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declare isl_tab_get_ctx in isl_tab.h
[isl.git] / isl_test.c
blobae43aed2659f3c0cbb524af60780ef9eb10a282e
1 /*
2 * Copyright 2008-2009 Katholieke Universiteit Leuven
3 *
4 * Use of this software is governed by the MIT 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_private.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 #include <isl/ast_build.h>
26
27 #define ARRAY_SIZE(array) (sizeof(array)/sizeof(*array))
28
29 static char *srcdir;
30
31 static char *get_filename(isl_ctx *ctx, const char *name, const char *suffix) {
32 char *filename;
33 int length;
34 char *pattern = "%s/test_inputs/%s.%s";
35
36 length = strlen(pattern) - 6 + strlen(srcdir) + strlen(name)
37 + strlen(suffix) + 1;
38 filename = isl_alloc_array(ctx, char, length);
39
40 if (!filename)
41 return NULL;
42
43 sprintf(filename, pattern, srcdir, name, suffix);
44
45 return filename;
46 }
47
48 void test_parse_map(isl_ctx *ctx, const char *str)
49 {
50 isl_map *map;
51
52 map = isl_map_read_from_str(ctx, str);
53 assert(map);
54 isl_map_free(map);
55 }
56
57 int test_parse_map_equal(isl_ctx *ctx, const char *str, const char *str2)
58 {
59 isl_map *map, *map2;
60 int equal;
61
62 map = isl_map_read_from_str(ctx, str);
63 map2 = isl_map_read_from_str(ctx, str2);
64 equal = isl_map_is_equal(map, map2);
65 isl_map_free(map);
66 isl_map_free(map2);
67
68 if (equal < 0)
69 return -1;
70 if (!equal)
71 isl_die(ctx, isl_error_unknown, "maps not equal",
72 return -1);
73
74 return 0;
75 }
76
77 void test_parse_pwqp(isl_ctx *ctx, const char *str)
78 {
79 isl_pw_qpolynomial *pwqp;
80
81 pwqp = isl_pw_qpolynomial_read_from_str(ctx, str);
82 assert(pwqp);
83 isl_pw_qpolynomial_free(pwqp);
84 }
85
86 static void test_parse_pwaff(isl_ctx *ctx, const char *str)
87 {
88 isl_pw_aff *pwaff;
89
90 pwaff = isl_pw_aff_read_from_str(ctx, str);
91 assert(pwaff);
92 isl_pw_aff_free(pwaff);
93 }
94
95 int test_parse(struct isl_ctx *ctx)
96 {
97 isl_map *map, *map2;
98 const char *str, *str2;
99
100 str = "{ [i] -> [-i] }";
101 map = isl_map_read_from_str(ctx, str);
102 assert(map);
103 isl_map_free(map);
104
105 str = "{ A[i] -> L[([i/3])] }";
106 map = isl_map_read_from_str(ctx, str);
107 assert(map);
108 isl_map_free(map);
109
110 test_parse_map(ctx, "{[[s] -> A[i]] -> [[s+1] -> A[i]]}");
111 test_parse_map(ctx, "{ [p1, y1, y2] -> [2, y1, y2] : "
112 "p1 = 1 && (y1 <= y2 || y2 = 0) }");
113
114 str = "{ [x,y] : [([x/2]+y)/3] >= 1 }";
115 str2 = "{ [x, y] : 2y >= 6 - x }";
116 if (test_parse_map_equal(ctx, str, str2) < 0)
117 return -1;
118
119 if (test_parse_map_equal(ctx, "{ [x,y] : x <= min(y, 2*y+3) }",
120 "{ [x,y] : x <= y, 2*y + 3 }") < 0)
121 return -1;
122 str = "{ [x, y] : (y <= x and y >= -3) or (2y <= -3 + x and y <= -4) }";
123 if (test_parse_map_equal(ctx, "{ [x,y] : x >= min(y, 2*y+3) }",
124 str) < 0)
125 return -1;
126
127 str = "{[new,old] -> [new+1-2*[(new+1)/2],old+1-2*[(old+1)/2]]}";
128 map = isl_map_read_from_str(ctx, str);
129 str = "{ [new, old] -> [o0, o1] : "
130 "exists (e0 = [(-1 - new + o0)/2], e1 = [(-1 - old + o1)/2]: "
131 "2e0 = -1 - new + o0 and 2e1 = -1 - old + o1 and o0 >= 0 and "
132 "o0 <= 1 and o1 >= 0 and o1 <= 1) }";
133 map2 = isl_map_read_from_str(ctx, str);
134 assert(isl_map_is_equal(map, map2));
135 isl_map_free(map);
136 isl_map_free(map2);
137
138 str = "{[new,old] -> [new+1-2*[(new+1)/2],old+1-2*[(old+1)/2]]}";
139 map = isl_map_read_from_str(ctx, str);
140 str = "{[new,old] -> [(new+1)%2,(old+1)%2]}";
141 map2 = isl_map_read_from_str(ctx, str);
142 assert(isl_map_is_equal(map, map2));
143 isl_map_free(map);
144 isl_map_free(map2);
145
146 str = "[n] -> { [c1] : c1>=0 and c1<=floord(n-4,3) }";
147 str2 = "[n] -> { [c1] : c1 >= 0 and 3c1 <= -4 + n }";
148 if (test_parse_map_equal(ctx, str, str2) < 0)
149 return -1;
150
151 str = "{ [i,j] -> [i] : i < j; [i,j] -> [j] : j <= i }";
152 str2 = "{ [i,j] -> [min(i,j)] }";
153 if (test_parse_map_equal(ctx, str, str2) < 0)
154 return -1;
155
156 str = "{ [i,j] : i != j }";
157 str2 = "{ [i,j] : i < j or i > j }";
158 if (test_parse_map_equal(ctx, str, str2) < 0)
159 return -1;
160
161 str = "{ [i,j] : (i+1)*2 >= j }";
162 str2 = "{ [i, j] : j <= 2 + 2i }";
163 if (test_parse_map_equal(ctx, str, str2) < 0)
164 return -1;
165
166 str = "{ [i] -> [i > 0 ? 4 : 5] }";
167 str2 = "{ [i] -> [5] : i <= 0; [i] -> [4] : i >= 1 }";
168 if (test_parse_map_equal(ctx, str, str2) < 0)
169 return -1;
170
171 str = "[N=2,M] -> { [i=[(M+N)/4]] }";
172 str2 = "[N, M] -> { [i] : N = 2 and 4i <= 2 + M and 4i >= -1 + M }";
173 if (test_parse_map_equal(ctx, str, str2) < 0)
174 return -1;
175
176 str = "{ [x] : x >= 0 }";
177 str2 = "{ [x] : x-0 >= 0 }";
178 if (test_parse_map_equal(ctx, str, str2) < 0)
179 return -1;
180
181 str = "{ [i] : ((i > 10)) }";
182 str2 = "{ [i] : i >= 11 }";
183 if (test_parse_map_equal(ctx, str, str2) < 0)
184 return -1;
185
186 str = "{ [i] -> [0] }";
187 str2 = "{ [i] -> [0 * i] }";
188 if (test_parse_map_equal(ctx, str, str2) < 0)
189 return -1;
190
191 test_parse_pwqp(ctx, "{ [i] -> i + [ (i + [i/3])/2 ] }");
192 test_parse_map(ctx, "{ S1[i] -> [([i/10]),i%10] : 0 <= i <= 45 }");
193 test_parse_pwaff(ctx, "{ [i] -> [i + 1] : i > 0; [a] -> [a] : a < 0 }");
194 test_parse_pwqp(ctx, "{ [x] -> ([(x)/2] * [(x)/3]) }");
195
196 if (test_parse_map_equal(ctx, "{ [a] -> [b] : (not false) }",
197 "{ [a] -> [b] : true }") < 0)
198 return -1;
199
200 if (test_parse_map_equal(ctx, "{ [i] : i/2 <= 5 }",
201 "{ [i] : i <= 10 }") < 0)
202 return -1;
203
204 if (test_parse_map_equal(ctx, "{Sym=[n] [i] : i <= n }",
205 "[n] -> { [i] : i <= n }") < 0)
206 return -1;
207
208 if (test_parse_map_equal(ctx, "{ [*] }", "{ [a] }") < 0)
209 return -1;
210
211 return 0;
212 }
213
214 void test_read(struct isl_ctx *ctx)
215 {
216 char *filename;
217 FILE *input;
218 struct isl_basic_set *bset1, *bset2;
219 const char *str = "{[y]: Exists ( alpha : 2alpha = y)}";
220
221 filename = get_filename(ctx, "set", "omega");
222 assert(filename);
223 input = fopen(filename, "r");
224 assert(input);
225
226 bset1 = isl_basic_set_read_from_file(ctx, input);
227 bset2 = isl_basic_set_read_from_str(ctx, str);
228
229 assert(isl_basic_set_is_equal(bset1, bset2) == 1);
230
231 isl_basic_set_free(bset1);
232 isl_basic_set_free(bset2);
233 free(filename);
234
235 fclose(input);
236 }
237
238 void test_bounded(struct isl_ctx *ctx)
239 {
240 isl_set *set;
241 int bounded;
242
243 set = isl_set_read_from_str(ctx, "[n] -> {[i] : 0 <= i <= n }");
244 bounded = isl_set_is_bounded(set);
245 assert(bounded);
246 isl_set_free(set);
247
248 set = isl_set_read_from_str(ctx, "{[n, i] : 0 <= i <= n }");
249 bounded = isl_set_is_bounded(set);
250 assert(!bounded);
251 isl_set_free(set);
252
253 set = isl_set_read_from_str(ctx, "[n] -> {[i] : i <= n }");
254 bounded = isl_set_is_bounded(set);
255 assert(!bounded);
256 isl_set_free(set);
257 }
258
259 /* Construct the basic set { [i] : 5 <= i <= N } */
260 void test_construction(struct isl_ctx *ctx)
261 {
262 isl_int v;
263 isl_space *dim;
264 isl_local_space *ls;
265 struct isl_basic_set *bset;
266 struct isl_constraint *c;
267
268 isl_int_init(v);
269
270 dim = isl_space_set_alloc(ctx, 1, 1);
271 bset = isl_basic_set_universe(isl_space_copy(dim));
272 ls = isl_local_space_from_space(dim);
273
274 c = isl_inequality_alloc(isl_local_space_copy(ls));
275 isl_int_set_si(v, -1);
276 isl_constraint_set_coefficient(c, isl_dim_set, 0, v);
277 isl_int_set_si(v, 1);
278 isl_constraint_set_coefficient(c, isl_dim_param, 0, v);
279 bset = isl_basic_set_add_constraint(bset, c);
280
281 c = isl_inequality_alloc(isl_local_space_copy(ls));
282 isl_int_set_si(v, 1);
283 isl_constraint_set_coefficient(c, isl_dim_set, 0, v);
284 isl_int_set_si(v, -5);
285 isl_constraint_set_constant(c, v);
286 bset = isl_basic_set_add_constraint(bset, c);
287
288 isl_local_space_free(ls);
289 isl_basic_set_free(bset);
290
291 isl_int_clear(v);
292 }
293
294 void test_dim(struct isl_ctx *ctx)
295 {
296 const char *str;
297 isl_map *map1, *map2;
298
299 map1 = isl_map_read_from_str(ctx,
300 "[n] -> { [i] -> [j] : exists (a = [i/10] : i - 10a <= n ) }");
301 map1 = isl_map_add_dims(map1, isl_dim_in, 1);
302 map2 = isl_map_read_from_str(ctx,
303 "[n] -> { [i,k] -> [j] : exists (a = [i/10] : i - 10a <= n ) }");
304 assert(isl_map_is_equal(map1, map2));
305 isl_map_free(map2);
306
307 map1 = isl_map_project_out(map1, isl_dim_in, 0, 1);
308 map2 = isl_map_read_from_str(ctx, "[n] -> { [i] -> [j] : n >= 0 }");
309 assert(isl_map_is_equal(map1, map2));
310
311 isl_map_free(map1);
312 isl_map_free(map2);
313
314 str = "[n] -> { [i] -> [] : exists a : 0 <= i <= n and i = 2 a }";
315 map1 = isl_map_read_from_str(ctx, str);
316 str = "{ [i] -> [j] : exists a : 0 <= i <= j and i = 2 a }";
317 map2 = isl_map_read_from_str(ctx, str);
318 map1 = isl_map_move_dims(map1, isl_dim_out, 0, isl_dim_param, 0, 1);
319 assert(isl_map_is_equal(map1, map2));
320
321 isl_map_free(map1);
322 isl_map_free(map2);
323 }
324
325 static int test_div(isl_ctx *ctx)
326 {
327 unsigned n;
328 const char *str;
329 int empty;
330 isl_int v;
331 isl_space *dim;
332 isl_set *set;
333 isl_local_space *ls;
334 struct isl_basic_set *bset;
335 struct isl_constraint *c;
336
337 isl_int_init(v);
338
339 /* test 1 */
340 dim = isl_space_set_alloc(ctx, 0, 3);
341 bset = isl_basic_set_universe(isl_space_copy(dim));
342 ls = isl_local_space_from_space(dim);
343
344 c = isl_equality_alloc(isl_local_space_copy(ls));
345 isl_int_set_si(v, -1);
346 isl_constraint_set_constant(c, v);
347 isl_int_set_si(v, 1);
348 isl_constraint_set_coefficient(c, isl_dim_set, 0, v);
349 isl_int_set_si(v, 3);
350 isl_constraint_set_coefficient(c, isl_dim_set, 1, v);
351 bset = isl_basic_set_add_constraint(bset, c);
352
353 c = isl_equality_alloc(isl_local_space_copy(ls));
354 isl_int_set_si(v, 1);
355 isl_constraint_set_constant(c, v);
356 isl_int_set_si(v, -1);
357 isl_constraint_set_coefficient(c, isl_dim_set, 0, v);
358 isl_int_set_si(v, 3);
359 isl_constraint_set_coefficient(c, isl_dim_set, 2, v);
360 bset = isl_basic_set_add_constraint(bset, c);
361
362 bset = isl_basic_set_project_out(bset, isl_dim_set, 1, 2);
363
364 assert(bset && bset->n_div == 1);
365 isl_local_space_free(ls);
366 isl_basic_set_free(bset);
367
368 /* test 2 */
369 dim = isl_space_set_alloc(ctx, 0, 3);
370 bset = isl_basic_set_universe(isl_space_copy(dim));
371 ls = isl_local_space_from_space(dim);
372
373 c = isl_equality_alloc(isl_local_space_copy(ls));
374 isl_int_set_si(v, 1);
375 isl_constraint_set_constant(c, v);
376 isl_int_set_si(v, -1);
377 isl_constraint_set_coefficient(c, isl_dim_set, 0, v);
378 isl_int_set_si(v, 3);
379 isl_constraint_set_coefficient(c, isl_dim_set, 1, v);
380 bset = isl_basic_set_add_constraint(bset, c);
381
382 c = isl_equality_alloc(isl_local_space_copy(ls));
383 isl_int_set_si(v, -1);
384 isl_constraint_set_constant(c, v);
385 isl_int_set_si(v, 1);
386 isl_constraint_set_coefficient(c, isl_dim_set, 0, v);
387 isl_int_set_si(v, 3);
388 isl_constraint_set_coefficient(c, isl_dim_set, 2, v);
389 bset = isl_basic_set_add_constraint(bset, c);
390
391 bset = isl_basic_set_project_out(bset, isl_dim_set, 1, 2);
392
393 assert(bset && bset->n_div == 1);
394 isl_local_space_free(ls);
395 isl_basic_set_free(bset);
396
397 /* test 3 */
398 dim = isl_space_set_alloc(ctx, 0, 3);
399 bset = isl_basic_set_universe(isl_space_copy(dim));
400 ls = isl_local_space_from_space(dim);
401
402 c = isl_equality_alloc(isl_local_space_copy(ls));
403 isl_int_set_si(v, 1);
404 isl_constraint_set_constant(c, v);
405 isl_int_set_si(v, -1);
406 isl_constraint_set_coefficient(c, isl_dim_set, 0, v);
407 isl_int_set_si(v, 3);
408 isl_constraint_set_coefficient(c, isl_dim_set, 1, v);
409 bset = isl_basic_set_add_constraint(bset, c);
410
411 c = isl_equality_alloc(isl_local_space_copy(ls));
412 isl_int_set_si(v, -3);
413 isl_constraint_set_constant(c, v);
414 isl_int_set_si(v, 1);
415 isl_constraint_set_coefficient(c, isl_dim_set, 0, v);
416 isl_int_set_si(v, 4);
417 isl_constraint_set_coefficient(c, isl_dim_set, 2, v);
418 bset = isl_basic_set_add_constraint(bset, c);
419
420 bset = isl_basic_set_project_out(bset, isl_dim_set, 1, 2);
421
422 assert(bset && bset->n_div == 1);
423 isl_local_space_free(ls);
424 isl_basic_set_free(bset);
425
426 /* test 4 */
427 dim = isl_space_set_alloc(ctx, 0, 3);
428 bset = isl_basic_set_universe(isl_space_copy(dim));
429 ls = isl_local_space_from_space(dim);
430
431 c = isl_equality_alloc(isl_local_space_copy(ls));
432 isl_int_set_si(v, 2);
433 isl_constraint_set_constant(c, v);
434 isl_int_set_si(v, -1);
435 isl_constraint_set_coefficient(c, isl_dim_set, 0, v);
436 isl_int_set_si(v, 3);
437 isl_constraint_set_coefficient(c, isl_dim_set, 1, v);
438 bset = isl_basic_set_add_constraint(bset, c);
439
440 c = isl_equality_alloc(isl_local_space_copy(ls));
441 isl_int_set_si(v, -1);
442 isl_constraint_set_constant(c, v);
443 isl_int_set_si(v, 1);
444 isl_constraint_set_coefficient(c, isl_dim_set, 0, v);
445 isl_int_set_si(v, 6);
446 isl_constraint_set_coefficient(c, isl_dim_set, 2, v);
447 bset = isl_basic_set_add_constraint(bset, c);
448
449 bset = isl_basic_set_project_out(bset, isl_dim_set, 1, 2);
450
451 assert(isl_basic_set_is_empty(bset));
452 isl_local_space_free(ls);
453 isl_basic_set_free(bset);
454
455 /* test 5 */
456 dim = isl_space_set_alloc(ctx, 0, 3);
457 bset = isl_basic_set_universe(isl_space_copy(dim));
458 ls = isl_local_space_from_space(dim);
459
460 c = isl_equality_alloc(isl_local_space_copy(ls));
461 isl_int_set_si(v, -1);
462 isl_constraint_set_coefficient(c, isl_dim_set, 0, v);
463 isl_int_set_si(v, 3);
464 isl_constraint_set_coefficient(c, isl_dim_set, 2, v);
465 bset = isl_basic_set_add_constraint(bset, c);
466
467 c = isl_equality_alloc(isl_local_space_copy(ls));
468 isl_int_set_si(v, 1);
469 isl_constraint_set_coefficient(c, isl_dim_set, 0, v);
470 isl_int_set_si(v, -3);
471 isl_constraint_set_coefficient(c, isl_dim_set, 1, v);
472 bset = isl_basic_set_add_constraint(bset, c);
473
474 bset = isl_basic_set_project_out(bset, isl_dim_set, 2, 1);
475
476 assert(bset && bset->n_div == 0);
477 isl_basic_set_free(bset);
478 isl_local_space_free(ls);
479
480 /* test 6 */
481 dim = isl_space_set_alloc(ctx, 0, 3);
482 bset = isl_basic_set_universe(isl_space_copy(dim));
483 ls = isl_local_space_from_space(dim);
484
485 c = isl_equality_alloc(isl_local_space_copy(ls));
486 isl_int_set_si(v, -1);
487 isl_constraint_set_coefficient(c, isl_dim_set, 0, v);
488 isl_int_set_si(v, 6);
489 isl_constraint_set_coefficient(c, isl_dim_set, 2, v);
490 bset = isl_basic_set_add_constraint(bset, c);
491
492 c = isl_equality_alloc(isl_local_space_copy(ls));
493 isl_int_set_si(v, 1);
494 isl_constraint_set_coefficient(c, isl_dim_set, 0, v);
495 isl_int_set_si(v, -3);
496 isl_constraint_set_coefficient(c, isl_dim_set, 1, v);
497 bset = isl_basic_set_add_constraint(bset, c);
498
499 bset = isl_basic_set_project_out(bset, isl_dim_set, 2, 1);
500
501 assert(bset && bset->n_div == 1);
502 isl_basic_set_free(bset);
503 isl_local_space_free(ls);
504
505 /* test 7 */
506 /* This test is a bit tricky. We set up an equality
507 * a + 3b + 3c = 6 e0
508 * Normalization of divs creates _two_ divs
509 * a = 3 e0
510 * c - b - e0 = 2 e1
511 * Afterwards e0 is removed again because it has coefficient -1
512 * and we end up with the original equality and div again.
513 * Perhaps we can avoid the introduction of this temporary div.
