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isl_basic_map_project_out: extract out insert_div_rows
[isl.git] / isl_test.c
blobde8f986f45ac419713296f1757d8b786e27bff72
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;
723 int n;
724
725 test_affine_hull_case(ctx, "affine2");
726 test_affine_hull_case(ctx, "affine");
727 test_affine_hull_case(ctx, "affine3");
728
729 str = "[m] -> { [i0] : exists (e0, e1: e1 <= 1 + i0 and "
730 "m >= 3 and 4i0 <= 2 + m and e1 >= i0 and "
731 "e1 >= 0 and e1 <= 2 and e1 >= 1 + 2e0 and "
732 "2e1 <= 1 + m + 4e0 and 2e1 >= 2 - m + 4i0 - 4e0) }";
733 set = isl_set_read_from_str(ctx, str);
734 bset = isl_set_affine_hull(set);
735 n = isl_basic_set_dim(bset, isl_dim_div);
736 isl_basic_set_free(bset);
737 if (n != 0)
738 isl_die(ctx, isl_error_unknown, "not expecting any divs",
739 return -1);
740
741 return 0;
742 }
743
744 void test_convex_hull_case(struct isl_ctx *ctx, const char *name)
745 {
746 char *filename;
747 FILE *input;
748 struct isl_basic_set *bset1, *bset2;
749 struct isl_set *set;
750
751 filename = get_filename(ctx, name, "polylib");
752 assert(filename);
753 input = fopen(filename, "r");
754 assert(input);
755
756 bset1 = isl_basic_set_read_from_file(ctx, input);
757 bset2 = isl_basic_set_read_from_file(ctx, input);
758
759 set = isl_basic_set_union(bset1, bset2);
760 bset1 = isl_set_convex_hull(set);
761
762 bset2 = isl_basic_set_read_from_file(ctx, input);
763
764 assert(isl_basic_set_is_equal(bset1, bset2) == 1);
765
766 isl_basic_set_free(bset1);
767 isl_basic_set_free(bset2);
768 free(filename);
769
770 fclose(input);
771 }
772
773 void test_convex_hull_algo(struct isl_ctx *ctx, int convex)
774 {
775 const char *str1, *str2;
776 isl_set *set1, *set2;
777 int orig_convex = ctx->opt->convex;
778 ctx->opt->convex = convex;
779
780 test_convex_hull_case(ctx, "convex0");
781 test_convex_hull_case(ctx, "convex1");
782 test_convex_hull_case(ctx, "convex2");
783 test_convex_hull_case(ctx, "convex3");
784 test_convex_hull_case(ctx, "convex4");
785 test_convex_hull_case(ctx, "convex5");
786 test_convex_hull_case(ctx, "convex6");
787 test_convex_hull_case(ctx, "convex7");
788 test_convex_hull_case(ctx, "convex8");
789 test_convex_hull_case(ctx, "convex9");
790 test_convex_hull_case(ctx, "convex10");
791 test_convex_hull_case(ctx, "convex11");
792 test_convex_hull_case(ctx, "convex12");
793 test_convex_hull_case(ctx, "convex13");
794 test_convex_hull_case(ctx, "convex14");
795 test_convex_hull_case(ctx, "convex15");
796
797 str1 = "{ [i0, i1, i2] : (i2 = 1 and i0 = 0 and i1 >= 0) or "
798 "(i0 = 1 and i1 = 0 and i2 = 1) or "
799 "(i0 = 0 and i1 = 0 and i2 = 0) }";
800 str2 = "{ [i0, i1, i2] : i0 >= 0 and i2 >= i0 and i2 <= 1 and i1 >= 0 }";
801 set1 = isl_set_read_from_str(ctx, str1);
802 set2 = isl_set_read_from_str(ctx, str2);
803 set1 = isl_set_from_basic_set(isl_set_convex_hull(set1));
804 assert(isl_set_is_equal(set1, set2));
805 isl_set_free(set1);
806 isl_set_free(set2);
807
808 ctx->opt->convex = orig_convex;
809 }
810
811 void test_convex_hull(struct isl_ctx *ctx)
812 {
813 test_convex_hull_algo(ctx, ISL_CONVEX_HULL_FM);
814 test_convex_hull_algo(ctx, ISL_CONVEX_HULL_WRAP);
815 }
816
817 void test_gist_case(struct isl_ctx *ctx, const char *name)
818 {
819 char *filename;
820 FILE *input;
821 struct isl_basic_set *bset1, *bset2;
822
823 filename = get_filename(ctx, name, "polylib");
824 assert(filename);
825 input = fopen(filename, "r");
826 assert(input);
827
828 bset1 = isl_basic_set_read_from_file(ctx, input);
829 bset2 = isl_basic_set_read_from_file(ctx, input);
830
831 bset1 = isl_basic_set_gist(bset1, bset2);
832
833 bset2 = isl_basic_set_read_from_file(ctx, input);
834
835 assert(isl_basic_set_is_equal(bset1, bset2) == 1);
836
837 isl_basic_set_free(bset1);
838 isl_basic_set_free(bset2);
839 free(filename);
840
841 fclose(input);
842 }
843
844 void test_gist(struct isl_ctx *ctx)
845 {
846 const char *str;
847 isl_basic_set *bset1, *bset2;
848
849 test_gist_case(ctx, "gist1");
850
851 str = "[p0, p2, p3, p5, p6, p10] -> { [] : "
852 "exists (e0 = [(15 + p0 + 15p6 + 15p10)/16], e1 = [(p5)/8], "
853 "e2 = [(p6)/128], e3 = [(8p2 - p5)/128], "
854 "e4 = [(128p3 - p6)/4096]: 8e1 = p5 and 128e2 = p6 and "
855 "128e3 = 8p2 - p5 and 4096e4 = 128p3 - p6 and p2 >= 0 and "
856 "16e0 >= 16 + 16p6 + 15p10 and p2 <= 15 and p3 >= 0 and "
857 "p3 <= 31 and p6 >= 128p3 and p5 >= 8p2 and p10 >= 0 and "
858 "16e0 <= 15 + p0 + 15p6 + 15p10 and 16e0 >= p0 + 15p6 + 15p10 and "
859 "p10 <= 15 and p10 <= -1 + p0 - p6) }";
860 bset1 = isl_basic_set_read_from_str(ctx, str);
861 str = "[p0, p2, p3, p5, p6, p10] -> { [] : exists (e0 = [(p5)/8], "
862 "e1 = [(p6)/128], e2 = [(8p2 - p5)/128], "
863 "e3 = [(128p3 - p6)/4096]: 8e0 = p5 and 128e1 = p6 and "
864 "128e2 = 8p2 - p5 and 4096e3 = 128p3 - p6 and p5 >= -7 and "
865 "p2 >= 0 and 8p2 <= -1 + p0 and p2 <= 15 and p3 >= 0 and "
866 "p3 <= 31 and 128p3 <= -1 + p0 and p6 >= -127 and "
867 "p5 <= -1 + p0 and p6 <= -1 + p0 and p6 >= 128p3 and "
868 "p0 >= 1 and p5 >= 8p2 and p10 >= 0 and p10 <= 15 ) }";
869 bset2 = isl_basic_set_read_from_str(ctx, str);
870 bset1 = isl_basic_set_gist(bset1, bset2);
871 assert(bset1 && bset1->n_div == 0);
872 isl_basic_set_free(bset1);
873 }
874
875 int test_coalesce_set(isl_ctx *ctx, const char *str, int check_one)
876 {
877 isl_set *set, *set2;
878 int equal;
879 int one;
880
881 set = isl_set_read_from_str(ctx, str);
882 set = isl_set_coalesce(set);
883 set2 = isl_set_read_from_str(ctx, str);
884 equal = isl_set_is_equal(set, set2);
885 one = set && set->n == 1;
886 isl_set_free(set);
887 isl_set_free(set2);
888
889 if (equal < 0)
890 return -1;
891 if (!equal)
892 isl_die(ctx, isl_error_unknown,
893 "coalesced set not equal to input", return -1);
894 if (check_one && !one)
895 isl_die(ctx, isl_error_unknown,
896 "coalesced set should not be a union", return -1);
897
898 return 0;
899 }
900
901 int test_coalesce_unbounded_wrapping(isl_ctx *ctx)
902 {
903 int r = 0;
904 int bounded;
905
906 bounded = isl_options_get_coalesce_bounded_wrapping(ctx);
907 isl_options_set_coalesce_bounded_wrapping(ctx, 0);
908
909 if (test_coalesce_set(ctx,
910 "{[x,y,z] : y + 2 >= 0 and x - y + 1 >= 0 and "
911 "-x - y + 1 >= 0 and -3 <= z <= 3;"
912 "[x,y,z] : -x+z + 20 >= 0 and -x-z + 20 >= 0 and "
913 "x-z + 20 >= 0 and x+z + 20 >= 0 and "
914 "-10 <= y <= 0}", 1) < 0)
915 goto error;
916 if (test_coalesce_set(ctx,
917 "{[x,y] : 0 <= x,y <= 10; [5,y]: 4 <=y <= 11}", 1) < 0)
918 goto error;
919 if (test_coalesce_set(ctx,
920 "{[x,0,0] : -5 <= x <= 5; [0,y,1] : -5 <= y <= 5 }", 1) < 0)
921 goto error;
922
923 if (0) {
924 error:
925 r = -1;
926 }
927
928 isl_options_set_coalesce_bounded_wrapping(ctx, bounded);
929
930 return r;
931 }
932
933 int test_coalesce(struct isl_ctx *ctx)
934 {
935 const char *str;
936 struct isl_set *set, *set2;
937 struct isl_map *map, *map2;
938
939 set = isl_set_read_from_str(ctx,
940 "{[x,y]: x >= 0 & x <= 10 & y >= 0 & y <= 10 or "
941 "y >= x & x >= 2 & 5 >= y }");
942 set = isl_set_coalesce(set);
943 assert(set && set->n == 1);
944 isl_set_free(set);
945
946 set = isl_set_read_from_str(ctx,
947 "{[x,y]: y >= 0 & 2x + y <= 30 & y <= 10 & x >= 0 or "
948 "x + y >= 10 & y <= x & x + y <= 20 & y >= 0}");
949 set = isl_set_coalesce(set);
950 assert(set && set->n == 1);
951 isl_set_free(set);
952
953 set = isl_set_read_from_str(ctx,
954 "{[x,y]: y >= 0 & 2x + y <= 30 & y <= 10 & x >= 0 or "
955 "x + y >= 10 & y <= x & x + y <= 19 & y >= 0}");
956 set = isl_set_coalesce(set);
957 assert(set && set->n == 2);
958 isl_set_free(set);
959
960 set = isl_set_read_from_str(ctx,
961 "{[x,y]: y >= 0 & x <= 5 & y <= x or "
962 "y >= 0 & x >= 6 & x <= 10 & y <= x}");
963 set = isl_set_coalesce(set);
964 assert(set && set->n == 1);
965 isl_set_free(set);
966
967 set = isl_set_read_from_str(ctx,
968 "{[x,y]: y >= 0 & x <= 5 & y <= x or "
969 "y >= 0 & x >= 7 & x <= 10 & y <= x}");
970 set = isl_set_coalesce(set);
971 assert(set && set->n == 2);
972 isl_set_free(set);
973
974 set = isl_set_read_from_str(ctx,
975 "{[x,y]: y >= 0 & x <= 5 & y <= x or "
976 "y >= 0 & x >= 6 & x <= 10 & y + 1 <= x}");
977 set = isl_set_coalesce(set);
978 assert(set && set->n == 2);
979 isl_set_free(set);
980
981 set = isl_set_read_from_str(ctx,
982 "{[x,y]: y >= 0 & x <= 5 & y <= x or "
983 "y >= 0 & x = 6 & y <= 6}");
984 set = isl_set_coalesce(set);
985 assert(set && set->n == 1);
986 isl_set_free(set);
987
988 set = isl_set_read_from_str(ctx,
989 "{[x,y]: y >= 0 & x <= 5 & y <= x or "
990 "y >= 0 & x = 7 & y <= 6}");
991 set = isl_set_coalesce(set);
992 assert(set && set->n == 2);
993 isl_set_free(set);
994
995 set = isl_set_read_from_str(ctx,
996 "{[x,y]: y >= 0 & x <= 5 & y <= x or "
997 "y >= 0 & x = 6 & y <= 5}");
998 set = isl_set_coalesce(set);
999 assert(set && set->n == 1);
1000 set2 = isl_set_read_from_str(ctx,
1001 "{[x,y]: y >= 0 & x <= 5 & y <= x or "
1002 "y >= 0 & x = 6 & y <= 5}");
1003 assert(isl_set_is_equal(set, set2));
1004 isl_set_free(set);
1005 isl_set_free(set2);
1006
1007 set = isl_set_read_from_str(ctx,
1008 "{[x,y]: y >= 0 & x <= 5 & y <= x or "
1009 "y >= 0 & x = 6 & y <= 7}");
1010 set = isl_set_coalesce(set);
1011 assert(set && set->n == 2);
1012 isl_set_free(set);
1013
1014 set = isl_set_read_from_str(ctx,
1015 "[n] -> { [i] : i = 1 and n >= 2 or 2 <= i and i <= n }");
1016 set = isl_set_coalesce(set);
1017 assert(set && set->n == 1);
1018 set2 = isl_set_read_from_str(ctx,
1019 "[n] -> { [i] : i = 1 and n >= 2 or 2 <= i and i <= n }");
1020 assert(isl_set_is_equal(set, set2));
1021 isl_set_free(set);
1022 isl_set_free(set2);
1023
1024 set = isl_set_read_from_str(ctx,
1025 "{[x,y] : x >= 0 and y >= 0 or 0 <= y and y <= 5 and x = -1}");
1026 set = isl_set_coalesce(set);
1027 set2 = isl_set_read_from_str(ctx,
1028 "{[x,y] : x >= 0 and y >= 0 or 0 <= y and y <= 5 and x = -1}");
1029 assert(isl_set_is_equal(set, set2));
1030 isl_set_free(set);
1031 isl_set_free(set2);
1032
1033 set = isl_set_read_from_str(ctx,
1034 "[n] -> { [i] : 1 <= i and i <= n - 1 or "
1035 "2 <= i and i <= n }");
1036 set = isl_set_coalesce(set);
1037 assert(set && set->n == 1);
1038 set2 = isl_set_read_from_str(ctx,
1039 "[n] -> { [i] : 1 <= i and i <= n - 1 or "
1040 "2 <= i and i <= n }");
1041 assert(isl_set_is_equal(set, set2));
1042 isl_set_free(set);
1043 isl_set_free(set2);
1044
1045 map = isl_map_read_from_str(ctx,
1046 "[n] -> { [i0] -> [o0] : exists (e0 = [(i0)/4], e1 = [(o0)/4], "
1047 "e2 = [(n)/2], e3 = [(-2 + i0)/4], e4 = [(-2 + o0)/4], "
1048 "e5 = [(-2n + i0)/4]: 2e2 = n and 4e3 = -2 + i0 and "
1049 "4e4 = -2 + o0 and i0 >= 8 + 2n and o0 >= 2 + i0 and "
1050 "o0 <= 56 + 2n and o0 <= -12 + 4n and i0 <= 57 + 2n and "
1051 "i0 <= -11 + 4n and o0 >= 6 + 2n and 4e0 <= i0 and "
1052 "4e0 >= -3 + i0 and 4e1 <= o0 and 4e1 >= -3 + o0 and "
1053 "4e5 <= -2n + i0 and 4e5 >= -3 - 2n + i0);"
1054 "[i0] -> [o0] : exists (e0 = [(i0)/4], e1 = [(o0)/4], "
1055 "e2 = [(n)/2], e3 = [(-2 + i0)/4], e4 = [(-2 + o0)/4], "
1056 "e5 = [(-2n + i0)/4]: 2e2 = n and 4e3 = -2 + i0 and "
1057 "4e4 = -2 + o0 and 2e0 >= 3 + n and e0 <= -4 + n and "
1058 "2e0 <= 27 + n and e1 <= -4 + n and 2e1 <= 27 + n and "
1059 "2e1 >= 2 + n and e1 >= 1 + e0 and i0 >= 7 + 2n and "
1060 "i0 <= -11 + 4n and i0 <= 57 + 2n and 4e0 <= -2 + i0 and "
1061 "4e0 >= -3 + i0 and o0 >= 6 + 2n and o0 <= -11 + 4n and "
1062 "o0 <= 57 + 2n and 4e1 <= -2 + o0 and 4e1 >= -3 + o0 and "
1063 "4e5 <= -2n + i0 and 4e5 >= -3 - 2n + i0 ) }");
1064 map = isl_map_coalesce(map);
1065 map2 = isl_map_read_from_str(ctx,
1066 "[n] -> { [i0] -> [o0] : exists (e0 = [(i0)/4], e1 = [(o0)/4], "
1067 "e2 = [(n)/2], e3 = [(-2 + i0)/4], e4 = [(-2 + o0)/4], "
1068 "e5 = [(-2n + i0)/4]: 2e2 = n and 4e3 = -2 + i0 and "
1069 "4e4 = -2 + o0 and i0 >= 8 + 2n and o0 >= 2 + i0 and "
1070 "o0 <= 56 + 2n and o0 <= -12 + 4n and i0 <= 57 + 2n and "
1071 "i0 <= -11 + 4n and o0 >= 6 + 2n and 4e0 <= i0 and "
1072 "4e0 >= -3 + i0 and 4e1 <= o0 and 4e1 >= -3 + o0 and "
1073 "4e5 <= -2n + i0 and 4e5 >= -3 - 2n + i0);"
1074 "[i0] -> [o0] : exists (e0 = [(i0)/4], e1 = [(o0)/4], "
1075 "e2 = [(n)/2], e3 = [(-2 + i0)/4], e4 = [(-2 + o0)/4], "
1076 "e5 = [(-2n + i0)/4]: 2e2 = n and 4e3 = -2 + i0 and "
1077 "4e4 = -2 + o0 and 2e0 >= 3 + n and e0 <= -4 + n and "
1078 "2e0 <= 27 + n and e1 <= -4 + n and 2e1 <= 27 + n and "
1079 "2e1 >= 2 + n and e1 >= 1 + e0 and i0 >= 7 + 2n and "
1080 "i0 <= -11 + 4n and i0 <= 57 + 2n and 4e0 <= -2 + i0 and "
1081 "4e0 >= -3 + i0 and o0 >= 6 + 2n and o0 <= -11 + 4n and "
1082 "o0 <= 57 + 2n and 4e1 <= -2 + o0 and 4e1 >= -3 + o0 and "
1083 "4e5 <= -2n + i0 and 4e5 >= -3 - 2n + i0 ) }");
1084 assert(isl_map_is_equal(map, map2));
1085 isl_map_free(map);
1086 isl_map_free(map2);
1087
1088 str = "[n, m] -> { [] -> [o0, o2, o3] : (o3 = 1 and o0 >= 1 + m and "
1089 "o0 <= n + m and o2 <= m and o0 >= 2 + n and o2 >= 3) or "
1090 "(o0 >= 2 + n and o0 >= 1 + m and o0 <= n + m and n >= 1 and "
1091 "o3 <= -1 + o2 and o3 >= 1 - m + o2 and o3 >= 2 and o3 <= n) }";
1092 map = isl_map_read_from_str(ctx, str);
1093 map = isl_map_coalesce(map);
1094 map2 = isl_map_read_from_str(ctx, str);
1095 assert(isl_map_is_equal(map, map2));
1096 isl_map_free(map);
1097 isl_map_free(map2);
1098
1099 str = "[M, N] -> { [i0, i1, i2, i3, i4, i5, i6] -> "
1100 "[o0, o1, o2, o3, o4, o5, o6] : "
1101 "(o6 <= -4 + 2M - 2N + i0 + i1 - i2 + i6 - o0 - o1 + o2 and "
1102 "o3 <= -2 + i3 and o6 >= 2 + i0 + i3 + i6 - o0 - o3 and "
1103 "o6 >= 2 - M + N + i3 + i4 + i6 - o3 - o4 and o0 <= -1 + i0 and "
1104 "o4 >= 4 - 3M + 3N - i0 - i1 + i2 + 2i3 + i4 + o0 + o1 - o2 - 2o3 "
1105 "and o6 <= -3 + 2M - 2N + i3 + i4 - i5 + i6 - o3 - o4 + o5 and "
1106 "2o6 <= -5 + 5M - 5N + 2i0 + i1 - i2 - i5 + 2i6 - 2o0 - o1 + o2 + o5 "
1107 "and o6 >= 2i0 + i1 + i6 - 2o0 - o1 and "
1108 "3o6 <= -5 + 4M - 4N + 2i0 + i1 - i2 + 2i3 + i4 - i5 + 3i6 "
1109 "- 2o0 - o1 + o2 - 2o3 - o4 + o5) or "
1110 "(N >= 2 and o3 <= -1 + i3 and o0 <= -1 + i0 and "
1111 "o6 >= i3 + i6 - o3 and M >= 0 and "
1112 "2o6 >= 1 + i0 + i3 + 2i6 - o0 - o3 and "
1113 "o6 >= 1 - M + i0 + i6 - o0 and N >= 2M and o6 >= i0 + i6 - o0) }";
