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[isl.git] / isl_test.c
blobe458e588c6e50efae16d7a57f650f210eec50d86
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/set.h>
16 #include <isl/flow.h>
17 #include <isl/constraint.h>
18 #include <isl/polynomial.h>
19 #include <isl/union_map.h>
20 #include <isl_factorization.h>
21 #include <isl/schedule.h>
22
23 static char *srcdir;
24
25 static char *get_filename(isl_ctx *ctx, const char *name, const char *suffix) {
26 char *filename;
27 int length;
28 char *pattern = "%s/test_inputs/%s.%s";
29
30 length = strlen(pattern) - 6 + strlen(srcdir) + strlen(name)
31 + strlen(suffix) + 1;
32 filename = isl_alloc_array(ctx, char, length);
33
34 if (!filename)
35 return NULL;
36
37 sprintf(filename, pattern, srcdir, name, suffix);
38
39 return filename;
40 }
41
42 void test_parse_map(isl_ctx *ctx, const char *str)
43 {
44 isl_map *map;
45
46 map = isl_map_read_from_str(ctx, str, -1);
47 assert(map);
48 isl_map_free(map);
49 }
50
51 void test_parse_map_equal(isl_ctx *ctx, const char *str, const char *str2)
52 {
53 isl_map *map, *map2;
54
55 map = isl_map_read_from_str(ctx, str, -1);
56 map2 = isl_map_read_from_str(ctx, str2, -1);
57 assert(map && map2 && isl_map_is_equal(map, map2));
58 isl_map_free(map);
59 isl_map_free(map2);
60 }
61
62 void test_parse_pwqp(isl_ctx *ctx, const char *str)
63 {
64 isl_pw_qpolynomial *pwqp;
65
66 pwqp = isl_pw_qpolynomial_read_from_str(ctx, str);
67 assert(pwqp);
68 isl_pw_qpolynomial_free(pwqp);
69 }
70
71 void test_parse(struct isl_ctx *ctx)
72 {
73 isl_map *map, *map2;
74 const char *str, *str2;
75
76 str = "{ [i] -> [-i] }";
77 map = isl_map_read_from_str(ctx, str, -1);
78 assert(map);
79 isl_map_free(map);
80
81 str = "{ A[i] -> L[([i/3])] }";
82 map = isl_map_read_from_str(ctx, str, -1);
83 assert(map);
84 isl_map_free(map);
85
86 test_parse_map(ctx, "{[[s] -> A[i]] -> [[s+1] -> A[i]]}");
87 test_parse_map(ctx, "{ [p1, y1, y2] -> [2, y1, y2] : "
88 "p1 = 1 && (y1 <= y2 || y2 = 0) }");
89
90 str = "{ [x,y] : [([x/2]+y)/3] >= 1 }";
91 str2 = "{ [x, y] : 2y >= 6 - x }";
92 test_parse_map_equal(ctx, str, str2);
93
94 test_parse_map_equal(ctx, "{ [x,y] : x <= min(y, 2*y+3) }",
95 "{ [x,y] : x <= y, 2*y + 3 }");
96 str = "{ [x, y] : (y <= x and y >= -3) or (2y <= -3 + x and y <= -4) }";
97 test_parse_map_equal(ctx, "{ [x,y] : x >= min(y, 2*y+3) }", str);
98
99 str = "{[new,old] -> [new+1-2*[(new+1)/2],old+1-2*[(old+1)/2]]}";
100 map = isl_map_read_from_str(ctx, str, -1);
101 str = "{ [new, old] -> [o0, o1] : "
102 "exists (e0 = [(-1 - new + o0)/2], e1 = [(-1 - old + o1)/2]: "
103 "2e0 = -1 - new + o0 and 2e1 = -1 - old + o1 and o0 >= 0 and "
104 "o0 <= 1 and o1 >= 0 and o1 <= 1) }";
105 map2 = isl_map_read_from_str(ctx, str, -1);
106 assert(isl_map_is_equal(map, map2));
107 isl_map_free(map);
108 isl_map_free(map2);
109
110 str = "{[new,old] -> [new+1-2*[(new+1)/2],old+1-2*[(old+1)/2]]}";
111 map = isl_map_read_from_str(ctx, str, -1);
112 str = "{[new,old] -> [(new+1)%2,(old+1)%2]}";
113 map2 = isl_map_read_from_str(ctx, str, -1);
114 assert(isl_map_is_equal(map, map2));
115 isl_map_free(map);
116 isl_map_free(map2);
117
118 str = "[n] -> { [c1] : c1>=0 and c1<=floord(n-4,3) }";
119 str2 = "[n] -> { [c1] : c1 >= 0 and 3c1 <= -4 + n }";
120 test_parse_map_equal(ctx, str, str2);
121
122 test_parse_pwqp(ctx, "{ [i] -> i + [ (i + [i/3])/2 ] }");
123 test_parse_map(ctx, "{ S1[i] -> [([i/10]),i%10] : 0 <= i <= 45 }");
124 }
125
126 void test_read(struct isl_ctx *ctx)
127 {
128 char *filename;
129 FILE *input;
130 struct isl_basic_set *bset1, *bset2;
131 const char *str = "{[y]: Exists ( alpha : 2alpha = y)}";
132
133 filename = get_filename(ctx, "set", "omega");
134 assert(filename);
135 input = fopen(filename, "r");
136 assert(input);
137
138 bset1 = isl_basic_set_read_from_file(ctx, input, 0);
139 bset2 = isl_basic_set_read_from_str(ctx, str, 0);
140
141 assert(isl_basic_set_is_equal(bset1, bset2) == 1);
142
143 isl_basic_set_free(bset1);
144 isl_basic_set_free(bset2);
145 free(filename);
146
147 fclose(input);
148 }
149
150 void test_bounded(struct isl_ctx *ctx)
151 {
152 isl_set *set;
153 int bounded;
154
155 set = isl_set_read_from_str(ctx, "[n] -> {[i] : 0 <= i <= n }", -1);
156 bounded = isl_set_is_bounded(set);
157 assert(bounded);
158 isl_set_free(set);
159
160 set = isl_set_read_from_str(ctx, "{[n, i] : 0 <= i <= n }", -1);
161 bounded = isl_set_is_bounded(set);
162 assert(!bounded);
163 isl_set_free(set);
164
165 set = isl_set_read_from_str(ctx, "[n] -> {[i] : i <= n }", -1);
166 bounded = isl_set_is_bounded(set);
167 assert(!bounded);
168 isl_set_free(set);
169 }
170
171 /* Construct the basic set { [i] : 5 <= i <= N } */
172 void test_construction(struct isl_ctx *ctx)
173 {
174 isl_int v;
175 struct isl_dim *dim;
176 struct isl_basic_set *bset;
177 struct isl_constraint *c;
178
179 isl_int_init(v);
180
181 dim = isl_dim_set_alloc(ctx, 1, 1);
182 bset = isl_basic_set_universe(dim);
183
184 c = isl_inequality_alloc(isl_basic_set_get_dim(bset));
185 isl_int_set_si(v, -1);
186 isl_constraint_set_coefficient(c, isl_dim_set, 0, v);
187 isl_int_set_si(v, 1);
188 isl_constraint_set_coefficient(c, isl_dim_param, 0, v);
189 bset = isl_basic_set_add_constraint(bset, c);
190
191 c = isl_inequality_alloc(isl_basic_set_get_dim(bset));
192 isl_int_set_si(v, 1);
193 isl_constraint_set_coefficient(c, isl_dim_set, 0, v);
194 isl_int_set_si(v, -5);
195 isl_constraint_set_constant(c, v);
196 bset = isl_basic_set_add_constraint(bset, c);
197
198 isl_basic_set_free(bset);
199
200 isl_int_clear(v);
201 }
202
203 void test_dim(struct isl_ctx *ctx)
204 {
205 const char *str;
206 isl_map *map1, *map2;
207
208 map1 = isl_map_read_from_str(ctx,
209 "[n] -> { [i] -> [j] : exists (a = [i/10] : i - 10a <= n ) }", -1);
210 map1 = isl_map_add_dims(map1, isl_dim_in, 1);
211 map2 = isl_map_read_from_str(ctx,
212 "[n] -> { [i,k] -> [j] : exists (a = [i/10] : i - 10a <= n ) }", -1);
213 assert(isl_map_is_equal(map1, map2));
214 isl_map_free(map2);
215
216 map1 = isl_map_project_out(map1, isl_dim_in, 0, 1);
217 map2 = isl_map_read_from_str(ctx, "[n] -> { [i] -> [j] : n >= 0 }", -1);
218 assert(isl_map_is_equal(map1, map2));
219
220 isl_map_free(map1);
221 isl_map_free(map2);
222
223 str = "[n] -> { [i] -> [] : exists a : 0 <= i <= n and i = 2 a }";
224 map1 = isl_map_read_from_str(ctx, str, -1);
225 str = "{ [i] -> [j] : exists a : 0 <= i <= j and i = 2 a }";
226 map2 = isl_map_read_from_str(ctx, str, -1);
227 map1 = isl_map_move_dims(map1, isl_dim_out, 0, isl_dim_param, 0, 1);
228 assert(isl_map_is_equal(map1, map2));
229
230 isl_map_free(map1);
231 isl_map_free(map2);
232 }
233
234 void test_div(struct isl_ctx *ctx)
235 {
236 isl_int v;
237 int pos;
238 struct isl_dim *dim;
239 struct isl_div *div;
240 struct isl_basic_set *bset;
241 struct isl_constraint *c;
242
243 isl_int_init(v);
244
245 /* test 1 */
246 dim = isl_dim_set_alloc(ctx, 0, 1);
247 bset = isl_basic_set_universe(dim);
248
249 c = isl_equality_alloc(isl_basic_set_get_dim(bset));
250 isl_int_set_si(v, -1);
251 isl_constraint_set_constant(c, v);
252 isl_int_set_si(v, 1);
253 isl_constraint_set_coefficient(c, isl_dim_set, 0, v);
254 div = isl_div_alloc(isl_basic_set_get_dim(bset));
255 c = isl_constraint_add_div(c, div, &pos);
256 isl_int_set_si(v, 3);
257 isl_constraint_set_coefficient(c, isl_dim_div, pos, v);
258 bset = isl_basic_set_add_constraint(bset, c);
259
260 c = isl_equality_alloc(isl_basic_set_get_dim(bset));
261 isl_int_set_si(v, 1);
262 isl_constraint_set_constant(c, v);
263 isl_int_set_si(v, -1);
264 isl_constraint_set_coefficient(c, isl_dim_set, 0, v);
265 div = isl_div_alloc(isl_basic_set_get_dim(bset));
266 c = isl_constraint_add_div(c, div, &pos);
267 isl_int_set_si(v, 3);
268 isl_constraint_set_coefficient(c, isl_dim_div, pos, v);
269 bset = isl_basic_set_add_constraint(bset, c);
270
271 assert(bset && bset->n_div == 1);
272 isl_basic_set_free(bset);
273
274 /* test 2 */
275 dim = isl_dim_set_alloc(ctx, 0, 1);
276 bset = isl_basic_set_universe(dim);
277
278 c = isl_equality_alloc(isl_basic_set_get_dim(bset));
279 isl_int_set_si(v, 1);
280 isl_constraint_set_constant(c, v);
281 isl_int_set_si(v, -1);
282 isl_constraint_set_coefficient(c, isl_dim_set, 0, v);
283 div = isl_div_alloc(isl_basic_set_get_dim(bset));
284 c = isl_constraint_add_div(c, div, &pos);
285 isl_int_set_si(v, 3);
286 isl_constraint_set_coefficient(c, isl_dim_div, pos, v);
287 bset = isl_basic_set_add_constraint(bset, c);
288
289 c = isl_equality_alloc(isl_basic_set_get_dim(bset));
290 isl_int_set_si(v, -1);
291 isl_constraint_set_constant(c, v);
292 isl_int_set_si(v, 1);
293 isl_constraint_set_coefficient(c, isl_dim_set, 0, v);
294 div = isl_div_alloc(isl_basic_set_get_dim(bset));
295 c = isl_constraint_add_div(c, div, &pos);
296 isl_int_set_si(v, 3);
297 isl_constraint_set_coefficient(c, isl_dim_div, pos, v);
298 bset = isl_basic_set_add_constraint(bset, c);
299
300 assert(bset && bset->n_div == 1);
301 isl_basic_set_free(bset);
302
303 /* test 3 */
304 dim = isl_dim_set_alloc(ctx, 0, 1);
305 bset = isl_basic_set_universe(dim);
306
307 c = isl_equality_alloc(isl_basic_set_get_dim(bset));
308 isl_int_set_si(v, 1);
309 isl_constraint_set_constant(c, v);
310 isl_int_set_si(v, -1);
311 isl_constraint_set_coefficient(c, isl_dim_set, 0, v);
312 div = isl_div_alloc(isl_basic_set_get_dim(bset));
313 c = isl_constraint_add_div(c, div, &pos);
314 isl_int_set_si(v, 3);
315 isl_constraint_set_coefficient(c, isl_dim_div, pos, v);
316 bset = isl_basic_set_add_constraint(bset, c);
317
318 c = isl_equality_alloc(isl_basic_set_get_dim(bset));
319 isl_int_set_si(v, -3);
320 isl_constraint_set_constant(c, v);
321 isl_int_set_si(v, 1);
322 isl_constraint_set_coefficient(c, isl_dim_set, 0, v);
323 div = isl_div_alloc(isl_basic_set_get_dim(bset));
324 c = isl_constraint_add_div(c, div, &pos);
325 isl_int_set_si(v, 4);
326 isl_constraint_set_coefficient(c, isl_dim_div, pos, v);
327 bset = isl_basic_set_add_constraint(bset, c);
328
329 assert(bset && bset->n_div == 1);
330 isl_basic_set_free(bset);
331
332 /* test 4 */
333 dim = isl_dim_set_alloc(ctx, 0, 1);
334 bset = isl_basic_set_universe(dim);
335
336 c = isl_equality_alloc(isl_basic_set_get_dim(bset));
337 isl_int_set_si(v, 2);
338 isl_constraint_set_constant(c, v);
339 isl_int_set_si(v, -1);
340 isl_constraint_set_coefficient(c, isl_dim_set, 0, v);
341 div = isl_div_alloc(isl_basic_set_get_dim(bset));
342 c = isl_constraint_add_div(c, div, &pos);
343 isl_int_set_si(v, 3);
344 isl_constraint_set_coefficient(c, isl_dim_div, pos, v);
345 bset = isl_basic_set_add_constraint(bset, c);
346
347 c = isl_equality_alloc(isl_basic_set_get_dim(bset));
348 isl_int_set_si(v, -1);
349 isl_constraint_set_constant(c, v);
350 isl_int_set_si(v, 1);
351 isl_constraint_set_coefficient(c, isl_dim_set, 0, v);
352 div = isl_div_alloc(isl_basic_set_get_dim(bset));
353 c = isl_constraint_add_div(c, div, &pos);
354 isl_int_set_si(v, 6);
355 isl_constraint_set_coefficient(c, isl_dim_div, pos, v);
356 bset = isl_basic_set_add_constraint(bset, c);
357
358 assert(isl_basic_set_is_empty(bset));
359 isl_basic_set_free(bset);
360
361 /* test 5 */
362 dim = isl_dim_set_alloc(ctx, 0, 2);
363 bset = isl_basic_set_universe(dim);
364
365 c = isl_equality_alloc(isl_basic_set_get_dim(bset));
366 isl_int_set_si(v, -1);
367 isl_constraint_set_coefficient(c, isl_dim_set, 0, v);
368 div = isl_div_alloc(isl_basic_set_get_dim(bset));
369 c = isl_constraint_add_div(c, div, &pos);
370 isl_int_set_si(v, 3);
371 isl_constraint_set_coefficient(c, isl_dim_div, pos, v);
372 bset = isl_basic_set_add_constraint(bset, c);
373
374 c = isl_equality_alloc(isl_basic_set_get_dim(bset));
375 isl_int_set_si(v, 1);
376 isl_constraint_set_coefficient(c, isl_dim_set, 0, v);
377 isl_int_set_si(v, -3);
378 isl_constraint_set_coefficient(c, isl_dim_set, 1, v);
379 bset = isl_basic_set_add_constraint(bset, c);
380
381 assert(bset && bset->n_div == 0);
382 isl_basic_set_free(bset);
383
384 /* test 6 */
385 dim = isl_dim_set_alloc(ctx, 0, 2);
386 bset = isl_basic_set_universe(dim);
387
388 c = isl_equality_alloc(isl_basic_set_get_dim(bset));
389 isl_int_set_si(v, -1);
390 isl_constraint_set_coefficient(c, isl_dim_set, 0, v);
391 div = isl_div_alloc(isl_basic_set_get_dim(bset));
392 c = isl_constraint_add_div(c, div, &pos);
393 isl_int_set_si(v, 6);
394 isl_constraint_set_coefficient(c, isl_dim_div, pos, v);
395 bset = isl_basic_set_add_constraint(bset, c);
396
397 c = isl_equality_alloc(isl_basic_set_get_dim(bset));
398 isl_int_set_si(v, 1);
399 isl_constraint_set_coefficient(c, isl_dim_set, 0, v);
400 isl_int_set_si(v, -3);
401 isl_constraint_set_coefficient(c, isl_dim_set, 1, v);
402 bset = isl_basic_set_add_constraint(bset, c);
403
404 assert(bset && bset->n_div == 1);
405 isl_basic_set_free(bset);
406
407 /* test 7 */
408 /* This test is a bit tricky. We set up an equality
409 * a + 3b + 3c = 6 e0
410 * Normalization of divs creates _two_ divs
411 * a = 3 e0
412 * c - b - e0 = 2 e1
413 * Afterwards e0 is removed again because it has coefficient -1
414 * and we end up with the original equality and div again.
