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add doc/SubmittingPatches to the distribution
[isl.git] / isl_test.c
blob8bf31f3645fe1b9664c5af2a552f12908f81e4a7
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 #define ARRAY_SIZE(array) (sizeof(array)/sizeof(*array))
27
28 static char *srcdir;
29
30 static char *get_filename(isl_ctx *ctx, const char *name, const char *suffix) {
31 char *filename;
32 int length;
33 char *pattern = "%s/test_inputs/%s.%s";
34
35 length = strlen(pattern) - 6 + strlen(srcdir) + strlen(name)
36 + strlen(suffix) + 1;
37 filename = isl_alloc_array(ctx, char, length);
38
39 if (!filename)
40 return NULL;
41
42 sprintf(filename, pattern, srcdir, name, suffix);
43
44 return filename;
45 }
46
47 void test_parse_map(isl_ctx *ctx, const char *str)
48 {
49 isl_map *map;
50
51 map = isl_map_read_from_str(ctx, str);
52 assert(map);
53 isl_map_free(map);
54 }
55
56 int test_parse_map_equal(isl_ctx *ctx, const char *str, const char *str2)
57 {
58 isl_map *map, *map2;
59 int equal;
60
61 map = isl_map_read_from_str(ctx, str);
62 map2 = isl_map_read_from_str(ctx, str2);
63 equal = isl_map_is_equal(map, map2);
64 isl_map_free(map);
65 isl_map_free(map2);
66
67 if (equal < 0)
68 return -1;
69 if (!equal)
70 isl_die(ctx, isl_error_unknown, "maps not equal",
71 return -1);
72
73 return 0;
74 }
75
76 void test_parse_pwqp(isl_ctx *ctx, const char *str)
77 {
78 isl_pw_qpolynomial *pwqp;
79
80 pwqp = isl_pw_qpolynomial_read_from_str(ctx, str);
81 assert(pwqp);
82 isl_pw_qpolynomial_free(pwqp);
83 }
84
85 static void test_parse_pwaff(isl_ctx *ctx, const char *str)
86 {
87 isl_pw_aff *pwaff;
88
89 pwaff = isl_pw_aff_read_from_str(ctx, str);
90 assert(pwaff);
91 isl_pw_aff_free(pwaff);
92 }
93
94 int test_parse(struct isl_ctx *ctx)
95 {
96 isl_map *map, *map2;
97 const char *str, *str2;
98
99 str = "{ [i] -> [-i] }";
100 map = isl_map_read_from_str(ctx, str);
101 assert(map);
102 isl_map_free(map);
103
104 str = "{ A[i] -> L[([i/3])] }";
105 map = isl_map_read_from_str(ctx, str);
106 assert(map);
107 isl_map_free(map);
108
109 test_parse_map(ctx, "{[[s] -> A[i]] -> [[s+1] -> A[i]]}");
110 test_parse_map(ctx, "{ [p1, y1, y2] -> [2, y1, y2] : "
111 "p1 = 1 && (y1 <= y2 || y2 = 0) }");
112
113 str = "{ [x,y] : [([x/2]+y)/3] >= 1 }";
114 str2 = "{ [x, y] : 2y >= 6 - x }";
115 if (test_parse_map_equal(ctx, str, str2) < 0)
116 return -1;
117
118 if (test_parse_map_equal(ctx, "{ [x,y] : x <= min(y, 2*y+3) }",
119 "{ [x,y] : x <= y, 2*y + 3 }") < 0)
120 return -1;
121 str = "{ [x, y] : (y <= x and y >= -3) or (2y <= -3 + x and y <= -4) }";
122 if (test_parse_map_equal(ctx, "{ [x,y] : x >= min(y, 2*y+3) }",
123 str) < 0)
124 return -1;
125
126 str = "{[new,old] -> [new+1-2*[(new+1)/2],old+1-2*[(old+1)/2]]}";
127 map = isl_map_read_from_str(ctx, str);
128 str = "{ [new, old] -> [o0, o1] : "
129 "exists (e0 = [(-1 - new + o0)/2], e1 = [(-1 - old + o1)/2]: "
130 "2e0 = -1 - new + o0 and 2e1 = -1 - old + o1 and o0 >= 0 and "
131 "o0 <= 1 and o1 >= 0 and o1 <= 1) }";
132 map2 = isl_map_read_from_str(ctx, str);
133 assert(isl_map_is_equal(map, map2));
134 isl_map_free(map);
135 isl_map_free(map2);
136
137 str = "{[new,old] -> [new+1-2*[(new+1)/2],old+1-2*[(old+1)/2]]}";
138 map = isl_map_read_from_str(ctx, str);
139 str = "{[new,old] -> [(new+1)%2,(old+1)%2]}";
140 map2 = isl_map_read_from_str(ctx, str);
141 assert(isl_map_is_equal(map, map2));
142 isl_map_free(map);
143 isl_map_free(map2);
144
145 str = "[n] -> { [c1] : c1>=0 and c1<=floord(n-4,3) }";
146 str2 = "[n] -> { [c1] : c1 >= 0 and 3c1 <= -4 + n }";
147 if (test_parse_map_equal(ctx, str, str2) < 0)
148 return -1;
149
150 str = "{ [i,j] -> [i] : i < j; [i,j] -> [j] : j <= i }";
151 str2 = "{ [i,j] -> [min(i,j)] }";
152 if (test_parse_map_equal(ctx, str, str2) < 0)
153 return -1;
154
155 str = "{ [i,j] : i != j }";
156 str2 = "{ [i,j] : i < j or i > j }";
157 if (test_parse_map_equal(ctx, str, str2) < 0)
158 return -1;
159
160 str = "{ [i,j] : (i+1)*2 >= j }";
161 str2 = "{ [i, j] : j <= 2 + 2i }";
162 if (test_parse_map_equal(ctx, str, str2) < 0)
163 return -1;
164
165 str = "{ [i] -> [i > 0 ? 4 : 5] }";
166 str2 = "{ [i] -> [5] : i <= 0; [i] -> [4] : i >= 1 }";
167 if (test_parse_map_equal(ctx, str, str2) < 0)
168 return -1;
169
170 str = "[N=2,M] -> { [i=[(M+N)/4]] }";
171 str2 = "[N, M] -> { [i] : N = 2 and 4i <= 2 + M and 4i >= -1 + M }";
172 if (test_parse_map_equal(ctx, str, str2) < 0)
173 return -1;
174
175 str = "{ [x] : x >= 0 }";
176 str2 = "{ [x] : x-0 >= 0 }";
177 if (test_parse_map_equal(ctx, str, str2) < 0)
178 return -1;
179
180 str = "{ [i] : ((i > 10)) }";
181 str2 = "{ [i] : i >= 11 }";
182 if (test_parse_map_equal(ctx, str, str2) < 0)
183 return -1;
184
185 str = "{ [i] -> [0] }";
186 str2 = "{ [i] -> [0 * i] }";
187 if (test_parse_map_equal(ctx, str, str2) < 0)
188 return -1;
189
190 test_parse_pwqp(ctx, "{ [i] -> i + [ (i + [i/3])/2 ] }");
191 test_parse_map(ctx, "{ S1[i] -> [([i/10]),i%10] : 0 <= i <= 45 }");
192 test_parse_pwaff(ctx, "{ [i] -> [i + 1] : i > 0; [a] -> [a] : a < 0 }");
193 test_parse_pwqp(ctx, "{ [x] -> ([(x)/2] * [(x)/3]) }");
194
195 if (test_parse_map_equal(ctx, "{ [a] -> [b] : (not false) }",
196 "{ [a] -> [b] : true }") < 0)
197 return -1;
198
199 return 0;
200 }
201
202 void test_read(struct isl_ctx *ctx)
203 {
204 char *filename;
205 FILE *input;
206 struct isl_basic_set *bset1, *bset2;
207 const char *str = "{[y]: Exists ( alpha : 2alpha = y)}";
208
209 filename = get_filename(ctx, "set", "omega");
210 assert(filename);
211 input = fopen(filename, "r");
212 assert(input);
213
214 bset1 = isl_basic_set_read_from_file(ctx, input);
215 bset2 = isl_basic_set_read_from_str(ctx, str);
216
217 assert(isl_basic_set_is_equal(bset1, bset2) == 1);
218
219 isl_basic_set_free(bset1);
220 isl_basic_set_free(bset2);
221 free(filename);
222
223 fclose(input);
224 }
225
226 void test_bounded(struct isl_ctx *ctx)
227 {
228 isl_set *set;
229 int bounded;
230
231 set = isl_set_read_from_str(ctx, "[n] -> {[i] : 0 <= i <= n }");
232 bounded = isl_set_is_bounded(set);
233 assert(bounded);
234 isl_set_free(set);
235
236 set = isl_set_read_from_str(ctx, "{[n, i] : 0 <= i <= n }");
237 bounded = isl_set_is_bounded(set);
238 assert(!bounded);
239 isl_set_free(set);
240
241 set = isl_set_read_from_str(ctx, "[n] -> {[i] : i <= n }");
242 bounded = isl_set_is_bounded(set);
243 assert(!bounded);
244 isl_set_free(set);
245 }
246
247 /* Construct the basic set { [i] : 5 <= i <= N } */
248 void test_construction(struct isl_ctx *ctx)
249 {
250 isl_int v;
251 isl_space *dim;
252 isl_local_space *ls;
253 struct isl_basic_set *bset;
254 struct isl_constraint *c;
255
256 isl_int_init(v);
257
258 dim = isl_space_set_alloc(ctx, 1, 1);
259 bset = isl_basic_set_universe(isl_space_copy(dim));
260 ls = isl_local_space_from_space(dim);
261
262 c = isl_inequality_alloc(isl_local_space_copy(ls));
263 isl_int_set_si(v, -1);
264 isl_constraint_set_coefficient(c, isl_dim_set, 0, v);
265 isl_int_set_si(v, 1);
266 isl_constraint_set_coefficient(c, isl_dim_param, 0, v);
267 bset = isl_basic_set_add_constraint(bset, c);
268
269 c = isl_inequality_alloc(isl_local_space_copy(ls));
270 isl_int_set_si(v, 1);
271 isl_constraint_set_coefficient(c, isl_dim_set, 0, v);
272 isl_int_set_si(v, -5);
273 isl_constraint_set_constant(c, v);
274 bset = isl_basic_set_add_constraint(bset, c);
275
276 isl_local_space_free(ls);
277 isl_basic_set_free(bset);
278
279 isl_int_clear(v);
280 }
281
282 void test_dim(struct isl_ctx *ctx)
283 {
284 const char *str;
285 isl_map *map1, *map2;
286
287 map1 = isl_map_read_from_str(ctx,
288 "[n] -> { [i] -> [j] : exists (a = [i/10] : i - 10a <= n ) }");
289 map1 = isl_map_add_dims(map1, isl_dim_in, 1);
290 map2 = isl_map_read_from_str(ctx,
291 "[n] -> { [i,k] -> [j] : exists (a = [i/10] : i - 10a <= n ) }");
292 assert(isl_map_is_equal(map1, map2));
293 isl_map_free(map2);
294
295 map1 = isl_map_project_out(map1, isl_dim_in, 0, 1);
296 map2 = isl_map_read_from_str(ctx, "[n] -> { [i] -> [j] : n >= 0 }");
297 assert(isl_map_is_equal(map1, map2));
298
299 isl_map_free(map1);
300 isl_map_free(map2);
301
302 str = "[n] -> { [i] -> [] : exists a : 0 <= i <= n and i = 2 a }";
303 map1 = isl_map_read_from_str(ctx, str);
304 str = "{ [i] -> [j] : exists a : 0 <= i <= j and i = 2 a }";
305 map2 = isl_map_read_from_str(ctx, str);
306 map1 = isl_map_move_dims(map1, isl_dim_out, 0, isl_dim_param, 0, 1);
307 assert(isl_map_is_equal(map1, map2));
308
309 isl_map_free(map1);
310 isl_map_free(map2);
311 }
312
313 static int test_div(isl_ctx *ctx)
314 {
315 const char *str;
316 isl_int v;
317 isl_space *dim;
318 isl_set *set;
319 isl_local_space *ls;
320 struct isl_basic_set *bset;
321 struct isl_constraint *c;
322
323 isl_int_init(v);
324
325 /* test 1 */
326 dim = isl_space_set_alloc(ctx, 0, 3);
327 bset = isl_basic_set_universe(isl_space_copy(dim));
328 ls = isl_local_space_from_space(dim);
329
330 c = isl_equality_alloc(isl_local_space_copy(ls));
331 isl_int_set_si(v, -1);
332 isl_constraint_set_constant(c, v);
333 isl_int_set_si(v, 1);
334 isl_constraint_set_coefficient(c, isl_dim_set, 0, v);
335 isl_int_set_si(v, 3);
336 isl_constraint_set_coefficient(c, isl_dim_set, 1, v);
337 bset = isl_basic_set_add_constraint(bset, c);
338
339 c = isl_equality_alloc(isl_local_space_copy(ls));
340 isl_int_set_si(v, 1);
341 isl_constraint_set_constant(c, v);
342 isl_int_set_si(v, -1);
343 isl_constraint_set_coefficient(c, isl_dim_set, 0, v);
344 isl_int_set_si(v, 3);
345 isl_constraint_set_coefficient(c, isl_dim_set, 2, v);
346 bset = isl_basic_set_add_constraint(bset, c);
347
348 bset = isl_basic_set_project_out(bset, isl_dim_set, 1, 2);
349
350 assert(bset && bset->n_div == 1);
351 isl_local_space_free(ls);
352 isl_basic_set_free(bset);
353
354 /* test 2 */
355 dim = isl_space_set_alloc(ctx, 0, 3);
356 bset = isl_basic_set_universe(isl_space_copy(dim));
357 ls = isl_local_space_from_space(dim);
358
359 c = isl_equality_alloc(isl_local_space_copy(ls));
360 isl_int_set_si(v, 1);
361 isl_constraint_set_constant(c, v);
362 isl_int_set_si(v, -1);
363 isl_constraint_set_coefficient(c, isl_dim_set, 0, v);
364 isl_int_set_si(v, 3);
365 isl_constraint_set_coefficient(c, isl_dim_set, 1, v);
366 bset = isl_basic_set_add_constraint(bset, c);
367
368 c = isl_equality_alloc(isl_local_space_copy(ls));
369 isl_int_set_si(v, -1);
370 isl_constraint_set_constant(c, v);
371 isl_int_set_si(v, 1);
372 isl_constraint_set_coefficient(c, isl_dim_set, 0, v);
373 isl_int_set_si(v, 3);
374 isl_constraint_set_coefficient(c, isl_dim_set, 2, v);
375 bset = isl_basic_set_add_constraint(bset, c);
376
377 bset = isl_basic_set_project_out(bset, isl_dim_set, 1, 2);
378
379 assert(bset && bset->n_div == 1);
380 isl_local_space_free(ls);
381 isl_basic_set_free(bset);
382
383 /* test 3 */
384 dim = isl_space_set_alloc(ctx, 0, 3);
385 bset = isl_basic_set_universe(isl_space_copy(dim));
386 ls = isl_local_space_from_space(dim);
387
388 c = isl_equality_alloc(isl_local_space_copy(ls));
389 isl_int_set_si(v, 1);
390 isl_constraint_set_constant(c, v);
391 isl_int_set_si(v, -1);
392 isl_constraint_set_coefficient(c, isl_dim_set, 0, v);
393 isl_int_set_si(v, 3);
394 isl_constraint_set_coefficient(c, isl_dim_set, 1, v);
395 bset = isl_basic_set_add_constraint(bset, c);
396
397 c = isl_equality_alloc(isl_local_space_copy(ls));
398 isl_int_set_si(v, -3);
399 isl_constraint_set_constant(c, v);
400 isl_int_set_si(v, 1);
401 isl_constraint_set_coefficient(c, isl_dim_set, 0, v);
402 isl_int_set_si(v, 4);
403 isl_constraint_set_coefficient(c, isl_dim_set, 2, v);
404 bset = isl_basic_set_add_constraint(bset, c);
405
406 bset = isl_basic_set_project_out(bset, isl_dim_set, 1, 2);
407
408 assert(bset && bset->n_div == 1);
409 isl_local_space_free(ls);
410 isl_basic_set_free(bset);
411
412 /* test 4 */
413 dim = isl_space_set_alloc(ctx, 0, 3);
414 bset = isl_basic_set_universe(isl_space_copy(dim));
415 ls = isl_local_space_from_space(dim);
416
417 c = isl_equality_alloc(isl_local_space_copy(ls));
418 isl_int_set_si(v, 2);
419 isl_constraint_set_constant(c, v);
420 isl_int_set_si(v, -1);
421 isl_constraint_set_coefficient(c, isl_dim_set, 0, v);
422 isl_int_set_si(v, 3);
423 isl_constraint_set_coefficient(c, isl_dim_set, 1, v);
424 bset = isl_basic_set_add_constraint(bset, c);
425
426 c = isl_equality_alloc(isl_local_space_copy(ls));
427 isl_int_set_si(v, -1);
428 isl_constraint_set_constant(c, v);
429 isl_int_set_si(v, 1);
430 isl_constraint_set_coefficient(c, isl_dim_set, 0, v);
431 isl_int_set_si(v, 6);
432 isl_constraint_set_coefficient(c, isl_dim_set, 2, v);
433 bset = isl_basic_set_add_constraint(bset, c);
434
435 bset = isl_basic_set_project_out(bset, isl_dim_set, 1, 2);
436
437 assert(isl_basic_set_is_empty(bset));
438 isl_local_space_free(ls);
439 isl_basic_set_free(bset);
440
441 /* test 5 */
442 dim = isl_space_set_alloc(ctx, 0, 3);
443 bset = isl_basic_set_universe(isl_space_copy(dim));
444 ls = isl_local_space_from_space(dim);
445
446 c = isl_equality_alloc(isl_local_space_copy(ls));
447 isl_int_set_si(v, -1);
448 isl_constraint_set_coefficient(c, isl_dim_set, 0, v);
449 isl_int_set_si(v, 3);
450 isl_constraint_set_coefficient(c, isl_dim_set, 2, v);
451 bset = isl_basic_set_add_constraint(bset, c);
452
453 c = isl_equality_alloc(isl_local_space_copy(ls));
454 isl_int_set_si(v, 1);
455 isl_constraint_set_coefficient(c, isl_dim_set, 0, v);
456 isl_int_set_si(v, -3);
457 isl_constraint_set_coefficient(c, isl_dim_set, 1, v);
458 bset = isl_basic_set_add_constraint(bset, c);
459
460 bset = isl_basic_set_project_out(bset, isl_dim_set, 2, 1);
461
462 assert(bset && bset->n_div == 0);
463 isl_basic_set_free(bset);
464 isl_local_space_free(ls);
465
466 /* test 6 */
467 dim = isl_space_set_alloc(ctx, 0, 3);
468 bset = isl_basic_set_universe(isl_space_copy(dim));
469 ls = isl_local_space_from_space(dim);
470
471 c = isl_equality_alloc(isl_local_space_copy(ls));
472 isl_int_set_si(v, -1);
473 isl_constraint_set_coefficient(c, isl_dim_set, 0, v);
474 isl_int_set_si(v, 6);
475 isl_constraint_set_coefficient(c, isl_dim_set, 2, v);
476 bset = isl_basic_set_add_constraint(bset, c);
477
478 c = isl_equality_alloc(isl_local_space_copy(ls));
479 isl_int_set_si(v, 1);
480 isl_constraint_set_coefficient(c, isl_dim_set, 0, v);
481 isl_int_set_si(v, -3);
482 isl_constraint_set_coefficient(c, isl_dim_set, 1, v);
483 bset = isl_basic_set_add_constraint(bset, c);
484
485 bset = isl_basic_set_project_out(bset, isl_dim_set, 2, 1);
486
487 assert(bset && bset->n_div == 1);
488 isl_basic_set_free(bset);
489 isl_local_space_free(ls);
490
491 /* test 7 */
492 /* This test is a bit tricky. We set up an equality
493 * a + 3b + 3c = 6 e0
494 * Normalization of divs creates _two_ divs
495 * a = 3 e0
496 * c - b - e0 = 2 e1
497 * Afterwards e0 is removed again because it has coefficient -1
498 * and we end up with the original equality and div again.