514 */
515 dim = isl_space_set_alloc(ctx, 0, 4);
516 bset = isl_basic_set_universe(isl_space_copy(dim));
517 ls = isl_local_space_from_space(dim);
518
519 c = isl_equality_alloc(isl_local_space_copy(ls));
520 isl_int_set_si(v, -1);
521 isl_constraint_set_coefficient(c, isl_dim_set, 0, v);
522 isl_int_set_si(v, -3);
523 isl_constraint_set_coefficient(c, isl_dim_set, 1, v);
524 isl_int_set_si(v, -3);
525 isl_constraint_set_coefficient(c, isl_dim_set, 2, v);
526 isl_int_set_si(v, 6);
527 isl_constraint_set_coefficient(c, isl_dim_set, 3, v);
528 bset = isl_basic_set_add_constraint(bset, c);
529
530 bset = isl_basic_set_project_out(bset, isl_dim_set, 3, 1);
531
532 /* Test disabled for now */
533 /*
534 assert(bset && bset->n_div == 1);
535 */
536 isl_local_space_free(ls);
537 isl_basic_set_free(bset);
538
539 /* test 8 */
540 dim = isl_space_set_alloc(ctx, 0, 5);
541 bset = isl_basic_set_universe(isl_space_copy(dim));
542 ls = isl_local_space_from_space(dim);
543
544 c = isl_equality_alloc(isl_local_space_copy(ls));
545 isl_int_set_si(v, -1);
546 isl_constraint_set_coefficient(c, isl_dim_set, 0, v);
547 isl_int_set_si(v, -3);
548 isl_constraint_set_coefficient(c, isl_dim_set, 1, v);
549 isl_int_set_si(v, -3);
550 isl_constraint_set_coefficient(c, isl_dim_set, 3, v);
551 isl_int_set_si(v, 6);
552 isl_constraint_set_coefficient(c, isl_dim_set, 4, v);
553 bset = isl_basic_set_add_constraint(bset, c);
554
555 c = isl_equality_alloc(isl_local_space_copy(ls));
556 isl_int_set_si(v, -1);
557 isl_constraint_set_coefficient(c, isl_dim_set, 0, v);
558 isl_int_set_si(v, 1);
559 isl_constraint_set_coefficient(c, isl_dim_set, 2, v);
560 isl_int_set_si(v, 1);
561 isl_constraint_set_constant(c, v);
562 bset = isl_basic_set_add_constraint(bset, c);
563
564 bset = isl_basic_set_project_out(bset, isl_dim_set, 4, 1);
565
566 /* Test disabled for now */
567 /*
568 assert(bset && bset->n_div == 1);
569 */
570 isl_local_space_free(ls);
571 isl_basic_set_free(bset);
572
573 /* test 9 */
574 dim = isl_space_set_alloc(ctx, 0, 4);
575 bset = isl_basic_set_universe(isl_space_copy(dim));
576 ls = isl_local_space_from_space(dim);
577
578 c = isl_equality_alloc(isl_local_space_copy(ls));
579 isl_int_set_si(v, 1);
580 isl_constraint_set_coefficient(c, isl_dim_set, 0, v);
581 isl_int_set_si(v, -1);
582 isl_constraint_set_coefficient(c, isl_dim_set, 1, v);
583 isl_int_set_si(v, -2);
584 isl_constraint_set_coefficient(c, isl_dim_set, 2, v);
585 bset = isl_basic_set_add_constraint(bset, c);
586
587 c = isl_equality_alloc(isl_local_space_copy(ls));
588 isl_int_set_si(v, -1);
589 isl_constraint_set_coefficient(c, isl_dim_set, 0, v);
590 isl_int_set_si(v, 3);
591 isl_constraint_set_coefficient(c, isl_dim_set, 3, v);
592 isl_int_set_si(v, 2);
593 isl_constraint_set_constant(c, v);
594 bset = isl_basic_set_add_constraint(bset, c);
595
596 bset = isl_basic_set_project_out(bset, isl_dim_set, 2, 2);
597
598 bset = isl_basic_set_fix_si(bset, isl_dim_set, 0, 2);
599
600 assert(!isl_basic_set_is_empty(bset));
601
602 isl_local_space_free(ls);
603 isl_basic_set_free(bset);
604
605 /* test 10 */
606 dim = isl_space_set_alloc(ctx, 0, 3);
607 bset = isl_basic_set_universe(isl_space_copy(dim));
608 ls = isl_local_space_from_space(dim);
609
610 c = isl_equality_alloc(isl_local_space_copy(ls));
611 isl_int_set_si(v, 1);
612 isl_constraint_set_coefficient(c, isl_dim_set, 0, v);
613 isl_int_set_si(v, -2);
614 isl_constraint_set_coefficient(c, isl_dim_set, 2, v);
615 bset = isl_basic_set_add_constraint(bset, c);
616
617 bset = isl_basic_set_project_out(bset, isl_dim_set, 2, 1);
618
619 bset = isl_basic_set_fix_si(bset, isl_dim_set, 0, 2);
620
621 isl_local_space_free(ls);
622 isl_basic_set_free(bset);
623
624 isl_int_clear(v);
625
626 str = "{ [i] : exists (e0, e1: 3e1 >= 1 + 2e0 and "
627 "8e1 <= -1 + 5i - 5e0 and 2e1 >= 1 + 2i - 5e0) }";
628 set = isl_set_read_from_str(ctx, str);
629 set = isl_set_compute_divs(set);
630 isl_set_free(set);
631 if (!set)
632 return -1;
633
634 str = "{ [i,j] : 2*[i/2] + 3 * [j/4] <= 10 and 2 i = j }";
635 bset = isl_basic_set_read_from_str(ctx, str);
636 n = isl_basic_set_dim(bset, isl_dim_div);
637 isl_basic_set_free(bset);
638 if (!bset)
639 return -1;
640 if (n != 0)
641 isl_die(ctx, isl_error_unknown,
642 "expecting no existentials", return -1);
643
644 str = "{ [i,j,k] : 3 + i + 2j >= 0 and 2 * [(i+2j)/4] <= k }";
645 set = isl_set_read_from_str(ctx, str);
646 set = isl_set_remove_divs_involving_dims(set, isl_dim_set, 0, 2);
647 set = isl_set_fix_si(set, isl_dim_set, 2, -3);
648 empty = isl_set_is_empty(set);
649 isl_set_free(set);
650 if (empty < 0)
651 return -1;
652 if (!empty)
653 isl_die(ctx, isl_error_unknown,
654 "result not as accurate as expected", return -1);
655
656 return 0;
657 }
658
659 void test_application_case(struct isl_ctx *ctx, const char *name)
660 {
661 char *filename;
662 FILE *input;
663 struct isl_basic_set *bset1, *bset2;
664 struct isl_basic_map *bmap;
665
666 filename = get_filename(ctx, name, "omega");
667 assert(filename);
668 input = fopen(filename, "r");
669 assert(input);
670
671 bset1 = isl_basic_set_read_from_file(ctx, input);
672 bmap = isl_basic_map_read_from_file(ctx, input);
673
674 bset1 = isl_basic_set_apply(bset1, bmap);
675
676 bset2 = isl_basic_set_read_from_file(ctx, input);
677
678 assert(isl_basic_set_is_equal(bset1, bset2) == 1);
679
680 isl_basic_set_free(bset1);
681 isl_basic_set_free(bset2);
682 free(filename);
683
684 fclose(input);
685 }
686
687 void test_application(struct isl_ctx *ctx)
688 {
689 test_application_case(ctx, "application");
690 test_application_case(ctx, "application2");
691 }
692
693 void test_affine_hull_case(struct isl_ctx *ctx, const char *name)
694 {
695 char *filename;
696 FILE *input;
697 struct isl_basic_set *bset1, *bset2;
698
699 filename = get_filename(ctx, name, "polylib");
700 assert(filename);
701 input = fopen(filename, "r");
702 assert(input);
703
704 bset1 = isl_basic_set_read_from_file(ctx, input);
705 bset2 = isl_basic_set_read_from_file(ctx, input);
706
707 bset1 = isl_basic_set_affine_hull(bset1);
708
709 assert(isl_basic_set_is_equal(bset1, bset2) == 1);
710
711 isl_basic_set_free(bset1);
712 isl_basic_set_free(bset2);
713 free(filename);
714
715 fclose(input);
716 }
717
718 int test_affine_hull(struct isl_ctx *ctx)
719 {
720 const char *str;
721 isl_set *set;
722 isl_basic_set *bset, *bset2;
723 int n;
724 int subset;
725
726 test_affine_hull_case(ctx, "affine2");
727 test_affine_hull_case(ctx, "affine");
728 test_affine_hull_case(ctx, "affine3");
729
730 str = "[m] -> { [i0] : exists (e0, e1: e1 <= 1 + i0 and "
731 "m >= 3 and 4i0 <= 2 + m and e1 >= i0 and "
732 "e1 >= 0 and e1 <= 2 and e1 >= 1 + 2e0 and "
733 "2e1 <= 1 + m + 4e0 and 2e1 >= 2 - m + 4i0 - 4e0) }";
734 set = isl_set_read_from_str(ctx, str);
735 bset = isl_set_affine_hull(set);
736 n = isl_basic_set_dim(bset, isl_dim_div);
737 isl_basic_set_free(bset);
738 if (n != 0)
739 isl_die(ctx, isl_error_unknown, "not expecting any divs",
740 return -1);
741
742 /* Check that isl_map_affine_hull is not confused by
743 * the reordering of divs in isl_map_align_divs.
744 */
745 str = "{ [a, b, c, 0] : exists (e0 = [(b)/32], e1 = [(c)/32]: "
746 "32e0 = b and 32e1 = c); "
747 "[a, 0, c, 0] : exists (e0 = [(c)/32]: 32e0 = c) }";
748 set = isl_set_read_from_str(ctx, str);
749 bset = isl_set_affine_hull(set);
750 isl_basic_set_free(bset);
751 if (!bset)
752 return -1;
753
754 str = "{ [a] : exists e0, e1, e2: 32e1 = 31 + 31a + 31e0 and "
755 "32e2 = 31 + 31e0 }";
756 set = isl_set_read_from_str(ctx, str);
757 bset = isl_set_affine_hull(set);
758 str = "{ [a] : exists e : a = 32 e }";
759 bset2 = isl_basic_set_read_from_str(ctx, str);
760 subset = isl_basic_set_is_subset(bset, bset2);
761 isl_basic_set_free(bset);
762 isl_basic_set_free(bset2);
763 if (subset < 0)
764 return -1;
765 if (!subset)
766 isl_die(ctx, isl_error_unknown, "not as accurate as expected",
767 return -1);
768
769 return 0;
770 }
771
772 void test_convex_hull_case(struct isl_ctx *ctx, const char *name)
773 {
774 char *filename;
775 FILE *input;
776 struct isl_basic_set *bset1, *bset2;
777 struct isl_set *set;
778
779 filename = get_filename(ctx, name, "polylib");
780 assert(filename);
781 input = fopen(filename, "r");
782 assert(input);
783
784 bset1 = isl_basic_set_read_from_file(ctx, input);
785 bset2 = isl_basic_set_read_from_file(ctx, input);
786
787 set = isl_basic_set_union(bset1, bset2);
788 bset1 = isl_set_convex_hull(set);
789
790 bset2 = isl_basic_set_read_from_file(ctx, input);
791
792 assert(isl_basic_set_is_equal(bset1, bset2) == 1);
793
794 isl_basic_set_free(bset1);
795 isl_basic_set_free(bset2);
796 free(filename);
797
798 fclose(input);
799 }
800
801 void test_convex_hull_algo(struct isl_ctx *ctx, int convex)
802 {
803 const char *str1, *str2;
804 isl_set *set1, *set2;
805 int orig_convex = ctx->opt->convex;
806 ctx->opt->convex = convex;
807
808 test_convex_hull_case(ctx, "convex0");
809 test_convex_hull_case(ctx, "convex1");
810 test_convex_hull_case(ctx, "convex2");
811 test_convex_hull_case(ctx, "convex3");
812 test_convex_hull_case(ctx, "convex4");
813 test_convex_hull_case(ctx, "convex5");
814 test_convex_hull_case(ctx, "convex6");
815 test_convex_hull_case(ctx, "convex7");
816 test_convex_hull_case(ctx, "convex8");
817 test_convex_hull_case(ctx, "convex9");
818 test_convex_hull_case(ctx, "convex10");
819 test_convex_hull_case(ctx, "convex11");
820 test_convex_hull_case(ctx, "convex12");
821 test_convex_hull_case(ctx, "convex13");
822 test_convex_hull_case(ctx, "convex14");
823 test_convex_hull_case(ctx, "convex15");
824
825 str1 = "{ [i0, i1, i2] : (i2 = 1 and i0 = 0 and i1 >= 0) or "
826 "(i0 = 1 and i1 = 0 and i2 = 1) or "
827 "(i0 = 0 and i1 = 0 and i2 = 0) }";
828 str2 = "{ [i0, i1, i2] : i0 >= 0 and i2 >= i0 and i2 <= 1 and i1 >= 0 }";
829 set1 = isl_set_read_from_str(ctx, str1);
830 set2 = isl_set_read_from_str(ctx, str2);
831 set1 = isl_set_from_basic_set(isl_set_convex_hull(set1));
832 assert(isl_set_is_equal(set1, set2));
833 isl_set_free(set1);
834 isl_set_free(set2);
835
836 ctx->opt->convex = orig_convex;
837 }
838
839 void test_convex_hull(struct isl_ctx *ctx)
840 {
841 test_convex_hull_algo(ctx, ISL_CONVEX_HULL_FM);
842 test_convex_hull_algo(ctx, ISL_CONVEX_HULL_WRAP);
843 }
844
845 void test_gist_case(struct isl_ctx *ctx, const char *name)
846 {
847 char *filename;
848 FILE *input;
849 struct isl_basic_set *bset1, *bset2;
850
851 filename = get_filename(ctx, name, "polylib");
852 assert(filename);
853 input = fopen(filename, "r");
854 assert(input);
855
856 bset1 = isl_basic_set_read_from_file(ctx, input);
857 bset2 = isl_basic_set_read_from_file(ctx, input);
858
859 bset1 = isl_basic_set_gist(bset1, bset2);
860
861 bset2 = isl_basic_set_read_from_file(ctx, input);
862
863 assert(isl_basic_set_is_equal(bset1, bset2) == 1);
864
865 isl_basic_set_free(bset1);
866 isl_basic_set_free(bset2);
867 free(filename);
868
869 fclose(input);
870 }
871
872 void test_gist(struct isl_ctx *ctx)
873 {
874 const char *str;
875 isl_basic_set *bset1, *bset2;
876
877 test_gist_case(ctx, "gist1");
878
879 str = "[p0, p2, p3, p5, p6, p10] -> { [] : "
880 "exists (e0 = [(15 + p0 + 15p6 + 15p10)/16], e1 = [(p5)/8], "
881 "e2 = [(p6)/128], e3 = [(8p2 - p5)/128], "
882 "e4 = [(128p3 - p6)/4096]: 8e1 = p5 and 128e2 = p6 and "
883 "128e3 = 8p2 - p5 and 4096e4 = 128p3 - p6 and p2 >= 0 and "
884 "16e0 >= 16 + 16p6 + 15p10 and p2 <= 15 and p3 >= 0 and "
885 "p3 <= 31 and p6 >= 128p3 and p5 >= 8p2 and p10 >= 0 and "
886 "16e0 <= 15 + p0 + 15p6 + 15p10 and 16e0 >= p0 + 15p6 + 15p10 and "
887 "p10 <= 15 and p10 <= -1 + p0 - p6) }";
888 bset1 = isl_basic_set_read_from_str(ctx, str);
889 str = "[p0, p2, p3, p5, p6, p10] -> { [] : exists (e0 = [(p5)/8], "
890 "e1 = [(p6)/128], e2 = [(8p2 - p5)/128], "
891 "e3 = [(128p3 - p6)/4096]: 8e0 = p5 and 128e1 = p6 and "
892 "128e2 = 8p2 - p5 and 4096e3 = 128p3 - p6 and p5 >= -7 and "
893 "p2 >= 0 and 8p2 <= -1 + p0 and p2 <= 15 and p3 >= 0 and "
894 "p3 <= 31 and 128p3 <= -1 + p0 and p6 >= -127 and "
895 "p5 <= -1 + p0 and p6 <= -1 + p0 and p6 >= 128p3 and "
896 "p0 >= 1 and p5 >= 8p2 and p10 >= 0 and p10 <= 15 ) }";
897 bset2 = isl_basic_set_read_from_str(ctx, str);
898 bset1 = isl_basic_set_gist(bset1, bset2);
899 assert(bset1 && bset1->n_div == 0);
900 isl_basic_set_free(bset1);
901 }
902
903 int test_coalesce_set(isl_ctx *ctx, const char *str, int check_one)
904 {
905 isl_set *set, *set2;
906 int equal;
907 int one;
908
909 set = isl_set_read_from_str(ctx, str);
910 set = isl_set_coalesce(set);
911 set2 = isl_set_read_from_str(ctx, str);
912 equal = isl_set_is_equal(set, set2);
913 one = set && set->n == 1;
914 isl_set_free(set);
915 isl_set_free(set2);
916
917 if (equal < 0)
918 return -1;
919 if (!equal)
920 isl_die(ctx, isl_error_unknown,
921 "coalesced set not equal to input", return -1);
922 if (check_one && !one)
923 isl_die(ctx, isl_error_unknown,
924 "coalesced set should not be a union", return -1);
925
926 return 0;
927 }
928
929 int test_coalesce_unbounded_wrapping(isl_ctx *ctx)
930 {
931 int r = 0;
932 int bounded;
933
934 bounded = isl_options_get_coalesce_bounded_wrapping(ctx);
935 isl_options_set_coalesce_bounded_wrapping(ctx, 0);
936
937 if (test_coalesce_set(ctx,
938 "{[x,y,z] : y + 2 >= 0 and x - y + 1 >= 0 and "
939 "-x - y + 1 >= 0 and -3 <= z <= 3;"
940 "[x,y,z] : -x+z + 20 >= 0 and -x-z + 20 >= 0 and "
941 "x-z + 20 >= 0 and x+z + 20 >= 0 and "
942 "-10 <= y <= 0}", 1) < 0)
943 goto error;
944 if (test_coalesce_set(ctx,
945 "{[x,y] : 0 <= x,y <= 10; [5,y]: 4 <=y <= 11}", 1) < 0)
946 goto error;
947 if (test_coalesce_set(ctx,
948 "{[x,0,0] : -5 <= x <= 5; [0,y,1] : -5 <= y <= 5 }", 1) < 0)
949 goto error;
950
951 if (0) {
952 error:
953 r = -1;
954 }
955
956 isl_options_set_coalesce_bounded_wrapping(ctx, bounded);
957
958 return r;
959 }
960
961 /* Inputs for coalescing tests.
962 * "str" is a string representation of the input set.
963 * "single_disjunct" is set if we expect the result to consist of
964 * a single disjunct.
965 */
966 struct {
967 int single_disjunct;
968 const char *str;
969 } coalesce_tests[] = {
970 { 1, "{[x,y]: x >= 0 & x <= 10 & y >= 0 & y <= 10 or "
971 "y >= x & x >= 2 & 5 >= y }" },
972 { 1, "{[x,y]: y >= 0 & 2x + y <= 30 & y <= 10 & x >= 0 or "
973 "x + y >= 10 & y <= x & x + y <= 20 & y >= 0}" },
974 { 0, "{[x,y]: y >= 0 & 2x + y <= 30 & y <= 10 & x >= 0 or "
975 "x + y >= 10 & y <= x & x + y <= 19 & y >= 0}" },
976 { 1, "{[x,y]: y >= 0 & x <= 5 & y <= x or "
977 "y >= 0 & x >= 6 & x <= 10 & y <= x}" },
978 { 0, "{[x,y]: y >= 0 & x <= 5 & y <= x or "
979 "y >= 0 & x >= 7 & x <= 10 & y <= x}" },
980 { 0, "{[x,y]: y >= 0 & x <= 5 & y <= x or "
981 "y >= 0 & x >= 6 & x <= 10 & y + 1 <= x}" },
982 { 1, "{[x,y]: y >= 0 & x <= 5 & y <= x or y >= 0 & x = 6 & y <= 6}" },
983 { 0, "{[x,y]: y >= 0 & x <= 5 & y <= x or y >= 0 & x = 7 & y <= 6}" },
984 { 1, "{[x,y]: y >= 0 & x <= 5 & y <= x or y >= 0 & x = 6 & y <= 5}" },
985 { 0, "{[x,y]: y >= 0 & x <= 5 & y <= x or y >= 0 & x = 6 & y <= 7}" },
986 { 1, "[n] -> { [i] : i = 1 and n >= 2 or 2 <= i and i <= n }" },
987 { 0, "{[x,y] : x >= 0 and y >= 0 or 0 <= y and y <= 5 and x = -1}" },
988 { 1, "[n] -> { [i] : 1 <= i and i <= n - 1 or 2 <= i and i <= n }" },
989 { 0, "[n] -> { [[i0] -> [o0]] : exists (e0 = [(i0)/4], e1 = [(o0)/4], "
990 "e2 = [(n)/2], e3 = [(-2 + i0)/4], e4 = [(-2 + o0)/4], "
991 "e5 = [(-2n + i0)/4]: 2e2 = n and 4e3 = -2 + i0 and "
992 "4e4 = -2 + o0 and i0 >= 8 + 2n and o0 >= 2 + i0 and "
993 "o0 <= 56 + 2n and o0 <= -12 + 4n and i0 <= 57 + 2n and "
994 "i0 <= -11 + 4n and o0 >= 6 + 2n and 4e0 <= i0 and "
995 "4e0 >= -3 + i0 and 4e1 <= o0 and 4e1 >= -3 + o0 and "
996 "4e5 <= -2n + i0 and 4e5 >= -3 - 2n + i0);"
997 "[[i0] -> [o0]] : exists (e0 = [(i0)/4], e1 = [(o0)/4], "
998 "e2 = [(n)/2], e3 = [(-2 + i0)/4], e4 = [(-2 + o0)/4], "
999 "e5 = [(-2n + i0)/4]: 2e2 = n and 4e3 = -2 + i0 and "
1000 "4e4 = -2 + o0 and 2e0 >= 3 + n and e0 <= -4 + n and "
1001 "2e0 <= 27 + n and e1 <= -4 + n and 2e1 <= 27 + n and "
1002 "2e1 >= 2 + n and e1 >= 1 + e0 and i0 >= 7 + 2n and "
1003 "i0 <= -11 + 4n and i0 <= 57 + 2n and 4e0 <= -2 + i0 and "
1004 "4e0 >= -3 + i0 and o0 >= 6 + 2n and o0 <= -11 + 4n and "
1005 "o0 <= 57 + 2n and 4e1 <= -2 + o0 and 4e1 >= -3 + o0 and "
1006 "4e5 <= -2n + i0 and 4e5 >= -3 - 2n + i0 ) }" },
1007 { 0, "[n, m] -> { [o0, o2, o3] : (o3 = 1 and o0 >= 1 + m and "
1008 "o0 <= n + m and o2 <= m and o0 >= 2 + n and o2 >= 3) or "
1009 "(o0 >= 2 + n and o0 >= 1 + m and o0 <= n + m and n >= 1 and "
1010 "o3 <= -1 + o2 and o3 >= 1 - m + o2 and o3 >= 2 and o3 <= n) }" },
1011 { 0, "[M, N] -> { [[i0, i1, i2, i3, i4, i5, i6] -> "
1012 "[o0, o1, o2, o3, o4, o5, o6]] : "
1013 "(o6 <= -4 + 2M - 2N + i0 + i1 - i2 + i6 - o0 - o1 + o2 and "
1014 "o3 <= -2 + i3 and o6 >= 2 + i0 + i3 + i6 - o0 - o3 and "
1015 "o6 >= 2 - M + N + i3 + i4 + i6 - o3 - o4 and o0 <= -1 + i0 and "
1016 "o4 >= 4 - 3M + 3N - i0 - i1 + i2 + 2i3 + i4 + o0 + o1 - o2 - 2o3 "
1017 "and o6 <= -3 + 2M - 2N + i3 + i4 - i5 + i6 - o3 - o4 + o5 and "
1018 "2o6 <= -5 + 5M - 5N + 2i0 + i1 - i2 - i5 + 2i6 - 2o0 - o1 + o2 + o5 "
1019 "and o6 >= 2i0 + i1 + i6 - 2o0 - o1 and "
1020 "3o6 <= -5 + 4M - 4N + 2i0 + i1 - i2 + 2i3 + i4 - i5 + 3i6 "
1021 "- 2o0 - o1 + o2 - 2o3 - o4 + o5) or "
1022 "(N >= 2 and o3 <= -1 + i3 and o0 <= -1 + i0 and "
1023 "o6 >= i3 + i6 - o3 and M >= 0 and "
1024 "2o6 >= 1 + i0 + i3 + 2i6 - o0 - o3 and "
1025 "o6 >= 1 - M + i0 + i6 - o0 and N >= 2M and o6 >= i0 + i6 - o0) }" },
1026 { 0, "[M, N] -> { [o0] : (o0 = 0 and M >= 1 and N >= 2) or "
1027 "(o0 = 0 and M >= 1 and N >= 2M and N >= 2 + M) or "
1028 "(o0 = 0 and M >= 2 and N >= 3) or "
1029 "(M = 0 and o0 = 0 and N >= 3) }" },
1030 { 0, "{ [i0, i1, i2, i3] : (i1 = 10i0 and i0 >= 1 and 10i0 <= 100 and "
1031 "i3 <= 9 + 10 i2 and i3 >= 1 + 10i2 and i3 >= 0) or "
1032 "(i1 <= 9 + 10i0 and i1 >= 1 + 10i0 and i2 >= 0 and "
1033 "i0 >= 0 and i1 <= 100 and i3 <= 9 + 10i2 and i3 >= 1 + 10i2) }" },
1034 { 0, "[M] -> { [i1] : (i1 >= 2 and i1 <= M) or (i1 = M and M >= 1) }" },
1035 { 0, "{[x,y] : x,y >= 0; [x,y] : 10 <= x <= 20 and y >= -1 }" },
1036 { 1, "{ [x, y] : (x >= 1 and y >= 1 and x <= 2 and y <= 2) or "
1037 "(y = 3 and x = 1) }" },
1038 { 1, "[M] -> { [i0, i1, i2, i3, i4] : (i1 >= 3 and i4 >= 2 + i2 and "
1039 "i2 >= 2 and i0 >= 2 and i3 >= 1 + i2 and i0 <= M and "
1040 "i1 <= M and i3 <= M and i4 <= M) or "
1041 "(i1 >= 2 and i4 >= 1 + i2 and i2 >= 2 and i0 >= 2 and "
1042 "i3 >= 1 + i2 and i0 <= M and i1 <= -1 + M and i3 <= M and "
1043 "i4 <= -1 + M) }" },
1044 { 1, "{ [x, y] : (x >= 0 and y >= 0 and x <= 10 and y <= 10) or "
1045 "(x >= 1 and y >= 1 and x <= 11 and y <= 11) }" },
1046 { 0, "{[x,0] : x >= 0; [x,1] : x <= 20}" },
1047 { 1, "{ [x, 1 - x] : 0 <= x <= 1; [0,0] }" },
1048 { 1, "{ [0,0]; [i,i] : 1 <= i <= 10 }" },
1049 { 0, "{ [0,0]; [i,j] : 1 <= i,j <= 10 }" },
1050 { 1, "{ [0,0]; [i,2i] : 1 <= i <= 10 }" },
1051 { 0, "{ [0,0]; [i,2i] : 2 <= i <= 10 }" },
1052 { 0, "{ [1,0]; [i,2i] : 1 <= i <= 10 }" },
1053 { 0, "{ [0,1]; [i,2i] : 1 <= i <= 10 }" },
1054 { 0, "{ [a, b] : exists e : 2e = a and "
1055 "a >= 0 and (a <= 3 or (b <= 0 and b >= -4 + a)) }" },
1056 { 0, "{ [i, j, i', j'] : i <= 2 and j <= 2 and "
1057 "j' >= -1 + 2i + j - 2i' and i' <= -1 + i and "
1058 "j >= 1 and j' <= i + j - i' and i >= 1; "
1059 "[1, 1, 1, 1] }" },
1060 { 1, "{ [i,j] : exists a,b : i = 2a and j = 3b; "
1061 "[i,j] : exists a : j = 3a }" },
1062 { 1, "{ [a, b, c] : (c <= 7 - b and b <= 1 and b >= 0 and "
1063 "c >= 3 + b and b <= 3 + 8a and b >= -26 + 8a and "
1064 "a >= 3) or "
1065 "(b <= 1 and c <= 7 and b >= 0 and c >= 4 + b and "
1066 "b <= 3 + 8a and b >= -26 + 8a and a >= 3) }" },
1067 { 1, "{ [a, 0, c] : c >= 1 and c <= 29 and c >= -1 + 8a and "
1068 "c <= 6 + 8a and a >= 3; "
1069 "[a, -1, c] : c >= 1 and c <= 30 and c >= 8a and "
1070 "c <= 7 + 8a and a >= 3 and a <= 4 }" },
1071 { 1, "{ [x,y] : 0 <= x <= 2 and y >= 0 and x + 2y <= 4; "
1072 "[x,0] : 3 <= x <= 4 }" },
1073 { 1, "{ [x,y] : 0 <= x <= 3 and y >= 0 and x + 3y <= 6; "
1074 "[x,0] : 4 <= x <= 5 }" },
1075 { 0, "{ [x,y] : 0 <= x <= 2 and y >= 0 and x + 2y <= 4; "
1076 "[x,0] : 3 <= x <= 5 }" },
1077 { 0, "{ [x,y] : 0 <= x <= 2 and y >= 0 and x + y <= 4; "
1078 "[x,0] : 3 <= x <= 4 }" },
1079 { 1 , "{ [i0, i1] : i0 <= 122 and i0 >= 1 and 128i1 >= -249 + i0 and "
1080 "i1 <= 0; "
1081 "[i0, 0] : i0 >= 123 and i0 <= 124 }" },
1082 };
1083
1084 /* Test the functionality of isl_set_coalesce.