1114 map = isl_map_read_from_str(ctx, str);
1115 map = isl_map_coalesce(map);
1116 map2 = isl_map_read_from_str(ctx, str);
1117 assert(isl_map_is_equal(map, map2));
1118 isl_map_free(map);
1119 isl_map_free(map2);
1120
1121 str = "[M, N] -> { [] -> [o0] : (o0 = 0 and M >= 1 and N >= 2) or "
1122 "(o0 = 0 and M >= 1 and N >= 2M and N >= 2 + M) or "
1123 "(o0 = 0 and M >= 2 and N >= 3) or "
1124 "(M = 0 and o0 = 0 and N >= 3) }";
1125 map = isl_map_read_from_str(ctx, str);
1126 map = isl_map_coalesce(map);
1127 map2 = isl_map_read_from_str(ctx, str);
1128 assert(isl_map_is_equal(map, map2));
1129 isl_map_free(map);
1130 isl_map_free(map2);
1131
1132 str = "{ [i0, i1, i2, i3] : (i1 = 10i0 and i0 >= 1 and 10i0 <= 100 and "
1133 "i3 <= 9 + 10 i2 and i3 >= 1 + 10i2 and i3 >= 0) or "
1134 "(i1 <= 9 + 10i0 and i1 >= 1 + 10i0 and i2 >= 0 and "
1135 "i0 >= 0 and i1 <= 100 and i3 <= 9 + 10i2 and i3 >= 1 + 10i2) }";
1136 map = isl_map_read_from_str(ctx, str);
1137 map = isl_map_coalesce(map);
1138 map2 = isl_map_read_from_str(ctx, str);
1139 assert(isl_map_is_equal(map, map2));
1140 isl_map_free(map);
1141 isl_map_free(map2);
1142
1143 test_coalesce_set(ctx,
1144 "[M] -> { [i1] : (i1 >= 2 and i1 <= M) or "
1145 "(i1 = M and M >= 1) }", 0);
1146 test_coalesce_set(ctx,
1147 "{[x,y] : x,y >= 0; [x,y] : 10 <= x <= 20 and y >= -1 }", 0);
1148 test_coalesce_set(ctx,
1149 "{ [x, y] : (x >= 1 and y >= 1 and x <= 2 and y <= 2) or "
1150 "(y = 3 and x = 1) }", 1);
1151 test_coalesce_set(ctx,
1152 "[M] -> { [i0, i1, i2, i3, i4] : (i1 >= 3 and i4 >= 2 + i2 and "
1153 "i2 >= 2 and i0 >= 2 and i3 >= 1 + i2 and i0 <= M and "
1154 "i1 <= M and i3 <= M and i4 <= M) or "
1155 "(i1 >= 2 and i4 >= 1 + i2 and i2 >= 2 and i0 >= 2 and "
1156 "i3 >= 1 + i2 and i0 <= M and i1 <= -1 + M and i3 <= M and "
1157 "i4 <= -1 + M) }", 1);
1158 test_coalesce_set(ctx,
1159 "{ [x, y] : (x >= 0 and y >= 0 and x <= 10 and y <= 10) or "
1160 "(x >= 1 and y >= 1 and x <= 11 and y <= 11) }", 1);
1161 if (test_coalesce_unbounded_wrapping(ctx) < 0)
1162 return -1;
1163 if (test_coalesce_set(ctx, "{[x,0] : x >= 0; [x,1] : x <= 20}", 0) < 0)
1164 return -1;
1165 if (test_coalesce_set(ctx, "{ [x, 1 - x] : 0 <= x <= 1; [0,0] }", 1) < 0)
1166 return -1;
1167 if (test_coalesce_set(ctx, "{ [0,0]; [i,i] : 1 <= i <= 10 }", 1) < 0)
1168 return -1;
1169 if (test_coalesce_set(ctx, "{ [0,0]; [i,j] : 1 <= i,j <= 10 }", 0) < 0)
1170 return -1;
1171 if (test_coalesce_set(ctx, "{ [0,0]; [i,2i] : 1 <= i <= 10 }", 1) < 0)
1172 return -1;
1173 if (test_coalesce_set(ctx, "{ [0,0]; [i,2i] : 2 <= i <= 10 }", 0) < 0)
1174 return -1;
1175 if (test_coalesce_set(ctx, "{ [1,0]; [i,2i] : 1 <= i <= 10 }", 0) < 0)
1176 return -1;
1177 if (test_coalesce_set(ctx, "{ [0,1]; [i,2i] : 1 <= i <= 10 }", 0) < 0)
1178 return -1;
1179 if (test_coalesce_set(ctx, "{ [a, b] : exists e : 2e = a and "
1180 "a >= 0 and (a <= 3 or (b <= 0 and b >= -4 + a)) }", 0) < 0)
1181 return -1;
1182 if (test_coalesce_set(ctx,
1183 "{ [i, j, i', j'] : i <= 2 and j <= 2 and "
1184 "j' >= -1 + 2i + j - 2i' and i' <= -1 + i and "
1185 "j >= 1 and j' <= i + j - i' and i >= 1; "
1186 "[1, 1, 1, 1] }", 0) < 0)
1187 return -1;
1188 if (test_coalesce_set(ctx, "{ [i,j] : exists a,b : i = 2a and j = 3b; "
1189 "[i,j] : exists a : j = 3a }", 1) < 0)
1190 return -1;
1191 if (test_coalesce_set(ctx,
1192 "{ [a, b, c] : (c <= 7 - b and b <= 1 and b >= 0 and "
1193 "c >= 3 + b and b <= 3 + 8a and b >= -26 + 8a and "
1194 "a >= 3) or "
1195 "(b <= 1 and c <= 7 and b >= 0 and c >= 4 + b and "
1196 "b <= 3 + 8a and b >= -26 + 8a and a >= 3) }", 1) < 0)
1197 return -1;
1198 if (test_coalesce_set(ctx,
1199 "{ [a, 0, c] : c >= 1 and c <= 29 and c >= -1 + 8a and "
1200 "c <= 6 + 8a and a >= 3; "
1201 "[a, -1, c] : c >= 1 and c <= 30 and c >= 8a and "
1202 "c <= 7 + 8a and a >= 3 and a <= 4 }", 1) < 0)
1203 return -1;
1204 return 0;
1205 }
1206
1207 void test_closure(struct isl_ctx *ctx)
1208 {
1209 const char *str;
1210 isl_set *dom;
1211 isl_map *up, *right;
1212 isl_map *map, *map2;
1213 int exact;
1214
1215 /* COCOA example 1 */
1216 map = isl_map_read_from_str(ctx,
1217 "[n] -> { [i,j] -> [i2,j2] : i2 = i + 1 and j2 = j + 1 and "
1218 "1 <= i and i < n and 1 <= j and j < n or "
1219 "i2 = i + 1 and j2 = j - 1 and "
1220 "1 <= i and i < n and 2 <= j and j <= n }");
1221 map = isl_map_power(map, &exact);
1222 assert(exact);
1223 isl_map_free(map);
1224
1225 /* COCOA example 1 */
1226 map = isl_map_read_from_str(ctx,
1227 "[n] -> { [i,j] -> [i2,j2] : i2 = i + 1 and j2 = j + 1 and "
1228 "1 <= i and i < n and 1 <= j and j < n or "
1229 "i2 = i + 1 and j2 = j - 1 and "
1230 "1 <= i and i < n and 2 <= j and j <= n }");
1231 map = isl_map_transitive_closure(map, &exact);
1232 assert(exact);
1233 map2 = isl_map_read_from_str(ctx,
1234 "[n] -> { [i,j] -> [i2,j2] : exists (k1,k2,k : "
1235 "1 <= i and i < n and 1 <= j and j <= n and "
1236 "2 <= i2 and i2 <= n and 1 <= j2 and j2 <= n and "
1237 "i2 = i + k1 + k2 and j2 = j + k1 - k2 and "
1238 "k1 >= 0 and k2 >= 0 and k1 + k2 = k and k >= 1 )}");
1239 assert(isl_map_is_equal(map, map2));
1240 isl_map_free(map2);
1241 isl_map_free(map);
1242
1243 map = isl_map_read_from_str(ctx,
1244 "[n] -> { [x] -> [y] : y = x + 1 and 0 <= x and x <= n and "
1245 " 0 <= y and y <= n }");
1246 map = isl_map_transitive_closure(map, &exact);
1247 map2 = isl_map_read_from_str(ctx,
1248 "[n] -> { [x] -> [y] : y > x and 0 <= x and x <= n and "
1249 " 0 <= y and y <= n }");
1250 assert(isl_map_is_equal(map, map2));
1251 isl_map_free(map2);
1252 isl_map_free(map);
1253
1254 /* COCOA example 2 */
1255 map = isl_map_read_from_str(ctx,
1256 "[n] -> { [i,j] -> [i2,j2] : i2 = i + 2 and j2 = j + 2 and "
1257 "1 <= i and i < n - 1 and 1 <= j and j < n - 1 or "
1258 "i2 = i + 2 and j2 = j - 2 and "
1259 "1 <= i and i < n - 1 and 3 <= j and j <= n }");
1260 map = isl_map_transitive_closure(map, &exact);
1261 assert(exact);
1262 map2 = isl_map_read_from_str(ctx,
1263 "[n] -> { [i,j] -> [i2,j2] : exists (k1,k2,k : "
1264 "1 <= i and i < n - 1 and 1 <= j and j <= n and "
1265 "3 <= i2 and i2 <= n and 1 <= j2 and j2 <= n and "
1266 "i2 = i + 2 k1 + 2 k2 and j2 = j + 2 k1 - 2 k2 and "
1267 "k1 >= 0 and k2 >= 0 and k1 + k2 = k and k >= 1) }");
1268 assert(isl_map_is_equal(map, map2));
1269 isl_map_free(map);
1270 isl_map_free(map2);
1271
1272 /* COCOA Fig.2 left */
1273 map = isl_map_read_from_str(ctx,
1274 "[n] -> { [i,j] -> [i2,j2] : i2 = i + 2 and j2 = j and "
1275 "i <= 2 j - 3 and i <= n - 2 and j <= 2 i - 1 and "
1276 "j <= n or "
1277 "i2 = i and j2 = j + 2 and i <= 2 j - 1 and i <= n and "
1278 "j <= 2 i - 3 and j <= n - 2 or "
1279 "i2 = i + 1 and j2 = j + 1 and i <= 2 j - 1 and "
1280 "i <= n - 1 and j <= 2 i - 1 and j <= n - 1 }");
1281 map = isl_map_transitive_closure(map, &exact);
1282 assert(exact);
1283 isl_map_free(map);
1284
1285 /* COCOA Fig.2 right */
1286 map = isl_map_read_from_str(ctx,
1287 "[n] -> { [i,j] -> [i2,j2] : i2 = i + 3 and j2 = j and "
1288 "i <= 2 j - 4 and i <= n - 3 and j <= 2 i - 1 and "
1289 "j <= n or "
1290 "i2 = i and j2 = j + 3 and i <= 2 j - 1 and i <= n and "
1291 "j <= 2 i - 4 and j <= n - 3 or "
1292 "i2 = i + 1 and j2 = j + 1 and i <= 2 j - 1 and "
1293 "i <= n - 1 and j <= 2 i - 1 and j <= n - 1 }");
1294 map = isl_map_power(map, &exact);
1295 assert(exact);
1296 isl_map_free(map);
1297
1298 /* COCOA Fig.2 right */
1299 map = isl_map_read_from_str(ctx,
1300 "[n] -> { [i,j] -> [i2,j2] : i2 = i + 3 and j2 = j and "
1301 "i <= 2 j - 4 and i <= n - 3 and j <= 2 i - 1 and "
1302 "j <= n or "
1303 "i2 = i and j2 = j + 3 and i <= 2 j - 1 and i <= n and "
1304 "j <= 2 i - 4 and j <= n - 3 or "
1305 "i2 = i + 1 and j2 = j + 1 and i <= 2 j - 1 and "
1306 "i <= n - 1 and j <= 2 i - 1 and j <= n - 1 }");
1307 map = isl_map_transitive_closure(map, &exact);
1308 assert(exact);
1309 map2 = isl_map_read_from_str(ctx,
1310 "[n] -> { [i,j] -> [i2,j2] : exists (k1,k2,k3,k : "
1311 "i <= 2 j - 1 and i <= n and j <= 2 i - 1 and "
1312 "j <= n and 3 + i + 2 j <= 3 n and "
1313 "3 + 2 i + j <= 3n and i2 <= 2 j2 -1 and i2 <= n and "
1314 "i2 <= 3 j2 - 4 and j2 <= 2 i2 -1 and j2 <= n and "
1315 "13 + 4 j2 <= 11 i2 and i2 = i + 3 k1 + k3 and "
1316 "j2 = j + 3 k2 + k3 and k1 >= 0 and k2 >= 0 and "
1317 "k3 >= 0 and k1 + k2 + k3 = k and k > 0) }");
1318 assert(isl_map_is_equal(map, map2));
1319 isl_map_free(map2);
1320 isl_map_free(map);
1321
1322 /* COCOA Fig.1 right */
1323 dom = isl_set_read_from_str(ctx,
1324 "{ [x,y] : x >= 0 and -2 x + 3 y >= 0 and x <= 3 and "
1325 "2 x - 3 y + 3 >= 0 }");
1326 right = isl_map_read_from_str(ctx,
1327 "{ [x,y] -> [x2,y2] : x2 = x + 1 and y2 = y }");
1328 up = isl_map_read_from_str(ctx,
1329 "{ [x,y] -> [x2,y2] : x2 = x and y2 = y + 1 }");
1330 right = isl_map_intersect_domain(right, isl_set_copy(dom));
1331 right = isl_map_intersect_range(right, isl_set_copy(dom));
1332 up = isl_map_intersect_domain(up, isl_set_copy(dom));
1333 up = isl_map_intersect_range(up, dom);
1334 map = isl_map_union(up, right);
1335 map = isl_map_transitive_closure(map, &exact);
1336 assert(exact);
1337 map2 = isl_map_read_from_str(ctx,
1338 "{ [0,0] -> [0,1]; [0,0] -> [1,1]; [0,1] -> [1,1]; "
1339 " [2,2] -> [3,2]; [2,2] -> [3,3]; [3,2] -> [3,3] }");
1340 assert(isl_map_is_equal(map, map2));
1341 isl_map_free(map2);
1342 isl_map_free(map);
1343
1344 /* COCOA Theorem 1 counter example */
1345 map = isl_map_read_from_str(ctx,
1346 "{ [i,j] -> [i2,j2] : i = 0 and 0 <= j and j <= 1 and "
1347 "i2 = 1 and j2 = j or "
1348 "i = 0 and j = 0 and i2 = 0 and j2 = 1 }");
1349 map = isl_map_transitive_closure(map, &exact);
1350 assert(exact);
1351 isl_map_free(map);
1352
1353 map = isl_map_read_from_str(ctx,
1354 "[m,n] -> { [i,j] -> [i2,j2] : i2 = i and j2 = j + 2 and "
1355 "1 <= i,i2 <= n and 1 <= j,j2 <= m or "
1356 "i2 = i + 1 and 3 <= j2 - j <= 4 and "
1357 "1 <= i,i2 <= n and 1 <= j,j2 <= m }");
1358 map = isl_map_transitive_closure(map, &exact);
1359 assert(exact);
1360 isl_map_free(map);
1361
1362 /* Kelly et al 1996, fig 12 */
1363 map = isl_map_read_from_str(ctx,
1364 "[n] -> { [i,j] -> [i2,j2] : i2 = i and j2 = j + 1 and "
1365 "1 <= i,j,j+1 <= n or "
1366 "j = n and j2 = 1 and i2 = i + 1 and "
1367 "1 <= i,i+1 <= n }");
1368 map = isl_map_transitive_closure(map, &exact);
1369 assert(exact);
1370 map2 = isl_map_read_from_str(ctx,
1371 "[n] -> { [i,j] -> [i2,j2] : 1 <= j < j2 <= n and "
1372 "1 <= i <= n and i = i2 or "
1373 "1 <= i < i2 <= n and 1 <= j <= n and "
1374 "1 <= j2 <= n }");
1375 assert(isl_map_is_equal(map, map2));
1376 isl_map_free(map2);
1377 isl_map_free(map);
1378
1379 /* Omega's closure4 */
1380 map = isl_map_read_from_str(ctx,
1381 "[m,n] -> { [x,y] -> [x2,y2] : x2 = x and y2 = y + 1 and "
1382 "1 <= x,y <= 10 or "
1383 "x2 = x + 1 and y2 = y and "
1384 "1 <= x <= 20 && 5 <= y <= 15 }");
1385 map = isl_map_transitive_closure(map, &exact);
1386 assert(exact);
1387 isl_map_free(map);
1388
1389 map = isl_map_read_from_str(ctx,
1390 "[n] -> { [x] -> [y]: 1 <= n <= y - x <= 10 }");
1391 map = isl_map_transitive_closure(map, &exact);
1392 assert(!exact);
1393 map2 = isl_map_read_from_str(ctx,
1394 "[n] -> { [x] -> [y] : 1 <= n <= 10 and y >= n + x }");
1395 assert(isl_map_is_equal(map, map2));
1396 isl_map_free(map);
1397 isl_map_free(map2);
1398
1399 str = "[n, m] -> { [i0, i1, i2, i3] -> [o0, o1, o2, o3] : "
1400 "i3 = 1 and o0 = i0 and o1 = -1 + i1 and o2 = -1 + i2 and "
1401 "o3 = -2 + i2 and i1 <= -1 + i0 and i1 >= 1 - m + i0 and "
1402 "i1 >= 2 and i1 <= n and i2 >= 3 and i2 <= 1 + n and i2 <= m }";
1403 map = isl_map_read_from_str(ctx, str);
1404 map = isl_map_transitive_closure(map, &exact);
1405 assert(exact);
1406 map2 = isl_map_read_from_str(ctx, str);
1407 assert(isl_map_is_equal(map, map2));
1408 isl_map_free(map);
1409 isl_map_free(map2);
1410
1411 str = "{[0] -> [1]; [2] -> [3]}";
1412 map = isl_map_read_from_str(ctx, str);
1413 map = isl_map_transitive_closure(map, &exact);
1414 assert(exact);
1415 map2 = isl_map_read_from_str(ctx, str);
1416 assert(isl_map_is_equal(map, map2));
1417 isl_map_free(map);
1418 isl_map_free(map2);
1419
1420 str = "[n] -> { [[i0, i1, 1, 0, i0] -> [i5, 1]] -> "
1421 "[[i0, -1 + i1, 2, 0, i0] -> [-1 + i5, 2]] : "
1422 "exists (e0 = [(3 - n)/3]: i5 >= 2 and i1 >= 2 and "
1423 "3i0 <= -1 + n and i1 <= -1 + n and i5 <= -1 + n and "
1424 "3e0 >= 1 - n and 3e0 <= 2 - n and 3i0 >= -2 + n); "
1425 "[[i0, i1, 2, 0, i0] -> [i5, 1]] -> "
1426 "[[i0, i1, 1, 0, i0] -> [-1 + i5, 2]] : "
1427 "exists (e0 = [(3 - n)/3]: i5 >= 2 and i1 >= 1 and "
1428 "3i0 <= -1 + n and i1 <= -1 + n and i5 <= -1 + n and "
1429 "3e0 >= 1 - n and 3e0 <= 2 - n and 3i0 >= -2 + n); "
1430 "[[i0, i1, 1, 0, i0] -> [i5, 2]] -> "
1431 "[[i0, -1 + i1, 2, 0, i0] -> [i5, 1]] : "
1432 "exists (e0 = [(3 - n)/3]: i1 >= 2 and i5 >= 1 and "
1433 "3i0 <= -1 + n and i1 <= -1 + n and i5 <= -1 + n and "
1434 "3e0 >= 1 - n and 3e0 <= 2 - n and 3i0 >= -2 + n); "
1435 "[[i0, i1, 2, 0, i0] -> [i5, 2]] -> "
1436 "[[i0, i1, 1, 0, i0] -> [i5, 1]] : "
1437 "exists (e0 = [(3 - n)/3]: i5 >= 1 and i1 >= 1 and "
1438 "3i0 <= -1 + n and i1 <= -1 + n and i5 <= -1 + n and "
1439 "3e0 >= 1 - n and 3e0 <= 2 - n and 3i0 >= -2 + n) }";
1440 map = isl_map_read_from_str(ctx, str);
1441 map = isl_map_transitive_closure(map, NULL);
1442 assert(map);
1443 isl_map_free(map);
1444 }
1445
1446 void test_lex(struct isl_ctx *ctx)
1447 {
1448 isl_space *dim;
1449 isl_map *map;
1450
1451 dim = isl_space_set_alloc(ctx, 0, 0);
1452 map = isl_map_lex_le(dim);
1453 assert(!isl_map_is_empty(map));
1454 isl_map_free(map);
1455 }
1456
1457 void test_lexmin(struct isl_ctx *ctx)
1458 {
1459 const char *str;
1460 isl_basic_map *bmap;
1461 isl_map *map, *map2;
1462 isl_set *set;
1463 isl_set *set2;
1464 isl_pw_multi_aff *pma;
1465
1466 str = "[p0, p1] -> { [] -> [] : "
1467 "exists (e0 = [(2p1)/3], e1, e2, e3 = [(3 - p1 + 3e0)/3], "
1468 "e4 = [(p1)/3], e5 = [(p1 + 3e4)/3]: "
1469 "3e0 >= -2 + 2p1 and 3e0 >= p1 and 3e3 >= 1 - p1 + 3e0 and "
1470 "3e0 <= 2p1 and 3e3 >= -2 + p1 and 3e3 <= -1 + p1 and p1 >= 3 and "
1471 "3e5 >= -2 + 2p1 and 3e5 >= p1 and 3e5 <= -1 + p1 + 3e4 and "
