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configure.ac: remove spurious ","
[isl.git] / isl_test.c
blob4cb7de37c2be74d30ef388ab17b3c2a0e847d634
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 #include <isl_options_private.h>
24 #include <isl/vertices.h>
25
26 static char *srcdir;
27
28 static char *get_filename(isl_ctx *ctx, const char *name, const char *suffix) {
29 char *filename;
30 int length;
31 char *pattern = "%s/test_inputs/%s.%s";
32
33 length = strlen(pattern) - 6 + strlen(srcdir) + strlen(name)
34 + strlen(suffix) + 1;
35 filename = isl_alloc_array(ctx, char, length);
36
37 if (!filename)
38 return NULL;
39
40 sprintf(filename, pattern, srcdir, name, suffix);
41
42 return filename;
43 }
44
45 void test_parse_map(isl_ctx *ctx, const char *str)
46 {
47 isl_map *map;
48
49 map = isl_map_read_from_str(ctx, str);
50 assert(map);
51 isl_map_free(map);
52 }
53
54 void test_parse_map_equal(isl_ctx *ctx, const char *str, const char *str2)
55 {
56 isl_map *map, *map2;
57
58 map = isl_map_read_from_str(ctx, str);
59 map2 = isl_map_read_from_str(ctx, str2);
60 assert(map && map2 && isl_map_is_equal(map, map2));
61 isl_map_free(map);
62 isl_map_free(map2);
63 }
64
65 void test_parse_pwqp(isl_ctx *ctx, const char *str)
66 {
67 isl_pw_qpolynomial *pwqp;
68
69 pwqp = isl_pw_qpolynomial_read_from_str(ctx, str);
70 assert(pwqp);
71 isl_pw_qpolynomial_free(pwqp);
72 }
73
74 static void test_parse_pwaff(isl_ctx *ctx, const char *str)
75 {
76 isl_pw_aff *pwaff;
77
78 pwaff = isl_pw_aff_read_from_str(ctx, str);
79 assert(pwaff);
80 isl_pw_aff_free(pwaff);
81 }
82
83 void test_parse(struct isl_ctx *ctx)
84 {
85 isl_map *map, *map2;
86 const char *str, *str2;
87
88 str = "{ [i] -> [-i] }";
89 map = isl_map_read_from_str(ctx, str);
90 assert(map);
91 isl_map_free(map);
92
93 str = "{ A[i] -> L[([i/3])] }";
94 map = isl_map_read_from_str(ctx, str);
95 assert(map);
96 isl_map_free(map);
97
98 test_parse_map(ctx, "{[[s] -> A[i]] -> [[s+1] -> A[i]]}");
99 test_parse_map(ctx, "{ [p1, y1, y2] -> [2, y1, y2] : "
100 "p1 = 1 && (y1 <= y2 || y2 = 0) }");
101
102 str = "{ [x,y] : [([x/2]+y)/3] >= 1 }";
103 str2 = "{ [x, y] : 2y >= 6 - x }";
104 test_parse_map_equal(ctx, str, str2);
105
106 test_parse_map_equal(ctx, "{ [x,y] : x <= min(y, 2*y+3) }",
107 "{ [x,y] : x <= y, 2*y + 3 }");
108 str = "{ [x, y] : (y <= x and y >= -3) or (2y <= -3 + x and y <= -4) }";
109 test_parse_map_equal(ctx, "{ [x,y] : x >= min(y, 2*y+3) }", str);
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);
113 str = "{ [new, old] -> [o0, o1] : "
114 "exists (e0 = [(-1 - new + o0)/2], e1 = [(-1 - old + o1)/2]: "
115 "2e0 = -1 - new + o0 and 2e1 = -1 - old + o1 and o0 >= 0 and "
116 "o0 <= 1 and o1 >= 0 and o1 <= 1) }";
117 map2 = isl_map_read_from_str(ctx, str);
118 assert(isl_map_is_equal(map, map2));
119 isl_map_free(map);
120 isl_map_free(map2);
121
122 str = "{[new,old] -> [new+1-2*[(new+1)/2],old+1-2*[(old+1)/2]]}";
123 map = isl_map_read_from_str(ctx, str);
124 str = "{[new,old] -> [(new+1)%2,(old+1)%2]}";
125 map2 = isl_map_read_from_str(ctx, str);
126 assert(isl_map_is_equal(map, map2));
127 isl_map_free(map);
128 isl_map_free(map2);
129
130 str = "[n] -> { [c1] : c1>=0 and c1<=floord(n-4,3) }";
131 str2 = "[n] -> { [c1] : c1 >= 0 and 3c1 <= -4 + n }";
132 test_parse_map_equal(ctx, str, str2);
133
134 str = "{ [i,j] -> [i] : i < j; [i,j] -> [j] : j <= i }";
135 str2 = "{ [i,j] -> [min(i,j)] }";
136 test_parse_map_equal(ctx, str, str2);
137
138 str = "{ [i,j] : i != j }";
139 str2 = "{ [i,j] : i < j or i > j }";
140 test_parse_map_equal(ctx, str, str2);
141
142 str = "{ [i,j] : (i+1)*2 >= j }";
143 str2 = "{ [i, j] : j <= 2 + 2i }";
144 test_parse_map_equal(ctx, str, str2);
145
146 str = "{ [i] -> [i > 0 ? 4 : 5] }";
147 str2 = "{ [i] -> [5] : i <= 0; [i] -> [4] : i >= 1 }";
148 test_parse_map_equal(ctx, str, str2);
149
150 str = "[N=2,M] -> { [i=[(M+N)/4]] }";
151 str2 = "[N, M] -> { [i] : N = 2 and 4i <= 2 + M and 4i >= -1 + M }";
152 test_parse_map_equal(ctx, str, str2);
153
154 str = "{ [x] : x >= 0 }";
155 str2 = "{ [x] : x-0 >= 0 }";
156 test_parse_map_equal(ctx, str, str2);
157
158 str = "{ [i] : ((i > 10)) }";
159 str2 = "{ [i] : i >= 11 }";
160 test_parse_map_equal(ctx, str, str2);
161
162 str = "{ [i] -> [0] }";
163 str2 = "{ [i] -> [0 * i] }";
164 test_parse_map_equal(ctx, str, str2);
165
166 test_parse_pwqp(ctx, "{ [i] -> i + [ (i + [i/3])/2 ] }");
167 test_parse_map(ctx, "{ S1[i] -> [([i/10]),i%10] : 0 <= i <= 45 }");
168 test_parse_pwaff(ctx, "{ [i] -> [i + 1] : i > 0; [a] -> [a] : a < 0 }");
169 test_parse_pwqp(ctx, "{ [x] -> ([(x)/2] * [(x)/3]) }");
170 }
171
172 void test_read(struct isl_ctx *ctx)
173 {
174 char *filename;
175 FILE *input;
176 struct isl_basic_set *bset1, *bset2;
177 const char *str = "{[y]: Exists ( alpha : 2alpha = y)}";
178
179 filename = get_filename(ctx, "set", "omega");
180 assert(filename);
181 input = fopen(filename, "r");
182 assert(input);
183
184 bset1 = isl_basic_set_read_from_file(ctx, input);
185 bset2 = isl_basic_set_read_from_str(ctx, str);
186
187 assert(isl_basic_set_is_equal(bset1, bset2) == 1);
188
189 isl_basic_set_free(bset1);
190 isl_basic_set_free(bset2);
191 free(filename);
192
193 fclose(input);
194 }
195
196 void test_bounded(struct isl_ctx *ctx)
197 {
198 isl_set *set;
199 int bounded;
200
201 set = isl_set_read_from_str(ctx, "[n] -> {[i] : 0 <= i <= n }");
202 bounded = isl_set_is_bounded(set);
203 assert(bounded);
204 isl_set_free(set);
205
206 set = isl_set_read_from_str(ctx, "{[n, i] : 0 <= i <= n }");
207 bounded = isl_set_is_bounded(set);
208 assert(!bounded);
209 isl_set_free(set);
210
211 set = isl_set_read_from_str(ctx, "[n] -> {[i] : i <= n }");
212 bounded = isl_set_is_bounded(set);
213 assert(!bounded);
214 isl_set_free(set);
215 }
216
217 /* Construct the basic set { [i] : 5 <= i <= N } */
218 void test_construction(struct isl_ctx *ctx)
219 {
220 isl_int v;
221 isl_space *dim;
222 isl_local_space *ls;
223 struct isl_basic_set *bset;
224 struct isl_constraint *c;
225
226 isl_int_init(v);
227
228 dim = isl_space_set_alloc(ctx, 1, 1);
229 bset = isl_basic_set_universe(isl_space_copy(dim));
230 ls = isl_local_space_from_space(dim);
231
232 c = isl_inequality_alloc(isl_local_space_copy(ls));
233 isl_int_set_si(v, -1);
234 isl_constraint_set_coefficient(c, isl_dim_set, 0, v);
235 isl_int_set_si(v, 1);
236 isl_constraint_set_coefficient(c, isl_dim_param, 0, v);
237 bset = isl_basic_set_add_constraint(bset, c);
238
239 c = isl_inequality_alloc(isl_local_space_copy(ls));
240 isl_int_set_si(v, 1);
241 isl_constraint_set_coefficient(c, isl_dim_set, 0, v);
242 isl_int_set_si(v, -5);
243 isl_constraint_set_constant(c, v);
244 bset = isl_basic_set_add_constraint(bset, c);
245
246 isl_local_space_free(ls);
247 isl_basic_set_free(bset);
248
249 isl_int_clear(v);
250 }
251
252 void test_dim(struct isl_ctx *ctx)
253 {
254 const char *str;
255 isl_map *map1, *map2;
256
257 map1 = isl_map_read_from_str(ctx,
258 "[n] -> { [i] -> [j] : exists (a = [i/10] : i - 10a <= n ) }");
259 map1 = isl_map_add_dims(map1, isl_dim_in, 1);
260 map2 = isl_map_read_from_str(ctx,
261 "[n] -> { [i,k] -> [j] : exists (a = [i/10] : i - 10a <= n ) }");
262 assert(isl_map_is_equal(map1, map2));
263 isl_map_free(map2);
264
265 map1 = isl_map_project_out(map1, isl_dim_in, 0, 1);
266 map2 = isl_map_read_from_str(ctx, "[n] -> { [i] -> [j] : n >= 0 }");
267 assert(isl_map_is_equal(map1, map2));
268
269 isl_map_free(map1);
270 isl_map_free(map2);
271
272 str = "[n] -> { [i] -> [] : exists a : 0 <= i <= n and i = 2 a }";
273 map1 = isl_map_read_from_str(ctx, str);
274 str = "{ [i] -> [j] : exists a : 0 <= i <= j and i = 2 a }";
275 map2 = isl_map_read_from_str(ctx, str);
276 map1 = isl_map_move_dims(map1, isl_dim_out, 0, isl_dim_param, 0, 1);
277 assert(isl_map_is_equal(map1, map2));
278
279 isl_map_free(map1);
280 isl_map_free(map2);
281 }
282
283 void test_div(struct isl_ctx *ctx)
284 {
285 isl_int v;
286 isl_space *dim;
287 isl_local_space *ls;
288 struct isl_basic_set *bset;
289 struct isl_constraint *c;
290
291 isl_int_init(v);
292
293 /* test 1 */
294 dim = isl_space_set_alloc(ctx, 0, 3);
295 bset = isl_basic_set_universe(isl_space_copy(dim));
296 ls = isl_local_space_from_space(dim);
297
298 c = isl_equality_alloc(isl_local_space_copy(ls));
299 isl_int_set_si(v, -1);
300 isl_constraint_set_constant(c, v);
301 isl_int_set_si(v, 1);
302 isl_constraint_set_coefficient(c, isl_dim_set, 0, v);
303 isl_int_set_si(v, 3);
304 isl_constraint_set_coefficient(c, isl_dim_set, 1, v);
305 bset = isl_basic_set_add_constraint(bset, c);
306
307 c = isl_equality_alloc(isl_local_space_copy(ls));
308 isl_int_set_si(v, 1);
309 isl_constraint_set_constant(c, v);
310 isl_int_set_si(v, -1);
311 isl_constraint_set_coefficient(c, isl_dim_set, 0, v);
312 isl_int_set_si(v, 3);
313 isl_constraint_set_coefficient(c, isl_dim_set, 2, v);
314 bset = isl_basic_set_add_constraint(bset, c);
315
316 bset = isl_basic_set_project_out(bset, isl_dim_set, 1, 2);
317
318 assert(bset && bset->n_div == 1);
319 isl_local_space_free(ls);
320 isl_basic_set_free(bset);
321
322 /* test 2 */
323 dim = isl_space_set_alloc(ctx, 0, 3);
324 bset = isl_basic_set_universe(isl_space_copy(dim));
325 ls = isl_local_space_from_space(dim);
326
327 c = isl_equality_alloc(isl_local_space_copy(ls));
328 isl_int_set_si(v, 1);
329 isl_constraint_set_constant(c, v);
330 isl_int_set_si(v, -1);
331 isl_constraint_set_coefficient(c, isl_dim_set, 0, v);
332 isl_int_set_si(v, 3);
333 isl_constraint_set_coefficient(c, isl_dim_set, 1, v);
334 bset = isl_basic_set_add_constraint(bset, c);
335
336 c = isl_equality_alloc(isl_local_space_copy(ls));
337 isl_int_set_si(v, -1);
338 isl_constraint_set_constant(c, v);
339 isl_int_set_si(v, 1);
340 isl_constraint_set_coefficient(c, isl_dim_set, 0, v);
341 isl_int_set_si(v, 3);
342 isl_constraint_set_coefficient(c, isl_dim_set, 2, v);
343 bset = isl_basic_set_add_constraint(bset, c);
344
345 bset = isl_basic_set_project_out(bset, isl_dim_set, 1, 2);
346
347 assert(bset && bset->n_div == 1);
348 isl_local_space_free(ls);
349 isl_basic_set_free(bset);
350
351 /* test 3 */
352 dim = isl_space_set_alloc(ctx, 0, 3);
353 bset = isl_basic_set_universe(isl_space_copy(dim));
354 ls = isl_local_space_from_space(dim);
355
356 c = isl_equality_alloc(isl_local_space_copy(ls));
357 isl_int_set_si(v, 1);
358 isl_constraint_set_constant(c, v);
359 isl_int_set_si(v, -1);
360 isl_constraint_set_coefficient(c, isl_dim_set, 0, v);
361 isl_int_set_si(v, 3);
362 isl_constraint_set_coefficient(c, isl_dim_set, 1, v);
363 bset = isl_basic_set_add_constraint(bset, c);
364
365 c = isl_equality_alloc(isl_local_space_copy(ls));
366 isl_int_set_si(v, -3);
367 isl_constraint_set_constant(c, v);
368 isl_int_set_si(v, 1);
369 isl_constraint_set_coefficient(c, isl_dim_set, 0, v);
370 isl_int_set_si(v, 4);
371 isl_constraint_set_coefficient(c, isl_dim_set, 2, v);
372 bset = isl_basic_set_add_constraint(bset, c);
373
374 bset = isl_basic_set_project_out(bset, isl_dim_set, 1, 2);
375
376 assert(bset && bset->n_div == 1);
377 isl_local_space_free(ls);
378 isl_basic_set_free(bset);
379
380 /* test 4 */
381 dim = isl_space_set_alloc(ctx, 0, 3);
382 bset = isl_basic_set_universe(isl_space_copy(dim));
383 ls = isl_local_space_from_space(dim);
384
385 c = isl_equality_alloc(isl_local_space_copy(ls));
386 isl_int_set_si(v, 2);
387 isl_constraint_set_constant(c, v);
388 isl_int_set_si(v, -1);
389 isl_constraint_set_coefficient(c, isl_dim_set, 0, v);
390 isl_int_set_si(v, 3);
391 isl_constraint_set_coefficient(c, isl_dim_set, 1, v);
392 bset = isl_basic_set_add_constraint(bset, c);
393
394 c = isl_equality_alloc(isl_local_space_copy(ls));
395 isl_int_set_si(v, -1);
396 isl_constraint_set_constant(c, v);
397 isl_int_set_si(v, 1);
398 isl_constraint_set_coefficient(c, isl_dim_set, 0, v);
399 isl_int_set_si(v, 6);
400 isl_constraint_set_coefficient(c, isl_dim_set, 2, v);
401 bset = isl_basic_set_add_constraint(bset, c);
402
403 bset = isl_basic_set_project_out(bset, isl_dim_set, 1, 2);
404
405 assert(isl_basic_set_is_empty(bset));
406 isl_local_space_free(ls);
407 isl_basic_set_free(bset);
408
409 /* test 5 */
410 dim = isl_space_set_alloc(ctx, 0, 3);
411 bset = isl_basic_set_universe(isl_space_copy(dim));
412 ls = isl_local_space_from_space(dim);
413
414 c = isl_equality_alloc(isl_local_space_copy(ls));
415 isl_int_set_si(v, -1);
416 isl_constraint_set_coefficient(c, isl_dim_set, 0, v);
417 isl_int_set_si(v, 3);
418 isl_constraint_set_coefficient(c, isl_dim_set, 2, v);
419 bset = isl_basic_set_add_constraint(bset, c);
420
421 c = isl_equality_alloc(isl_local_space_copy(ls));
422 isl_int_set_si(v, 1);
423 isl_constraint_set_coefficient(c, isl_dim_set, 0, v);
424 isl_int_set_si(v, -3);
425 isl_constraint_set_coefficient(c, isl_dim_set, 1, v);
426 bset = isl_basic_set_add_constraint(bset, c);
427
428 bset = isl_basic_set_project_out(bset, isl_dim_set, 2, 1);
429
430 assert(bset && bset->n_div == 0);
431 isl_basic_set_free(bset);
432 isl_local_space_free(ls);
433
434 /* test 6 */
435 dim = isl_space_set_alloc(ctx, 0, 3);
436 bset = isl_basic_set_universe(isl_space_copy(dim));
437 ls = isl_local_space_from_space(dim);
438
439 c = isl_equality_alloc(isl_local_space_copy(ls));
440 isl_int_set_si(v, -1);
441 isl_constraint_set_coefficient(c, isl_dim_set, 0, v);
442 isl_int_set_si(v, 6);
443 isl_constraint_set_coefficient(c, isl_dim_set, 2, v);
444 bset = isl_basic_set_add_constraint(bset, c);
445
446 c = isl_equality_alloc(isl_local_space_copy(ls));
447 isl_int_set_si(v, 1);
448 isl_constraint_set_coefficient(c, isl_dim_set, 0, v);
449 isl_int_set_si(v, -3);
450 isl_constraint_set_coefficient(c, isl_dim_set, 1, v);
451 bset = isl_basic_set_add_constraint(bset, c);
452
453 bset = isl_basic_set_project_out(bset, isl_dim_set, 2, 1);
454
455 assert(bset && bset->n_div == 1);
456 isl_basic_set_free(bset);
457 isl_local_space_free(ls);
458
459 /* test 7 */
460 /* This test is a bit tricky. We set up an equality
461 * a + 3b + 3c = 6 e0
462 * Normalization of divs creates _two_ divs
463 * a = 3 e0
464 * c - b - e0 = 2 e1
465 * Afterwards e0 is removed again because it has coefficient -1
466 * and we end up with the original equality and div again.
