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isl_union_map: construct new isl_union_map on operations that change dimensions
[isl.git] / isl_test.c
blob14f633d69054773bf2b358a6ecd1caa78a550b5a
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_read(struct isl_ctx *ctx)
22 {
23 char filename[PATH_MAX];
24 FILE *input;
25 int n;
26 struct isl_basic_set *bset1, *bset2;
27 const char *str = "{[y]: Exists ( alpha : 2alpha = y)}";
28
29 n = snprintf(filename, sizeof(filename),
30 "%s/test_inputs/set.omega", srcdir);
31 assert(n < sizeof(filename));
32 input = fopen(filename, "r");
33 assert(input);
34
35 bset1 = isl_basic_set_read_from_file(ctx, input, 0);
36 bset2 = isl_basic_set_read_from_str(ctx, str, 0);
37
38 assert(isl_basic_set_is_equal(bset1, bset2) == 1);
39
40 isl_basic_set_free(bset1);
41 isl_basic_set_free(bset2);
42
43 fclose(input);
44 }
45
46 void test_bounded(struct isl_ctx *ctx)
47 {
48 isl_set *set;
49 int bounded;
50
51 set = isl_set_read_from_str(ctx, "[n] -> {[i] : 0 <= i <= n }", -1);
52 bounded = isl_set_is_bounded(set);
53 assert(bounded);
54 isl_set_free(set);
55
56 set = isl_set_read_from_str(ctx, "{[n, i] : 0 <= i <= n }", -1);
57 bounded = isl_set_is_bounded(set);
58 assert(!bounded);
59 isl_set_free(set);
60
61 set = isl_set_read_from_str(ctx, "[n] -> {[i] : i <= n }", -1);
62 bounded = isl_set_is_bounded(set);
63 assert(!bounded);
64 isl_set_free(set);
65 }
66
67 /* Construct the basic set { [i] : 5 <= i <= N } */
68 void test_construction(struct isl_ctx *ctx)
69 {
70 isl_int v;
71 struct isl_dim *dim;
72 struct isl_basic_set *bset;
73 struct isl_constraint *c;
74
75 isl_int_init(v);
76
77 dim = isl_dim_set_alloc(ctx, 1, 1);
78 bset = isl_basic_set_universe(dim);
79
80 c = isl_inequality_alloc(isl_basic_set_get_dim(bset));
81 isl_int_set_si(v, -1);
82 isl_constraint_set_coefficient(c, isl_dim_set, 0, v);
83 isl_int_set_si(v, 1);
84 isl_constraint_set_coefficient(c, isl_dim_param, 0, v);
85 bset = isl_basic_set_add_constraint(bset, c);
86
87 c = isl_inequality_alloc(isl_basic_set_get_dim(bset));
88 isl_int_set_si(v, 1);
89 isl_constraint_set_coefficient(c, isl_dim_set, 0, v);
90 isl_int_set_si(v, -5);
91 isl_constraint_set_constant(c, v);
92 bset = isl_basic_set_add_constraint(bset, c);
93
94 isl_basic_set_free(bset);
95
96 isl_int_clear(v);
97 }
98
99 void test_dim(struct isl_ctx *ctx)
100 {
101 const char *str;
102 isl_map *map1, *map2;
103
104 map1 = isl_map_read_from_str(ctx,
105 "[n] -> { [i] -> [j] : exists (a = [i/10] : i - 10a <= n ) }", -1);
106 map1 = isl_map_add(map1, isl_dim_in, 1);
107 map2 = isl_map_read_from_str(ctx,
108 "[n] -> { [i,k] -> [j] : exists (a = [i/10] : i - 10a <= n ) }", -1);
109 assert(isl_map_is_equal(map1, map2));
110 isl_map_free(map2);
111
112 map1 = isl_map_project_out(map1, isl_dim_in, 0, 1);
113 map2 = isl_map_read_from_str(ctx, "[n] -> { [i] -> [j] : n >= 0 }", -1);
114 assert(isl_map_is_equal(map1, map2));
115
116 isl_map_free(map1);
117 isl_map_free(map2);
118
119 str = "[n] -> { [i] -> [] : exists a : 0 <= i <= n and i = 2 a }";
120 map1 = isl_map_read_from_str(ctx, str, -1);
121 str = "{ [i] -> [j] : exists a : 0 <= i <= j and i = 2 a }";
122 map2 = isl_map_read_from_str(ctx, str, -1);
123 map1 = isl_map_move_dims(map1, isl_dim_out, 0, isl_dim_param, 0, 1);
124 assert(isl_map_is_equal(map1, map2));
125
126 isl_map_free(map1);
127 isl_map_free(map2);
128 }
129
130 void test_div(struct isl_ctx *ctx)
131 {
132 isl_int v;
133 int pos;
134 struct isl_dim *dim;
135 struct isl_div *div;
136 struct isl_basic_set *bset;
137 struct isl_constraint *c;
138
139 isl_int_init(v);
140
141 /* test 1 */
142 dim = isl_dim_set_alloc(ctx, 0, 1);
143 bset = isl_basic_set_universe(dim);
144
145 c = isl_equality_alloc(isl_basic_set_get_dim(bset));
146 isl_int_set_si(v, -1);
147 isl_constraint_set_constant(c, v);
148 isl_int_set_si(v, 1);
149 isl_constraint_set_coefficient(c, isl_dim_set, 0, v);
150 div = isl_div_alloc(isl_basic_set_get_dim(bset));
151 c = isl_constraint_add_div(c, div, &pos);
152 isl_int_set_si(v, 3);
153 isl_constraint_set_coefficient(c, isl_dim_div, pos, v);
154 bset = isl_basic_set_add_constraint(bset, c);
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 assert(bset && bset->n_div == 1);
168 isl_basic_set_free(bset);
169
170 /* test 2 */
171 dim = isl_dim_set_alloc(ctx, 0, 1);
172 bset = isl_basic_set_universe(dim);
173
174 c = isl_equality_alloc(isl_basic_set_get_dim(bset));
175 isl_int_set_si(v, 1);
176 isl_constraint_set_constant(c, v);
177 isl_int_set_si(v, -1);
178 isl_constraint_set_coefficient(c, isl_dim_set, 0, v);
179 div = isl_div_alloc(isl_basic_set_get_dim(bset));
180 c = isl_constraint_add_div(c, div, &pos);
181 isl_int_set_si(v, 3);
182 isl_constraint_set_coefficient(c, isl_dim_div, pos, v);
183 bset = isl_basic_set_add_constraint(bset, c);
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 assert(bset && bset->n_div == 1);
197 isl_basic_set_free(bset);
198
199 /* test 3 */
200 dim = isl_dim_set_alloc(ctx, 0, 1);
201 bset = isl_basic_set_universe(dim);
202
203 c = isl_equality_alloc(isl_basic_set_get_dim(bset));
204 isl_int_set_si(v, 1);
205 isl_constraint_set_constant(c, v);
206 isl_int_set_si(v, -1);
207 isl_constraint_set_coefficient(c, isl_dim_set, 0, v);
208 div = isl_div_alloc(isl_basic_set_get_dim(bset));
209 c = isl_constraint_add_div(c, div, &pos);
210 isl_int_set_si(v, 3);
211 isl_constraint_set_coefficient(c, isl_dim_div, pos, v);
212 bset = isl_basic_set_add_constraint(bset, c);
213
214 c = isl_equality_alloc(isl_basic_set_get_dim(bset));
215 isl_int_set_si(v, -3);
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, 4);
222 isl_constraint_set_coefficient(c, isl_dim_div, pos, v);
223 bset = isl_basic_set_add_constraint(bset, c);
224
225 assert(bset && bset->n_div == 1);
226 isl_basic_set_free(bset);
227