415 * Perhaps we can avoid the introduction of this temporary div.
416 */
417 dim = isl_dim_set_alloc(ctx, 0, 3);
418 bset = isl_basic_set_universe(dim);
419
420 c = isl_equality_alloc(isl_basic_set_get_dim(bset));
421 isl_int_set_si(v, -1);
422 isl_constraint_set_coefficient(c, isl_dim_set, 0, v);
423 isl_int_set_si(v, -3);
424 isl_constraint_set_coefficient(c, isl_dim_set, 1, v);
425 isl_int_set_si(v, -3);
426 isl_constraint_set_coefficient(c, isl_dim_set, 2, v);
427 div = isl_div_alloc(isl_basic_set_get_dim(bset));
428 c = isl_constraint_add_div(c, div, &pos);
429 isl_int_set_si(v, 6);
430 isl_constraint_set_coefficient(c, isl_dim_div, pos, v);
431 bset = isl_basic_set_add_constraint(bset, c);
432
433 /* Test disabled for now */
434 /*
435 assert(bset && bset->n_div == 1);
436 */
437 isl_basic_set_free(bset);
438
439 /* test 8 */
440 dim = isl_dim_set_alloc(ctx, 0, 4);
441 bset = isl_basic_set_universe(dim);
442
443 c = isl_equality_alloc(isl_basic_set_get_dim(bset));
444 isl_int_set_si(v, -1);
445 isl_constraint_set_coefficient(c, isl_dim_set, 0, v);
446 isl_int_set_si(v, -3);
447 isl_constraint_set_coefficient(c, isl_dim_set, 1, v);
448 isl_int_set_si(v, -3);
449 isl_constraint_set_coefficient(c, isl_dim_set, 3, v);
450 div = isl_div_alloc(isl_basic_set_get_dim(bset));
451 c = isl_constraint_add_div(c, div, &pos);
452 isl_int_set_si(v, 6);
453 isl_constraint_set_coefficient(c, isl_dim_div, pos, v);
454 bset = isl_basic_set_add_constraint(bset, c);
455
456 c = isl_equality_alloc(isl_basic_set_get_dim(bset));
457 isl_int_set_si(v, -1);
458 isl_constraint_set_coefficient(c, isl_dim_set, 0, v);
459 isl_int_set_si(v, 1);
460 isl_constraint_set_coefficient(c, isl_dim_set, 2, v);
461 isl_int_set_si(v, 1);
462 isl_constraint_set_constant(c, v);
463 bset = isl_basic_set_add_constraint(bset, c);
464
465 /* Test disabled for now */
466 /*
467 assert(bset && bset->n_div == 1);
468 */
469 isl_basic_set_free(bset);
470
471 /* test 9 */
472 dim = isl_dim_set_alloc(ctx, 0, 2);
473 bset = isl_basic_set_universe(dim);
474
475 c = isl_equality_alloc(isl_basic_set_get_dim(bset));
476 isl_int_set_si(v, 1);
477 isl_constraint_set_coefficient(c, isl_dim_set, 0, v);
478 isl_int_set_si(v, -1);
479 isl_constraint_set_coefficient(c, isl_dim_set, 1, v);
480 div = isl_div_alloc(isl_basic_set_get_dim(bset));
481 c = isl_constraint_add_div(c, div, &pos);
482 isl_int_set_si(v, -2);
483 isl_constraint_set_coefficient(c, isl_dim_div, pos, v);
484 bset = isl_basic_set_add_constraint(bset, c);
485
486 c = isl_equality_alloc(isl_basic_set_get_dim(bset));
487 isl_int_set_si(v, -1);
488 isl_constraint_set_coefficient(c, isl_dim_set, 0, v);
489 div = isl_div_alloc(isl_basic_set_get_dim(bset));
490 c = isl_constraint_add_div(c, div, &pos);
491 isl_int_set_si(v, 3);
492 isl_constraint_set_coefficient(c, isl_dim_div, pos, v);
493 isl_int_set_si(v, 2);
494 isl_constraint_set_constant(c, v);
495 bset = isl_basic_set_add_constraint(bset, c);
496
497 bset = isl_basic_set_fix_si(bset, isl_dim_set, 0, 2);
498
499 assert(!isl_basic_set_is_empty(bset));
500
501 isl_basic_set_free(bset);
502
503 /* test 10 */
504 dim = isl_dim_set_alloc(ctx, 0, 2);
505 bset = isl_basic_set_universe(dim);
506
507 c = isl_equality_alloc(isl_basic_set_get_dim(bset));
508 isl_int_set_si(v, 1);
509 isl_constraint_set_coefficient(c, isl_dim_set, 0, v);
510 div = isl_div_alloc(isl_basic_set_get_dim(bset));
511 c = isl_constraint_add_div(c, div, &pos);
512 isl_int_set_si(v, -2);
513 isl_constraint_set_coefficient(c, isl_dim_div, pos, v);
514 bset = isl_basic_set_add_constraint(bset, c);
515
516 bset = isl_basic_set_fix_si(bset, isl_dim_set, 0, 2);
517
518 isl_basic_set_free(bset);
519
520 isl_int_clear(v);
521 }
522
523 void test_application_case(struct isl_ctx *ctx, const char *name)
524 {
525 char *filename;
526 FILE *input;
527 struct isl_basic_set *bset1, *bset2;
528 struct isl_basic_map *bmap;
529
530 filename = get_filename(ctx, name, "omega");
531 assert(filename);
532 input = fopen(filename, "r");
533 assert(input);
534
535 bset1 = isl_basic_set_read_from_file(ctx, input, 0);
536 bmap = isl_basic_map_read_from_file(ctx, input, 0);
537
538 bset1 = isl_basic_set_apply(bset1, bmap);
539
540 bset2 = isl_basic_set_read_from_file(ctx, input, 0);
541
542 assert(isl_basic_set_is_equal(bset1, bset2) == 1);
543
544 isl_basic_set_free(bset1);
545 isl_basic_set_free(bset2);
546 free(filename);
547
548 fclose(input);
549 }
550
551 void test_application(struct isl_ctx *ctx)
552 {
553 test_application_case(ctx, "application");
554 test_application_case(ctx, "application2");
555 }
556
557 void test_affine_hull_case(struct isl_ctx *ctx, const char *name)
558 {
559 char *filename;
560 FILE *input;
561 struct isl_basic_set *bset1, *bset2;
562
563 filename = get_filename(ctx, name, "polylib");
564 assert(filename);
565 input = fopen(filename, "r");
566 assert(input);
567
568 bset1 = isl_basic_set_read_from_file(ctx, input, 0);
569 bset2 = isl_basic_set_read_from_file(ctx, input, 0);
570
571 bset1 = isl_basic_set_affine_hull(bset1);
572
573 assert(isl_basic_set_is_equal(bset1, bset2) == 1);
574
575 isl_basic_set_free(bset1);
576 isl_basic_set_free(bset2);
577 free(filename);
578
579 fclose(input);
580 }
581
582 void test_affine_hull(struct isl_ctx *ctx)
583 {
584 test_affine_hull_case(ctx, "affine2");
585 test_affine_hull_case(ctx, "affine");
586 test_affine_hull_case(ctx, "affine3");
587 }
588
589 void test_convex_hull_case(struct isl_ctx *ctx, const char *name)
590 {
591 char *filename;
592 FILE *input;
593 struct isl_basic_set *bset1, *bset2;
594 struct isl_set *set;
595
596 filename = get_filename(ctx, name, "polylib");
597 assert(filename);
598 input = fopen(filename, "r");
599 assert(input);
600
601 bset1 = isl_basic_set_read_from_file(ctx, input, 0);
602 bset2 = isl_basic_set_read_from_file(ctx, input, 0);
603
604 set = isl_basic_set_union(bset1, bset2);
605 bset1 = isl_set_convex_hull(set);
606
607 bset2 = isl_basic_set_read_from_file(ctx, input, 0);
608
609 assert(isl_basic_set_is_equal(bset1, bset2) == 1);
610
611 isl_basic_set_free(bset1);
612 isl_basic_set_free(bset2);
613 free(filename);
614
615 fclose(input);
616 }
617
618 void test_convex_hull_algo(struct isl_ctx *ctx, int convex)
619 {
620 const char *str1, *str2;
621 isl_set *set1, *set2;
622 int orig_convex = ctx->opt->convex;
623 ctx->opt->convex = convex;
624
625 test_convex_hull_case(ctx, "convex0");
626 test_convex_hull_case(ctx, "convex1");
627 test_convex_hull_case(ctx, "convex2");
628 test_convex_hull_case(ctx, "convex3");
629 test_convex_hull_case(ctx, "convex4");
630 test_convex_hull_case(ctx, "convex5");
631 test_convex_hull_case(ctx, "convex6");
632 test_convex_hull_case(ctx, "convex7");
633 test_convex_hull_case(ctx, "convex8");
634 test_convex_hull_case(ctx, "convex9");
635 test_convex_hull_case(ctx, "convex10");
636 test_convex_hull_case(ctx, "convex11");
637 test_convex_hull_case(ctx, "convex12");
638 test_convex_hull_case(ctx, "convex13");
639 test_convex_hull_case(ctx, "convex14");
640 test_convex_hull_case(ctx, "convex15");
641
642 str1 = "{ [i0, i1, i2] : (i2 = 1 and i0 = 0 and i1 >= 0) or "
643 "(i0 = 1 and i1 = 0 and i2 = 1) or "
644 "(i0 = 0 and i1 = 0 and i2 = 0) }";
645 str2 = "{ [i0, i1, i2] : i0 >= 0 and i2 >= i0 and i2 <= 1 and i1 >= 0 }";
646 set1 = isl_set_read_from_str(ctx, str1, -1);
647 set2 = isl_set_read_from_str(ctx, str2, -1);
648 set1 = isl_set_from_basic_set(isl_set_convex_hull(set1));
649 assert(isl_set_is_equal(set1, set2));
650 isl_set_free(set1);
651 isl_set_free(set2);
652
653 ctx->opt->convex = orig_convex;
654 }
655
656 void test_convex_hull(struct isl_ctx *ctx)
657 {
658 test_convex_hull_algo(ctx, ISL_CONVEX_HULL_FM);
659 test_convex_hull_algo(ctx, ISL_CONVEX_HULL_WRAP);
660 }
661
662 void test_gist_case(struct isl_ctx *ctx, const char *name)
663 {
664 char *filename;
665 FILE *input;
666 struct isl_basic_set *bset1, *bset2;
667
668 filename = get_filename(ctx, name, "polylib");
669 assert(filename);
670 input = fopen(filename, "r");
671 assert(input);
672
673 bset1 = isl_basic_set_read_from_file(ctx, input, 0);
674 bset2 = isl_basic_set_read_from_file(ctx, input, 0);
675
676 bset1 = isl_basic_set_gist(bset1, bset2);
677
678 bset2 = isl_basic_set_read_from_file(ctx, input, 0);
679
680 assert(isl_basic_set_is_equal(bset1, bset2) == 1);
681
682 isl_basic_set_free(bset1);
683 isl_basic_set_free(bset2);
684 free(filename);
685
686 fclose(input);
687 }
688
689 void test_gist(struct isl_ctx *ctx)
690 {
691 const char *str;
692 isl_basic_set *bset1, *bset2;
693
694 test_gist_case(ctx, "gist1");
695
696 str = "[p0, p2, p3, p5, p6, p10] -> { [] : "
697 "exists (e0 = [(15 + p0 + 15p6 + 15p10)/16], e1 = [(p5)/8], "
698 "e2 = [(p6)/128], e3 = [(8p2 - p5)/128], "
699 "e4 = [(128p3 - p6)/4096]: 8e1 = p5 and 128e2 = p6 and "
700 "128e3 = 8p2 - p5 and 4096e4 = 128p3 - p6 and p2 >= 0 and "
701 "16e0 >= 16 + 16p6 + 15p10 and p2 <= 15 and p3 >= 0 and "
702 "p3 <= 31 and p6 >= 128p3 and p5 >= 8p2 and p10 >= 0 and "
703 "16e0 <= 15 + p0 + 15p6 + 15p10 and 16e0 >= p0 + 15p6 + 15p10 and "
704 "p10 <= 15 and p10 <= -1 + p0 - p6) }";
705 bset1 = isl_basic_set_read_from_str(ctx, str, -1);
706 str = "[p0, p2, p3, p5, p6, p10] -> { [] : exists (e0 = [(p5)/8], "
707 "e1 = [(p6)/128], e2 = [(8p2 - p5)/128], "
708 "e3 = [(128p3 - p6)/4096]: 8e0 = p5 and 128e1 = p6 and "
709 "128e2 = 8p2 - p5 and 4096e3 = 128p3 - p6 and p5 >= -7 and "
710 "p2 >= 0 and 8p2 <= -1 + p0 and p2 <= 15 and p3 >= 0 and "