467 * Perhaps we can avoid the introduction of this temporary div.
468 */
469 dim = isl_space_set_alloc(ctx, 0, 4);
470 bset = isl_basic_set_universe(isl_space_copy(dim));
471 ls = isl_local_space_from_space(dim);
472
473 c = isl_equality_alloc(isl_local_space_copy(ls));
474 isl_int_set_si(v, -1);
475 isl_constraint_set_coefficient(c, isl_dim_set, 0, v);
476 isl_int_set_si(v, -3);
477 isl_constraint_set_coefficient(c, isl_dim_set, 1, v);
478 isl_int_set_si(v, -3);
479 isl_constraint_set_coefficient(c, isl_dim_set, 2, v);
480 isl_int_set_si(v, 6);
481 isl_constraint_set_coefficient(c, isl_dim_set, 3, v);
482 bset = isl_basic_set_add_constraint(bset, c);
483
484 bset = isl_basic_set_project_out(bset, isl_dim_set, 3, 1);
485
486 /* Test disabled for now */
487 /*
488 assert(bset && bset->n_div == 1);
489 */
490 isl_local_space_free(ls);
491 isl_basic_set_free(bset);
492
493 /* test 8 */
494 dim = isl_space_set_alloc(ctx, 0, 5);
495 bset = isl_basic_set_universe(isl_space_copy(dim));
496 ls = isl_local_space_from_space(dim);
497
498 c = isl_equality_alloc(isl_local_space_copy(ls));
499 isl_int_set_si(v, -1);
500 isl_constraint_set_coefficient(c, isl_dim_set, 0, v);
501 isl_int_set_si(v, -3);
502 isl_constraint_set_coefficient(c, isl_dim_set, 1, v);
503 isl_int_set_si(v, -3);
504 isl_constraint_set_coefficient(c, isl_dim_set, 3, v);
505 isl_int_set_si(v, 6);
506 isl_constraint_set_coefficient(c, isl_dim_set, 4, v);
507 bset = isl_basic_set_add_constraint(bset, c);
508
509 c = isl_equality_alloc(isl_local_space_copy(ls));
510 isl_int_set_si(v, -1);
511 isl_constraint_set_coefficient(c, isl_dim_set, 0, v);
512 isl_int_set_si(v, 1);
513 isl_constraint_set_coefficient(c, isl_dim_set, 2, v);
514 isl_int_set_si(v, 1);
515 isl_constraint_set_constant(c, v);
516 bset = isl_basic_set_add_constraint(bset, c);
517
518 bset = isl_basic_set_project_out(bset, isl_dim_set, 4, 1);
519
520 /* Test disabled for now */
521 /*
522 assert(bset && bset->n_div == 1);
523 */
524 isl_local_space_free(ls);
525 isl_basic_set_free(bset);
526
527 /* test 9 */
528 dim = isl_space_set_alloc(ctx, 0, 4);
529 bset = isl_basic_set_universe(isl_space_copy(dim));
530 ls = isl_local_space_from_space(dim);
531
532 c = isl_equality_alloc(isl_local_space_copy(ls));
533 isl_int_set_si(v, 1);
534 isl_constraint_set_coefficient(c, isl_dim_set, 0, v);
535 isl_int_set_si(v, -1);
536 isl_constraint_set_coefficient(c, isl_dim_set, 1, v);
537 isl_int_set_si(v, -2);
538 isl_constraint_set_coefficient(c, isl_dim_set, 2, v);
539 bset = isl_basic_set_add_constraint(bset, c);
540
541 c = isl_equality_alloc(isl_local_space_copy(ls));
542 isl_int_set_si(v, -1);
543 isl_constraint_set_coefficient(c, isl_dim_set, 0, v);
544 isl_int_set_si(v, 3);
545 isl_constraint_set_coefficient(c, isl_dim_set, 3, v);
546 isl_int_set_si(v, 2);
547 isl_constraint_set_constant(c, v);
548 bset = isl_basic_set_add_constraint(bset, c);
549
550 bset = isl_basic_set_project_out(bset, isl_dim_set, 2, 2);
551
552 bset = isl_basic_set_fix_si(bset, isl_dim_set, 0, 2);
553
554 assert(!isl_basic_set_is_empty(bset));
555
556 isl_local_space_free(ls);
557 isl_basic_set_free(bset);
558
559 /* test 10 */
560 dim = isl_space_set_alloc(ctx, 0, 3);
561 bset = isl_basic_set_universe(isl_space_copy(dim));
562 ls = isl_local_space_from_space(dim);
563
564 c = isl_equality_alloc(isl_local_space_copy(ls));
565 isl_int_set_si(v, 1);
566 isl_constraint_set_coefficient(c, isl_dim_set, 0, v);
567 isl_int_set_si(v, -2);
568 isl_constraint_set_coefficient(c, isl_dim_set, 2, v);
569 bset = isl_basic_set_add_constraint(bset, c);
570
571 bset = isl_basic_set_project_out(bset, isl_dim_set, 2, 1);
572
573 bset = isl_basic_set_fix_si(bset, isl_dim_set, 0, 2);
574
575 isl_local_space_free(ls);
576 isl_basic_set_free(bset);
577
578 isl_int_clear(v);
579 }
580
581 void test_application_case(struct isl_ctx *ctx, const char *name)
582 {
583 char *filename;
584 FILE *input;
585 struct isl_basic_set *bset1, *bset2;
586 struct isl_basic_map *bmap;
587
588 filename = get_filename(ctx, name, "omega");
589 assert(filename);
590 input = fopen(filename, "r");
591 assert(input);
592
593 bset1 = isl_basic_set_read_from_file(ctx, input);
594 bmap = isl_basic_map_read_from_file(ctx, input);
595
596 bset1 = isl_basic_set_apply(bset1, bmap);
597
598 bset2 = isl_basic_set_read_from_file(ctx, input);
599
600 assert(isl_basic_set_is_equal(bset1, bset2) == 1);
601
602 isl_basic_set_free(bset1);
603 isl_basic_set_free(bset2);
604 free(filename);
605
606 fclose(input);
607 }
608
609 void test_application(struct isl_ctx *ctx)
610 {
611 test_application_case(ctx, "application");
612 test_application_case(ctx, "application2");
613 }
614
615 void test_affine_hull_case(struct isl_ctx *ctx, const char *name)
616 {
617 char *filename;
618 FILE *input;
619 struct isl_basic_set *bset1, *bset2;
620
621 filename = get_filename(ctx, name, "polylib");
622 assert(filename);
623 input = fopen(filename, "r");
624 assert(input);
625
626 bset1 = isl_basic_set_read_from_file(ctx, input);
627 bset2 = isl_basic_set_read_from_file(ctx, input);
628
629 bset1 = isl_basic_set_affine_hull(bset1);
630
631 assert(isl_basic_set_is_equal(bset1, bset2) == 1);
632
633 isl_basic_set_free(bset1);
634 isl_basic_set_free(bset2);
635 free(filename);
636
637 fclose(input);
638 }
639
640 int test_affine_hull(struct isl_ctx *ctx)
641 {
642 const char *str;
643 isl_set *set;
644 isl_basic_set *bset;
645 int n;
646
647 test_affine_hull_case(ctx, "affine2");
648 test_affine_hull_case(ctx, "affine");
649 test_affine_hull_case(ctx, "affine3");
650
651 str = "[m] -> { [i0] : exists (e0, e1: e1 <= 1 + i0 and "
652 "m >= 3 and 4i0 <= 2 + m and e1 >= i0 and "
653 "e1 >= 0 and e1 <= 2 and e1 >= 1 + 2e0 and "
654 "2e1 <= 1 + m + 4e0 and 2e1 >= 2 - m + 4i0 - 4e0) }";
655 set = isl_set_read_from_str(ctx, str);
656 bset = isl_set_affine_hull(set);
657 n = isl_basic_set_dim(bset, isl_dim_div);
658 isl_basic_set_free(bset);
659 if (n != 0)
660 isl_die(ctx, isl_error_unknown, "not expecting any divs",
661 return -1);
662
663 return 0;
664 }
665
666 void test_convex_hull_case(struct isl_ctx *ctx, const char *name)
667 {
668 char *filename;
669 FILE *input;
670 struct isl_basic_set *bset1, *bset2;
671 struct isl_set *set;
672
673 filename = get_filename(ctx, name, "polylib");
674 assert(filename);
675 input = fopen(filename, "r");
676 assert(input);
677
678 bset1 = isl_basic_set_read_from_file(ctx, input);
679 bset2 = isl_basic_set_read_from_file(ctx, input);
680
681 set = isl_basic_set_union(bset1, bset2);
682 bset1 = isl_set_convex_hull(set);
683
684 bset2 = isl_basic_set_read_from_file(ctx, input);
685
686 assert(isl_basic_set_is_equal(bset1, bset2) == 1);
687
688 isl_basic_set_free(bset1);
689 isl_basic_set_free(bset2);
690 free(filename);
691
692 fclose(input);
693 }
694
695 void test_convex_hull_algo(struct isl_ctx *ctx, int convex)
696 {
697 const char *str1, *str2;
698 isl_set *set1, *set2;
699 int orig_convex = ctx->opt->convex;
700 ctx->opt->convex = convex;
701
702 test_convex_hull_case(ctx, "convex0");
703 test_convex_hull_case(ctx, "convex1");
704 test_convex_hull_case(ctx, "convex2");
705 test_convex_hull_case(ctx, "convex3");
706 test_convex_hull_case(ctx, "convex4");
707 test_convex_hull_case(ctx, "convex5");
708 test_convex_hull_case(ctx, "convex6");
709 test_convex_hull_case(ctx, "convex7");
710 test_convex_hull_case(ctx, "convex8");
711 test_convex_hull_case(ctx, "convex9");
712 test_convex_hull_case(ctx, "convex10");
713 test_convex_hull_case(ctx, "convex11");
714 test_convex_hull_case(ctx, "convex12");
715 test_convex_hull_case(ctx, "convex13");
716 test_convex_hull_case(ctx, "convex14");
717 test_convex_hull_case(ctx, "convex15");
718
719 str1 = "{ [i0, i1, i2] : (i2 = 1 and i0 = 0 and i1 >= 0) or "
720 "(i0 = 1 and i1 = 0 and i2 = 1) or "
721 "(i0 = 0 and i1 = 0 and i2 = 0) }";
722 str2 = "{ [i0, i1, i2] : i0 >= 0 and i2 >= i0 and i2 <= 1 and i1 >= 0 }";
723 set1 = isl_set_read_from_str(ctx, str1);
724 set2 = isl_set_read_from_str(ctx, str2);
725 set1 = isl_set_from_basic_set(isl_set_convex_hull(set1));
726 assert(isl_set_is_equal(set1, set2));
727 isl_set_free(set1);
728 isl_set_free(set2);
729
730 ctx->opt->convex = orig_convex;
731 }
732
733 void test_convex_hull(struct isl_ctx *ctx)
734 {
735 test_convex_hull_algo(ctx, ISL_CONVEX_HULL_FM);
736 test_convex_hull_algo(ctx, ISL_CONVEX_HULL_WRAP);
737 }
738
739 void test_gist_case(struct isl_ctx *ctx, const char *name)
740 {
741 char *filename;
742 FILE *input;
743 struct isl_basic_set *bset1, *bset2;
744
745 filename = get_filename(ctx, name, "polylib");
746 assert(filename);
747 input = fopen(filename, "r");
748 assert(input);
749
750 bset1 = isl_basic_set_read_from_file(ctx, input);
751 bset2 = isl_basic_set_read_from_file(ctx, input);
752
753 bset1 = isl_basic_set_gist(bset1, bset2);
754
755 bset2 = isl_basic_set_read_from_file(ctx, input);
756
757 assert(isl_basic_set_is_equal(bset1, bset2) == 1);
758
759 isl_basic_set_free(bset1);
760 isl_basic_set_free(bset2);
761 free(filename);
762
763 fclose(input);
764 }
765
766 void test_gist(struct isl_ctx *ctx)
767 {
768 const char *str;
769 isl_basic_set *bset1, *bset2;
770
771 test_gist_case(ctx, "gist1");
772
773 str = "[p0, p2, p3, p5, p6, p10] -> { [] : "
774 "exists (e0 = [(15 + p0 + 15p6 + 15p10)/16], e1 = [(p5)/8], "
775 "e2 = [(p6)/128], e3 = [(8p2 - p5)/128], "
776 "e4 = [(128p3 - p6)/4096]: 8e1 = p5 and 128e2 = p6 and "
777 "128e3 = 8p2 - p5 and 4096e4 = 128p3 - p6 and p2 >= 0 and "
778 "16e0 >= 16 + 16p6 + 15p10 and p2 <= 15 and p3 >= 0 and "
779 "p3 <= 31 and p6 >= 128p3 and p5 >= 8p2 and p10 >= 0 and "
780 "16e0 <= 15 + p0 + 15p6 + 15p10 and 16e0 >= p0 + 15p6 + 15p10 and "
781 "p10 <= 15 and p10 <= -1 + p0 - p6) }";
782 bset1 = isl_basic_set_read_from_str(ctx, str);
783 str = "[p0, p2, p3, p5, p6, p10] -> { [] : exists (e0 = [(p5)/8], "
784 "e1 = [(p6)/128], e2 = [(8p2 - p5)/128], "
785 "e3 = [(128p3 - p6)/4096]: 8e0 = p5 and 128e1 = p6 and "
786 "128e2 = 8p2 - p5 and 4096e3 = 128p3 - p6 and p5 >= -7 and "
787 "p2 >= 0 and 8p2 <= -1 + p0 and p2 <= 15 and p3 >= 0 and "
788 "p3 <= 31 and 128p3 <= -1 + p0 and p6 >= -127 and "
789 "p5 <= -1 + p0 and p6 <= -1 + p0 and p6 >= 128p3 and "
790 "p0 >= 1 and p5 >= 8p2 and p10 >= 0 and p10 <= 15 ) }";
791 bset2 = isl_basic_set_read_from_str(ctx, str);
792 bset1 = isl_basic_set_gist(bset1, bset2);
793 assert(bset1 && bset1->n_div == 0);
794 isl_basic_set_free(bset1);
795 }
796
797 int test_coalesce_set(isl_ctx *ctx, const char *str, int check_one)
798 {
799 isl_set *set, *set2;
800 int equal;
801 int one;
802
803 set = isl_set_read_from_str(ctx, str);
804 set = isl_set_coalesce(set);
805 set2 = isl_set_read_from_str(ctx, str);
806 equal = isl_set_is_equal(set, set2);
807 one = set && set->n == 1;
808 isl_set_free(set);
809 isl_set_free(set2);
810
811 if (equal < 0)
812 return -1;
813 if (!equal)
814 isl_die(ctx, isl_error_unknown,
815 "coalesced set not equal to input", return -1);
816 if (check_one && !one)
817 isl_die(ctx, isl_error_unknown,
818 "coalesced set should not be a union", return -1);
819
820 return 0;
821 }
822
823 int test_coalesce(struct isl_ctx *ctx)
824 {
825 const char *str;
826 struct isl_set *set, *set2;
827 struct isl_map *map, *map2;
828
829 set = isl_set_read_from_str(ctx,
830 "{[x,y]: x >= 0 & x <= 10 & y >= 0 & y <= 10 or "
831 "y >= x & x >= 2 & 5 >= y }");
832 set = isl_set_coalesce(set);
833 assert(set && set->n == 1);
834 isl_set_free(set);
835
836 set = isl_set_read_from_str(ctx,
837 "{[x,y]: y >= 0 & 2x + y <= 30 & y <= 10 & x >= 0 or "
838 "x + y >= 10 & y <= x & x + y <= 20 & y >= 0}");
839 set = isl_set_coalesce(set);
