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isl_map_read_from_str: parse tuple entries with leading minus sign
[isl.git] / isl_test.c
blob24aca70d777a3e33b405157efbe112ab564960e6
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 #include <isl_polynomial.h>
18
19 static char *srcdir;
20
21 void test_parse(struct isl_ctx *ctx)
22 {
23 isl_map *map;
24 const char *str;
25
26 str = "{ [i] -> [-i] }";
27 map = isl_map_read_from_str(ctx, str, -1);
28 assert(map);
29 isl_map_free(map);
30 }
31
32 void test_read(struct isl_ctx *ctx)
33 {
34 char filename[PATH_MAX];
35 FILE *input;
36 int n;
37 struct isl_basic_set *bset1, *bset2;
38 const char *str = "{[y]: Exists ( alpha : 2alpha = y)}";
39
40 n = snprintf(filename, sizeof(filename),
41 "%s/test_inputs/set.omega", srcdir);
42 assert(n < sizeof(filename));
43 input = fopen(filename, "r");
44 assert(input);
45
46 bset1 = isl_basic_set_read_from_file(ctx, input, 0);
47 bset2 = isl_basic_set_read_from_str(ctx, str, 0);
48
49 assert(isl_basic_set_is_equal(bset1, bset2) == 1);
50
51 isl_basic_set_free(bset1);
52 isl_basic_set_free(bset2);
53
54 fclose(input);
55 }
56
57 void test_bounded(struct isl_ctx *ctx)
58 {
59 isl_set *set;
60 int bounded;
61
62 set = isl_set_read_from_str(ctx, "[n] -> {[i] : 0 <= i <= n }", -1);
63 bounded = isl_set_is_bounded(set);
64 assert(bounded);
65 isl_set_free(set);
66
67 set = isl_set_read_from_str(ctx, "{[n, i] : 0 <= i <= n }", -1);
68 bounded = isl_set_is_bounded(set);
69 assert(!bounded);
70 isl_set_free(set);
71
72 set = isl_set_read_from_str(ctx, "[n] -> {[i] : i <= n }", -1);
73 bounded = isl_set_is_bounded(set);
74 assert(!bounded);
75 isl_set_free(set);
76 }
77
78 /* Construct the basic set { [i] : 5 <= i <= N } */
79 void test_construction(struct isl_ctx *ctx)
80 {
81 isl_int v;
82 struct isl_dim *dim;
83 struct isl_basic_set *bset;
84 struct isl_constraint *c;
85
86 isl_int_init(v);
87
88 dim = isl_dim_set_alloc(ctx, 1, 1);
89 bset = isl_basic_set_universe(dim);
90
91 c = isl_inequality_alloc(isl_basic_set_get_dim(bset));
92 isl_int_set_si(v, -1);
93 isl_constraint_set_coefficient(c, isl_dim_set, 0, v);
94 isl_int_set_si(v, 1);
95 isl_constraint_set_coefficient(c, isl_dim_param, 0, v);
96 bset = isl_basic_set_add_constraint(bset, c);
97
98 c = isl_inequality_alloc(isl_basic_set_get_dim(bset));
99 isl_int_set_si(v, 1);
100 isl_constraint_set_coefficient(c, isl_dim_set, 0, v);
101 isl_int_set_si(v, -5);
102 isl_constraint_set_constant(c, v);
103 bset = isl_basic_set_add_constraint(bset, c);
104
105 isl_basic_set_free(bset);
106
107 isl_int_clear(v);
108 }
109
110 void test_dim(struct isl_ctx *ctx)
111 {
112 const char *str;
113 isl_map *map1, *map2;
114
115 map1 = isl_map_read_from_str(ctx,
116 "[n] -> { [i] -> [j] : exists (a = [i/10] : i - 10a <= n ) }", -1);
117 map1 = isl_map_add(map1, isl_dim_in, 1);
118 map2 = isl_map_read_from_str(ctx,
119 "[n] -> { [i,k] -> [j] : exists (a = [i/10] : i - 10a <= n ) }", -1);
120 assert(isl_map_is_equal(map1, map2));
121 isl_map_free(map2);
122
123 map1 = isl_map_project_out(map1, isl_dim_in, 0, 1);
124 map2 = isl_map_read_from_str(ctx, "[n] -> { [i] -> [j] : n >= 0 }", -1);
125 assert(isl_map_is_equal(map1, map2));
126
127 isl_map_free(map1);
128 isl_map_free(map2);
129
130 str = "[n] -> { [i] -> [] : exists a : 0 <= i <= n and i = 2 a }";
131 map1 = isl_map_read_from_str(ctx, str, -1);
132 str = "{ [i] -> [j] : exists a : 0 <= i <= j and i = 2 a }";
133 map2 = isl_map_read_from_str(ctx, str, -1);
134 map1 = isl_map_move_dims(map1, isl_dim_out, 0, isl_dim_param, 0, 1);
135 assert(isl_map_is_equal(map1, map2));
136
137 isl_map_free(map1);
138 isl_map_free(map2);
139 }
140
141 void test_div(struct isl_ctx *ctx)
142 {
143 isl_int v;
144 int pos;
145 struct isl_dim *dim;
146 struct isl_div *div;
147 struct isl_basic_set *bset;
148 struct isl_constraint *c;
149
150 isl_int_init(v);
151
152 /* test 1 */
153 dim = isl_dim_set_alloc(ctx, 0, 1);
154 bset = isl_basic_set_universe(dim);
155
156 c = isl_equality_alloc(isl_basic_set_get_dim(bset));
157 isl_int_set_si(v, -1);
158 isl_constraint_set_constant(c, v);
159 isl_int_set_si(v, 1);
160 isl_constraint_set_coefficient(c, isl_dim_set, 0, v);
161 div = isl_div_alloc(isl_basic_set_get_dim(bset));
162 c = isl_constraint_add_div(c, div, &pos);
163 isl_int_set_si(v, 3);
164 isl_constraint_set_coefficient(c, isl_dim_div, pos, v);
165 bset = isl_basic_set_add_constraint(bset, c);
166
167 c = isl_equality_alloc(isl_basic_set_get_dim(bset));
168 isl_int_set_si(v, 1);
169 isl_constraint_set_constant(c, v);
170 isl_int_set_si(v, -1);
171 isl_constraint_set_coefficient(c, isl_dim_set, 0, v);
172 div = isl_div_alloc(isl_basic_set_get_dim(bset));
173 c = isl_constraint_add_div(c, div, &pos);
174 isl_int_set_si(v, 3);
175 isl_constraint_set_coefficient(c, isl_dim_div, pos, v);
176 bset = isl_basic_set_add_constraint(bset, c);
177
178 assert(bset && bset->n_div == 1);
179 isl_basic_set_free(bset);
180
181 /* test 2 */
182 dim = isl_dim_set_alloc(ctx, 0, 1);
183 bset = isl_basic_set_universe(dim);
184
185 c = isl_equality_alloc(isl_basic_set_get_dim(bset));
186 isl_int_set_si(v, 1);
187 isl_constraint_set_constant(c, v);
188 isl_int_set_si(v, -1);
189 isl_constraint_set_coefficient(c, isl_dim_set, 0, v);
190 div = isl_div_alloc(isl_basic_set_get_dim(bset));
191 c = isl_constraint_add_div(c, div, &pos);
192 isl_int_set_si(v, 3);
193 isl_constraint_set_coefficient(c, isl_dim_div, pos, v);
194 bset = isl_basic_set_add_constraint(bset, c);
195
196 c = isl_equality_alloc(isl_basic_set_get_dim(bset));
197 isl_int_set_si(v, -1);
198 isl_constraint_set_constant(c, v);
199 isl_int_set_si(v, 1);
200 isl_constraint_set_coefficient(c, isl_dim_set, 0, v);
201 div = isl_div_alloc(isl_basic_set_get_dim(bset));
202 c = isl_constraint_add_div(c, div, &pos);
203 isl_int_set_si(v, 3);
204 isl_constraint_set_coefficient(c, isl_dim_div, pos, v);
205 bset = isl_basic_set_add_constraint(bset, c);
206
207 assert(bset && bset->n_div == 1);
208 isl_basic_set_free(bset);
209
