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isl_ast_build_get_stride_constraint: combine multiple strides
[isl.git] / isl_test.c
blob7986d9371012b824faa8ee82c675a7c106382e77
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 /* Check that isl_map_affine_hull is not confused by
742 * the reordering of divs in isl_map_align_divs.
743 */
744 str = "{ [a, b, c, 0] : exists (e0 = [(b)/32], e1 = [(c)/32]: "
745 "32e0 = b and 32e1 = c); "
746 "[a, 0, c, 0] : exists (e0 = [(c)/32]: 32e0 = c) }";
747 set = isl_set_read_from_str(ctx, str);
748 bset = isl_set_affine_hull(set);
749 isl_basic_set_free(bset);
750 if (!bset)
751 return -1;
752
753 return 0;
754 }
755
756 void test_convex_hull_case(struct isl_ctx *ctx, const char *name)
757 {
758 char *filename;
759 FILE *input;
760 struct isl_basic_set *bset1, *bset2;
761 struct isl_set *set;
762
763 filename = get_filename(ctx, name, "polylib");
764 assert(filename);
765 input = fopen(filename, "r");
766 assert(input);
767
768 bset1 = isl_basic_set_read_from_file(ctx, input);
769 bset2 = isl_basic_set_read_from_file(ctx, input);
770
771 set = isl_basic_set_union(bset1, bset2);
772 bset1 = isl_set_convex_hull(set);
773
774 bset2 = isl_basic_set_read_from_file(ctx, input);
775
776 assert(isl_basic_set_is_equal(bset1, bset2) == 1);
777
778 isl_basic_set_free(bset1);
779 isl_basic_set_free(bset2);
780 free(filename);
781
782 fclose(input);
783 }
784
785 void test_convex_hull_algo(struct isl_ctx *ctx, int convex)
786 {
787 const char *str1, *str2;
788 isl_set *set1, *set2;
789 int orig_convex = ctx->opt->convex;
790 ctx->opt->convex = convex;
791
792 test_convex_hull_case(ctx, "convex0");
793 test_convex_hull_case(ctx, "convex1");
794 test_convex_hull_case(ctx, "convex2");
795 test_convex_hull_case(ctx, "convex3");
796 test_convex_hull_case(ctx, "convex4");
797 test_convex_hull_case(ctx, "convex5");
798 test_convex_hull_case(ctx, "convex6");
799 test_convex_hull_case(ctx, "convex7");
800 test_convex_hull_case(ctx, "convex8");
801 test_convex_hull_case(ctx, "convex9");
802 test_convex_hull_case(ctx, "convex10");
803 test_convex_hull_case(ctx, "convex11");
804 test_convex_hull_case(ctx, "convex12");
805 test_convex_hull_case(ctx, "convex13");
806 test_convex_hull_case(ctx, "convex14");
807 test_convex_hull_case(ctx, "convex15");
808
809 str1 = "{ [i0, i1, i2] : (i2 = 1 and i0 = 0 and i1 >= 0) or "
810 "(i0 = 1 and i1 = 0 and i2 = 1) or "
811 "(i0 = 0 and i1 = 0 and i2 = 0) }";
812 str2 = "{ [i0, i1, i2] : i0 >= 0 and i2 >= i0 and i2 <= 1 and i1 >= 0 }";
813 set1 = isl_set_read_from_str(ctx, str1);
814 set2 = isl_set_read_from_str(ctx, str2);
815 set1 = isl_set_from_basic_set(isl_set_convex_hull(set1));
816 assert(isl_set_is_equal(set1, set2));
817 isl_set_free(set1);
818 isl_set_free(set2);
819
820 ctx->opt->convex = orig_convex;
821 }
822
823 void test_convex_hull(struct isl_ctx *ctx)
824 {
825 test_convex_hull_algo(ctx, ISL_CONVEX_HULL_FM);
826 test_convex_hull_algo(ctx, ISL_CONVEX_HULL_WRAP);
827 }
828
829 void test_gist_case(struct isl_ctx *ctx, const char *name)
830 {
831 char *filename;
832 FILE *input;
833 struct isl_basic_set *bset1, *bset2;
834
835 filename = get_filename(ctx, name, "polylib");
836 assert(filename);
837 input = fopen(filename, "r");
838 assert(input);
839
840 bset1 = isl_basic_set_read_from_file(ctx, input);
841 bset2 = isl_basic_set_read_from_file(ctx, input);
842
843 bset1 = isl_basic_set_gist(bset1, bset2);
844
845 bset2 = isl_basic_set_read_from_file(ctx, input);
846
847 assert(isl_basic_set_is_equal(bset1, bset2) == 1);
848
849 isl_basic_set_free(bset1);
850 isl_basic_set_free(bset2);
851 free(filename);
852
853 fclose(input);
854 }
855
856 void test_gist(struct isl_ctx *ctx)
857 {
858 const char *str;
859 isl_basic_set *bset1, *bset2;
860
861 test_gist_case(ctx, "gist1");
862
863 str = "[p0, p2, p3, p5, p6, p10] -> { [] : "
864 "exists (e0 = [(15 + p0 + 15p6 + 15p10)/16], e1 = [(p5)/8], "
865 "e2 = [(p6)/128], e3 = [(8p2 - p5)/128], "
866 "e4 = [(128p3 - p6)/4096]: 8e1 = p5 and 128e2 = p6 and "
867 "128e3 = 8p2 - p5 and 4096e4 = 128p3 - p6 and p2 >= 0 and "
868 "16e0 >= 16 + 16p6 + 15p10 and p2 <= 15 and p3 >= 0 and "
869 "p3 <= 31 and p6 >= 128p3 and p5 >= 8p2 and p10 >= 0 and "
870 "16e0 <= 15 + p0 + 15p6 + 15p10 and 16e0 >= p0 + 15p6 + 15p10 and "
871 "p10 <= 15 and p10 <= -1 + p0 - p6) }";
872 bset1 = isl_basic_set_read_from_str(ctx, str);
873 str = "[p0, p2, p3, p5, p6, p10] -> { [] : exists (e0 = [(p5)/8], "
874 "e1 = [(p6)/128], e2 = [(8p2 - p5)/128], "
875 "e3 = [(128p3 - p6)/4096]: 8e0 = p5 and 128e1 = p6 and "
876 "128e2 = 8p2 - p5 and 4096e3 = 128p3 - p6 and p5 >= -7 and "
877 "p2 >= 0 and 8p2 <= -1 + p0 and p2 <= 15 and p3 >= 0 and "
878 "p3 <= 31 and 128p3 <= -1 + p0 and p6 >= -127 and "
879 "p5 <= -1 + p0 and p6 <= -1 + p0 and p6 >= 128p3 and "
880 "p0 >= 1 and p5 >= 8p2 and p10 >= 0 and p10 <= 15 ) }";
881 bset2 = isl_basic_set_read_from_str(ctx, str);
882 bset1 = isl_basic_set_gist(bset1, bset2);
883 assert(bset1 && bset1->n_div == 0);
884 isl_basic_set_free(bset1);
885 }
886
887 int test_coalesce_set(isl_ctx *ctx, const char *str, int check_one)
888 {
889 isl_set *set, *set2;
890 int equal;
891 int one;
892
893 set = isl_set_read_from_str(ctx, str);
894 set = isl_set_coalesce(set);
895 set2 = isl_set_read_from_str(ctx, str);
896 equal = isl_set_is_equal(set, set2);
897 one = set && set->n == 1;
898 isl_set_free(set);
899 isl_set_free(set2);
900
901 if (equal < 0)
902 return -1;
903 if (!equal)
904 isl_die(ctx, isl_error_unknown,
905 "coalesced set not equal to input", return -1);
906 if (check_one && !one)
907 isl_die(ctx, isl_error_unknown,
908 "coalesced set should not be a union", return -1);
909
910 return 0;
911 }
912
913 int test_coalesce_unbounded_wrapping(isl_ctx *ctx)
914 {
915 int r = 0;
916 int bounded;
917
918 bounded = isl_options_get_coalesce_bounded_wrapping(ctx);
919 isl_options_set_coalesce_bounded_wrapping(ctx, 0);
920
921 if (test_coalesce_set(ctx,
922 "{[x,y,z] : y + 2 >= 0 and x - y + 1 >= 0 and "
923 "-x - y + 1 >= 0 and -3 <= z <= 3;"
924 "[x,y,z] : -x+z + 20 >= 0 and -x-z + 20 >= 0 and "
925 "x-z + 20 >= 0 and x+z + 20 >= 0 and "
926 "-10 <= y <= 0}", 1) < 0)
927 goto error;
928 if (test_coalesce_set(ctx,
929 "{[x,y] : 0 <= x,y <= 10; [5,y]: 4 <=y <= 11}", 1) < 0)
930 goto error;
931 if (test_coalesce_set(ctx,
932 "{[x,0,0] : -5 <= x <= 5; [0,y,1] : -5 <= y <= 5 }", 1) < 0)
933 goto error;
934
935 if (0) {
936 error:
937 r = -1;
938 }
939
940 isl_options_set_coalesce_bounded_wrapping(ctx, bounded);
941
942 return r;
943 }
944
945 /* Inputs for coalescing tests.
946 * "str" is a string representation of the input set.
947 * "single_disjunct" is set if we expect the result to consist of
948 * a single disjunct.
949 */
950 struct {
951 int single_disjunct;
952 const char *str;
953 } coalesce_tests[] = {
954 { 1, "{[x,y]: x >= 0 & x <= 10 & y >= 0 & y <= 10 or "
955 "y >= x & x >= 2 & 5 >= y }" },
956 { 1, "{[x,y]: y >= 0 & 2x + y <= 30 & y <= 10 & x >= 0 or "
957 "x + y >= 10 & y <= x & x + y <= 20 & y >= 0}" },
958 { 0, "{[x,y]: y >= 0 & 2x + y <= 30 & y <= 10 & x >= 0 or "
959 "x + y >= 10 & y <= x & x + y <= 19 & y >= 0}" },
960 { 1, "{[x,y]: y >= 0 & x <= 5 & y <= x or "
961 "y >= 0 & x >= 6 & x <= 10 & y <= x}" },
962 { 0, "{[x,y]: y >= 0 & x <= 5 & y <= x or "
963 "y >= 0 & x >= 7 & x <= 10 & y <= x}" },
964 { 0, "{[x,y]: y >= 0 & x <= 5 & y <= x or "
965 "y >= 0 & x >= 6 & x <= 10 & y + 1 <= x}" },
966 { 1, "{[x,y]: y >= 0 & x <= 5 & y <= x or y >= 0 & x = 6 & y <= 6}" },
967 { 0, "{[x,y]: y >= 0 & x <= 5 & y <= x or y >= 0 & x = 7 & y <= 6}" },
968 { 1, "{[x,y]: y >= 0 & x <= 5 & y <= x or y >= 0 & x = 6 & y <= 5}" },
969 { 0, "{[x,y]: y >= 0 & x <= 5 & y <= x or y >= 0 & x = 6 & y <= 7}" },
970 { 1, "[n] -> { [i] : i = 1 and n >= 2 or 2 <= i and i <= n }" },
971 { 0, "{[x,y] : x >= 0 and y >= 0 or 0 <= y and y <= 5 and x = -1}" },
972 { 1, "[n] -> { [i] : 1 <= i and i <= n - 1 or 2 <= i and i <= n }" },
973 { 0, "[n] -> { [[i0] -> [o0]] : exists (e0 = [(i0)/4], e1 = [(o0)/4], "
974 "e2 = [(n)/2], e3 = [(-2 + i0)/4], e4 = [(-2 + o0)/4], "
975 "e5 = [(-2n + i0)/4]: 2e2 = n and 4e3 = -2 + i0 and "
976 "4e4 = -2 + o0 and i0 >= 8 + 2n and o0 >= 2 + i0 and "
977 "o0 <= 56 + 2n and o0 <= -12 + 4n and i0 <= 57 + 2n and "
978 "i0 <= -11 + 4n and o0 >= 6 + 2n and 4e0 <= i0 and "
979 "4e0 >= -3 + i0 and 4e1 <= o0 and 4e1 >= -3 + o0 and "
980 "4e5 <= -2n + i0 and 4e5 >= -3 - 2n + i0);"
981 "[[i0] -> [o0]] : exists (e0 = [(i0)/4], e1 = [(o0)/4], "
982 "e2 = [(n)/2], e3 = [(-2 + i0)/4], e4 = [(-2 + o0)/4], "
983 "e5 = [(-2n + i0)/4]: 2e2 = n and 4e3 = -2 + i0 and "
984 "4e4 = -2 + o0 and 2e0 >= 3 + n and e0 <= -4 + n and "
985 "2e0 <= 27 + n and e1 <= -4 + n and 2e1 <= 27 + n and "
986 "2e1 >= 2 + n and e1 >= 1 + e0 and i0 >= 7 + 2n and "
987 "i0 <= -11 + 4n and i0 <= 57 + 2n and 4e0 <= -2 + i0 and "
988 "4e0 >= -3 + i0 and o0 >= 6 + 2n and o0 <= -11 + 4n and "
989 "o0 <= 57 + 2n and 4e1 <= -2 + o0 and 4e1 >= -3 + o0 and "
990 "4e5 <= -2n + i0 and 4e5 >= -3 - 2n + i0 ) }" },
991 { 0, "[n, m] -> { [o0, o2, o3] : (o3 = 1 and o0 >= 1 + m and "
992 "o0 <= n + m and o2 <= m and o0 >= 2 + n and o2 >= 3) or "
993 "(o0 >= 2 + n and o0 >= 1 + m and o0 <= n + m and n >= 1 and "
994 "o3 <= -1 + o2 and o3 >= 1 - m + o2 and o3 >= 2 and o3 <= n) }" },
995 { 0, "[M, N] -> { [[i0, i1, i2, i3, i4, i5, i6] -> "
996 "[o0, o1, o2, o3, o4, o5, o6]] : "
997 "(o6 <= -4 + 2M - 2N + i0 + i1 - i2 + i6 - o0 - o1 + o2 and "
998 "o3 <= -2 + i3 and o6 >= 2 + i0 + i3 + i6 - o0 - o3 and "
999 "o6 >= 2 - M + N + i3 + i4 + i6 - o3 - o4 and o0 <= -1 + i0 and "
1000 "o4 >= 4 - 3M + 3N - i0 - i1 + i2 + 2i3 + i4 + o0 + o1 - o2 - 2o3 "
1001 "and o6 <= -3 + 2M - 2N + i3 + i4 - i5 + i6 - o3 - o4 + o5 and "
1002 "2o6 <= -5 + 5M - 5N + 2i0 + i1 - i2 - i5 + 2i6 - 2o0 - o1 + o2 + o5 "
1003 "and o6 >= 2i0 + i1 + i6 - 2o0 - o1 and "
1004 "3o6 <= -5 + 4M - 4N + 2i0 + i1 - i2 + 2i3 + i4 - i5 + 3i6 "
1005 "- 2o0 - o1 + o2 - 2o3 - o4 + o5) or "
1006 "(N >= 2 and o3 <= -1 + i3 and o0 <= -1 + i0 and "
1007 "o6 >= i3 + i6 - o3 and M >= 0 and "
1008 "2o6 >= 1 + i0 + i3 + 2i6 - o0 - o3 and "
1009 "o6 >= 1 - M + i0 + i6 - o0 and N >= 2M and o6 >= i0 + i6 - o0) }" },
1010 { 0, "[M, N] -> { [o0] : (o0 = 0 and M >= 1 and N >= 2) or "
1011 "(o0 = 0 and M >= 1 and N >= 2M and N >= 2 + M) or "
1012 "(o0 = 0 and M >= 2 and N >= 3) or "
1013 "(M = 0 and o0 = 0 and N >= 3) }" },
1014 { 0, "{ [i0, i1, i2, i3] : (i1 = 10i0 and i0 >= 1 and 10i0 <= 100 and "
1015 "i3 <= 9 + 10 i2 and i3 >= 1 + 10i2 and i3 >= 0) or "
1016 "(i1 <= 9 + 10i0 and i1 >= 1 + 10i0 and i2 >= 0 and "
1017 "i0 >= 0 and i1 <= 100 and i3 <= 9 + 10i2 and i3 >= 1 + 10i2) }" },
1018 { 0, "[M] -> { [i1] : (i1 >= 2 and i1 <= M) or (i1 = M and M >= 1) }" },
1019 { 0, "{[x,y] : x,y >= 0; [x,y] : 10 <= x <= 20 and y >= -1 }" },
1020 { 1, "{ [x, y] : (x >= 1 and y >= 1 and x <= 2 and y <= 2) or "
1021 "(y = 3 and x = 1) }" },
1022 { 1, "[M] -> { [i0, i1, i2, i3, i4] : (i1 >= 3 and i4 >= 2 + i2 and "
1023 "i2 >= 2 and i0 >= 2 and i3 >= 1 + i2 and i0 <= M and "
1024 "i1 <= M and i3 <= M and i4 <= M) or "
1025 "(i1 >= 2 and i4 >= 1 + i2 and i2 >= 2 and i0 >= 2 and "
1026 "i3 >= 1 + i2 and i0 <= M and i1 <= -1 + M and i3 <= M and "
1027 "i4 <= -1 + M) }" },
1028 { 1, "{ [x, y] : (x >= 0 and y >= 0 and x <= 10 and y <= 10) or "
1029 "(x >= 1 and y >= 1 and x <= 11 and y <= 11) }" },
1030 { 0, "{[x,0] : x >= 0; [x,1] : x <= 20}" },
1031 { 1, "{ [x, 1 - x] : 0 <= x <= 1; [0,0] }" },
1032 { 1, "{ [0,0]; [i,i] : 1 <= i <= 10 }" },
1033 { 0, "{ [0,0]; [i,j] : 1 <= i,j <= 10 }" },
1034 { 1, "{ [0,0]; [i,2i] : 1 <= i <= 10 }" },
1035 { 0, "{ [0,0]; [i,2i] : 2 <= i <= 10 }" },
1036 { 0, "{ [1,0]; [i,2i] : 1 <= i <= 10 }" },
1037 { 0, "{ [0,1]; [i,2i] : 1 <= i <= 10 }" },
1038 { 0, "{ [a, b] : exists e : 2e = a and "
1039 "a >= 0 and (a <= 3 or (b <= 0 and b >= -4 + a)) }" },
1040 { 0, "{ [i, j, i', j'] : i <= 2 and j <= 2 and "
1041 "j' >= -1 + 2i + j - 2i' and i' <= -1 + i and "
1042 "j >= 1 and j' <= i + j - i' and i >= 1; "
1043 "[1, 1, 1, 1] }" },
1044 { 1, "{ [i,j] : exists a,b : i = 2a and j = 3b; "
1045 "[i,j] : exists a : j = 3a }" },
1046 { 1, "{ [a, b, c] : (c <= 7 - b and b <= 1 and b >= 0 and "
1047 "c >= 3 + b and b <= 3 + 8a and b >= -26 + 8a and "
1048 "a >= 3) or "
1049 "(b <= 1 and c <= 7 and b >= 0 and c >= 4 + b and "
1050 "b <= 3 + 8a and b >= -26 + 8a and a >= 3) }" },
1051 { 1, "{ [a, 0, c] : c >= 1 and c <= 29 and c >= -1 + 8a and "
1052 "c <= 6 + 8a and a >= 3; "
1053 "[a, -1, c] : c >= 1 and c <= 30 and c >= 8a and "
1054 "c <= 7 + 8a and a >= 3 and a <= 4 }" },
1055 { 1, "{ [x,y] : 0 <= x <= 2 and y >= 0 and x + 2y <= 4; "
1056 "[x,0] : 3 <= x <= 4 }" },
1057 { 1, "{ [x,y] : 0 <= x <= 3 and y >= 0 and x + 3y <= 6; "
1058 "[x,0] : 4 <= x <= 5 }" },
1059 { 0, "{ [x,y] : 0 <= x <= 2 and y >= 0 and x + 2y <= 4; "
1060 "[x,0] : 3 <= x <= 5 }" },
1061 { 0, "{ [x,y] : 0 <= x <= 2 and y >= 0 and x + y <= 4; "
1062 "[x,0] : 3 <= x <= 4 }" },
1063 { 1 , "{ [i0, i1] : i0 <= 122 and i0 >= 1 and 128i1 >= -249 + i0 and "
1064 "i1 <= 0; "
1065 "[i0, 0] : i0 >= 123 and i0 <= 124 }" },
1066 };
1067
1068 /* Test the functionality of isl_set_coalesce.
