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isl_access_info: change interface for specifying restrictions
[isl.git] / isl_test.c
blob4d9945e5f7ec843676def037a6d1084033d41529
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 int test_parse_map_equal(isl_ctx *ctx, const char *str, const char *str2)
55 {
56 isl_map *map, *map2;
57 int equal;
58
59 map = isl_map_read_from_str(ctx, str);
60 map2 = isl_map_read_from_str(ctx, str2);
61 equal = isl_map_is_equal(map, map2);
62 isl_map_free(map);
63 isl_map_free(map2);
64
65 if (equal < 0)
66 return -1;
67 if (!equal)
68 isl_die(ctx, isl_error_unknown, "maps not equal",
69 return -1);
70
71 return 0;
72 }
73
74 void test_parse_pwqp(isl_ctx *ctx, const char *str)
75 {
76 isl_pw_qpolynomial *pwqp;
77
78 pwqp = isl_pw_qpolynomial_read_from_str(ctx, str);
79 assert(pwqp);
80 isl_pw_qpolynomial_free(pwqp);
81 }
82
83 static void test_parse_pwaff(isl_ctx *ctx, const char *str)
84 {
85 isl_pw_aff *pwaff;
86
87 pwaff = isl_pw_aff_read_from_str(ctx, str);
88 assert(pwaff);
89 isl_pw_aff_free(pwaff);
90 }
91
92 int test_parse(struct isl_ctx *ctx)
93 {
94 isl_map *map, *map2;
95 const char *str, *str2;
96
97 str = "{ [i] -> [-i] }";
98 map = isl_map_read_from_str(ctx, str);
99 assert(map);
100 isl_map_free(map);
101
102 str = "{ A[i] -> L[([i/3])] }";
103 map = isl_map_read_from_str(ctx, str);
104 assert(map);
105 isl_map_free(map);
106
107 test_parse_map(ctx, "{[[s] -> A[i]] -> [[s+1] -> A[i]]}");
108 test_parse_map(ctx, "{ [p1, y1, y2] -> [2, y1, y2] : "
109 "p1 = 1 && (y1 <= y2 || y2 = 0) }");
110
111 str = "{ [x,y] : [([x/2]+y)/3] >= 1 }";
112 str2 = "{ [x, y] : 2y >= 6 - x }";
113 if (test_parse_map_equal(ctx, str, str2) < 0)
114 return -1;
115
116 if (test_parse_map_equal(ctx, "{ [x,y] : x <= min(y, 2*y+3) }",
117 "{ [x,y] : x <= y, 2*y + 3 }") < 0)
118 return -1;
119 str = "{ [x, y] : (y <= x and y >= -3) or (2y <= -3 + x and y <= -4) }";
120 if (test_parse_map_equal(ctx, "{ [x,y] : x >= min(y, 2*y+3) }",
121 str) < 0)
122 return -1;
123
124 str = "{[new,old] -> [new+1-2*[(new+1)/2],old+1-2*[(old+1)/2]]}";
125 map = isl_map_read_from_str(ctx, str);
126 str = "{ [new, old] -> [o0, o1] : "
127 "exists (e0 = [(-1 - new + o0)/2], e1 = [(-1 - old + o1)/2]: "
128 "2e0 = -1 - new + o0 and 2e1 = -1 - old + o1 and o0 >= 0 and "
129 "o0 <= 1 and o1 >= 0 and o1 <= 1) }";
130 map2 = isl_map_read_from_str(ctx, str);
131 assert(isl_map_is_equal(map, map2));
132 isl_map_free(map);
133 isl_map_free(map2);
134
135 str = "{[new,old] -> [new+1-2*[(new+1)/2],old+1-2*[(old+1)/2]]}";
136 map = isl_map_read_from_str(ctx, str);
137 str = "{[new,old] -> [(new+1)%2,(old+1)%2]}";
138 map2 = isl_map_read_from_str(ctx, str);
139 assert(isl_map_is_equal(map, map2));
140 isl_map_free(map);
141 isl_map_free(map2);
142
143 str = "[n] -> { [c1] : c1>=0 and c1<=floord(n-4,3) }";
144 str2 = "[n] -> { [c1] : c1 >= 0 and 3c1 <= -4 + n }";
145 if (test_parse_map_equal(ctx, str, str2) < 0)
146 return -1;
147
148 str = "{ [i,j] -> [i] : i < j; [i,j] -> [j] : j <= i }";
149 str2 = "{ [i,j] -> [min(i,j)] }";
150 if (test_parse_map_equal(ctx, str, str2) < 0)
151 return -1;
152
153 str = "{ [i,j] : i != j }";
154 str2 = "{ [i,j] : i < j or i > j }";
155 if (test_parse_map_equal(ctx, str, str2) < 0)
156 return -1;
157
158 str = "{ [i,j] : (i+1)*2 >= j }";
159 str2 = "{ [i, j] : j <= 2 + 2i }";
160 if (test_parse_map_equal(ctx, str, str2) < 0)
161 return -1;
162
163 str = "{ [i] -> [i > 0 ? 4 : 5] }";
164 str2 = "{ [i] -> [5] : i <= 0; [i] -> [4] : i >= 1 }";
165 if (test_parse_map_equal(ctx, str, str2) < 0)
166 return -1;
167
168 str = "[N=2,M] -> { [i=[(M+N)/4]] }";
169 str2 = "[N, M] -> { [i] : N = 2 and 4i <= 2 + M and 4i >= -1 + M }";
170 if (test_parse_map_equal(ctx, str, str2) < 0)
171 return -1;
172
173 str = "{ [x] : x >= 0 }";
174 str2 = "{ [x] : x-0 >= 0 }";
175 if (test_parse_map_equal(ctx, str, str2) < 0)
176 return -1;
177
178 str = "{ [i] : ((i > 10)) }";
179 str2 = "{ [i] : i >= 11 }";
180 if (test_parse_map_equal(ctx, str, str2) < 0)
181 return -1;
182
183 str = "{ [i] -> [0] }";
184 str2 = "{ [i] -> [0 * i] }";
185 if (test_parse_map_equal(ctx, str, str2) < 0)
186 return -1;
187
188 test_parse_pwqp(ctx, "{ [i] -> i + [ (i + [i/3])/2 ] }");
189 test_parse_map(ctx, "{ S1[i] -> [([i/10]),i%10] : 0 <= i <= 45 }");
190 test_parse_pwaff(ctx, "{ [i] -> [i + 1] : i > 0; [a] -> [a] : a < 0 }");
191 test_parse_pwqp(ctx, "{ [x] -> ([(x)/2] * [(x)/3]) }");
192
193 if (test_parse_map_equal(ctx, "{ [a] -> [b] : (not false) }",
194 "{ [a] -> [b] : true }") < 0)
195 return -1;
196
197 return 0;
198 }
199
200 void test_read(struct isl_ctx *ctx)
201 {
202 char *filename;
203 FILE *input;
204 struct isl_basic_set *bset1, *bset2;
205 const char *str = "{[y]: Exists ( alpha : 2alpha = y)}";
206
207 filename = get_filename(ctx, "set", "omega");
208 assert(filename);
209 input = fopen(filename, "r");
210 assert(input);
211
212 bset1 = isl_basic_set_read_from_file(ctx, input);
213 bset2 = isl_basic_set_read_from_str(ctx, str);
214
215 assert(isl_basic_set_is_equal(bset1, bset2) == 1);
216
217 isl_basic_set_free(bset1);
218 isl_basic_set_free(bset2);
219 free(filename);
220
221 fclose(input);
222 }
223
224 void test_bounded(struct isl_ctx *ctx)
225 {
226 isl_set *set;
227 int bounded;
228
229 set = isl_set_read_from_str(ctx, "[n] -> {[i] : 0 <= i <= n }");
230 bounded = isl_set_is_bounded(set);
231 assert(bounded);
232 isl_set_free(set);
233
234 set = isl_set_read_from_str(ctx, "{[n, i] : 0 <= i <= n }");
235 bounded = isl_set_is_bounded(set);
236 assert(!bounded);
237 isl_set_free(set);
238
239 set = isl_set_read_from_str(ctx, "[n] -> {[i] : i <= n }");
240 bounded = isl_set_is_bounded(set);
241 assert(!bounded);
242 isl_set_free(set);
243 }
244
245 /* Construct the basic set { [i] : 5 <= i <= N } */
246 void test_construction(struct isl_ctx *ctx)
247 {
248 isl_int v;
249 isl_space *dim;
250 isl_local_space *ls;
251 struct isl_basic_set *bset;
252 struct isl_constraint *c;
253
254 isl_int_init(v);
255
256 dim = isl_space_set_alloc(ctx, 1, 1);
257 bset = isl_basic_set_universe(isl_space_copy(dim));
258 ls = isl_local_space_from_space(dim);
259
260 c = isl_inequality_alloc(isl_local_space_copy(ls));
261 isl_int_set_si(v, -1);
262 isl_constraint_set_coefficient(c, isl_dim_set, 0, v);
263 isl_int_set_si(v, 1);
264 isl_constraint_set_coefficient(c, isl_dim_param, 0, v);
265 bset = isl_basic_set_add_constraint(bset, c);
266
267 c = isl_inequality_alloc(isl_local_space_copy(ls));
268 isl_int_set_si(v, 1);
269 isl_constraint_set_coefficient(c, isl_dim_set, 0, v);
270 isl_int_set_si(v, -5);
271 isl_constraint_set_constant(c, v);
272 bset = isl_basic_set_add_constraint(bset, c);
273
274 isl_local_space_free(ls);
275 isl_basic_set_free(bset);
276
277 isl_int_clear(v);
278 }
279
280 void test_dim(struct isl_ctx *ctx)
281 {
282 const char *str;
283 isl_map *map1, *map2;
284
285 map1 = isl_map_read_from_str(ctx,
286 "[n] -> { [i] -> [j] : exists (a = [i/10] : i - 10a <= n ) }");
287 map1 = isl_map_add_dims(map1, isl_dim_in, 1);
288 map2 = isl_map_read_from_str(ctx,
289 "[n] -> { [i,k] -> [j] : exists (a = [i/10] : i - 10a <= n ) }");
290 assert(isl_map_is_equal(map1, map2));
291 isl_map_free(map2);
292
293 map1 = isl_map_project_out(map1, isl_dim_in, 0, 1);
294 map2 = isl_map_read_from_str(ctx, "[n] -> { [i] -> [j] : n >= 0 }");
295 assert(isl_map_is_equal(map1, map2));
296
297 isl_map_free(map1);
298 isl_map_free(map2);
299
300 str = "[n] -> { [i] -> [] : exists a : 0 <= i <= n and i = 2 a }";
301 map1 = isl_map_read_from_str(ctx, str);
302 str = "{ [i] -> [j] : exists a : 0 <= i <= j and i = 2 a }";
303 map2 = isl_map_read_from_str(ctx, str);
304 map1 = isl_map_move_dims(map1, isl_dim_out, 0, isl_dim_param, 0, 1);
305 assert(isl_map_is_equal(map1, map2));
306
307 isl_map_free(map1);
308 isl_map_free(map2);
309 }
310
311 void test_div(struct isl_ctx *ctx)
312 {
313 isl_int v;
314 isl_space *dim;
315 isl_local_space *ls;
316 struct isl_basic_set *bset;
317 struct isl_constraint *c;
318
319 isl_int_init(v);
320
321 /* test 1 */
322 dim = isl_space_set_alloc(ctx, 0, 3);
323 bset = isl_basic_set_universe(isl_space_copy(dim));
324 ls = isl_local_space_from_space(dim);
325
326 c = isl_equality_alloc(isl_local_space_copy(ls));
327 isl_int_set_si(v, -1);
328 isl_constraint_set_constant(c, v);
329 isl_int_set_si(v, 1);
330 isl_constraint_set_coefficient(c, isl_dim_set, 0, v);
331 isl_int_set_si(v, 3);
332 isl_constraint_set_coefficient(c, isl_dim_set, 1, v);
333 bset = isl_basic_set_add_constraint(bset, c);
334
335 c = isl_equality_alloc(isl_local_space_copy(ls));
336 isl_int_set_si(v, 1);
337 isl_constraint_set_constant(c, v);
338 isl_int_set_si(v, -1);
339 isl_constraint_set_coefficient(c, isl_dim_set, 0, v);
340 isl_int_set_si(v, 3);
341 isl_constraint_set_coefficient(c, isl_dim_set, 2, v);
342 bset = isl_basic_set_add_constraint(bset, c);
343
344 bset = isl_basic_set_project_out(bset, isl_dim_set, 1, 2);
345
346 assert(bset && bset->n_div == 1);
347 isl_local_space_free(ls);
348 isl_basic_set_free(bset);
349
350 /* test 2 */
351 dim = isl_space_set_alloc(ctx, 0, 3);
352 bset = isl_basic_set_universe(isl_space_copy(dim));
353 ls = isl_local_space_from_space(dim);
354
355 c = isl_equality_alloc(isl_local_space_copy(ls));
356 isl_int_set_si(v, 1);
357 isl_constraint_set_constant(c, v);
358 isl_int_set_si(v, -1);
359 isl_constraint_set_coefficient(c, isl_dim_set, 0, v);
360 isl_int_set_si(v, 3);
361 isl_constraint_set_coefficient(c, isl_dim_set, 1, v);
362 bset = isl_basic_set_add_constraint(bset, c);
363
364 c = isl_equality_alloc(isl_local_space_copy(ls));
365 isl_int_set_si(v, -1);
366 isl_constraint_set_constant(c, v);
367 isl_int_set_si(v, 1);
368 isl_constraint_set_coefficient(c, isl_dim_set, 0, v);
369 isl_int_set_si(v, 3);
370 isl_constraint_set_coefficient(c, isl_dim_set, 2, v);
371 bset = isl_basic_set_add_constraint(bset, c);
372
373 bset = isl_basic_set_project_out(bset, isl_dim_set, 1, 2);
374
375 assert(bset && bset->n_div == 1);
376 isl_local_space_free(ls);
377 isl_basic_set_free(bset);
378
379 /* test 3 */
380 dim = isl_space_set_alloc(ctx, 0, 3);
381 bset = isl_basic_set_universe(isl_space_copy(dim));
382 ls = isl_local_space_from_space(dim);
383
384 c = isl_equality_alloc(isl_local_space_copy(ls));
385 isl_int_set_si(v, 1);
386 isl_constraint_set_constant(c, v);
387 isl_int_set_si(v, -1);
388 isl_constraint_set_coefficient(c, isl_dim_set, 0, v);
389 isl_int_set_si(v, 3);
390 isl_constraint_set_coefficient(c, isl_dim_set, 1, v);
391 bset = isl_basic_set_add_constraint(bset, c);
392
393 c = isl_equality_alloc(isl_local_space_copy(ls));
394 isl_int_set_si(v, -3);
395 isl_constraint_set_constant(c, v);
396 isl_int_set_si(v, 1);
397 isl_constraint_set_coefficient(c, isl_dim_set, 0, v);
398 isl_int_set_si(v, 4);
399 isl_constraint_set_coefficient(c, isl_dim_set, 2, v);
400 bset = isl_basic_set_add_constraint(bset, c);
401
402 bset = isl_basic_set_project_out(bset, isl_dim_set, 1, 2);
403
404 assert(bset && bset->n_div == 1);
405 isl_local_space_free(ls);
406 isl_basic_set_free(bset);
407
408 /* test 4 */
409 dim = isl_space_set_alloc(ctx, 0, 3);
410 bset = isl_basic_set_universe(isl_space_copy(dim));
411 ls = isl_local_space_from_space(dim);
412
413 c = isl_equality_alloc(isl_local_space_copy(ls));
414 isl_int_set_si(v, 2);
415 isl_constraint_set_constant(c, v);
416 isl_int_set_si(v, -1);
417 isl_constraint_set_coefficient(c, isl_dim_set, 0, v);
418 isl_int_set_si(v, 3);
419 isl_constraint_set_coefficient(c, isl_dim_set, 1, v);
420 bset = isl_basic_set_add_constraint(bset, c);
421
422 c = isl_equality_alloc(isl_local_space_copy(ls));
423 isl_int_set_si(v, -1);
424 isl_constraint_set_constant(c, v);
425 isl_int_set_si(v, 1);
426 isl_constraint_set_coefficient(c, isl_dim_set, 0, v);
427 isl_int_set_si(v, 6);
428 isl_constraint_set_coefficient(c, isl_dim_set, 2, v);
429 bset = isl_basic_set_add_constraint(bset, c);
430
431 bset = isl_basic_set_project_out(bset, isl_dim_set, 1, 2);
432
433 assert(isl_basic_set_is_empty(bset));
434 isl_local_space_free(ls);
435 isl_basic_set_free(bset);
436
437 /* test 5 */
438 dim = isl_space_set_alloc(ctx, 0, 3);
439 bset = isl_basic_set_universe(isl_space_copy(dim));
440 ls = isl_local_space_from_space(dim);
441
442 c = isl_equality_alloc(isl_local_space_copy(ls));
443 isl_int_set_si(v, -1);
444 isl_constraint_set_coefficient(c, isl_dim_set, 0, v);
445 isl_int_set_si(v, 3);
446 isl_constraint_set_coefficient(c, isl_dim_set, 2, v);
447 bset = isl_basic_set_add_constraint(bset, c);
448
449 c = isl_equality_alloc(isl_local_space_copy(ls));
450 isl_int_set_si(v, 1);
451 isl_constraint_set_coefficient(c, isl_dim_set, 0, v);
452 isl_int_set_si(v, -3);
453 isl_constraint_set_coefficient(c, isl_dim_set, 1, v);
454 bset = isl_basic_set_add_constraint(bset, c);
455
456 bset = isl_basic_set_project_out(bset, isl_dim_set, 2, 1);
457
458 assert(bset && bset->n_div == 0);
459 isl_basic_set_free(bset);
460 isl_local_space_free(ls);
461
462 /* test 6 */
463 dim = isl_space_set_alloc(ctx, 0, 3);
464 bset = isl_basic_set_universe(isl_space_copy(dim));
465 ls = isl_local_space_from_space(dim);
466
467 c = isl_equality_alloc(isl_local_space_copy(ls));
468 isl_int_set_si(v, -1);
469 isl_constraint_set_coefficient(c, isl_dim_set, 0, v);
470 isl_int_set_si(v, 6);
471 isl_constraint_set_coefficient(c, isl_dim_set, 2, v);
472 bset = isl_basic_set_add_constraint(bset, c);
473
474 c = isl_equality_alloc(isl_local_space_copy(ls));
475 isl_int_set_si(v, 1);
476 isl_constraint_set_coefficient(c, isl_dim_set, 0, v);
477 isl_int_set_si(v, -3);
478 isl_constraint_set_coefficient(c, isl_dim_set, 1, v);
479 bset = isl_basic_set_add_constraint(bset, c);
480
481 bset = isl_basic_set_project_out(bset, isl_dim_set, 2, 1);
482
483 assert(bset && bset->n_div == 1);
484 isl_basic_set_free(bset);
485 isl_local_space_free(ls);
486
487 /* test 7 */
488 /* This test is a bit tricky. We set up an equality
489 * a + 3b + 3c = 6 e0
490 * Normalization of divs creates _two_ divs
491 * a = 3 e0
492 * c - b - e0 = 2 e1
493 * Afterwards e0 is removed again because it has coefficient -1
494 * and we end up with the original equality and div again.