210 /* test 3 */
211 dim = isl_dim_set_alloc(ctx, 0, 1);
212 bset = isl_basic_set_universe(dim);
213
214 c = isl_equality_alloc(isl_basic_set_get_dim(bset));
215 isl_int_set_si(v, 1);
216 isl_constraint_set_constant(c, v);
217 isl_int_set_si(v, -1);
218 isl_constraint_set_coefficient(c, isl_dim_set, 0, v);
219 div = isl_div_alloc(isl_basic_set_get_dim(bset));
220 c = isl_constraint_add_div(c, div, &pos);
221 isl_int_set_si(v, 3);
222 isl_constraint_set_coefficient(c, isl_dim_div, pos, v);
223 bset = isl_basic_set_add_constraint(bset, c);
224
225 c = isl_equality_alloc(isl_basic_set_get_dim(bset));
226 isl_int_set_si(v, -3);
227 isl_constraint_set_constant(c, v);
228 isl_int_set_si(v, 1);
229 isl_constraint_set_coefficient(c, isl_dim_set, 0, v);
230 div = isl_div_alloc(isl_basic_set_get_dim(bset));
231 c = isl_constraint_add_div(c, div, &pos);
232 isl_int_set_si(v, 4);
233 isl_constraint_set_coefficient(c, isl_dim_div, pos, v);
234 bset = isl_basic_set_add_constraint(bset, c);
235
236 assert(bset && bset->n_div == 1);
237 isl_basic_set_free(bset);
238
239 /* test 4 */
240 dim = isl_dim_set_alloc(ctx, 0, 1);
241 bset = isl_basic_set_universe(dim);
242
243 c = isl_equality_alloc(isl_basic_set_get_dim(bset));
244 isl_int_set_si(v, 2);
245 isl_constraint_set_constant(c, v);
246 isl_int_set_si(v, -1);
247 isl_constraint_set_coefficient(c, isl_dim_set, 0, v);
248 div = isl_div_alloc(isl_basic_set_get_dim(bset));
249 c = isl_constraint_add_div(c, div, &pos);
250 isl_int_set_si(v, 3);
251 isl_constraint_set_coefficient(c, isl_dim_div, pos, v);
252 bset = isl_basic_set_add_constraint(bset, c);
253
254 c = isl_equality_alloc(isl_basic_set_get_dim(bset));
255 isl_int_set_si(v, -1);
256 isl_constraint_set_constant(c, v);
257 isl_int_set_si(v, 1);
258 isl_constraint_set_coefficient(c, isl_dim_set, 0, v);
259 div = isl_div_alloc(isl_basic_set_get_dim(bset));
260 c = isl_constraint_add_div(c, div, &pos);
261 isl_int_set_si(v, 6);
262 isl_constraint_set_coefficient(c, isl_dim_div, pos, v);
263 bset = isl_basic_set_add_constraint(bset, c);
264
265 assert(isl_basic_set_is_empty(bset));
266 isl_basic_set_free(bset);
267
268 /* test 5 */
269 dim = isl_dim_set_alloc(ctx, 0, 2);
270 bset = isl_basic_set_universe(dim);
271
272 c = isl_equality_alloc(isl_basic_set_get_dim(bset));
273 isl_int_set_si(v, -1);
274 isl_constraint_set_coefficient(c, isl_dim_set, 0, v);
275 div = isl_div_alloc(isl_basic_set_get_dim(bset));
276 c = isl_constraint_add_div(c, div, &pos);
277 isl_int_set_si(v, 3);
278 isl_constraint_set_coefficient(c, isl_dim_div, pos, v);
279 bset = isl_basic_set_add_constraint(bset, c);
280
281 c = isl_equality_alloc(isl_basic_set_get_dim(bset));
282 isl_int_set_si(v, 1);
283 isl_constraint_set_coefficient(c, isl_dim_set, 0, v);
284 isl_int_set_si(v, -3);
285 isl_constraint_set_coefficient(c, isl_dim_set, 1, v);
286 bset = isl_basic_set_add_constraint(bset, c);
287
288 assert(bset && bset->n_div == 0);
289 isl_basic_set_free(bset);
290
291 /* test 6 */
292 dim = isl_dim_set_alloc(ctx, 0, 2);
293 bset = isl_basic_set_universe(dim);
294
295 c = isl_equality_alloc(isl_basic_set_get_dim(bset));
296 isl_int_set_si(v, -1);
297 isl_constraint_set_coefficient(c, isl_dim_set, 0, v);
298 div = isl_div_alloc(isl_basic_set_get_dim(bset));
299 c = isl_constraint_add_div(c, div, &pos);
300 isl_int_set_si(v, 6);
301 isl_constraint_set_coefficient(c, isl_dim_div, pos, v);
302 bset = isl_basic_set_add_constraint(bset, c);
303
304 c = isl_equality_alloc(isl_basic_set_get_dim(bset));
305 isl_int_set_si(v, 1);
306 isl_constraint_set_coefficient(c, isl_dim_set, 0, v);
307 isl_int_set_si(v, -3);
308 isl_constraint_set_coefficient(c, isl_dim_set, 1, v);
309 bset = isl_basic_set_add_constraint(bset, c);
310
311 assert(bset && bset->n_div == 1);
312 isl_basic_set_free(bset);
313
314 /* test 7 */
315 /* This test is a bit tricky. We set up an equality
316 * a + 3b + 3c = 6 e0
317 * Normalization of divs creates _two_ divs
318 * a = 3 e0
319 * c - b - e0 = 2 e1
320 * Afterwards e0 is removed again because it has coefficient -1
321 * and we end up with the original equality and div again.
322 * Perhaps we can avoid the introduction of this temporary div.
323 */
324 dim = isl_dim_set_alloc(ctx, 0, 3);
325 bset = isl_basic_set_universe(dim);
326
327 c = isl_equality_alloc(isl_basic_set_get_dim(bset));
328 isl_int_set_si(v, -1);
329 isl_constraint_set_coefficient(c, isl_dim_set, 0, v);
330 isl_int_set_si(v, -3);
331 isl_constraint_set_coefficient(c, isl_dim_set, 1, v);
332 isl_int_set_si(v, -3);
333 isl_constraint_set_coefficient(c, isl_dim_set, 2, v);
334 div = isl_div_alloc(isl_basic_set_get_dim(bset));
335 c = isl_constraint_add_div(c, div, &pos);
336 isl_int_set_si(v, 6);
337 isl_constraint_set_coefficient(c, isl_dim_div, pos, v);
338 bset = isl_basic_set_add_constraint(bset, c);
339
340 /* Test disabled for now */
341 /*
342 assert(bset && bset->n_div == 1);
343 */
344 isl_basic_set_free(bset);
345
346 /* test 8 */
347 dim = isl_dim_set_alloc(ctx, 0, 4);
348 bset = isl_basic_set_universe(dim);
349
350 c = isl_equality_alloc(isl_basic_set_get_dim(bset));
351 isl_int_set_si(v, -1);
352 isl_constraint_set_coefficient(c, isl_dim_set, 0, v);
353 isl_int_set_si(v, -3);
354 isl_constraint_set_coefficient(c, isl_dim_set, 1, v);
355 isl_int_set_si(v, -3);
356 isl_constraint_set_coefficient(c, isl_dim_set, 3, v);
357 div = isl_div_alloc(isl_basic_set_get_dim(bset));
358 c = isl_constraint_add_div(c, div, &pos);
359 isl_int_set_si(v, 6);
360 isl_constraint_set_coefficient(c, isl_dim_div, pos, v);
361 bset = isl_basic_set_add_constraint(bset, c);
362
363 c = isl_equality_alloc(isl_basic_set_get_dim(bset));
364 isl_int_set_si(v, -1);
365 isl_constraint_set_coefficient(c, isl_dim_set, 0, v);
366 isl_int_set_si(v, 1);
367 isl_constraint_set_coefficient(c, isl_dim_set, 2, v);
368 isl_int_set_si(v, 1);
369 isl_constraint_set_constant(c, v);
370 bset = isl_basic_set_add_constraint(bset, c);
371
372 /* Test disabled for now */
373 /*
374 assert(bset && bset->n_div == 1);
375 */