499 * Perhaps we can avoid the introduction of this temporary div.
500 */
501 dim = isl_space_set_alloc(ctx, 0, 4);
502 bset = isl_basic_set_universe(isl_space_copy(dim));
503 ls = isl_local_space_from_space(dim);
504
505 c = isl_equality_alloc(isl_local_space_copy(ls));
506 isl_int_set_si(v, -1);
507 isl_constraint_set_coefficient(c, isl_dim_set, 0, v);
508 isl_int_set_si(v, -3);
509 isl_constraint_set_coefficient(c, isl_dim_set, 1, v);
510 isl_int_set_si(v, -3);
511 isl_constraint_set_coefficient(c, isl_dim_set, 2, v);
512 isl_int_set_si(v, 6);
513 isl_constraint_set_coefficient(c, isl_dim_set, 3, v);
514 bset = isl_basic_set_add_constraint(bset, c);
515
516 bset = isl_basic_set_project_out(bset, isl_dim_set, 3, 1);
517
518 /* Test disabled for now */
519 /*
520 assert(bset && bset->n_div == 1);
521 */
522 isl_local_space_free(ls);
523 isl_basic_set_free(bset);
524
525 /* test 8 */
526 dim = isl_space_set_alloc(ctx, 0, 5);
527 bset = isl_basic_set_universe(isl_space_copy(dim));
528 ls = isl_local_space_from_space(dim);
529
530 c = isl_equality_alloc(isl_local_space_copy(ls));
531 isl_int_set_si(v, -1);
532 isl_constraint_set_coefficient(c, isl_dim_set, 0, v);
533 isl_int_set_si(v, -3);
534 isl_constraint_set_coefficient(c, isl_dim_set, 1, v);
535 isl_int_set_si(v, -3);
536 isl_constraint_set_coefficient(c, isl_dim_set, 3, v);
537 isl_int_set_si(v, 6);
538 isl_constraint_set_coefficient(c, isl_dim_set, 4, v);
539 bset = isl_basic_set_add_constraint(bset, c);
540
541 c = isl_equality_alloc(isl_local_space_copy(ls));
542 isl_int_set_si(v, -1);
543 isl_constraint_set_coefficient(c, isl_dim_set, 0, v);
544 isl_int_set_si(v, 1);
545 isl_constraint_set_coefficient(c, isl_dim_set, 2, v);
546 isl_int_set_si(v, 1);
547 isl_constraint_set_constant(c, v);
548 bset = isl_basic_set_add_constraint(bset, c);
549
550 bset = isl_basic_set_project_out(bset, isl_dim_set, 4, 1);
551
552 /* Test disabled for now */
553 /*
554 assert(bset && bset->n_div == 1);
555 */
556 isl_local_space_free(ls);
557 isl_basic_set_free(bset);
558
559 /* test 9 */
560 dim = isl_space_set_alloc(ctx, 0, 4);
561 bset = isl_basic_set_universe(isl_space_copy(dim));
562 ls = isl_local_space_from_space(dim);
563
564 c = isl_equality_alloc(isl_local_space_copy(ls));
565 isl_int_set_si(v, 1);
566 isl_constraint_set_coefficient(c, isl_dim_set, 0, v);
567 isl_int_set_si(v, -1);
568 isl_constraint_set_coefficient(c, isl_dim_set, 1, v);
569 isl_int_set_si(v, -2);
570 isl_constraint_set_coefficient(c, isl_dim_set, 2, v);
571 bset = isl_basic_set_add_constraint(bset, c);
572
573 c = isl_equality_alloc(isl_local_space_copy(ls));
574 isl_int_set_si(v, -1);
575 isl_constraint_set_coefficient(c, isl_dim_set, 0, v);
576 isl_int_set_si(v, 3);
577 isl_constraint_set_coefficient(c, isl_dim_set, 3, v);
578 isl_int_set_si(v, 2);
579 isl_constraint_set_constant(c, v);
580 bset = isl_basic_set_add_constraint(bset, c);
581
582 bset = isl_basic_set_project_out(bset, isl_dim_set, 2, 2);
583
584 bset = isl_basic_set_fix_si(bset, isl_dim_set, 0, 2);
585
586 assert(!isl_basic_set_is_empty(bset));
587
588 isl_local_space_free(ls);
589 isl_basic_set_free(bset);
590
591 /* test 10 */
592 dim = isl_space_set_alloc(ctx, 0, 3);
593 bset = isl_basic_set_universe(isl_space_copy(dim));
594 ls = isl_local_space_from_space(dim);
595
596 c = isl_equality_alloc(isl_local_space_copy(ls));
597 isl_int_set_si(v, 1);
598 isl_constraint_set_coefficient(c, isl_dim_set, 0, v);
599 isl_int_set_si(v, -2);
600 isl_constraint_set_coefficient(c, isl_dim_set, 2, v);
601 bset = isl_basic_set_add_constraint(bset, c);
602
603 bset = isl_basic_set_project_out(bset, isl_dim_set, 2, 1);
604
605 bset = isl_basic_set_fix_si(bset, isl_dim_set, 0, 2);
606
607 isl_local_space_free(ls);
608 isl_basic_set_free(bset);
609
610 isl_int_clear(v);
611
612 str = "{ [i] : exists (e0, e1: 3e1 >= 1 + 2e0 and "
613 "8e1 <= -1 + 5i - 5e0 and 2e1 >= 1 + 2i - 5e0) }";
614 set = isl_set_read_from_str(ctx, str);
615 set = isl_set_compute_divs(set);
616 isl_set_free(set);
617 if (!set)
618 return -1;
619
620 return 0;
621 }
622
623 void test_application_case(struct isl_ctx *ctx, const char *name)
624 {
625 char *filename;
626 FILE *input;
627 struct isl_basic_set *bset1, *bset2;
628 struct isl_basic_map *bmap;
629
630 filename = get_filename(ctx, name, "omega");
631 assert(filename);
632 input = fopen(filename, "r");
633 assert(input);
634
635 bset1 = isl_basic_set_read_from_file(ctx, input);
636 bmap = isl_basic_map_read_from_file(ctx, input);
637
638 bset1 = isl_basic_set_apply(bset1, bmap);
639
640 bset2 = isl_basic_set_read_from_file(ctx, input);
641
642 assert(isl_basic_set_is_equal(bset1, bset2) == 1);
643
644 isl_basic_set_free(bset1);
645 isl_basic_set_free(bset2);
646 free(filename);
647
648 fclose(input);
649 }
650
651 void test_application(struct isl_ctx *ctx)
652 {
653 test_application_case(ctx, "application");
654 test_application_case(ctx, "application2");
655 }
656
657 void test_affine_hull_case(struct isl_ctx *ctx, const char *name)
658 {
659 char *filename;
660 FILE *input;
661 struct isl_basic_set *bset1, *bset2;
662
663 filename = get_filename(ctx, name, "polylib");
664 assert(filename);
665 input = fopen(filename, "r");
666 assert(input);
667
668 bset1 = isl_basic_set_read_from_file(ctx, input);
669 bset2 = isl_basic_set_read_from_file(ctx, input);
670
671 bset1 = isl_basic_set_affine_hull(bset1);
672
673 assert(isl_basic_set_is_equal(bset1, bset2) == 1);
674
675 isl_basic_set_free(bset1);
676 isl_basic_set_free(bset2);
677 free(filename);
678
679 fclose(input);
680 }
681
682 int test_affine_hull(struct isl_ctx *ctx)
683 {
684 const char *str;
685 isl_set *set;
686 isl_basic_set *bset;
687 int n;
688
689 test_affine_hull_case(ctx, "affine2");
690 test_affine_hull_case(ctx, "affine");
691 test_affine_hull_case(ctx, "affine3");
692
693 str = "[m] -> { [i0] : exists (e0, e1: e1 <= 1 + i0 and "
694 "m >= 3 and 4i0 <= 2 + m and e1 >= i0 and "
695 "e1 >= 0 and e1 <= 2 and e1 >= 1 + 2e0 and "
696 "2e1 <= 1 + m + 4e0 and 2e1 >= 2 - m + 4i0 - 4e0) }";
697 set = isl_set_read_from_str(ctx, str);
698 bset = isl_set_affine_hull(set);
699 n = isl_basic_set_dim(bset, isl_dim_div);
700 isl_basic_set_free(bset);
701 if (n != 0)
702 isl_die(ctx, isl_error_unknown, "not expecting any divs",
703 return -1);
704
705 return 0;
706 }
707
708 void test_convex_hull_case(struct isl_ctx *ctx, const char *name)
709 {
710 char *filename;
711 FILE *input;
712 struct isl_basic_set *bset1, *bset2;
713 struct isl_set *set;
714
715 filename = get_filename(ctx, name, "polylib");
716 assert(filename);
717 input = fopen(filename, "r");
718 assert(input);
719
720 bset1 = isl_basic_set_read_from_file(ctx, input);
721 bset2 = isl_basic_set_read_from_file(ctx, input);
722
723 set = isl_basic_set_union(bset1, bset2);
724 bset1 = isl_set_convex_hull(set);
725
726 bset2 = isl_basic_set_read_from_file(ctx, input);
727
728 assert(isl_basic_set_is_equal(bset1, bset2) == 1);
729
730 isl_basic_set_free(bset1);
731 isl_basic_set_free(bset2);
732 free(filename);
733
734 fclose(input);
735 }
736
737 void test_convex_hull_algo(struct isl_ctx *ctx, int convex)
738 {
739 const char *str1, *str2;
740 isl_set *set1, *set2;
741 int orig_convex = ctx->opt->convex;
742 ctx->opt->convex = convex;
743
744 test_convex_hull_case(ctx, "convex0");
745 test_convex_hull_case(ctx, "convex1");
746 test_convex_hull_case(ctx, "convex2");
747 test_convex_hull_case(ctx, "convex3");
748 test_convex_hull_case(ctx, "convex4");
749 test_convex_hull_case(ctx, "convex5");
750 test_convex_hull_case(ctx, "convex6");
751 test_convex_hull_case(ctx, "convex7");
752 test_convex_hull_case(ctx, "convex8");
753 test_convex_hull_case(ctx, "convex9");
754 test_convex_hull_case(ctx, "convex10");
755 test_convex_hull_case(ctx, "convex11");
756 test_convex_hull_case(ctx, "convex12");
757 test_convex_hull_case(ctx, "convex13");
758 test_convex_hull_case(ctx, "convex14");
759 test_convex_hull_case(ctx, "convex15");
760
761 str1 = "{ [i0, i1, i2] : (i2 = 1 and i0 = 0 and i1 >= 0) or "
762 "(i0 = 1 and i1 = 0 and i2 = 1) or "
763 "(i0 = 0 and i1 = 0 and i2 = 0) }";
764 str2 = "{ [i0, i1, i2] : i0 >= 0 and i2 >= i0 and i2 <= 1 and i1 >= 0 }";
765 set1 = isl_set_read_from_str(ctx, str1);
766 set2 = isl_set_read_from_str(ctx, str2);
767 set1 = isl_set_from_basic_set(isl_set_convex_hull(set1));
768 assert(isl_set_is_equal(set1, set2));
769 isl_set_free(set1);
770 isl_set_free(set2);
771
772 ctx->opt->convex = orig_convex;
773 }
774
775 void test_convex_hull(struct isl_ctx *ctx)
776 {
777 test_convex_hull_algo(ctx, ISL_CONVEX_HULL_FM);
778 test_convex_hull_algo(ctx, ISL_CONVEX_HULL_WRAP);
779 }
780
781 void test_gist_case(struct isl_ctx *ctx, const char *name)
782 {
783 char *filename;
784 FILE *input;
785 struct isl_basic_set *bset1, *bset2;
786
787 filename = get_filename(ctx, name, "polylib");
788 assert(filename);
789 input = fopen(filename, "r");
790 assert(input);
791
792 bset1 = isl_basic_set_read_from_file(ctx, input);
793 bset2 = isl_basic_set_read_from_file(ctx, input);
794
795 bset1 = isl_basic_set_gist(bset1, bset2);
796
797 bset2 = isl_basic_set_read_from_file(ctx, input);
798
799 assert(isl_basic_set_is_equal(bset1, bset2) == 1);
800
801 isl_basic_set_free(bset1);
802 isl_basic_set_free(bset2);
803 free(filename);
804
805 fclose(input);
806 }
807
808 void test_gist(struct isl_ctx *ctx)
809 {
810 const char *str;
811 isl_basic_set *bset1, *bset2;
812
813 test_gist_case(ctx, "gist1");
814
815 str = "[p0, p2, p3, p5, p6, p10] -> { [] : "
816 "exists (e0 = [(15 + p0 + 15p6 + 15p10)/16], e1 = [(p5)/8], "
817 "e2 = [(p6)/128], e3 = [(8p2 - p5)/128], "
818 "e4 = [(128p3 - p6)/4096]: 8e1 = p5 and 128e2 = p6 and "
819 "128e3 = 8p2 - p5 and 4096e4 = 128p3 - p6 and p2 >= 0 and "
820 "16e0 >= 16 + 16p6 + 15p10 and p2 <= 15 and p3 >= 0 and "
821 "p3 <= 31 and p6 >= 128p3 and p5 >= 8p2 and p10 >= 0 and "
822 "16e0 <= 15 + p0 + 15p6 + 15p10 and 16e0 >= p0 + 15p6 + 15p10 and "
823 "p10 <= 15 and p10 <= -1 + p0 - p6) }";
824 bset1 = isl_basic_set_read_from_str(ctx, str);
825 str = "[p0, p2, p3, p5, p6, p10] -> { [] : exists (e0 = [(p5)/8], "
826 "e1 = [(p6)/128], e2 = [(8p2 - p5)/128], "
827 "e3 = [(128p3 - p6)/4096]: 8e0 = p5 and 128e1 = p6 and "
828 "128e2 = 8p2 - p5 and 4096e3 = 128p3 - p6 and p5 >= -7 and "
829 "p2 >= 0 and 8p2 <= -1 + p0 and p2 <= 15 and p3 >= 0 and "
830 "p3 <= 31 and 128p3 <= -1 + p0 and p6 >= -127 and "
831 "p5 <= -1 + p0 and p6 <= -1 + p0 and p6 >= 128p3 and "
832 "p0 >= 1 and p5 >= 8p2 and p10 >= 0 and p10 <= 15 ) }";
833 bset2 = isl_basic_set_read_from_str(ctx, str);
834 bset1 = isl_basic_set_gist(bset1, bset2);
835 assert(bset1 && bset1->n_div == 0);
836 isl_basic_set_free(bset1);
837 }
838
839 int test_coalesce_set(isl_ctx *ctx, const char *str, int check_one)
840 {
841 isl_set *set, *set2;
842 int equal;
843 int one;
844
845 set = isl_set_read_from_str(ctx, str);
846 set = isl_set_coalesce(set);
847 set2 = isl_set_read_from_str(ctx, str);
848 equal = isl_set_is_equal(set, set2);
849 one = set && set->n == 1;
850 isl_set_free(set);
851 isl_set_free(set2);
852
853 if (equal < 0)
854 return -1;
855 if (!equal)
856 isl_die(ctx, isl_error_unknown,
857 "coalesced set not equal to input", return -1);
858 if (check_one && !one)
859 isl_die(ctx, isl_error_unknown,
860 "coalesced set should not be a union", return -1);
861
862 return 0;
863 }
864
865 int test_coalesce_unbounded_wrapping(isl_ctx *ctx)
866 {
867 int r = 0;
868 int bounded;
869
870 bounded = isl_options_get_coalesce_bounded_wrapping(ctx);
871 isl_options_set_coalesce_bounded_wrapping(ctx, 0);
872
873 if (test_coalesce_set(ctx,
874 "{[x,y,z] : y + 2 >= 0 and x - y + 1 >= 0 and "
875 "-x - y + 1 >= 0 and -3 <= z <= 3;"
876 "[x,y,z] : -x+z + 20 >= 0 and -x-z + 20 >= 0 and "
877 "x-z + 20 >= 0 and x+z + 20 >= 0 and "
878 "-10 <= y <= 0}", 1) < 0)
879 goto error;
880 if (test_coalesce_set(ctx,
881 "{[x,y] : 0 <= x,y <= 10; [5,y]: 4 <=y <= 11}", 1) < 0)
882 goto error;
883 if (test_coalesce_set(ctx,
884 "{[x,0,0] : -5 <= x <= 5; [0,y,1] : -5 <= y <= 5 }", 1) < 0)
885 goto error;
886
887 if (0) {
888 error:
889 r = -1;
890 }
891
892 isl_options_set_coalesce_bounded_wrapping(ctx, bounded);
893