1085 * That is, check that the output is always equal to the input
1086 * and in some cases that the result consists of a single disjunct.
1087 */
1088 static int test_coalesce(struct isl_ctx *ctx)
1089 {
1090 int i;
1091
1092 for (i = 0; i < ARRAY_SIZE(coalesce_tests); ++i) {
1093 const char *str = coalesce_tests[i].str;
1094 int check_one = coalesce_tests[i].single_disjunct;
1095 if (test_coalesce_set(ctx, str, check_one) < 0)
1096 return -1;
1097 }
1098
1099 if (test_coalesce_unbounded_wrapping(ctx) < 0)
1100 return -1;
1101
1102 return 0;
1103 }
1104
1105 void test_closure(struct isl_ctx *ctx)
1106 {
1107 const char *str;
1108 isl_set *dom;
1109 isl_map *up, *right;
1110 isl_map *map, *map2;
1111 int exact;
1112
1113 /* COCOA example 1 */
1114 map = isl_map_read_from_str(ctx,
1115 "[n] -> { [i,j] -> [i2,j2] : i2 = i + 1 and j2 = j + 1 and "
1116 "1 <= i and i < n and 1 <= j and j < n or "
1117 "i2 = i + 1 and j2 = j - 1 and "
1118 "1 <= i and i < n and 2 <= j and j <= n }");
1119 map = isl_map_power(map, &exact);
1120 assert(exact);
1121 isl_map_free(map);
1122
1123 /* COCOA example 1 */
1124 map = isl_map_read_from_str(ctx,
1125 "[n] -> { [i,j] -> [i2,j2] : i2 = i + 1 and j2 = j + 1 and "
1126 "1 <= i and i < n and 1 <= j and j < n or "
1127 "i2 = i + 1 and j2 = j - 1 and "
1128 "1 <= i and i < n and 2 <= j and j <= n }");
1129 map = isl_map_transitive_closure(map, &exact);
1130 assert(exact);
1131 map2 = isl_map_read_from_str(ctx,
1132 "[n] -> { [i,j] -> [i2,j2] : exists (k1,k2,k : "
1133 "1 <= i and i < n and 1 <= j and j <= n and "
1134 "2 <= i2 and i2 <= n and 1 <= j2 and j2 <= n and "
1135 "i2 = i + k1 + k2 and j2 = j + k1 - k2 and "
1136 "k1 >= 0 and k2 >= 0 and k1 + k2 = k and k >= 1 )}");
1137 assert(isl_map_is_equal(map, map2));
1138 isl_map_free(map2);
1139 isl_map_free(map);
1140
1141 map = isl_map_read_from_str(ctx,
1142 "[n] -> { [x] -> [y] : y = x + 1 and 0 <= x and x <= n and "
1143 " 0 <= y and y <= n }");
1144 map = isl_map_transitive_closure(map, &exact);
1145 map2 = isl_map_read_from_str(ctx,
1146 "[n] -> { [x] -> [y] : y > x and 0 <= x and x <= n and "
1147 " 0 <= y and y <= n }");
1148 assert(isl_map_is_equal(map, map2));
1149 isl_map_free(map2);
1150 isl_map_free(map);
1151
1152 /* COCOA example 2 */
1153 map = isl_map_read_from_str(ctx,
1154 "[n] -> { [i,j] -> [i2,j2] : i2 = i + 2 and j2 = j + 2 and "
1155 "1 <= i and i < n - 1 and 1 <= j and j < n - 1 or "
1156 "i2 = i + 2 and j2 = j - 2 and "
1157 "1 <= i and i < n - 1 and 3 <= j and j <= n }");
1158 map = isl_map_transitive_closure(map, &exact);
1159 assert(exact);
1160 map2 = isl_map_read_from_str(ctx,
1161 "[n] -> { [i,j] -> [i2,j2] : exists (k1,k2,k : "
1162 "1 <= i and i < n - 1 and 1 <= j and j <= n and "
1163 "3 <= i2 and i2 <= n and 1 <= j2 and j2 <= n and "
1164 "i2 = i + 2 k1 + 2 k2 and j2 = j + 2 k1 - 2 k2 and "
1165 "k1 >= 0 and k2 >= 0 and k1 + k2 = k and k >= 1) }");
1166 assert(isl_map_is_equal(map, map2));
1167 isl_map_free(map);
1168 isl_map_free(map2);
1169
1170 /* COCOA Fig.2 left */
1171 map = isl_map_read_from_str(ctx,
1172 "[n] -> { [i,j] -> [i2,j2] : i2 = i + 2 and j2 = j and "
1173 "i <= 2 j - 3 and i <= n - 2 and j <= 2 i - 1 and "
1174 "j <= n or "
1175 "i2 = i and j2 = j + 2 and i <= 2 j - 1 and i <= n and "
1176 "j <= 2 i - 3 and j <= n - 2 or "
1177 "i2 = i + 1 and j2 = j + 1 and i <= 2 j - 1 and "
1178 "i <= n - 1 and j <= 2 i - 1 and j <= n - 1 }");
1179 map = isl_map_transitive_closure(map, &exact);
1180 assert(exact);
1181 isl_map_free(map);
1182
1183 /* COCOA Fig.2 right */
1184 map = isl_map_read_from_str(ctx,
1185 "[n] -> { [i,j] -> [i2,j2] : i2 = i + 3 and j2 = j and "
1186 "i <= 2 j - 4 and i <= n - 3 and j <= 2 i - 1 and "
1187 "j <= n or "
1188 "i2 = i and j2 = j + 3 and i <= 2 j - 1 and i <= n and "
1189 "j <= 2 i - 4 and j <= n - 3 or "
1190 "i2 = i + 1 and j2 = j + 1 and i <= 2 j - 1 and "
1191 "i <= n - 1 and j <= 2 i - 1 and j <= n - 1 }");
1192 map = isl_map_power(map, &exact);
1193 assert(exact);
1194 isl_map_free(map);
1195
1196 /* COCOA Fig.2 right */
1197 map = isl_map_read_from_str(ctx,
1198 "[n] -> { [i,j] -> [i2,j2] : i2 = i + 3 and j2 = j and "
1199 "i <= 2 j - 4 and i <= n - 3 and j <= 2 i - 1 and "
1200 "j <= n or "
1201 "i2 = i and j2 = j + 3 and i <= 2 j - 1 and i <= n and "
1202 "j <= 2 i - 4 and j <= n - 3 or "
1203 "i2 = i + 1 and j2 = j + 1 and i <= 2 j - 1 and "
1204 "i <= n - 1 and j <= 2 i - 1 and j <= n - 1 }");
1205 map = isl_map_transitive_closure(map, &exact);
1206 assert(exact);
1207 map2 = isl_map_read_from_str(ctx,
1208 "[n] -> { [i,j] -> [i2,j2] : exists (k1,k2,k3,k : "
1209 "i <= 2 j - 1 and i <= n and j <= 2 i - 1 and "
1210 "j <= n and 3 + i + 2 j <= 3 n and "
1211 "3 + 2 i + j <= 3n and i2 <= 2 j2 -1 and i2 <= n and "
1212 "i2 <= 3 j2 - 4 and j2 <= 2 i2 -1 and j2 <= n and "
1213 "13 + 4 j2 <= 11 i2 and i2 = i + 3 k1 + k3 and "
1214 "j2 = j + 3 k2 + k3 and k1 >= 0 and k2 >= 0 and "
1215 "k3 >= 0 and k1 + k2 + k3 = k and k > 0) }");
1216 assert(isl_map_is_equal(map, map2));
1217 isl_map_free(map2);
1218 isl_map_free(map);
1219
1220 /* COCOA Fig.1 right */
1221 dom = isl_set_read_from_str(ctx,
1222 "{ [x,y] : x >= 0 and -2 x + 3 y >= 0 and x <= 3 and "
1223 "2 x - 3 y + 3 >= 0 }");
1224 right = isl_map_read_from_str(ctx,
1225 "{ [x,y] -> [x2,y2] : x2 = x + 1 and y2 = y }");
1226 up = isl_map_read_from_str(ctx,
1227 "{ [x,y] -> [x2,y2] : x2 = x and y2 = y + 1 }");
1228 right = isl_map_intersect_domain(right, isl_set_copy(dom));
1229 right = isl_map_intersect_range(right, isl_set_copy(dom));
1230 up = isl_map_intersect_domain(up, isl_set_copy(dom));
1231 up = isl_map_intersect_range(up, dom);
1232 map = isl_map_union(up, right);
1233 map = isl_map_transitive_closure(map, &exact);
1234 assert(exact);
1235 map2 = isl_map_read_from_str(ctx,
1236 "{ [0,0] -> [0,1]; [0,0] -> [1,1]; [0,1] -> [1,1]; "
1237 " [2,2] -> [3,2]; [2,2] -> [3,3]; [3,2] -> [3,3] }");
1238 assert(isl_map_is_equal(map, map2));
1239 isl_map_free(map2);
1240 isl_map_free(map);
1241
1242 /* COCOA Theorem 1 counter example */
1243 map = isl_map_read_from_str(ctx,
1244 "{ [i,j] -> [i2,j2] : i = 0 and 0 <= j and j <= 1 and "
1245 "i2 = 1 and j2 = j or "
1246 "i = 0 and j = 0 and i2 = 0 and j2 = 1 }");
1247 map = isl_map_transitive_closure(map, &exact);
1248 assert(exact);
1249 isl_map_free(map);
1250
1251 map = isl_map_read_from_str(ctx,
1252 "[m,n] -> { [i,j] -> [i2,j2] : i2 = i and j2 = j + 2 and "
1253 "1 <= i,i2 <= n and 1 <= j,j2 <= m or "
1254 "i2 = i + 1 and 3 <= j2 - j <= 4 and "
1255 "1 <= i,i2 <= n and 1 <= j,j2 <= m }");
1256 map = isl_map_transitive_closure(map, &exact);
1257 assert(exact);
1258 isl_map_free(map);
1259
1260 /* Kelly et al 1996, fig 12 */
1261 map = isl_map_read_from_str(ctx,
1262 "[n] -> { [i,j] -> [i2,j2] : i2 = i and j2 = j + 1 and "
1263 "1 <= i,j,j+1 <= n or "
1264 "j = n and j2 = 1 and i2 = i + 1 and "
1265 "1 <= i,i+1 <= n }");
1266 map = isl_map_transitive_closure(map, &exact);
1267 assert(exact);
1268 map2 = isl_map_read_from_str(ctx,
1269 "[n] -> { [i,j] -> [i2,j2] : 1 <= j < j2 <= n and "
1270 "1 <= i <= n and i = i2 or "
1271 "1 <= i < i2 <= n and 1 <= j <= n and "
1272 "1 <= j2 <= n }");
1273 assert(isl_map_is_equal(map, map2));
1274 isl_map_free(map2);
1275 isl_map_free(map);
1276
1277 /* Omega's closure4 */
1278 map = isl_map_read_from_str(ctx,
1279 "[m,n] -> { [x,y] -> [x2,y2] : x2 = x and y2 = y + 1 and "
1280 "1 <= x,y <= 10 or "
1281 "x2 = x + 1 and y2 = y and "
1282 "1 <= x <= 20 && 5 <= y <= 15 }");
1283 map = isl_map_transitive_closure(map, &exact);
1284 assert(exact);
1285 isl_map_free(map);
1286
1287 map = isl_map_read_from_str(ctx,
1288 "[n] -> { [x] -> [y]: 1 <= n <= y - x <= 10 }");
1289 map = isl_map_transitive_closure(map, &exact);
1290 assert(!exact);
1291 map2 = isl_map_read_from_str(ctx,
1292 "[n] -> { [x] -> [y] : 1 <= n <= 10 and y >= n + x }");
1293 assert(isl_map_is_equal(map, map2));
1294 isl_map_free(map);
1295 isl_map_free(map2);
1296
1297 str = "[n, m] -> { [i0, i1, i2, i3] -> [o0, o1, o2, o3] : "
1298 "i3 = 1 and o0 = i0 and o1 = -1 + i1 and o2 = -1 + i2 and "
1299 "o3 = -2 + i2 and i1 <= -1 + i0 and i1 >= 1 - m + i0 and "
1300 "i1 >= 2 and i1 <= n and i2 >= 3 and i2 <= 1 + n and i2 <= m }";
1301 map = isl_map_read_from_str(ctx, str);
1302 map = isl_map_transitive_closure(map, &exact);
1303 assert(exact);
1304 map2 = isl_map_read_from_str(ctx, str);
1305 assert(isl_map_is_equal(map, map2));
1306 isl_map_free(map);
1307 isl_map_free(map2);
1308
1309 str = "{[0] -> [1]; [2] -> [3]}";
1310 map = isl_map_read_from_str(ctx, str);
1311 map = isl_map_transitive_closure(map, &exact);
1312 assert(exact);
1313 map2 = isl_map_read_from_str(ctx, str);
1314 assert(isl_map_is_equal(map, map2));
1315 isl_map_free(map);
1316 isl_map_free(map2);
1317
1318 str = "[n] -> { [[i0, i1, 1, 0, i0] -> [i5, 1]] -> "
1319 "[[i0, -1 + i1, 2, 0, i0] -> [-1 + i5, 2]] : "
1320 "exists (e0 = [(3 - n)/3]: i5 >= 2 and i1 >= 2 and "
1321 "3i0 <= -1 + n and i1 <= -1 + n and i5 <= -1 + n and "
1322 "3e0 >= 1 - n and 3e0 <= 2 - n and 3i0 >= -2 + n); "
1323 "[[i0, i1, 2, 0, i0] -> [i5, 1]] -> "
1324 "[[i0, i1, 1, 0, i0] -> [-1 + i5, 2]] : "
1325 "exists (e0 = [(3 - n)/3]: i5 >= 2 and i1 >= 1 and "
1326 "3i0 <= -1 + n and i1 <= -1 + n and i5 <= -1 + n and "
1327 "3e0 >= 1 - n and 3e0 <= 2 - n and 3i0 >= -2 + n); "
1328 "[[i0, i1, 1, 0, i0] -> [i5, 2]] -> "
1329 "[[i0, -1 + i1, 2, 0, i0] -> [i5, 1]] : "
1330 "exists (e0 = [(3 - n)/3]: i1 >= 2 and i5 >= 1 and "
1331 "3i0 <= -1 + n and i1 <= -1 + n and i5 <= -1 + n and "
1332 "3e0 >= 1 - n and 3e0 <= 2 - n and 3i0 >= -2 + n); "
1333 "[[i0, i1, 2, 0, i0] -> [i5, 2]] -> "
1334 "[[i0, i1, 1, 0, i0] -> [i5, 1]] : "
1335 "exists (e0 = [(3 - n)/3]: i5 >= 1 and i1 >= 1 and "
1336 "3i0 <= -1 + n and i1 <= -1 + n and i5 <= -1 + n and "
1337 "3e0 >= 1 - n and 3e0 <= 2 - n and 3i0 >= -2 + n) }";
1338 map = isl_map_read_from_str(ctx, str);
1339 map = isl_map_transitive_closure(map, NULL);
1340 assert(map);
1341 isl_map_free(map);
1342 }
1343
1344 void test_lex(struct isl_ctx *ctx)
1345 {
1346 isl_space *dim;
1347 isl_map *map;
1348
1349 dim = isl_space_set_alloc(ctx, 0, 0);
1350 map = isl_map_lex_le(dim);
1351 assert(!isl_map_is_empty(map));
1352 isl_map_free(map);
1353 }
1354
1355 static int test_lexmin(struct isl_ctx *ctx)
1356 {
1357 int equal;
1358 const char *str;
1359 isl_basic_map *bmap;
1360 isl_map *map, *map2;
1361 isl_set *set;
1362 isl_set *set2;
1363 isl_pw_multi_aff *pma;
1364
1365 str = "[p0, p1] -> { [] -> [] : "
1366 "exists (e0 = [(2p1)/3], e1, e2, e3 = [(3 - p1 + 3e0)/3], "
1367 "e4 = [(p1)/3], e5 = [(p1 + 3e4)/3]: "
1368 "3e0 >= -2 + 2p1 and 3e0 >= p1 and 3e3 >= 1 - p1 + 3e0 and "
1369 "3e0 <= 2p1 and 3e3 >= -2 + p1 and 3e3 <= -1 + p1 and p1 >= 3 and "
1370 "3e5 >= -2 + 2p1 and 3e5 >= p1 and 3e5 <= -1 + p1 + 3e4 and "
1371 "3e4 <= p1 and 3e4 >= -2 + p1 and e3 <= -1 + e0 and "
1372 "3e4 >= 6 - p1 + 3e1 and 3e1 >= p1 and 3e5 >= -2 + p1 + 3e4 and "
1373 "2e4 >= 3 - p1 + 2e1 and e4 <= e1 and 3e3 <= 2 - p1 + 3e0 and "
1374 "e5 >= 1 + e1 and 3e4 >= 6 - 2p1 + 3e1 and "
1375 "p0 >= 2 and p1 >= p0 and 3e2 >= p1 and 3e4 >= 6 - p1 + 3e2 and "
1376 "e2 <= e1 and e3 >= 1 and e4 <= e2) }";
1377 map = isl_map_read_from_str(ctx, str);
1378 map = isl_map_lexmin(map);
1379 isl_map_free(map);
1380
1381 str = "[C] -> { [obj,a,b,c] : obj <= 38 a + 7 b + 10 c and "
1382 "a + b <= 1 and c <= 10 b and c <= C and a,b,c,C >= 0 }";
1383 set = isl_set_read_from_str(ctx, str);
1384 set = isl_set_lexmax(set);
1385 str = "[C] -> { [obj,a,b,c] : C = 8 }";
1386 set2 = isl_set_read_from_str(ctx, str);
1387 set = isl_set_intersect(set, set2);
1388 assert(!isl_set_is_empty(set));
1389 isl_set_free(set);
1390
1391 str = "{ [x] -> [y] : x <= y <= 10; [x] -> [5] : -8 <= x <= 8 }";
1392 map = isl_map_read_from_str(ctx, str);
1393 map = isl_map_lexmin(map);
1394 str = "{ [x] -> [5] : 6 <= x <= 8; "
1395 "[x] -> [x] : x <= 5 or (9 <= x <= 10) }";
1396 map2 = isl_map_read_from_str(ctx, str);
1397 assert(isl_map_is_equal(map, map2));
1398 isl_map_free(map);
1399 isl_map_free(map2);
1400
1401 str = "{ [x] -> [y] : 4y = x or 4y = -1 + x or 4y = -2 + x }";
1402 map = isl_map_read_from_str(ctx, str);
1403 map2 = isl_map_copy(map);
1404 map = isl_map_lexmin(map);
1405 assert(isl_map_is_equal(map, map2));
1406 isl_map_free(map);
1407 isl_map_free(map2);
1408
1409 str = "{ [x] -> [y] : x = 4y; [x] -> [y] : x = 2y }";
1410 map = isl_map_read_from_str(ctx, str);
1411 map = isl_map_lexmin(map);
1412 str = "{ [x] -> [y] : (4y = x and x >= 0) or "
1413 "(exists (e0 = [(x)/4], e1 = [(-2 + x)/4]: 2y = x and "
1414 "4e1 = -2 + x and 4e0 <= -1 + x and 4e0 >= -3 + x)) or "
1415 "(exists (e0 = [(x)/4]: 2y = x and 4e0 = x and x <= -4)) }";
1416 map2 = isl_map_read_from_str(ctx, str);
1417 assert(isl_map_is_equal(map, map2));
1418 isl_map_free(map);
1419 isl_map_free(map2);
1420
1421 str = "{ [i] -> [i', j] : j = i - 8i' and i' >= 0 and i' <= 7 and "
1422 " 8i' <= i and 8i' >= -7 + i }";
1423 bmap = isl_basic_map_read_from_str(ctx, str);
1424 pma = isl_basic_map_lexmin_pw_multi_aff(isl_basic_map_copy(bmap));
1425 map2 = isl_map_from_pw_multi_aff(pma);
1426 map = isl_map_from_basic_map(bmap);
1427 assert(isl_map_is_equal(map, map2));
1428 isl_map_free(map);
1429 isl_map_free(map2);
1430
1431 str = "{ T[a] -> S[b, c] : a = 4b-2c and c >= b }";
1432 map = isl_map_read_from_str(ctx, str);
1433 map = isl_map_lexmin(map);
1434 str = "{ T[a] -> S[b, c] : 2b = a and 2c = a }";
1435 map2 = isl_map_read_from_str(ctx, str);
1436 assert(isl_map_is_equal(map, map2));
1437 isl_map_free(map);
1438 isl_map_free(map2);
1439
1440 str = "[i] -> { [i', j] : j = i - 8i' and i' >= 0 and i' <= 7 and "
1441 " 8i' <= i and 8i' >= -7 + i }";
1442 set = isl_set_read_from_str(ctx, str);
1443 pma = isl_set_lexmin_pw_multi_aff(isl_set_copy(set));
1444 set2 = isl_set_from_pw_multi_aff(pma);
1445 equal = isl_set_is_equal(set, set2);
1446 isl_set_free(set);
1447 isl_set_free(set2);
1448 if (equal < 0)
1449 return -1;
1450 if (!equal)
1451 isl_die(ctx, isl_error_unknown,
1452 "unexpected difference between set and "
1453 "piecewise affine expression", return -1);
1454
1455 return 0;
1456 }
1457
1458 struct must_may {
1459 isl_map *must;
1460 isl_map *may;
1461 };
1462
1463 static int collect_must_may(__isl_take isl_map *dep, int must,
1464 void *dep_user, void *user)
1465 {
1466 struct must_may *mm = (struct must_may *)user;
1467
1468 if (must)
1469 mm->must = isl_map_union(mm->must, dep);
1470 else
1471 mm->may = isl_map_union(mm->may, dep);
1472
1473 return 0;
1474 }
1475
1476 static int common_space(void *first, void *second)
1477 {
1478 int depth = *(int *)first;
1479 return 2 * depth;
1480 }
1481
1482 static int map_is_equal(__isl_keep isl_map *map, const char *str)
1483 {
1484 isl_map *map2;
1485 int equal;
1486
1487 if (!map)
1488 return -1;
1489
1490 map2 = isl_map_read_from_str(map->ctx, str);
1491 equal = isl_map_is_equal(map, map2);
1492 isl_map_free(map2);
1493
1494 return equal;
1495 }
1496
1497 static int map_check_equal(__isl_keep isl_map *map, const char *str)
1498 {
1499 int equal;
1500
1501 equal = map_is_equal(map, str);
1502 if (equal < 0)
1503 return -1;
1504 if (!equal)
1505 isl_die(isl_map_get_ctx(map), isl_error_unknown,
1506 "result not as expected", return -1);
1507 return 0;
1508 }
1509
1510 void test_dep(struct isl_ctx *ctx)
1511 {
1512 const char *str;
1513 isl_space *dim;
1514 isl_map *map;
1515 isl_access_info *ai;
1516 isl_flow *flow;
1517 int depth;
1518 struct must_may mm;
1519
1520 depth = 3;
1521
1522 str = "{ [2,i,0] -> [i] : 0 <= i <= 10 }";
1523 map = isl_map_read_from_str(ctx, str);
1524 ai = isl_access_info_alloc(map, &depth, &common_space, 2);
1525
1526 str = "{ [0,i,0] -> [i] : 0 <= i <= 10 }";
1527 map = isl_map_read_from_str(ctx, str);
1528 ai = isl_access_info_add_source(ai, map, 1, &depth);
1529
1530 str = "{ [1,i,0] -> [5] : 0 <= i <= 10 }";
1531 map = isl_map_read_from_str(ctx, str);
1532 ai = isl_access_info_add_source(ai, map, 1, &depth);
1533
1534 flow = isl_access_info_compute_flow(ai);
1535 dim = isl_space_alloc(ctx, 0, 3, 3);