228 /* test 4 */
229 dim = isl_dim_set_alloc(ctx, 0, 1);
230 bset = isl_basic_set_universe(dim);
231
232 c = isl_equality_alloc(isl_basic_set_get_dim(bset));
233 isl_int_set_si(v, 2);
234 isl_constraint_set_constant(c, v);
235 isl_int_set_si(v, -1);
236 isl_constraint_set_coefficient(c, isl_dim_set, 0, v);
237 div = isl_div_alloc(isl_basic_set_get_dim(bset));
238 c = isl_constraint_add_div(c, div, &pos);
239 isl_int_set_si(v, 3);
240 isl_constraint_set_coefficient(c, isl_dim_div, pos, v);
241 bset = isl_basic_set_add_constraint(bset, c);
242
243 c = isl_equality_alloc(isl_basic_set_get_dim(bset));
244 isl_int_set_si(v, -1);
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, 6);
251 isl_constraint_set_coefficient(c, isl_dim_div, pos, v);
252 bset = isl_basic_set_add_constraint(bset, c);
253
254 assert(isl_basic_set_is_empty(bset));
255 isl_basic_set_free(bset);
256
257 /* test 5 */
258 dim = isl_dim_set_alloc(ctx, 0, 2);
259 bset = isl_basic_set_universe(dim);
260
261 c = isl_equality_alloc(isl_basic_set_get_dim(bset));
262 isl_int_set_si(v, -1);
263 isl_constraint_set_coefficient(c, isl_dim_set, 0, v);
264 div = isl_div_alloc(isl_basic_set_get_dim(bset));
265 c = isl_constraint_add_div(c, div, &pos);
266 isl_int_set_si(v, 3);
267 isl_constraint_set_coefficient(c, isl_dim_div, pos, v);
268 bset = isl_basic_set_add_constraint(bset, c);
269
270 c = isl_equality_alloc(isl_basic_set_get_dim(bset));
271 isl_int_set_si(v, 1);
272 isl_constraint_set_coefficient(c, isl_dim_set, 0, v);
273 isl_int_set_si(v, -3);
274 isl_constraint_set_coefficient(c, isl_dim_set, 1, v);
275 bset = isl_basic_set_add_constraint(bset, c);
276
277 assert(bset && bset->n_div == 0);
278 isl_basic_set_free(bset);
279
280 /* test 6 */
281 dim = isl_dim_set_alloc(ctx, 0, 2);
282 bset = isl_basic_set_universe(dim);
283
284 c = isl_equality_alloc(isl_basic_set_get_dim(bset));
285 isl_int_set_si(v, -1);
286 isl_constraint_set_coefficient(c, isl_dim_set, 0, v);
287 div = isl_div_alloc(isl_basic_set_get_dim(bset));
288 c = isl_constraint_add_div(c, div, &pos);
289 isl_int_set_si(v, 6);
290 isl_constraint_set_coefficient(c, isl_dim_div, pos, v);
291 bset = isl_basic_set_add_constraint(bset, c);
292
293 c = isl_equality_alloc(isl_basic_set_get_dim(bset));
294 isl_int_set_si(v, 1);
295 isl_constraint_set_coefficient(c, isl_dim_set, 0, v);
296 isl_int_set_si(v, -3);
297 isl_constraint_set_coefficient(c, isl_dim_set, 1, v);
298 bset = isl_basic_set_add_constraint(bset, c);
299
300 assert(bset && bset->n_div == 1);
301 isl_basic_set_free(bset);
302
303 /* test 7 */
304 /* This test is a bit tricky. We set up an equality
305 * a + 3b + 3c = 6 e0
306 * Normalization of divs creates _two_ divs
307 * a = 3 e0
308 * c - b - e0 = 2 e1
309 * Afterwards e0 is removed again because it has coefficient -1
310 * and we end up with the original equality and div again.
311 * Perhaps we can avoid the introduction of this temporary div.
312 */
313 dim = isl_dim_set_alloc(ctx, 0, 3);
314 bset = isl_basic_set_universe(dim);
315
316 c = isl_equality_alloc(isl_basic_set_get_dim(bset));
317 isl_int_set_si(v, -1);
318 isl_constraint_set_coefficient(c, isl_dim_set, 0, v);
319 isl_int_set_si(v, -3);
320 isl_constraint_set_coefficient(c, isl_dim_set, 1, v);
321 isl_int_set_si(v, -3);
322 isl_constraint_set_coefficient(c, isl_dim_set, 2, v);
323 div = isl_div_alloc(isl_basic_set_get_dim(bset));
324 c = isl_constraint_add_div(c, div, &pos);
325 isl_int_set_si(v, 6);
326 isl_constraint_set_coefficient(c, isl_dim_div, pos, v);
327 bset = isl_basic_set_add_constraint(bset, c);
328
329 /* Test disabled for now */
330 /*
331 assert(bset && bset->n_div == 1);
332 */
333 isl_basic_set_free(bset);
334
335 /* test 8 */
336 dim = isl_dim_set_alloc(ctx, 0, 4);
337 bset = isl_basic_set_universe(dim);
338
339 c = isl_equality_alloc(isl_basic_set_get_dim(bset));
340 isl_int_set_si(v, -1);
341 isl_constraint_set_coefficient(c, isl_dim_set, 0, v);
342 isl_int_set_si(v, -3);
343 isl_constraint_set_coefficient(c, isl_dim_set, 1, v);
344 isl_int_set_si(v, -3);
345 isl_constraint_set_coefficient(c, isl_dim_set, 3, v);
346 div = isl_div_alloc(isl_basic_set_get_dim(bset));
347 c = isl_constraint_add_div(c, div, &pos);
348 isl_int_set_si(v, 6);
349 isl_constraint_set_coefficient(c, isl_dim_div, pos, v);
350 bset = isl_basic_set_add_constraint(bset, c);
351
352 c = isl_equality_alloc(isl_basic_set_get_dim(bset));
353 isl_int_set_si(v, -1);
354 isl_constraint_set_coefficient(c, isl_dim_set, 0, v);
355 isl_int_set_si(v, 1);
356 isl_constraint_set_coefficient(c, isl_dim_set, 2, v);
357 isl_int_set_si(v, 1);
358 isl_constraint_set_constant(c, v);
359 bset = isl_basic_set_add_constraint(bset, c);
360
361 /* Test disabled for now */
362 /*
363 assert(bset && bset->n_div == 1);
364 */
365 isl_basic_set_free(bset);
366
367 /* test 9 */
368 dim = isl_dim_set_alloc(ctx, 0, 2);
369 bset = isl_basic_set_universe(dim);
370
371 c = isl_equality_alloc(isl_basic_set_get_dim(bset));
372 isl_int_set_si(v, 1);
373 isl_constraint_set_coefficient(c, isl_dim_set, 0, v);
374 isl_int_set_si(v, -1);
375 isl_constraint_set_coefficient(c, isl_dim_set, 1, v);
376 div = isl_div_alloc(isl_basic_set_get_dim(bset));
377 c = isl_constraint_add_div(c, div, &pos);
378 isl_int_set_si(v, -2);
379 isl_constraint_set_coefficient(c, isl_dim_div, pos, v);
380 bset = isl_basic_set_add_constraint(bset, c);
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 div = isl_div_alloc(isl_basic_set_get_dim(bset));
386 c = isl_constraint_add_div(c, div, &pos);
387 isl_int_set_si(v, 3);
388 isl_constraint_set_coefficient(c, isl_dim_div, pos, v);
389 isl_int_set_si(v, 2);
390 isl_constraint_set_constant(c, v);
391 bset = isl_basic_set_add_constraint(bset, c);
392
393 bset = isl_basic_set_fix_si(bset, isl_dim_set, 0, 2);
394
395 assert(!isl_basic_set_is_empty(bset));