894 return r;
895 }
896
897 int test_coalesce(struct isl_ctx *ctx)
898 {
899 const char *str;
900 struct isl_set *set, *set2;
901 struct isl_map *map, *map2;
902
903 set = isl_set_read_from_str(ctx,
904 "{[x,y]: x >= 0 & x <= 10 & y >= 0 & y <= 10 or "
905 "y >= x & x >= 2 & 5 >= y }");
906 set = isl_set_coalesce(set);
907 assert(set && set->n == 1);
908 isl_set_free(set);
909
910 set = isl_set_read_from_str(ctx,
911 "{[x,y]: y >= 0 & 2x + y <= 30 & y <= 10 & x >= 0 or "
912 "x + y >= 10 & y <= x & x + y <= 20 & y >= 0}");
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 & 2x + y <= 30 & y <= 10 & x >= 0 or "
919 "x + y >= 10 & y <= x & x + y <= 19 & y >= 0}");
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 <= x}");
927 set = isl_set_coalesce(set);
928 assert(set && set->n == 1);
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 >= 7 & x <= 10 & y <= x}");
934 set = isl_set_coalesce(set);
935 assert(set && set->n == 2);
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 >= 6 & x <= 10 & y + 1 <= x}");
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 <= 6}");
948 set = isl_set_coalesce(set);
949 assert(set && set->n == 1);
950 isl_set_free(set);
951
952 set = isl_set_read_from_str(ctx,
953 "{[x,y]: y >= 0 & x <= 5 & y <= x or "
954 "y >= 0 & x = 7 & y <= 6}");
955 set = isl_set_coalesce(set);
956 assert(set && set->n == 2);
957 isl_set_free(set);
958
959 set = isl_set_read_from_str(ctx,
960 "{[x,y]: y >= 0 & x <= 5 & y <= x or "
961 "y >= 0 & x = 6 & y <= 5}");
962 set = isl_set_coalesce(set);
963 assert(set && set->n == 1);
964 set2 = isl_set_read_from_str(ctx,
965 "{[x,y]: y >= 0 & x <= 5 & y <= x or "
966 "y >= 0 & x = 6 & y <= 5}");
967 assert(isl_set_is_equal(set, set2));
968 isl_set_free(set);
969 isl_set_free(set2);
970
971 set = isl_set_read_from_str(ctx,
972 "{[x,y]: y >= 0 & x <= 5 & y <= x or "
973 "y >= 0 & x = 6 & y <= 7}");
974 set = isl_set_coalesce(set);
975 assert(set && set->n == 2);
976 isl_set_free(set);
977
978 set = isl_set_read_from_str(ctx,
979 "[n] -> { [i] : i = 1 and n >= 2 or 2 <= i and i <= n }");
980 set = isl_set_coalesce(set);
981 assert(set && set->n == 1);
982 set2 = isl_set_read_from_str(ctx,
983 "[n] -> { [i] : i = 1 and n >= 2 or 2 <= i and i <= n }");
984 assert(isl_set_is_equal(set, set2));
985 isl_set_free(set);
986 isl_set_free(set2);
987
988 set = isl_set_read_from_str(ctx,
989 "{[x,y] : x >= 0 and y >= 0 or 0 <= y and y <= 5 and x = -1}");
990 set = isl_set_coalesce(set);
991 set2 = isl_set_read_from_str(ctx,
992 "{[x,y] : x >= 0 and y >= 0 or 0 <= y and y <= 5 and x = -1}");
993 assert(isl_set_is_equal(set, set2));
994 isl_set_free(set);
995 isl_set_free(set2);
996
997 set = isl_set_read_from_str(ctx,
998 "[n] -> { [i] : 1 <= i and i <= n - 1 or "
999 "2 <= i and i <= n }");
1000 set = isl_set_coalesce(set);
1001 assert(set && set->n == 1);
1002 set2 = isl_set_read_from_str(ctx,
1003 "[n] -> { [i] : 1 <= i and i <= n - 1 or "
1004 "2 <= i and i <= n }");
1005 assert(isl_set_is_equal(set, set2));
1006 isl_set_free(set);
1007 isl_set_free(set2);
1008
1009 map = isl_map_read_from_str(ctx,
1010 "[n] -> { [i0] -> [o0] : exists (e0 = [(i0)/4], e1 = [(o0)/4], "
1011 "e2 = [(n)/2], e3 = [(-2 + i0)/4], e4 = [(-2 + o0)/4], "
1012 "e5 = [(-2n + i0)/4]: 2e2 = n and 4e3 = -2 + i0 and "
1013 "4e4 = -2 + o0 and i0 >= 8 + 2n and o0 >= 2 + i0 and "
1014 "o0 <= 56 + 2n and o0 <= -12 + 4n and i0 <= 57 + 2n and "
1015 "i0 <= -11 + 4n and o0 >= 6 + 2n and 4e0 <= i0 and "
1016 "4e0 >= -3 + i0 and 4e1 <= o0 and 4e1 >= -3 + o0 and "
1017 "4e5 <= -2n + i0 and 4e5 >= -3 - 2n + i0);"
1018 "[i0] -> [o0] : exists (e0 = [(i0)/4], e1 = [(o0)/4], "
1019 "e2 = [(n)/2], e3 = [(-2 + i0)/4], e4 = [(-2 + o0)/4], "
1020 "e5 = [(-2n + i0)/4]: 2e2 = n and 4e3 = -2 + i0 and "
1021 "4e4 = -2 + o0 and 2e0 >= 3 + n and e0 <= -4 + n and "
1022 "2e0 <= 27 + n and e1 <= -4 + n and 2e1 <= 27 + n and "
1023 "2e1 >= 2 + n and e1 >= 1 + e0 and i0 >= 7 + 2n and "
1024 "i0 <= -11 + 4n and i0 <= 57 + 2n and 4e0 <= -2 + i0 and "
1025 "4e0 >= -3 + i0 and o0 >= 6 + 2n and o0 <= -11 + 4n and "
1026 "o0 <= 57 + 2n and 4e1 <= -2 + o0 and 4e1 >= -3 + o0 and "
1027 "4e5 <= -2n + i0 and 4e5 >= -3 - 2n + i0 ) }");
1028 map = isl_map_coalesce(map);
1029 map2 = isl_map_read_from_str(ctx,
1030 "[n] -> { [i0] -> [o0] : exists (e0 = [(i0)/4], e1 = [(o0)/4], "
1031 "e2 = [(n)/2], e3 = [(-2 + i0)/4], e4 = [(-2 + o0)/4], "
1032 "e5 = [(-2n + i0)/4]: 2e2 = n and 4e3 = -2 + i0 and "
1033 "4e4 = -2 + o0 and i0 >= 8 + 2n and o0 >= 2 + i0 and "
1034 "o0 <= 56 + 2n and o0 <= -12 + 4n and i0 <= 57 + 2n and "
1035 "i0 <= -11 + 4n and o0 >= 6 + 2n and 4e0 <= i0 and "
1036 "4e0 >= -3 + i0 and 4e1 <= o0 and 4e1 >= -3 + o0 and "
1037 "4e5 <= -2n + i0 and 4e5 >= -3 - 2n + i0);"
1038 "[i0] -> [o0] : exists (e0 = [(i0)/4], e1 = [(o0)/4], "
1039 "e2 = [(n)/2], e3 = [(-2 + i0)/4], e4 = [(-2 + o0)/4], "
1040 "e5 = [(-2n + i0)/4]: 2e2 = n and 4e3 = -2 + i0 and "
1041 "4e4 = -2 + o0 and 2e0 >= 3 + n and e0 <= -4 + n and "
1042 "2e0 <= 27 + n and e1 <= -4 + n and 2e1 <= 27 + n and "
1043 "2e1 >= 2 + n and e1 >= 1 + e0 and i0 >= 7 + 2n and "
1044 "i0 <= -11 + 4n and i0 <= 57 + 2n and 4e0 <= -2 + i0 and "
1045 "4e0 >= -3 + i0 and o0 >= 6 + 2n and o0 <= -11 + 4n and "
1046 "o0 <= 57 + 2n and 4e1 <= -2 + o0 and 4e1 >= -3 + o0 and "
1047 "4e5 <= -2n + i0 and 4e5 >= -3 - 2n + i0 ) }");
1048 assert(isl_map_is_equal(map, map2));
1049 isl_map_free(map);
1050 isl_map_free(map2);
1051
1052 str = "[n, m] -> { [] -> [o0, o2, o3] : (o3 = 1 and o0 >= 1 + m and "
1053 "o0 <= n + m and o2 <= m and o0 >= 2 + n and o2 >= 3) or "
1054 "(o0 >= 2 + n and o0 >= 1 + m and o0 <= n + m and n >= 1 and "
1055 "o3 <= -1 + o2 and o3 >= 1 - m + o2 and o3 >= 2 and o3 <= n) }";
1056 map = isl_map_read_from_str(ctx, str);
1057 map = isl_map_coalesce(map);
1058 map2 = isl_map_read_from_str(ctx, str);
1059 assert(isl_map_is_equal(map, map2));
1060 isl_map_free(map);
1061 isl_map_free(map2);
1062
1063 str = "[M, N] -> { [i0, i1, i2, i3, i4, i5, i6] -> "
1064 "[o0, o1, o2, o3, o4, o5, o6] : "
1065 "(o6 <= -4 + 2M - 2N + i0 + i1 - i2 + i6 - o0 - o1 + o2 and "
1066 "o3 <= -2 + i3 and o6 >= 2 + i0 + i3 + i6 - o0 - o3 and "
1067 "o6 >= 2 - M + N + i3 + i4 + i6 - o3 - o4 and o0 <= -1 + i0 and "
1068 "o4 >= 4 - 3M + 3N - i0 - i1 + i2 + 2i3 + i4 + o0 + o1 - o2 - 2o3 "
1069 "and o6 <= -3 + 2M - 2N + i3 + i4 - i5 + i6 - o3 - o4 + o5 and "
1070 "2o6 <= -5 + 5M - 5N + 2i0 + i1 - i2 - i5 + 2i6 - 2o0 - o1 + o2 + o5 "
1071 "and o6 >= 2i0 + i1 + i6 - 2o0 - o1 and "
1072 "3o6 <= -5 + 4M - 4N + 2i0 + i1 - i2 + 2i3 + i4 - i5 + 3i6 "
1073 "- 2o0 - o1 + o2 - 2o3 - o4 + o5) or "
1074 "(N >= 2 and o3 <= -1 + i3 and o0 <= -1 + i0 and "
1075 "o6 >= i3 + i6 - o3 and M >= 0 and "
1076 "2o6 >= 1 + i0 + i3 + 2i6 - o0 - o3 and "
1077 "o6 >= 1 - M + i0 + i6 - o0 and N >= 2M and o6 >= i0 + i6 - o0) }";
1078 map = isl_map_read_from_str(ctx, str);
1079 map = isl_map_coalesce(map);
1080 map2 = isl_map_read_from_str(ctx, str);
1081 assert(isl_map_is_equal(map, map2));
1082 isl_map_free(map);
1083 isl_map_free(map2);
1084
1085 str = "[M, N] -> { [] -> [o0] : (o0 = 0 and M >= 1 and N >= 2) or "
1086 "(o0 = 0 and M >= 1 and N >= 2M and N >= 2 + M) or "
1087 "(o0 = 0 and M >= 2 and N >= 3) or "
1088 "(M = 0 and o0 = 0 and N >= 3) }";
1089 map = isl_map_read_from_str(ctx, str);
1090 map = isl_map_coalesce(map);
1091 map2 = isl_map_read_from_str(ctx, str);
1092 assert(isl_map_is_equal(map, map2));
1093 isl_map_free(map);
1094 isl_map_free(map2);
1095
1096 str = "{ [i0, i1, i2, i3] : (i1 = 10i0 and i0 >= 1 and 10i0 <= 100 and "
1097 "i3 <= 9 + 10 i2 and i3 >= 1 + 10i2 and i3 >= 0) or "
1098 "(i1 <= 9 + 10i0 and i1 >= 1 + 10i0 and i2 >= 0 and "
1099 "i0 >= 0 and i1 <= 100 and i3 <= 9 + 10i2 and i3 >= 1 + 10i2) }";
1100 map = isl_map_read_from_str(ctx, str);
1101 map = isl_map_coalesce(map);
1102 map2 = isl_map_read_from_str(ctx, str);
1103 assert(isl_map_is_equal(map, map2));
1104 isl_map_free(map);
1105 isl_map_free(map2);
1106
1107 test_coalesce_set(ctx,
1108 "[M] -> { [i1] : (i1 >= 2 and i1 <= M) or "
1109 "(i1 = M and M >= 1) }", 0);
1110 test_coalesce_set(ctx,
1111 "{[x,y] : x,y >= 0; [x,y] : 10 <= x <= 20 and y >= -1 }", 0);
1112 test_coalesce_set(ctx,
1113 "{ [x, y] : (x >= 1 and y >= 1 and x <= 2 and y <= 2) or "
1114 "(y = 3 and x = 1) }", 1);
1115 test_coalesce_set(ctx,
1116 "[M] -> { [i0, i1, i2, i3, i4] : (i1 >= 3 and i4 >= 2 + i2 and "
1117 "i2 >= 2 and i0 >= 2 and i3 >= 1 + i2 and i0 <= M and "
1118 "i1 <= M and i3 <= M and i4 <= M) or "
1119 "(i1 >= 2 and i4 >= 1 + i2 and i2 >= 2 and i0 >= 2 and "
1120 "i3 >= 1 + i2 and i0 <= M and i1 <= -1 + M and i3 <= M and "
1121 "i4 <= -1 + M) }", 1);
1122 test_coalesce_set(ctx,
1123 "{ [x, y] : (x >= 0 and y >= 0 and x <= 10 and y <= 10) or "
1124 "(x >= 1 and y >= 1 and x <= 11 and y <= 11) }", 1);
1125 if (test_coalesce_unbounded_wrapping(ctx) < 0)
1126 return -1;
1127 if (test_coalesce_set(ctx, "{[x,0] : x >= 0; [x,1] : x <= 20}", 0) < 0)
1128 return -1;
1129 if (test_coalesce_set(ctx, "{ [x, 1 - x] : 0 <= x <= 1; [0,0] }", 1) < 0)
1130 return -1;
1131 if (test_coalesce_set(ctx, "{ [0,0]; [i,i] : 1 <= i <= 10 }", 1) < 0)
1132 return -1;
1133 if (test_coalesce_set(ctx, "{ [0,0]; [i,j] : 1 <= i,j <= 10 }", 0) < 0)
1134 return -1;
1135 if (test_coalesce_set(ctx, "{ [0,0]; [i,2i] : 1 <= i <= 10 }", 1) < 0)
1136 return -1;
1137 if (test_coalesce_set(ctx, "{ [0,0]; [i,2i] : 2 <= i <= 10 }", 0) < 0)
1138 return -1;
1139 if (test_coalesce_set(ctx, "{ [1,0]; [i,2i] : 1 <= i <= 10 }", 0) < 0)
1140 return -1;
1141 if (test_coalesce_set(ctx, "{ [0,1]; [i,2i] : 1 <= i <= 10 }", 0) < 0)
1142 return -1;
1143 if (test_coalesce_set(ctx, "{ [a, b] : exists e : 2e = a and "
1144 "a >= 0 and (a <= 3 or (b <= 0 and b >= -4 + a)) }", 0) < 0)
1145 return -1;
1146 if (test_coalesce_set(ctx,
1147 "{ [i, j, i', j'] : i <= 2 and j <= 2 and "
1148 "j' >= -1 + 2i + j - 2i' and i' <= -1 + i and "
1149 "j >= 1 and j' <= i + j - i' and i >= 1; "
1150 "[1, 1, 1, 1] }", 0) < 0)
1151 return -1;
1152 if (test_coalesce_set(ctx, "{ [i,j] : exists a,b : i = 2a and j = 3b; "
1153 "[i,j] : exists a : j = 3a }", 1) < 0)
1154 return -1;
1155 return 0;
1156 }
1157
1158 void test_closure(struct isl_ctx *ctx)
1159 {
1160 const char *str;
1161 isl_set *dom;
1162 isl_map *up, *right;
1163 isl_map *map, *map2;
1164 int exact;
1165
1166 /* COCOA example 1 */
1167 map = isl_map_read_from_str(ctx,
1168 "[n] -> { [i,j] -> [i2,j2] : i2 = i + 1 and j2 = j + 1 and "
1169 "1 <= i and i < n and 1 <= j and j < n or "
1170 "i2 = i + 1 and j2 = j - 1 and "
1171 "1 <= i and i < n and 2 <= j and j <= n }");
1172 map = isl_map_power(map, &exact);
1173 assert(exact);
1174 isl_map_free(map);
1175
1176 /* COCOA example 1 */
1177 map = isl_map_read_from_str(ctx,
1178 "[n] -> { [i,j] -> [i2,j2] : i2 = i + 1 and j2 = j + 1 and "
1179 "1 <= i and i < n and 1 <= j and j < n or "
1180 "i2 = i + 1 and j2 = j - 1 and "
1181 "1 <= i and i < n and 2 <= j and j <= n }");
1182 map = isl_map_transitive_closure(map, &exact);
1183 assert(exact);
1184 map2 = isl_map_read_from_str(ctx,
1185 "[n] -> { [i,j] -> [i2,j2] : exists (k1,k2,k : "
1186 "1 <= i and i < n and 1 <= j and j <= n and "
1187 "2 <= i2 and i2 <= n and 1 <= j2 and j2 <= n and "
1188 "i2 = i + k1 + k2 and j2 = j + k1 - k2 and "
1189 "k1 >= 0 and k2 >= 0 and k1 + k2 = k and k >= 1 )}");
1190 assert(isl_map_is_equal(map, map2));
1191 isl_map_free(map2);
1192 isl_map_free(map);
1193
1194 map = isl_map_read_from_str(ctx,
1195 "[n] -> { [x] -> [y] : y = x + 1 and 0 <= x and x <= n and "
1196 " 0 <= y and y <= n }");
1197 map = isl_map_transitive_closure(map, &exact);
1198 map2 = isl_map_read_from_str(ctx,
1199 "[n] -> { [x] -> [y] : y > x and 0 <= x and x <= n and "
1200 " 0 <= y and y <= n }");
1201 assert(isl_map_is_equal(map, map2));
1202 isl_map_free(map2);
1203 isl_map_free(map);
1204
1205 /* COCOA example 2 */
1206 map = isl_map_read_from_str(ctx,
1207 "[n] -> { [i,j] -> [i2,j2] : i2 = i + 2 and j2 = j + 2 and "
1208 "1 <= i and i < n - 1 and 1 <= j and j < n - 1 or "
1209 "i2 = i + 2 and j2 = j - 2 and "
1210 "1 <= i and i < n - 1 and 3 <= j and j <= n }");
1211 map = isl_map_transitive_closure(map, &exact);
1212 assert(exact);