376 isl_basic_set_free(bset);
377
378 /* test 9 */
379 dim = isl_dim_set_alloc(ctx, 0, 2);
380 bset = isl_basic_set_universe(dim);
381
382 c = isl_equality_alloc(isl_basic_set_get_dim(bset));
383 isl_int_set_si(v, 1);
384 isl_constraint_set_coefficient(c, isl_dim_set, 0, v);
385 isl_int_set_si(v, -1);
386 isl_constraint_set_coefficient(c, isl_dim_set, 1, v);
387 div = isl_div_alloc(isl_basic_set_get_dim(bset));
388 c = isl_constraint_add_div(c, div, &pos);
389 isl_int_set_si(v, -2);
390 isl_constraint_set_coefficient(c, isl_dim_div, pos, v);
391 bset = isl_basic_set_add_constraint(bset, c);
392
393 c = isl_equality_alloc(isl_basic_set_get_dim(bset));
394 isl_int_set_si(v, -1);
395 isl_constraint_set_coefficient(c, isl_dim_set, 0, v);
396 div = isl_div_alloc(isl_basic_set_get_dim(bset));
397 c = isl_constraint_add_div(c, div, &pos);
398 isl_int_set_si(v, 3);
399 isl_constraint_set_coefficient(c, isl_dim_div, pos, v);
400 isl_int_set_si(v, 2);
401 isl_constraint_set_constant(c, v);
402 bset = isl_basic_set_add_constraint(bset, c);
403
404 bset = isl_basic_set_fix_si(bset, isl_dim_set, 0, 2);
405
406 assert(!isl_basic_set_is_empty(bset));
407
408 isl_basic_set_free(bset);
409
410 /* test 10 */
411 dim = isl_dim_set_alloc(ctx, 0, 2);
412 bset = isl_basic_set_universe(dim);
413
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 div = isl_div_alloc(isl_basic_set_get_dim(bset));
418 c = isl_constraint_add_div(c, div, &pos);
419 isl_int_set_si(v, -2);
420 isl_constraint_set_coefficient(c, isl_dim_div, pos, v);
421 bset = isl_basic_set_add_constraint(bset, c);
422
423 bset = isl_basic_set_fix_si(bset, isl_dim_set, 0, 2);
424
425 isl_basic_set_free(bset);
426
427 isl_int_clear(v);
428 }
429
430 void test_application_case(struct isl_ctx *ctx, const char *name)
431 {
432 char filename[PATH_MAX];
433 FILE *input;
434 int n;
435 struct isl_basic_set *bset1, *bset2;
436 struct isl_basic_map *bmap;
437
438 n = snprintf(filename, sizeof(filename),
439 "%s/test_inputs/%s.omega", srcdir, name);
440 assert(n < sizeof(filename));
441 input = fopen(filename, "r");
442 assert(input);
443
444 bset1 = isl_basic_set_read_from_file(ctx, input, 0);
445 bmap = isl_basic_map_read_from_file(ctx, input, 0);
446
447 bset1 = isl_basic_set_apply(bset1, bmap);
448
449 bset2 = isl_basic_set_read_from_file(ctx, input, 0);
450
451 assert(isl_basic_set_is_equal(bset1, bset2) == 1);
452
453 isl_basic_set_free(bset1);
454 isl_basic_set_free(bset2);
455
456 fclose(input);
457 }
458
459 void test_application(struct isl_ctx *ctx)
460 {
461 test_application_case(ctx, "application");
462 test_application_case(ctx, "application2");
463 }
464
465 void test_affine_hull_case(struct isl_ctx *ctx, const char *name)
466 {
467 char filename[PATH_MAX];
468 FILE *input;
469 int n;
470 struct isl_basic_set *bset1, *bset2;
471
472 n = snprintf(filename, sizeof(filename),
473 "%s/test_inputs/%s.polylib", srcdir, name);
474 assert(n < sizeof(filename));
475 input = fopen(filename, "r");
476 assert(input);
477
478 bset1 = isl_basic_set_read_from_file(ctx, input, 0);
479 bset2 = isl_basic_set_read_from_file(ctx, input, 0);
480
481 bset1 = isl_basic_set_affine_hull(bset1);
482
483 assert(isl_basic_set_is_equal(bset1, bset2) == 1);
484
485 isl_basic_set_free(bset1);
486 isl_basic_set_free(bset2);
487
488 fclose(input);
489 }
490
491 void test_affine_hull(struct isl_ctx *ctx)
492 {
493 test_affine_hull_case(ctx, "affine2");
494 test_affine_hull_case(ctx, "affine");
495 test_affine_hull_case(ctx, "affine3");
496 }
497
498 void test_convex_hull_case(struct isl_ctx *ctx, const char *name)
499 {
500 char filename[PATH_MAX];
501 FILE *input;
502 int n;
503 struct isl_basic_set *bset1, *bset2;
504 struct isl_set *set;
505
506 n = snprintf(filename, sizeof(filename),
507 "%s/test_inputs/%s.polylib", srcdir, name);
508 assert(n < sizeof(filename));
509 input = fopen(filename, "r");
510 assert(input);
511
512 bset1 = isl_basic_set_read_from_file(ctx, input, 0);
513 bset2 = isl_basic_set_read_from_file(ctx, input, 0);
514
515 set = isl_basic_set_union(bset1, bset2);
516 bset1 = isl_set_convex_hull(set);
517
518 bset2 = isl_basic_set_read_from_file(ctx, input, 0);
519
520 assert(isl_basic_set_is_equal(bset1, bset2) == 1);
521
522 isl_basic_set_free(bset1);
523 isl_basic_set_free(bset2);
524
525 fclose(input);
526 }
527
528 void test_convex_hull(struct isl_ctx *ctx)
529 {
530 const char *str1, *str2;
531 isl_set *set1, *set2;
532
533 test_convex_hull_case(ctx, "convex0");
534 test_convex_hull_case(ctx, "convex1");
535 test_convex_hull_case(ctx, "convex2");
536 test_convex_hull_case(ctx, "convex3");
537 test_convex_hull_case(ctx, "convex4");
538 test_convex_hull_case(ctx, "convex5");
539 test_convex_hull_case(ctx, "convex6");
540 test_convex_hull_case(ctx, "convex7");
541 test_convex_hull_case(ctx, "convex8");
542 test_convex_hull_case(ctx, "convex9");
543 test_convex_hull_case(ctx, "convex10");
544 test_convex_hull_case(ctx, "convex11");
545 test_convex_hull_case(ctx, "convex12");
546 test_convex_hull_case(ctx, "convex13");
547 test_convex_hull_case(ctx, "convex14");
548 test_convex_hull_case(ctx, "convex15");
549
550 str1 = "{ [i0, i1, i2] : (i2 = 1 and i0 = 0 and i1 >= 0) or "
551 "(i0 = 1 and i1 = 0 and i2 = 1) or "
552 "(i0 = 0 and i1 = 0 and i2 = 0) }";
553 str2 = "{ [i0, i1, i2] : i0 >= 0 and i2 >= i0 and i2 <= 1 and i1 >= 0 }";
554 set1 = isl_set_read_from_str(ctx, str1, -1);
555 set2 = isl_set_read_from_str(ctx, str2, -1);
556 set1 = isl_set_from_basic_set(isl_set_convex_hull(set1));
557 assert(isl_set_is_equal(set1, set2));
558 isl_set_free(set1);
559 isl_set_free(set2);
560 }
561
562 void test_gist_case(struct isl_ctx *ctx, const char *name)
563 {
564 char filename[PATH_MAX];
565 FILE *input;
566 int n;
567 struct isl_basic_set *bset1, *bset2;
568
569 n = snprintf(filename, sizeof(filename),
570 "%s/test_inputs/%s.polylib", srcdir, name);
571 assert(n < sizeof(filename));
572 input = fopen(filename, "r");
573 assert(input);
574
575 bset1 = isl_basic_set_read_from_file(ctx, input, 0);