495 * Perhaps we can avoid the introduction of this temporary div.
496 */
497 dim = isl_space_set_alloc(ctx, 0, 4);
498 bset = isl_basic_set_universe(isl_space_copy(dim));
499 ls = isl_local_space_from_space(dim);
500
501 c = isl_equality_alloc(isl_local_space_copy(ls));
502 isl_int_set_si(v, -1);
503 isl_constraint_set_coefficient(c, isl_dim_set, 0, v);
504 isl_int_set_si(v, -3);
505 isl_constraint_set_coefficient(c, isl_dim_set, 1, v);
506 isl_int_set_si(v, -3);
507 isl_constraint_set_coefficient(c, isl_dim_set, 2, v);
508 isl_int_set_si(v, 6);
509 isl_constraint_set_coefficient(c, isl_dim_set, 3, v);
510 bset = isl_basic_set_add_constraint(bset, c);
511
512 bset = isl_basic_set_project_out(bset, isl_dim_set, 3, 1);
513
514 /* Test disabled for now */
515 /*
516 assert(bset && bset->n_div == 1);
517 */
518 isl_local_space_free(ls);
519 isl_basic_set_free(bset);
520
521 /* test 8 */
522 dim = isl_space_set_alloc(ctx, 0, 5);
523 bset = isl_basic_set_universe(isl_space_copy(dim));
524 ls = isl_local_space_from_space(dim);
525
526 c = isl_equality_alloc(isl_local_space_copy(ls));
527 isl_int_set_si(v, -1);
528 isl_constraint_set_coefficient(c, isl_dim_set, 0, v);
529 isl_int_set_si(v, -3);
530 isl_constraint_set_coefficient(c, isl_dim_set, 1, v);
531 isl_int_set_si(v, -3);
532 isl_constraint_set_coefficient(c, isl_dim_set, 3, v);
533 isl_int_set_si(v, 6);
534 isl_constraint_set_coefficient(c, isl_dim_set, 4, v);
535 bset = isl_basic_set_add_constraint(bset, c);
536
537 c = isl_equality_alloc(isl_local_space_copy(ls));
538 isl_int_set_si(v, -1);
539 isl_constraint_set_coefficient(c, isl_dim_set, 0, v);
540 isl_int_set_si(v, 1);
541 isl_constraint_set_coefficient(c, isl_dim_set, 2, v);
542 isl_int_set_si(v, 1);
543 isl_constraint_set_constant(c, v);
544 bset = isl_basic_set_add_constraint(bset, c);
545
546 bset = isl_basic_set_project_out(bset, isl_dim_set, 4, 1);
547
548 /* Test disabled for now */
549 /*
550 assert(bset && bset->n_div == 1);
551 */
552 isl_local_space_free(ls);
553 isl_basic_set_free(bset);
554
555 /* test 9 */
556 dim = isl_space_set_alloc(ctx, 0, 4);
557 bset = isl_basic_set_universe(isl_space_copy(dim));
558 ls = isl_local_space_from_space(dim);
559
560 c = isl_equality_alloc(isl_local_space_copy(ls));
561 isl_int_set_si(v, 1);
562 isl_constraint_set_coefficient(c, isl_dim_set, 0, v);
563 isl_int_set_si(v, -1);
564 isl_constraint_set_coefficient(c, isl_dim_set, 1, v);
565 isl_int_set_si(v, -2);
566 isl_constraint_set_coefficient(c, isl_dim_set, 2, v);
567 bset = isl_basic_set_add_constraint(bset, c);
568
569 c = isl_equality_alloc(isl_local_space_copy(ls));
570 isl_int_set_si(v, -1);
571 isl_constraint_set_coefficient(c, isl_dim_set, 0, v);
572 isl_int_set_si(v, 3);
573 isl_constraint_set_coefficient(c, isl_dim_set, 3, v);
574 isl_int_set_si(v, 2);
575 isl_constraint_set_constant(c, v);
576 bset = isl_basic_set_add_constraint(bset, c);
577
578 bset = isl_basic_set_project_out(bset, isl_dim_set, 2, 2);
579
580 bset = isl_basic_set_fix_si(bset, isl_dim_set, 0, 2);
581
582 assert(!isl_basic_set_is_empty(bset));
583
584 isl_local_space_free(ls);
585 isl_basic_set_free(bset);
586
587 /* test 10 */
588 dim = isl_space_set_alloc(ctx, 0, 3);
589 bset = isl_basic_set_universe(isl_space_copy(dim));
590 ls = isl_local_space_from_space(dim);
591
592 c = isl_equality_alloc(isl_local_space_copy(ls));
593 isl_int_set_si(v, 1);
594 isl_constraint_set_coefficient(c, isl_dim_set, 0, v);
595 isl_int_set_si(v, -2);
596 isl_constraint_set_coefficient(c, isl_dim_set, 2, v);
597 bset = isl_basic_set_add_constraint(bset, c);
598
599 bset = isl_basic_set_project_out(bset, isl_dim_set, 2, 1);
600
601 bset = isl_basic_set_fix_si(bset, isl_dim_set, 0, 2);
602
603 isl_local_space_free(ls);
604 isl_basic_set_free(bset);
605
606 isl_int_clear(v);
607 }
608
609 void test_application_case(struct isl_ctx *ctx, const char *name)
610 {
611 char *filename;
612 FILE *input;
613 struct isl_basic_set *bset1, *bset2;
614 struct isl_basic_map *bmap;
615
616 filename = get_filename(ctx, name, "omega");
617 assert(filename);
618 input = fopen(filename, "r");
619 assert(input);
620
621 bset1 = isl_basic_set_read_from_file(ctx, input);
622 bmap = isl_basic_map_read_from_file(ctx, input);
623
624 bset1 = isl_basic_set_apply(bset1, bmap);
625
626 bset2 = isl_basic_set_read_from_file(ctx, input);
627
628 assert(isl_basic_set_is_equal(bset1, bset2) == 1);
629
630 isl_basic_set_free(bset1);
631 isl_basic_set_free(bset2);
632 free(filename);
633
634 fclose(input);
635 }
636
637 void test_application(struct isl_ctx *ctx)
638 {
639 test_application_case(ctx, "application");
640 test_application_case(ctx, "application2");
641 }
642
643 void test_affine_hull_case(struct isl_ctx *ctx, const char *name)
644 {
645 char *filename;
646 FILE *input;
647 struct isl_basic_set *bset1, *bset2;
648
649 filename = get_filename(ctx, name, "polylib");
650 assert(filename);
651 input = fopen(filename, "r");
652 assert(input);
653
654 bset1 = isl_basic_set_read_from_file(ctx, input);
655 bset2 = isl_basic_set_read_from_file(ctx, input);
656
657 bset1 = isl_basic_set_affine_hull(bset1);
658
659 assert(isl_basic_set_is_equal(bset1, bset2) == 1);
660
661 isl_basic_set_free(bset1);
662 isl_basic_set_free(bset2);
663 free(filename);
664
665 fclose(input);
666 }
667
668 int test_affine_hull(struct isl_ctx *ctx)
669 {
670 const char *str;
671 isl_set *set;
672 isl_basic_set *bset;
673 int n;
674
675 test_affine_hull_case(ctx, "affine2");
676 test_affine_hull_case(ctx, "affine");
677 test_affine_hull_case(ctx, "affine3");
678
679 str = "[m] -> { [i0] : exists (e0, e1: e1 <= 1 + i0 and "
680 "m >= 3 and 4i0 <= 2 + m and e1 >= i0 and "
681 "e1 >= 0 and e1 <= 2 and e1 >= 1 + 2e0 and "
682 "2e1 <= 1 + m + 4e0 and 2e1 >= 2 - m + 4i0 - 4e0) }";
683 set = isl_set_read_from_str(ctx, str);
684 bset = isl_set_affine_hull(set);
685 n = isl_basic_set_dim(bset, isl_dim_div);
686 isl_basic_set_free(bset);
687 if (n != 0)
688 isl_die(ctx, isl_error_unknown, "not expecting any divs",
689 return -1);
690
691 return 0;
692 }
693
694 void test_convex_hull_case(struct isl_ctx *ctx, const char *name)
695 {
696 char *filename;
697 FILE *input;
698 struct isl_basic_set *bset1, *bset2;
699 struct isl_set *set;
700
701 filename = get_filename(ctx, name, "polylib");
702 assert(filename);
703 input = fopen(filename, "r");
704 assert(input);
705
706 bset1 = isl_basic_set_read_from_file(ctx, input);
707 bset2 = isl_basic_set_read_from_file(ctx, input);
708
709 set = isl_basic_set_union(bset1, bset2);
710 bset1 = isl_set_convex_hull(set);
711
712 bset2 = isl_basic_set_read_from_file(ctx, input);
713
714 assert(isl_basic_set_is_equal(bset1, bset2) == 1);
715
716 isl_basic_set_free(bset1);
717 isl_basic_set_free(bset2);
718 free(filename);
719
720 fclose(input);
721 }
722
723 void test_convex_hull_algo(struct isl_ctx *ctx, int convex)
724 {
725 const char *str1, *str2;
726 isl_set *set1, *set2;
727 int orig_convex = ctx->opt->convex;
728 ctx->opt->convex = convex;
729
730 test_convex_hull_case(ctx, "convex0");
731 test_convex_hull_case(ctx, "convex1");
732 test_convex_hull_case(ctx, "convex2");
733 test_convex_hull_case(ctx, "convex3");
734 test_convex_hull_case(ctx, "convex4");
735 test_convex_hull_case(ctx, "convex5");
736 test_convex_hull_case(ctx, "convex6");
737 test_convex_hull_case(ctx, "convex7");
738 test_convex_hull_case(ctx, "convex8");
739 test_convex_hull_case(ctx, "convex9");
740 test_convex_hull_case(ctx, "convex10");
741 test_convex_hull_case(ctx, "convex11");
742 test_convex_hull_case(ctx, "convex12");
743 test_convex_hull_case(ctx, "convex13");
744 test_convex_hull_case(ctx, "convex14");
745 test_convex_hull_case(ctx, "convex15");
746
747 str1 = "{ [i0, i1, i2] : (i2 = 1 and i0 = 0 and i1 >= 0) or "
748 "(i0 = 1 and i1 = 0 and i2 = 1) or "
749 "(i0 = 0 and i1 = 0 and i2 = 0) }";
750 str2 = "{ [i0, i1, i2] : i0 >= 0 and i2 >= i0 and i2 <= 1 and i1 >= 0 }";
751 set1 = isl_set_read_from_str(ctx, str1);
752 set2 = isl_set_read_from_str(ctx, str2);
753 set1 = isl_set_from_basic_set(isl_set_convex_hull(set1));
754 assert(isl_set_is_equal(set1, set2));
755 isl_set_free(set1);
756 isl_set_free(set2);
757
758 ctx->opt->convex = orig_convex;
759 }
760
761 void test_convex_hull(struct isl_ctx *ctx)
762 {
763 test_convex_hull_algo(ctx, ISL_CONVEX_HULL_FM);
764 test_convex_hull_algo(ctx, ISL_CONVEX_HULL_WRAP);
765 }
766
767 void test_gist_case(struct isl_ctx *ctx, const char *name)
768 {
769 char *filename;
770 FILE *input;
771 struct isl_basic_set *bset1, *bset2;
772
773 filename = get_filename(ctx, name, "polylib");
774 assert(filename);
775 input = fopen(filename, "r");
776 assert(input);
777
778 bset1 = isl_basic_set_read_from_file(ctx, input);
779 bset2 = isl_basic_set_read_from_file(ctx, input);
780
781 bset1 = isl_basic_set_gist(bset1, bset2);
782
783 bset2 = isl_basic_set_read_from_file(ctx, input);
784
785 assert(isl_basic_set_is_equal(bset1, bset2) == 1);
786
787 isl_basic_set_free(bset1);
788 isl_basic_set_free(bset2);
789 free(filename);
790
791 fclose(input);
792 }
793
794 void test_gist(struct isl_ctx *ctx)
795 {
796 const char *str;
797 isl_basic_set *bset1, *bset2;
798
799 test_gist_case(ctx, "gist1");
800
801 str = "[p0, p2, p3, p5, p6, p10] -> { [] : "
802 "exists (e0 = [(15 + p0 + 15p6 + 15p10)/16], e1 = [(p5)/8], "
803 "e2 = [(p6)/128], e3 = [(8p2 - p5)/128], "
804 "e4 = [(128p3 - p6)/4096]: 8e1 = p5 and 128e2 = p6 and "
805 "128e3 = 8p2 - p5 and 4096e4 = 128p3 - p6 and p2 >= 0 and "
806 "16e0 >= 16 + 16p6 + 15p10 and p2 <= 15 and p3 >= 0 and "
807 "p3 <= 31 and p6 >= 128p3 and p5 >= 8p2 and p10 >= 0 and "
808 "16e0 <= 15 + p0 + 15p6 + 15p10 and 16e0 >= p0 + 15p6 + 15p10 and "
809 "p10 <= 15 and p10 <= -1 + p0 - p6) }";
810 bset1 = isl_basic_set_read_from_str(ctx, str);
811 str = "[p0, p2, p3, p5, p6, p10] -> { [] : exists (e0 = [(p5)/8], "
812 "e1 = [(p6)/128], e2 = [(8p2 - p5)/128], "
813 "e3 = [(128p3 - p6)/4096]: 8e0 = p5 and 128e1 = p6 and "
814 "128e2 = 8p2 - p5 and 4096e3 = 128p3 - p6 and p5 >= -7 and "
815 "p2 >= 0 and 8p2 <= -1 + p0 and p2 <= 15 and p3 >= 0 and "
816 "p3 <= 31 and 128p3 <= -1 + p0 and p6 >= -127 and "
817 "p5 <= -1 + p0 and p6 <= -1 + p0 and p6 >= 128p3 and "
818 "p0 >= 1 and p5 >= 8p2 and p10 >= 0 and p10 <= 15 ) }";
819 bset2 = isl_basic_set_read_from_str(ctx, str);
820 bset1 = isl_basic_set_gist(bset1, bset2);
821 assert(bset1 && bset1->n_div == 0);
822 isl_basic_set_free(bset1);
823 }
824
825 int test_coalesce_set(isl_ctx *ctx, const char *str, int check_one)
826 {
827 isl_set *set, *set2;
828 int equal;
829 int one;
830
831 set = isl_set_read_from_str(ctx, str);
832 set = isl_set_coalesce(set);
833 set2 = isl_set_read_from_str(ctx, str);
834 equal = isl_set_is_equal(set, set2);
835 one = set && set->n == 1;
836 isl_set_free(set);
837 isl_set_free(set2);
838
839 if (equal < 0)
840 return -1;
841 if (!equal)
842 isl_die(ctx, isl_error_unknown,
843 "coalesced set not equal to input", return -1);
844 if (check_one && !one)
845 isl_die(ctx, isl_error_unknown,
846 "coalesced set should not be a union", return -1);
847
848 return 0;
849 }
850
851 int test_coalesce_unbounded_wrapping(isl_ctx *ctx)
852 {
853 int r = 0;
854 int bounded;
855
856 bounded = isl_options_get_coalesce_bounded_wrapping(ctx);
857 isl_options_set_coalesce_bounded_wrapping(ctx, 0);
858
859 if (test_coalesce_set(ctx,
860 "{[x,y,z] : y + 2 >= 0 and x - y + 1 >= 0 and "
861 "-x - y + 1 >= 0 and -3 <= z <= 3;"
862 "[x,y,z] : -x+z + 20 >= 0 and -x-z + 20 >= 0 and "
863 "x-z + 20 >= 0 and x+z + 20 >= 0 and "
864 "-10 <= y <= 0}", 1) < 0)
865 goto error;
866 if (test_coalesce_set(ctx,
867 "{[x,y] : 0 <= x,y <= 10; [5,y]: 4 <=y <= 11}", 1) < 0)
868 goto error;
869 if (test_coalesce_set(ctx,
870 "{[x,0,0] : -5 <= x <= 5; [0,y,1] : -5 <= y <= 5 }", 1) < 0)
871 goto error;
872
873 if (0) {
874 error:
875 r = -1;
876 }
877
878 isl_options_set_coalesce_bounded_wrapping(ctx, bounded);