1069 * That is, check that the output is always equal to the input
1070 * and in some cases that the result consists of a single disjunct.
1071 */
1072 static int test_coalesce(struct isl_ctx *ctx)
1073 {
1074 int i;
1075
1076 for (i = 0; i < ARRAY_SIZE(coalesce_tests); ++i) {
1077 const char *str = coalesce_tests[i].str;
1078 int check_one = coalesce_tests[i].single_disjunct;
1079 if (test_coalesce_set(ctx, str, check_one) < 0)
1080 return -1;
1081 }
1082
1083 if (test_coalesce_unbounded_wrapping(ctx) < 0)
1084 return -1;
1085
1086 return 0;
1087 }
1088
1089 void test_closure(struct isl_ctx *ctx)
1090 {
1091 const char *str;
1092 isl_set *dom;
1093 isl_map *up, *right;
1094 isl_map *map, *map2;
1095 int exact;
1096
1097 /* COCOA example 1 */
1098 map = isl_map_read_from_str(ctx,
1099 "[n] -> { [i,j] -> [i2,j2] : i2 = i + 1 and j2 = j + 1 and "
1100 "1 <= i and i < n and 1 <= j and j < n or "
1101 "i2 = i + 1 and j2 = j - 1 and "
1102 "1 <= i and i < n and 2 <= j and j <= n }");
1103 map = isl_map_power(map, &exact);
1104 assert(exact);
1105 isl_map_free(map);
1106
1107 /* COCOA example 1 */
1108 map = isl_map_read_from_str(ctx,
1109 "[n] -> { [i,j] -> [i2,j2] : i2 = i + 1 and j2 = j + 1 and "
1110 "1 <= i and i < n and 1 <= j and j < n or "
1111 "i2 = i + 1 and j2 = j - 1 and "
1112 "1 <= i and i < n and 2 <= j and j <= n }");
1113 map = isl_map_transitive_closure(map, &exact);
1114 assert(exact);
1115 map2 = isl_map_read_from_str(ctx,
1116 "[n] -> { [i,j] -> [i2,j2] : exists (k1,k2,k : "
1117 "1 <= i and i < n and 1 <= j and j <= n and "
1118 "2 <= i2 and i2 <= n and 1 <= j2 and j2 <= n and "
1119 "i2 = i + k1 + k2 and j2 = j + k1 - k2 and "
1120 "k1 >= 0 and k2 >= 0 and k1 + k2 = k and k >= 1 )}");
1121 assert(isl_map_is_equal(map, map2));
1122 isl_map_free(map2);
1123 isl_map_free(map);
1124
1125 map = isl_map_read_from_str(ctx,
1126 "[n] -> { [x] -> [y] : y = x + 1 and 0 <= x and x <= n and "
1127 " 0 <= y and y <= n }");
1128 map = isl_map_transitive_closure(map, &exact);
1129 map2 = isl_map_read_from_str(ctx,
1130 "[n] -> { [x] -> [y] : y > x and 0 <= x and x <= n and "
1131 " 0 <= y and y <= n }");
1132 assert(isl_map_is_equal(map, map2));
1133 isl_map_free(map2);
1134 isl_map_free(map);
1135
1136 /* COCOA example 2 */
1137 map = isl_map_read_from_str(ctx,
1138 "[n] -> { [i,j] -> [i2,j2] : i2 = i + 2 and j2 = j + 2 and "
1139 "1 <= i and i < n - 1 and 1 <= j and j < n - 1 or "
1140 "i2 = i + 2 and j2 = j - 2 and "
1141 "1 <= i and i < n - 1 and 3 <= j and j <= n }");
1142 map = isl_map_transitive_closure(map, &exact);
1143 assert(exact);
1144 map2 = isl_map_read_from_str(ctx,
1145 "[n] -> { [i,j] -> [i2,j2] : exists (k1,k2,k : "
1146 "1 <= i and i < n - 1 and 1 <= j and j <= n and "
1147 "3 <= i2 and i2 <= n and 1 <= j2 and j2 <= n and "
1148 "i2 = i + 2 k1 + 2 k2 and j2 = j + 2 k1 - 2 k2 and "
1149 "k1 >= 0 and k2 >= 0 and k1 + k2 = k and k >= 1) }");
1150 assert(isl_map_is_equal(map, map2));
1151 isl_map_free(map);
1152 isl_map_free(map2);
1153
1154 /* COCOA Fig.2 left */
1155 map = isl_map_read_from_str(ctx,
1156 "[n] -> { [i,j] -> [i2,j2] : i2 = i + 2 and j2 = j and "
1157 "i <= 2 j - 3 and i <= n - 2 and j <= 2 i - 1 and "
1158 "j <= n or "
1159 "i2 = i and j2 = j + 2 and i <= 2 j - 1 and i <= n and "
1160 "j <= 2 i - 3 and j <= n - 2 or "
1161 "i2 = i + 1 and j2 = j + 1 and i <= 2 j - 1 and "
1162 "i <= n - 1 and j <= 2 i - 1 and j <= n - 1 }");
1163 map = isl_map_transitive_closure(map, &exact);
1164 assert(exact);
1165 isl_map_free(map);
1166
1167 /* COCOA Fig.2 right */
1168 map = isl_map_read_from_str(ctx,
1169 "[n] -> { [i,j] -> [i2,j2] : i2 = i + 3 and j2 = j and "
1170 "i <= 2 j - 4 and i <= n - 3 and j <= 2 i - 1 and "
1171 "j <= n or "
1172 "i2 = i and j2 = j + 3 and i <= 2 j - 1 and i <= n and "
1173 "j <= 2 i - 4 and j <= n - 3 or "
1174 "i2 = i + 1 and j2 = j + 1 and i <= 2 j - 1 and "
1175 "i <= n - 1 and j <= 2 i - 1 and j <= n - 1 }");
1176 map = isl_map_power(map, &exact);
1177 assert(exact);
1178 isl_map_free(map);
1179
1180 /* COCOA Fig.2 right */
1181 map = isl_map_read_from_str(ctx,
1182 "[n] -> { [i,j] -> [i2,j2] : i2 = i + 3 and j2 = j and "
1183 "i <= 2 j - 4 and i <= n - 3 and j <= 2 i - 1 and "
1184 "j <= n or "
1185 "i2 = i and j2 = j + 3 and i <= 2 j - 1 and i <= n and "
1186 "j <= 2 i - 4 and j <= n - 3 or "
1187 "i2 = i + 1 and j2 = j + 1 and i <= 2 j - 1 and "
1188 "i <= n - 1 and j <= 2 i - 1 and j <= n - 1 }");
1189 map = isl_map_transitive_closure(map, &exact);
1190 assert(exact);
1191 map2 = isl_map_read_from_str(ctx,
1192 "[n] -> { [i,j] -> [i2,j2] : exists (k1,k2,k3,k : "
1193 "i <= 2 j - 1 and i <= n and j <= 2 i - 1 and "
1194 "j <= n and 3 + i + 2 j <= 3 n and "
1195 "3 + 2 i + j <= 3n and i2 <= 2 j2 -1 and i2 <= n and "
1196 "i2 <= 3 j2 - 4 and j2 <= 2 i2 -1 and j2 <= n and "
1197 "13 + 4 j2 <= 11 i2 and i2 = i + 3 k1 + k3 and "
1198 "j2 = j + 3 k2 + k3 and k1 >= 0 and k2 >= 0 and "
1199 "k3 >= 0 and k1 + k2 + k3 = k and k > 0) }");
1200 assert(isl_map_is_equal(map, map2));
1201 isl_map_free(map2);
1202 isl_map_free(map);
1203
1204 /* COCOA Fig.1 right */
1205 dom = isl_set_read_from_str(ctx,
1206 "{ [x,y] : x >= 0 and -2 x + 3 y >= 0 and x <= 3 and "
1207 "2 x - 3 y + 3 >= 0 }");
1208 right = isl_map_read_from_str(ctx,
1209 "{ [x,y] -> [x2,y2] : x2 = x + 1 and y2 = y }");
1210 up = isl_map_read_from_str(ctx,
1211 "{ [x,y] -> [x2,y2] : x2 = x and y2 = y + 1 }");
1212 right = isl_map_intersect_domain(right, isl_set_copy(dom));
1213 right = isl_map_intersect_range(right, isl_set_copy(dom));
1214 up = isl_map_intersect_domain(up, isl_set_copy(dom));
1215 up = isl_map_intersect_range(up, dom);
1216 map = isl_map_union(up, right);
1217 map = isl_map_transitive_closure(map, &exact);
1218 assert(exact);
1219 map2 = isl_map_read_from_str(ctx,
1220 "{ [0,0] -> [0,1]; [0,0] -> [1,1]; [0,1] -> [1,1]; "
1221 " [2,2] -> [3,2]; [2,2] -> [3,3]; [3,2] -> [3,3] }");
1222 assert(isl_map_is_equal(map, map2));
1223 isl_map_free(map2);
1224 isl_map_free(map);
1225
1226 /* COCOA Theorem 1 counter example */
1227 map = isl_map_read_from_str(ctx,
1228 "{ [i,j] -> [i2,j2] : i = 0 and 0 <= j and j <= 1 and "
1229 "i2 = 1 and j2 = j or "
1230 "i = 0 and j = 0 and i2 = 0 and j2 = 1 }");
1231 map = isl_map_transitive_closure(map, &exact);
1232 assert(exact);
1233 isl_map_free(map);
1234
1235 map = isl_map_read_from_str(ctx,
1236 "[m,n] -> { [i,j] -> [i2,j2] : i2 = i and j2 = j + 2 and "
1237 "1 <= i,i2 <= n and 1 <= j,j2 <= m or "
1238 "i2 = i + 1 and 3 <= j2 - j <= 4 and "
1239 "1 <= i,i2 <= n and 1 <= j,j2 <= m }");
1240 map = isl_map_transitive_closure(map, &exact);
1241 assert(exact);
1242 isl_map_free(map);
1243
1244 /* Kelly et al 1996, fig 12 */
1245 map = isl_map_read_from_str(ctx,
1246 "[n] -> { [i,j] -> [i2,j2] : i2 = i and j2 = j + 1 and "
1247 "1 <= i,j,j+1 <= n or "
1248 "j = n and j2 = 1 and i2 = i + 1 and "
1249 "1 <= i,i+1 <= n }");
1250 map = isl_map_transitive_closure(map, &exact);
1251 assert(exact);
1252 map2 = isl_map_read_from_str(ctx,
1253 "[n] -> { [i,j] -> [i2,j2] : 1 <= j < j2 <= n and "
1254 "1 <= i <= n and i = i2 or "
1255 "1 <= i < i2 <= n and 1 <= j <= n and "
1256 "1 <= j2 <= n }");
1257 assert(isl_map_is_equal(map, map2));
1258 isl_map_free(map2);
1259 isl_map_free(map);
1260
1261 /* Omega's closure4 */
1262 map = isl_map_read_from_str(ctx,
1263 "[m,n] -> { [x,y] -> [x2,y2] : x2 = x and y2 = y + 1 and "
1264 "1 <= x,y <= 10 or "
1265 "x2 = x + 1 and y2 = y and "
1266 "1 <= x <= 20 && 5 <= y <= 15 }");
1267 map = isl_map_transitive_closure(map, &exact);
1268 assert(exact);
1269 isl_map_free(map);
1270
1271 map = isl_map_read_from_str(ctx,
1272 "[n] -> { [x] -> [y]: 1 <= n <= y - x <= 10 }");
1273 map = isl_map_transitive_closure(map, &exact);
1274 assert(!exact);
1275 map2 = isl_map_read_from_str(ctx,
1276 "[n] -> { [x] -> [y] : 1 <= n <= 10 and y >= n + x }");
1277 assert(isl_map_is_equal(map, map2));
1278 isl_map_free(map);
1279 isl_map_free(map2);
1280
1281 str = "[n, m] -> { [i0, i1, i2, i3] -> [o0, o1, o2, o3] : "
1282 "i3 = 1 and o0 = i0 and o1 = -1 + i1 and o2 = -1 + i2 and "
1283 "o3 = -2 + i2 and i1 <= -1 + i0 and i1 >= 1 - m + i0 and "
1284 "i1 >= 2 and i1 <= n and i2 >= 3 and i2 <= 1 + n and i2 <= m }";
1285 map = isl_map_read_from_str(ctx, str);
1286 map = isl_map_transitive_closure(map, &exact);
1287 assert(exact);
1288 map2 = isl_map_read_from_str(ctx, str);
1289 assert(isl_map_is_equal(map, map2));
1290 isl_map_free(map);
1291 isl_map_free(map2);
1292
1293 str = "{[0] -> [1]; [2] -> [3]}";
1294 map = isl_map_read_from_str(ctx, str);
1295 map = isl_map_transitive_closure(map, &exact);
1296 assert(exact);
1297 map2 = isl_map_read_from_str(ctx, str);
1298 assert(isl_map_is_equal(map, map2));
1299 isl_map_free(map);
1300 isl_map_free(map2);
1301
1302 str = "[n] -> { [[i0, i1, 1, 0, i0] -> [i5, 1]] -> "
1303 "[[i0, -1 + i1, 2, 0, i0] -> [-1 + i5, 2]] : "
1304 "exists (e0 = [(3 - n)/3]: i5 >= 2 and i1 >= 2 and "
1305 "3i0 <= -1 + n and i1 <= -1 + n and i5 <= -1 + n and "
1306 "3e0 >= 1 - n and 3e0 <= 2 - n and 3i0 >= -2 + n); "
1307 "[[i0, i1, 2, 0, i0] -> [i5, 1]] -> "
1308 "[[i0, i1, 1, 0, i0] -> [-1 + i5, 2]] : "
1309 "exists (e0 = [(3 - n)/3]: i5 >= 2 and i1 >= 1 and "
1310 "3i0 <= -1 + n and i1 <= -1 + n and i5 <= -1 + n and "
1311 "3e0 >= 1 - n and 3e0 <= 2 - n and 3i0 >= -2 + n); "
1312 "[[i0, i1, 1, 0, i0] -> [i5, 2]] -> "
1313 "[[i0, -1 + i1, 2, 0, i0] -> [i5, 1]] : "
1314 "exists (e0 = [(3 - n)/3]: i1 >= 2 and i5 >= 1 and "
1315 "3i0 <= -1 + n and i1 <= -1 + n and i5 <= -1 + n and "
1316 "3e0 >= 1 - n and 3e0 <= 2 - n and 3i0 >= -2 + n); "
1317 "[[i0, i1, 2, 0, i0] -> [i5, 2]] -> "
1318 "[[i0, i1, 1, 0, i0] -> [i5, 1]] : "
1319 "exists (e0 = [(3 - n)/3]: i5 >= 1 and i1 >= 1 and "
1320 "3i0 <= -1 + n and i1 <= -1 + n and i5 <= -1 + n and "
1321 "3e0 >= 1 - n and 3e0 <= 2 - n and 3i0 >= -2 + n) }";
1322 map = isl_map_read_from_str(ctx, str);
1323 map = isl_map_transitive_closure(map, NULL);
1324 assert(map);
1325 isl_map_free(map);
1326 }
1327
1328 void test_lex(struct isl_ctx *ctx)
1329 {
1330 isl_space *dim;
1331 isl_map *map;
1332
1333 dim = isl_space_set_alloc(ctx, 0, 0);
1334 map = isl_map_lex_le(dim);
1335 assert(!isl_map_is_empty(map));
1336 isl_map_free(map);
1337 }
1338
1339 static int test_lexmin(struct isl_ctx *ctx)
1340 {
1341 int equal;
1342 const char *str;
1343 isl_basic_map *bmap;
1344 isl_map *map, *map2;
1345 isl_set *set;
1346 isl_set *set2;
1347 isl_pw_multi_aff *pma;
1348
1349 str = "[p0, p1] -> { [] -> [] : "
1350 "exists (e0 = [(2p1)/3], e1, e2, e3 = [(3 - p1 + 3e0)/3], "
1351 "e4 = [(p1)/3], e5 = [(p1 + 3e4)/3]: "
1352 "3e0 >= -2 + 2p1 and 3e0 >= p1 and 3e3 >= 1 - p1 + 3e0 and "
1353 "3e0 <= 2p1 and 3e3 >= -2 + p1 and 3e3 <= -1 + p1 and p1 >= 3 and "
1354 "3e5 >= -2 + 2p1 and 3e5 >= p1 and 3e5 <= -1 + p1 + 3e4 and "
1355 "3e4 <= p1 and 3e4 >= -2 + p1 and e3 <= -1 + e0 and "
1356 "3e4 >= 6 - p1 + 3e1 and 3e1 >= p1 and 3e5 >= -2 + p1 + 3e4 and "
1357 "2e4 >= 3 - p1 + 2e1 and e4 <= e1 and 3e3 <= 2 - p1 + 3e0 and "
1358 "e5 >= 1 + e1 and 3e4 >= 6 - 2p1 + 3e1 and "
1359 "p0 >= 2 and p1 >= p0 and 3e2 >= p1 and 3e4 >= 6 - p1 + 3e2 and "
1360 "e2 <= e1 and e3 >= 1 and e4 <= e2) }";
1361 map = isl_map_read_from_str(ctx, str);
1362 map = isl_map_lexmin(map);
1363 isl_map_free(map);
1364
1365 str = "[C] -> { [obj,a,b,c] : obj <= 38 a + 7 b + 10 c and "
1366 "a + b <= 1 and c <= 10 b and c <= C and a,b,c,C >= 0 }";
1367 set = isl_set_read_from_str(ctx, str);
1368 set = isl_set_lexmax(set);
1369 str = "[C] -> { [obj,a,b,c] : C = 8 }";
1370 set2 = isl_set_read_from_str(ctx, str);
1371 set = isl_set_intersect(set, set2);
1372 assert(!isl_set_is_empty(set));
1373 isl_set_free(set);
1374
1375 str = "{ [x] -> [y] : x <= y <= 10; [x] -> [5] : -8 <= x <= 8 }";
1376 map = isl_map_read_from_str(ctx, str);
1377 map = isl_map_lexmin(map);
1378 str = "{ [x] -> [5] : 6 <= x <= 8; "
1379 "[x] -> [x] : x <= 5 or (9 <= x <= 10) }";
1380 map2 = isl_map_read_from_str(ctx, str);
1381 assert(isl_map_is_equal(map, map2));
1382 isl_map_free(map);
1383 isl_map_free(map2);
1384
1385 str = "{ [x] -> [y] : 4y = x or 4y = -1 + x or 4y = -2 + x }";
1386 map = isl_map_read_from_str(ctx, str);
1387 map2 = isl_map_copy(map);
1388 map = isl_map_lexmin(map);
1389 assert(isl_map_is_equal(map, map2));
1390 isl_map_free(map);
1391 isl_map_free(map2);
1392
1393 str = "{ [x] -> [y] : x = 4y; [x] -> [y] : x = 2y }";
1394 map = isl_map_read_from_str(ctx, str);
1395 map = isl_map_lexmin(map);
1396 str = "{ [x] -> [y] : (4y = x and x >= 0) or "
1397 "(exists (e0 = [(x)/4], e1 = [(-2 + x)/4]: 2y = x and "
1398 "4e1 = -2 + x and 4e0 <= -1 + x and 4e0 >= -3 + x)) or "
1399 "(exists (e0 = [(x)/4]: 2y = x and 4e0 = x and x <= -4)) }";
1400 map2 = isl_map_read_from_str(ctx, str);
1401 assert(isl_map_is_equal(map, map2));
1402 isl_map_free(map);
1403 isl_map_free(map2);
1404
1405 str = "{ [i] -> [i', j] : j = i - 8i' and i' >= 0 and i' <= 7 and "
1406 " 8i' <= i and 8i' >= -7 + i }";
1407 bmap = isl_basic_map_read_from_str(ctx, str);
1408 pma = isl_basic_map_lexmin_pw_multi_aff(isl_basic_map_copy(bmap));
1409 map2 = isl_map_from_pw_multi_aff(pma);
1410 map = isl_map_from_basic_map(bmap);
1411 assert(isl_map_is_equal(map, map2));
1412 isl_map_free(map);
1413 isl_map_free(map2);
1414
1415 str = "{ T[a] -> S[b, c] : a = 4b-2c and c >= b }";
1416 map = isl_map_read_from_str(ctx, str);
1417 map = isl_map_lexmin(map);
1418 str = "{ T[a] -> S[b, c] : 2b = a and 2c = a }";
1419 map2 = isl_map_read_from_str(ctx, str);
1420 assert(isl_map_is_equal(map, map2));