711 "p3 <= 31 and 128p3 <= -1 + p0 and p6 >= -127 and "
712 "p5 <= -1 + p0 and p6 <= -1 + p0 and p6 >= 128p3 and "
713 "p0 >= 1 and p5 >= 8p2 and p10 >= 0 and p10 <= 15 ) }";
714 bset2 = isl_basic_set_read_from_str(ctx, str, -1);
715 bset1 = isl_basic_set_gist(bset1, bset2);
716 assert(bset1 && bset1->n_div == 0);
717 isl_basic_set_free(bset1);
718 }
719
720 void test_coalesce_set(isl_ctx *ctx, const char *str, int check_one)
721 {
722 isl_set *set, *set2;
723
724 set = isl_set_read_from_str(ctx, str, -1);
725 set = isl_set_coalesce(set);
726 set2 = isl_set_read_from_str(ctx, str, -1);
727 assert(isl_set_is_equal(set, set2));
728 if (check_one)
729 assert(set && set->n == 1);
730 isl_set_free(set);
731 isl_set_free(set2);
732 }
733
734 void test_coalesce(struct isl_ctx *ctx)
735 {
736 const char *str;
737 struct isl_set *set, *set2;
738 struct isl_map *map, *map2;
739
740 set = isl_set_read_from_str(ctx,
741 "{[x,y]: x >= 0 & x <= 10 & y >= 0 & y <= 10 or "
742 "y >= x & x >= 2 & 5 >= y }", -1);
743 set = isl_set_coalesce(set);
744 assert(set && set->n == 1);
745 isl_set_free(set);
746
747 set = isl_set_read_from_str(ctx,
748 "{[x,y]: y >= 0 & 2x + y <= 30 & y <= 10 & x >= 0 or "
749 "x + y >= 10 & y <= x & x + y <= 20 & y >= 0}", -1);
750 set = isl_set_coalesce(set);
751 assert(set && set->n == 1);
752 isl_set_free(set);
753
754 set = isl_set_read_from_str(ctx,
755 "{[x,y]: y >= 0 & 2x + y <= 30 & y <= 10 & x >= 0 or "
756 "x + y >= 10 & y <= x & x + y <= 19 & y >= 0}", -1);
757 set = isl_set_coalesce(set);
758 assert(set && set->n == 2);
759 isl_set_free(set);
760
761 set = isl_set_read_from_str(ctx,
762 "{[x,y]: y >= 0 & x <= 5 & y <= x or "
763 "y >= 0 & x >= 6 & x <= 10 & y <= x}", -1);
764 set = isl_set_coalesce(set);
765 assert(set && set->n == 1);
766 isl_set_free(set);
767
768 set = isl_set_read_from_str(ctx,
769 "{[x,y]: y >= 0 & x <= 5 & y <= x or "
770 "y >= 0 & x >= 7 & x <= 10 & y <= x}", -1);
771 set = isl_set_coalesce(set);
772 assert(set && set->n == 2);
773 isl_set_free(set);
774
775 set = isl_set_read_from_str(ctx,
776 "{[x,y]: y >= 0 & x <= 5 & y <= x or "
777 "y >= 0 & x >= 6 & x <= 10 & y + 1 <= x}", -1);
778 set = isl_set_coalesce(set);
779 assert(set && set->n == 2);
780 isl_set_free(set);
781
782 set = isl_set_read_from_str(ctx,
783 "{[x,y]: y >= 0 & x <= 5 & y <= x or "
784 "y >= 0 & x = 6 & y <= 6}", -1);
785 set = isl_set_coalesce(set);
786 assert(set && set->n == 1);
787 isl_set_free(set);
788
789 set = isl_set_read_from_str(ctx,
790 "{[x,y]: y >= 0 & x <= 5 & y <= x or "
791 "y >= 0 & x = 7 & y <= 6}", -1);
792 set = isl_set_coalesce(set);
793 assert(set && set->n == 2);
794 isl_set_free(set);
795
796 set = isl_set_read_from_str(ctx,
797 "{[x,y]: y >= 0 & x <= 5 & y <= x or "
798 "y >= 0 & x = 6 & y <= 5}", -1);
799 set = isl_set_coalesce(set);
800 assert(set && set->n == 1);
801 set2 = isl_set_read_from_str(ctx,
802 "{[x,y]: y >= 0 & x <= 5 & y <= x or "
803 "y >= 0 & x = 6 & y <= 5}", -1);
804 assert(isl_set_is_equal(set, set2));
805 isl_set_free(set);
806 isl_set_free(set2);
807
808 set = isl_set_read_from_str(ctx,
809 "{[x,y]: y >= 0 & x <= 5 & y <= x or "
810 "y >= 0 & x = 6 & y <= 7}", -1);
811 set = isl_set_coalesce(set);
812 assert(set && set->n == 2);
813 isl_set_free(set);
814
815 set = isl_set_read_from_str(ctx,
816 "[n] -> { [i] : i = 1 and n >= 2 or 2 <= i and i <= n }", -1);
817 set = isl_set_coalesce(set);
818 assert(set && set->n == 1);
819 set2 = isl_set_read_from_str(ctx,
820 "[n] -> { [i] : i = 1 and n >= 2 or 2 <= i and i <= n }", -1);
821 assert(isl_set_is_equal(set, set2));
822 isl_set_free(set);
823 isl_set_free(set2);
824
825 set = isl_set_read_from_str(ctx,
826 "{[x,y] : x >= 0 and y >= 0 or 0 <= y and y <= 5 and x = -1}", -1);
827 set = isl_set_coalesce(set);
828 set2 = isl_set_read_from_str(ctx,
829 "{[x,y] : x >= 0 and y >= 0 or 0 <= y and y <= 5 and x = -1}", -1);
830 assert(isl_set_is_equal(set, set2));
831 isl_set_free(set);
832 isl_set_free(set2);
833
834 set = isl_set_read_from_str(ctx,
835 "[n] -> { [i] : 1 <= i and i <= n - 1 or "
836 "2 <= i and i <= n }", -1);
837 set = isl_set_coalesce(set);
838 assert(set && set->n == 1);
839 set2 = isl_set_read_from_str(ctx,
840 "[n] -> { [i] : 1 <= i and i <= n - 1 or "
841 "2 <= i and i <= n }", -1);
842 assert(isl_set_is_equal(set, set2));
843 isl_set_free(set);
844 isl_set_free(set2);
845
846 map = isl_map_read_from_str(ctx,
847 "[n] -> { [i0] -> [o0] : exists (e0 = [(i0)/4], e1 = [(o0)/4], "
848 "e2 = [(n)/2], e3 = [(-2 + i0)/4], e4 = [(-2 + o0)/4], "
849 "e5 = [(-2n + i0)/4]: 2e2 = n and 4e3 = -2 + i0 and "
850 "4e4 = -2 + o0 and i0 >= 8 + 2n and o0 >= 2 + i0 and "
851 "o0 <= 56 + 2n and o0 <= -12 + 4n and i0 <= 57 + 2n and "
852 "i0 <= -11 + 4n and o0 >= 6 + 2n and 4e0 <= i0 and "
853 "4e0 >= -3 + i0 and 4e1 <= o0 and 4e1 >= -3 + o0 and "
854 "4e5 <= -2n + i0 and 4e5 >= -3 - 2n + i0);"
855 "[i0] -> [o0] : exists (e0 = [(i0)/4], e1 = [(o0)/4], "
856 "e2 = [(n)/2], e3 = [(-2 + i0)/4], e4 = [(-2 + o0)/4], "
857 "e5 = [(-2n + i0)/4]: 2e2 = n and 4e3 = -2 + i0 and "
858 "4e4 = -2 + o0 and 2e0 >= 3 + n and e0 <= -4 + n and "
859 "2e0 <= 27 + n and e1 <= -4 + n and 2e1 <= 27 + n and "
860 "2e1 >= 2 + n and e1 >= 1 + e0 and i0 >= 7 + 2n and "
861 "i0 <= -11 + 4n and i0 <= 57 + 2n and 4e0 <= -2 + i0 and "
862 "4e0 >= -3 + i0 and o0 >= 6 + 2n and o0 <= -11 + 4n and "
863 "o0 <= 57 + 2n and 4e1 <= -2 + o0 and 4e1 >= -3 + o0 and "
864 "4e5 <= -2n + i0 and 4e5 >= -3 - 2n + i0 ) }", -1);
865 map = isl_map_coalesce(map);
866 map2 = isl_map_read_from_str(ctx,
867 "[n] -> { [i0] -> [o0] : exists (e0 = [(i0)/4], e1 = [(o0)/4], "
868 "e2 = [(n)/2], e3 = [(-2 + i0)/4], e4 = [(-2 + o0)/4], "
869 "e5 = [(-2n + i0)/4]: 2e2 = n and 4e3 = -2 + i0 and "
870 "4e4 = -2 + o0 and i0 >= 8 + 2n and o0 >= 2 + i0 and "
871 "o0 <= 56 + 2n and o0 <= -12 + 4n and i0 <= 57 + 2n and "
872 "i0 <= -11 + 4n and o0 >= 6 + 2n and 4e0 <= i0 and "
873 "4e0 >= -3 + i0 and 4e1 <= o0 and 4e1 >= -3 + o0 and "
874 "4e5 <= -2n + i0 and 4e5 >= -3 - 2n + i0);"
875 "[i0] -> [o0] : exists (e0 = [(i0)/4], e1 = [(o0)/4], "
876 "e2 = [(n)/2], e3 = [(-2 + i0)/4], e4 = [(-2 + o0)/4], "
877 "e5 = [(-2n + i0)/4]: 2e2 = n and 4e3 = -2 + i0 and "
878 "4e4 = -2 + o0 and 2e0 >= 3 + n and e0 <= -4 + n and "
879 "2e0 <= 27 + n and e1 <= -4 + n and 2e1 <= 27 + n and "
880 "2e1 >= 2 + n and e1 >= 1 + e0 and i0 >= 7 + 2n and "
881 "i0 <= -11 + 4n and i0 <= 57 + 2n and 4e0 <= -2 + i0 and "
882 "4e0 >= -3 + i0 and o0 >= 6 + 2n and o0 <= -11 + 4n and "
883 "o0 <= 57 + 2n and 4e1 <= -2 + o0 and 4e1 >= -3 + o0 and "
884 "4e5 <= -2n + i0 and 4e5 >= -3 - 2n + i0 ) }", -1);
885 assert(isl_map_is_equal(map, map2));
886 isl_map_free(map);
887 isl_map_free(map2);
888
889 str = "[n, m] -> { [] -> [o0, o2, o3] : (o3 = 1 and o0 >= 1 + m and "
890 "o0 <= n + m and o2 <= m and o0 >= 2 + n and o2 >= 3) or "
891 "(o0 >= 2 + n and o0 >= 1 + m and o0 <= n + m and n >= 1 and "
892 "o3 <= -1 + o2 and o3 >= 1 - m + o2 and o3 >= 2 and o3 <= n) }";
893 map = isl_map_read_from_str(ctx, str, -1);
894 map = isl_map_coalesce(map);
895 map2 = isl_map_read_from_str(ctx, str, -1);
896 assert(isl_map_is_equal(map, map2));
897 isl_map_free(map);
898 isl_map_free(map2);
899
900 str = "[M, N] -> { [i0, i1, i2, i3, i4, i5, i6] -> "
901 "[o0, o1, o2, o3, o4, o5, o6] : "
902 "(o6 <= -4 + 2M - 2N + i0 + i1 - i2 + i6 - o0 - o1 + o2 and "
903 "o3 <= -2 + i3 and o6 >= 2 + i0 + i3 + i6 - o0 - o3 and "
904 "o6 >= 2 - M + N + i3 + i4 + i6 - o3 - o4 and o0 <= -1 + i0 and "
905 "o4 >= 4 - 3M + 3N - i0 - i1 + i2 + 2i3 + i4 + o0 + o1 - o2 - 2o3 "
906 "and o6 <= -3 + 2M - 2N + i3 + i4 - i5 + i6 - o3 - o4 + o5 and "
907 "2o6 <= -5 + 5M - 5N + 2i0 + i1 - i2 - i5 + 2i6 - 2o0 - o1 + o2 + o5 "
908 "and o6 >= 2i0 + i1 + i6 - 2o0 - o1 and "
909 "3o6 <= -5 + 4M - 4N + 2i0 + i1 - i2 + 2i3 + i4 - i5 + 3i6 "
910 "- 2o0 - o1 + o2 - 2o3 - o4 + o5) or "
911 "(N >= 2 and o3 <= -1 + i3 and o0 <= -1 + i0 and "
912 "o6 >= i3 + i6 - o3 and M >= 0 and "
913 "2o6 >= 1 + i0 + i3 + 2i6 - o0 - o3 and "
914 "o6 >= 1 - M + i0 + i6 - o0 and N >= 2M and o6 >= i0 + i6 - o0) }";
915 map = isl_map_read_from_str(ctx, str, -1);
916 map = isl_map_coalesce(map);
917 map2 = isl_map_read_from_str(ctx, str, -1);
918 assert(isl_map_is_equal(map, map2));
919 isl_map_free(map);
920 isl_map_free(map2);
921
922 str = "[M, N] -> { [] -> [o0] : (o0 = 0 and M >= 1 and N >= 2) or "
923 "(o0 = 0 and M >= 1 and N >= 2M and N >= 2 + M) or "
924 "(o0 = 0 and M >= 2 and N >= 3) or "
925 "(M = 0 and o0 = 0 and N >= 3) }";
926 map = isl_map_read_from_str(ctx, str, -1);
927 map = isl_map_coalesce(map);
928 map2 = isl_map_read_from_str(ctx, str, -1);
929 assert(isl_map_is_equal(map, map2));
930 isl_map_free(map);
931 isl_map_free(map2);
932
933 str = "{ [i0, i1, i2, i3] : (i1 = 10i0 and i0 >= 1 and 10i0 <= 100 and "
934 "i3 <= 9 + 10 i2 and i3 >= 1 + 10i2 and i3 >= 0) or "
935 "(i1 <= 9 + 10i0 and i1 >= 1 + 10i0 and i2 >= 0 and "
936 "i0 >= 0 and i1 <= 100 and i3 <= 9 + 10i2 and i3 >= 1 + 10i2) }";
937 map = isl_map_read_from_str(ctx, str, -1);
938 map = isl_map_coalesce(map);
939 map2 = isl_map_read_from_str(ctx, str, -1);
940 assert(isl_map_is_equal(map, map2));
941 isl_map_free(map);
942 isl_map_free(map2);
943
944 test_coalesce_set(ctx,
945 "[M] -> { [i1] : (i1 >= 2 and i1 <= M) or "
946 "(i1 = M and M >= 1) }", 0);
947 test_coalesce_set(ctx,
948 "{[x,y] : x,y >= 0; [x,y] : 10 <= x <= 20 and y >= -1 }", 0);
949 test_coalesce_set(ctx,
950 "{ [x, y] : (x >= 1 and y >= 1 and x <= 2 and y <= 2) or "