1213 map2 = isl_map_read_from_str(ctx,
1214 "[n] -> { [i,j] -> [i2,j2] : exists (k1,k2,k : "
1215 "1 <= i and i < n - 1 and 1 <= j and j <= n and "
1216 "3 <= i2 and i2 <= n and 1 <= j2 and j2 <= n and "
1217 "i2 = i + 2 k1 + 2 k2 and j2 = j + 2 k1 - 2 k2 and "
1218 "k1 >= 0 and k2 >= 0 and k1 + k2 = k and k >= 1) }");
1219 assert(isl_map_is_equal(map, map2));
1220 isl_map_free(map);
1221 isl_map_free(map2);
1222
1223 /* COCOA Fig.2 left */
1224 map = isl_map_read_from_str(ctx,
1225 "[n] -> { [i,j] -> [i2,j2] : i2 = i + 2 and j2 = j and "
1226 "i <= 2 j - 3 and i <= n - 2 and j <= 2 i - 1 and "
1227 "j <= n or "
1228 "i2 = i and j2 = j + 2 and i <= 2 j - 1 and i <= n and "
1229 "j <= 2 i - 3 and j <= n - 2 or "
1230 "i2 = i + 1 and j2 = j + 1 and i <= 2 j - 1 and "
1231 "i <= n - 1 and j <= 2 i - 1 and j <= n - 1 }");
1232 map = isl_map_transitive_closure(map, &exact);
1233 assert(exact);
1234 isl_map_free(map);
1235
1236 /* COCOA Fig.2 right */
1237 map = isl_map_read_from_str(ctx,
1238 "[n] -> { [i,j] -> [i2,j2] : i2 = i + 3 and j2 = j and "
1239 "i <= 2 j - 4 and i <= n - 3 and j <= 2 i - 1 and "
1240 "j <= n or "
1241 "i2 = i and j2 = j + 3 and i <= 2 j - 1 and i <= n and "
1242 "j <= 2 i - 4 and j <= n - 3 or "
1243 "i2 = i + 1 and j2 = j + 1 and i <= 2 j - 1 and "
1244 "i <= n - 1 and j <= 2 i - 1 and j <= n - 1 }");
1245 map = isl_map_power(map, &exact);
1246 assert(exact);
1247 isl_map_free(map);
1248
1249 /* COCOA Fig.2 right */
1250 map = isl_map_read_from_str(ctx,
1251 "[n] -> { [i,j] -> [i2,j2] : i2 = i + 3 and j2 = j and "
1252 "i <= 2 j - 4 and i <= n - 3 and j <= 2 i - 1 and "
1253 "j <= n or "
1254 "i2 = i and j2 = j + 3 and i <= 2 j - 1 and i <= n and "
1255 "j <= 2 i - 4 and j <= n - 3 or "
1256 "i2 = i + 1 and j2 = j + 1 and i <= 2 j - 1 and "
1257 "i <= n - 1 and j <= 2 i - 1 and j <= n - 1 }");
1258 map = isl_map_transitive_closure(map, &exact);
1259 assert(exact);
1260 map2 = isl_map_read_from_str(ctx,
1261 "[n] -> { [i,j] -> [i2,j2] : exists (k1,k2,k3,k : "
1262 "i <= 2 j - 1 and i <= n and j <= 2 i - 1 and "
1263 "j <= n and 3 + i + 2 j <= 3 n and "
1264 "3 + 2 i + j <= 3n and i2 <= 2 j2 -1 and i2 <= n and "
1265 "i2 <= 3 j2 - 4 and j2 <= 2 i2 -1 and j2 <= n and "
1266 "13 + 4 j2 <= 11 i2 and i2 = i + 3 k1 + k3 and "
1267 "j2 = j + 3 k2 + k3 and k1 >= 0 and k2 >= 0 and "
1268 "k3 >= 0 and k1 + k2 + k3 = k and k > 0) }");
1269 assert(isl_map_is_equal(map, map2));
1270 isl_map_free(map2);
1271 isl_map_free(map);
1272
1273 /* COCOA Fig.1 right */
1274 dom = isl_set_read_from_str(ctx,
1275 "{ [x,y] : x >= 0 and -2 x + 3 y >= 0 and x <= 3 and "
1276 "2 x - 3 y + 3 >= 0 }");
1277 right = isl_map_read_from_str(ctx,
1278 "{ [x,y] -> [x2,y2] : x2 = x + 1 and y2 = y }");
1279 up = isl_map_read_from_str(ctx,
1280 "{ [x,y] -> [x2,y2] : x2 = x and y2 = y + 1 }");
1281 right = isl_map_intersect_domain(right, isl_set_copy(dom));
1282 right = isl_map_intersect_range(right, isl_set_copy(dom));
1283 up = isl_map_intersect_domain(up, isl_set_copy(dom));
1284 up = isl_map_intersect_range(up, dom);
1285 map = isl_map_union(up, right);
1286 map = isl_map_transitive_closure(map, &exact);
1287 assert(exact);
1288 map2 = isl_map_read_from_str(ctx,
1289 "{ [0,0] -> [0,1]; [0,0] -> [1,1]; [0,1] -> [1,1]; "
1290 " [2,2] -> [3,2]; [2,2] -> [3,3]; [3,2] -> [3,3] }");
1291 assert(isl_map_is_equal(map, map2));
1292 isl_map_free(map2);
1293 isl_map_free(map);
1294
1295 /* COCOA Theorem 1 counter example */
1296 map = isl_map_read_from_str(ctx,
1297 "{ [i,j] -> [i2,j2] : i = 0 and 0 <= j and j <= 1 and "
1298 "i2 = 1 and j2 = j or "
1299 "i = 0 and j = 0 and i2 = 0 and j2 = 1 }");
1300 map = isl_map_transitive_closure(map, &exact);
1301 assert(exact);
1302 isl_map_free(map);
1303
1304 map = isl_map_read_from_str(ctx,
1305 "[m,n] -> { [i,j] -> [i2,j2] : i2 = i and j2 = j + 2 and "
1306 "1 <= i,i2 <= n and 1 <= j,j2 <= m or "
1307 "i2 = i + 1 and 3 <= j2 - j <= 4 and "
1308 "1 <= i,i2 <= n and 1 <= j,j2 <= m }");
1309 map = isl_map_transitive_closure(map, &exact);
1310 assert(exact);
1311 isl_map_free(map);
1312
1313 /* Kelly et al 1996, fig 12 */
1314 map = isl_map_read_from_str(ctx,
1315 "[n] -> { [i,j] -> [i2,j2] : i2 = i and j2 = j + 1 and "
1316 "1 <= i,j,j+1 <= n or "
1317 "j = n and j2 = 1 and i2 = i + 1 and "
1318 "1 <= i,i+1 <= n }");
1319 map = isl_map_transitive_closure(map, &exact);
1320 assert(exact);
1321 map2 = isl_map_read_from_str(ctx,
1322 "[n] -> { [i,j] -> [i2,j2] : 1 <= j < j2 <= n and "
1323 "1 <= i <= n and i = i2 or "
1324 "1 <= i < i2 <= n and 1 <= j <= n and "
1325 "1 <= j2 <= n }");
1326 assert(isl_map_is_equal(map, map2));
1327 isl_map_free(map2);
1328 isl_map_free(map);
1329
1330 /* Omega's closure4 */
1331 map = isl_map_read_from_str(ctx,
1332 "[m,n] -> { [x,y] -> [x2,y2] : x2 = x and y2 = y + 1 and "
1333 "1 <= x,y <= 10 or "
1334 "x2 = x + 1 and y2 = y and "
1335 "1 <= x <= 20 && 5 <= y <= 15 }");
1336 map = isl_map_transitive_closure(map, &exact);
1337 assert(exact);
1338 isl_map_free(map);
1339
1340 map = isl_map_read_from_str(ctx,
1341 "[n] -> { [x] -> [y]: 1 <= n <= y - x <= 10 }");
1342 map = isl_map_transitive_closure(map, &exact);
1343 assert(!exact);
1344 map2 = isl_map_read_from_str(ctx,
1345 "[n] -> { [x] -> [y] : 1 <= n <= 10 and y >= n + x }");
1346 assert(isl_map_is_equal(map, map2));
1347 isl_map_free(map);
1348 isl_map_free(map2);
1349
1350 str = "[n, m] -> { [i0, i1, i2, i3] -> [o0, o1, o2, o3] : "
1351 "i3 = 1 and o0 = i0 and o1 = -1 + i1 and o2 = -1 + i2 and "
1352 "o3 = -2 + i2 and i1 <= -1 + i0 and i1 >= 1 - m + i0 and "
1353 "i1 >= 2 and i1 <= n and i2 >= 3 and i2 <= 1 + n and i2 <= m }";
1354 map = isl_map_read_from_str(ctx, str);
1355 map = isl_map_transitive_closure(map, &exact);
1356 assert(exact);
1357 map2 = isl_map_read_from_str(ctx, str);
1358 assert(isl_map_is_equal(map, map2));
1359 isl_map_free(map);
1360 isl_map_free(map2);
1361
1362 str = "{[0] -> [1]; [2] -> [3]}";
1363 map = isl_map_read_from_str(ctx, str);
1364 map = isl_map_transitive_closure(map, &exact);
1365 assert(exact);
1366 map2 = isl_map_read_from_str(ctx, str);
1367 assert(isl_map_is_equal(map, map2));
1368 isl_map_free(map);
1369 isl_map_free(map2);
1370
1371 str = "[n] -> { [[i0, i1, 1, 0, i0] -> [i5, 1]] -> "
1372 "[[i0, -1 + i1, 2, 0, i0] -> [-1 + i5, 2]] : "
1373 "exists (e0 = [(3 - n)/3]: i5 >= 2 and i1 >= 2 and "
1374 "3i0 <= -1 + n and i1 <= -1 + n and i5 <= -1 + n and "
1375 "3e0 >= 1 - n and 3e0 <= 2 - n and 3i0 >= -2 + n); "
1376 "[[i0, i1, 2, 0, i0] -> [i5, 1]] -> "
1377 "[[i0, i1, 1, 0, i0] -> [-1 + i5, 2]] : "
1378 "exists (e0 = [(3 - n)/3]: i5 >= 2 and i1 >= 1 and "
1379 "3i0 <= -1 + n and i1 <= -1 + n and i5 <= -1 + n and "
1380 "3e0 >= 1 - n and 3e0 <= 2 - n and 3i0 >= -2 + n); "
1381 "[[i0, i1, 1, 0, i0] -> [i5, 2]] -> "
1382 "[[i0, -1 + i1, 2, 0, i0] -> [i5, 1]] : "
1383 "exists (e0 = [(3 - n)/3]: i1 >= 2 and i5 >= 1 and "
1384 "3i0 <= -1 + n and i1 <= -1 + n and i5 <= -1 + n and "
1385 "3e0 >= 1 - n and 3e0 <= 2 - n and 3i0 >= -2 + n); "
1386 "[[i0, i1, 2, 0, i0] -> [i5, 2]] -> "
1387 "[[i0, i1, 1, 0, i0] -> [i5, 1]] : "
1388 "exists (e0 = [(3 - n)/3]: i5 >= 1 and i1 >= 1 and "
1389 "3i0 <= -1 + n and i1 <= -1 + n and i5 <= -1 + n and "
1390 "3e0 >= 1 - n and 3e0 <= 2 - n and 3i0 >= -2 + n) }";
1391 map = isl_map_read_from_str(ctx, str);
1392 map = isl_map_transitive_closure(map, NULL);
1393 assert(map);
1394 isl_map_free(map);
1395 }
1396
1397 void test_lex(struct isl_ctx *ctx)
1398 {
1399 isl_space *dim;
1400 isl_map *map;
1401
1402 dim = isl_space_set_alloc(ctx, 0, 0);
1403 map = isl_map_lex_le(dim);
1404 assert(!isl_map_is_empty(map));
1405 isl_map_free(map);
1406 }
1407
1408 void test_lexmin(struct isl_ctx *ctx)
1409 {
1410 const char *str;
1411 isl_basic_map *bmap;
1412 isl_map *map, *map2;
1413 isl_set *set;
1414 isl_set *set2;
1415 isl_pw_multi_aff *pma;
1416
1417 str = "[p0, p1] -> { [] -> [] : "
1418 "exists (e0 = [(2p1)/3], e1, e2, e3 = [(3 - p1 + 3e0)/3], "
1419 "e4 = [(p1)/3], e5 = [(p1 + 3e4)/3]: "
1420 "3e0 >= -2 + 2p1 and 3e0 >= p1 and 3e3 >= 1 - p1 + 3e0 and "
1421 "3e0 <= 2p1 and 3e3 >= -2 + p1 and 3e3 <= -1 + p1 and p1 >= 3 and "
1422 "3e5 >= -2 + 2p1 and 3e5 >= p1 and 3e5 <= -1 + p1 + 3e4 and "
1423 "3e4 <= p1 and 3e4 >= -2 + p1 and e3 <= -1 + e0 and "
1424 "3e4 >= 6 - p1 + 3e1 and 3e1 >= p1 and 3e5 >= -2 + p1 + 3e4 and "
1425 "2e4 >= 3 - p1 + 2e1 and e4 <= e1 and 3e3 <= 2 - p1 + 3e0 and "
1426 "e5 >= 1 + e1 and 3e4 >= 6 - 2p1 + 3e1 and "
1427 "p0 >= 2 and p1 >= p0 and 3e2 >= p1 and 3e4 >= 6 - p1 + 3e2 and "
1428 "e2 <= e1 and e3 >= 1 and e4 <= e2) }";
1429 map = isl_map_read_from_str(ctx, str);
1430 map = isl_map_lexmin(map);
1431 isl_map_free(map);
1432
1433 str = "[C] -> { [obj,a,b,c] : obj <= 38 a + 7 b + 10 c and "
1434 "a + b <= 1 and c <= 10 b and c <= C and a,b,c,C >= 0 }";
1435 set = isl_set_read_from_str(ctx, str);
1436 set = isl_set_lexmax(set);
1437 str = "[C] -> { [obj,a,b,c] : C = 8 }";
1438 set2 = isl_set_read_from_str(ctx, str);
1439 set = isl_set_intersect(set, set2);
1440 assert(!isl_set_is_empty(set));
1441 isl_set_free(set);
1442
1443 str = "{ [x] -> [y] : x <= y <= 10; [x] -> [5] : -8 <= x <= 8 }";
1444 map = isl_map_read_from_str(ctx, str);
1445 map = isl_map_lexmin(map);
1446 str = "{ [x] -> [5] : 6 <= x <= 8; "
1447 "[x] -> [x] : x <= 5 or (9 <= x <= 10) }";
1448 map2 = isl_map_read_from_str(ctx, str);
1449 assert(isl_map_is_equal(map, map2));
1450 isl_map_free(map);
1451 isl_map_free(map2);
1452
1453 str = "{ [x] -> [y] : 4y = x or 4y = -1 + x or 4y = -2 + x }";
1454 map = isl_map_read_from_str(ctx, str);
1455 map2 = isl_map_copy(map);
1456 map = isl_map_lexmin(map);
1457 assert(isl_map_is_equal(map, map2));
1458 isl_map_free(map);
1459 isl_map_free(map2);
1460
1461 str = "{ [x] -> [y] : x = 4y; [x] -> [y] : x = 2y }";
1462 map = isl_map_read_from_str(ctx, str);
1463 map = isl_map_lexmin(map);
1464 str = "{ [x] -> [y] : (4y = x and x >= 0) or "
1465 "(exists (e0 = [(x)/4], e1 = [(-2 + x)/4]: 2y = x and "
1466 "4e1 = -2 + x and 4e0 <= -1 + x and 4e0 >= -3 + x)) or "
1467 "(exists (e0 = [(x)/4]: 2y = x and 4e0 = x and x <= -4)) }";
1468 map2 = isl_map_read_from_str(ctx, str);
1469 assert(isl_map_is_equal(map, map2));
1470 isl_map_free(map);
1471 isl_map_free(map2);
1472
1473 str = "{ [i] -> [i', j] : j = i - 8i' and i' >= 0 and i' <= 7 and "
1474 " 8i' <= i and 8i' >= -7 + i }";
1475 bmap = isl_basic_map_read_from_str(ctx, str);
1476 pma = isl_basic_map_lexmin_pw_multi_aff(isl_basic_map_copy(bmap));
1477 map2 = isl_map_from_pw_multi_aff(pma);
1478 map = isl_map_from_basic_map(bmap);
1479 assert(isl_map_is_equal(map, map2));
1480 isl_map_free(map);
1481 isl_map_free(map2);
1482
1483 str = "{ T[a] -> S[b, c] : a = 4b-2c and c >= b }";
1484 map = isl_map_read_from_str(ctx, str);
1485 map = isl_map_lexmin(map);
1486 str = "{ T[a] -> S[b, c] : 2b = a and 2c = a }";
1487 map2 = isl_map_read_from_str(ctx, str);
1488 assert(isl_map_is_equal(map, map2));
1489 isl_map_free(map);
1490 isl_map_free(map2);
1491 }
1492
1493 struct must_may {
1494 isl_map *must;
1495 isl_map *may;
1496 };
1497
1498 static int collect_must_may(__isl_take isl_map *dep, int must,
1499 void *dep_user, void *user)
1500 {
1501 struct must_may *mm = (struct must_may *)user;
1502
1503 if (must)
1504 mm->must = isl_map_union(mm->must, dep);
1505 else
1506 mm->may = isl_map_union(mm->may, dep);
1507
1508 return 0;
1509 }
1510
1511 static int common_space(void *first, void *second)
1512 {
1513 int depth = *(int *)first;
1514 return 2 * depth;
1515 }
1516
1517 static int map_is_equal(__isl_keep isl_map *map, const char *str)
1518 {
1519 isl_map *map2;
1520 int equal;
1521
1522 if (!map)
1523 return -1;
1524
1525 map2 = isl_map_read_from_str(map->ctx, str);
1526 equal = isl_map_is_equal(map, map2);
1527 isl_map_free(map2);
1528
1529 return equal;
1530 }
1531
1532 static int map_check_equal(__isl_keep isl_map *map, const char *str)
1533 {
1534 int equal;
1535
1536 equal = map_is_equal(map, str);
1537 if (equal < 0)
1538 return -1;
1539 if (!equal)
1540 isl_die(isl_map_get_ctx(map), isl_error_unknown,
1541 "result not as expected", return -1);
1542 return 0;
1543 }
1544
1545 void test_dep(struct isl_ctx *ctx)
1546 {
1547 const char *str;