1421 isl_map_free(map);
1422 isl_map_free(map2);
1423
1424 str = "[i] -> { [i', j] : j = i - 8i' and i' >= 0 and i' <= 7 and "
1425 " 8i' <= i and 8i' >= -7 + i }";
1426 set = isl_set_read_from_str(ctx, str);
1427 pma = isl_set_lexmin_pw_multi_aff(isl_set_copy(set));
1428 set2 = isl_set_from_pw_multi_aff(pma);
1429 equal = isl_set_is_equal(set, set2);
1430 isl_set_free(set);
1431 isl_set_free(set2);
1432 if (equal < 0)
1433 return -1;
1434 if (!equal)
1435 isl_die(ctx, isl_error_unknown,
1436 "unexpected difference between set and "
1437 "piecewise affine expression", return -1);
1438
1439 return 0;
1440 }
1441
1442 struct must_may {
1443 isl_map *must;
1444 isl_map *may;
1445 };
1446
1447 static int collect_must_may(__isl_take isl_map *dep, int must,
1448 void *dep_user, void *user)
1449 {
1450 struct must_may *mm = (struct must_may *)user;
1451
1452 if (must)
1453 mm->must = isl_map_union(mm->must, dep);
1454 else
1455 mm->may = isl_map_union(mm->may, dep);
1456
1457 return 0;
1458 }
1459
1460 static int common_space(void *first, void *second)
1461 {
1462 int depth = *(int *)first;
1463 return 2 * depth;
1464 }
1465
1466 static int map_is_equal(__isl_keep isl_map *map, const char *str)
1467 {
1468 isl_map *map2;
1469 int equal;
1470
1471 if (!map)
1472 return -1;
1473
1474 map2 = isl_map_read_from_str(map->ctx, str);
1475 equal = isl_map_is_equal(map, map2);
1476 isl_map_free(map2);
1477
1478 return equal;
1479 }
1480
1481 static int map_check_equal(__isl_keep isl_map *map, const char *str)
1482 {
1483 int equal;
1484
1485 equal = map_is_equal(map, str);
1486 if (equal < 0)
1487 return -1;
1488 if (!equal)
1489 isl_die(isl_map_get_ctx(map), isl_error_unknown,
1490 "result not as expected", return -1);
1491 return 0;
1492 }
1493
1494 void test_dep(struct isl_ctx *ctx)
1495 {
1496 const char *str;
1497 isl_space *dim;
1498 isl_map *map;
1499 isl_access_info *ai;
1500 isl_flow *flow;
1501 int depth;
1502 struct must_may mm;
1503
1504 depth = 3;
1505
1506 str = "{ [2,i,0] -> [i] : 0 <= i <= 10 }";
1507 map = isl_map_read_from_str(ctx, str);
1508 ai = isl_access_info_alloc(map, &depth, &common_space, 2);
1509
1510 str = "{ [0,i,0] -> [i] : 0 <= i <= 10 }";
1511 map = isl_map_read_from_str(ctx, str);
1512 ai = isl_access_info_add_source(ai, map, 1, &depth);
1513
1514 str = "{ [1,i,0] -> [5] : 0 <= i <= 10 }";
1515 map = isl_map_read_from_str(ctx, str);
1516 ai = isl_access_info_add_source(ai, map, 1, &depth);
1517
1518 flow = isl_access_info_compute_flow(ai);
1519 dim = isl_space_alloc(ctx, 0, 3, 3);
1520 mm.must = isl_map_empty(isl_space_copy(dim));
1521 mm.may = isl_map_empty(dim);
1522
1523 isl_flow_foreach(flow, collect_must_may, &mm);
1524
1525 str = "{ [0,i,0] -> [2,i,0] : (0 <= i <= 4) or (6 <= i <= 10); "
1526 " [1,10,0] -> [2,5,0] }";
1527 assert(map_is_equal(mm.must, str));
1528 str = "{ [i,j,k] -> [l,m,n] : 1 = 0 }";
1529 assert(map_is_equal(mm.may, str));
1530
1531 isl_map_free(mm.must);
1532 isl_map_free(mm.may);
1533 isl_flow_free(flow);
1534
1535
1536 str = "{ [2,i,0] -> [i] : 0 <= i <= 10 }";
1537 map = isl_map_read_from_str(ctx, str);
1538 ai = isl_access_info_alloc(map, &depth, &common_space, 2);
1539
1540 str = "{ [0,i,0] -> [i] : 0 <= i <= 10 }";
1541 map = isl_map_read_from_str(ctx, str);
1542 ai = isl_access_info_add_source(ai, map, 1, &depth);
1543
1544 str = "{ [1,i,0] -> [5] : 0 <= i <= 10 }";
1545 map = isl_map_read_from_str(ctx, str);
1546 ai = isl_access_info_add_source(ai, map, 0, &depth);
1547
1548 flow = isl_access_info_compute_flow(ai);
1549 dim = isl_space_alloc(ctx, 0, 3, 3);
1550 mm.must = isl_map_empty(isl_space_copy(dim));
1551 mm.may = isl_map_empty(dim);
1552
1553 isl_flow_foreach(flow, collect_must_may, &mm);
1554
1555 str = "{ [0,i,0] -> [2,i,0] : (0 <= i <= 4) or (6 <= i <= 10) }";
1556 assert(map_is_equal(mm.must, str));
1557 str = "{ [0,5,0] -> [2,5,0]; [1,i,0] -> [2,5,0] : 0 <= i <= 10 }";
1558 assert(map_is_equal(mm.may, str));
1559
1560 isl_map_free(mm.must);
1561 isl_map_free(mm.may);
1562 isl_flow_free(flow);
1563
1564
1565 str = "{ [2,i,0] -> [i] : 0 <= i <= 10 }";
1566 map = isl_map_read_from_str(ctx, str);
1567 ai = isl_access_info_alloc(map, &depth, &common_space, 2);
1568
1569 str = "{ [0,i,0] -> [i] : 0 <= i <= 10 }";
1570 map = isl_map_read_from_str(ctx, str);
1571 ai = isl_access_info_add_source(ai, map, 0, &depth);
1572
1573 str = "{ [1,i,0] -> [5] : 0 <= i <= 10 }";
1574 map = isl_map_read_from_str(ctx, str);
1575 ai = isl_access_info_add_source(ai, map, 0, &depth);
1576
1577 flow = isl_access_info_compute_flow(ai);
1578 dim = isl_space_alloc(ctx, 0, 3, 3);
1579 mm.must = isl_map_empty(isl_space_copy(dim));
1580 mm.may = isl_map_empty(dim);
1581
1582 isl_flow_foreach(flow, collect_must_may, &mm);
1583
1584 str = "{ [0,i,0] -> [2,i,0] : 0 <= i <= 10; "
1585 " [1,i,0] -> [2,5,0] : 0 <= i <= 10 }";
1586 assert(map_is_equal(mm.may, str));
1587 str = "{ [i,j,k] -> [l,m,n] : 1 = 0 }";
1588 assert(map_is_equal(mm.must, str));
1589
1590 isl_map_free(mm.must);
1591 isl_map_free(mm.may);
1592 isl_flow_free(flow);
1593
1594
1595 str = "{ [0,i,2] -> [i] : 0 <= i <= 10 }";
1596 map = isl_map_read_from_str(ctx, str);
1597 ai = isl_access_info_alloc(map, &depth, &common_space, 2);
1598
1599 str = "{ [0,i,0] -> [i] : 0 <= i <= 10 }";
1600 map = isl_map_read_from_str(ctx, str);
1601 ai = isl_access_info_add_source(ai, map, 0, &depth);
1602
1603 str = "{ [0,i,1] -> [5] : 0 <= i <= 10 }";
1604 map = isl_map_read_from_str(ctx, str);
1605 ai = isl_access_info_add_source(ai, map, 0, &depth);
1606
1607 flow = isl_access_info_compute_flow(ai);
1608 dim = isl_space_alloc(ctx, 0, 3, 3);
1609 mm.must = isl_map_empty(isl_space_copy(dim));
1610 mm.may = isl_map_empty(dim);
1611
1612 isl_flow_foreach(flow, collect_must_may, &mm);
1613
1614 str = "{ [0,i,0] -> [0,i,2] : 0 <= i <= 10; "
1615 " [0,i,1] -> [0,5,2] : 0 <= i <= 5 }";
1616 assert(map_is_equal(mm.may, str));
1617 str = "{ [i,j,k] -> [l,m,n] : 1 = 0 }";
1618 assert(map_is_equal(mm.must, str));
1619
1620 isl_map_free(mm.must);
1621 isl_map_free(mm.may);
1622 isl_flow_free(flow);
1623
1624
1625 str = "{ [0,i,1] -> [i] : 0 <= i <= 10 }";
1626 map = isl_map_read_from_str(ctx, str);
1627 ai = isl_access_info_alloc(map, &depth, &common_space, 2);
1628
1629 str = "{ [0,i,0] -> [i] : 0 <= i <= 10 }";
1630 map = isl_map_read_from_str(ctx, str);
1631 ai = isl_access_info_add_source(ai, map, 0, &depth);
1632
1633 str = "{ [0,i,2] -> [5] : 0 <= i <= 10 }";
1634 map = isl_map_read_from_str(ctx, str);
1635 ai = isl_access_info_add_source(ai, map, 0, &depth);
1636
1637 flow = isl_access_info_compute_flow(ai);
1638 dim = isl_space_alloc(ctx, 0, 3, 3);
1639 mm.must = isl_map_empty(isl_space_copy(dim));
1640 mm.may = isl_map_empty(dim);
1641
1642 isl_flow_foreach(flow, collect_must_may, &mm);
1643
1644 str = "{ [0,i,0] -> [0,i,1] : 0 <= i <= 10; "
1645 " [0,i,2] -> [0,5,1] : 0 <= i <= 4 }";
1646 assert(map_is_equal(mm.may, str));
1647 str = "{ [i,j,k] -> [l,m,n] : 1 = 0 }";
1648 assert(map_is_equal(mm.must, str));
1649
1650 isl_map_free(mm.must);
1651 isl_map_free(mm.may);
1652 isl_flow_free(flow);
1653
1654
1655 depth = 5;
1656
1657 str = "{ [1,i,0,0,0] -> [i,j] : 0 <= i <= 10 and 0 <= j <= 10 }";
1658 map = isl_map_read_from_str(ctx, str);
1659 ai = isl_access_info_alloc(map, &depth, &common_space, 1);
1660
1661 str = "{ [0,i,0,j,0] -> [i,j] : 0 <= i <= 10 and 0 <= j <= 10 }";
1662 map = isl_map_read_from_str(ctx, str);
1663 ai = isl_access_info_add_source(ai, map, 1, &depth);
1664
1665 flow = isl_access_info_compute_flow(ai);
1666 dim = isl_space_alloc(ctx, 0, 5, 5);
1667 mm.must = isl_map_empty(isl_space_copy(dim));
1668 mm.may = isl_map_empty(dim);
1669
1670 isl_flow_foreach(flow, collect_must_may, &mm);
1671
1672 str = "{ [0,i,0,j,0] -> [1,i,0,0,0] : 0 <= i,j <= 10 }";
1673 assert(map_is_equal(mm.must, str));
1674 str = "{ [0,0,0,0,0] -> [0,0,0,0,0] : 1 = 0 }";
1675 assert(map_is_equal(mm.may, str));
1676
1677 isl_map_free(mm.must);
1678 isl_map_free(mm.may);
1679 isl_flow_free(flow);
1680 }
1681
1682 int test_sv(isl_ctx *ctx)
1683 {
1684 const char *str;
1685 isl_map *map;
1686 isl_union_map *umap;
1687 int sv;
1688
1689 str = "[N] -> { [i] -> [f] : 0 <= i <= N and 0 <= i - 10 f <= 9 }";
1690 map = isl_map_read_from_str(ctx, str);
1691 sv = isl_map_is_single_valued(map);
1692 isl_map_free(map);
1693 if (sv < 0)
1694 return -1;
1695 if (!sv)
1696 isl_die(ctx, isl_error_internal,
1697 "map not detected as single valued", return -1);
1698
1699 str = "[N] -> { [i] -> [f] : 0 <= i <= N and 0 <= i - 10 f <= 10 }";
1700 map = isl_map_read_from_str(ctx, str);
1701 sv = isl_map_is_single_valued(map);
1702 isl_map_free(map);
1703 if (sv < 0)
1704 return -1;
1705 if (sv)
1706 isl_die(ctx, isl_error_internal,
1707 "map detected as single valued", return -1);
1708
1709 str = "{ S1[i] -> [i] : 0 <= i <= 9; S2[i] -> [i] : 0 <= i <= 9 }";
1710 umap = isl_union_map_read_from_str(ctx, str);
1711 sv = isl_union_map_is_single_valued(umap);
1712 isl_union_map_free(umap);
1713 if (sv < 0)
1714 return -1;
1715 if (!sv)
1716 isl_die(ctx, isl_error_internal,
1717 "map not detected as single valued", return -1);
1718
1719 str = "{ [i] -> S1[i] : 0 <= i <= 9; [i] -> S2[i] : 0 <= i <= 9 }";
1720 umap = isl_union_map_read_from_str(ctx, str);
1721 sv = isl_union_map_is_single_valued(umap);
1722 isl_union_map_free(umap);
1723 if (sv < 0)
1724 return -1;
1725 if (sv)
1726 isl_die(ctx, isl_error_internal,
1727 "map detected as single valued", return -1);
1728
1729 return 0;
1730 }
1731
1732 void test_bijective_case(struct isl_ctx *ctx, const char *str, int bijective)
1733 {
1734 isl_map *map;
1735
1736 map = isl_map_read_from_str(ctx, str);
1737 if (bijective)
1738 assert(isl_map_is_bijective(map));
1739 else
1740 assert(!isl_map_is_bijective(map));
1741 isl_map_free(map);
1742 }
1743
1744 void test_bijective(struct isl_ctx *ctx)
1745 {
1746 test_bijective_case(ctx, "[N,M]->{[i,j] -> [i]}", 0);
1747 test_bijective_case(ctx, "[N,M]->{[i,j] -> [i] : j=i}", 1);
1748 test_bijective_case(ctx, "[N,M]->{[i,j] -> [i] : j=0}", 1);
1749 test_bijective_case(ctx, "[N,M]->{[i,j] -> [i] : j=N}", 1);
1750 test_bijective_case(ctx, "[N,M]->{[i,j] -> [j,i]}", 1);
1751 test_bijective_case(ctx, "[N,M]->{[i,j] -> [i+j]}", 0);
1752 test_bijective_case(ctx, "[N,M]->{[i,j] -> []}", 0);
1753 test_bijective_case(ctx, "[N,M]->{[i,j] -> [i,j,N]}", 1);
1754 test_bijective_case(ctx, "[N,M]->{[i,j] -> [2i]}", 0);
1755 test_bijective_case(ctx, "[N,M]->{[i,j] -> [i,i]}", 0);
1756 test_bijective_case(ctx, "[N,M]->{[i,j] -> [2i,i]}", 0);
1757 test_bijective_case(ctx, "[N,M]->{[i,j] -> [2i,j]}", 1);
1758 test_bijective_case(ctx, "[N,M]->{[i,j] -> [x,y] : 2x=i & y =j}", 1);
1759 }
1760
1761 void test_pwqp(struct isl_ctx *ctx)
1762 {
1763 const char *str;
1764 isl_set *set;
1765 isl_pw_qpolynomial *pwqp1, *pwqp2;
1766
1767 str = "{ [i,j,k] -> 1 + 9 * [i/5] + 7 * [j/11] + 4 * [k/13] }";
1768 pwqp1 = isl_pw_qpolynomial_read_from_str(ctx, str);
1769
1770 pwqp1 = isl_pw_qpolynomial_move_dims(pwqp1, isl_dim_param, 0,
1771 isl_dim_in, 1, 1);
1772
1773 str = "[j] -> { [i,k] -> 1 + 9 * [i/5] + 7 * [j/11] + 4 * [k/13] }";
1774 pwqp2 = isl_pw_qpolynomial_read_from_str(ctx, str);
1775
1776 pwqp1 = isl_pw_qpolynomial_sub(pwqp1, pwqp2);
1777
1778 assert(isl_pw_qpolynomial_is_zero(pwqp1));
1779
1780 isl_pw_qpolynomial_free(pwqp1);
1781
1782 str = "{ [i] -> i }";
1783 pwqp1 = isl_pw_qpolynomial_read_from_str(ctx, str);
1784 str = "{ [k] : exists a : k = 2a }";
1785 set = isl_set_read_from_str(ctx, str);
1786 pwqp1 = isl_pw_qpolynomial_gist(pwqp1, set);
1787 str = "{ [i] -> i }";
1788 pwqp2 = isl_pw_qpolynomial_read_from_str(ctx, str);
1789
1790 pwqp1 = isl_pw_qpolynomial_sub(pwqp1, pwqp2);
1791
1792 assert(isl_pw_qpolynomial_is_zero(pwqp1));
1793
1794 isl_pw_qpolynomial_free(pwqp1);
1795
1796 str = "{ [i] -> i + [ (i + [i/3])/2 ] }";
1797 pwqp1 = isl_pw_qpolynomial_read_from_str(ctx, str);
1798 str = "{ [10] }";
1799 set = isl_set_read_from_str(ctx, str);
1800 pwqp1 = isl_pw_qpolynomial_gist(pwqp1, set);
1801 str = "{ [i] -> 16 }";
1802 pwqp2 = isl_pw_qpolynomial_read_from_str(ctx, str);
1803
1804 pwqp1 = isl_pw_qpolynomial_sub(pwqp1, pwqp2);
1805
1806 assert(isl_pw_qpolynomial_is_zero(pwqp1));
1807
1808 isl_pw_qpolynomial_free(pwqp1);
1809
1810 str = "{ [i] -> ([(i)/2]) }";
1811 pwqp1 = isl_pw_qpolynomial_read_from_str(ctx, str);
1812 str = "{ [k] : exists a : k = 2a+1 }";
1813 set = isl_set_read_from_str(ctx, str);
1814 pwqp1 = isl_pw_qpolynomial_gist(pwqp1, set);
1815 str = "{ [i] -> -1/2 + 1/2 * i }";
1816 pwqp2 = isl_pw_qpolynomial_read_from_str(ctx, str);
1817
1818 pwqp1 = isl_pw_qpolynomial_sub(pwqp1, pwqp2);
1819
1820 assert(isl_pw_qpolynomial_is_zero(pwqp1));
1821
1822 isl_pw_qpolynomial_free(pwqp1);
1823
1824 str = "{ [i] -> ([([i/2] + [i/2])/5]) }";
1825 pwqp1 = isl_pw_qpolynomial_read_from_str(ctx, str);
1826 str = "{ [i] -> ([(2 * [i/2])/5]) }";
1827 pwqp2 = isl_pw_qpolynomial_read_from_str(ctx, str);
1828
1829 pwqp1 = isl_pw_qpolynomial_sub(pwqp1, pwqp2);
1830
1831 assert(isl_pw_qpolynomial_is_zero(pwqp1));
1832
1833 isl_pw_qpolynomial_free(pwqp1);
1834
1835 str = "{ [x] -> ([x/2] + [(x+1)/2]) }";
1836 pwqp1 = isl_pw_qpolynomial_read_from_str(ctx, str);
1837 str = "{ [x] -> x }";
1838 pwqp2 = isl_pw_qpolynomial_read_from_str(ctx, str);
1839
1840 pwqp1 = isl_pw_qpolynomial_sub(pwqp1, pwqp2);
1841
1842 assert(isl_pw_qpolynomial_is_zero(pwqp1));
1843
1844 isl_pw_qpolynomial_free(pwqp1);
1845
1846 str = "{ [i] -> ([i/2]) : i >= 0; [i] -> ([i/3]) : i < 0 }";
1847 pwqp1 = isl_pw_qpolynomial_read_from_str(ctx, str);