576 bset2 = isl_basic_set_read_from_file(ctx, input, 0);
577
578 bset1 = isl_basic_set_gist(bset1, bset2);
579
580 bset2 = isl_basic_set_read_from_file(ctx, input, 0);
581
582 assert(isl_basic_set_is_equal(bset1, bset2) == 1);
583
584 isl_basic_set_free(bset1);
585 isl_basic_set_free(bset2);
586
587 fclose(input);
588 }
589
590 void test_gist(struct isl_ctx *ctx)
591 {
592 test_gist_case(ctx, "gist1");
593 }
594
595 void test_coalesce_set(isl_ctx *ctx, const char *str, int check_one)
596 {
597 isl_set *set, *set2;
598
599 set = isl_set_read_from_str(ctx, str, -1);
600 set = isl_set_coalesce(set);
601 set2 = isl_set_read_from_str(ctx, str, -1);
602 assert(isl_set_is_equal(set, set2));
603 if (check_one)
604 assert(set && set->n == 1);
605 isl_set_free(set);
606 isl_set_free(set2);
607 }
608
609 void test_coalesce(struct isl_ctx *ctx)
610 {
611 const char *str;
612 struct isl_set *set, *set2;
613 struct isl_map *map, *map2;
614
615 set = isl_set_read_from_str(ctx,
616 "{[x,y]: x >= 0 & x <= 10 & y >= 0 & y <= 10 or "
617 "y >= x & x >= 2 & 5 >= y }", -1);
618 set = isl_set_coalesce(set);
619 assert(set && set->n == 1);
620 isl_set_free(set);
621
622 set = isl_set_read_from_str(ctx,
623 "{[x,y]: y >= 0 & 2x + y <= 30 & y <= 10 & x >= 0 or "
624 "x + y >= 10 & y <= x & x + y <= 20 & y >= 0}", -1);
625 set = isl_set_coalesce(set);
626 assert(set && set->n == 1);
627 isl_set_free(set);
628
629 set = isl_set_read_from_str(ctx,
630 "{[x,y]: y >= 0 & 2x + y <= 30 & y <= 10 & x >= 0 or "
631 "x + y >= 10 & y <= x & x + y <= 19 & y >= 0}", -1);
632 set = isl_set_coalesce(set);
633 assert(set && set->n == 2);
634 isl_set_free(set);
635
636 set = isl_set_read_from_str(ctx,
637 "{[x,y]: y >= 0 & x <= 5 & y <= x or "
638 "y >= 0 & x >= 6 & x <= 10 & y <= x}", -1);
639 set = isl_set_coalesce(set);
640 assert(set && set->n == 1);
641 isl_set_free(set);
642
643 set = isl_set_read_from_str(ctx,
644 "{[x,y]: y >= 0 & x <= 5 & y <= x or "
645 "y >= 0 & x >= 7 & x <= 10 & y <= x}", -1);
646 set = isl_set_coalesce(set);
647 assert(set && set->n == 2);
648 isl_set_free(set);
649
650 set = isl_set_read_from_str(ctx,
651 "{[x,y]: y >= 0 & x <= 5 & y <= x or "
652 "y >= 0 & x >= 6 & x <= 10 & y + 1 <= x}", -1);
653 set = isl_set_coalesce(set);
654 assert(set && set->n == 2);
655 isl_set_free(set);
656
657 set = isl_set_read_from_str(ctx,
658 "{[x,y]: y >= 0 & x <= 5 & y <= x or "
659 "y >= 0 & x = 6 & y <= 6}", -1);
660 set = isl_set_coalesce(set);
661 assert(set && set->n == 1);
662 isl_set_free(set);
663
664 set = isl_set_read_from_str(ctx,
665 "{[x,y]: y >= 0 & x <= 5 & y <= x or "
666 "y >= 0 & x = 7 & y <= 6}", -1);
667 set = isl_set_coalesce(set);
668 assert(set && set->n == 2);
669 isl_set_free(set);
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 <= 5}", -1);
674 set = isl_set_coalesce(set);
675 assert(set && set->n == 1);
676 set2 = isl_set_read_from_str(ctx,
677 "{[x,y]: y >= 0 & x <= 5 & y <= x or "
678 "y >= 0 & x = 6 & y <= 5}", -1);
679 assert(isl_set_is_equal(set, set2));
680 isl_set_free(set);
681 isl_set_free(set2);
682
683 set = isl_set_read_from_str(ctx,
684 "{[x,y]: y >= 0 & x <= 5 & y <= x or "
685 "y >= 0 & x = 6 & y <= 7}", -1);
686 set = isl_set_coalesce(set);
687 assert(set && set->n == 2);
688 isl_set_free(set);
689
690 set = isl_set_read_from_str(ctx,
691 "[n] -> { [i] : i = 1 and n >= 2 or 2 <= i and i <= n }", -1);
692 set = isl_set_coalesce(set);
693 assert(set && set->n == 1);
694 set2 = isl_set_read_from_str(ctx,
695 "[n] -> { [i] : i = 1 and n >= 2 or 2 <= i and i <= n }", -1);
696 assert(isl_set_is_equal(set, set2));
697 isl_set_free(set);
698 isl_set_free(set2);
699
700 set = isl_set_read_from_str(ctx,
701 "{[x,y] : x >= 0 and y >= 0 or 0 <= y and y <= 5 and x = -1}", -1);
702 set = isl_set_coalesce(set);
703 set2 = isl_set_read_from_str(ctx,
704 "{[x,y] : x >= 0 and y >= 0 or 0 <= y and y <= 5 and x = -1}", -1);
705 assert(isl_set_is_equal(set, set2));
706 isl_set_free(set);
707 isl_set_free(set2);
708
709 set = isl_set_read_from_str(ctx,
710 "[n] -> { [i] : 1 <= i and i <= n - 1 or "
711 "2 <= i and i <= n }", -1);
712 set = isl_set_coalesce(set);
713 assert(set && set->n == 1);
714 set2 = isl_set_read_from_str(ctx,
715 "[n] -> { [i] : 1 <= i and i <= n - 1 or "
716 "2 <= i and i <= n }", -1);
717 assert(isl_set_is_equal(set, set2));
718 isl_set_free(set);
719 isl_set_free(set2);
720
721 map = isl_map_read_from_str(ctx,
722 "[n] -> { [i0] -> [o0] : exists (e0 = [(i0)/4], e1 = [(o0)/4], "
723 "e2 = [(n)/2], e3 = [(-2 + i0)/4], e4 = [(-2 + o0)/4], "
724 "e5 = [(-2n + i0)/4]: 2e2 = n and 4e3 = -2 + i0 and "
725 "4e4 = -2 + o0 and i0 >= 8 + 2n and o0 >= 2 + i0 and "
726 "o0 <= 56 + 2n and o0 <= -12 + 4n and i0 <= 57 + 2n and "
727 "i0 <= -11 + 4n and o0 >= 6 + 2n and 4e0 <= i0 and "
728 "4e0 >= -3 + i0 and 4e1 <= o0 and 4e1 >= -3 + o0 and "
729 "4e5 <= -2n + i0 and 4e5 >= -3 - 2n + i0);"
730 "[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 2e0 >= 3 + n and e0 <= -4 + n and "
734 "2e0 <= 27 + n and e1 <= -4 + n and 2e1 <= 27 + n and "
735 "2e1 >= 2 + n and e1 >= 1 + e0 and i0 >= 7 + 2n and "
736 "i0 <= -11 + 4n and i0 <= 57 + 2n and 4e0 <= -2 + i0 and "
737 "4e0 >= -3 + i0 and o0 >= 6 + 2n and o0 <= -11 + 4n and "
738 "o0 <= 57 + 2n and 4e1 <= -2 + o0 and 4e1 >= -3 + o0 and "
739 "4e5 <= -2n + i0 and 4e5 >= -3 - 2n + i0 ) }", -1);
740 map = isl_map_coalesce(map);
741 map2 = isl_map_read_from_str(ctx,
742 "[n] -> { [i0] -> [o0] : exists (e0 = [(i0)/4], e1 = [(o0)/4], "
743 "e2 = [(n)/2], e3 = [(-2 + i0)/4], e4 = [(-2 + o0)/4], "
744 "e5 = [(-2n + i0)/4]: 2e2 = n and 4e3 = -2 + i0 and "
745 "4e4 = -2 + o0 and i0 >= 8 + 2n and o0 >= 2 + i0 and "
746 "o0 <= 56 + 2n and o0 <= -12 + 4n and i0 <= 57 + 2n and "
747 "i0 <= -11 + 4n and o0 >= 6 + 2n and 4e0 <= i0 and "
748 "4e0 >= -3 + i0 and 4e1 <= o0 and 4e1 >= -3 + o0 and "
749 "4e5 <= -2n + i0 and 4e5 >= -3 - 2n + i0);"
750 "[i0] -> [o0] : exists (e0 = [(i0)/4], e1 = [(o0)/4], "
751 "e2 = [(n)/2], e3 = [(-2 + i0)/4], e4 = [(-2 + o0)/4], "