951 "(y = 3 and x = 1) }", 1);
952 test_coalesce_set(ctx,
953 "[M] -> { [i0, i1, i2, i3, i4] : (i1 >= 3 and i4 >= 2 + i2 and "
954 "i2 >= 2 and i0 >= 2 and i3 >= 1 + i2 and i0 <= M and "
955 "i1 <= M and i3 <= M and i4 <= M) or "
956 "(i1 >= 2 and i4 >= 1 + i2 and i2 >= 2 and i0 >= 2 and "
957 "i3 >= 1 + i2 and i0 <= M and i1 <= -1 + M and i3 <= M and "
958 "i4 <= -1 + M) }", 1);
959 test_coalesce_set(ctx,
960 "{ [x, y] : (x >= 0 and y >= 0 and x <= 10 and y <= 10) or "
961 "(x >= 1 and y >= 1 and x <= 11 and y <= 11) }", 1);
962 test_coalesce_set(ctx,
963 "{[x,y,z] : y + 2 >= 0 and x - y + 1 >= 0 and "
964 "-x - y + 1 >= 0 and -3 <= z <= 3;"
965 "[x,y,z] : -x+z + 20 >= 0 and -x-z + 20 >= 0 and "
966 "x-z + 20 >= 0 and x+z + 20 >= 0 and -10 <= y <= 0}", 1);
967 test_coalesce_set(ctx,
968 "{[x,y] : 0 <= x,y <= 10; [5,y]: 4 <=y <= 11}", 1);
969 test_coalesce_set(ctx, "{[x,0] : x >= 0; [x,1] : x <= 20}", 0);
970 test_coalesce_set(ctx,
971 "{[x,0,0] : -5 <= x <= 5; [0,y,1] : -5 <= y <= 5 }", 1);
972 test_coalesce_set(ctx, "{ [x, 1 - x] : 0 <= x <= 1; [0,0] }", 1);
973 test_coalesce_set(ctx, "{ [0,0]; [i,i] : 1 <= i <= 10 }", 1);
974 test_coalesce_set(ctx, "{ [0,0]; [i,j] : 1 <= i,j <= 10 }", 0);
975 test_coalesce_set(ctx, "{ [0,0]; [i,2i] : 1 <= i <= 10 }", 1);
976 test_coalesce_set(ctx, "{ [0,0]; [i,2i] : 2 <= i <= 10 }", 0);
977 test_coalesce_set(ctx, "{ [1,0]; [i,2i] : 1 <= i <= 10 }", 0);
978 test_coalesce_set(ctx, "{ [0,1]; [i,2i] : 1 <= i <= 10 }", 0);
979 }
980
981 void test_closure(struct isl_ctx *ctx)
982 {
983 const char *str;
984 isl_set *dom;
985 isl_map *up, *right;
986 isl_map *map, *map2;
987 int exact;
988
989 /* COCOA example 1 */
990 map = isl_map_read_from_str(ctx,
991 "[n] -> { [i,j] -> [i2,j2] : i2 = i + 1 and j2 = j + 1 and "
992 "1 <= i and i < n and 1 <= j and j < n or "
993 "i2 = i + 1 and j2 = j - 1 and "
994 "1 <= i and i < n and 2 <= j and j <= n }", -1);
995 map = isl_map_power(map, &exact);
996 assert(exact);
997 isl_map_free(map);
998
999 /* COCOA example 1 */
1000 map = isl_map_read_from_str(ctx,
1001 "[n] -> { [i,j] -> [i2,j2] : i2 = i + 1 and j2 = j + 1 and "
1002 "1 <= i and i < n and 1 <= j and j < n or "
1003 "i2 = i + 1 and j2 = j - 1 and "
1004 "1 <= i and i < n and 2 <= j and j <= n }", -1);
1005 map = isl_map_transitive_closure(map, &exact);
1006 assert(exact);
1007 map2 = isl_map_read_from_str(ctx,
1008 "[n] -> { [i,j] -> [i2,j2] : exists (k1,k2,k : "
1009 "1 <= i and i < n and 1 <= j and j <= n and "
1010 "2 <= i2 and i2 <= n and 1 <= j2 and j2 <= n and "
1011 "i2 = i + k1 + k2 and j2 = j + k1 - k2 and "
1012 "k1 >= 0 and k2 >= 0 and k1 + k2 = k and k >= 1 )}", -1);
1013 assert(isl_map_is_equal(map, map2));
1014 isl_map_free(map2);
1015 isl_map_free(map);
1016
1017 map = isl_map_read_from_str(ctx,
1018 "[n] -> { [x] -> [y] : y = x + 1 and 0 <= x and x <= n and "
1019 " 0 <= y and y <= n }", -1);
1020 map = isl_map_transitive_closure(map, &exact);
1021 map2 = isl_map_read_from_str(ctx,
1022 "[n] -> { [x] -> [y] : y > x and 0 <= x and x <= n and "
1023 " 0 <= y and y <= n }", -1);
1024 assert(isl_map_is_equal(map, map2));
1025 isl_map_free(map2);
1026 isl_map_free(map);
1027
1028 /* COCOA example 2 */
1029 map = isl_map_read_from_str(ctx,
1030 "[n] -> { [i,j] -> [i2,j2] : i2 = i + 2 and j2 = j + 2 and "
1031 "1 <= i and i < n - 1 and 1 <= j and j < n - 1 or "
1032 "i2 = i + 2 and j2 = j - 2 and "
1033 "1 <= i and i < n - 1 and 3 <= j and j <= n }", -1);
1034 map = isl_map_transitive_closure(map, &exact);
1035 assert(exact);
1036 map2 = isl_map_read_from_str(ctx,
1037 "[n] -> { [i,j] -> [i2,j2] : exists (k1,k2,k : "
1038 "1 <= i and i < n - 1 and 1 <= j and j <= n and "
1039 "3 <= i2 and i2 <= n and 1 <= j2 and j2 <= n and "
1040 "i2 = i + 2 k1 + 2 k2 and j2 = j + 2 k1 - 2 k2 and "
1041 "k1 >= 0 and k2 >= 0 and k1 + k2 = k and k >= 1) }", -1);
1042 assert(isl_map_is_equal(map, map2));
1043 isl_map_free(map);
1044 isl_map_free(map2);
1045
1046 /* COCOA Fig.2 left */
1047 map = isl_map_read_from_str(ctx,
1048 "[n] -> { [i,j] -> [i2,j2] : i2 = i + 2 and j2 = j and "
1049 "i <= 2 j - 3 and i <= n - 2 and j <= 2 i - 1 and "
1050 "j <= n or "
1051 "i2 = i and j2 = j + 2 and i <= 2 j - 1 and i <= n and "
1052 "j <= 2 i - 3 and j <= n - 2 or "
1053 "i2 = i + 1 and j2 = j + 1 and i <= 2 j - 1 and "
1054 "i <= n - 1 and j <= 2 i - 1 and j <= n - 1 }", -1);
1055 map = isl_map_transitive_closure(map, &exact);
1056 assert(exact);
1057 isl_map_free(map);
1058
1059 /* COCOA Fig.2 right */
1060 map = isl_map_read_from_str(ctx,
1061 "[n] -> { [i,j] -> [i2,j2] : i2 = i + 3 and j2 = j and "
1062 "i <= 2 j - 4 and i <= n - 3 and j <= 2 i - 1 and "
1063 "j <= n or "
1064 "i2 = i and j2 = j + 3 and i <= 2 j - 1 and i <= n and "
1065 "j <= 2 i - 4 and j <= n - 3 or "
1066 "i2 = i + 1 and j2 = j + 1 and i <= 2 j - 1 and "
1067 "i <= n - 1 and j <= 2 i - 1 and j <= n - 1 }", -1);
1068 map = isl_map_power(map, &exact);
1069 assert(exact);
1070 isl_map_free(map);
1071
1072 /* COCOA Fig.2 right */
1073 map = isl_map_read_from_str(ctx,
1074 "[n] -> { [i,j] -> [i2,j2] : i2 = i + 3 and j2 = j and "
1075 "i <= 2 j - 4 and i <= n - 3 and j <= 2 i - 1 and "
1076 "j <= n or "
1077 "i2 = i and j2 = j + 3 and i <= 2 j - 1 and i <= n and "
1078 "j <= 2 i - 4 and j <= n - 3 or "
1079 "i2 = i + 1 and j2 = j + 1 and i <= 2 j - 1 and "
1080 "i <= n - 1 and j <= 2 i - 1 and j <= n - 1 }", -1);
1081 map = isl_map_transitive_closure(map, &exact);
1082 assert(exact);
1083 map2 = isl_map_read_from_str(ctx,
1084 "[n] -> { [i,j] -> [i2,j2] : exists (k1,k2,k3,k : "
1085 "i <= 2 j - 1 and i <= n and j <= 2 i - 1 and "
1086 "j <= n and 3 + i + 2 j <= 3 n and "
1087 "3 + 2 i + j <= 3n and i2 <= 2 j2 -1 and i2 <= n and "
1088 "i2 <= 3 j2 - 4 and j2 <= 2 i2 -1 and j2 <= n and "
1089 "13 + 4 j2 <= 11 i2 and i2 = i + 3 k1 + k3 and "
1090 "j2 = j + 3 k2 + k3 and k1 >= 0 and k2 >= 0 and "
1091 "k3 >= 0 and k1 + k2 + k3 = k and k > 0) }", -1);
1092 assert(isl_map_is_equal(map, map2));
1093 isl_map_free(map2);
1094 isl_map_free(map);
1095
1096 /* COCOA Fig.1 right */
1097 dom = isl_set_read_from_str(ctx,
1098 "{ [x,y] : x >= 0 and -2 x + 3 y >= 0 and x <= 3 and "
1099 "2 x - 3 y + 3 >= 0 }", -1);
1100 right = isl_map_read_from_str(ctx,
1101 "{ [x,y] -> [x2,y2] : x2 = x + 1 and y2 = y }", -1);
1102 up = isl_map_read_from_str(ctx,
1103 "{ [x,y] -> [x2,y2] : x2 = x and y2 = y + 1 }", -1);
1104 right = isl_map_intersect_domain(right, isl_set_copy(dom));
1105 right = isl_map_intersect_range(right, isl_set_copy(dom));
1106 up = isl_map_intersect_domain(up, isl_set_copy(dom));
1107 up = isl_map_intersect_range(up, dom);
1108 map = isl_map_union(up, right);
1109 map = isl_map_transitive_closure(map, &exact);
1110 assert(exact);
1111 map2 = isl_map_read_from_str(ctx,
1112 "{ [0,0] -> [0,1]; [0,0] -> [1,1]; [0,1] -> [1,1]; "
1113 " [2,2] -> [3,2]; [2,2] -> [3,3]; [3,2] -> [3,3] }", -1);
1114 assert(isl_map_is_equal(map, map2));
1115 isl_map_free(map2);
1116 isl_map_free(map);
1117
1118 /* COCOA Theorem 1 counter example */
1119 map = isl_map_read_from_str(ctx,
1120 "{ [i,j] -> [i2,j2] : i = 0 and 0 <= j and j <= 1 and "
1121 "i2 = 1 and j2 = j or "
1122 "i = 0 and j = 0 and i2 = 0 and j2 = 1 }", -1);
1123 map = isl_map_transitive_closure(map, &exact);
1124 assert(exact);
1125 isl_map_free(map);
1126
1127 map = isl_map_read_from_str(ctx,
1128 "[m,n] -> { [i,j] -> [i2,j2] : i2 = i and j2 = j + 2 and "
1129 "1 <= i,i2 <= n and 1 <= j,j2 <= m or "
1130 "i2 = i + 1 and 3 <= j2 - j <= 4 and "
1131 "1 <= i,i2 <= n and 1 <= j,j2 <= m }", -1);
1132 map = isl_map_transitive_closure(map, &exact);
1133 assert(exact);
1134 isl_map_free(map);
1135
1136 /* Kelly et al 1996, fig 12 */
1137 map = isl_map_read_from_str(ctx,
1138 "[n] -> { [i,j] -> [i2,j2] : i2 = i and j2 = j + 1 and "
1139 "1 <= i,j,j+1 <= n or "
1140 "j = n and j2 = 1 and i2 = i + 1 and "
1141 "1 <= i,i+1 <= n }", -1);
1142 map = isl_map_transitive_closure(map, &exact);
1143 assert(exact);
1144 map2 = isl_map_read_from_str(ctx,
1145 "[n] -> { [i,j] -> [i2,j2] : 1 <= j < j2 <= n and "
1146 "1 <= i <= n and i = i2 or "
1147 "1 <= i < i2 <= n and 1 <= j <= n and "
1148 "1 <= j2 <= n }", -1);
1149 assert(isl_map_is_equal(map, map2));
1150 isl_map_free(map2);
1151 isl_map_free(map);
1152
1153 /* Omega's closure4 */
1154 map = isl_map_read_from_str(ctx,
1155 "[m,n] -> { [x,y] -> [x2,y2] : x2 = x and y2 = y + 1 and "
1156 "1 <= x,y <= 10 or "
1157 "x2 = x + 1 and y2 = y and "
1158 "1 <= x <= 20 && 5 <= y <= 15 }", -1);
1159 map = isl_map_transitive_closure(map, &exact);
1160 assert(exact);
1161 isl_map_free(map);
1162
1163 map = isl_map_read_from_str(ctx,
1164 "[n] -> { [x] -> [y]: 1 <= n <= y - x <= 10 }", -1);
1165 map = isl_map_transitive_closure(map, &exact);
1166 assert(!exact);
1167 map2 = isl_map_read_from_str(ctx,
1168 "[n] -> { [x] -> [y] : 1 <= n <= 10 and y >= n + x }", -1);
1169 assert(isl_map_is_equal(map, map2));
1170 isl_map_free(map);
1171 isl_map_free(map2);
1172
1173 str = "[n, m] -> { [i0, i1, i2, i3] -> [o0, o1, o2, o3] : "
1174 "i3 = 1 and o0 = i0 and o1 = -1 + i1 and o2 = -1 + i2 and "
1175 "o3 = -2 + i2 and i1 <= -1 + i0 and i1 >= 1 - m + i0 and "
1176 "i1 >= 2 and i1 <= n and i2 >= 3 and i2 <= 1 + n and i2 <= m }";
1177 map = isl_map_read_from_str(ctx, str, -1);
1178 map = isl_map_transitive_closure(map, &exact);
1179 assert(exact);
1180 map2 = isl_map_read_from_str(ctx, str, -1);
1181 assert(isl_map_is_equal(map, map2));
1182 isl_map_free(map);
1183 isl_map_free(map2);
1184
