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add private isl_local_space_realign
[isl.git] / isl_test.c
blob610e67c1787596404acf9f8491922d7b0779ec63
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_private.h>
14 #include <isl_map_private.h>
15 #include <isl/aff.h>
16 #include <isl/set.h>
17 #include <isl/flow.h>
18 #include <isl/constraint.h>
19 #include <isl/polynomial.h>
20 #include <isl/union_map.h>
21 #include <isl_factorization.h>
22 #include <isl/schedule.h>
23
24 static char *srcdir;
25
26 static char *get_filename(isl_ctx *ctx, const char *name, const char *suffix) {
27 char *filename;
28 int length;
29 char *pattern = "%s/test_inputs/%s.%s";
30
31 length = strlen(pattern) - 6 + strlen(srcdir) + strlen(name)
32 + strlen(suffix) + 1;
33 filename = isl_alloc_array(ctx, char, length);
34
35 if (!filename)
36 return NULL;
37
38 sprintf(filename, pattern, srcdir, name, suffix);
39
40 return filename;
41 }
42
43 void test_parse_map(isl_ctx *ctx, const char *str)
44 {
45 isl_map *map;
46
47 map = isl_map_read_from_str(ctx, str, -1);
48 assert(map);
49 isl_map_free(map);
50 }
51
52 void test_parse_map_equal(isl_ctx *ctx, const char *str, const char *str2)
53 {
54 isl_map *map, *map2;
55
56 map = isl_map_read_from_str(ctx, str, -1);
57 map2 = isl_map_read_from_str(ctx, str2, -1);
58 assert(map && map2 && isl_map_is_equal(map, map2));
59 isl_map_free(map);
60 isl_map_free(map2);
61 }
62
63 void test_parse_pwqp(isl_ctx *ctx, const char *str)
64 {
65 isl_pw_qpolynomial *pwqp;
66
67 pwqp = isl_pw_qpolynomial_read_from_str(ctx, str);
68 assert(pwqp);
69 isl_pw_qpolynomial_free(pwqp);
70 }
71
72 void test_parse(struct isl_ctx *ctx)
73 {
74 isl_map *map, *map2;
75 const char *str, *str2;
76
77 str = "{ [i] -> [-i] }";
78 map = isl_map_read_from_str(ctx, str, -1);
79 assert(map);
80 isl_map_free(map);
81
82 str = "{ A[i] -> L[([i/3])] }";
83 map = isl_map_read_from_str(ctx, str, -1);
84 assert(map);
85 isl_map_free(map);
86
87 test_parse_map(ctx, "{[[s] -> A[i]] -> [[s+1] -> A[i]]}");
88 test_parse_map(ctx, "{ [p1, y1, y2] -> [2, y1, y2] : "
89 "p1 = 1 && (y1 <= y2 || y2 = 0) }");
90
91 str = "{ [x,y] : [([x/2]+y)/3] >= 1 }";
92 str2 = "{ [x, y] : 2y >= 6 - x }";
93 test_parse_map_equal(ctx, str, str2);
94
95 test_parse_map_equal(ctx, "{ [x,y] : x <= min(y, 2*y+3) }",
96 "{ [x,y] : x <= y, 2*y + 3 }");
97 str = "{ [x, y] : (y <= x and y >= -3) or (2y <= -3 + x and y <= -4) }";
98 test_parse_map_equal(ctx, "{ [x,y] : x >= min(y, 2*y+3) }", str);
99
100 str = "{[new,old] -> [new+1-2*[(new+1)/2],old+1-2*[(old+1)/2]]}";
101 map = isl_map_read_from_str(ctx, str, -1);
102 str = "{ [new, old] -> [o0, o1] : "
103 "exists (e0 = [(-1 - new + o0)/2], e1 = [(-1 - old + o1)/2]: "
104 "2e0 = -1 - new + o0 and 2e1 = -1 - old + o1 and o0 >= 0 and "
105 "o0 <= 1 and o1 >= 0 and o1 <= 1) }";
106 map2 = isl_map_read_from_str(ctx, str, -1);
107 assert(isl_map_is_equal(map, map2));
108 isl_map_free(map);
109 isl_map_free(map2);
110
111 str = "{[new,old] -> [new+1-2*[(new+1)/2],old+1-2*[(old+1)/2]]}";
112 map = isl_map_read_from_str(ctx, str, -1);
113 str = "{[new,old] -> [(new+1)%2,(old+1)%2]}";
114 map2 = isl_map_read_from_str(ctx, str, -1);
115 assert(isl_map_is_equal(map, map2));
116 isl_map_free(map);
117 isl_map_free(map2);
118
119 str = "[n] -> { [c1] : c1>=0 and c1<=floord(n-4,3) }";
120 str2 = "[n] -> { [c1] : c1 >= 0 and 3c1 <= -4 + n }";
121 test_parse_map_equal(ctx, str, str2);
122
123 test_parse_pwqp(ctx, "{ [i] -> i + [ (i + [i/3])/2 ] }");
124 test_parse_map(ctx, "{ S1[i] -> [([i/10]),i%10] : 0 <= i <= 45 }");
125 }
126
127 void test_read(struct isl_ctx *ctx)
128 {
129 char *filename;
130 FILE *input;
131 struct isl_basic_set *bset1, *bset2;
132 const char *str = "{[y]: Exists ( alpha : 2alpha = y)}";
133
134 filename = get_filename(ctx, "set", "omega");
135 assert(filename);
136 input = fopen(filename, "r");
137 assert(input);
138
139 bset1 = isl_basic_set_read_from_file(ctx, input, 0);
140 bset2 = isl_basic_set_read_from_str(ctx, str, 0);
141
142 assert(isl_basic_set_is_equal(bset1, bset2) == 1);
143
144 isl_basic_set_free(bset1);
145 isl_basic_set_free(bset2);
146 free(filename);
147
148 fclose(input);
149 }
150
151 void test_bounded(struct isl_ctx *ctx)
152 {
153 isl_set *set;
154 int bounded;
155
156 set = isl_set_read_from_str(ctx, "[n] -> {[i] : 0 <= i <= n }", -1);
157 bounded = isl_set_is_bounded(set);
158 assert(bounded);
159 isl_set_free(set);
160
161 set = isl_set_read_from_str(ctx, "{[n, i] : 0 <= i <= n }", -1);
162 bounded = isl_set_is_bounded(set);
163 assert(!bounded);
164 isl_set_free(set);
165
166 set = isl_set_read_from_str(ctx, "[n] -> {[i] : i <= n }", -1);
167 bounded = isl_set_is_bounded(set);
168 assert(!bounded);
169 isl_set_free(set);
170 }
171
172 /* Construct the basic set { [i] : 5 <= i <= N } */
173 void test_construction(struct isl_ctx *ctx)
174 {
175 isl_int v;
176 struct isl_dim *dim;
177 struct isl_basic_set *bset;
178 struct isl_constraint *c;
179
180 isl_int_init(v);
181
182 dim = isl_dim_set_alloc(ctx, 1, 1);
183 bset = isl_basic_set_universe(dim);
184
185 c = isl_inequality_alloc(isl_basic_set_get_dim(bset));
186 isl_int_set_si(v, -1);
187 isl_constraint_set_coefficient(c, isl_dim_set, 0, v);
188 isl_int_set_si(v, 1);
189 isl_constraint_set_coefficient(c, isl_dim_param, 0, v);
190 bset = isl_basic_set_add_constraint(bset, c);
191
192 c = isl_inequality_alloc(isl_basic_set_get_dim(bset));
193 isl_int_set_si(v, 1);
194 isl_constraint_set_coefficient(c, isl_dim_set, 0, v);
195 isl_int_set_si(v, -5);
196 isl_constraint_set_constant(c, v);
197 bset = isl_basic_set_add_constraint(bset, c);
198
199 isl_basic_set_free(bset);
200
201 isl_int_clear(v);
202 }
203
204 void test_dim(struct isl_ctx *ctx)
205 {
206 const char *str;
207 isl_map *map1, *map2;
208
209 map1 = isl_map_read_from_str(ctx,
210 "[n] -> { [i] -> [j] : exists (a = [i/10] : i - 10a <= n ) }", -1);
211 map1 = isl_map_add_dims(map1, isl_dim_in, 1);
212 map2 = isl_map_read_from_str(ctx,
213 "[n] -> { [i,k] -> [j] : exists (a = [i/10] : i - 10a <= n ) }", -1);
214 assert(isl_map_is_equal(map1, map2));
215 isl_map_free(map2);
216
217 map1 = isl_map_project_out(map1, isl_dim_in, 0, 1);
218 map2 = isl_map_read_from_str(ctx, "[n] -> { [i] -> [j] : n >= 0 }", -1);
219 assert(isl_map_is_equal(map1, map2));
220
221 isl_map_free(map1);
222 isl_map_free(map2);
223
224 str = "[n] -> { [i] -> [] : exists a : 0 <= i <= n and i = 2 a }";
225 map1 = isl_map_read_from_str(ctx, str, -1);
226 str = "{ [i] -> [j] : exists a : 0 <= i <= j and i = 2 a }";
227 map2 = isl_map_read_from_str(ctx, str, -1);
228 map1 = isl_map_move_dims(map1, isl_dim_out, 0, isl_dim_param, 0, 1);
229 assert(isl_map_is_equal(map1, map2));
230
231 isl_map_free(map1);
232 isl_map_free(map2);
233 }
234
235 void test_div(struct isl_ctx *ctx)
236 {
237 isl_int v;
238 struct isl_dim *dim;
239 struct isl_basic_set *bset;
240 struct isl_constraint *c;
241
242 isl_int_init(v);
243
244 /* test 1 */
245 dim = isl_dim_set_alloc(ctx, 0, 3);
246 bset = isl_basic_set_universe(dim);
247
248 c = isl_equality_alloc(isl_basic_set_get_dim(bset));
249 isl_int_set_si(v, -1);
250 isl_constraint_set_constant(c, v);
251 isl_int_set_si(v, 1);
252 isl_constraint_set_coefficient(c, isl_dim_set, 0, v);
253 isl_int_set_si(v, 3);
254 isl_constraint_set_coefficient(c, isl_dim_set, 1, v);
255 bset = isl_basic_set_add_constraint(bset, c);
256
257 c = isl_equality_alloc(isl_basic_set_get_dim(bset));
258 isl_int_set_si(v, 1);
259 isl_constraint_set_constant(c, v);
260 isl_int_set_si(v, -1);
261 isl_constraint_set_coefficient(c, isl_dim_set, 0, v);
262 isl_int_set_si(v, 3);
263 isl_constraint_set_coefficient(c, isl_dim_set, 2, v);
264 bset = isl_basic_set_add_constraint(bset, c);
265
266 bset = isl_basic_set_project_out(bset, isl_dim_set, 1, 2);
267
268 assert(bset && bset->n_div == 1);
269 isl_basic_set_free(bset);
270
271 /* test 2 */
272 dim = isl_dim_set_alloc(ctx, 0, 3);
273 bset = isl_basic_set_universe(dim);
274
275 c = isl_equality_alloc(isl_basic_set_get_dim(bset));
276 isl_int_set_si(v, 1);
277 isl_constraint_set_constant(c, v);
278 isl_int_set_si(v, -1);
279 isl_constraint_set_coefficient(c, isl_dim_set, 0, v);
280 isl_int_set_si(v, 3);
281 isl_constraint_set_coefficient(c, isl_dim_set, 1, v);
282 bset = isl_basic_set_add_constraint(bset, c);
283
284 c = isl_equality_alloc(isl_basic_set_get_dim(bset));
285 isl_int_set_si(v, -1);
286 isl_constraint_set_constant(c, v);
287 isl_int_set_si(v, 1);
288 isl_constraint_set_coefficient(c, isl_dim_set, 0, v);
289 isl_int_set_si(v, 3);
290 isl_constraint_set_coefficient(c, isl_dim_set, 2, v);
291 bset = isl_basic_set_add_constraint(bset, c);
292
293 bset = isl_basic_set_project_out(bset, isl_dim_set, 1, 2);
294
295 assert(bset && bset->n_div == 1);
296 isl_basic_set_free(bset);
297
298 /* test 3 */
299 dim = isl_dim_set_alloc(ctx, 0, 3);
300 bset = isl_basic_set_universe(dim);
301
302 c = isl_equality_alloc(isl_basic_set_get_dim(bset));
303 isl_int_set_si(v, 1);
304 isl_constraint_set_constant(c, v);
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 c = isl_equality_alloc(isl_basic_set_get_dim(bset));
312 isl_int_set_si(v, -3);
313 isl_constraint_set_constant(c, v);
314 isl_int_set_si(v, 1);
315 isl_constraint_set_coefficient(c, isl_dim_set, 0, v);
316 isl_int_set_si(v, 4);
317 isl_constraint_set_coefficient(c, isl_dim_set, 2, v);
318 bset = isl_basic_set_add_constraint(bset, c);
319
320 bset = isl_basic_set_project_out(bset, isl_dim_set, 1, 2);
321
322 assert(bset && bset->n_div == 1);
323 isl_basic_set_free(bset);
324
325 /* test 4 */
326 dim = isl_dim_set_alloc(ctx, 0, 3);
327 bset = isl_basic_set_universe(dim);
328
329 c = isl_equality_alloc(isl_basic_set_get_dim(bset));
330 isl_int_set_si(v, 2);
331 isl_constraint_set_constant(c, v);
332 isl_int_set_si(v, -1);
333 isl_constraint_set_coefficient(c, isl_dim_set, 0, v);
334 isl_int_set_si(v, 3);
335 isl_constraint_set_coefficient(c, isl_dim_set, 1, v);
336 bset = isl_basic_set_add_constraint(bset, c);
337
338 c = isl_equality_alloc(isl_basic_set_get_dim(bset));
339 isl_int_set_si(v, -1);
340 isl_constraint_set_constant(c, v);
341 isl_int_set_si(v, 1);
342 isl_constraint_set_coefficient(c, isl_dim_set, 0, v);
343 isl_int_set_si(v, 6);
344 isl_constraint_set_coefficient(c, isl_dim_set, 2, v);
345 bset = isl_basic_set_add_constraint(bset, c);
346
347 bset = isl_basic_set_project_out(bset, isl_dim_set, 1, 2);
348
349 assert(isl_basic_set_is_empty(bset));
350 isl_basic_set_free(bset);
351
352 /* test 5 */
353 dim = isl_dim_set_alloc(ctx, 0, 3);
354 bset = isl_basic_set_universe(dim);
355
356 c = isl_equality_alloc(isl_basic_set_get_dim(bset));
357 isl_int_set_si(v, -1);
358 isl_constraint_set_coefficient(c, isl_dim_set, 0, v);
359 isl_int_set_si(v, 3);
360 isl_constraint_set_coefficient(c, isl_dim_set, 2, 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, -3);
367 isl_constraint_set_coefficient(c, isl_dim_set, 1, v);
368 bset = isl_basic_set_add_constraint(bset, c);
369
370 bset = isl_basic_set_project_out(bset, isl_dim_set, 2, 1);
371
372 assert(bset && bset->n_div == 0);
373 isl_basic_set_free(bset);
374
375 /* test 6 */
376 dim = isl_dim_set_alloc(ctx, 0, 3);
377 bset = isl_basic_set_universe(dim);
378
379 c = isl_equality_alloc(isl_basic_set_get_dim(bset));
380 isl_int_set_si(v, -1);
381 isl_constraint_set_coefficient(c, isl_dim_set, 0, v);
382 isl_int_set_si(v, 6);
383 isl_constraint_set_coefficient(c, isl_dim_set, 2, v);
384 bset = isl_basic_set_add_constraint(bset, c);
385
386 c = isl_equality_alloc(isl_basic_set_get_dim(bset));
387 isl_int_set_si(v, 1);
388 isl_constraint_set_coefficient(c, isl_dim_set, 0, v);
389 isl_int_set_si(v, -3);
390 isl_constraint_set_coefficient(c, isl_dim_set, 1, v);
391 bset = isl_basic_set_add_constraint(bset, c);
392
393 bset = isl_basic_set_project_out(bset, isl_dim_set, 2, 1);
394
395 assert(bset && bset->n_div == 1);
396 isl_basic_set_free(bset);
397
398 /* test 7 */
399 /* This test is a bit tricky. We set up an equality
400 * a + 3b + 3c = 6 e0
401 * Normalization of divs creates _two_ divs
402 * a = 3 e0
403 * c - b - e0 = 2 e1
404 * Afterwards e0 is removed again because it has coefficient -1
405 * and we end up with the original equality and div again.