1536 mm.must = isl_map_empty(isl_space_copy(dim));
1537 mm.may = isl_map_empty(dim);
1538
1539 isl_flow_foreach(flow, collect_must_may, &mm);
1540
1541 str = "{ [0,i,0] -> [2,i,0] : (0 <= i <= 4) or (6 <= i <= 10); "
1542 " [1,10,0] -> [2,5,0] }";
1543 assert(map_is_equal(mm.must, str));
1544 str = "{ [i,j,k] -> [l,m,n] : 1 = 0 }";
1545 assert(map_is_equal(mm.may, str));
1546
1547 isl_map_free(mm.must);
1548 isl_map_free(mm.may);
1549 isl_flow_free(flow);
1550
1551
1552 str = "{ [2,i,0] -> [i] : 0 <= i <= 10 }";
1553 map = isl_map_read_from_str(ctx, str);
1554 ai = isl_access_info_alloc(map, &depth, &common_space, 2);
1555
1556 str = "{ [0,i,0] -> [i] : 0 <= i <= 10 }";
1557 map = isl_map_read_from_str(ctx, str);
1558 ai = isl_access_info_add_source(ai, map, 1, &depth);
1559
1560 str = "{ [1,i,0] -> [5] : 0 <= i <= 10 }";
1561 map = isl_map_read_from_str(ctx, str);
1562 ai = isl_access_info_add_source(ai, map, 0, &depth);
1563
1564 flow = isl_access_info_compute_flow(ai);
1565 dim = isl_space_alloc(ctx, 0, 3, 3);
1566 mm.must = isl_map_empty(isl_space_copy(dim));
1567 mm.may = isl_map_empty(dim);
1568
1569 isl_flow_foreach(flow, collect_must_may, &mm);
1570
1571 str = "{ [0,i,0] -> [2,i,0] : (0 <= i <= 4) or (6 <= i <= 10) }";
1572 assert(map_is_equal(mm.must, str));
1573 str = "{ [0,5,0] -> [2,5,0]; [1,i,0] -> [2,5,0] : 0 <= i <= 10 }";
1574 assert(map_is_equal(mm.may, str));
1575
1576 isl_map_free(mm.must);
1577 isl_map_free(mm.may);
1578 isl_flow_free(flow);
1579
1580
1581 str = "{ [2,i,0] -> [i] : 0 <= i <= 10 }";
1582 map = isl_map_read_from_str(ctx, str);
1583 ai = isl_access_info_alloc(map, &depth, &common_space, 2);
1584
1585 str = "{ [0,i,0] -> [i] : 0 <= i <= 10 }";
1586 map = isl_map_read_from_str(ctx, str);
1587 ai = isl_access_info_add_source(ai, map, 0, &depth);
1588
1589 str = "{ [1,i,0] -> [5] : 0 <= i <= 10 }";
1590 map = isl_map_read_from_str(ctx, str);
1591 ai = isl_access_info_add_source(ai, map, 0, &depth);
1592
1593 flow = isl_access_info_compute_flow(ai);
1594 dim = isl_space_alloc(ctx, 0, 3, 3);
1595 mm.must = isl_map_empty(isl_space_copy(dim));
1596 mm.may = isl_map_empty(dim);
1597
1598 isl_flow_foreach(flow, collect_must_may, &mm);
1599
1600 str = "{ [0,i,0] -> [2,i,0] : 0 <= i <= 10; "
1601 " [1,i,0] -> [2,5,0] : 0 <= i <= 10 }";
1602 assert(map_is_equal(mm.may, str));
1603 str = "{ [i,j,k] -> [l,m,n] : 1 = 0 }";
1604 assert(map_is_equal(mm.must, str));
1605
1606 isl_map_free(mm.must);
1607 isl_map_free(mm.may);
1608 isl_flow_free(flow);
1609
1610
1611 str = "{ [0,i,2] -> [i] : 0 <= i <= 10 }";
1612 map = isl_map_read_from_str(ctx, str);
1613 ai = isl_access_info_alloc(map, &depth, &common_space, 2);
1614
1615 str = "{ [0,i,0] -> [i] : 0 <= i <= 10 }";
1616 map = isl_map_read_from_str(ctx, str);
1617 ai = isl_access_info_add_source(ai, map, 0, &depth);
1618
1619 str = "{ [0,i,1] -> [5] : 0 <= i <= 10 }";
1620 map = isl_map_read_from_str(ctx, str);
1621 ai = isl_access_info_add_source(ai, map, 0, &depth);
1622
1623 flow = isl_access_info_compute_flow(ai);
1624 dim = isl_space_alloc(ctx, 0, 3, 3);
1625 mm.must = isl_map_empty(isl_space_copy(dim));
1626 mm.may = isl_map_empty(dim);
1627
1628 isl_flow_foreach(flow, collect_must_may, &mm);
1629
1630 str = "{ [0,i,0] -> [0,i,2] : 0 <= i <= 10; "
1631 " [0,i,1] -> [0,5,2] : 0 <= i <= 5 }";
1632 assert(map_is_equal(mm.may, str));
1633 str = "{ [i,j,k] -> [l,m,n] : 1 = 0 }";
1634 assert(map_is_equal(mm.must, str));
1635
1636 isl_map_free(mm.must);
1637 isl_map_free(mm.may);
1638 isl_flow_free(flow);
1639
1640
1641 str = "{ [0,i,1] -> [i] : 0 <= i <= 10 }";
1642 map = isl_map_read_from_str(ctx, str);
1643 ai = isl_access_info_alloc(map, &depth, &common_space, 2);
1644
1645 str = "{ [0,i,0] -> [i] : 0 <= i <= 10 }";
1646 map = isl_map_read_from_str(ctx, str);
1647 ai = isl_access_info_add_source(ai, map, 0, &depth);
1648
1649 str = "{ [0,i,2] -> [5] : 0 <= i <= 10 }";
1650 map = isl_map_read_from_str(ctx, str);
1651 ai = isl_access_info_add_source(ai, map, 0, &depth);
1652
1653 flow = isl_access_info_compute_flow(ai);
1654 dim = isl_space_alloc(ctx, 0, 3, 3);
1655 mm.must = isl_map_empty(isl_space_copy(dim));
1656 mm.may = isl_map_empty(dim);
1657
1658 isl_flow_foreach(flow, collect_must_may, &mm);
1659
1660 str = "{ [0,i,0] -> [0,i,1] : 0 <= i <= 10; "
1661 " [0,i,2] -> [0,5,1] : 0 <= i <= 4 }";
1662 assert(map_is_equal(mm.may, str));
1663 str = "{ [i,j,k] -> [l,m,n] : 1 = 0 }";
1664 assert(map_is_equal(mm.must, str));
1665
1666 isl_map_free(mm.must);
1667 isl_map_free(mm.may);
1668 isl_flow_free(flow);
1669
1670
1671 depth = 5;
1672
1673 str = "{ [1,i,0,0,0] -> [i,j] : 0 <= i <= 10 and 0 <= j <= 10 }";
1674 map = isl_map_read_from_str(ctx, str);
1675 ai = isl_access_info_alloc(map, &depth, &common_space, 1);
1676
1677 str = "{ [0,i,0,j,0] -> [i,j] : 0 <= i <= 10 and 0 <= j <= 10 }";
1678 map = isl_map_read_from_str(ctx, str);
1679 ai = isl_access_info_add_source(ai, map, 1, &depth);
1680
1681 flow = isl_access_info_compute_flow(ai);
1682 dim = isl_space_alloc(ctx, 0, 5, 5);
1683 mm.must = isl_map_empty(isl_space_copy(dim));
1684 mm.may = isl_map_empty(dim);
1685
1686 isl_flow_foreach(flow, collect_must_may, &mm);
1687
1688 str = "{ [0,i,0,j,0] -> [1,i,0,0,0] : 0 <= i,j <= 10 }";
1689 assert(map_is_equal(mm.must, str));
1690 str = "{ [0,0,0,0,0] -> [0,0,0,0,0] : 1 = 0 }";
1691 assert(map_is_equal(mm.may, str));
1692
1693 isl_map_free(mm.must);
1694 isl_map_free(mm.may);
1695 isl_flow_free(flow);
1696 }
1697
1698 int test_sv(isl_ctx *ctx)
1699 {
1700 const char *str;
1701 isl_map *map;
1702 isl_union_map *umap;
1703 int sv;
1704
1705 str = "[N] -> { [i] -> [f] : 0 <= i <= N and 0 <= i - 10 f <= 9 }";
1706 map = isl_map_read_from_str(ctx, str);
1707 sv = isl_map_is_single_valued(map);
1708 isl_map_free(map);
1709 if (sv < 0)
1710 return -1;
1711 if (!sv)
1712 isl_die(ctx, isl_error_internal,
1713 "map not detected as single valued", return -1);
1714
1715 str = "[N] -> { [i] -> [f] : 0 <= i <= N and 0 <= i - 10 f <= 10 }";
1716 map = isl_map_read_from_str(ctx, str);
1717 sv = isl_map_is_single_valued(map);
1718 isl_map_free(map);
1719 if (sv < 0)
1720 return -1;
1721 if (sv)
1722 isl_die(ctx, isl_error_internal,
1723 "map detected as single valued", return -1);
1724
1725 str = "{ S1[i] -> [i] : 0 <= i <= 9; S2[i] -> [i] : 0 <= i <= 9 }";
1726 umap = isl_union_map_read_from_str(ctx, str);
1727 sv = isl_union_map_is_single_valued(umap);
1728 isl_union_map_free(umap);
1729 if (sv < 0)
1730 return -1;
1731 if (!sv)
1732 isl_die(ctx, isl_error_internal,
1733 "map not detected as single valued", return -1);
1734
1735 str = "{ [i] -> S1[i] : 0 <= i <= 9; [i] -> S2[i] : 0 <= i <= 9 }";
1736 umap = isl_union_map_read_from_str(ctx, str);
1737 sv = isl_union_map_is_single_valued(umap);
1738 isl_union_map_free(umap);
1739 if (sv < 0)
1740 return -1;
1741 if (sv)
1742 isl_die(ctx, isl_error_internal,
1743 "map detected as single valued", return -1);
1744
1745 return 0;
1746 }
1747
1748 void test_bijective_case(struct isl_ctx *ctx, const char *str, int bijective)
1749 {
1750 isl_map *map;
1751
1752 map = isl_map_read_from_str(ctx, str);
1753 if (bijective)
1754 assert(isl_map_is_bijective(map));
1755 else
1756 assert(!isl_map_is_bijective(map));
1757 isl_map_free(map);
1758 }
1759
1760 void test_bijective(struct isl_ctx *ctx)
1761 {
1762 test_bijective_case(ctx, "[N,M]->{[i,j] -> [i]}", 0);
1763 test_bijective_case(ctx, "[N,M]->{[i,j] -> [i] : j=i}", 1);
1764 test_bijective_case(ctx, "[N,M]->{[i,j] -> [i] : j=0}", 1);
1765 test_bijective_case(ctx, "[N,M]->{[i,j] -> [i] : j=N}", 1);
1766 test_bijective_case(ctx, "[N,M]->{[i,j] -> [j,i]}", 1);
1767 test_bijective_case(ctx, "[N,M]->{[i,j] -> [i+j]}", 0);
1768 test_bijective_case(ctx, "[N,M]->{[i,j] -> []}", 0);
1769 test_bijective_case(ctx, "[N,M]->{[i,j] -> [i,j,N]}", 1);
1770 test_bijective_case(ctx, "[N,M]->{[i,j] -> [2i]}", 0);
1771 test_bijective_case(ctx, "[N,M]->{[i,j] -> [i,i]}", 0);
1772 test_bijective_case(ctx, "[N,M]->{[i,j] -> [2i,i]}", 0);
1773 test_bijective_case(ctx, "[N,M]->{[i,j] -> [2i,j]}", 1);
1774 test_bijective_case(ctx, "[N,M]->{[i,j] -> [x,y] : 2x=i & y =j}", 1);
1775 }
1776
1777 void test_pwqp(struct isl_ctx *ctx)
1778 {
1779 const char *str;
1780 isl_set *set;
1781 isl_pw_qpolynomial *pwqp1, *pwqp2;
1782
1783 str = "{ [i,j,k] -> 1 + 9 * [i/5] + 7 * [j/11] + 4 * [k/13] }";
1784 pwqp1 = isl_pw_qpolynomial_read_from_str(ctx, str);
1785
1786 pwqp1 = isl_pw_qpolynomial_move_dims(pwqp1, isl_dim_param, 0,
1787 isl_dim_in, 1, 1);
1788
1789 str = "[j] -> { [i,k] -> 1 + 9 * [i/5] + 7 * [j/11] + 4 * [k/13] }";
1790 pwqp2 = isl_pw_qpolynomial_read_from_str(ctx, str);
1791
1792 pwqp1 = isl_pw_qpolynomial_sub(pwqp1, pwqp2);
1793
1794 assert(isl_pw_qpolynomial_is_zero(pwqp1));
1795
1796 isl_pw_qpolynomial_free(pwqp1);
1797
1798 str = "{ [i] -> i }";
1799 pwqp1 = isl_pw_qpolynomial_read_from_str(ctx, str);
1800 str = "{ [k] : exists a : k = 2a }";
1801 set = isl_set_read_from_str(ctx, str);
1802 pwqp1 = isl_pw_qpolynomial_gist(pwqp1, set);
1803 str = "{ [i] -> i }";
1804 pwqp2 = isl_pw_qpolynomial_read_from_str(ctx, str);
1805
1806 pwqp1 = isl_pw_qpolynomial_sub(pwqp1, pwqp2);
1807
1808 assert(isl_pw_qpolynomial_is_zero(pwqp1));
1809
1810 isl_pw_qpolynomial_free(pwqp1);
1811
1812 str = "{ [i] -> i + [ (i + [i/3])/2 ] }";
1813 pwqp1 = isl_pw_qpolynomial_read_from_str(ctx, str);
1814 str = "{ [10] }";
1815 set = isl_set_read_from_str(ctx, str);
1816 pwqp1 = isl_pw_qpolynomial_gist(pwqp1, set);
1817 str = "{ [i] -> 16 }";
1818 pwqp2 = isl_pw_qpolynomial_read_from_str(ctx, str);
1819
1820 pwqp1 = isl_pw_qpolynomial_sub(pwqp1, pwqp2);
1821
1822 assert(isl_pw_qpolynomial_is_zero(pwqp1));
1823
1824 isl_pw_qpolynomial_free(pwqp1);
1825
1826 str = "{ [i] -> ([(i)/2]) }";
1827 pwqp1 = isl_pw_qpolynomial_read_from_str(ctx, str);
1828 str = "{ [k] : exists a : k = 2a+1 }";
1829 set = isl_set_read_from_str(ctx, str);
1830 pwqp1 = isl_pw_qpolynomial_gist(pwqp1, set);
1831 str = "{ [i] -> -1/2 + 1/2 * i }";
1832 pwqp2 = isl_pw_qpolynomial_read_from_str(ctx, str);
1833
1834 pwqp1 = isl_pw_qpolynomial_sub(pwqp1, pwqp2);
1835
1836 assert(isl_pw_qpolynomial_is_zero(pwqp1));
1837
1838 isl_pw_qpolynomial_free(pwqp1);
1839
1840 str = "{ [i] -> ([([i/2] + [i/2])/5]) }";
1841 pwqp1 = isl_pw_qpolynomial_read_from_str(ctx, str);
1842 str = "{ [i] -> ([(2 * [i/2])/5]) }";
1843 pwqp2 = isl_pw_qpolynomial_read_from_str(ctx, str);
1844
1845 pwqp1 = isl_pw_qpolynomial_sub(pwqp1, pwqp2);
1846
1847 assert(isl_pw_qpolynomial_is_zero(pwqp1));
1848
1849 isl_pw_qpolynomial_free(pwqp1);
1850
1851 str = "{ [x] -> ([x/2] + [(x+1)/2]) }";
1852 pwqp1 = isl_pw_qpolynomial_read_from_str(ctx, str);
1853 str = "{ [x] -> x }";
1854 pwqp2 = isl_pw_qpolynomial_read_from_str(ctx, str);
1855
1856 pwqp1 = isl_pw_qpolynomial_sub(pwqp1, pwqp2);
1857
1858 assert(isl_pw_qpolynomial_is_zero(pwqp1));
1859
1860 isl_pw_qpolynomial_free(pwqp1);
1861
1862 str = "{ [i] -> ([i/2]) : i >= 0; [i] -> ([i/3]) : i < 0 }";
1863 pwqp1 = isl_pw_qpolynomial_read_from_str(ctx, str);
1864 pwqp2 = isl_pw_qpolynomial_read_from_str(ctx, str);
1865 pwqp1 = isl_pw_qpolynomial_coalesce(pwqp1);
1866 pwqp1 = isl_pw_qpolynomial_sub(pwqp1, pwqp2);
1867 assert(isl_pw_qpolynomial_is_zero(pwqp1));
1868 isl_pw_qpolynomial_free(pwqp1);
1869 }
1870
1871 void test_split_periods(isl_ctx *ctx)
1872 {
1873 const char *str;
1874 isl_pw_qpolynomial *pwqp;
1875
1876 str = "{ [U,V] -> 1/3 * U + 2/3 * V - [(U + 2V)/3] + [U/2] : "
1877 "U + 2V + 3 >= 0 and - U -2V >= 0 and - U + 10 >= 0 and "
1878 "U >= 0; [U,V] -> U^2 : U >= 100 }";
1879 pwqp = isl_pw_qpolynomial_read_from_str(ctx, str);
1880
1881 pwqp = isl_pw_qpolynomial_split_periods(pwqp, 2);
1882 assert(pwqp);
1883
1884 isl_pw_qpolynomial_free(pwqp);
1885 }
1886
1887 void test_union(isl_ctx *ctx)
1888 {
1889 const char *str;
1890 isl_union_set *uset1, *uset2;
1891 isl_union_map *umap1, *umap2;
1892
1893 str = "{ [i] : 0 <= i <= 1 }";
1894 uset1 = isl_union_set_read_from_str(ctx, str);
1895 str = "{ [1] -> [0] }";
1896 umap1 = isl_union_map_read_from_str(ctx, str);
1897
1898 umap2 = isl_union_set_lex_gt_union_set(isl_union_set_copy(uset1), uset1);
1899 assert(isl_union_map_is_equal(umap1, umap2));
1900
1901 isl_union_map_free(umap1);
1902 isl_union_map_free(umap2);
1903
1904 str = "{ A[i] -> B[i]; B[i] -> C[i]; A[0] -> C[1] }";
1905 umap1 = isl_union_map_read_from_str(ctx, str);
1906 str = "{ A[i]; B[i] }";
1907 uset1 = isl_union_set_read_from_str(ctx, str);
1908
1909 uset2 = isl_union_map_domain(umap1);
1910
1911 assert(isl_union_set_is_equal(uset1, uset2));
1912
1913 isl_union_set_free(uset1);
1914 isl_union_set_free(uset2);
1915 }
1916
1917 void test_bound(isl_ctx *ctx)
1918 {
1919 const char *str;
1920 isl_pw_qpolynomial *pwqp;
1921 isl_pw_qpolynomial_fold *pwf;
1922
1923 str = "{ [[a, b, c, d] -> [e]] -> 0 }";
1924 pwqp = isl_pw_qpolynomial_read_from_str(ctx, str);
1925 pwf = isl_pw_qpolynomial_bound(pwqp, isl_fold_max, NULL);
1926 assert(isl_pw_qpolynomial_fold_dim(pwf, isl_dim_in) == 4);
1927 isl_pw_qpolynomial_fold_free(pwf);
1928
1929 str = "{ [[x]->[x]] -> 1 : exists a : x = 2 a }";
1930 pwqp = isl_pw_qpolynomial_read_from_str(ctx, str);
1931 pwf = isl_pw_qpolynomial_bound(pwqp, isl_fold_max, NULL);
1932 assert(isl_pw_qpolynomial_fold_dim(pwf, isl_dim_in) == 1);
1933 isl_pw_qpolynomial_fold_free(pwf);
1934 }
1935
1936 void test_lift(isl_ctx *ctx)
1937 {
1938 const char *str;
1939 isl_basic_map *bmap;
1940 isl_basic_set *bset;
1941
1942 str = "{ [i0] : exists e0 : i0 = 4e0 }";
1943 bset = isl_basic_set_read_from_str(ctx, str);
1944 bset = isl_basic_set_lift(bset);
1945 bmap = isl_basic_map_from_range(bset);
1946 bset = isl_basic_map_domain(bmap);
1947 isl_basic_set_free(bset);
1948 }
1949
1950 struct {
1951 const char *set1;
1952 const char *set2;
1953 int subset;
1954 } subset_tests[] = {
1955 { "{ [112, 0] }",
1956 "{ [i0, i1] : exists (e0 = [(i0 - i1)/16], e1: "
1957 "16e0 <= i0 - i1 and 16e0 >= -15 + i0 - i1 and "
1958 "16e1 <= i1 and 16e0 >= -i1 and 16e1 >= -i0 + i1) }", 1 },
1959 { "{ [65] }",
1960 "{ [i] : exists (e0 = [(255i)/256], e1 = [(127i + 65e0)/191], "
1961 "e2 = [(3i + 61e1)/65], e3 = [(52i + 12e2)/61], "
1962 "e4 = [(2i + e3)/3], e5 = [(4i + e3)/4], e6 = [(8i + e3)/12]: "
1963 "3e4 = 2i + e3 and 4e5 = 4i + e3 and 12e6 = 8i + e3 and "
1964 "i <= 255 and 64e3 >= -45 + 67i and i >= 0 and "
1965 "256e0 <= 255i and 256e0 >= -255 + 255i and "
1966 "191e1 <= 127i + 65e0 and 191e1 >= -190 + 127i + 65e0 and "
1967 "65e2 <= 3i + 61e1 and 65e2 >= -64 + 3i + 61e1 and "
1968 "61e3 <= 52i + 12e2 and 61e3 >= -60 + 52i + 12e2) }", 1 },
1969 { "{ [i] : 0 <= i <= 10 }", "{ rat: [i] : 0 <= i <= 10 }", 1 },
1970 { "{ rat: [i] : 0 <= i <= 10 }", "{ [i] : 0 <= i <= 10 }", 0 },
1971 { "{ rat: [0] }", "{ [i] : 0 <= i <= 10 }", 1 },
1972 { "{ rat: [(1)/2] }", "{ [i] : 0 <= i <= 10 }", 0 },
1973 };
1974
1975 static int test_subset(isl_ctx *ctx)
1976 {
1977 int i;
1978 isl_set *set1, *set2;
1979 int subset;
1980
1981 for (i = 0; i < ARRAY_SIZE(subset_tests); ++i) {
1982 set1 = isl_set_read_from_str(ctx, subset_tests[i].set1);
1983 set2 = isl_set_read_from_str(ctx, subset_tests[i].set2);
1984 subset = isl_set_is_subset(set1, set2);
1985 isl_set_free(set1);
1986 isl_set_free(set2);
1987 if (subset < 0)
1988 return -1;
1989 if (subset != subset_tests[i].subset)
1990 isl_die(ctx, isl_error_unknown,
1991 "incorrect subset result", return -1);
1992 }
1993
1994 return 0;
1995 }
1996
1997 struct {
1998 const char *minuend;
1999 const char *subtrahend;
2000 const char *difference;
2001 } subtract_domain_tests[] = {
2002 { "{ A[i] -> B[i] }", "{ A[i] }", "{ }" },
2003 { "{ A[i] -> B[i] }", "{ B[i] }", "{ A[i] -> B[i] }" },
2004 { "{ A[i] -> B[i] }", "{ A[i] : i > 0 }", "{ A[i] -> B[i] : i <= 0 }" },
2005 };
2006
2007 static int test_subtract(isl_ctx *ctx)
2008 {
2009 int i;
2010 isl_union_map *umap1, *umap2;
2011 isl_union_set *uset;
2012 int equal;
2013
2014 for (i = 0; i < ARRAY_SIZE(subtract_domain_tests); ++i) {
2015 umap1 = isl_union_map_read_from_str(ctx,
2016 subtract_domain_tests[i].minuend);
2017 uset = isl_union_set_read_from_str(ctx,