1548 isl_space *dim;
1549 isl_map *map;
1550 isl_access_info *ai;
1551 isl_flow *flow;
1552 int depth;
1553 struct must_may mm;
1554
1555 depth = 3;
1556
1557 str = "{ [2,i,0] -> [i] : 0 <= i <= 10 }";
1558 map = isl_map_read_from_str(ctx, str);
1559 ai = isl_access_info_alloc(map, &depth, &common_space, 2);
1560
1561 str = "{ [0,i,0] -> [i] : 0 <= i <= 10 }";
1562 map = isl_map_read_from_str(ctx, str);
1563 ai = isl_access_info_add_source(ai, map, 1, &depth);
1564
1565 str = "{ [1,i,0] -> [5] : 0 <= i <= 10 }";
1566 map = isl_map_read_from_str(ctx, str);
1567 ai = isl_access_info_add_source(ai, map, 1, &depth);
1568
1569 flow = isl_access_info_compute_flow(ai);
1570 dim = isl_space_alloc(ctx, 0, 3, 3);
1571 mm.must = isl_map_empty(isl_space_copy(dim));
1572 mm.may = isl_map_empty(dim);
1573
1574 isl_flow_foreach(flow, collect_must_may, &mm);
1575
1576 str = "{ [0,i,0] -> [2,i,0] : (0 <= i <= 4) or (6 <= i <= 10); "
1577 " [1,10,0] -> [2,5,0] }";
1578 assert(map_is_equal(mm.must, str));
1579 str = "{ [i,j,k] -> [l,m,n] : 1 = 0 }";
1580 assert(map_is_equal(mm.may, str));
1581
1582 isl_map_free(mm.must);
1583 isl_map_free(mm.may);
1584 isl_flow_free(flow);
1585
1586
1587 str = "{ [2,i,0] -> [i] : 0 <= i <= 10 }";
1588 map = isl_map_read_from_str(ctx, str);
1589 ai = isl_access_info_alloc(map, &depth, &common_space, 2);
1590
1591 str = "{ [0,i,0] -> [i] : 0 <= i <= 10 }";
1592 map = isl_map_read_from_str(ctx, str);
1593 ai = isl_access_info_add_source(ai, map, 1, &depth);
1594
1595 str = "{ [1,i,0] -> [5] : 0 <= i <= 10 }";
1596 map = isl_map_read_from_str(ctx, str);
1597 ai = isl_access_info_add_source(ai, map, 0, &depth);
1598
1599 flow = isl_access_info_compute_flow(ai);
1600 dim = isl_space_alloc(ctx, 0, 3, 3);
1601 mm.must = isl_map_empty(isl_space_copy(dim));
1602 mm.may = isl_map_empty(dim);
1603
1604 isl_flow_foreach(flow, collect_must_may, &mm);
1605
1606 str = "{ [0,i,0] -> [2,i,0] : (0 <= i <= 4) or (6 <= i <= 10) }";
1607 assert(map_is_equal(mm.must, str));
1608 str = "{ [0,5,0] -> [2,5,0]; [1,i,0] -> [2,5,0] : 0 <= i <= 10 }";
1609 assert(map_is_equal(mm.may, str));
1610
1611 isl_map_free(mm.must);
1612 isl_map_free(mm.may);
1613 isl_flow_free(flow);
1614
1615
1616 str = "{ [2,i,0] -> [i] : 0 <= i <= 10 }";
1617 map = isl_map_read_from_str(ctx, str);
1618 ai = isl_access_info_alloc(map, &depth, &common_space, 2);
1619
1620 str = "{ [0,i,0] -> [i] : 0 <= i <= 10 }";
1621 map = isl_map_read_from_str(ctx, str);
1622 ai = isl_access_info_add_source(ai, map, 0, &depth);
1623
1624 str = "{ [1,i,0] -> [5] : 0 <= i <= 10 }";
1625 map = isl_map_read_from_str(ctx, str);
1626 ai = isl_access_info_add_source(ai, map, 0, &depth);
1627
1628 flow = isl_access_info_compute_flow(ai);
1629 dim = isl_space_alloc(ctx, 0, 3, 3);
1630 mm.must = isl_map_empty(isl_space_copy(dim));
1631 mm.may = isl_map_empty(dim);
1632
1633 isl_flow_foreach(flow, collect_must_may, &mm);
1634
1635 str = "{ [0,i,0] -> [2,i,0] : 0 <= i <= 10; "
1636 " [1,i,0] -> [2,5,0] : 0 <= i <= 10 }";
1637 assert(map_is_equal(mm.may, str));
1638 str = "{ [i,j,k] -> [l,m,n] : 1 = 0 }";
1639 assert(map_is_equal(mm.must, str));
1640
1641 isl_map_free(mm.must);
1642 isl_map_free(mm.may);
1643 isl_flow_free(flow);
1644
1645
1646 str = "{ [0,i,2] -> [i] : 0 <= i <= 10 }";
1647 map = isl_map_read_from_str(ctx, str);
1648 ai = isl_access_info_alloc(map, &depth, &common_space, 2);
1649
1650 str = "{ [0,i,0] -> [i] : 0 <= i <= 10 }";
1651 map = isl_map_read_from_str(ctx, str);
1652 ai = isl_access_info_add_source(ai, map, 0, &depth);
1653
1654 str = "{ [0,i,1] -> [5] : 0 <= i <= 10 }";
1655 map = isl_map_read_from_str(ctx, str);
1656 ai = isl_access_info_add_source(ai, map, 0, &depth);
1657
1658 flow = isl_access_info_compute_flow(ai);
1659 dim = isl_space_alloc(ctx, 0, 3, 3);
1660 mm.must = isl_map_empty(isl_space_copy(dim));
1661 mm.may = isl_map_empty(dim);
1662
1663 isl_flow_foreach(flow, collect_must_may, &mm);
1664
1665 str = "{ [0,i,0] -> [0,i,2] : 0 <= i <= 10; "
1666 " [0,i,1] -> [0,5,2] : 0 <= i <= 5 }";
1667 assert(map_is_equal(mm.may, str));
1668 str = "{ [i,j,k] -> [l,m,n] : 1 = 0 }";
1669 assert(map_is_equal(mm.must, str));
1670
1671 isl_map_free(mm.must);
1672 isl_map_free(mm.may);
1673 isl_flow_free(flow);
1674
1675
1676 str = "{ [0,i,1] -> [i] : 0 <= i <= 10 }";
1677 map = isl_map_read_from_str(ctx, str);
1678 ai = isl_access_info_alloc(map, &depth, &common_space, 2);
1679
1680 str = "{ [0,i,0] -> [i] : 0 <= i <= 10 }";
1681 map = isl_map_read_from_str(ctx, str);
1682 ai = isl_access_info_add_source(ai, map, 0, &depth);
1683
1684 str = "{ [0,i,2] -> [5] : 0 <= i <= 10 }";
1685 map = isl_map_read_from_str(ctx, str);
1686 ai = isl_access_info_add_source(ai, map, 0, &depth);
1687
1688 flow = isl_access_info_compute_flow(ai);
1689 dim = isl_space_alloc(ctx, 0, 3, 3);
1690 mm.must = isl_map_empty(isl_space_copy(dim));
1691 mm.may = isl_map_empty(dim);
1692
1693 isl_flow_foreach(flow, collect_must_may, &mm);
1694
1695 str = "{ [0,i,0] -> [0,i,1] : 0 <= i <= 10; "
1696 " [0,i,2] -> [0,5,1] : 0 <= i <= 4 }";
1697 assert(map_is_equal(mm.may, str));
1698 str = "{ [i,j,k] -> [l,m,n] : 1 = 0 }";
1699 assert(map_is_equal(mm.must, str));
1700
1701 isl_map_free(mm.must);
1702 isl_map_free(mm.may);
1703 isl_flow_free(flow);
1704
1705
1706 depth = 5;
1707
1708 str = "{ [1,i,0,0,0] -> [i,j] : 0 <= i <= 10 and 0 <= j <= 10 }";
1709 map = isl_map_read_from_str(ctx, str);
1710 ai = isl_access_info_alloc(map, &depth, &common_space, 1);
1711
1712 str = "{ [0,i,0,j,0] -> [i,j] : 0 <= i <= 10 and 0 <= j <= 10 }";
1713 map = isl_map_read_from_str(ctx, str);
1714 ai = isl_access_info_add_source(ai, map, 1, &depth);
1715
1716 flow = isl_access_info_compute_flow(ai);
1717 dim = isl_space_alloc(ctx, 0, 5, 5);
1718 mm.must = isl_map_empty(isl_space_copy(dim));
1719 mm.may = isl_map_empty(dim);
1720
1721 isl_flow_foreach(flow, collect_must_may, &mm);
1722
1723 str = "{ [0,i,0,j,0] -> [1,i,0,0,0] : 0 <= i,j <= 10 }";
1724 assert(map_is_equal(mm.must, str));
1725 str = "{ [0,0,0,0,0] -> [0,0,0,0,0] : 1 = 0 }";
1726 assert(map_is_equal(mm.may, str));
1727
1728 isl_map_free(mm.must);
1729 isl_map_free(mm.may);
1730 isl_flow_free(flow);
1731 }
1732
1733 int test_sv(isl_ctx *ctx)
1734 {
1735 const char *str;
1736 isl_map *map;
1737 isl_union_map *umap;
1738 int sv;
1739
1740 str = "[N] -> { [i] -> [f] : 0 <= i <= N and 0 <= i - 10 f <= 9 }";
1741 map = isl_map_read_from_str(ctx, str);
1742 sv = isl_map_is_single_valued(map);
1743 isl_map_free(map);
1744 if (sv < 0)
1745 return -1;
1746 if (!sv)
1747 isl_die(ctx, isl_error_internal,
1748 "map not detected as single valued", return -1);
1749
1750 str = "[N] -> { [i] -> [f] : 0 <= i <= N and 0 <= i - 10 f <= 10 }";
1751 map = isl_map_read_from_str(ctx, str);
1752 sv = isl_map_is_single_valued(map);
1753 isl_map_free(map);
1754 if (sv < 0)
1755 return -1;
1756 if (sv)
1757 isl_die(ctx, isl_error_internal,
1758 "map detected as single valued", return -1);
1759
1760 str = "{ S1[i] -> [i] : 0 <= i <= 9; S2[i] -> [i] : 0 <= i <= 9 }";
1761 umap = isl_union_map_read_from_str(ctx, str);
1762 sv = isl_union_map_is_single_valued(umap);
1763 isl_union_map_free(umap);
1764 if (sv < 0)
1765 return -1;
1766 if (!sv)
1767 isl_die(ctx, isl_error_internal,
1768 "map not detected as single valued", return -1);
1769
1770 str = "{ [i] -> S1[i] : 0 <= i <= 9; [i] -> S2[i] : 0 <= i <= 9 }";
1771 umap = isl_union_map_read_from_str(ctx, str);
1772 sv = isl_union_map_is_single_valued(umap);
1773 isl_union_map_free(umap);
1774 if (sv < 0)
1775 return -1;
1776 if (sv)
1777 isl_die(ctx, isl_error_internal,
1778 "map detected as single valued", return -1);
1779
1780 return 0;
1781 }
1782
1783 void test_bijective_case(struct isl_ctx *ctx, const char *str, int bijective)
1784 {
1785 isl_map *map;
1786
1787 map = isl_map_read_from_str(ctx, str);
1788 if (bijective)
1789 assert(isl_map_is_bijective(map));
1790 else
1791 assert(!isl_map_is_bijective(map));
1792 isl_map_free(map);
1793 }
1794
1795 void test_bijective(struct isl_ctx *ctx)
1796 {
1797 test_bijective_case(ctx, "[N,M]->{[i,j] -> [i]}", 0);
1798 test_bijective_case(ctx, "[N,M]->{[i,j] -> [i] : j=i}", 1);
1799 test_bijective_case(ctx, "[N,M]->{[i,j] -> [i] : j=0}", 1);
1800 test_bijective_case(ctx, "[N,M]->{[i,j] -> [i] : j=N}", 1);
1801 test_bijective_case(ctx, "[N,M]->{[i,j] -> [j,i]}", 1);
1802 test_bijective_case(ctx, "[N,M]->{[i,j] -> [i+j]}", 0);
1803 test_bijective_case(ctx, "[N,M]->{[i,j] -> []}", 0);
1804 test_bijective_case(ctx, "[N,M]->{[i,j] -> [i,j,N]}", 1);
1805 test_bijective_case(ctx, "[N,M]->{[i,j] -> [2i]}", 0);
1806 test_bijective_case(ctx, "[N,M]->{[i,j] -> [i,i]}", 0);
1807 test_bijective_case(ctx, "[N,M]->{[i,j] -> [2i,i]}", 0);
1808 test_bijective_case(ctx, "[N,M]->{[i,j] -> [2i,j]}", 1);
1809 test_bijective_case(ctx, "[N,M]->{[i,j] -> [x,y] : 2x=i & y =j}", 1);
1810 }
1811
1812 void test_pwqp(struct isl_ctx *ctx)
1813 {
1814 const char *str;
1815 isl_set *set;
1816 isl_pw_qpolynomial *pwqp1, *pwqp2;
1817
1818 str = "{ [i,j,k] -> 1 + 9 * [i/5] + 7 * [j/11] + 4 * [k/13] }";
1819 pwqp1 = isl_pw_qpolynomial_read_from_str(ctx, str);
1820
1821 pwqp1 = isl_pw_qpolynomial_move_dims(pwqp1, isl_dim_param, 0,
1822 isl_dim_in, 1, 1);
1823
1824 str = "[j] -> { [i,k] -> 1 + 9 * [i/5] + 7 * [j/11] + 4 * [k/13] }";
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 }";
1834 pwqp1 = isl_pw_qpolynomial_read_from_str(ctx, str);
1835 str = "{ [k] : exists a : k = 2a }";
1836 set = isl_set_read_from_str(ctx, str);
1837 pwqp1 = isl_pw_qpolynomial_gist(pwqp1, set);
1838 str = "{ [i] -> i }";
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 + [ (i + [i/3])/2 ] }";
1848 pwqp1 = isl_pw_qpolynomial_read_from_str(ctx, str);
1849 str = "{ [10] }";
1850 set = isl_set_read_from_str(ctx, str);
1851 pwqp1 = isl_pw_qpolynomial_gist(pwqp1, set);
1852 str = "{ [i] -> 16 }";
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]) }";
1862 pwqp1 = isl_pw_qpolynomial_read_from_str(ctx, str);
1863 str = "{ [k] : exists a : k = 2a+1 }";
1864 set = isl_set_read_from_str(ctx, str);
1865 pwqp1 = isl_pw_qpolynomial_gist(pwqp1, set);
1866 str = "{ [i] -> -1/2 + 1/2 * i }";
1867 pwqp2 = isl_pw_qpolynomial_read_from_str(ctx, str);
1868
1869 pwqp1 = isl_pw_qpolynomial_sub(pwqp1, pwqp2);
1870
1871 assert(isl_pw_qpolynomial_is_zero(pwqp1));
1872
1873 isl_pw_qpolynomial_free(pwqp1);
1874
1875 str = "{ [i] -> ([([i/2] + [i/2])/5]) }";
1876 pwqp1 = isl_pw_qpolynomial_read_from_str(ctx, str);
1877 str = "{ [i] -> ([(2 * [i/2])/5]) }";
1878 pwqp2 = isl_pw_qpolynomial_read_from_str(ctx, str);
1879
1880 pwqp1 = isl_pw_qpolynomial_sub(pwqp1, pwqp2);
1881
1882 assert(isl_pw_qpolynomial_is_zero(pwqp1));
1883
1884 isl_pw_qpolynomial_free(pwqp1);
1885
1886 str = "{ [x] -> ([x/2] + [(x+1)/2]) }";
1887 pwqp1 = isl_pw_qpolynomial_read_from_str(ctx, str);
1888 str = "{ [x] -> x }";
1889 pwqp2 = isl_pw_qpolynomial_read_from_str(ctx, str);
1890
1891 pwqp1 = isl_pw_qpolynomial_sub(pwqp1, pwqp2);
1892
1893 assert(isl_pw_qpolynomial_is_zero(pwqp1));
1894
1895 isl_pw_qpolynomial_free(pwqp1);
1896
1897 str = "{ [i] -> ([i/2]) : i >= 0; [i] -> ([i/3]) : i < 0 }";
1898 pwqp1 = isl_pw_qpolynomial_read_from_str(ctx, str);
1899 pwqp2 = isl_pw_qpolynomial_read_from_str(ctx, str);
1900 pwqp1 = isl_pw_qpolynomial_coalesce(pwqp1);
1901 pwqp1 = isl_pw_qpolynomial_sub(pwqp1, pwqp2);
1902 assert(isl_pw_qpolynomial_is_zero(pwqp1));
1903 isl_pw_qpolynomial_free(pwqp1);
1904 }
1905
1906 void test_split_periods(isl_ctx *ctx)
1907 {
1908 const char *str;
1909 isl_pw_qpolynomial *pwqp;
1910
1911 str = "{ [U,V] -> 1/3 * U + 2/3 * V - [(U + 2V)/3] + [U/2] : "
1912 "U + 2V + 3 >= 0 and - U -2V >= 0 and - U + 10 >= 0 and "
1913 "U >= 0; [U,V] -> U^2 : U >= 100 }";
1914 pwqp = isl_pw_qpolynomial_read_from_str(ctx, str);
1915
1916 pwqp = isl_pw_qpolynomial_split_periods(pwqp, 2);
1917 assert(pwqp);
1918
1919 isl_pw_qpolynomial_free(pwqp);
1920 }
1921
1922 void test_union(isl_ctx *ctx)
1923 {
1924 const char *str;
1925 isl_union_set *uset1, *uset2;
1926 isl_union_map *umap1, *umap2;
1927
1928 str = "{ [i] : 0 <= i <= 1 }";
1929 uset1 = isl_union_set_read_from_str(ctx, str);
1930 str = "{ [1] -> [0] }";
1931 umap1 = isl_union_map_read_from_str(ctx, str);