879
880 return r;
881 }
882
883 int test_coalesce(struct isl_ctx *ctx)
884 {
885 const char *str;
886 struct isl_set *set, *set2;
887 struct isl_map *map, *map2;
888
889 set = isl_set_read_from_str(ctx,
890 "{[x,y]: x >= 0 & x <= 10 & y >= 0 & y <= 10 or "
891 "y >= x & x >= 2 & 5 >= y }");
892 set = isl_set_coalesce(set);
893 assert(set && set->n == 1);
894 isl_set_free(set);
895
896 set = isl_set_read_from_str(ctx,
897 "{[x,y]: y >= 0 & 2x + y <= 30 & y <= 10 & x >= 0 or "
898 "x + y >= 10 & y <= x & x + y <= 20 & y >= 0}");
899 set = isl_set_coalesce(set);
900 assert(set && set->n == 1);
901 isl_set_free(set);
902
903 set = isl_set_read_from_str(ctx,
904 "{[x,y]: y >= 0 & 2x + y <= 30 & y <= 10 & x >= 0 or "
905 "x + y >= 10 & y <= x & x + y <= 19 & y >= 0}");
906 set = isl_set_coalesce(set);
907 assert(set && set->n == 2);
908 isl_set_free(set);
909
910 set = isl_set_read_from_str(ctx,
911 "{[x,y]: y >= 0 & x <= 5 & y <= x or "
912 "y >= 0 & x >= 6 & x <= 10 & y <= x}");
913 set = isl_set_coalesce(set);
914 assert(set && set->n == 1);
915 isl_set_free(set);
916
917 set = isl_set_read_from_str(ctx,
918 "{[x,y]: y >= 0 & x <= 5 & y <= x or "
919 "y >= 0 & x >= 7 & x <= 10 & y <= x}");
920 set = isl_set_coalesce(set);
921 assert(set && set->n == 2);
922 isl_set_free(set);
923
924 set = isl_set_read_from_str(ctx,
925 "{[x,y]: y >= 0 & x <= 5 & y <= x or "
926 "y >= 0 & x >= 6 & x <= 10 & y + 1 <= x}");
927 set = isl_set_coalesce(set);
928 assert(set && set->n == 2);
929 isl_set_free(set);
930
931 set = isl_set_read_from_str(ctx,
932 "{[x,y]: y >= 0 & x <= 5 & y <= x or "
933 "y >= 0 & x = 6 & y <= 6}");
934 set = isl_set_coalesce(set);
935 assert(set && set->n == 1);
936 isl_set_free(set);
937
938 set = isl_set_read_from_str(ctx,
939 "{[x,y]: y >= 0 & x <= 5 & y <= x or "
940 "y >= 0 & x = 7 & y <= 6}");
941 set = isl_set_coalesce(set);
942 assert(set && set->n == 2);
943 isl_set_free(set);
944
945 set = isl_set_read_from_str(ctx,
946 "{[x,y]: y >= 0 & x <= 5 & y <= x or "
947 "y >= 0 & x = 6 & y <= 5}");
948 set = isl_set_coalesce(set);
949 assert(set && set->n == 1);
950 set2 = isl_set_read_from_str(ctx,
951 "{[x,y]: y >= 0 & x <= 5 & y <= x or "
952 "y >= 0 & x = 6 & y <= 5}");
953 assert(isl_set_is_equal(set, set2));
954 isl_set_free(set);
955 isl_set_free(set2);
956
957 set = isl_set_read_from_str(ctx,
958 "{[x,y]: y >= 0 & x <= 5 & y <= x or "
959 "y >= 0 & x = 6 & y <= 7}");
960 set = isl_set_coalesce(set);
961 assert(set && set->n == 2);
962 isl_set_free(set);
963
964 set = isl_set_read_from_str(ctx,
965 "[n] -> { [i] : i = 1 and n >= 2 or 2 <= i and i <= n }");
966 set = isl_set_coalesce(set);
967 assert(set && set->n == 1);
968 set2 = isl_set_read_from_str(ctx,
969 "[n] -> { [i] : i = 1 and n >= 2 or 2 <= i and i <= n }");
970 assert(isl_set_is_equal(set, set2));
971 isl_set_free(set);
972 isl_set_free(set2);
973
974 set = isl_set_read_from_str(ctx,
975 "{[x,y] : x >= 0 and y >= 0 or 0 <= y and y <= 5 and x = -1}");
976 set = isl_set_coalesce(set);
977 set2 = isl_set_read_from_str(ctx,
978 "{[x,y] : x >= 0 and y >= 0 or 0 <= y and y <= 5 and x = -1}");
979 assert(isl_set_is_equal(set, set2));
980 isl_set_free(set);
981 isl_set_free(set2);
982
983 set = isl_set_read_from_str(ctx,
984 "[n] -> { [i] : 1 <= i and i <= n - 1 or "
985 "2 <= i and i <= n }");
986 set = isl_set_coalesce(set);
987 assert(set && set->n == 1);
988 set2 = isl_set_read_from_str(ctx,
989 "[n] -> { [i] : 1 <= i and i <= n - 1 or "
990 "2 <= i and i <= n }");
991 assert(isl_set_is_equal(set, set2));
992 isl_set_free(set);
993 isl_set_free(set2);
994
995 map = isl_map_read_from_str(ctx,
996 "[n] -> { [i0] -> [o0] : exists (e0 = [(i0)/4], e1 = [(o0)/4], "
997 "e2 = [(n)/2], e3 = [(-2 + i0)/4], e4 = [(-2 + o0)/4], "
998 "e5 = [(-2n + i0)/4]: 2e2 = n and 4e3 = -2 + i0 and "
999 "4e4 = -2 + o0 and i0 >= 8 + 2n and o0 >= 2 + i0 and "
1000 "o0 <= 56 + 2n and o0 <= -12 + 4n and i0 <= 57 + 2n and "
1001 "i0 <= -11 + 4n and o0 >= 6 + 2n and 4e0 <= i0 and "
1002 "4e0 >= -3 + i0 and 4e1 <= o0 and 4e1 >= -3 + o0 and "
1003 "4e5 <= -2n + i0 and 4e5 >= -3 - 2n + i0);"
1004 "[i0] -> [o0] : exists (e0 = [(i0)/4], e1 = [(o0)/4], "
1005 "e2 = [(n)/2], e3 = [(-2 + i0)/4], e4 = [(-2 + o0)/4], "
1006 "e5 = [(-2n + i0)/4]: 2e2 = n and 4e3 = -2 + i0 and "
1007 "4e4 = -2 + o0 and 2e0 >= 3 + n and e0 <= -4 + n and "
1008 "2e0 <= 27 + n and e1 <= -4 + n and 2e1 <= 27 + n and "
1009 "2e1 >= 2 + n and e1 >= 1 + e0 and i0 >= 7 + 2n and "
1010 "i0 <= -11 + 4n and i0 <= 57 + 2n and 4e0 <= -2 + i0 and "
1011 "4e0 >= -3 + i0 and o0 >= 6 + 2n and o0 <= -11 + 4n and "
1012 "o0 <= 57 + 2n and 4e1 <= -2 + o0 and 4e1 >= -3 + o0 and "
1013 "4e5 <= -2n + i0 and 4e5 >= -3 - 2n + i0 ) }");
1014 map = isl_map_coalesce(map);
1015 map2 = isl_map_read_from_str(ctx,
1016 "[n] -> { [i0] -> [o0] : exists (e0 = [(i0)/4], e1 = [(o0)/4], "
1017 "e2 = [(n)/2], e3 = [(-2 + i0)/4], e4 = [(-2 + o0)/4], "
1018 "e5 = [(-2n + i0)/4]: 2e2 = n and 4e3 = -2 + i0 and "
1019 "4e4 = -2 + o0 and i0 >= 8 + 2n and o0 >= 2 + i0 and "
1020 "o0 <= 56 + 2n and o0 <= -12 + 4n and i0 <= 57 + 2n and "
1021 "i0 <= -11 + 4n and o0 >= 6 + 2n and 4e0 <= i0 and "
1022 "4e0 >= -3 + i0 and 4e1 <= o0 and 4e1 >= -3 + o0 and "
1023 "4e5 <= -2n + i0 and 4e5 >= -3 - 2n + i0);"
1024 "[i0] -> [o0] : exists (e0 = [(i0)/4], e1 = [(o0)/4], "
1025 "e2 = [(n)/2], e3 = [(-2 + i0)/4], e4 = [(-2 + o0)/4], "
1026 "e5 = [(-2n + i0)/4]: 2e2 = n and 4e3 = -2 + i0 and "
1027 "4e4 = -2 + o0 and 2e0 >= 3 + n and e0 <= -4 + n and "
1028 "2e0 <= 27 + n and e1 <= -4 + n and 2e1 <= 27 + n and "
1029 "2e1 >= 2 + n and e1 >= 1 + e0 and i0 >= 7 + 2n and "
1030 "i0 <= -11 + 4n and i0 <= 57 + 2n and 4e0 <= -2 + i0 and "
1031 "4e0 >= -3 + i0 and o0 >= 6 + 2n and o0 <= -11 + 4n and "
1032 "o0 <= 57 + 2n and 4e1 <= -2 + o0 and 4e1 >= -3 + o0 and "
1033 "4e5 <= -2n + i0 and 4e5 >= -3 - 2n + i0 ) }");
1034 assert(isl_map_is_equal(map, map2));
1035 isl_map_free(map);
1036 isl_map_free(map2);
1037
1038 str = "[n, m] -> { [] -> [o0, o2, o3] : (o3 = 1 and o0 >= 1 + m and "
1039 "o0 <= n + m and o2 <= m and o0 >= 2 + n and o2 >= 3) or "
1040 "(o0 >= 2 + n and o0 >= 1 + m and o0 <= n + m and n >= 1 and "
1041 "o3 <= -1 + o2 and o3 >= 1 - m + o2 and o3 >= 2 and o3 <= n) }";
1042 map = isl_map_read_from_str(ctx, str);
1043 map = isl_map_coalesce(map);
1044 map2 = isl_map_read_from_str(ctx, str);
1045 assert(isl_map_is_equal(map, map2));
1046 isl_map_free(map);
1047 isl_map_free(map2);
1048
1049 str = "[M, N] -> { [i0, i1, i2, i3, i4, i5, i6] -> "
1050 "[o0, o1, o2, o3, o4, o5, o6] : "
1051 "(o6 <= -4 + 2M - 2N + i0 + i1 - i2 + i6 - o0 - o1 + o2 and "
1052 "o3 <= -2 + i3 and o6 >= 2 + i0 + i3 + i6 - o0 - o3 and "
1053 "o6 >= 2 - M + N + i3 + i4 + i6 - o3 - o4 and o0 <= -1 + i0 and "
1054 "o4 >= 4 - 3M + 3N - i0 - i1 + i2 + 2i3 + i4 + o0 + o1 - o2 - 2o3 "
1055 "and o6 <= -3 + 2M - 2N + i3 + i4 - i5 + i6 - o3 - o4 + o5 and "
1056 "2o6 <= -5 + 5M - 5N + 2i0 + i1 - i2 - i5 + 2i6 - 2o0 - o1 + o2 + o5 "
1057 "and o6 >= 2i0 + i1 + i6 - 2o0 - o1 and "
1058 "3o6 <= -5 + 4M - 4N + 2i0 + i1 - i2 + 2i3 + i4 - i5 + 3i6 "
1059 "- 2o0 - o1 + o2 - 2o3 - o4 + o5) or "
1060 "(N >= 2 and o3 <= -1 + i3 and o0 <= -1 + i0 and "
1061 "o6 >= i3 + i6 - o3 and M >= 0 and "
1062 "2o6 >= 1 + i0 + i3 + 2i6 - o0 - o3 and "
1063 "o6 >= 1 - M + i0 + i6 - o0 and N >= 2M and o6 >= i0 + i6 - o0) }";
1064 map = isl_map_read_from_str(ctx, str);
1065 map = isl_map_coalesce(map);
1066 map2 = isl_map_read_from_str(ctx, str);
1067 assert(isl_map_is_equal(map, map2));
1068 isl_map_free(map);
1069 isl_map_free(map2);
1070
1071 str = "[M, N] -> { [] -> [o0] : (o0 = 0 and M >= 1 and N >= 2) or "
1072 "(o0 = 0 and M >= 1 and N >= 2M and N >= 2 + M) or "
1073 "(o0 = 0 and M >= 2 and N >= 3) or "
1074 "(M = 0 and o0 = 0 and N >= 3) }";
1075 map = isl_map_read_from_str(ctx, str);
1076 map = isl_map_coalesce(map);
1077 map2 = isl_map_read_from_str(ctx, str);
1078 assert(isl_map_is_equal(map, map2));
1079 isl_map_free(map);
1080 isl_map_free(map2);
1081
1082 str = "{ [i0, i1, i2, i3] : (i1 = 10i0 and i0 >= 1 and 10i0 <= 100 and "
1083 "i3 <= 9 + 10 i2 and i3 >= 1 + 10i2 and i3 >= 0) or "
1084 "(i1 <= 9 + 10i0 and i1 >= 1 + 10i0 and i2 >= 0 and "
1085 "i0 >= 0 and i1 <= 100 and i3 <= 9 + 10i2 and i3 >= 1 + 10i2) }";
1086 map = isl_map_read_from_str(ctx, str);
1087 map = isl_map_coalesce(map);
1088 map2 = isl_map_read_from_str(ctx, str);
1089 assert(isl_map_is_equal(map, map2));
1090 isl_map_free(map);
1091 isl_map_free(map2);
1092
1093 test_coalesce_set(ctx,
1094 "[M] -> { [i1] : (i1 >= 2 and i1 <= M) or "
1095 "(i1 = M and M >= 1) }", 0);
1096 test_coalesce_set(ctx,
1097 "{[x,y] : x,y >= 0; [x,y] : 10 <= x <= 20 and y >= -1 }", 0);
1098 test_coalesce_set(ctx,
1099 "{ [x, y] : (x >= 1 and y >= 1 and x <= 2 and y <= 2) or "
1100 "(y = 3 and x = 1) }", 1);
1101 test_coalesce_set(ctx,
1102 "[M] -> { [i0, i1, i2, i3, i4] : (i1 >= 3 and i4 >= 2 + i2 and "
1103 "i2 >= 2 and i0 >= 2 and i3 >= 1 + i2 and i0 <= M and "
1104 "i1 <= M and i3 <= M and i4 <= M) or "
1105 "(i1 >= 2 and i4 >= 1 + i2 and i2 >= 2 and i0 >= 2 and "
1106 "i3 >= 1 + i2 and i0 <= M and i1 <= -1 + M and i3 <= M and "
1107 "i4 <= -1 + M) }", 1);
1108 test_coalesce_set(ctx,
1109 "{ [x, y] : (x >= 0 and y >= 0 and x <= 10 and y <= 10) or "
1110 "(x >= 1 and y >= 1 and x <= 11 and y <= 11) }", 1);
1111 if (test_coalesce_unbounded_wrapping(ctx) < 0)
1112 return -1;
1113 if (test_coalesce_set(ctx, "{[x,0] : x >= 0; [x,1] : x <= 20}", 0) < 0)
1114 return -1;
1115 if (test_coalesce_set(ctx, "{ [x, 1 - x] : 0 <= x <= 1; [0,0] }", 1) < 0)
1116 return -1;
1117 if (test_coalesce_set(ctx, "{ [0,0]; [i,i] : 1 <= i <= 10 }", 1) < 0)
1118 return -1;
1119 if (test_coalesce_set(ctx, "{ [0,0]; [i,j] : 1 <= i,j <= 10 }", 0) < 0)
1120 return -1;
1121 if (test_coalesce_set(ctx, "{ [0,0]; [i,2i] : 1 <= i <= 10 }", 1) < 0)
1122 return -1;
1123 if (test_coalesce_set(ctx, "{ [0,0]; [i,2i] : 2 <= i <= 10 }", 0) < 0)
1124 return -1;
1125 if (test_coalesce_set(ctx, "{ [1,0]; [i,2i] : 1 <= i <= 10 }", 0) < 0)
1126 return -1;
1127 if (test_coalesce_set(ctx, "{ [0,1]; [i,2i] : 1 <= i <= 10 }", 0) < 0)
1128 return -1;
1129 if (test_coalesce_set(ctx, "{ [a, b] : exists e : 2e = a and "
1130 "a >= 0 and (a <= 3 or (b <= 0 and b >= -4 + a)) }", 0) < 0)
1131 return -1;
1132 if (test_coalesce_set(ctx,
1133 "{ [i, j, i', j'] : i <= 2 and j <= 2 and "
1134 "j' >= -1 + 2i + j - 2i' and i' <= -1 + i and "
1135 "j >= 1 and j' <= i + j - i' and i >= 1; "
1136 "[1, 1, 1, 1] }", 0) < 0)
1137 return -1;
1138 if (test_coalesce_set(ctx, "{ [i,j] : exists a,b : i = 2a and j = 3b; "
1139 "[i,j] : exists a : j = 3a }", 1) < 0)
1140 return -1;
1141 return 0;
1142 }
1143
1144 void test_closure(struct isl_ctx *ctx)
1145 {
1146 const char *str;
1147 isl_set *dom;
1148 isl_map *up, *right;
1149 isl_map *map, *map2;
1150 int exact;
1151
1152 /* COCOA example 1 */
1153 map = isl_map_read_from_str(ctx,
1154 "[n] -> { [i,j] -> [i2,j2] : i2 = i + 1 and j2 = j + 1 and "
1155 "1 <= i and i < n and 1 <= j and j < n or "
1156 "i2 = i + 1 and j2 = j - 1 and "
1157 "1 <= i and i < n and 2 <= j and j <= n }");
1158 map = isl_map_power(map, &exact);
1159 assert(exact);
1160 isl_map_free(map);
1161
1162 /* COCOA example 1 */
1163 map = isl_map_read_from_str(ctx,
1164 "[n] -> { [i,j] -> [i2,j2] : i2 = i + 1 and j2 = j + 1 and "
1165 "1 <= i and i < n and 1 <= j and j < n or "
1166 "i2 = i + 1 and j2 = j - 1 and "
1167 "1 <= i and i < n and 2 <= j and j <= n }");
1168 map = isl_map_transitive_closure(map, &exact);
1169 assert(exact);
1170 map2 = isl_map_read_from_str(ctx,
1171 "[n] -> { [i,j] -> [i2,j2] : exists (k1,k2,k : "
1172 "1 <= i and i < n and 1 <= j and j <= n and "
1173 "2 <= i2 and i2 <= n and 1 <= j2 and j2 <= n and "
1174 "i2 = i + k1 + k2 and j2 = j + k1 - k2 and "
1175 "k1 >= 0 and k2 >= 0 and k1 + k2 = k and k >= 1 )}");
1176 assert(isl_map_is_equal(map, map2));