2018 subtract_domain_tests[i].subtrahend);
2019 umap2 = isl_union_map_read_from_str(ctx,
2020 subtract_domain_tests[i].difference);
2021 umap1 = isl_union_map_subtract_domain(umap1, uset);
2022 equal = isl_union_map_is_equal(umap1, umap2);
2023 isl_union_map_free(umap1);
2024 isl_union_map_free(umap2);
2025 if (equal < 0)
2026 return -1;
2027 if (!equal)
2028 isl_die(ctx, isl_error_unknown,
2029 "incorrect subtract domain result", return -1);
2030 }
2031
2032 return 0;
2033 }
2034
2035 int test_factorize(isl_ctx *ctx)
2036 {
2037 const char *str;
2038 isl_basic_set *bset;
2039 isl_factorizer *f;
2040
2041 str = "{ [i0, i1, i2, i3, i4, i5, i6, i7] : 3i5 <= 2 - 2i0 and "
2042 "i0 >= -2 and i6 >= 1 + i3 and i7 >= 0 and 3i5 >= -2i0 and "
2043 "2i4 <= i2 and i6 >= 1 + 2i0 + 3i1 and i4 <= -1 and "
2044 "i6 >= 1 + 2i0 + 3i5 and i6 <= 2 + 2i0 + 3i5 and "
2045 "3i5 <= 2 - 2i0 - i2 + 3i4 and i6 <= 2 + 2i0 + 3i1 and "
2046 "i0 <= -1 and i7 <= i2 + i3 - 3i4 - i6 and "
2047 "3i5 >= -2i0 - i2 + 3i4 }";
2048 bset = isl_basic_set_read_from_str(ctx, str);
2049 f = isl_basic_set_factorizer(bset);
2050 isl_basic_set_free(bset);
2051 isl_factorizer_free(f);
2052 if (!f)
2053 isl_die(ctx, isl_error_unknown,
2054 "failed to construct factorizer", return -1);
2055
2056 str = "{ [i0, i1, i2, i3, i4, i5, i6, i7, i8, i9, i10, i11, i12] : "
2057 "i12 <= 2 + i0 - i11 and 2i8 >= -i4 and i11 >= i1 and "
2058 "3i5 <= -i2 and 2i11 >= -i4 - 2i7 and i11 <= 3 + i0 + 3i9 and "
2059 "i11 <= -i4 - 2i7 and i12 >= -i10 and i2 >= -2 and "
2060 "i11 >= i1 + 3i10 and i11 >= 1 + i0 + 3i9 and "
2061 "i11 <= 1 - i4 - 2i8 and 6i6 <= 6 - i2 and 3i6 >= 1 - i2 and "
2062 "i11 <= 2 + i1 and i12 <= i4 + i11 and i12 >= i0 - i11 and "
2063 "3i5 >= -2 - i2 and i12 >= -1 + i4 + i11 and 3i3 <= 3 - i2 and "
2064 "9i6 <= 11 - i2 + 6i5 and 3i3 >= 1 - i2 and "
2065 "9i6 <= 5 - i2 + 6i3 and i12 <= -1 and i2 <= 0 }";
2066 bset = isl_basic_set_read_from_str(ctx, str);
2067 f = isl_basic_set_factorizer(bset);
2068 isl_basic_set_free(bset);
2069 isl_factorizer_free(f);
2070 if (!f)
2071 isl_die(ctx, isl_error_unknown,
2072 "failed to construct factorizer", return -1);
2073
2074 return 0;
2075 }
2076
2077 static int check_injective(__isl_take isl_map *map, void *user)
2078 {
2079 int *injective = user;
2080
2081 *injective = isl_map_is_injective(map);
2082 isl_map_free(map);
2083
2084 if (*injective < 0 || !*injective)
2085 return -1;
2086
2087 return 0;
2088 }
2089
2090 int test_one_schedule(isl_ctx *ctx, const char *d, const char *w,
2091 const char *r, const char *s, int tilable, int parallel)
2092 {
2093 int i;
2094 isl_union_set *D;
2095 isl_union_map *W, *R, *S;
2096 isl_union_map *empty;
2097 isl_union_map *dep_raw, *dep_war, *dep_waw, *dep;
2098 isl_union_map *validity, *proximity;
2099 isl_union_map *schedule;
2100 isl_union_map *test;
2101 isl_union_set *delta;
2102 isl_union_set *domain;
2103 isl_set *delta_set;
2104 isl_set *slice;
2105 isl_set *origin;
2106 isl_schedule *sched;
2107 int is_nonneg, is_parallel, is_tilable, is_injection, is_complete;
2108
2109 D = isl_union_set_read_from_str(ctx, d);
2110 W = isl_union_map_read_from_str(ctx, w);
2111 R = isl_union_map_read_from_str(ctx, r);
2112 S = isl_union_map_read_from_str(ctx, s);
2113
2114 W = isl_union_map_intersect_domain(W, isl_union_set_copy(D));
2115 R = isl_union_map_intersect_domain(R, isl_union_set_copy(D));
2116
2117 empty = isl_union_map_empty(isl_union_map_get_space(S));
2118 isl_union_map_compute_flow(isl_union_map_copy(R),
2119 isl_union_map_copy(W), empty,
2120 isl_union_map_copy(S),
2121 &dep_raw, NULL, NULL, NULL);
2122 isl_union_map_compute_flow(isl_union_map_copy(W),
2123 isl_union_map_copy(W),
2124 isl_union_map_copy(R),
2125 isl_union_map_copy(S),
2126 &dep_waw, &dep_war, NULL, NULL);
2127
2128 dep = isl_union_map_union(dep_waw, dep_war);
2129 dep = isl_union_map_union(dep, dep_raw);
2130 validity = isl_union_map_copy(dep);
2131 proximity = isl_union_map_copy(dep);
2132
2133 sched = isl_union_set_compute_schedule(isl_union_set_copy(D),
2134 validity, proximity);
2135 schedule = isl_schedule_get_map(sched);
2136 isl_schedule_free(sched);
2137 isl_union_map_free(W);
2138 isl_union_map_free(R);
2139 isl_union_map_free(S);
2140
2141 is_injection = 1;
2142 isl_union_map_foreach_map(schedule, &check_injective, &is_injection);
2143
2144 domain = isl_union_map_domain(isl_union_map_copy(schedule));
2145 is_complete = isl_union_set_is_subset(D, domain);
2146 isl_union_set_free(D);
2147 isl_union_set_free(domain);
2148
2149 test = isl_union_map_reverse(isl_union_map_copy(schedule));
2150 test = isl_union_map_apply_range(test, dep);
2151 test = isl_union_map_apply_range(test, schedule);
2152
2153 delta = isl_union_map_deltas(test);
2154 if (isl_union_set_n_set(delta) == 0) {
2155 is_tilable = 1;
2156 is_parallel = 1;
2157 is_nonneg = 1;
2158 isl_union_set_free(delta);
2159 } else {
2160 delta_set = isl_set_from_union_set(delta);
2161
2162 slice = isl_set_universe(isl_set_get_space(delta_set));
2163 for (i = 0; i < tilable; ++i)
2164 slice = isl_set_lower_bound_si(slice, isl_dim_set, i, 0);
2165 is_tilable = isl_set_is_subset(delta_set, slice);
2166 isl_set_free(slice);
2167
2168 slice = isl_set_universe(isl_set_get_space(delta_set));
2169 for (i = 0; i < parallel; ++i)
2170 slice = isl_set_fix_si(slice, isl_dim_set, i, 0);
2171 is_parallel = isl_set_is_subset(delta_set, slice);
2172 isl_set_free(slice);
2173
2174 origin = isl_set_universe(isl_set_get_space(delta_set));
2175 for (i = 0; i < isl_set_dim(origin, isl_dim_set); ++i)
2176 origin = isl_set_fix_si(origin, isl_dim_set, i, 0);
2177
2178 delta_set = isl_set_union(delta_set, isl_set_copy(origin));
2179 delta_set = isl_set_lexmin(delta_set);
2180
2181 is_nonneg = isl_set_is_equal(delta_set, origin);
2182
2183 isl_set_free(origin);
2184 isl_set_free(delta_set);
2185 }
2186
2187 if (is_nonneg < 0 || is_parallel < 0 || is_tilable < 0 ||
2188 is_injection < 0 || is_complete < 0)
2189 return -1;
2190 if (!is_complete)
2191 isl_die(ctx, isl_error_unknown,
2192 "generated schedule incomplete", return -1);
2193 if (!is_injection)
2194 isl_die(ctx, isl_error_unknown,
2195 "generated schedule not injective on each statement",
2196 return -1);
2197 if (!is_nonneg)
2198 isl_die(ctx, isl_error_unknown,
2199 "negative dependences in generated schedule",
2200 return -1);
2201 if (!is_tilable)
2202 isl_die(ctx, isl_error_unknown,
2203 "generated schedule not as tilable as expected",
2204 return -1);
2205 if (!is_parallel)
2206 isl_die(ctx, isl_error_unknown,
2207 "generated schedule not as parallel as expected",
2208 return -1);
2209
2210 return 0;
2211 }
2212
2213 static __isl_give isl_union_map *compute_schedule(isl_ctx *ctx,
2214 const char *domain, const char *validity, const char *proximity)
2215 {
2216 isl_union_set *dom;
2217 isl_union_map *dep;
2218 isl_union_map *prox;
2219 isl_schedule *schedule;
2220 isl_union_map *sched;
2221
2222 dom = isl_union_set_read_from_str(ctx, domain);
2223 dep = isl_union_map_read_from_str(ctx, validity);
2224 prox = isl_union_map_read_from_str(ctx, proximity);
2225 schedule = isl_union_set_compute_schedule(dom, dep, prox);
2226 sched = isl_schedule_get_map(schedule);
2227 isl_schedule_free(schedule);
2228
2229 return sched;
2230 }
2231
2232 /* Check that a schedule can be constructed on the given domain
2233 * with the given validity and proximity constraints.
2234 */
2235 static int test_has_schedule(isl_ctx *ctx, const char *domain,
2236 const char *validity, const char *proximity)
2237 {
2238 isl_union_map *sched;
2239
2240 sched = compute_schedule(ctx, domain, validity, proximity);
2241 if (!sched)
2242 return -1;
2243
2244 isl_union_map_free(sched);
2245 return 0;
2246 }
2247
2248 int test_special_schedule(isl_ctx *ctx, const char *domain,
2249 const char *validity, const char *proximity, const char *expected_sched)
2250 {
2251 isl_union_map *sched1, *sched2;
2252 int equal;
2253
2254 sched1 = compute_schedule(ctx, domain, validity, proximity);
2255 sched2 = isl_union_map_read_from_str(ctx, expected_sched);
2256
2257 equal = isl_union_map_is_equal(sched1, sched2);
2258 isl_union_map_free(sched1);
2259 isl_union_map_free(sched2);
2260
2261 if (equal < 0)
2262 return -1;
2263 if (!equal)
2264 isl_die(ctx, isl_error_unknown, "unexpected schedule",
2265 return -1);
2266
2267 return 0;
2268 }
2269
2270 /* Check that the schedule map is properly padded, even after being
2271 * reconstructed from the band forest.
2272 */
2273 static int test_padded_schedule(isl_ctx *ctx)
2274 {
2275 const char *str;
2276 isl_union_set *D;
2277 isl_union_map *validity, *proximity;
2278 isl_schedule *sched;
2279 isl_union_map *map1, *map2;
2280 isl_band_list *list;
2281 int equal;
2282
2283 str = "[N] -> { S0[i] : 0 <= i <= N; S1[i, j] : 0 <= i, j <= N }";
2284 D = isl_union_set_read_from_str(ctx, str);
2285 validity = isl_union_map_empty(isl_union_set_get_space(D));
2286 proximity = isl_union_map_copy(validity);
2287 sched = isl_union_set_compute_schedule(D, validity, proximity);
2288 map1 = isl_schedule_get_map(sched);
2289 list = isl_schedule_get_band_forest(sched);
2290 isl_band_list_free(list);
2291 map2 = isl_schedule_get_map(sched);
2292 isl_schedule_free(sched);
2293 equal = isl_union_map_is_equal(map1, map2);
2294 isl_union_map_free(map1);
2295 isl_union_map_free(map2);
2296
2297 if (equal < 0)
2298 return -1;
2299 if (!equal)
2300 isl_die(ctx, isl_error_unknown,
2301 "reconstructed schedule map not the same as original",
2302 return -1);
2303
2304 return 0;
2305 }
2306
2307 int test_schedule(isl_ctx *ctx)
2308 {
2309 const char *D, *W, *R, *V, *P, *S;
2310
2311 /* Handle resulting schedule with zero bands. */
2312 if (test_one_schedule(ctx, "{[]}", "{}", "{}", "{[] -> []}", 0, 0) < 0)
2313 return -1;
2314
2315 /* Jacobi */
2316 D = "[T,N] -> { S1[t,i] : 1 <= t <= T and 2 <= i <= N - 1 }";
2317 W = "{ S1[t,i] -> a[t,i] }";
2318 R = "{ S1[t,i] -> a[t-1,i]; S1[t,i] -> a[t-1,i-1]; "
2319 "S1[t,i] -> a[t-1,i+1] }";
2320 S = "{ S1[t,i] -> [t,i] }";
2321 if (test_one_schedule(ctx, D, W, R, S, 2, 0) < 0)
2322 return -1;
2323
2324 /* Fig. 5 of CC2008 */
2325 D = "[N] -> { S_0[i, j] : i >= 0 and i <= -1 + N and j >= 2 and "
2326 "j <= -1 + N }";
2327 W = "[N] -> { S_0[i, j] -> a[i, j] : i >= 0 and i <= -1 + N and "
2328 "j >= 2 and j <= -1 + N }";
2329 R = "[N] -> { S_0[i, j] -> a[j, i] : i >= 0 and i <= -1 + N and "
2330 "j >= 2 and j <= -1 + N; "
2331 "S_0[i, j] -> a[i, -1 + j] : i >= 0 and i <= -1 + N and "
2332 "j >= 2 and j <= -1 + N }";
2333 S = "[N] -> { S_0[i, j] -> [0, i, 0, j, 0] }";
2334 if (test_one_schedule(ctx, D, W, R, S, 2, 0) < 0)
2335 return -1;
2336
2337 D = "{ S1[i] : 0 <= i <= 10; S2[i] : 0 <= i <= 9 }";
2338 W = "{ S1[i] -> a[i] }";
2339 R = "{ S2[i] -> a[i+1] }";
2340 S = "{ S1[i] -> [0,i]; S2[i] -> [1,i] }";
2341 if (test_one_schedule(ctx, D, W, R, S, 1, 1) < 0)
2342 return -1;
2343
2344 D = "{ S1[i] : 0 <= i < 10; S2[i] : 0 <= i < 10 }";
2345 W = "{ S1[i] -> a[i] }";
2346 R = "{ S2[i] -> a[9-i] }";
2347 S = "{ S1[i] -> [0,i]; S2[i] -> [1,i] }";
2348 if (test_one_schedule(ctx, D, W, R, S, 1, 1) < 0)
2349 return -1;
2350
2351 D = "[N] -> { S1[i] : 0 <= i < N; S2[i] : 0 <= i < N }";
2352 W = "{ S1[i] -> a[i] }";
2353 R = "[N] -> { S2[i] -> a[N-1-i] }";
2354 S = "{ S1[i] -> [0,i]; S2[i] -> [1,i] }";
2355 if (test_one_schedule(ctx, D, W, R, S, 1, 1) < 0)
2356 return -1;
2357
2358 D = "{ S1[i] : 0 < i < 10; S2[i] : 0 <= i < 10 }";
2359 W = "{ S1[i] -> a[i]; S2[i] -> b[i] }";
2360 R = "{ S2[i] -> a[i]; S1[i] -> b[i-1] }";
2361 S = "{ S1[i] -> [i,0]; S2[i] -> [i,1] }";
2362 if (test_one_schedule(ctx, D, W, R, S, 0, 0) < 0)
2363 return -1;
2364
2365 D = "[N] -> { S1[i] : 1 <= i <= N; S2[i,j] : 1 <= i,j <= N }";
2366 W = "{ S1[i] -> a[0,i]; S2[i,j] -> a[i,j] }";
2367 R = "{ S2[i,j] -> a[i-1,j] }";
2368 S = "{ S1[i] -> [0,i,0]; S2[i,j] -> [1,i,j] }";
2369 if (test_one_schedule(ctx, D, W, R, S, 2, 1) < 0)
2370 return -1;
2371
2372 D = "[N] -> { S1[i] : 1 <= i <= N; S2[i,j] : 1 <= i,j <= N }";
2373 W = "{ S1[i] -> a[i,0]; S2[i,j] -> a[i,j] }";
2374 R = "{ S2[i,j] -> a[i,j-1] }";
2375 S = "{ S1[i] -> [0,i,0]; S2[i,j] -> [1,i,j] }";
2376 if (test_one_schedule(ctx, D, W, R, S, 2, 1) < 0)
2377 return -1;
2378
2379 D = "[N] -> { S_0[]; S_1[i] : i >= 0 and i <= -1 + N; S_2[] }";
2380 W = "[N] -> { S_0[] -> a[0]; S_2[] -> b[0]; "
2381 "S_1[i] -> a[1 + i] : i >= 0 and i <= -1 + N }";
2382 R = "[N] -> { S_2[] -> a[N]; S_1[i] -> a[i] : i >= 0 and i <= -1 + N }";
2383 S = "[N] -> { S_1[i] -> [1, i, 0]; S_2[] -> [2, 0, 1]; "
2384 "S_0[] -> [0, 0, 0] }";
2385 if (test_one_schedule(ctx, D, W, R, S, 1, 0) < 0)
2386 return -1;
2387 ctx->opt->schedule_parametric = 0;
2388 if (test_one_schedule(ctx, D, W, R, S, 0, 0) < 0)
2389 return -1;
2390 ctx->opt->schedule_parametric = 1;
2391
2392 D = "[N] -> { S1[i] : 1 <= i <= N; S2[i] : 1 <= i <= N; "
2393 "S3[i,j] : 1 <= i,j <= N; S4[i] : 1 <= i <= N }";
2394 W = "{ S1[i] -> a[i,0]; S2[i] -> a[0,i]; S3[i,j] -> a[i,j] }";
2395 R = "[N] -> { S3[i,j] -> a[i-1,j]; S3[i,j] -> a[i,j-1]; "
2396 "S4[i] -> a[i,N] }";
2397 S = "{ S1[i] -> [0,i,0]; S2[i] -> [1,i,0]; S3[i,j] -> [2,i,j]; "
2398 "S4[i] -> [4,i,0] }";
2399 if (test_one_schedule(ctx, D, W, R, S, 2, 0) < 0)
2400 return -1;
2401
2402 D = "[N] -> { S_0[i, j] : i >= 1 and i <= N and j >= 1 and j <= N }";
2403 W = "[N] -> { S_0[i, j] -> s[0] : i >= 1 and i <= N and j >= 1 and "
2404 "j <= N }";
2405 R = "[N] -> { S_0[i, j] -> s[0] : i >= 1 and i <= N and j >= 1 and "
2406 "j <= N; "
2407 "S_0[i, j] -> a[i, j] : i >= 1 and i <= N and j >= 1 and "
2408 "j <= N }";
2409 S = "[N] -> { S_0[i, j] -> [0, i, 0, j, 0] }";
2410 if (test_one_schedule(ctx, D, W, R, S, 0, 0) < 0)
2411 return -1;
2412
2413 D = "[N] -> { S_0[t] : t >= 0 and t <= -1 + N; "
2414 " S_2[t] : t >= 0 and t <= -1 + N; "
2415 " S_1[t, i] : t >= 0 and t <= -1 + N and i >= 0 and "
2416 "i <= -1 + N }";
2417 W = "[N] -> { S_0[t] -> a[t, 0] : t >= 0 and t <= -1 + N; "
2418 " S_2[t] -> b[t] : t >= 0 and t <= -1 + N; "
2419 " S_1[t, i] -> a[t, 1 + i] : t >= 0 and t <= -1 + N and "
2420 "i >= 0 and i <= -1 + N }";
2421 R = "[N] -> { S_1[t, i] -> a[t, i] : t >= 0 and t <= -1 + N and "
2422 "i >= 0 and i <= -1 + N; "
2423 " S_2[t] -> a[t, N] : t >= 0 and t <= -1 + N }";
2424 S = "[N] -> { S_2[t] -> [0, t, 2]; S_1[t, i] -> [0, t, 1, i, 0]; "
2425 " S_0[t] -> [0, t, 0] }";
2426
2427 if (test_one_schedule(ctx, D, W, R, S, 2, 1) < 0)
2428 return -1;
2429 ctx->opt->schedule_parametric = 0;
2430 if (test_one_schedule(ctx, D, W, R, S, 0, 0) < 0)
2431 return -1;
2432 ctx->opt->schedule_parametric = 1;
2433
2434 D = "[N] -> { S1[i,j] : 0 <= i,j < N; S2[i,j] : 0 <= i,j < N }";
2435 S = "{ S1[i,j] -> [0,i,j]; S2[i,j] -> [1,i,j] }";
2436 if (test_one_schedule(ctx, D, "{}", "{}", S, 2, 2) < 0)
2437 return -1;
2438
2439 D = "[M, N] -> { S_1[i] : i >= 0 and i <= -1 + M; "
2440 "S_0[i, j] : i >= 0 and i <= -1 + M and j >= 0 and j <= -1 + N }";
2441 W = "[M, N] -> { S_0[i, j] -> a[j] : i >= 0 and i <= -1 + M and "
2442 "j >= 0 and j <= -1 + N; "
2443 "S_1[i] -> b[0] : i >= 0 and i <= -1 + M }";
2444 R = "[M, N] -> { S_0[i, j] -> a[0] : i >= 0 and i <= -1 + M and "
2445 "j >= 0 and j <= -1 + N; "
2446 "S_1[i] -> b[0] : i >= 0 and i <= -1 + M }";
2447 S = "[M, N] -> { S_1[i] -> [1, i, 0]; S_0[i, j] -> [0, i, 0, j, 0] }";
2448 if (test_one_schedule(ctx, D, W, R, S, 0, 0) < 0)
2449 return -1;
2450
2451 D = "{ S_0[i] : i >= 0 }";
2452 W = "{ S_0[i] -> a[i] : i >= 0 }";
2453 R = "{ S_0[i] -> a[0] : i >= 0 }";
2454 S = "{ S_0[i] -> [0, i, 0] }";
2455 if (test_one_schedule(ctx, D, W, R, S, 0, 0) < 0)
2456 return -1;
2457
2458 D = "{ S_0[i] : i >= 0; S_1[i] : i >= 0 }";
2459 W = "{ S_0[i] -> a[i] : i >= 0; S_1[i] -> b[i] : i >= 0 }";
2460 R = "{ S_0[i] -> b[0] : i >= 0; S_1[i] -> a[i] : i >= 0 }";
2461 S = "{ S_1[i] -> [0, i, 1]; S_0[i] -> [0, i, 0] }";
2462 if (test_one_schedule(ctx, D, W, R, S, 0, 0) < 0)
2463 return -1;
2464
2465 D = "[n] -> { S_0[j, k] : j <= -1 + n and j >= 0 and "
2466 "k <= -1 + n and k >= 0 }";
2467 W = "[n] -> { S_0[j, k] -> B[j] : j <= -1 + n and j >= 0 and " "k <= -1 + n and k >= 0 }";