1932
1933 umap2 = isl_union_set_lex_gt_union_set(isl_union_set_copy(uset1), uset1);
1934 assert(isl_union_map_is_equal(umap1, umap2));
1935
1936 isl_union_map_free(umap1);
1937 isl_union_map_free(umap2);
1938
1939 str = "{ A[i] -> B[i]; B[i] -> C[i]; A[0] -> C[1] }";
1940 umap1 = isl_union_map_read_from_str(ctx, str);
1941 str = "{ A[i]; B[i] }";
1942 uset1 = isl_union_set_read_from_str(ctx, str);
1943
1944 uset2 = isl_union_map_domain(umap1);
1945
1946 assert(isl_union_set_is_equal(uset1, uset2));
1947
1948 isl_union_set_free(uset1);
1949 isl_union_set_free(uset2);
1950 }
1951
1952 void test_bound(isl_ctx *ctx)
1953 {
1954 const char *str;
1955 isl_pw_qpolynomial *pwqp;
1956 isl_pw_qpolynomial_fold *pwf;
1957
1958 str = "{ [[a, b, c, d] -> [e]] -> 0 }";
1959 pwqp = isl_pw_qpolynomial_read_from_str(ctx, str);
1960 pwf = isl_pw_qpolynomial_bound(pwqp, isl_fold_max, NULL);
1961 assert(isl_pw_qpolynomial_fold_dim(pwf, isl_dim_in) == 4);
1962 isl_pw_qpolynomial_fold_free(pwf);
1963
1964 str = "{ [[x]->[x]] -> 1 : exists a : x = 2 a }";
1965 pwqp = isl_pw_qpolynomial_read_from_str(ctx, str);
1966 pwf = isl_pw_qpolynomial_bound(pwqp, isl_fold_max, NULL);
1967 assert(isl_pw_qpolynomial_fold_dim(pwf, isl_dim_in) == 1);
1968 isl_pw_qpolynomial_fold_free(pwf);
1969 }
1970
1971 void test_lift(isl_ctx *ctx)
1972 {
1973 const char *str;
1974 isl_basic_map *bmap;
1975 isl_basic_set *bset;
1976
1977 str = "{ [i0] : exists e0 : i0 = 4e0 }";
1978 bset = isl_basic_set_read_from_str(ctx, str);
1979 bset = isl_basic_set_lift(bset);
1980 bmap = isl_basic_map_from_range(bset);
1981 bset = isl_basic_map_domain(bmap);
1982 isl_basic_set_free(bset);
1983 }
1984
1985 void test_subset(isl_ctx *ctx)
1986 {
1987 const char *str;
1988 isl_set *set1, *set2;
1989
1990 str = "{ [112, 0] }";
1991 set1 = isl_set_read_from_str(ctx, str);
1992 str = "{ [i0, i1] : exists (e0 = [(i0 - i1)/16], e1: "
1993 "16e0 <= i0 - i1 and 16e0 >= -15 + i0 - i1 and "
1994 "16e1 <= i1 and 16e0 >= -i1 and 16e1 >= -i0 + i1) }";
1995 set2 = isl_set_read_from_str(ctx, str);
1996 assert(isl_set_is_subset(set1, set2));
1997 isl_set_free(set1);
1998 isl_set_free(set2);
1999 }
2000
2001 int test_factorize(isl_ctx *ctx)
2002 {
2003 const char *str;
2004 isl_basic_set *bset;
2005 isl_factorizer *f;
2006
2007 str = "{ [i0, i1, i2, i3, i4, i5, i6, i7] : 3i5 <= 2 - 2i0 and "
2008 "i0 >= -2 and i6 >= 1 + i3 and i7 >= 0 and 3i5 >= -2i0 and "
2009 "2i4 <= i2 and i6 >= 1 + 2i0 + 3i1 and i4 <= -1 and "
2010 "i6 >= 1 + 2i0 + 3i5 and i6 <= 2 + 2i0 + 3i5 and "
2011 "3i5 <= 2 - 2i0 - i2 + 3i4 and i6 <= 2 + 2i0 + 3i1 and "
2012 "i0 <= -1 and i7 <= i2 + i3 - 3i4 - i6 and "
2013 "3i5 >= -2i0 - i2 + 3i4 }";
2014 bset = isl_basic_set_read_from_str(ctx, str);
2015 f = isl_basic_set_factorizer(bset);
2016 isl_basic_set_free(bset);
2017 isl_factorizer_free(f);
2018 if (!f)
2019 isl_die(ctx, isl_error_unknown,
2020 "failed to construct factorizer", return -1);
2021
2022 str = "{ [i0, i1, i2, i3, i4, i5, i6, i7, i8, i9, i10, i11, i12] : "
2023 "i12 <= 2 + i0 - i11 and 2i8 >= -i4 and i11 >= i1 and "
2024 "3i5 <= -i2 and 2i11 >= -i4 - 2i7 and i11 <= 3 + i0 + 3i9 and "
2025 "i11 <= -i4 - 2i7 and i12 >= -i10 and i2 >= -2 and "
2026 "i11 >= i1 + 3i10 and i11 >= 1 + i0 + 3i9 and "
2027 "i11 <= 1 - i4 - 2i8 and 6i6 <= 6 - i2 and 3i6 >= 1 - i2 and "
2028 "i11 <= 2 + i1 and i12 <= i4 + i11 and i12 >= i0 - i11 and "
2029 "3i5 >= -2 - i2 and i12 >= -1 + i4 + i11 and 3i3 <= 3 - i2 and "
2030 "9i6 <= 11 - i2 + 6i5 and 3i3 >= 1 - i2 and "
2031 "9i6 <= 5 - i2 + 6i3 and i12 <= -1 and i2 <= 0 }";
2032 bset = isl_basic_set_read_from_str(ctx, str);
2033 f = isl_basic_set_factorizer(bset);
2034 isl_basic_set_free(bset);
2035 isl_factorizer_free(f);
2036 if (!f)
2037 isl_die(ctx, isl_error_unknown,
2038 "failed to construct factorizer", return -1);
2039
2040 return 0;
2041 }
2042
2043 static int check_injective(__isl_take isl_map *map, void *user)
2044 {
2045 int *injective = user;
2046
2047 *injective = isl_map_is_injective(map);
2048 isl_map_free(map);
2049
2050 if (*injective < 0 || !*injective)
2051 return -1;
2052
2053 return 0;
2054 }
2055
2056 int test_one_schedule(isl_ctx *ctx, const char *d, const char *w,
2057 const char *r, const char *s, int tilable, int parallel)
2058 {
2059 int i;
2060 isl_union_set *D;
2061 isl_union_map *W, *R, *S;
2062 isl_union_map *empty;
2063 isl_union_map *dep_raw, *dep_war, *dep_waw, *dep;
2064 isl_union_map *validity, *proximity;
2065 isl_union_map *schedule;
2066 isl_union_map *test;
2067 isl_union_set *delta;
2068 isl_union_set *domain;
2069 isl_set *delta_set;
2070 isl_set *slice;
2071 isl_set *origin;
2072 isl_schedule *sched;
2073 int is_nonneg, is_parallel, is_tilable, is_injection, is_complete;
2074
2075 D = isl_union_set_read_from_str(ctx, d);
2076 W = isl_union_map_read_from_str(ctx, w);
2077 R = isl_union_map_read_from_str(ctx, r);
2078 S = isl_union_map_read_from_str(ctx, s);
2079
2080 W = isl_union_map_intersect_domain(W, isl_union_set_copy(D));
2081 R = isl_union_map_intersect_domain(R, isl_union_set_copy(D));
2082
2083 empty = isl_union_map_empty(isl_union_map_get_space(S));
2084 isl_union_map_compute_flow(isl_union_map_copy(R),
2085 isl_union_map_copy(W), empty,
2086 isl_union_map_copy(S),
2087 &dep_raw, NULL, NULL, NULL);
2088 isl_union_map_compute_flow(isl_union_map_copy(W),
2089 isl_union_map_copy(W),
2090 isl_union_map_copy(R),
2091 isl_union_map_copy(S),
2092 &dep_waw, &dep_war, NULL, NULL);
2093
2094 dep = isl_union_map_union(dep_waw, dep_war);
2095 dep = isl_union_map_union(dep, dep_raw);
2096 validity = isl_union_map_copy(dep);
2097 proximity = isl_union_map_copy(dep);
2098
2099 sched = isl_union_set_compute_schedule(isl_union_set_copy(D),
2100 validity, proximity);
2101 schedule = isl_schedule_get_map(sched);
2102 isl_schedule_free(sched);
2103 isl_union_map_free(W);
2104 isl_union_map_free(R);
2105 isl_union_map_free(S);
2106
2107 is_injection = 1;
2108 isl_union_map_foreach_map(schedule, &check_injective, &is_injection);
2109
2110 domain = isl_union_map_domain(isl_union_map_copy(schedule));
2111 is_complete = isl_union_set_is_subset(D, domain);
2112 isl_union_set_free(D);
2113 isl_union_set_free(domain);
2114
2115 test = isl_union_map_reverse(isl_union_map_copy(schedule));
2116 test = isl_union_map_apply_range(test, dep);
2117 test = isl_union_map_apply_range(test, schedule);
2118
2119 delta = isl_union_map_deltas(test);
2120 if (isl_union_set_n_set(delta) == 0) {
2121 is_tilable = 1;
2122 is_parallel = 1;
2123 is_nonneg = 1;
2124 isl_union_set_free(delta);
2125 } else {
2126 delta_set = isl_set_from_union_set(delta);
2127
2128 slice = isl_set_universe(isl_set_get_space(delta_set));
2129 for (i = 0; i < tilable; ++i)
2130 slice = isl_set_lower_bound_si(slice, isl_dim_set, i, 0);
2131 is_tilable = isl_set_is_subset(delta_set, slice);
2132 isl_set_free(slice);
2133
2134 slice = isl_set_universe(isl_set_get_space(delta_set));
2135 for (i = 0; i < parallel; ++i)
2136 slice = isl_set_fix_si(slice, isl_dim_set, i, 0);
2137 is_parallel = isl_set_is_subset(delta_set, slice);
2138 isl_set_free(slice);
2139
2140 origin = isl_set_universe(isl_set_get_space(delta_set));
2141 for (i = 0; i < isl_set_dim(origin, isl_dim_set); ++i)
2142 origin = isl_set_fix_si(origin, isl_dim_set, i, 0);
2143
2144 delta_set = isl_set_union(delta_set, isl_set_copy(origin));
2145 delta_set = isl_set_lexmin(delta_set);
2146
2147 is_nonneg = isl_set_is_equal(delta_set, origin);
2148
2149 isl_set_free(origin);
2150 isl_set_free(delta_set);
2151 }
2152
2153 if (is_nonneg < 0 || is_parallel < 0 || is_tilable < 0 ||
2154 is_injection < 0 || is_complete < 0)
2155 return -1;
2156 if (!is_complete)
2157 isl_die(ctx, isl_error_unknown,
2158 "generated schedule incomplete", return -1);
2159 if (!is_injection)
2160 isl_die(ctx, isl_error_unknown,
2161 "generated schedule not injective on each statement",
2162 return -1);
2163 if (!is_nonneg)
2164 isl_die(ctx, isl_error_unknown,
2165 "negative dependences in generated schedule",
2166 return -1);
2167 if (!is_tilable)
2168 isl_die(ctx, isl_error_unknown,
2169 "generated schedule not as tilable as expected",
2170 return -1);
2171 if (!is_parallel)
2172 isl_die(ctx, isl_error_unknown,
2173 "generated schedule not as parallel as expected",
2174 return -1);
2175
2176 return 0;
2177 }
2178
2179 int test_special_schedule(isl_ctx *ctx, const char *domain,
2180 const char *validity, const char *proximity, const char *expected_sched)
2181 {
2182 isl_union_set *dom;
2183 isl_union_map *dep;
2184 isl_union_map *prox;
2185 isl_union_map *sched1, *sched2;
2186 isl_schedule *schedule;
2187 int equal;
2188
2189 dom = isl_union_set_read_from_str(ctx, domain);
2190 dep = isl_union_map_read_from_str(ctx, validity);
2191 prox = isl_union_map_read_from_str(ctx, proximity);
2192 schedule = isl_union_set_compute_schedule(dom, dep, prox);
2193 sched1 = isl_schedule_get_map(schedule);
2194 isl_schedule_free(schedule);
2195
2196 sched2 = isl_union_map_read_from_str(ctx, expected_sched);
2197
2198 equal = isl_union_map_is_equal(sched1, sched2);
2199 isl_union_map_free(sched1);
2200 isl_union_map_free(sched2);
2201
2202 if (equal < 0)
2203 return -1;
2204 if (!equal)
2205 isl_die(ctx, isl_error_unknown, "unexpected schedule",
2206 return -1);
2207
2208 return 0;
2209 }
2210
2211 int test_schedule(isl_ctx *ctx)
2212 {
2213 const char *D, *W, *R, *V, *P, *S;
2214
2215 /* Jacobi */
2216 D = "[T,N] -> { S1[t,i] : 1 <= t <= T and 2 <= i <= N - 1 }";
2217 W = "{ S1[t,i] -> a[t,i] }";
2218 R = "{ S1[t,i] -> a[t-1,i]; S1[t,i] -> a[t-1,i-1]; "
2219 "S1[t,i] -> a[t-1,i+1] }";
2220 S = "{ S1[t,i] -> [t,i] }";
2221 if (test_one_schedule(ctx, D, W, R, S, 2, 0) < 0)
2222 return -1;
2223
2224 /* Fig. 5 of CC2008 */
2225 D = "[N] -> { S_0[i, j] : i >= 0 and i <= -1 + N and j >= 2 and "
2226 "j <= -1 + N }";
2227 W = "[N] -> { S_0[i, j] -> a[i, j] : i >= 0 and i <= -1 + N and "
2228 "j >= 2 and j <= -1 + N }";
2229 R = "[N] -> { S_0[i, j] -> a[j, i] : i >= 0 and i <= -1 + N and "
2230 "j >= 2 and j <= -1 + N; "
2231 "S_0[i, j] -> a[i, -1 + j] : i >= 0 and i <= -1 + N and "
2232 "j >= 2 and j <= -1 + N }";
2233 S = "[N] -> { S_0[i, j] -> [0, i, 0, j, 0] }";
2234 if (test_one_schedule(ctx, D, W, R, S, 2, 0) < 0)
2235 return -1;
2236
2237 D = "{ S1[i] : 0 <= i <= 10; S2[i] : 0 <= i <= 9 }";
2238 W = "{ S1[i] -> a[i] }";
2239 R = "{ S2[i] -> a[i+1] }";
2240 S = "{ S1[i] -> [0,i]; S2[i] -> [1,i] }";
2241 if (test_one_schedule(ctx, D, W, R, S, 1, 1) < 0)
2242 return -1;
2243
2244 D = "{ S1[i] : 0 <= i < 10; S2[i] : 0 <= i < 10 }";
2245 W = "{ S1[i] -> a[i] }";
2246 R = "{ S2[i] -> a[9-i] }";
2247 S = "{ S1[i] -> [0,i]; S2[i] -> [1,i] }";
2248 if (test_one_schedule(ctx, D, W, R, S, 1, 1) < 0)
2249 return -1;
2250
2251 D = "[N] -> { S1[i] : 0 <= i < N; S2[i] : 0 <= i < N }";
2252 W = "{ S1[i] -> a[i] }";
2253 R = "[N] -> { S2[i] -> a[N-1-i] }";
2254 S = "{ S1[i] -> [0,i]; S2[i] -> [1,i] }";
2255 if (test_one_schedule(ctx, D, W, R, S, 1, 1) < 0)
2256 return -1;
2257
2258 D = "{ S1[i] : 0 < i < 10; S2[i] : 0 <= i < 10 }";
2259 W = "{ S1[i] -> a[i]; S2[i] -> b[i] }";
2260 R = "{ S2[i] -> a[i]; S1[i] -> b[i-1] }";
2261 S = "{ S1[i] -> [i,0]; S2[i] -> [i,1] }";
2262 if (test_one_schedule(ctx, D, W, R, S, 0, 0) < 0)
2263 return -1;
2264
2265 D = "[N] -> { S1[i] : 1 <= i <= N; S2[i,j] : 1 <= i,j <= N }";
2266 W = "{ S1[i] -> a[0,i]; S2[i,j] -> a[i,j] }";
2267 R = "{ S2[i,j] -> a[i-1,j] }";
2268 S = "{ S1[i] -> [0,i,0]; S2[i,j] -> [1,i,j] }";
2269 if (test_one_schedule(ctx, D, W, R, S, 2, 1) < 0)
2270 return -1;
2271
2272 D = "[N] -> { S1[i] : 1 <= i <= N; S2[i,j] : 1 <= i,j <= N }";
2273 W = "{ S1[i] -> a[i,0]; S2[i,j] -> a[i,j] }";
2274 R = "{ S2[i,j] -> a[i,j-1] }";
2275 S = "{ S1[i] -> [0,i,0]; S2[i,j] -> [1,i,j] }";
2276 if (test_one_schedule(ctx, D, W, R, S, 2, 1) < 0)
2277 return -1;
2278
2279 D = "[N] -> { S_0[]; S_1[i] : i >= 0 and i <= -1 + N; S_2[] }";
2280 W = "[N] -> { S_0[] -> a[0]; S_2[] -> b[0]; "
2281 "S_1[i] -> a[1 + i] : i >= 0 and i <= -1 + N }";
2282 R = "[N] -> { S_2[] -> a[N]; S_1[i] -> a[i] : i >= 0 and i <= -1 + N }";
2283 S = "[N] -> { S_1[i] -> [1, i, 0]; S_2[] -> [2, 0, 1]; "
2284 "S_0[] -> [0, 0, 0] }";