1177 isl_map_free(map2);
1178 isl_map_free(map);
1179
1180 map = isl_map_read_from_str(ctx,
1181 "[n] -> { [x] -> [y] : y = x + 1 and 0 <= x and x <= n and "
1182 " 0 <= y and y <= n }");
1183 map = isl_map_transitive_closure(map, &exact);
1184 map2 = isl_map_read_from_str(ctx,
1185 "[n] -> { [x] -> [y] : y > x and 0 <= x and x <= n and "
1186 " 0 <= y and y <= n }");
1187 assert(isl_map_is_equal(map, map2));
1188 isl_map_free(map2);
1189 isl_map_free(map);
1190
1191 /* COCOA example 2 */
1192 map = isl_map_read_from_str(ctx,
1193 "[n] -> { [i,j] -> [i2,j2] : i2 = i + 2 and j2 = j + 2 and "
1194 "1 <= i and i < n - 1 and 1 <= j and j < n - 1 or "
1195 "i2 = i + 2 and j2 = j - 2 and "
1196 "1 <= i and i < n - 1 and 3 <= j and j <= n }");
1197 map = isl_map_transitive_closure(map, &exact);
1198 assert(exact);
1199 map2 = isl_map_read_from_str(ctx,
1200 "[n] -> { [i,j] -> [i2,j2] : exists (k1,k2,k : "
1201 "1 <= i and i < n - 1 and 1 <= j and j <= n and "
1202 "3 <= i2 and i2 <= n and 1 <= j2 and j2 <= n and "
1203 "i2 = i + 2 k1 + 2 k2 and j2 = j + 2 k1 - 2 k2 and "
1204 "k1 >= 0 and k2 >= 0 and k1 + k2 = k and k >= 1) }");
1205 assert(isl_map_is_equal(map, map2));
1206 isl_map_free(map);
1207 isl_map_free(map2);
1208
1209 /* COCOA Fig.2 left */
1210 map = isl_map_read_from_str(ctx,
1211 "[n] -> { [i,j] -> [i2,j2] : i2 = i + 2 and j2 = j and "
1212 "i <= 2 j - 3 and i <= n - 2 and j <= 2 i - 1 and "
1213 "j <= n or "
1214 "i2 = i and j2 = j + 2 and i <= 2 j - 1 and i <= n and "
1215 "j <= 2 i - 3 and j <= n - 2 or "
1216 "i2 = i + 1 and j2 = j + 1 and i <= 2 j - 1 and "
1217 "i <= n - 1 and j <= 2 i - 1 and j <= n - 1 }");
1218 map = isl_map_transitive_closure(map, &exact);
1219 assert(exact);
1220 isl_map_free(map);
1221
1222 /* COCOA Fig.2 right */
1223 map = isl_map_read_from_str(ctx,
1224 "[n] -> { [i,j] -> [i2,j2] : i2 = i + 3 and j2 = j and "
1225 "i <= 2 j - 4 and i <= n - 3 and j <= 2 i - 1 and "
1226 "j <= n or "
1227 "i2 = i and j2 = j + 3 and i <= 2 j - 1 and i <= n and "
1228 "j <= 2 i - 4 and j <= n - 3 or "
1229 "i2 = i + 1 and j2 = j + 1 and i <= 2 j - 1 and "
1230 "i <= n - 1 and j <= 2 i - 1 and j <= n - 1 }");
1231 map = isl_map_power(map, &exact);
1232 assert(exact);
1233 isl_map_free(map);
1234
1235 /* COCOA Fig.2 right */
1236 map = isl_map_read_from_str(ctx,
1237 "[n] -> { [i,j] -> [i2,j2] : i2 = i + 3 and j2 = j and "
1238 "i <= 2 j - 4 and i <= n - 3 and j <= 2 i - 1 and "
1239 "j <= n or "
1240 "i2 = i and j2 = j + 3 and i <= 2 j - 1 and i <= n and "
1241 "j <= 2 i - 4 and j <= n - 3 or "
1242 "i2 = i + 1 and j2 = j + 1 and i <= 2 j - 1 and "
1243 "i <= n - 1 and j <= 2 i - 1 and j <= n - 1 }");
1244 map = isl_map_transitive_closure(map, &exact);
1245 assert(exact);
1246 map2 = isl_map_read_from_str(ctx,
1247 "[n] -> { [i,j] -> [i2,j2] : exists (k1,k2,k3,k : "
1248 "i <= 2 j - 1 and i <= n and j <= 2 i - 1 and "
1249 "j <= n and 3 + i + 2 j <= 3 n and "
1250 "3 + 2 i + j <= 3n and i2 <= 2 j2 -1 and i2 <= n and "
1251 "i2 <= 3 j2 - 4 and j2 <= 2 i2 -1 and j2 <= n and "
1252 "13 + 4 j2 <= 11 i2 and i2 = i + 3 k1 + k3 and "
1253 "j2 = j + 3 k2 + k3 and k1 >= 0 and k2 >= 0 and "
1254 "k3 >= 0 and k1 + k2 + k3 = k and k > 0) }");
1255 assert(isl_map_is_equal(map, map2));
1256 isl_map_free(map2);
1257 isl_map_free(map);
1258
1259 /* COCOA Fig.1 right */
1260 dom = isl_set_read_from_str(ctx,
1261 "{ [x,y] : x >= 0 and -2 x + 3 y >= 0 and x <= 3 and "
1262 "2 x - 3 y + 3 >= 0 }");
1263 right = isl_map_read_from_str(ctx,
1264 "{ [x,y] -> [x2,y2] : x2 = x + 1 and y2 = y }");
1265 up = isl_map_read_from_str(ctx,
1266 "{ [x,y] -> [x2,y2] : x2 = x and y2 = y + 1 }");
1267 right = isl_map_intersect_domain(right, isl_set_copy(dom));
1268 right = isl_map_intersect_range(right, isl_set_copy(dom));
1269 up = isl_map_intersect_domain(up, isl_set_copy(dom));
1270 up = isl_map_intersect_range(up, dom);
1271 map = isl_map_union(up, right);
1272 map = isl_map_transitive_closure(map, &exact);
1273 assert(exact);
1274 map2 = isl_map_read_from_str(ctx,
1275 "{ [0,0] -> [0,1]; [0,0] -> [1,1]; [0,1] -> [1,1]; "
1276 " [2,2] -> [3,2]; [2,2] -> [3,3]; [3,2] -> [3,3] }");
1277 assert(isl_map_is_equal(map, map2));
1278 isl_map_free(map2);
1279 isl_map_free(map);
1280
1281 /* COCOA Theorem 1 counter example */
1282 map = isl_map_read_from_str(ctx,
1283 "{ [i,j] -> [i2,j2] : i = 0 and 0 <= j and j <= 1 and "
1284 "i2 = 1 and j2 = j or "
1285 "i = 0 and j = 0 and i2 = 0 and j2 = 1 }");
1286 map = isl_map_transitive_closure(map, &exact);
1287 assert(exact);
1288 isl_map_free(map);
1289
1290 map = isl_map_read_from_str(ctx,
1291 "[m,n] -> { [i,j] -> [i2,j2] : i2 = i and j2 = j + 2 and "
1292 "1 <= i,i2 <= n and 1 <= j,j2 <= m or "
1293 "i2 = i + 1 and 3 <= j2 - j <= 4 and "
1294 "1 <= i,i2 <= n and 1 <= j,j2 <= m }");
1295 map = isl_map_transitive_closure(map, &exact);
1296 assert(exact);
1297 isl_map_free(map);
1298
1299 /* Kelly et al 1996, fig 12 */
1300 map = isl_map_read_from_str(ctx,
1301 "[n] -> { [i,j] -> [i2,j2] : i2 = i and j2 = j + 1 and "
1302 "1 <= i,j,j+1 <= n or "
1303 "j = n and j2 = 1 and i2 = i + 1 and "
1304 "1 <= i,i+1 <= n }");
1305 map = isl_map_transitive_closure(map, &exact);
1306 assert(exact);
1307 map2 = isl_map_read_from_str(ctx,
1308 "[n] -> { [i,j] -> [i2,j2] : 1 <= j < j2 <= n and "
1309 "1 <= i <= n and i = i2 or "
1310 "1 <= i < i2 <= n and 1 <= j <= n and "
1311 "1 <= j2 <= n }");
1312 assert(isl_map_is_equal(map, map2));
1313 isl_map_free(map2);
1314 isl_map_free(map);
1315
1316 /* Omega's closure4 */
1317 map = isl_map_read_from_str(ctx,
1318 "[m,n] -> { [x,y] -> [x2,y2] : x2 = x and y2 = y + 1 and "
1319 "1 <= x,y <= 10 or "
1320 "x2 = x + 1 and y2 = y and "
1321 "1 <= x <= 20 && 5 <= y <= 15 }");
1322 map = isl_map_transitive_closure(map, &exact);
1323 assert(exact);
1324 isl_map_free(map);
1325
1326 map = isl_map_read_from_str(ctx,
1327 "[n] -> { [x] -> [y]: 1 <= n <= y - x <= 10 }");
1328 map = isl_map_transitive_closure(map, &exact);
1329 assert(!exact);
1330 map2 = isl_map_read_from_str(ctx,
1331 "[n] -> { [x] -> [y] : 1 <= n <= 10 and y >= n + x }");
1332 assert(isl_map_is_equal(map, map2));
1333 isl_map_free(map);
1334 isl_map_free(map2);
1335
1336 str = "[n, m] -> { [i0, i1, i2, i3] -> [o0, o1, o2, o3] : "
1337 "i3 = 1 and o0 = i0 and o1 = -1 + i1 and o2 = -1 + i2 and "
1338 "o3 = -2 + i2 and i1 <= -1 + i0 and i1 >= 1 - m + i0 and "
1339 "i1 >= 2 and i1 <= n and i2 >= 3 and i2 <= 1 + n and i2 <= m }";
1340 map = isl_map_read_from_str(ctx, str);
1341 map = isl_map_transitive_closure(map, &exact);
1342 assert(exact);
1343 map2 = isl_map_read_from_str(ctx, str);
1344 assert(isl_map_is_equal(map, map2));
1345 isl_map_free(map);
1346 isl_map_free(map2);
1347
1348 str = "{[0] -> [1]; [2] -> [3]}";
1349 map = isl_map_read_from_str(ctx, str);
1350 map = isl_map_transitive_closure(map, &exact);
1351 assert(exact);
1352 map2 = isl_map_read_from_str(ctx, str);
1353 assert(isl_map_is_equal(map, map2));
1354 isl_map_free(map);
1355 isl_map_free(map2);
1356
1357 str = "[n] -> { [[i0, i1, 1, 0, i0] -> [i5, 1]] -> "
1358 "[[i0, -1 + i1, 2, 0, i0] -> [-1 + i5, 2]] : "
1359 "exists (e0 = [(3 - n)/3]: i5 >= 2 and i1 >= 2 and "
1360 "3i0 <= -1 + n and i1 <= -1 + n and i5 <= -1 + n and "
1361 "3e0 >= 1 - n and 3e0 <= 2 - n and 3i0 >= -2 + n); "
1362 "[[i0, i1, 2, 0, i0] -> [i5, 1]] -> "
1363 "[[i0, i1, 1, 0, i0] -> [-1 + i5, 2]] : "
1364 "exists (e0 = [(3 - n)/3]: i5 >= 2 and i1 >= 1 and "
1365 "3i0 <= -1 + n and i1 <= -1 + n and i5 <= -1 + n and "
1366 "3e0 >= 1 - n and 3e0 <= 2 - n and 3i0 >= -2 + n); "
1367 "[[i0, i1, 1, 0, i0] -> [i5, 2]] -> "
1368 "[[i0, -1 + i1, 2, 0, i0] -> [i5, 1]] : "
1369 "exists (e0 = [(3 - n)/3]: i1 >= 2 and i5 >= 1 and "
1370 "3i0 <= -1 + n and i1 <= -1 + n and i5 <= -1 + n and "
1371 "3e0 >= 1 - n and 3e0 <= 2 - n and 3i0 >= -2 + n); "
1372 "[[i0, i1, 2, 0, i0] -> [i5, 2]] -> "
1373 "[[i0, i1, 1, 0, i0] -> [i5, 1]] : "
1374 "exists (e0 = [(3 - n)/3]: i5 >= 1 and i1 >= 1 and "
1375 "3i0 <= -1 + n and i1 <= -1 + n and i5 <= -1 + n and "
1376 "3e0 >= 1 - n and 3e0 <= 2 - n and 3i0 >= -2 + n) }";
1377 map = isl_map_read_from_str(ctx, str);
1378 map = isl_map_transitive_closure(map, NULL);
1379 assert(map);
1380 isl_map_free(map);
1381 }
1382
1383 void test_lex(struct isl_ctx *ctx)
1384 {
1385 isl_space *dim;
1386 isl_map *map;
1387
1388 dim = isl_space_set_alloc(ctx, 0, 0);
1389 map = isl_map_lex_le(dim);
1390 assert(!isl_map_is_empty(map));
1391 isl_map_free(map);
1392 }
1393
1394 void test_lexmin(struct isl_ctx *ctx)
1395 {
1396 const char *str;
1397 isl_basic_map *bmap;
1398 isl_map *map, *map2;
1399 isl_set *set;
1400 isl_set *set2;
1401 isl_pw_multi_aff *pma;
1402
1403 str = "[p0, p1] -> { [] -> [] : "
1404 "exists (e0 = [(2p1)/3], e1, e2, e3 = [(3 - p1 + 3e0)/3], "
1405 "e4 = [(p1)/3], e5 = [(p1 + 3e4)/3]: "
1406 "3e0 >= -2 + 2p1 and 3e0 >= p1 and 3e3 >= 1 - p1 + 3e0 and "
1407 "3e0 <= 2p1 and 3e3 >= -2 + p1 and 3e3 <= -1 + p1 and p1 >= 3 and "
1408 "3e5 >= -2 + 2p1 and 3e5 >= p1 and 3e5 <= -1 + p1 + 3e4 and "
1409 "3e4 <= p1 and 3e4 >= -2 + p1 and e3 <= -1 + e0 and "
1410 "3e4 >= 6 - p1 + 3e1 and 3e1 >= p1 and 3e5 >= -2 + p1 + 3e4 and "
1411 "2e4 >= 3 - p1 + 2e1 and e4 <= e1 and 3e3 <= 2 - p1 + 3e0 and "
1412 "e5 >= 1 + e1 and 3e4 >= 6 - 2p1 + 3e1 and "
1413 "p0 >= 2 and p1 >= p0 and 3e2 >= p1 and 3e4 >= 6 - p1 + 3e2 and "
1414 "e2 <= e1 and e3 >= 1 and e4 <= e2) }";
1415 map = isl_map_read_from_str(ctx, str);
1416 map = isl_map_lexmin(map);
1417 isl_map_free(map);
1418
1419 str = "[C] -> { [obj,a,b,c] : obj <= 38 a + 7 b + 10 c and "
1420 "a + b <= 1 and c <= 10 b and c <= C and a,b,c,C >= 0 }";
1421 set = isl_set_read_from_str(ctx, str);
1422 set = isl_set_lexmax(set);
1423 str = "[C] -> { [obj,a,b,c] : C = 8 }";
1424 set2 = isl_set_read_from_str(ctx, str);
1425 set = isl_set_intersect(set, set2);
1426 assert(!isl_set_is_empty(set));
1427 isl_set_free(set);
1428
1429 str = "{ [x] -> [y] : x <= y <= 10; [x] -> [5] : -8 <= x <= 8 }";
1430 map = isl_map_read_from_str(ctx, str);
1431 map = isl_map_lexmin(map);
1432 str = "{ [x] -> [5] : 6 <= x <= 8; "
1433 "[x] -> [x] : x <= 5 or (9 <= x <= 10) }";
1434 map2 = isl_map_read_from_str(ctx, str);
1435 assert(isl_map_is_equal(map, map2));
1436 isl_map_free(map);
1437 isl_map_free(map2);
1438
1439 str = "{ [x] -> [y] : 4y = x or 4y = -1 + x or 4y = -2 + x }";
1440 map = isl_map_read_from_str(ctx, str);
1441 map2 = isl_map_copy(map);
1442 map = isl_map_lexmin(map);
1443 assert(isl_map_is_equal(map, map2));
1444 isl_map_free(map);
1445 isl_map_free(map2);
1446
1447 str = "{ [x] -> [y] : x = 4y; [x] -> [y] : x = 2y }";
1448 map = isl_map_read_from_str(ctx, str);
1449 map = isl_map_lexmin(map);
1450 str = "{ [x] -> [y] : (4y = x and x >= 0) or "
1451 "(exists (e0 = [(x)/4], e1 = [(-2 + x)/4]: 2y = x and "
1452 "4e1 = -2 + x and 4e0 <= -1 + x and 4e0 >= -3 + x)) or "
1453 "(exists (e0 = [(x)/4]: 2y = x and 4e0 = x and x <= -4)) }";
1454 map2 = isl_map_read_from_str(ctx, str);
1455 assert(isl_map_is_equal(map, map2));
1456 isl_map_free(map);
1457 isl_map_free(map2);
1458
1459 str = "{ [i] -> [i', j] : j = i - 8i' and i' >= 0 and i' <= 7 and "
1460 " 8i' <= i and 8i' >= -7 + i }";
1461 bmap = isl_basic_map_read_from_str(ctx, str);
1462 pma = isl_basic_map_lexmin_pw_multi_aff(isl_basic_map_copy(bmap));
1463 map2 = isl_map_from_pw_multi_aff(pma);
1464 map = isl_map_from_basic_map(bmap);
1465 assert(isl_map_is_equal(map, map2));
1466 isl_map_free(map);
1467 isl_map_free(map2);
1468
1469 str = "{ T[a] -> S[b, c] : a = 4b-2c and c >= b }";
1470 map = isl_map_read_from_str(ctx, str);
1471 map = isl_map_lexmin(map);
1472 str = "{ T[a] -> S[b, c] : 2b = a and 2c = a }";
1473 map2 = isl_map_read_from_str(ctx, str);
1474 assert(isl_map_is_equal(map, map2));
1475 isl_map_free(map);
1476 isl_map_free(map2);
1477 }
1478
1479 struct must_may {
1480 isl_map *must;
1481 isl_map *may;
1482 };
1483
