map_free(mm.may);
1290 isl_flow_free(flow);
1291
1292
1293 depth = 5;
1294
1295 str = "{ [1,i,0,0,0] -> [i,j] : 0 <= i <= 10 and 0 <= j <= 10 }";
1296 map = isl_map_read_from_str(ctx, str, -1);
1297 ai = isl_access_info_alloc(map, &depth, &common_space, 1);
1298
1299 str = "{ [0,i,0,j,0] -> [i,j] : 0 <= i <= 10 and 0 <= j <= 10 }";
1300 map = isl_map_read_from_str(ctx, str, -1);
1301 ai = isl_access_info_add_source(ai, map, 1, &depth);
1302
1303 flow = isl_access_info_compute_flow(ai);
1304 dim = isl_dim_alloc(ctx, 0, 5, 5);
1305 mm.must = isl_map_empty(isl_dim_copy(dim));
1306 mm.may = isl_map_empty(dim);
1307
1308 isl_flow_foreach(flow, collect_must_may, &mm);
1309
1310 str = "{ [0,i,0,j,0] -> [1,i,0,0,0] : 0 <= i,j <= 10 }";
1311 assert(map_is_equal(mm.must, str));
1312 str = "{ [0,0,0,0,0] -> [0,0,0,0,0] : 1 = 0 }";
1313 assert(map_is_equal(mm.may, str));
1314
1315 isl_map_free(mm.must);
1316 isl_map_free(mm.may);
1317 isl_flow_free(flow);
1318 }
1319
1320 void test_sv(struct isl_ctx *ctx)
1321 {
1322 const char *str;
1323 isl_map *map;
1324
1325 str = "[N] -> { [i] -> [f] : 0 <= i <= N and 0 <= i - 10 f <= 9 }";
1326 map = isl_map_read_from_str(ctx, str, -1);
1327 assert(isl_map_is_single_valued(map));
1328 isl_map_free(map);
1329
1330 str = "[N] -> { [i] -> [f] : 0 <= i <= N and 0 <= i - 10 f <= 10 }";
1331 map = isl_map_read_from_str(ctx, str, -1);
1332 assert(!isl_map_is_single_valued(map));
1333 isl_map_free(map);
1334 }
1335
1336 void test_bijective_case(struct isl_ctx *ctx, const char *str, int bijective)
1337 {
1338 isl_map *map;
1339
1340 map = isl_map_read_from_str(ctx, str, -1);
1341 if (bijective)
1342 assert(isl_map_is_bijective(map));
1343 else
1344 assert(!isl_map_is_bijective(map));
1345 isl_map_free(map);
1346 }
1347
1348 void test_bijective(struct isl_ctx *ctx)
1349 {
1350 test_bijective_case(ctx, "[N,M]->{[i,j] -> [i]}", 0);
1351 test_bijective_case(ctx, "[N,M]->{[i,j] -> [i] : j=i}", 1);
1352 test_bijective_case(ctx, "[N,M]->{[i,j] -> [i] : j=0}", 1);
1353 test_bijective_case(ctx, "[N,M]->{[i,j] -> [i] : j=N}", 1);
1354 test_bijective_case(ctx, "[N,M]->{[i,j] -> [j,i]}", 1);
1355 test_bijective_case(ctx, "[N,M]->{[i,j] -> [i+j]}", 0);
1356 test_bijective_case(ctx, "[N,M]->{[i,j] -> []}", 0);
1357 test_bijective_case(ctx, "[N,M]->{[i,j] -> [i,j,N]}", 1);
1358 test_bijective_case(ctx, "[N,M]->{[i,j] -> [2i]}", 0);
1359 test_bijective_case(ctx, "[N,M]->{[i,j] -> [i,i]}", 0);
1360 test_bijective_case(ctx, "[N,M]->{[i,j] -> [2i,i]}", 0);
1361 test_bijective_case(ctx, "[N,M]->{[i,j] -> [2i,j]}", 1);
1362 test_bijective_case(ctx, "[N,M]->{[i,j] -> [x,y] : 2x=i & y =j}", 1);
1363 }
1364
1365 int main()
1366 {
1367 struct isl_ctx *ctx;
1368
1369 srcdir = getenv("srcdir");
1370 assert(srcdir);
1371
1372 ctx = isl_ctx_alloc();
1373 test_lex(ctx);
1374 test_sv(ctx);
1375 test_bijective(ctx);
1376 test_dep(ctx);
1377 test_read(ctx);
1378 test_bounded(ctx);
1379 test_construction(ctx);
1380 test_dim(ctx);
1381 test_div(ctx);
1382 test_application(ctx);
1383 test_affine_hull(ctx);
1384 test_convex_hull(ctx);
1385 test_gist(ctx);
1386 test_coalesce(ctx);
1387 test_closure(ctx);
1388 test_lexmin(ctx);
1389 isl_ctx_free(ctx);
1390 return 0;
1391 }
Integer set library