406 * Perhaps we can avoid the introduction of this temporary div.
407 */
408 dim = isl_dim_set_alloc(ctx, 0, 4);
409 bset = isl_basic_set_universe(dim);
410
411 c = isl_equality_alloc(isl_basic_set_get_dim(bset));
412 isl_int_set_si(v, -1);
413 isl_constraint_set_coefficient(c, isl_dim_set, 0, v);
414 isl_int_set_si(v, -3);
415 isl_constraint_set_coefficient(c, isl_dim_set, 1, v);
416 isl_int_set_si(v, -3);
417 isl_constraint_set_coefficient(c, isl_dim_set, 2, v);
418 isl_int_set_si(v, 6);
419 isl_constraint_set_coefficient(c, isl_dim_set, 3, v);
420 bset = isl_basic_set_add_constraint(bset, c);
421
422 bset = isl_basic_set_project_out(bset, isl_dim_set, 3, 1);
423
424 /* Test disabled for now */
425 /*
426 assert(bset && bset->n_div == 1);
427 */
428 isl_basic_set_free(bset);
429
430 /* test 8 */
431 dim = isl_dim_set_alloc(ctx, 0, 5);
432 bset = isl_basic_set_universe(dim);
433
434 c = isl_equality_alloc(isl_basic_set_get_dim(bset));
435 isl_int_set_si(v, -1);
436 isl_constraint_set_coefficient(c, isl_dim_set, 0, v);
437 isl_int_set_si(v, -3);
438 isl_constraint_set_coefficient(c, isl_dim_set, 1, v);
439 isl_int_set_si(v, -3);
440 isl_constraint_set_coefficient(c, isl_dim_set, 3, v);
441 isl_int_set_si(v, 6);
442 isl_constraint_set_coefficient(c, isl_dim_set, 4, v);
443 bset = isl_basic_set_add_constraint(bset, c);
444
445 c = isl_equality_alloc(isl_basic_set_get_dim(bset));
446 isl_int_set_si(v, -1);
447 isl_constraint_set_coefficient(c, isl_dim_set, 0, v);
448 isl_int_set_si(v, 1);
449 isl_constraint_set_coefficient(c, isl_dim_set, 2, v);
450 isl_int_set_si(v, 1);
451 isl_constraint_set_constant(c, v);
452 bset = isl_basic_set_add_constraint(bset, c);
453
454 bset = isl_basic_set_project_out(bset, isl_dim_set, 4, 1);
455
456 /* Test disabled for now */
457 /*
458 assert(bset && bset->n_div == 1);
459 */
460 isl_basic_set_free(bset);
461
462 /* test 9 */
463 dim = isl_dim_set_alloc(ctx, 0, 4);
464 bset = isl_basic_set_universe(dim);
465
466 c = isl_equality_alloc(isl_basic_set_get_dim(bset));
467 isl_int_set_si(v, 1);
468 isl_constraint_set_coefficient(c, isl_dim_set, 0, v);
469 isl_int_set_si(v, -1);
470 isl_constraint_set_coefficient(c, isl_dim_set, 1, v);
471 isl_int_set_si(v, -2);
472 isl_constraint_set_coefficient(c, isl_dim_set, 2, v);
473 bset = isl_basic_set_add_constraint(bset, c);
474
475 c = isl_equality_alloc(isl_basic_set_get_dim(bset));
476 isl_int_set_si(v, -1);
477 isl_constraint_set_coefficient(c, isl_dim_set, 0, v);
478 isl_int_set_si(v, 3);
479 isl_constraint_set_coefficient(c, isl_dim_set, 3, v);
480 isl_int_set_si(v, 2);
481 isl_constraint_set_constant(c, v);
482 bset = isl_basic_set_add_constraint(bset, c);
483
484 bset = isl_basic_set_project_out(bset, isl_dim_set, 2, 2);
485
486 bset = isl_basic_set_fix_si(bset, isl_dim_set, 0, 2);
487
488 assert(!isl_basic_set_is_empty(bset));
489
490 isl_basic_set_free(bset);
491
492 /* test 10 */
493 dim = isl_dim_set_alloc(ctx, 0, 3);
494 bset = isl_basic_set_universe(dim);
495
496 c = isl_equality_alloc(isl_basic_set_get_dim(bset));
497 isl_int_set_si(v, 1);
498 isl_constraint_set_coefficient(c, isl_dim_set, 0, v);
499 isl_int_set_si(v, -2);
500 isl_constraint_set_coefficient(c, isl_dim_set, 2, v);
501 bset = isl_basic_set_add_constraint(bset, c);
502
503 bset = isl_basic_set_project_out(bset, isl_dim_set, 2, 1);
504
505 bset = isl_basic_set_fix_si(bset, isl_dim_set, 0, 2);
506
507 isl_basic_set_free(bset);
508
509 isl_int_clear(v);
510 }
511
512 void test_application_case(struct isl_ctx *ctx, const char *name)
513 {
514 char *filename;
515 FILE *input;
516 struct isl_basic_set *bset1, *bset2;
517 struct isl_basic_map *bmap;
518
519 filename = get_filename(ctx, name, "omega");
520 assert(filename);
521 input = fopen(filename, "r");
522 assert(input);
523
524 bset1 = isl_basic_set_read_from_file(ctx, input, 0);
525 bmap = isl_basic_map_read_from_file(ctx, input, 0);
526
527 bset1 = isl_basic_set_apply(bset1, bmap);
528
529 bset2 = isl_basic_set_read_from_file(ctx, input, 0);
530
531 assert(isl_basic_set_is_equal(bset1, bset2) == 1);
532
533 isl_basic_set_free(bset1);
534 isl_basic_set_free(bset2);
535 free(filename);
536
537 fclose(input);
538 }
539
540 void test_application(struct isl_ctx *ctx)
541 {
542 test_application_case(ctx, "application");
543 test_application_case(ctx, "application2");
544 }
545
546 void test_affine_hull_case(struct isl_ctx *ctx, const char *name)
547 {
548 char *filename;
549 FILE *input;
550 struct isl_basic_set *bset1, *bset2;
551
552 filename = get_filename(ctx, name, "polylib");
553 assert(filename);
554 input = fopen(filename, "r");
555 assert(input);
556
557 bset1 = isl_basic_set_read_from_file(ctx, input, 0);
558 bset2 = isl_basic_set_read_from_file(ctx, input, 0);
559
560 bset1 = isl_basic_set_affine_hull(bset1);
561
562 assert(isl_basic_set_is_equal(bset1, bset2) == 1);
563
564 isl_basic_set_free(bset1);
565 isl_basic_set_free(bset2);
566 free(filename);
567
568 fclose(input);
569 }
570
571 void test_affine_hull(struct isl_ctx *ctx)
572 {
573 test_affine_hull_case(ctx, "affine2");
574 test_affine_hull_case(ctx, "affine");
575 test_affine_hull_case(ctx, "affine3");
576 }
577
578 void test_convex_hull_case(struct isl_ctx *ctx, const char *name)
579 {
580 char *filename;
581 FILE *input;
582 struct isl_basic_set *bset1, *bset2;
583 struct isl_set *set;
584
585 filename = get_filename(ctx, name, "polylib");
586 assert(filename);
587 input = fopen(filename, "r");
588 assert(input);
589
590 bset1 = isl_basic_set_read_from_file(ctx, input, 0);
591 bset2 = isl_basic_set_read_from_file(ctx, input, 0);
592
593 set = isl_basic_set_union(bset1, bset2);
594 bset1 = isl_set_convex_hull(set);
595
596 bset2 = isl_basic_set_read_from_file(ctx, input, 0);
597
598 assert(isl_basic_set_is_equal(bset1, bset2) == 1);
599
600 isl_basic_set_free(bset1);
601 isl_basic_set_free(bset2);
602 free(filename);
603
604 fclose(input);
605 }
606
607 void test_convex_hull_algo(struct isl_ctx *ctx, int convex)
608 {
609 const char *str1, *str2;
610 isl_set *set1, *set2;
611 int orig_convex = ctx->opt->convex;
612 ctx->opt->convex = convex;
613
614 test_convex_hull_case(ctx, "convex0");
615 test_convex_hull_case(ctx, "convex1");
616 test_convex_hull_case(ctx, "convex2");
617 test_convex_hull_case(ctx, "convex3");
618 test_convex_hull_case(ctx, "convex4");
619 test_convex_hull_case(ctx, "convex5");
620 test_convex_hull_case(ctx, "convex6");
621 test_convex_hull_case(ctx, "convex7");
622 test_convex_hull_case(ctx, "convex8");
623 test_convex_hull_case(ctx, "convex9");
624 test_convex_hull_case(ctx, "convex10");
625 test_convex_hull_case(ctx, "convex11");
626 test_convex_hull_case(ctx, "convex12");
627 test_convex_hull_case(ctx, "convex13");
628 test_convex_hull_case(ctx, "convex14");
629 test_convex_hull_case(ctx, "convex15");
630
631 str1 = "{ [i0, i1, i2] : (i2 = 1 and i0 = 0 and i1 >= 0) or "
632 "(i0 = 1 and i1 = 0 and i2 = 1) or "
633 "(i0 = 0 and i1 = 0 and i2 = 0) }";
634 str2 = "{ [i0, i1, i2] : i0 >= 0 and i2 >= i0 and i2 <= 1 and i1 >= 0 }";
635 set1 = isl_set_read_from_str(ctx, str1, -1);
636 set2 = isl_set_read_from_str(ctx, str2, -1);
637 set1 = isl_set_from_basic_set(isl_set_convex_hull(set1));
638 assert(isl_set_is_equal(set1, set2));
639 isl_set_free(set1);
640 isl_set_free(set2);
641
642 ctx->opt->convex = orig_convex;
643 }
644
645 void test_convex_hull(struct isl_ctx *ctx)
646 {
647 test_convex_hull_algo(ctx, ISL_CONVEX_HULL_FM);
648 test_convex_hull_algo(ctx, ISL_CONVEX_HULL_WRAP);
649 }
650
651 void test_gist_case(struct isl_ctx *ctx, const char *name)
652 {
653 char *filename;
654 FILE *input;
655 struct isl_basic_set *bset1, *bset2;
656
657 filename = get_filename(ctx, name, "polylib");
658 assert(filename);
659 input = fopen(filename, "r");
660 assert(input);
661
662 bset1 = isl_basic_set_read_from_file(ctx, input, 0);
663 bset2 = isl_basic_set_read_from_file(ctx, input, 0);
664
665 bset1 = isl_basic_set_gist(bset1, bset2);
666
667 bset2 = isl_basic_set_read_from_file(ctx, input, 0);
668
669 assert(isl_basic_set_is_equal(bset1, bset2) == 1);
670
671 isl_basic_set_free(bset1);
672 isl_basic_set_free(bset2);
673 free(filename);
674
675 fclose(input);
676 }
677
678 void test_gist(struct isl_ctx *ctx)
679 {
680 const char *str;
681 isl_basic_set *bset1, *bset2;
682
683 test_gist_case(ctx, "gist1");
684
685 str = "[p0, p2, p3, p5, p6, p10] -> { [] : "
686 "exists (e0 = [(15 + p0 + 15p6 + 15p10)/16], e1 = [(p5)/8], "
687 "e2 = [(p6)/128], e3 = [(8p2 - p5)/128], "
688 "e4 = [(128p3 - p6)/4096]: 8e1 = p5 and 128e2 = p6 and "
689 "128e3 = 8p2 - p5 and 4096e4 = 128p3 - p6 and p2 >= 0 and "
690 "16e0 >= 16 + 16p6 + 15p10 and p2 <= 15 and p3 >= 0 and "
691 "p3 <= 31 and p6 >= 128p3 and p5 >= 8p2 and p10 >= 0 and "
692 "16e0 <= 15 + p0 + 15p6 + 15p10 and 16e0 >= p0 + 15p6 + 15p10 and "
693 "p10 <= 15 and p10 <= -1 + p0 - p6) }";
694 bset1 = isl_basic_set_read_from_str(ctx, str, -1);
695 str = "[p0, p2, p3, p5, p6, p10] -> { [] : exists (e0 = [(p5)/8], "
696 "e1 = [(p6)/128], e2 = [(8p2 - p5)/128], "
697 "e3 = [(128p3 - p6)/4096]: 8e0 = p5 and 128e1 = p6 and "
698 "128e2 = 8p2 - p5 and 4096e3 = 128p3 - p6 and p5 >= -7 and "
699 "p2 >= 0 and 8p2 <= -1 + p0 and p2 <= 15 and p3 >= 0 and "
700 "p3 <= 31 and 128p3 <= -1 + p0 and p6 >= -127 and "
701 "p5 <= -1 + p0 and p6 <= -1 + p0 and p6 >= 128p3 and "
702 "p0 >= 1 and p5 >= 8p2 and p10 >= 0 and p10 <= 15 ) }";
703 bset2 = isl_basic_set_read_from_str(ctx, str, -1);
704 bset1 = isl_basic_set_gist(bset1, bset2);
705 assert(bset1 && bset1->n_div == 0);
706 isl_basic_set_free(bset1);
707 }
708
709 void test_coalesce_set(isl_ctx *ctx, const char *str, int check_one)
710 {
711 isl_set *set, *set2;
712
713 set = isl_set_read_from_str(ctx, str, -1);
714 set = isl_set_coalesce(set);
715 set2 = isl_set_read_from_str(ctx, str, -1);
716 assert(isl_set_is_equal(set, set2));