1185 str = "{[0] -> [1]; [2] -> [3]}";
1186 map = isl_map_read_from_str(ctx, str, -1);
1187 map = isl_map_transitive_closure(map, &exact);
1188 assert(exact);
1189 map2 = isl_map_read_from_str(ctx, str, -1);
1190 assert(isl_map_is_equal(map, map2));
1191 isl_map_free(map);
1192 isl_map_free(map2);
1193
1194 str = "[n] -> { [[i0, i1, 1, 0, i0] -> [i5, 1]] -> "
1195 "[[i0, -1 + i1, 2, 0, i0] -> [-1 + i5, 2]] : "
1196 "exists (e0 = [(3 - n)/3]: i5 >= 2 and i1 >= 2 and "
1197 "3i0 <= -1 + n and i1 <= -1 + n and i5 <= -1 + n and "
1198 "3e0 >= 1 - n and 3e0 <= 2 - n and 3i0 >= -2 + n); "
1199 "[[i0, i1, 2, 0, i0] -> [i5, 1]] -> "
1200 "[[i0, i1, 1, 0, i0] -> [-1 + i5, 2]] : "
1201 "exists (e0 = [(3 - n)/3]: i5 >= 2 and i1 >= 1 and "
1202 "3i0 <= -1 + n and i1 <= -1 + n and i5 <= -1 + n and "
1203 "3e0 >= 1 - n and 3e0 <= 2 - n and 3i0 >= -2 + n); "
1204 "[[i0, i1, 1, 0, i0] -> [i5, 2]] -> "
1205 "[[i0, -1 + i1, 2, 0, i0] -> [i5, 1]] : "
1206 "exists (e0 = [(3 - n)/3]: i1 >= 2 and i5 >= 1 and "
1207 "3i0 <= -1 + n and i1 <= -1 + n and i5 <= -1 + n and "
1208 "3e0 >= 1 - n and 3e0 <= 2 - n and 3i0 >= -2 + n); "
1209 "[[i0, i1, 2, 0, i0] -> [i5, 2]] -> "
1210 "[[i0, i1, 1, 0, i0] -> [i5, 1]] : "
1211 "exists (e0 = [(3 - n)/3]: i5 >= 1 and i1 >= 1 and "
1212 "3i0 <= -1 + n and i1 <= -1 + n and i5 <= -1 + n and "
1213 "3e0 >= 1 - n and 3e0 <= 2 - n and 3i0 >= -2 + n) }";
1214 map = isl_map_read_from_str(ctx, str, -1);
1215 map = isl_map_transitive_closure(map, NULL);
1216 assert(map);
1217 isl_map_free(map);
1218 }
1219
1220 void test_lex(struct isl_ctx *ctx)
1221 {
1222 isl_dim *dim;
1223 isl_map *map;
1224
1225 dim = isl_dim_alloc(ctx, 0, 0, 0);
1226 map = isl_map_lex_le(dim);
1227 assert(!isl_map_is_empty(map));
1228 isl_map_free(map);
1229 }
1230
1231 static int consume_lexmin(__isl_take isl_basic_set *dom,
1232 __isl_take isl_aff_list *list, void *user)
1233 {
1234 isl_dim *dim;
1235 isl_basic_map *bmap;
1236 isl_map **map = user;
1237
1238 dim = isl_basic_set_get_dim(dom);
1239 bmap = isl_basic_map_from_aff_list(dim, list);
1240 bmap = isl_basic_map_intersect_domain(bmap, dom);
1241
1242 *map = isl_map_union(*map, isl_map_from_basic_map(bmap));
1243
1244 return 0;
1245 }
1246
1247 void test_lexmin(struct isl_ctx *ctx)
1248 {
1249 const char *str;
1250 isl_basic_map *bmap;
1251 isl_map *map, *map2;
1252 isl_set *set;
1253 isl_set *set2;
1254
1255 str = "[p0, p1] -> { [] -> [] : "
1256 "exists (e0 = [(2p1)/3], e1, e2, e3 = [(3 - p1 + 3e0)/3], "
1257 "e4 = [(p1)/3], e5 = [(p1 + 3e4)/3]: "
1258 "3e0 >= -2 + 2p1 and 3e0 >= p1 and 3e3 >= 1 - p1 + 3e0 and "
1259 "3e0 <= 2p1 and 3e3 >= -2 + p1 and 3e3 <= -1 + p1 and p1 >= 3 and "
1260 "3e5 >= -2 + 2p1 and 3e5 >= p1 and 3e5 <= -1 + p1 + 3e4 and "
1261 "3e4 <= p1 and 3e4 >= -2 + p1 and e3 <= -1 + e0 and "
1262 "3e4 >= 6 - p1 + 3e1 and 3e1 >= p1 and 3e5 >= -2 + p1 + 3e4 and "
1263 "2e4 >= 3 - p1 + 2e1 and e4 <= e1 and 3e3 <= 2 - p1 + 3e0 and "
1264 "e5 >= 1 + e1 and 3e4 >= 6 - 2p1 + 3e1 and "
1265 "p0 >= 2 and p1 >= p0 and 3e2 >= p1 and 3e4 >= 6 - p1 + 3e2 and "
1266 "e2 <= e1 and e3 >= 1 and e4 <= e2) }";
1267 map = isl_map_read_from_str(ctx, str, -1);
1268 map = isl_map_lexmin(map);
1269 isl_map_free(map);
1270
1271 str = "[C] -> { [obj,a,b,c] : obj <= 38 a + 7 b + 10 c and "
1272 "a + b <= 1 and c <= 10 b and c <= C and a,b,c,C >= 0 }";
1273 set = isl_set_read_from_str(ctx, str, -1);
1274 set = isl_set_lexmax(set);
1275 str = "[C] -> { [obj,a,b,c] : C = 8 }";
1276 set2 = isl_set_read_from_str(ctx, str, -1);
1277 set = isl_set_intersect(set, set2);
1278 assert(!isl_set_is_empty(set));
1279 isl_set_free(set);
1280
1281 str = "{ [x] -> [y] : x <= y <= 10; [x] -> [5] : -8 <= x <= 8 }";
1282 map = isl_map_read_from_str(ctx, str, -1);
1283 map = isl_map_lexmin(map);
1284 str = "{ [x] -> [5] : 6 <= x <= 8; "
1285 "[x] -> [x] : x <= 5 or (9 <= x <= 10) }";
1286 map2 = isl_map_read_from_str(ctx, str, -1);
1287 assert(isl_map_is_equal(map, map2));
1288 isl_map_free(map);
1289 isl_map_free(map2);
1290
1291 str = "{ [x] -> [y] : 4y = x or 4y = -1 + x or 4y = -2 + x }";
1292 map = isl_map_read_from_str(ctx, str, -1);
1293 map2 = isl_map_copy(map);
1294 map = isl_map_lexmin(map);
1295 assert(isl_map_is_equal(map, map2));
1296 isl_map_free(map);
1297 isl_map_free(map2);
1298
1299 str = "{ [x] -> [y] : x = 4y; [x] -> [y] : x = 2y }";
1300 map = isl_map_read_from_str(ctx, str, -1);
1301 map = isl_map_lexmin(map);
1302 str = "{ [x] -> [y] : (4y = x and x >= 0) or "
1303 "(exists (e0 = [(x)/4], e1 = [(-2 + x)/4]: 2y = x and "
1304 "4e1 = -2 + x and 4e0 <= -1 + x and 4e0 >= -3 + x)) or "
1305 "(exists (e0 = [(x)/4]: 2y = x and 4e0 = x and x <= -4)) }";
1306 map2 = isl_map_read_from_str(ctx, str, -1);
1307 assert(isl_map_is_equal(map, map2));
1308 isl_map_free(map);
1309 isl_map_free(map2);
1310
1311 str = "{ [i] -> [i', j] : j = i - 8i' and i' >= 0 and i' <= 7 and "
1312 " 8i' <= i and 8i' >= -7 + i }";
1313 bmap = isl_basic_map_read_from_str(ctx, str, -1);
1314 map2 = isl_map_empty(isl_basic_map_get_dim(bmap));
1315 isl_basic_map_foreach_lexmin(bmap, &consume_lexmin, &map2);
1316 map = isl_map_from_basic_map(bmap);
1317 assert(isl_map_is_equal(map, map2));
1318 isl_map_free(map);
1319 isl_map_free(map2);
1320 }
1321
1322 struct must_may {
1323 isl_map *must;
1324 isl_map *may;
1325 };
1326
1327 static int collect_must_may(__isl_take isl_map *dep, int must,
1328 void *dep_user, void *user)
1329 {
1330 struct must_may *mm = (struct must_may *)user;
1331
1332 if (must)
1333 mm->must = isl_map_union(mm->must, dep);
1334 else
1335 mm->may = isl_map_union(mm->may, dep);
1336
1337 return 0;
1338 }
1339
1340 static int common_space(void *first, void *second)
1341 {
1342 int depth = *(int *)first;
1343 return 2 * depth;
1344 }
1345
1346 static int map_is_equal(__isl_keep isl_map *map, const char *str)
1347 {
1348 isl_map *map2;
1349 int equal;
1350
1351 if (!map)
1352 return -1;
1353
1354 map2 = isl_map_read_from_str(map->ctx, str, -1);
1355 equal = isl_map_is_equal(map, map2);
1356 isl_map_free(map2);
1357
1358 return equal;
1359 }
1360
1361 void test_dep(struct isl_ctx *ctx)
1362 {
1363 const char *str;
1364 isl_dim *dim;
1365 isl_map *map;
1366 isl_access_info *ai;
1367 isl_flow *flow;
1368 int depth;
1369 struct must_may mm;
1370
1371 depth = 3;
1372
1373 str = "{ [2,i,0] -> [i] : 0 <= i <= 10 }";
1374 map = isl_map_read_from_str(ctx, str, -1);
1375 ai = isl_access_info_alloc(map, &depth, &common_space, 2);
1376
1377 str = "{ [0,i,0] -> [i] : 0 <= i <= 10 }";
1378 map = isl_map_read_from_str(ctx, str, -1);
1379 ai = isl_access_info_add_source(ai, map, 1, &depth);
1380
1381 str = "{ [1,i,0] -> [5] : 0 <= i <= 10 }";
1382 map = isl_map_read_from_str(ctx, str, -1);
1383 ai = isl_access_info_add_source(ai, map, 1, &depth);
1384
1385 flow = isl_access_info_compute_flow(ai);
1386 dim = isl_dim_alloc(ctx, 0, 3, 3);
1387 mm.must = isl_map_empty(isl_dim_copy(dim));
1388 mm.may = isl_map_empty(dim);
1389
1390 isl_flow_foreach(flow, collect_must_may, &mm);
1391
1392 str = "{ [0,i,0] -> [2,i,0] : (0 <= i <= 4) or (6 <= i <= 10); "
1393 " [1,10,0] -> [2,5,0] }";
1394 assert(map_is_equal(mm.must, str));
1395 str = "{ [i,j,k] -> [l,m,n] : 1 = 0 }";
1396 assert(map_is_equal(mm.may, str));
1397
1398 isl_map_free(mm.must);
1399 isl_map_free(mm.may);
1400 isl_flow_free(flow);
1401
1402
1403 str = "{ [2,i,0] -> [i] : 0 <= i <= 10 }";
1404 map = isl_map_read_from_str(ctx, str, -1);
1405 ai = isl_access_info_alloc(map, &depth, &common_space, 2);
1406
1407 str = "{ [0,i,0] -> [i] : 0 <= i <= 10 }";
1408 map = isl_map_read_from_str(ctx, str, -1);
1409 ai = isl_access_info_add_source(ai, map, 1, &depth);
1410
1411 str = "{ [1,i,0] -> [5] : 0 <= i <= 10 }";
1412 map = isl_map_read_from_str(ctx, str, -1);
1413 ai = isl_access_info_add_source(ai, map, 0, &depth);
1414
1415 flow = isl_access_info_compute_flow(ai);
1416 dim = isl_dim_alloc(ctx, 0, 3, 3);
1417 mm.must = isl_map_empty(isl_dim_copy(dim));
1418 mm.may = isl_map_empty(dim);
1419
1420 isl_flow_foreach(flow, collect_must_may, &mm);
1421
1422 str = "{ [0,i,0] -> [2,i,0] : (0 <= i <= 4) or (6 <= i <= 10) }";
1423 assert(map_is_equal(mm.must, str));
1424 str = "{ [0,5,0] -> [2,5,0]; [1,i,0] -> [2,5,0] : 0 <= i <= 10 }";
1425 assert(map_is_equal(mm.may, str));
1426
1427 isl_map_free(mm.must);
1428 isl_map_free(mm.may);
1429 isl_flow_free(flow);
1430
1431
1432 str = "{ [2,i,0] -> [i] : 0 <= i <= 10 }";
1433 map = isl_map_read_from_str(ctx, str, -1);
1434 ai = isl_access_info_alloc(map, &depth, &common_space, 2);
1435
1436 str = "{ [0,i,0] -> [i] : 0 <= i <= 10 }";
1437 map = isl_map_read_from_str(ctx, str, -1);
1438 ai = isl_access_info_add_source(ai, map, 0, &depth);
1439
1440 str = "{ [1,i,0] -> [5] : 0 <= i <= 10 }";
1441 map = isl_map_read_from_str(ctx, str, -1);
1442 ai = isl_access_info_add_source(ai, map, 0, &depth);
1443
1444 flow = isl_access_info_compute_flow(ai);
1445 dim = isl_dim_alloc(ctx, 0, 3, 3);
1446 mm.must = isl_map_empty(isl_dim_copy(dim));
1447 mm.may = isl_map_empty(dim);
1448
1449 isl_flow_foreach(flow, collect_must_may, &mm);
1450
1451 str = "{ [0,i,0] -> [2,i,0] : 0 <= i <= 10; "
1452 " [1,i,0] -> [2,5,0] : 0 <= i <= 10 }";
1453 assert(map_is_equal(mm.may, str));
1454 str = "{ [i,j,k] -> [l,m,n] : 1 = 0 }";
1455 assert(map_is_equal(mm.must, str));
1456
1457 isl_map_free(mm.must);
1458 isl_map_free(mm.may);
1459 isl_flow_free(flow);
1460
1461
1462 str = "{ [0,i,2] -> [i] : 0 <= i <= 10 }";
1463 map = isl_map_read_from_str(ctx, str, -1);