1848 pwqp2 = isl_pw_qpolynomial_read_from_str(ctx, str);
1849 pwqp1 = isl_pw_qpolynomial_coalesce(pwqp1);
1850 pwqp1 = isl_pw_qpolynomial_sub(pwqp1, pwqp2);
1851 assert(isl_pw_qpolynomial_is_zero(pwqp1));
1852 isl_pw_qpolynomial_free(pwqp1);
1853 }
1854
1855 void test_split_periods(isl_ctx *ctx)
1856 {
1857 const char *str;
1858 isl_pw_qpolynomial *pwqp;
1859
1860 str = "{ [U,V] -> 1/3 * U + 2/3 * V - [(U + 2V)/3] + [U/2] : "
1861 "U + 2V + 3 >= 0 and - U -2V >= 0 and - U + 10 >= 0 and "
1862 "U >= 0; [U,V] -> U^2 : U >= 100 }";
1863 pwqp = isl_pw_qpolynomial_read_from_str(ctx, str);
1864
1865 pwqp = isl_pw_qpolynomial_split_periods(pwqp, 2);
1866 assert(pwqp);
1867
1868 isl_pw_qpolynomial_free(pwqp);
1869 }
1870
1871 void test_union(isl_ctx *ctx)
1872 {
1873 const char *str;
1874 isl_union_set *uset1, *uset2;
1875 isl_union_map *umap1, *umap2;
1876
1877 str = "{ [i] : 0 <= i <= 1 }";
1878 uset1 = isl_union_set_read_from_str(ctx, str);
1879 str = "{ [1] -> [0] }";
1880 umap1 = isl_union_map_read_from_str(ctx, str);
1881
1882 umap2 = isl_union_set_lex_gt_union_set(isl_union_set_copy(uset1), uset1);
1883 assert(isl_union_map_is_equal(umap1, umap2));
1884
1885 isl_union_map_free(umap1);
1886 isl_union_map_free(umap2);
1887
1888 str = "{ A[i] -> B[i]; B[i] -> C[i]; A[0] -> C[1] }";
1889 umap1 = isl_union_map_read_from_str(ctx, str);
1890 str = "{ A[i]; B[i] }";
1891 uset1 = isl_union_set_read_from_str(ctx, str);
1892
1893 uset2 = isl_union_map_domain(umap1);
1894
1895 assert(isl_union_set_is_equal(uset1, uset2));
1896
1897 isl_union_set_free(uset1);
1898 isl_union_set_free(uset2);
1899 }
1900
1901 void test_bound(isl_ctx *ctx)
1902 {
1903 const char *str;
1904 isl_pw_qpolynomial *pwqp;
1905 isl_pw_qpolynomial_fold *pwf;
1906
1907 str = "{ [[a, b, c, d] -> [e]] -> 0 }";
1908 pwqp = isl_pw_qpolynomial_read_from_str(ctx, str);
1909 pwf = isl_pw_qpolynomial_bound(pwqp, isl_fold_max, NULL);
1910 assert(isl_pw_qpolynomial_fold_dim(pwf, isl_dim_in) == 4);
1911 isl_pw_qpolynomial_fold_free(pwf);
1912
1913 str = "{ [[x]->[x]] -> 1 : exists a : x = 2 a }";
1914 pwqp = isl_pw_qpolynomial_read_from_str(ctx, str);
1915 pwf = isl_pw_qpolynomial_bound(pwqp, isl_fold_max, NULL);
1916 assert(isl_pw_qpolynomial_fold_dim(pwf, isl_dim_in) == 1);
1917 isl_pw_qpolynomial_fold_free(pwf);
1918 }
1919
1920 void test_lift(isl_ctx *ctx)
1921 {
1922 const char *str;
1923 isl_basic_map *bmap;
1924 isl_basic_set *bset;
1925
1926 str = "{ [i0] : exists e0 : i0 = 4e0 }";
1927 bset = isl_basic_set_read_from_str(ctx, str);
1928 bset = isl_basic_set_lift(bset);
1929 bmap = isl_basic_map_from_range(bset);
1930 bset = isl_basic_map_domain(bmap);
1931 isl_basic_set_free(bset);
1932 }
1933
1934 struct {
1935 const char *set1;
1936 const char *set2;
1937 int subset;
1938 } subset_tests[] = {
1939 { "{ [112, 0] }",
1940 "{ [i0, i1] : exists (e0 = [(i0 - i1)/16], e1: "
1941 "16e0 <= i0 - i1 and 16e0 >= -15 + i0 - i1 and "
1942 "16e1 <= i1 and 16e0 >= -i1 and 16e1 >= -i0 + i1) }", 1 },
1943 { "{ [65] }",
1944 "{ [i] : exists (e0 = [(255i)/256], e1 = [(127i + 65e0)/191], "
1945 "e2 = [(3i + 61e1)/65], e3 = [(52i + 12e2)/61], "
1946 "e4 = [(2i + e3)/3], e5 = [(4i + e3)/4], e6 = [(8i + e3)/12]: "
1947 "3e4 = 2i + e3 and 4e5 = 4i + e3 and 12e6 = 8i + e3 and "
1948 "i <= 255 and 64e3 >= -45 + 67i and i >= 0 and "
1949 "256e0 <= 255i and 256e0 >= -255 + 255i and "
1950 "191e1 <= 127i + 65e0 and 191e1 >= -190 + 127i + 65e0 and "
1951 "65e2 <= 3i + 61e1 and 65e2 >= -64 + 3i + 61e1 and "
1952 "61e3 <= 52i + 12e2 and 61e3 >= -60 + 52i + 12e2) }", 1 },
1953 { "{ [i] : 0 <= i <= 10 }", "{ rat: [i] : 0 <= i <= 10 }", 1 },
1954 { "{ rat: [i] : 0 <= i <= 10 }", "{ [i] : 0 <= i <= 10 }", 0 },
1955 { "{ rat: [0] }", "{ [i] : 0 <= i <= 10 }", 1 },
1956 { "{ rat: [(1)/2] }", "{ [i] : 0 <= i <= 10 }", 0 },
1957 };
1958
1959 static int test_subset(isl_ctx *ctx)
1960 {
1961 int i;
1962 isl_set *set1, *set2;
1963 int subset;
1964
1965 for (i = 0; i < ARRAY_SIZE(subset_tests); ++i) {
1966 set1 = isl_set_read_from_str(ctx, subset_tests[i].set1);
1967 set2 = isl_set_read_from_str(ctx, subset_tests[i].set2);
1968 subset = isl_set_is_subset(set1, set2);
1969 isl_set_free(set1);
1970 isl_set_free(set2);
1971 if (subset < 0)
1972 return -1;
1973 if (subset != subset_tests[i].subset)
1974 isl_die(ctx, isl_error_unknown,
1975 "incorrect subset result", return -1);
1976 }
1977
1978 return 0;
1979 }
1980
1981 struct {
1982 const char *minuend;
1983 const char *subtrahend;
1984 const char *difference;
1985 } subtract_domain_tests[] = {
1986 { "{ A[i] -> B[i] }", "{ A[i] }", "{ }" },
1987 { "{ A[i] -> B[i] }", "{ B[i] }", "{ A[i] -> B[i] }" },
1988 { "{ A[i] -> B[i] }", "{ A[i] : i > 0 }", "{ A[i] -> B[i] : i <= 0 }" },
1989 };
1990
1991 static int test_subtract(isl_ctx *ctx)
1992 {
1993 int i;
1994 isl_union_map *umap1, *umap2;
1995 isl_union_set *uset;
1996 int equal;
1997
1998 for (i = 0; i < ARRAY_SIZE(subtract_domain_tests); ++i) {
1999 umap1 = isl_union_map_read_from_str(ctx,
2000 subtract_domain_tests[i].minuend);
2001 uset = isl_union_set_read_from_str(ctx,
2002 subtract_domain_tests[i].subtrahend);
2003 umap2 = isl_union_map_read_from_str(ctx,
2004 subtract_domain_tests[i].difference);
2005 umap1 = isl_union_map_subtract_domain(umap1, uset);
2006 equal = isl_union_map_is_equal(umap1, umap2);
2007 isl_union_map_free(umap1);
2008 isl_union_map_free(umap2);
2009 if (equal < 0)
2010 return -1;
2011 if (!equal)
2012 isl_die(ctx, isl_error_unknown,
2013 "incorrect subtract domain result", return -1);
2014 }
2015
2016 return 0;
2017 }
2018
2019 int test_factorize(isl_ctx *ctx)
2020 {
2021 const char *str;
2022 isl_basic_set *bset;
2023 isl_factorizer *f;
2024
2025 str = "{ [i0, i1, i2, i3, i4, i5, i6, i7] : 3i5 <= 2 - 2i0 and "
2026 "i0 >= -2 and i6 >= 1 + i3 and i7 >= 0 and 3i5 >= -2i0 and "
2027 "2i4 <= i2 and i6 >= 1 + 2i0 + 3i1 and i4 <= -1 and "
2028 "i6 >= 1 + 2i0 + 3i5 and i6 <= 2 + 2i0 + 3i5 and "
2029 "3i5 <= 2 - 2i0 - i2 + 3i4 and i6 <= 2 + 2i0 + 3i1 and "
2030 "i0 <= -1 and i7 <= i2 + i3 - 3i4 - i6 and "
2031 "3i5 >= -2i0 - i2 + 3i4 }";
2032 bset = isl_basic_set_read_from_str(ctx, str);
2033 f = isl_basic_set_factorizer(bset);
2034 isl_basic_set_free(bset);
2035 isl_factorizer_free(f);
2036 if (!f)
2037 isl_die(ctx, isl_error_unknown,
2038 "failed to construct factorizer", return -1);
2039
2040 str = "{ [i0, i1, i2, i3, i4, i5, i6, i7, i8, i9, i10, i11, i12] : "
2041 "i12 <= 2 + i0 - i11 and 2i8 >= -i4 and i11 >= i1 and "
2042 "3i5 <= -i2 and 2i11 >= -i4 - 2i7 and i11 <= 3 + i0 + 3i9 and "
2043 "i11 <= -i4 - 2i7 and i12 >= -i10 and i2 >= -2 and "
2044 "i11 >= i1 + 3i10 and i11 >= 1 + i0 + 3i9 and "
2045 "i11 <= 1 - i4 - 2i8 and 6i6 <= 6 - i2 and 3i6 >= 1 - i2 and "
2046 "i11 <= 2 + i1 and i12 <= i4 + i11 and i12 >= i0 - i11 and "
2047 "3i5 >= -2 - i2 and i12 >= -1 + i4 + i11 and 3i3 <= 3 - i2 and "
2048 "9i6 <= 11 - i2 + 6i5 and 3i3 >= 1 - i2 and "
2049 "9i6 <= 5 - i2 + 6i3 and i12 <= -1 and i2 <= 0 }";
2050 bset = isl_basic_set_read_from_str(ctx, str);
2051 f = isl_basic_set_factorizer(bset);
2052 isl_basic_set_free(bset);
2053 isl_factorizer_free(f);
2054 if (!f)
2055 isl_die(ctx, isl_error_unknown,
2056 "failed to construct factorizer", return -1);
2057
2058 return 0;
2059 }
2060
2061 static int check_injective(__isl_take isl_map *map, void *user)
2062 {
2063 int *injective = user;
2064
2065 *injective = isl_map_is_injective(map);
2066 isl_map_free(map);
2067
2068 if (*injective < 0 || !*injective)
2069 return -1;
2070
2071 return 0;
2072 }
2073
2074 int test_one_schedule(isl_ctx *ctx, const char *d, const char *w,
2075 const char *r, const char *s, int tilable, int parallel)
2076 {
2077 int i;
2078 isl_union_set *D;
2079 isl_union_map *W, *R, *S;
2080 isl_union_map *empty;
2081 isl_union_map *dep_raw, *dep_war, *dep_waw, *dep;
2082 isl_union_map *validity, *proximity;
2083 isl_union_map *schedule;
2084 isl_union_map *test;
2085 isl_union_set *delta;
2086 isl_union_set *domain;
2087 isl_set *delta_set;
2088 isl_set *slice;
2089 isl_set *origin;
2090 isl_schedule *sched;
2091 int is_nonneg, is_parallel, is_tilable, is_injection, is_complete;
2092
2093 D = isl_union_set_read_from_str(ctx, d);
2094 W = isl_union_map_read_from_str(ctx, w);
2095 R = isl_union_map_read_from_str(ctx, r);
2096 S = isl_union_map_read_from_str(ctx, s);
2097
2098 W = isl_union_map_intersect_domain(W, isl_union_set_copy(D));
2099 R = isl_union_map_intersect_domain(R, isl_union_set_copy(D));
2100
2101 empty = isl_union_map_empty(isl_union_map_get_space(S));
2102 isl_union_map_compute_flow(isl_union_map_copy(R),
2103 isl_union_map_copy(W), empty,
2104 isl_union_map_copy(S),
2105 &dep_raw, NULL, NULL, NULL);
2106 isl_union_map_compute_flow(isl_union_map_copy(W),
2107 isl_union_map_copy(W),
2108 isl_union_map_copy(R),
2109 isl_union_map_copy(S),
2110 &dep_waw, &dep_war, NULL, NULL);
2111
2112 dep = isl_union_map_union(dep_waw, dep_war);
2113 dep = isl_union_map_union(dep, dep_raw);
2114 validity = isl_union_map_copy(dep);
2115 proximity = isl_union_map_copy(dep);
2116
2117 sched = isl_union_set_compute_schedule(isl_union_set_copy(D),
2118 validity, proximity);
2119 schedule = isl_schedule_get_map(sched);
2120 isl_schedule_free(sched);
2121 isl_union_map_free(W);
2122 isl_union_map_free(R);
2123 isl_union_map_free(S);
2124
2125 is_injection = 1;
2126 isl_union_map_foreach_map(schedule, &check_injective, &is_injection);
2127
2128 domain = isl_union_map_domain(isl_union_map_copy(schedule));
2129 is_complete = isl_union_set_is_subset(D, domain);
2130 isl_union_set_free(D);
2131 isl_union_set_free(domain);
2132
2133 test = isl_union_map_reverse(isl_union_map_copy(schedule));
2134 test = isl_union_map_apply_range(test, dep);
2135 test = isl_union_map_apply_range(test, schedule);
2136
2137 delta = isl_union_map_deltas(test);
2138 if (isl_union_set_n_set(delta) == 0) {
2139 is_tilable = 1;
2140 is_parallel = 1;
2141 is_nonneg = 1;
2142 isl_union_set_free(delta);
2143 } else {
2144 delta_set = isl_set_from_union_set(delta);
2145
2146 slice = isl_set_universe(isl_set_get_space(delta_set));
2147 for (i = 0; i < tilable; ++i)
2148 slice = isl_set_lower_bound_si(slice, isl_dim_set, i, 0);
2149 is_tilable = isl_set_is_subset(delta_set, slice);
2150 isl_set_free(slice);
2151
2152 slice = isl_set_universe(isl_set_get_space(delta_set));
2153 for (i = 0; i < parallel; ++i)
2154 slice = isl_set_fix_si(slice, isl_dim_set, i, 0);
2155 is_parallel = isl_set_is_subset(delta_set, slice);
2156 isl_set_free(slice);
2157
2158 origin = isl_set_universe(isl_set_get_space(delta_set));
2159 for (i = 0; i < isl_set_dim(origin, isl_dim_set); ++i)
2160 origin = isl_set_fix_si(origin, isl_dim_set, i, 0);
2161
2162 delta_set = isl_set_union(delta_set, isl_set_copy(origin));
2163 delta_set = isl_set_lexmin(delta_set);
2164
2165 is_nonneg = isl_set_is_equal(delta_set, origin);
2166
2167 isl_set_free(origin);
2168 isl_set_free(delta_set);
2169 }
2170
2171 if (is_nonneg < 0 || is_parallel < 0 || is_tilable < 0 ||
2172 is_injection < 0 || is_complete < 0)
2173 return -1;
2174 if (!is_complete)
2175 isl_die(ctx, isl_error_unknown,
2176 "generated schedule incomplete", return -1);
2177 if (!is_injection)
2178 isl_die(ctx, isl_error_unknown,
2179 "generated schedule not injective on each statement",
2180 return -1);
2181 if (!is_nonneg)
2182 isl_die(ctx, isl_error_unknown,
2183 "negative dependences in generated schedule",
2184 return -1);
2185 if (!is_tilable)
2186 isl_die(ctx, isl_error_unknown,
2187 "generated schedule not as tilable as expected",
2188 return -1);
2189 if (!is_parallel)
2190 isl_die(ctx, isl_error_unknown,
2191 "generated schedule not as parallel as expected",
2192 return -1);
2193
2194 return 0;
2195 }
2196
2197 static __isl_give isl_union_map *compute_schedule(isl_ctx *ctx,
2198 const char *domain, const char *validity, const char *proximity)
2199 {
2200 isl_union_set *dom;
2201 isl_union_map *dep;
2202 isl_union_map *prox;
2203 isl_schedule *schedule;
2204 isl_union_map *sched;
2205
2206 dom = isl_union_set_read_from_str(ctx, domain);
2207 dep = isl_union_map_read_from_str(ctx, validity);
2208 prox = isl_union_map_read_from_str(ctx, proximity);
2209 schedule = isl_union_set_compute_schedule(dom, dep, prox);
2210 sched = isl_schedule_get_map(schedule);
2211 isl_schedule_free(schedule);
2212
2213 return sched;
2214 }
2215
2216 /* Check that a schedule can be constructed on the given domain
2217 * with the given validity and proximity constraints.
2218 */
2219 static int test_has_schedule(isl_ctx *ctx, const char *domain,
2220 const char *validity, const char *proximity)
2221 {
2222 isl_union_map *sched;
2223
2224 sched = compute_schedule(ctx, domain, validity, proximity);
2225 if (!sched)
2226 return -1;
2227
2228 isl_union_map_free(sched);
2229 return 0;
2230 }
2231
2232 int test_special_schedule(isl_ctx *ctx, const char *domain,
2233 const char *validity, const char *proximity, const char *expected_sched)
2234 {
2235 isl_union_map *sched1, *sched2;
2236 int equal;
2237
2238 sched1 = compute_schedule(ctx, domain, validity, proximity);
2239 sched2 = isl_union_map_read_from_str(ctx, expected_sched);
2240
2241 equal = isl_union_map_is_equal(sched1, sched2);
2242 isl_union_map_free(sched1);
2243 isl_union_map_free(sched2);
2244
2245 if (equal < 0)
2246 return -1;
2247 if (!equal)
2248 isl_die(ctx, isl_error_unknown, "unexpected schedule",
2249 return -1);
2250
2251 return 0;
2252 }
2253
2254 /* Check that the schedule map is properly padded, even after being
2255 * reconstructed from the band forest.