2468 R = "[n] -> { S_0[j, k] -> B[j] : j <= -1 + n and j >= 0 and "
2469 "k <= -1 + n and k >= 0; "
2470 "S_0[j, k] -> B[k] : j <= -1 + n and j >= 0 and "
2471 "k <= -1 + n and k >= 0; "
2472 "S_0[j, k] -> A[k] : j <= -1 + n and j >= 0 and "
2473 "k <= -1 + n and k >= 0 }";
2474 S = "[n] -> { S_0[j, k] -> [2, j, k] }";
2475 ctx->opt->schedule_outer_zero_distance = 1;
2476 if (test_one_schedule(ctx, D, W, R, S, 0, 0) < 0)
2477 return -1;
2478 ctx->opt->schedule_outer_zero_distance = 0;
2479
2480 D = "{Stmt_for_body24[i0, i1, i2, i3]:"
2481 "i0 >= 0 and i0 <= 1 and i1 >= 0 and i1 <= 6 and i2 >= 2 and "
2482 "i2 <= 6 - i1 and i3 >= 0 and i3 <= -1 + i2;"
2483 "Stmt_for_body24[i0, i1, 1, 0]:"
2484 "i0 >= 0 and i0 <= 1 and i1 >= 0 and i1 <= 5;"
2485 "Stmt_for_body7[i0, i1, i2]:"
2486 "i0 >= 0 and i0 <= 1 and i1 >= 0 and i1 <= 7 and i2 >= 0 and "
2487 "i2 <= 7 }";
2488
2489 V = "{Stmt_for_body24[0, i1, i2, i3] -> "
2490 "Stmt_for_body24[1, i1, i2, i3]:"
2491 "i3 >= 0 and i3 <= -1 + i2 and i1 >= 0 and i2 <= 6 - i1 and "
2492 "i2 >= 1;"
2493 "Stmt_for_body24[0, i1, i2, i3] -> "
2494 "Stmt_for_body7[1, 1 + i1 + i3, 1 + i1 + i2]:"
2495 "i3 <= -1 + i2 and i2 <= 6 - i1 and i2 >= 1 and i1 >= 0 and "
2496 "i3 >= 0;"
2497 "Stmt_for_body24[0, i1, i2, i3] ->"
2498 "Stmt_for_body7[1, i1, 1 + i1 + i3]:"
2499 "i3 >= 0 and i2 <= 6 - i1 and i1 >= 0 and i3 <= -1 + i2;"
2500 "Stmt_for_body7[0, i1, i2] -> Stmt_for_body7[1, i1, i2]:"
2501 "(i2 >= 1 + i1 and i2 <= 6 and i1 >= 0 and i1 <= 4) or "
2502 "(i2 >= 3 and i2 <= 7 and i1 >= 1 and i2 >= 1 + i1) or "
2503 "(i2 >= 0 and i2 <= i1 and i2 >= -7 + i1 and i1 <= 7);"
2504 "Stmt_for_body7[0, i1, 1 + i1] -> Stmt_for_body7[1, i1, 1 + i1]:"
2505 "i1 <= 6 and i1 >= 0;"
2506 "Stmt_for_body7[0, 0, 7] -> Stmt_for_body7[1, 0, 7];"
2507 "Stmt_for_body7[i0, i1, i2] -> "
2508 "Stmt_for_body24[i0, o1, -1 + i2 - o1, -1 + i1 - o1]:"
2509 "i0 >= 0 and i0 <= 1 and o1 >= 0 and i2 >= 1 + i1 and "
2510 "o1 <= -2 + i2 and i2 <= 7 and o1 <= -1 + i1;"
2511 "Stmt_for_body7[i0, i1, i2] -> "
2512 "Stmt_for_body24[i0, i1, o2, -1 - i1 + i2]:"
2513 "i0 >= 0 and i0 <= 1 and i1 >= 0 and o2 >= -i1 + i2 and "
2514 "o2 >= 1 and o2 <= 6 - i1 and i2 >= 1 + i1 }";
2515 P = V;
2516 S = "{ Stmt_for_body24[i0, i1, i2, i3] -> "
2517 "[i0, 5i0 + i1, 6i0 + i1 + i2, 1 + 6i0 + i1 + i2 + i3, 1];"
2518 "Stmt_for_body7[i0, i1, i2] -> [0, 5i0, 6i0 + i1, 6i0 + i2, 0] }";
2519
2520 if (test_special_schedule(ctx, D, V, P, S) < 0)
2521 return -1;
2522
2523 D = "{ S_0[i, j] : i >= 1 and i <= 10 and j >= 1 and j <= 8 }";
2524 V = "{ S_0[i, j] -> S_0[i, 1 + j] : i >= 1 and i <= 10 and "
2525 "j >= 1 and j <= 7;"
2526 "S_0[i, j] -> S_0[1 + i, j] : i >= 1 and i <= 9 and "
2527 "j >= 1 and j <= 8 }";
2528 P = "{ }";
2529 S = "{ S_0[i, j] -> [i + j, j] }";
2530 ctx->opt->schedule_algorithm = ISL_SCHEDULE_ALGORITHM_FEAUTRIER;
2531 if (test_special_schedule(ctx, D, V, P, S) < 0)
2532 return -1;
2533 ctx->opt->schedule_algorithm = ISL_SCHEDULE_ALGORITHM_ISL;
2534
2535 /* Fig. 1 from Feautrier's "Some Efficient Solutions..." pt. 2, 1992 */
2536 D = "[N] -> { S_0[i, j] : i >= 0 and i <= -1 + N and "
2537 "j >= 0 and j <= -1 + i }";
2538 V = "[N] -> { S_0[i, j] -> S_0[i, 1 + j] : j <= -2 + i and "
2539 "i <= -1 + N and j >= 0;"
2540 "S_0[i, -1 + i] -> S_0[1 + i, 0] : i >= 1 and "
2541 "i <= -2 + N }";
2542 P = "{ }";
2543 S = "{ S_0[i, j] -> [i, j] }";
2544 ctx->opt->schedule_algorithm = ISL_SCHEDULE_ALGORITHM_FEAUTRIER;
2545 if (test_special_schedule(ctx, D, V, P, S) < 0)
2546 return -1;
2547 ctx->opt->schedule_algorithm = ISL_SCHEDULE_ALGORITHM_ISL;
2548
2549 /* Test both algorithms on a case with only proximity dependences. */
2550 D = "{ S[i,j] : 0 <= i <= 10 }";
2551 V = "{ }";
2552 P = "{ S[i,j] -> S[i+1,j] : 0 <= i,j <= 10 }";
2553 S = "{ S[i, j] -> [j, i] }";
2554 ctx->opt->schedule_algorithm = ISL_SCHEDULE_ALGORITHM_FEAUTRIER;
2555 if (test_special_schedule(ctx, D, V, P, S) < 0)
2556 return -1;
2557 ctx->opt->schedule_algorithm = ISL_SCHEDULE_ALGORITHM_ISL;
2558 if (test_special_schedule(ctx, D, V, P, S) < 0)
2559 return -1;
2560
2561 D = "{ A[a]; B[] }";
2562 V = "{}";
2563 P = "{ A[a] -> B[] }";
2564 if (test_has_schedule(ctx, D, V, P) < 0)
2565 return -1;
2566
2567 if (test_padded_schedule(ctx) < 0)
2568 return -1;
2569
2570 return 0;
2571 }
2572
2573 int test_plain_injective(isl_ctx *ctx, const char *str, int injective)
2574 {
2575 isl_union_map *umap;
2576 int test;
2577
2578 umap = isl_union_map_read_from_str(ctx, str);
2579 test = isl_union_map_plain_is_injective(umap);
2580 isl_union_map_free(umap);
2581 if (test < 0)
2582 return -1;
2583 if (test == injective)
2584 return 0;
2585 if (injective)
2586 isl_die(ctx, isl_error_unknown,
2587 "map not detected as injective", return -1);
2588 else
2589 isl_die(ctx, isl_error_unknown,
2590 "map detected as injective", return -1);
2591 }
2592
2593 int test_injective(isl_ctx *ctx)
2594 {
2595 const char *str;
2596
2597 if (test_plain_injective(ctx, "{S[i,j] -> A[0]; T[i,j] -> B[1]}", 0))
2598 return -1;
2599 if (test_plain_injective(ctx, "{S[] -> A[0]; T[] -> B[0]}", 1))
2600 return -1;
2601 if (test_plain_injective(ctx, "{S[] -> A[0]; T[] -> A[1]}", 1))
2602 return -1;
2603 if (test_plain_injective(ctx, "{S[] -> A[0]; T[] -> A[0]}", 0))
2604 return -1;
2605 if (test_plain_injective(ctx, "{S[i] -> A[i,0]; T[i] -> A[i,1]}", 1))
2606 return -1;
2607 if (test_plain_injective(ctx, "{S[i] -> A[i]; T[i] -> A[i]}", 0))
2608 return -1;
2609 if (test_plain_injective(ctx, "{S[] -> A[0,0]; T[] -> A[0,1]}", 1))
2610 return -1;
2611 if (test_plain_injective(ctx, "{S[] -> A[0,0]; T[] -> A[1,0]}", 1))
2612 return -1;
2613
2614 str = "{S[] -> A[0,0]; T[] -> A[0,1]; U[] -> A[1,0]}";
2615 if (test_plain_injective(ctx, str, 1))
2616 return -1;
2617 str = "{S[] -> A[0,0]; T[] -> A[0,1]; U[] -> A[0,0]}";
2618 if (test_plain_injective(ctx, str, 0))
2619 return -1;
2620
2621 return 0;
2622 }
2623
2624 static int aff_plain_is_equal(__isl_keep isl_aff *aff, const char *str)
2625 {
2626 isl_aff *aff2;
2627 int equal;
2628
2629 if (!aff)
2630 return -1;
2631
2632 aff2 = isl_aff_read_from_str(isl_aff_get_ctx(aff), str);
2633 equal = isl_aff_plain_is_equal(aff, aff2);
2634 isl_aff_free(aff2);
2635
2636 return equal;
2637 }
2638
2639 static int aff_check_plain_equal(__isl_keep isl_aff *aff, const char *str)
2640 {
2641 int equal;
2642
2643 equal = aff_plain_is_equal(aff, str);
2644 if (equal < 0)
2645 return -1;
2646 if (!equal)
2647 isl_die(isl_aff_get_ctx(aff), isl_error_unknown,
2648 "result not as expected", return -1);
2649 return 0;
2650 }
2651
2652 int test_aff(isl_ctx *ctx)
2653 {
2654 const char *str;
2655 isl_set *set;
2656 isl_space *space;
2657 isl_local_space *ls;
2658 isl_aff *aff;
2659 int zero, equal;
2660
2661 space = isl_space_set_alloc(ctx, 0, 1);
2662 ls = isl_local_space_from_space(space);
2663 aff = isl_aff_zero_on_domain(ls);
2664
2665 aff = isl_aff_add_coefficient_si(aff, isl_dim_in, 0, 1);
2666 aff = isl_aff_scale_down_ui(aff, 3);
2667 aff = isl_aff_floor(aff);
2668 aff = isl_aff_add_coefficient_si(aff, isl_dim_in, 0, 1);
2669 aff = isl_aff_scale_down_ui(aff, 2);
2670 aff = isl_aff_floor(aff);
2671 aff = isl_aff_add_coefficient_si(aff, isl_dim_in, 0, 1);
2672
2673 str = "{ [10] }";
2674 set = isl_set_read_from_str(ctx, str);
2675 aff = isl_aff_gist(aff, set);
2676
2677 aff = isl_aff_add_constant_si(aff, -16);
2678 zero = isl_aff_plain_is_zero(aff);
2679 isl_aff_free(aff);
2680
2681 if (zero < 0)
2682 return -1;
2683 if (!zero)
2684 isl_die(ctx, isl_error_unknown, "unexpected result", return -1);
2685
2686 aff = isl_aff_read_from_str(ctx, "{ [-1] }");
2687 aff = isl_aff_scale_down_ui(aff, 64);
2688 aff = isl_aff_floor(aff);
2689 equal = aff_check_plain_equal(aff, "{ [-1] }");
2690 isl_aff_free(aff);
2691 if (equal < 0)
2692 return -1;
2693
2694 return 0;
2695 }
2696
2697 int test_dim_max(isl_ctx *ctx)
2698 {
2699 int equal;
2700 const char *str;
2701 isl_set *set1, *set2;
2702 isl_set *set;
2703 isl_map *map;
2704 isl_pw_aff *pwaff;
2705
2706 str = "[N] -> { [i] : 0 <= i <= min(N,10) }";
2707 set = isl_set_read_from_str(ctx, str);
2708 pwaff = isl_set_dim_max(set, 0);
2709 set1 = isl_set_from_pw_aff(pwaff);
2710 str = "[N] -> { [10] : N >= 10; [N] : N <= 9 and N >= 0 }";
2711 set2 = isl_set_read_from_str(ctx, str);
2712 equal = isl_set_is_equal(set1, set2);
2713 isl_set_free(set1);
2714 isl_set_free(set2);
2715 if (equal < 0)
2716 return -1;
2717 if (!equal)
2718 isl_die(ctx, isl_error_unknown, "unexpected result", return -1);
2719
2720 str = "[N] -> { [i] : 0 <= i <= max(2N,N+6) }";
2721 set = isl_set_read_from_str(ctx, str);
2722 pwaff = isl_set_dim_max(set, 0);
2723 set1 = isl_set_from_pw_aff(pwaff);
2724 str = "[N] -> { [6 + N] : -6 <= N <= 5; [2N] : N >= 6 }";
2725 set2 = isl_set_read_from_str(ctx, str);
2726 equal = isl_set_is_equal(set1, set2);
2727 isl_set_free(set1);
2728 isl_set_free(set2);
2729 if (equal < 0)
2730 return -1;
2731 if (!equal)
2732 isl_die(ctx, isl_error_unknown, "unexpected result", return -1);
2733
2734 str = "[N] -> { [i] : 0 <= i <= 2N or 0 <= i <= N+6 }";
2735 set = isl_set_read_from_str(ctx, str);
2736 pwaff = isl_set_dim_max(set, 0);
2737 set1 = isl_set_from_pw_aff(pwaff);
2738 str = "[N] -> { [6 + N] : -6 <= N <= 5; [2N] : N >= 6 }";
2739 set2 = isl_set_read_from_str(ctx, str);
2740 equal = isl_set_is_equal(set1, set2);
2741 isl_set_free(set1);
2742 isl_set_free(set2);
2743 if (equal < 0)
2744 return -1;
2745 if (!equal)
2746 isl_die(ctx, isl_error_unknown, "unexpected result", return -1);
2747
2748 str = "[N,M] -> { [i,j] -> [([i/16]), i%16, ([j/16]), j%16] : "
2749 "0 <= i < N and 0 <= j < M }";
2750 map = isl_map_read_from_str(ctx, str);
2751 set = isl_map_range(map);
2752
2753 pwaff = isl_set_dim_max(isl_set_copy(set), 0);
2754 set1 = isl_set_from_pw_aff(pwaff);
2755 str = "[N,M] -> { [([(N-1)/16])] : M,N > 0 }";
2756 set2 = isl_set_read_from_str(ctx, str);
2757 equal = isl_set_is_equal(set1, set2);
2758 isl_set_free(set1);
2759 isl_set_free(set2);
2760
2761 pwaff = isl_set_dim_max(isl_set_copy(set), 3);
2762 set1 = isl_set_from_pw_aff(pwaff);
2763 str = "[N,M] -> { [t] : t = min(M-1,15) and M,N > 0 }";
2764 set2 = isl_set_read_from_str(ctx, str);
2765 if (equal >= 0 && equal)
2766 equal = isl_set_is_equal(set1, set2);
2767 isl_set_free(set1);
2768 isl_set_free(set2);
2769
2770 isl_set_free(set);
2771
2772 if (equal < 0)
2773 return -1;
2774 if (!equal)
2775 isl_die(ctx, isl_error_unknown, "unexpected result", return -1);
2776
2777 /* Check that solutions are properly merged. */
2778 str = "[n] -> { [a, b, c] : c >= -4a - 2b and "
2779 "c <= -1 + n - 4a - 2b and c >= -2b and "
2780 "4a >= -4 + n and c >= 0 }";
2781 set = isl_set_read_from_str(ctx, str);
2782 pwaff = isl_set_dim_min(set, 2);
2783 set1 = isl_set_from_pw_aff(pwaff);
2784 str = "[n] -> { [(0)] : n >= 1 }";
2785 set2 = isl_set_read_from_str(ctx, str);
2786 equal = isl_set_is_equal(set1, set2);
2787 isl_set_free(set1);
2788 isl_set_free(set2);
2789
2790 if (equal < 0)
2791 return -1;
2792 if (!equal)
2793 isl_die(ctx, isl_error_unknown, "unexpected result", return -1);
2794
2795 return 0;
2796 }
2797
2798 int test_product(isl_ctx *ctx)
2799 {
2800 const char *str;
2801 isl_set *set;
2802 isl_union_set *uset1, *uset2;
2803 int ok;
2804
2805 str = "{ A[i] }";
2806 set = isl_set_read_from_str(ctx, str);
2807 set = isl_set_product(set, isl_set_copy(set));
2808 ok = isl_set_is_wrapping(set);
2809 isl_set_free(set);
2810 if (ok < 0)
2811 return -1;
2812 if (!ok)
2813 isl_die(ctx, isl_error_unknown, "unexpected result", return -1);
2814
2815 str = "{ [] }";
2816 uset1 = isl_union_set_read_from_str(ctx, str);
2817 uset1 = isl_union_set_product(uset1, isl_union_set_copy(uset1));
2818 str = "{ [[] -> []] }";
2819 uset2 = isl_union_set_read_from_str(ctx, str);
2820 ok = isl_union_set_is_equal(uset1, uset2);
2821 isl_union_set_free(uset1);
2822 isl_union_set_free(uset2);
2823 if (ok < 0)
2824 return -1;
2825 if (!ok)
2826 isl_die(ctx, isl_error_unknown, "unexpected result", return -1);
2827
2828 return 0;
2829 }
2830
2831 int test_equal(isl_ctx *ctx)
2832 {
2833 const char *str;
2834 isl_set *set, *set2;
2835 int equal;
2836
2837 str = "{ S_6[i] }";
2838 set = isl_set_read_from_str(ctx, str);
2839 str = "{ S_7[i] }";
2840 set2 = isl_set_read_from_str(ctx, str);
2841 equal = isl_set_is_equal(set, set2);
2842 isl_set_free(set);
2843 isl_set_free(set2);
2844 if (equal < 0)
2845 return -1;
2846 if (equal)
2847 isl_die(ctx, isl_error_unknown, "unexpected result", return -1);
2848
2849 return 0;
2850 }
2851
2852 static int test_plain_fixed(isl_ctx *ctx, __isl_take isl_map *map,
2853 enum isl_dim_type type, unsigned pos, int fixed)
2854 {
2855 int test;
2856
2857 test = isl_map_plain_is_fixed(map, type, pos, NULL);
2858 isl_map_free(map);
2859 if (test < 0)
2860 return -1;
2861 if (test == fixed)
2862 return 0;
2863 if (fixed)
2864 isl_die(ctx, isl_error_unknown,
2865 "map not detected as fixed", return -1);
2866 else
2867 isl_die(ctx, isl_error_unknown,
2868 "map detected as fixed", return -1);
2869 }
2870
2871 int test_fixed(isl_ctx *ctx)
2872 {
2873 const char *str;
2874 isl_map *map;
2875
2876 str = "{ [i] -> [i] }";
2877 map = isl_map_read_from_str(ctx, str);
2878 if (test_plain_fixed(ctx, map, isl_dim_out, 0, 0))
2879 return -1;
2880 str = "{ [i] -> [1] }";
2881 map = isl_map_read_from_str(ctx, str);
2882 if (test_plain_fixed(ctx, map, isl_dim_out, 0, 1))
2883 return -1;
2884 str = "{ S_1[p1] -> [o0] : o0 = -2 and p1 >= 1 and p1 <= 7 }";
2885 map = isl_map_read_from_str(ctx, str);
2886 if (test_plain_fixed(ctx, map, isl_dim_out, 0, 1))
2887 return -1;
2888 map = isl_map_read_from_str(ctx, str);
2889 map = isl_map_neg(map);
2890 if (test_plain_fixed(ctx, map, isl_dim_out, 0, 1))
2891 return -1;
2892
2893 return 0;
2894 }
2895
2896 int test_vertices(isl_ctx *ctx)
2897 {
2898 const char *str;
2899 isl_basic_set *bset;
2900 isl_vertices *vertices;
2901
2902 str = "{ A[t, i] : t = 12 and i >= 4 and i <= 12 }";
2903 bset = isl_basic_set_read_from_str(ctx, str);
2904 vertices = isl_basic_set_compute_vertices(bset);
2905 isl_basic_set_free(bset);
2906 isl_vertices_free(vertices);
2907 if (!vertices)
2908 return -1;
2909
2910 str = "{ A[t, i] : t = 14 and i = 1 }";
2911 bset = isl_basic_set_read_from_str(ctx, str);
2912 vertices = isl_basic_set_compute_vertices(bset);
2913 isl_basic_set_free(bset);
2914 isl_vertices_free(vertices);
2915 if (!vertices)
2916 return -1;
2917
2918 return 0;
2919 }
2920
2921 int test_union_pw(isl_ctx *ctx)
2922 {
2923 int equal;
2924 const char *str;
2925 isl_union_set *uset;
2926 isl_union_pw_qpolynomial *upwqp1, *upwqp2;
2927
2928 str = "{ [x] -> x^2 }";
2929 upwqp1 = isl_union_pw_qpolynomial_read_from_str(ctx, str);
2930 upwqp2 = isl_union_pw_qpolynomial_copy(upwqp1);
2931 uset = isl_union_pw_qpolynomial_domain(upwqp1);
2932 upwqp1 = isl_union_pw_qpolynomial_copy(upwqp2);
2933 upwqp1 = isl_union_pw_qpolynomial_intersect_domain(upwqp1, uset);
2934 equal = isl_union_pw_qpolynomial_plain_is_equal(upwqp1, upwqp2);
2935 isl_union_pw_qpolynomial_free(upwqp1);
2936 isl_union_pw_qpolynomial_free(upwqp2);
2937 if (equal < 0)
2938 return -1;
2939 if (!equal)
2940 isl_die(ctx, isl_error_unknown, "unexpected result", return -1);
2941
2942 return 0;
2943 }
2944
2945 int test_output(isl_ctx *ctx)
2946 {
2947 char *s;
2948 const char *str;
2949 isl_pw_aff *pa;
2950 isl_printer *p;
2951 int equal;
2952
2953 str = "[x] -> { [1] : x % 4 <= 2; [2] : x = 3 }";
2954 pa = isl_pw_aff_read_from_str(ctx, str);
2955
2956 p = isl_printer_to_str(ctx);
2957 p = isl_printer_set_output_format(p, ISL_FORMAT_C);
2958 p = isl_printer_print_pw_aff(p, pa);
2959 s = isl_printer_get_str(p);
2960 isl_printer_free(p);
2961 isl_pw_aff_free(pa);
2962 if (!s)
2963 equal = -1;
2964 else
2965 equal = !strcmp(s, "(2 - x + 4*floord(x, 4) >= 0) ? (1) : 2");
2966 free(s);
2967 if (equal < 0)
2968 return -1;
2969 if (!equal)
2970 isl_die(ctx, isl_error_unknown, "unexpected result", return -1);
2971
2972 return 0;
2973 }
2974
2975 int test_sample(isl_ctx *ctx)
2976 {
2977 const char *str;
2978 isl_basic_set *bset1, *bset2;