1484 static int collect_must_may(__isl_take isl_map *dep, int must,
1485 void *dep_user, void *user)
1486 {
1487 struct must_may *mm = (struct must_may *)user;
1488
1489 if (must)
1490 mm->must = isl_map_union(mm->must, dep);
1491 else
1492 mm->may = isl_map_union(mm->may, dep);
1493
1494 return 0;
1495 }
1496
1497 static int common_space(void *first, void *second)
1498 {
1499 int depth = *(int *)first;
1500 return 2 * depth;
1501 }
1502
1503 static int map_is_equal(__isl_keep isl_map *map, const char *str)
1504 {
1505 isl_map *map2;
1506 int equal;
1507
1508 if (!map)
1509 return -1;
1510
1511 map2 = isl_map_read_from_str(map->ctx, str);
1512 equal = isl_map_is_equal(map, map2);
1513 isl_map_free(map2);
1514
1515 return equal;
1516 }
1517
1518 static int map_check_equal(__isl_keep isl_map *map, const char *str)
1519 {
1520 int equal;
1521
1522 equal = map_is_equal(map, str);
1523 if (equal < 0)
1524 return -1;
1525 if (!equal)
1526 isl_die(isl_map_get_ctx(map), isl_error_unknown,
1527 "result not as expected", return -1);
1528 return 0;
1529 }
1530
1531 void test_dep(struct isl_ctx *ctx)
1532 {
1533 const char *str;
1534 isl_space *dim;
1535 isl_map *map;
1536 isl_access_info *ai;
1537 isl_flow *flow;
1538 int depth;
1539 struct must_may mm;
1540
1541 depth = 3;
1542
1543 str = "{ [2,i,0] -> [i] : 0 <= i <= 10 }";
1544 map = isl_map_read_from_str(ctx, str);
1545 ai = isl_access_info_alloc(map, &depth, &common_space, 2);
1546
1547 str = "{ [0,i,0] -> [i] : 0 <= i <= 10 }";
1548 map = isl_map_read_from_str(ctx, str);
1549 ai = isl_access_info_add_source(ai, map, 1, &depth);
1550
1551 str = "{ [1,i,0] -> [5] : 0 <= i <= 10 }";
1552 map = isl_map_read_from_str(ctx, str);
1553 ai = isl_access_info_add_source(ai, map, 1, &depth);
1554
1555 flow = isl_access_info_compute_flow(ai);
1556 dim = isl_space_alloc(ctx, 0, 3, 3);
1557 mm.must = isl_map_empty(isl_space_copy(dim));
1558 mm.may = isl_map_empty(dim);
1559
1560 isl_flow_foreach(flow, collect_must_may, &mm);
1561
1562 str = "{ [0,i,0] -> [2,i,0] : (0 <= i <= 4) or (6 <= i <= 10); "
1563 " [1,10,0] -> [2,5,0] }";
1564 assert(map_is_equal(mm.must, str));
1565 str = "{ [i,j,k] -> [l,m,n] : 1 = 0 }";
1566 assert(map_is_equal(mm.may, str));
1567
1568 isl_map_free(mm.must);
1569 isl_map_free(mm.may);
1570 isl_flow_free(flow);
1571
1572
1573 str = "{ [2,i,0] -> [i] : 0 <= i <= 10 }";
1574 map = isl_map_read_from_str(ctx, str);
1575 ai = isl_access_info_alloc(map, &depth, &common_space, 2);
1576
1577 str = "{ [0,i,0] -> [i] : 0 <= i <= 10 }";
1578 map = isl_map_read_from_str(ctx, str);
1579 ai = isl_access_info_add_source(ai, map, 1, &depth);
1580
1581 str = "{ [1,i,0] -> [5] : 0 <= i <= 10 }";
1582 map = isl_map_read_from_str(ctx, str);
1583 ai = isl_access_info_add_source(ai, map, 0, &depth);
1584
1585 flow = isl_access_info_compute_flow(ai);
1586 dim = isl_space_alloc(ctx, 0, 3, 3);
1587 mm.must = isl_map_empty(isl_space_copy(dim));
1588 mm.may = isl_map_empty(dim);
1589
1590 isl_flow_foreach(flow, collect_must_may, &mm);
1591
1592 str = "{ [0,i,0] -> [2,i,0] : (0 <= i <= 4) or (6 <= i <= 10) }";
1593 assert(map_is_equal(mm.must, str));
1594 str = "{ [0,5,0] -> [2,5,0]; [1,i,0] -> [2,5,0] : 0 <= i <= 10 }";
1595 assert(map_is_equal(mm.may, str));
1596
1597 isl_map_free(mm.must);
1598 isl_map_free(mm.may);
1599 isl_flow_free(flow);
1600
1601
1602 str = "{ [2,i,0] -> [i] : 0 <= i <= 10 }";
1603 map = isl_map_read_from_str(ctx, str);
1604 ai = isl_access_info_alloc(map, &depth, &common_space, 2);
1605
1606 str = "{ [0,i,0] -> [i] : 0 <= i <= 10 }";
1607 map = isl_map_read_from_str(ctx, str);
1608 ai = isl_access_info_add_source(ai, map, 0, &depth);
1609
1610 str = "{ [1,i,0] -> [5] : 0 <= i <= 10 }";
1611 map = isl_map_read_from_str(ctx, str);
1612 ai = isl_access_info_add_source(ai, map, 0, &depth);
1613
1614 flow = isl_access_info_compute_flow(ai);
1615 dim = isl_space_alloc(ctx, 0, 3, 3);
1616 mm.must = isl_map_empty(isl_space_copy(dim));
1617 mm.may = isl_map_empty(dim);
1618
1619 isl_flow_foreach(flow, collect_must_may, &mm);
1620
1621 str = "{ [0,i,0] -> [2,i,0] : 0 <= i <= 10; "
1622 " [1,i,0] -> [2,5,0] : 0 <= i <= 10 }";
1623 assert(map_is_equal(mm.may, str));
1624 str = "{ [i,j,k] -> [l,m,n] : 1 = 0 }";
1625 assert(map_is_equal(mm.must, str));
1626
1627 isl_map_free(mm.must);
1628 isl_map_free(mm.may);
1629 isl_flow_free(flow);
1630
1631
1632 str = "{ [0,i,2] -> [i] : 0 <= i <= 10 }";
1633 map = isl_map_read_from_str(ctx, str);
1634 ai = isl_access_info_alloc(map, &depth, &common_space, 2);
1635
1636 str = "{ [0,i,0] -> [i] : 0 <= i <= 10 }";
1637 map = isl_map_read_from_str(ctx, str);
1638 ai = isl_access_info_add_source(ai, map, 0, &depth);
1639
1640 str = "{ [0,i,1] -> [5] : 0 <= i <= 10 }";
1641 map = isl_map_read_from_str(ctx, str);
1642 ai = isl_access_info_add_source(ai, map, 0, &depth);
1643
1644 flow = isl_access_info_compute_flow(ai);
1645 dim = isl_space_alloc(ctx, 0, 3, 3);
1646 mm.must = isl_map_empty(isl_space_copy(dim));
1647 mm.may = isl_map_empty(dim);
1648
1649 isl_flow_foreach(flow, collect_must_may, &mm);
1650
1651 str = "{ [0,i,0] -> [0,i,2] : 0 <= i <= 10; "
1652 " [0,i,1] -> [0,5,2] : 0 <= i <= 5 }";
1653 assert(map_is_equal(mm.may, str));
1654 str = "{ [i,j,k] -> [l,m,n] : 1 = 0 }";
1655 assert(map_is_equal(mm.must, str));
1656
1657 isl_map_free(mm.must);
1658 isl_map_free(mm.may);
1659 isl_flow_free(flow);
1660
1661
1662 str = "{ [0,i,1] -> [i] : 0 <= i <= 10 }";
1663 map = isl_map_read_from_str(ctx, str);
1664 ai = isl_access_info_alloc(map, &depth, &common_space, 2);
1665
1666 str = "{ [0,i,0] -> [i] : 0 <= i <= 10 }";
1667 map = isl_map_read_from_str(ctx, str);
1668 ai = isl_access_info_add_source(ai, map, 0, &depth);
1669
1670 str = "{ [0,i,2] -> [5] : 0 <= i <= 10 }";
1671 map = isl_map_read_from_str(ctx, str);
1672 ai = isl_access_info_add_source(ai, map, 0, &depth);
1673
1674 flow = isl_access_info_compute_flow(ai);
1675 dim = isl_space_alloc(ctx, 0, 3, 3);
1676 mm.must = isl_map_empty(isl_space_copy(dim));
1677 mm.may = isl_map_empty(dim);
1678
1679 isl_flow_foreach(flow, collect_must_may, &mm);
1680
1681 str = "{ [0,i,0] -> [0,i,1] : 0 <= i <= 10; "
1682 " [0,i,2] -> [0,5,1] : 0 <= i <= 4 }";
1683 assert(map_is_equal(mm.may, str));
1684 str = "{ [i,j,k] -> [l,m,n] : 1 = 0 }";
1685 assert(map_is_equal(mm.must, str));
1686
1687 isl_map_free(mm.must);
1688 isl_map_free(mm.may);
1689 isl_flow_free(flow);
1690
1691
1692 depth = 5;
1693
1694 str = "{ [1,i,0,0,0] -> [i,j] : 0 <= i <= 10 and 0 <= j <= 10 }";
1695 map = isl_map_read_from_str(ctx, str);
1696 ai = isl_access_info_alloc(map, &depth, &common_space, 1);
1697
1698 str = "{ [0,i,0,j,0] -> [i,j] : 0 <= i <= 10 and 0 <= j <= 10 }";
1699 map = isl_map_read_from_str(ctx, str);
1700 ai = isl_access_info_add_source(ai, map, 1, &depth);
1701
1702 flow = isl_access_info_compute_flow(ai);
1703 dim = isl_space_alloc(ctx, 0, 5, 5);
1704 mm.must = isl_map_empty(isl_space_copy(dim));
1705 mm.may = isl_map_empty(dim);
1706
1707 isl_flow_foreach(flow, collect_must_may, &mm);
1708
1709 str = "{ [0,i,0,j,0] -> [1,i,0,0,0] : 0 <= i,j <= 10 }";
1710 assert(map_is_equal(mm.must, str));
1711 str = "{ [0,0,0,0,0] -> [0,0,0,0,0] : 1 = 0 }";
1712 assert(map_is_equal(mm.may, str));
1713
1714 isl_map_free(mm.must);
1715 isl_map_free(mm.may);
1716 isl_flow_free(flow);
1717 }
1718
1719 int test_sv(isl_ctx *ctx)
1720 {
1721 const char *str;
1722 isl_map *map;
1723 isl_union_map *umap;
1724 int sv;
1725
1726 str = "[N] -> { [i] -> [f] : 0 <= i <= N and 0 <= i - 10 f <= 9 }";
1727 map = isl_map_read_from_str(ctx, str);
1728 sv = isl_map_is_single_valued(map);
1729 isl_map_free(map);
1730 if (sv < 0)
1731 return -1;
1732 if (!sv)
1733 isl_die(ctx, isl_error_internal,
1734 "map not detected as single valued", return -1);
1735
1736 str = "[N] -> { [i] -> [f] : 0 <= i <= N and 0 <= i - 10 f <= 10 }";
1737 map = isl_map_read_from_str(ctx, str);
1738 sv = isl_map_is_single_valued(map);
1739 isl_map_free(map);
1740 if (sv < 0)
1741 return -1;
1742 if (sv)
1743 isl_die(ctx, isl_error_internal,
1744 "map detected as single valued", return -1);
1745
1746 str = "{ S1[i] -> [i] : 0 <= i <= 9; S2[i] -> [i] : 0 <= i <= 9 }";
1747 umap = isl_union_map_read_from_str(ctx, str);
1748 sv = isl_union_map_is_single_valued(umap);
1749 isl_union_map_free(umap);
1750 if (sv < 0)
1751 return -1;
1752 if (!sv)
1753 isl_die(ctx, isl_error_internal,
1754 "map not detected as single valued", return -1);
1755
1756 str = "{ [i] -> S1[i] : 0 <= i <= 9; [i] -> S2[i] : 0 <= i <= 9 }";
1757 umap = isl_union_map_read_from_str(ctx, str);
1758 sv = isl_union_map_is_single_valued(umap);
1759 isl_union_map_free(umap);
1760 if (sv < 0)
1761 return -1;
1762 if (sv)
1763 isl_die(ctx, isl_error_internal,
1764 "map detected as single valued", return -1);
1765
1766 return 0;
1767 }
1768
1769 void test_bijective_case(struct isl_ctx *ctx, const char *str, int bijective)
1770 {
1771 isl_map *map;
1772
1773 map = isl_map_read_from_str(ctx, str);
1774 if (bijective)
1775 assert(isl_map_is_bijective(map));
1776 else
1777 assert(!isl_map_is_bijective(map));
1778 isl_map_free(map);
1779 }
1780
1781 void test_bijective(struct isl_ctx *ctx)
1782 {
1783 test_bijective_case(ctx, "[N,M]->{[i,j] -> [i]}", 0);
1784 test_bijective_case(ctx, "[N,M]->{[i,j] -> [i] : j=i}", 1);
1785 test_bijective_case(ctx, "[N,M]->{[i,j] -> [i] : j=0}", 1);
1786 test_bijective_case(ctx, "[N,M]->{[i,j] -> [i] : j=N}", 1);
1787 test_bijective_case(ctx, "[N,M]->{[i,j] -> [j,i]}", 1);
1788 test_bijective_case(ctx, "[N,M]->{[i,j] -> [i+j]}", 0);
1789 test_bijective_case(ctx, "[N,M]->{[i,j] -> []}", 0);
1790 test_bijective_case(ctx, "[N,M]->{[i,j] -> [i,j,N]}", 1);
1791 test_bijective_case(ctx, "[N,M]->{[i,j] -> [2i]}", 0);
1792 test_bijective_case(ctx, "[N,M]->{[i,j] -> [i,i]}", 0);
1793 test_bijective_case(ctx, "[N,M]->{[i,j] -> [2i,i]}", 0);
1794 test_bijective_case(ctx, "[N,M]->{[i,j] -> [2i,j]}", 1);
1795 test_bijective_case(ctx, "[N,M]->{[i,j] -> [x,y] : 2x=i & y =j}", 1);
1796 }
1797
1798 void test_pwqp(struct isl_ctx *ctx)
1799 {
1800 const char *str;
1801 isl_set *set;
1802 isl_pw_qpolynomial *pwqp1, *pwqp2;
1803
1804 str = "{ [i,j,k] -> 1 + 9 * [i/5] + 7 * [j/11] + 4 * [k/13] }";
1805 pwqp1 = isl_pw_qpolynomial_read_from_str(ctx, str);
1806
1807 pwqp1 = isl_pw_qpolynomial_move_dims(pwqp1, isl_dim_param, 0,
1808 isl_dim_in, 1, 1);
1809
1810 str = "[j] -> { [i,k] -> 1 + 9 * [i/5] + 7 * [j/11] + 4 * [k/13] }";
1811 pwqp2 = isl_pw_qpolynomial_read_from_str(ctx, str);
1812
1813 pwqp1 = isl_pw_qpolynomial_sub(pwqp1, pwqp2);
1814
1815 assert(isl_pw_qpolynomial_is_zero(pwqp1));
1816
1817 isl_pw_qpolynomial_free(pwqp1);
1818
1819 str = "{ [i] -> i }";
1820 pwqp1 = isl_pw_qpolynomial_read_from_str(ctx, str);
1821 str = "{ [k] : exists a : k = 2a }";
1822 set = isl_set_read_from_str(ctx, str);
1823 pwqp1 = isl_pw_qpolynomial_gist(pwqp1, set);
1824 str = "{ [i] -> i }";
1825 pwqp2 = isl_pw_qpolynomial_read_from_str(ctx, str);
1826
1827 pwqp1 = isl_pw_qpolynomial_sub(pwqp1, pwqp2);
1828
1829 assert(isl_pw_qpolynomial_is_zero(pwqp1));
1830
1831 isl_pw_qpolynomial_free(pwqp1);
1832
1833 str = "{ [i] -> i + [ (i + [i/3])/2 ] }";
1834 pwqp1 = isl_pw_qpolynomial_read_from_str(ctx, str);
1835 str = "{ [10] }";
1836 set = isl_set_read_from_str(ctx, str);
1837 pwqp1 = isl_pw_qpolynomial_gist(pwqp1, set);
1838 str = "{ [i] -> 16 }";
1839 pwqp2 = isl_pw_qpolynomial_read_from_str(ctx, str);
1840
1841 pwqp1 = isl_pw_qpolynomial_sub(pwqp1, pwqp2);
1842
1843 assert(isl_pw_qpolynomial_is_zero(pwqp1));
1844
1845 isl_pw_qpolynomial_free(pwqp1);
1846
1847 str = "{ [i] -> ([(i)/2]) }";
1848 pwqp1 = isl_pw_qpolynomial_read_from_str(ctx, str);
1849 str = "{ [k] : exists a : k = 2a+1 }";
1850 set = isl_set_read_from_str(ctx, str);
1851 pwqp1 = isl_pw_qpolynomial_gist(pwqp1, set);
1852 str = "{ [i] -> -1/2 + 1/2 * i }";
1853 pwqp2 = isl_pw_qpolynomial_read_from_str(ctx, str);
1854