752 "e5 = [(-2n + i0)/4]: 2e2 = n and 4e3 = -2 + i0 and "
753 "4e4 = -2 + o0 and 2e0 >= 3 + n and e0 <= -4 + n and "
754 "2e0 <= 27 + n and e1 <= -4 + n and 2e1 <= 27 + n and "
755 "2e1 >= 2 + n and e1 >= 1 + e0 and i0 >= 7 + 2n and "
756 "i0 <= -11 + 4n and i0 <= 57 + 2n and 4e0 <= -2 + i0 and "
757 "4e0 >= -3 + i0 and o0 >= 6 + 2n and o0 <= -11 + 4n and "
758 "o0 <= 57 + 2n and 4e1 <= -2 + o0 and 4e1 >= -3 + o0 and "
759 "4e5 <= -2n + i0 and 4e5 >= -3 - 2n + i0 ) }", -1);
760 assert(isl_map_is_equal(map, map2));
761 isl_map_free(map);
762 isl_map_free(map2);
763
764 str = "[n, m] -> { [] -> [o0, o2, o3] : (o3 = 1 and o0 >= 1 + m and "
765 "o0 <= n + m and o2 <= m and o0 >= 2 + n and o2 >= 3) or "
766 "(o0 >= 2 + n and o0 >= 1 + m and o0 <= n + m and n >= 1 and "
767 "o3 <= -1 + o2 and o3 >= 1 - m + o2 and o3 >= 2 and o3 <= n) }";
768 map = isl_map_read_from_str(ctx, str, -1);
769 map = isl_map_coalesce(map);
770 map2 = isl_map_read_from_str(ctx, str, -1);
771 assert(isl_map_is_equal(map, map2));
772 isl_map_free(map);
773 isl_map_free(map2);
774
775 str = "[M, N] -> { [i0, i1, i2, i3, i4, i5, i6] -> "
776 "[o0, o1, o2, o3, o4, o5, o6] : "
777 "(o6 <= -4 + 2M - 2N + i0 + i1 - i2 + i6 - o0 - o1 + o2 and "
778 "o3 <= -2 + i3 and o6 >= 2 + i0 + i3 + i6 - o0 - o3 and "
779 "o6 >= 2 - M + N + i3 + i4 + i6 - o3 - o4 and o0 <= -1 + i0 and "
780 "o4 >= 4 - 3M + 3N - i0 - i1 + i2 + 2i3 + i4 + o0 + o1 - o2 - 2o3 "
781 "and o6 <= -3 + 2M - 2N + i3 + i4 - i5 + i6 - o3 - o4 + o5 and "
782 "2o6 <= -5 + 5M - 5N + 2i0 + i1 - i2 - i5 + 2i6 - 2o0 - o1 + o2 + o5 "
783 "and o6 >= 2i0 + i1 + i6 - 2o0 - o1 and "
784 "3o6 <= -5 + 4M - 4N + 2i0 + i1 - i2 + 2i3 + i4 - i5 + 3i6 "
785 "- 2o0 - o1 + o2 - 2o3 - o4 + o5) or "
786 "(N >= 2 and o3 <= -1 + i3 and o0 <= -1 + i0 and "
787 "o6 >= i3 + i6 - o3 and M >= 0 and "
788 "2o6 >= 1 + i0 + i3 + 2i6 - o0 - o3 and "
789 "o6 >= 1 - M + i0 + i6 - o0 and N >= 2M and o6 >= i0 + i6 - o0) }";
790 map = isl_map_read_from_str(ctx, str, -1);
791 map = isl_map_coalesce(map);
792 map2 = isl_map_read_from_str(ctx, str, -1);
793 assert(isl_map_is_equal(map, map2));
794 isl_map_free(map);
795 isl_map_free(map2);
796
797 str = "[M, N] -> { [] -> [o0] : (o0 = 0 and M >= 1 and N >= 2) or "
798 "(o0 = 0 and M >= 1 and N >= 2M and N >= 2 + M) or "
799 "(o0 = 0 and M >= 2 and N >= 3) or "
800 "(M = 0 and o0 = 0 and N >= 3) }";
801 map = isl_map_read_from_str(ctx, str, -1);
802 map = isl_map_coalesce(map);
803 map2 = isl_map_read_from_str(ctx, str, -1);
804 assert(isl_map_is_equal(map, map2));
805 isl_map_free(map);
806 isl_map_free(map2);
807
808 str = "{ [i0, i1, i2, i3] : (i1 = 10i0 and i0 >= 1 and 10i0 <= 100 and "
809 "i3 <= 9 + 10 i2 and i3 >= 1 + 10i2 and i3 >= 0) or "
810 "(i1 <= 9 + 10i0 and i1 >= 1 + 10i0 and i2 >= 0 and "
811 "i0 >= 0 and i1 <= 100 and i3 <= 9 + 10i2 and i3 >= 1 + 10i2) }";
812 map = isl_map_read_from_str(ctx, str, -1);
813 map = isl_map_coalesce(map);
814 map2 = isl_map_read_from_str(ctx, str, -1);
815 assert(isl_map_is_equal(map, map2));
816 isl_map_free(map);
817 isl_map_free(map2);
818
819 test_coalesce_set(ctx,
820 "[M] -> { [i1] : (i1 >= 2 and i1 <= M) or "
821 "(i1 = M and M >= 1) }", 0);
822 test_coalesce_set(ctx,
823 "{[x,y] : x,y >= 0; [x,y] : 10 <= x <= 20 and y >= -1 }", 0);
824 test_coalesce_set(ctx,
825 "{ [x, y] : (x >= 1 and y >= 1 and x <= 2 and y <= 2) or "
826 "(y = 3 and x = 1) }", 1);
827 test_coalesce_set(ctx,
828 "[M] -> { [i0, i1, i2, i3, i4] : (i1 >= 3 and i4 >= 2 + i2 and "
829 "i2 >= 2 and i0 >= 2 and i3 >= 1 + i2 and i0 <= M and "
830 "i1 <= M and i3 <= M and i4 <= M) or "
831 "(i1 >= 2 and i4 >= 1 + i2 and i2 >= 2 and i0 >= 2 and "
832 "i3 >= 1 + i2 and i0 <= M and i1 <= -1 + M and i3 <= M and "
833 "i4 <= -1 + M) }", 1);
834 test_coalesce_set(ctx,
835 "{ [x, y] : (x >= 0 and y >= 0 and x <= 10 and y <= 10) or "
836 "(x >= 1 and y >= 1 and x <= 11 and y <= 11) }", 1);
837 test_coalesce_set(ctx,
838 "{[x,y,z] : y + 2 >= 0 and x - y + 1 >= 0 and "
839 "-x - y + 1 >= 0 and -3 <= z <= 3;"
840 "[x,y,z] : -x+z + 20 >= 0 and -x-z + 20 >= 0 and "
841 "x-z + 20 >= 0 and x+z + 20 >= 0 and -10 <= y <= 0}", 1);
842 test_coalesce_set(ctx,
843 "{[x,y] : 0 <= x,y <= 10; [5,y]: 4 <=y <= 11}", 1);
844 }
845
846 void test_closure(struct isl_ctx *ctx)
847 {
848 const char *str;
849 isl_set *dom;
850 isl_map *up, *right;
851 isl_map *map, *map2;
852 int exact;
853
854 /* COCOA example 1 */
855 map = isl_map_read_from_str(ctx,
856 "[n,k] -> { [i,j] -> [i2,j2] : i2 = i + 1 and j2 = j + 1 and "
857 "1 <= i and i < n and 1 <= j and j < n or "
858 "i2 = i + 1 and j2 = j - 1 and "
859 "1 <= i and i < n and 2 <= j and j <= n }", -1);
860 map = isl_map_power(map, 1, &exact);
861 assert(exact);
862 isl_map_free(map);
863
864 /* COCOA example 1 */
865 map = isl_map_read_from_str(ctx,
866 "[n] -> { [i,j] -> [i2,j2] : i2 = i + 1 and j2 = j + 1 and "
867 "1 <= i and i < n and 1 <= j and j < n or "
868 "i2 = i + 1 and j2 = j - 1 and "
869 "1 <= i and i < n and 2 <= j and j <= n }", -1);
870 map = isl_map_transitive_closure(map, &exact);
871 assert(exact);
872 map2 = isl_map_read_from_str(ctx,
873 "[n] -> { [i,j] -> [i2,j2] : exists (k1,k2,k : "
874 "1 <= i and i < n and 1 <= j and j <= n and "
875 "2 <= i2 and i2 <= n and 1 <= j2 and j2 <= n and "
876 "i2 = i + k1 + k2 and j2 = j + k1 - k2 and "
877 "k1 >= 0 and k2 >= 0 and k1 + k2 = k and k >= 1 )}", -1);
878 assert(isl_map_is_equal(map, map2));
879 isl_map_free(map2);
880 isl_map_free(map);
881
882 map = isl_map_read_from_str(ctx,
883 "[n] -> { [x] -> [y] : y = x + 1 and 0 <= x and x <= n and "
884 " 0 <= y and y <= n }", -1);
885 map = isl_map_transitive_closure(map, &exact);
886 map2 = isl_map_read_from_str(ctx,
887 "[n] -> { [x] -> [y] : y > x and 0 <= x and x <= n and "
888 " 0 <= y and y <= n }", -1);
889 assert(isl_map_is_equal(map, map2));
890 isl_map_free(map2);
891 isl_map_free(map);
892
893 /* COCOA example 2 */
894 map = isl_map_read_from_str(ctx,
895 "[n] -> { [i,j] -> [i2,j2] : i2 = i + 2 and j2 = j + 2 and "