717 if (check_one)
718 assert(set && set->n == 1);
719 isl_set_free(set);
720 isl_set_free(set2);
721 }
722
723 void test_coalesce(struct isl_ctx *ctx)
724 {
725 const char *str;
726 struct isl_set *set, *set2;
727 struct isl_map *map, *map2;
728
729 set = isl_set_read_from_str(ctx,
730 "{[x,y]: x >= 0 & x <= 10 & y >= 0 & y <= 10 or "
731 "y >= x & x >= 2 & 5 >= y }", -1);
732 set = isl_set_coalesce(set);
733 assert(set && set->n == 1);
734 isl_set_free(set);
735
736 set = isl_set_read_from_str(ctx,
737 "{[x,y]: y >= 0 & 2x + y <= 30 & y <= 10 & x >= 0 or "
738 "x + y >= 10 & y <= x & x + y <= 20 & y >= 0}", -1);
739 set = isl_set_coalesce(set);
740 assert(set && set->n == 1);
741 isl_set_free(set);
742
743 set = isl_set_read_from_str(ctx,
744 "{[x,y]: y >= 0 & 2x + y <= 30 & y <= 10 & x >= 0 or "
745 "x + y >= 10 & y <= x & x + y <= 19 & y >= 0}", -1);
746 set = isl_set_coalesce(set);
747 assert(set && set->n == 2);
748 isl_set_free(set);
749
750 set = isl_set_read_from_str(ctx,
751 "{[x,y]: y >= 0 & x <= 5 & y <= x or "
752 "y >= 0 & x >= 6 & x <= 10 & y <= x}", -1);
753 set = isl_set_coalesce(set);
754 assert(set && set->n == 1);
755 isl_set_free(set);
756
757 set = isl_set_read_from_str(ctx,
758 "{[x,y]: y >= 0 & x <= 5 & y <= x or "
759 "y >= 0 & x >= 7 & x <= 10 & y <= x}", -1);
760 set = isl_set_coalesce(set);
761 assert(set && set->n == 2);
762 isl_set_free(set);
763
764 set = isl_set_read_from_str(ctx,
765 "{[x,y]: y >= 0 & x <= 5 & y <= x or "
766 "y >= 0 & x >= 6 & x <= 10 & y + 1 <= x}", -1);
767 set = isl_set_coalesce(set);
768 assert(set && set->n == 2);
769 isl_set_free(set);
770
771 set = isl_set_read_from_str(ctx,
772 "{[x,y]: y >= 0 & x <= 5 & y <= x or "
773 "y >= 0 & x = 6 & y <= 6}", -1);
774 set = isl_set_coalesce(set);
775 assert(set && set->n == 1);
776 isl_set_free(set);
777
778 set = isl_set_read_from_str(ctx,
779 "{[x,y]: y >= 0 & x <= 5 & y <= x or "
780 "y >= 0 & x = 7 & y <= 6}", -1);
781 set = isl_set_coalesce(set);
782 assert(set && set->n == 2);
783 isl_set_free(set);
784
785 set = isl_set_read_from_str(ctx,
786 "{[x,y]: y >= 0 & x <= 5 & y <= x or "
787 "y >= 0 & x = 6 & y <= 5}", -1);
788 set = isl_set_coalesce(set);
789 assert(set && set->n == 1);
790 set2 = isl_set_read_from_str(ctx,
791 "{[x,y]: y >= 0 & x <= 5 & y <= x or "
792 "y >= 0 & x = 6 & y <= 5}", -1);
793 assert(isl_set_is_equal(set, set2));
794 isl_set_free(set);
795 isl_set_free(set2);
796
797 set = isl_set_read_from_str(ctx,
798 "{[x,y]: y >= 0 & x <= 5 & y <= x or "
799 "y >= 0 & x = 6 & y <= 7}", -1);
800 set = isl_set_coalesce(set);
801 assert(set && set->n == 2);
802 isl_set_free(set);
803
804 set = isl_set_read_from_str(ctx,
805 "[n] -> { [i] : i = 1 and n >= 2 or 2 <= i and i <= n }", -1);
806 set = isl_set_coalesce(set);
807 assert(set && set->n == 1);
808 set2 = isl_set_read_from_str(ctx,
809 "[n] -> { [i] : i = 1 and n >= 2 or 2 <= i and i <= n }", -1);
810 assert(isl_set_is_equal(set, set2));
811 isl_set_free(set);
812 isl_set_free(set2);
813
814 set = isl_set_read_from_str(ctx,
815 "{[x,y] : x >= 0 and y >= 0 or 0 <= y and y <= 5 and x = -1}", -1);
816 set = isl_set_coalesce(set);
817 set2 = isl_set_read_from_str(ctx,
818 "{[x,y] : x >= 0 and y >= 0 or 0 <= y and y <= 5 and x = -1}", -1);
819 assert(isl_set_is_equal(set, set2));
820 isl_set_free(set);
821 isl_set_free(set2);
822
823 set = isl_set_read_from_str(ctx,
824 "[n] -> { [i] : 1 <= i and i <= n - 1 or "
825 "2 <= i and i <= n }", -1);
826 set = isl_set_coalesce(set);
827 assert(set && set->n == 1);
828 set2 = isl_set_read_from_str(ctx,
829 "[n] -> { [i] : 1 <= i and i <= n - 1 or "
830 "2 <= i and i <= n }", -1);
831 assert(isl_set_is_equal(set, set2));
832 isl_set_free(set);
833 isl_set_free(set2);
834
835 map = isl_map_read_from_str(ctx,
836 "[n] -> { [i0] -> [o0] : exists (e0 = [(i0)/4], e1 = [(o0)/4], "
837 "e2 = [(n)/2], e3 = [(-2 + i0)/4], e4 = [(-2 + o0)/4], "
838 "e5 = [(-2n + i0)/4]: 2e2 = n and 4e3 = -2 + i0 and "
839 "4e4 = -2 + o0 and i0 >= 8 + 2n and o0 >= 2 + i0 and "
840 "o0 <= 56 + 2n and o0 <= -12 + 4n and i0 <= 57 + 2n and "
841 "i0 <= -11 + 4n and o0 >= 6 + 2n and 4e0 <= i0 and "
842 "4e0 >= -3 + i0 and 4e1 <= o0 and 4e1 >= -3 + o0 and "
843 "4e5 <= -2n + i0 and 4e5 >= -3 - 2n + i0);"
844 "[i0] -> [o0] : exists (e0 = [(i0)/4], e1 = [(o0)/4], "
845 "e2 = [(n)/2], e3 = [(-2 + i0)/4], e4 = [(-2 + o0)/4], "
846 "e5 = [(-2n + i0)/4]: 2e2 = n and 4e3 = -2 + i0 and "
847 "4e4 = -2 + o0 and 2e0 >= 3 + n and e0 <= -4 + n and "
848 "2e0 <= 27 + n and e1 <= -4 + n and 2e1 <= 27 + n and "
849 "2e1 >= 2 + n and e1 >= 1 + e0 and i0 >= 7 + 2n and "
850 "i0 <= -11 + 4n and i0 <= 57 + 2n and 4e0 <= -2 + i0 and "
851 "4e0 >= -3 + i0 and o0 >= 6 + 2n and o0 <= -11 + 4n and "
852 "o0 <= 57 + 2n and 4e1 <= -2 + o0 and 4e1 >= -3 + o0 and "
853 "4e5 <= -2n + i0 and 4e5 >= -3 - 2n + i0 ) }", -1);
854 map = isl_map_coalesce(map);
855 map2 = isl_map_read_from_str(ctx,
856 "[n] -> { [i0] -> [o0] : exists (e0 = [(i0)/4], e1 = [(o0)/4], "
857 "e2 = [(n)/2], e3 = [(-2 + i0)/4], e4 = [(-2 + o0)/4], "
858 "e5 = [(-2n + i0)/4]: 2e2 = n and 4e3 = -2 + i0 and "
859 "4e4 = -2 + o0 and i0 >= 8 + 2n and o0 >= 2 + i0 and "
860 "o0 <= 56 + 2n and o0 <= -12 + 4n and i0 <= 57 + 2n and "
861 "i0 <= -11 + 4n and o0 >= 6 + 2n and 4e0 <= i0 and "
862 "4e0 >= -3 + i0 and 4e1 <= o0 and 4e1 >= -3 + o0 and "
863 "4e5 <= -2n + i0 and 4e5 >= -3 - 2n + i0);"
864 "[i0] -> [o0] : exists (e0 = [(i0)/4], e1 = [(o0)/4], "
865 "e2 = [(n)/2], e3 = [(-2 + i0)/4], e4 = [(-2 + o0)/4], "
866 "e5 = [(-2n + i0)/4]: 2e2 = n and 4e3 = -2 + i0 and "
867 "4e4 = -2 + o0 and 2e0 >= 3 + n and e0 <= -4 + n and "
868 "2e0 <= 27 + n and e1 <= -4 + n and 2e1 <= 27 + n and "
869 "2e1 >= 2 + n and e1 >= 1 + e0 and i0 >= 7 + 2n and "
870 "i0 <= -11 + 4n and i0 <= 57 + 2n and 4e0 <= -2 + i0 and "
871 "4e0 >= -3 + i0 and o0 >= 6 + 2n and o0 <= -11 + 4n and "
872 "o0 <= 57 + 2n and 4e1 <= -2 + o0 and 4e1 >= -3 + o0 and "
873 "4e5 <= -2n + i0 and 4e5 >= -3 - 2n + i0 ) }", -1);
874 assert(isl_map_is_equal(map, map2));
875 isl_map_free(map);
876 isl_map_free(map2);
877
878 str = "[n, m] -> { [] -> [o0, o2, o3] : (o3 = 1 and o0 >= 1 + m and "
879 "o0 <= n + m and o2 <= m and o0 >= 2 + n and o2 >= 3) or "
880 "(o0 >= 2 + n and o0 >= 1 + m and o0 <= n + m and n >= 1 and "
881 "o3 <= -1 + o2 and o3 >= 1 - m + o2 and o3 >= 2 and o3 <= n) }";
882 map = isl_map_read_from_str(ctx, str, -1);
883 map = isl_map_coalesce(map);
884 map2 = isl_map_read_from_str(ctx, str, -1);
885 assert(isl_map_is_equal(map, map2));
886 isl_map_free(map);
887 isl_map_free(map2);
888
889 str = "[M, N] -> { [i0, i1, i2, i3, i4, i5, i6] -> "
890 "[o0, o1, o2, o3, o4, o5, o6] : "
891 "(o6 <= -4 + 2M - 2N + i0 + i1 - i2 + i6 - o0 - o1 + o2 and "
892 "o3 <= -2 + i3 and o6 >= 2 + i0 + i3 + i6 - o0 - o3 and "
893 "o6 >= 2 - M + N + i3 + i4 + i6 - o3 - o4 and o0 <= -1 + i0 and "
894 "o4 >= 4 - 3M + 3N - i0 - i1 + i2 + 2i3 + i4 + o0 + o1 - o2 - 2o3 "
895 "and o6 <= -3 + 2M - 2N + i3 + i4 - i5 + i6 - o3 - o4 + o5 and "
896 "2o6 <= -5 + 5M - 5N + 2i0 + i1 - i2 - i5 + 2i6 - 2o0 - o1 + o2 + o5 "
897 "and o6 >= 2i0 + i1 + i6 - 2o0 - o1 and "
898 "3o6 <= -5 + 4M - 4N + 2i0 + i1 - i2 + 2i3 + i4 - i5 + 3i6 "
899 "- 2o0 - o1 + o2 - 2o3 - o4 + o5) or "
900 "(N >= 2 and o3 <= -1 + i3 and o0 <= -1 + i0 and "
901 "o6 >= i3 + i6 - o3 and M >= 0 and "
902 "2o6 >= 1 + i0 + i3 + 2i6 - o0 - o3 and "
903 "o6 >= 1 - M + i0 + i6 - o0 and N >= 2M and o6 >= i0 + i6 - o0) }";
904 map = isl_map_read_from_str(ctx, str, -1);
905 map = isl_map_coalesce(map);
906 map2 = isl_map_read_from_str(ctx, str, -1);
907 assert(isl_map_is_equal(map, map2));
908 isl_map_free(map);
909 isl_map_free(map2);
910
911 str = "[M, N] -> { [] -> [o0] : (o0 = 0 and M >= 1 and N >= 2) or "
912 "(o0 = 0 and M >= 1 and N >= 2M and N >= 2 + M) or "
913 "(o0 = 0 and M >= 2 and N >= 3) or "
914 "(M = 0 and o0 = 0 and N >= 3) }";
915 map = isl_map_read_from_str(ctx, str, -1);
916 map = isl_map_coalesce(map);
917 map2 = isl_map_read_from_str(ctx, str, -1);
918 assert(isl_map_is_equal(map, map2));
919 isl_map_free(map);
920 isl_map_free(map2);
921
922 str = "{ [i0, i1, i2, i3] : (i1 = 10i0 and i0 >= 1 and 10i0 <= 100 and "
923 "i3 <= 9 + 10 i2 and i3 >= 1 + 10i2 and i3 >= 0) or "
924 "(i1 <= 9 + 10i0 and i1 >= 1 + 10i0 and i2 >= 0 and "
925 "i0 >= 0 and i1 <= 100 and i3 <= 9 + 10i2 and i3 >= 1 + 10i2) }";
926 map = isl_map_read_from_str(ctx, str, -1);
927 map = isl_map_coalesce(map);
928 map2 = isl_map_read_from_str(ctx, str, -1);
929 assert(isl_map_is_equal(map, map2));
930 isl_map_free(map);
931 isl_map_free(map2);
932
933 test_coalesce_set(ctx,
934 "[M] -> { [i1] : (i1 >= 2 and i1 <= M) or "
935 "(i1 = M and M >= 1) }", 0);
936 test_coalesce_set(ctx,
937 "{[x,y] : x,y >= 0; [x,y] : 10 <= x <= 20 and y >= -1 }", 0);
938 test_coalesce_set(ctx,
939 "{ [x, y] : (x >= 1 and y >= 1 and x <= 2 and y <= 2) or "
940 "(y = 3 and x = 1) }", 1);
941 test_coalesce_set(ctx,
942 "[M] -> { [i0, i1, i2, i3, i4] : (i1 >= 3 and i4 >= 2 + i2 and "
943 "i2 >= 2 and i0 >= 2 and i3 >= 1 + i2 and i0 <= M and "
944 "i1 <= M and i3 <= M and i4 <= M) or "
945 "(i1 >= 2 and i4 >= 1 + i2 and i2 >= 2 and i0 >= 2 and "
946 "i3 >= 1 + i2 and i0 <= M and i1 <= -1 + M and i3 <= M and "
947 "i4 <= -1 + M) }", 1);
948 test_coalesce_set(ctx,
949 "{ [x, y] : (x >= 0 and y >= 0 and x <= 10 and y <= 10) or "
950 "(x >= 1 and y >= 1 and x <= 11 and y <= 11) }", 1);
951 test_coalesce_set(ctx,
952 "{[x,y,z] : y + 2 >= 0 and x - y + 1 >= 0 and "
953 "-x - y + 1 >= 0 and -3 <= z <= 3;"
954 "[x,y,z] : -x+z + 20 >= 0 and -x-z + 20 >= 0 and "
955 "x-z + 20 >= 0 and x+z + 20 >= 0 and -10 <= y <= 0}", 1);
956 test_coalesce_set(ctx,
957 "{[x,y] : 0 <= x,y <= 10; [5,y]: 4 <=y <= 11}", 1);
958 test_coalesce_set(ctx, "{[x,0] : x >= 0; [x,1] : x <= 20}", 0);
959 test_coalesce_set(ctx,