396
397 isl_basic_set_free(bset);
398
399 /* test 10 */
400 dim = isl_dim_set_alloc(ctx, 0, 2);
401 bset = isl_basic_set_universe(dim);
402
403 c = isl_equality_alloc(isl_basic_set_get_dim(bset));
404 isl_int_set_si(v, 1);
405 isl_constraint_set_coefficient(c, isl_dim_set, 0, v);
406 div = isl_div_alloc(isl_basic_set_get_dim(bset));
407 c = isl_constraint_add_div(c, div, &pos);
408 isl_int_set_si(v, -2);
409 isl_constraint_set_coefficient(c, isl_dim_div, pos, v);
410 bset = isl_basic_set_add_constraint(bset, c);
411
412 bset = isl_basic_set_fix_si(bset, isl_dim_set, 0, 2);
413
414 isl_basic_set_free(bset);
415
416 isl_int_clear(v);
417 }
418
419 void test_application_case(struct isl_ctx *ctx, const char *name)
420 {
421 char filename[PATH_MAX];
422 FILE *input;
423 int n;
424 struct isl_basic_set *bset1, *bset2;
425 struct isl_basic_map *bmap;
426
427 n = snprintf(filename, sizeof(filename),
428 "%s/test_inputs/%s.omega", srcdir, name);
429 assert(n < sizeof(filename));
430 input = fopen(filename, "r");
431 assert(input);
432
433 bset1 = isl_basic_set_read_from_file(ctx, input, 0);
434 bmap = isl_basic_map_read_from_file(ctx, input, 0);
435
436 bset1 = isl_basic_set_apply(bset1, bmap);
437
438 bset2 = isl_basic_set_read_from_file(ctx, input, 0);
439
440 assert(isl_basic_set_is_equal(bset1, bset2) == 1);
441
442 isl_basic_set_free(bset1);
443 isl_basic_set_free(bset2);
444
445 fclose(input);
446 }
447
448 void test_application(struct isl_ctx *ctx)
449 {
450 test_application_case(ctx, "application");
451 test_application_case(ctx, "application2");
452 }
453
454 void test_affine_hull_case(struct isl_ctx *ctx, const char *name)
455 {
456 char filename[PATH_MAX];
457 FILE *input;
458 int n;
459 struct isl_basic_set *bset1, *bset2;
460
461 n = snprintf(filename, sizeof(filename),
462 "%s/test_inputs/%s.polylib", srcdir, name);
463 assert(n < sizeof(filename));
464 input = fopen(filename, "r");
465 assert(input);
466
467 bset1 = isl_basic_set_read_from_file(ctx, input, 0);
468 bset2 = isl_basic_set_read_from_file(ctx, input, 0);
469
470 bset1 = isl_basic_set_affine_hull(bset1);
471
472 assert(isl_basic_set_is_equal(bset1, bset2) == 1);
473
474 isl_basic_set_free(bset1);
475 isl_basic_set_free(bset2);
476
477 fclose(input);
478 }
479
480 void test_affine_hull(struct isl_ctx *ctx)
481 {
482 test_affine_hull_case(ctx, "affine2");
483 test_affine_hull_case(ctx, "affine");
484 test_affine_hull_case(ctx, "affine3");
485 }
486
487 void test_convex_hull_case(struct isl_ctx *ctx, const char *name)
488 {
489 char filename[PATH_MAX];
490 FILE *input;
491 int n;
492 struct isl_basic_set *bset1, *bset2;
493 struct isl_set *set;
494
495 n = snprintf(filename, sizeof(filename),
496 "%s/test_inputs/%s.polylib", srcdir, name);
497 assert(n < sizeof(filename));
498 input = fopen(filename, "r");
499 assert(input);
500
501 bset1 = isl_basic_set_read_from_file(ctx, input, 0);
502 bset2 = isl_basic_set_read_from_file(ctx, input, 0);
503
504 set = isl_basic_set_union(bset1, bset2);
505 bset1 = isl_set_convex_hull(set);
506
507 bset2 = isl_basic_set_read_from_file(ctx, input, 0);
508
509 assert(isl_basic_set_is_equal(bset1, bset2) == 1);
510
511 isl_basic_set_free(bset1);
512 isl_basic_set_free(bset2);
513
514 fclose(input);
515 }
516
517 void test_convex_hull(struct isl_ctx *ctx)
518 {
519 const char *str1, *str2;
520 isl_set *set1, *set2;
521
522 test_convex_hull_case(ctx, "convex0");
523 test_convex_hull_case(ctx, "convex1");
524 test_convex_hull_case(ctx, "convex2");
525 test_convex_hull_case(ctx, "convex3");
526 test_convex_hull_case(ctx, "convex4");
527 test_convex_hull_case(ctx, "convex5");
528 test_convex_hull_case(ctx, "convex6");
529 test_convex_hull_case(ctx, "convex7");
530 test_convex_hull_case(ctx, "convex8");
531 test_convex_hull_case(ctx, "convex9");
532 test_convex_hull_case(ctx, "convex10");
533 test_convex_hull_case(ctx, "convex11");
534 test_convex_hull_case(ctx, "convex12");
535 test_convex_hull_case(ctx, "convex13");
536 test_convex_hull_case(ctx, "convex14");
537 test_convex_hull_case(ctx, "convex15");
538
539 str1 = "{ [i0, i1, i2] : (i2 = 1 and i0 = 0 and i1 >= 0) or "
540 "(i0 = 1 and i1 = 0 and i2 = 1) or "
541 "(i0 = 0 and i1 = 0 and i2 = 0) }";
542 str2 = "{ [i0, i1, i2] : i0 >= 0 and i2 >= i0 and i2 <= 1 and i1 >= 0 }";
543 set1 = isl_set_read_from_str(ctx, str1, -1);
544 set2 = isl_set_read_from_str(ctx, str2, -1);
545 set1 = isl_set_from_basic_set(isl_set_convex_hull(set1));
546 assert(isl_set_is_equal(set1, set2));
547 isl_set_free(set1);
548 isl_set_free(set2);
549 }
550
551 void test_gist_case(struct isl_ctx *ctx, const char *name)
552 {
553 char filename[PATH_MAX];
554 FILE *input;
555 int n;
556 struct isl_basic_set *bset1, *bset2;
557
558 n = snprintf(filename, sizeof(filename),
559 "%s/test_inputs/%s.polylib", srcdir, name);
560 assert(n < sizeof(filename));
561 input = fopen(filename, "r");
562 assert(input);
563
564 bset1 = isl_basic_set_read_from_file(ctx, input, 0);
565 bset2 = isl_basic_set_read_from_file(ctx, input, 0);
566
567 bset1 = isl_basic_set_gist(bset1, bset2);
568
569 bset2 = isl_basic_set_read_from_file(ctx, input, 0);
570
571 assert(isl_basic_set_is_equal(bset1, bset2) == 1);
572
573 isl_basic_set_free(bset1);
574 isl_basic_set_free(bset2);
575
576 fclose(input);
577 }
578
579 void test_gist(struct isl_ctx *ctx)
580 {
581 test_gist_case(ctx, "gist1");
582 }
583
584 void test_coalesce_set(isl_ctx *ctx, const char *str, int check_one)
585 {
586 isl_set *set, *set2;
587
588 set = isl_set_read_from_str(ctx, str, -1);
589 set = isl_set_coalesce(set);
590 set2 = isl_set_read_from_str(ctx, str, -1);
591 assert(isl_set_is_equal(set, set2));
592 if (check_one)
593 assert(set && set->n == 1);
594 isl_set_free(set);
595 isl_set_free(set2);
596 }
597
598 void test_coalesce(struct isl_ctx *ctx)