1464 ai = isl_access_info_alloc(map, &depth, &common_space, 2);
1465
1466 str = "{ [0,i,0] -> [i] : 0 <= i <= 10 }";
1467 map = isl_map_read_from_str(ctx, str, -1);
1468 ai = isl_access_info_add_source(ai, map, 0, &depth);
1469
1470 str = "{ [0,i,1] -> [5] : 0 <= i <= 10 }";
1471 map = isl_map_read_from_str(ctx, str, -1);
1472 ai = isl_access_info_add_source(ai, map, 0, &depth);
1473
1474 flow = isl_access_info_compute_flow(ai);
1475 dim = isl_dim_alloc(ctx, 0, 3, 3);
1476 mm.must = isl_map_empty(isl_dim_copy(dim));
1477 mm.may = isl_map_empty(dim);
1478
1479 isl_flow_foreach(flow, collect_must_may, &mm);
1480
1481 str = "{ [0,i,0] -> [0,i,2] : 0 <= i <= 10; "
1482 " [0,i,1] -> [0,5,2] : 0 <= i <= 5 }";
1483 assert(map_is_equal(mm.may, str));
1484 str = "{ [i,j,k] -> [l,m,n] : 1 = 0 }";
1485 assert(map_is_equal(mm.must, str));
1486
1487 isl_map_free(mm.must);
1488 isl_map_free(mm.may);
1489 isl_flow_free(flow);
1490
1491
1492 str = "{ [0,i,1] -> [i] : 0 <= i <= 10 }";
1493 map = isl_map_read_from_str(ctx, str, -1);
1494 ai = isl_access_info_alloc(map, &depth, &common_space, 2);
1495
1496 str = "{ [0,i,0] -> [i] : 0 <= i <= 10 }";
1497 map = isl_map_read_from_str(ctx, str, -1);
1498 ai = isl_access_info_add_source(ai, map, 0, &depth);
1499
1500 str = "{ [0,i,2] -> [5] : 0 <= i <= 10 }";
1501 map = isl_map_read_from_str(ctx, str, -1);
1502 ai = isl_access_info_add_source(ai, map, 0, &depth);
1503
1504 flow = isl_access_info_compute_flow(ai);
1505 dim = isl_dim_alloc(ctx, 0, 3, 3);
1506 mm.must = isl_map_empty(isl_dim_copy(dim));
1507 mm.may = isl_map_empty(dim);
1508
1509 isl_flow_foreach(flow, collect_must_may, &mm);
1510
1511 str = "{ [0,i,0] -> [0,i,1] : 0 <= i <= 10; "
1512 " [0,i,2] -> [0,5,1] : 0 <= i <= 4 }";
1513 assert(map_is_equal(mm.may, str));
1514 str = "{ [i,j,k] -> [l,m,n] : 1 = 0 }";
1515 assert(map_is_equal(mm.must, str));
1516
1517 isl_map_free(mm.must);
1518 isl_map_free(mm.may);
1519 isl_flow_free(flow);
1520
1521
1522 depth = 5;
1523
1524 str = "{ [1,i,0,0,0] -> [i,j] : 0 <= i <= 10 and 0 <= j <= 10 }";
1525 map = isl_map_read_from_str(ctx, str, -1);
1526 ai = isl_access_info_alloc(map, &depth, &common_space, 1);
1527
1528 str = "{ [0,i,0,j,0] -> [i,j] : 0 <= i <= 10 and 0 <= j <= 10 }";
1529 map = isl_map_read_from_str(ctx, str, -1);
1530 ai = isl_access_info_add_source(ai, map, 1, &depth);
1531
1532 flow = isl_access_info_compute_flow(ai);
1533 dim = isl_dim_alloc(ctx, 0, 5, 5);
1534 mm.must = isl_map_empty(isl_dim_copy(dim));
1535 mm.may = isl_map_empty(dim);
1536
1537 isl_flow_foreach(flow, collect_must_may, &mm);
1538
1539 str = "{ [0,i,0,j,0] -> [1,i,0,0,0] : 0 <= i,j <= 10 }";
1540 assert(map_is_equal(mm.must, str));
1541 str = "{ [0,0,0,0,0] -> [0,0,0,0,0] : 1 = 0 }";
1542 assert(map_is_equal(mm.may, str));
1543
1544 isl_map_free(mm.must);
1545 isl_map_free(mm.may);
1546 isl_flow_free(flow);
1547 }
1548
1549 int test_sv(isl_ctx *ctx)
1550 {
1551 const char *str;
1552 isl_map *map;
1553 isl_union_map *umap;
1554 int sv;
1555
1556 str = "[N] -> { [i] -> [f] : 0 <= i <= N and 0 <= i - 10 f <= 9 }";
1557 map = isl_map_read_from_str(ctx, str, -1);
1558 sv = isl_map_is_single_valued(map);
1559 isl_map_free(map);
1560 if (sv < 0)
1561 return -1;
1562 if (!sv)
1563 isl_die(ctx, isl_error_internal,
1564 "map not detected as single valued", return -1);
1565
1566 str = "[N] -> { [i] -> [f] : 0 <= i <= N and 0 <= i - 10 f <= 10 }";
1567 map = isl_map_read_from_str(ctx, str, -1);
1568 sv = isl_map_is_single_valued(map);
1569 isl_map_free(map);
1570 if (sv < 0)
1571 return -1;
1572 if (sv)
1573 isl_die(ctx, isl_error_internal,
1574 "map detected as single valued", return -1);
1575
1576 str = "{ S1[i] -> [i] : 0 <= i <= 9; S2[i] -> [i] : 0 <= i <= 9 }";
1577 umap = isl_union_map_read_from_str(ctx, str);
1578 sv = isl_union_map_is_single_valued(umap);
1579 isl_union_map_free(umap);
1580 if (sv < 0)
1581 return -1;
1582 if (!sv)
1583 isl_die(ctx, isl_error_internal,
1584 "map not detected as single valued", return -1);
1585
1586 str = "{ [i] -> S1[i] : 0 <= i <= 9; [i] -> S2[i] : 0 <= i <= 9 }";
1587 umap = isl_union_map_read_from_str(ctx, str);
1588 sv = isl_union_map_is_single_valued(umap);
1589 isl_union_map_free(umap);
1590 if (sv < 0)
1591 return -1;
1592 if (sv)
1593 isl_die(ctx, isl_error_internal,
1594 "map detected as single valued", return -1);
1595
1596 return 0;
1597 }
1598
1599 void test_bijective_case(struct isl_ctx *ctx, const char *str, int bijective)
1600 {
1601 isl_map *map;
1602
1603 map = isl_map_read_from_str(ctx, str, -1);
1604 if (bijective)
1605 assert(isl_map_is_bijective(map));
1606 else
1607 assert(!isl_map_is_bijective(map));
1608 isl_map_free(map);
1609 }
1610
1611 void test_bijective(struct isl_ctx *ctx)
1612 {
1613 test_bijective_case(ctx, "[N,M]->{[i,j] -> [i]}", 0);
1614 test_bijective_case(ctx, "[N,M]->{[i,j] -> [i] : j=i}", 1);
1615 test_bijective_case(ctx, "[N,M]->{[i,j] -> [i] : j=0}", 1);
1616 test_bijective_case(ctx, "[N,M]->{[i,j] -> [i] : j=N}", 1);
1617 test_bijective_case(ctx, "[N,M]->{[i,j] -> [j,i]}", 1);
1618 test_bijective_case(ctx, "[N,M]->{[i,j] -> [i+j]}", 0);
1619 test_bijective_case(ctx, "[N,M]->{[i,j] -> []}", 0);
1620 test_bijective_case(ctx, "[N,M]->{[i,j] -> [i,j,N]}", 1);
1621 test_bijective_case(ctx, "[N,M]->{[i,j] -> [2i]}", 0);
1622 test_bijective_case(ctx, "[N,M]->{[i,j] -> [i,i]}", 0);
1623 test_bijective_case(ctx, "[N,M]->{[i,j] -> [2i,i]}", 0);
1624 test_bijective_case(ctx, "[N,M]->{[i,j] -> [2i,j]}", 1);
1625 test_bijective_case(ctx, "[N,M]->{[i,j] -> [x,y] : 2x=i & y =j}", 1);
1626 }
1627
1628 void test_pwqp(struct isl_ctx *ctx)
1629 {
1630 const char *str;
1631 isl_set *set;
1632 isl_pw_qpolynomial *pwqp1, *pwqp2;
1633
1634 str = "{ [i,j,k] -> 1 + 9 * [i/5] + 7 * [j/11] + 4 * [k/13] }";
1635 pwqp1 = isl_pw_qpolynomial_read_from_str(ctx, str);
1636
1637 pwqp1 = isl_pw_qpolynomial_move_dims(pwqp1, isl_dim_param, 0,
1638 isl_dim_set, 1, 1);
1639
1640 str = "[j] -> { [i,k] -> 1 + 9 * [i/5] + 7 * [j/11] + 4 * [k/13] }";
1641 pwqp2 = isl_pw_qpolynomial_read_from_str(ctx, str);
1642
1643 pwqp1 = isl_pw_qpolynomial_sub(pwqp1, pwqp2);
1644
1645 assert(isl_pw_qpolynomial_is_zero(pwqp1));
1646
1647 isl_pw_qpolynomial_free(pwqp1);
1648
1649 str = "{ [i] -> i }";
1650 pwqp1 = isl_pw_qpolynomial_read_from_str(ctx, str);
1651 str = "{ [k] : exists a : k = 2a }";
1652 set = isl_set_read_from_str(ctx, str, 0);
1653 pwqp1 = isl_pw_qpolynomial_gist(pwqp1, set);
1654 str = "{ [i] -> i }";
1655 pwqp2 = isl_pw_qpolynomial_read_from_str(ctx, str);
1656
1657 pwqp1 = isl_pw_qpolynomial_sub(pwqp1, pwqp2);
1658
1659 assert(isl_pw_qpolynomial_is_zero(pwqp1));
1660
1661 isl_pw_qpolynomial_free(pwqp1);
1662
1663 str = "{ [i] -> i + [ (i + [i/3])/2 ] }";
1664 pwqp1 = isl_pw_qpolynomial_read_from_str(ctx, str);
1665 str = "{ [10] }";
1666 set = isl_set_read_from_str(ctx, str, 0);
1667 pwqp1 = isl_pw_qpolynomial_gist(pwqp1, set);
1668 str = "{ [i] -> 16 }";
1669 pwqp2 = isl_pw_qpolynomial_read_from_str(ctx, str);
1670
1671 pwqp1 = isl_pw_qpolynomial_sub(pwqp1, pwqp2);
1672
1673 assert(isl_pw_qpolynomial_is_zero(pwqp1));
1674
1675 isl_pw_qpolynomial_free(pwqp1);
1676
1677 str = "{ [i] -> ([(i)/2]) }";
1678 pwqp1 = isl_pw_qpolynomial_read_from_str(ctx, str);
1679 str = "{ [k] : exists a : k = 2a+1 }";
1680 set = isl_set_read_from_str(ctx, str, 0);
1681 pwqp1 = isl_pw_qpolynomial_gist(pwqp1, set);
1682 str = "{ [i] -> -1/2 + 1/2 * i }";
1683 pwqp2 = isl_pw_qpolynomial_read_from_str(ctx, str);
1684
1685 pwqp1 = isl_pw_qpolynomial_sub(pwqp1, pwqp2);
1686
1687 assert(isl_pw_qpolynomial_is_zero(pwqp1));
1688
1689 isl_pw_qpolynomial_free(pwqp1);
1690
1691 str = "{ [i] -> ([([i/2] + [i/2])/5]) }";
1692 pwqp1 = isl_pw_qpolynomial_read_from_str(ctx, str);
1693 str = "{ [i] -> ([(2 * [i/2])/5]) }";
1694 pwqp2 = isl_pw_qpolynomial_read_from_str(ctx, str);
1695
1696 pwqp1 = isl_pw_qpolynomial_sub(pwqp1, pwqp2);
1697
1698 assert(isl_pw_qpolynomial_is_zero(pwqp1));
1699
1700 isl_pw_qpolynomial_free(pwqp1);
1701
1702 str = "{ [x] -> ([x/2] + [(x+1)/2]) }";
1703 pwqp1 = isl_pw_qpolynomial_read_from_str(ctx, str);
1704 str = "{ [x] -> x }";
1705 pwqp2 = isl_pw_qpolynomial_read_from_str(ctx, str);
1706
1707 pwqp1 = isl_pw_qpolynomial_sub(pwqp1, pwqp2);
1708
1709 assert(isl_pw_qpolynomial_is_zero(pwqp1));
1710
1711 isl_pw_qpolynomial_free(pwqp1);
1712
1713 str = "{ [i] -> ([i/2]) : i >= 0; [i] -> ([i/3]) : i < 0 }";
1714 pwqp1 = isl_pw_qpolynomial_read_from_str(ctx, str);
1715 pwqp2 = isl_pw_qpolynomial_read_from_str(ctx, str);
1716 pwqp1 = isl_pw_qpolynomial_coalesce(pwqp1);
1717 pwqp1 = isl_pw_qpolynomial_sub(pwqp1, pwqp2);
1718 assert(isl_pw_qpolynomial_is_zero(pwqp1));
1719 isl_pw_qpolynomial_free(pwqp1);
1720 }
1721
1722 void test_split_periods(isl_ctx *ctx)
1723 {
1724 const char *str;
1725 isl_pw_qpolynomial *pwqp;
1726
1727 str = "{ [U,V] -> 1/3 * U + 2/3 * V - [(U + 2V)/3] + [U/2] : "
1728 "U + 2V + 3 >= 0 and - U -2V >= 0 and - U + 10 >= 0 and "
1729 "U >= 0; [U,V] -> U^2 : U >= 100 }";
1730 pwqp = isl_pw_qpolynomial_read_from_str(ctx, str);
1731
1732 pwqp = isl_pw_qpolynomial_split_periods(pwqp, 2);
1733 assert(pwqp);
1734
1735 isl_pw_qpolynomial_free(pwqp);
1736 }
1737
1738 void test_union(isl_ctx *ctx)
1739 {
1740 const char *str;
1741 isl_union_set *uset1, *uset2;
1742 isl_union_map *umap1, *umap2;
1743
1744 str = "{ [i] : 0 <= i <= 1 }";
1745 uset1 = isl_union_set_read_from_str(ctx, str);
1746 str = "{ [1] -> [0] }";
1747 umap1 = isl_union_map_read_from_str(ctx, str);
1748