1472 "3e4 <= p1 and 3e4 >= -2 + p1 and e3 <= -1 + e0 and "
1473 "3e4 >= 6 - p1 + 3e1 and 3e1 >= p1 and 3e5 >= -2 + p1 + 3e4 and "
1474 "2e4 >= 3 - p1 + 2e1 and e4 <= e1 and 3e3 <= 2 - p1 + 3e0 and "
1475 "e5 >= 1 + e1 and 3e4 >= 6 - 2p1 + 3e1 and "
1476 "p0 >= 2 and p1 >= p0 and 3e2 >= p1 and 3e4 >= 6 - p1 + 3e2 and "
1477 "e2 <= e1 and e3 >= 1 and e4 <= e2) }";
1478 map = isl_map_read_from_str(ctx, str);
1479 map = isl_map_lexmin(map);
1480 isl_map_free(map);
1481
1482 str = "[C] -> { [obj,a,b,c] : obj <= 38 a + 7 b + 10 c and "
1483 "a + b <= 1 and c <= 10 b and c <= C and a,b,c,C >= 0 }";
1484 set = isl_set_read_from_str(ctx, str);
1485 set = isl_set_lexmax(set);
1486 str = "[C] -> { [obj,a,b,c] : C = 8 }";
1487 set2 = isl_set_read_from_str(ctx, str);
1488 set = isl_set_intersect(set, set2);
1489 assert(!isl_set_is_empty(set));
1490 isl_set_free(set);
1491
1492 str = "{ [x] -> [y] : x <= y <= 10; [x] -> [5] : -8 <= x <= 8 }";
1493 map = isl_map_read_from_str(ctx, str);
1494 map = isl_map_lexmin(map);
1495 str = "{ [x] -> [5] : 6 <= x <= 8; "
1496 "[x] -> [x] : x <= 5 or (9 <= x <= 10) }";
1497 map2 = isl_map_read_from_str(ctx, str);
1498 assert(isl_map_is_equal(map, map2));
1499 isl_map_free(map);
1500 isl_map_free(map2);
1501
1502 str = "{ [x] -> [y] : 4y = x or 4y = -1 + x or 4y = -2 + x }";
1503 map = isl_map_read_from_str(ctx, str);
1504 map2 = isl_map_copy(map);
1505 map = isl_map_lexmin(map);
1506 assert(isl_map_is_equal(map, map2));
1507 isl_map_free(map);
1508 isl_map_free(map2);
1509
1510 str = "{ [x] -> [y] : x = 4y; [x] -> [y] : x = 2y }";
1511 map = isl_map_read_from_str(ctx, str);
1512 map = isl_map_lexmin(map);
1513 str = "{ [x] -> [y] : (4y = x and x >= 0) or "
1514 "(exists (e0 = [(x)/4], e1 = [(-2 + x)/4]: 2y = x and "
1515 "4e1 = -2 + x and 4e0 <= -1 + x and 4e0 >= -3 + x)) or "
1516 "(exists (e0 = [(x)/4]: 2y = x and 4e0 = x and x <= -4)) }";
1517 map2 = isl_map_read_from_str(ctx, str);
1518 assert(isl_map_is_equal(map, map2));
1519 isl_map_free(map);
1520 isl_map_free(map2);
1521
1522 str = "{ [i] -> [i', j] : j = i - 8i' and i' >= 0 and i' <= 7 and "
1523 " 8i' <= i and 8i' >= -7 + i }";
1524 bmap = isl_basic_map_read_from_str(ctx, str);
1525 pma = isl_basic_map_lexmin_pw_multi_aff(isl_basic_map_copy(bmap));
1526 map2 = isl_map_from_pw_multi_aff(pma);
1527 map = isl_map_from_basic_map(bmap);
1528 assert(isl_map_is_equal(map, map2));
1529 isl_map_free(map);
1530 isl_map_free(map2);
1531
1532 str = "{ T[a] -> S[b, c] : a = 4b-2c and c >= b }";
1533 map = isl_map_read_from_str(ctx, str);
1534 map = isl_map_lexmin(map);
1535 str = "{ T[a] -> S[b, c] : 2b = a and 2c = a }";
1536 map2 = isl_map_read_from_str(ctx, str);
1537 assert(isl_map_is_equal(map, map2));
1538 isl_map_free(map);
1539 isl_map_free(map2);
1540 }
1541
1542 struct must_may {
1543 isl_map *must;
1544 isl_map *may;
1545 };
1546
1547 static int collect_must_may(__isl_take isl_map *dep, int must,
1548 void *dep_user, void *user)
1549 {
1550 struct must_may *mm = (struct must_may *)user;
1551
1552 if (must)
1553 mm->must = isl_map_union(mm->must, dep);
1554 else
1555 mm->may = isl_map_union(mm->may, dep);
1556
1557 return 0;
1558 }
1559
1560 static int common_space(void *first, void *second)
1561 {
1562 int depth = *(int *)first;
1563 return 2 * depth;
1564 }
1565
1566 static int map_is_equal(__isl_keep isl_map *map, const char *str)
1567 {
1568 isl_map *map2;
1569 int equal;
1570
1571 if (!map)
1572 return -1;
1573
1574 map2 = isl_map_read_from_str(map->ctx, str);
1575 equal = isl_map_is_equal(map, map2);
1576 isl_map_free(map2);
1577
1578 return equal;
1579 }
1580
1581 static int map_check_equal(__isl_keep isl_map *map, const char *str)
1582 {
1583 int equal;
1584
1585 equal = map_is_equal(map, str);
1586 if (equal < 0)
1587 return -1;
1588 if (!equal)
1589 isl_die(isl_map_get_ctx(map), isl_error_unknown,
1590 "result not as expected", return -1);
1591 return 0;
1592 }
1593
1594 void test_dep(struct isl_ctx *ctx)
1595 {
1596 const char *str;
1597 isl_space *dim;
1598 isl_map *map;
1599 isl_access_info *ai;
1600 isl_flow *flow;
1601 int depth;
1602 struct must_may mm;
1603
1604 depth = 3;
1605
1606 str = "{ [2,i,0] -> [i] : 0 <= i <= 10 }";
1607 map = isl_map_read_from_str(ctx, str);
1608 ai = isl_access_info_alloc(map, &depth, &common_space, 2);
1609
1610 str = "{ [0,i,0] -> [i] : 0 <= i <= 10 }";
1611 map = isl_map_read_from_str(ctx, str);
1612 ai = isl_access_info_add_source(ai, map, 1, &depth);
1613
1614 str = "{ [1,i,0] -> [5] : 0 <= i <= 10 }";
1615 map = isl_map_read_from_str(ctx, str);
1616 ai = isl_access_info_add_source(ai, map, 1, &depth);
1617
1618 flow = isl_access_info_compute_flow(ai);
1619 dim = isl_space_alloc(ctx, 0, 3, 3);
1620 mm.must = isl_map_empty(isl_space_copy(dim));
1621 mm.may = isl_map_empty(dim);
1622
1623 isl_flow_foreach(flow, collect_must_may, &mm);
1624
1625 str = "{ [0,i,0] -> [2,i,0] : (0 <= i <= 4) or (6 <= i <= 10); "
1626 " [1,10,0] -> [2,5,0] }";
1627 assert(map_is_equal(mm.must, str));
1628 str = "{ [i,j,k] -> [l,m,n] : 1 = 0 }";
1629 assert(map_is_equal(mm.may, str));
1630
1631 isl_map_free(mm.must);
1632 isl_map_free(mm.may);
1633 isl_flow_free(flow);
1634
1635
1636 str = "{ [2,i,0] -> [i] : 0 <= i <= 10 }";
1637 map = isl_map_read_from_str(ctx, str);
1638 ai = isl_access_info_alloc(map, &depth, &common_space, 2);
1639
1640 str = "{ [0,i,0] -> [i] : 0 <= i <= 10 }";
1641 map = isl_map_read_from_str(ctx, str);
1642 ai = isl_access_info_add_source(ai, map, 1, &depth);
1643
1644 str = "{ [1,i,0] -> [5] : 0 <= i <= 10 }";
1645 map = isl_map_read_from_str(ctx, str);
1646 ai = isl_access_info_add_source(ai, map, 0, &depth);
1647
1648 flow = isl_access_info_compute_flow(ai);
1649 dim = isl_space_alloc(ctx, 0, 3, 3);
1650 mm.must = isl_map_empty(isl_space_copy(dim));
1651 mm.may = isl_map_empty(dim);
1652
1653 isl_flow_foreach(flow, collect_must_may, &mm);
1654
1655 str = "{ [0,i,0] -> [2,i,0] : (0 <= i <= 4) or (6 <= i <= 10) }";
1656 assert(map_is_equal(mm.must, str));
1657 str = "{ [0,5,0] -> [2,5,0]; [1,i,0] -> [2,5,0] : 0 <= i <= 10 }";
1658 assert(map_is_equal(mm.may, str));
1659
1660 isl_map_free(mm.must);
1661 isl_map_free(mm.may);
1662 isl_flow_free(flow);
1663
1664
1665 str = "{ [2,i,0] -> [i] : 0 <= i <= 10 }";
1666 map = isl_map_read_from_str(ctx, str);
1667 ai = isl_access_info_alloc(map, &depth, &common_space, 2);
1668
1669 str = "{ [0,i,0] -> [i] : 0 <= i <= 10 }";
1670 map = isl_map_read_from_str(ctx, str);
1671 ai = isl_access_info_add_source(ai, map, 0, &depth);
1672
1673 str = "{ [1,i,0] -> [5] : 0 <= i <= 10 }";
1674 map = isl_map_read_from_str(ctx, str);
1675 ai = isl_access_info_add_source(ai, map, 0, &depth);
1676
1677 flow = isl_access_info_compute_flow(ai);
1678 dim = isl_space_alloc(ctx, 0, 3, 3);
1679 mm.must = isl_map_empty(isl_space_copy(dim));
1680 mm.may = isl_map_empty(dim);
1681
1682 isl_flow_foreach(flow, collect_must_may, &mm);
1683
1684 str = "{ [0,i,0] -> [2,i,0] : 0 <= i <= 10; "
1685 " [1,i,0] -> [2,5,0] : 0 <= i <= 10 }";
1686 assert(map_is_equal(mm.may, str));
1687 str = "{ [i,j,k] -> [l,m,n] : 1 = 0 }";
1688 assert(map_is_equal(mm.must, str));
1689
1690 isl_map_free(mm.must);
1691 isl_map_free(mm.may);
1692 isl_flow_free(flow);
1693
1694
1695 str = "{ [0,i,2] -> [i] : 0 <= i <= 10 }";
1696 map = isl_map_read_from_str(ctx, str);
1697 ai = isl_access_info_alloc(map, &depth, &common_space, 2);
1698
1699 str = "{ [0,i,0] -> [i] : 0 <= i <= 10 }";
1700 map = isl_map_read_from_str(ctx, str);
1701 ai = isl_access_info_add_source(ai, map, 0, &depth);
1702
1703 str = "{ [0,i,1] -> [5] : 0 <= i <= 10 }";
1704 map = isl_map_read_from_str(ctx, str);
1705 ai = isl_access_info_add_source(ai, map, 0, &depth);
1706
1707 flow = isl_access_info_compute_flow(ai);
1708 dim = isl_space_alloc(ctx, 0, 3, 3);
1709 mm.must = isl_map_empty(isl_space_copy(dim));
1710 mm.may = isl_map_empty(dim);
1711
1712 isl_flow_foreach(flow, collect_must_may, &mm);
1713
1714 str = "{ [0,i,0] -> [0,i,2] : 0 <= i <= 10; "
1715 " [0,i,1] -> [0,5,2] : 0 <= i <= 5 }";
1716 assert(map_is_equal(mm.may, str));
1717 str = "{ [i,j,k] -> [l,m,n] : 1 = 0 }";
1718 assert(map_is_equal(mm.must, str));
1719
1720 isl_map_free(mm.must);
1721 isl_map_free(mm.may);
1722 isl_flow_free(flow);
1723
1724
1725 str = "{ [0,i,1] -> [i] : 0 <= i <= 10 }";
1726 map = isl_map_read_from_str(ctx, str);
1727 ai = isl_access_info_alloc(map, &depth, &common_space, 2);
1728
1729 str = "{ [0,i,0] -> [i] : 0 <= i <= 10 }";
1730 map = isl_map_read_from_str(ctx, str);
1731 ai = isl_access_info_add_source(ai, map, 0, &depth);
1732
1733 str = "{ [0,i,2] -> [5] : 0 <= i <= 10 }";
1734 map = isl_map_read_from_str(ctx, str);
1735 ai = isl_access_info_add_source(ai, map, 0, &depth);
1736
1737 flow = isl_access_info_compute_flow(ai);
1738 dim = isl_space_alloc(ctx, 0, 3, 3);
1739 mm.must = isl_map_empty(isl_space_copy(dim));
1740 mm.may = isl_map_empty(dim);
1741
1742 isl_flow_foreach(flow, collect_must_may, &mm);
1743
1744 str = "{ [0,i,0] -> [0,i,1] : 0 <= i <= 10; "
1745 " [0,i,2] -> [0,5,1] : 0 <= i <= 4 }";
1746 assert(map_is_equal(mm.may, str));
1747 str = "{ [i,j,k] -> [l,m,n] : 1 = 0 }";
1748 assert(map_is_equal(mm.must, str));
1749
1750 isl_map_free(mm.must);
1751 isl_map_free(mm.may);
1752 isl_flow_free(flow);
1753
1754
1755 depth = 5;
1756
1757 str = "{ [1,i,0,0,0] -> [i,j] : 0 <= i <= 10 and 0 <= j <= 10 }";
1758 map = isl_map_read_from_str(ctx, str);
1759 ai = isl_access_info_alloc(map, &depth, &common_space, 1);
1760
1761 str = "{ [0,i,0,j,0] -> [i,j] : 0 <= i <= 10 and 0 <= j <= 10 }";
1762 map = isl_map_read_from_str(ctx, str);
1763 ai = isl_access_info_add_source(ai, map, 1, &depth);
1764
1765 flow = isl_access_info_compute_flow(ai);
1766 dim = isl_space_alloc(ctx, 0, 5, 5);
1767 mm.must = isl_map_empty(isl_space_copy(dim));
1768 mm.may = isl_map_empty(dim);
1769
1770 isl_flow_foreach(flow, collect_must_may, &mm);
1771
1772 str = "{ [0,i,0,j,0] -> [1,i,0,0,0] : 0 <= i,j <= 10 }";
1773 assert(map_is_equal(mm.must, str));
1774 str = "{ [0,0,0,0,0] -> [0,0,0,0,0] : 1 = 0 }";
1775 assert(map_is_equal(mm.may, str));
1776
1777 isl_map_free(mm.must);
1778 isl_map_free(mm.may);
1779 isl_flow_free(flow);
1780 }
1781
1782 int test_sv(isl_ctx *ctx)
1783 {
1784 const char *str;
1785 isl_map *map;
1786 isl_union_map *umap;
1787 int sv;
1788
1789 str = "[N] -> { [i] -> [f] : 0 <= i <= N and 0 <= i - 10 f <= 9 }";
1790 map = isl_map_read_from_str(ctx, str);
1791 sv = isl_map_is_single_valued(map);
1792 isl_map_free(map);
1793 if (sv < 0)
1794 return -1;
1795 if (!sv)
1796 isl_die(ctx, isl_error_internal,
1797 "map not detected as single valued", return -1);
1798
1799 str = "[N] -> { [i] -> [f] : 0 <= i <= N and 0 <= i - 10 f <= 10 }";
1800 map = isl_map_read_from_str(ctx, str);
1801 sv = isl_map_is_single_valued(map);
1802 isl_map_free(map);
1803 if (sv < 0)
1804 return -1;
1805 if (sv)
1806 isl_die(ctx, isl_error_internal,
1807 "map detected as single valued", return -1);
1808
1809 str = "{ S1[i] -> [i] : 0 <= i <= 9; S2[i] -> [i] : 0 <= i <= 9 }";
1810 umap = isl_union_map_read_from_str(ctx, str);
1811 sv = isl_union_map_is_single_valued(umap);
1812 isl_union_map_free(umap);
1813 if (sv < 0)
1814 return -1;
1815 if (!sv)
1816 isl_die(ctx, isl_error_internal,
1817 "map not detected as single valued", return -1);
1818
1819 str = "{ [i] -> S1[i] : 0 <= i <= 9; [i] -> S2[i] : 0 <= i <= 9 }";
1820 umap = isl_union_map_read_from_str(ctx, str);
1821 sv = isl_union_map_is_single_valued(umap);
1822 isl_union_map_free(umap);
1823 if (sv < 0)
1824 return -1;
1825 if (sv)
1826 isl_die(ctx, isl_error_internal,
1827 "map detected as single valued", return -1);
1828
1829 return 0;
1830 }
1831
1832 void test_bijective_case(struct isl_ctx *ctx, const char *str, int bijective)
1833 {
1834 isl_map *map;
1835
1836 map = isl_map_read_from_str(ctx, str);
1837 if (bijective)
1838 assert(isl_map_is_bijective(map));
1839 else
1840 assert(!isl_map_is_bijective(map));
1841 isl_map_free(map);
1842 }
1843
1844 void test_bijective(struct isl_ctx *ctx)
1845 {
1846 test_bijective_case(ctx, "[N,M]->{[i,j] -> [i]}", 0);
1847 test_bijective_case(ctx, "[N,M]->{[i,j] -> [i] : j=i}", 1);
1848 test_bijective_case(ctx, "[N,M]->{[i,j] -> [i] : j=0}", 1);
1849 test_bijective_case(ctx, "[N,M]->{[i,j] -> [i] : j=N}", 1);
1850 test_bijective_case(ctx, "[N,M]->{[i,j] -> [j,i]}", 1);
1851 test_bijective_case(ctx, "[N,M]->{[i,j] -> [i+j]}", 0);
1852 test_bijective_case(ctx, "[N,M]->{[i,j] -> []}", 0);
1853 test_bijective_case(ctx, "[N,M]->{[i,j] -> [i,j,N]}", 1);
1854 test_bijective_case(ctx, "[N,M]->{[i,j] -> [2i]}", 0);
1855 test_bijective_case(ctx, "[N,M]->{[i,j] -> [i,i]}", 0);
1856 test_bijective_case(ctx, "[N,M]->{[i,j] -> [2i,i]}", 0);
1857 test_bijective_case(ctx, "[N,M]->{[i,j] -> [2i,j]}", 1);
1858 test_bijective_case(ctx, "[N,M]->{[i,j] -> [x,y] : 2x=i & y =j}", 1);
1859 }
1860
1861 void test_pwqp(struct isl_ctx *ctx)
1862 {
1863 const char *str;
1864 isl_set *set;
1865 isl_pw_qpolynomial *pwqp1, *pwqp2;
1866
1867 str = "{ [i,j,k] -> 1 + 9 * [i/5] + 7 * [j/11] + 4 * [k/13] }";
1868 pwqp1 = isl_pw_qpolynomial_read_from_str(ctx, str);
1869
1870 pwqp1 = isl_pw_qpolynomial_move_dims(pwqp1, isl_dim_param, 0,
1871 isl_dim_in, 1, 1);
1872
1873 str = "[j] -> { [i,k] -> 1 + 9 * [i/5] + 7 * [j/11] + 4 * [k/13] }";
1874 pwqp2 = isl_pw_qpolynomial_read_from_str(ctx, str);
1875
1876 pwqp1 = isl_pw_qpolynomial_sub(pwqp1, pwqp2);
1877
1878 assert(isl_pw_qpolynomial_is_zero(pwqp1));
1879
1880 isl_pw_qpolynomial_free(pwqp1);
1881
1882 str = "{ [i] -> i }";
1883 pwqp1 = isl_pw_qpolynomial_read_from_str(ctx, str);
1884 str = "{ [k] : exists a : k = 2a }";
1885 set = isl_set_read_from_str(ctx, str);
1886 pwqp1 = isl_pw_qpolynomial_gist(pwqp1, set);
1887 str = "{ [i] -> i }";
1888 pwqp2 = isl_pw_qpolynomial_read_from_str(ctx, str);
1889
1890 pwqp1 = isl_pw_qpolynomial_sub(pwqp1, pwqp2);
1891
1892 assert(isl_pw_qpolynomial_is_zero(pwqp1));
1893
1894 isl_pw_qpolynomial_free(pwqp1);
1895
1896 str = "{ [i] -> i + [ (i + [i/3])/2 ] }";
1897 pwqp1 = isl_pw_qpolynomial_read_from_str(ctx, str);
1898 str = "{ [10] }";