599 {
600 const char *str;
601 struct isl_set *set, *set2;
602 struct isl_map *map, *map2;
603
604 set = isl_set_read_from_str(ctx,
605 "{[x,y]: x >= 0 & x <= 10 & y >= 0 & y <= 10 or "
606 "y >= x & x >= 2 & 5 >= y }", -1);
607 set = isl_set_coalesce(set);
608 assert(set && set->n == 1);
609 isl_set_free(set);
610
611 set = isl_set_read_from_str(ctx,
612 "{[x,y]: y >= 0 & 2x + y <= 30 & y <= 10 & x >= 0 or "
613 "x + y >= 10 & y <= x & x + y <= 20 & y >= 0}", -1);
614 set = isl_set_coalesce(set);
615 assert(set && set->n == 1);
616 isl_set_free(set);
617
618 set = isl_set_read_from_str(ctx,
619 "{[x,y]: y >= 0 & 2x + y <= 30 & y <= 10 & x >= 0 or "
620 "x + y >= 10 & y <= x & x + y <= 19 & y >= 0}", -1);
621 set = isl_set_coalesce(set);
622 assert(set && set->n == 2);
623 isl_set_free(set);
624
625 set = isl_set_read_from_str(ctx,
626 "{[x,y]: y >= 0 & x <= 5 & y <= x or "
627 "y >= 0 & x >= 6 & x <= 10 & y <= x}", -1);
628 set = isl_set_coalesce(set);
629 assert(set && set->n == 1);
630 isl_set_free(set);
631
632 set = isl_set_read_from_str(ctx,
633 "{[x,y]: y >= 0 & x <= 5 & y <= x or "
634 "y >= 0 & x >= 7 & x <= 10 & y <= x}", -1);
635 set = isl_set_coalesce(set);
636 assert(set && set->n == 2);
637 isl_set_free(set);
638
639 set = isl_set_read_from_str(ctx,
640 "{[x,y]: y >= 0 & x <= 5 & y <= x or "
641 "y >= 0 & x >= 6 & x <= 10 & y + 1 <= x}", -1);
642 set = isl_set_coalesce(set);
643 assert(set && set->n == 2);
644 isl_set_free(set);
645
646 set = isl_set_read_from_str(ctx,
647 "{[x,y]: y >= 0 & x <= 5 & y <= x or "
648 "y >= 0 & x = 6 & y <= 6}", -1);
649 set = isl_set_coalesce(set);
650 assert(set && set->n == 1);
651 isl_set_free(set);
652
653 set = isl_set_read_from_str(ctx,
654 "{[x,y]: y >= 0 & x <= 5 & y <= x or "
655 "y >= 0 & x = 7 & y <= 6}", -1);
656 set = isl_set_coalesce(set);
657 assert(set && set->n == 2);
658 isl_set_free(set);
659
660 set = isl_set_read_from_str(ctx,
661 "{[x,y]: y >= 0 & x <= 5 & y <= x or "
662 "y >= 0 & x = 6 & y <= 5}", -1);
663 set = isl_set_coalesce(set);
664 assert(set && set->n == 1);
665 set2 = isl_set_read_from_str(ctx,
666 "{[x,y]: y >= 0 & x <= 5 & y <= x or "
667 "y >= 0 & x = 6 & y <= 5}", -1);
668 assert(isl_set_is_equal(set, set2));
669 isl_set_free(set);
670 isl_set_free(set2);
671
672 set = isl_set_read_from_str(ctx,
673 "{[x,y]: y >= 0 & x <= 5 & y <= x or "
674 "y >= 0 & x = 6 & y <= 7}", -1);
675 set = isl_set_coalesce(set);
676 assert(set && set->n == 2);
677 isl_set_free(set);
678
679 set = isl_set_read_from_str(ctx,
680 "[n] -> { [i] : i = 1 and n >= 2 or 2 <= i and i <= n }", -1);
681 set = isl_set_coalesce(set);
682 assert(set && set->n == 1);
683 set2 = isl_set_read_from_str(ctx,
684 "[n] -> { [i] : i = 1 and n >= 2 or 2 <= i and i <= n }", -1);
685 assert(isl_set_is_equal(set, set2));
686 isl_set_free(set);
687 isl_set_free(set2);
688
689 set = isl_set_read_from_str(ctx,
690 "{[x,y] : x >= 0 and y >= 0 or 0 <= y and y <= 5 and x = -1}", -1);
691 set = isl_set_coalesce(set);
692 set2 = isl_set_read_from_str(ctx,
693 "{[x,y] : x >= 0 and y >= 0 or 0 <= y and y <= 5 and x = -1}", -1);
694 assert(isl_set_is_equal(set, set2));
695 isl_set_free(set);
696 isl_set_free(set2);
697
698 set = isl_set_read_from_str(ctx,
699 "[n] -> { [i] : 1 <= i and i <= n - 1 or "
700 "2 <= i and i <= n }", -1);
701 set = isl_set_coalesce(set);
702 assert(set && set->n == 1);
703 set2 = isl_set_read_from_str(ctx,
704 "[n] -> { [i] : 1 <= i and i <= n - 1 or "
705 "2 <= i and i <= n }", -1);
706 assert(isl_set_is_equal(set, set2));
707 isl_set_free(set);
708 isl_set_free(set2);
709
710 map = isl_map_read_from_str(ctx,
711 "[n] -> { [i0] -> [o0] : exists (e0 = [(i0)/4], e1 = [(o0)/4], "
712 "e2 = [(n)/2], e3 = [(-2 + i0)/4], e4 = [(-2 + o0)/4], "
713 "e5 = [(-2n + i0)/4]: 2e2 = n and 4e3 = -2 + i0 and "
714 "4e4 = -2 + o0 and i0 >= 8 + 2n and o0 >= 2 + i0 and "
715 "o0 <= 56 + 2n and o0 <= -12 + 4n and i0 <= 57 + 2n and "
716 "i0 <= -11 + 4n and o0 >= 6 + 2n and 4e0 <= i0 and "
717 "4e0 >= -3 + i0 and 4e1 <= o0 and 4e1 >= -3 + o0 and "
718 "4e5 <= -2n + i0 and 4e5 >= -3 - 2n + i0);"
719 "[i0] -> [o0] : exists (e0 = [(i0)/4], e1 = [(o0)/4], "
720 "e2 = [(n)/2], e3 = [(-2 + i0)/4], e4 = [(-2 + o0)/4], "
721 "e5 = [(-2n + i0)/4]: 2e2 = n and 4e3 = -2 + i0 and "
722 "4e4 = -2 + o0 and 2e0 >= 3 + n and e0 <= -4 + n and "
723 "2e0 <= 27 + n and e1 <= -4 + n and 2e1 <= 27 + n and "
724 "2e1 >= 2 + n and e1 >= 1 + e0 and i0 >= 7 + 2n and "
725 "i0 <= -11 + 4n and i0 <= 57 + 2n and 4e0 <= -2 + i0 and "
726 "4e0 >= -3 + i0 and o0 >= 6 + 2n and o0 <= -11 + 4n and "
727 "o0 <= 57 + 2n and 4e1 <= -2 + o0 and 4e1 >= -3 + o0 and "
728 "4e5 <= -2n + i0 and 4e5 >= -3 - 2n + i0 ) }", -1);
729 map = isl_map_coalesce(map);
730 map2 = isl_map_read_from_str(ctx,
731 "[n] -> { [i0] -> [o0] : exists (e0 = [(i0)/4], e1 = [(o0)/4], "
732 "e2 = [(n)/2], e3 = [(-2 + i0)/4], e4 = [(-2 + o0)/4], "
733 "e5 = [(-2n + i0)/4]: 2e2 = n and 4e3 = -2 + i0 and "
734 "4e4 = -2 + o0 and i0 >= 8 + 2n and o0 >= 2 + i0 and "
735 "o0 <= 56 + 2n and o0 <= -12 + 4n and i0 <= 57 + 2n and "
736 "i0 <= -11 + 4n and o0 >= 6 + 2n and 4e0 <= i0 and "
737 "4e0 >= -3 + i0 and 4e1 <= o0 and 4e1 >= -3 + o0 and "
738 "4e5 <= -2n + i0 and 4e5 >= -3 - 2n + i0);"
739 "[i0] -> [o0] : exists (e0 = [(i0)/4], e1 = [(o0)/4], "
740 "e2 = [(n)/2], e3 = [(-2 + i0)/4], e4 = [(-2 + o0)/4], "
741 "e5 = [(-2n + i0)/4]: 2e2 = n and 4e3 = -2 + i0 and "
742 "4e4 = -2 + o0 and 2e0 >= 3 + n and e0 <= -4 + n and "
743 "2e0 <= 27 + n and e1 <= -4 + n and 2e1 <= 27 + n and "
744 "2e1 >= 2 + n and e1 >= 1 + e0 and i0 >= 7 + 2n and "
745 "i0 <= -11 + 4n and i0 <= 57 + 2n and 4e0 <= -2 + i0 and "
746 "4e0 >= -3 + i0 and o0 >= 6 + 2n and o0 <= -11 + 4n and "
747 "o0 <= 57 + 2n and 4e1 <= -2 + o0 and 4e1 >= -3 + o0 and "