1749 umap2 = isl_union_set_lex_gt_union_set(isl_union_set_copy(uset1), uset1);
1750 assert(isl_union_map_is_equal(umap1, umap2));
1751
1752 isl_union_map_free(umap1);
1753 isl_union_map_free(umap2);
1754
1755 str = "{ A[i] -> B[i]; B[i] -> C[i]; A[0] -> C[1] }";
1756 umap1 = isl_union_map_read_from_str(ctx, str);
1757 str = "{ A[i]; B[i] }";
1758 uset1 = isl_union_set_read_from_str(ctx, str);
1759
1760 uset2 = isl_union_map_domain(umap1);
1761
1762 assert(isl_union_set_is_equal(uset1, uset2));
1763
1764 isl_union_set_free(uset1);
1765 isl_union_set_free(uset2);
1766 }
1767
1768 void test_bound(isl_ctx *ctx)
1769 {
1770 const char *str;
1771 isl_pw_qpolynomial *pwqp;
1772 isl_pw_qpolynomial_fold *pwf;
1773
1774 str = "{ [[a, b, c, d] -> [e]] -> 0 }";
1775 pwqp = isl_pw_qpolynomial_read_from_str(ctx, str);
1776 pwf = isl_pw_qpolynomial_bound(pwqp, isl_fold_max, NULL);
1777 assert(isl_pw_qpolynomial_fold_dim(pwf, isl_dim_set) == 4);
1778 isl_pw_qpolynomial_fold_free(pwf);
1779
1780 str = "{ [[x]->[x]] -> 1 : exists a : x = 2 a }";
1781 pwqp = isl_pw_qpolynomial_read_from_str(ctx, str);
1782 pwf = isl_pw_qpolynomial_bound(pwqp, isl_fold_max, NULL);
1783 assert(isl_pw_qpolynomial_fold_dim(pwf, isl_dim_set) == 1);
1784 isl_pw_qpolynomial_fold_free(pwf);
1785 }
1786
1787 void test_lift(isl_ctx *ctx)
1788 {
1789 const char *str;
1790 isl_basic_map *bmap;
1791 isl_basic_set *bset;
1792
1793 str = "{ [i0] : exists e0 : i0 = 4e0 }";
1794 bset = isl_basic_set_read_from_str(ctx, str, 0);
1795 bset = isl_basic_set_lift(bset);
1796 bmap = isl_basic_map_from_range(bset);
1797 bset = isl_basic_map_domain(bmap);
1798 isl_basic_set_free(bset);
1799 }
1800
1801 void test_subset(isl_ctx *ctx)
1802 {
1803 const char *str;
1804 isl_set *set1, *set2;
1805
1806 str = "{ [112, 0] }";
1807 set1 = isl_set_read_from_str(ctx, str, 0);
1808 str = "{ [i0, i1] : exists (e0 = [(i0 - i1)/16], e1: "
1809 "16e0 <= i0 - i1 and 16e0 >= -15 + i0 - i1 and "
1810 "16e1 <= i1 and 16e0 >= -i1 and 16e1 >= -i0 + i1) }";
1811 set2 = isl_set_read_from_str(ctx, str, 0);
1812 assert(isl_set_is_subset(set1, set2));
1813 isl_set_free(set1);
1814 isl_set_free(set2);
1815 }
1816
1817 void test_factorize(isl_ctx *ctx)
1818 {
1819 const char *str;
1820 isl_basic_set *bset;
1821 isl_factorizer *f;
1822
1823 str = "{ [i0, i1, i2, i3, i4, i5, i6, i7] : 3i5 <= 2 - 2i0 and "
1824 "i0 >= -2 and i6 >= 1 + i3 and i7 >= 0 and 3i5 >= -2i0 and "
1825 "2i4 <= i2 and i6 >= 1 + 2i0 + 3i1 and i4 <= -1 and "
1826 "i6 >= 1 + 2i0 + 3i5 and i6 <= 2 + 2i0 + 3i5 and "
1827 "3i5 <= 2 - 2i0 - i2 + 3i4 and i6 <= 2 + 2i0 + 3i1 and "
1828 "i0 <= -1 and i7 <= i2 + i3 - 3i4 - i6 and "
1829 "3i5 >= -2i0 - i2 + 3i4 }";
1830 bset = isl_basic_set_read_from_str(ctx, str, 0);
1831 f = isl_basic_set_factorizer(bset);
1832 assert(f);
1833 isl_basic_set_free(bset);
1834 isl_factorizer_free(f);
1835
1836 str = "{ [i0, i1, i2, i3, i4, i5, i6, i7, i8, i9, i10, i11, i12] : "
1837 "i12 <= 2 + i0 - i11 and 2i8 >= -i4 and i11 >= i1 and "
1838 "3i5 <= -i2 and 2i11 >= -i4 - 2i7 and i11 <= 3 + i0 + 3i9 and "
1839 "i11 <= -i4 - 2i7 and i12 >= -i10 and i2 >= -2 and "
1840 "i11 >= i1 + 3i10 and i11 >= 1 + i0 + 3i9 and "
1841 "i11 <= 1 - i4 - 2i8 and 6i6 <= 6 - i2 and 3i6 >= 1 - i2 and "
1842 "i11 <= 2 + i1 and i12 <= i4 + i11 and i12 >= i0 - i11 and "
1843 "3i5 >= -2 - i2 and i12 >= -1 + i4 + i11 and 3i3 <= 3 - i2 and "
1844 "9i6 <= 11 - i2 + 6i5 and 3i3 >= 1 - i2 and "
1845 "9i6 <= 5 - i2 + 6i3 and i12 <= -1 and i2 <= 0 }";
1846 bset = isl_basic_set_read_from_str(ctx, str, 0);
1847 f = isl_basic_set_factorizer(bset);
1848 assert(f);
1849 isl_basic_set_free(bset);
1850 isl_factorizer_free(f);
1851 }
1852
1853 static int check_injective(__isl_take isl_map *map, void *user)
1854 {
1855 int *injective = user;
1856
1857 *injective = isl_map_is_injective(map);
1858 isl_map_free(map);
1859
1860 if (*injective < 0 || !*injective)
1861 return -1;
1862
1863 return 0;
1864 }
1865
1866 int test_one_schedule(isl_ctx *ctx, const char *d, const char *w,
1867 const char *r, const char *s, int tilable, int parallel)
1868 {
1869 int i;
1870 isl_union_set *D;
1871 isl_union_map *W, *R, *S;
1872 isl_union_map *empty;
1873 isl_union_map *dep_raw, *dep_war, *dep_waw, *dep;
1874 isl_union_map *validity, *proximity;
1875 isl_union_map *schedule;
1876 isl_union_map *test;
1877 isl_union_set *delta;
1878 isl_union_set *domain;
1879 isl_set *delta_set;
1880 isl_set *slice;
1881 isl_set *origin;
1882 isl_schedule *sched;
1883 int is_nonneg, is_parallel, is_tilable, is_injection, is_complete;
1884
1885 D = isl_union_set_read_from_str(ctx, d);
1886 W = isl_union_map_read_from_str(ctx, w);
1887 R = isl_union_map_read_from_str(ctx, r);
1888 S = isl_union_map_read_from_str(ctx, s);
1889
1890 W = isl_union_map_intersect_domain(W, isl_union_set_copy(D));
1891 R = isl_union_map_intersect_domain(R, isl_union_set_copy(D));
1892
1893 empty = isl_union_map_empty(isl_union_map_get_dim(S));
1894 isl_union_map_compute_flow(isl_union_map_copy(R),
1895 isl_union_map_copy(W), empty,
1896 isl_union_map_copy(S),
1897 &dep_raw, NULL, NULL, NULL);
1898 isl_union_map_compute_flow(isl_union_map_copy(W),
1899 isl_union_map_copy(W),
1900 isl_union_map_copy(R),
1901 isl_union_map_copy(S),
1902 &dep_waw, &dep_war, NULL, NULL);
1903
1904 dep = isl_union_map_union(dep_waw, dep_war);
1905 dep = isl_union_map_union(dep, dep_raw);
1906 validity = isl_union_map_copy(dep);
1907 proximity = isl_union_map_copy(dep);
1908
1909 sched = isl_union_set_compute_schedule(isl_union_set_copy(D),
1910 validity, proximity);
1911 schedule = isl_schedule_get_map(sched);
1912 isl_schedule_free(sched);
1913 isl_union_map_free(W);
1914 isl_union_map_free(R);
1915 isl_union_map_free(S);
1916
1917 is_injection = 1;
1918 isl_union_map_foreach_map(schedule, &check_injective, &is_injection);
1919
1920 domain = isl_union_map_domain(isl_union_map_copy(schedule));
1921 is_complete = isl_union_set_is_subset(D, domain);
1922 isl_union_set_free(D);
1923 isl_union_set_free(domain);
1924
1925 test = isl_union_map_reverse(isl_union_map_copy(schedule));
1926 test = isl_union_map_apply_range(test, dep);
1927 test = isl_union_map_apply_range(test, schedule);
1928
1929 delta = isl_union_map_deltas(test);
1930 if (isl_union_set_n_set(delta) == 0) {
1931 is_tilable = 1;
1932 is_parallel = 1;
1933 is_nonneg = 1;
1934 } else {
1935 delta_set = isl_union_set_copy_set(delta);
1936
1937 slice = isl_set_universe(isl_set_get_dim(delta_set));
1938 for (i = 0; i < tilable; ++i)
1939 slice = isl_set_lower_bound_si(slice, isl_dim_set, i, 0);
1940 is_tilable = isl_set_is_subset(delta_set, slice);
1941 isl_set_free(slice);
1942
1943 slice = isl_set_universe(isl_set_get_dim(delta_set));
1944 for (i = 0; i < parallel; ++i)
1945 slice = isl_set_fix_si(slice, isl_dim_set, i, 0);
1946 is_parallel = isl_set_is_subset(delta_set, slice);
1947 isl_set_free(slice);
1948
1949 origin = isl_set_universe(isl_set_get_dim(delta_set));
1950 for (i = 0; i < isl_set_dim(origin, isl_dim_set); ++i)
1951 origin = isl_set_fix_si(origin, isl_dim_set, i, 0);
1952
1953 delta_set = isl_set_union(delta_set, isl_set_copy(origin));
1954 delta_set = isl_set_lexmin(delta_set);
1955
1956 is_nonneg = isl_set_is_equal(delta_set, origin);
1957
1958 isl_set_free(origin);
1959 isl_set_free(delta_set);
1960 }
1961 isl_union_set_free(delta);
1962
1963 if (is_nonneg < 0 || is_parallel < 0 || is_tilable < 0 ||
1964 is_injection < 0 || is_complete < 0)
1965 return -1;
1966 if (!is_complete)
1967 isl_die(ctx, isl_error_unknown,
1968 "generated schedule incomplete", return -1);
1969 if (!is_injection)
1970 isl_die(ctx, isl_error_unknown,
1971 "generated schedule not injective on each statement",
1972 return -1);
1973 if (!is_nonneg)
1974 isl_die(ctx, isl_error_unknown,
1975 "negative dependences in generated schedule",
1976 return -1);
1977 if (!is_tilable)
1978 isl_die(ctx, isl_error_unknown,
1979 "generated schedule not as tilable as expected",
1980 return -1);
1981 if (!is_parallel)
1982 isl_die(ctx, isl_error_unknown,
1983 "generated schedule not as parallel as expected",
1984 return -1);
1985
1986 return 0;
1987 }
1988
1989 int test_special_schedule(isl_ctx *ctx)
1990 {
1991 const char *str;
1992 isl_union_set *dom;
1993 isl_union_map *empty;
1994 isl_union_map *dep;
1995 isl_union_map *sched1, *sched2;
1996 isl_schedule *schedule;
1997 int equal;
1998
1999 str = "{ S[i,j] : 0 <= i <= 10 }";
2000 dom = isl_union_set_read_from_str(ctx, str);
2001 str = "{ S[i,j] -> S[i+1,j] : 0 <= i,j <= 10 }";
2002 dep = isl_union_map_read_from_str(ctx, str);
2003 empty = isl_union_map_read_from_str(ctx, "{}");
2004 schedule = isl_union_set_compute_schedule(dom, empty, dep);
2005 sched1 = isl_schedule_get_map(schedule);
2006 isl_schedule_free(schedule);
2007
2008 str = "{ S[i, j] -> [j, i] }";
2009 sched2 = isl_union_map_read_from_str(ctx, str);
2010
2011 equal = isl_union_map_is_equal(sched1, sched2);
2012 isl_union_map_free(sched1);
2013 isl_union_map_free(sched2);
2014
2015 if (equal < 0)
2016 return -1;
2017 if (!equal)
2018 isl_die(ctx, isl_error_unknown, "unexpected schedule",
2019 return -1);
2020
2021 return 0;
2022 }
2023
2024 int test_schedule(isl_ctx *ctx)
2025 {
2026 const char *D, *W, *R, *S;
2027
2028 /* Jacobi */
2029 D = "[T,N] -> { S1[t,i] : 1 <= t <= T and 2 <= i <= N - 1 }";
2030 W = "{ S1[t,i] -> a[t,i] }";
2031 R = "{ S1[t,i] -> a[t-1,i]; S1[t,i] -> a[t-1,i-1]; "
2032 "S1[t,i] -> a[t-1,i+1] }";
2033 S = "{ S1[t,i] -> [t,i] }";
2034 if (test_one_schedule(ctx, D, W, R, S, 2, 0) < 0)