1899 set = isl_set_read_from_str(ctx, str);
1900 pwqp1 = isl_pw_qpolynomial_gist(pwqp1, set);
1901 str = "{ [i] -> 16 }";
1902 pwqp2 = isl_pw_qpolynomial_read_from_str(ctx, str);
1903
1904 pwqp1 = isl_pw_qpolynomial_sub(pwqp1, pwqp2);
1905
1906 assert(isl_pw_qpolynomial_is_zero(pwqp1));
1907
1908 isl_pw_qpolynomial_free(pwqp1);
1909
1910 str = "{ [i] -> ([(i)/2]) }";
1911 pwqp1 = isl_pw_qpolynomial_read_from_str(ctx, str);
1912 str = "{ [k] : exists a : k = 2a+1 }";
1913 set = isl_set_read_from_str(ctx, str);
1914 pwqp1 = isl_pw_qpolynomial_gist(pwqp1, set);
1915 str = "{ [i] -> -1/2 + 1/2 * i }";
1916 pwqp2 = isl_pw_qpolynomial_read_from_str(ctx, str);
1917
1918 pwqp1 = isl_pw_qpolynomial_sub(pwqp1, pwqp2);
1919
1920 assert(isl_pw_qpolynomial_is_zero(pwqp1));
1921
1922 isl_pw_qpolynomial_free(pwqp1);
1923
1924 str = "{ [i] -> ([([i/2] + [i/2])/5]) }";
1925 pwqp1 = isl_pw_qpolynomial_read_from_str(ctx, str);
1926 str = "{ [i] -> ([(2 * [i/2])/5]) }";
1927 pwqp2 = isl_pw_qpolynomial_read_from_str(ctx, str);
1928
1929 pwqp1 = isl_pw_qpolynomial_sub(pwqp1, pwqp2);
1930
1931 assert(isl_pw_qpolynomial_is_zero(pwqp1));
1932
1933 isl_pw_qpolynomial_free(pwqp1);
1934
1935 str = "{ [x] -> ([x/2] + [(x+1)/2]) }";
1936 pwqp1 = isl_pw_qpolynomial_read_from_str(ctx, str);
1937 str = "{ [x] -> x }";
1938 pwqp2 = isl_pw_qpolynomial_read_from_str(ctx, str);
1939
1940 pwqp1 = isl_pw_qpolynomial_sub(pwqp1, pwqp2);
1941
1942 assert(isl_pw_qpolynomial_is_zero(pwqp1));
1943
1944 isl_pw_qpolynomial_free(pwqp1);
1945
1946 str = "{ [i] -> ([i/2]) : i >= 0; [i] -> ([i/3]) : i < 0 }";
1947 pwqp1 = isl_pw_qpolynomial_read_from_str(ctx, str);
1948 pwqp2 = isl_pw_qpolynomial_read_from_str(ctx, str);
1949 pwqp1 = isl_pw_qpolynomial_coalesce(pwqp1);
1950 pwqp1 = isl_pw_qpolynomial_sub(pwqp1, pwqp2);
1951 assert(isl_pw_qpolynomial_is_zero(pwqp1));
1952 isl_pw_qpolynomial_free(pwqp1);
1953 }
1954
1955 void test_split_periods(isl_ctx *ctx)
1956 {
1957 const char *str;
1958 isl_pw_qpolynomial *pwqp;
1959
1960 str = "{ [U,V] -> 1/3 * U + 2/3 * V - [(U + 2V)/3] + [U/2] : "
1961 "U + 2V + 3 >= 0 and - U -2V >= 0 and - U + 10 >= 0 and "
1962 "U >= 0; [U,V] -> U^2 : U >= 100 }";
1963 pwqp = isl_pw_qpolynomial_read_from_str(ctx, str);
1964
1965 pwqp = isl_pw_qpolynomial_split_periods(pwqp, 2);
1966 assert(pwqp);
1967
1968 isl_pw_qpolynomial_free(pwqp);
1969 }
1970
1971 void test_union(isl_ctx *ctx)
1972 {
1973 const char *str;
1974 isl_union_set *uset1, *uset2;
1975 isl_union_map *umap1, *umap2;
1976
1977 str = "{ [i] : 0 <= i <= 1 }";
1978 uset1 = isl_union_set_read_from_str(ctx, str);
1979 str = "{ [1] -> [0] }";
1980 umap1 = isl_union_map_read_from_str(ctx, str);
1981
1982 umap2 = isl_union_set_lex_gt_union_set(isl_union_set_copy(uset1), uset1);
1983 assert(isl_union_map_is_equal(umap1, umap2));
1984
1985 isl_union_map_free(umap1);
1986 isl_union_map_free(umap2);
1987
1988 str = "{ A[i] -> B[i]; B[i] -> C[i]; A[0] -> C[1] }";
1989 umap1 = isl_union_map_read_from_str(ctx, str);
1990 str = "{ A[i]; B[i] }";
1991 uset1 = isl_union_set_read_from_str(ctx, str);
1992
1993 uset2 = isl_union_map_domain(umap1);
1994
1995 assert(isl_union_set_is_equal(uset1, uset2));
1996
1997 isl_union_set_free(uset1);
1998 isl_union_set_free(uset2);
1999 }
2000
2001 void test_bound(isl_ctx *ctx)
2002 {
2003 const char *str;
2004 isl_pw_qpolynomial *pwqp;
2005 isl_pw_qpolynomial_fold *pwf;
2006
2007 str = "{ [[a, b, c, d] -> [e]] -> 0 }";
2008 pwqp = isl_pw_qpolynomial_read_from_str(ctx, str);
2009 pwf = isl_pw_qpolynomial_bound(pwqp, isl_fold_max, NULL);
2010 assert(isl_pw_qpolynomial_fold_dim(pwf, isl_dim_in) == 4);
2011 isl_pw_qpolynomial_fold_free(pwf);
2012
2013 str = "{ [[x]->[x]] -> 1 : exists a : x = 2 a }";
2014 pwqp = isl_pw_qpolynomial_read_from_str(ctx, str);
2015 pwf = isl_pw_qpolynomial_bound(pwqp, isl_fold_max, NULL);
2016 assert(isl_pw_qpolynomial_fold_dim(pwf, isl_dim_in) == 1);
2017 isl_pw_qpolynomial_fold_free(pwf);
2018 }
2019
2020 void test_lift(isl_ctx *ctx)
2021 {
2022 const char *str;
2023 isl_basic_map *bmap;
2024 isl_basic_set *bset;
2025
2026 str = "{ [i0] : exists e0 : i0 = 4e0 }";
2027 bset = isl_basic_set_read_from_str(ctx, str);
2028 bset = isl_basic_set_lift(bset);
2029 bmap = isl_basic_map_from_range(bset);
2030 bset = isl_basic_map_domain(bmap);
2031 isl_basic_set_free(bset);
2032 }
2033
2034 struct {
2035 const char *set1;
2036 const char *set2;
2037 int subset;
2038 } subset_tests[] = {
2039 { "{ [112, 0] }",
2040 "{ [i0, i1] : exists (e0 = [(i0 - i1)/16], e1: "
2041 "16e0 <= i0 - i1 and 16e0 >= -15 + i0 - i1 and "
2042 "16e1 <= i1 and 16e0 >= -i1 and 16e1 >= -i0 + i1) }", 1 },
2043 { "{ [65] }",
2044 "{ [i] : exists (e0 = [(255i)/256], e1 = [(127i + 65e0)/191], "
2045 "e2 = [(3i + 61e1)/65], e3 = [(52i + 12e2)/61], "
2046 "e4 = [(2i + e3)/3], e5 = [(4i + e3)/4], e6 = [(8i + e3)/12]: "
2047 "3e4 = 2i + e3 and 4e5 = 4i + e3 and 12e6 = 8i + e3 and "
2048 "i <= 255 and 64e3 >= -45 + 67i and i >= 0 and "
2049 "256e0 <= 255i and 256e0 >= -255 + 255i and "
2050 "191e1 <= 127i + 65e0 and 191e1 >= -190 + 127i + 65e0 and "
2051 "65e2 <= 3i + 61e1 and 65e2 >= -64 + 3i + 61e1 and "
2052 "61e3 <= 52i + 12e2 and 61e3 >= -60 + 52i + 12e2) }", 1 },
2053 { "{ [i] : 0 <= i <= 10 }", "{ rat: [i] : 0 <= i <= 10 }", 1 },
2054 { "{ rat: [i] : 0 <= i <= 10 }", "{ [i] : 0 <= i <= 10 }", 0 },
2055 { "{ rat: [0] }", "{ [i] : 0 <= i <= 10 }", 1 },
2056 { "{ rat: [(1)/2] }", "{ [i] : 0 <= i <= 10 }", 0 },
2057 };
2058
2059 static int test_subset(isl_ctx *ctx)
2060 {
2061 int i;
2062 isl_set *set1, *set2;
2063 int subset;
2064
2065 for (i = 0; i < ARRAY_SIZE(subset_tests); ++i) {
2066 set1 = isl_set_read_from_str(ctx, subset_tests[i].set1);
2067 set2 = isl_set_read_from_str(ctx, subset_tests[i].set2);
2068 subset = isl_set_is_subset(set1, set2);
2069 isl_set_free(set1);
2070 isl_set_free(set2);
2071 if (subset < 0)
2072 return -1;
2073 if (subset != subset_tests[i].subset)
2074 isl_die(ctx, isl_error_unknown,
2075 "incorrect subset result", return -1);
2076 }
2077
2078 return 0;
2079 }
2080
2081 struct {
2082 const char *minuend;
2083 const char *subtrahend;
2084 const char *difference;
2085 } subtract_domain_tests[] = {
2086 { "{ A[i] -> B[i] }", "{ A[i] }", "{ }" },
2087 { "{ A[i] -> B[i] }", "{ B[i] }", "{ A[i] -> B[i] }" },
2088 { "{ A[i] -> B[i] }", "{ A[i] : i > 0 }", "{ A[i] -> B[i] : i <= 0 }" },
2089 };
2090
2091 static int test_subtract(isl_ctx *ctx)
2092 {
2093 int i;
2094 isl_union_map *umap1, *umap2;
2095 isl_union_set *uset;
2096 int equal;
2097
2098 for (i = 0; i < ARRAY_SIZE(subtract_domain_tests); ++i) {
2099 umap1 = isl_union_map_read_from_str(ctx,
2100 subtract_domain_tests[i].minuend);
2101 uset = isl_union_set_read_from_str(ctx,
2102 subtract_domain_tests[i].subtrahend);
2103 umap2 = isl_union_map_read_from_str(ctx,
2104 subtract_domain_tests[i].difference);
2105 umap1 = isl_union_map_subtract_domain(umap1, uset);
2106 equal = isl_union_map_is_equal(umap1, umap2);
2107 isl_union_map_free(umap1);
2108 isl_union_map_free(umap2);
2109 if (equal < 0)
2110 return -1;
2111 if (!equal)
2112 isl_die(ctx, isl_error_unknown,
2113 "incorrect subtract domain result", return -1);
2114 }
2115
2116 return 0;
2117 }
2118
2119 int test_factorize(isl_ctx *ctx)
2120 {
2121 const char *str;
2122 isl_basic_set *bset;
2123 isl_factorizer *f;
2124
2125 str = "{ [i0, i1, i2, i3, i4, i5, i6, i7] : 3i5 <= 2 - 2i0 and "
2126 "i0 >= -2 and i6 >= 1 + i3 and i7 >= 0 and 3i5 >= -2i0 and "
2127 "2i4 <= i2 and i6 >= 1 + 2i0 + 3i1 and i4 <= -1 and "
2128 "i6 >= 1 + 2i0 + 3i5 and i6 <= 2 + 2i0 + 3i5 and "
2129 "3i5 <= 2 - 2i0 - i2 + 3i4 and i6 <= 2 + 2i0 + 3i1 and "
2130 "i0 <= -1 and i7 <= i2 + i3 - 3i4 - i6 and "
2131 "3i5 >= -2i0 - i2 + 3i4 }";
2132 bset = isl_basic_set_read_from_str(ctx, str);
2133 f = isl_basic_set_factorizer(bset);
2134 isl_basic_set_free(bset);
2135 isl_factorizer_free(f);
2136 if (!f)
2137 isl_die(ctx, isl_error_unknown,
2138 "failed to construct factorizer", return -1);
2139
2140 str = "{ [i0, i1, i2, i3, i4, i5, i6, i7, i8, i9, i10, i11, i12] : "
2141 "i12 <= 2 + i0 - i11 and 2i8 >= -i4 and i11 >= i1 and "
2142 "3i5 <= -i2 and 2i11 >= -i4 - 2i7 and i11 <= 3 + i0 + 3i9 and "
2143 "i11 <= -i4 - 2i7 and i12 >= -i10 and i2 >= -2 and "
2144 "i11 >= i1 + 3i10 and i11 >= 1 + i0 + 3i9 and "
2145 "i11 <= 1 - i4 - 2i8 and 6i6 <= 6 - i2 and 3i6 >= 1 - i2 and "
2146 "i11 <= 2 + i1 and i12 <= i4 + i11 and i12 >= i0 - i11 and "
2147 "3i5 >= -2 - i2 and i12 >= -1 + i4 + i11 and 3i3 <= 3 - i2 and "
2148 "9i6 <= 11 - i2 + 6i5 and 3i3 >= 1 - i2 and "
2149 "9i6 <= 5 - i2 + 6i3 and i12 <= -1 and i2 <= 0 }";
2150 bset = isl_basic_set_read_from_str(ctx, str);
2151 f = isl_basic_set_factorizer(bset);
2152 isl_basic_set_free(bset);
2153 isl_factorizer_free(f);
2154 if (!f)
2155 isl_die(ctx, isl_error_unknown,
2156 "failed to construct factorizer", return -1);
2157
2158 return 0;
2159 }
2160
2161 static int check_injective(__isl_take isl_map *map, void *user)
2162 {
2163 int *injective = user;
2164
2165 *injective = isl_map_is_injective(map);
2166 isl_map_free(map);
2167
2168 if (*injective < 0 || !*injective)
2169 return -1;
2170
2171 return 0;
2172 }
2173
2174 int test_one_schedule(isl_ctx *ctx, const char *d, const char *w,
2175 const char *r, const char *s, int tilable, int parallel)
2176 {
2177 int i;
2178 isl_union_set *D;
2179 isl_union_map *W, *R, *S;
2180 isl_union_map *empty;
2181 isl_union_map *dep_raw, *dep_war, *dep_waw, *dep;
2182 isl_union_map *validity, *proximity;
2183 isl_union_map *schedule;
2184 isl_union_map *test;
2185 isl_union_set *delta;
2186 isl_union_set *domain;
2187 isl_set *delta_set;
2188 isl_set *slice;
2189 isl_set *origin;
2190 isl_schedule *sched;
2191 int is_nonneg, is_parallel, is_tilable, is_injection, is_complete;
2192
2193 D = isl_union_set_read_from_str(ctx, d);
2194 W = isl_union_map_read_from_str(ctx, w);
2195 R = isl_union_map_read_from_str(ctx, r);
2196 S = isl_union_map_read_from_str(ctx, s);
2197
2198 W = isl_union_map_intersect_domain(W, isl_union_set_copy(D));
2199 R = isl_union_map_intersect_domain(R, isl_union_set_copy(D));
2200
2201 empty = isl_union_map_empty(isl_union_map_get_space(S));
2202 isl_union_map_compute_flow(isl_union_map_copy(R),
2203 isl_union_map_copy(W), empty,
2204 isl_union_map_copy(S),
2205 &dep_raw, NULL, NULL, NULL);
2206 isl_union_map_compute_flow(isl_union_map_copy(W),
2207 isl_union_map_copy(W),
2208 isl_union_map_copy(R),
2209 isl_union_map_copy(S),
2210 &dep_waw, &dep_war, NULL, NULL);
2211
2212 dep = isl_union_map_union(dep_waw, dep_war);
2213 dep = isl_union_map_union(dep, dep_raw);
2214 validity = isl_union_map_copy(dep);
2215 proximity = isl_union_map_copy(dep);
2216
2217 sched = isl_union_set_compute_schedule(isl_union_set_copy(D),
2218 validity, proximity);
2219 schedule = isl_schedule_get_map(sched);
2220 isl_schedule_free(sched);
2221 isl_union_map_free(W);
2222 isl_union_map_free(R);
2223 isl_union_map_free(S);
2224
2225 is_injection = 1;
2226 isl_union_map_foreach_map(schedule, &check_injective, &is_injection);
2227
2228 domain = isl_union_map_domain(isl_union_map_copy(schedule));
2229 is_complete = isl_union_set_is_subset(D, domain);
2230 isl_union_set_free(D);
2231 isl_union_set_free(domain);
2232
2233 test = isl_union_map_reverse(isl_union_map_copy(schedule));
2234 test = isl_union_map_apply_range(test, dep);
2235 test = isl_union_map_apply_range(test, schedule);
2236
2237 delta = isl_union_map_deltas(test);
2238 if (isl_union_set_n_set(delta) == 0) {
2239 is_tilable = 1;
2240 is_parallel = 1;
2241 is_nonneg = 1;
2242 isl_union_set_free(delta);
2243 } else {
2244 delta_set = isl_set_from_union_set(delta);
2245
2246 slice = isl_set_universe(isl_set_get_space(delta_set));
2247 for (i = 0; i < tilable; ++i)
2248 slice = isl_set_lower_bound_si(slice, isl_dim_set, i, 0);
2249 is_tilable = isl_set_is_subset(delta_set, slice);
2250 isl_set_free(slice);
2251
2252 slice = isl_set_universe(isl_set_get_space(delta_set));
2253 for (i = 0; i < parallel; ++i)
2254 slice = isl_set_fix_si(slice, isl_dim_set, i, 0);
2255 is_parallel = isl_set_is_subset(delta_set, slice);
2256 isl_set_free(slice);
2257
2258 origin = isl_set_universe(isl_set_get_space(delta_set));
2259 for (i = 0; i < isl_set_dim(origin, isl_dim_set); ++i)
2260 origin = isl_set_fix_si(origin, isl_dim_set, i, 0);
2261
2262 delta_set = isl_set_union(delta_set, isl_set_copy(origin));
2263 delta_set = isl_set_lexmin(delta_set);
2264
2265 is_nonneg = isl_set_is_equal(delta_set, origin);
2266
2267 isl_set_free(origin);
2268 isl_set_free(delta_set);
2269 }
2270
2271 if (is_nonneg < 0 || is_parallel < 0 || is_tilable < 0 ||
2272 is_injection < 0 || is_complete < 0)
2273 return -1;
2274 if (!is_complete)
2275 isl_die(ctx, isl_error_unknown,
2276 "generated schedule incomplete", return -1);
2277 if (!is_injection)
2278 isl_die(ctx, isl_error_unknown,
2279 "generated schedule not injective on each statement",
2280 return -1);
2281 if (!is_nonneg)
2282 isl_die(ctx, isl_error_unknown,
2283 "negative dependences in generated schedule",
2284 return -1);
2285 if (!is_tilable)
2286 isl_die(ctx, isl_error_unknown,
2287 "generated schedule not as tilable as expected",
2288 return -1);
2289 if (!is_parallel)
2290 isl_die(ctx, isl_error_unknown,
2291 "generated schedule not as parallel as expected",
2292 return -1);
2293
2294 return 0;
2295 }
2296
2297 static __isl_give isl_union_map *compute_schedule(isl_ctx *ctx,
2298 const char *domain, const char *validity, const char *proximity)
2299 {
2300 isl_union_set *dom;
2301 isl_union_map *dep;
2302 isl_union_map *prox;
2303 isl_schedule *schedule;
2304 isl_union_map *sched;
2305
2306 dom = isl_union_set_read_from_str(ctx, domain);
2307 dep = isl_union_map_read_from_str(ctx, validity);
2308 prox = isl_union_map_read_from_str(ctx, proximity);
2309 schedule = isl_union_set_compute_schedule(dom, dep, prox);
2310 sched = isl_schedule_get_map(schedule);
2311 isl_schedule_free(schedule);
2312
2313 return sched;
2314 }
2315
2316 /* Check that a schedule can be constructed on the given domain
2317 * with the given validity and proximity constraints.