748 "4e5 <= -2n + i0 and 4e5 >= -3 - 2n + i0 ) }", -1);
749 assert(isl_map_is_equal(map, map2));
750 isl_map_free(map);
751 isl_map_free(map2);
752
753 str = "[n, m] -> { [] -> [o0, o2, o3] : (o3 = 1 and o0 >= 1 + m and "
754 "o0 <= n + m and o2 <= m and o0 >= 2 + n and o2 >= 3) or "
755 "(o0 >= 2 + n and o0 >= 1 + m and o0 <= n + m and n >= 1 and "
756 "o3 <= -1 + o2 and o3 >= 1 - m + o2 and o3 >= 2 and o3 <= n) }";
757 map = isl_map_read_from_str(ctx, str, -1);
758 map = isl_map_coalesce(map);
759 map2 = isl_map_read_from_str(ctx, str, -1);
760 assert(isl_map_is_equal(map, map2));
761 isl_map_free(map);
762 isl_map_free(map2);
763
764 str = "[M, N] -> { [i0, i1, i2, i3, i4, i5, i6] -> "
765 "[o0, o1, o2, o3, o4, o5, o6] : "
766 "(o6 <= -4 + 2M - 2N + i0 + i1 - i2 + i6 - o0 - o1 + o2 and "
767 "o3 <= -2 + i3 and o6 >= 2 + i0 + i3 + i6 - o0 - o3 and "
768 "o6 >= 2 - M + N + i3 + i4 + i6 - o3 - o4 and o0 <= -1 + i0 and "
769 "o4 >= 4 - 3M + 3N - i0 - i1 + i2 + 2i3 + i4 + o0 + o1 - o2 - 2o3 "
770 "and o6 <= -3 + 2M - 2N + i3 + i4 - i5 + i6 - o3 - o4 + o5 and "
771 "2o6 <= -5 + 5M - 5N + 2i0 + i1 - i2 - i5 + 2i6 - 2o0 - o1 + o2 + o5 "
772 "and o6 >= 2i0 + i1 + i6 - 2o0 - o1 and "
773 "3o6 <= -5 + 4M - 4N + 2i0 + i1 - i2 + 2i3 + i4 - i5 + 3i6 "
774 "- 2o0 - o1 + o2 - 2o3 - o4 + o5) or "
775 "(N >= 2 and o3 <= -1 + i3 and o0 <= -1 + i0 and "
776 "o6 >= i3 + i6 - o3 and M >= 0 and "
777 "2o6 >= 1 + i0 + i3 + 2i6 - o0 - o3 and "
778 "o6 >= 1 - M + i0 + i6 - o0 and N >= 2M and o6 >= i0 + i6 - o0) }";
779 map = isl_map_read_from_str(ctx, str, -1);
780 map = isl_map_coalesce(map);
781 map2 = isl_map_read_from_str(ctx, str, -1);
782 assert(isl_map_is_equal(map, map2));
783 isl_map_free(map);
784 isl_map_free(map2);
785
786 str = "[M, N] -> { [] -> [o0] : (o0 = 0 and M >= 1 and N >= 2) or "
787 "(o0 = 0 and M >= 1 and N >= 2M and N >= 2 + M) or "
788 "(o0 = 0 and M >= 2 and N >= 3) or "
789 "(M = 0 and o0 = 0 and N >= 3) }";
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 = "{ [i0, i1, i2, i3] : (i1 = 10i0 and i0 >= 1 and 10i0 <= 100 and "
798 "i3 <= 9 + 10 i2 and i3 >= 1 + 10i2 and i3 >= 0) or "
799 "(i1 <= 9 + 10i0 and i1 >= 1 + 10i0 and i2 >= 0 and "
800 "i0 >= 0 and i1 <= 100 and i3 <= 9 + 10i2 and i3 >= 1 + 10i2) }";
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 test_coalesce_set(ctx,
809 "[M] -> { [i1] : (i1 >= 2 and i1 <= M) or "
810 "(i1 = M and M >= 1) }", 0);
811 test_coalesce_set(ctx,
812 "{[x,y] : x,y >= 0; [x,y] : 10 <= x <= 20 and y >= -1 }", 0);
813 test_coalesce_set(ctx,
814 "{ [x, y] : (x >= 1 and y >= 1 and x <= 2 and y <= 2) or "
815 "(y = 3 and x = 1) }", 1);
816 test_coalesce_set(ctx,
817 "[M] -> { [i0, i1, i2, i3, i4] : (i1 >= 3 and i4 >= 2 + i2 and "
818 "i2 >= 2 and i0 >= 2 and i3 >= 1 + i2 and i0 <= M and "
819 "i1 <= M and i3 <= M and i4 <= M) or "
820 "(i1 >= 2 and i4 >= 1 + i2 and i2 >= 2 and i0 >= 2 and "
821 "i3 >= 1 + i2 and i0 <= M and i1 <= -1 + M and i3 <= M and "
822 "i4 <= -1 + M) }", 1);
823 test_coalesce_set(ctx,
824 "{ [x, y] : (x >= 0 and y >= 0 and x <= 10 and y <= 10) or "
825 "(x >= 1 and y >= 1 and x <= 11 and y <= 11) }", 1);
826 test_coalesce_set(ctx,
827 "{[x,y,z] : y + 2 >= 0 and x - y + 1 >= 0 and "
828 "-x - y + 1 >= 0 and -3 <= z <= 3;"
829 "[x,y,z] : -x+z + 20 >= 0 and -x-z + 20 >= 0 and "
830 "x-z + 20 >= 0 and x+z + 20 >= 0 and -10 <= y <= 0}", 1);
831 test_coalesce_set(ctx,
832 "{[x,y] : 0 <= x,y <= 10; [5,y]: 4 <=y <= 11}", 1);
833 }
834
835 void test_closure(struct isl_ctx *ctx)
836 {
837 const char *str;
838 isl_set *dom;
839 isl_map *up, *right;
840 isl_map *map, *map2;
841 int exact;
842
843 /* COCOA example 1 */
844 map = isl_map_read_from_str(ctx,
845 "[n,k] -> { [i,j] -> [i2,j2] : i2 = i + 1 and j2 = j + 1 and "
846 "1 <= i and i < n and 1 <= j and j < n or "
847 "i2 = i + 1 and j2 = j - 1 and "
848 "1 <= i and i < n and 2 <= j and j <= n }", -1);
849 map = isl_map_power(map, 1, &exact);
850 assert(exact);
851 isl_map_free(map);
852
853 /* COCOA example 1 */
854 map = isl_map_read_from_str(ctx,
855 "[n] -> { [i,j] -> [i2,j2] : i2 = i + 1 and j2 = j + 1 and "
856 "1 <= i and i < n and 1 <= j and j < n or "
857 "i2 = i + 1 and j2 = j - 1 and "
858 "1 <= i and i < n and 2 <= j and j <= n }", -1);
859 map = isl_map_transitive_closure(map, &exact);
860 assert(exact);
861 map2 = isl_map_read_from_str(ctx,
862 "[n] -> { [i,j] -> [i2,j2] : exists (k1,k2,k : "
863 "1 <= i and i < n and 1 <= j and j <= n and "
864 "2 <= i2 and i2 <= n and 1 <= j2 and j2 <= n and "
865 "i2 = i + k1 + k2 and j2 = j + k1 - k2 and "
866 "k1 >= 0 and k2 >= 0 and k1 + k2 = k and k >= 1 )}", -1);
867 assert(isl_map_is_equal(map, map2));
868 isl_map_free(map2);
869 isl_map_free(map);
870
871 map = isl_map_read_from_str(ctx,
872 "[n] -> { [x] -> [y] : y = x + 1 and 0 <= x and x <= n and "
873 " 0 <= y and y <= n }", -1);
874 map = isl_map_transitive_closure(map, &exact);
875 map2 = isl_map_read_from_str(ctx,
876 "[n] -> { [x] -> [y] : y > x and 0 <= x and x <= n and "
877 " 0 <= y and y <= n }", -1);
878 assert(isl_map_is_equal(map, map2));
879 isl_map_free(map2);
880 isl_map_free(map);
881
882 /* COCOA example 2 */
883 map = isl_map_read_from_str(ctx,
884 "[n] -> { [i,j] -> [i2,j2] : i2 = i + 2 and j2 = j + 2 and "
885 "1 <= i and i < n - 1 and 1 <= j and j < n - 1 or "
886 "i2 = i + 2 and j2 = j - 2 and "
887 "1 <= i and i < n - 1 and 3 <= j and j <= n }", -1);
888 map = isl_map_transitive_closure(map, &exact);
889 assert(exact);
890 map2 = isl_map_read_from_str(ctx,
891 "[n] -> { [i,j] -> [i2,j2] : exists (k1,k2,k : "
892 "1 <= i and i < n - 1 and 1 <= j and j <= n and "
893 "3 <= i2 and i2 <= n and 1 <= j2 and j2 <= n and "
894 "i2 = i + 2 k1 + 2 k2 and j2 = j + 2 k1 - 2 k2 and "
895 "k1 >= 0 and k2 >= 0 and k1 + k2 = k and k >= 1) }", -1);
896 assert(isl_map_is_equal(map, map2));
897 isl_map_free(map);