840 assert(set && set->n == 1);
841 isl_set_free(set);
842
843 set = isl_set_read_from_str(ctx,
844 "{[x,y]: y >= 0 & 2x + y <= 30 & y <= 10 & x >= 0 or "
845 "x + y >= 10 & y <= x & x + y <= 19 & y >= 0}");
846 set = isl_set_coalesce(set);
847 assert(set && set->n == 2);
848 isl_set_free(set);
849
850 set = isl_set_read_from_str(ctx,
851 "{[x,y]: y >= 0 & x <= 5 & y <= x or "
852 "y >= 0 & x >= 6 & x <= 10 & y <= x}");
853 set = isl_set_coalesce(set);
854 assert(set && set->n == 1);
855 isl_set_free(set);
856
857 set = isl_set_read_from_str(ctx,
858 "{[x,y]: y >= 0 & x <= 5 & y <= x or "
859 "y >= 0 & x >= 7 & x <= 10 & y <= x}");
860 set = isl_set_coalesce(set);
861 assert(set && set->n == 2);
862 isl_set_free(set);
863
864 set = isl_set_read_from_str(ctx,
865 "{[x,y]: y >= 0 & x <= 5 & y <= x or "
866 "y >= 0 & x >= 6 & x <= 10 & y + 1 <= x}");
867 set = isl_set_coalesce(set);
868 assert(set && set->n == 2);
869 isl_set_free(set);
870
871 set = isl_set_read_from_str(ctx,
872 "{[x,y]: y >= 0 & x <= 5 & y <= x or "
873 "y >= 0 & x = 6 & y <= 6}");
874 set = isl_set_coalesce(set);
875 assert(set && set->n == 1);
876 isl_set_free(set);
877
878 set = isl_set_read_from_str(ctx,
879 "{[x,y]: y >= 0 & x <= 5 & y <= x or "
880 "y >= 0 & x = 7 & y <= 6}");
881 set = isl_set_coalesce(set);
882 assert(set && set->n == 2);
883 isl_set_free(set);
884
885 set = isl_set_read_from_str(ctx,
886 "{[x,y]: y >= 0 & x <= 5 & y <= x or "
887 "y >= 0 & x = 6 & y <= 5}");
888 set = isl_set_coalesce(set);
889 assert(set && set->n == 1);
890 set2 = isl_set_read_from_str(ctx,
891 "{[x,y]: y >= 0 & x <= 5 & y <= x or "
892 "y >= 0 & x = 6 & y <= 5}");
893 assert(isl_set_is_equal(set, set2));
894 isl_set_free(set);
895 isl_set_free(set2);
896
897 set = isl_set_read_from_str(ctx,
898 "{[x,y]: y >= 0 & x <= 5 & y <= x or "
899 "y >= 0 & x = 6 & y <= 7}");
900 set = isl_set_coalesce(set);
901 assert(set && set->n == 2);
902 isl_set_free(set);
903
904 set = isl_set_read_from_str(ctx,
905 "[n] -> { [i] : i = 1 and n >= 2 or 2 <= i and i <= n }");
906 set = isl_set_coalesce(set);
907 assert(set && set->n == 1);
908 set2 = isl_set_read_from_str(ctx,
909 "[n] -> { [i] : i = 1 and n >= 2 or 2 <= i and i <= n }");
910 assert(isl_set_is_equal(set, set2));
911 isl_set_free(set);
912 isl_set_free(set2);
913
914 set = isl_set_read_from_str(ctx,
915 "{[x,y] : x >= 0 and y >= 0 or 0 <= y and y <= 5 and x = -1}");
916 set = isl_set_coalesce(set);
917 set2 = isl_set_read_from_str(ctx,
918 "{[x,y] : x >= 0 and y >= 0 or 0 <= y and y <= 5 and x = -1}");
919 assert(isl_set_is_equal(set, set2));
920 isl_set_free(set);
921 isl_set_free(set2);
922
923 set = isl_set_read_from_str(ctx,
924 "[n] -> { [i] : 1 <= i and i <= n - 1 or "
925 "2 <= i and i <= n }");
926 set = isl_set_coalesce(set);
927 assert(set && set->n == 1);
928 set2 = isl_set_read_from_str(ctx,
929 "[n] -> { [i] : 1 <= i and i <= n - 1 or "
930 "2 <= i and i <= n }");
931 assert(isl_set_is_equal(set, set2));
932 isl_set_free(set);
933 isl_set_free(set2);
934
935 map = isl_map_read_from_str(ctx,
936 "[n] -> { [i0] -> [o0] : exists (e0 = [(i0)/4], e1 = [(o0)/4], "
937 "e2 = [(n)/2], e3 = [(-2 + i0)/4], e4 = [(-2 + o0)/4], "
938 "e5 = [(-2n + i0)/4]: 2e2 = n and 4e3 = -2 + i0 and "
939 "4e4 = -2 + o0 and i0 >= 8 + 2n and o0 >= 2 + i0 and "
940 "o0 <= 56 + 2n and o0 <= -12 + 4n and i0 <= 57 + 2n and "
941 "i0 <= -11 + 4n and o0 >= 6 + 2n and 4e0 <= i0 and "
942 "4e0 >= -3 + i0 and 4e1 <= o0 and 4e1 >= -3 + o0 and "
943 "4e5 <= -2n + i0 and 4e5 >= -3 - 2n + i0);"
944 "[i0] -> [o0] : exists (e0 = [(i0)/4], e1 = [(o0)/4], "
945 "e2 = [(n)/2], e3 = [(-2 + i0)/4], e4 = [(-2 + o0)/4], "
946 "e5 = [(-2n + i0)/4]: 2e2 = n and 4e3 = -2 + i0 and "
947 "4e4 = -2 + o0 and 2e0 >= 3 + n and e0 <= -4 + n and "
948 "2e0 <= 27 + n and e1 <= -4 + n and 2e1 <= 27 + n and "
949 "2e1 >= 2 + n and e1 >= 1 + e0 and i0 >= 7 + 2n and "
950 "i0 <= -11 + 4n and i0 <= 57 + 2n and 4e0 <= -2 + i0 and "
951 "4e0 >= -3 + i0 and o0 >= 6 + 2n and o0 <= -11 + 4n and "
952 "o0 <= 57 + 2n and 4e1 <= -2 + o0 and 4e1 >= -3 + o0 and "
953 "4e5 <= -2n + i0 and 4e5 >= -3 - 2n + i0 ) }");
954 map = isl_map_coalesce(map);
955 map2 = isl_map_read_from_str(ctx,
956 "[n] -> { [i0] -> [o0] : exists (e0 = [(i0)/4], e1 = [(o0)/4], "
957 "e2 = [(n)/2], e3 = [(-2 + i0)/4], e4 = [(-2 + o0)/4], "
958 "e5 = [(-2n + i0)/4]: 2e2 = n and 4e3 = -2 + i0 and "
959 "4e4 = -2 + o0 and i0 >= 8 + 2n and o0 >= 2 + i0 and "
960 "o0 <= 56 + 2n and o0 <= -12 + 4n and i0 <= 57 + 2n and "
961 "i0 <= -11 + 4n and o0 >= 6 + 2n and 4e0 <= i0 and "
962 "4e0 >= -3 + i0 and 4e1 <= o0 and 4e1 >= -3 + o0 and "
963 "4e5 <= -2n + i0 and 4e5 >= -3 - 2n + i0);"
964 "[i0] -> [o0] : exists (e0 = [(i0)/4], e1 = [(o0)/4], "
965 "e2 = [(n)/2], e3 = [(-2 + i0)/4], e4 = [(-2 + o0)/4], "
966 "e5 = [(-2n + i0)/4]: 2e2 = n and 4e3 = -2 + i0 and "
967 "4e4 = -2 + o0 and 2e0 >= 3 + n and e0 <= -4 + n and "
968 "2e0 <= 27 + n and e1 <= -4 + n and 2e1 <= 27 + n and "
969 "2e1 >= 2 + n and e1 >= 1 + e0 and i0 >= 7 + 2n and "
970 "i0 <= -11 + 4n and i0 <= 57 + 2n and 4e0 <= -2 + i0 and "
971 "4e0 >= -3 + i0 and o0 >= 6 + 2n and o0 <= -11 + 4n and "
972 "o0 <= 57 + 2n and 4e1 <= -2 + o0 and 4e1 >= -3 + o0 and "
973 "4e5 <= -2n + i0 and 4e5 >= -3 - 2n + i0 ) }");
974 assert(isl_map_is_equal(map, map2));
975 isl_map_free(map);
976 isl_map_free(map2);
977
978 str = "[n, m] -> { [] -> [o0, o2, o3] : (o3 = 1 and o0 >= 1 + m and "
979 "o0 <= n + m and o2 <= m and o0 >= 2 + n and o2 >= 3) or "
980 "(o0 >= 2 + n and o0 >= 1 + m and o0 <= n + m and n >= 1 and "
981 "o3 <= -1 + o2 and o3 >= 1 - m + o2 and o3 >= 2 and o3 <= n) }";
982 map = isl_map_read_from_str(ctx, str);
983 map = isl_map_coalesce(map);
984 map2 = isl_map_read_from_str(ctx, str);
985 assert(isl_map_is_equal(map, map2));
986 isl_map_free(map);
987 isl_map_free(map2);
988
989 str = "[M, N] -> { [i0, i1, i2, i3, i4, i5, i6] -> "
990 "[o0, o1, o2, o3, o4, o5, o6] : "
991 "(o6 <= -4 + 2M - 2N + i0 + i1 - i2 + i6 - o0 - o1 + o2 and "
992 "o3 <= -2 + i3 and o6 >= 2 + i0 + i3 + i6 - o0 - o3 and "
993 "o6 >= 2 - M + N + i3 + i4 + i6 - o3 - o4 and o0 <= -1 + i0 and "
994 "o4 >= 4 - 3M + 3N - i0 - i1 + i2 + 2i3 + i4 + o0 + o1 - o2 - 2o3 "
995 "and o6 <= -3 + 2M - 2N + i3 + i4 - i5 + i6 - o3 - o4 + o5 and "
996 "2o6 <= -5 + 5M - 5N + 2i0 + i1 - i2 - i5 + 2i6 - 2o0 - o1 + o2 + o5 "
997 "and o6 >= 2i0 + i1 + i6 - 2o0 - o1 and "
998 "3o6 <= -5 + 4M - 4N + 2i0 + i1 - i2 + 2i3 + i4 - i5 + 3i6 "
999 "- 2o0 - o1 + o2 - 2o3 - o4 + o5) or "
1000 "(N >= 2 and o3 <= -1 + i3 and o0 <= -1 + i0 and "
1001 "o6 >= i3 + i6 - o3 and M >= 0 and "
1002 "2o6 >= 1 + i0 + i3 + 2i6 - o0 - o3 and "
1003 "o6 >= 1 - M + i0 + i6 - o0 and N >= 2M and o6 >= i0 + i6 - o0) }";
1004 map = isl_map_read_from_str(ctx, str);
1005 map = isl_map_coalesce(map);
1006 map2 = isl_map_read_from_str(ctx, str);
1007 assert(isl_map_is_equal(map, map2));
1008 isl_map_free(map);
1009 isl_map_free(map2);
1010
1011 str = "[M, N] -> { [] -> [o0] : (o0 = 0 and M >= 1 and N >= 2) or "
1012 "(o0 = 0 and M >= 1 and N >= 2M and N >= 2 + M) or "
1013 "(o0 = 0 and M >= 2 and N >= 3) or "
1014 "(M = 0 and o0 = 0 and N >= 3) }";
1015 map = isl_map_read_from_str(ctx, str);
1016 map = isl_map_coalesce(map);
1017 map2 = isl_map_read_from_str(ctx, str);
1018 assert(isl_map_is_equal(map, map2));
1019 isl_map_free(map);
1020 isl_map_free(map2);
1021
1022 str = "{ [i0, i1, i2, i3] : (i1 = 10i0 and i0 >= 1 and 10i0 <= 100 and "
1023 "i3 <= 9 + 10 i2 and i3 >= 1 + 10i2 and i3 >= 0) or "
1024 "(i1 <= 9 + 10i0 and i1 >= 1 + 10i0 and i2 >= 0 and "
1025 "i0 >= 0 and i1 <= 100 and i3 <= 9 + 10i2 and i3 >= 1 + 10i2) }";
1026 map = isl_map_read_from_str(ctx, str);
1027 map = isl_map_coalesce(map);
1028 map2 = isl_map_read_from_str(ctx, str);
1029 assert(isl_map_is_equal(map, map2));
1030 isl_map_free(map);
1031 isl_map_free(map2);
1032
1033 test_coalesce_set(ctx,
1034 "[M] -> { [i1] : (i1 >= 2 and i1 <= M) or "
1035 "(i1 = M and M >= 1) }", 0);
1036 test_coalesce_set(ctx,
1037 "{[x,y] : x,y >= 0; [x,y] : 10 <= x <= 20 and y >= -1 }", 0);
1038 test_coalesce_set(ctx,
1039 "{ [x, y] : (x >= 1 and y >= 1 and x <= 2 and y <= 2) or "
1040 "(y = 3 and x = 1) }", 1);
1041 test_coalesce_set(ctx,
1042 "[M] -> { [i0, i1, i2, i3, i4] : (i1 >= 3 and i4 >= 2 + i2 and "
1043 "i2 >= 2 and i0 >= 2 and i3 >= 1 + i2 and i0 <= M and "
1044 "i1 <= M and i3 <= M and i4 <= M) or "
1045 "(i1 >= 2 and i4 >= 1 + i2 and i2 >= 2 and i0 >= 2 and "
1046 "i3 >= 1 + i2 and i0 <= M and i1 <= -1 + M and i3 <= M and "
1047 "i4 <= -1 + M) }", 1);
1048 test_coalesce_set(ctx,
1049 "{ [x, y] : (x >= 0 and y >= 0 and x <= 10 and y <= 10) or "
1050 "(x >= 1 and y >= 1 and x <= 11 and y <= 11) }", 1);
1051 test_coalesce_set(ctx,
1052 "{[x,y,z] : y + 2 >= 0 and x - y + 1 >= 0 and "
1053 "-x - y + 1 >= 0 and -3 <= z <= 3;"
1054 "[x,y,z] : -x+z + 20 >= 0 and -x-z + 20 >= 0 and "
1055 "x-z + 20 >= 0 and x+z + 20 >= 0 and -10 <= y <= 0}", 1);
1056 if (test_coalesce_set(ctx,
1057 "{[x,y] : 0 <= x,y <= 10; [5,y]: 4 <=y <= 11}", 1) < 0)
1058 return -1;
1059 if (test_coalesce_set(ctx, "{[x,0] : x >= 0; [x,1] : x <= 20}", 0) < 0)
1060 return -1;
1061 if (test_coalesce_set(ctx,
1062 "{[x,0,0] : -5 <= x <= 5; [0,y,1] : -5 <= y <= 5 }", 1) < 0)
1063 return -1;
1064 if (test_coalesce_set(ctx, "{ [x, 1 - x] : 0 <= x <= 1; [0,0] }", 1) < 0)
1065 return -1;
1066 if (test_coalesce_set(ctx, "{ [0,0]; [i,i] : 1 <= i <= 10 }", 1) < 0)
1067 return -1;
1068 if (test_coalesce_set(ctx, "{ [0,0]; [i,j] : 1 <= i,j <= 10 }", 0) < 0)
1069 return -1;
1070 if (test_coalesce_set(ctx, "{ [0,0]; [i,2i] : 1 <= i <= 10 }", 1) < 0)
1071 return -1;
1072 if (test_coalesce_set(ctx, "{ [0,0]; [i,2i] : 2 <= i <= 10 }", 0) < 0)
1073 return -1;
1074 if (test_coalesce_set(ctx, "{ [1,0]; [i,2i] : 1 <= i <= 10 }", 0) < 0)
1075 return -1;
1076 if (test_coalesce_set(ctx, "{ [0,1]; [i,2i] : 1 <= i <= 10 }", 0) < 0)
1077 return -1;
1078 if (test_coalesce_set(ctx, "{ [a, b] : exists e : 2e = a and "
1079 "a >= 0 and (a <= 3 or (b <= 0 and b >= -4 + a)) }", 0) < 0)
1080 return -1;
1081 return 0;
1082 }
1083
1084 void test_closure(struct isl_ctx *ctx)
1085 {
1086 const char *str;
1087 isl_set *dom;
1088 isl_map *up, *right;
1089 isl_map *map, *map2;
1090 int exact;
1091
1092 /* COCOA example 1 */
1093 map = isl_map_read_from_str(ctx,
1094 "[n] -> { [i,j] -> [i2,j2] : i2 = i + 1 and j2 = j + 1 and "
1095 "1 <= i and i < n and 1 <= j and j < n or "
1096 "i2 = i + 1 and j2 = j - 1 and "
1097 "1 <= i and i < n and 2 <= j and j <= n }");
1098 map = isl_map_power(map, &exact);
1099 assert(exact);
1100 isl_map_free(map);
1101
1102 /* COCOA example 1 */
1103 map = isl_map_read_from_str(ctx,
1104 "[n] -> { [i,j] -> [i2,j2] : i2 = i + 1 and j2 = j + 1 and "
1105 "1 <= i and i < n and 1 <= j and j < n or "
1106 "i2 = i + 1 and j2 = j - 1 and "
1107 "1 <= i and i < n and 2 <= j and j <= n }");
1108 map = isl_map_transitive_closure(map, &exact);
1109 assert(exact);
1110 map2 = isl_map_read_from_str(ctx,
1111 "[n] -> { [i,j] -> [i2,j2] : exists (k1,k2,k : "
1112 "1 <= i and i < n and 1 <= j and j <= n and "
1113 "2 <= i2 and i2 <= n and 1 <= j2 and j2 <= n and "
1114 "i2 = i + k1 + k2 and j2 = j + k1 - k2 and "
1115 "k1 >= 0 and k2 >= 0 and k1 + k2 = k and k >= 1 )}");
1116 assert(isl_map_is_equal(map, map2));
1117 isl_map_free(map2);
1118 isl_map_free(map);
1119
1120 map = isl_map_read_from_str(ctx,
1121 "[n] -> { [x] -> [y] : y = x + 1 and 0 <= x and x <= n and "
1122 " 0 <= y and y <= n }");
1123 map = isl_map_transitive_closure(map, &exact);
1124 map2 = isl_map_read_from_str(ctx,
1125 "[n] -> { [x] -> [y] : y > x and 0 <= x and x <= n and "
1126 " 0 <= y and y <= n }");