960 "{[x,0,0] : -5 <= x <= 5; [0,y,1] : -5 <= y <= 5 }", 1);
961 test_coalesce_set(ctx, "{ [x, 1 - x] : 0 <= x <= 1; [0,0] }", 1);
962 test_coalesce_set(ctx, "{ [0,0]; [i,i] : 1 <= i <= 10 }", 1);
963 test_coalesce_set(ctx, "{ [0,0]; [i,j] : 1 <= i,j <= 10 }", 0);
964 test_coalesce_set(ctx, "{ [0,0]; [i,2i] : 1 <= i <= 10 }", 1);
965 test_coalesce_set(ctx, "{ [0,0]; [i,2i] : 2 <= i <= 10 }", 0);
966 test_coalesce_set(ctx, "{ [1,0]; [i,2i] : 1 <= i <= 10 }", 0);
967 test_coalesce_set(ctx, "{ [0,1]; [i,2i] : 1 <= i <= 10 }", 0);
968 }
969
970 void test_closure(struct isl_ctx *ctx)
971 {
972 const char *str;
973 isl_set *dom;
974 isl_map *up, *right;
975 isl_map *map, *map2;
976 int exact;
977
978 /* COCOA example 1 */
979 map = isl_map_read_from_str(ctx,
980 "[n] -> { [i,j] -> [i2,j2] : i2 = i + 1 and j2 = j + 1 and "
981 "1 <= i and i < n and 1 <= j and j < n or "
982 "i2 = i + 1 and j2 = j - 1 and "
983 "1 <= i and i < n and 2 <= j and j <= n }", -1);
984 map = isl_map_power(map, &exact);
985 assert(exact);
986 isl_map_free(map);
987
988 /* COCOA example 1 */
989 map = isl_map_read_from_str(ctx,
990 "[n] -> { [i,j] -> [i2,j2] : i2 = i + 1 and j2 = j + 1 and "
991 "1 <= i and i < n and 1 <= j and j < n or "
992 "i2 = i + 1 and j2 = j - 1 and "
993 "1 <= i and i < n and 2 <= j and j <= n }", -1);
994 map = isl_map_transitive_closure(map, &exact);
995 assert(exact);
996 map2 = isl_map_read_from_str(ctx,
997 "[n] -> { [i,j] -> [i2,j2] : exists (k1,k2,k : "
998 "1 <= i and i < n and 1 <= j and j <= n and "
999 "2 <= i2 and i2 <= n and 1 <= j2 and j2 <= n and "
1000 "i2 = i + k1 + k2 and j2 = j + k1 - k2 and "
1001 "k1 >= 0 and k2 >= 0 and k1 + k2 = k and k >= 1 )}", -1);
1002 assert(isl_map_is_equal(map, map2));
1003 isl_map_free(map2);
1004 isl_map_free(map);
1005
1006 map = isl_map_read_from_str(ctx,
1007 "[n] -> { [x] -> [y] : y = x + 1 and 0 <= x and x <= n and "
1008 " 0 <= y and y <= n }", -1);
1009 map = isl_map_transitive_closure(map, &exact);
1010 map2 = isl_map_read_from_str(ctx,
1011 "[n] -> { [x] -> [y] : y > x and 0 <= x and x <= n and "
1012 " 0 <= y and y <= n }", -1);
1013 assert(isl_map_is_equal(map, map2));
1014 isl_map_free(map2);
1015 isl_map_free(map);
1016
1017 /* COCOA example 2 */
1018 map = isl_map_read_from_str(ctx,
1019 "[n] -> { [i,j] -> [i2,j2] : i2 = i + 2 and j2 = j + 2 and "
1020 "1 <= i and i < n - 1 and 1 <= j and j < n - 1 or "
1021 "i2 = i + 2 and j2 = j - 2 and "
1022 "1 <= i and i < n - 1 and 3 <= j and j <= n }", -1);
1023 map = isl_map_transitive_closure(map, &exact);
1024 assert(exact);
1025 map2 = isl_map_read_from_str(ctx,
1026 "[n] -> { [i,j] -> [i2,j2] : exists (k1,k2,k : "
1027 "1 <= i and i < n - 1 and 1 <= j and j <= n and "
1028 "3 <= i2 and i2 <= n and 1 <= j2 and j2 <= n and "
1029 "i2 = i + 2 k1 + 2 k2 and j2 = j + 2 k1 - 2 k2 and "
1030 "k1 >= 0 and k2 >= 0 and k1 + k2 = k and k >= 1) }", -1);
1031 assert(isl_map_is_equal(map, map2));
1032 isl_map_free(map);
1033 isl_map_free(map2);
1034
1035 /* COCOA Fig.2 left */
1036 map = isl_map_read_from_str(ctx,
1037 "[n] -> { [i,j] -> [i2,j2] : i2 = i + 2 and j2 = j and "
1038 "i <= 2 j - 3 and i <= n - 2 and j <= 2 i - 1 and "
1039 "j <= n or "
1040 "i2 = i and j2 = j + 2 and i <= 2 j - 1 and i <= n and "
1041 "j <= 2 i - 3 and j <= n - 2 or "
1042 "i2 = i + 1 and j2 = j + 1 and i <= 2 j - 1 and "
1043 "i <= n - 1 and j <= 2 i - 1 and j <= n - 1 }", -1);
1044 map = isl_map_transitive_closure(map, &exact);
1045 assert(exact);
1046 isl_map_free(map);
1047
1048 /* COCOA Fig.2 right */
1049 map = isl_map_read_from_str(ctx,
1050 "[n] -> { [i,j] -> [i2,j2] : i2 = i + 3 and j2 = j and "
1051 "i <= 2 j - 4 and i <= n - 3 and j <= 2 i - 1 and "
1052 "j <= n or "
1053 "i2 = i and j2 = j + 3 and i <= 2 j - 1 and i <= n and "
1054 "j <= 2 i - 4 and j <= n - 3 or "
1055 "i2 = i + 1 and j2 = j + 1 and i <= 2 j - 1 and "
1056 "i <= n - 1 and j <= 2 i - 1 and j <= n - 1 }", -1);
1057 map = isl_map_power(map, &exact);
1058 assert(exact);
1059 isl_map_free(map);
1060
1061 /* COCOA Fig.2 right */
1062 map = isl_map_read_from_str(ctx,
1063 "[n] -> { [i,j] -> [i2,j2] : i2 = i + 3 and j2 = j and "
1064 "i <= 2 j - 4 and i <= n - 3 and j <= 2 i - 1 and "
1065 "j <= n or "
1066 "i2 = i and j2 = j + 3 and i <= 2 j - 1 and i <= n and "
1067 "j <= 2 i - 4 and j <= n - 3 or "
1068 "i2 = i + 1 and j2 = j + 1 and i <= 2 j - 1 and "
1069 "i <= n - 1 and j <= 2 i - 1 and j <= n - 1 }", -1);
1070 map = isl_map_transitive_closure(map, &exact);
1071 assert(exact);
1072 map2 = isl_map_read_from_str(ctx,
1073 "[n] -> { [i,j] -> [i2,j2] : exists (k1,k2,k3,k : "
1074 "i <= 2 j - 1 and i <= n and j <= 2 i - 1 and "
1075 "j <= n and 3 + i + 2 j <= 3 n and "
1076 "3 + 2 i + j <= 3n and i2 <= 2 j2 -1 and i2 <= n and "
1077 "i2 <= 3 j2 - 4 and j2 <= 2 i2 -1 and j2 <= n and "
1078 "13 + 4 j2 <= 11 i2 and i2 = i + 3 k1 + k3 and "
1079 "j2 = j + 3 k2 + k3 and k1 >= 0 and k2 >= 0 and "
1080 "k3 >= 0 and k1 + k2 + k3 = k and k > 0) }", -1);
1081 assert(isl_map_is_equal(map, map2));
1082 isl_map_free(map2);
1083 isl_map_free(map);
1084
1085 /* COCOA Fig.1 right */
1086 dom = isl_set_read_from_str(ctx,
1087 "{ [x,y] : x >= 0 and -2 x + 3 y >= 0 and x <= 3 and "
1088 "2 x - 3 y + 3 >= 0 }", -1);
1089 right = isl_map_read_from_str(ctx,
1090 "{ [x,y] -> [x2,y2] : x2 = x + 1 and y2 = y }", -1);
1091 up = isl_map_read_from_str(ctx,
1092 "{ [x,y] -> [x2,y2] : x2 = x and y2 = y + 1 }", -1);
1093 right = isl_map_intersect_domain(right, isl_set_copy(dom));
1094 right = isl_map_intersect_range(right, isl_set_copy(dom));
1095 up = isl_map_intersect_domain(up, isl_set_copy(dom));
1096 up = isl_map_intersect_range(up, dom);
1097 map = isl_map_union(up, right);
1098 map = isl_map_transitive_closure(map, &exact);
1099 assert(exact);
1100 map2 = isl_map_read_from_str(ctx,
1101 "{ [0,0] -> [0,1]; [0,0] -> [1,1]; [0,1] -> [1,1]; "
1102 " [2,2] -> [3,2]; [2,2] -> [3,3]; [3,2] -> [3,3] }", -1);
1103 assert(isl_map_is_equal(map, map2));
1104 isl_map_free(map2);
1105 isl_map_free(map);
1106
1107 /* COCOA Theorem 1 counter example */
1108 map = isl_map_read_from_str(ctx,
1109 "{ [i,j] -> [i2,j2] : i = 0 and 0 <= j and j <= 1 and "
1110 "i2 = 1 and j2 = j or "
1111 "i = 0 and j = 0 and i2 = 0 and j2 = 1 }", -1);
1112 map = isl_map_transitive_closure(map, &exact);
1113 assert(exact);
1114 isl_map_free(map);
1115
1116 map = isl_map_read_from_str(ctx,
1117 "[m,n] -> { [i,j] -> [i2,j2] : i2 = i and j2 = j + 2 and "
1118 "1 <= i,i2 <= n and 1 <= j,j2 <= m or "
1119 "i2 = i + 1 and 3 <= j2 - j <= 4 and "
1120 "1 <= i,i2 <= n and 1 <= j,j2 <= m }", -1);
1121 map = isl_map_transitive_closure(map, &exact);
1122 assert(exact);
1123 isl_map_free(map);
1124
1125 /* Kelly et al 1996, fig 12 */
1126 map = isl_map_read_from_str(ctx,
1127 "[n] -> { [i,j] -> [i2,j2] : i2 = i and j2 = j + 1 and "
1128 "1 <= i,j,j+1 <= n or "
1129 "j = n and j2 = 1 and i2 = i + 1 and "
1130 "1 <= i,i+1 <= n }", -1);
1131 map = isl_map_transitive_closure(map, &exact);
1132 assert(exact);
1133 map2 = isl_map_read_from_str(ctx,
1134 "[n] -> { [i,j] -> [i2,j2] : 1 <= j < j2 <= n and "
1135 "1 <= i <= n and i = i2 or "
1136 "1 <= i < i2 <= n and 1 <= j <= n and "
1137 "1 <= j2 <= n }", -1);
1138 assert(isl_map_is_equal(map, map2));
1139 isl_map_free(map2);
1140 isl_map_free(map);
1141
1142 /* Omega's closure4 */
1143 map = isl_map_read_from_str(ctx,
1144 "[m,n] -> { [x,y] -> [x2,y2] : x2 = x and y2 = y + 1 and "
1145 "1 <= x,y <= 10 or "
1146 "x2 = x + 1 and y2 = y and "
1147 "1 <= x <= 20 && 5 <= y <= 15 }", -1);
1148 map = isl_map_transitive_closure(map, &exact);
1149 assert(exact);
1150 isl_map_free(map);
1151
1152 map = isl_map_read_from_str(ctx,
1153 "[n] -> { [x] -> [y]: 1 <= n <= y - x <= 10 }", -1);
1154 map = isl_map_transitive_closure(map, &exact);
1155 assert(!exact);
1156 map2 = isl_map_read_from_str(ctx,
1157 "[n] -> { [x] -> [y] : 1 <= n <= 10 and y >= n + x }", -1);
1158 assert(isl_map_is_equal(map, map2));
1159 isl_map_free(map);
1160 isl_map_free(map2);
1161
1162 str = "[n, m] -> { [i0, i1, i2, i3] -> [o0, o1, o2, o3] : "
1163 "i3 = 1 and o0 = i0 and o1 = -1 + i1 and o2 = -1 + i2 and "
1164 "o3 = -2 + i2 and i1 <= -1 + i0 and i1 >= 1 - m + i0 and "
1165 "i1 >= 2 and i1 <= n and i2 >= 3 and i2 <= 1 + n and i2 <= m }";
1166 map = isl_map_read_from_str(ctx, str, -1);
1167 map = isl_map_transitive_closure(map, &exact);
1168 assert(exact);
1169 map2 = isl_map_read_from_str(ctx, str, -1);
1170 assert(isl_map_is_equal(map, map2));
1171 isl_map_free(map);
1172 isl_map_free(map2);
1173
1174 str = "{[0] -> [1]; [2] -> [3]}";
1175 map = isl_map_read_from_str(ctx, str, -1);
1176 map = isl_map_transitive_closure(map, &exact);
1177 assert(exact);
1178 map2 = isl_map_read_from_str(ctx, str, -1);
1179 assert(isl_map_is_equal(map, map2));
1180 isl_map_free(map);
1181 isl_map_free(map2);
1182
1183 str = "[n] -> { [[i0, i1, 1, 0, i0] -> [i5, 1]] -> "
1184 "[[i0, -1 + i1, 2, 0, i0] -> [-1 + i5, 2]] : "
1185 "exists (e0 = [(3 - n)/3]: i5 >= 2 and i1 >= 2 and "
1186 "3i0 <= -1 + n and i1 <= -1 + n and i5 <= -1 + n and "
1187 "3e0 >= 1 - n and 3e0 <= 2 - n and 3i0 >= -2 + n); "
1188 "[[i0, i1, 2, 0, i0] -> [i5, 1]] -> "
1189 "[[i0, i1, 1, 0, i0] -> [-1 + i5, 2]] : "
1190 "exists (e0 = [(3 - n)/3]: i5 >= 2 and i1 >= 1 and "
1191 "3i0 <= -1 + n and i1 <= -1 + n and i5 <= -1 + n and "
1192 "3e0 >= 1 - n and 3e0 <= 2 - n and 3i0 >= -2 + n); "
1193 "[[i0, i1, 1, 0, i0] -> [i5, 2]] -> "
1194 "[[i0, -1 + i1, 2, 0, i0] -> [i5, 1]] : "
1195 "exists (e0 = [(3 - n)/3]: i1 >= 2 and i5 >= 1 and "
1196 "3i0 <= -1 + n and i1 <= -1 + n and i5 <= -1 + n and "
1197 "3e0 >= 1 - n and 3e0 <= 2 - n and 3i0 >= -2 + n); "
1198 "[[i0, i1, 2, 0, i0] -> [i5, 2]] -> "
1199 "[[i0, i1, 1, 0, i0] -> [i5, 1]] : "
1200 "exists (e0 = [(3 - n)/3]: i5 >= 1 and i1 >= 1 and "
1201 "3i0 <= -1 + n and i1 <= -1 + n and i5 <= -1 + n and "