2318 */
2319 static int test_has_schedule(isl_ctx *ctx, const char *domain,
2320 const char *validity, const char *proximity)
2321 {
2322 isl_union_map *sched;
2323
2324 sched = compute_schedule(ctx, domain, validity, proximity);
2325 if (!sched)
2326 return -1;
2327
2328 isl_union_map_free(sched);
2329 return 0;
2330 }
2331
2332 int test_special_schedule(isl_ctx *ctx, const char *domain,
2333 const char *validity, const char *proximity, const char *expected_sched)
2334 {
2335 isl_union_map *sched1, *sched2;
2336 int equal;
2337
2338 sched1 = compute_schedule(ctx, domain, validity, proximity);
2339 sched2 = isl_union_map_read_from_str(ctx, expected_sched);
2340
2341 equal = isl_union_map_is_equal(sched1, sched2);
2342 isl_union_map_free(sched1);
2343 isl_union_map_free(sched2);
2344
2345 if (equal < 0)
2346 return -1;
2347 if (!equal)
2348 isl_die(ctx, isl_error_unknown, "unexpected schedule",
2349 return -1);
2350
2351 return 0;
2352 }
2353
2354 int test_schedule(isl_ctx *ctx)
2355 {
2356 const char *D, *W, *R, *V, *P, *S;
2357
2358 /* Handle resulting schedule with zero bands. */
2359 if (test_one_schedule(ctx, "{[]}", "{}", "{}", "{[] -> []}", 0, 0) < 0)
2360 return -1;
2361
2362 /* Jacobi */
2363 D = "[T,N] -> { S1[t,i] : 1 <= t <= T and 2 <= i <= N - 1 }";
2364 W = "{ S1[t,i] -> a[t,i] }";
2365 R = "{ S1[t,i] -> a[t-1,i]; S1[t,i] -> a[t-1,i-1]; "
2366 "S1[t,i] -> a[t-1,i+1] }";
2367 S = "{ S1[t,i] -> [t,i] }";
2368 if (test_one_schedule(ctx, D, W, R, S, 2, 0) < 0)
2369 return -1;
2370
2371 /* Fig. 5 of CC2008 */
2372 D = "[N] -> { S_0[i, j] : i >= 0 and i <= -1 + N and j >= 2 and "
2373 "j <= -1 + N }";
2374 W = "[N] -> { S_0[i, j] -> a[i, j] : i >= 0 and i <= -1 + N and "
2375 "j >= 2 and j <= -1 + N }";
2376 R = "[N] -> { S_0[i, j] -> a[j, i] : i >= 0 and i <= -1 + N and "
2377 "j >= 2 and j <= -1 + N; "
2378 "S_0[i, j] -> a[i, -1 + j] : i >= 0 and i <= -1 + N and "
2379 "j >= 2 and j <= -1 + N }";
2380 S = "[N] -> { S_0[i, j] -> [0, i, 0, j, 0] }";
2381 if (test_one_schedule(ctx, D, W, R, S, 2, 0) < 0)
2382 return -1;
2383
2384 D = "{ S1[i] : 0 <= i <= 10; S2[i] : 0 <= i <= 9 }";
2385 W = "{ S1[i] -> a[i] }";
2386 R = "{ S2[i] -> a[i+1] }";
2387 S = "{ S1[i] -> [0,i]; S2[i] -> [1,i] }";
2388 if (test_one_schedule(ctx, D, W, R, S, 1, 1) < 0)
2389 return -1;
2390
2391 D = "{ S1[i] : 0 <= i < 10; S2[i] : 0 <= i < 10 }";
2392 W = "{ S1[i] -> a[i] }";
2393 R = "{ S2[i] -> a[9-i] }";
2394 S = "{ S1[i] -> [0,i]; S2[i] -> [1,i] }";
2395 if (test_one_schedule(ctx, D, W, R, S, 1, 1) < 0)
2396 return -1;
2397
2398 D = "[N] -> { S1[i] : 0 <= i < N; S2[i] : 0 <= i < N }";
2399 W = "{ S1[i] -> a[i] }";
2400 R = "[N] -> { S2[i] -> a[N-1-i] }";
2401 S = "{ S1[i] -> [0,i]; S2[i] -> [1,i] }";
2402 if (test_one_schedule(ctx, D, W, R, S, 1, 1) < 0)
2403 return -1;
2404
2405 D = "{ S1[i] : 0 < i < 10; S2[i] : 0 <= i < 10 }";
2406 W = "{ S1[i] -> a[i]; S2[i] -> b[i] }";
2407 R = "{ S2[i] -> a[i]; S1[i] -> b[i-1] }";
2408 S = "{ S1[i] -> [i,0]; S2[i] -> [i,1] }";
2409 if (test_one_schedule(ctx, D, W, R, S, 0, 0) < 0)
2410 return -1;
2411
2412 D = "[N] -> { S1[i] : 1 <= i <= N; S2[i,j] : 1 <= i,j <= N }";
2413 W = "{ S1[i] -> a[0,i]; S2[i,j] -> a[i,j] }";
2414 R = "{ S2[i,j] -> a[i-1,j] }";
2415 S = "{ S1[i] -> [0,i,0]; S2[i,j] -> [1,i,j] }";
2416 if (test_one_schedule(ctx, D, W, R, S, 2, 1) < 0)
2417 return -1;
2418
2419 D = "[N] -> { S1[i] : 1 <= i <= N; S2[i,j] : 1 <= i,j <= N }";
2420 W = "{ S1[i] -> a[i,0]; S2[i,j] -> a[i,j] }";
2421 R = "{ S2[i,j] -> a[i,j-1] }";
2422 S = "{ S1[i] -> [0,i,0]; S2[i,j] -> [1,i,j] }";
2423 if (test_one_schedule(ctx, D, W, R, S, 2, 1) < 0)
2424 return -1;
2425
2426 D = "[N] -> { S_0[]; S_1[i] : i >= 0 and i <= -1 + N; S_2[] }";
2427 W = "[N] -> { S_0[] -> a[0]; S_2[] -> b[0]; "
2428 "S_1[i] -> a[1 + i] : i >= 0 and i <= -1 + N }";
2429 R = "[N] -> { S_2[] -> a[N]; S_1[i] -> a[i] : i >= 0 and i <= -1 + N }";
2430 S = "[N] -> { S_1[i] -> [1, i, 0]; S_2[] -> [2, 0, 1]; "
2431 "S_0[] -> [0, 0, 0] }";
2432 if (test_one_schedule(ctx, D, W, R, S, 1, 0) < 0)
2433 return -1;
2434 ctx->opt->schedule_parametric = 0;
2435 if (test_one_schedule(ctx, D, W, R, S, 0, 0) < 0)
2436 return -1;
2437 ctx->opt->schedule_parametric = 1;
2438
2439 D = "[N] -> { S1[i] : 1 <= i <= N; S2[i] : 1 <= i <= N; "
2440 "S3[i,j] : 1 <= i,j <= N; S4[i] : 1 <= i <= N }";
2441 W = "{ S1[i] -> a[i,0]; S2[i] -> a[0,i]; S3[i,j] -> a[i,j] }";
2442 R = "[N] -> { S3[i,j] -> a[i-1,j]; S3[i,j] -> a[i,j-1]; "
2443 "S4[i] -> a[i,N] }";
2444 S = "{ S1[i] -> [0,i,0]; S2[i] -> [1,i,0]; S3[i,j] -> [2,i,j]; "
2445 "S4[i] -> [4,i,0] }";
2446 if (test_one_schedule(ctx, D, W, R, S, 2, 0) < 0)
2447 return -1;
2448
2449 D = "[N] -> { S_0[i, j] : i >= 1 and i <= N and j >= 1 and j <= N }";
2450 W = "[N] -> { S_0[i, j] -> s[0] : i >= 1 and i <= N and j >= 1 and "
2451 "j <= N }";
2452 R = "[N] -> { S_0[i, j] -> s[0] : i >= 1 and i <= N and j >= 1 and "
2453 "j <= N; "
2454 "S_0[i, j] -> a[i, j] : i >= 1 and i <= N and j >= 1 and "
2455 "j <= N }";
2456 S = "[N] -> { S_0[i, j] -> [0, i, 0, j, 0] }";
2457 if (test_one_schedule(ctx, D, W, R, S, 0, 0) < 0)
2458 return -1;
2459
2460 D = "[N] -> { S_0[t] : t >= 0 and t <= -1 + N; "
2461 " S_2[t] : t >= 0 and t <= -1 + N; "
2462 " S_1[t, i] : t >= 0 and t <= -1 + N and i >= 0 and "
2463 "i <= -1 + N }";
2464 W = "[N] -> { S_0[t] -> a[t, 0] : t >= 0 and t <= -1 + N; "
2465 " S_2[t] -> b[t] : t >= 0 and t <= -1 + N; "
2466 " S_1[t, i] -> a[t, 1 + i] : t >= 0 and t <= -1 + N and "
2467 "i >= 0 and i <= -1 + N }";
2468 R = "[N] -> { S_1[t, i] -> a[t, i] : t >= 0 and t <= -1 + N and "
2469 "i >= 0 and i <= -1 + N; "
2470 " S_2[t] -> a[t, N] : t >= 0 and t <= -1 + N }";
2471 S = "[N] -> { S_2[t] -> [0, t, 2]; S_1[t, i] -> [0, t, 1, i, 0]; "
2472 " S_0[t] -> [0, t, 0] }";
2473
2474 if (test_one_schedule(ctx, D, W, R, S, 2, 1) < 0)
2475 return -1;
2476 ctx->opt->schedule_parametric = 0;
2477 if (test_one_schedule(ctx, D, W, R, S, 0, 0) < 0)
2478 return -1;
2479 ctx->opt->schedule_parametric = 1;
2480
2481 D = "[N] -> { S1[i,j] : 0 <= i,j < N; S2[i,j] : 0 <= i,j < N }";
2482 S = "{ S1[i,j] -> [0,i,j]; S2[i,j] -> [1,i,j] }";
2483 if (test_one_schedule(ctx, D, "{}", "{}", S, 2, 2) < 0)
2484 return -1;
2485
2486 D = "[M, N] -> { S_1[i] : i >= 0 and i <= -1 + M; "
2487 "S_0[i, j] : i >= 0 and i <= -1 + M and j >= 0 and j <= -1 + N }";
2488 W = "[M, N] -> { S_0[i, j] -> a[j] : i >= 0 and i <= -1 + M and "
2489 "j >= 0 and j <= -1 + N; "
2490 "S_1[i] -> b[0] : i >= 0 and i <= -1 + M }";
2491 R = "[M, N] -> { S_0[i, j] -> a[0] : i >= 0 and i <= -1 + M and "
2492 "j >= 0 and j <= -1 + N; "
2493 "S_1[i] -> b[0] : i >= 0 and i <= -1 + M }";
2494 S = "[M, N] -> { S_1[i] -> [1, i, 0]; S_0[i, j] -> [0, i, 0, j, 0] }";
2495 if (test_one_schedule(ctx, D, W, R, S, 0, 0) < 0)
2496 return -1;
2497
2498 D = "{ S_0[i] : i >= 0 }";
2499 W = "{ S_0[i] -> a[i] : i >= 0 }";
2500 R = "{ S_0[i] -> a[0] : i >= 0 }";
2501 S = "{ S_0[i] -> [0, i, 0] }";
2502 if (test_one_schedule(ctx, D, W, R, S, 0, 0) < 0)
2503 return -1;
2504
2505 D = "{ S_0[i] : i >= 0; S_1[i] : i >= 0 }";
2506 W = "{ S_0[i] -> a[i] : i >= 0; S_1[i] -> b[i] : i >= 0 }";
2507 R = "{ S_0[i] -> b[0] : i >= 0; S_1[i] -> a[i] : i >= 0 }";
2508 S = "{ S_1[i] -> [0, i, 1]; S_0[i] -> [0, i, 0] }";
2509 if (test_one_schedule(ctx, D, W, R, S, 0, 0) < 0)
2510 return -1;
2511
2512 D = "[n] -> { S_0[j, k] : j <= -1 + n and j >= 0 and "
2513 "k <= -1 + n and k >= 0 }";
2514 W = "[n] -> { S_0[j, k] -> B[j] : j <= -1 + n and j >= 0 and " "k <= -1 + n and k >= 0 }";
2515 R = "[n] -> { S_0[j, k] -> B[j] : j <= -1 + n and j >= 0 and "
2516 "k <= -1 + n and k >= 0; "
2517 "S_0[j, k] -> B[k] : j <= -1 + n and j >= 0 and "
2518 "k <= -1 + n and k >= 0; "
2519 "S_0[j, k] -> A[k] : j <= -1 + n and j >= 0 and "
2520 "k <= -1 + n and k >= 0 }";
2521 S = "[n] -> { S_0[j, k] -> [2, j, k] }";
2522 ctx->opt->schedule_outer_zero_distance = 1;
2523 if (test_one_schedule(ctx, D, W, R, S, 0, 0) < 0)
2524 return -1;
2525 ctx->opt->schedule_outer_zero_distance = 0;
2526
2527 D = "{Stmt_for_body24[i0, i1, i2, i3]:"
2528 "i0 >= 0 and i0 <= 1 and i1 >= 0 and i1 <= 6 and i2 >= 2 and "
2529 "i2 <= 6 - i1 and i3 >= 0 and i3 <= -1 + i2;"
2530 "Stmt_for_body24[i0, i1, 1, 0]:"
2531 "i0 >= 0 and i0 <= 1 and i1 >= 0 and i1 <= 5;"
2532 "Stmt_for_body7[i0, i1, i2]:"
2533 "i0 >= 0 and i0 <= 1 and i1 >= 0 and i1 <= 7 and i2 >= 0 and "
2534 "i2 <= 7 }";
2535
2536 V = "{Stmt_for_body24[0, i1, i2, i3] -> "
2537 "Stmt_for_body24[1, i1, i2, i3]:"
2538 "i3 >= 0 and i3 <= -1 + i2 and i1 >= 0 and i2 <= 6 - i1 and "
2539 "i2 >= 1;"
2540 "Stmt_for_body24[0, i1, i2, i3] -> "
2541 "Stmt_for_body7[1, 1 + i1 + i3, 1 + i1 + i2]:"
2542 "i3 <= -1 + i2 and i2 <= 6 - i1 and i2 >= 1 and i1 >= 0 and "
2543 "i3 >= 0;"
2544 "Stmt_for_body24[0, i1, i2, i3] ->"
2545 "Stmt_for_body7[1, i1, 1 + i1 + i3]:"
2546 "i3 >= 0 and i2 <= 6 - i1 and i1 >= 0 and i3 <= -1 + i2;"
2547 "Stmt_for_body7[0, i1, i2] -> Stmt_for_body7[1, i1, i2]:"
2548 "(i2 >= 1 + i1 and i2 <= 6 and i1 >= 0 and i1 <= 4) or "
2549 "(i2 >= 3 and i2 <= 7 and i1 >= 1 and i2 >= 1 + i1) or "
2550 "(i2 >= 0 and i2 <= i1 and i2 >= -7 + i1 and i1 <= 7);"
2551 "Stmt_for_body7[0, i1, 1 + i1] -> Stmt_for_body7[1, i1, 1 + i1]:"
2552 "i1 <= 6 and i1 >= 0;"
2553 "Stmt_for_body7[0, 0, 7] -> Stmt_for_body7[1, 0, 7];"
2554 "Stmt_for_body7[i0, i1, i2] -> "
2555 "Stmt_for_body24[i0, o1, -1 + i2 - o1, -1 + i1 - o1]:"
2556 "i0 >= 0 and i0 <= 1 and o1 >= 0 and i2 >= 1 + i1 and "
2557 "o1 <= -2 + i2 and i2 <= 7 and o1 <= -1 + i1;"
2558 "Stmt_for_body7[i0, i1, i2] -> "
2559 "Stmt_for_body24[i0, i1, o2, -1 - i1 + i2]:"
2560 "i0 >= 0 and i0 <= 1 and i1 >= 0 and o2 >= -i1 + i2 and "
2561 "o2 >= 1 and o2 <= 6 - i1 and i2 >= 1 + i1 }";
2562 P = V;
2563 S = "{ Stmt_for_body24[i0, i1, i2, i3] -> "
2564 "[i0, 5i0 + i1, 6i0 + i1 + i2, 1 + 6i0 + i1 + i2 + i3, 1];"
2565 "Stmt_for_body7[i0, i1, i2] -> [0, 5i0, 6i0 + i1, 6i0 + i2, 0] }";
2566
2567 if (test_special_schedule(ctx, D, V, P, S) < 0)
2568 return -1;
2569
2570 D = "{ S_0[i, j] : i >= 1 and i <= 10 and j >= 1 and j <= 8 }";
2571 V = "{ S_0[i, j] -> S_0[i, 1 + j] : i >= 1 and i <= 10 and "
2572 "j >= 1 and j <= 7;"
2573 "S_0[i, j] -> S_0[1 + i, j] : i >= 1 and i <= 9 and "
2574 "j >= 1 and j <= 8 }";
2575 P = "{ }";
2576 S = "{ S_0[i, j] -> [i + j, j] }";
2577 ctx->opt->schedule_algorithm = ISL_SCHEDULE_ALGORITHM_FEAUTRIER;
2578 if (test_special_schedule(ctx, D, V, P, S) < 0)
2579 return -1;
2580 ctx->opt->schedule_algorithm = ISL_SCHEDULE_ALGORITHM_ISL;
2581
2582 /* Fig. 1 from Feautrier's "Some Efficient Solutions..." pt. 2, 1992 */
2583 D = "[N] -> { S_0[i, j] : i >= 0 and i <= -1 + N and "
2584 "j >= 0 and j <= -1 + i }";
2585 V = "[N] -> { S_0[i, j] -> S_0[i, 1 + j] : j <= -2 + i and "
2586 "i <= -1 + N and j >= 0;"
2587 "S_0[i, -1 + i] -> S_0[1 + i, 0] : i >= 1 and "
2588 "i <= -2 + N }";
2589 P = "{ }";
2590 S = "{ S_0[i, j] -> [i, j] }";
2591 ctx->opt->schedule_algorithm = ISL_SCHEDULE_ALGORITHM_FEAUTRIER;
2592 if (test_special_schedule(ctx, D, V, P, S) < 0)
2593 return -1;
2594 ctx->opt->schedule_algorithm = ISL_SCHEDULE_ALGORITHM_ISL;
2595
2596 /* Test both algorithms on a case with only proximity dependences. */
2597 D = "{ S[i,j] : 0 <= i <= 10 }";
2598 V = "{ }";
2599 P = "{ S[i,j] -> S[i+1,j] : 0 <= i,j <= 10 }";
2600 S = "{ S[i, j] -> [j, i] }";
2601 ctx->opt->schedule_algorithm = ISL_SCHEDULE_ALGORITHM_FEAUTRIER;
2602 if (test_special_schedule(ctx, D, V, P, S) < 0)
2603 return -1;
2604 ctx->opt->schedule_algorithm = ISL_SCHEDULE_ALGORITHM_ISL;
2605 if (test_special_schedule(ctx, D, V, P, S) < 0)
2606 return -1;
2607
2608 D = "{ A[a]; B[] }";
2609 V = "{}";
2610 P = "{ A[a] -> B[] }";
2611 if (test_has_schedule(ctx, D, V, P) < 0)
2612 return -1;
2613
2614 return 0;
2615 }
2616
2617 int test_plain_injective(isl_ctx *ctx, const char *str, int injective)
2618 {
2619 isl_union_map *umap;
2620 int test;
2621
2622 umap = isl_union_map_read_from_str(ctx, str);
2623 test = isl_union_map_plain_is_injective(umap);
2624 isl_union_map_free(umap);
2625 if (test < 0)
2626 return -1;
2627 if (test == injective)
2628 return 0;
2629 if (injective)
2630 isl_die(ctx, isl_error_unknown,
2631 "map not detected as injective", return -1);
2632 else
2633 isl_die(ctx, isl_error_unknown,
2634 "map detected as injective", return -1);