1127 assert(isl_map_is_equal(map, map2));
1128 isl_map_free(map2);
1129 isl_map_free(map);
1130
1131 /* COCOA example 2 */
1132 map = isl_map_read_from_str(ctx,
1133 "[n] -> { [i,j] -> [i2,j2] : i2 = i + 2 and j2 = j + 2 and "
1134 "1 <= i and i < n - 1 and 1 <= j and j < n - 1 or "
1135 "i2 = i + 2 and j2 = j - 2 and "
1136 "1 <= i and i < n - 1 and 3 <= j and j <= n }");
1137 map = isl_map_transitive_closure(map, &exact);
1138 assert(exact);
1139 map2 = isl_map_read_from_str(ctx,
1140 "[n] -> { [i,j] -> [i2,j2] : exists (k1,k2,k : "
1141 "1 <= i and i < n - 1 and 1 <= j and j <= n and "
1142 "3 <= i2 and i2 <= n and 1 <= j2 and j2 <= n and "
1143 "i2 = i + 2 k1 + 2 k2 and j2 = j + 2 k1 - 2 k2 and "
1144 "k1 >= 0 and k2 >= 0 and k1 + k2 = k and k >= 1) }");
1145 assert(isl_map_is_equal(map, map2));
1146 isl_map_free(map);
1147 isl_map_free(map2);
1148
1149 /* COCOA Fig.2 left */
1150 map = isl_map_read_from_str(ctx,
1151 "[n] -> { [i,j] -> [i2,j2] : i2 = i + 2 and j2 = j and "
1152 "i <= 2 j - 3 and i <= n - 2 and j <= 2 i - 1 and "
1153 "j <= n or "
1154 "i2 = i and j2 = j + 2 and i <= 2 j - 1 and i <= n and "
1155 "j <= 2 i - 3 and j <= n - 2 or "
1156 "i2 = i + 1 and j2 = j + 1 and i <= 2 j - 1 and "
1157 "i <= n - 1 and j <= 2 i - 1 and j <= n - 1 }");
1158 map = isl_map_transitive_closure(map, &exact);
1159 assert(exact);
1160 isl_map_free(map);
1161
1162 /* COCOA Fig.2 right */
1163 map = isl_map_read_from_str(ctx,
1164 "[n] -> { [i,j] -> [i2,j2] : i2 = i + 3 and j2 = j and "
1165 "i <= 2 j - 4 and i <= n - 3 and j <= 2 i - 1 and "
1166 "j <= n or "
1167 "i2 = i and j2 = j + 3 and i <= 2 j - 1 and i <= n and "
1168 "j <= 2 i - 4 and j <= n - 3 or "
1169 "i2 = i + 1 and j2 = j + 1 and i <= 2 j - 1 and "
1170 "i <= n - 1 and j <= 2 i - 1 and j <= n - 1 }");
1171 map = isl_map_power(map, &exact);
1172 assert(exact);
1173 isl_map_free(map);
1174
1175 /* COCOA Fig.2 right */
1176 map = isl_map_read_from_str(ctx,
1177 "[n] -> { [i,j] -> [i2,j2] : i2 = i + 3 and j2 = j and "
1178 "i <= 2 j - 4 and i <= n - 3 and j <= 2 i - 1 and "
1179 "j <= n or "
1180 "i2 = i and j2 = j + 3 and i <= 2 j - 1 and i <= n and "
1181 "j <= 2 i - 4 and j <= n - 3 or "
1182 "i2 = i + 1 and j2 = j + 1 and i <= 2 j - 1 and "
1183 "i <= n - 1 and j <= 2 i - 1 and j <= n - 1 }");
1184 map = isl_map_transitive_closure(map, &exact);
1185 assert(exact);
1186 map2 = isl_map_read_from_str(ctx,
1187 "[n] -> { [i,j] -> [i2,j2] : exists (k1,k2,k3,k : "
1188 "i <= 2 j - 1 and i <= n and j <= 2 i - 1 and "
1189 "j <= n and 3 + i + 2 j <= 3 n and "
1190 "3 + 2 i + j <= 3n and i2 <= 2 j2 -1 and i2 <= n and "
1191 "i2 <= 3 j2 - 4 and j2 <= 2 i2 -1 and j2 <= n and "
1192 "13 + 4 j2 <= 11 i2 and i2 = i + 3 k1 + k3 and "
1193 "j2 = j + 3 k2 + k3 and k1 >= 0 and k2 >= 0 and "
1194 "k3 >= 0 and k1 + k2 + k3 = k and k > 0) }");
1195 assert(isl_map_is_equal(map, map2));
1196 isl_map_free(map2);
1197 isl_map_free(map);
1198
1199 /* COCOA Fig.1 right */
1200 dom = isl_set_read_from_str(ctx,
1201 "{ [x,y] : x >= 0 and -2 x + 3 y >= 0 and x <= 3 and "
1202 "2 x - 3 y + 3 >= 0 }");
1203 right = isl_map_read_from_str(ctx,
1204 "{ [x,y] -> [x2,y2] : x2 = x + 1 and y2 = y }");
1205 up = isl_map_read_from_str(ctx,
1206 "{ [x,y] -> [x2,y2] : x2 = x and y2 = y + 1 }");
1207 right = isl_map_intersect_domain(right, isl_set_copy(dom));
1208 right = isl_map_intersect_range(right, isl_set_copy(dom));
1209 up = isl_map_intersect_domain(up, isl_set_copy(dom));
1210 up = isl_map_intersect_range(up, dom);
1211 map = isl_map_union(up, right);
1212 map = isl_map_transitive_closure(map, &exact);
1213 assert(exact);
1214 map2 = isl_map_read_from_str(ctx,
1215 "{ [0,0] -> [0,1]; [0,0] -> [1,1]; [0,1] -> [1,1]; "
1216 " [2,2] -> [3,2]; [2,2] -> [3,3]; [3,2] -> [3,3] }");
1217 assert(isl_map_is_equal(map, map2));
1218 isl_map_free(map2);
1219 isl_map_free(map);
1220
1221 /* COCOA Theorem 1 counter example */
1222 map = isl_map_read_from_str(ctx,
1223 "{ [i,j] -> [i2,j2] : i = 0 and 0 <= j and j <= 1 and "
1224 "i2 = 1 and j2 = j or "
1225 "i = 0 and j = 0 and i2 = 0 and j2 = 1 }");
1226 map = isl_map_transitive_closure(map, &exact);
1227 assert(exact);
1228 isl_map_free(map);
1229
1230 map = isl_map_read_from_str(ctx,
1231 "[m,n] -> { [i,j] -> [i2,j2] : i2 = i and j2 = j + 2 and "
1232 "1 <= i,i2 <= n and 1 <= j,j2 <= m or "
1233 "i2 = i + 1 and 3 <= j2 - j <= 4 and "
1234 "1 <= i,i2 <= n and 1 <= j,j2 <= m }");
1235 map = isl_map_transitive_closure(map, &exact);
1236 assert(exact);
1237 isl_map_free(map);
1238
1239 /* Kelly et al 1996, fig 12 */
1240 map = isl_map_read_from_str(ctx,
1241 "[n] -> { [i,j] -> [i2,j2] : i2 = i and j2 = j + 1 and "
1242 "1 <= i,j,j+1 <= n or "
1243 "j = n and j2 = 1 and i2 = i + 1 and "
1244 "1 <= i,i+1 <= n }");
1245 map = isl_map_transitive_closure(map, &exact);
1246 assert(exact);
1247 map2 = isl_map_read_from_str(ctx,
1248 "[n] -> { [i,j] -> [i2,j2] : 1 <= j < j2 <= n and "
1249 "1 <= i <= n and i = i2 or "
1250 "1 <= i < i2 <= n and 1 <= j <= n and "
1251 "1 <= j2 <= n }");
1252 assert(isl_map_is_equal(map, map2));
1253 isl_map_free(map2);
1254 isl_map_free(map);
1255
1256 /* Omega's closure4 */
1257 map = isl_map_read_from_str(ctx,
1258 "[m,n] -> { [x,y] -> [x2,y2] : x2 = x and y2 = y + 1 and "
1259 "1 <= x,y <= 10 or "
1260 "x2 = x + 1 and y2 = y and "
1261 "1 <= x <= 20 && 5 <= y <= 15 }");
1262 map = isl_map_transitive_closure(map, &exact);
1263 assert(exact);
1264 isl_map_free(map);
1265
1266 map = isl_map_read_from_str(ctx,
1267 "[n] -> { [x] -> [y]: 1 <= n <= y - x <= 10 }");
1268 map = isl_map_transitive_closure(map, &exact);
1269 assert(!exact);
1270 map2 = isl_map_read_from_str(ctx,
1271 "[n] -> { [x] -> [y] : 1 <= n <= 10 and y >= n + x }");
1272 assert(isl_map_is_equal(map, map2));
1273 isl_map_free(map);
1274 isl_map_free(map2);
1275
1276 str = "[n, m] -> { [i0, i1, i2, i3] -> [o0, o1, o2, o3] : "
1277 "i3 = 1 and o0 = i0 and o1 = -1 + i1 and o2 = -1 + i2 and "
1278 "o3 = -2 + i2 and i1 <= -1 + i0 and i1 >= 1 - m + i0 and "
1279 "i1 >= 2 and i1 <= n and i2 >= 3 and i2 <= 1 + n and i2 <= m }";
1280 map = isl_map_read_from_str(ctx, str);
1281 map = isl_map_transitive_closure(map, &exact);
1282 assert(exact);
1283 map2 = isl_map_read_from_str(ctx, str);
1284 assert(isl_map_is_equal(map, map2));
1285 isl_map_free(map);
1286 isl_map_free(map2);
1287
1288 str = "{[0] -> [1]; [2] -> [3]}";
1289 map = isl_map_read_from_str(ctx, str);
1290 map = isl_map_transitive_closure(map, &exact);
1291 assert(exact);
1292 map2 = isl_map_read_from_str(ctx, str);
1293 assert(isl_map_is_equal(map, map2));
1294 isl_map_free(map);
1295 isl_map_free(map2);
1296
1297 str = "[n] -> { [[i0, i1, 1, 0, i0] -> [i5, 1]] -> "
1298 "[[i0, -1 + i1, 2, 0, i0] -> [-1 + i5, 2]] : "
1299 "exists (e0 = [(3 - n)/3]: i5 >= 2 and i1 >= 2 and "
1300 "3i0 <= -1 + n and i1 <= -1 + n and i5 <= -1 + n and "
1301 "3e0 >= 1 - n and 3e0 <= 2 - n and 3i0 >= -2 + n); "
1302 "[[i0, i1, 2, 0, i0] -> [i5, 1]] -> "
1303 "[[i0, i1, 1, 0, i0] -> [-1 + i5, 2]] : "
1304 "exists (e0 = [(3 - n)/3]: i5 >= 2 and i1 >= 1 and "
1305 "3i0 <= -1 + n and i1 <= -1 + n and i5 <= -1 + n and "
1306 "3e0 >= 1 - n and 3e0 <= 2 - n and 3i0 >= -2 + n); "
1307 "[[i0, i1, 1, 0, i0] -> [i5, 2]] -> "
1308 "[[i0, -1 + i1, 2, 0, i0] -> [i5, 1]] : "
1309 "exists (e0 = [(3 - n)/3]: i1 >= 2 and i5 >= 1 and "
1310 "3i0 <= -1 + n and i1 <= -1 + n and i5 <= -1 + n and "
1311 "3e0 >= 1 - n and 3e0 <= 2 - n and 3i0 >= -2 + n); "
1312 "[[i0, i1, 2, 0, i0] -> [i5, 2]] -> "
1313 "[[i0, i1, 1, 0, i0] -> [i5, 1]] : "
1314 "exists (e0 = [(3 - n)/3]: i5 >= 1 and i1 >= 1 and "
1315 "3i0 <= -1 + n and i1 <= -1 + n and i5 <= -1 + n and "
1316 "3e0 >= 1 - n and 3e0 <= 2 - n and 3i0 >= -2 + n) }";
1317 map = isl_map_read_from_str(ctx, str);
1318 map = isl_map_transitive_closure(map, NULL);
1319 assert(map);
1320 isl_map_free(map);
1321 }
1322
1323 void test_lex(struct isl_ctx *ctx)
1324 {
1325 isl_space *dim;
1326 isl_map *map;
1327
1328 dim = isl_space_set_alloc(ctx, 0, 0);
1329 map = isl_map_lex_le(dim);
1330 assert(!isl_map_is_empty(map));
1331 isl_map_free(map);
1332 }
1333
1334 void test_lexmin(struct isl_ctx *ctx)
1335 {
1336 const char *str;
1337 isl_basic_map *bmap;
1338 isl_map *map, *map2;
1339 isl_set *set;
1340 isl_set *set2;
1341 isl_pw_multi_aff *pma;
1342
1343 str = "[p0, p1] -> { [] -> [] : "
1344 "exists (e0 = [(2p1)/3], e1, e2, e3 = [(3 - p1 + 3e0)/3], "
1345 "e4 = [(p1)/3], e5 = [(p1 + 3e4)/3]: "
1346 "3e0 >= -2 + 2p1 and 3e0 >= p1 and 3e3 >= 1 - p1 + 3e0 and "
1347 "3e0 <= 2p1 and 3e3 >= -2 + p1 and 3e3 <= -1 + p1 and p1 >= 3 and "
1348 "3e5 >= -2 + 2p1 and 3e5 >= p1 and 3e5 <= -1 + p1 + 3e4 and "
1349 "3e4 <= p1 and 3e4 >= -2 + p1 and e3 <= -1 + e0 and "
1350 "3e4 >= 6 - p1 + 3e1 and 3e1 >= p1 and 3e5 >= -2 + p1 + 3e4 and "
1351 "2e4 >= 3 - p1 + 2e1 and e4 <= e1 and 3e3 <= 2 - p1 + 3e0 and "
1352 "e5 >= 1 + e1 and 3e4 >= 6 - 2p1 + 3e1 and "
1353 "p0 >= 2 and p1 >= p0 and 3e2 >= p1 and 3e4 >= 6 - p1 + 3e2 and "
1354 "e2 <= e1 and e3 >= 1 and e4 <= e2) }";
1355 map = isl_map_read_from_str(ctx, str);
1356 map = isl_map_lexmin(map);
1357 isl_map_free(map);
1358
1359 str = "[C] -> { [obj,a,b,c] : obj <= 38 a + 7 b + 10 c and "
1360 "a + b <= 1 and c <= 10 b and c <= C and a,b,c,C >= 0 }";
1361 set = isl_set_read_from_str(ctx, str);
1362 set = isl_set_lexmax(set);
1363 str = "[C] -> { [obj,a,b,c] : C = 8 }";
1364 set2 = isl_set_read_from_str(ctx, str);
1365 set = isl_set_intersect(set, set2);
1366 assert(!isl_set_is_empty(set));
1367 isl_set_free(set);
1368
1369 str = "{ [x] -> [y] : x <= y <= 10; [x] -> [5] : -8 <= x <= 8 }";
1370 map = isl_map_read_from_str(ctx, str);
1371 map = isl_map_lexmin(map);
1372 str = "{ [x] -> [5] : 6 <= x <= 8; "
1373 "[x] -> [x] : x <= 5 or (9 <= x <= 10) }";
1374 map2 = isl_map_read_from_str(ctx, str);
1375 assert(isl_map_is_equal(map, map2));
1376 isl_map_free(map);
1377 isl_map_free(map2);
1378
1379 str = "{ [x] -> [y] : 4y = x or 4y = -1 + x or 4y = -2 + x }";
1380 map = isl_map_read_from_str(ctx, str);
1381 map2 = isl_map_copy(map);
1382 map = isl_map_lexmin(map);
1383 assert(isl_map_is_equal(map, map2));
1384 isl_map_free(map);
1385 isl_map_free(map2);
1386
1387 str = "{ [x] -> [y] : x = 4y; [x] -> [y] : x = 2y }";
1388 map = isl_map_read_from_str(ctx, str);
1389 map = isl_map_lexmin(map);
1390 str = "{ [x] -> [y] : (4y = x and x >= 0) or "
1391 "(exists (e0 = [(x)/4], e1 = [(-2 + x)/4]: 2y = x and "
1392 "4e1 = -2 + x and 4e0 <= -1 + x and 4e0 >= -3 + x)) or "
1393 "(exists (e0 = [(x)/4]: 2y = x and 4e0 = x and x <= -4)) }";
1394 map2 = isl_map_read_from_str(ctx, str);
1395 assert(isl_map_is_equal(map, map2));
1396 isl_map_free(map);
1397 isl_map_free(map2);
1398
1399 str = "{ [i] -> [i', j] : j = i - 8i' and i' >= 0 and i' <= 7 and "
1400 " 8i' <= i and 8i' >= -7 + i }";
1401 bmap = isl_basic_map_read_from_str(ctx, str);
1402 pma = isl_basic_map_lexmin_pw_multi_aff(isl_basic_map_copy(bmap));
1403 map2 = isl_map_from_pw_multi_aff(pma);
1404 map = isl_map_from_basic_map(bmap);
1405 assert(isl_map_is_equal(map, map2));
1406 isl_map_free(map);
1407 isl_map_free(map2);
1408
1409 str = "{ T[a] -> S[b, c] : a = 4b-2c and c >= b }";
1410 map = isl_map_read_from_str(ctx, str);
1411 map = isl_map_lexmin(map);
1412 str = "{ T[a] -> S[b, c] : 2b = a and 2c = a }";
1413 map2 = isl_map_read_from_str(ctx, str);
1414 assert(isl_map_is_equal(map, map2));
1415 isl_map_free(map);
1416 isl_map_free(map2);
1417 }
1418
1419 struct must_may {
1420 isl_map *must;
1421 isl_map *may;
1422 };
1423
1424 static int collect_must_may(__isl_take isl_map *dep, int must,
1425 void *dep_user, void *user)
1426 {
1427 struct must_may *mm = (struct must_may *)user;