1202 "3e0 >= 1 - n and 3e0 <= 2 - n and 3i0 >= -2 + n) }";
1203 map = isl_map_read_from_str(ctx, str, -1);
1204 map = isl_map_transitive_closure(map, NULL);
1205 assert(map);
1206 isl_map_free(map);
1207 }
1208
1209 void test_lex(struct isl_ctx *ctx)
1210 {
1211 isl_dim *dim;
1212 isl_map *map;
1213
1214 dim = isl_dim_alloc(ctx, 0, 0, 0);
1215 map = isl_map_lex_le(dim);
1216 assert(!isl_map_is_empty(map));
1217 isl_map_free(map);
1218 }
1219
1220 static int consume_lexmin(__isl_take isl_basic_set *dom,
1221 __isl_take isl_aff_list *list, void *user)
1222 {
1223 isl_dim *dim;
1224 isl_basic_map *bmap;
1225 isl_map **map = user;
1226
1227 dim = isl_basic_set_get_dim(dom);
1228 bmap = isl_basic_map_from_aff_list(dim, list);
1229 bmap = isl_basic_map_intersect_domain(bmap, dom);
1230
1231 *map = isl_map_union(*map, isl_map_from_basic_map(bmap));
1232
1233 return 0;
1234 }
1235
1236 void test_lexmin(struct isl_ctx *ctx)
1237 {
1238 const char *str;
1239 isl_basic_map *bmap;
1240 isl_map *map, *map2;
1241 isl_set *set;
1242 isl_set *set2;
1243
1244 str = "[p0, p1] -> { [] -> [] : "
1245 "exists (e0 = [(2p1)/3], e1, e2, e3 = [(3 - p1 + 3e0)/3], "
1246 "e4 = [(p1)/3], e5 = [(p1 + 3e4)/3]: "
1247 "3e0 >= -2 + 2p1 and 3e0 >= p1 and 3e3 >= 1 - p1 + 3e0 and "
1248 "3e0 <= 2p1 and 3e3 >= -2 + p1 and 3e3 <= -1 + p1 and p1 >= 3 and "
1249 "3e5 >= -2 + 2p1 and 3e5 >= p1 and 3e5 <= -1 + p1 + 3e4 and "
1250 "3e4 <= p1 and 3e4 >= -2 + p1 and e3 <= -1 + e0 and "
1251 "3e4 >= 6 - p1 + 3e1 and 3e1 >= p1 and 3e5 >= -2 + p1 + 3e4 and "
1252 "2e4 >= 3 - p1 + 2e1 and e4 <= e1 and 3e3 <= 2 - p1 + 3e0 and "
1253 "e5 >= 1 + e1 and 3e4 >= 6 - 2p1 + 3e1 and "
1254 "p0 >= 2 and p1 >= p0 and 3e2 >= p1 and 3e4 >= 6 - p1 + 3e2 and "
1255 "e2 <= e1 and e3 >= 1 and e4 <= e2) }";
1256 map = isl_map_read_from_str(ctx, str, -1);
1257 map = isl_map_lexmin(map);
1258 isl_map_free(map);
1259
1260 str = "[C] -> { [obj,a,b,c] : obj <= 38 a + 7 b + 10 c and "
1261 "a + b <= 1 and c <= 10 b and c <= C and a,b,c,C >= 0 }";
1262 set = isl_set_read_from_str(ctx, str, -1);
1263 set = isl_set_lexmax(set);
1264 str = "[C] -> { [obj,a,b,c] : C = 8 }";
1265 set2 = isl_set_read_from_str(ctx, str, -1);
1266 set = isl_set_intersect(set, set2);
1267 assert(!isl_set_is_empty(set));
1268 isl_set_free(set);
1269
1270 str = "{ [x] -> [y] : x <= y <= 10; [x] -> [5] : -8 <= x <= 8 }";
1271 map = isl_map_read_from_str(ctx, str, -1);
1272 map = isl_map_lexmin(map);
1273 str = "{ [x] -> [5] : 6 <= x <= 8; "
1274 "[x] -> [x] : x <= 5 or (9 <= x <= 10) }";
1275 map2 = isl_map_read_from_str(ctx, str, -1);
1276 assert(isl_map_is_equal(map, map2));
1277 isl_map_free(map);
1278 isl_map_free(map2);
1279
1280 str = "{ [x] -> [y] : 4y = x or 4y = -1 + x or 4y = -2 + x }";
1281 map = isl_map_read_from_str(ctx, str, -1);
1282 map2 = isl_map_copy(map);
1283 map = isl_map_lexmin(map);
1284 assert(isl_map_is_equal(map, map2));
1285 isl_map_free(map);
1286 isl_map_free(map2);
1287
1288 str = "{ [x] -> [y] : x = 4y; [x] -> [y] : x = 2y }";
1289 map = isl_map_read_from_str(ctx, str, -1);
1290 map = isl_map_lexmin(map);
1291 str = "{ [x] -> [y] : (4y = x and x >= 0) or "
1292 "(exists (e0 = [(x)/4], e1 = [(-2 + x)/4]: 2y = x and "
1293 "4e1 = -2 + x and 4e0 <= -1 + x and 4e0 >= -3 + x)) or "
1294 "(exists (e0 = [(x)/4]: 2y = x and 4e0 = x and x <= -4)) }";
1295 map2 = isl_map_read_from_str(ctx, str, -1);
1296 assert(isl_map_is_equal(map, map2));
1297 isl_map_free(map);
1298 isl_map_free(map2);
1299
1300 str = "{ [i] -> [i', j] : j = i - 8i' and i' >= 0 and i' <= 7 and "
1301 " 8i' <= i and 8i' >= -7 + i }";
1302 bmap = isl_basic_map_read_from_str(ctx, str, -1);
1303 map2 = isl_map_empty(isl_basic_map_get_dim(bmap));
1304 isl_basic_map_foreach_lexmin(bmap, &consume_lexmin, &map2);
1305 map = isl_map_from_basic_map(bmap);
1306 assert(isl_map_is_equal(map, map2));
1307 isl_map_free(map);
1308 isl_map_free(map2);
1309 }
1310
1311 struct must_may {
1312 isl_map *must;
1313 isl_map *may;
1314 };
1315
1316 static int collect_must_may(__isl_take isl_map *dep, int must,
1317 void *dep_user, void *user)
1318 {
1319 struct must_may *mm = (struct must_may *)user;
1320
1321 if (must)
1322 mm->must = isl_map_union(mm->must, dep);
1323 else
1324 mm->may = isl_map_union(mm->may, dep);
1325
1326 return 0;
1327 }
1328
1329 static int common_space(void *first, void *second)
1330 {
1331 int depth = *(int *)first;
1332 return 2 * depth;
1333 }
1334
1335 static int map_is_equal(__isl_keep isl_map *map, const char *str)
1336 {
1337 isl_map *map2;
1338 int equal;
1339
1340 if (!map)
1341 return -1;
1342
1343 map2 = isl_map_read_from_str(map->ctx, str, -1);
1344 equal = isl_map_is_equal(map, map2);
1345 isl_map_free(map2);
1346
1347 return equal;
1348 }
1349
1350 void test_dep(struct isl_ctx *ctx)
1351 {
1352 const char *str;
1353 isl_dim *dim;
1354 isl_map *map;
1355 isl_access_info *ai;
1356 isl_flow *flow;
1357 int depth;
1358 struct must_may mm;
1359
1360 depth = 3;
1361
1362 str = "{ [2,i,0] -> [i] : 0 <= i <= 10 }";
1363 map = isl_map_read_from_str(ctx, str, -1);
1364 ai = isl_access_info_alloc(map, &depth, &common_space, 2);
1365
1366 str = "{ [0,i,0] -> [i] : 0 <= i <= 10 }";
1367 map = isl_map_read_from_str(ctx, str, -1);
1368 ai = isl_access_info_add_source(ai, map, 1, &depth);
1369
1370 str = "{ [1,i,0] -> [5] : 0 <= i <= 10 }";
1371 map = isl_map_read_from_str(ctx, str, -1);
1372 ai = isl_access_info_add_source(ai, map, 1, &depth);
1373
1374 flow = isl_access_info_compute_flow(ai);
1375 dim = isl_dim_alloc(ctx, 0, 3, 3);
1376 mm.must = isl_map_empty(isl_dim_copy(dim));
1377 mm.may = isl_map_empty(dim);
1378
1379 isl_flow_foreach(flow, collect_must_may, &mm);
1380
1381 str = "{ [0,i,0] -> [2,i,0] : (0 <= i <= 4) or (6 <= i <= 10); "
1382 " [1,10,0] -> [2,5,0] }";
1383 assert(map_is_equal(mm.must, str));
1384 str = "{ [i,j,k] -> [l,m,n] : 1 = 0 }";
1385 assert(map_is_equal(mm.may, str));
1386
1387 isl_map_free(mm.must);
1388 isl_map_free(mm.may);
1389 isl_flow_free(flow);
1390
1391
1392 str = "{ [2,i,0] -> [i] : 0 <= i <= 10 }";
1393 map = isl_map_read_from_str(ctx, str, -1);
1394 ai = isl_access_info_alloc(map, &depth, &common_space, 2);
1395
1396 str = "{ [0,i,0] -> [i] : 0 <= i <= 10 }";
1397 map = isl_map_read_from_str(ctx, str, -1);
1398 ai = isl_access_info_add_source(ai, map, 1, &depth);
1399
1400 str = "{ [1,i,0] -> [5] : 0 <= i <= 10 }";
1401 map = isl_map_read_from_str(ctx, str, -1);
1402 ai = isl_access_info_add_source(ai, map, 0, &depth);
1403
1404 flow = isl_access_info_compute_flow(ai);
1405 dim = isl_dim_alloc(ctx, 0, 3, 3);
1406 mm.must = isl_map_empty(isl_dim_copy(dim));
1407 mm.may = isl_map_empty(dim);
1408
1409 isl_flow_foreach(flow, collect_must_may, &mm);
1410
1411 str = "{ [0,i,0] -> [2,i,0] : (0 <= i <= 4) or (6 <= i <= 10) }";
1412 assert(map_is_equal(mm.must, str));
1413 str = "{ [0,5,0] -> [2,5,0]; [1,i,0] -> [2,5,0] : 0 <= i <= 10 }";
1414 assert(map_is_equal(mm.may, str));
1415
1416 isl_map_free(mm.must);
1417 isl_map_free(mm.may);
1418 isl_flow_free(flow);
1419
1420
1421 str = "{ [2,i,0] -> [i] : 0 <= i <= 10 }";
1422 map = isl_map_read_from_str(ctx, str, -1);
1423 ai = isl_access_info_alloc(map, &depth, &common_space, 2);
1424
1425 str = "{ [0,i,0] -> [i] : 0 <= i <= 10 }";
1426 map = isl_map_read_from_str(ctx, str, -1);
1427 ai = isl_access_info_add_source(ai, map, 0, &depth);
1428
1429 str = "{ [1,i,0] -> [5] : 0 <= i <= 10 }";
1430 map = isl_map_read_from_str(ctx, str, -1);
1431 ai = isl_access_info_add_source(ai, map, 0, &depth);
1432
1433 flow = isl_access_info_compute_flow(ai);
1434 dim = isl_dim_alloc(ctx, 0, 3, 3);
1435 mm.must = isl_map_empty(isl_dim_copy(dim));
1436 mm.may = isl_map_empty(dim);
1437
1438 isl_flow_foreach(flow, collect_must_may, &mm);
1439
1440 str = "{ [0,i,0] -> [2,i,0] : 0 <= i <= 10; "
1441 " [1,i,0] -> [2,5,0] : 0 <= i <= 10 }";
1442 assert(map_is_equal(mm.may, str));
1443 str = "{ [i,j,k] -> [l,m,n] : 1 = 0 }";
1444 assert(map_is_equal(mm.must, str));
1445
1446 isl_map_free(mm.must);
1447 isl_map_free(mm.may);
1448 isl_flow_free(flow);
1449
1450
1451 str = "{ [0,i,2] -> [i] : 0 <= i <= 10 }";
1452 map = isl_map_read_from_str(ctx, str, -1);
1453 ai = isl_access_info_alloc(map, &depth, &common_space, 2);
1454
1455 str = "{ [0,i,0] -> [i] : 0 <= i <= 10 }";
1456 map = isl_map_read_from_str(ctx, str, -1);
1457 ai = isl_access_info_add_source(ai, map, 0, &depth);
1458
1459 str = "{ [0,i,1] -> [5] : 0 <= i <= 10 }";
1460 map = isl_map_read_from_str(ctx, str, -1);
1461 ai = isl_access_info_add_source(ai, map, 0, &depth);
1462
1463 flow = isl_access_info_compute_flow(ai);
1464 dim = isl_dim_alloc(ctx, 0, 3, 3);
1465 mm.must = isl_map_empty(isl_dim_copy(dim));
1466 mm.may = isl_map_empty(dim);
1467
1468 isl_flow_foreach(flow, collect_must_may, &mm);
1469
1470 str = "{ [0,i,0] -> [0,i,2] : 0 <= i <= 10; "
1471 " [0,i,1] -> [0,5,2] : 0 <= i <= 5 }";
1472 assert(map_is_equal(mm.may, str));
1473 str = "{ [i,j,k] -> [l,m,n] : 1 = 0 }";
1474 assert(map_is_equal(mm.must, str));
1475
1476 isl_map_free(mm.must);
1477 isl_map_free(mm.may);
1478 isl_flow_free(flow);
1479
1480
1481 str = "{ [0,i,1] -> [i] : 0 <= i <= 10 }";
1482 map = isl_map_read_from_str(ctx, str, -1);
1483 ai = isl_access_info_alloc(map, &depth, &common_space, 2);
1484
1485 str = "{ [0,i,0] -> [i] : 0 <= i <= 10 }";
1486 map = isl_map_read_from_str(ctx, str, -1);
1487 ai = isl_access_info_add_source(ai, map, 0, &depth);
1488
1489 str = "{ [0,i,2] -> [5] : 0 <= i <= 10 }";
1490 map = isl_map_read_from_str(ctx, str, -1);
1491 ai = isl_access_info_add_source(ai, map, 0, &depth);
1492
1493 flow = isl_access_info_compute_flow(ai);
1494 dim = isl_dim_alloc(ctx, 0, 3, 3);
1495 mm.must = isl_map_empty(isl_dim_copy(dim));
1496 mm.may = isl_map_empty(dim);
1497
1498 isl_flow_foreach(flow, collect_must_may, &mm);
1499
1500 str = "{ [0,i,0] -> [0,i,1] : 0 <= i <= 10; "