2635 }
2636
2637 int test_injective(isl_ctx *ctx)
2638 {
2639 const char *str;
2640
2641 if (test_plain_injective(ctx, "{S[i,j] -> A[0]; T[i,j] -> B[1]}", 0))
2642 return -1;
2643 if (test_plain_injective(ctx, "{S[] -> A[0]; T[] -> B[0]}", 1))
2644 return -1;
2645 if (test_plain_injective(ctx, "{S[] -> A[0]; T[] -> A[1]}", 1))
2646 return -1;
2647 if (test_plain_injective(ctx, "{S[] -> A[0]; T[] -> A[0]}", 0))
2648 return -1;
2649 if (test_plain_injective(ctx, "{S[i] -> A[i,0]; T[i] -> A[i,1]}", 1))
2650 return -1;
2651 if (test_plain_injective(ctx, "{S[i] -> A[i]; T[i] -> A[i]}", 0))
2652 return -1;
2653 if (test_plain_injective(ctx, "{S[] -> A[0,0]; T[] -> A[0,1]}", 1))
2654 return -1;
2655 if (test_plain_injective(ctx, "{S[] -> A[0,0]; T[] -> A[1,0]}", 1))
2656 return -1;
2657
2658 str = "{S[] -> A[0,0]; T[] -> A[0,1]; U[] -> A[1,0]}";
2659 if (test_plain_injective(ctx, str, 1))
2660 return -1;
2661 str = "{S[] -> A[0,0]; T[] -> A[0,1]; U[] -> A[0,0]}";
2662 if (test_plain_injective(ctx, str, 0))
2663 return -1;
2664
2665 return 0;
2666 }
2667
2668 static int aff_plain_is_equal(__isl_keep isl_aff *aff, const char *str)
2669 {
2670 isl_aff *aff2;
2671 int equal;
2672
2673 if (!aff)
2674 return -1;
2675
2676 aff2 = isl_aff_read_from_str(isl_aff_get_ctx(aff), str);
2677 equal = isl_aff_plain_is_equal(aff, aff2);
2678 isl_aff_free(aff2);
2679
2680 return equal;
2681 }
2682
2683 static int aff_check_plain_equal(__isl_keep isl_aff *aff, const char *str)
2684 {
2685 int equal;
2686
2687 equal = aff_plain_is_equal(aff, str);
2688 if (equal < 0)
2689 return -1;
2690 if (!equal)
2691 isl_die(isl_aff_get_ctx(aff), isl_error_unknown,
2692 "result not as expected", return -1);
2693 return 0;
2694 }
2695
2696 int test_aff(isl_ctx *ctx)
2697 {
2698 const char *str;
2699 isl_set *set;
2700 isl_space *space;
2701 isl_local_space *ls;
2702 isl_aff *aff;
2703 int zero, equal;
2704
2705 space = isl_space_set_alloc(ctx, 0, 1);
2706 ls = isl_local_space_from_space(space);
2707 aff = isl_aff_zero_on_domain(ls);
2708
2709 aff = isl_aff_add_coefficient_si(aff, isl_dim_in, 0, 1);
2710 aff = isl_aff_scale_down_ui(aff, 3);
2711 aff = isl_aff_floor(aff);
2712 aff = isl_aff_add_coefficient_si(aff, isl_dim_in, 0, 1);
2713 aff = isl_aff_scale_down_ui(aff, 2);
2714 aff = isl_aff_floor(aff);
2715 aff = isl_aff_add_coefficient_si(aff, isl_dim_in, 0, 1);
2716
2717 str = "{ [10] }";
2718 set = isl_set_read_from_str(ctx, str);
2719 aff = isl_aff_gist(aff, set);
2720
2721 aff = isl_aff_add_constant_si(aff, -16);
2722 zero = isl_aff_plain_is_zero(aff);
2723 isl_aff_free(aff);
2724
2725 if (zero < 0)
2726 return -1;
2727 if (!zero)
2728 isl_die(ctx, isl_error_unknown, "unexpected result", return -1);
2729
2730 aff = isl_aff_read_from_str(ctx, "{ [-1] }");
2731 aff = isl_aff_scale_down_ui(aff, 64);
2732 aff = isl_aff_floor(aff);
2733 equal = aff_check_plain_equal(aff, "{ [-1] }");
2734 isl_aff_free(aff);
2735 if (equal < 0)
2736 return -1;
2737
2738 return 0;
2739 }
2740
2741 int test_dim_max(isl_ctx *ctx)
2742 {
2743 int equal;
2744 const char *str;
2745 isl_set *set1, *set2;
2746 isl_set *set;
2747 isl_map *map;
2748 isl_pw_aff *pwaff;
2749
2750 str = "[N] -> { [i] : 0 <= i <= min(N,10) }";
2751 set = isl_set_read_from_str(ctx, str);
2752 pwaff = isl_set_dim_max(set, 0);
2753 set1 = isl_set_from_pw_aff(pwaff);
2754 str = "[N] -> { [10] : N >= 10; [N] : N <= 9 and N >= 0 }";
2755 set2 = isl_set_read_from_str(ctx, str);
2756 equal = isl_set_is_equal(set1, set2);
2757 isl_set_free(set1);
2758 isl_set_free(set2);
2759 if (equal < 0)
2760 return -1;
2761 if (!equal)
2762 isl_die(ctx, isl_error_unknown, "unexpected result", return -1);
2763
2764 str = "[N] -> { [i] : 0 <= i <= max(2N,N+6) }";
2765 set = isl_set_read_from_str(ctx, str);
2766 pwaff = isl_set_dim_max(set, 0);
2767 set1 = isl_set_from_pw_aff(pwaff);
2768 str = "[N] -> { [6 + N] : -6 <= N <= 5; [2N] : N >= 6 }";
2769 set2 = isl_set_read_from_str(ctx, str);
2770 equal = isl_set_is_equal(set1, set2);
2771 isl_set_free(set1);
2772 isl_set_free(set2);
2773 if (equal < 0)
2774 return -1;
2775 if (!equal)
2776 isl_die(ctx, isl_error_unknown, "unexpected result", return -1);
2777
2778 str = "[N] -> { [i] : 0 <= i <= 2N or 0 <= i <= N+6 }";
2779 set = isl_set_read_from_str(ctx, str);
2780 pwaff = isl_set_dim_max(set, 0);
2781 set1 = isl_set_from_pw_aff(pwaff);
2782 str = "[N] -> { [6 + N] : -6 <= N <= 5; [2N] : N >= 6 }";
2783 set2 = isl_set_read_from_str(ctx, str);
2784 equal = isl_set_is_equal(set1, set2);
2785 isl_set_free(set1);
2786 isl_set_free(set2);
2787 if (equal < 0)
2788 return -1;
2789 if (!equal)
2790 isl_die(ctx, isl_error_unknown, "unexpected result", return -1);
2791
2792 str = "[N,M] -> { [i,j] -> [([i/16]), i%16, ([j/16]), j%16] : "
2793 "0 <= i < N and 0 <= j < M }";
2794 map = isl_map_read_from_str(ctx, str);
2795 set = isl_map_range(map);
2796
2797 pwaff = isl_set_dim_max(isl_set_copy(set), 0);
2798 set1 = isl_set_from_pw_aff(pwaff);
2799 str = "[N,M] -> { [([(N-1)/16])] : M,N > 0 }";
2800 set2 = isl_set_read_from_str(ctx, str);
2801 equal = isl_set_is_equal(set1, set2);
2802 isl_set_free(set1);
2803 isl_set_free(set2);
2804
2805 pwaff = isl_set_dim_max(isl_set_copy(set), 3);
2806 set1 = isl_set_from_pw_aff(pwaff);
2807 str = "[N,M] -> { [t] : t = min(M-1,15) and M,N > 0 }";
2808 set2 = isl_set_read_from_str(ctx, str);
2809 if (equal >= 0 && equal)
2810 equal = isl_set_is_equal(set1, set2);
2811 isl_set_free(set1);
2812 isl_set_free(set2);
2813
2814 isl_set_free(set);
2815
2816 if (equal < 0)
2817 return -1;
2818 if (!equal)
2819 isl_die(ctx, isl_error_unknown, "unexpected result", return -1);
2820
2821 return 0;
2822 }
2823
2824 int test_product(isl_ctx *ctx)
2825 {
2826 const char *str;
2827 isl_set *set;
2828 isl_union_set *uset1, *uset2;
2829 int ok;
2830
2831 str = "{ A[i] }";
2832 set = isl_set_read_from_str(ctx, str);
2833 set = isl_set_product(set, isl_set_copy(set));
2834 ok = isl_set_is_wrapping(set);
2835 isl_set_free(set);
2836 if (ok < 0)
2837 return -1;
2838 if (!ok)
2839 isl_die(ctx, isl_error_unknown, "unexpected result", return -1);
2840
2841 str = "{ [] }";
2842 uset1 = isl_union_set_read_from_str(ctx, str);
2843 uset1 = isl_union_set_product(uset1, isl_union_set_copy(uset1));
2844 str = "{ [[] -> []] }";
2845 uset2 = isl_union_set_read_from_str(ctx, str);
2846 ok = isl_union_set_is_equal(uset1, uset2);
2847 isl_union_set_free(uset1);
2848 isl_union_set_free(uset2);
2849 if (ok < 0)
2850 return -1;
2851 if (!ok)
2852 isl_die(ctx, isl_error_unknown, "unexpected result", return -1);
2853
2854 return 0;
2855 }
2856
2857 int test_equal(isl_ctx *ctx)
2858 {
2859 const char *str;
2860 isl_set *set, *set2;
2861 int equal;
2862
2863 str = "{ S_6[i] }";
2864 set = isl_set_read_from_str(ctx, str);
2865 str = "{ S_7[i] }";
2866 set2 = isl_set_read_from_str(ctx, str);
2867 equal = isl_set_is_equal(set, set2);
2868 isl_set_free(set);
2869 isl_set_free(set2);
2870 if (equal < 0)
2871 return -1;
2872 if (equal)
2873 isl_die(ctx, isl_error_unknown, "unexpected result", return -1);
2874
2875 return 0;
2876 }
2877
2878 static int test_plain_fixed(isl_ctx *ctx, __isl_take isl_map *map,
2879 enum isl_dim_type type, unsigned pos, int fixed)
2880 {
2881 int test;
2882
2883 test = isl_map_plain_is_fixed(map, type, pos, NULL);
2884 isl_map_free(map);
2885 if (test < 0)
2886 return -1;
2887 if (test == fixed)
2888 return 0;
2889 if (fixed)
2890 isl_die(ctx, isl_error_unknown,
2891 "map not detected as fixed", return -1);
2892 else
2893 isl_die(ctx, isl_error_unknown,
2894 "map detected as fixed", return -1);
2895 }
2896
2897 int test_fixed(isl_ctx *ctx)
2898 {
2899 const char *str;
2900 isl_map *map;
2901
2902 str = "{ [i] -> [i] }";
2903 map = isl_map_read_from_str(ctx, str);
2904 if (test_plain_fixed(ctx, map, isl_dim_out, 0, 0))
2905 return -1;
2906 str = "{ [i] -> [1] }";
2907 map = isl_map_read_from_str(ctx, str);
2908 if (test_plain_fixed(ctx, map, isl_dim_out, 0, 1))
2909 return -1;
2910 str = "{ S_1[p1] -> [o0] : o0 = -2 and p1 >= 1 and p1 <= 7 }";
2911 map = isl_map_read_from_str(ctx, str);
2912 if (test_plain_fixed(ctx, map, isl_dim_out, 0, 1))
2913 return -1;
2914 map = isl_map_read_from_str(ctx, str);
2915 map = isl_map_neg(map);
2916 if (test_plain_fixed(ctx, map, isl_dim_out, 0, 1))
2917 return -1;
2918
2919 return 0;
2920 }
2921
2922 int test_vertices(isl_ctx *ctx)
2923 {
2924 const char *str;
2925 isl_basic_set *bset;
2926 isl_vertices *vertices;
2927
2928 str = "{ A[t, i] : t = 12 and i >= 4 and i <= 12 }";
2929 bset = isl_basic_set_read_from_str(ctx, str);
2930 vertices = isl_basic_set_compute_vertices(bset);
2931 isl_basic_set_free(bset);
2932 isl_vertices_free(vertices);
2933 if (!vertices)
2934 return -1;
2935
2936 str = "{ A[t, i] : t = 14 and i = 1 }";
2937 bset = isl_basic_set_read_from_str(ctx, str);
2938 vertices = isl_basic_set_compute_vertices(bset);
2939 isl_basic_set_free(bset);
2940 isl_vertices_free(vertices);
2941 if (!vertices)
2942 return -1;
2943
2944 return 0;
2945 }
2946
2947 int test_union_pw(isl_ctx *ctx)
2948 {
2949 int equal;
2950 const char *str;
2951 isl_union_set *uset;
2952 isl_union_pw_qpolynomial *upwqp1, *upwqp2;
2953
2954 str = "{ [x] -> x^2 }";
2955 upwqp1 = isl_union_pw_qpolynomial_read_from_str(ctx, str);
2956 upwqp2 = isl_union_pw_qpolynomial_copy(upwqp1);
2957 uset = isl_union_pw_qpolynomial_domain(upwqp1);
2958 upwqp1 = isl_union_pw_qpolynomial_copy(upwqp2);
2959 upwqp1 = isl_union_pw_qpolynomial_intersect_domain(upwqp1, uset);
2960 equal = isl_union_pw_qpolynomial_plain_is_equal(upwqp1, upwqp2);
2961 isl_union_pw_qpolynomial_free(upwqp1);
2962 isl_union_pw_qpolynomial_free(upwqp2);
2963 if (equal < 0)
2964 return -1;
2965 if (!equal)
2966 isl_die(ctx, isl_error_unknown, "unexpected result", return -1);
2967
2968 return 0;
2969 }
2970
2971 int test_output(isl_ctx *ctx)
2972 {
2973 char *s;
2974 const char *str;
2975 isl_pw_aff *pa;
2976 isl_printer *p;
2977 int equal;
2978
2979 str = "[x] -> { [1] : x % 4 <= 2; [2] : x = 3 }";
2980 pa = isl_pw_aff_read_from_str(ctx, str);
2981
2982 p = isl_printer_to_str(ctx);
2983 p = isl_printer_set_output_format(p, ISL_FORMAT_C);
2984 p = isl_printer_print_pw_aff(p, pa);
2985 s = isl_printer_get_str(p);
2986 isl_printer_free(p);
2987 isl_pw_aff_free(pa);
2988 if (!s)
2989 equal = -1;
2990 else
2991 equal = !strcmp(s, "(2 - x + 4*floord(x, 4) >= 0) ? (1) : 2");
2992 free(s);
2993 if (equal < 0)
2994 return -1;
2995 if (!equal)
2996 isl_die(ctx, isl_error_unknown, "unexpected result", return -1);
2997
2998 return 0;
2999 }
3000
3001 int test_sample(isl_ctx *ctx)
3002 {
3003 const char *str;
3004 isl_basic_set *bset1, *bset2;
3005 int empty, subset;
3006
3007 str = "{ [a, b, c, d, e, f, g, h, i, j, k] : "
3008 "3i >= 1073741823b - c - 1073741823e + f and c >= 0 and "
3009 "3i >= -1 + 3221225466b + c + d - 3221225466e - f and "
3010 "2e >= a - b and 3e <= 2a and 3k <= -a and f <= -1 + a and "
3011 "3i <= 4 - a + 4b + 2c - e - 2f and 3k <= -a + c - f and "
3012 "3h >= -2 + a and 3g >= -3 - a and 3k >= -2 - a and "
3013 "3i >= -2 - a - 2c + 3e + 2f and 3h <= a + c - f and "
3014 "3h >= a + 2147483646b + 2c - 2147483646e - 2f and "
3015 "3g <= -1 - a and 3i <= 1 + c + d - f and a <= 1073741823 and "
3016 "f >= 1 - a + 1073741822b + c + d - 1073741822e and "
3017 "3i >= 1 + 2b - 2c + e + 2f + 3g and "
3018 "1073741822f <= 1073741822 - a + 1073741821b + 1073741822c +"
3019 "d - 1073741821e and "
3020 "3j <= 3 - a + 3b and 3g <= -2 - 2b + c + d - e - f and "
3021 "3j >= 1 - a + b + 2e and "
3022 "3f >= -3 + a + 3221225462b + 3c + d - 3221225465e and "
3023 "3i <= 4 - a + 4b - e and "
3024 "f <= 1073741822 + 1073741822b - 1073741822e and 3h <= a and "
3025 "f >= 0 and 2e <= 4 - a + 5b - d and 2e <= a - b + d and "
3026 "c <= -1 + a and 3i >= -2 - a + 3e and "
3027 "1073741822e <= 1073741823 - a + 1073741822b + c and "
3028 "3g >= -4 + 3221225464b + 3c + d - 3221225467e - 3f and "
3029 "3i >= -1 + 3221225466b + 3c + d - 3221225466e - 3f and "
3030 "1073741823e >= 1 + 1073741823b - d and "
3031 "3i >= 1073741823b + c - 1073741823e - f and "
3032 "3i >= 1 + 2b + e + 3g }";
3033 bset1 = isl_basic_set_read_from_str(ctx, str);
3034 bset2 = isl_basic_set_sample(isl_basic_set_copy(bset1));
3035 empty = isl_basic_set_is_empty(bset2);