2256 */
2257 static int test_padded_schedule(isl_ctx *ctx)
2258 {
2259 const char *str;
2260 isl_union_set *D;
2261 isl_union_map *validity, *proximity;
2262 isl_schedule *sched;
2263 isl_union_map *map1, *map2;
2264 isl_band_list *list;
2265 int equal;
2266
2267 str = "[N] -> { S0[i] : 0 <= i <= N; S1[i, j] : 0 <= i, j <= N }";
2268 D = isl_union_set_read_from_str(ctx, str);
2269 validity = isl_union_map_empty(isl_union_set_get_space(D));
2270 proximity = isl_union_map_copy(validity);
2271 sched = isl_union_set_compute_schedule(D, validity, proximity);
2272 map1 = isl_schedule_get_map(sched);
2273 list = isl_schedule_get_band_forest(sched);
2274 isl_band_list_free(list);
2275 map2 = isl_schedule_get_map(sched);
2276 isl_schedule_free(sched);
2277 equal = isl_union_map_is_equal(map1, map2);
2278 isl_union_map_free(map1);
2279 isl_union_map_free(map2);
2280
2281 if (equal < 0)
2282 return -1;
2283 if (!equal)
2284 isl_die(ctx, isl_error_unknown,
2285 "reconstructed schedule map not the same as original",
2286 return -1);
2287
2288 return 0;
2289 }
2290
2291 int test_schedule(isl_ctx *ctx)
2292 {
2293 const char *D, *W, *R, *V, *P, *S;
2294
2295 /* Handle resulting schedule with zero bands. */
2296 if (test_one_schedule(ctx, "{[]}", "{}", "{}", "{[] -> []}", 0, 0) < 0)
2297 return -1;
2298
2299 /* Jacobi */
2300 D = "[T,N] -> { S1[t,i] : 1 <= t <= T and 2 <= i <= N - 1 }";
2301 W = "{ S1[t,i] -> a[t,i] }";
2302 R = "{ S1[t,i] -> a[t-1,i]; S1[t,i] -> a[t-1,i-1]; "
2303 "S1[t,i] -> a[t-1,i+1] }";
2304 S = "{ S1[t,i] -> [t,i] }";
2305 if (test_one_schedule(ctx, D, W, R, S, 2, 0) < 0)
2306 return -1;
2307
2308 /* Fig. 5 of CC2008 */
2309 D = "[N] -> { S_0[i, j] : i >= 0 and i <= -1 + N and j >= 2 and "
2310 "j <= -1 + N }";
2311 W = "[N] -> { S_0[i, j] -> a[i, j] : i >= 0 and i <= -1 + N and "
2312 "j >= 2 and j <= -1 + N }";
2313 R = "[N] -> { S_0[i, j] -> a[j, i] : i >= 0 and i <= -1 + N and "
2314 "j >= 2 and j <= -1 + N; "
2315 "S_0[i, j] -> a[i, -1 + j] : i >= 0 and i <= -1 + N and "
2316 "j >= 2 and j <= -1 + N }";
2317 S = "[N] -> { S_0[i, j] -> [0, i, 0, j, 0] }";
2318 if (test_one_schedule(ctx, D, W, R, S, 2, 0) < 0)
2319 return -1;
2320
2321 D = "{ S1[i] : 0 <= i <= 10; S2[i] : 0 <= i <= 9 }";
2322 W = "{ S1[i] -> a[i] }";
2323 R = "{ S2[i] -> a[i+1] }";
2324 S = "{ S1[i] -> [0,i]; S2[i] -> [1,i] }";
2325 if (test_one_schedule(ctx, D, W, R, S, 1, 1) < 0)
2326 return -1;
2327
2328 D = "{ S1[i] : 0 <= i < 10; S2[i] : 0 <= i < 10 }";
2329 W = "{ S1[i] -> a[i] }";
2330 R = "{ S2[i] -> a[9-i] }";
2331 S = "{ S1[i] -> [0,i]; S2[i] -> [1,i] }";
2332 if (test_one_schedule(ctx, D, W, R, S, 1, 1) < 0)
2333 return -1;
2334
2335 D = "[N] -> { S1[i] : 0 <= i < N; S2[i] : 0 <= i < N }";
2336 W = "{ S1[i] -> a[i] }";
2337 R = "[N] -> { S2[i] -> a[N-1-i] }";
2338 S = "{ S1[i] -> [0,i]; S2[i] -> [1,i] }";
2339 if (test_one_schedule(ctx, D, W, R, S, 1, 1) < 0)
2340 return -1;
2341
2342 D = "{ S1[i] : 0 < i < 10; S2[i] : 0 <= i < 10 }";
2343 W = "{ S1[i] -> a[i]; S2[i] -> b[i] }";
2344 R = "{ S2[i] -> a[i]; S1[i] -> b[i-1] }";
2345 S = "{ S1[i] -> [i,0]; S2[i] -> [i,1] }";
2346 if (test_one_schedule(ctx, D, W, R, S, 0, 0) < 0)
2347 return -1;
2348
2349 D = "[N] -> { S1[i] : 1 <= i <= N; S2[i,j] : 1 <= i,j <= N }";
2350 W = "{ S1[i] -> a[0,i]; S2[i,j] -> a[i,j] }";
2351 R = "{ S2[i,j] -> a[i-1,j] }";
2352 S = "{ S1[i] -> [0,i,0]; S2[i,j] -> [1,i,j] }";
2353 if (test_one_schedule(ctx, D, W, R, S, 2, 1) < 0)
2354 return -1;
2355
2356 D = "[N] -> { S1[i] : 1 <= i <= N; S2[i,j] : 1 <= i,j <= N }";
2357 W = "{ S1[i] -> a[i,0]; S2[i,j] -> a[i,j] }";
2358 R = "{ S2[i,j] -> a[i,j-1] }";
2359 S = "{ S1[i] -> [0,i,0]; S2[i,j] -> [1,i,j] }";
2360 if (test_one_schedule(ctx, D, W, R, S, 2, 1) < 0)
2361 return -1;
2362
2363 D = "[N] -> { S_0[]; S_1[i] : i >= 0 and i <= -1 + N; S_2[] }";
2364 W = "[N] -> { S_0[] -> a[0]; S_2[] -> b[0]; "
2365 "S_1[i] -> a[1 + i] : i >= 0 and i <= -1 + N }";
2366 R = "[N] -> { S_2[] -> a[N]; S_1[i] -> a[i] : i >= 0 and i <= -1 + N }";
2367 S = "[N] -> { S_1[i] -> [1, i, 0]; S_2[] -> [2, 0, 1]; "
2368 "S_0[] -> [0, 0, 0] }";
2369 if (test_one_schedule(ctx, D, W, R, S, 1, 0) < 0)
2370 return -1;
2371 ctx->opt->schedule_parametric = 0;
2372 if (test_one_schedule(ctx, D, W, R, S, 0, 0) < 0)
2373 return -1;
2374 ctx->opt->schedule_parametric = 1;
2375
2376 D = "[N] -> { S1[i] : 1 <= i <= N; S2[i] : 1 <= i <= N; "
2377 "S3[i,j] : 1 <= i,j <= N; S4[i] : 1 <= i <= N }";
2378 W = "{ S1[i] -> a[i,0]; S2[i] -> a[0,i]; S3[i,j] -> a[i,j] }";
2379 R = "[N] -> { S3[i,j] -> a[i-1,j]; S3[i,j] -> a[i,j-1]; "
2380 "S4[i] -> a[i,N] }";
2381 S = "{ S1[i] -> [0,i,0]; S2[i] -> [1,i,0]; S3[i,j] -> [2,i,j]; "
2382 "S4[i] -> [4,i,0] }";
2383 if (test_one_schedule(ctx, D, W, R, S, 2, 0) < 0)
2384 return -1;
2385
2386 D = "[N] -> { S_0[i, j] : i >= 1 and i <= N and j >= 1 and j <= N }";
2387 W = "[N] -> { S_0[i, j] -> s[0] : i >= 1 and i <= N and j >= 1 and "
2388 "j <= N }";
2389 R = "[N] -> { S_0[i, j] -> s[0] : i >= 1 and i <= N and j >= 1 and "
2390 "j <= N; "
2391 "S_0[i, j] -> a[i, j] : i >= 1 and i <= N and j >= 1 and "
2392 "j <= N }";
2393 S = "[N] -> { S_0[i, j] -> [0, i, 0, j, 0] }";
2394 if (test_one_schedule(ctx, D, W, R, S, 0, 0) < 0)
2395 return -1;
2396
2397 D = "[N] -> { S_0[t] : t >= 0 and t <= -1 + N; "
2398 " S_2[t] : t >= 0 and t <= -1 + N; "
2399 " S_1[t, i] : t >= 0 and t <= -1 + N and i >= 0 and "
2400 "i <= -1 + N }";
2401 W = "[N] -> { S_0[t] -> a[t, 0] : t >= 0 and t <= -1 + N; "
2402 " S_2[t] -> b[t] : t >= 0 and t <= -1 + N; "
2403 " S_1[t, i] -> a[t, 1 + i] : t >= 0 and t <= -1 + N and "
2404 "i >= 0 and i <= -1 + N }";
2405 R = "[N] -> { S_1[t, i] -> a[t, i] : t >= 0 and t <= -1 + N and "
2406 "i >= 0 and i <= -1 + N; "
2407 " S_2[t] -> a[t, N] : t >= 0 and t <= -1 + N }";
2408 S = "[N] -> { S_2[t] -> [0, t, 2]; S_1[t, i] -> [0, t, 1, i, 0]; "
2409 " S_0[t] -> [0, t, 0] }";
2410
2411 if (test_one_schedule(ctx, D, W, R, S, 2, 1) < 0)
2412 return -1;
2413 ctx->opt->schedule_parametric = 0;
2414 if (test_one_schedule(ctx, D, W, R, S, 0, 0) < 0)
2415 return -1;
2416 ctx->opt->schedule_parametric = 1;
2417
2418 D = "[N] -> { S1[i,j] : 0 <= i,j < N; S2[i,j] : 0 <= i,j < N }";
2419 S = "{ S1[i,j] -> [0,i,j]; S2[i,j] -> [1,i,j] }";
2420 if (test_one_schedule(ctx, D, "{}", "{}", S, 2, 2) < 0)
2421 return -1;
2422
2423 D = "[M, N] -> { S_1[i] : i >= 0 and i <= -1 + M; "
2424 "S_0[i, j] : i >= 0 and i <= -1 + M and j >= 0 and j <= -1 + N }";
2425 W = "[M, N] -> { S_0[i, j] -> a[j] : i >= 0 and i <= -1 + M and "
2426 "j >= 0 and j <= -1 + N; "
2427 "S_1[i] -> b[0] : i >= 0 and i <= -1 + M }";
2428 R = "[M, N] -> { S_0[i, j] -> a[0] : i >= 0 and i <= -1 + M and "
2429 "j >= 0 and j <= -1 + N; "
2430 "S_1[i] -> b[0] : i >= 0 and i <= -1 + M }";
2431 S = "[M, N] -> { S_1[i] -> [1, i, 0]; S_0[i, j] -> [0, i, 0, j, 0] }";
2432 if (test_one_schedule(ctx, D, W, R, S, 0, 0) < 0)
2433 return -1;
2434
2435 D = "{ S_0[i] : i >= 0 }";
2436 W = "{ S_0[i] -> a[i] : i >= 0 }";
2437 R = "{ S_0[i] -> a[0] : i >= 0 }";
2438 S = "{ S_0[i] -> [0, i, 0] }";
2439 if (test_one_schedule(ctx, D, W, R, S, 0, 0) < 0)
2440 return -1;
2441
2442 D = "{ S_0[i] : i >= 0; S_1[i] : i >= 0 }";
2443 W = "{ S_0[i] -> a[i] : i >= 0; S_1[i] -> b[i] : i >= 0 }";
2444 R = "{ S_0[i] -> b[0] : i >= 0; S_1[i] -> a[i] : i >= 0 }";
2445 S = "{ S_1[i] -> [0, i, 1]; S_0[i] -> [0, i, 0] }";
2446 if (test_one_schedule(ctx, D, W, R, S, 0, 0) < 0)
2447 return -1;
2448
2449 D = "[n] -> { S_0[j, k] : j <= -1 + n and j >= 0 and "
2450 "k <= -1 + n and k >= 0 }";
2451 W = "[n] -> { S_0[j, k] -> B[j] : j <= -1 + n and j >= 0 and " "k <= -1 + n and k >= 0 }";
2452 R = "[n] -> { S_0[j, k] -> B[j] : j <= -1 + n and j >= 0 and "
2453 "k <= -1 + n and k >= 0; "
2454 "S_0[j, k] -> B[k] : j <= -1 + n and j >= 0 and "
2455 "k <= -1 + n and k >= 0; "
2456 "S_0[j, k] -> A[k] : j <= -1 + n and j >= 0 and "
2457 "k <= -1 + n and k >= 0 }";
2458 S = "[n] -> { S_0[j, k] -> [2, j, k] }";
2459 ctx->opt->schedule_outer_zero_distance = 1;
2460 if (test_one_schedule(ctx, D, W, R, S, 0, 0) < 0)
2461 return -1;
2462 ctx->opt->schedule_outer_zero_distance = 0;
2463
2464 D = "{Stmt_for_body24[i0, i1, i2, i3]:"
2465 "i0 >= 0 and i0 <= 1 and i1 >= 0 and i1 <= 6 and i2 >= 2 and "
2466 "i2 <= 6 - i1 and i3 >= 0 and i3 <= -1 + i2;"
2467 "Stmt_for_body24[i0, i1, 1, 0]:"
2468 "i0 >= 0 and i0 <= 1 and i1 >= 0 and i1 <= 5;"
2469 "Stmt_for_body7[i0, i1, i2]:"
2470 "i0 >= 0 and i0 <= 1 and i1 >= 0 and i1 <= 7 and i2 >= 0 and "
2471 "i2 <= 7 }";
2472
2473 V = "{Stmt_for_body24[0, i1, i2, i3] -> "
2474 "Stmt_for_body24[1, i1, i2, i3]:"
2475 "i3 >= 0 and i3 <= -1 + i2 and i1 >= 0 and i2 <= 6 - i1 and "
2476 "i2 >= 1;"
2477 "Stmt_for_body24[0, i1, i2, i3] -> "
2478 "Stmt_for_body7[1, 1 + i1 + i3, 1 + i1 + i2]:"
2479 "i3 <= -1 + i2 and i2 <= 6 - i1 and i2 >= 1 and i1 >= 0 and "
2480 "i3 >= 0;"
2481 "Stmt_for_body24[0, i1, i2, i3] ->"
2482 "Stmt_for_body7[1, i1, 1 + i1 + i3]:"
2483 "i3 >= 0 and i2 <= 6 - i1 and i1 >= 0 and i3 <= -1 + i2;"
2484 "Stmt_for_body7[0, i1, i2] -> Stmt_for_body7[1, i1, i2]:"
2485 "(i2 >= 1 + i1 and i2 <= 6 and i1 >= 0 and i1 <= 4) or "
2486 "(i2 >= 3 and i2 <= 7 and i1 >= 1 and i2 >= 1 + i1) or "
2487 "(i2 >= 0 and i2 <= i1 and i2 >= -7 + i1 and i1 <= 7);"
2488 "Stmt_for_body7[0, i1, 1 + i1] -> Stmt_for_body7[1, i1, 1 + i1]:"
2489 "i1 <= 6 and i1 >= 0;"
2490 "Stmt_for_body7[0, 0, 7] -> Stmt_for_body7[1, 0, 7];"
2491 "Stmt_for_body7[i0, i1, i2] -> "
2492 "Stmt_for_body24[i0, o1, -1 + i2 - o1, -1 + i1 - o1]:"
2493 "i0 >= 0 and i0 <= 1 and o1 >= 0 and i2 >= 1 + i1 and "
2494 "o1 <= -2 + i2 and i2 <= 7 and o1 <= -1 + i1;"
2495 "Stmt_for_body7[i0, i1, i2] -> "
2496 "Stmt_for_body24[i0, i1, o2, -1 - i1 + i2]:"
2497 "i0 >= 0 and i0 <= 1 and i1 >= 0 and o2 >= -i1 + i2 and "
2498 "o2 >= 1 and o2 <= 6 - i1 and i2 >= 1 + i1 }";
2499 P = V;
2500 S = "{ Stmt_for_body24[i0, i1, i2, i3] -> "
2501 "[i0, 5i0 + i1, 6i0 + i1 + i2, 1 + 6i0 + i1 + i2 + i3, 1];"
2502 "Stmt_for_body7[i0, i1, i2] -> [0, 5i0, 6i0 + i1, 6i0 + i2, 0] }";
2503
2504 if (test_special_schedule(ctx, D, V, P, S) < 0)
2505 return -1;
2506
2507 D = "{ S_0[i, j] : i >= 1 and i <= 10 and j >= 1 and j <= 8 }";
2508 V = "{ S_0[i, j] -> S_0[i, 1 + j] : i >= 1 and i <= 10 and "
2509 "j >= 1 and j <= 7;"
2510 "S_0[i, j] -> S_0[1 + i, j] : i >= 1 and i <= 9 and "
2511 "j >= 1 and j <= 8 }";
2512 P = "{ }";
2513 S = "{ S_0[i, j] -> [i + j, j] }";
2514 ctx->opt->schedule_algorithm = ISL_SCHEDULE_ALGORITHM_FEAUTRIER;
2515 if (test_special_schedule(ctx, D, V, P, S) < 0)
2516 return -1;
2517 ctx->opt->schedule_algorithm = ISL_SCHEDULE_ALGORITHM_ISL;
2518
2519 /* Fig. 1 from Feautrier's "Some Efficient Solutions..." pt. 2, 1992 */
2520 D = "[N] -> { S_0[i, j] : i >= 0 and i <= -1 + N and "
2521 "j >= 0 and j <= -1 + i }";
2522 V = "[N] -> { S_0[i, j] -> S_0[i, 1 + j] : j <= -2 + i and "
2523 "i <= -1 + N and j >= 0;"
2524 "S_0[i, -1 + i] -> S_0[1 + i, 0] : i >= 1 and "
2525 "i <= -2 + N }";
2526 P = "{ }";
2527 S = "{ S_0[i, j] -> [i, j] }";
2528 ctx->opt->schedule_algorithm = ISL_SCHEDULE_ALGORITHM_FEAUTRIER;
2529 if (test_special_schedule(ctx, D, V, P, S) < 0)
2530 return -1;
2531 ctx->opt->schedule_algorithm = ISL_SCHEDULE_ALGORITHM_ISL;
2532
2533 /* Test both algorithms on a case with only proximity dependences. */
2534 D = "{ S[i,j] : 0 <= i <= 10 }";
2535 V = "{ }";
2536 P = "{ S[i,j] -> S[i+1,j] : 0 <= i,j <= 10 }";
2537 S = "{ S[i, j] -> [j, i] }";
2538 ctx->opt->schedule_algorithm = ISL_SCHEDULE_ALGORITHM_FEAUTRIER;
2539 if (test_special_schedule(ctx, D, V, P, S) < 0)
2540 return -1;
2541 ctx->opt->schedule_algorithm = ISL_SCHEDULE_ALGORITHM_ISL;
2542 if (test_special_schedule(ctx, D, V, P, S) < 0)
2543 return -1;
2544
2545 D = "{ A[a]; B[] }";
2546 V = "{}";
2547 P = "{ A[a] -> B[] }";
2548 if (test_has_schedule(ctx, D, V, P) < 0)
2549 return -1;
2550
2551 if (test_padded_schedule(ctx) < 0)
2552 return -1;
2553
2554 return 0;
2555 }
2556
2557 int test_plain_injective(isl_ctx *ctx, const char *str, int injective)
2558 {
2559 isl_union_map *umap;
2560 int test;
2561
2562 umap = isl_union_map_read_from_str(ctx, str);
2563 test = isl_union_map_plain_is_injective(umap);
2564 isl_union_map_free(umap);
2565 if (test < 0)
2566 return -1;
2567 if (test == injective)
2568 return 0;
2569 if (injective)
2570 isl_die(ctx, isl_error_unknown,
2571 "map not detected as injective", return -1);
2572 else
2573 isl_die(ctx, isl_error_unknown,
2574 "map detected as injective", return -1);
2575 }
2576
2577 int test_injective(isl_ctx *ctx)
2578 {
2579 const char *str;
2580
2581 if (test_plain_injective(ctx, "{S[i,j] -> A[0]; T[i,j] -> B[1]}", 0))
2582 return -1;
2583 if (test_plain_injective(ctx, "{S[] -> A[0]; T[] -> B[0]}", 1))
2584 return -1;
2585 if (test_plain_injective(ctx, "{S[] -> A[0]; T[] -> A[1]}", 1))
2586 return -1;
2587 if (test_plain_injective(ctx, "{S[] -> A[0]; T[] -> A[0]}", 0))
2588 return -1;
2589 if (test_plain_injective(ctx, "{S[i] -> A[i,0]; T[i] -> A[i,1]}", 1))
2590 return -1;
2591 if (test_plain_injective(ctx, "{S[i] -> A[i]; T[i] -> A[i]}", 0))
2592 return -1;
2593 if (test_plain_injective(ctx, "{S[] -> A[0,0]; T[] -> A[0,1]}", 1))
2594 return -1;
2595 if (test_plain_injective(ctx, "{S[] -> A[0,0]; T[] -> A[1,0]}", 1))
2596 return -1;
2597
2598 str = "{S[] -> A[0,0]; T[] -> A[0,1]; U[] -> A[1,0]}";
2599 if (test_plain_injective(ctx, str, 1))
2600 return -1;
2601 str = "{S[] -> A[0,0]; T[] -> A[0,1]; U[] -> A[0,0]}";
2602 if (test_plain_injective(ctx, str, 0))
2603 return -1;
2604
2605 return 0;
2606 }
2607
2608 static int aff_plain_is_equal(__isl_keep isl_aff *aff, const char *str)
2609 {
2610 isl_aff *aff2;
2611 int equal;
2612
2613 if (!aff)
2614 return -1;
2615
2616 aff2 = isl_aff_read_from_str(isl_aff_get_ctx(aff), str);
2617 equal = isl_aff_plain_is_equal(aff, aff2);
2618 isl_aff_free(aff2);
2619
2620 return equal;
2621 }
2622
2623 static int aff_check_plain_equal(__isl_keep isl_aff *aff, const char *str)
2624 {
2625 int equal;
2626
2627 equal = aff_plain_is_equal(aff, str);
2628 if (equal < 0)
2629 return -1;
2630 if (!equal)
2631 isl_die(isl_aff_get_ctx(aff), isl_error_unknown,
2632 "result not as expected", return -1);
2633 return 0;