896 "1 <= i and i < n - 1 and 1 <= j and j < n - 1 or "
897 "i2 = i + 2 and j2 = j - 2 and "
898 "1 <= i and i < n - 1 and 3 <= j and j <= n }", -1);
899 map = isl_map_transitive_closure(map, &exact);
900 assert(exact);
901 map2 = isl_map_read_from_str(ctx,
902 "[n] -> { [i,j] -> [i2,j2] : exists (k1,k2,k : "
903 "1 <= i and i < n - 1 and 1 <= j and j <= n and "
904 "3 <= i2 and i2 <= n and 1 <= j2 and j2 <= n and "
905 "i2 = i + 2 k1 + 2 k2 and j2 = j + 2 k1 - 2 k2 and "
906 "k1 >= 0 and k2 >= 0 and k1 + k2 = k and k >= 1) }", -1);
907 assert(isl_map_is_equal(map, map2));
908 isl_map_free(map);
909 isl_map_free(map2);
910
911 /* COCOA Fig.2 left */
912 map = isl_map_read_from_str(ctx,
913 "[n] -> { [i,j] -> [i2,j2] : i2 = i + 2 and j2 = j and "
914 "i <= 2 j - 3 and i <= n - 2 and j <= 2 i - 1 and "
915 "j <= n or "
916 "i2 = i and j2 = j + 2 and i <= 2 j - 1 and i <= n and "
917 "j <= 2 i - 3 and j <= n - 2 or "
918 "i2 = i + 1 and j2 = j + 1 and i <= 2 j - 1 and "
919 "i <= n - 1 and j <= 2 i - 1 and j <= n - 1 }", -1);
920 map = isl_map_transitive_closure(map, &exact);
921 assert(exact);
922 isl_map_free(map);
923
924 /* COCOA Fig.2 right */
925 map = isl_map_read_from_str(ctx,
926 "[n,k] -> { [i,j] -> [i2,j2] : i2 = i + 3 and j2 = j and "
927 "i <= 2 j - 4 and i <= n - 3 and j <= 2 i - 1 and "
928 "j <= n or "
929 "i2 = i and j2 = j + 3 and i <= 2 j - 1 and i <= n and "
930 "j <= 2 i - 4 and j <= n - 3 or "
931 "i2 = i + 1 and j2 = j + 1 and i <= 2 j - 1 and "
932 "i <= n - 1 and j <= 2 i - 1 and j <= n - 1 }", -1);
933 map = isl_map_power(map, 1, &exact);
934 assert(exact);
935 isl_map_free(map);
936
937 /* COCOA Fig.2 right */
938 map = isl_map_read_from_str(ctx,
939 "[n] -> { [i,j] -> [i2,j2] : i2 = i + 3 and j2 = j and "
940 "i <= 2 j - 4 and i <= n - 3 and j <= 2 i - 1 and "
941 "j <= n or "
942 "i2 = i and j2 = j + 3 and i <= 2 j - 1 and i <= n and "
943 "j <= 2 i - 4 and j <= n - 3 or "
944 "i2 = i + 1 and j2 = j + 1 and i <= 2 j - 1 and "
945 "i <= n - 1 and j <= 2 i - 1 and j <= n - 1 }", -1);
946 map = isl_map_transitive_closure(map, &exact);
947 assert(exact);
948 map2 = isl_map_read_from_str(ctx,
949 "[n] -> { [i,j] -> [i2,j2] : exists (k1,k2,k3,k : "
950 "i <= 2 j - 1 and i <= n and j <= 2 i - 1 and "
951 "j <= n and 3 + i + 2 j <= 3 n and "
952 "3 + 2 i + j <= 3n and i2 <= 2 j2 -1 and i2 <= n and "
953 "i2 <= 3 j2 - 4 and j2 <= 2 i2 -1 and j2 <= n and "
954 "13 + 4 j2 <= 11 i2 and i2 = i + 3 k1 + k3 and "
955 "j2 = j + 3 k2 + k3 and k1 >= 0 and k2 >= 0 and "
956 "k3 >= 0 and k1 + k2 + k3 = k and k > 0) }", -1);
957 assert(isl_map_is_equal(map, map2));
958 isl_map_free(map2);
959 isl_map_free(map);
960
961 /* COCOA Fig.1 right */
962 dom = isl_set_read_from_str(ctx,
963 "{ [x,y] : x >= 0 and -2 x + 3 y >= 0 and x <= 3 and "
964 "2 x - 3 y + 3 >= 0 }", -1);
965 right = isl_map_read_from_str(ctx,
966 "{ [x,y] -> [x2,y2] : x2 = x + 1 and y2 = y }", -1);
967 up = isl_map_read_from_str(ctx,
968 "{ [x,y] -> [x2,y2] : x2 = x and y2 = y + 1 }", -1);
969 right = isl_map_intersect_domain(right, isl_set_copy(dom));
970 right = isl_map_intersect_range(right, isl_set_copy(dom));
971 up = isl_map_intersect_domain(up, isl_set_copy(dom));
972 up = isl_map_intersect_range(up, dom);
973 map = isl_map_union(up, right);
974 map = isl_map_transitive_closure(map, &exact);
975 assert(exact);
976 map2 = isl_map_read_from_str(ctx,
977 "{ [0,0] -> [0,1]; [0,0] -> [1,1]; [0,1] -> [1,1]; "
978 " [2,2] -> [3,2]; [2,2] -> [3,3]; [3,2] -> [3,3] }", -1);
979 assert(isl_map_is_equal(map, map2));
980 isl_map_free(map2);
981 isl_map_free(map);
982
983 /* COCOA Theorem 1 counter example */
984 map = isl_map_read_from_str(ctx,
985 "{ [i,j] -> [i2,j2] : i = 0 and 0 <= j and j <= 1 and "
986 "i2 = 1 and j2 = j or "
987 "i = 0 and j = 0 and i2 = 0 and j2 = 1 }", -1);
988 map = isl_map_transitive_closure(map, &exact);
989 assert(exact);
990 isl_map_free(map);
991
992 map = isl_map_read_from_str(ctx,
993 "[m,n] -> { [i,j] -> [i2,j2] : i2 = i and j2 = j + 2 and "
994 "1 <= i,i2 <= n and 1 <= j,j2 <= m or "
995 "i2 = i + 1 and 3 <= j2 - j <= 4 and "
996 "1 <= i,i2 <= n and 1 <= j,j2 <= m }", -1);
997 map = isl_map_transitive_closure(map, &exact);
998 assert(exact);
999 isl_map_free(map);
1000
1001 /* Kelly et al 1996, fig 12 */
1002 map = isl_map_read_from_str(ctx,
1003 "[n] -> { [i,j] -> [i2,j2] : i2 = i and j2 = j + 1 and "
1004 "1 <= i,j,j+1 <= n or "
1005 "j = n and j2 = 1 and i2 = i + 1 and "
1006 "1 <= i,i+1 <= n }", -1);
1007 map = isl_map_transitive_closure(map, &exact);
1008 assert(exact);
1009 map2 = isl_map_read_from_str(ctx,
1010 "[n] -> { [i,j] -> [i2,j2] : 1 <= j < j2 <= n and "
1011 "1 <= i <= n and i = i2 or "
1012 "1 <= i < i2 <= n and 1 <= j <= n and "
1013 "1 <= j2 <= n }", -1);
1014 assert(isl_map_is_equal(map, map2));
1015 isl_map_free(map2);
1016 isl_map_free(map);
1017
1018 /* Omega's closure4 */
1019 map = isl_map_read_from_str(ctx,
1020 "[m,n] -> { [x,y] -> [x2,y2] : x2 = x and y2 = y + 1 and "
1021 "1 <= x,y <= 10 or "
1022 "x2 = x + 1 and y2 = y and "
1023 "1 <= x <= 20 && 5 <= y <= 15 }", -1);
1024 map = isl_map_transitive_closure(map, &exact);
1025 assert(exact);
1026 isl_map_free(map);
1027
1028 map = isl_map_read_from_str(ctx,
1029 "[n] -> { [x] -> [y]: 1 <= n <= y - x <= 10 }", -1);
1030 map = isl_map_transitive_closure(map, &exact);
1031 assert(!exact);
1032 map2 = isl_map_read_from_str(ctx,
1033 "[n] -> { [x] -> [y] : 1 <= n <= 10 and y >= n + x }", -1);
1034 assert(isl_map_is_equal(map, map2));
1035 isl_map_free(map);
1036 isl_map_free(map2);
1037
1038 str = "[n, m] -> { [i0, i1, i2, i3] -> [o0, o1, o2, o3] : "
1039 "i3 = 1 and o0 = i0 and o1 = -1 + i1 and o2 = -1 + i2 and "
1040 "o3 = -2 + i2 and i1 <= -1 + i0 and i1 >= 1 - m + i0 and "
1041 "i1 >= 2 and i1 <= n and i2 >= 3 and i2 <= 1 + n and i2 <= m }";
1042 map = isl_map_read_from_str(ctx, str, -1);
1043 map = isl_map_transitive_closure(map, &exact);
1044 assert(exact);
1045 map2 = isl_map_read_from_str(ctx, str, -1);
1046 assert(isl_map_is_equal(map, map2));