3036 subset = isl_basic_set_is_subset(bset2, bset1);
3037 isl_basic_set_free(bset1);
3038 isl_basic_set_free(bset2);
3039 if (empty < 0 || subset < 0)
3040 return -1;
3041 if (empty)
3042 isl_die(ctx, isl_error_unknown, "point not found", return -1);
3043 if (!subset)
3044 isl_die(ctx, isl_error_unknown, "bad point found", return -1);
3045
3046 return 0;
3047 }
3048
3049 int test_fixed_power(isl_ctx *ctx)
3050 {
3051 const char *str;
3052 isl_map *map;
3053 isl_int exp;
3054 int equal;
3055
3056 isl_int_init(exp);
3057 str = "{ [i] -> [i + 1] }";
3058 map = isl_map_read_from_str(ctx, str);
3059 isl_int_set_si(exp, 23);
3060 map = isl_map_fixed_power(map, exp);
3061 equal = map_check_equal(map, "{ [i] -> [i + 23] }");
3062 isl_int_clear(exp);
3063 isl_map_free(map);
3064 if (equal < 0)
3065 return -1;
3066
3067 return 0;
3068 }
3069
3070 int test_slice(isl_ctx *ctx)
3071 {
3072 const char *str;
3073 isl_map *map;
3074 int equal;
3075
3076 str = "{ [i] -> [j] }";
3077 map = isl_map_read_from_str(ctx, str);
3078 map = isl_map_equate(map, isl_dim_in, 0, isl_dim_out, 0);
3079 equal = map_check_equal(map, "{ [i] -> [i] }");
3080 isl_map_free(map);
3081 if (equal < 0)
3082 return -1;
3083
3084 str = "{ [i] -> [j] }";
3085 map = isl_map_read_from_str(ctx, str);
3086 map = isl_map_equate(map, isl_dim_in, 0, isl_dim_in, 0);
3087 equal = map_check_equal(map, "{ [i] -> [j] }");
3088 isl_map_free(map);
3089 if (equal < 0)
3090 return -1;
3091
3092 str = "{ [i] -> [j] }";
3093 map = isl_map_read_from_str(ctx, str);
3094 map = isl_map_oppose(map, isl_dim_in, 0, isl_dim_out, 0);
3095 equal = map_check_equal(map, "{ [i] -> [-i] }");
3096 isl_map_free(map);
3097 if (equal < 0)
3098 return -1;
3099
3100 str = "{ [i] -> [j] }";
3101 map = isl_map_read_from_str(ctx, str);
3102 map = isl_map_oppose(map, isl_dim_in, 0, isl_dim_in, 0);
3103 equal = map_check_equal(map, "{ [0] -> [j] }");
3104 isl_map_free(map);
3105 if (equal < 0)
3106 return -1;
3107
3108 str = "{ [i] -> [j] }";
3109 map = isl_map_read_from_str(ctx, str);
3110 map = isl_map_order_gt(map, isl_dim_in, 0, isl_dim_out, 0);
3111 equal = map_check_equal(map, "{ [i] -> [j] : i > j }");
3112 isl_map_free(map);
3113 if (equal < 0)
3114 return -1;
3115
3116 str = "{ [i] -> [j] }";
3117 map = isl_map_read_from_str(ctx, str);
3118 map = isl_map_order_gt(map, isl_dim_in, 0, isl_dim_in, 0);
3119 equal = map_check_equal(map, "{ [i] -> [j] : false }");
3120 isl_map_free(map);
3121 if (equal < 0)
3122 return -1;
3123
3124 return 0;
3125 }
3126
3127 int test_eliminate(isl_ctx *ctx)
3128 {
3129 const char *str;
3130 isl_map *map;
3131 int equal;
3132
3133 str = "{ [i] -> [j] : i = 2j }";
3134 map = isl_map_read_from_str(ctx, str);
3135 map = isl_map_eliminate(map, isl_dim_out, 0, 1);
3136 equal = map_check_equal(map, "{ [i] -> [j] : exists a : i = 2a }");
3137 isl_map_free(map);
3138 if (equal < 0)
3139 return -1;
3140
3141 return 0;
3142 }
3143
3144 /* Check that isl_set_dim_residue_class detects that the values of j
3145 * in the set below are all odd and that it does not detect any spurious
3146 * strides.
3147 */
3148 static int test_residue_class(isl_ctx *ctx)
3149 {
3150 const char *str;
3151 isl_set *set;
3152 isl_int m, r;
3153 int res;
3154
3155 str = "{ [i,j] : j = 4 i + 1 and 0 <= i <= 100; "
3156 "[i,j] : j = 4 i + 3 and 500 <= i <= 600 }";
3157 set = isl_set_read_from_str(ctx, str);
3158 isl_int_init(m);
3159 isl_int_init(r);
3160 res = isl_set_dim_residue_class(set, 1, &m, &r);
3161 if (res >= 0 &&
3162 (isl_int_cmp_si(m, 2) != 0 || isl_int_cmp_si(r, 1) != 0))
3163 isl_die(ctx, isl_error_unknown, "incorrect residue class",
3164 res = -1);
3165 isl_int_clear(r);
3166 isl_int_clear(m);
3167 isl_set_free(set);
3168
3169 return res;
3170 }
3171
3172 int test_align_parameters(isl_ctx *ctx)
3173 {
3174 const char *str;
3175 isl_space *space;
3176 isl_multi_aff *ma1, *ma2;
3177 int equal;
3178
3179 str = "{ A[B[] -> C[]] -> D[E[] -> F[]] }";
3180 ma1 = isl_multi_aff_read_from_str(ctx, str);
3181
3182 space = isl_space_params_alloc(ctx, 1);
3183 space = isl_space_set_dim_name(space, isl_dim_param, 0, "N");
3184 ma1 = isl_multi_aff_align_params(ma1, space);
3185
3186 str = "[N] -> { A[B[] -> C[]] -> D[E[] -> F[]] }";
3187 ma2 = isl_multi_aff_read_from_str(ctx, str);
3188
3189 equal = isl_multi_aff_plain_is_equal(ma1, ma2);
3190
3191 isl_multi_aff_free(ma1);
3192 isl_multi_aff_free(ma2);
3193
3194 if (equal < 0)
3195 return -1;
3196 if (!equal)
3197 isl_die(ctx, isl_error_unknown,
3198 "result not as expected", return -1);
3199
3200 return 0;
3201 }
3202
3203 static int test_list(isl_ctx *ctx)
3204 {
3205 isl_id *a, *b, *c, *d, *id;
3206 isl_id_list *list;
3207 int ok;
3208
3209 a = isl_id_alloc(ctx, "a", NULL);
3210 b = isl_id_alloc(ctx, "b", NULL);
3211 c = isl_id_alloc(ctx, "c", NULL);
3212 d = isl_id_alloc(ctx, "d", NULL);
3213
3214 list = isl_id_list_alloc(ctx, 4);
3215 list = isl_id_list_add(list, a);
3216 list = isl_id_list_add(list, b);
3217 list = isl_id_list_add(list, c);
3218 list = isl_id_list_add(list, d);
3219 list = isl_id_list_drop(list, 1, 1);
3220
3221 if (isl_id_list_n_id(list) != 3) {
3222 isl_id_list_free(list);
3223 isl_die(ctx, isl_error_unknown,
3224 "unexpected number of elements in list", return -1);
3225 }
3226
3227 id = isl_id_list_get_id(list, 0);
3228 ok = id == a;
3229 isl_id_free(id);
3230 id = isl_id_list_get_id(list, 1);
3231 ok = ok && id == c;
3232 isl_id_free(id);
3233 id = isl_id_list_get_id(list, 2);
3234 ok = ok && id == d;
3235 isl_id_free(id);
3236
3237 isl_id_list_free(list);
3238
3239 if (!ok)
3240 isl_die(ctx, isl_error_unknown,
3241 "unexpected elements in list", return -1);
3242
3243 return 0;
3244 }
3245
3246 const char *set_conversion_tests[] = {
3247 "[N] -> { [i] : N - 1 <= 2 i <= N }",
3248 "[N] -> { [i] : exists a : i = 4 a and N - 1 <= i <= N }",
3249 "[N] -> { [i,j] : exists a : i = 4 a and N - 1 <= i, 2j <= N }",
3250 "[N] -> { [[i]->[j]] : exists a : i = 4 a and N - 1 <= i, 2j <= N }",
3251 };
3252
3253 /* Check that converting from isl_set to isl_pw_multi_aff and back
3254 * to isl_set produces the original isl_set.
3255 */
3256 static int test_set_conversion(isl_ctx *ctx)
3257 {
3258 int i;
3259 const char *str;
3260 isl_set *set1, *set2;
3261 isl_pw_multi_aff *pma;
3262 int equal;
3263
3264 for (i = 0; i < ARRAY_SIZE(set_conversion_tests); ++i) {
3265 str = set_conversion_tests[i];
3266 set1 = isl_set_read_from_str(ctx, str);
3267 pma = isl_pw_multi_aff_from_set(isl_set_copy(set1));
3268 set2 = isl_set_from_pw_multi_aff(pma);
3269 equal = isl_set_is_equal(set1, set2);
3270 isl_set_free(set1);
3271 isl_set_free(set2);
3272
3273 if (equal < 0)
3274 return -1;
3275 if (!equal)
3276 isl_die(ctx, isl_error_unknown, "bad conversion",
3277 return -1);
3278 }
3279
3280 return 0;
3281 }
3282
3283 /* Check that converting from isl_map to isl_pw_multi_aff and back
3284 * to isl_map produces the original isl_map.
3285 */
3286 static int test_map_conversion(isl_ctx *ctx)
3287 {
3288 const char *str;
3289 isl_map *map1, *map2;
3290 isl_pw_multi_aff *pma;
3291 int equal;
3292
3293 str = "{ [a, b, c, d] -> s0[a, b, e, f] : "
3294 "exists (e0 = [(a - 2c)/3], e1 = [(-4 + b - 5d)/9], "
3295 "e2 = [(-d + f)/9]: 3e0 = a - 2c and 9e1 = -4 + b - 5d and "
3296 "9e2 = -d + f and f >= 0 and f <= 8 and 9e >= -5 - 2a and "
3297 "9e <= -2 - 2a) }";
3298 map1 = isl_map_read_from_str(ctx, str);
3299 pma = isl_pw_multi_aff_from_map(isl_map_copy(map1));
3300 map2 = isl_map_from_pw_multi_aff(pma);
3301 equal = isl_map_is_equal(map1, map2);
3302 isl_map_free(map1);
3303 isl_map_free(map2);
3304
3305 if (equal < 0)
3306 return -1;
3307 if (!equal)
3308 isl_die(ctx, isl_error_unknown, "bad conversion", return -1);
3309
3310 return 0;
3311 }
3312
3313 static int test_conversion(isl_ctx *ctx)
3314 {
3315 if (test_set_conversion(ctx) < 0)
3316 return -1;
3317 if (test_map_conversion(ctx) < 0)
3318 return -1;
3319 return 0;
3320 }
3321
3322 /* Check that isl_basic_map_curry does not modify input.
3323 */
3324 static int test_curry(isl_ctx *ctx)
3325 {
3326 const char *str;
3327 isl_basic_map *bmap1, *bmap2;
3328 int equal;
3329
3330 str = "{ [A[] -> B[]] -> C[] }";
3331 bmap1 = isl_basic_map_read_from_str(ctx, str);
3332 bmap2 = isl_basic_map_curry(isl_basic_map_copy(bmap1));
3333 equal = isl_basic_map_is_equal(bmap1, bmap2);
3334 isl_basic_map_free(bmap1);
3335 isl_basic_map_free(bmap2);
3336
3337 if (equal < 0)
3338 return -1;
3339 if (equal)
3340 isl_die(ctx, isl_error_unknown,
3341 "curried map should not be equal to original",
3342 return -1);
3343
3344 return 0;
3345 }
3346
3347 struct {
3348 const char *set;
3349 const char *ma;
3350 const char *res;
3351 } preimage_tests[] = {
3352 { "{ B[i,j] : 0 <= i < 10 and 0 <= j < 100 }",
3353 "{ A[j,i] -> B[i,j] }",
3354 "{ A[j,i] : 0 <= i < 10 and 0 <= j < 100 }" },
3355 { "{ rat: B[i,j] : 0 <= i, j and 3 i + 5 j <= 100 }",
3356 "{ A[a,b] -> B[a/2,b/6] }",
3357 "{ rat: A[a,b] : 0 <= a, b and 9 a + 5 b <= 600 }" },
3358 { "{ B[i,j] : 0 <= i, j and 3 i + 5 j <= 100 }",
3359 "{ A[a,b] -> B[a/2,b/6] }",
3360 "{ A[a,b] : 0 <= a, b and 9 a + 5 b <= 600 and "
3361 "exists i,j : a = 2 i and b = 6 j }" },
3362 { "[n] -> { S[i] : 0 <= i <= 100 }", "[n] -> { S[n] }",
3363 "[n] -> { : 0 <= n <= 100 }" },
3364 { "{ B[i] : 0 <= i < 100 and exists a : i = 4 a }",
3365 "{ A[a] -> B[2a] }",
3366 "{ A[a] : 0 <= a < 50 and exists b : a = 2 b }" },
3367 { "{ B[i] : 0 <= i < 100 and exists a : i = 4 a }",
3368 "{ A[a] -> B[([a/2])] }",
3369 "{ A[a] : 0 <= a < 200 and exists b : [a/2] = 4 b }" },
3370 { "{ B[i,j,k] : 0 <= i,j,k <= 100 }",
3371 "{ A[a] -> B[a,a,a/3] }",
3372 "{ A[a] : 0 <= a <= 100 and exists b : a = 3 b }" },
3373 { "{ B[i,j] : j = [(i)/2] } ", "{ A[i,j] -> B[i/3,j] }",
3374 "{ A[i,j] : j = [(i)/6] and exists a : i = 3 a }" },
3375 };
3376
3377 int test_preimage(isl_ctx *ctx)
3378 {
3379 int i;
3380 isl_basic_set *bset1, *bset2;
3381 isl_multi_aff *ma;
3382 int equal;
3383
3384 for (i = 0; i < ARRAY_SIZE(preimage_tests); ++i) {
3385 bset1 = isl_basic_set_read_from_str(ctx, preimage_tests[i].set);
3386 ma = isl_multi_aff_read_from_str(ctx, preimage_tests[i].ma);
3387 bset2 = isl_basic_set_read_from_str(ctx, preimage_tests[i].res);
3388 bset1 = isl_basic_set_preimage_multi_aff(bset1, ma);
3389 equal = isl_basic_set_is_equal(bset1, bset2);
3390 isl_basic_set_free(bset1);
3391 isl_basic_set_free(bset2);
3392 if (equal < 0)
3393 return -1;
3394 if (!equal)
3395 isl_die(ctx, isl_error_unknown, "bad preimage",
3396 return -1);
3397 }
3398
3399 return 0;
3400 }
3401
3402 struct {
3403 const char *ma1;
3404 const char *ma;
3405 const char *res;
3406 } pullback_tests[] = {
3407 { "{ B[i,j] -> C[i + 2j] }" , "{ A[a,b] -> B[b,a] }",
3408 "{ A[a,b] -> C[b + 2a] }" },
3409 { "{ B[i] -> C[2i] }", "{ A[a] -> B[(a)/2] }", "{ A[a] -> C[a] }" },
3410 { "{ B[i] -> C[(i)/2] }", "{ A[a] -> B[2a] }", "{ A[a] -> C[a] }" },
3411 { "{ B[i] -> C[(i)/2] }", "{ A[a] -> B[(a)/3] }",
3412 "{ A[a] -> C[(a)/6] }" },
3413 { "{ B[i] -> C[2i] }", "{ A[a] -> B[5a] }", "{ A[a] -> C[10a] }" },
3414 { "{ B[i] -> C[2i] }", "{ A[a] -> B[(a)/3] }",
3415 "{ A[a] -> C[(2a)/3] }" },
3416 { "{ B[i,j] -> C[i + j] }", "{ A[a] -> B[a,a] }", "{ A[a] -> C[2a] }"},
3417 { "{ B[a] -> C[a,a] }", "{ A[i,j] -> B[i + j] }",
3418 "{ A[i,j] -> C[i + j, i + j] }"},
3419 { "{ B[i] -> C[([i/2])] }", "{ B[5] }", "{ C[2] }" },
3420 { "[n] -> { B[i,j] -> C[([i/2]) + 2j] }",
3421 "[n] -> { B[n,[n/3]] }", "[n] -> { C[([n/2]) + 2*[n/3]] }", },
3422 };
3423
3424 static int test_pullback(isl_ctx *ctx)
3425 {
3426 int i;
3427 isl_multi_aff *ma1, *ma2;
3428 isl_multi_aff *ma;
3429 int equal;
3430
3431 for (i = 0; i < ARRAY_SIZE(pullback_tests); ++i) {
3432 ma1 = isl_multi_aff_read_from_str(ctx, pullback_tests[i].ma1);
3433 ma = isl_multi_aff_read_from_str(ctx, pullback_tests[i].ma);
3434 ma2 = isl_multi_aff_read_from_str(ctx, pullback_tests[i].res);
3435 ma1 = isl_multi_aff_pullback_multi_aff(ma1, ma);
3436 equal = isl_multi_aff_plain_is_equal(ma1, ma2);
3437 isl_multi_aff_free(ma1);
3438 isl_multi_aff_free(ma2);
3439 if (equal < 0)
3440 return -1;
3441 if (!equal)
3442 isl_die(ctx, isl_error_unknown, "bad pullback",
3443 return -1);
3444 }
3445
3446 return 0;
3447 }
3448
3449 /* Check that negation is printed correctly.