2979 int empty, subset;
2980
2981 str = "{ [a, b, c, d, e, f, g, h, i, j, k] : "
2982 "3i >= 1073741823b - c - 1073741823e + f and c >= 0 and "
2983 "3i >= -1 + 3221225466b + c + d - 3221225466e - f and "
2984 "2e >= a - b and 3e <= 2a and 3k <= -a and f <= -1 + a and "
2985 "3i <= 4 - a + 4b + 2c - e - 2f and 3k <= -a + c - f and "
2986 "3h >= -2 + a and 3g >= -3 - a and 3k >= -2 - a and "
2987 "3i >= -2 - a - 2c + 3e + 2f and 3h <= a + c - f and "
2988 "3h >= a + 2147483646b + 2c - 2147483646e - 2f and "
2989 "3g <= -1 - a and 3i <= 1 + c + d - f and a <= 1073741823 and "
2990 "f >= 1 - a + 1073741822b + c + d - 1073741822e and "
2991 "3i >= 1 + 2b - 2c + e + 2f + 3g and "
2992 "1073741822f <= 1073741822 - a + 1073741821b + 1073741822c +"
2993 "d - 1073741821e and "
2994 "3j <= 3 - a + 3b and 3g <= -2 - 2b + c + d - e - f and "
2995 "3j >= 1 - a + b + 2e and "
2996 "3f >= -3 + a + 3221225462b + 3c + d - 3221225465e and "
2997 "3i <= 4 - a + 4b - e and "
2998 "f <= 1073741822 + 1073741822b - 1073741822e and 3h <= a and "
2999 "f >= 0 and 2e <= 4 - a + 5b - d and 2e <= a - b + d and "
3000 "c <= -1 + a and 3i >= -2 - a + 3e and "
3001 "1073741822e <= 1073741823 - a + 1073741822b + c and "
3002 "3g >= -4 + 3221225464b + 3c + d - 3221225467e - 3f and "
3003 "3i >= -1 + 3221225466b + 3c + d - 3221225466e - 3f and "
3004 "1073741823e >= 1 + 1073741823b - d and "
3005 "3i >= 1073741823b + c - 1073741823e - f and "
3006 "3i >= 1 + 2b + e + 3g }";
3007 bset1 = isl_basic_set_read_from_str(ctx, str);
3008 bset2 = isl_basic_set_sample(isl_basic_set_copy(bset1));
3009 empty = isl_basic_set_is_empty(bset2);
3010 subset = isl_basic_set_is_subset(bset2, bset1);
3011 isl_basic_set_free(bset1);
3012 isl_basic_set_free(bset2);
3013 if (empty < 0 || subset < 0)
3014 return -1;
3015 if (empty)
3016 isl_die(ctx, isl_error_unknown, "point not found", return -1);
3017 if (!subset)
3018 isl_die(ctx, isl_error_unknown, "bad point found", return -1);
3019
3020 return 0;
3021 }
3022
3023 int test_fixed_power(isl_ctx *ctx)
3024 {
3025 const char *str;
3026 isl_map *map;
3027 isl_int exp;
3028 int equal;
3029
3030 isl_int_init(exp);
3031 str = "{ [i] -> [i + 1] }";
3032 map = isl_map_read_from_str(ctx, str);
3033 isl_int_set_si(exp, 23);
3034 map = isl_map_fixed_power(map, exp);
3035 equal = map_check_equal(map, "{ [i] -> [i + 23] }");
3036 isl_int_clear(exp);
3037 isl_map_free(map);
3038 if (equal < 0)
3039 return -1;
3040
3041 return 0;
3042 }
3043
3044 int test_slice(isl_ctx *ctx)
3045 {
3046 const char *str;
3047 isl_map *map;
3048 int equal;
3049
3050 str = "{ [i] -> [j] }";
3051 map = isl_map_read_from_str(ctx, str);
3052 map = isl_map_equate(map, isl_dim_in, 0, isl_dim_out, 0);
3053 equal = map_check_equal(map, "{ [i] -> [i] }");
3054 isl_map_free(map);
3055 if (equal < 0)
3056 return -1;
3057
3058 str = "{ [i] -> [j] }";
3059 map = isl_map_read_from_str(ctx, str);
3060 map = isl_map_equate(map, isl_dim_in, 0, isl_dim_in, 0);
3061 equal = map_check_equal(map, "{ [i] -> [j] }");
3062 isl_map_free(map);
3063 if (equal < 0)
3064 return -1;
3065
3066 str = "{ [i] -> [j] }";
3067 map = isl_map_read_from_str(ctx, str);
3068 map = isl_map_oppose(map, isl_dim_in, 0, isl_dim_out, 0);
3069 equal = map_check_equal(map, "{ [i] -> [-i] }");
3070 isl_map_free(map);
3071 if (equal < 0)
3072 return -1;
3073
3074 str = "{ [i] -> [j] }";
3075 map = isl_map_read_from_str(ctx, str);
3076 map = isl_map_oppose(map, isl_dim_in, 0, isl_dim_in, 0);
3077 equal = map_check_equal(map, "{ [0] -> [j] }");
3078 isl_map_free(map);
3079 if (equal < 0)
3080 return -1;
3081
3082 str = "{ [i] -> [j] }";
3083 map = isl_map_read_from_str(ctx, str);
3084 map = isl_map_order_gt(map, isl_dim_in, 0, isl_dim_out, 0);
3085 equal = map_check_equal(map, "{ [i] -> [j] : i > j }");
3086 isl_map_free(map);
3087 if (equal < 0)
3088 return -1;
3089
3090 str = "{ [i] -> [j] }";
3091 map = isl_map_read_from_str(ctx, str);
3092 map = isl_map_order_gt(map, isl_dim_in, 0, isl_dim_in, 0);
3093 equal = map_check_equal(map, "{ [i] -> [j] : false }");
3094 isl_map_free(map);
3095 if (equal < 0)
3096 return -1;
3097
3098 return 0;
3099 }
3100
3101 int test_eliminate(isl_ctx *ctx)
3102 {
3103 const char *str;
3104 isl_map *map;
3105 int equal;
3106
3107 str = "{ [i] -> [j] : i = 2j }";
3108 map = isl_map_read_from_str(ctx, str);
3109 map = isl_map_eliminate(map, isl_dim_out, 0, 1);
3110 equal = map_check_equal(map, "{ [i] -> [j] : exists a : i = 2a }");
3111 isl_map_free(map);
3112 if (equal < 0)
3113 return -1;
3114
3115 return 0;
3116 }
3117
3118 /* Check that isl_set_dim_residue_class detects that the values of j
3119 * in the set below are all odd and that it does not detect any spurious
3120 * strides.
3121 */
3122 static int test_residue_class(isl_ctx *ctx)
3123 {
3124 const char *str;
3125 isl_set *set;
3126 isl_int m, r;
3127 int res;
3128
3129 str = "{ [i,j] : j = 4 i + 1 and 0 <= i <= 100; "
3130 "[i,j] : j = 4 i + 3 and 500 <= i <= 600 }";
3131 set = isl_set_read_from_str(ctx, str);
3132 isl_int_init(m);
3133 isl_int_init(r);
3134 res = isl_set_dim_residue_class(set, 1, &m, &r);
3135 if (res >= 0 &&
3136 (isl_int_cmp_si(m, 2) != 0 || isl_int_cmp_si(r, 1) != 0))
3137 isl_die(ctx, isl_error_unknown, "incorrect residue class",
3138 res = -1);
3139 isl_int_clear(r);
3140 isl_int_clear(m);
3141 isl_set_free(set);
3142
3143 return res;
3144 }
3145
3146 int test_align_parameters(isl_ctx *ctx)
3147 {
3148 const char *str;
3149 isl_space *space;
3150 isl_multi_aff *ma1, *ma2;
3151 int equal;
3152
3153 str = "{ A[B[] -> C[]] -> D[E[] -> F[]] }";
3154 ma1 = isl_multi_aff_read_from_str(ctx, str);
3155
3156 space = isl_space_params_alloc(ctx, 1);
3157 space = isl_space_set_dim_name(space, isl_dim_param, 0, "N");
3158 ma1 = isl_multi_aff_align_params(ma1, space);
3159
3160 str = "[N] -> { A[B[] -> C[]] -> D[E[] -> F[]] }";
3161 ma2 = isl_multi_aff_read_from_str(ctx, str);
3162
3163 equal = isl_multi_aff_plain_is_equal(ma1, ma2);
3164
3165 isl_multi_aff_free(ma1);
3166 isl_multi_aff_free(ma2);
3167
3168 if (equal < 0)
3169 return -1;
3170 if (!equal)
3171 isl_die(ctx, isl_error_unknown,
3172 "result not as expected", return -1);
3173
3174 return 0;
3175 }
3176
3177 static int test_list(isl_ctx *ctx)
3178 {
3179 isl_id *a, *b, *c, *d, *id;
3180 isl_id_list *list;
3181 int ok;
3182
3183 a = isl_id_alloc(ctx, "a", NULL);
3184 b = isl_id_alloc(ctx, "b", NULL);
3185 c = isl_id_alloc(ctx, "c", NULL);
3186 d = isl_id_alloc(ctx, "d", NULL);
3187
3188 list = isl_id_list_alloc(ctx, 4);
3189 list = isl_id_list_add(list, a);
3190 list = isl_id_list_add(list, b);
3191 list = isl_id_list_add(list, c);
3192 list = isl_id_list_add(list, d);
3193 list = isl_id_list_drop(list, 1, 1);
3194
3195 if (isl_id_list_n_id(list) != 3) {
3196 isl_id_list_free(list);
3197 isl_die(ctx, isl_error_unknown,
3198 "unexpected number of elements in list", return -1);
3199 }
3200
3201 id = isl_id_list_get_id(list, 0);
3202 ok = id == a;
3203 isl_id_free(id);
3204 id = isl_id_list_get_id(list, 1);
3205 ok = ok && id == c;
3206 isl_id_free(id);
3207 id = isl_id_list_get_id(list, 2);
3208 ok = ok && id == d;
3209 isl_id_free(id);
3210
3211 isl_id_list_free(list);
3212
3213 if (!ok)
3214 isl_die(ctx, isl_error_unknown,
3215 "unexpected elements in list", return -1);
3216
3217 return 0;
3218 }
3219
3220 const char *set_conversion_tests[] = {
3221 "[N] -> { [i] : N - 1 <= 2 i <= N }",
3222 "[N] -> { [i] : exists a : i = 4 a and N - 1 <= i <= N }",
3223 "[N] -> { [i,j] : exists a : i = 4 a and N - 1 <= i, 2j <= N }",
3224 "[N] -> { [[i]->[j]] : exists a : i = 4 a and N - 1 <= i, 2j <= N }",
3225 };
3226
3227 /* Check that converting from isl_set to isl_pw_multi_aff and back
3228 * to isl_set produces the original isl_set.
3229 */
3230 static int test_set_conversion(isl_ctx *ctx)
3231 {
3232 int i;
3233 const char *str;
3234 isl_set *set1, *set2;
3235 isl_pw_multi_aff *pma;
3236 int equal;
3237
3238 for (i = 0; i < ARRAY_SIZE(set_conversion_tests); ++i) {
3239 str = set_conversion_tests[i];
3240 set1 = isl_set_read_from_str(ctx, str);
3241 pma = isl_pw_multi_aff_from_set(isl_set_copy(set1));
3242 set2 = isl_set_from_pw_multi_aff(pma);
3243 equal = isl_set_is_equal(set1, set2);
3244 isl_set_free(set1);
3245 isl_set_free(set2);
3246
3247 if (equal < 0)
3248 return -1;
3249 if (!equal)
3250 isl_die(ctx, isl_error_unknown, "bad conversion",
3251 return -1);
3252 }
3253
3254 return 0;
3255 }
3256
3257 /* Check that converting from isl_map to isl_pw_multi_aff and back
3258 * to isl_map produces the original isl_map.
3259 */
3260 static int test_map_conversion(isl_ctx *ctx)
3261 {
3262 const char *str;
3263 isl_map *map1, *map2;
3264 isl_pw_multi_aff *pma;
3265 int equal;
3266
3267 str = "{ [a, b, c, d] -> s0[a, b, e, f] : "
3268 "exists (e0 = [(a - 2c)/3], e1 = [(-4 + b - 5d)/9], "
3269 "e2 = [(-d + f)/9]: 3e0 = a - 2c and 9e1 = -4 + b - 5d and "
3270 "9e2 = -d + f and f >= 0 and f <= 8 and 9e >= -5 - 2a and "
3271 "9e <= -2 - 2a) }";
3272 map1 = isl_map_read_from_str(ctx, str);
3273 pma = isl_pw_multi_aff_from_map(isl_map_copy(map1));
3274 map2 = isl_map_from_pw_multi_aff(pma);
3275 equal = isl_map_is_equal(map1, map2);
3276 isl_map_free(map1);
3277 isl_map_free(map2);
3278
3279 if (equal < 0)
3280 return -1;
3281 if (!equal)
3282 isl_die(ctx, isl_error_unknown, "bad conversion", return -1);
3283
3284 return 0;
3285 }
3286
3287 static int test_conversion(isl_ctx *ctx)
3288 {
3289 if (test_set_conversion(ctx) < 0)
3290 return -1;
3291 if (test_map_conversion(ctx) < 0)
3292 return -1;
3293 return 0;
3294 }
3295
3296 /* Check that isl_basic_map_curry does not modify input.
3297 */
3298 static int test_curry(isl_ctx *ctx)
3299 {
3300 const char *str;
3301 isl_basic_map *bmap1, *bmap2;
3302 int equal;
3303
3304 str = "{ [A[] -> B[]] -> C[] }";
3305 bmap1 = isl_basic_map_read_from_str(ctx, str);
3306 bmap2 = isl_basic_map_curry(isl_basic_map_copy(bmap1));
3307 equal = isl_basic_map_is_equal(bmap1, bmap2);
3308 isl_basic_map_free(bmap1);
3309 isl_basic_map_free(bmap2);
3310
3311 if (equal < 0)
3312 return -1;
3313 if (equal)
3314 isl_die(ctx, isl_error_unknown,
3315 "curried map should not be equal to original",
3316 return -1);
3317
3318 return 0;
3319 }
3320
3321 struct {
3322 const char *set;
3323 const char *ma;
3324 const char *res;
3325 } preimage_tests[] = {
3326 { "{ B[i,j] : 0 <= i < 10 and 0 <= j < 100 }",
3327 "{ A[j,i] -> B[i,j] }",
3328 "{ A[j,i] : 0 <= i < 10 and 0 <= j < 100 }" },
3329 { "{ rat: B[i,j] : 0 <= i, j and 3 i + 5 j <= 100 }",
3330 "{ A[a,b] -> B[a/2,b/6] }",
3331 "{ rat: A[a,b] : 0 <= a, b and 9 a + 5 b <= 600 }" },
3332 { "{ B[i,j] : 0 <= i, j and 3 i + 5 j <= 100 }",
3333 "{ A[a,b] -> B[a/2,b/6] }",
3334 "{ A[a,b] : 0 <= a, b and 9 a + 5 b <= 600 and "
3335 "exists i,j : a = 2 i and b = 6 j }" },
3336 { "[n] -> { S[i] : 0 <= i <= 100 }", "[n] -> { S[n] }",
3337 "[n] -> { : 0 <= n <= 100 }" },
3338 { "{ B[i] : 0 <= i < 100 and exists a : i = 4 a }",
3339 "{ A[a] -> B[2a] }",
3340 "{ A[a] : 0 <= a < 50 and exists b : a = 2 b }" },
3341 { "{ B[i] : 0 <= i < 100 and exists a : i = 4 a }",
3342 "{ A[a] -> B[([a/2])] }",
3343 "{ A[a] : 0 <= a < 200 and exists b : [a/2] = 4 b }" },
3344 { "{ B[i,j,k] : 0 <= i,j,k <= 100 }",
3345 "{ A[a] -> B[a,a,a/3] }",
3346 "{ A[a] : 0 <= a <= 100 and exists b : a = 3 b }" },
3347 { "{ B[i,j] : j = [(i)/2] } ", "{ A[i,j] -> B[i/3,j] }",
3348 "{ A[i,j] : j = [(i)/6] and exists a : i = 3 a }" },
3349 };
3350
3351 static int test_preimage_basic_set(isl_ctx *ctx)
3352 {
3353 int i;
3354 isl_basic_set *bset1, *bset2;
3355 isl_multi_aff *ma;
3356 int equal;
3357
3358 for (i = 0; i < ARRAY_SIZE(preimage_tests); ++i) {
3359 bset1 = isl_basic_set_read_from_str(ctx, preimage_tests[i].set);
3360 ma = isl_multi_aff_read_from_str(ctx, preimage_tests[i].ma);
3361 bset2 = isl_basic_set_read_from_str(ctx, preimage_tests[i].res);
3362 bset1 = isl_basic_set_preimage_multi_aff(bset1, ma);
3363 equal = isl_basic_set_is_equal(bset1, bset2);
3364 isl_basic_set_free(bset1);
3365 isl_basic_set_free(bset2);
3366 if (equal < 0)
3367 return -1;
3368 if (!equal)
3369 isl_die(ctx, isl_error_unknown, "bad preimage",
3370 return -1);
3371 }
3372
3373 return 0;
3374 }
3375
3376 struct {
3377 const char *map;
3378 const char *ma;
3379 const char *res;
3380 } preimage_domain_tests[] = {
3381 { "{ B[i,j] -> C[2i + 3j] : 0 <= i < 10 and 0 <= j < 100 }",
3382 "{ A[j,i] -> B[i,j] }",
3383 "{ A[j,i] -> C[2i + 3j] : 0 <= i < 10 and 0 <= j < 100 }" },
3384 { "{ B[i] -> C[i]; D[i] -> E[i] }",
3385 "{ A[i] -> B[i + 1] }",
3386 "{ A[i] -> C[i + 1] }" },
3387 { "{ B[i] -> C[i]; B[i] -> E[i] }",
3388 "{ A[i] -> B[i + 1] }",
3389 "{ A[i] -> C[i + 1]; A[i] -> E[i + 1] }" },
3390 { "{ B[i] -> C[([i/2])] }",
3391 "{ A[i] -> B[2i] }",
3392 "{ A[i] -> C[i] }" },
3393 { "{ B[i,j] -> C[([i/2]), ([(i+j)/3])] }",
3394 "{ A[i] -> B[([i/5]), ([i/7])] }",
3395 "{ A[i] -> C[([([i/5])/2]), ([(([i/5])+([i/7]))/3])] }" },
3396 { "[N] -> { B[i] -> C[([N/2]), i, ([N/3])] }",
3397 "[N] -> { A[] -> B[([N/5])] }",
3398 "[N] -> { A[] -> C[([N/2]), ([N/5]), ([N/3])] }" },
3399 { "{ B[i] -> C[i] : exists a : i = 5 a }",
3400 "{ A[i] -> B[2i] }",
3401 "{ A[i] -> C[2i] : exists a : 2i = 5 a }" },
3402 { "{ B[i] -> C[i] : exists a : i = 2 a; "
3403 "B[i] -> D[i] : exists a : i = 2 a + 1 }",
3404 "{ A[i] -> B[2i] }",
3405 "{ A[i] -> C[2i] }" },
3406 };
3407
3408 static int test_preimage_union_map(isl_ctx *ctx)
3409 {
3410 int i;
3411 isl_union_map *umap1, *umap2;
3412 isl_multi_aff *ma;
3413 int equal;
3414
3415 for (i = 0; i < ARRAY_SIZE(preimage_domain_tests); ++i) {
3416 umap1 = isl_union_map_read_from_str(ctx,
3417 preimage_domain_tests[i].map);
3418 ma = isl_multi_aff_read_from_str(ctx,
3419 preimage_domain_tests[i].ma);
3420 umap2 = isl_union_map_read_from_str(ctx,
3421 preimage_domain_tests[i].res);
3422 umap1 = isl_union_map_preimage_domain_multi_aff(umap1, ma);
3423 equal = isl_union_map_is_equal(umap1, umap2);
3424 isl_union_map_free(umap1);
3425 isl_union_map_free(umap2);
3426 if (equal < 0)
3427 return -1;
3428 if (!equal)
3429 isl_die(ctx, isl_error_unknown, "bad preimage",
3430 return -1);
3431 }
3432
3433 return 0;
3434 }
3435
3436 static int test_preimage(isl_ctx *ctx)
3437 {
3438 if (test_preimage_basic_set(ctx) < 0)
3439 return -1;
3440 if (test_preimage_union_map(ctx) < 0)
3441 return -1;
3442
3443 return 0;
3444 }
3445
3446 struct {
3447 const char *ma1;
3448 const char *ma;
3449 const char *res;
3450 } pullback_tests[] = {
3451 { "{ B[i,j] -> C[i + 2j] }" , "{ A[a,b] -> B[b,a] }",
3452 "{ A[a,b] -> C[b + 2a] }" },
3453 { "{ B[i] -> C[2i] }", "{ A[a] -> B[(a)/2] }", "{ A[a] -> C[a] }" },
3454 { "{ B[i] -> C[(i)/2] }", "{ A[a] -> B[2a] }", "{ A[a] -> C[a] }" },
3455 { "{ B[i] -> C[(i)/2] }", "{ A[a] -> B[(a)/3] }",
3456 "{ A[a] -> C[(a)/6] }" },
3457 { "{ B[i] -> C[2i] }", "{ A[a] -> B[5a] }", "{ A[a] -> C[10a] }" },
3458 { "{ B[i] -> C[2i] }", "{ A[a] -> B[(a)/3] }",
3459 "{ A[a] -> C[(2a)/3] }" },
3460 { "{ B[i,j] -> C[i + j] }", "{ A[a] -> B[a,a] }", "{ A[a] -> C[2a] }"},
3461 { "{ B[a] -> C[a,a] }", "{ A[i,j] -> B[i + j] }",
3462 "{ A[i,j] -> C[i + j, i + j] }"},
3463 { "{ B[i] -> C[([i/2])] }", "{ B[5] }", "{ C[2] }" },
3464 { "[n] -> { B[i,j] -> C[([i/2]) + 2j] }",
3465 "[n] -> { B[n,[n/3]] }", "[n] -> { C[([n/2]) + 2*[n/3]] }", },
3466 };
3467
3468 static int test_pullback(isl_ctx *ctx)
3469 {
3470 int i;
3471 isl_multi_aff *ma1, *ma2;
3472 isl_multi_aff *ma;
3473 int equal;
3474
3475 for (i = 0; i < ARRAY_SIZE(pullback_tests); ++i) {
3476 ma1 = isl_multi_aff_read_from_str(ctx, pullback_tests[i].ma1);
3477 ma = isl_multi_aff_read_from_str(ctx, pullback_tests[i].ma);
3478 ma2 = isl_multi_aff_read_from_str(ctx, pullback_tests[i].res);
3479 ma1 = isl_multi_aff_pullback_multi_aff(ma1, ma);
3480 equal = isl_multi_aff_plain_is_equal(ma1, ma2);
3481 isl_multi_aff_free(ma1);
3482 isl_multi_aff_free(ma2);
3483 if (equal < 0)
3484 return -1;
3485 if (!equal)
3486 isl_die(ctx, isl_error_unknown, "bad pullback",
3487 return -1);
3488 }
3489
3490 return 0;
3491 }
3492
3493 /* Check that negation is printed correctly.