1047 isl_map_free(map);
1048 isl_map_free(map2);
1049
1050 str = "{[0] -> [1]; [2] -> [3]}";
1051 map = isl_map_read_from_str(ctx, str, -1);
1052 map = isl_map_transitive_closure(map, &exact);
1053 assert(exact);
1054 map2 = isl_map_read_from_str(ctx, str, -1);
1055 assert(isl_map_is_equal(map, map2));
1056 isl_map_free(map);
1057 isl_map_free(map2);
1058 }
1059
1060 void test_lex(struct isl_ctx *ctx)
1061 {
1062 isl_dim *dim;
1063 isl_map *map;
1064
1065 dim = isl_dim_alloc(ctx, 0, 0, 0);
1066 map = isl_map_lex_le(dim);
1067 assert(!isl_map_is_empty(map));
1068 isl_map_free(map);
1069 }
1070
1071 void test_lexmin(struct isl_ctx *ctx)
1072 {
1073 const char *str;
1074 isl_map *map;
1075 isl_set *set;
1076 isl_set *set2;
1077
1078 str = "[p0, p1] -> { [] -> [] : "
1079 "exists (e0 = [(2p1)/3], e1, e2, e3 = [(3 - p1 + 3e0)/3], "
1080 "e4 = [(p1)/3], e5 = [(p1 + 3e4)/3]: "
1081 "3e0 >= -2 + 2p1 and 3e0 >= p1 and 3e3 >= 1 - p1 + 3e0 and "
1082 "3e0 <= 2p1 and 3e3 >= -2 + p1 and 3e3 <= -1 + p1 and p1 >= 3 and "
1083 "3e5 >= -2 + 2p1 and 3e5 >= p1 and 3e5 <= -1 + p1 + 3e4 and "
1084 "3e4 <= p1 and 3e4 >= -2 + p1 and e3 <= -1 + e0 and "
1085 "3e4 >= 6 - p1 + 3e1 and 3e1 >= p1 and 3e5 >= -2 + p1 + 3e4 and "
1086 "2e4 >= 3 - p1 + 2e1 and e4 <= e1 and 3e3 <= 2 - p1 + 3e0 and "
1087 "e5 >= 1 + e1 and 3e4 >= 6 - 2p1 + 3e1 and "
1088 "p0 >= 2 and p1 >= p0 and 3e2 >= p1 and 3e4 >= 6 - p1 + 3e2 and "
1089 "e2 <= e1 and e3 >= 1 and e4 <= e2) }";
1090 map = isl_map_read_from_str(ctx, str, -1);
1091 map = isl_map_lexmin(map);
1092 isl_map_free(map);
1093
1094 str = "[C] -> { [obj,a,b,c] : obj <= 38 a + 7 b + 10 c and "
1095 "a + b <= 1 and c <= 10 b and c <= C and a,b,c,C >= 0 }";
1096 set = isl_set_read_from_str(ctx, str, -1);
1097 set = isl_set_lexmax(set);
1098 str = "[C] -> { [obj,a,b,c] : C = 8 }";
1099 set2 = isl_set_read_from_str(ctx, str, -1);
1100 set = isl_set_intersect(set, set2);
1101 assert(!isl_set_is_empty(set));
1102 isl_set_free(set);
1103 }
1104
1105 struct must_may {
1106 isl_map *must;
1107 isl_map *may;
1108 };
1109
1110 static int collect_must_may(__isl_take isl_map *dep, int must,
1111 void *dep_user, void *user)
1112 {
1113 struct must_may *mm = (struct must_may *)user;
1114
1115 if (must)
1116 mm->must = isl_map_union(mm->must, dep);
1117 else
1118 mm->may = isl_map_union(mm->may, dep);
1119
1120 return 0;
1121 }
1122
1123 static int common_space(void *first, void *second)
1124 {
1125 int depth = *(int *)first;
1126 return 2 * depth;
1127 }
1128
1129 static int map_is_equal(__isl_keep isl_map *map, const char *str)
1130 {
1131 isl_map *map2;
1132 int equal;
1133
1134 if (!map)
1135 return -1;
1136
1137 map2 = isl_map_read_from_str(map->ctx, str, -1);
1138 equal = isl_map_is_equal(map, map2);
1139 isl_map_free(map2);
1140
1141 return equal;
1142 }
1143
1144 void test_dep(struct isl_ctx *ctx)
1145 {
1146 const char *str;
1147 isl_dim *dim;
1148 isl_map *map;
1149 isl_access_info *ai;
1150 isl_flow *flow;
1151 int depth;
1152 struct must_may mm;
1153
1154 depth = 3;
1155
1156 str = "{ [2,i,0] -> [i] : 0 <= i <= 10 }";
1157 map = isl_map_read_from_str(ctx, str, -1);
1158 ai = isl_access_info_alloc(map, &depth, &common_space, 2);
1159
1160 str = "{ [0,i,0] -> [i] : 0 <= i <= 10 }";
1161 map = isl_map_read_from_str(ctx, str, -1);
1162 ai = isl_access_info_add_source(ai, map, 1, &depth);
1163
1164 str = "{ [1,i,0] -> [5] : 0 <= i <= 10 }";
1165 map = isl_map_read_from_str(ctx, str, -1);
1166 ai = isl_access_info_add_source(ai, map, 1, &depth);
1167
1168 flow = isl_access_info_compute_flow(ai);
1169 dim = isl_dim_alloc(ctx, 0, 3, 3);
1170 mm.must = isl_map_empty(isl_dim_copy(dim));
1171 mm.may = isl_map_empty(dim);
1172
1173 isl_flow_foreach(flow, collect_must_may, &mm);
1174
1175 str = "{ [0,i,0] -> [2,i,0] : (0 <= i <= 4) or (6 <= i <= 10); "
1176 " [1,10,0] -> [2,5,0] }";
1177 assert(map_is_equal(mm.must, str));
1178 str = "{ [i,j,k] -> [l,m,n] : 1 = 0 }";
1179 assert(map_is_equal(mm.may, str));
1180
1181 isl_map_free(mm.must);
1182 isl_map_free(mm.may);
1183 isl_flow_free(flow);
1184
1185
1186 str = "{ [2,i,0] -> [i] : 0 <= i <= 10 }";
1187 map = isl_map_read_from_str(ctx, str, -1);
1188 ai = isl_access_info_alloc(map, &depth, &common_space, 2);
1189
1190 str = "{ [0,i,0] -> [i] : 0 <= i <= 10 }";
1191 map = isl_map_read_from_str(ctx, str, -1);
1192 ai = isl_access_info_add_source(ai, map, 1, &depth);
1193
1194 str = "{ [1,i,0] -> [5] : 0 <= i <= 10 }";
1195 map = isl_map_read_from_str(ctx, str, -1);
1196 ai = isl_access_info_add_source(ai, map, 0, &depth);
1197
1198 flow = isl_access_info_compute_flow(ai);
1199 dim = isl_dim_alloc(ctx, 0, 3, 3);
1200 mm.must = isl_map_empty(isl_dim_copy(dim));
1201 mm.may = isl_map_empty(dim);
1202
1203 isl_flow_foreach(flow, collect_must_may, &mm);
1204
1205 str = "{ [0,i,0] -> [2,i,0] : (0 <= i <= 4) or (6 <= i <= 10) }";
1206 assert(map_is_equal(mm.must, str));
1207 str = "{ [0,5,0] -> [2,5,0]; [1,i,0] -> [2,5,0] : 0 <= i <= 10 }";
1208 assert(map_is_equal(mm.may, str));
1209
1210 isl_map_free(mm.must);
1211 isl_map_free(mm.may);
1212 isl_flow_free(flow);
1213
1214
1215 str = "{ [2,i,0] -> [i] : 0 <= i <= 10 }";
1216 map = isl_map_read_from_str(ctx, str, -1);
1217 ai = isl_access_info_alloc(map, &depth, &common_space, 2);
1218
1219 str = "{ [0,i,0] -> [i] : 0 <= i <= 10 }";
1220 map = isl_map_read_from_str(ctx, str, -1);
1221 ai = isl_access_info_add_source(ai, map, 0, &depth);
1222
1223 str = "{ [1,i,0] -> [5] : 0 <= i <= 10 }";
1224 map = isl_map_read_from_str(ctx, str, -1);
1225 ai = isl_access_info_add_source(ai, map, 0, &depth);
1226
1227 flow = isl_access_info_compute_flow(ai);
1228 dim = isl_dim_alloc(ctx, 0, 3, 3);
1229 mm.must = isl_map_empty(isl_dim_copy(dim));
1230 mm.may = isl_map_empty(dim);
1231
1232 isl_flow_foreach(flow, collect_must_may, &mm);
1233
1234 str = "{ [0,i,0] -> [2,i,0] : 0 <= i <= 10; "
1235 " [1,i,0] -> [2,5,0] : 0 <= i <= 10 }";
1236 assert(map_is_equal(mm.may, str));
1237 str = "{ [i,j,k] -> [l,m,n] : 1 = 0 }";
1238 assert(map_is_equal(mm.must, str));