1855 pwqp1 = isl_pw_qpolynomial_sub(pwqp1, pwqp2);
1856
1857 assert(isl_pw_qpolynomial_is_zero(pwqp1));
1858
1859 isl_pw_qpolynomial_free(pwqp1);
1860
1861 str = "{ [i] -> ([([i/2] + [i/2])/5]) }";
1862 pwqp1 = isl_pw_qpolynomial_read_from_str(ctx, str);
1863 str = "{ [i] -> ([(2 * [i/2])/5]) }";
1864 pwqp2 = isl_pw_qpolynomial_read_from_str(ctx, str);
1865
1866 pwqp1 = isl_pw_qpolynomial_sub(pwqp1, pwqp2);
1867
1868 assert(isl_pw_qpolynomial_is_zero(pwqp1));
1869
1870 isl_pw_qpolynomial_free(pwqp1);
1871
1872 str = "{ [x] -> ([x/2] + [(x+1)/2]) }";
1873 pwqp1 = isl_pw_qpolynomial_read_from_str(ctx, str);
1874 str = "{ [x] -> x }";
1875 pwqp2 = isl_pw_qpolynomial_read_from_str(ctx, str);
1876
1877 pwqp1 = isl_pw_qpolynomial_sub(pwqp1, pwqp2);
1878
1879 assert(isl_pw_qpolynomial_is_zero(pwqp1));
1880
1881 isl_pw_qpolynomial_free(pwqp1);
1882
1883 str = "{ [i] -> ([i/2]) : i >= 0; [i] -> ([i/3]) : i < 0 }";
1884 pwqp1 = isl_pw_qpolynomial_read_from_str(ctx, str);
1885 pwqp2 = isl_pw_qpolynomial_read_from_str(ctx, str);
1886 pwqp1 = isl_pw_qpolynomial_coalesce(pwqp1);
1887 pwqp1 = isl_pw_qpolynomial_sub(pwqp1, pwqp2);
1888 assert(isl_pw_qpolynomial_is_zero(pwqp1));
1889 isl_pw_qpolynomial_free(pwqp1);
1890 }
1891
1892 void test_split_periods(isl_ctx *ctx)
1893 {
1894 const char *str;
1895 isl_pw_qpolynomial *pwqp;
1896
1897 str = "{ [U,V] -> 1/3 * U + 2/3 * V - [(U + 2V)/3] + [U/2] : "
1898 "U + 2V + 3 >= 0 and - U -2V >= 0 and - U + 10 >= 0 and "
1899 "U >= 0; [U,V] -> U^2 : U >= 100 }";
1900 pwqp = isl_pw_qpolynomial_read_from_str(ctx, str);
1901
1902 pwqp = isl_pw_qpolynomial_split_periods(pwqp, 2);
1903 assert(pwqp);
1904
1905 isl_pw_qpolynomial_free(pwqp);
1906 }
1907
1908 void test_union(isl_ctx *ctx)
1909 {
1910 const char *str;
1911 isl_union_set *uset1, *uset2;
1912 isl_union_map *umap1, *umap2;
1913
1914 str = "{ [i] : 0 <= i <= 1 }";
1915 uset1 = isl_union_set_read_from_str(ctx, str);
1916 str = "{ [1] -> [0] }";
1917 umap1 = isl_union_map_read_from_str(ctx, str);
1918
1919 umap2 = isl_union_set_lex_gt_union_set(isl_union_set_copy(uset1), uset1);
1920 assert(isl_union_map_is_equal(umap1, umap2));
1921
1922 isl_union_map_free(umap1);
1923 isl_union_map_free(umap2);
1924
1925 str = "{ A[i] -> B[i]; B[i] -> C[i]; A[0] -> C[1] }";
1926 umap1 = isl_union_map_read_from_str(ctx, str);
1927 str = "{ A[i]; B[i] }";
1928 uset1 = isl_union_set_read_from_str(ctx, str);
1929
1930 uset2 = isl_union_map_domain(umap1);
1931
1932 assert(isl_union_set_is_equal(uset1, uset2));
1933
1934 isl_union_set_free(uset1);
1935 isl_union_set_free(uset2);
1936 }
1937
1938 void test_bound(isl_ctx *ctx)
1939 {
1940 const char *str;
1941 isl_pw_qpolynomial *pwqp;
1942 isl_pw_qpolynomial_fold *pwf;
1943
1944 str = "{ [[a, b, c, d] -> [e]] -> 0 }";
1945 pwqp = isl_pw_qpolynomial_read_from_str(ctx, str);
1946 pwf = isl_pw_qpolynomial_bound(pwqp, isl_fold_max, NULL);
1947 assert(isl_pw_qpolynomial_fold_dim(pwf, isl_dim_in) == 4);
1948 isl_pw_qpolynomial_fold_free(pwf);
1949
1950 str = "{ [[x]->[x]] -> 1 : exists a : x = 2 a }";
1951 pwqp = isl_pw_qpolynomial_read_from_str(ctx, str);
1952 pwf = isl_pw_qpolynomial_bound(pwqp, isl_fold_max, NULL);
1953 assert(isl_pw_qpolynomial_fold_dim(pwf, isl_dim_in) == 1);
1954 isl_pw_qpolynomial_fold_free(pwf);
1955 }
1956
1957 void test_lift(isl_ctx *ctx)
1958 {
1959 const char *str;
1960 isl_basic_map *bmap;
1961 isl_basic_set *bset;
1962
1963 str = "{ [i0] : exists e0 : i0 = 4e0 }";
1964 bset = isl_basic_set_read_from_str(ctx, str);
1965 bset = isl_basic_set_lift(bset);
1966 bmap = isl_basic_map_from_range(bset);
1967 bset = isl_basic_map_domain(bmap);
1968 isl_basic_set_free(bset);
1969 }
1970
1971 void test_subset(isl_ctx *ctx)
1972 {
1973 const char *str;
1974 isl_set *set1, *set2;
1975
1976 str = "{ [112, 0] }";
1977 set1 = isl_set_read_from_str(ctx, str);
1978 str = "{ [i0, i1] : exists (e0 = [(i0 - i1)/16], e1: "
1979 "16e0 <= i0 - i1 and 16e0 >= -15 + i0 - i1 and "
1980 "16e1 <= i1 and 16e0 >= -i1 and 16e1 >= -i0 + i1) }";
1981 set2 = isl_set_read_from_str(ctx, str);
1982 assert(isl_set_is_subset(set1, set2));
1983 isl_set_free(set1);
1984 isl_set_free(set2);
1985 }
1986
1987 void test_factorize(isl_ctx *ctx)
1988 {
1989 const char *str;
1990 isl_basic_set *bset;
1991 isl_factorizer *f;
1992
1993 str = "{ [i0, i1, i2, i3, i4, i5, i6, i7] : 3i5 <= 2 - 2i0 and "
1994 "i0 >= -2 and i6 >= 1 + i3 and i7 >= 0 and 3i5 >= -2i0 and "
1995 "2i4 <= i2 and i6 >= 1 + 2i0 + 3i1 and i4 <= -1 and "
1996 "i6 >= 1 + 2i0 + 3i5 and i6 <= 2 + 2i0 + 3i5 and "
1997 "3i5 <= 2 - 2i0 - i2 + 3i4 and i6 <= 2 + 2i0 + 3i1 and "
1998 "i0 <= -1 and i7 <= i2 + i3 - 3i4 - i6 and "
1999 "3i5 >= -2i0 - i2 + 3i4 }";
2000 bset = isl_basic_set_read_from_str(ctx, str);
2001 f = isl_basic_set_factorizer(bset);
2002 assert(f);
2003 isl_basic_set_free(bset);
2004 isl_factorizer_free(f);
2005
2006 str = "{ [i0, i1, i2, i3, i4, i5, i6, i7, i8, i9, i10, i11, i12] : "
2007 "i12 <= 2 + i0 - i11 and 2i8 >= -i4 and i11 >= i1 and "
2008 "3i5 <= -i2 and 2i11 >= -i4 - 2i7 and i11 <= 3 + i0 + 3i9 and "
2009 "i11 <= -i4 - 2i7 and i12 >= -i10 and i2 >= -2 and "
2010 "i11 >= i1 + 3i10 and i11 >= 1 + i0 + 3i9 and "
2011 "i11 <= 1 - i4 - 2i8 and 6i6 <= 6 - i2 and 3i6 >= 1 - i2 and "
2012 "i11 <= 2 + i1 and i12 <= i4 + i11 and i12 >= i0 - i11 and "
2013 "3i5 >= -2 - i2 and i12 >= -1 + i4 + i11 and 3i3 <= 3 - i2 and "
2014 "9i6 <= 11 - i2 + 6i5 and 3i3 >= 1 - i2 and "
2015 "9i6 <= 5 - i2 + 6i3 and i12 <= -1 and i2 <= 0 }";
2016 bset = isl_basic_set_read_from_str(ctx, str);
2017 f = isl_basic_set_factorizer(bset);
2018 assert(f);
2019 isl_basic_set_free(bset);
2020 isl_factorizer_free(f);
2021 }
2022
2023 static int check_injective(__isl_take isl_map *map, void *user)
2024 {
2025 int *injective = user;
2026
2027 *injective = isl_map_is_injective(map);
2028 isl_map_free(map);
2029
2030 if (*injective < 0 || !*injective)
2031 return -1;
2032
2033 return 0;
2034 }
2035
2036 int test_one_schedule(isl_ctx *ctx, const char *d, const char *w,
2037 const char *r, const char *s, int tilable, int parallel)
2038 {
2039 int i;
2040 isl_union_set *D;
2041 isl_union_map *W, *R, *S;
2042 isl_union_map *empty;
2043 isl_union_map *dep_raw, *dep_war, *dep_waw, *dep;
2044 isl_union_map *validity, *proximity;
2045 isl_union_map *schedule;
2046 isl_union_map *test;
2047 isl_union_set *delta;
2048 isl_union_set *domain;
2049 isl_set *delta_set;
2050 isl_set *slice;
2051 isl_set *origin;
2052 isl_schedule *sched;
2053 int is_nonneg, is_parallel, is_tilable, is_injection, is_complete;
2054
2055 D = isl_union_set_read_from_str(ctx, d);
2056 W = isl_union_map_read_from_str(ctx, w);
2057 R = isl_union_map_read_from_str(ctx, r);
2058 S = isl_union_map_read_from_str(ctx, s);
2059
2060 W = isl_union_map_intersect_domain(W, isl_union_set_copy(D));
2061 R = isl_union_map_intersect_domain(R, isl_union_set_copy(D));
2062
2063 empty = isl_union_map_empty(isl_union_map_get_space(S));
2064 isl_union_map_compute_flow(isl_union_map_copy(R),
2065 isl_union_map_copy(W), empty,
2066 isl_union_map_copy(S),
2067 &dep_raw, NULL, NULL, NULL);
2068 isl_union_map_compute_flow(isl_union_map_copy(W),
2069 isl_union_map_copy(W),
2070 isl_union_map_copy(R),
2071 isl_union_map_copy(S),
2072 &dep_waw, &dep_war, NULL, NULL);
2073
2074 dep = isl_union_map_union(dep_waw, dep_war);
2075 dep = isl_union_map_union(dep, dep_raw);
2076 validity = isl_union_map_copy(dep);
2077 proximity = isl_union_map_copy(dep);
2078
2079 sched = isl_union_set_compute_schedule(isl_union_set_copy(D),
2080 validity, proximity);
2081 schedule = isl_schedule_get_map(sched);
2082 isl_schedule_free(sched);
2083 isl_union_map_free(W);
2084 isl_union_map_free(R);
2085 isl_union_map_free(S);
2086
2087 is_injection = 1;
2088 isl_union_map_foreach_map(schedule, &check_injective, &is_injection);
2089
2090 domain = isl_union_map_domain(isl_union_map_copy(schedule));
2091 is_complete = isl_union_set_is_subset(D, domain);
2092 isl_union_set_free(D);
2093 isl_union_set_free(domain);
2094
2095 test = isl_union_map_reverse(isl_union_map_copy(schedule));
2096 test = isl_union_map_apply_range(test, dep);
2097 test = isl_union_map_apply_range(test, schedule);
2098
2099 delta = isl_union_map_deltas(test);
2100 if (isl_union_set_n_set(delta) == 0) {
2101 is_tilable = 1;
2102 is_parallel = 1;
2103 is_nonneg = 1;
2104 isl_union_set_free(delta);
2105 } else {
2106 delta_set = isl_set_from_union_set(delta);
2107
2108 slice = isl_set_universe(isl_set_get_space(delta_set));
2109 for (i = 0; i < tilable; ++i)
2110 slice = isl_set_lower_bound_si(slice, isl_dim_set, i, 0);
2111 is_tilable = isl_set_is_subset(delta_set, slice);
2112 isl_set_free(slice);
2113
2114 slice = isl_set_universe(isl_set_get_space(delta_set));
2115 for (i = 0; i < parallel; ++i)
2116 slice = isl_set_fix_si(slice, isl_dim_set, i, 0);
2117 is_parallel = isl_set_is_subset(delta_set, slice);
2118 isl_set_free(slice);
2119
2120 origin = isl_set_universe(isl_set_get_space(delta_set));
2121 for (i = 0; i < isl_set_dim(origin, isl_dim_set); ++i)
2122 origin = isl_set_fix_si(origin, isl_dim_set, i, 0);
2123
2124 delta_set = isl_set_union(delta_set, isl_set_copy(origin));
2125 delta_set = isl_set_lexmin(delta_set);
2126
2127 is_nonneg = isl_set_is_equal(delta_set, origin);
2128
2129 isl_set_free(origin);
2130 isl_set_free(delta_set);
2131 }
2132
2133 if (is_nonneg < 0 || is_parallel < 0 || is_tilable < 0 ||
2134 is_injection < 0 || is_complete < 0)
2135 return -1;
2136 if (!is_complete)
2137 isl_die(ctx, isl_error_unknown,
2138 "generated schedule incomplete", return -1);
2139 if (!is_injection)
2140 isl_die(ctx, isl_error_unknown,
2141 "generated schedule not injective on each statement",
2142 return -1);
2143 if (!is_nonneg)
2144 isl_die(ctx, isl_error_unknown,
2145 "negative dependences in generated schedule",
2146 return -1);
2147 if (!is_tilable)
2148 isl_die(ctx, isl_error_unknown,
2149 "generated schedule not as tilable as expected",
2150 return -1);
2151 if (!is_parallel)
2152 isl_die(ctx, isl_error_unknown,
2153 "generated schedule not as parallel as expected",
2154 return -1);
2155
2156 return 0;
2157 }
2158
2159 int test_special_schedule(isl_ctx *ctx, const char *domain,
2160 const char *validity, const char *proximity, const char *expected_sched)
2161 {
2162 isl_union_set *dom;
2163 isl_union_map *dep;
2164 isl_union_map *prox;
2165 isl_union_map *sched1, *sched2;
2166 isl_schedule *schedule;
2167 int equal;
2168
2169 dom = isl_union_set_read_from_str(ctx, domain);
2170 dep = isl_union_map_read_from_str(ctx, validity);
2171 prox = isl_union_map_read_from_str(ctx, proximity);
2172 schedule = isl_union_set_compute_schedule(dom, dep, prox);
2173 sched1 = isl_schedule_get_map(schedule);
2174 isl_schedule_free(schedule);
2175
2176 sched2 = isl_union_map_read_from_str(ctx, expected_sched);
2177
2178 equal = isl_union_map_is_equal(sched1, sched2);
2179 isl_union_map_free(sched1);
2180 isl_union_map_free(sched2);
2181
2182 if (equal < 0)
2183 return -1;
2184 if (!equal)
2185 isl_die(ctx, isl_error_unknown, "unexpected schedule",
2186 return -1);
2187
2188 return 0;
2189 }
2190
2191 int test_schedule(isl_ctx *ctx)
2192 {
2193 const char *D, *W, *R, *V, *P, *S;
2194
2195 /* Jacobi */
2196 D = "[T,N] -> { S1[t,i] : 1 <= t <= T and 2 <= i <= N - 1 }";
2197 W = "{ S1[t,i] -> a[t,i] }";
2198 R = "{ S1[t,i] -> a[t-1,i]; S1[t,i] -> a[t-1,i-1]; "
2199 "S1[t,i] -> a[t-1,i+1] }";
2200 S = "{ S1[t,i] -> [t,i] }";
2201 if (test_one_schedule(ctx, D, W, R, S, 2, 0) < 0)
2202 return -1;
2203
2204 /* Fig. 5 of CC2008 */
2205 D = "[N] -> { S_0[i, j] : i >= 0 and i <= -1 + N and j >= 2 and "
2206 "j <= -1 + N }";
2207 W = "[N] -> { S_0[i, j] -> a[i, j] : i >= 0 and i <= -1 + N and "
2208 "j >= 2 and j <= -1 + N }";
2209 R = "[N] -> { S_0[i, j] -> a[j, i] : i >= 0 and i <= -1 + N and "
2210 "j >= 2 and j <= -1 + N; "
2211 "S_0[i, j] -> a[i, -1 + j] : i >= 0 and i <= -1 + N and "
2212 "j >= 2 and j <= -1 + N }";