2035 return -1;
2036
2037 /* Fig. 5 of CC2008 */
2038 D = "[N] -> { S_0[i, j] : i >= 0 and i <= -1 + N and j >= 2 and "
2039 "j <= -1 + N }";
2040 W = "[N] -> { S_0[i, j] -> a[i, j] : i >= 0 and i <= -1 + N and "
2041 "j >= 2 and j <= -1 + N }";
2042 R = "[N] -> { S_0[i, j] -> a[j, i] : i >= 0 and i <= -1 + N and "
2043 "j >= 2 and j <= -1 + N; "
2044 "S_0[i, j] -> a[i, -1 + j] : i >= 0 and i <= -1 + N and "
2045 "j >= 2 and j <= -1 + N }";
2046 S = "[N] -> { S_0[i, j] -> [0, i, 0, j, 0] }";
2047 if (test_one_schedule(ctx, D, W, R, S, 2, 0) < 0)
2048 return -1;
2049
2050 D = "{ S1[i] : 0 <= i <= 10; S2[i] : 0 <= i <= 9 }";
2051 W = "{ S1[i] -> a[i] }";
2052 R = "{ S2[i] -> a[i+1] }";
2053 S = "{ S1[i] -> [0,i]; S2[i] -> [1,i] }";
2054 if (test_one_schedule(ctx, D, W, R, S, 1, 1) < 0)
2055 return -1;
2056
2057 D = "{ S1[i] : 0 <= i < 10; S2[i] : 0 <= i < 10 }";
2058 W = "{ S1[i] -> a[i] }";
2059 R = "{ S2[i] -> a[9-i] }";
2060 S = "{ S1[i] -> [0,i]; S2[i] -> [1,i] }";
2061 if (test_one_schedule(ctx, D, W, R, S, 1, 1) < 0)
2062 return -1;
2063
2064 D = "[N] -> { S1[i] : 0 <= i < N; S2[i] : 0 <= i < N }";
2065 W = "{ S1[i] -> a[i] }";
2066 R = "[N] -> { S2[i] -> a[N-1-i] }";
2067 S = "{ S1[i] -> [0,i]; S2[i] -> [1,i] }";
2068 if (test_one_schedule(ctx, D, W, R, S, 1, 1) < 0)
2069 return -1;
2070
2071 D = "{ S1[i] : 0 < i < 10; S2[i] : 0 <= i < 10 }";
2072 W = "{ S1[i] -> a[i]; S2[i] -> b[i] }";
2073 R = "{ S2[i] -> a[i]; S1[i] -> b[i-1] }";
2074 S = "{ S1[i] -> [i,0]; S2[i] -> [i,1] }";
2075 if (test_one_schedule(ctx, D, W, R, S, 0, 0) < 0)
2076 return -1;
2077
2078 D = "[N] -> { S1[i] : 1 <= i <= N; S2[i,j] : 1 <= i,j <= N }";
2079 W = "{ S1[i] -> a[0,i]; S2[i,j] -> a[i,j] }";
2080 R = "{ S2[i,j] -> a[i-1,j] }";
2081 S = "{ S1[i] -> [0,i,0]; S2[i,j] -> [1,i,j] }";
2082 if (test_one_schedule(ctx, D, W, R, S, 2, 1) < 0)
2083 return -1;
2084
2085 D = "[N] -> { S1[i] : 1 <= i <= N; S2[i,j] : 1 <= i,j <= N }";
2086 W = "{ S1[i] -> a[i,0]; S2[i,j] -> a[i,j] }";
2087 R = "{ S2[i,j] -> a[i,j-1] }";
2088 S = "{ S1[i] -> [0,i,0]; S2[i,j] -> [1,i,j] }";
2089 if (test_one_schedule(ctx, D, W, R, S, 2, 1) < 0)
2090 return -1;
2091
2092 D = "[N] -> { S_0[]; S_1[i] : i >= 0 and i <= -1 + N; S_2[] }";
2093 W = "[N] -> { S_0[] -> a[0]; S_2[] -> b[0]; "
2094 "S_1[i] -> a[1 + i] : i >= 0 and i <= -1 + N }";
2095 R = "[N] -> { S_2[] -> a[N]; S_1[i] -> a[i] : i >= 0 and i <= -1 + N }";
2096 S = "[N] -> { S_1[i] -> [1, i, 0]; S_2[] -> [2, 0, 1]; "
2097 "S_0[] -> [0, 0, 0] }";
2098 if (test_one_schedule(ctx, D, W, R, S, 1, 0) < 0)
2099 return -1;
2100 ctx->opt->schedule_parametric = 0;
2101 if (test_one_schedule(ctx, D, W, R, S, 0, 0) < 0)
2102 return -1;
2103 ctx->opt->schedule_parametric = 1;
2104
2105 D = "[N] -> { S1[i] : 1 <= i <= N; S2[i] : 1 <= i <= N; "
2106 "S3[i,j] : 1 <= i,j <= N; S4[i] : 1 <= i <= N }";
2107 W = "{ S1[i] -> a[i,0]; S2[i] -> a[0,i]; S3[i,j] -> a[i,j] }";
2108 R = "[N] -> { S3[i,j] -> a[i-1,j]; S3[i,j] -> a[i,j-1]; "
2109 "S4[i] -> a[i,N] }";
2110 S = "{ S1[i] -> [0,i,0]; S2[i] -> [1,i,0]; S3[i,j] -> [2,i,j]; "
2111 "S4[i] -> [4,i,0] }";
2112 if (test_one_schedule(ctx, D, W, R, S, 2, 0) < 0)
2113 return -1;
2114
2115 D = "[N] -> { S_0[i, j] : i >= 1 and i <= N and j >= 1 and j <= N }";
2116 W = "[N] -> { S_0[i, j] -> s[0] : i >= 1 and i <= N and j >= 1 and "
2117 "j <= N }";
2118 R = "[N] -> { S_0[i, j] -> s[0] : i >= 1 and i <= N and j >= 1 and "
2119 "j <= N; "
2120 "S_0[i, j] -> a[i, j] : i >= 1 and i <= N and j >= 1 and "
2121 "j <= N }";
2122 S = "[N] -> { S_0[i, j] -> [0, i, 0, j, 0] }";
2123 if (test_one_schedule(ctx, D, W, R, S, 0, 0) < 0)
2124 return -1;
2125
2126 D = "[N] -> { S_0[t] : t >= 0 and t <= -1 + N; "
2127 " S_2[t] : t >= 0 and t <= -1 + N; "
2128 " S_1[t, i] : t >= 0 and t <= -1 + N and i >= 0 and "
2129 "i <= -1 + N }";
2130 W = "[N] -> { S_0[t] -> a[t, 0] : t >= 0 and t <= -1 + N; "
2131 " S_2[t] -> b[t] : t >= 0 and t <= -1 + N; "
2132 " S_1[t, i] -> a[t, 1 + i] : t >= 0 and t <= -1 + N and "
2133 "i >= 0 and i <= -1 + N }";
2134 R = "[N] -> { S_1[t, i] -> a[t, i] : t >= 0 and t <= -1 + N and "
2135 "i >= 0 and i <= -1 + N; "
2136 " S_2[t] -> a[t, N] : t >= 0 and t <= -1 + N }";
2137 S = "[N] -> { S_2[t] -> [0, t, 2]; S_1[t, i] -> [0, t, 1, i, 0]; "
2138 " S_0[t] -> [0, t, 0] }";
2139
2140 if (test_one_schedule(ctx, D, W, R, S, 2, 1) < 0)
2141 return -1;
2142 ctx->opt->schedule_parametric = 0;
2143 if (test_one_schedule(ctx, D, W, R, S, 0, 0) < 0)
2144 return -1;
2145 ctx->opt->schedule_parametric = 1;
2146
2147 D = "[N] -> { S1[i,j] : 0 <= i,j < N; S2[i,j] : 0 <= i,j < N }";
2148 S = "{ S1[i,j] -> [0,i,j]; S2[i,j] -> [1,i,j] }";
2149 if (test_one_schedule(ctx, D, "{}", "{}", S, 2, 2) < 0)
2150 return -1;
2151
2152 D = "[M, N] -> { S_1[i] : i >= 0 and i <= -1 + M; "
2153 "S_0[i, j] : i >= 0 and i <= -1 + M and j >= 0 and j <= -1 + N }";
2154 W = "[M, N] -> { S_0[i, j] -> a[j] : i >= 0 and i <= -1 + M and "
2155 "j >= 0 and j <= -1 + N; "
2156 "S_1[i] -> b[0] : i >= 0 and i <= -1 + M }";
2157 R = "[M, N] -> { S_0[i, j] -> a[0] : i >= 0 and i <= -1 + M and "
2158 "j >= 0 and j <= -1 + N; "
2159 "S_1[i] -> b[0] : i >= 0 and i <= -1 + M }";
2160 S = "[M, N] -> { S_1[i] -> [1, i, 0]; S_0[i, j] -> [0, i, 0, j, 0] }";
2161 if (test_one_schedule(ctx, D, W, R, S, 0, 0) < 0)
2162 return -1;
2163
2164 D = "{ S_0[i] : i >= 0 }";
2165 W = "{ S_0[i] -> a[i] : i >= 0 }";
2166 R = "{ S_0[i] -> a[0] : i >= 0 }";
2167 S = "{ S_0[i] -> [0, i, 0] }";
2168 if (test_one_schedule(ctx, D, W, R, S, 0, 0) < 0)
2169 return -1;
2170
2171 D = "{ S_0[i] : i >= 0; S_1[i] : i >= 0 }";
2172 W = "{ S_0[i] -> a[i] : i >= 0; S_1[i] -> b[i] : i >= 0 }";
2173 R = "{ S_0[i] -> b[0] : i >= 0; S_1[i] -> a[i] : i >= 0 }";
2174 S = "{ S_1[i] -> [0, i, 1]; S_0[i] -> [0, i, 0] }";
2175 if (test_one_schedule(ctx, D, W, R, S, 0, 0) < 0)
2176 return -1;
2177
2178 return test_special_schedule(ctx);
2179 }
2180
2181 int test_plain_injective(isl_ctx *ctx, const char *str, int injective)
2182 {
2183 isl_union_map *umap;
2184 int test;
2185
2186 umap = isl_union_map_read_from_str(ctx, str);
2187 test = isl_union_map_plain_is_injective(umap);
2188 isl_union_map_free(umap);
2189 if (test < 0)
2190 return -1;
2191 if (test == injective)
2192 return 0;
2193 if (injective)
2194 isl_die(ctx, isl_error_unknown,
2195 "map not detected as injective", return -1);
2196 else
2197 isl_die(ctx, isl_error_unknown,
2198 "map detected as injective", return -1);
2199 }
2200
2201 int test_injective(isl_ctx *ctx)
2202 {
2203 const char *str;
2204
2205 if (test_plain_injective(ctx, "{S[i,j] -> A[0]; T[i,j] -> B[1]}", 0))
2206 return -1;
2207 if (test_plain_injective(ctx, "{S[] -> A[0]; T[] -> B[0]}", 1))
2208 return -1;
2209 if (test_plain_injective(ctx, "{S[] -> A[0]; T[] -> A[1]}", 1))
2210 return -1;
2211 if (test_plain_injective(ctx, "{S[] -> A[0]; T[] -> A[0]}", 0))
2212 return -1;
2213 if (test_plain_injective(ctx, "{S[i] -> A[i,0]; T[i] -> A[i,1]}", 1))
2214 return -1;
2215 if (test_plain_injective(ctx, "{S[i] -> A[i]; T[i] -> A[i]}", 0))
2216 return -1;
2217 if (test_plain_injective(ctx, "{S[] -> A[0,0]; T[] -> A[0,1]}", 1))
2218 return -1;
2219 if (test_plain_injective(ctx, "{S[] -> A[0,0]; T[] -> A[1,0]}", 1))
2220 return -1;
2221
2222 str = "{S[] -> A[0,0]; T[] -> A[0,1]; U[] -> A[1,0]}";
2223 if (test_plain_injective(ctx, str, 1))
2224 return -1;
2225 str = "{S[] -> A[0,0]; T[] -> A[0,1]; U[] -> A[0,0]}";
2226 if (test_plain_injective(ctx, str, 0))
2227 return -1;
2228
2229 return 0;
2230 }
2231
2232 int test_aff(isl_ctx *ctx)
2233 {
2234 const char *str;
2235 isl_set *set;
2236 isl_dim *dim;
2237 isl_local_space *ls;
2238 isl_aff *aff;
2239 int zero;
2240
2241 dim = isl_dim_set_alloc(ctx, 0, 1);
2242 ls = isl_local_space_from_dim(dim);
2243 aff = isl_aff_zero(ls);
2244
2245 aff = isl_aff_add_coefficient_si(aff, isl_dim_set, 0, 1);
2246 aff = isl_aff_scale_down_ui(aff, 3);
2247 aff = isl_aff_floor(aff);
2248 aff = isl_aff_add_coefficient_si(aff, isl_dim_set, 0, 1);
2249 aff = isl_aff_scale_down_ui(aff, 2);
2250 aff = isl_aff_floor(aff);
2251 aff = isl_aff_add_coefficient_si(aff, isl_dim_set, 0, 1);
2252
2253 str = "{ [10] }";
2254 set = isl_set_read_from_str(ctx, str, 0);
2255 aff = isl_aff_gist(aff, set);
2256
2257 aff = isl_aff_add_constant_si(aff, -16);
2258 zero = isl_aff_plain_is_zero(aff);
2259 isl_aff_free(aff);
2260
2261 if (zero < 0)
2262 return -1;
2263 if (!zero)
2264 isl_die(ctx, isl_error_unknown, "unexpected result", return -1);
2265
2266 return 0;
2267 }
2268
2269 int main()
2270 {
2271 struct isl_ctx *ctx;
2272
2273 srcdir = getenv("srcdir");
2274 assert(srcdir);
2275
2276 ctx = isl_ctx_alloc();
2277 if (test_aff(ctx) < 0)
2278 goto error;
2279 if (test_injective(ctx) < 0)
2280 goto error;
2281 if (test_schedule(ctx) < 0)
2282 goto error;
2283 test_factorize(ctx);
2284 test_subset(ctx);
2285 test_lift(ctx);
2286 test_bound(ctx);
2287 test_union(ctx);
2288 test_split_periods(ctx);
2289 test_parse(ctx);
2290 test_pwqp(ctx);
2291 test_lex(ctx);
2292 if (test_sv(ctx) < 0)
2293 goto error;
2294 test_bijective(ctx);
2295 test_dep(ctx);
2296 test_read(ctx);
2297 test_bounded(ctx);
2298 test_construction(ctx);
2299 test_dim(ctx);
2300 test_div(ctx);
2301 test_application(ctx);
2302 test_affine_hull(ctx);
2303 test_convex_hull(ctx);
2304 test_gist(ctx);
2305 test_coalesce(ctx);
2306 test_closure(ctx);
2307 test_lexmin(ctx);
2308 isl_ctx_free(ctx);
2309 return 0;
2310 error:
2311 isl_ctx_free(ctx);
2312 return -1;
2313 }
Integer set library