1239
1240 isl_map_free(mm.must);
1241 isl_map_free(mm.may);
1242 isl_flow_free(flow);
1243
1244
1245 str = "{ [0,i,2] -> [i] : 0 <= i <= 10 }";
1246 map = isl_map_read_from_str(ctx, str, -1);
1247 ai = isl_access_info_alloc(map, &depth, &common_space, 2);
1248
1249 str = "{ [0,i,0] -> [i] : 0 <= i <= 10 }";
1250 map = isl_map_read_from_str(ctx, str, -1);
1251 ai = isl_access_info_add_source(ai, map, 0, &depth);
1252
1253 str = "{ [0,i,1] -> [5] : 0 <= i <= 10 }";
1254 map = isl_map_read_from_str(ctx, str, -1);
1255 ai = isl_access_info_add_source(ai, map, 0, &depth);
1256
1257 flow = isl_access_info_compute_flow(ai);
1258 dim = isl_dim_alloc(ctx, 0, 3, 3);
1259 mm.must = isl_map_empty(isl_dim_copy(dim));
1260 mm.may = isl_map_empty(dim);
1261
1262 isl_flow_foreach(flow, collect_must_may, &mm);
1263
1264 str = "{ [0,i,0] -> [0,i,2] : 0 <= i <= 10; "
1265 " [0,i,1] -> [0,5,2] : 0 <= i <= 5 }";
1266 assert(map_is_equal(mm.may, str));
1267 str = "{ [i,j,k] -> [l,m,n] : 1 = 0 }";
1268 assert(map_is_equal(mm.must, str));
1269
1270 isl_map_free(mm.must);
1271 isl_map_free(mm.may);
1272 isl_flow_free(flow);
1273
1274
1275 str = "{ [0,i,1] -> [i] : 0 <= i <= 10 }";
1276 map = isl_map_read_from_str(ctx, str, -1);
1277 ai = isl_access_info_alloc(map, &depth, &common_space, 2);
1278
1279 str = "{ [0,i,0] -> [i] : 0 <= i <= 10 }";
1280 map = isl_map_read_from_str(ctx, str, -1);
1281 ai = isl_access_info_add_source(ai, map, 0, &depth);
1282
1283 str = "{ [0,i,2] -> [5] : 0 <= i <= 10 }";
1284 map = isl_map_read_from_str(ctx, str, -1);
1285 ai = isl_access_info_add_source(ai, map, 0, &depth);
1286
1287 flow = isl_access_info_compute_flow(ai);
1288 dim = isl_dim_alloc(ctx, 0, 3, 3);
1289 mm.must = isl_map_empty(isl_dim_copy(dim));
1290 mm.may = isl_map_empty(dim);
1291
1292 isl_flow_foreach(flow, collect_must_may, &mm);
1293
1294 str = "{ [0,i,0] -> [0,i,1] : 0 <= i <= 10; "
1295 " [0,i,2] -> [0,5,1] : 0 <= i <= 4 }";
1296 assert(map_is_equal(mm.may, str));
1297 str = "{ [i,j,k] -> [l,m,n] : 1 = 0 }";
1298 assert(map_is_equal(mm.must, str));
1299
1300 isl_map_free(mm.must);
1301 isl_map_free(mm.may);
1302 isl_flow_free(flow);
1303
1304
1305 depth = 5;
1306
1307 str = "{ [1,i,0,0,0] -> [i,j] : 0 <= i <= 10 and 0 <= j <= 10 }";
1308 map = isl_map_read_from_str(ctx, str, -1);
1309 ai = isl_access_info_alloc(map, &depth, &common_space, 1);
1310
1311 str = "{ [0,i,0,j,0] -> [i,j] : 0 <= i <= 10 and 0 <= j <= 10 }";
1312 map = isl_map_read_from_str(ctx, str, -1);
1313 ai = isl_access_info_add_source(ai, map, 1, &depth);
1314
1315 flow = isl_access_info_compute_flow(ai);
1316 dim = isl_dim_alloc(ctx, 0, 5, 5);
1317 mm.must = isl_map_empty(isl_dim_copy(dim));
1318 mm.may = isl_map_empty(dim);
1319
1320 isl_flow_foreach(flow, collect_must_may, &mm);
1321
1322 str = "{ [0,i,0,j,0] -> [1,i,0,0,0] : 0 <= i,j <= 10 }";
1323 assert(map_is_equal(mm.must, str));
1324 str = "{ [0,0,0,0,0] -> [0,0,0,0,0] : 1 = 0 }";
1325 assert(map_is_equal(mm.may, str));
1326
1327 isl_map_free(mm.must);
1328 isl_map_free(mm.may);
1329 isl_flow_free(flow);
1330 }
1331
1332 void test_sv(struct isl_ctx *ctx)
1333 {
1334 const char *str;
1335 isl_map *map;
1336
1337 str = "[N] -> { [i] -> [f] : 0 <= i <= N and 0 <= i - 10 f <= 9 }";
1338 map = isl_map_read_from_str(ctx, str, -1);
1339 assert(isl_map_is_single_valued(map));
1340 isl_map_free(map);
1341
1342 str = "[N] -> { [i] -> [f] : 0 <= i <= N and 0 <= i - 10 f <= 10 }";
1343 map = isl_map_read_from_str(ctx, str, -1);
1344 assert(!isl_map_is_single_valued(map));
1345 isl_map_free(map);
1346 }
1347
1348 void test_bijective_case(struct isl_ctx *ctx, const char *str, int bijective)
1349 {
1350 isl_map *map;
1351
1352 map = isl_map_read_from_str(ctx, str, -1);
1353 if (bijective)
1354 assert(isl_map_is_bijective(map));
1355 else
1356 assert(!isl_map_is_bijective(map));
1357 isl_map_free(map);
1358 }
1359
1360 void test_bijective(struct isl_ctx *ctx)
1361 {
1362 test_bijective_case(ctx, "[N,M]->{[i,j] -> [i]}", 0);
1363 test_bijective_case(ctx, "[N,M]->{[i,j] -> [i] : j=i}", 1);
1364 test_bijective_case(ctx, "[N,M]->{[i,j] -> [i] : j=0}", 1);
1365 test_bijective_case(ctx, "[N,M]->{[i,j] -> [i] : j=N}", 1);
1366 test_bijective_case(ctx, "[N,M]->{[i,j] -> [j,i]}", 1);
1367 test_bijective_case(ctx, "[N,M]->{[i,j] -> [i+j]}", 0);
1368 test_bijective_case(ctx, "[N,M]->{[i,j] -> []}", 0);
1369 test_bijective_case(ctx, "[N,M]->{[i,j] -> [i,j,N]}", 1);
1370 test_bijective_case(ctx, "[N,M]->{[i,j] -> [2i]}", 0);
1371 test_bijective_case(ctx, "[N,M]->{[i,j] -> [i,i]}", 0);
1372 test_bijective_case(ctx, "[N,M]->{[i,j] -> [2i,i]}", 0);
1373 test_bijective_case(ctx, "[N,M]->{[i,j] -> [2i,j]}", 1);
1374 test_bijective_case(ctx, "[N,M]->{[i,j] -> [x,y] : 2x=i & y =j}", 1);
1375 }
1376
1377 void test_pwqp(struct isl_ctx *ctx)
1378 {
1379 const char *str;
1380 isl_pw_qpolynomial *pwqp1, *pwqp2;
1381
1382 str = "{ [i,j,k] -> 1 + 9 * [i/5] + 7 * [j/11] + 4 * [k/13] }";
1383 pwqp1 = isl_pw_qpolynomial_read_from_str(ctx, str);
1384
1385 pwqp1 = isl_pw_qpolynomial_move_dims(pwqp1, isl_dim_param, 0,
1386 isl_dim_set, 1, 1);
1387
1388 str = "[j] -> { [i,k] -> 1 + 9 * [i/5] + 7 * [j/11] + 4 * [k/13] }";
1389 pwqp2 = isl_pw_qpolynomial_read_from_str(ctx, str);
1390
1391 pwqp1 = isl_pw_qpolynomial_sub(pwqp1, pwqp2);
1392
1393 assert(isl_pw_qpolynomial_is_zero(pwqp1));
1394
1395 isl_pw_qpolynomial_free(pwqp1);
1396 }
1397
1398 int main()
1399 {
1400 struct isl_ctx *ctx;
1401
1402 srcdir = getenv("srcdir");
1403 assert(srcdir);
1404
1405 ctx = isl_ctx_alloc();
1406 test_parse(ctx);
1407 test_pwqp(ctx);
1408 test_lex(ctx);
1409 test_sv(ctx);
1410 test_bijective(ctx);
1411 test_dep(ctx);
1412 test_read(ctx);
1413 test_bounded(ctx);
1414 test_construction(ctx);
1415 test_dim(ctx);
1416 test_div(ctx);
1417 test_application(ctx);
1418 test_affine_hull(ctx);
1419 test_convex_hull(ctx);
1420 test_gist(ctx);
1421 test_coalesce(ctx);
1422 test_closure(ctx);
1423 test_lexmin(ctx);
1424 isl_ctx_free(ctx);
1425 return 0;
1426 }
Integer set library