2285 if (test_one_schedule(ctx, D, W, R, S, 1, 0) < 0)
2286 return -1;
2287 ctx->opt->schedule_parametric = 0;
2288 if (test_one_schedule(ctx, D, W, R, S, 0, 0) < 0)
2289 return -1;
2290 ctx->opt->schedule_parametric = 1;
2291
2292 D = "[N] -> { S1[i] : 1 <= i <= N; S2[i] : 1 <= i <= N; "
2293 "S3[i,j] : 1 <= i,j <= N; S4[i] : 1 <= i <= N }";
2294 W = "{ S1[i] -> a[i,0]; S2[i] -> a[0,i]; S3[i,j] -> a[i,j] }";
2295 R = "[N] -> { S3[i,j] -> a[i-1,j]; S3[i,j] -> a[i,j-1]; "
2296 "S4[i] -> a[i,N] }";
2297 S = "{ S1[i] -> [0,i,0]; S2[i] -> [1,i,0]; S3[i,j] -> [2,i,j]; "
2298 "S4[i] -> [4,i,0] }";
2299 if (test_one_schedule(ctx, D, W, R, S, 2, 0) < 0)
2300 return -1;
2301
2302 D = "[N] -> { S_0[i, j] : i >= 1 and i <= N and j >= 1 and j <= N }";
2303 W = "[N] -> { S_0[i, j] -> s[0] : i >= 1 and i <= N and j >= 1 and "
2304 "j <= N }";
2305 R = "[N] -> { S_0[i, j] -> s[0] : i >= 1 and i <= N and j >= 1 and "
2306 "j <= N; "
2307 "S_0[i, j] -> a[i, j] : i >= 1 and i <= N and j >= 1 and "
2308 "j <= N }";
2309 S = "[N] -> { S_0[i, j] -> [0, i, 0, j, 0] }";
2310 if (test_one_schedule(ctx, D, W, R, S, 0, 0) < 0)
2311 return -1;
2312
2313 D = "[N] -> { S_0[t] : t >= 0 and t <= -1 + N; "
2314 " S_2[t] : t >= 0 and t <= -1 + N; "
2315 " S_1[t, i] : t >= 0 and t <= -1 + N and i >= 0 and "
2316 "i <= -1 + N }";
2317 W = "[N] -> { S_0[t] -> a[t, 0] : t >= 0 and t <= -1 + N; "
2318 " S_2[t] -> b[t] : t >= 0 and t <= -1 + N; "
2319 " S_1[t, i] -> a[t, 1 + i] : t >= 0 and t <= -1 + N and "
2320 "i >= 0 and i <= -1 + N }";
2321 R = "[N] -> { S_1[t, i] -> a[t, i] : t >= 0 and t <= -1 + N and "
2322 "i >= 0 and i <= -1 + N; "
2323 " S_2[t] -> a[t, N] : t >= 0 and t <= -1 + N }";
2324 S = "[N] -> { S_2[t] -> [0, t, 2]; S_1[t, i] -> [0, t, 1, i, 0]; "
2325 " S_0[t] -> [0, t, 0] }";
2326
2327 if (test_one_schedule(ctx, D, W, R, S, 2, 1) < 0)
2328 return -1;
2329 ctx->opt->schedule_parametric = 0;
2330 if (test_one_schedule(ctx, D, W, R, S, 0, 0) < 0)
2331 return -1;
2332 ctx->opt->schedule_parametric = 1;
2333
2334 D = "[N] -> { S1[i,j] : 0 <= i,j < N; S2[i,j] : 0 <= i,j < N }";
2335 S = "{ S1[i,j] -> [0,i,j]; S2[i,j] -> [1,i,j] }";
2336 if (test_one_schedule(ctx, D, "{}", "{}", S, 2, 2) < 0)
2337 return -1;
2338
2339 D = "[M, N] -> { S_1[i] : i >= 0 and i <= -1 + M; "
2340 "S_0[i, j] : i >= 0 and i <= -1 + M and j >= 0 and j <= -1 + N }";
2341 W = "[M, N] -> { S_0[i, j] -> a[j] : i >= 0 and i <= -1 + M and "
2342 "j >= 0 and j <= -1 + N; "
2343 "S_1[i] -> b[0] : i >= 0 and i <= -1 + M }";
2344 R = "[M, N] -> { S_0[i, j] -> a[0] : i >= 0 and i <= -1 + M and "
2345 "j >= 0 and j <= -1 + N; "
2346 "S_1[i] -> b[0] : i >= 0 and i <= -1 + M }";
2347 S = "[M, N] -> { S_1[i] -> [1, i, 0]; S_0[i, j] -> [0, i, 0, j, 0] }";
2348 if (test_one_schedule(ctx, D, W, R, S, 0, 0) < 0)
2349 return -1;
2350
2351 D = "{ S_0[i] : i >= 0 }";
2352 W = "{ S_0[i] -> a[i] : i >= 0 }";
2353 R = "{ S_0[i] -> a[0] : i >= 0 }";
2354 S = "{ S_0[i] -> [0, i, 0] }";
2355 if (test_one_schedule(ctx, D, W, R, S, 0, 0) < 0)
2356 return -1;
2357
2358 D = "{ S_0[i] : i >= 0; S_1[i] : i >= 0 }";
2359 W = "{ S_0[i] -> a[i] : i >= 0; S_1[i] -> b[i] : i >= 0 }";
2360 R = "{ S_0[i] -> b[0] : i >= 0; S_1[i] -> a[i] : i >= 0 }";
2361 S = "{ S_1[i] -> [0, i, 1]; S_0[i] -> [0, i, 0] }";
2362 if (test_one_schedule(ctx, D, W, R, S, 0, 0) < 0)
2363 return -1;
2364
2365 D = "[n] -> { S_0[j, k] : j <= -1 + n and j >= 0 and "
2366 "k <= -1 + n and k >= 0 }";
2367 W = "[n] -> { S_0[j, k] -> B[j] : j <= -1 + n and j >= 0 and " "k <= -1 + n and k >= 0 }";
2368 R = "[n] -> { S_0[j, k] -> B[j] : j <= -1 + n and j >= 0 and "
2369 "k <= -1 + n and k >= 0; "
2370 "S_0[j, k] -> B[k] : j <= -1 + n and j >= 0 and "
2371 "k <= -1 + n and k >= 0; "
2372 "S_0[j, k] -> A[k] : j <= -1 + n and j >= 0 and "
2373 "k <= -1 + n and k >= 0 }";
2374 S = "[n] -> { S_0[j, k] -> [2, j, k] }";
2375 ctx->opt->schedule_outer_zero_distance = 1;
2376 if (test_one_schedule(ctx, D, W, R, S, 0, 0) < 0)
2377 return -1;
2378 ctx->opt->schedule_outer_zero_distance = 0;
2379
2380 D = "{Stmt_for_body24[i0, i1, i2, i3]:"
2381 "i0 >= 0 and i0 <= 1 and i1 >= 0 and i1 <= 6 and i2 >= 2 and "
2382 "i2 <= 6 - i1 and i3 >= 0 and i3 <= -1 + i2;"
2383 "Stmt_for_body24[i0, i1, 1, 0]:"
2384 "i0 >= 0 and i0 <= 1 and i1 >= 0 and i1 <= 5;"
2385 "Stmt_for_body7[i0, i1, i2]:"
2386 "i0 >= 0 and i0 <= 1 and i1 >= 0 and i1 <= 7 and i2 >= 0 and "
2387 "i2 <= 7 }";
2388
2389 V = "{Stmt_for_body24[0, i1, i2, i3] -> "
2390 "Stmt_for_body24[1, i1, i2, i3]:"
2391 "i3 >= 0 and i3 <= -1 + i2 and i1 >= 0 and i2 <= 6 - i1 and "
2392 "i2 >= 1;"
2393 "Stmt_for_body24[0, i1, i2, i3] -> "
2394 "Stmt_for_body7[1, 1 + i1 + i3, 1 + i1 + i2]:"
2395 "i3 <= -1 + i2 and i2 <= 6 - i1 and i2 >= 1 and i1 >= 0 and "
2396 "i3 >= 0;"
2397 "Stmt_for_body24[0, i1, i2, i3] ->"
2398 "Stmt_for_body7[1, i1, 1 + i1 + i3]:"
2399 "i3 >= 0 and i2 <= 6 - i1 and i1 >= 0 and i3 <= -1 + i2;"
2400 "Stmt_for_body7[0, i1, i2] -> Stmt_for_body7[1, i1, i2]:"
2401 "(i2 >= 1 + i1 and i2 <= 6 and i1 >= 0 and i1 <= 4) or "
2402 "(i2 >= 3 and i2 <= 7 and i1 >= 1 and i2 >= 1 + i1) or "
2403 "(i2 >= 0 and i2 <= i1 and i2 >= -7 + i1 and i1 <= 7);"
2404 "Stmt_for_body7[0, i1, 1 + i1] -> Stmt_for_body7[1, i1, 1 + i1]:"
2405 "i1 <= 6 and i1 >= 0;"
2406 "Stmt_for_body7[0, 0, 7] -> Stmt_for_body7[1, 0, 7];"
2407 "Stmt_for_body7[i0, i1, i2] -> "
2408 "Stmt_for_body24[i0, o1, -1 + i2 - o1, -1 + i1 - o1]:"
2409 "i0 >= 0 and i0 <= 1 and o1 >= 0 and i2 >= 1 + i1 and "
2410 "o1 <= -2 + i2 and i2 <= 7 and o1 <= -1 + i1;"
2411 "Stmt_for_body7[i0, i1, i2] -> "
2412 "Stmt_for_body24[i0, i1, o2, -1 - i1 + i2]:"
2413 "i0 >= 0 and i0 <= 1 and i1 >= 0 and o2 >= -i1 + i2 and "
2414 "o2 >= 1 and o2 <= 6 - i1 and i2 >= 1 + i1 }";
2415 P = V;
2416 S = "{ Stmt_for_body24[i0, i1, i2, i3] -> "
2417 "[i0, 5i0 + i1, 6i0 + i1 + i2, 1 + 6i0 + i1 + i2 + i3, 1];"
2418 "Stmt_for_body7[i0, i1, i2] -> [0, 5i0, 6i0 + i1, 6i0 + i2, 0] }";
2419
2420 if (test_special_schedule(ctx, D, V, P, S) < 0)
2421 return -1;
2422
2423 D = "{ S_0[i, j] : i >= 1 and i <= 10 and j >= 1 and j <= 8 }";
2424 V = "{ S_0[i, j] -> S_0[i, 1 + j] : i >= 1 and i <= 10 and "
2425 "j >= 1 and j <= 7;"
2426 "S_0[i, j] -> S_0[1 + i, j] : i >= 1 and i <= 9 and "
2427 "j >= 1 and j <= 8 }";
2428 P = "{ }";
2429 S = "{ S_0[i, j] -> [i + j, j] }";
2430 ctx->opt->schedule_algorithm = ISL_SCHEDULE_ALGORITHM_FEAUTRIER;
2431 if (test_special_schedule(ctx, D, V, P, S) < 0)
2432 return -1;
2433 ctx->opt->schedule_algorithm = ISL_SCHEDULE_ALGORITHM_ISL;
2434
2435 /* Fig. 1 from Feautrier's "Some Efficient Solutions..." pt. 2, 1992 */
2436 D = "[N] -> { S_0[i, j] : i >= 0 and i <= -1 + N and "
2437 "j >= 0 and j <= -1 + i }";
2438 V = "[N] -> { S_0[i, j] -> S_0[i, 1 + j] : j <= -2 + i and "
2439 "i <= -1 + N and j >= 0;"
2440 "S_0[i, -1 + i] -> S_0[1 + i, 0] : i >= 1 and "
2441 "i <= -2 + N }";
2442 P = "{ }";
2443 S = "{ S_0[i, j] -> [i, j] }";
2444 ctx->opt->schedule_algorithm = ISL_SCHEDULE_ALGORITHM_FEAUTRIER;
2445 if (test_special_schedule(ctx, D, V, P, S) < 0)
2446 return -1;
2447 ctx->opt->schedule_algorithm = ISL_SCHEDULE_ALGORITHM_ISL;
2448
2449 /* Test both algorithms on a case with only proximity dependences. */
2450 D = "{ S[i,j] : 0 <= i <= 10 }";
2451 V = "{ }";
2452 P = "{ S[i,j] -> S[i+1,j] : 0 <= i,j <= 10 }";
2453 S = "{ S[i, j] -> [j, i] }";
2454 ctx->opt->schedule_algorithm = ISL_SCHEDULE_ALGORITHM_FEAUTRIER;
2455 if (test_special_schedule(ctx, D, V, P, S) < 0)
2456 return -1;
2457 ctx->opt->schedule_algorithm = ISL_SCHEDULE_ALGORITHM_ISL;
2458 return test_special_schedule(ctx, D, V, P, S);
2459 }
2460
2461 int test_plain_injective(isl_ctx *ctx, const char *str, int injective)
2462 {
2463 isl_union_map *umap;
2464 int test;
2465
2466 umap = isl_union_map_read_from_str(ctx, str);
2467 test = isl_union_map_plain_is_injective(umap);
2468 isl_union_map_free(umap);
2469 if (test < 0)
2470 return -1;
2471 if (test == injective)
2472 return 0;
2473 if (injective)
2474 isl_die(ctx, isl_error_unknown,
2475 "map not detected as injective", return -1);
2476 else
2477 isl_die(ctx, isl_error_unknown,
2478 "map detected as injective", return -1);
2479 }
2480
2481 int test_injective(isl_ctx *ctx)
2482 {
2483 const char *str;
2484
2485 if (test_plain_injective(ctx, "{S[i,j] -> A[0]; T[i,j] -> B[1]}", 0))
2486 return -1;
2487 if (test_plain_injective(ctx, "{S[] -> A[0]; T[] -> B[0]}", 1))
2488 return -1;
2489 if (test_plain_injective(ctx, "{S[] -> A[0]; T[] -> A[1]}", 1))
2490 return -1;
2491 if (test_plain_injective(ctx, "{S[] -> A[0]; T[] -> A[0]}", 0))
2492 return -1;
2493 if (test_plain_injective(ctx, "{S[i] -> A[i,0]; T[i] -> A[i,1]}", 1))
2494 return -1;
2495 if (test_plain_injective(ctx, "{S[i] -> A[i]; T[i] -> A[i]}", 0))
2496 return -1;
2497 if (test_plain_injective(ctx, "{S[] -> A[0,0]; T[] -> A[0,1]}", 1))
2498 return -1;
2499 if (test_plain_injective(ctx, "{S[] -> A[0,0]; T[] -> A[1,0]}", 1))
2500 return -1;
2501
2502 str = "{S[] -> A[0,0]; T[] -> A[0,1]; U[] -> A[1,0]}";
2503 if (test_plain_injective(ctx, str, 1))
2504 return -1;
2505 str = "{S[] -> A[0,0]; T[] -> A[0,1]; U[] -> A[0,0]}";
2506 if (test_plain_injective(ctx, str, 0))
2507 return -1;
2508
2509 return 0;
2510 }
2511
2512 static int aff_plain_is_equal(__isl_keep isl_aff *aff, const char *str)
2513 {
2514 isl_aff *aff2;
2515 int equal;
2516
2517 if (!aff)
2518 return -1;
2519
2520 aff2 = isl_aff_read_from_str(isl_aff_get_ctx(aff), str);
2521 equal = isl_aff_plain_is_equal(aff, aff2);
2522 isl_aff_free(aff2);
2523
2524 return equal;
2525 }
2526
2527 static int aff_check_plain_equal(__isl_keep isl_aff *aff, const char *str)
2528 {
2529 int equal;
2530
2531 equal = aff_plain_is_equal(aff, str);
2532 if (equal < 0)
2533 return -1;
2534 if (!equal)
2535 isl_die(isl_aff_get_ctx(aff), isl_error_unknown,
2536 "result not as expected", return -1);
2537 return 0;
2538 }
2539
2540 int test_aff(isl_ctx *ctx)
2541 {
2542 const char *str;
2543 isl_set *set;
2544 isl_space *space;
2545 isl_local_space *ls;
2546 isl_aff *aff;
2547 int zero, equal;
2548
2549 space = isl_space_set_alloc(ctx, 0, 1);
2550 ls = isl_local_space_from_space(space);
2551 aff = isl_aff_zero_on_domain(ls);
2552
2553 aff = isl_aff_add_coefficient_si(aff, isl_dim_in, 0, 1);
2554 aff = isl_aff_scale_down_ui(aff, 3);
2555 aff = isl_aff_floor(aff);
2556 aff = isl_aff_add_coefficient_si(aff, isl_dim_in, 0, 1);
2557 aff = isl_aff_scale_down_ui(aff, 2);
2558 aff = isl_aff_floor(aff);
2559 aff = isl_aff_add_coefficient_si(aff, isl_dim_in, 0, 1);
2560
2561 str = "{ [10] }";
2562 set = isl_set_read_from_str(ctx, str);
2563 aff = isl_aff_gist(aff, set);
2564
2565 aff = isl_aff_add_constant_si(aff, -16);
2566 zero = isl_aff_plain_is_zero(aff);
2567 isl_aff_free(aff);
2568
2569 if (zero < 0)
2570 return -1;
2571 if (!zero)
2572 isl_die(ctx, isl_error_unknown, "unexpected result", return -1);
2573
2574 aff = isl_aff_read_from_str(ctx, "{ [-1] }");
2575 aff = isl_aff_scale_down_ui(aff, 64);
2576 aff = isl_aff_floor(aff);
2577 equal = aff_check_plain_equal(aff, "{ [-1] }");
2578 isl_aff_free(aff);
2579 if (equal < 0)
2580 return -1;
2581
2582 return 0;
2583 }
2584
2585 int test_dim_max(isl_ctx *ctx)
2586 {
2587 int equal;
2588 const char *str;
2589 isl_set *set1, *set2;
2590 isl_set *set;
2591 isl_map *map;
2592 isl_pw_aff *pwaff;
2593
2594 str = "[N] -> { [i] : 0 <= i <= min(N,10) }";
2595 set = isl_set_read_from_str(ctx, str);
2596 pwaff = isl_set_dim_max(set, 0);
2597 set1 = isl_set_from_pw_aff(pwaff);
2598 str = "[N] -> { [10] : N >= 10; [N] : N <= 9 and N >= 0 }";
2599 set2 = isl_set_read_from_str(ctx, str);
2600 equal = isl_set_is_equal(set1, set2);
2601 isl_set_free(set1);
2602 isl_set_free(set2);
2603 if (equal < 0)
2604 return -1;
2605 if (!equal)
2606 isl_die(ctx, isl_error_unknown, "unexpected result", return -1);
2607
2608 str = "[N] -> { [i] : 0 <= i <= max(2N,N+6) }";
2609 set = isl_set_read_from_str(ctx, str);
2610 pwaff = isl_set_dim_max(set, 0);
2611 set1 = isl_set_from_pw_aff(pwaff);
2612 str = "[N] -> { [6 + N] : -6 <= N <= 5; [2N] : N >= 6 }";
2613 set2 = isl_set_read_from_str(ctx, str);
2614 equal = isl_set_is_equal(set1, set2);
2615 isl_set_free(set1);
2616 isl_set_free(set2);
2617 if (equal < 0)
2618 return -1;