3494 */
3495 static int test_ast(isl_ctx *ctx)
3496 {
3497 isl_ast_expr *expr, *expr1, *expr2, *expr3;
3498 char *str;
3499 int ok;
3500
3501 expr1 = isl_ast_expr_from_id(isl_id_alloc(ctx, "A", NULL));
3502 expr2 = isl_ast_expr_from_id(isl_id_alloc(ctx, "B", NULL));
3503 expr = isl_ast_expr_add(expr1, expr2);
3504 expr = isl_ast_expr_neg(expr);
3505 str = isl_ast_expr_to_str(expr);
3506 ok = str ? !strcmp(str, "-(A + B)") : -1;
3507 free(str);
3508 isl_ast_expr_free(expr);
3509
3510 if (ok < 0)
3511 return -1;
3512 if (!ok)
3513 isl_die(ctx, isl_error_unknown,
3514 "isl_ast_expr printed incorrectly", return -1);
3515
3516 expr1 = isl_ast_expr_from_id(isl_id_alloc(ctx, "A", NULL));
3517 expr2 = isl_ast_expr_from_id(isl_id_alloc(ctx, "B", NULL));
3518 expr = isl_ast_expr_add(expr1, expr2);
3519 expr3 = isl_ast_expr_from_id(isl_id_alloc(ctx, "C", NULL));
3520 expr = isl_ast_expr_sub(expr3, expr);
3521 str = isl_ast_expr_to_str(expr);
3522 ok = str ? !strcmp(str, "C - (A + B)") : -1;
3523 free(str);
3524 isl_ast_expr_free(expr);
3525
3526 if (ok < 0)
3527 return -1;
3528 if (!ok)
3529 isl_die(ctx, isl_error_unknown,
3530 "isl_ast_expr printed incorrectly", return -1);
3531
3532 return 0;
3533 }
3534
3535 /* Internal data structure for before_for and after_for callbacks.
3536 *
3537 * depth is the current depth
3538 * before is the number of times before_for has been called
3539 * after is the number of times after_for has been called
3540 */
3541 struct isl_test_codegen_data {
3542 int depth;
3543 int before;
3544 int after;
3545 };
3546
3547 /* This function is called before each for loop in the AST generated
3548 * from test_ast_gen1.
3549 *
3550 * Increment the number of calls and the depth.
3551 * Check that the space returned by isl_ast_build_get_schedule_space
3552 * matches the target space of the schedule returned by
3553 * isl_ast_build_get_schedule.
3554 * Return an isl_id that is checked by the corresponding call
3555 * to after_for.
3556 */
3557 static __isl_give isl_id *before_for(__isl_keep isl_ast_build *build,
3558 void *user)
3559 {
3560 struct isl_test_codegen_data *data = user;
3561 isl_ctx *ctx;
3562 isl_space *space;
3563 isl_union_map *schedule;
3564 isl_union_set *uset;
3565 isl_set *set;
3566 int empty;
3567 char name[] = "d0";
3568
3569 ctx = isl_ast_build_get_ctx(build);
3570
3571 if (data->before >= 3)
3572 isl_die(ctx, isl_error_unknown,
3573 "unexpected number of for nodes", return NULL);
3574 if (data->depth >= 2)
3575 isl_die(ctx, isl_error_unknown,
3576 "unexpected depth", return NULL);
3577
3578 snprintf(name, sizeof(name), "d%d", data->depth);
3579 data->before++;
3580 data->depth++;
3581
3582 schedule = isl_ast_build_get_schedule(build);
3583 uset = isl_union_map_range(schedule);
3584 if (!uset)
3585 return NULL;
3586 if (isl_union_set_n_set(uset) != 1) {
3587 isl_union_set_free(uset);
3588 isl_die(ctx, isl_error_unknown,
3589 "expecting single range space", return NULL);
3590 }
3591
3592 space = isl_ast_build_get_schedule_space(build);
3593 set = isl_union_set_extract_set(uset, space);
3594 isl_union_set_free(uset);
3595 empty = isl_set_is_empty(set);
3596 isl_set_free(set);
3597
3598 if (empty < 0)
3599 return NULL;
3600 if (empty)
3601 isl_die(ctx, isl_error_unknown,
3602 "spaces don't match", return NULL);
3603
3604 return isl_id_alloc(ctx, name, NULL);
3605 }
3606
3607 /* This function is called after each for loop in the AST generated
3608 * from test_ast_gen1.
3609 *
3610 * Increment the number of calls and decrement the depth.
3611 * Check that the annotation attached to the node matches
3612 * the isl_id returned by the corresponding call to before_for.
3613 */
3614 static __isl_give isl_ast_node *after_for(__isl_take isl_ast_node *node,
3615 __isl_keep isl_ast_build *build, void *user)
3616 {
3617 struct isl_test_codegen_data *data = user;
3618 isl_id *id;
3619 const char *name;
3620 int valid;
3621
3622 data->after++;
3623 data->depth--;
3624
3625 if (data->after > data->before)
3626 isl_die(isl_ast_node_get_ctx(node), isl_error_unknown,
3627 "mismatch in number of for nodes",
3628 return isl_ast_node_free(node));
3629
3630 id = isl_ast_node_get_annotation(node);
3631 if (!id)
3632 isl_die(isl_ast_node_get_ctx(node), isl_error_unknown,
3633 "missing annotation", return isl_ast_node_free(node));
3634
3635 name = isl_id_get_name(id);
3636 valid = name && atoi(name + 1) == data->depth;
3637 isl_id_free(id);
3638
3639 if (!valid)
3640 isl_die(isl_ast_node_get_ctx(node), isl_error_unknown,
3641 "wrong annotation", return isl_ast_node_free(node));
3642
3643 return node;
3644 }
3645
3646 /* Check that the before_each_for and after_each_for callbacks
3647 * are called for each for loop in the generated code,
3648 * that they are called in the right order and that the isl_id
3649 * returned from the before_each_for callback is attached to
3650 * the isl_ast_node passed to the corresponding after_each_for call.
3651 */
3652 static int test_ast_gen1(isl_ctx *ctx)
3653 {
3654 const char *str;
3655 isl_set *set;
3656 isl_union_map *schedule;
3657 isl_ast_build *build;
3658 isl_ast_node *tree;
3659 struct isl_test_codegen_data data;
3660
3661 str = "[N] -> { : N >= 10 }";
3662 set = isl_set_read_from_str(ctx, str);
3663 str = "[N] -> { A[i,j] -> S[8,i,3,j] : 0 <= i,j <= N; "
3664 "B[i,j] -> S[8,j,9,i] : 0 <= i,j <= N }";
3665 schedule = isl_union_map_read_from_str(ctx, str);
3666
3667 data.before = 0;
3668 data.after = 0;
3669 data.depth = 0;
3670 build = isl_ast_build_from_context(set);
3671 build = isl_ast_build_set_before_each_for(build,
3672 &before_for, &data);
3673 build = isl_ast_build_set_after_each_for(build,
3674 &after_for, &data);
3675 tree = isl_ast_build_ast_from_schedule(build, schedule);
3676 isl_ast_build_free(build);
3677 if (!tree)
3678 return -1;
3679
3680 isl_ast_node_free(tree);
3681
3682 if (data.before != 3 || data.after != 3)
3683 isl_die(ctx, isl_error_unknown,
3684 "unexpected number of for nodes", return -1);
3685
3686 return 0;
3687 }
3688
3689 /* Check that the AST generator handles domains that are integrally disjoint
3690 * but not ratinoally disjoint.
3691 */
3692 static int test_ast_gen2(isl_ctx *ctx)
3693 {
3694 const char *str;
3695 isl_set *set;
3696 isl_union_map *schedule;
3697 isl_union_map *options;
3698 isl_ast_build *build;
3699 isl_ast_node *tree;
3700
3701 str = "{ A[i,j] -> [i,j] : 0 <= i,j <= 1 }";
3702 schedule = isl_union_map_read_from_str(ctx, str);
3703 set = isl_set_universe(isl_space_params_alloc(ctx, 0));
3704 build = isl_ast_build_from_context(set);
3705
3706 str = "{ [i,j] -> atomic[1] : i + j = 1; [i,j] -> unroll[1] : i = j }";
3707 options = isl_union_map_read_from_str(ctx, str);
3708 build = isl_ast_build_set_options(build, options);
3709 tree = isl_ast_build_ast_from_schedule(build, schedule);
3710 isl_ast_build_free(build);
3711 if (!tree)
3712 return -1;
3713 isl_ast_node_free(tree);
3714
3715 return 0;
3716 }
3717
3718 /* Increment *user on each call.
3719 */
3720 static __isl_give isl_ast_node *count_domains(__isl_take isl_ast_node *node,
3721 __isl_keep isl_ast_build *build, void *user)
3722 {
3723 int *n = user;
3724
3725 (*n)++;
3726
3727 return node;
3728 }
3729
3730 /* Test that unrolling tries to minimize the number of instances.
3731 * In particular, for the schedule given below, make sure it generates
3732 * 3 nodes (rather than 101).
3733 */
3734 static int test_ast_gen3(isl_ctx *ctx)
3735 {
3736 const char *str;
3737 isl_set *set;
3738 isl_union_map *schedule;
3739 isl_union_map *options;
3740 isl_ast_build *build;
3741 isl_ast_node *tree;
3742 int n_domain = 0;
3743
3744 str = "[n] -> { A[i] -> [i] : 0 <= i <= 100 and n <= i <= n + 2 }";
3745 schedule = isl_union_map_read_from_str(ctx, str);
3746 set = isl_set_universe(isl_space_params_alloc(ctx, 0));
3747
3748 str = "{ [i] -> unroll[0] }";
3749 options = isl_union_map_read_from_str(ctx, str);
3750
3751 build = isl_ast_build_from_context(set);
3752 build = isl_ast_build_set_options(build, options);
3753 build = isl_ast_build_set_at_each_domain(build,
3754 &count_domains, &n_domain);
3755 tree = isl_ast_build_ast_from_schedule(build, schedule);
3756 isl_ast_build_free(build);
3757 if (!tree)
3758 return -1;
3759
3760 isl_ast_node_free(tree);
3761
3762 if (n_domain != 3)
3763 isl_die(ctx, isl_error_unknown,
3764 "unexpected number of for nodes", return -1);
3765
3766 return 0;
3767 }
3768
3769 /* Check that if the ast_build_exploit_nested_bounds options is set,
3770 * we do not get an outer if node in the generated AST,
3771 * while we do get such an outer if node if the options is not set.
3772 */
3773 static int test_ast_gen4(isl_ctx *ctx)
3774 {
3775 const char *str;
3776 isl_set *set;
3777 isl_union_map *schedule;
3778 isl_ast_build *build;
3779 isl_ast_node *tree;
3780 enum isl_ast_node_type type;
3781 int enb;
3782
3783 enb = isl_options_get_ast_build_exploit_nested_bounds(ctx);
3784 str = "[N,M] -> { A[i,j] -> [i,j] : 0 <= i <= N and 0 <= j <= M }";
3785
3786 isl_options_set_ast_build_exploit_nested_bounds(ctx, 1);
3787
3788 schedule = isl_union_map_read_from_str(ctx, str);
3789 set = isl_set_universe(isl_space_params_alloc(ctx, 0));
3790 build = isl_ast_build_from_context(set);
3791 tree = isl_ast_build_ast_from_schedule(build, schedule);
3792 isl_ast_build_free(build);
3793 if (!tree)
3794 return -1;
3795
3796 type = isl_ast_node_get_type(tree);
3797 isl_ast_node_free(tree);
3798
3799 if (type == isl_ast_node_if)
3800 isl_die(ctx, isl_error_unknown,
3801 "not expecting if node", return -1);
3802
3803 isl_options_set_ast_build_exploit_nested_bounds(ctx, 0);
3804
3805 schedule = isl_union_map_read_from_str(ctx, str);
3806 set = isl_set_universe(isl_space_params_alloc(ctx, 0));
3807 build = isl_ast_build_from_context(set);
3808 tree = isl_ast_build_ast_from_schedule(build, schedule);
3809 isl_ast_build_free(build);
3810 if (!tree)
3811 return -1;
3812
3813 type = isl_ast_node_get_type(tree);
3814 isl_ast_node_free(tree);
3815
3816 if (type != isl_ast_node_if)
3817 isl_die(ctx, isl_error_unknown,
3818 "expecting if node", return -1);
3819
3820 isl_options_set_ast_build_exploit_nested_bounds(ctx, enb);
3821
3822 return 0;
3823 }
3824
3825 /* This function is called for each leaf in the AST generated
3826 * from test_ast_gen5.
3827 *
3828 * We finalize the AST generation by extending the outer schedule
3829 * with a zero-dimensional schedule. If this results in any for loops,
3830 * then this means that we did not pass along enough information
3831 * about the outer schedule to the inner AST generation.
3832 */
3833 static __isl_give isl_ast_node *create_leaf(__isl_take isl_ast_build *build,
3834 void *user)
3835 {
3836 isl_union_map *schedule, *extra;
3837 isl_ast_node *tree;
3838
3839 schedule = isl_ast_build_get_schedule(build);
3840 extra = isl_union_map_copy(schedule);
3841 extra = isl_union_map_from_domain(isl_union_map_domain(extra));
3842 schedule = isl_union_map_range_product(schedule, extra);
3843 tree = isl_ast_build_ast_from_schedule(build, schedule);
3844 isl_ast_build_free(build);
3845
3846 if (!tree)
3847 return NULL;
3848
3849 if (isl_ast_node_get_type(tree) == isl_ast_node_for)
3850 isl_die(isl_ast_node_get_ctx(tree), isl_error_unknown,
3851 "code should not contain any for loop",
3852 return isl_ast_node_free(tree));
3853
3854 return tree;
3855 }
3856
3857 /* Check that we do not lose any information when going back and
3858 * forth between internal and external schedule.
3859 *
3860 * In particular, we create an AST where we unroll the only
3861 * non-constant dimension in the schedule. We therefore do
3862 * not expect any for loops in the AST. However, older versions
3863 * of isl would not pass along enough information about the outer
3864 * schedule when performing an inner code generation from a create_leaf
3865 * callback, resulting in the inner code generation producing a for loop.
3866 */
3867 static int test_ast_gen5(isl_ctx *ctx)
3868 {
3869 const char *str;
3870 isl_set *set;
3871 isl_union_map *schedule, *options;
3872 isl_ast_build *build;
3873 isl_ast_node *tree;
3874
3875 str = "{ A[] -> [1, 1, 2]; B[i] -> [1, i, 0] : i >= 1 and i <= 2 }";
3876 schedule = isl_union_map_read_from_str(ctx, str);
3877
3878 str = "{ [a, b, c] -> unroll[1] : exists (e0 = [(a)/4]: "
3879 "4e0 >= -1 + a - b and 4e0 <= -2 + a + b) }";
3880 options = isl_union_map_read_from_str(ctx, str);
3881
3882 set = isl_set_universe(isl_space_params_alloc(ctx, 0));
3883 build = isl_ast_build_from_context(set);
3884 build = isl_ast_build_set_options(build, options);
3885 build = isl_ast_build_set_create_leaf(build, &create_leaf, NULL);
3886 tree = isl_ast_build_ast_from_schedule(build, schedule);
3887 isl_ast_build_free(build);
3888 isl_ast_node_free(tree);
3889 if (!tree)
3890 return -1;
3891
3892 return 0;
3893 }
3894
3895 static int test_ast_gen(isl_ctx *ctx)
3896 {
3897 if (test_ast_gen1(ctx) < 0)
3898 return -1;
3899 if (test_ast_gen2(ctx) < 0)
3900 return -1;
3901 if (test_ast_gen3(ctx) < 0)
3902 return -1;
3903 if (test_ast_gen4(ctx) < 0)
3904 return -1;
3905 if (test_ast_gen5(ctx) < 0)
3906 return -1;
3907 return 0;
3908 }
3909
3910 /* Check if dropping output dimensions from an isl_pw_multi_aff
3911 * works properly.
3912 */
3913 static int test_pw_multi_aff(isl_ctx *ctx)
3914 {
3915 const char *str;
3916 isl_pw_multi_aff *pma1, *pma2;
3917 int equal;
3918
3919 str = "{ [i,j] -> [i+j, 4i-j] }";
3920 pma1 = isl_pw_multi_aff_read_from_str(ctx, str);
3921 str = "{ [i,j] -> [4i-j] }";
3922 pma2 = isl_pw_multi_aff_read_from_str(ctx, str);
3923
3924 pma1 = isl_pw_multi_aff_drop_dims(pma1, isl_dim_out, 0, 1);
3925
3926 equal = isl_pw_multi_aff_plain_is_equal(pma1, pma2);
3927
3928 isl_pw_multi_aff_free(pma1);
3929 isl_pw_multi_aff_free(pma2);
3930 if (equal < 0)
3931 return -1;
3932 if (!equal)
3933 isl_die(ctx, isl_error_unknown,
3934 "expressions not equal", return -1);
3935
3936 return 0;
3937 }
3938
3939 /* This is a regression test for a bug where isl_basic_map_simplify
3940 * would end up in an infinite loop. In particular, we construct
3941 * an empty basic set that is not obviously empty.
3942 * isl_basic_set_is_empty marks the basic set as empty.
3943 * After projecting out i3, the variable can be dropped completely,
3944 * but isl_basic_map_simplify refrains from doing so if the basic set
3945 * is empty and would end up in an infinite loop if it didn't test
3946 * explicitly for empty basic maps in the outer loop.
3947 */
3948 static int test_simplify(isl_ctx *ctx)
3949 {
3950 const char *str;
3951 isl_basic_set *bset;
3952 int empty;
3953
3954 str = "{ [i0, i1, i2, i3] : i0 >= -2 and 6i2 <= 4 + i0 + 5i1 and "
3955 "i2 <= 22 and 75i2 <= 111 + 13i0 + 60i1 and "
3956 "25i2 >= 38 + 6i0 + 20i1 and i0 <= -1 and i2 >= 20 and "
3957 "i3 >= i2 }";
3958 bset = isl_basic_set_read_from_str(ctx, str);
3959 empty = isl_basic_set_is_empty(bset);
3960 bset = isl_basic_set_project_out(bset, isl_dim_set, 3, 1);
3961 isl_basic_set_free(bset);
3962 if (!bset)
3963 return -1;
3964 if (!empty)
3965 isl_die(ctx, isl_error_unknown,
3966 "basic set should be empty", return -1);
3967
3968 return 0;
3969 }
3970
3971 /* This is a regression test for a bug where isl_tab_basic_map_partial_lexopt
3972 * with gbr context would fail to disable the use of the shifted tableau
3973 * when transferring equalities for the input to the context, resulting
3974 * in invalid sample values.
3975 */
3976 static int test_partial_lexmin(isl_ctx *ctx)
3977 {
3978 const char *str;
3979 isl_basic_set *bset;
3980 isl_basic_map *bmap;
3981 isl_map *map;
3982
3983 str = "{ [1, b, c, 1 - c] -> [e] : 2e <= -c and 2e >= -3 + c }";
3984 bmap = isl_basic_map_read_from_str(ctx, str);
3985 str = "{ [a, b, c, d] : c <= 1 and 2d >= 6 - 4b - c }";
3986 bset = isl_basic_set_read_from_str(ctx, str);
3987 map = isl_basic_map_partial_lexmin(bmap, bset, NULL);
3988 isl_map_free(map);
3989
3990 if (!map)
3991 return -1;
3992
3993 return 0;
3994 }
3995
3996 /* Check that the variable compression performed on the existentially
3997 * quantified variables inside isl_basic_set_compute_divs is not confused
3998 * by the implicit equalities among the parameters.
3999 */
4000 static int test_compute_divs(isl_ctx *ctx)
4001 {
4002 const char *str;
4003 isl_basic_set *bset;
4004 isl_set *set;
4005
4006 str = "[a, b, c, d, e] -> { [] : exists (e0: 2d = b and a <= 124 and "
4007 "b <= 2046 and b >= 0 and b <= 60 + 64a and 2e >= b + 2c and "
4008 "2e >= b and 2e <= 1 + b and 2e <= 1 + b + 2c and "
4009 "32768e0 >= -124 + a and 2097152e0 <= 60 + 64a - b) }";
4010 bset = isl_basic_set_read_from_str(ctx, str);
4011 set = isl_basic_set_compute_divs(bset);
4012 isl_set_free(set);
4013 if (!set)
4014 return -1;
4015
4016 return 0;
4017 }
4018
4019 struct {
4020 const char *name;
4021 int (*fn)(isl_ctx *ctx);
4022 } tests [] = {
4023 { "compute divs", &test_compute_divs },
4024 { "partial lexmin", &test_partial_lexmin },
4025 { "simplify", &test_simplify },
4026 { "curry", &test_curry },
4027 { "piecewise multi affine expressions", &test_pw_multi_aff },
4028 { "conversion", &test_conversion },
4029 { "list", &test_list },
4030 { "align parameters", &test_align_parameters },
4031 { "preimage", &test_preimage },
4032 { "pullback", &test_pullback },
4033 { "AST", &test_ast },
4034 { "AST generation", &test_ast_gen },
4035 { "eliminate", &test_eliminate },
4036 { "residue class", &test_residue_class },
4037 { "div", &test_div },
4038 { "slice", &test_slice },
4039 { "fixed power", &test_fixed_power },
4040 { "sample", &test_sample },
4041 { "output", &test_output },
4042 { "vertices", &test_vertices },
4043 { "fixed", &test_fixed },
4044 { "equal", &test_equal },
4045 { "product", &test_product },
4046 { "dim_max", &test_dim_max },
4047 { "affine", &test_aff },
4048 { "injective", &test_injective },
4049 { "schedule", &test_schedule },
4050 { "union_pw", &test_union_pw },
4051 { "parse", &test_parse },
4052 { "single-valued", &test_sv },
4053 { "affine hull", &test_affine_hull },
4054 { "coalesce", &test_coalesce },
4055 { "factorize", &test_factorize },
4056 { "subset", &test_subset },
4057 { "subtract", &test_subtract },
4058 { "lexmin", &test_lexmin },
4059 };
4060
4061 int main()
4062 {
4063 int i;
4064 struct isl_ctx *ctx;
4065
4066 srcdir = getenv("srcdir");
4067 assert(srcdir);
4068
4069 ctx = isl_ctx_alloc();
4070 for (i = 0; i < ARRAY_SIZE(tests); ++i) {
4071 printf("%s\n", tests[i].name);
4072 if (tests[i].fn(ctx) < 0)
4073 goto error;
4074 }
4075 test_lift(ctx);
4076 test_bound(ctx);
4077 test_union(ctx);
4078 test_split_periods(ctx);
4079 test_pwqp(ctx);
4080 test_lex(ctx);
4081 test_bijective(ctx);
4082 test_dep(ctx);
4083 test_read(ctx);
4084 test_bounded(ctx);
4085 test_construction(ctx);
4086 test_dim(ctx);
4087 test_application(ctx);
4088 test_convex_hull(ctx);
4089 test_gist(ctx);
4090 test_closure(ctx);
4091 isl_ctx_free(ctx);
4092 return 0;
4093 error:
4094 isl_ctx_free(ctx);
4095 return -1;
4096 }
Integer set library