3450 */
3451 static int test_ast(isl_ctx *ctx)
3452 {
3453 isl_ast_expr *expr, *expr1, *expr2, *expr3;
3454 char *str;
3455 int ok;
3456
3457 expr1 = isl_ast_expr_from_id(isl_id_alloc(ctx, "A", NULL));
3458 expr2 = isl_ast_expr_from_id(isl_id_alloc(ctx, "B", NULL));
3459 expr = isl_ast_expr_add(expr1, expr2);
3460 expr = isl_ast_expr_neg(expr);
3461 str = isl_ast_expr_to_str(expr);
3462 ok = str ? !strcmp(str, "-(A + B)") : -1;
3463 free(str);
3464 isl_ast_expr_free(expr);
3465
3466 if (ok < 0)
3467 return -1;
3468 if (!ok)
3469 isl_die(ctx, isl_error_unknown,
3470 "isl_ast_expr printed incorrectly", return -1);
3471
3472 expr1 = isl_ast_expr_from_id(isl_id_alloc(ctx, "A", NULL));
3473 expr2 = isl_ast_expr_from_id(isl_id_alloc(ctx, "B", NULL));
3474 expr = isl_ast_expr_add(expr1, expr2);
3475 expr3 = isl_ast_expr_from_id(isl_id_alloc(ctx, "C", NULL));
3476 expr = isl_ast_expr_sub(expr3, expr);
3477 str = isl_ast_expr_to_str(expr);
3478 ok = str ? !strcmp(str, "C - (A + B)") : -1;
3479 free(str);
3480 isl_ast_expr_free(expr);
3481
3482 if (ok < 0)
3483 return -1;
3484 if (!ok)
3485 isl_die(ctx, isl_error_unknown,
3486 "isl_ast_expr printed incorrectly", return -1);
3487
3488 return 0;
3489 }
3490
3491 /* Internal data structure for before_for and after_for callbacks.
3492 *
3493 * depth is the current depth
3494 * before is the number of times before_for has been called
3495 * after is the number of times after_for has been called
3496 */
3497 struct isl_test_codegen_data {
3498 int depth;
3499 int before;
3500 int after;
3501 };
3502
3503 /* This function is called before each for loop in the AST generated
3504 * from test_ast_gen1.
3505 *
3506 * Increment the number of calls and the depth.
3507 * Check that the space returned by isl_ast_build_get_schedule_space
3508 * matches the target space of the schedule returned by
3509 * isl_ast_build_get_schedule.
3510 * Return an isl_id that is checked by the corresponding call
3511 * to after_for.
3512 */
3513 static __isl_give isl_id *before_for(__isl_keep isl_ast_build *build,
3514 void *user)
3515 {
3516 struct isl_test_codegen_data *data = user;
3517 isl_ctx *ctx;
3518 isl_space *space;
3519 isl_union_map *schedule;
3520 isl_union_set *uset;
3521 isl_set *set;
3522 int empty;
3523 char name[] = "d0";
3524
3525 ctx = isl_ast_build_get_ctx(build);
3526
3527 if (data->before >= 3)
3528 isl_die(ctx, isl_error_unknown,
3529 "unexpected number of for nodes", return NULL);
3530 if (data->depth >= 2)
3531 isl_die(ctx, isl_error_unknown,
3532 "unexpected depth", return NULL);
3533
3534 snprintf(name, sizeof(name), "d%d", data->depth);
3535 data->before++;
3536 data->depth++;
3537
3538 schedule = isl_ast_build_get_schedule(build);
3539 uset = isl_union_map_range(schedule);
3540 if (!uset)
3541 return NULL;
3542 if (isl_union_set_n_set(uset) != 1) {
3543 isl_union_set_free(uset);
3544 isl_die(ctx, isl_error_unknown,
3545 "expecting single range space", return NULL);
3546 }
3547
3548 space = isl_ast_build_get_schedule_space(build);
3549 set = isl_union_set_extract_set(uset, space);
3550 isl_union_set_free(uset);
3551 empty = isl_set_is_empty(set);
3552 isl_set_free(set);
3553
3554 if (empty < 0)
3555 return NULL;
3556 if (empty)
3557 isl_die(ctx, isl_error_unknown,
3558 "spaces don't match", return NULL);
3559
3560 return isl_id_alloc(ctx, name, NULL);
3561 }
3562
3563 /* This function is called after each for loop in the AST generated
3564 * from test_ast_gen1.
3565 *
3566 * Increment the number of calls and decrement the depth.
3567 * Check that the annotation attached to the node matches
3568 * the isl_id returned by the corresponding call to before_for.
3569 */
3570 static __isl_give isl_ast_node *after_for(__isl_take isl_ast_node *node,
3571 __isl_keep isl_ast_build *build, void *user)
3572 {
3573 struct isl_test_codegen_data *data = user;
3574 isl_id *id;
3575 const char *name;
3576 int valid;
3577
3578 data->after++;
3579 data->depth--;
3580
3581 if (data->after > data->before)
3582 isl_die(isl_ast_node_get_ctx(node), isl_error_unknown,
3583 "mismatch in number of for nodes",
3584 return isl_ast_node_free(node));
3585
3586 id = isl_ast_node_get_annotation(node);
3587 if (!id)
3588 isl_die(isl_ast_node_get_ctx(node), isl_error_unknown,
3589 "missing annotation", return isl_ast_node_free(node));
3590
3591 name = isl_id_get_name(id);
3592 valid = name && atoi(name + 1) == data->depth;
3593 isl_id_free(id);
3594
3595 if (!valid)
3596 isl_die(isl_ast_node_get_ctx(node), isl_error_unknown,
3597 "wrong annotation", return isl_ast_node_free(node));
3598
3599 return node;
3600 }
3601
3602 /* Check that the before_each_for and after_each_for callbacks
3603 * are called for each for loop in the generated code,
3604 * that they are called in the right order and that the isl_id
3605 * returned from the before_each_for callback is attached to
3606 * the isl_ast_node passed to the corresponding after_each_for call.
3607 */
3608 static int test_ast_gen1(isl_ctx *ctx)
3609 {
3610 const char *str;
3611 isl_set *set;
3612 isl_union_map *schedule;
3613 isl_ast_build *build;
3614 isl_ast_node *tree;
3615 struct isl_test_codegen_data data;
3616
3617 str = "[N] -> { : N >= 10 }";
3618 set = isl_set_read_from_str(ctx, str);
3619 str = "[N] -> { A[i,j] -> S[8,i,3,j] : 0 <= i,j <= N; "
3620 "B[i,j] -> S[8,j,9,i] : 0 <= i,j <= N }";
3621 schedule = isl_union_map_read_from_str(ctx, str);
3622
3623 data.before = 0;
3624 data.after = 0;
3625 data.depth = 0;
3626 build = isl_ast_build_from_context(set);
3627 build = isl_ast_build_set_before_each_for(build,
3628 &before_for, &data);
3629 build = isl_ast_build_set_after_each_for(build,
3630 &after_for, &data);
3631 tree = isl_ast_build_ast_from_schedule(build, schedule);
3632 isl_ast_build_free(build);
3633 if (!tree)
3634 return -1;
3635
3636 isl_ast_node_free(tree);
3637
3638 if (data.before != 3 || data.after != 3)
3639 isl_die(ctx, isl_error_unknown,
3640 "unexpected number of for nodes", return -1);
3641
3642 return 0;
3643 }
3644
3645 /* Check that the AST generator handles domains that are integrally disjoint
3646 * but not ratinoally disjoint.
3647 */
3648 static int test_ast_gen2(isl_ctx *ctx)
3649 {
3650 const char *str;
3651 isl_set *set;
3652 isl_union_map *schedule;
3653 isl_union_map *options;
3654 isl_ast_build *build;
3655 isl_ast_node *tree;
3656
3657 str = "{ A[i,j] -> [i,j] : 0 <= i,j <= 1 }";
3658 schedule = isl_union_map_read_from_str(ctx, str);
3659 set = isl_set_universe(isl_space_params_alloc(ctx, 0));
3660 build = isl_ast_build_from_context(set);
3661
3662 str = "{ [i,j] -> atomic[1] : i + j = 1; [i,j] -> unroll[1] : i = j }";
3663 options = isl_union_map_read_from_str(ctx, str);
3664 build = isl_ast_build_set_options(build, options);
3665 tree = isl_ast_build_ast_from_schedule(build, schedule);
3666 isl_ast_build_free(build);
3667 if (!tree)
3668 return -1;
3669 isl_ast_node_free(tree);
3670
3671 return 0;
3672 }
3673
3674 /* Increment *user on each call.
3675 */
3676 static __isl_give isl_ast_node *count_domains(__isl_take isl_ast_node *node,
3677 __isl_keep isl_ast_build *build, void *user)
3678 {
3679 int *n = user;
3680
3681 (*n)++;
3682
3683 return node;
3684 }
3685
3686 /* Test that unrolling tries to minimize the number of instances.
3687 * In particular, for the schedule given below, make sure it generates
3688 * 3 nodes (rather than 101).
3689 */
3690 static int test_ast_gen3(isl_ctx *ctx)
3691 {
3692 const char *str;
3693 isl_set *set;
3694 isl_union_map *schedule;
3695 isl_union_map *options;
3696 isl_ast_build *build;
3697 isl_ast_node *tree;
3698 int n_domain = 0;
3699
3700 str = "[n] -> { A[i] -> [i] : 0 <= i <= 100 and n <= i <= n + 2 }";
3701 schedule = isl_union_map_read_from_str(ctx, str);
3702 set = isl_set_universe(isl_space_params_alloc(ctx, 0));
3703
3704 str = "{ [i] -> unroll[0] }";
3705 options = isl_union_map_read_from_str(ctx, str);
3706
3707 build = isl_ast_build_from_context(set);
3708 build = isl_ast_build_set_options(build, options);
3709 build = isl_ast_build_set_at_each_domain(build,
3710 &count_domains, &n_domain);
3711 tree = isl_ast_build_ast_from_schedule(build, schedule);
3712 isl_ast_build_free(build);
3713 if (!tree)
3714 return -1;
3715
3716 isl_ast_node_free(tree);
3717
3718 if (n_domain != 3)
3719 isl_die(ctx, isl_error_unknown,
3720 "unexpected number of for nodes", return -1);
3721
3722 return 0;
3723 }
3724
3725 /* Check that if the ast_build_exploit_nested_bounds options is set,
3726 * we do not get an outer if node in the generated AST,
3727 * while we do get such an outer if node if the options is not set.
3728 */
3729 static int test_ast_gen4(isl_ctx *ctx)
3730 {
3731 const char *str;
3732 isl_set *set;
3733 isl_union_map *schedule;
3734 isl_ast_build *build;
3735 isl_ast_node *tree;
3736 enum isl_ast_node_type type;
3737 int enb;
3738
3739 enb = isl_options_get_ast_build_exploit_nested_bounds(ctx);
3740 str = "[N,M] -> { A[i,j] -> [i,j] : 0 <= i <= N and 0 <= j <= M }";
3741
3742 isl_options_set_ast_build_exploit_nested_bounds(ctx, 1);
3743
3744 schedule = isl_union_map_read_from_str(ctx, str);
3745 set = isl_set_universe(isl_space_params_alloc(ctx, 0));
3746 build = isl_ast_build_from_context(set);
3747 tree = isl_ast_build_ast_from_schedule(build, schedule);
3748 isl_ast_build_free(build);
3749 if (!tree)
3750 return -1;
3751
3752 type = isl_ast_node_get_type(tree);
3753 isl_ast_node_free(tree);
3754
3755 if (type == isl_ast_node_if)
3756 isl_die(ctx, isl_error_unknown,
3757 "not expecting if node", return -1);
3758
3759 isl_options_set_ast_build_exploit_nested_bounds(ctx, 0);
3760
3761 schedule = isl_union_map_read_from_str(ctx, str);
3762 set = isl_set_universe(isl_space_params_alloc(ctx, 0));
3763 build = isl_ast_build_from_context(set);
3764 tree = isl_ast_build_ast_from_schedule(build, schedule);
3765 isl_ast_build_free(build);
3766 if (!tree)
3767 return -1;
3768
3769 type = isl_ast_node_get_type(tree);
3770 isl_ast_node_free(tree);
3771
3772 if (type != isl_ast_node_if)
3773 isl_die(ctx, isl_error_unknown,
3774 "expecting if node", return -1);
3775
3776 isl_options_set_ast_build_exploit_nested_bounds(ctx, enb);
3777
3778 return 0;
3779 }
3780
3781 static int test_ast_gen(isl_ctx *ctx)
3782 {
3783 if (test_ast_gen1(ctx) < 0)
3784 return -1;
3785 if (test_ast_gen2(ctx) < 0)
3786 return -1;
3787 if (test_ast_gen3(ctx) < 0)
3788 return -1;
3789 if (test_ast_gen4(ctx) < 0)
3790 return -1;
3791 return 0;
3792 }
3793
3794 /* Check if dropping output dimensions from an isl_pw_multi_aff
3795 * works properly.
3796 */
3797 static int test_pw_multi_aff(isl_ctx *ctx)
3798 {
3799 const char *str;
3800 isl_pw_multi_aff *pma1, *pma2;
3801 int equal;
3802
3803 str = "{ [i,j] -> [i+j, 4i-j] }";
3804 pma1 = isl_pw_multi_aff_read_from_str(ctx, str);
3805 str = "{ [i,j] -> [4i-j] }";
3806 pma2 = isl_pw_multi_aff_read_from_str(ctx, str);
3807
3808 pma1 = isl_pw_multi_aff_drop_dims(pma1, isl_dim_out, 0, 1);
3809
3810 equal = isl_pw_multi_aff_plain_is_equal(pma1, pma2);
3811
3812 isl_pw_multi_aff_free(pma1);
3813 isl_pw_multi_aff_free(pma2);
3814 if (equal < 0)
3815 return -1;
3816 if (!equal)
3817 isl_die(ctx, isl_error_unknown,
3818 "expressions not equal", return -1);
3819
3820 return 0;
3821 }
3822
3823 /* This is a regression test for a bug where isl_basic_map_simplify
3824 * would end up in an infinite loop. In particular, we construct
3825 * an empty basic set that is not obviously empty.
3826 * isl_basic_set_is_empty marks the basic set as empty.
3827 * After projecting out i3, the variable can be dropped completely,
3828 * but isl_basic_map_simplify refrains from doing so if the basic set
3829 * is empty and would end up in an infinite loop if it didn't test
3830 * explicitly for empty basic maps in the outer loop.
3831 */
3832 static int test_simplify(isl_ctx *ctx)
3833 {
3834 const char *str;
3835 isl_basic_set *bset;
3836 int empty;
3837
3838 str = "{ [i0, i1, i2, i3] : i0 >= -2 and 6i2 <= 4 + i0 + 5i1 and "
3839 "i2 <= 22 and 75i2 <= 111 + 13i0 + 60i1 and "
3840 "25i2 >= 38 + 6i0 + 20i1 and i0 <= -1 and i2 >= 20 and "
3841 "i3 >= i2 }";
3842 bset = isl_basic_set_read_from_str(ctx, str);
3843 empty = isl_basic_set_is_empty(bset);
3844 bset = isl_basic_set_project_out(bset, isl_dim_set, 3, 1);
3845 isl_basic_set_free(bset);
3846 if (!bset)
3847 return -1;
3848 if (!empty)
3849 isl_die(ctx, isl_error_unknown,
3850 "basic set should be empty", return -1);
3851
3852 return 0;
3853 }
3854
3855 struct {
3856 const char *name;
3857 int (*fn)(isl_ctx *ctx);
3858 } tests [] = {
3859 { "simplify", &test_simplify },
3860 { "curry", &test_curry },
3861 { "piecewise multi affine expressions", &test_pw_multi_aff },
3862 { "conversion", &test_conversion },
3863 { "list", &test_list },
3864 { "align parameters", &test_align_parameters },
3865 { "preimage", &test_preimage },
3866 { "pullback", &test_pullback },
3867 { "AST", &test_ast },
3868 { "AST generation", &test_ast_gen },
3869 { "eliminate", &test_eliminate },
3870 { "residue class", &test_residue_class },
3871 { "div", &test_div },
3872 { "slice", &test_slice },
3873 { "fixed power", &test_fixed_power },
3874 { "sample", &test_sample },
3875 { "output", &test_output },
3876 { "vertices", &test_vertices },
3877 { "fixed", &test_fixed },
3878 { "equal", &test_equal },
3879 { "product", &test_product },
3880 { "dim_max", &test_dim_max },
3881 { "affine", &test_aff },
3882 { "injective", &test_injective },
3883 { "schedule", &test_schedule },
3884 { "union_pw", &test_union_pw },
3885 { "parse", &test_parse },
3886 { "single-valued", &test_sv },
3887 { "affine hull", &test_affine_hull },
3888 { "coalesce", &test_coalesce },
3889 { "factorize", &test_factorize },
3890 { "subset", &test_subset },
3891 { "subtract", &test_subtract },
3892 };
3893
3894 int main()
3895 {
3896 int i;
3897 struct isl_ctx *ctx;
3898
3899 srcdir = getenv("srcdir");
3900 assert(srcdir);
3901
3902 ctx = isl_ctx_alloc();
3903 for (i = 0; i < ARRAY_SIZE(tests); ++i) {
3904 printf("%s\n", tests[i].name);
3905 if (tests[i].fn(ctx) < 0)
3906 goto error;
3907 }
3908 test_lift(ctx);
3909 test_bound(ctx);
3910 test_union(ctx);
3911 test_split_periods(ctx);
3912 test_pwqp(ctx);
3913 test_lex(ctx);
3914 test_bijective(ctx);
3915 test_dep(ctx);
3916 test_read(ctx);
3917 test_bounded(ctx);
3918 test_construction(ctx);
3919 test_dim(ctx);
3920 test_application(ctx);
3921 test_convex_hull(ctx);
3922 test_gist(ctx);
3923 test_closure(ctx);
3924 test_lexmin(ctx);
3925 isl_ctx_free(ctx);
3926 return 0;
3927 error:
3928 isl_ctx_free(ctx);
3929 return -1;
3930 }
Integer set library