1501 " [0,i,2] -> [0,5,1] : 0 <= i <= 4 }";
1502 assert(map_is_equal(mm.may, str));
1503 str = "{ [i,j,k] -> [l,m,n] : 1 = 0 }";
1504 assert(map_is_equal(mm.must, str));
1505
1506 isl_map_free(mm.must);
1507 isl_map_free(mm.may);
1508 isl_flow_free(flow);
1509
1510
1511 depth = 5;
1512
1513 str = "{ [1,i,0,0,0] -> [i,j] : 0 <= i <= 10 and 0 <= j <= 10 }";
1514 map = isl_map_read_from_str(ctx, str, -1);
1515 ai = isl_access_info_alloc(map, &depth, &common_space, 1);
1516
1517 str = "{ [0,i,0,j,0] -> [i,j] : 0 <= i <= 10 and 0 <= j <= 10 }";
1518 map = isl_map_read_from_str(ctx, str, -1);
1519 ai = isl_access_info_add_source(ai, map, 1, &depth);
1520
1521 flow = isl_access_info_compute_flow(ai);
1522 dim = isl_dim_alloc(ctx, 0, 5, 5);
1523 mm.must = isl_map_empty(isl_dim_copy(dim));
1524 mm.may = isl_map_empty(dim);
1525
1526 isl_flow_foreach(flow, collect_must_may, &mm);
1527
1528 str = "{ [0,i,0,j,0] -> [1,i,0,0,0] : 0 <= i,j <= 10 }";
1529 assert(map_is_equal(mm.must, str));
1530 str = "{ [0,0,0,0,0] -> [0,0,0,0,0] : 1 = 0 }";
1531 assert(map_is_equal(mm.may, str));
1532
1533 isl_map_free(mm.must);
1534 isl_map_free(mm.may);
1535 isl_flow_free(flow);
1536 }
1537
1538 int test_sv(isl_ctx *ctx)
1539 {
1540 const char *str;
1541 isl_map *map;
1542 isl_union_map *umap;
1543 int sv;
1544
1545 str = "[N] -> { [i] -> [f] : 0 <= i <= N and 0 <= i - 10 f <= 9 }";
1546 map = isl_map_read_from_str(ctx, str, -1);
1547 sv = isl_map_is_single_valued(map);
1548 isl_map_free(map);
1549 if (sv < 0)
1550 return -1;
1551 if (!sv)
1552 isl_die(ctx, isl_error_internal,
1553 "map not detected as single valued", return -1);
1554
1555 str = "[N] -> { [i] -> [f] : 0 <= i <= N and 0 <= i - 10 f <= 10 }";
1556 map = isl_map_read_from_str(ctx, str, -1);
1557 sv = isl_map_is_single_valued(map);
1558 isl_map_free(map);
1559 if (sv < 0)
1560 return -1;
1561 if (sv)
1562 isl_die(ctx, isl_error_internal,
1563 "map detected as single valued", return -1);
1564
1565 str = "{ S1[i] -> [i] : 0 <= i <= 9; S2[i] -> [i] : 0 <= i <= 9 }";
1566 umap = isl_union_map_read_from_str(ctx, str);
1567 sv = isl_union_map_is_single_valued(umap);
1568 isl_union_map_free(umap);
1569 if (sv < 0)
1570 return -1;
1571 if (!sv)
1572 isl_die(ctx, isl_error_internal,
1573 "map not detected as single valued", return -1);
1574
1575 str = "{ [i] -> S1[i] : 0 <= i <= 9; [i] -> S2[i] : 0 <= i <= 9 }";
1576 umap = isl_union_map_read_from_str(ctx, str);
1577 sv = isl_union_map_is_single_valued(umap);
1578 isl_union_map_free(umap);
1579 if (sv < 0)
1580 return -1;
1581 if (sv)
1582 isl_die(ctx, isl_error_internal,
1583 "map detected as single valued", return -1);
1584
1585 return 0;
1586 }
1587
1588 void test_bijective_case(struct isl_ctx *ctx, const char *str, int bijective)
1589 {
1590 isl_map *map;
1591
1592 map = isl_map_read_from_str(ctx, str, -1);
1593 if (bijective)
1594 assert(isl_map_is_bijective(map));
1595 else
1596 assert(!isl_map_is_bijective(map));
1597 isl_map_free(map);
1598 }
1599
1600 void test_bijective(struct isl_ctx *ctx)
1601 {
1602 test_bijective_case(ctx, "[N,M]->{[i,j] -> [i]}", 0);
1603 test_bijective_case(ctx, "[N,M]->{[i,j] -> [i] : j=i}", 1);
1604 test_bijective_case(ctx, "[N,M]->{[i,j] -> [i] : j=0}", 1);
1605 test_bijective_case(ctx, "[N,M]->{[i,j] -> [i] : j=N}", 1);
1606 test_bijective_case(ctx, "[N,M]->{[i,j] -> [j,i]}", 1);
1607 test_bijective_case(ctx, "[N,M]->{[i,j] -> [i+j]}", 0);
1608 test_bijective_case(ctx, "[N,M]->{[i,j] -> []}", 0);
1609 test_bijective_case(ctx, "[N,M]->{[i,j] -> [i,j,N]}", 1);
1610 test_bijective_case(ctx, "[N,M]->{[i,j] -> [2i]}", 0);
1611 test_bijective_case(ctx, "[N,M]->{[i,j] -> [i,i]}", 0);
1612 test_bijective_case(ctx, "[N,M]->{[i,j] -> [2i,i]}", 0);
1613 test_bijective_case(ctx, "[N,M]->{[i,j] -> [2i,j]}", 1);
1614 test_bijective_case(ctx, "[N,M]->{[i,j] -> [x,y] : 2x=i & y =j}", 1);
1615 }
1616
1617 void test_pwqp(struct isl_ctx *ctx)
1618 {
1619 const char *str;
1620 isl_set *set;
1621 isl_pw_qpolynomial *pwqp1, *pwqp2;
1622
1623 str = "{ [i,j,k] -> 1 + 9 * [i/5] + 7 * [j/11] + 4 * [k/13] }";
1624 pwqp1 = isl_pw_qpolynomial_read_from_str(ctx, str);
1625
1626 pwqp1 = isl_pw_qpolynomial_move_dims(pwqp1, isl_dim_param, 0,
1627 isl_dim_set, 1, 1);
1628
1629 str = "[j] -> { [i,k] -> 1 + 9 * [i/5] + 7 * [j/11] + 4 * [k/13] }";
1630 pwqp2 = isl_pw_qpolynomial_read_from_str(ctx, str);
1631
1632 pwqp1 = isl_pw_qpolynomial_sub(pwqp1, pwqp2);
1633
1634 assert(isl_pw_qpolynomial_is_zero(pwqp1));
1635
1636 isl_pw_qpolynomial_free(pwqp1);
1637
1638 str = "{ [i] -> i }";
1639 pwqp1 = isl_pw_qpolynomial_read_from_str(ctx, str);
1640 str = "{ [k] : exists a : k = 2a }";
1641 set = isl_set_read_from_str(ctx, str, 0);
1642 pwqp1 = isl_pw_qpolynomial_gist(pwqp1, set);
1643 str = "{ [i] -> i }";
1644 pwqp2 = isl_pw_qpolynomial_read_from_str(ctx, str);
1645
1646 pwqp1 = isl_pw_qpolynomial_sub(pwqp1, pwqp2);
1647
1648 assert(isl_pw_qpolynomial_is_zero(pwqp1));
1649
1650 isl_pw_qpolynomial_free(pwqp1);
1651
1652 str = "{ [i] -> i + [ (i + [i/3])/2 ] }";
1653 pwqp1 = isl_pw_qpolynomial_read_from_str(ctx, str);
1654 str = "{ [10] }";
1655 set = isl_set_read_from_str(ctx, str, 0);
1656 pwqp1 = isl_pw_qpolynomial_gist(pwqp1, set);
1657 str = "{ [i] -> 16 }";
1658 pwqp2 = isl_pw_qpolynomial_read_from_str(ctx, str);
1659
1660 pwqp1 = isl_pw_qpolynomial_sub(pwqp1, pwqp2);
1661
1662 assert(isl_pw_qpolynomial_is_zero(pwqp1));
1663
1664 isl_pw_qpolynomial_free(pwqp1);
1665
1666 str = "{ [i] -> ([(i)/2]) }";
1667 pwqp1 = isl_pw_qpolynomial_read_from_str(ctx, str);
1668 str = "{ [k] : exists a : k = 2a+1 }";
1669 set = isl_set_read_from_str(ctx, str, 0);
1670 pwqp1 = isl_pw_qpolynomial_gist(pwqp1, set);
1671 str = "{ [i] -> -1/2 + 1/2 * i }";
1672 pwqp2 = isl_pw_qpolynomial_read_from_str(ctx, str);
1673
1674 pwqp1 = isl_pw_qpolynomial_sub(pwqp1, pwqp2);
1675
1676 assert(isl_pw_qpolynomial_is_zero(pwqp1));
1677
1678 isl_pw_qpolynomial_free(pwqp1);
1679
1680 str = "{ [i] -> ([([i/2] + [i/2])/5]) }";
1681 pwqp1 = isl_pw_qpolynomial_read_from_str(ctx, str);
1682 str = "{ [i] -> ([(2 * [i/2])/5]) }";
1683 pwqp2 = isl_pw_qpolynomial_read_from_str(ctx, str);
1684
1685 pwqp1 = isl_pw_qpolynomial_sub(pwqp1, pwqp2);
1686
1687 assert(isl_pw_qpolynomial_is_zero(pwqp1));
1688
1689 isl_pw_qpolynomial_free(pwqp1);
1690
1691 str = "{ [x] -> ([x/2] + [(x+1)/2]) }";
1692 pwqp1 = isl_pw_qpolynomial_read_from_str(ctx, str);
1693 str = "{ [x] -> x }";
1694 pwqp2 = isl_pw_qpolynomial_read_from_str(ctx, str);
1695
1696 pwqp1 = isl_pw_qpolynomial_sub(pwqp1, pwqp2);
1697
1698 assert(isl_pw_qpolynomial_is_zero(pwqp1));
1699
1700 isl_pw_qpolynomial_free(pwqp1);
1701
1702 str = "{ [i] -> ([i/2]) : i >= 0; [i] -> ([i/3]) : i < 0 }";
1703 pwqp1 = isl_pw_qpolynomial_read_from_str(ctx, str);
1704 pwqp2 = isl_pw_qpolynomial_read_from_str(ctx, str);
1705 pwqp1 = isl_pw_qpolynomial_coalesce(pwqp1);
1706 pwqp1 = isl_pw_qpolynomial_sub(pwqp1, pwqp2);
1707 assert(isl_pw_qpolynomial_is_zero(pwqp1));
1708 isl_pw_qpolynomial_free(pwqp1);
1709 }
1710
1711 void test_split_periods(isl_ctx *ctx)
1712 {
1713 const char *str;
1714 isl_pw_qpolynomial *pwqp;
1715
1716 str = "{ [U,V] -> 1/3 * U + 2/3 * V - [(U + 2V)/3] + [U/2] : "
1717 "U + 2V + 3 >= 0 and - U -2V >= 0 and - U + 10 >= 0 and "
1718 "U >= 0; [U,V] -> U^2 : U >= 100 }";
1719 pwqp = isl_pw_qpolynomial_read_from_str(ctx, str);
1720
1721 pwqp = isl_pw_qpolynomial_split_periods(pwqp, 2);
1722 assert(pwqp);
1723
1724 isl_pw_qpolynomial_free(pwqp);
1725 }
1726
1727 void test_union(isl_ctx *ctx)
1728 {
1729 const char *str;
1730 isl_union_set *uset1, *uset2;
1731 isl_union_map *umap1, *umap2;
1732
1733 str = "{ [i] : 0 <= i <= 1 }";
1734 uset1 = isl_union_set_read_from_str(ctx, str);
1735 str = "{ [1] -> [0] }";
1736 umap1 = isl_union_map_read_from_str(ctx, str);
1737
1738 umap2 = isl_union_set_lex_gt_union_set(isl_union_set_copy(uset1), uset1);
1739 assert(isl_union_map_is_equal(umap1, umap2));
1740
1741 isl_union_map_free(umap1);
1742 isl_union_map_free(umap2);
1743
1744 str = "{ A[i] -> B[i]; B[i] -> C[i]; A[0] -> C[1] }";
1745 umap1 = isl_union_map_read_from_str(ctx, str);
1746 str = "{ A[i]; B[i] }";
1747 uset1 = isl_union_set_read_from_str(ctx, str);
1748
1749 uset2 = isl_union_map_domain(umap1);
1750
1751 assert(isl_union_set_is_equal(uset1, uset2));
1752
1753 isl_union_set_free(uset1);
1754 isl_union_set_free(uset2);
1755 }
1756
1757 void test_bound(isl_ctx *ctx)
1758 {
1759 const char *str;
1760 isl_pw_qpolynomial *pwqp;
1761 isl_pw_qpolynomial_fold *pwf;
1762
1763 str = "{ [[a, b, c, d] -> [e]] -> 0 }";
1764 pwqp = isl_pw_qpolynomial_read_from_str(ctx, str);
1765 pwf = isl_pw_qpolynomial_bound(pwqp, isl_fold_max, NULL);
1766 assert(isl_pw_qpolynomial_fold_dim(pwf, isl_dim_set) == 4);
1767 isl_pw_qpolynomial_fold_free(pwf);
1768
1769 str = "{ [[x]->[x]] -> 1 : exists a : x = 2 a }";
1770 pwqp = isl_pw_qpolynomial_read_from_str(ctx, str);
1771 pwf = isl_pw_qpolynomial_bound(pwqp, isl_fold_max, NULL);
1772 assert(isl_pw_qpolynomial_fold_dim(pwf, isl_dim_set) == 1);
1773 isl_pw_qpolynomial_fold_free(pwf);
1774 }
1775
1776 void test_lift(isl_ctx *ctx)
1777 {
1778 const char *str;
1779 isl_basic_map *bmap;
1780 isl_basic_set *bset;
1781
1782 str = "{ [i0] : exists e0 : i0 = 4e0 }";
1783 bset = isl_basic_set_read_from_str(ctx, str, 0);
1784 bset = isl_basic_set_lift(bset);
1785 bmap = isl_basic_map_from_range(bset);
1786 bset = isl_basic_map_domain(bmap);
1787 isl_basic_set_free(bset);
1788 }
1789
1790 void test_subset(isl_ctx *ctx)
1791 {
1792 const char *str;
1793 isl_set *set1, *set2;
1794
1795 str = "{ [112, 0] }";
1796 set1 = isl_set_read_from_str(ctx, str, 0);
1797 str = "{ [i0, i1] : exists (e0 = [(i0 - i1)/16], e1: "
1798 "16e0 <= i0 - i1 and 16e0 >= -15 + i0 - i1 and "
1799 "16e1 <= i1 and 16e0 >= -i1 and 16e1 >= -i0 + i1) }";
1800 set2 = isl_set_read_from_str(ctx, str, 0);