898 isl_map_free(map2);
899
900 /* COCOA Fig.2 left */
901 map = isl_map_read_from_str(ctx,
902 "[n] -> { [i,j] -> [i2,j2] : i2 = i + 2 and j2 = j and "
903 "i <= 2 j - 3 and i <= n - 2 and j <= 2 i - 1 and "
904 "j <= n or "
905 "i2 = i and j2 = j + 2 and i <= 2 j - 1 and i <= n and "
906 "j <= 2 i - 3 and j <= n - 2 or "
907 "i2 = i + 1 and j2 = j + 1 and i <= 2 j - 1 and "
908 "i <= n - 1 and j <= 2 i - 1 and j <= n - 1 }", -1);
909 map = isl_map_transitive_closure(map, &exact);
910 assert(exact);
911 isl_map_free(map);
912
913 /* COCOA Fig.2 right */
914 map = isl_map_read_from_str(ctx,
915 "[n,k] -> { [i,j] -> [i2,j2] : i2 = i + 3 and j2 = j and "
916 "i <= 2 j - 4 and i <= n - 3 and j <= 2 i - 1 and "
917 "j <= n or "
918 "i2 = i and j2 = j + 3 and i <= 2 j - 1 and i <= n and "
919 "j <= 2 i - 4 and j <= n - 3 or "
920 "i2 = i + 1 and j2 = j + 1 and i <= 2 j - 1 and "
921 "i <= n - 1 and j <= 2 i - 1 and j <= n - 1 }", -1);
922 map = isl_map_power(map, 1, &exact);
923 assert(exact);
924 isl_map_free(map);
925
926 /* COCOA Fig.2 right */
927 map = isl_map_read_from_str(ctx,
928 "[n] -> { [i,j] -> [i2,j2] : i2 = i + 3 and j2 = j and "
929 "i <= 2 j - 4 and i <= n - 3 and j <= 2 i - 1 and "
930 "j <= n or "
931 "i2 = i and j2 = j + 3 and i <= 2 j - 1 and i <= n and "
932 "j <= 2 i - 4 and j <= n - 3 or "
933 "i2 = i + 1 and j2 = j + 1 and i <= 2 j - 1 and "
934 "i <= n - 1 and j <= 2 i - 1 and j <= n - 1 }", -1);
935 map = isl_map_transitive_closure(map, &exact);
936 assert(exact);
937 map2 = isl_map_read_from_str(ctx,
938 "[n] -> { [i,j] -> [i2,j2] : exists (k1,k2,k3,k : "
939 "i <= 2 j - 1 and i <= n and j <= 2 i - 1 and "
940 "j <= n and 3 + i + 2 j <= 3 n and "
941 "3 + 2 i + j <= 3n and i2 <= 2 j2 -1 and i2 <= n and "
942 "i2 <= 3 j2 - 4 and j2 <= 2 i2 -1 and j2 <= n and "
943 "13 + 4 j2 <= 11 i2 and i2 = i + 3 k1 + k3 and "
944 "j2 = j + 3 k2 + k3 and k1 >= 0 and k2 >= 0 and "
945 "k3 >= 0 and k1 + k2 + k3 = k and k > 0) }", -1);
946 assert(isl_map_is_equal(map, map2));
947 isl_map_free(map2);
948 isl_map_free(map);
949
950 /* COCOA Fig.1 right */
951 dom = isl_set_read_from_str(ctx,
952 "{ [x,y] : x >= 0 and -2 x + 3 y >= 0 and x <= 3 and "
953 "2 x - 3 y + 3 >= 0 }", -1);
954 right = isl_map_read_from_str(ctx,
955 "{ [x,y] -> [x2,y2] : x2 = x + 1 and y2 = y }", -1);
956 up = isl_map_read_from_str(ctx,
957 "{ [x,y] -> [x2,y2] : x2 = x and y2 = y + 1 }", -1);
958 right = isl_map_intersect_domain(right, isl_set_copy(dom));
959 right = isl_map_intersect_range(right, isl_set_copy(dom));
960 up = isl_map_intersect_domain(up, isl_set_copy(dom));
961 up = isl_map_intersect_range(up, dom);
962 map = isl_map_union(up, right);
963 map = isl_map_transitive_closure(map, &exact);
964 assert(exact);
965 map2 = isl_map_read_from_str(ctx,
966 "{ [0,0] -> [0,1]; [0,0] -> [1,1]; [0,1] -> [1,1]; "
967 " [2,2] -> [3,2]; [2,2] -> [3,3]; [3,2] -> [3,3] }", -1);
968 assert(isl_map_is_equal(map, map2));
969 isl_map_free(map2);
970 isl_map_free(map);
971
972 /* COCOA Theorem 1 counter example */
973 map = isl_map_read_from_str(ctx,
974 "{ [i,j] -> [i2,j2] : i = 0 and 0 <= j and j <= 1 and "
975 "i2 = 1 and j2 = j or "
976 "i = 0 and j = 0 and i2 = 0 and j2 = 1 }", -1);
977 map = isl_map_transitive_closure(map, &exact);
978 assert(exact);
979 isl_map_free(map);
980
981 map = isl_map_read_from_str(ctx,
982 "[m,n] -> { [i,j] -> [i2,j2] : i2 = i and j2 = j + 2 and "
983 "1 <= i,i2 <= n and 1 <= j,j2 <= m or "
984 "i2 = i + 1 and 3 <= j2 - j <= 4 and "
985 "1 <= i,i2 <= n and 1 <= j,j2 <= m }", -1);
986 map = isl_map_transitive_closure(map, &exact);
987 assert(exact);
988 isl_map_free(map);
989
990 /* Kelly et al 1996, fig 12 */
991 map = isl_map_read_from_str(ctx,
992 "[n] -> { [i,j] -> [i2,j2] : i2 = i and j2 = j + 1 and "
993 "1 <= i,j,j+1 <= n or "
994 "j = n and j2 = 1 and i2 = i + 1 and "
995 "1 <= i,i+1 <= n }", -1);
996 map = isl_map_transitive_closure(map, &exact);
997 assert(exact);
998 map2 = isl_map_read_from_str(ctx,
999 "[n] -> { [i,j] -> [i2,j2] : 1 <= j < j2 <= n and "
1000 "1 <= i <= n and i = i2 or "
1001 "1 <= i < i2 <= n and 1 <= j <= n and "
1002 "1 <= j2 <= n }", -1);
1003 assert(isl_map_is_equal(map, map2));
1004 isl_map_free(map2);
1005 isl_map_free(map);
1006
1007 /* Omega's closure4 */
1008 map = isl_map_read_from_str(ctx,
1009 "[m,n] -> { [x,y] -> [x2,y2] : x2 = x and y2 = y + 1 and "
1010 "1 <= x,y <= 10 or "
1011 "x2 = x + 1 and y2 = y and "
1012 "1 <= x <= 20 && 5 <= y <= 15 }", -1);
1013 map = isl_map_transitive_closure(map, &exact);
1014 assert(exact);
1015 isl_map_free(map);
1016
1017 map = isl_map_read_from_str(ctx,
1018 "[n] -> { [x] -> [y]: 1 <= n <= y - x <= 10 }", -1);
1019 map = isl_map_transitive_closure(map, &exact);
1020 assert(!exact);
1021 map2 = isl_map_read_from_str(ctx,
1022 "[n] -> { [x] -> [y] : 1 <= n <= 10 and y >= n + x }", -1);
1023 assert(isl_map_is_equal(map, map2));
1024 isl_map_free(map);
1025 isl_map_free(map2);
1026
1027 str = "[n, m] -> { [i0, i1, i2, i3] -> [o0, o1, o2, o3] : "
1028 "i3 = 1 and o0 = i0 and o1 = -1 + i1 and o2 = -1 + i2 and "
1029 "o3 = -2 + i2 and i1 <= -1 + i0 and i1 >= 1 - m + i0 and "
1030 "i1 >= 2 and i1 <= n and i2 >= 3 and i2 <= 1 + n and i2 <= m }";
1031 map = isl_map_read_from_str(ctx, str, -1);
1032 map = isl_map_transitive_closure(map, &exact);
1033 assert(exact);
1034 map2 = isl_map_read_from_str(ctx, str, -1);
1035 assert(isl_map_is_equal(map, map2));
1036 isl_map_free(map);
1037 isl_map_free(map2);
1038
1039 str = "{[0] -> [1]; [2] -> [3]}";
1040 map = isl_map_read_from_str(ctx, str, -1);
1041 map = isl_map_transitive_closure(map, &exact);
1042 assert(exact);
1043 map2 = isl_map_read_from_str(ctx, str, -1);
1044 assert(isl_map_is_equal(map, map2));
1045 isl_map_free(map);
1046 isl_map_free(map2);
1047 }
1048
1049 void test_lex(struct isl_ctx *ctx)