2634 }
2635
2636 int test_aff(isl_ctx *ctx)
2637 {
2638 const char *str;
2639 isl_set *set;
2640 isl_space *space;
2641 isl_local_space *ls;
2642 isl_aff *aff;
2643 int zero, equal;
2644
2645 space = isl_space_set_alloc(ctx, 0, 1);
2646 ls = isl_local_space_from_space(space);
2647 aff = isl_aff_zero_on_domain(ls);
2648
2649 aff = isl_aff_add_coefficient_si(aff, isl_dim_in, 0, 1);
2650 aff = isl_aff_scale_down_ui(aff, 3);
2651 aff = isl_aff_floor(aff);
2652 aff = isl_aff_add_coefficient_si(aff, isl_dim_in, 0, 1);
2653 aff = isl_aff_scale_down_ui(aff, 2);
2654 aff = isl_aff_floor(aff);
2655 aff = isl_aff_add_coefficient_si(aff, isl_dim_in, 0, 1);
2656
2657 str = "{ [10] }";
2658 set = isl_set_read_from_str(ctx, str);
2659 aff = isl_aff_gist(aff, set);
2660
2661 aff = isl_aff_add_constant_si(aff, -16);
2662 zero = isl_aff_plain_is_zero(aff);
2663 isl_aff_free(aff);
2664
2665 if (zero < 0)
2666 return -1;
2667 if (!zero)
2668 isl_die(ctx, isl_error_unknown, "unexpected result", return -1);
2669
2670 aff = isl_aff_read_from_str(ctx, "{ [-1] }");
2671 aff = isl_aff_scale_down_ui(aff, 64);
2672 aff = isl_aff_floor(aff);
2673 equal = aff_check_plain_equal(aff, "{ [-1] }");
2674 isl_aff_free(aff);
2675 if (equal < 0)
2676 return -1;
2677
2678 return 0;
2679 }
2680
2681 int test_dim_max(isl_ctx *ctx)
2682 {
2683 int equal;
2684 const char *str;
2685 isl_set *set1, *set2;
2686 isl_set *set;
2687 isl_map *map;
2688 isl_pw_aff *pwaff;
2689
2690 str = "[N] -> { [i] : 0 <= i <= min(N,10) }";
2691 set = isl_set_read_from_str(ctx, str);
2692 pwaff = isl_set_dim_max(set, 0);
2693 set1 = isl_set_from_pw_aff(pwaff);
2694 str = "[N] -> { [10] : N >= 10; [N] : N <= 9 and N >= 0 }";
2695 set2 = isl_set_read_from_str(ctx, str);
2696 equal = isl_set_is_equal(set1, set2);
2697 isl_set_free(set1);
2698 isl_set_free(set2);
2699 if (equal < 0)
2700 return -1;
2701 if (!equal)
2702 isl_die(ctx, isl_error_unknown, "unexpected result", return -1);
2703
2704 str = "[N] -> { [i] : 0 <= i <= max(2N,N+6) }";
2705 set = isl_set_read_from_str(ctx, str);
2706 pwaff = isl_set_dim_max(set, 0);
2707 set1 = isl_set_from_pw_aff(pwaff);
2708 str = "[N] -> { [6 + N] : -6 <= N <= 5; [2N] : N >= 6 }";
2709 set2 = isl_set_read_from_str(ctx, str);
2710 equal = isl_set_is_equal(set1, set2);
2711 isl_set_free(set1);
2712 isl_set_free(set2);
2713 if (equal < 0)
2714 return -1;
2715 if (!equal)
2716 isl_die(ctx, isl_error_unknown, "unexpected result", return -1);
2717
2718 str = "[N] -> { [i] : 0 <= i <= 2N or 0 <= i <= N+6 }";
2719 set = isl_set_read_from_str(ctx, str);
2720 pwaff = isl_set_dim_max(set, 0);
2721 set1 = isl_set_from_pw_aff(pwaff);
2722 str = "[N] -> { [6 + N] : -6 <= N <= 5; [2N] : N >= 6 }";
2723 set2 = isl_set_read_from_str(ctx, str);
2724 equal = isl_set_is_equal(set1, set2);
2725 isl_set_free(set1);
2726 isl_set_free(set2);
2727 if (equal < 0)
2728 return -1;
2729 if (!equal)
2730 isl_die(ctx, isl_error_unknown, "unexpected result", return -1);
2731
2732 str = "[N,M] -> { [i,j] -> [([i/16]), i%16, ([j/16]), j%16] : "
2733 "0 <= i < N and 0 <= j < M }";
2734 map = isl_map_read_from_str(ctx, str);
2735 set = isl_map_range(map);
2736
2737 pwaff = isl_set_dim_max(isl_set_copy(set), 0);
2738 set1 = isl_set_from_pw_aff(pwaff);
2739 str = "[N,M] -> { [([(N-1)/16])] : M,N > 0 }";
2740 set2 = isl_set_read_from_str(ctx, str);
2741 equal = isl_set_is_equal(set1, set2);
2742 isl_set_free(set1);
2743 isl_set_free(set2);
2744
2745 pwaff = isl_set_dim_max(isl_set_copy(set), 3);
2746 set1 = isl_set_from_pw_aff(pwaff);
2747 str = "[N,M] -> { [t] : t = min(M-1,15) and M,N > 0 }";
2748 set2 = isl_set_read_from_str(ctx, str);
2749 if (equal >= 0 && equal)
2750 equal = isl_set_is_equal(set1, set2);
2751 isl_set_free(set1);
2752 isl_set_free(set2);
2753
2754 isl_set_free(set);
2755
2756 if (equal < 0)
2757 return -1;
2758 if (!equal)
2759 isl_die(ctx, isl_error_unknown, "unexpected result", return -1);
2760
2761 /* Check that solutions are properly merged. */
2762 str = "[n] -> { [a, b, c] : c >= -4a - 2b and "
2763 "c <= -1 + n - 4a - 2b and c >= -2b and "
2764 "4a >= -4 + n and c >= 0 }";
2765 set = isl_set_read_from_str(ctx, str);
2766 pwaff = isl_set_dim_min(set, 2);
2767 set1 = isl_set_from_pw_aff(pwaff);
2768 str = "[n] -> { [(0)] : n >= 1 }";
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
2774 if (equal < 0)
2775 return -1;
2776 if (!equal)
2777 isl_die(ctx, isl_error_unknown, "unexpected result", return -1);
2778
2779 return 0;
2780 }
2781
2782 int test_product(isl_ctx *ctx)
2783 {
2784 const char *str;
2785 isl_set *set;
2786 isl_union_set *uset1, *uset2;
2787 int ok;
2788
2789 str = "{ A[i] }";
2790 set = isl_set_read_from_str(ctx, str);
2791 set = isl_set_product(set, isl_set_copy(set));
2792 ok = isl_set_is_wrapping(set);
2793 isl_set_free(set);
2794 if (ok < 0)
2795 return -1;
2796 if (!ok)
2797 isl_die(ctx, isl_error_unknown, "unexpected result", return -1);
2798
2799 str = "{ [] }";
2800 uset1 = isl_union_set_read_from_str(ctx, str);
2801 uset1 = isl_union_set_product(uset1, isl_union_set_copy(uset1));
2802 str = "{ [[] -> []] }";
2803 uset2 = isl_union_set_read_from_str(ctx, str);
2804 ok = isl_union_set_is_equal(uset1, uset2);
2805 isl_union_set_free(uset1);
2806 isl_union_set_free(uset2);
2807 if (ok < 0)
2808 return -1;
2809 if (!ok)
2810 isl_die(ctx, isl_error_unknown, "unexpected result", return -1);
2811
2812 return 0;
2813 }
2814
2815 int test_equal(isl_ctx *ctx)
2816 {
2817 const char *str;
2818 isl_set *set, *set2;
2819 int equal;
2820
2821 str = "{ S_6[i] }";
2822 set = isl_set_read_from_str(ctx, str);
2823 str = "{ S_7[i] }";
2824 set2 = isl_set_read_from_str(ctx, str);
2825 equal = isl_set_is_equal(set, set2);
2826 isl_set_free(set);
2827 isl_set_free(set2);
2828 if (equal < 0)
2829 return -1;
2830 if (equal)
2831 isl_die(ctx, isl_error_unknown, "unexpected result", return -1);
2832
2833 return 0;
2834 }
2835
2836 static int test_plain_fixed(isl_ctx *ctx, __isl_take isl_map *map,
2837 enum isl_dim_type type, unsigned pos, int fixed)
2838 {
2839 int test;
2840
2841 test = isl_map_plain_is_fixed(map, type, pos, NULL);
2842 isl_map_free(map);
2843 if (test < 0)
2844 return -1;
2845 if (test == fixed)
2846 return 0;
2847 if (fixed)
2848 isl_die(ctx, isl_error_unknown,
2849 "map not detected as fixed", return -1);
2850 else
2851 isl_die(ctx, isl_error_unknown,
2852 "map detected as fixed", return -1);
2853 }
2854
2855 int test_fixed(isl_ctx *ctx)
2856 {
2857 const char *str;
2858 isl_map *map;
2859
2860 str = "{ [i] -> [i] }";
2861 map = isl_map_read_from_str(ctx, str);
2862 if (test_plain_fixed(ctx, map, isl_dim_out, 0, 0))
2863 return -1;
2864 str = "{ [i] -> [1] }";
2865 map = isl_map_read_from_str(ctx, str);
2866 if (test_plain_fixed(ctx, map, isl_dim_out, 0, 1))
2867 return -1;
2868 str = "{ S_1[p1] -> [o0] : o0 = -2 and p1 >= 1 and p1 <= 7 }";
2869 map = isl_map_read_from_str(ctx, str);
2870 if (test_plain_fixed(ctx, map, isl_dim_out, 0, 1))
2871 return -1;
2872 map = isl_map_read_from_str(ctx, str);
2873 map = isl_map_neg(map);
2874 if (test_plain_fixed(ctx, map, isl_dim_out, 0, 1))
2875 return -1;
2876
2877 return 0;
2878 }
2879
2880 int test_vertices(isl_ctx *ctx)
2881 {
2882 const char *str;
2883 isl_basic_set *bset;
2884 isl_vertices *vertices;
2885
2886 str = "{ A[t, i] : t = 12 and i >= 4 and i <= 12 }";
2887 bset = isl_basic_set_read_from_str(ctx, str);
2888 vertices = isl_basic_set_compute_vertices(bset);
2889 isl_basic_set_free(bset);
2890 isl_vertices_free(vertices);
2891 if (!vertices)
2892 return -1;
2893
2894 str = "{ A[t, i] : t = 14 and i = 1 }";
2895 bset = isl_basic_set_read_from_str(ctx, str);
2896 vertices = isl_basic_set_compute_vertices(bset);
2897 isl_basic_set_free(bset);
2898 isl_vertices_free(vertices);
2899 if (!vertices)
2900 return -1;
2901
2902 return 0;
2903 }
2904
2905 int test_union_pw(isl_ctx *ctx)
2906 {
2907 int equal;
2908 const char *str;
2909 isl_union_set *uset;
2910 isl_union_pw_qpolynomial *upwqp1, *upwqp2;
2911
2912 str = "{ [x] -> x^2 }";
2913 upwqp1 = isl_union_pw_qpolynomial_read_from_str(ctx, str);
2914 upwqp2 = isl_union_pw_qpolynomial_copy(upwqp1);
2915 uset = isl_union_pw_qpolynomial_domain(upwqp1);
2916 upwqp1 = isl_union_pw_qpolynomial_copy(upwqp2);
2917 upwqp1 = isl_union_pw_qpolynomial_intersect_domain(upwqp1, uset);
2918 equal = isl_union_pw_qpolynomial_plain_is_equal(upwqp1, upwqp2);
2919 isl_union_pw_qpolynomial_free(upwqp1);
2920 isl_union_pw_qpolynomial_free(upwqp2);
2921 if (equal < 0)
2922 return -1;
2923 if (!equal)
2924 isl_die(ctx, isl_error_unknown, "unexpected result", return -1);
2925
2926 return 0;
2927 }
2928
2929 int test_output(isl_ctx *ctx)
2930 {
2931 char *s;
2932 const char *str;
2933 isl_pw_aff *pa;
2934 isl_printer *p;
2935 int equal;
2936
2937 str = "[x] -> { [1] : x % 4 <= 2; [2] : x = 3 }";
2938 pa = isl_pw_aff_read_from_str(ctx, str);
2939
2940 p = isl_printer_to_str(ctx);
2941 p = isl_printer_set_output_format(p, ISL_FORMAT_C);
2942 p = isl_printer_print_pw_aff(p, pa);
2943 s = isl_printer_get_str(p);
2944 isl_printer_free(p);
2945 isl_pw_aff_free(pa);
2946 if (!s)
2947 equal = -1;
2948 else
2949 equal = !strcmp(s, "(2 - x + 4*floord(x, 4) >= 0) ? (1) : 2");
2950 free(s);
2951 if (equal < 0)
2952 return -1;
2953 if (!equal)
2954 isl_die(ctx, isl_error_unknown, "unexpected result", return -1);
2955
2956 return 0;
2957 }
2958
2959 int test_sample(isl_ctx *ctx)
2960 {
2961 const char *str;
2962 isl_basic_set *bset1, *bset2;
2963 int empty, subset;
2964
2965 str = "{ [a, b, c, d, e, f, g, h, i, j, k] : "
2966 "3i >= 1073741823b - c - 1073741823e + f and c >= 0 and "
2967 "3i >= -1 + 3221225466b + c + d - 3221225466e - f and "
2968 "2e >= a - b and 3e <= 2a and 3k <= -a and f <= -1 + a and "
2969 "3i <= 4 - a + 4b + 2c - e - 2f and 3k <= -a + c - f and "
2970 "3h >= -2 + a and 3g >= -3 - a and 3k >= -2 - a and "
2971 "3i >= -2 - a - 2c + 3e + 2f and 3h <= a + c - f and "
2972 "3h >= a + 2147483646b + 2c - 2147483646e - 2f and "
2973 "3g <= -1 - a and 3i <= 1 + c + d - f and a <= 1073741823 and "
2974 "f >= 1 - a + 1073741822b + c + d - 1073741822e and "
2975 "3i >= 1 + 2b - 2c + e + 2f + 3g and "
2976 "1073741822f <= 1073741822 - a + 1073741821b + 1073741822c +"
2977 "d - 1073741821e and "
2978 "3j <= 3 - a + 3b and 3g <= -2 - 2b + c + d - e - f and "
2979 "3j >= 1 - a + b + 2e and "
2980 "3f >= -3 + a + 3221225462b + 3c + d - 3221225465e and "
2981 "3i <= 4 - a + 4b - e and "
2982 "f <= 1073741822 + 1073741822b - 1073741822e and 3h <= a and "
2983 "f >= 0 and 2e <= 4 - a + 5b - d and 2e <= a - b + d and "
2984 "c <= -1 + a and 3i >= -2 - a + 3e and "
2985 "1073741822e <= 1073741823 - a + 1073741822b + c and "
2986 "3g >= -4 + 3221225464b + 3c + d - 3221225467e - 3f and "
2987 "3i >= -1 + 3221225466b + 3c + d - 3221225466e - 3f and "
2988 "1073741823e >= 1 + 1073741823b - d and "
2989 "3i >= 1073741823b + c - 1073741823e - f and "
2990 "3i >= 1 + 2b + e + 3g }";
2991 bset1 = isl_basic_set_read_from_str(ctx, str);
2992 bset2 = isl_basic_set_sample(isl_basic_set_copy(bset1));
2993 empty = isl_basic_set_is_empty(bset2);
2994 subset = isl_basic_set_is_subset(bset2, bset1);
2995 isl_basic_set_free(bset1);
2996 isl_basic_set_free(bset2);
2997 if (empty < 0 || subset < 0)
2998 return -1;
2999 if (empty)
3000 isl_die(ctx, isl_error_unknown, "point not found", return -1);
3001 if (!subset)
3002 isl_die(ctx, isl_error_unknown, "bad point found", return -1);
3003
3004 return 0;
3005 }
3006
3007 int test_fixed_power(isl_ctx *ctx)
3008 {
3009 const char *str;
3010 isl_map *map;
3011 isl_int exp;
3012 int equal;
3013
3014 isl_int_init(exp);
3015 str = "{ [i] -> [i + 1] }";
3016 map = isl_map_read_from_str(ctx, str);
3017 isl_int_set_si(exp, 23);
3018 map = isl_map_fixed_power(map, exp);
3019 equal = map_check_equal(map, "{ [i] -> [i + 23] }");
3020 isl_int_clear(exp);
3021 isl_map_free(map);
3022 if (equal < 0)
3023 return -1;
3024
3025 return 0;
3026 }
3027
3028 int test_slice(isl_ctx *ctx)
3029 {
3030 const char *str;
3031 isl_map *map;
3032 int equal;
3033
3034 str = "{ [i] -> [j] }";
3035 map = isl_map_read_from_str(ctx, str);
3036 map = isl_map_equate(map, isl_dim_in, 0, isl_dim_out, 0);
3037 equal = map_check_equal(map, "{ [i] -> [i] }");
3038 isl_map_free(map);
3039 if (equal < 0)
3040 return -1;
3041
3042 str = "{ [i] -> [j] }";
3043 map = isl_map_read_from_str(ctx, str);
3044 map = isl_map_equate(map, isl_dim_in, 0, isl_dim_in, 0);
3045 equal = map_check_equal(map, "{ [i] -> [j] }");
3046 isl_map_free(map);
3047 if (equal < 0)
3048 return -1;
3049
3050 str = "{ [i] -> [j] }";
3051 map = isl_map_read_from_str(ctx, str);
3052 map = isl_map_oppose(map, isl_dim_in, 0, isl_dim_out, 0);
3053 equal = map_check_equal(map, "{ [i] -> [-i] }");
3054 isl_map_free(map);
3055 if (equal < 0)
3056 return -1;
3057
3058 str = "{ [i] -> [j] }";
3059 map = isl_map_read_from_str(ctx, str);
3060 map = isl_map_oppose(map, isl_dim_in, 0, isl_dim_in, 0);
3061 equal = map_check_equal(map, "{ [0] -> [j] }");
3062 isl_map_free(map);
3063 if (equal < 0)
3064 return -1;
3065
3066 str = "{ [i] -> [j] }";
3067 map = isl_map_read_from_str(ctx, str);
3068 map = isl_map_order_gt(map, isl_dim_in, 0, isl_dim_out, 0);
3069 equal = map_check_equal(map, "{ [i] -> [j] : i > j }");
3070 isl_map_free(map);
3071 if (equal < 0)
3072 return -1;
3073
3074 str = "{ [i] -> [j] }";
3075 map = isl_map_read_from_str(ctx, str);
3076 map = isl_map_order_gt(map, isl_dim_in, 0, isl_dim_in, 0);
3077 equal = map_check_equal(map, "{ [i] -> [j] : false }");
3078 isl_map_free(map);
3079 if (equal < 0)
3080 return -1;
3081
3082 return 0;
3083 }
3084
3085 int test_eliminate(isl_ctx *ctx)
3086 {
3087 const char *str;
3088 isl_map *map;
3089 int equal;
3090
3091 str = "{ [i] -> [j] : i = 2j }";
3092 map = isl_map_read_from_str(ctx, str);
3093 map = isl_map_eliminate(map, isl_dim_out, 0, 1);
3094 equal = map_check_equal(map, "{ [i] -> [j] : exists a : i = 2a }");
3095 isl_map_free(map);
3096 if (equal < 0)
3097 return -1;
3098
3099 return 0;
3100 }
3101
3102 /* Check that isl_set_dim_residue_class detects that the values of j
3103 * in the set below are all odd and that it does not detect any spurious
3104 * strides.