1801 assert(isl_set_is_subset(set1, set2));
1802 isl_set_free(set1);
1803 isl_set_free(set2);
1804 }
1805
1806 void test_factorize(isl_ctx *ctx)
1807 {
1808 const char *str;
1809 isl_basic_set *bset;
1810 isl_factorizer *f;
1811
1812 str = "{ [i0, i1, i2, i3, i4, i5, i6, i7] : 3i5 <= 2 - 2i0 and "
1813 "i0 >= -2 and i6 >= 1 + i3 and i7 >= 0 and 3i5 >= -2i0 and "
1814 "2i4 <= i2 and i6 >= 1 + 2i0 + 3i1 and i4 <= -1 and "
1815 "i6 >= 1 + 2i0 + 3i5 and i6 <= 2 + 2i0 + 3i5 and "
1816 "3i5 <= 2 - 2i0 - i2 + 3i4 and i6 <= 2 + 2i0 + 3i1 and "
1817 "i0 <= -1 and i7 <= i2 + i3 - 3i4 - i6 and "
1818 "3i5 >= -2i0 - i2 + 3i4 }";
1819 bset = isl_basic_set_read_from_str(ctx, str, 0);
1820 f = isl_basic_set_factorizer(bset);
1821 assert(f);
1822 isl_basic_set_free(bset);
1823 isl_factorizer_free(f);
1824
1825 str = "{ [i0, i1, i2, i3, i4, i5, i6, i7, i8, i9, i10, i11, i12] : "
1826 "i12 <= 2 + i0 - i11 and 2i8 >= -i4 and i11 >= i1 and "
1827 "3i5 <= -i2 and 2i11 >= -i4 - 2i7 and i11 <= 3 + i0 + 3i9 and "
1828 "i11 <= -i4 - 2i7 and i12 >= -i10 and i2 >= -2 and "
1829 "i11 >= i1 + 3i10 and i11 >= 1 + i0 + 3i9 and "
1830 "i11 <= 1 - i4 - 2i8 and 6i6 <= 6 - i2 and 3i6 >= 1 - i2 and "
1831 "i11 <= 2 + i1 and i12 <= i4 + i11 and i12 >= i0 - i11 and "
1832 "3i5 >= -2 - i2 and i12 >= -1 + i4 + i11 and 3i3 <= 3 - i2 and "
1833 "9i6 <= 11 - i2 + 6i5 and 3i3 >= 1 - i2 and "
1834 "9i6 <= 5 - i2 + 6i3 and i12 <= -1 and i2 <= 0 }";
1835 bset = isl_basic_set_read_from_str(ctx, str, 0);
1836 f = isl_basic_set_factorizer(bset);
1837 assert(f);
1838 isl_basic_set_free(bset);
1839 isl_factorizer_free(f);
1840 }
1841
1842 static int check_injective(__isl_take isl_map *map, void *user)
1843 {
1844 int *injective = user;
1845
1846 *injective = isl_map_is_injective(map);
1847 isl_map_free(map);
1848
1849 if (*injective < 0 || !*injective)
1850 return -1;
1851
1852 return 0;
1853 }
1854
1855 int test_one_schedule(isl_ctx *ctx, const char *d, const char *w,
1856 const char *r, const char *s, int tilable, int parallel)
1857 {
1858 int i;
1859 isl_union_set *D;
1860 isl_union_map *W, *R, *S;
1861 isl_union_map *empty;
1862 isl_union_map *dep_raw, *dep_war, *dep_waw, *dep;
1863 isl_union_map *validity, *proximity;
1864 isl_union_map *schedule;
1865 isl_union_map *test;
1866 isl_union_set *delta;
1867 isl_union_set *domain;
1868 isl_set *delta_set;
1869 isl_set *slice;
1870 isl_set *origin;
1871 isl_schedule *sched;
1872 int is_nonneg, is_parallel, is_tilable, is_injection, is_complete;
1873
1874 D = isl_union_set_read_from_str(ctx, d);
1875 W = isl_union_map_read_from_str(ctx, w);
1876 R = isl_union_map_read_from_str(ctx, r);
1877 S = isl_union_map_read_from_str(ctx, s);
1878
1879 W = isl_union_map_intersect_domain(W, isl_union_set_copy(D));
1880 R = isl_union_map_intersect_domain(R, isl_union_set_copy(D));
1881
1882 empty = isl_union_map_empty(isl_union_map_get_dim(S));
1883 isl_union_map_compute_flow(isl_union_map_copy(R),
1884 isl_union_map_copy(W), empty,
1885 isl_union_map_copy(S),
1886 &dep_raw, NULL, NULL, NULL);
1887 isl_union_map_compute_flow(isl_union_map_copy(W),
1888 isl_union_map_copy(W),
1889 isl_union_map_copy(R),
1890 isl_union_map_copy(S),
1891 &dep_waw, &dep_war, NULL, NULL);
1892
1893 dep = isl_union_map_union(dep_waw, dep_war);
1894 dep = isl_union_map_union(dep, dep_raw);
1895 validity = isl_union_map_copy(dep);
1896 proximity = isl_union_map_copy(dep);
1897
1898 sched = isl_union_set_compute_schedule(isl_union_set_copy(D),
1899 validity, proximity);
1900 schedule = isl_schedule_get_map(sched);
1901 isl_schedule_free(sched);
1902 isl_union_map_free(W);
1903 isl_union_map_free(R);
1904 isl_union_map_free(S);
1905
1906 is_injection = 1;
1907 isl_union_map_foreach_map(schedule, &check_injective, &is_injection);
1908
1909 domain = isl_union_map_domain(isl_union_map_copy(schedule));
1910 is_complete = isl_union_set_is_subset(D, domain);
1911 isl_union_set_free(D);
1912 isl_union_set_free(domain);
1913
1914 test = isl_union_map_reverse(isl_union_map_copy(schedule));
1915 test = isl_union_map_apply_range(test, dep);
1916 test = isl_union_map_apply_range(test, schedule);
1917
1918 delta = isl_union_map_deltas(test);
1919 if (isl_union_set_n_set(delta) == 0) {
1920 is_tilable = 1;
1921 is_parallel = 1;
1922 is_nonneg = 1;
1923 } else {
1924 delta_set = isl_union_set_copy_set(delta);
1925
1926 slice = isl_set_universe(isl_set_get_dim(delta_set));
1927 for (i = 0; i < tilable; ++i)
1928 slice = isl_set_lower_bound_si(slice, isl_dim_set, i, 0);
1929 is_tilable = isl_set_is_subset(delta_set, slice);
1930 isl_set_free(slice);
1931
1932 slice = isl_set_universe(isl_set_get_dim(delta_set));
1933 for (i = 0; i < parallel; ++i)
1934 slice = isl_set_fix_si(slice, isl_dim_set, i, 0);
1935 is_parallel = isl_set_is_subset(delta_set, slice);
1936 isl_set_free(slice);
1937
1938 origin = isl_set_universe(isl_set_get_dim(delta_set));
1939 for (i = 0; i < isl_set_dim(origin, isl_dim_set); ++i)
1940 origin = isl_set_fix_si(origin, isl_dim_set, i, 0);
1941
1942 delta_set = isl_set_union(delta_set, isl_set_copy(origin));
1943 delta_set = isl_set_lexmin(delta_set);
1944
1945 is_nonneg = isl_set_is_equal(delta_set, origin);
1946
1947 isl_set_free(origin);
1948 isl_set_free(delta_set);
1949 }
1950 isl_union_set_free(delta);
1951
1952 if (is_nonneg < 0 || is_parallel < 0 || is_tilable < 0 ||
1953 is_injection < 0 || is_complete < 0)
1954 return -1;
1955 if (!is_complete)
1956 isl_die(ctx, isl_error_unknown,
1957 "generated schedule incomplete", return -1);
1958 if (!is_injection)
1959 isl_die(ctx, isl_error_unknown,
1960 "generated schedule not injective on each statement",
1961 return -1);
1962 if (!is_nonneg)
1963 isl_die(ctx, isl_error_unknown,
1964 "negative dependences in generated schedule",
1965 return -1);
1966 if (!is_tilable)
1967 isl_die(ctx, isl_error_unknown,
1968 "generated schedule not as tilable as expected",
1969 return -1);
1970 if (!is_parallel)
1971 isl_die(ctx, isl_error_unknown,
1972 "generated schedule not as parallel as expected",
1973 return -1);
1974
1975 return 0;
1976 }
1977
1978 int test_special_schedule(isl_ctx *ctx)
1979 {
1980 const char *str;
1981 isl_union_set *dom;
1982 isl_union_map *empty;
1983 isl_union_map *dep;
1984 isl_union_map *sched1, *sched2;
1985 isl_schedule *schedule;
1986 int equal;
1987
1988 str = "{ S[i,j] : 0 <= i <= 10 }";
1989 dom = isl_union_set_read_from_str(ctx, str);
1990 str = "{ S[i,j] -> S[i+1,j] : 0 <= i,j <= 10 }";
1991 dep = isl_union_map_read_from_str(ctx, str);
1992 empty = isl_union_map_read_from_str(ctx, "{}");
1993 schedule = isl_union_set_compute_schedule(dom, empty, dep);
1994 sched1 = isl_schedule_get_map(schedule);
1995 isl_schedule_free(schedule);
1996
1997 str = "{ S[i, j] -> [j, i] }";
1998 sched2 = isl_union_map_read_from_str(ctx, str);
1999
2000 equal = isl_union_map_is_equal(sched1, sched2);
2001 isl_union_map_free(sched1);
2002 isl_union_map_free(sched2);
2003
2004 if (equal < 0)
2005 return -1;
2006 if (!equal)
2007 isl_die(ctx, isl_error_unknown, "unexpected schedule",
2008 return -1);
2009
2010 return 0;
2011 }
2012
2013 int test_schedule(isl_ctx *ctx)
2014 {
2015 const char *D, *W, *R, *S;
2016
2017 /* Jacobi */
2018 D = "[T,N] -> { S1[t,i] : 1 <= t <= T and 2 <= i <= N - 1 }";
2019 W = "{ S1[t,i] -> a[t,i] }";
2020 R = "{ S1[t,i] -> a[t-1,i]; S1[t,i] -> a[t-1,i-1]; "
2021 "S1[t,i] -> a[t-1,i+1] }";
2022 S = "{ S1[t,i] -> [t,i] }";
2023 if (test_one_schedule(ctx, D, W, R, S, 2, 0) < 0)
2024 return -1;
2025
2026 /* Fig. 5 of CC2008 */
2027 D = "[N] -> { S_0[i, j] : i >= 0 and i <= -1 + N and j >= 2 and "
2028 "j <= -1 + N }";
2029 W = "[N] -> { S_0[i, j] -> a[i, j] : i >= 0 and i <= -1 + N and "
2030 "j >= 2 and j <= -1 + N }";
2031 R = "[N] -> { S_0[i, j] -> a[j, i] : i >= 0 and i <= -1 + N and "
2032 "j >= 2 and j <= -1 + N; "
2033 "S_0[i, j] -> a[i, -1 + j] : i >= 0 and i <= -1 + N and "
2034 "j >= 2 and j <= -1 + N }";
2035 S = "[N] -> { S_0[i, j] -> [0, i, 0, j, 0] }";
2036 if (test_one_schedule(ctx, D, W, R, S, 2, 0) < 0)
2037 return -1;
2038
2039 D = "{ S1[i] : 0 <= i <= 10; S2[i] : 0 <= i <= 9 }";
2040 W = "{ S1[i] -> a[i] }";
2041 R = "{ S2[i] -> a[i+1] }";
2042 S = "{ S1[i] -> [0,i]; S2[i] -> [1,i] }";
2043 if (test_one_schedule(ctx, D, W, R, S, 1, 1) < 0)
2044 return -1;
2045
2046 D = "{ S1[i] : 0 <= i < 10; S2[i] : 0 <= i < 10 }";
2047 W = "{ S1[i] -> a[i] }";
2048 R = "{ S2[i] -> a[9-i] }";
2049 S = "{ S1[i] -> [0,i]; S2[i] -> [1,i] }";
2050 if (test_one_schedule(ctx, D, W, R, S, 1, 1) < 0)
2051 return -1;
2052
2053 D = "[N] -> { S1[i] : 0 <= i < N; S2[i] : 0 <= i < N }";
2054 W = "{ S1[i] -> a[i] }";
2055 R = "[N] -> { S2[i] -> a[N-1-i] }";
2056 S = "{ S1[i] -> [0,i]; S2[i] -> [1,i] }";
2057 if (test_one_schedule(ctx, D, W, R, S, 1, 1) < 0)
2058 return -1;
2059
2060 D = "{ S1[i] : 0 < i < 10; S2[i] : 0 <= i < 10 }";
2061 W = "{ S1[i] -> a[i]; S2[i] -> b[i] }";
2062 R = "{ S2[i] -> a[i]; S1[i] -> b[i-1] }";
2063 S = "{ S1[i] -> [i,0]; S2[i] -> [i,1] }";
2064 if (test_one_schedule(ctx, D, W, R, S, 0, 0) < 0)
2065 return -1;
2066
2067 D = "[N] -> { S1[i] : 1 <= i <= N; S2[i,j] : 1 <= i,j <= N }";
2068 W = "{ S1[i] -> a[0,i]; S2[i,j] -> a[i,j] }";
2069 R = "{ S2[i,j] -> a[i-1,j] }";
2070 S = "{ S1[i] -> [0,i,0]; S2[i,j] -> [1,i,j] }";
2071 if (test_one_schedule(ctx, D, W, R, S, 2, 1) < 0)
2072 return -1;
2073
2074 D = "[N] -> { S1[i] : 1 <= i <= N; S2[i,j] : 1 <= i,j <= N }";
2075 W = "{ S1[i] -> a[i,0]; S2[i,j] -> a[i,j] }";
2076 R = "{ S2[i,j] -> a[i,j-1] }";
2077 S = "{ S1[i] -> [0,i,0]; S2[i,j] -> [1,i,j] }";
2078 if (test_one_schedule(ctx, D, W, R, S, 2, 1) < 0)
2079 return -1;
2080
2081 D = "[N] -> { S_0[]; S_1[i] : i >= 0 and i <= -1 + N; S_2[] }";
2082 W = "[N] -> { S_0[] -> a[0]; S_2[] -> b[0]; "
2083 "S_1[i] -> a[1 + i] : i >= 0 and i <= -1 + N }";
2084 R = "[N] -> { S_2[] -> a[N]; S_1[i] -> a[i] : i >= 0 and i <= -1 + N }";