1428
1429 if (must)
1430 mm->must = isl_map_union(mm->must, dep);
1431 else
1432 mm->may = isl_map_union(mm->may, dep);
1433
1434 return 0;
1435 }
1436
1437 static int common_space(void *first, void *second)
1438 {
1439 int depth = *(int *)first;
1440 return 2 * depth;
1441 }
1442
1443 static int map_is_equal(__isl_keep isl_map *map, const char *str)
1444 {
1445 isl_map *map2;
1446 int equal;
1447
1448 if (!map)
1449 return -1;
1450
1451 map2 = isl_map_read_from_str(map->ctx, str);
1452 equal = isl_map_is_equal(map, map2);
1453 isl_map_free(map2);
1454
1455 return equal;
1456 }
1457
1458 void test_dep(struct isl_ctx *ctx)
1459 {
1460 const char *str;
1461 isl_space *dim;
1462 isl_map *map;
1463 isl_access_info *ai;
1464 isl_flow *flow;
1465 int depth;
1466 struct must_may mm;
1467
1468 depth = 3;
1469
1470 str = "{ [2,i,0] -> [i] : 0 <= i <= 10 }";
1471 map = isl_map_read_from_str(ctx, str);
1472 ai = isl_access_info_alloc(map, &depth, &common_space, 2);
1473
1474 str = "{ [0,i,0] -> [i] : 0 <= i <= 10 }";
1475 map = isl_map_read_from_str(ctx, str);
1476 ai = isl_access_info_add_source(ai, map, 1, &depth);
1477
1478 str = "{ [1,i,0] -> [5] : 0 <= i <= 10 }";
1479 map = isl_map_read_from_str(ctx, str);
1480 ai = isl_access_info_add_source(ai, map, 1, &depth);
1481
1482 flow = isl_access_info_compute_flow(ai);
1483 dim = isl_space_alloc(ctx, 0, 3, 3);
1484 mm.must = isl_map_empty(isl_space_copy(dim));
1485 mm.may = isl_map_empty(dim);
1486
1487 isl_flow_foreach(flow, collect_must_may, &mm);
1488
1489 str = "{ [0,i,0] -> [2,i,0] : (0 <= i <= 4) or (6 <= i <= 10); "
1490 " [1,10,0] -> [2,5,0] }";
1491 assert(map_is_equal(mm.must, str));
1492 str = "{ [i,j,k] -> [l,m,n] : 1 = 0 }";
1493 assert(map_is_equal(mm.may, str));
1494
1495 isl_map_free(mm.must);
1496 isl_map_free(mm.may);
1497 isl_flow_free(flow);
1498
1499
1500 str = "{ [2,i,0] -> [i] : 0 <= i <= 10 }";
1501 map = isl_map_read_from_str(ctx, str);
1502 ai = isl_access_info_alloc(map, &depth, &common_space, 2);
1503
1504 str = "{ [0,i,0] -> [i] : 0 <= i <= 10 }";
1505 map = isl_map_read_from_str(ctx, str);
1506 ai = isl_access_info_add_source(ai, map, 1, &depth);
1507
1508 str = "{ [1,i,0] -> [5] : 0 <= i <= 10 }";
1509 map = isl_map_read_from_str(ctx, str);
1510 ai = isl_access_info_add_source(ai, map, 0, &depth);
1511
1512 flow = isl_access_info_compute_flow(ai);
1513 dim = isl_space_alloc(ctx, 0, 3, 3);
1514 mm.must = isl_map_empty(isl_space_copy(dim));
1515 mm.may = isl_map_empty(dim);
1516
1517 isl_flow_foreach(flow, collect_must_may, &mm);
1518
1519 str = "{ [0,i,0] -> [2,i,0] : (0 <= i <= 4) or (6 <= i <= 10) }";
1520 assert(map_is_equal(mm.must, str));
1521 str = "{ [0,5,0] -> [2,5,0]; [1,i,0] -> [2,5,0] : 0 <= i <= 10 }";
1522 assert(map_is_equal(mm.may, str));
1523
1524 isl_map_free(mm.must);
1525 isl_map_free(mm.may);
1526 isl_flow_free(flow);
1527
1528
1529 str = "{ [2,i,0] -> [i] : 0 <= i <= 10 }";
1530 map = isl_map_read_from_str(ctx, str);
1531 ai = isl_access_info_alloc(map, &depth, &common_space, 2);
1532
1533 str = "{ [0,i,0] -> [i] : 0 <= i <= 10 }";
1534 map = isl_map_read_from_str(ctx, str);
1535 ai = isl_access_info_add_source(ai, map, 0, &depth);
1536
1537 str = "{ [1,i,0] -> [5] : 0 <= i <= 10 }";
1538 map = isl_map_read_from_str(ctx, str);
1539 ai = isl_access_info_add_source(ai, map, 0, &depth);
1540
1541 flow = isl_access_info_compute_flow(ai);
1542 dim = isl_space_alloc(ctx, 0, 3, 3);
1543 mm.must = isl_map_empty(isl_space_copy(dim));
1544 mm.may = isl_map_empty(dim);
1545
1546 isl_flow_foreach(flow, collect_must_may, &mm);
1547
1548 str = "{ [0,i,0] -> [2,i,0] : 0 <= i <= 10; "
1549 " [1,i,0] -> [2,5,0] : 0 <= i <= 10 }";
1550 assert(map_is_equal(mm.may, str));
1551 str = "{ [i,j,k] -> [l,m,n] : 1 = 0 }";
1552 assert(map_is_equal(mm.must, str));
1553
1554 isl_map_free(mm.must);
1555 isl_map_free(mm.may);
1556 isl_flow_free(flow);
1557
1558
1559 str = "{ [0,i,2] -> [i] : 0 <= i <= 10 }";
1560 map = isl_map_read_from_str(ctx, str);
1561 ai = isl_access_info_alloc(map, &depth, &common_space, 2);
1562
1563 str = "{ [0,i,0] -> [i] : 0 <= i <= 10 }";
1564 map = isl_map_read_from_str(ctx, str);
1565 ai = isl_access_info_add_source(ai, map, 0, &depth);
1566
1567 str = "{ [0,i,1] -> [5] : 0 <= i <= 10 }";
1568 map = isl_map_read_from_str(ctx, str);
1569 ai = isl_access_info_add_source(ai, map, 0, &depth);
1570
1571 flow = isl_access_info_compute_flow(ai);
1572 dim = isl_space_alloc(ctx, 0, 3, 3);
1573 mm.must = isl_map_empty(isl_space_copy(dim));
1574 mm.may = isl_map_empty(dim);
1575
1576 isl_flow_foreach(flow, collect_must_may, &mm);
1577
1578 str = "{ [0,i,0] -> [0,i,2] : 0 <= i <= 10; "
1579 " [0,i,1] -> [0,5,2] : 0 <= i <= 5 }";
1580 assert(map_is_equal(mm.may, str));
1581 str = "{ [i,j,k] -> [l,m,n] : 1 = 0 }";
1582 assert(map_is_equal(mm.must, str));
1583
1584 isl_map_free(mm.must);
1585 isl_map_free(mm.may);
1586 isl_flow_free(flow);
1587
1588
1589 str = "{ [0,i,1] -> [i] : 0 <= i <= 10 }";
1590 map = isl_map_read_from_str(ctx, str);
1591 ai = isl_access_info_alloc(map, &depth, &common_space, 2);
1592
1593 str = "{ [0,i,0] -> [i] : 0 <= i <= 10 }";
1594 map = isl_map_read_from_str(ctx, str);
1595 ai = isl_access_info_add_source(ai, map, 0, &depth);
1596
1597 str = "{ [0,i,2] -> [5] : 0 <= i <= 10 }";
1598 map = isl_map_read_from_str(ctx, str);
1599 ai = isl_access_info_add_source(ai, map, 0, &depth);
1600
1601 flow = isl_access_info_compute_flow(ai);
1602 dim = isl_space_alloc(ctx, 0, 3, 3);
1603 mm.must = isl_map_empty(isl_space_copy(dim));
1604 mm.may = isl_map_empty(dim);
1605
1606 isl_flow_foreach(flow, collect_must_may, &mm);
1607
1608 str = "{ [0,i,0] -> [0,i,1] : 0 <= i <= 10; "
1609 " [0,i,2] -> [0,5,1] : 0 <= i <= 4 }";
1610 assert(map_is_equal(mm.may, str));
1611 str = "{ [i,j,k] -> [l,m,n] : 1 = 0 }";
1612 assert(map_is_equal(mm.must, str));
1613
1614 isl_map_free(mm.must);
1615 isl_map_free(mm.may);
1616 isl_flow_free(flow);
1617
1618
1619 depth = 5;
1620
1621 str = "{ [1,i,0,0,0] -> [i,j] : 0 <= i <= 10 and 0 <= j <= 10 }";
1622 map = isl_map_read_from_str(ctx, str);
1623 ai = isl_access_info_alloc(map, &depth, &common_space, 1);
1624
1625 str = "{ [0,i,0,j,0] -> [i,j] : 0 <= i <= 10 and 0 <= j <= 10 }";
1626 map = isl_map_read_from_str(ctx, str);
1627 ai = isl_access_info_add_source(ai, map, 1, &depth);
1628
1629 flow = isl_access_info_compute_flow(ai);
1630 dim = isl_space_alloc(ctx, 0, 5, 5);
1631 mm.must = isl_map_empty(isl_space_copy(dim));
1632 mm.may = isl_map_empty(dim);
1633
1634 isl_flow_foreach(flow, collect_must_may, &mm);
1635
1636 str = "{ [0,i,0,j,0] -> [1,i,0,0,0] : 0 <= i,j <= 10 }";
1637 assert(map_is_equal(mm.must, str));
1638 str = "{ [0,0,0,0,0] -> [0,0,0,0,0] : 1 = 0 }";
1639 assert(map_is_equal(mm.may, str));
1640
1641 isl_map_free(mm.must);
1642 isl_map_free(mm.may);
1643 isl_flow_free(flow);
1644 }
1645
1646 int test_sv(isl_ctx *ctx)
1647 {
1648 const char *str;
1649 isl_map *map;
1650 isl_union_map *umap;
1651 int sv;
1652
1653 str = "[N] -> { [i] -> [f] : 0 <= i <= N and 0 <= i - 10 f <= 9 }";
1654 map = isl_map_read_from_str(ctx, str);
1655 sv = isl_map_is_single_valued(map);
1656 isl_map_free(map);
1657 if (sv < 0)
1658 return -1;
1659 if (!sv)
1660 isl_die(ctx, isl_error_internal,
1661 "map not detected as single valued", return -1);
1662
1663 str = "[N] -> { [i] -> [f] : 0 <= i <= N and 0 <= i - 10 f <= 10 }";
1664 map = isl_map_read_from_str(ctx, str);
1665 sv = isl_map_is_single_valued(map);
1666 isl_map_free(map);
1667 if (sv < 0)
1668 return -1;
1669 if (sv)
1670 isl_die(ctx, isl_error_internal,
1671 "map detected as single valued", return -1);
1672
1673 str = "{ S1[i] -> [i] : 0 <= i <= 9; S2[i] -> [i] : 0 <= i <= 9 }";
1674 umap = isl_union_map_read_from_str(ctx, str);
1675 sv = isl_union_map_is_single_valued(umap);
1676 isl_union_map_free(umap);
1677 if (sv < 0)
1678 return -1;
1679 if (!sv)
1680 isl_die(ctx, isl_error_internal,
1681 "map not detected as single valued", return -1);
1682
1683 str = "{ [i] -> S1[i] : 0 <= i <= 9; [i] -> S2[i] : 0 <= i <= 9 }";
1684 umap = isl_union_map_read_from_str(ctx, str);
1685 sv = isl_union_map_is_single_valued(umap);
1686 isl_union_map_free(umap);
1687 if (sv < 0)
1688 return -1;
1689 if (sv)
1690 isl_die(ctx, isl_error_internal,
1691 "map detected as single valued", return -1);
1692
1693 return 0;
1694 }
1695
1696 void test_bijective_case(struct isl_ctx *ctx, const char *str, int bijective)
1697 {
1698 isl_map *map;
1699
1700 map = isl_map_read_from_str(ctx, str);
1701 if (bijective)
1702 assert(isl_map_is_bijective(map));
1703 else
1704 assert(!isl_map_is_bijective(map));
1705 isl_map_free(map);
1706 }
1707
1708 void test_bijective(struct isl_ctx *ctx)
1709 {
1710 test_bijective_case(ctx, "[N,M]->{[i,j] -> [i]}", 0);
1711 test_bijective_case(ctx, "[N,M]->{[i,j] -> [i] : j=i}", 1);
1712 test_bijective_case(ctx, "[N,M]->{[i,j] -> [i] : j=0}", 1);
1713 test_bijective_case(ctx, "[N,M]->{[i,j] -> [i] : j=N}", 1);
1714 test_bijective_case(ctx, "[N,M]->{[i,j] -> [j,i]}", 1);
1715 test_bijective_case(ctx, "[N,M]->{[i,j] -> [i+j]}", 0);
1716 test_bijective_case(ctx, "[N,M]->{[i,j] -> []}", 0);
1717 test_bijective_case(ctx, "[N,M]->{[i,j] -> [i,j,N]}", 1);
1718 test_bijective_case(ctx, "[N,M]->{[i,j] -> [2i]}", 0);
1719 test_bijective_case(ctx, "[N,M]->{[i,j] -> [i,i]}", 0);
1720 test_bijective_case(ctx, "[N,M]->{[i,j] -> [2i,i]}", 0);
1721 test_bijective_case(ctx, "[N,M]->{[i,j] -> [2i,j]}", 1);
1722 test_bijective_case(ctx, "[N,M]->{[i,j] -> [x,y] : 2x=i & y =j}", 1);
1723 }
1724
1725 void test_pwqp(struct isl_ctx *ctx)
1726 {
1727 const char *str;
1728 isl_set *set;
1729 isl_pw_qpolynomial *pwqp1, *pwqp2;
1730
1731 str = "{ [i,j,k] -> 1 + 9 * [i/5] + 7 * [j/11] + 4 * [k/13] }";
1732 pwqp1 = isl_pw_qpolynomial_read_from_str(ctx, str);
1733
1734 pwqp1 = isl_pw_qpolynomial_move_dims(pwqp1, isl_dim_param, 0,
1735 isl_dim_in, 1, 1);
1736
1737 str = "[j] -> { [i,k] -> 1 + 9 * [i/5] + 7 * [j/11] + 4 * [k/13] }";
1738 pwqp2 = isl_pw_qpolynomial_read_from_str(ctx, str);
1739
1740 pwqp1 = isl_pw_qpolynomial_sub(pwqp1, pwqp2);
1741
1742 assert(isl_pw_qpolynomial_is_zero(pwqp1));
1743
1744 isl_pw_qpolynomial_free(pwqp1);
1745
1746 str = "{ [i] -> i }";
1747 pwqp1 = isl_pw_qpolynomial_read_from_str(ctx, str);
1748 str = "{ [k] : exists a : k = 2a }";
1749 set = isl_set_read_from_str(ctx, str);
1750 pwqp1 = isl_pw_qpolynomial_gist(pwqp1, set);
1751 str = "{ [i] -> i }";
1752 pwqp2 = isl_pw_qpolynomial_read_from_str(ctx, str);
1753
1754 pwqp1 = isl_pw_qpolynomial_sub(pwqp1, pwqp2);
1755
1756 assert(isl_pw_qpolynomial_is_zero(pwqp1));
1757
1758 isl_pw_qpolynomial_free(pwqp1);
1759
1760 str = "{ [i] -> i + [ (i + [i/3])/2 ] }";
1761 pwqp1 = isl_pw_qpolynomial_read_from_str(ctx, str);
1762 str = "{ [10] }";
1763 set = isl_set_read_from_str(ctx, str);
1764 pwqp1 = isl_pw_qpolynomial_gist(pwqp1, set);
1765 str = "{ [i] -> 16 }";
1766 pwqp2 = isl_pw_qpolynomial_read_from_str(ctx, str);
1767
1768 pwqp1 = isl_pw_qpolynomial_sub(pwqp1, pwqp2);
1769
1770 assert(isl_pw_qpolynomial_is_zero(pwqp1));
1771
1772 isl_pw_qpolynomial_free(pwqp1);
1773
1774 str = "{ [i] -> ([(i)/2]) }";
1775 pwqp1 = isl_pw_qpolynomial_read_from_str(ctx, str);
1776 str = "{ [k] : exists a : k = 2a+1 }";
1777 set = isl_set_read_from_str(ctx, str);
1778 pwqp1 = isl_pw_qpolynomial_gist(pwqp1, set);
1779 str = "{ [i] -> -1/2 + 1/2 * i }";
1780 pwqp2 = isl_pw_qpolynomial_read_from_str(ctx, str);
1781
1782 pwqp1 = isl_pw_qpolynomial_sub(pwqp1, pwqp2);
1783
1784 assert(isl_pw_qpolynomial_is_zero(pwqp1));
1785
1786 isl_pw_qpolynomial_free(pwqp1);
1787
1788 str = "{ [i] -> ([([i/2] + [i/2])/5]) }";