2213 S = "[N] -> { S_0[i, j] -> [0, i, 0, j, 0] }";
2214 if (test_one_schedule(ctx, D, W, R, S, 2, 0) < 0)
2215 return -1;
2216
2217 D = "{ S1[i] : 0 <= i <= 10; S2[i] : 0 <= i <= 9 }";
2218 W = "{ S1[i] -> a[i] }";
2219 R = "{ S2[i] -> a[i+1] }";
2220 S = "{ S1[i] -> [0,i]; S2[i] -> [1,i] }";
2221 if (test_one_schedule(ctx, D, W, R, S, 1, 1) < 0)
2222 return -1;
2223
2224 D = "{ S1[i] : 0 <= i < 10; S2[i] : 0 <= i < 10 }";
2225 W = "{ S1[i] -> a[i] }";
2226 R = "{ S2[i] -> a[9-i] }";
2227 S = "{ S1[i] -> [0,i]; S2[i] -> [1,i] }";
2228 if (test_one_schedule(ctx, D, W, R, S, 1, 1) < 0)
2229 return -1;
2230
2231 D = "[N] -> { S1[i] : 0 <= i < N; S2[i] : 0 <= i < N }";
2232 W = "{ S1[i] -> a[i] }";
2233 R = "[N] -> { S2[i] -> a[N-1-i] }";
2234 S = "{ S1[i] -> [0,i]; S2[i] -> [1,i] }";
2235 if (test_one_schedule(ctx, D, W, R, S, 1, 1) < 0)
2236 return -1;
2237
2238 D = "{ S1[i] : 0 < i < 10; S2[i] : 0 <= i < 10 }";
2239 W = "{ S1[i] -> a[i]; S2[i] -> b[i] }";
2240 R = "{ S2[i] -> a[i]; S1[i] -> b[i-1] }";
2241 S = "{ S1[i] -> [i,0]; S2[i] -> [i,1] }";
2242 if (test_one_schedule(ctx, D, W, R, S, 0, 0) < 0)
2243 return -1;
2244
2245 D = "[N] -> { S1[i] : 1 <= i <= N; S2[i,j] : 1 <= i,j <= N }";
2246 W = "{ S1[i] -> a[0,i]; S2[i,j] -> a[i,j] }";
2247 R = "{ S2[i,j] -> a[i-1,j] }";
2248 S = "{ S1[i] -> [0,i,0]; S2[i,j] -> [1,i,j] }";
2249 if (test_one_schedule(ctx, D, W, R, S, 2, 1) < 0)
2250 return -1;
2251
2252 D = "[N] -> { S1[i] : 1 <= i <= N; S2[i,j] : 1 <= i,j <= N }";
2253 W = "{ S1[i] -> a[i,0]; S2[i,j] -> a[i,j] }";
2254 R = "{ S2[i,j] -> a[i,j-1] }";
2255 S = "{ S1[i] -> [0,i,0]; S2[i,j] -> [1,i,j] }";
2256 if (test_one_schedule(ctx, D, W, R, S, 2, 1) < 0)
2257 return -1;
2258
2259 D = "[N] -> { S_0[]; S_1[i] : i >= 0 and i <= -1 + N; S_2[] }";
2260 W = "[N] -> { S_0[] -> a[0]; S_2[] -> b[0]; "
2261 "S_1[i] -> a[1 + i] : i >= 0 and i <= -1 + N }";
2262 R = "[N] -> { S_2[] -> a[N]; S_1[i] -> a[i] : i >= 0 and i <= -1 + N }";
2263 S = "[N] -> { S_1[i] -> [1, i, 0]; S_2[] -> [2, 0, 1]; "
2264 "S_0[] -> [0, 0, 0] }";
2265 if (test_one_schedule(ctx, D, W, R, S, 1, 0) < 0)
2266 return -1;
2267 ctx->opt->schedule_parametric = 0;
2268 if (test_one_schedule(ctx, D, W, R, S, 0, 0) < 0)
2269 return -1;
2270 ctx->opt->schedule_parametric = 1;
2271
2272 D = "[N] -> { S1[i] : 1 <= i <= N; S2[i] : 1 <= i <= N; "
2273 "S3[i,j] : 1 <= i,j <= N; S4[i] : 1 <= i <= N }";
2274 W = "{ S1[i] -> a[i,0]; S2[i] -> a[0,i]; S3[i,j] -> a[i,j] }";
2275 R = "[N] -> { S3[i,j] -> a[i-1,j]; S3[i,j] -> a[i,j-1]; "
2276 "S4[i] -> a[i,N] }";
2277 S = "{ S1[i] -> [0,i,0]; S2[i] -> [1,i,0]; S3[i,j] -> [2,i,j]; "
2278 "S4[i] -> [4,i,0] }";
2279 if (test_one_schedule(ctx, D, W, R, S, 2, 0) < 0)
2280 return -1;
2281
2282 D = "[N] -> { S_0[i, j] : i >= 1 and i <= N and j >= 1 and j <= N }";
2283 W = "[N] -> { S_0[i, j] -> s[0] : i >= 1 and i <= N and j >= 1 and "
2284 "j <= N }";
2285 R = "[N] -> { S_0[i, j] -> s[0] : i >= 1 and i <= N and j >= 1 and "
2286 "j <= N; "
2287 "S_0[i, j] -> a[i, j] : i >= 1 and i <= N and j >= 1 and "
2288 "j <= N }";
2289 S = "[N] -> { S_0[i, j] -> [0, i, 0, j, 0] }";
2290 if (test_one_schedule(ctx, D, W, R, S, 0, 0) < 0)
2291 return -1;
2292
2293 D = "[N] -> { S_0[t] : t >= 0 and t <= -1 + N; "
2294 " S_2[t] : t >= 0 and t <= -1 + N; "
2295 " S_1[t, i] : t >= 0 and t <= -1 + N and i >= 0 and "
2296 "i <= -1 + N }";
2297 W = "[N] -> { S_0[t] -> a[t, 0] : t >= 0 and t <= -1 + N; "
2298 " S_2[t] -> b[t] : t >= 0 and t <= -1 + N; "
2299 " S_1[t, i] -> a[t, 1 + i] : t >= 0 and t <= -1 + N and "
2300 "i >= 0 and i <= -1 + N }";
2301 R = "[N] -> { S_1[t, i] -> a[t, i] : t >= 0 and t <= -1 + N and "
2302 "i >= 0 and i <= -1 + N; "
2303 " S_2[t] -> a[t, N] : t >= 0 and t <= -1 + N }";
2304 S = "[N] -> { S_2[t] -> [0, t, 2]; S_1[t, i] -> [0, t, 1, i, 0]; "
2305 " S_0[t] -> [0, t, 0] }";
2306
2307 if (test_one_schedule(ctx, D, W, R, S, 2, 1) < 0)
2308 return -1;
2309 ctx->opt->schedule_parametric = 0;
2310 if (test_one_schedule(ctx, D, W, R, S, 0, 0) < 0)
2311 return -1;
2312 ctx->opt->schedule_parametric = 1;
2313
2314 D = "[N] -> { S1[i,j] : 0 <= i,j < N; S2[i,j] : 0 <= i,j < N }";
2315 S = "{ S1[i,j] -> [0,i,j]; S2[i,j] -> [1,i,j] }";
2316 if (test_one_schedule(ctx, D, "{}", "{}", S, 2, 2) < 0)
2317 return -1;
2318
2319 D = "[M, N] -> { S_1[i] : i >= 0 and i <= -1 + M; "
2320 "S_0[i, j] : i >= 0 and i <= -1 + M and j >= 0 and j <= -1 + N }";
2321 W = "[M, N] -> { S_0[i, j] -> a[j] : i >= 0 and i <= -1 + M and "
2322 "j >= 0 and j <= -1 + N; "
2323 "S_1[i] -> b[0] : i >= 0 and i <= -1 + M }";
2324 R = "[M, N] -> { S_0[i, j] -> a[0] : i >= 0 and i <= -1 + M and "
2325 "j >= 0 and j <= -1 + N; "
2326 "S_1[i] -> b[0] : i >= 0 and i <= -1 + M }";
2327 S = "[M, N] -> { S_1[i] -> [1, i, 0]; S_0[i, j] -> [0, i, 0, j, 0] }";
2328 if (test_one_schedule(ctx, D, W, R, S, 0, 0) < 0)
2329 return -1;
2330
2331 D = "{ S_0[i] : i >= 0 }";
2332 W = "{ S_0[i] -> a[i] : i >= 0 }";
2333 R = "{ S_0[i] -> a[0] : i >= 0 }";
2334 S = "{ S_0[i] -> [0, i, 0] }";
2335 if (test_one_schedule(ctx, D, W, R, S, 0, 0) < 0)
2336 return -1;
2337
2338 D = "{ S_0[i] : i >= 0; S_1[i] : i >= 0 }";
2339 W = "{ S_0[i] -> a[i] : i >= 0; S_1[i] -> b[i] : i >= 0 }";
2340 R = "{ S_0[i] -> b[0] : i >= 0; S_1[i] -> a[i] : i >= 0 }";
2341 S = "{ S_1[i] -> [0, i, 1]; S_0[i] -> [0, i, 0] }";
2342 if (test_one_schedule(ctx, D, W, R, S, 0, 0) < 0)
2343 return -1;
2344
2345 D = "[n] -> { S_0[j, k] : j <= -1 + n and j >= 0 and "
2346 "k <= -1 + n and k >= 0 }";
2347 W = "[n] -> { S_0[j, k] -> B[j] : j <= -1 + n and j >= 0 and " "k <= -1 + n and k >= 0 }";
2348 R = "[n] -> { S_0[j, k] -> B[j] : j <= -1 + n and j >= 0 and "
2349 "k <= -1 + n and k >= 0; "
2350 "S_0[j, k] -> B[k] : j <= -1 + n and j >= 0 and "
2351 "k <= -1 + n and k >= 0; "
2352 "S_0[j, k] -> A[k] : j <= -1 + n and j >= 0 and "
2353 "k <= -1 + n and k >= 0 }";
2354 S = "[n] -> { S_0[j, k] -> [2, j, k] }";
2355 ctx->opt->schedule_outer_zero_distance = 1;
2356 if (test_one_schedule(ctx, D, W, R, S, 0, 0) < 0)
2357 return -1;
2358 ctx->opt->schedule_outer_zero_distance = 0;
2359
2360 D = "{Stmt_for_body24[i0, i1, i2, i3]:"
2361 "i0 >= 0 and i0 <= 1 and i1 >= 0 and i1 <= 6 and i2 >= 2 and "
2362 "i2 <= 6 - i1 and i3 >= 0 and i3 <= -1 + i2;"
2363 "Stmt_for_body24[i0, i1, 1, 0]:"
2364 "i0 >= 0 and i0 <= 1 and i1 >= 0 and i1 <= 5;"
2365 "Stmt_for_body7[i0, i1, i2]:"
2366 "i0 >= 0 and i0 <= 1 and i1 >= 0 and i1 <= 7 and i2 >= 0 and "
2367 "i2 <= 7 }";
2368
2369 V = "{Stmt_for_body24[0, i1, i2, i3] -> "
2370 "Stmt_for_body24[1, i1, i2, i3]:"
2371 "i3 >= 0 and i3 <= -1 + i2 and i1 >= 0 and i2 <= 6 - i1 and "
2372 "i2 >= 1;"
2373 "Stmt_for_body24[0, i1, i2, i3] -> "
2374 "Stmt_for_body7[1, 1 + i1 + i3, 1 + i1 + i2]:"
2375 "i3 <= -1 + i2 and i2 <= 6 - i1 and i2 >= 1 and i1 >= 0 and "
2376 "i3 >= 0;"
2377 "Stmt_for_body24[0, i1, i2, i3] ->"
2378 "Stmt_for_body7[1, i1, 1 + i1 + i3]:"
2379 "i3 >= 0 and i2 <= 6 - i1 and i1 >= 0 and i3 <= -1 + i2;"
2380 "Stmt_for_body7[0, i1, i2] -> Stmt_for_body7[1, i1, i2]:"
2381 "(i2 >= 1 + i1 and i2 <= 6 and i1 >= 0 and i1 <= 4) or "
2382 "(i2 >= 3 and i2 <= 7 and i1 >= 1 and i2 >= 1 + i1) or "
2383 "(i2 >= 0 and i2 <= i1 and i2 >= -7 + i1 and i1 <= 7);"
2384 "Stmt_for_body7[0, i1, 1 + i1] -> Stmt_for_body7[1, i1, 1 + i1]:"
2385 "i1 <= 6 and i1 >= 0;"
2386 "Stmt_for_body7[0, 0, 7] -> Stmt_for_body7[1, 0, 7];"
2387 "Stmt_for_body7[i0, i1, i2] -> "
2388 "Stmt_for_body24[i0, o1, -1 + i2 - o1, -1 + i1 - o1]:"
2389 "i0 >= 0 and i0 <= 1 and o1 >= 0 and i2 >= 1 + i1 and "
2390 "o1 <= -2 + i2 and i2 <= 7 and o1 <= -1 + i1;"
2391 "Stmt_for_body7[i0, i1, i2] -> "
2392 "Stmt_for_body24[i0, i1, o2, -1 - i1 + i2]:"
2393 "i0 >= 0 and i0 <= 1 and i1 >= 0 and o2 >= -i1 + i2 and "
2394 "o2 >= 1 and o2 <= 6 - i1 and i2 >= 1 + i1 }";
2395 P = V;
2396 S = "{ Stmt_for_body24[i0, i1, i2, i3] -> "
2397 "[i0, 5i0 + i1, 6i0 + i1 + i2, 1 + 6i0 + i1 + i2 + i3, 1];"
2398 "Stmt_for_body7[i0, i1, i2] -> [0, 5i0, 6i0 + i1, 6i0 + i2, 0] }";
2399
2400 if (test_special_schedule(ctx, D, V, P, S) < 0)
2401 return -1;
2402
2403 D = "{ S_0[i, j] : i >= 1 and i <= 10 and j >= 1 and j <= 8 }";
2404 V = "{ S_0[i, j] -> S_0[i, 1 + j] : i >= 1 and i <= 10 and "
2405 "j >= 1 and j <= 7;"
2406 "S_0[i, j] -> S_0[1 + i, j] : i >= 1 and i <= 9 and "
2407 "j >= 1 and j <= 8 }";
2408 P = "{ }";
2409 S = "{ S_0[i, j] -> [i + j, j] }";
2410 ctx->opt->schedule_algorithm = ISL_SCHEDULE_ALGORITHM_FEAUTRIER;
2411 if (test_special_schedule(ctx, D, V, P, S) < 0)
2412 return -1;
2413 ctx->opt->schedule_algorithm = ISL_SCHEDULE_ALGORITHM_ISL;
2414
2415 /* Fig. 1 from Feautrier's "Some Efficient Solutions..." pt. 2, 1992 */
2416 D = "[N] -> { S_0[i, j] : i >= 0 and i <= -1 + N and "
2417 "j >= 0 and j <= -1 + i }";
2418 V = "[N] -> { S_0[i, j] -> S_0[i, 1 + j] : j <= -2 + i and "
2419 "i <= -1 + N and j >= 0;"
2420 "S_0[i, -1 + i] -> S_0[1 + i, 0] : i >= 1 and "
2421 "i <= -2 + N }";
2422 P = "{ }";
2423 S = "{ S_0[i, j] -> [i, j] }";
2424 ctx->opt->schedule_algorithm = ISL_SCHEDULE_ALGORITHM_FEAUTRIER;
2425 if (test_special_schedule(ctx, D, V, P, S) < 0)
2426 return -1;
2427 ctx->opt->schedule_algorithm = ISL_SCHEDULE_ALGORITHM_ISL;
2428
2429 /* Test both algorithms on a case with only proximity dependences. */
2430 D = "{ S[i,j] : 0 <= i <= 10 }";
2431 V = "{ }";
2432 P = "{ S[i,j] -> S[i+1,j] : 0 <= i,j <= 10 }";
2433 S = "{ S[i, j] -> [j, i] }";
2434 ctx->opt->schedule_algorithm = ISL_SCHEDULE_ALGORITHM_FEAUTRIER;
2435 if (test_special_schedule(ctx, D, V, P, S) < 0)
2436 return -1;
2437 ctx->opt->schedule_algorithm = ISL_SCHEDULE_ALGORITHM_ISL;
2438 return test_special_schedule(ctx, D, V, P, S);
2439 }
2440
2441 int test_plain_injective(isl_ctx *ctx, const char *str, int injective)
2442 {
2443 isl_union_map *umap;
2444 int test;
2445
2446 umap = isl_union_map_read_from_str(ctx, str);
2447 test = isl_union_map_plain_is_injective(umap);
2448 isl_union_map_free(umap);
2449 if (test < 0)
2450 return -1;
2451 if (test == injective)
2452 return 0;
2453 if (injective)
2454 isl_die(ctx, isl_error_unknown,
2455 "map not detected as injective", return -1);
2456 else
2457 isl_die(ctx, isl_error_unknown,
2458 "map detected as injective", return -1);
2459 }
2460
2461 int test_injective(isl_ctx *ctx)
2462 {
2463 const char *str;
2464
2465 if (test_plain_injective(ctx, "{S[i,j] -> A[0]; T[i,j] -> B[1]}", 0))
2466 return -1;
2467 if (test_plain_injective(ctx, "{S[] -> A[0]; T[] -> B[0]}", 1))
2468 return -1;
2469 if (test_plain_injective(ctx, "{S[] -> A[0]; T[] -> A[1]}", 1))
2470 return -1;
2471 if (test_plain_injective(ctx, "{S[] -> A[0]; T[] -> A[0]}", 0))
2472 return -1;
2473 if (test_plain_injective(ctx, "{S[i] -> A[i,0]; T[i] -> A[i,1]}", 1))
2474 return -1;
2475 if (test_plain_injective(ctx, "{S[i] -> A[i]; T[i] -> A[i]}", 0))
2476 return -1;
2477 if (test_plain_injective(ctx, "{S[] -> A[0,0]; T[] -> A[0,1]}", 1))
2478 return -1;
2479 if (test_plain_injective(ctx, "{S[] -> A[0,0]; T[] -> A[1,0]}", 1))
2480 return -1;
2481
2482 str = "{S[] -> A[0,0]; T[] -> A[0,1]; U[] -> A[1,0]}";
2483 if (test_plain_injective(ctx, str, 1))
2484 return -1;
2485 str = "{S[] -> A[0,0]; T[] -> A[0,1]; U[] -> A[0,0]}";
2486 if (test_plain_injective(ctx, str, 0))
2487 return -1;
2488
2489 return 0;
2490 }
2491
2492 int test_aff(isl_ctx *ctx)
2493 {
2494 const char *str;
2495 isl_set *set;
2496 isl_space *dim;
2497 isl_local_space *ls;
2498 isl_aff *aff;
2499 int zero;
2500
2501 dim = isl_space_set_alloc(ctx, 0, 1);
2502 ls = isl_local_space_from_space(dim);
2503 aff = isl_aff_zero_on_domain(ls);
2504
2505 aff = isl_aff_add_coefficient_si(aff, isl_dim_in, 0, 1);
2506 aff = isl_aff_scale_down_ui(aff, 3);
2507 aff = isl_aff_floor(aff);
2508 aff = isl_aff_add_coefficient_si(aff, isl_dim_in, 0, 1);
2509 aff = isl_aff_scale_down_ui(aff, 2);
2510 aff = isl_aff_floor(aff);
2511 aff = isl_aff_add_coefficient_si(aff, isl_dim_in, 0, 1);
2512