1050 {
1051 isl_dim *dim;
1052 isl_map *map;
1053
1054 dim = isl_dim_alloc(ctx, 0, 0, 0);
1055 map = isl_map_lex_le(dim);
1056 assert(!isl_map_is_empty(map));
1057 isl_map_free(map);
1058 }
1059
1060 void test_lexmin(struct isl_ctx *ctx)
1061 {
1062 const char *str;
1063 isl_map *map;
1064 isl_set *set;
1065 isl_set *set2;
1066
1067 str = "[p0, p1] -> { [] -> [] : "
1068 "exists (e0 = [(2p1)/3], e1, e2, e3 = [(3 - p1 + 3e0)/3], "
1069 "e4 = [(p1)/3], e5 = [(p1 + 3e4)/3]: "
1070 "3e0 >= -2 + 2p1 and 3e0 >= p1 and 3e3 >= 1 - p1 + 3e0 and "
1071 "3e0 <= 2p1 and 3e3 >= -2 + p1 and 3e3 <= -1 + p1 and p1 >= 3 and "
1072 "3e5 >= -2 + 2p1 and 3e5 >= p1 and 3e5 <= -1 + p1 + 3e4 and "
1073 "3e4 <= p1 and 3e4 >= -2 + p1 and e3 <= -1 + e0 and "
1074 "3e4 >= 6 - p1 + 3e1 and 3e1 >= p1 and 3e5 >= -2 + p1 + 3e4 and "
1075 "2e4 >= 3 - p1 + 2e1 and e4 <= e1 and 3e3 <= 2 - p1 + 3e0 and "
1076 "e5 >= 1 + e1 and 3e4 >= 6 - 2p1 + 3e1 and "
1077 "p0 >= 2 and p1 >= p0 and 3e2 >= p1 and 3e4 >= 6 - p1 + 3e2 and "
1078 "e2 <= e1 and e3 >= 1 and e4 <= e2) }";
1079 map = isl_map_read_from_str(ctx, str, -1);
1080 map = isl_map_lexmin(map);
1081 isl_map_free(map);
1082
1083 str = "[C] -> { [obj,a,b,c] : obj <= 38 a + 7 b + 10 c and "
1084 "a + b <= 1 and c <= 10 b and c <= C and a,b,c,C >= 0 }";
1085 set = isl_set_read_from_str(ctx, str, -1);
1086 set = isl_set_lexmax(set);
1087 str = "[C] -> { [obj,a,b,c] : C = 8 }";
1088 set2 = isl_set_read_from_str(ctx, str, -1);
1089 set = isl_set_intersect(set, set2);
1090 assert(!isl_set_is_empty(set));
1091 isl_set_free(set);
1092 }
1093
1094 struct must_may {
1095 isl_map *must;
1096 isl_map *may;
1097 };
1098
1099 static int collect_must_may(__isl_take isl_map *dep, int must,
1100 void *dep_user, void *user)
1101 {
1102 struct must_may *mm = (struct must_may *)user;
1103
1104 if (must)
1105 mm->must = isl_map_union(mm->must, dep);
1106 else
1107 mm->may = isl_map_union(mm->may, dep);
1108
1109 return 0;
1110 }
1111
1112 static int common_space(void *first, void *second)
1113 {
1114 int depth = *(int *)first;
1115 return 2 * depth;
1116 }
1117
1118 static int map_is_equal(__isl_keep isl_map *map, const char *str)
1119 {
1120 isl_map *map2;
1121 int equal;
1122
1123 if (!map)
1124 return -1;
1125
1126 map2 = isl_map_read_from_str(map->ctx, str, -1);
1127 equal = isl_map_is_equal(map, map2);
1128 isl_map_free(map2);
1129
1130 return equal;
1131 }
1132
1133 void test_dep(struct isl_ctx *ctx)
1134 {
1135 const char *str;
1136 isl_dim *dim;
1137 isl_map *map;
1138 isl_access_info *ai;
1139 isl_flow *flow;
1140 int depth;
1141 struct must_may mm;
1142
1143 depth = 3;
1144
1145 str = "{ [2,i,0] -> [i] : 0 <= i <= 10 }";
1146 map = isl_map_read_from_str(ctx, str, -1);
1147 ai = isl_access_info_alloc(map, &depth, &common_space, 2);
1148
1149 str = "{ [0,i,0] -> [i] : 0 <= i <= 10 }";
1150 map = isl_map_read_from_str(ctx, str, -1);
1151 ai = isl_access_info_add_source(ai, map, 1, &depth);
1152
1153 str = "{ [1,i,0] -> [5] : 0 <= i <= 10 }";
1154 map = isl_map_read_from_str(ctx, str, -1);
1155 ai = isl_access_info_add_source(ai, map, 1, &depth);
1156
1157 flow = isl_access_info_compute_flow(ai);
1158 dim = isl_dim_alloc(ctx, 0, 3, 3);
1159 mm.must = isl_map_empty(isl_dim_copy(dim));
1160 mm.may = isl_map_empty(dim);
1161
1162 isl_flow_foreach(flow, collect_must_may, &mm);
1163
1164 str = "{ [0,i,0] -> [2,i,0] : (0 <= i <= 4) or (6 <= i <= 10); "
1165 " [1,10,0] -> [2,5,0] }";
1166 assert(map_is_equal(mm.must, str));
1167 str = "{ [i,j,k] -> [l,m,n] : 1 = 0 }";
1168 assert(map_is_equal(mm.may, str));
1169
1170 isl_map_free(mm.must);
1171 isl_map_free(mm.may);
1172 isl_flow_free(flow);
1173
1174
1175 str = "{ [2,i,0] -> [i] : 0 <= i <= 10 }";
1176 map = isl_map_read_from_str(ctx, str, -1);
1177 ai = isl_access_info_alloc(map, &depth, &common_space, 2);
1178
1179 str = "{ [0,i,0] -> [i] : 0 <= i <= 10 }";
1180 map = isl_map_read_from_str(ctx, str, -1);
1181 ai = isl_access_info_add_source(ai, map, 1, &depth);
1182
1183 str = "{ [1,i,0] -> [5] : 0 <= i <= 10 }";
1184 map = isl_map_read_from_str(ctx, str, -1);
1185 ai = isl_access_info_add_source(ai, map, 0, &depth);
1186
1187 flow = isl_access_info_compute_flow(ai);
1188 dim = isl_dim_alloc(ctx, 0, 3, 3);
1189 mm.must = isl_map_empty(isl_dim_copy(dim));
1190 mm.may = isl_map_empty(dim);
1191
1192 isl_flow_foreach(flow, collect_must_may, &mm);
1193
1194 str = "{ [0,i,0] -> [2,i,0] : (0 <= i <= 4) or (6 <= i <= 10) }";
1195 assert(map_is_equal(mm.must, str));
1196 str = "{ [0,5,0] -> [2,5,0]; [1,i,0] -> [2,5,0] : 0 <= i <= 10 }";
1197 assert(map_is_equal(mm.may, str));
1198
1199 isl_map_free(mm.must);
1200 isl_map_free(mm.may);
1201 isl_flow_free(flow);
1202
1203
1204 str = "{ [2,i,0] -> [i] : 0 <= i <= 10 }";
1205 map = isl_map_read_from_str(ctx, str, -1);
1206 ai = isl_access_info_alloc(map, &depth, &common_space, 2);
1207
1208 str = "{ [0,i,0] -> [i] : 0 <= i <= 10 }";
1209 map = isl_map_read_from_str(ctx, str, -1);
1210 ai = isl_access_info_add_source(ai, map, 0, &depth);
1211
1212 str = "{ [1,i,0] -> [5] : 0 <= i <= 10 }";
1213 map = isl_map_read_from_str(ctx, str, -1);
1214 ai = isl_access_info_add_source(ai, map, 0, &depth);
1215
1216 flow = isl_access_info_compute_flow(ai);
1217 dim = isl_dim_alloc(ctx, 0, 3, 3);
1218 mm.must = isl_map_empty(isl_dim_copy(dim));
1219 mm.may = isl_map_empty(dim);
1220
1221 isl_flow_foreach(flow, collect_must_may, &mm);
1222
1223 str = "{ [0,i,0] -> [2,i,0] : 0 <= i <= 10; "
1224 " [1,i,0] -> [2,5,0] : 0 <= i <= 10 }";
1225 assert(map_is_equal(mm.may, str));
1226 str = "{ [i,j,k] -> [l,m,n] : 1 = 0 }";
1227 assert(map_is_equal(mm.must, str));
1228
1229 isl_map_free(mm.must);
1230 isl_map_free(mm.may);
1231 isl_flow_free(flow);
1232
1233
1234 str = "{ [0,i,2] -> [i] : 0 <= i <= 10 }";
1235 map = isl_map_read_from_str(ctx, str, -1);