3105 */
3106 static int test_residue_class(isl_ctx *ctx)
3107 {
3108 const char *str;
3109 isl_set *set;
3110 isl_int m, r;
3111 int res;
3112
3113 str = "{ [i,j] : j = 4 i + 1 and 0 <= i <= 100; "
3114 "[i,j] : j = 4 i + 3 and 500 <= i <= 600 }";
3115 set = isl_set_read_from_str(ctx, str);
3116 isl_int_init(m);
3117 isl_int_init(r);
3118 res = isl_set_dim_residue_class(set, 1, &m, &r);
3119 if (res >= 0 &&
3120 (isl_int_cmp_si(m, 2) != 0 || isl_int_cmp_si(r, 1) != 0))
3121 isl_die(ctx, isl_error_unknown, "incorrect residue class",
3122 res = -1);
3123 isl_int_clear(r);
3124 isl_int_clear(m);
3125 isl_set_free(set);
3126
3127 return res;
3128 }
3129
3130 int test_align_parameters(isl_ctx *ctx)
3131 {
3132 const char *str;
3133 isl_space *space;
3134 isl_multi_aff *ma1, *ma2;
3135 int equal;
3136
3137 str = "{ A[B[] -> C[]] -> D[E[] -> F[]] }";
3138 ma1 = isl_multi_aff_read_from_str(ctx, str);
3139
3140 space = isl_space_params_alloc(ctx, 1);
3141 space = isl_space_set_dim_name(space, isl_dim_param, 0, "N");
3142 ma1 = isl_multi_aff_align_params(ma1, space);
3143
3144 str = "[N] -> { A[B[] -> C[]] -> D[E[] -> F[]] }";
3145 ma2 = isl_multi_aff_read_from_str(ctx, str);
3146
3147 equal = isl_multi_aff_plain_is_equal(ma1, ma2);
3148
3149 isl_multi_aff_free(ma1);
3150 isl_multi_aff_free(ma2);
3151
3152 if (equal < 0)
3153 return -1;
3154 if (!equal)
3155 isl_die(ctx, isl_error_unknown,
3156 "result not as expected", return -1);
3157
3158 return 0;
3159 }
3160
3161 static int test_list(isl_ctx *ctx)
3162 {
3163 isl_id *a, *b, *c, *d, *id;
3164 isl_id_list *list;
3165 int ok;
3166
3167 a = isl_id_alloc(ctx, "a", NULL);
3168 b = isl_id_alloc(ctx, "b", NULL);
3169 c = isl_id_alloc(ctx, "c", NULL);
3170 d = isl_id_alloc(ctx, "d", NULL);
3171
3172 list = isl_id_list_alloc(ctx, 4);
3173 list = isl_id_list_add(list, a);
3174 list = isl_id_list_add(list, b);
3175 list = isl_id_list_add(list, c);
3176 list = isl_id_list_add(list, d);
3177 list = isl_id_list_drop(list, 1, 1);
3178
3179 if (isl_id_list_n_id(list) != 3) {
3180 isl_id_list_free(list);
3181 isl_die(ctx, isl_error_unknown,
3182 "unexpected number of elements in list", return -1);
3183 }
3184
3185 id = isl_id_list_get_id(list, 0);
3186 ok = id == a;
3187 isl_id_free(id);
3188 id = isl_id_list_get_id(list, 1);
3189 ok = ok && id == c;
3190 isl_id_free(id);
3191 id = isl_id_list_get_id(list, 2);
3192 ok = ok && id == d;
3193 isl_id_free(id);
3194
3195 isl_id_list_free(list);
3196
3197 if (!ok)
3198 isl_die(ctx, isl_error_unknown,
3199 "unexpected elements in list", return -1);
3200
3201 return 0;
3202 }
3203
3204 const char *set_conversion_tests[] = {
3205 "[N] -> { [i] : N - 1 <= 2 i <= N }",
3206 "[N] -> { [i] : exists a : i = 4 a and N - 1 <= i <= N }",
3207 "[N] -> { [i,j] : exists a : i = 4 a and N - 1 <= i, 2j <= N }",
3208 "[N] -> { [[i]->[j]] : exists a : i = 4 a and N - 1 <= i, 2j <= N }",
3209 };
3210
3211 /* Check that converting from isl_set to isl_pw_multi_aff and back
3212 * to isl_set produces the original isl_set.
3213 */
3214 static int test_set_conversion(isl_ctx *ctx)
3215 {
3216 int i;
3217 const char *str;
3218 isl_set *set1, *set2;
3219 isl_pw_multi_aff *pma;
3220 int equal;
3221
3222 for (i = 0; i < ARRAY_SIZE(set_conversion_tests); ++i) {
3223 str = set_conversion_tests[i];
3224 set1 = isl_set_read_from_str(ctx, str);
3225 pma = isl_pw_multi_aff_from_set(isl_set_copy(set1));
3226 set2 = isl_set_from_pw_multi_aff(pma);
3227 equal = isl_set_is_equal(set1, set2);
3228 isl_set_free(set1);
3229 isl_set_free(set2);
3230
3231 if (equal < 0)
3232 return -1;
3233 if (!equal)
3234 isl_die(ctx, isl_error_unknown, "bad conversion",
3235 return -1);
3236 }
3237
3238 return 0;
3239 }
3240
3241 /* Check that converting from isl_map to isl_pw_multi_aff and back
3242 * to isl_map produces the original isl_map.
3243 */
3244 static int test_map_conversion(isl_ctx *ctx)
3245 {
3246 const char *str;
3247 isl_map *map1, *map2;
3248 isl_pw_multi_aff *pma;
3249 int equal;
3250
3251 str = "{ [a, b, c, d] -> s0[a, b, e, f] : "
3252 "exists (e0 = [(a - 2c)/3], e1 = [(-4 + b - 5d)/9], "
3253 "e2 = [(-d + f)/9]: 3e0 = a - 2c and 9e1 = -4 + b - 5d and "
3254 "9e2 = -d + f and f >= 0 and f <= 8 and 9e >= -5 - 2a and "
3255 "9e <= -2 - 2a) }";
3256 map1 = isl_map_read_from_str(ctx, str);
3257 pma = isl_pw_multi_aff_from_map(isl_map_copy(map1));
3258 map2 = isl_map_from_pw_multi_aff(pma);
3259 equal = isl_map_is_equal(map1, map2);
3260 isl_map_free(map1);
3261 isl_map_free(map2);
3262
3263 if (equal < 0)
3264 return -1;
3265 if (!equal)
3266 isl_die(ctx, isl_error_unknown, "bad conversion", return -1);
3267
3268 return 0;
3269 }
3270
3271 static int test_conversion(isl_ctx *ctx)
3272 {
3273 if (test_set_conversion(ctx) < 0)
3274 return -1;
3275 if (test_map_conversion(ctx) < 0)
3276 return -1;
3277 return 0;
3278 }
3279
3280 /* Check that isl_basic_map_curry does not modify input.
3281 */
3282 static int test_curry(isl_ctx *ctx)
3283 {
3284 const char *str;
3285 isl_basic_map *bmap1, *bmap2;
3286 int equal;
3287
3288 str = "{ [A[] -> B[]] -> C[] }";
3289 bmap1 = isl_basic_map_read_from_str(ctx, str);
3290 bmap2 = isl_basic_map_curry(isl_basic_map_copy(bmap1));
3291 equal = isl_basic_map_is_equal(bmap1, bmap2);
3292 isl_basic_map_free(bmap1);
3293 isl_basic_map_free(bmap2);
3294
3295 if (equal < 0)
3296 return -1;
3297 if (equal)
3298 isl_die(ctx, isl_error_unknown,
3299 "curried map should not be equal to original",
3300 return -1);
3301
3302 return 0;
3303 }
3304
3305 struct {
3306 const char *set;
3307 const char *ma;
3308 const char *res;
3309 } preimage_tests[] = {
3310 { "{ B[i,j] : 0 <= i < 10 and 0 <= j < 100 }",
3311 "{ A[j,i] -> B[i,j] }",
3312 "{ A[j,i] : 0 <= i < 10 and 0 <= j < 100 }" },
3313 { "{ rat: B[i,j] : 0 <= i, j and 3 i + 5 j <= 100 }",
3314 "{ A[a,b] -> B[a/2,b/6] }",
3315 "{ rat: A[a,b] : 0 <= a, b and 9 a + 5 b <= 600 }" },
3316 { "{ B[i,j] : 0 <= i, j and 3 i + 5 j <= 100 }",
3317 "{ A[a,b] -> B[a/2,b/6] }",
3318 "{ A[a,b] : 0 <= a, b and 9 a + 5 b <= 600 and "
3319 "exists i,j : a = 2 i and b = 6 j }" },
3320 { "[n] -> { S[i] : 0 <= i <= 100 }", "[n] -> { S[n] }",
3321 "[n] -> { : 0 <= n <= 100 }" },
3322 { "{ B[i] : 0 <= i < 100 and exists a : i = 4 a }",
3323 "{ A[a] -> B[2a] }",
3324 "{ A[a] : 0 <= a < 50 and exists b : a = 2 b }" },
3325 { "{ B[i] : 0 <= i < 100 and exists a : i = 4 a }",
3326 "{ A[a] -> B[([a/2])] }",
3327 "{ A[a] : 0 <= a < 200 and exists b : [a/2] = 4 b }" },
3328 { "{ B[i,j,k] : 0 <= i,j,k <= 100 }",
3329 "{ A[a] -> B[a,a,a/3] }",
3330 "{ A[a] : 0 <= a <= 100 and exists b : a = 3 b }" },
3331 { "{ B[i,j] : j = [(i)/2] } ", "{ A[i,j] -> B[i/3,j] }",
3332 "{ A[i,j] : j = [(i)/6] and exists a : i = 3 a }" },
3333 };
3334
3335 static int test_preimage_basic_set(isl_ctx *ctx)
3336 {
3337 int i;
3338 isl_basic_set *bset1, *bset2;
3339 isl_multi_aff *ma;
3340 int equal;
3341
3342 for (i = 0; i < ARRAY_SIZE(preimage_tests); ++i) {
3343 bset1 = isl_basic_set_read_from_str(ctx, preimage_tests[i].set);
3344 ma = isl_multi_aff_read_from_str(ctx, preimage_tests[i].ma);
3345 bset2 = isl_basic_set_read_from_str(ctx, preimage_tests[i].res);
3346 bset1 = isl_basic_set_preimage_multi_aff(bset1, ma);
3347 equal = isl_basic_set_is_equal(bset1, bset2);
3348 isl_basic_set_free(bset1);
3349 isl_basic_set_free(bset2);
3350 if (equal < 0)
3351 return -1;
3352 if (!equal)
3353 isl_die(ctx, isl_error_unknown, "bad preimage",
3354 return -1);
3355 }
3356
3357 return 0;
3358 }
3359
3360 struct {
3361 const char *map;
3362 const char *ma;
3363 const char *res;
3364 } preimage_domain_tests[] = {
3365 { "{ B[i,j] -> C[2i + 3j] : 0 <= i < 10 and 0 <= j < 100 }",
3366 "{ A[j,i] -> B[i,j] }",
3367 "{ A[j,i] -> C[2i + 3j] : 0 <= i < 10 and 0 <= j < 100 }" },
3368 { "{ B[i] -> C[i]; D[i] -> E[i] }",
3369 "{ A[i] -> B[i + 1] }",
3370 "{ A[i] -> C[i + 1] }" },
3371 { "{ B[i] -> C[i]; B[i] -> E[i] }",
3372 "{ A[i] -> B[i + 1] }",
3373 "{ A[i] -> C[i + 1]; A[i] -> E[i + 1] }" },
3374 { "{ B[i] -> C[([i/2])] }",
3375 "{ A[i] -> B[2i] }",
3376 "{ A[i] -> C[i] }" },
3377 { "{ B[i,j] -> C[([i/2]), ([(i+j)/3])] }",
3378 "{ A[i] -> B[([i/5]), ([i/7])] }",
3379 "{ A[i] -> C[([([i/5])/2]), ([(([i/5])+([i/7]))/3])] }" },
3380 { "[N] -> { B[i] -> C[([N/2]), i, ([N/3])] }",
3381 "[N] -> { A[] -> B[([N/5])] }",
3382 "[N] -> { A[] -> C[([N/2]), ([N/5]), ([N/3])] }" },
3383 { "{ B[i] -> C[i] : exists a : i = 5 a }",
3384 "{ A[i] -> B[2i] }",
3385 "{ A[i] -> C[2i] : exists a : 2i = 5 a }" },
3386 { "{ B[i] -> C[i] : exists a : i = 2 a; "
3387 "B[i] -> D[i] : exists a : i = 2 a + 1 }",
3388 "{ A[i] -> B[2i] }",
3389 "{ A[i] -> C[2i] }" },
3390 };
3391
3392 static int test_preimage_union_map(isl_ctx *ctx)
3393 {
3394 int i;
3395 isl_union_map *umap1, *umap2;
3396 isl_multi_aff *ma;
3397 int equal;
3398
3399 for (i = 0; i < ARRAY_SIZE(preimage_domain_tests); ++i) {
3400 umap1 = isl_union_map_read_from_str(ctx,
3401 preimage_domain_tests[i].map);
3402 ma = isl_multi_aff_read_from_str(ctx,
3403 preimage_domain_tests[i].ma);
3404 umap2 = isl_union_map_read_from_str(ctx,
3405 preimage_domain_tests[i].res);
3406 umap1 = isl_union_map_preimage_domain_multi_aff(umap1, ma);
3407 equal = isl_union_map_is_equal(umap1, umap2);
3408 isl_union_map_free(umap1);
3409 isl_union_map_free(umap2);
3410 if (equal < 0)
3411 return -1;
3412 if (!equal)
3413 isl_die(ctx, isl_error_unknown, "bad preimage",
3414 return -1);
3415 }
3416
3417 return 0;
3418 }
3419
3420 static int test_preimage(isl_ctx *ctx)
3421 {
3422 if (test_preimage_basic_set(ctx) < 0)
3423 return -1;
3424 if (test_preimage_union_map(ctx) < 0)
3425 return -1;
3426
3427 return 0;
3428 }
3429
3430 struct {
3431 const char *ma1;
3432 const char *ma;
3433 const char *res;
3434 } pullback_tests[] = {
3435 { "{ B[i,j] -> C[i + 2j] }" , "{ A[a,b] -> B[b,a] }",
3436 "{ A[a,b] -> C[b + 2a] }" },
3437 { "{ B[i] -> C[2i] }", "{ A[a] -> B[(a)/2] }", "{ A[a] -> C[a] }" },
3438 { "{ B[i] -> C[(i)/2] }", "{ A[a] -> B[2a] }", "{ A[a] -> C[a] }" },
3439 { "{ B[i] -> C[(i)/2] }", "{ A[a] -> B[(a)/3] }",
3440 "{ A[a] -> C[(a)/6] }" },
3441 { "{ B[i] -> C[2i] }", "{ A[a] -> B[5a] }", "{ A[a] -> C[10a] }" },
3442 { "{ B[i] -> C[2i] }", "{ A[a] -> B[(a)/3] }",
3443 "{ A[a] -> C[(2a)/3] }" },
3444 { "{ B[i,j] -> C[i + j] }", "{ A[a] -> B[a,a] }", "{ A[a] -> C[2a] }"},
3445 { "{ B[a] -> C[a,a] }", "{ A[i,j] -> B[i + j] }",
3446 "{ A[i,j] -> C[i + j, i + j] }"},
3447 { "{ B[i] -> C[([i/2])] }", "{ B[5] }", "{ C[2] }" },
3448 { "[n] -> { B[i,j] -> C[([i/2]) + 2j] }",
3449 "[n] -> { B[n,[n/3]] }", "[n] -> { C[([n/2]) + 2*[n/3]] }", },
3450 };
3451
3452 static int test_pullback(isl_ctx *ctx)
3453 {
3454 int i;
3455 isl_multi_aff *ma1, *ma2;
3456 isl_multi_aff *ma;
3457 int equal;
3458
3459 for (i = 0; i < ARRAY_SIZE(pullback_tests); ++i) {
3460 ma1 = isl_multi_aff_read_from_str(ctx, pullback_tests[i].ma1);
3461 ma = isl_multi_aff_read_from_str(ctx, pullback_tests[i].ma);
3462 ma2 = isl_multi_aff_read_from_str(ctx, pullback_tests[i].res);
3463 ma1 = isl_multi_aff_pullback_multi_aff(ma1, ma);
3464 equal = isl_multi_aff_plain_is_equal(ma1, ma2);
3465 isl_multi_aff_free(ma1);
3466 isl_multi_aff_free(ma2);
3467 if (equal < 0)
3468 return -1;
3469 if (!equal)
3470 isl_die(ctx, isl_error_unknown, "bad pullback",
3471 return -1);
3472 }
3473
3474 return 0;
3475 }
3476
3477 /* Check that negation is printed correctly.
3478 */
3479 static int test_ast(isl_ctx *ctx)
3480 {
3481 isl_ast_expr *expr, *expr1, *expr2, *expr3;
3482 char *str;
3483 int ok;
3484
3485 expr1 = isl_ast_expr_from_id(isl_id_alloc(ctx, "A", NULL));
3486 expr2 = isl_ast_expr_from_id(isl_id_alloc(ctx, "B", NULL));
3487 expr = isl_ast_expr_add(expr1, expr2);
3488 expr = isl_ast_expr_neg(expr);
3489 str = isl_ast_expr_to_str(expr);
3490 ok = str ? !strcmp(str, "-(A + B)") : -1;
3491 free(str);
3492 isl_ast_expr_free(expr);
3493
3494 if (ok < 0)
3495 return -1;
3496 if (!ok)
3497 isl_die(ctx, isl_error_unknown,
3498 "isl_ast_expr printed incorrectly", return -1);
3499
3500 expr1 = isl_ast_expr_from_id(isl_id_alloc(ctx, "A", NULL));
3501 expr2 = isl_ast_expr_from_id(isl_id_alloc(ctx, "B", NULL));
3502 expr = isl_ast_expr_add(expr1, expr2);
3503 expr3 = isl_ast_expr_from_id(isl_id_alloc(ctx, "C", NULL));
3504 expr = isl_ast_expr_sub(expr3, expr);
3505 str = isl_ast_expr_to_str(expr);
3506 ok = str ? !strcmp(str, "C - (A + B)") : -1;
3507 free(str);
3508 isl_ast_expr_free(expr);
3509
3510 if (ok < 0)
3511 return -1;
3512 if (!ok)
3513 isl_die(ctx, isl_error_unknown,
3514 "isl_ast_expr printed incorrectly", return -1);
3515
3516 return 0;
3517 }
3518
3519 /* Internal data structure for before_for and after_for callbacks.
3520 *
3521 * depth is the current depth
3522 * before is the number of times before_for has been called
3523 * after is the number of times after_for has been called
3524 */
3525 struct isl_test_codegen_data {
3526 int depth;
3527 int before;
3528 int after;
3529 };
3530
3531 /* This function is called before each for loop in the AST generated
3532 * from test_ast_gen1.
3533 *
3534 * Increment the number of calls and the depth.
3535 * Check that the space returned by isl_ast_build_get_schedule_space
3536 * matches the target space of the schedule returned by
3537 * isl_ast_build_get_schedule.
3538 * Return an isl_id that is checked by the corresponding call
3539 * to after_for.