1789 pwqp1 = isl_pw_qpolynomial_read_from_str(ctx, str);
1790 str = "{ [i] -> ([(2 * [i/2])/5]) }";
1791 pwqp2 = isl_pw_qpolynomial_read_from_str(ctx, str);
1792
1793 pwqp1 = isl_pw_qpolynomial_sub(pwqp1, pwqp2);
1794
1795 assert(isl_pw_qpolynomial_is_zero(pwqp1));
1796
1797 isl_pw_qpolynomial_free(pwqp1);
1798
1799 str = "{ [x] -> ([x/2] + [(x+1)/2]) }";
1800 pwqp1 = isl_pw_qpolynomial_read_from_str(ctx, str);
1801 str = "{ [x] -> x }";
1802 pwqp2 = isl_pw_qpolynomial_read_from_str(ctx, str);
1803
1804 pwqp1 = isl_pw_qpolynomial_sub(pwqp1, pwqp2);
1805
1806 assert(isl_pw_qpolynomial_is_zero(pwqp1));
1807
1808 isl_pw_qpolynomial_free(pwqp1);
1809
1810 str = "{ [i] -> ([i/2]) : i >= 0; [i] -> ([i/3]) : i < 0 }";
1811 pwqp1 = isl_pw_qpolynomial_read_from_str(ctx, str);
1812 pwqp2 = isl_pw_qpolynomial_read_from_str(ctx, str);
1813 pwqp1 = isl_pw_qpolynomial_coalesce(pwqp1);
1814 pwqp1 = isl_pw_qpolynomial_sub(pwqp1, pwqp2);
1815 assert(isl_pw_qpolynomial_is_zero(pwqp1));
1816 isl_pw_qpolynomial_free(pwqp1);
1817 }
1818
1819 void test_split_periods(isl_ctx *ctx)
1820 {
1821 const char *str;
1822 isl_pw_qpolynomial *pwqp;
1823
1824 str = "{ [U,V] -> 1/3 * U + 2/3 * V - [(U + 2V)/3] + [U/2] : "
1825 "U + 2V + 3 >= 0 and - U -2V >= 0 and - U + 10 >= 0 and "
1826 "U >= 0; [U,V] -> U^2 : U >= 100 }";
1827 pwqp = isl_pw_qpolynomial_read_from_str(ctx, str);
1828
1829 pwqp = isl_pw_qpolynomial_split_periods(pwqp, 2);
1830 assert(pwqp);
1831
1832 isl_pw_qpolynomial_free(pwqp);
1833 }
1834
1835 void test_union(isl_ctx *ctx)
1836 {
1837 const char *str;
1838 isl_union_set *uset1, *uset2;
1839 isl_union_map *umap1, *umap2;
1840
1841 str = "{ [i] : 0 <= i <= 1 }";
1842 uset1 = isl_union_set_read_from_str(ctx, str);
1843 str = "{ [1] -> [0] }";
1844 umap1 = isl_union_map_read_from_str(ctx, str);
1845
1846 umap2 = isl_union_set_lex_gt_union_set(isl_union_set_copy(uset1), uset1);
1847 assert(isl_union_map_is_equal(umap1, umap2));
1848
1849 isl_union_map_free(umap1);
1850 isl_union_map_free(umap2);
1851
1852 str = "{ A[i] -> B[i]; B[i] -> C[i]; A[0] -> C[1] }";
1853 umap1 = isl_union_map_read_from_str(ctx, str);
1854 str = "{ A[i]; B[i] }";
1855 uset1 = isl_union_set_read_from_str(ctx, str);
1856
1857 uset2 = isl_union_map_domain(umap1);
1858
1859 assert(isl_union_set_is_equal(uset1, uset2));
1860
1861 isl_union_set_free(uset1);
1862 isl_union_set_free(uset2);
1863 }
1864
1865 void test_bound(isl_ctx *ctx)
1866 {
1867 const char *str;
1868 isl_pw_qpolynomial *pwqp;
1869 isl_pw_qpolynomial_fold *pwf;
1870
1871 str = "{ [[a, b, c, d] -> [e]] -> 0 }";
1872 pwqp = isl_pw_qpolynomial_read_from_str(ctx, str);
1873 pwf = isl_pw_qpolynomial_bound(pwqp, isl_fold_max, NULL);
1874 assert(isl_pw_qpolynomial_fold_dim(pwf, isl_dim_in) == 4);
1875 isl_pw_qpolynomial_fold_free(pwf);
1876
1877 str = "{ [[x]->[x]] -> 1 : exists a : x = 2 a }";
1878 pwqp = isl_pw_qpolynomial_read_from_str(ctx, str);
1879 pwf = isl_pw_qpolynomial_bound(pwqp, isl_fold_max, NULL);
1880 assert(isl_pw_qpolynomial_fold_dim(pwf, isl_dim_in) == 1);
1881 isl_pw_qpolynomial_fold_free(pwf);
1882 }
1883
1884 void test_lift(isl_ctx *ctx)
1885 {
1886 const char *str;
1887 isl_basic_map *bmap;
1888 isl_basic_set *bset;
1889
1890 str = "{ [i0] : exists e0 : i0 = 4e0 }";
1891 bset = isl_basic_set_read_from_str(ctx, str);
1892 bset = isl_basic_set_lift(bset);
1893 bmap = isl_basic_map_from_range(bset);
1894 bset = isl_basic_map_domain(bmap);
1895 isl_basic_set_free(bset);
1896 }
1897
1898 void test_subset(isl_ctx *ctx)
1899 {
1900 const char *str;
1901 isl_set *set1, *set2;
1902
1903 str = "{ [112, 0] }";
1904 set1 = isl_set_read_from_str(ctx, str);
1905 str = "{ [i0, i1] : exists (e0 = [(i0 - i1)/16], e1: "
1906 "16e0 <= i0 - i1 and 16e0 >= -15 + i0 - i1 and "
1907 "16e1 <= i1 and 16e0 >= -i1 and 16e1 >= -i0 + i1) }";
1908 set2 = isl_set_read_from_str(ctx, str);
1909 assert(isl_set_is_subset(set1, set2));
1910 isl_set_free(set1);
1911 isl_set_free(set2);
1912 }
1913
1914 void test_factorize(isl_ctx *ctx)
1915 {
1916 const char *str;
1917 isl_basic_set *bset;
1918 isl_factorizer *f;
1919
1920 str = "{ [i0, i1, i2, i3, i4, i5, i6, i7] : 3i5 <= 2 - 2i0 and "
1921 "i0 >= -2 and i6 >= 1 + i3 and i7 >= 0 and 3i5 >= -2i0 and "
1922 "2i4 <= i2 and i6 >= 1 + 2i0 + 3i1 and i4 <= -1 and "
1923 "i6 >= 1 + 2i0 + 3i5 and i6 <= 2 + 2i0 + 3i5 and "
1924 "3i5 <= 2 - 2i0 - i2 + 3i4 and i6 <= 2 + 2i0 + 3i1 and "
1925 "i0 <= -1 and i7 <= i2 + i3 - 3i4 - i6 and "
1926 "3i5 >= -2i0 - i2 + 3i4 }";
1927 bset = isl_basic_set_read_from_str(ctx, str);
1928 f = isl_basic_set_factorizer(bset);
1929 assert(f);
1930 isl_basic_set_free(bset);
1931 isl_factorizer_free(f);
1932
1933 str = "{ [i0, i1, i2, i3, i4, i5, i6, i7, i8, i9, i10, i11, i12] : "
1934 "i12 <= 2 + i0 - i11 and 2i8 >= -i4 and i11 >= i1 and "
1935 "3i5 <= -i2 and 2i11 >= -i4 - 2i7 and i11 <= 3 + i0 + 3i9 and "
1936 "i11 <= -i4 - 2i7 and i12 >= -i10 and i2 >= -2 and "
1937 "i11 >= i1 + 3i10 and i11 >= 1 + i0 + 3i9 and "
1938 "i11 <= 1 - i4 - 2i8 and 6i6 <= 6 - i2 and 3i6 >= 1 - i2 and "
1939 "i11 <= 2 + i1 and i12 <= i4 + i11 and i12 >= i0 - i11 and "
1940 "3i5 >= -2 - i2 and i12 >= -1 + i4 + i11 and 3i3 <= 3 - i2 and "
1941 "9i6 <= 11 - i2 + 6i5 and 3i3 >= 1 - i2 and "
1942 "9i6 <= 5 - i2 + 6i3 and i12 <= -1 and i2 <= 0 }";
1943 bset = isl_basic_set_read_from_str(ctx, str);
1944 f = isl_basic_set_factorizer(bset);
1945 assert(f);
1946 isl_basic_set_free(bset);
1947 isl_factorizer_free(f);
1948 }
1949
1950 static int check_injective(__isl_take isl_map *map, void *user)
1951 {
1952 int *injective = user;
1953
1954 *injective = isl_map_is_injective(map);
1955 isl_map_free(map);
1956
1957 if (*injective < 0 || !*injective)
1958 return -1;
1959
1960 return 0;
1961 }
1962
1963 int test_one_schedule(isl_ctx *ctx, const char *d, const char *w,
1964 const char *r, const char *s, int tilable, int parallel)
1965 {
1966 int i;
1967 isl_union_set *D;
1968 isl_union_map *W, *R, *S;
1969 isl_union_map *empty;
1970 isl_union_map *dep_raw, *dep_war, *dep_waw, *dep;
1971 isl_union_map *validity, *proximity;
1972 isl_union_map *schedule;
1973 isl_union_map *test;
1974 isl_union_set *delta;
1975 isl_union_set *domain;
1976 isl_set *delta_set;
1977 isl_set *slice;
1978 isl_set *origin;
1979 isl_schedule *sched;
1980 int is_nonneg, is_parallel, is_tilable, is_injection, is_complete;
1981
1982 D = isl_union_set_read_from_str(ctx, d);
1983 W = isl_union_map_read_from_str(ctx, w);
1984 R = isl_union_map_read_from_str(ctx, r);
1985 S = isl_union_map_read_from_str(ctx, s);
1986
1987 W = isl_union_map_intersect_domain(W, isl_union_set_copy(D));
1988 R = isl_union_map_intersect_domain(R, isl_union_set_copy(D));
1989
1990 empty = isl_union_map_empty(isl_union_map_get_space(S));
1991 isl_union_map_compute_flow(isl_union_map_copy(R),
1992 isl_union_map_copy(W), empty,
1993 isl_union_map_copy(S),
1994 &dep_raw, NULL, NULL, NULL);
1995 isl_union_map_compute_flow(isl_union_map_copy(W),
1996 isl_union_map_copy(W),
1997 isl_union_map_copy(R),
1998 isl_union_map_copy(S),
1999 &dep_waw, &dep_war, NULL, NULL);
2000
2001 dep = isl_union_map_union(dep_waw, dep_war);
2002 dep = isl_union_map_union(dep, dep_raw);
2003 validity = isl_union_map_copy(dep);
2004 proximity = isl_union_map_copy(dep);
2005
2006 sched = isl_union_set_compute_schedule(isl_union_set_copy(D),
2007 validity, proximity);
2008 schedule = isl_schedule_get_map(sched);
2009 isl_schedule_free(sched);
2010 isl_union_map_free(W);
2011 isl_union_map_free(R);
2012 isl_union_map_free(S);
2013
2014 is_injection = 1;
2015 isl_union_map_foreach_map(schedule, &check_injective, &is_injection);
2016
2017 domain = isl_union_map_domain(isl_union_map_copy(schedule));
2018 is_complete = isl_union_set_is_subset(D, domain);
2019 isl_union_set_free(D);
2020 isl_union_set_free(domain);
2021
2022 test = isl_union_map_reverse(isl_union_map_copy(schedule));
2023 test = isl_union_map_apply_range(test, dep);
2024 test = isl_union_map_apply_range(test, schedule);
2025
2026 delta = isl_union_map_deltas(test);
2027 if (isl_union_set_n_set(delta) == 0) {
2028 is_tilable = 1;
2029 is_parallel = 1;
2030 is_nonneg = 1;
2031 isl_union_set_free(delta);
2032 } else {
2033 delta_set = isl_set_from_union_set(delta);
2034
2035 slice = isl_set_universe(isl_set_get_space(delta_set));
2036 for (i = 0; i < tilable; ++i)
2037 slice = isl_set_lower_bound_si(slice, isl_dim_set, i, 0);
2038 is_tilable = isl_set_is_subset(delta_set, slice);
2039 isl_set_free(slice);
2040
2041 slice = isl_set_universe(isl_set_get_space(delta_set));
2042 for (i = 0; i < parallel; ++i)
2043 slice = isl_set_fix_si(slice, isl_dim_set, i, 0);
2044 is_parallel = isl_set_is_subset(delta_set, slice);
2045 isl_set_free(slice);
2046
2047 origin = isl_set_universe(isl_set_get_space(delta_set));
2048 for (i = 0; i < isl_set_dim(origin, isl_dim_set); ++i)
2049 origin = isl_set_fix_si(origin, isl_dim_set, i, 0);
2050
2051 delta_set = isl_set_union(delta_set, isl_set_copy(origin));
2052 delta_set = isl_set_lexmin(delta_set);
2053
2054 is_nonneg = isl_set_is_equal(delta_set, origin);
2055
2056 isl_set_free(origin);
2057 isl_set_free(delta_set);
2058 }
2059
2060 if (is_nonneg < 0 || is_parallel < 0 || is_tilable < 0 ||
2061 is_injection < 0 || is_complete < 0)
2062 return -1;
2063 if (!is_complete)
2064 isl_die(ctx, isl_error_unknown,
2065 "generated schedule incomplete", return -1);
2066 if (!is_injection)
2067 isl_die(ctx, isl_error_unknown,
2068 "generated schedule not injective on each statement",
2069 return -1);
2070 if (!is_nonneg)
2071 isl_die(ctx, isl_error_unknown,
2072 "negative dependences in generated schedule",
2073 return -1);
2074 if (!is_tilable)
2075 isl_die(ctx, isl_error_unknown,
2076 "generated schedule not as tilable as expected",
2077 return -1);
2078 if (!is_parallel)
2079 isl_die(ctx, isl_error_unknown,
2080 "generated schedule not as parallel as expected",
2081 return -1);
2082
2083 return 0;
2084 }
2085
2086 int test_special_schedule(isl_ctx *ctx, const char *domain,
2087 const char *validity, const char *proximity, const char *expected_sched)
2088 {
2089 isl_union_set *dom;
2090 isl_union_map *dep;
2091 isl_union_map *prox;
2092 isl_union_map *sched1, *sched2;
2093 isl_schedule *schedule;
2094 int equal;
2095
2096 dom = isl_union_set_read_from_str(ctx, domain);
2097 dep = isl_union_map_read_from_str(ctx, validity);
2098 prox = isl_union_map_read_from_str(ctx, proximity);
2099 schedule = isl_union_set_compute_schedule(dom, dep, prox);
2100 sched1 = isl_schedule_get_map(schedule);
2101 isl_schedule_free(schedule);
2102
2103 sched2 = isl_union_map_read_from_str(ctx, expected_sched);
2104
2105 equal = isl_union_map_is_equal(sched1, sched2);
2106 isl_union_map_free(sched1);
2107 isl_union_map_free(sched2);
2108
2109 if (equal < 0)
2110 return -1;
2111 if (!equal)
2112 isl_die(ctx, isl_error_unknown, "unexpected schedule",
2113 return -1);
2114
2115 return 0;
2116 }
2117
2118 int test_schedule(isl_ctx *ctx)
2119 {
2120 const char *D, *W, *R, *V, *P, *S;
2121
2122 /* Jacobi */
2123 D = "[T,N] -> { S1[t,i] : 1 <= t <= T and 2 <= i <= N - 1 }";
2124 W = "{ S1[t,i] -> a[t,i] }";
2125 R = "{ S1[t,i] -> a[t-1,i]; S1[t,i] -> a[t-1,i-1]; "
2126 "S1[t,i] -> a[t-1,i+1] }";
2127 S = "{ S1[t,i] -> [t,i] }";
2128 if (test_one_schedule(ctx, D, W, R, S, 2, 0) < 0)
2129 return -1;
2130
2131 /* Fig. 5 of CC2008 */
2132 D = "[N] -> { S_0[i, j] : i >= 0 and i <= -1 + N and j >= 2 and "
2133 "j <= -1 + N }";
2134 W = "[N] -> { S_0[i, j] -> a[i, j] : i >= 0 and i <= -1 + N and "
2135 "j >= 2 and j <= -1 + N }";
2136 R = "[N] -> { S_0[i, j] -> a[j, i] : i >= 0 and i <= -1 + N and "
2137 "j >= 2 and j <= -1 + N; "