2085 S = "[N] -> { S_1[i] -> [1, i, 0]; S_2[] -> [2, 0, 1]; "
2086 "S_0[] -> [0, 0, 0] }";
2087 if (test_one_schedule(ctx, D, W, R, S, 1, 0) < 0)
2088 return -1;
2089 ctx->opt->schedule_parametric = 0;
2090 if (test_one_schedule(ctx, D, W, R, S, 0, 0) < 0)
2091 return -1;
2092 ctx->opt->schedule_parametric = 1;
2093
2094 D = "[N] -> { S1[i] : 1 <= i <= N; S2[i] : 1 <= i <= N; "
2095 "S3[i,j] : 1 <= i,j <= N; S4[i] : 1 <= i <= N }";
2096 W = "{ S1[i] -> a[i,0]; S2[i] -> a[0,i]; S3[i,j] -> a[i,j] }";
2097 R = "[N] -> { S3[i,j] -> a[i-1,j]; S3[i,j] -> a[i,j-1]; "
2098 "S4[i] -> a[i,N] }";
2099 S = "{ S1[i] -> [0,i,0]; S2[i] -> [1,i,0]; S3[i,j] -> [2,i,j]; "
2100 "S4[i] -> [4,i,0] }";
2101 if (test_one_schedule(ctx, D, W, R, S, 2, 0) < 0)
2102 return -1;
2103
2104 D = "[N] -> { S_0[i, j] : i >= 1 and i <= N and j >= 1 and j <= N }";
2105 W = "[N] -> { S_0[i, j] -> s[0] : i >= 1 and i <= N and j >= 1 and "
2106 "j <= N }";
2107 R = "[N] -> { S_0[i, j] -> s[0] : i >= 1 and i <= N and j >= 1 and "
2108 "j <= N; "
2109 "S_0[i, j] -> a[i, j] : i >= 1 and i <= N and j >= 1 and "
2110 "j <= N }";
2111 S = "[N] -> { S_0[i, j] -> [0, i, 0, j, 0] }";
2112 if (test_one_schedule(ctx, D, W, R, S, 0, 0) < 0)
2113 return -1;
2114
2115 D = "[N] -> { S_0[t] : t >= 0 and t <= -1 + N; "
2116 " S_2[t] : t >= 0 and t <= -1 + N; "
2117 " S_1[t, i] : t >= 0 and t <= -1 + N and i >= 0 and "
2118 "i <= -1 + N }";
2119 W = "[N] -> { S_0[t] -> a[t, 0] : t >= 0 and t <= -1 + N; "
2120 " S_2[t] -> b[t] : t >= 0 and t <= -1 + N; "
2121 " S_1[t, i] -> a[t, 1 + i] : t >= 0 and t <= -1 + N and "
2122 "i >= 0 and i <= -1 + N }";
2123 R = "[N] -> { S_1[t, i] -> a[t, i] : t >= 0 and t <= -1 + N and "
2124 "i >= 0 and i <= -1 + N; "
2125 " S_2[t] -> a[t, N] : t >= 0 and t <= -1 + N }";
2126 S = "[N] -> { S_2[t] -> [0, t, 2]; S_1[t, i] -> [0, t, 1, i, 0]; "
2127 " S_0[t] -> [0, t, 0] }";
2128
2129 if (test_one_schedule(ctx, D, W, R, S, 2, 1) < 0)
2130 return -1;
2131 ctx->opt->schedule_parametric = 0;
2132 if (test_one_schedule(ctx, D, W, R, S, 0, 0) < 0)
2133 return -1;
2134 ctx->opt->schedule_parametric = 1;
2135
2136 D = "[N] -> { S1[i,j] : 0 <= i,j < N; S2[i,j] : 0 <= i,j < N }";
2137 S = "{ S1[i,j] -> [0,i,j]; S2[i,j] -> [1,i,j] }";
2138 if (test_one_schedule(ctx, D, "{}", "{}", S, 2, 2) < 0)
2139 return -1;
2140
2141 D = "[M, N] -> { S_1[i] : i >= 0 and i <= -1 + M; "
2142 "S_0[i, j] : i >= 0 and i <= -1 + M and j >= 0 and j <= -1 + N }";
2143 W = "[M, N] -> { S_0[i, j] -> a[j] : i >= 0 and i <= -1 + M and "
2144 "j >= 0 and j <= -1 + N; "
2145 "S_1[i] -> b[0] : i >= 0 and i <= -1 + M }";
2146 R = "[M, N] -> { S_0[i, j] -> a[0] : i >= 0 and i <= -1 + M and "
2147 "j >= 0 and j <= -1 + N; "
2148 "S_1[i] -> b[0] : i >= 0 and i <= -1 + M }";
2149 S = "[M, N] -> { S_1[i] -> [1, i, 0]; S_0[i, j] -> [0, i, 0, j, 0] }";
2150 if (test_one_schedule(ctx, D, W, R, S, 0, 0) < 0)
2151 return -1;
2152
2153 D = "{ S_0[i] : i >= 0 }";
2154 W = "{ S_0[i] -> a[i] : i >= 0 }";
2155 R = "{ S_0[i] -> a[0] : i >= 0 }";
2156 S = "{ S_0[i] -> [0, i, 0] }";
2157 if (test_one_schedule(ctx, D, W, R, S, 0, 0) < 0)
2158 return -1;
2159
2160 D = "{ S_0[i] : i >= 0; S_1[i] : i >= 0 }";
2161 W = "{ S_0[i] -> a[i] : i >= 0; S_1[i] -> b[i] : i >= 0 }";
2162 R = "{ S_0[i] -> b[0] : i >= 0; S_1[i] -> a[i] : i >= 0 }";
2163 S = "{ S_1[i] -> [0, i, 1]; S_0[i] -> [0, i, 0] }";
2164 if (test_one_schedule(ctx, D, W, R, S, 0, 0) < 0)
2165 return -1;
2166
2167 return test_special_schedule(ctx);
2168 }
2169
2170 int test_plain_injective(isl_ctx *ctx, const char *str, int injective)
2171 {
2172 isl_union_map *umap;
2173 int test;
2174
2175 umap = isl_union_map_read_from_str(ctx, str);
2176 test = isl_union_map_plain_is_injective(umap);
2177 isl_union_map_free(umap);
2178 if (test < 0)
2179 return -1;
2180 if (test == injective)
2181 return 0;
2182 if (injective)
2183 isl_die(ctx, isl_error_unknown,
2184 "map not detected as injective", return -1);
2185 else
2186 isl_die(ctx, isl_error_unknown,
2187 "map detected as injective", return -1);
2188 }
2189
2190 int test_injective(isl_ctx *ctx)
2191 {
2192 const char *str;
2193
2194 if (test_plain_injective(ctx, "{S[i,j] -> A[0]; T[i,j] -> B[1]}", 0))
2195 return -1;
2196 if (test_plain_injective(ctx, "{S[] -> A[0]; T[] -> B[0]}", 1))
2197 return -1;
2198 if (test_plain_injective(ctx, "{S[] -> A[0]; T[] -> A[1]}", 1))
2199 return -1;
2200 if (test_plain_injective(ctx, "{S[] -> A[0]; T[] -> A[0]}", 0))
2201 return -1;
2202 if (test_plain_injective(ctx, "{S[i] -> A[i,0]; T[i] -> A[i,1]}", 1))
2203 return -1;
2204 if (test_plain_injective(ctx, "{S[i] -> A[i]; T[i] -> A[i]}", 0))
2205 return -1;
2206 if (test_plain_injective(ctx, "{S[] -> A[0,0]; T[] -> A[0,1]}", 1))
2207 return -1;
2208 if (test_plain_injective(ctx, "{S[] -> A[0,0]; T[] -> A[1,0]}", 1))
2209 return -1;
2210
2211 str = "{S[] -> A[0,0]; T[] -> A[0,1]; U[] -> A[1,0]}";
2212 if (test_plain_injective(ctx, str, 1))
2213 return -1;
2214 str = "{S[] -> A[0,0]; T[] -> A[0,1]; U[] -> A[0,0]}";
2215 if (test_plain_injective(ctx, str, 0))
2216 return -1;
2217
2218 return 0;
2219 }
2220
2221 int test_aff(isl_ctx *ctx)
2222 {
2223 const char *str;
2224 isl_set *set;
2225 isl_dim *dim;
2226 isl_local_space *ls;
2227 isl_aff *aff;
2228 int zero;
2229
2230 dim = isl_dim_set_alloc(ctx, 0, 1);
2231 ls = isl_local_space_from_dim(dim);
2232 aff = isl_aff_zero(ls);
2233
2234 aff = isl_aff_add_coefficient_si(aff, isl_dim_set, 0, 1);
2235 aff = isl_aff_scale_down_ui(aff, 3);
2236 aff = isl_aff_floor(aff);
2237 aff = isl_aff_add_coefficient_si(aff, isl_dim_set, 0, 1);
2238 aff = isl_aff_scale_down_ui(aff, 2);
2239 aff = isl_aff_floor(aff);
2240 aff = isl_aff_add_coefficient_si(aff, isl_dim_set, 0, 1);
2241
2242 str = "{ [10] }";
2243 set = isl_set_read_from_str(ctx, str, 0);
2244 aff = isl_aff_gist(aff, set);
2245
2246 aff = isl_aff_add_constant_si(aff, -16);
2247 zero = isl_aff_plain_is_zero(aff);
2248 isl_aff_free(aff);
2249
2250 if (zero < 0)
2251 return -1;
2252 if (!zero)
2253 isl_die(ctx, isl_error_unknown, "unexpected result", return -1);
2254
2255 return 0;
2256 }
2257
2258 int test_dim_max(isl_ctx *ctx)
2259 {
2260 int equal;
2261 const char *str;
2262 isl_map *map, *map2;
2263 isl_set *set;
2264 isl_pw_aff *pwaff;
2265
2266 str = "[N] -> { [i] : 0 <= i <= min(N,10) }";
2267 set = isl_set_read_from_str(ctx, str, -1);
2268 pwaff = isl_set_dim_max(set, 0);
2269 map = isl_map_from_pw_aff(pwaff);
2270 str = "[N] -> { [] -> [10] : N >= 10; [] -> [N] : N <= 9 and N >= 0 }";
2271 map2 = isl_map_read_from_str(ctx, str, -1);
2272 equal = isl_map_is_equal(map, map2);
2273 isl_map_free(map);
2274 isl_map_free(map2);
2275 if (equal < 0)
2276 return -1;
2277 if (!equal)
2278 isl_die(ctx, isl_error_unknown, "unexpected result", return -1);
2279
2280 str = "[N] -> { [i] : 0 <= i <= max(2N,N+6) }";
2281 set = isl_set_read_from_str(ctx, str, -1);
2282 pwaff = isl_set_dim_max(set, 0);
2283 map = isl_map_from_pw_aff(pwaff);
2284 str = "[N] -> { [] -> [6 + N] : -6 <= N <= 5; [] -> [2N] : N >= 6 }";
2285 map2 = isl_map_read_from_str(ctx, str, -1);
2286 equal = isl_map_is_equal(map, map2);
2287 isl_map_free(map);
2288 isl_map_free(map2);
2289 if (equal < 0)
2290 return -1;
2291 if (!equal)
2292 isl_die(ctx, isl_error_unknown, "unexpected result", return -1);
2293
2294 str = "[N] -> { [i] : 0 <= i <= 2N or 0 <= i <= N+6 }";
2295 set = isl_set_read_from_str(ctx, str, -1);
2296 pwaff = isl_set_dim_max(set, 0);
2297 map = isl_map_from_pw_aff(pwaff);
2298 str = "[N] -> { [] -> [6 + N] : -6 <= N <= 5; [] -> [2N] : N >= 6 }";
2299 map2 = isl_map_read_from_str(ctx, str, -1);
2300 equal = isl_map_is_equal(map, map2);
2301 isl_map_free(map);
2302 isl_map_free(map2);
2303 if (equal < 0)
2304 return -1;
2305 if (!equal)
2306 isl_die(ctx, isl_error_unknown, "unexpected result", return -1);
2307
2308 str = "[N,M] -> { [i,j] -> [([i/16]), i%16, ([j/16]), j%16] : "
2309 "0 <= i < N and 0 <= j < M }";
2310 map = isl_map_read_from_str(ctx, str, -1);
2311 set = isl_map_range(map);
2312
2313 pwaff = isl_set_dim_max(isl_set_copy(set), 0);
2314 map = isl_map_from_pw_aff(pwaff);
2315 str = "[N,M] -> { [] -> [([(N-1)/16])] : M,N > 0 }";
2316 map2 = isl_map_read_from_str(ctx, str, -1);
2317 equal = isl_map_is_equal(map, map2);
2318 isl_map_free(map);
2319 isl_map_free(map2);
2320
2321 pwaff = isl_set_dim_max(isl_set_copy(set), 3);
2322 map = isl_map_from_pw_aff(pwaff);
2323 str = "[N,M] -> { [] -> [t] : t = min(M-1,15) and M,N > 0 }";
2324 map2 = isl_map_read_from_str(ctx, str, -1);
2325 if (equal >= 0 && equal)
2326 equal = isl_map_is_equal(map, map2);
2327 isl_map_free(map);
2328 isl_map_free(map2);
2329
2330 isl_set_free(set);
2331
2332 if (equal < 0)
2333 return -1;
2334 if (!equal)
2335 isl_die(ctx, isl_error_unknown, "unexpected result", return -1);
2336
2337 return 0;
2338 }
2339
2340 int main()
2341 {
2342 struct isl_ctx *ctx;
2343
2344 srcdir = getenv("srcdir");
2345 assert(srcdir);
2346
2347 ctx = isl_ctx_alloc();
2348 if (test_dim_max(ctx) < 0)
2349 goto error;
2350 if (test_aff(ctx) < 0)
2351 goto error;
2352 if (test_injective(ctx) < 0)
2353 goto error;
2354 if (test_schedule(ctx) < 0)
2355 goto error;
2356 test_factorize(ctx);
2357 test_subset(ctx);
2358 test_lift(ctx);
2359 test_bound(ctx);
2360 test_union(ctx);
2361 test_split_periods(ctx);
2362 test_parse(ctx);
2363 test_pwqp(ctx);
2364 test_lex(ctx);
2365 if (test_sv(ctx) < 0)
2366 goto error;
2367 test_bijective(ctx);
2368 test_dep(ctx);
2369 test_read(ctx);
2370 test_bounded(ctx);
2371 test_construction(ctx);
2372 test_dim(ctx);
2373 test_div(ctx);
2374 test_application(ctx);
2375 test_affine_hull(ctx);
2376 test_convex_hull(ctx);
2377 test_gist(ctx);
2378 test_coalesce(ctx);
2379 test_closure(ctx);
2380 test_lexmin(ctx);
2381 isl_ctx_free(ctx);
2382 return 0;
2383 error:
2384 isl_ctx_free(ctx);
2385 return -1;
2386 }
Integer set library