3540 */
3541 static __isl_give isl_id *before_for(__isl_keep isl_ast_build *build,
3542 void *user)
3543 {
3544 struct isl_test_codegen_data *data = user;
3545 isl_ctx *ctx;
3546 isl_space *space;
3547 isl_union_map *schedule;
3548 isl_union_set *uset;
3549 isl_set *set;
3550 int empty;
3551 char name[] = "d0";
3552
3553 ctx = isl_ast_build_get_ctx(build);
3554
3555 if (data->before >= 3)
3556 isl_die(ctx, isl_error_unknown,
3557 "unexpected number of for nodes", return NULL);
3558 if (data->depth >= 2)
3559 isl_die(ctx, isl_error_unknown,
3560 "unexpected depth", return NULL);
3561
3562 snprintf(name, sizeof(name), "d%d", data->depth);
3563 data->before++;
3564 data->depth++;
3565
3566 schedule = isl_ast_build_get_schedule(build);
3567 uset = isl_union_map_range(schedule);
3568 if (!uset)
3569 return NULL;
3570 if (isl_union_set_n_set(uset) != 1) {
3571 isl_union_set_free(uset);
3572 isl_die(ctx, isl_error_unknown,
3573 "expecting single range space", return NULL);
3574 }
3575
3576 space = isl_ast_build_get_schedule_space(build);
3577 set = isl_union_set_extract_set(uset, space);
3578 isl_union_set_free(uset);
3579 empty = isl_set_is_empty(set);
3580 isl_set_free(set);
3581
3582 if (empty < 0)
3583 return NULL;
3584 if (empty)
3585 isl_die(ctx, isl_error_unknown,
3586 "spaces don't match", return NULL);
3587
3588 return isl_id_alloc(ctx, name, NULL);
3589 }
3590
3591 /* This function is called after each for loop in the AST generated
3592 * from test_ast_gen1.
3593 *
3594 * Increment the number of calls and decrement the depth.
3595 * Check that the annotation attached to the node matches
3596 * the isl_id returned by the corresponding call to before_for.
3597 */
3598 static __isl_give isl_ast_node *after_for(__isl_take isl_ast_node *node,
3599 __isl_keep isl_ast_build *build, void *user)
3600 {
3601 struct isl_test_codegen_data *data = user;
3602 isl_id *id;
3603 const char *name;
3604 int valid;
3605
3606 data->after++;
3607 data->depth--;
3608
3609 if (data->after > data->before)
3610 isl_die(isl_ast_node_get_ctx(node), isl_error_unknown,
3611 "mismatch in number of for nodes",
3612 return isl_ast_node_free(node));
3613
3614 id = isl_ast_node_get_annotation(node);
3615 if (!id)
3616 isl_die(isl_ast_node_get_ctx(node), isl_error_unknown,
3617 "missing annotation", return isl_ast_node_free(node));
3618
3619 name = isl_id_get_name(id);
3620 valid = name && atoi(name + 1) == data->depth;
3621 isl_id_free(id);
3622
3623 if (!valid)
3624 isl_die(isl_ast_node_get_ctx(node), isl_error_unknown,
3625 "wrong annotation", return isl_ast_node_free(node));
3626
3627 return node;
3628 }
3629
3630 /* Check that the before_each_for and after_each_for callbacks
3631 * are called for each for loop in the generated code,
3632 * that they are called in the right order and that the isl_id
3633 * returned from the before_each_for callback is attached to
3634 * the isl_ast_node passed to the corresponding after_each_for call.
3635 */
3636 static int test_ast_gen1(isl_ctx *ctx)
3637 {
3638 const char *str;
3639 isl_set *set;
3640 isl_union_map *schedule;
3641 isl_ast_build *build;
3642 isl_ast_node *tree;
3643 struct isl_test_codegen_data data;
3644
3645 str = "[N] -> { : N >= 10 }";
3646 set = isl_set_read_from_str(ctx, str);
3647 str = "[N] -> { A[i,j] -> S[8,i,3,j] : 0 <= i,j <= N; "
3648 "B[i,j] -> S[8,j,9,i] : 0 <= i,j <= N }";
3649 schedule = isl_union_map_read_from_str(ctx, str);
3650
3651 data.before = 0;
3652 data.after = 0;
3653 data.depth = 0;
3654 build = isl_ast_build_from_context(set);
3655 build = isl_ast_build_set_before_each_for(build,
3656 &before_for, &data);
3657 build = isl_ast_build_set_after_each_for(build,
3658 &after_for, &data);
3659 tree = isl_ast_build_ast_from_schedule(build, schedule);
3660 isl_ast_build_free(build);
3661 if (!tree)
3662 return -1;
3663
3664 isl_ast_node_free(tree);
3665
3666 if (data.before != 3 || data.after != 3)
3667 isl_die(ctx, isl_error_unknown,
3668 "unexpected number of for nodes", return -1);
3669
3670 return 0;
3671 }
3672
3673 /* Check that the AST generator handles domains that are integrally disjoint
3674 * but not ratinoally disjoint.
3675 */
3676 static int test_ast_gen2(isl_ctx *ctx)
3677 {
3678 const char *str;
3679 isl_set *set;
3680 isl_union_map *schedule;
3681 isl_union_map *options;
3682 isl_ast_build *build;
3683 isl_ast_node *tree;
3684
3685 str = "{ A[i,j] -> [i,j] : 0 <= i,j <= 1 }";
3686 schedule = isl_union_map_read_from_str(ctx, str);
3687 set = isl_set_universe(isl_space_params_alloc(ctx, 0));
3688 build = isl_ast_build_from_context(set);
3689
3690 str = "{ [i,j] -> atomic[1] : i + j = 1; [i,j] -> unroll[1] : i = j }";
3691 options = isl_union_map_read_from_str(ctx, str);
3692 build = isl_ast_build_set_options(build, options);
3693 tree = isl_ast_build_ast_from_schedule(build, schedule);
3694 isl_ast_build_free(build);
3695 if (!tree)
3696 return -1;
3697 isl_ast_node_free(tree);
3698
3699 return 0;
3700 }
3701
3702 /* Increment *user on each call.
3703 */
3704 static __isl_give isl_ast_node *count_domains(__isl_take isl_ast_node *node,
3705 __isl_keep isl_ast_build *build, void *user)
3706 {
3707 int *n = user;
3708
3709 (*n)++;
3710
3711 return node;
3712 }
3713
3714 /* Test that unrolling tries to minimize the number of instances.
3715 * In particular, for the schedule given below, make sure it generates
3716 * 3 nodes (rather than 101).
3717 */
3718 static int test_ast_gen3(isl_ctx *ctx)
3719 {
3720 const char *str;
3721 isl_set *set;
3722 isl_union_map *schedule;
3723 isl_union_map *options;
3724 isl_ast_build *build;
3725 isl_ast_node *tree;
3726 int n_domain = 0;
3727
3728 str = "[n] -> { A[i] -> [i] : 0 <= i <= 100 and n <= i <= n + 2 }";
3729 schedule = isl_union_map_read_from_str(ctx, str);
3730 set = isl_set_universe(isl_space_params_alloc(ctx, 0));
3731
3732 str = "{ [i] -> unroll[0] }";
3733 options = isl_union_map_read_from_str(ctx, str);
3734
3735 build = isl_ast_build_from_context(set);
3736 build = isl_ast_build_set_options(build, options);
3737 build = isl_ast_build_set_at_each_domain(build,
3738 &count_domains, &n_domain);
3739 tree = isl_ast_build_ast_from_schedule(build, schedule);
3740 isl_ast_build_free(build);
3741 if (!tree)
3742 return -1;
3743
3744 isl_ast_node_free(tree);
3745
3746 if (n_domain != 3)
3747 isl_die(ctx, isl_error_unknown,
3748 "unexpected number of for nodes", return -1);
3749
3750 return 0;
3751 }
3752
3753 /* Check that if the ast_build_exploit_nested_bounds options is set,
3754 * we do not get an outer if node in the generated AST,
3755 * while we do get such an outer if node if the options is not set.
3756 */
3757 static int test_ast_gen4(isl_ctx *ctx)
3758 {
3759 const char *str;
3760 isl_set *set;
3761 isl_union_map *schedule;
3762 isl_ast_build *build;
3763 isl_ast_node *tree;
3764 enum isl_ast_node_type type;
3765 int enb;
3766
3767 enb = isl_options_get_ast_build_exploit_nested_bounds(ctx);
3768 str = "[N,M] -> { A[i,j] -> [i,j] : 0 <= i <= N and 0 <= j <= M }";
3769
3770 isl_options_set_ast_build_exploit_nested_bounds(ctx, 1);
3771
3772 schedule = isl_union_map_read_from_str(ctx, str);
3773 set = isl_set_universe(isl_space_params_alloc(ctx, 0));
3774 build = isl_ast_build_from_context(set);
3775 tree = isl_ast_build_ast_from_schedule(build, schedule);
3776 isl_ast_build_free(build);
3777 if (!tree)
3778 return -1;
3779
3780 type = isl_ast_node_get_type(tree);
3781 isl_ast_node_free(tree);
3782
3783 if (type == isl_ast_node_if)
3784 isl_die(ctx, isl_error_unknown,
3785 "not expecting if node", return -1);
3786
3787 isl_options_set_ast_build_exploit_nested_bounds(ctx, 0);
3788
3789 schedule = isl_union_map_read_from_str(ctx, str);
3790 set = isl_set_universe(isl_space_params_alloc(ctx, 0));
3791 build = isl_ast_build_from_context(set);
3792 tree = isl_ast_build_ast_from_schedule(build, schedule);
3793 isl_ast_build_free(build);
3794 if (!tree)
3795 return -1;
3796
3797 type = isl_ast_node_get_type(tree);
3798 isl_ast_node_free(tree);
3799
3800 if (type != isl_ast_node_if)
3801 isl_die(ctx, isl_error_unknown,
3802 "expecting if node", return -1);
3803
3804 isl_options_set_ast_build_exploit_nested_bounds(ctx, enb);
3805
3806 return 0;
3807 }
3808
3809 /* This function is called for each leaf in the AST generated
3810 * from test_ast_gen5.
3811 *
3812 * We finalize the AST generation by extending the outer schedule
3813 * with a zero-dimensional schedule. If this results in any for loops,
3814 * then this means that we did not pass along enough information
3815 * about the outer schedule to the inner AST generation.
3816 */
3817 static __isl_give isl_ast_node *create_leaf(__isl_take isl_ast_build *build,
3818 void *user)
3819 {
3820 isl_union_map *schedule, *extra;
3821 isl_ast_node *tree;
3822
3823 schedule = isl_ast_build_get_schedule(build);
3824 extra = isl_union_map_copy(schedule);
3825 extra = isl_union_map_from_domain(isl_union_map_domain(extra));
3826 schedule = isl_union_map_range_product(schedule, extra);
3827 tree = isl_ast_build_ast_from_schedule(build, schedule);
3828 isl_ast_build_free(build);
3829
3830 if (!tree)
3831 return NULL;
3832
3833 if (isl_ast_node_get_type(tree) == isl_ast_node_for)
3834 isl_die(isl_ast_node_get_ctx(tree), isl_error_unknown,
3835 "code should not contain any for loop",
3836 return isl_ast_node_free(tree));
3837
3838 return tree;
3839 }
3840
3841 /* Check that we do not lose any information when going back and
3842 * forth between internal and external schedule.
3843 *
3844 * In particular, we create an AST where we unroll the only
3845 * non-constant dimension in the schedule. We therefore do
3846 * not expect any for loops in the AST. However, older versions
3847 * of isl would not pass along enough information about the outer
3848 * schedule when performing an inner code generation from a create_leaf
3849 * callback, resulting in the inner code generation producing a for loop.
3850 */
3851 static int test_ast_gen5(isl_ctx *ctx)
3852 {
3853 const char *str;
3854 isl_set *set;
3855 isl_union_map *schedule, *options;
3856 isl_ast_build *build;
3857 isl_ast_node *tree;
3858
3859 str = "{ A[] -> [1, 1, 2]; B[i] -> [1, i, 0] : i >= 1 and i <= 2 }";
3860 schedule = isl_union_map_read_from_str(ctx, str);
3861
3862 str = "{ [a, b, c] -> unroll[1] : exists (e0 = [(a)/4]: "
3863 "4e0 >= -1 + a - b and 4e0 <= -2 + a + b) }";
3864 options = isl_union_map_read_from_str(ctx, str);
3865
3866 set = isl_set_universe(isl_space_params_alloc(ctx, 0));
3867 build = isl_ast_build_from_context(set);
3868 build = isl_ast_build_set_options(build, options);
3869 build = isl_ast_build_set_create_leaf(build, &create_leaf, NULL);
3870 tree = isl_ast_build_ast_from_schedule(build, schedule);
3871 isl_ast_build_free(build);
3872 isl_ast_node_free(tree);
3873 if (!tree)
3874 return -1;
3875
3876 return 0;
3877 }
3878
3879 static int test_ast_gen(isl_ctx *ctx)
3880 {
3881 if (test_ast_gen1(ctx) < 0)
3882 return -1;
3883 if (test_ast_gen2(ctx) < 0)
3884 return -1;
3885 if (test_ast_gen3(ctx) < 0)
3886 return -1;
3887 if (test_ast_gen4(ctx) < 0)
3888 return -1;
3889 if (test_ast_gen5(ctx) < 0)
3890 return -1;
3891 return 0;
3892 }
3893
3894 /* Check if dropping output dimensions from an isl_pw_multi_aff
3895 * works properly.
3896 */
3897 static int test_pw_multi_aff(isl_ctx *ctx)
3898 {
3899 const char *str;
3900 isl_pw_multi_aff *pma1, *pma2;
3901 int equal;
3902
3903 str = "{ [i,j] -> [i+j, 4i-j] }";
3904 pma1 = isl_pw_multi_aff_read_from_str(ctx, str);
3905 str = "{ [i,j] -> [4i-j] }";
3906 pma2 = isl_pw_multi_aff_read_from_str(ctx, str);
3907
3908 pma1 = isl_pw_multi_aff_drop_dims(pma1, isl_dim_out, 0, 1);
3909
3910 equal = isl_pw_multi_aff_plain_is_equal(pma1, pma2);
3911
3912 isl_pw_multi_aff_free(pma1);
3913 isl_pw_multi_aff_free(pma2);
3914 if (equal < 0)
3915 return -1;
3916 if (!equal)
3917 isl_die(ctx, isl_error_unknown,
3918 "expressions not equal", return -1);
3919
3920 return 0;
3921 }
3922
3923 /* This is a regression test for a bug where isl_basic_map_simplify
3924 * would end up in an infinite loop. In particular, we construct
3925 * an empty basic set that is not obviously empty.
3926 * isl_basic_set_is_empty marks the basic set as empty.
3927 * After projecting out i3, the variable can be dropped completely,
3928 * but isl_basic_map_simplify refrains from doing so if the basic set
3929 * is empty and would end up in an infinite loop if it didn't test
3930 * explicitly for empty basic maps in the outer loop.
3931 */
3932 static int test_simplify(isl_ctx *ctx)
3933 {
3934 const char *str;
3935 isl_basic_set *bset;
3936 int empty;
3937
3938 str = "{ [i0, i1, i2, i3] : i0 >= -2 and 6i2 <= 4 + i0 + 5i1 and "
3939 "i2 <= 22 and 75i2 <= 111 + 13i0 + 60i1 and "
3940 "25i2 >= 38 + 6i0 + 20i1 and i0 <= -1 and i2 >= 20 and "
3941 "i3 >= i2 }";
3942 bset = isl_basic_set_read_from_str(ctx, str);
3943 empty = isl_basic_set_is_empty(bset);
3944 bset = isl_basic_set_project_out(bset, isl_dim_set, 3, 1);
3945 isl_basic_set_free(bset);
3946 if (!bset)
3947 return -1;
3948 if (!empty)
3949 isl_die(ctx, isl_error_unknown,
3950 "basic set should be empty", return -1);
3951
3952 return 0;
3953 }
3954
3955 /* This is a regression test for a bug where isl_tab_basic_map_partial_lexopt
3956 * with gbr context would fail to disable the use of the shifted tableau
3957 * when transferring equalities for the input to the context, resulting
3958 * in invalid sample values.
3959 */
3960 static int test_partial_lexmin(isl_ctx *ctx)
3961 {
3962 const char *str;
3963 isl_basic_set *bset;
3964 isl_basic_map *bmap;
3965 isl_map *map;
3966
3967 str = "{ [1, b, c, 1 - c] -> [e] : 2e <= -c and 2e >= -3 + c }";
3968 bmap = isl_basic_map_read_from_str(ctx, str);
3969 str = "{ [a, b, c, d] : c <= 1 and 2d >= 6 - 4b - c }";
3970 bset = isl_basic_set_read_from_str(ctx, str);
3971 map = isl_basic_map_partial_lexmin(bmap, bset, NULL);
3972 isl_map_free(map);
3973
3974 if (!map)
3975 return -1;
3976
3977 return 0;
3978 }
3979
3980 /* Check that the variable compression performed on the existentially
3981 * quantified variables inside isl_basic_set_compute_divs is not confused
3982 * by the implicit equalities among the parameters.
3983 */
3984 static int test_compute_divs(isl_ctx *ctx)
3985 {
3986 const char *str;
3987 isl_basic_set *bset;
3988 isl_set *set;
3989
3990 str = "[a, b, c, d, e] -> { [] : exists (e0: 2d = b and a <= 124 and "
3991 "b <= 2046 and b >= 0 and b <= 60 + 64a and 2e >= b + 2c and "
3992 "2e >= b and 2e <= 1 + b and 2e <= 1 + b + 2c and "
3993 "32768e0 >= -124 + a and 2097152e0 <= 60 + 64a - b) }";
3994 bset = isl_basic_set_read_from_str(ctx, str);
3995 set = isl_basic_set_compute_divs(bset);
3996 isl_set_free(set);
3997 if (!set)
3998 return -1;
3999
4000 return 0;
4001 }
4002
4003 struct {
4004 const char *name;
4005 int (*fn)(isl_ctx *ctx);
4006 } tests [] = {
4007 { "compute divs", &test_compute_divs },
4008 { "partial lexmin", &test_partial_lexmin },
4009 { "simplify", &test_simplify },
4010 { "curry", &test_curry },
4011 { "piecewise multi affine expressions", &test_pw_multi_aff },
4012 { "conversion", &test_conversion },
4013 { "list", &test_list },
4014 { "align parameters", &test_align_parameters },
4015 { "preimage", &test_preimage },
4016 { "pullback", &test_pullback },
4017 { "AST", &test_ast },
4018 { "AST generation", &test_ast_gen },
4019 { "eliminate", &test_eliminate },
4020 { "residue class", &test_residue_class },
4021 { "div", &test_div },
4022 { "slice", &test_slice },
4023 { "fixed power", &test_fixed_power },
4024 { "sample", &test_sample },
4025 { "output", &test_output },
4026 { "vertices", &test_vertices },
4027 { "fixed", &test_fixed },
4028 { "equal", &test_equal },
4029 { "product", &test_product },
4030 { "dim_max", &test_dim_max },
4031 { "affine", &test_aff },
4032 { "injective", &test_injective },
4033 { "schedule", &test_schedule },
4034 { "union_pw", &test_union_pw },
4035 { "parse", &test_parse },
4036 { "single-valued", &test_sv },
4037 { "affine hull", &test_affine_hull },
4038 { "coalesce", &test_coalesce },
4039 { "factorize", &test_factorize },
4040 { "subset", &test_subset },
4041 { "subtract", &test_subtract },
4042 { "lexmin", &test_lexmin },
4043 };
4044
4045 int main()
4046 {
4047 int i;
4048 struct isl_ctx *ctx;
4049
4050 srcdir = getenv("srcdir");
4051 assert(srcdir);
4052
4053 ctx = isl_ctx_alloc();
4054 for (i = 0; i < ARRAY_SIZE(tests); ++i) {
4055 printf("%s\n", tests[i].name);
4056 if (tests[i].fn(ctx) < 0)
4057 goto error;
4058 }
4059 test_lift(ctx);
4060 test_bound(ctx);
4061 test_union(ctx);
4062 test_split_periods(ctx);
4063 test_pwqp(ctx);
4064 test_lex(ctx);
4065 test_bijective(ctx);
4066 test_dep(ctx);
4067 test_read(ctx);
4068 test_bounded(ctx);
4069 test_construction(ctx);
4070 test_dim(ctx);
4071 test_application(ctx);
4072 test_convex_hull(ctx);
4073 test_gist(ctx);
4074 test_closure(ctx);
4075 isl_ctx_free(ctx);
4076 return 0;
4077 error:
4078 isl_ctx_free(ctx);
4079 return -1;
4080 }
Integer set library