2138 "S_0[i, j] -> a[i, -1 + j] : i >= 0 and i <= -1 + N and "
2139 "j >= 2 and j <= -1 + N }";
2140 S = "[N] -> { S_0[i, j] -> [0, i, 0, j, 0] }";
2141 if (test_one_schedule(ctx, D, W, R, S, 2, 0) < 0)
2142 return -1;
2143
2144 D = "{ S1[i] : 0 <= i <= 10; S2[i] : 0 <= i <= 9 }";
2145 W = "{ S1[i] -> a[i] }";
2146 R = "{ S2[i] -> a[i+1] }";
2147 S = "{ S1[i] -> [0,i]; S2[i] -> [1,i] }";
2148 if (test_one_schedule(ctx, D, W, R, S, 1, 1) < 0)
2149 return -1;
2150
2151 D = "{ S1[i] : 0 <= i < 10; S2[i] : 0 <= i < 10 }";
2152 W = "{ S1[i] -> a[i] }";
2153 R = "{ S2[i] -> a[9-i] }";
2154 S = "{ S1[i] -> [0,i]; S2[i] -> [1,i] }";
2155 if (test_one_schedule(ctx, D, W, R, S, 1, 1) < 0)
2156 return -1;
2157
2158 D = "[N] -> { S1[i] : 0 <= i < N; S2[i] : 0 <= i < N }";
2159 W = "{ S1[i] -> a[i] }";
2160 R = "[N] -> { S2[i] -> a[N-1-i] }";
2161 S = "{ S1[i] -> [0,i]; S2[i] -> [1,i] }";
2162 if (test_one_schedule(ctx, D, W, R, S, 1, 1) < 0)
2163 return -1;
2164
2165 D = "{ S1[i] : 0 < i < 10; S2[i] : 0 <= i < 10 }";
2166 W = "{ S1[i] -> a[i]; S2[i] -> b[i] }";
2167 R = "{ S2[i] -> a[i]; S1[i] -> b[i-1] }";
2168 S = "{ S1[i] -> [i,0]; S2[i] -> [i,1] }";
2169 if (test_one_schedule(ctx, D, W, R, S, 0, 0) < 0)
2170 return -1;
2171
2172 D = "[N] -> { S1[i] : 1 <= i <= N; S2[i,j] : 1 <= i,j <= N }";
2173 W = "{ S1[i] -> a[0,i]; S2[i,j] -> a[i,j] }";
2174 R = "{ S2[i,j] -> a[i-1,j] }";
2175 S = "{ S1[i] -> [0,i,0]; S2[i,j] -> [1,i,j] }";
2176 if (test_one_schedule(ctx, D, W, R, S, 2, 1) < 0)
2177 return -1;
2178
2179 D = "[N] -> { S1[i] : 1 <= i <= N; S2[i,j] : 1 <= i,j <= N }";
2180 W = "{ S1[i] -> a[i,0]; S2[i,j] -> a[i,j] }";
2181 R = "{ S2[i,j] -> a[i,j-1] }";
2182 S = "{ S1[i] -> [0,i,0]; S2[i,j] -> [1,i,j] }";
2183 if (test_one_schedule(ctx, D, W, R, S, 2, 1) < 0)
2184 return -1;
2185
2186 D = "[N] -> { S_0[]; S_1[i] : i >= 0 and i <= -1 + N; S_2[] }";
2187 W = "[N] -> { S_0[] -> a[0]; S_2[] -> b[0]; "
2188 "S_1[i] -> a[1 + i] : i >= 0 and i <= -1 + N }";
2189 R = "[N] -> { S_2[] -> a[N]; S_1[i] -> a[i] : i >= 0 and i <= -1 + N }";
2190 S = "[N] -> { S_1[i] -> [1, i, 0]; S_2[] -> [2, 0, 1]; "
2191 "S_0[] -> [0, 0, 0] }";
2192 if (test_one_schedule(ctx, D, W, R, S, 1, 0) < 0)
2193 return -1;
2194 ctx->opt->schedule_parametric = 0;
2195 if (test_one_schedule(ctx, D, W, R, S, 0, 0) < 0)
2196 return -1;
2197 ctx->opt->schedule_parametric = 1;
2198
2199 D = "[N] -> { S1[i] : 1 <= i <= N; S2[i] : 1 <= i <= N; "
2200 "S3[i,j] : 1 <= i,j <= N; S4[i] : 1 <= i <= N }";
2201 W = "{ S1[i] -> a[i,0]; S2[i] -> a[0,i]; S3[i,j] -> a[i,j] }";
2202 R = "[N] -> { S3[i,j] -> a[i-1,j]; S3[i,j] -> a[i,j-1]; "
2203 "S4[i] -> a[i,N] }";
2204 S = "{ S1[i] -> [0,i,0]; S2[i] -> [1,i,0]; S3[i,j] -> [2,i,j]; "
2205 "S4[i] -> [4,i,0] }";
2206 if (test_one_schedule(ctx, D, W, R, S, 2, 0) < 0)
2207 return -1;
2208
2209 D = "[N] -> { S_0[i, j] : i >= 1 and i <= N and j >= 1 and j <= N }";
2210 W = "[N] -> { S_0[i, j] -> s[0] : i >= 1 and i <= N and j >= 1 and "
2211 "j <= N }";
2212 R = "[N] -> { S_0[i, j] -> s[0] : i >= 1 and i <= N and j >= 1 and "
2213 "j <= N; "
2214 "S_0[i, j] -> a[i, j] : i >= 1 and i <= N and j >= 1 and "
2215 "j <= N }";
2216 S = "[N] -> { S_0[i, j] -> [0, i, 0, j, 0] }";
2217 if (test_one_schedule(ctx, D, W, R, S, 0, 0) < 0)
2218 return -1;
2219
2220 D = "[N] -> { S_0[t] : t >= 0 and t <= -1 + N; "
2221 " S_2[t] : t >= 0 and t <= -1 + N; "
2222 " S_1[t, i] : t >= 0 and t <= -1 + N and i >= 0 and "
2223 "i <= -1 + N }";
2224 W = "[N] -> { S_0[t] -> a[t, 0] : t >= 0 and t <= -1 + N; "
2225 " S_2[t] -> b[t] : t >= 0 and t <= -1 + N; "
2226 " S_1[t, i] -> a[t, 1 + i] : t >= 0 and t <= -1 + N and "
2227 "i >= 0 and i <= -1 + N }";
2228 R = "[N] -> { S_1[t, i] -> a[t, i] : t >= 0 and t <= -1 + N and "
2229 "i >= 0 and i <= -1 + N; "
2230 " S_2[t] -> a[t, N] : t >= 0 and t <= -1 + N }";
2231 S = "[N] -> { S_2[t] -> [0, t, 2]; S_1[t, i] -> [0, t, 1, i, 0]; "
2232 " S_0[t] -> [0, t, 0] }";
2233
2234 if (test_one_schedule(ctx, D, W, R, S, 2, 1) < 0)
2235 return -1;
2236 ctx->opt->schedule_parametric = 0;
2237 if (test_one_schedule(ctx, D, W, R, S, 0, 0) < 0)
2238 return -1;
2239 ctx->opt->schedule_parametric = 1;
2240
2241 D = "[N] -> { S1[i,j] : 0 <= i,j < N; S2[i,j] : 0 <= i,j < N }";
2242 S = "{ S1[i,j] -> [0,i,j]; S2[i,j] -> [1,i,j] }";
2243 if (test_one_schedule(ctx, D, "{}", "{}", S, 2, 2) < 0)
2244 return -1;
2245
2246 D = "[M, N] -> { S_1[i] : i >= 0 and i <= -1 + M; "
2247 "S_0[i, j] : i >= 0 and i <= -1 + M and j >= 0 and j <= -1 + N }";
2248 W = "[M, N] -> { S_0[i, j] -> a[j] : i >= 0 and i <= -1 + M and "
2249 "j >= 0 and j <= -1 + N; "
2250 "S_1[i] -> b[0] : i >= 0 and i <= -1 + M }";
2251 R = "[M, N] -> { S_0[i, j] -> a[0] : i >= 0 and i <= -1 + M and "
2252 "j >= 0 and j <= -1 + N; "
2253 "S_1[i] -> b[0] : i >= 0 and i <= -1 + M }";
2254 S = "[M, N] -> { S_1[i] -> [1, i, 0]; S_0[i, j] -> [0, i, 0, j, 0] }";
2255 if (test_one_schedule(ctx, D, W, R, S, 0, 0) < 0)
2256 return -1;
2257
2258 D = "{ S_0[i] : i >= 0 }";
2259 W = "{ S_0[i] -> a[i] : i >= 0 }";
2260 R = "{ S_0[i] -> a[0] : i >= 0 }";
2261 S = "{ S_0[i] -> [0, i, 0] }";
2262 if (test_one_schedule(ctx, D, W, R, S, 0, 0) < 0)
2263 return -1;
2264
2265 D = "{ S_0[i] : i >= 0; S_1[i] : i >= 0 }";
2266 W = "{ S_0[i] -> a[i] : i >= 0; S_1[i] -> b[i] : i >= 0 }";
2267 R = "{ S_0[i] -> b[0] : i >= 0; S_1[i] -> a[i] : i >= 0 }";
2268 S = "{ S_1[i] -> [0, i, 1]; S_0[i] -> [0, i, 0] }";
2269 if (test_one_schedule(ctx, D, W, R, S, 0, 0) < 0)
2270 return -1;
2271
2272 D = "[n] -> { S_0[j, k] : j <= -1 + n and j >= 0 and "
2273 "k <= -1 + n and k >= 0 }";
2274 W = "[n] -> { S_0[j, k] -> B[j] : j <= -1 + n and j >= 0 and " "k <= -1 + n and k >= 0 }";
2275 R = "[n] -> { S_0[j, k] -> B[j] : j <= -1 + n and j >= 0 and "
2276 "k <= -1 + n and k >= 0; "
2277 "S_0[j, k] -> B[k] : j <= -1 + n and j >= 0 and "
2278 "k <= -1 + n and k >= 0; "
2279 "S_0[j, k] -> A[k] : j <= -1 + n and j >= 0 and "
2280 "k <= -1 + n and k >= 0 }";
2281 S = "[n] -> { S_0[j, k] -> [2, j, k] }";
2282 ctx->opt->schedule_outer_zero_distance = 1;
2283 if (test_one_schedule(ctx, D, W, R, S, 0, 0) < 0)
2284 return -1;
2285 ctx->opt->schedule_outer_zero_distance = 0;
2286
2287 D = "{Stmt_for_body24[i0, i1, i2, i3]:"
2288 "i0 >= 0 and i0 <= 1 and i1 >= 0 and i1 <= 6 and i2 >= 2 and "
2289 "i2 <= 6 - i1 and i3 >= 0 and i3 <= -1 + i2;"
2290 "Stmt_for_body24[i0, i1, 1, 0]:"
2291 "i0 >= 0 and i0 <= 1 and i1 >= 0 and i1 <= 5;"
2292 "Stmt_for_body7[i0, i1, i2]:"
2293 "i0 >= 0 and i0 <= 1 and i1 >= 0 and i1 <= 7 and i2 >= 0 and "
2294 "i2 <= 7 }";
2295
2296 V = "{Stmt_for_body24[0, i1, i2, i3] -> "
2297 "Stmt_for_body24[1, i1, i2, i3]:"
2298 "i3 >= 0 and i3 <= -1 + i2 and i1 >= 0 and i2 <= 6 - i1 and "
2299 "i2 >= 1;"
2300 "Stmt_for_body24[0, i1, i2, i3] -> "
2301 "Stmt_for_body7[1, 1 + i1 + i3, 1 + i1 + i2]:"
2302 "i3 <= -1 + i2 and i2 <= 6 - i1 and i2 >= 1 and i1 >= 0 and "
2303 "i3 >= 0;"
2304 "Stmt_for_body24[0, i1, i2, i3] ->"
2305 "Stmt_for_body7[1, i1, 1 + i1 + i3]:"
2306 "i3 >= 0 and i2 <= 6 - i1 and i1 >= 0 and i3 <= -1 + i2;"
2307 "Stmt_for_body7[0, i1, i2] -> Stmt_for_body7[1, i1, i2]:"
2308 "(i2 >= 1 + i1 and i2 <= 6 and i1 >= 0 and i1 <= 4) or "
2309 "(i2 >= 3 and i2 <= 7 and i1 >= 1 and i2 >= 1 + i1) or "
2310 "(i2 >= 0 and i2 <= i1 and i2 >= -7 + i1 and i1 <= 7);"
2311 "Stmt_for_body7[0, i1, 1 + i1] -> Stmt_for_body7[1, i1, 1 + i1]:"
2312 "i1 <= 6 and i1 >= 0;"
2313 "Stmt_for_body7[0, 0, 7] -> Stmt_for_body7[1, 0, 7];"
2314 "Stmt_for_body7[i0, i1, i2] -> "
2315 "Stmt_for_body24[i0, o1, -1 + i2 - o1, -1 + i1 - o1]:"
2316 "i0 >= 0 and i0 <= 1 and o1 >= 0 and i2 >= 1 + i1 and "
2317 "o1 <= -2 + i2 and i2 <= 7 and o1 <= -1 + i1;"
2318 "Stmt_for_body7[i0, i1, i2] -> "
2319 "Stmt_for_body24[i0, i1, o2, -1 - i1 + i2]:"
2320 "i0 >= 0 and i0 <= 1 and i1 >= 0 and o2 >= -i1 + i2 and "
2321 "o2 >= 1 and o2 <= 6 - i1 and i2 >= 1 + i1 }";
2322 P = V;
2323 S = "{ Stmt_for_body24[i0, i1, i2, i3] -> "
2324 "[i0, 5i0 + i1, 6i0 + i1 + i2, 1 + 6i0 + i1 + i2 + i3, 1];"
2325 "Stmt_for_body7[i0, i1, i2] -> [0, 5i0, 6i0 + i1, 6i0 + i2, 0] }";
2326
2327 if (test_special_schedule(ctx, D, V, P, S) < 0)
2328 return -1;
2329
2330 D = "{ S_0[i, j] : i >= 1 and i <= 10 and j >= 1 and j <= 8 }";
2331 V = "{ S_0[i, j] -> S_0[i, 1 + j] : i >= 1 and i <= 10 and "
2332 "j >= 1 and j <= 7;"
2333 "S_0[i, j] -> S_0[1 + i, j] : i >= 1 and i <= 9 and "
2334 "j >= 1 and j <= 8 }";
2335 P = "{ }";
2336 S = "{ S_0[i, j] -> [i + j, j] }";
2337 ctx->opt->schedule_algorithm = ISL_SCHEDULE_ALGORITHM_FEAUTRIER;
2338 if (test_special_schedule(ctx, D, V, P, S) < 0)
2339 return -1;
2340 ctx->opt->schedule_algorithm = ISL_SCHEDULE_ALGORITHM_ISL;
2341
2342 /* Fig. 1 from Feautrier's "Some Efficient Solutions..." pt. 2, 1992 */
2343 D = "[N] -> { S_0[i, j] : i >= 0 and i <= -1 + N and "
2344 "j >= 0 and j <= -1 + i }";
2345 V = "[N] -> { S_0[i, j] -> S_0[i, 1 + j] : j <= -2 + i and "
2346 "i <= -1 + N and j >= 0;"
2347 "S_0[i, -1 + i] -> S_0[1 + i, 0] : i >= 1 and "
2348 "i <= -2 + N }";
2349 P = "{ }";
2350 S = "{ S_0[i, j] -> [i, j] }";
2351 ctx->opt->schedule_algorithm = ISL_SCHEDULE_ALGORITHM_FEAUTRIER;
2352 if (test_special_schedule(ctx, D, V, P, S) < 0)
2353 return -1;
2354 ctx->opt->schedule_algorithm = ISL_SCHEDULE_ALGORITHM_ISL;
2355
2356 /* Test both algorithms on a case with only proximity dependences. */
2357 D = "{ S[i,j] : 0 <= i <= 10 }";
2358 V = "{ }";
2359 P = "{ S[i,j] -> S[i+1,j] : 0 <= i,j <= 10 }";
2360 S = "{ S[i, j] -> [j, i] }";
2361 ctx->opt->schedule_algorithm = ISL_SCHEDULE_ALGORITHM_FEAUTRIER;
2362 if (test_special_schedule(ctx, D, V, P, S) < 0)
2363 return -1;
2364 ctx->opt->schedule_algorithm = ISL_SCHEDULE_ALGORITHM_ISL;
2365 return test_special_schedule(ctx, D, V, P, S);
2366 }
2367
2368 int test_plain_injective(isl_ctx *ctx, const char *str, int injective)
2369 {
2370 isl_union_map *umap;
2371 int test;
2372
2373 umap = isl_union_map_read_from_str(ctx, str);
2374 test = isl_union_map_plain_is_injective(umap);
2375 isl_union_map_free(umap);
2376 if (test < 0)
2377 return -1;
2378 if (test == injective)
2379 return 0;
2380 if (injective)
2381 isl_die(ctx, isl_error_unknown,
2382 "map not detected as injective", return -1);
2383 else
2384 isl_die(ctx, isl_error_unknown,
2385 "map detected as injective", return -1);
2386 }
2387
2388 int test_injective(isl_ctx *ctx)
2389 {
2390 const char *str;
2391
2392 if (test_plain_injective(ctx, "{S[i,j] -> A[0]; T[i,j] -> B[1]}", 0))
2393 return -1;
2394 if (test_plain_injective(ctx, "{S[] -> A[0]; T[] -> B[0]}", 1))
2395 return -1;
2396 if (test_plain_injective(ctx, "{S[] -> A[0]; T[] -> A[1]}", 1))
2397 return -1;
2398 if (test_plain_injective(ctx, "{S[] -> A[0]; T[] -> A[0]}", 0))
2399 return -1;
2400 if (test_plain_injective(ctx, "{S[i] -> A[i,0]; T[i] -> A[i,1]}", 1))
2401 return -1;
2402 if (test_plain_injective(ctx, "{S[i] -> A[i]; T[i] -> A[i]}", 0))
2403 return -1;
2404 if (test_plain_injective(ctx, "{S[] -> A[0,0]; T[] -> A[0,1]}", 1))
2405 return -1;
2406 if (test_plain_injective(ctx, "{S[] -> A[0,0]; T[] -> A[1,0]}", 1))
2407 return -1;
2408
2409 str = "{S[] -> A[0,0]; T[] -> A[0,1]; U[] -> A[1,0]}";
2410 if (test_plain_injective(ctx, str, 1))
2411 return -1;
2412 str = "{S[] -> A[0,0]; T[] -> A[0,1]; U[] -> A[0,0]}";
2413 if (test_plain_injective(ctx, str, 0))
2414 return -1;
2415
2416 return 0;
2417 }
2418
2419 int test_aff(isl_ctx *ctx)
2420 {
2421 const char *str;
2422 isl_set *set;
2423 isl_space *dim;
2424 isl_local_space *ls;
2425 isl_aff *aff;
2426 int zero;
2427
2428 dim = isl_space_set_alloc(ctx, 0, 1);
2429 ls = isl_local_space_from_space(dim);
2430 aff = isl_aff_zero_on_domain(ls);
2431
2432 aff = isl_aff_add_coefficient_si(aff, isl_dim_in, 0, 1);