1236 ai = isl_access_info_alloc(map, &depth, &common_space, 2);
1237
1238 str = "{ [0,i,0] -> [i] : 0 <= i <= 10 }";
1239 map = isl_map_read_from_str(ctx, str, -1);
1240 ai = isl_access_info_add_source(ai, map, 0, &depth);
1241
1242 str = "{ [0,i,1] -> [5] : 0 <= i <= 10 }";
1243 map = isl_map_read_from_str(ctx, str, -1);
1244 ai = isl_access_info_add_source(ai, map, 0, &depth);
1245
1246 flow = isl_access_info_compute_flow(ai);
1247 dim = isl_dim_alloc(ctx, 0, 3, 3);
1248 mm.must = isl_map_empty(isl_dim_copy(dim));
1249 mm.may = isl_map_empty(dim);
1250
1251 isl_flow_foreach(flow, collect_must_may, &mm);
1252
1253 str = "{ [0,i,0] -> [0,i,2] : 0 <= i <= 10; "
1254 " [0,i,1] -> [0,5,2] : 0 <= i <= 5 }";
1255 assert(map_is_equal(mm.may, str));
1256 str = "{ [i,j,k] -> [l,m,n] : 1 = 0 }";
1257 assert(map_is_equal(mm.must, str));
1258
1259 isl_map_free(mm.must);
1260 isl_map_free(mm.may);
1261 isl_flow_free(flow);
1262
1263
1264 str = "{ [0,i,1] -> [i] : 0 <= i <= 10 }";
1265 map = isl_map_read_from_str(ctx, str, -1);
1266 ai = isl_access_info_alloc(map, &depth, &common_space, 2);
1267
1268 str = "{ [0,i,0] -> [i] : 0 <= i <= 10 }";
1269 map = isl_map_read_from_str(ctx, str, -1);
1270 ai = isl_access_info_add_source(ai, map, 0, &depth);
1271
1272 str = "{ [0,i,2] -> [5] : 0 <= i <= 10 }";
1273 map = isl_map_read_from_str(ctx, str, -1);
1274 ai = isl_access_info_add_source(ai, map, 0, &depth);
1275
1276 flow = isl_access_info_compute_flow(ai);
1277 dim = isl_dim_alloc(ctx, 0, 3, 3);
1278 mm.must = isl_map_empty(isl_dim_copy(dim));
1279 mm.may = isl_map_empty(dim);
1280
1281 isl_flow_foreach(flow, collect_must_may, &mm);
1282
1283 str = "{ [0,i,0] -> [0,i,1] : 0 <= i <= 10; "
1284 " [0,i,2] -> [0,5,1] : 0 <= i <= 4 }";
1285 assert(map_is_equal(mm.may, str));
1286 str = "{ [i,j,k] -> [l,m,n] : 1 = 0 }";
1287 assert(map_is_equal(mm.must, str));
1288
1289 isl_map_free(mm.must);
1290 isl_map_free(mm.may);
1291 isl_flow_free(flow);
1292
1293
1294 depth = 5;
1295
1296 str = "{ [1,i,0,0,0] -> [i,j] : 0 <= i <= 10 and 0 <= j <= 10 }";
1297 map = isl_map_read_from_str(ctx, str, -1);
1298 ai = isl_access_info_alloc(map, &depth, &common_space, 1);
1299
1300 str = "{ [0,i,0,j,0] -> [i,j] : 0 <= i <= 10 and 0 <= j <= 10 }";
1301 map = isl_map_read_from_str(ctx, str, -1);
1302 ai = isl_access_info_add_source(ai, map, 1, &depth);
1303
1304 flow = isl_access_info_compute_flow(ai);
1305 dim = isl_dim_alloc(ctx, 0, 5, 5);
1306 mm.must = isl_map_empty(isl_dim_copy(dim));
1307 mm.may = isl_map_empty(dim);
1308
1309 isl_flow_foreach(flow, collect_must_may, &mm);
1310
1311 str = "{ [0,i,0,j,0] -> [1,i,0,0,0] : 0 <= i,j <= 10 }";
1312 assert(map_is_equal(mm.must, str));
1313 str = "{ [0,0,0,0,0] -> [0,0,0,0,0] : 1 = 0 }";
1314 assert(map_is_equal(mm.may, str));
1315
1316 isl_map_free(mm.must);
1317 isl_map_free(mm.may);
1318 isl_flow_free(flow);
1319 }
1320
1321 void test_sv(struct isl_ctx *ctx)
1322 {
1323 const char *str;
1324 isl_map *map;
1325
1326 str = "[N] -> { [i] -> [f] : 0 <= i <= N and 0 <= i - 10 f <= 9 }";
1327 map = isl_map_read_from_str(ctx, str, -1);
1328 assert(isl_map_is_single_valued(map));
1329 isl_map_free(map);
1330
1331 str = "[N] -> { [i] -> [f] : 0 <= i <= N and 0 <= i - 10 f <= 10 }";
1332 map = isl_map_read_from_str(ctx, str, -1);
1333 assert(!isl_map_is_single_valued(map));
1334 isl_map_free(map);
1335 }
1336
1337 void test_bijective_case(struct isl_ctx *ctx, const char *str, int bijective)
1338 {
1339 isl_map *map;
1340
1341 map = isl_map_read_from_str(ctx, str, -1);
1342 if (bijective)
1343 assert(isl_map_is_bijective(map));
1344 else
1345 assert(!isl_map_is_bijective(map));
1346 isl_map_free(map);
1347 }
1348
1349 void test_bijective(struct isl_ctx *ctx)
1350 {
1351 test_bijective_case(ctx, "[N,M]->{[i,j] -> [i]}", 0);
1352 test_bijective_case(ctx, "[N,M]->{[i,j] -> [i] : j=i}", 1);
1353 test_bijective_case(ctx, "[N,M]->{[i,j] -> [i] : j=0}", 1);
1354 test_bijective_case(ctx, "[N,M]->{[i,j] -> [i] : j=N}", 1);
1355 test_bijective_case(ctx, "[N,M]->{[i,j] -> [j,i]}", 1);
1356 test_bijective_case(ctx, "[N,M]->{[i,j] -> [i+j]}", 0);
1357 test_bijective_case(ctx, "[N,M]->{[i,j] -> []}", 0);
1358 test_bijective_case(ctx, "[N,M]->{[i,j] -> [i,j,N]}", 1);
1359 test_bijective_case(ctx, "[N,M]->{[i,j] -> [2i]}", 0);
1360 test_bijective_case(ctx, "[N,M]->{[i,j] -> [i,i]}", 0);
1361 test_bijective_case(ctx, "[N,M]->{[i,j] -> [2i,i]}", 0);
1362 test_bijective_case(ctx, "[N,M]->{[i,j] -> [2i,j]}", 1);
1363 test_bijective_case(ctx, "[N,M]->{[i,j] -> [x,y] : 2x=i & y =j}", 1);
1364 }
1365
1366 void test_pwqp(struct isl_ctx *ctx)
1367 {
1368 const char *str;
1369 isl_pw_qpolynomial *pwqp1, *pwqp2;
1370
1371 str = "{ [i,j,k] -> 1 + 9 * [i/5] + 7 * [j/11] + 4 * [k/13] }";
1372 pwqp1 = isl_pw_qpolynomial_read_from_str(ctx, str);
1373
1374 pwqp1 = isl_pw_qpolynomial_move_dims(pwqp1, isl_dim_param, 0,
1375 isl_dim_set, 1, 1);
1376
1377 str = "[j] -> { [i,k] -> 1 + 9 * [i/5] + 7 * [j/11] + 4 * [k/13] }";
1378 pwqp2 = isl_pw_qpolynomial_read_from_str(ctx, str);
1379
1380 pwqp1 = isl_pw_qpolynomial_sub(pwqp1, pwqp2);
1381
1382 assert(isl_pw_qpolynomial_is_zero(pwqp1));
1383
1384 isl_pw_qpolynomial_free(pwqp1);
1385 }
1386
1387 int main()
1388 {
1389 struct isl_ctx *ctx;
1390
1391 srcdir = getenv("srcdir");
1392 assert(srcdir);
1393
1394 ctx = isl_ctx_alloc();
1395 test_pwqp(ctx);
1396 test_lex(ctx);
1397 test_sv(ctx);
1398 test_bijective(ctx);
1399 test_dep(ctx);
1400 test_read(ctx);
1401 test_bounded(ctx);
1402 test_construction(ctx);
1403 test_dim(ctx);
1404 test_div(ctx);
1405 test_application(ctx);
1406 test_affine_hull(ctx);
1407 test_convex_hull(ctx);
1408 test_gist(ctx);
1409 test_coalesce(ctx);
1410 test_closure(ctx);
1411 test_lexmin(ctx);
1412 isl_ctx_free(ctx);
1413 return 0;
1414 }
Integer set library