2619 if (!equal)
2620 isl_die(ctx, isl_error_unknown, "unexpected result", return -1);
2621
2622 str = "[N] -> { [i] : 0 <= i <= 2N or 0 <= i <= N+6 }";
2623 set = isl_set_read_from_str(ctx, str);
2624 pwaff = isl_set_dim_max(set, 0);
2625 set1 = isl_set_from_pw_aff(pwaff);
2626 str = "[N] -> { [6 + N] : -6 <= N <= 5; [2N] : N >= 6 }";
2627 set2 = isl_set_read_from_str(ctx, str);
2628 equal = isl_set_is_equal(set1, set2);
2629 isl_set_free(set1);
2630 isl_set_free(set2);
2631 if (equal < 0)
2632 return -1;
2633 if (!equal)
2634 isl_die(ctx, isl_error_unknown, "unexpected result", return -1);
2635
2636 str = "[N,M] -> { [i,j] -> [([i/16]), i%16, ([j/16]), j%16] : "
2637 "0 <= i < N and 0 <= j < M }";
2638 map = isl_map_read_from_str(ctx, str);
2639 set = isl_map_range(map);
2640
2641 pwaff = isl_set_dim_max(isl_set_copy(set), 0);
2642 set1 = isl_set_from_pw_aff(pwaff);
2643 str = "[N,M] -> { [([(N-1)/16])] : M,N > 0 }";
2644 set2 = isl_set_read_from_str(ctx, str);
2645 equal = isl_set_is_equal(set1, set2);
2646 isl_set_free(set1);
2647 isl_set_free(set2);
2648
2649 pwaff = isl_set_dim_max(isl_set_copy(set), 3);
2650 set1 = isl_set_from_pw_aff(pwaff);
2651 str = "[N,M] -> { [t] : t = min(M-1,15) and M,N > 0 }";
2652 set2 = isl_set_read_from_str(ctx, str);
2653 if (equal >= 0 && equal)
2654 equal = isl_set_is_equal(set1, set2);
2655 isl_set_free(set1);
2656 isl_set_free(set2);
2657
2658 isl_set_free(set);
2659
2660 if (equal < 0)
2661 return -1;
2662 if (!equal)
2663 isl_die(ctx, isl_error_unknown, "unexpected result", return -1);
2664
2665 return 0;
2666 }
2667
2668 int test_product(isl_ctx *ctx)
2669 {
2670 const char *str;
2671 isl_set *set;
2672 isl_union_set *uset1, *uset2;
2673 int ok;
2674
2675 str = "{ A[i] }";
2676 set = isl_set_read_from_str(ctx, str);
2677 set = isl_set_product(set, isl_set_copy(set));
2678 ok = isl_set_is_wrapping(set);
2679 isl_set_free(set);
2680 if (ok < 0)
2681 return -1;
2682 if (!ok)
2683 isl_die(ctx, isl_error_unknown, "unexpected result", return -1);
2684
2685 str = "{ [] }";
2686 uset1 = isl_union_set_read_from_str(ctx, str);
2687 uset1 = isl_union_set_product(uset1, isl_union_set_copy(uset1));
2688 str = "{ [[] -> []] }";
2689 uset2 = isl_union_set_read_from_str(ctx, str);
2690 ok = isl_union_set_is_equal(uset1, uset2);
2691 isl_union_set_free(uset1);
2692 isl_union_set_free(uset2);
2693 if (ok < 0)
2694 return -1;
2695 if (!ok)
2696 isl_die(ctx, isl_error_unknown, "unexpected result", return -1);
2697
2698 return 0;
2699 }
2700
2701 int test_equal(isl_ctx *ctx)
2702 {
2703 const char *str;
2704 isl_set *set, *set2;
2705 int equal;
2706
2707 str = "{ S_6[i] }";
2708 set = isl_set_read_from_str(ctx, str);
2709 str = "{ S_7[i] }";
2710 set2 = isl_set_read_from_str(ctx, str);
2711 equal = isl_set_is_equal(set, set2);
2712 isl_set_free(set);
2713 isl_set_free(set2);
2714 if (equal < 0)
2715 return -1;
2716 if (equal)
2717 isl_die(ctx, isl_error_unknown, "unexpected result", return -1);
2718
2719 return 0;
2720 }
2721
2722 static int test_plain_fixed(isl_ctx *ctx, __isl_take isl_map *map,
2723 enum isl_dim_type type, unsigned pos, int fixed)
2724 {
2725 int test;
2726
2727 test = isl_map_plain_is_fixed(map, type, pos, NULL);
2728 isl_map_free(map);
2729 if (test < 0)
2730 return -1;
2731 if (test == fixed)
2732 return 0;
2733 if (fixed)
2734 isl_die(ctx, isl_error_unknown,
2735 "map not detected as fixed", return -1);
2736 else
2737 isl_die(ctx, isl_error_unknown,
2738 "map detected as fixed", return -1);
2739 }
2740
2741 int test_fixed(isl_ctx *ctx)
2742 {
2743 const char *str;
2744 isl_map *map;
2745
2746 str = "{ [i] -> [i] }";
2747 map = isl_map_read_from_str(ctx, str);
2748 if (test_plain_fixed(ctx, map, isl_dim_out, 0, 0))
2749 return -1;
2750 str = "{ [i] -> [1] }";
2751 map = isl_map_read_from_str(ctx, str);
2752 if (test_plain_fixed(ctx, map, isl_dim_out, 0, 1))
2753 return -1;
2754 str = "{ S_1[p1] -> [o0] : o0 = -2 and p1 >= 1 and p1 <= 7 }";
2755 map = isl_map_read_from_str(ctx, str);
2756 if (test_plain_fixed(ctx, map, isl_dim_out, 0, 1))
2757 return -1;
2758 map = isl_map_read_from_str(ctx, str);
2759 map = isl_map_neg(map);
2760 if (test_plain_fixed(ctx, map, isl_dim_out, 0, 1))
2761 return -1;
2762
2763 return 0;
2764 }
2765
2766 int test_vertices(isl_ctx *ctx)
2767 {
2768 const char *str;
2769 isl_basic_set *bset;
2770 isl_vertices *vertices;
2771
2772 str = "{ A[t, i] : t = 12 and i >= 4 and i <= 12 }";
2773 bset = isl_basic_set_read_from_str(ctx, str);
2774 vertices = isl_basic_set_compute_vertices(bset);
2775 isl_basic_set_free(bset);
2776 isl_vertices_free(vertices);
2777 if (!vertices)
2778 return -1;
2779
2780 str = "{ A[t, i] : t = 14 and i = 1 }";
2781 bset = isl_basic_set_read_from_str(ctx, str);
2782 vertices = isl_basic_set_compute_vertices(bset);
2783 isl_basic_set_free(bset);
2784 isl_vertices_free(vertices);
2785 if (!vertices)
2786 return -1;
2787
2788 return 0;
2789 }
2790
2791 int test_union_pw(isl_ctx *ctx)
2792 {
2793 int equal;
2794 const char *str;
2795 isl_union_set *uset;
2796 isl_union_pw_qpolynomial *upwqp1, *upwqp2;
2797
2798 str = "{ [x] -> x^2 }";
2799 upwqp1 = isl_union_pw_qpolynomial_read_from_str(ctx, str);
2800 upwqp2 = isl_union_pw_qpolynomial_copy(upwqp1);
2801 uset = isl_union_pw_qpolynomial_domain(upwqp1);
2802 upwqp1 = isl_union_pw_qpolynomial_copy(upwqp2);
2803 upwqp1 = isl_union_pw_qpolynomial_intersect_domain(upwqp1, uset);
2804 equal = isl_union_pw_qpolynomial_plain_is_equal(upwqp1, upwqp2);
2805 isl_union_pw_qpolynomial_free(upwqp1);
2806 isl_union_pw_qpolynomial_free(upwqp2);
2807 if (equal < 0)
2808 return -1;
2809 if (!equal)
2810 isl_die(ctx, isl_error_unknown, "unexpected result", return -1);
2811
2812 return 0;
2813 }
2814
2815 int test_output(isl_ctx *ctx)
2816 {
2817 char *s;
2818 const char *str;
2819 isl_pw_aff *pa;
2820 isl_printer *p;
2821 int equal;
2822
2823 str = "[x] -> { [1] : x % 4 <= 2; [2] : x = 3 }";
2824 pa = isl_pw_aff_read_from_str(ctx, str);
2825
2826 p = isl_printer_to_str(ctx);
2827 p = isl_printer_set_output_format(p, ISL_FORMAT_C);
2828 p = isl_printer_print_pw_aff(p, pa);
2829 s = isl_printer_get_str(p);
2830 isl_printer_free(p);
2831 isl_pw_aff_free(pa);
2832 equal = !strcmp(s, "(2 - x + 4*floord(x, 4) >= 0) ? (1) : 2");
2833 free(s);
2834 if (equal < 0)
2835 return -1;
2836 if (!equal)
2837 isl_die(ctx, isl_error_unknown, "unexpected result", return -1);
2838
2839 return 0;
2840 }
2841
2842 int test_sample(isl_ctx *ctx)
2843 {
2844 const char *str;
2845 isl_basic_set *bset1, *bset2;
2846 int empty, subset;
2847
2848 str = "{ [a, b, c, d, e, f, g, h, i, j, k] : "
2849 "3i >= 1073741823b - c - 1073741823e + f and c >= 0 and "
2850 "3i >= -1 + 3221225466b + c + d - 3221225466e - f and "
2851 "2e >= a - b and 3e <= 2a and 3k <= -a and f <= -1 + a and "
2852 "3i <= 4 - a + 4b + 2c - e - 2f and 3k <= -a + c - f and "
2853 "3h >= -2 + a and 3g >= -3 - a and 3k >= -2 - a and "
2854 "3i >= -2 - a - 2c + 3e + 2f and 3h <= a + c - f and "
2855 "3h >= a + 2147483646b + 2c - 2147483646e - 2f and "
2856 "3g <= -1 - a and 3i <= 1 + c + d - f and a <= 1073741823 and "
2857 "f >= 1 - a + 1073741822b + c + d - 1073741822e and "
2858 "3i >= 1 + 2b - 2c + e + 2f + 3g and "
2859 "1073741822f <= 1073741822 - a + 1073741821b + 1073741822c +"
2860 "d - 1073741821e and "
2861 "3j <= 3 - a + 3b and 3g <= -2 - 2b + c + d - e - f and "
2862 "3j >= 1 - a + b + 2e and "
2863 "3f >= -3 + a + 3221225462b + 3c + d - 3221225465e and "
2864 "3i <= 4 - a + 4b - e and "
2865 "f <= 1073741822 + 1073741822b - 1073741822e and 3h <= a and "
2866 "f >= 0 and 2e <= 4 - a + 5b - d and 2e <= a - b + d and "
2867 "c <= -1 + a and 3i >= -2 - a + 3e and "
2868 "1073741822e <= 1073741823 - a + 1073741822b + c and "
2869 "3g >= -4 + 3221225464b + 3c + d - 3221225467e - 3f and "
2870 "3i >= -1 + 3221225466b + 3c + d - 3221225466e - 3f and "
2871 "1073741823e >= 1 + 1073741823b - d and "
2872 "3i >= 1073741823b + c - 1073741823e - f and "
2873 "3i >= 1 + 2b + e + 3g }";
2874 bset1 = isl_basic_set_read_from_str(ctx, str);
2875 bset2 = isl_basic_set_sample(isl_basic_set_copy(bset1));
2876 empty = isl_basic_set_is_empty(bset2);
2877 subset = isl_basic_set_is_subset(bset2, bset1);
2878 isl_basic_set_free(bset1);
2879 isl_basic_set_free(bset2);
2880 if (empty)
2881 isl_die(ctx, isl_error_unknown, "point not found", return -1);
2882 if (!subset)
2883 isl_die(ctx, isl_error_unknown, "bad point found", return -1);
2884
2885 return 0;
2886 }
2887
2888 int test_fixed_power(isl_ctx *ctx)
2889 {
2890 const char *str;
2891 isl_map *map;
2892 isl_int exp;
2893 int equal;
2894
2895 isl_int_init(exp);
2896 str = "{ [i] -> [i + 1] }";
2897 map = isl_map_read_from_str(ctx, str);
2898 isl_int_set_si(exp, 23);
2899 map = isl_map_fixed_power(map, exp);
2900 equal = map_check_equal(map, "{ [i] -> [i + 23] }");
2901 isl_int_clear(exp);
2902 isl_map_free(map);
2903 if (equal < 0)
2904 return -1;
2905
2906 return 0;
2907 }
2908
2909 int test_slice(isl_ctx *ctx)
2910 {
2911 const char *str;
2912 isl_map *map;
2913 int equal;
2914
2915 str = "{ [i] -> [j] }";
2916 map = isl_map_read_from_str(ctx, str);
2917 map = isl_map_equate(map, isl_dim_in, 0, isl_dim_out, 0);
2918 equal = map_check_equal(map, "{ [i] -> [i] }");
2919 isl_map_free(map);
2920 if (equal < 0)
2921 return -1;
2922
2923 str = "{ [i] -> [j] }";
2924 map = isl_map_read_from_str(ctx, str);
2925 map = isl_map_equate(map, isl_dim_in, 0, isl_dim_in, 0);
2926 equal = map_check_equal(map, "{ [i] -> [j] }");
2927 isl_map_free(map);
2928 if (equal < 0)
2929 return -1;
2930
2931 str = "{ [i] -> [j] }";
2932 map = isl_map_read_from_str(ctx, str);
2933 map = isl_map_oppose(map, isl_dim_in, 0, isl_dim_out, 0);
2934 equal = map_check_equal(map, "{ [i] -> [-i] }");
2935 isl_map_free(map);
2936 if (equal < 0)
2937 return -1;
2938
2939 str = "{ [i] -> [j] }";
2940 map = isl_map_read_from_str(ctx, str);
2941 map = isl_map_oppose(map, isl_dim_in, 0, isl_dim_in, 0);
2942 equal = map_check_equal(map, "{ [0] -> [j] }");
2943 isl_map_free(map);
2944 if (equal < 0)
2945 return -1;
2946
2947 str = "{ [i] -> [j] }";
2948 map = isl_map_read_from_str(ctx, str);
2949 map = isl_map_order_gt(map, isl_dim_in, 0, isl_dim_out, 0);
2950 equal = map_check_equal(map, "{ [i] -> [j] : i > j }");
2951 isl_map_free(map);
2952 if (equal < 0)
2953 return -1;
2954
2955 str = "{ [i] -> [j] }";
2956 map = isl_map_read_from_str(ctx, str);
2957 map = isl_map_order_gt(map, isl_dim_in, 0, isl_dim_in, 0);
2958 equal = map_check_equal(map, "{ [i] -> [j] : false }");
2959 isl_map_free(map);
2960 if (equal < 0)
2961 return -1;
2962
2963 return 0;
2964 }
2965
2966 struct {
2967 const char *name;
2968 int (*fn)(isl_ctx *ctx);
2969 } tests [] = {
2970 { "div", &test_div },
2971 { "slice", &test_slice },
2972 { "fixed power", &test_fixed_power },
2973 { "sample", &test_sample },
2974 { "output", &test_output },
2975 { "vertices", &test_vertices },
2976 { "fixed", &test_fixed },
2977 { "equal", &test_equal },
2978 { "product", &test_product },
2979 { "dim_max", &test_dim_max },
2980 { "affine", &test_aff },
2981 { "injective", &test_injective },
2982 { "schedule", &test_schedule },
2983 { "union_pw", &test_union_pw },
2984 { "parse", &test_parse },
2985 { "single-valued", &test_sv },
2986 { "affine hull", &test_affine_hull },
2987 { "coalesce", &test_coalesce },
2988 { "factorize", &test_factorize },
2989 };
2990
2991 int main()
2992 {
2993 int i;
2994 struct isl_ctx *ctx;
2995
2996 srcdir = getenv("srcdir");
2997 assert(srcdir);
2998
2999 ctx = isl_ctx_alloc();
3000 for (i = 0; i < ARRAY_SIZE(tests); ++i) {
3001 printf("%s\n", tests[i].name);
3002 if (tests[i].fn(ctx) < 0)
3003 goto error;
3004 }
3005 test_subset(ctx);
3006 test_lift(ctx);
3007 test_bound(ctx);
3008 test_union(ctx);
3009 test_split_periods(ctx);
3010 test_pwqp(ctx);
3011 test_lex(ctx);
3012 test_bijective(ctx);
3013 test_dep(ctx);
3014 test_read(ctx);
3015 test_bounded(ctx);
3016 test_construction(ctx);
3017 test_dim(ctx);
3018 test_application(ctx);
3019 test_convex_hull(ctx);
3020 test_gist(ctx);
3021 test_closure(ctx);
3022 test_lexmin(ctx);
3023 isl_ctx_free(ctx);
3024 return 0;
3025 error:
3026 isl_ctx_free(ctx);
3027 return -1;
3028 }
Integer set library