2513 str = "{ [10] }";
2514 set = isl_set_read_from_str(ctx, str);
2515 aff = isl_aff_gist(aff, set);
2516
2517 aff = isl_aff_add_constant_si(aff, -16);
2518 zero = isl_aff_plain_is_zero(aff);
2519 isl_aff_free(aff);
2520
2521 if (zero < 0)
2522 return -1;
2523 if (!zero)
2524 isl_die(ctx, isl_error_unknown, "unexpected result", return -1);
2525
2526 return 0;
2527 }
2528
2529 int test_dim_max(isl_ctx *ctx)
2530 {
2531 int equal;
2532 const char *str;
2533 isl_set *set1, *set2;
2534 isl_set *set;
2535 isl_map *map;
2536 isl_pw_aff *pwaff;
2537
2538 str = "[N] -> { [i] : 0 <= i <= min(N,10) }";
2539 set = isl_set_read_from_str(ctx, str);
2540 pwaff = isl_set_dim_max(set, 0);
2541 set1 = isl_set_from_pw_aff(pwaff);
2542 str = "[N] -> { [10] : N >= 10; [N] : N <= 9 and N >= 0 }";
2543 set2 = isl_set_read_from_str(ctx, str);
2544 equal = isl_set_is_equal(set1, set2);
2545 isl_set_free(set1);
2546 isl_set_free(set2);
2547 if (equal < 0)
2548 return -1;
2549 if (!equal)
2550 isl_die(ctx, isl_error_unknown, "unexpected result", return -1);
2551
2552 str = "[N] -> { [i] : 0 <= i <= max(2N,N+6) }";
2553 set = isl_set_read_from_str(ctx, str);
2554 pwaff = isl_set_dim_max(set, 0);
2555 set1 = isl_set_from_pw_aff(pwaff);
2556 str = "[N] -> { [6 + N] : -6 <= N <= 5; [2N] : N >= 6 }";
2557 set2 = isl_set_read_from_str(ctx, str);
2558 equal = isl_set_is_equal(set1, set2);
2559 isl_set_free(set1);
2560 isl_set_free(set2);
2561 if (equal < 0)
2562 return -1;
2563 if (!equal)
2564 isl_die(ctx, isl_error_unknown, "unexpected result", return -1);
2565
2566 str = "[N] -> { [i] : 0 <= i <= 2N or 0 <= i <= N+6 }";
2567 set = isl_set_read_from_str(ctx, str);
2568 pwaff = isl_set_dim_max(set, 0);
2569 set1 = isl_set_from_pw_aff(pwaff);
2570 str = "[N] -> { [6 + N] : -6 <= N <= 5; [2N] : N >= 6 }";
2571 set2 = isl_set_read_from_str(ctx, str);
2572 equal = isl_set_is_equal(set1, set2);
2573 isl_set_free(set1);
2574 isl_set_free(set2);
2575 if (equal < 0)
2576 return -1;
2577 if (!equal)
2578 isl_die(ctx, isl_error_unknown, "unexpected result", return -1);
2579
2580 str = "[N,M] -> { [i,j] -> [([i/16]), i%16, ([j/16]), j%16] : "
2581 "0 <= i < N and 0 <= j < M }";
2582 map = isl_map_read_from_str(ctx, str);
2583 set = isl_map_range(map);
2584
2585 pwaff = isl_set_dim_max(isl_set_copy(set), 0);
2586 set1 = isl_set_from_pw_aff(pwaff);
2587 str = "[N,M] -> { [([(N-1)/16])] : M,N > 0 }";
2588 set2 = isl_set_read_from_str(ctx, str);
2589 equal = isl_set_is_equal(set1, set2);
2590 isl_set_free(set1);
2591 isl_set_free(set2);
2592
2593 pwaff = isl_set_dim_max(isl_set_copy(set), 3);
2594 set1 = isl_set_from_pw_aff(pwaff);
2595 str = "[N,M] -> { [t] : t = min(M-1,15) and M,N > 0 }";
2596 set2 = isl_set_read_from_str(ctx, str);
2597 if (equal >= 0 && equal)
2598 equal = isl_set_is_equal(set1, set2);
2599 isl_set_free(set1);
2600 isl_set_free(set2);
2601
2602 isl_set_free(set);
2603
2604 if (equal < 0)
2605 return -1;
2606 if (!equal)
2607 isl_die(ctx, isl_error_unknown, "unexpected result", return -1);
2608
2609 return 0;
2610 }
2611
2612 int test_product(isl_ctx *ctx)
2613 {
2614 const char *str;
2615 isl_set *set;
2616 isl_union_set *uset1, *uset2;
2617 int ok;
2618
2619 str = "{ A[i] }";
2620 set = isl_set_read_from_str(ctx, str);
2621 set = isl_set_product(set, isl_set_copy(set));
2622 ok = isl_set_is_wrapping(set);
2623 isl_set_free(set);
2624 if (ok < 0)
2625 return -1;
2626 if (!ok)
2627 isl_die(ctx, isl_error_unknown, "unexpected result", return -1);
2628
2629 str = "{ [] }";
2630 uset1 = isl_union_set_read_from_str(ctx, str);
2631 uset1 = isl_union_set_product(uset1, isl_union_set_copy(uset1));
2632 str = "{ [[] -> []] }";
2633 uset2 = isl_union_set_read_from_str(ctx, str);
2634 ok = isl_union_set_is_equal(uset1, uset2);
2635 isl_union_set_free(uset1);
2636 isl_union_set_free(uset2);
2637 if (ok < 0)
2638 return -1;
2639 if (!ok)
2640 isl_die(ctx, isl_error_unknown, "unexpected result", return -1);
2641
2642 return 0;
2643 }
2644
2645 int test_equal(isl_ctx *ctx)
2646 {
2647 const char *str;
2648 isl_set *set, *set2;
2649 int equal;
2650
2651 str = "{ S_6[i] }";
2652 set = isl_set_read_from_str(ctx, str);
2653 str = "{ S_7[i] }";
2654 set2 = isl_set_read_from_str(ctx, str);
2655 equal = isl_set_is_equal(set, set2);
2656 isl_set_free(set);
2657 isl_set_free(set2);
2658 if (equal < 0)
2659 return -1;
2660 if (equal)
2661 isl_die(ctx, isl_error_unknown, "unexpected result", return -1);
2662
2663 return 0;
2664 }
2665
2666 static int test_plain_fixed(isl_ctx *ctx, __isl_take isl_map *map,
2667 enum isl_dim_type type, unsigned pos, int fixed)
2668 {
2669 int test;
2670
2671 test = isl_map_plain_is_fixed(map, type, pos, NULL);
2672 isl_map_free(map);
2673 if (test < 0)
2674 return -1;
2675 if (test == fixed)
2676 return 0;
2677 if (fixed)
2678 isl_die(ctx, isl_error_unknown,
2679 "map not detected as fixed", return -1);
2680 else
2681 isl_die(ctx, isl_error_unknown,
2682 "map detected as fixed", return -1);
2683 }
2684
2685 int test_fixed(isl_ctx *ctx)
2686 {
2687 const char *str;
2688 isl_map *map;
2689
2690 str = "{ [i] -> [i] }";
2691 map = isl_map_read_from_str(ctx, str);
2692 if (test_plain_fixed(ctx, map, isl_dim_out, 0, 0))
2693 return -1;
2694 str = "{ [i] -> [1] }";
2695 map = isl_map_read_from_str(ctx, str);
2696 if (test_plain_fixed(ctx, map, isl_dim_out, 0, 1))
2697 return -1;
2698 str = "{ S_1[p1] -> [o0] : o0 = -2 and p1 >= 1 and p1 <= 7 }";
2699 map = isl_map_read_from_str(ctx, str);
2700 if (test_plain_fixed(ctx, map, isl_dim_out, 0, 1))
2701 return -1;
2702 map = isl_map_read_from_str(ctx, str);
2703 map = isl_map_neg(map);
2704 if (test_plain_fixed(ctx, map, isl_dim_out, 0, 1))
2705 return -1;
2706
2707 return 0;
2708 }
2709
2710 int test_vertices(isl_ctx *ctx)
2711 {
2712 const char *str;
2713 isl_basic_set *bset;
2714 isl_vertices *vertices;
2715
2716 str = "{ A[t, i] : t = 12 and i >= 4 and i <= 12 }";
2717 bset = isl_basic_set_read_from_str(ctx, str);
2718 vertices = isl_basic_set_compute_vertices(bset);
2719 isl_basic_set_free(bset);
2720 isl_vertices_free(vertices);
2721 if (!vertices)
2722 return -1;
2723
2724 str = "{ A[t, i] : t = 14 and i = 1 }";
2725 bset = isl_basic_set_read_from_str(ctx, str);
2726 vertices = isl_basic_set_compute_vertices(bset);
2727 isl_basic_set_free(bset);
2728 isl_vertices_free(vertices);
2729 if (!vertices)
2730 return -1;
2731
2732 return 0;
2733 }
2734
2735 int test_union_pw(isl_ctx *ctx)
2736 {
2737 int equal;
2738 const char *str;
2739 isl_union_set *uset;
2740 isl_union_pw_qpolynomial *upwqp1, *upwqp2;
2741
2742 str = "{ [x] -> x^2 }";
2743 upwqp1 = isl_union_pw_qpolynomial_read_from_str(ctx, str);
2744 upwqp2 = isl_union_pw_qpolynomial_copy(upwqp1);
2745 uset = isl_union_pw_qpolynomial_domain(upwqp1);
2746 upwqp1 = isl_union_pw_qpolynomial_copy(upwqp2);
2747 upwqp1 = isl_union_pw_qpolynomial_intersect_domain(upwqp1, uset);
2748 equal = isl_union_pw_qpolynomial_plain_is_equal(upwqp1, upwqp2);
2749 isl_union_pw_qpolynomial_free(upwqp1);
2750 isl_union_pw_qpolynomial_free(upwqp2);
2751 if (equal < 0)
2752 return -1;
2753 if (!equal)
2754 isl_die(ctx, isl_error_unknown, "unexpected result", return -1);
2755
2756 return 0;
2757 }
2758
2759 int test_output(isl_ctx *ctx)
2760 {
2761 char *s;
2762 const char *str;
2763 isl_pw_aff *pa;
2764 isl_printer *p;
2765 int equal;
2766
2767 str = "[x] -> { [1] : x % 4 <= 2; [2] : x = 3 }";
2768 pa = isl_pw_aff_read_from_str(ctx, str);
2769
2770 p = isl_printer_to_str(ctx);
2771 p = isl_printer_set_output_format(p, ISL_FORMAT_C);
2772 p = isl_printer_print_pw_aff(p, pa);
2773 s = isl_printer_get_str(p);
2774 isl_printer_free(p);
2775 isl_pw_aff_free(pa);
2776 equal = !strcmp(s, "(2 - x + 4*floord(x, 4) >= 0) ? (1) : 2");
2777 free(s);
2778 if (equal < 0)
2779 return -1;
2780 if (!equal)
2781 isl_die(ctx, isl_error_unknown, "unexpected result", return -1);
2782
2783 return 0;
2784 }
2785
2786 int test_sample(isl_ctx *ctx)
2787 {
2788 const char *str;
2789 isl_basic_set *bset1, *bset2;
2790 int empty, subset;
2791
2792 str = "{ [a, b, c, d, e, f, g, h, i, j, k] : "
2793 "3i >= 1073741823b - c - 1073741823e + f and c >= 0 and "
2794 "3i >= -1 + 3221225466b + c + d - 3221225466e - f and "
2795 "2e >= a - b and 3e <= 2a and 3k <= -a and f <= -1 + a and "
2796 "3i <= 4 - a + 4b + 2c - e - 2f and 3k <= -a + c - f and "
2797 "3h >= -2 + a and 3g >= -3 - a and 3k >= -2 - a and "
2798 "3i >= -2 - a - 2c + 3e + 2f and 3h <= a + c - f and "
2799 "3h >= a + 2147483646b + 2c - 2147483646e - 2f and "
2800 "3g <= -1 - a and 3i <= 1 + c + d - f and a <= 1073741823 and "
2801 "f >= 1 - a + 1073741822b + c + d - 1073741822e and "
2802 "3i >= 1 + 2b - 2c + e + 2f + 3g and "
2803 "1073741822f <= 1073741822 - a + 1073741821b + 1073741822c +"
2804 "d - 1073741821e and "
2805 "3j <= 3 - a + 3b and 3g <= -2 - 2b + c + d - e - f and "
2806 "3j >= 1 - a + b + 2e and "
2807 "3f >= -3 + a + 3221225462b + 3c + d - 3221225465e and "
2808 "3i <= 4 - a + 4b - e and "
2809 "f <= 1073741822 + 1073741822b - 1073741822e and 3h <= a and "
2810 "f >= 0 and 2e <= 4 - a + 5b - d and 2e <= a - b + d and "
2811 "c <= -1 + a and 3i >= -2 - a + 3e and "
2812 "1073741822e <= 1073741823 - a + 1073741822b + c and "
2813 "3g >= -4 + 3221225464b + 3c + d - 3221225467e - 3f and "
2814 "3i >= -1 + 3221225466b + 3c + d - 3221225466e - 3f and "
2815 "1073741823e >= 1 + 1073741823b - d and "
2816 "3i >= 1073741823b + c - 1073741823e - f and "
2817 "3i >= 1 + 2b + e + 3g }";
2818 bset1 = isl_basic_set_read_from_str(ctx, str);
2819 bset2 = isl_basic_set_sample(isl_basic_set_copy(bset1));
2820 empty = isl_basic_set_is_empty(bset2);
2821 subset = isl_basic_set_is_subset(bset2, bset1);
2822 isl_basic_set_free(bset1);
2823 isl_basic_set_free(bset2);
2824 if (empty)
2825 isl_die(ctx, isl_error_unknown, "point not found", return -1);
2826 if (!subset)
2827 isl_die(ctx, isl_error_unknown, "bad point found", return -1);
2828
2829 return 0;
2830 }
2831
2832 int test_fixed_power(isl_ctx *ctx)
2833 {
2834 const char *str;
2835 isl_map *map;
2836 isl_int exp;
2837 int equal;
2838
2839 isl_int_init(exp);
2840 str = "{ [i] -> [i + 1] }";
2841 map = isl_map_read_from_str(ctx, str);
2842 isl_int_set_si(exp, 23);
2843 map = isl_map_fixed_power(map, exp);
2844 equal = map_check_equal(map, "{ [i] -> [i + 23] }");
2845 isl_int_clear(exp);
2846 isl_map_free(map);
2847 if (equal < 0)
2848 return -1;
2849
2850 return 0;
2851 }
2852
2853 int main()
2854 {
2855 struct isl_ctx *ctx;
2856
2857 srcdir = getenv("srcdir");
2858 assert(srcdir);
2859
2860 ctx = isl_ctx_alloc();
2861 if (test_fixed_power(ctx) < 0)
2862 goto error;
2863 if (test_sample(ctx) < 0)
2864 goto error;
2865 if (test_output(ctx) < 0)
2866 goto error;
2867 if (test_vertices(ctx) < 0)
2868 goto error;
2869 if (test_fixed(ctx) < 0)
2870 goto error;
2871 if (test_equal(ctx) < 0)
2872 goto error;
2873 if (test_product(ctx) < 0)
2874 goto error;
2875 if (test_dim_max(ctx) < 0)
2876 goto error;
2877 if (test_aff(ctx) < 0)
2878 goto error;
2879 if (test_injective(ctx) < 0)
2880 goto error;
2881 if (test_schedule(ctx) < 0)
2882 goto error;
2883 if (test_union_pw(ctx) < 0)
2884 goto error;
2885 test_factorize(ctx);
2886 test_subset(ctx);
2887 test_lift(ctx);
2888 test_bound(ctx);
2889 test_union(ctx);
2890 test_split_periods(ctx);
2891 if (test_parse(ctx) < 0)
2892 goto error;
2893 test_pwqp(ctx);
2894 test_lex(ctx);
2895 if (test_sv(ctx) < 0)
2896 goto error;
2897 test_bijective(ctx);
2898 test_dep(ctx);
2899 test_read(ctx);
2900 test_bounded(ctx);
2901 test_construction(ctx);
2902 test_dim(ctx);
2903 test_div(ctx);
2904 test_application(ctx);
2905 if (test_affine_hull(ctx) < 0)
2906 goto error;
2907 test_convex_hull(ctx);
2908 test_gist(ctx);
2909 if (test_coalesce(ctx) < 0)
2910 goto error;
2911 test_closure(ctx);
2912 test_lexmin(ctx);
2913 isl_ctx_free(ctx);
2914 return 0;
2915 error:
2916 isl_ctx_free(ctx);
2917 return -1;
2918 }
Integer set library