2433 aff = isl_aff_scale_down_ui(aff, 3);
2434 aff = isl_aff_floor(aff);
2435 aff = isl_aff_add_coefficient_si(aff, isl_dim_in, 0, 1);
2436 aff = isl_aff_scale_down_ui(aff, 2);
2437 aff = isl_aff_floor(aff);
2438 aff = isl_aff_add_coefficient_si(aff, isl_dim_in, 0, 1);
2439
2440 str = "{ [10] }";
2441 set = isl_set_read_from_str(ctx, str);
2442 aff = isl_aff_gist(aff, set);
2443
2444 aff = isl_aff_add_constant_si(aff, -16);
2445 zero = isl_aff_plain_is_zero(aff);
2446 isl_aff_free(aff);
2447
2448 if (zero < 0)
2449 return -1;
2450 if (!zero)
2451 isl_die(ctx, isl_error_unknown, "unexpected result", return -1);
2452
2453 return 0;
2454 }
2455
2456 int test_dim_max(isl_ctx *ctx)
2457 {
2458 int equal;
2459 const char *str;
2460 isl_set *set1, *set2;
2461 isl_set *set;
2462 isl_map *map;
2463 isl_pw_aff *pwaff;
2464
2465 str = "[N] -> { [i] : 0 <= i <= min(N,10) }";
2466 set = isl_set_read_from_str(ctx, str);
2467 pwaff = isl_set_dim_max(set, 0);
2468 set1 = isl_set_from_pw_aff(pwaff);
2469 str = "[N] -> { [10] : N >= 10; [N] : N <= 9 and N >= 0 }";
2470 set2 = isl_set_read_from_str(ctx, str);
2471 equal = isl_set_is_equal(set1, set2);
2472 isl_set_free(set1);
2473 isl_set_free(set2);
2474 if (equal < 0)
2475 return -1;
2476 if (!equal)
2477 isl_die(ctx, isl_error_unknown, "unexpected result", return -1);
2478
2479 str = "[N] -> { [i] : 0 <= i <= max(2N,N+6) }";
2480 set = isl_set_read_from_str(ctx, str);
2481 pwaff = isl_set_dim_max(set, 0);
2482 set1 = isl_set_from_pw_aff(pwaff);
2483 str = "[N] -> { [6 + N] : -6 <= N <= 5; [2N] : N >= 6 }";
2484 set2 = isl_set_read_from_str(ctx, str);
2485 equal = isl_set_is_equal(set1, set2);
2486 isl_set_free(set1);
2487 isl_set_free(set2);
2488 if (equal < 0)
2489 return -1;
2490 if (!equal)
2491 isl_die(ctx, isl_error_unknown, "unexpected result", return -1);
2492
2493 str = "[N] -> { [i] : 0 <= i <= 2N or 0 <= i <= N+6 }";
2494 set = isl_set_read_from_str(ctx, str);
2495 pwaff = isl_set_dim_max(set, 0);
2496 set1 = isl_set_from_pw_aff(pwaff);
2497 str = "[N] -> { [6 + N] : -6 <= N <= 5; [2N] : N >= 6 }";
2498 set2 = isl_set_read_from_str(ctx, str);
2499 equal = isl_set_is_equal(set1, set2);
2500 isl_set_free(set1);
2501 isl_set_free(set2);
2502 if (equal < 0)
2503 return -1;
2504 if (!equal)
2505 isl_die(ctx, isl_error_unknown, "unexpected result", return -1);
2506
2507 str = "[N,M] -> { [i,j] -> [([i/16]), i%16, ([j/16]), j%16] : "
2508 "0 <= i < N and 0 <= j < M }";
2509 map = isl_map_read_from_str(ctx, str);
2510 set = isl_map_range(map);
2511
2512 pwaff = isl_set_dim_max(isl_set_copy(set), 0);
2513 set1 = isl_set_from_pw_aff(pwaff);
2514 str = "[N,M] -> { [([(N-1)/16])] : M,N > 0 }";
2515 set2 = isl_set_read_from_str(ctx, str);
2516 equal = isl_set_is_equal(set1, set2);
2517 isl_set_free(set1);
2518 isl_set_free(set2);
2519
2520 pwaff = isl_set_dim_max(isl_set_copy(set), 3);
2521 set1 = isl_set_from_pw_aff(pwaff);
2522 str = "[N,M] -> { [t] : t = min(M-1,15) and M,N > 0 }";
2523 set2 = isl_set_read_from_str(ctx, str);
2524 if (equal >= 0 && equal)
2525 equal = isl_set_is_equal(set1, set2);
2526 isl_set_free(set1);
2527 isl_set_free(set2);
2528
2529 isl_set_free(set);
2530
2531 if (equal < 0)
2532 return -1;
2533 if (!equal)
2534 isl_die(ctx, isl_error_unknown, "unexpected result", return -1);
2535
2536 return 0;
2537 }
2538
2539 int test_product(isl_ctx *ctx)
2540 {
2541 const char *str;
2542 isl_set *set;
2543 isl_union_set *uset1, *uset2;
2544 int ok;
2545
2546 str = "{ A[i] }";
2547 set = isl_set_read_from_str(ctx, str);
2548 set = isl_set_product(set, isl_set_copy(set));
2549 ok = isl_set_is_wrapping(set);
2550 isl_set_free(set);
2551 if (ok < 0)
2552 return -1;
2553 if (!ok)
2554 isl_die(ctx, isl_error_unknown, "unexpected result", return -1);
2555
2556 str = "{ [] }";
2557 uset1 = isl_union_set_read_from_str(ctx, str);
2558 uset1 = isl_union_set_product(uset1, isl_union_set_copy(uset1));
2559 str = "{ [[] -> []] }";
2560 uset2 = isl_union_set_read_from_str(ctx, str);
2561 ok = isl_union_set_is_equal(uset1, uset2);
2562 isl_union_set_free(uset1);
2563 isl_union_set_free(uset2);
2564 if (ok < 0)
2565 return -1;
2566 if (!ok)
2567 isl_die(ctx, isl_error_unknown, "unexpected result", return -1);
2568
2569 return 0;
2570 }
2571
2572 int test_equal(isl_ctx *ctx)
2573 {
2574 const char *str;
2575 isl_set *set, *set2;
2576 int equal;
2577
2578 str = "{ S_6[i] }";
2579 set = isl_set_read_from_str(ctx, str);
2580 str = "{ S_7[i] }";
2581 set2 = isl_set_read_from_str(ctx, str);
2582 equal = isl_set_is_equal(set, set2);
2583 isl_set_free(set);
2584 isl_set_free(set2);
2585 if (equal < 0)
2586 return -1;
2587 if (equal)
2588 isl_die(ctx, isl_error_unknown, "unexpected result", return -1);
2589
2590 return 0;
2591 }
2592
2593 static int test_plain_fixed(isl_ctx *ctx, __isl_take isl_map *map,
2594 enum isl_dim_type type, unsigned pos, int fixed)
2595 {
2596 int test;
2597
2598 test = isl_map_plain_is_fixed(map, type, pos, NULL);
2599 isl_map_free(map);
2600 if (test < 0)
2601 return -1;
2602 if (test == fixed)
2603 return 0;
2604 if (fixed)
2605 isl_die(ctx, isl_error_unknown,
2606 "map not detected as fixed", return -1);
2607 else
2608 isl_die(ctx, isl_error_unknown,
2609 "map detected as fixed", return -1);
2610 }
2611
2612 int test_fixed(isl_ctx *ctx)
2613 {
2614 const char *str;
2615 isl_map *map;
2616
2617 str = "{ [i] -> [i] }";
2618 map = isl_map_read_from_str(ctx, str);
2619 if (test_plain_fixed(ctx, map, isl_dim_out, 0, 0))
2620 return -1;
2621 str = "{ [i] -> [1] }";
2622 map = isl_map_read_from_str(ctx, str);
2623 if (test_plain_fixed(ctx, map, isl_dim_out, 0, 1))
2624 return -1;
2625 str = "{ S_1[p1] -> [o0] : o0 = -2 and p1 >= 1 and p1 <= 7 }";
2626 map = isl_map_read_from_str(ctx, str);
2627 if (test_plain_fixed(ctx, map, isl_dim_out, 0, 1))
2628 return -1;
2629 map = isl_map_read_from_str(ctx, str);
2630 map = isl_map_neg(map);
2631 if (test_plain_fixed(ctx, map, isl_dim_out, 0, 1))
2632 return -1;
2633
2634 return 0;
2635 }
2636
2637 int test_vertices(isl_ctx *ctx)
2638 {
2639 const char *str;
2640 isl_basic_set *bset;
2641 isl_vertices *vertices;
2642
2643 str = "{ A[t, i] : t = 12 and i >= 4 and i <= 12 }";
2644 bset = isl_basic_set_read_from_str(ctx, str);
2645 vertices = isl_basic_set_compute_vertices(bset);
2646 isl_basic_set_free(bset);
2647 isl_vertices_free(vertices);
2648 if (!vertices)
2649 return -1;
2650
2651 str = "{ A[t, i] : t = 14 and i = 1 }";
2652 bset = isl_basic_set_read_from_str(ctx, str);
2653 vertices = isl_basic_set_compute_vertices(bset);
2654 isl_basic_set_free(bset);
2655 isl_vertices_free(vertices);
2656 if (!vertices)
2657 return -1;
2658
2659 return 0;
2660 }
2661
2662 int test_union_pw(isl_ctx *ctx)
2663 {
2664 int equal;
2665 const char *str;
2666 isl_union_set *uset;
2667 isl_union_pw_qpolynomial *upwqp1, *upwqp2;
2668
2669 str = "{ [x] -> x^2 }";
2670 upwqp1 = isl_union_pw_qpolynomial_read_from_str(ctx, str);
2671 upwqp2 = isl_union_pw_qpolynomial_copy(upwqp1);
2672 uset = isl_union_pw_qpolynomial_domain(upwqp1);
2673 upwqp1 = isl_union_pw_qpolynomial_copy(upwqp2);
2674 upwqp1 = isl_union_pw_qpolynomial_intersect_domain(upwqp1, uset);
2675 equal = isl_union_pw_qpolynomial_plain_is_equal(upwqp1, upwqp2);
2676 isl_union_pw_qpolynomial_free(upwqp1);
2677 isl_union_pw_qpolynomial_free(upwqp2);
2678 if (equal < 0)
2679 return -1;
2680 if (!equal)
2681 isl_die(ctx, isl_error_unknown, "unexpected result", return -1);
2682
2683 return 0;
2684 }
2685
2686 int test_output(isl_ctx *ctx)
2687 {
2688 char *s;
2689 const char *str;
2690 isl_pw_aff *pa;
2691 isl_printer *p;
2692 int equal;
2693
2694 str = "[x] -> { [1] : x % 4 <= 2; [2] : x = 3 }";
2695 pa = isl_pw_aff_read_from_str(ctx, str);
2696
2697 p = isl_printer_to_str(ctx);
2698 p = isl_printer_set_output_format(p, ISL_FORMAT_C);
2699 p = isl_printer_print_pw_aff(p, pa);
2700 s = isl_printer_get_str(p);
2701 isl_printer_free(p);
2702 isl_pw_aff_free(pa);
2703 equal = !strcmp(s, "(2 - x + 4*floord(x, 4) >= 0) ? (1) : 2");
2704 free(s);
2705 if (equal < 0)
2706 return -1;
2707 if (!equal)
2708 isl_die(ctx, isl_error_unknown, "unexpected result", return -1);
2709
2710 return 0;
2711 }
2712
2713 int test_sample(isl_ctx *ctx)
2714 {
2715 const char *str;
2716 isl_basic_set *bset1, *bset2;
2717 int empty, subset;
2718
2719 str = "{ [a, b, c, d, e, f, g, h, i, j, k] : "
2720 "3i >= 1073741823b - c - 1073741823e + f and c >= 0 and "
2721 "3i >= -1 + 3221225466b + c + d - 3221225466e - f and "
2722 "2e >= a - b and 3e <= 2a and 3k <= -a and f <= -1 + a and "
2723 "3i <= 4 - a + 4b + 2c - e - 2f and 3k <= -a + c - f and "
2724 "3h >= -2 + a and 3g >= -3 - a and 3k >= -2 - a and "
2725 "3i >= -2 - a - 2c + 3e + 2f and 3h <= a + c - f and "
2726 "3h >= a + 2147483646b + 2c - 2147483646e - 2f and "
2727 "3g <= -1 - a and 3i <= 1 + c + d - f and a <= 1073741823 and "
2728 "f >= 1 - a + 1073741822b + c + d - 1073741822e and "
2729 "3i >= 1 + 2b - 2c + e + 2f + 3g and "
2730 "1073741822f <= 1073741822 - a + 1073741821b + 1073741822c +"
2731 "d - 1073741821e and "
2732 "3j <= 3 - a + 3b and 3g <= -2 - 2b + c + d - e - f and "
2733 "3j >= 1 - a + b + 2e and "
2734 "3f >= -3 + a + 3221225462b + 3c + d - 3221225465e and "
2735 "3i <= 4 - a + 4b - e and "
2736 "f <= 1073741822 + 1073741822b - 1073741822e and 3h <= a and "
2737 "f >= 0 and 2e <= 4 - a + 5b - d and 2e <= a - b + d and "
2738 "c <= -1 + a and 3i >= -2 - a + 3e and "
2739 "1073741822e <= 1073741823 - a + 1073741822b + c and "
2740 "3g >= -4 + 3221225464b + 3c + d - 3221225467e - 3f and "
2741 "3i >= -1 + 3221225466b + 3c + d - 3221225466e - 3f and "
2742 "1073741823e >= 1 + 1073741823b - d and "
2743 "3i >= 1073741823b + c - 1073741823e - f and "
2744 "3i >= 1 + 2b + e + 3g }";
2745 bset1 = isl_basic_set_read_from_str(ctx, str);
2746 bset2 = isl_basic_set_sample(isl_basic_set_copy(bset1));
2747 empty = isl_basic_set_is_empty(bset2);
2748 subset = isl_basic_set_is_subset(bset2, bset1);
2749 isl_basic_set_free(bset1);
2750 isl_basic_set_free(bset2);
2751 if (empty)
2752 isl_die(ctx, isl_error_unknown, "point not found", return -1);
2753 if (!subset)
2754 isl_die(ctx, isl_error_unknown, "bad point found", return -1);
2755
2756 return 0;
2757 }
2758
2759 int main()
2760 {
2761 struct isl_ctx *ctx;
2762
2763 srcdir = getenv("srcdir");
2764 assert(srcdir);
2765
2766 ctx = isl_ctx_alloc();
2767 if (test_sample(ctx) < 0)
2768 goto error;
2769 if (test_output(ctx) < 0)
2770 goto error;
2771 if (test_vertices(ctx) < 0)
2772 goto error;
2773 if (test_fixed(ctx) < 0)
2774 goto error;
2775 if (test_equal(ctx) < 0)
2776 goto error;
2777 if (test_product(ctx) < 0)
2778 goto error;
2779 if (test_dim_max(ctx) < 0)
2780 goto error;
2781 if (test_aff(ctx) < 0)
2782 goto error;
2783 if (test_injective(ctx) < 0)
2784 goto error;
2785 if (test_schedule(ctx) < 0)
2786 goto error;
2787 if (test_union_pw(ctx) < 0)
2788 goto error;
2789 test_factorize(ctx);
2790 test_subset(ctx);
2791 test_lift(ctx);
2792 test_bound(ctx);
2793 test_union(ctx);
2794 test_split_periods(ctx);
2795 test_parse(ctx);
2796 test_pwqp(ctx);
2797 test_lex(ctx);
2798 if (test_sv(ctx) < 0)
2799 goto error;
2800 test_bijective(ctx);
2801 test_dep(ctx);
2802 test_read(ctx);
2803 test_bounded(ctx);
2804 test_construction(ctx);
2805 test_dim(ctx);
2806 test_div(ctx);
2807 test_application(ctx);
2808 if (test_affine_hull(ctx) < 0)
2809 goto error;
2810 test_convex_hull(ctx);
2811 test_gist(ctx);
2812 if (test_coalesce(ctx) < 0)
2813 goto error;
2814 test_closure(ctx);
2815 test_lexmin(ctx);
2816 isl_ctx_free(ctx);
2817 return 0;
2818 error:
2819 isl_ctx_free(ctx);
2820 return -1;
2821 }
Integer set library